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ION DYNAMICS AND ELECTRICAL RELAXATION PROCESS IN NASICON BASED PHOSPHATE GLASSES
Thesis
Submitted to Pondicherry University
in fulfillment for the award of the degree
of
DOCTOR OF PHILOSOPHY
in
Physics
by
S. Vinoth Rathan
Research Supervisor: Prof. G. Govindaraj
DEPARTMENT OF PHYSICS SCHOOL OF PHYSICAL, CHEMICAL AND APPLIED SCIENCES
PONDICHERRY UNIVERSITY PUDUCHERRY-605 014
INDIA
June 2011
Dedicated to the memory of my beloved mother
Department of Physics School of Physical, Chemical and Applied Sciences
PONDICHERRY UNIVERSITY PONDICHERRY – 605 014
INDIA
Phone: +91-0413-2654402(off.); +91-0413-2252018(Res.) Dr. G. GOVINDARAJ Fax: +91-413-2655183 Professor and Head e-mail: [email protected]
CERTIFICATE
This is to certify that Mr. S. Vinoth Rathan, Research Fellow, has carried out the work of the thesis entitled “ION DYNAMICS AND ELECTRICAL RELAXATION PROCESS IN
NASICON BASED PHOSPHATE GLASSES” for the degree of Doctor of Philosophy of Pondicherry University for the required period under the regulations in force. This thesis embodies a bonafide record of the work done by him under my guidance. The work is original and has not been submitted for the award of any Diploma or Degree of this or any other University. It is also stated that the entire thesis represents the independent work of Mr. S. Vinoth Rathan and was actually undertaken by the candidate under my guidance. Pondicherry Dr. G. Govindaraj June 2011
DECLARATION
I hereby declare that the work presented in this Ph. D thesis entitled, “ION DYNAMICS
AND ELECTRICAL RELAXATION PROCESS IN NASICON BASED PHOSPHATE
GLASSES”, is bonafied record of independent work done by me at the Department of Physics, School of Physical, Chemical and Applied Sciences Pondicherry University, Pondicherry – 605 014 under the supervision of Prof. G. Govindaraj. Head, Department of Physics, School of Physical, Chemical and Applied Sciences Pondicherry University, Pondicherry – 605 014. I further declare that the work reported herein does not form part of any other thesis or dissertation on the basis of which a degree or award was conferred earlier.
Mr. S. Vinoth Rathan Research Fellow
Department of Physics, SPCAS Pondicherry University Pondicherry – 605 014
Acknowledgements First I would like to thank Prof. G. Govindaraj for his expert guidance, support, and
patience throughout the duration of this final degree thesis, without his help, and encouragement this dissertation would not be possible. I would like to specifically appreciate all the dedication and knowledge that he has shared with me throughout my graduate study.
I am grateful to my doctoral committee members Prof. K. Porsezian and Prof. M. S. Pandian for their constructive suggestion and fruitful discussion at various stages of my research work.
I would also like to thank my seniors Dr. R. Murugaraj and Dr. C. R. Mariappan who have worked with me at initial stage of my research, for their several thoughtful discussions. I am also grateful to my lab mates Ms. Lakshmi Vijayan, Mr. Rajesh Cheruku and M.Phil Scholars Mr. Jobins Antony, Mr. Durairajan, Mr. Aashaq Hussain Shah and Mr. Ashok Jena for their whole hearted help and cooperation.
It’s my pleasure and privilege to extend my heartfelt thanks to all my associates and friends, Mr. R.V.J. Raja, Mr. N. Nallamuthu, Mr. S. Sabarinathan, Dr. B. Natarajan, Mr. R. Nagaraj Prakash, Mr. R. Murali, Mr. T. Udaya Kumar, Mr. S. Binukumar, Mr. Nithyananthan, Mr. R. Sanjivi and Ms. J. Anuradha for their timely help and for making these last five years, the most enjoyable ones!.
I wish to record my sincere thanks to the faculties and non-teaching staff members of Department of Physics and technical staff members of Central Instrumentation Facilities, Pondicherry University for extending helpful facilities to do my research. I am also gratified to all my colleagues in Sri Sairam Engineering College, Chennai who have greatly abetted in the effort I have done in thesis.
In addition, I would like to be grateful and extend my deep gratitude to my Amma (Mom) and Appa (Dad), who always believed in me despite my failures, loved me unconditionally and encouraged me to dream, explore and learn. Without them, I would not be where I am today. My affectionate thanks to my Anna, Anni and Tharnesh for their moral support and wishes throughout my course. Finally my special thanks to my wife Preethi for her lovely support, care and prayer.
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TABLE OF CONTENTS Page No. CHAPTER I INTRODUCTION 1.1 General 1
1.2 Classification of fast ion conductors 2
1.2.1 Crystalline and polycrystalline fast ion conductors 2
1.2.2 Fast ion conducting glasses 2
1.2.3 Fast ion conducting polymers 3
1.3 Review of fast ion conductors 4
1.4 Review of FIC glasses 6
1.5 Review of NASIGLAS compounds 8
1.6 Ion conduction mechanisms in glass 9
1.6.1 Anderson and Stuart model 11
1.6.2 The weak electrolyte model 12
1.6.3 Defect model 12
1.6.4 Random network model 13
1.7 Present work 14
CHAPTER II EXPERIMENTAL TECHNIQUES
2.1 Preparation of glasses 21
2.2 Physical Characterization 25
2.2.1. X-Ray Diffraction 25
2.2.2 Density Measurement 26
2.2.3 Thermal Analysis 26
2.3.4 Fourier Transform Infrared Spectroscopy Studies 28
2.3 Electrical properties 32
2.3.1. Impedance spectroscopy 33
2.3.2. AC response and conductivity 36
2.3.3. Electrical measurements 39
\
CHAPTER III IONIC CONDUCTIVITY IN TITANIUM AND NIOBIUM BASED NASICON GLASSES
3.1 Preview 45
3.2 Results and discussion 47
3.2.1 Synthesis and Characterization 47
3.2.2 Impedance spectroscopy studies 48
3.2.3 Dc conductivity analysis 56
3.2.4 Ac conductivity analysis 60
3.2.5 Electrical modulus behavior 70
3.2.6 Scaling 76
3.2.6 (a) Ac conductivity scaling 79
3.2.6 (b) Electric modulus scaling 83
Chapter IV MIXED ALKALI EFFECT IN NASICON GLASSES 4.1 Introduction 88
4.2 Synthesis and Characterization 90
4.3 Impedance spectroscopy and dc conductivity analysis 91
4.4 Ac conductivity analysis 96
4.5 Electric modulus 101
4.6 Scaling 103
4.6.1 Ac conductivity scaling 104
4.6.2 Electric modulus scaling 108
Chapter V INVESTIGATIONS ON DIVALENT ION SUBSTITUTED NASICON GLASSES
5. 1 Addition of divalent ions in NASICON glasses 113
5.1.1 Introduction 113
5.1.2 Synthesis and Characterization 114
5.1.3 Impedance spectroscopic studies 114
5.1.4 Ac conductivity studies 116
5.1.5 Dielectric properties 123
5.1.5(a) Permittivity studies 123
5.1.5 (b) Electric modulus analysis 126
5.1.6 Scaling studies in ac conductivity and electrical modulus 130
5.2 Effects of ZnO on electrical conductivity of NASICON type glasses 132
5.2.1 Introduction 132
5.2.2 Preparation and Characterization 133
5.2.3 Impedance spectroscopic studies 134
5.2.4 Composition dependence of dc conductivity 136
5.2.5 Ac electric response studies 139
5.2.6 Ac conductivity scaling studies 142
Chapter VI SUMMARY 149
Preface
The most commonly used experimental technique to characterize the dynamics of
mobile ions in disordered ionic solids is the electrical relaxation measurements. The present
thesis work was undertaken to study the ionic relaxation processes characterized by long and
short time scales in NASICON type phosphate glasses. The thesis consists of six chapters
and the contents of each chapter are as follows:
In first chapter, a general description of the interdisciplinary field of fast ionic
conductors and brief review of ionic materials reported. Since, the present work is on
NASICON materials, detailed literature survey of NASICON materials is presented. The
method of synthesis of the glasses and their characterization are presented in the second
chapter. Third chapter is directed towards the dynamics of different cations in the
NASICON based glass matrix with Ti4+ and Nb5+ as transition metal oxide in various
compositions of A5TiP3O12 (where A=Li, Na, Ag) and A4NbP3O12 (where A= Li, Na, Ag).
This involves insight in both the local structures of the host network and cation coordinated
within these systems. Fourth chapter deals with mixed alkali effect in NASICON type
glasses with composition changes in cations, e.g. (LixNa1-x)4NbP3O12 and (LixNa1-x)5TiP3O12.
The mixed alkali effect in electrical properties has been discussed using various formalisms
followed by the scaling behavior in NASICON glasses. In chapter five, electrical relaxation
and ion dynamics are studied with inclusion of divalent metal oxide maintaining constant
cation concentration in the NASICON glasses with variation in composition. The salient
features of the thesis are summarized in sixth chapter.
Three papers related to the subject matter of the thesis have been published in
reputed journals and five more are to be communicated.
Pondicherry S. Vinoth Rathan
June 2011
1
Chapter I
INTRODUCTION
1.1 General
Solid state ionics is an interdisciplinary science comprising physics, chemistry
and materials science involving all kinds of ionic transport in solids. The important
features of the solid state ionics is that it involves materials of varied morphology
including single crystals, sintered bodies, composites, glasses, amorphous thin films and
polymers. The electrical conductivity of these ionic materials is fairly high at low
temperature comparable with those of liquid electrolytes and molten salts and hence these
are termed as solid electrolytes. Solid electrolytes are also called as fast ionic conductors
(FIC) or superionic conductors. The recent interest in the field of solid state ionics is not
only to the technologists as it comprises potential materials such as batteries, fuel cells,
gas sensors, electrochromic display devices, pacemakers, analog potential memories etc.,
but also to the physicists because of their intricate conduction process [1, 2].
Solid electrolytes were first discussed by Faraday at the end of 19th century [3].
Nernst developed the stabilized zirconia which is one of the most widely used oxide solid
electrolyte in the oxygen sensors appeared as a resistive element in the heating type light
source called the Nernst Glower. Advanced researches in the area obviously begin with
discovery of unusual electrical conductivity in AgI by Tubant et al., [4] and the
investigation of Ag2HgI4 by Ketelaar [5]. The discovery of phase transition at 147oC in
AgI from the low conducting β-phase to the high conducting α-phase with an ionic
conductivity of 0.1Scm-1 is considered to be a break through in the physics of superionic
conductors. The most important discovery was β-alumina by Kemmer et al., which has
triggered the area of research with an optimum approach in the field of solid state ionics
[6]. Since then various kinds of solid conductors such as cation conductors, anion
conductors, oxide ion conductors, etc., have been found to have high conductivity at
various temperature in crystal, polycrystalline and glass phase. Past two decades, high
ionic conductors have also been found in polymeric forms and composite forms, i.e.,
dispersing insulating materials in ionic solids [7]. These different kinds of FICs with
diverse phases are being synthesized to meet the practical requirements and conditions.
2
Generally, the FIC materials commonly featured as: (i) crystal bonding is ionic in nature,
(ii) electrical conductivity is high (10-1–10-4S/cm), (iii) principle charge carriers are ions,
(iv) the electronic conductivity is negligible, (v) low activation energies for ion
migration, and (vi) special crystal structure with open tunnels or channels through which
the mobile ions move [1, 8-10].
1.2 Classification of fast ion conductors
The fast ionic conductors are classified primarily based on the microstructure and
phase as:
(a) Crystalline and polycrystalline fast ionic conductors.
(b) Fast ion conducting glasses.
(c) Fast ion conducting polymers.
(d) Fast ion conducting composites.
1.2.1 Crystalline and polycrystalline fast ion conductors
Crystalline fast ion conductors are characterized by the fast diffusion of one type
of ion through the defect in the crystalline framework [11]. Broadly the defects are
concentrated point defects or molten sublattice type defects. Mobile ions in most
crystalline FICs are monovalent. By the precise knowledge of the structure and the
flexibility of the compositions, numerous crystalline solid electrolytes are synthesized. As
a general rule FICs have a open crystal structure, which allows the rapid motion of ions.
Thermal agitation is not necessary to create the defects in the ion conducting sublattice,
since the sufficient number of empty sites are already available in the structure. Ionic
conduction in crystalline FICs is due to the motion of ions and or defect through the
vacancies in the lattice. Among the crystalline solid FICs, the highest conductivity is
exhibited by silver ion conductors.
1.2.2 Fast ion conducting glasses
Ionic conduction in glassy materials has been investigated since 1884, when
Warburg placed a dc electrical field on a glass, and observed an electrolytic Na+ transport.
Glass electrolytes characterized as amorphous structures are now widely used for solid
3
state ionic devices such as lithium ion batteries, sensors, fuel cells, electro-chromic
displays [12-15] etc. This is mainly owing to their dense, homogeneous and flexible
natures in comparison with crystals or ceramics. The glassy materials have several
advantages from a viewpoint of ion conduction in comparison with the crystalline such
as: (i) a wide range selection of compositions, (ii) isotropic properties, (iii) no grain
boundaries, (iv) easy film formation, and (v) resistance to environmental effects. On the
other hand, their amorphous structure and non equilibrium nature often hinder the
fundamental understanding of their ionic transport mechanism [16]. Generally the fast ion
conducting glasses are formed by three components; glass network former, metal oxides
acting as a glass network modifier and dopant cations. The glass network formers are
oxide materials of covalent nature, the assembly of oxygen tetrahedrals or trigonals [17].
1.2.3 Fast ion conducting polymers
Polymers based fast ionic conductors have received considerable attention
because of their potential applications in solid state batteries and electro-chromic devices
[18,19]. The area of polymeric electrolyte materials have been developed remarkably
after the discovery of the first ion conducting polymers in 1973, which was poly ethylene
oxide complexed with an alkali metal salt by Wright et al., [19], following that Armand
and coworkers examined the ionic conductivity of poly ethylene oxide and poly
propylene oxide salt complex and proposed their application as solid polymer electrolytes
in high-energy density batteries [20]. Most of the emphasis on polymer FICs has been
carried out on the improvement of the materials based polyethylene oxide and alkali
metal oxide. The area of polymer electrolytes has passed through various stages in
development. These promising materials can be classified into three categories, which
cover solid polymer electrolytes, polymer gel electrolytes and polyelectrolytes. Solid
polymer electrolytes are polymer salt complexes, which are obtained by dissolving a salt
in the polymer matrix. Polymer-gel electrolytes are prepared by incorporation of liquid
electrolytes into polymer matrix. Polyelectrolytes are polymers which contain ionic
centers as part of their constitutional repeating units. The transport of ions takes place
mainly in the amorphous phase in polymer electrolytes [21], however, Bruce et al., have
4
recently found that high ionic conductivity is also sustained in crystalline polymers [22].
Ion conduction in polymer electrolytes is a complex process, which is governed
preponderantly by local motion of polymer segments, long range ion motions and intra-
inter-chain transport of ions among the coordinating sites.
1.3 Review of fast ion conductors
The study of ionic conduction in solid state originated way back in 1838 when
Faraday discovered that PbF2 and Ag2S are good conductors of electricity [23]. These
solids are, the first ever discovered solid electrolyte. The discoveries of good Na+
mobility in glass by Warburg [24] as well as the first transference number measurements
by Warburg and Tegetmeier [25] are important contributions in the study of solid ionic
conductors. Katayama [27] in 1908 demonstrated that fast ionic conduction can be made
use of in potentiometric measurements. Yttria (Y2O3) stabilized zirconia (ZrO2), after
Nernst [26] in 1900, as well as AgI, after Tubant and Lorenz [4] in 1914, are among the
other FICs discovered in later stage of research. Another important discovery is that of
the first solid oxide fuel cell by Baur and Preis [28] in 1937 using yttria stabilized
zirconia as the electrolyte. The field of solid electrolytes did not seem to have gained
much in the later years until in 1957 Kiukkola and Wagner [29] carried out extensive
potentiometric measurements using solid electrolyte based electrochemical sensors.
Silver ion conducting solids, such as Ag3SI [30] and RbAg4I5 [31] were
discovered in the 1960s. The use of Ag3SI, by Takahashi and Yamamoto [32] and
RbAg4I5, by Argue and Owens [33] in electrochemical cells were demonstrated soon
after this. There was a burst of enthusiasm following the discovery of high ion mobility in
β-alumina (M2O.xAl2O3, where M = Li, Na, Ag, K, Rb, NH4 etc.) by Yao and Kummer
[34]. Na-β-alumina was successfully used in Na/S cell by Kummer and Weber [35]. The
discovery of β-alumina, an excellent solid electrolyte with a fairly rigid framework
structure, boosted researches for newer superionic conductors with skeleton structures.
This led to the synthesis of gallates and ferrites which are β-alumina type compounds
where the aluminum is replaced by Ga and Fe respectively. Lamellar structures of the
5
kind K072L072M028O2, where L=Se or In and M=Hf, Zr, Sn, and Na05In05Zr05S2 or
Na08Zr02S2 having high electrical conductivities were also synthesized [36].
Another advance in the mending of superionic solids was when Hong [37] and
Goodenough et al., [38] reported high conductivity in ‘skeleton’ structures involving
polyhedral units. The skeleton structure consists of a rigid (immobile) subarray
(sublattice) of ions which render a large number of three-dimensionally connected
interstitial sites suitable for long range motion of small monovalent cations [38]. Hong
reported synthesis and characterization of Na1+xZr2SixP3–xO12, where 0≤x≤3, now
popularly known as NASICON [38]. It is observed that the best conductor of the series is
Na3Zr2Si2PO12 (x=2) whose conductivity is comparable to Na-β-alumina above 443K.
The Na3Zr2Si2PO12 is the first reported Na+ ion conductor with three dimensional
conductivity. Hong reported the synthesis and structure of Li, Ag and K as yet another set
of counterparts of NASICON type of FICs at high temperature. The enormous ionic
substitutions possible in NaZr2(PO4)3 led to the synthesis of a very large number of
compounds which now find applications in diverse fields of materials science.
Goodenough et al., investigated the possibility of fast ion transport in various other
skeleton structures as well. The other skeleton structures examined includes high-
pressure-stabilized cubic Im3 phase of KSbO3 and NaSbO3, defect-pyrochlore structure
of the kind AB2X6, carnegieite structure of high-temperature NaAlSiO4 as well as the
NASICONs. While the Na3Zr2Si2PO12 is found to be the best in the series, NaSbO3 is
also a promising material for solid electrolyte applications.
Since 1970, a good number of studies focusing on the synthesis and
characterization of lithium ion conductors appeared. Search for the lithium ion
conductors are motivated by the small ionic radii of Li+, its lower weight, ease of
handling and its potential use in high energy density batteries. Li2SiO4 and Li4–3xAl3SiO4
(0≤x≤05) is one of the earliest superionic solids [39, 40] which shows high ionic
conductivity and has been the subject of many interesting studies. Some of the important
Li ion conductors that have attracted investigations are Li3N [41], Li-β-alumina [42],
NASICON type, LiZr2(PO4)3 [43], LiHf2P3O12 [44] etc., ternary chalcogenides like
LiInS2 [45], Li4B7O12X (X = Br, Cl or S) [46] and Li14Zn(GeO4)4 [37].
6
Silver containing NASICON materials are less studied compare to the alkali
containing NASICONs. Perret and Boudjada was the first to report silver containing
NASICON, AgSn2P3O12 [47]. Later many researchers have reported the preparation of
silver NASICONs AgTi2P3O12 and AgZr2P3O12, and study the crystal structure [48-50].
The catalytic activity of AgZr2P3O12 and AgHf2P3O12 in the butan-2-ol conversion to
butanes and methyl ethyl ketones have been studied by Arsalane et al. [51] and Youness
Birk et al.[52] respectively. d’Yvoire et al. have reported the preparation and
conductivity of Ag3M2P3O12 (M= Cr and Fe) [53, 54]. The electrical properties of silver
NASICONs AgTaMP3O12 (where M= Al, Ga, In, Cr, Fe and Y), AgSbMP3O12 (where
M= Al, Ga, Fe and Cr), and Ag3-2xTaxAl2-x(PO4)3 (x= 0.6 to 1.4) was studied by
Koteswara et al.,[55-57].
1.4 Review of FIC glasses
Many hundreds of glass compositions have been studied, but most of them have
been silver and alkali ion conductors. It is observed that the ionic conductivity in these
glassy electrolytes has never exceeded ~10-2 Scm-1 at 25oC. The only exception is AgI-
Ag2O-MxOy (MxOy=B2O3, GeO2, P2O5, MoO3) glass-ceramic composites which exhibit a
conductivity between 10-2 and 10-1 Scm-1 at 25oC [58, 59]. The higher conductivity of
these α-AgI doped materials arises from the α-AgI crystallites being homogeneously
dispersed in the superionic glass. Since then large number of silver ion conductor glasses
were developed for a number of related systems, including AgI mixed in various
proportions with chromates, arsenates, molybdates and phosphates. Malugani et al.,
investigated glass formation and their electrical properties in the systems AgX-AgPO3
(X=I, Br, C1) [60], MI2-AgPO3 (M=Cd, Hg, Pb) [61] and explained the responsible of
halides in rapid increase in conductivity. He also prepared non halide glasses AgPO3-
Ag2SO4 [62] and obtained considerably lower conductivities compared to halide glasses.
Kawamoto et al., [63,64] investigated the glass forming regions and electrical properties
of the systems Ag2S-GeS-GeS2, Ag2S-As2S3 and Ag2S-P2S5. Meanwhile, lithium ion
conducting glasses were investigated in detail as a solid electrolyte. As far as we know,
Otto [65] was the first to report glasses with exceptionally high Li ion conductivities in
lithium borate glasses at relatively low temperatures. Similar effects have also been
7
observed for alkali silicate glasses [66]. Significantly higher conductivities were
approached by Otto in the glassy system by incorporating more number of lithium ions in
the form of Li2SO4, LiC1 or LiF [67] when compared to glass containing Li2O alone.
Johnson et al., [67] investigated glasses and glass-ceramics with compositions related to
that of β-eucryptite, LiAlSiO4 and said that glass had higher conductivity compared to
their respective glass ceramic.
Evstrop'ev et al., [69] were the first to report FIC in phosphate glasses with
composition M2O-MF-Al(PO3)3 (M=Li, Na, K and Cs). Highest conductivity was
reported for the glass 30 Li2O-50LiF-20Al(PO3)3 with 10-2Scm-1 at 300°C. Malugani and
Robert [70] have investigated phosphate glasses LiPO3-LiX (X=I, Br, C1) and found that
conductivity was observed to increase with increasing halide content. Altogether
independent structure of LiI makes this enhancement in conductivity. At beginning,
conventional inorganic oxide glasses were studied, and later chalcogenide glasses
especially sulfide or oxysulfide glasses. Though different type of glasses such as halides,
oxide and sulfide glasses have been investigated each have their own advantages in
application. Since then, a large number of ion conducting glasses have been synthesized
with permanent glass formers. Glass et al., [71] prepared LiNbO3, LiTaO3, KNbO3, and
KTaO3 glasses by rapid quenching with enhanced conductivity compared to their
respective crystalline and single crystal.
In general the glassy electrolytes consist of three components: (i) a glass network
former, (ii) a network modifier M2XMAg, Cu, Li, Na; XO, S, Se and (iii) a dopant
salt MY (YI, Cl, Br, F). Many physical properties of these glasses show a nonlinear
behavior with mobile ion concentration. Ionic conductivity in glasses is quite dependent
on the nature and composition of the anion matrix. Also, the introduction of different
types of anion often leads to enhanced conductivities. The drastic increase of the dc
conductivity with increasing ion concentration is a common feature, observed in many
glassy materials. The conductivity maximum limitation is thought to be a generic feature
of FIC glasses. To date, however, there has been no definitive understanding provided for
this conductivity maximum, yet the implications of the conductivity maximum in the
performance of batteries and fuel cells are important. Susman et al., have achieved a best
conductivity in zirconia based silicate glass which was derived form the composition of
8
NASICON series [72], since then number of glasses with NASICON framework have
been synthesized and said to be NASIGLAS. The available monovalent ion conducting
NASICON type glasses and their studies are reviewed.
1.5 Review of NASIGLAS compounds
Colomban and Coworkers [73, 74] pointed out the possibility of the preparation
of various NASICON compounds AxBy(XO4)3 with A=Na, Li, K, Ag, Cu; B=Zr, Hf, Ti,
Sc, Fe, Cr; X=Si, P in both amorphous and crystalline form. Ahmad et al., [75, 76],
Niyompan et al., [77] and Ennas et al.,[78] prepared zirconia based glasses and studied
the electrical properties and short range orderliness in the sample. Na4Nb(PO4)3 (NNP)
NASICON materials was investigated by El Jazouli et al., [79] using Raman and optical
spectroscopic and concluded the similarity of phosphate unit in both crystal and glass
network. This was disproved by Prabakar and Rao [80] and Sales and Chakoumoko [81]
on the basis of magic-angle spinning 31P MAS-NMR spectroscopy and high performance
liquid chromatography measurements respectively. Greenblatt et al., [82] examined the
ionic conductivity of NNP glass (σ673K=3.1x10-3S/cm) and crystalline phase
(σ673K=3.1x10-5 S/cm) which shows interesting features.
Because of the ease of fabrication many scientist prepared various glasses with
high conductivity and good chemical stability in NASICON framework such as
Na3Ga2P3O12 by Berthet et al., [83], LiGe2(PO4)3 by Fu [84], AxByP3O12 (where A=Li,
Na, K and B=Fe, Ge, Ti, Ge, V and Nb) by Shobha and Rao [85, 86], A3Al2(PO4)3
(A=Na, Li) by Moreno-Real et al., [87] and Na3Al2(PO4)3F3 by Le Meins et al., [88]
Chowdari and Coworkers [89] reported about the lithium ion conducting glass and glass
ceramic of the composition Li1.4[Al0.4Ge1.6(PO4)3]. They also reported ionic conductivity
and X-ray photoelectron spectroscopy (XPS) studies of Li1+xM2-xAlx(PO4)3 (M=Ti & Ge)
[90]. Mariappan and Govindaraj has prepared number of NASICON type glasses as well
as ceramics and studied the electrical relaxation with various formalisms [91].
9
1.6 Ion conduction mechanisms in glass
In order to understand the transport mechanism, it is therefore essential to find a
connection between the microscopic structure and the ionic conductivity. Various
transport models have been proposed to explain the high ionic conductivity of FIC
glasses [92–96]. Most of these models are essentially based upon some specific
assumption about the microstructure in general and local environment of the mobile
cation in particular. Thus, in order to evaluate the different models and to understand the
origin of the diffusion mechanism it is essential to obtain more insight about the structure
and the nature of the conduction pathways. The ionic transport is strongly affected by the
short range order especially around the mobile ions, which is the consequence of the
chemical bonds between the mobile ions and coordinating other atoms. In conventional
alkali silicate glasses, the alkali cation is coordinated by non-bridging oxygens (NBO) in
the silicate network. The chemical bond strength between the lithium and the NBO is the
key factor of ionic transport. A glass looks homogeneous in mm scale; it may have
inhomogeneity in sub-micrometer scale and will have some ordered structure in Å scale.
Ionic transport is a phenomenon that a mobile ion starts from a locally ordered atomic
scale and diffuses to a macroscopic scale. During this process, the mobile ion experiences
various hierarchical structures. Conceptually, the ideas of fast ion conduction follow from
the ionic conductivity expression:
σ=nZeµ (1.1)
where n is the charge carrier density, Ze is the charge of the mobile particle, and µ is the
mobility of the charge carriers. Here n and µ are temperature dependent and they are
represented as:
b0
B
En n exp
k T
= −
(1.2)
and 0 s
B
µ Eµ exp
T k T
= −
(1.3)
where Eb is binding energy and Es is the strain energy or migration energy, kB is the
Boltzmann constant, T is temperature in Kelvin, n0, µ0 is the pre-exponential factors of
10
carrier density and mobility of the charge respectively. In general, the experimental data
on ionic conductivity in glasses in a limited temperature interval is represented as:
0 a
B
E(T) exp
T k T
σσ
= −
(1.4)
where Ea=Eb+Es is the total conductivity activation energy. The conductivity usually
shows Arrhenius temperature dependence. When a charge carrier is in a glass network, it
experiences two processes: dissociation and migration as shown in fig. 1.1 [97].
Fig. 1.1: Schematic diagram of ion transport in glass exhibiting the two activation
energies namely binding energy Eb and migration energy Es.
The charge carrier, usually a cation, dissociates from the anion, such as non-
bridging oxygen and then transports to the next available position through the pathway in
the glass network. Generally it is found that the pre-exponent, σ0 does not change much
with composition, so most researchers focus on the study of the behavior of the
conductivity activation energy. Two extreme conduction behaviors have been considered
in these glasses. One is the strong-electrolyte behavior which assumes the carrier density
Eb
Es
BO
BO
NBO NBO
Ene
rgy
r r
11
n is independent of temperature and all ions in the glass are mobile and the strain energy
dominates the dc conductivity [98-103]. Another is the weak-electrolyte behavior which
assumes that mobility, µ is independent of ion concentration or temperature and the
Coulomb energy dominates in the dc conductivity [94, 104]. While many models of ionic
conduction in glasses have been proposed, the most widely used models are as given
below
1.6.1 Anderson and Stuart model
Anderson and Stuart have proposed a model for the activation energy in ion
conducting glasses [92]. The activation energy for the dc conductivity, Ea, was
considered from a microscopic prospective. According to them, ionic transport in glasses
occurs by means of diffusion motion of mobile ions between energetically stable sites
located in the glass structure. The activation energy associated with such motion arises
from two contributions. The first one is Coulombic term associated with the removal of
an ion from its countervailing charged environment at one site to a position midway
between two neighboring sites without changing the structure of the glass and the second
one is associated with the strain energy which considerably deforms the structure to allow
the ions to pass through the gateway formed by the fully bonded bridging anion atoms
separating the two neighboring ion sites. The strain energy is represented as:
( )2
s D DE =4πG r-r (1.5)
where r is the cation radius, rD is the “doorway” radius in the glasses enough to
accommodate the cation, and G is the shear modulus of glass. This energy represents the
energy required to dilate the structure from its original radius rD out to the radius of the
cation r.
The coulomb energy or binding energy was estimated from the ionic crystal
theory, making some modification due to the difference between glass systems and ionic
crystals, and is shown in the following equation:
2
0b
0
βzz eE =
γ(r+r ) (1.6)
where z0 and r0 are the charge and radius of the O2- ion, respectively, β is a lattice
parameter depending on the distance between neighboring sites, z is the charge of cation,
12
γ is a covalency parameter, equal to dielectric constant in practical. So the total activation
energy according to Anderson-Stuart model is given by:
( )2
20a s b D D
0
βzz eE =E +E = +4πG r-r
γ(r+r ) (1.7)
The Anderson-Stuart model has been extensively applied to alkali oxide glasses, mixed
anion conductor, some chalcogenide glasses and even to new Li+ ion conducting glasses.
It can explain the conductivity behavior with the composition change in the glass.
1.6.2 The weak electrolyte model
In 1977, Ravaine and Souquet [93] have proposed the theory based on
correlations between the ionic conductivity and thermodynamic activity of fast ion
conducting glass called weak electrolyte model. They argue that the concentration of
moving charges is limited by the saturation of dissociated mobile ions and thus only a
very small fraction of cations participates in the transport of current. The weak electrolyte
model advocates the existence of two distinct carrier concentrations, mobile and
immobile carriers. In this model, carrier mobility is considered to be independent of the
glass composition and hence the structure.
1.6.3 Defect model
Glarum [96] have proposed a model based on the defects in glasses. In this the
interacting mobile ions can be taken into account by a defect pair as a first
approximation. Let us consider alkali ions in an alkali silicate glass. The alkali ion locates
near the NBO. If an alkali ion moves from one site near NBO to another site near the
other NBO, then the latter NBO is accompanied by two alkali ions. So, this pair of alkali
ions can be treated as a "defect" such as in lattice defect theory. The number of the
defects can be calculated by assuming the creation energy, and the motion of the "defect"
is dealt with conventional defect diffusion theory. The defects diffuse through the
material with a diffusion coefficient Ddef and have a number density ndef. Based on this
picture the ionic conductivity and dielectric relaxation of the defects can be calculated.
This model is further extended to the diffusion controlled relaxation theory by Elliott in
13
order to explain anomalous behavior of ac conductivity and nuclear magnetic resonance
relaxation time [95].
1.6.4 Random network model
Zachariasen analyzed the glass forming condition of oxide glasses based on
crystallographic point of view and concluded that the glass has a random network
structure formed by the corner sharing polyhedrons made of a metal atom at center and
oxygens at corners [17]. Typical silicate glass is actually composed of the SiO4
tetrahedrons shearing corner oxygens to form three dimensional networks. The oxygen at
the corner is bridging two silicon atoms and is called bridging oxygen (BO). Similarly, in
borate glass, BO3 planer triangles or boroxisole rings, and PO4 tetrahedrons in phosphate
glasses are the structural units to form networks. These oxides are called network forming
oxides or network formers, which can be regarded as inorganic polymers. A typical
phosphate glass is composed of PO4 tetrahedron and this tetrahedron is connected by
sharing two corner oxygens to form one dimensional network and rings. When alkali
oxide as Na2O is added to the phosphate glass, the introduced oxide ion partly destroys
the glass network to form non-bridging oxygen (NBO) connecting only one P atom.
Simultaneously, the introduced Na+ ion is rather weakly bounded the non-bridging
oxygen, such as P2O74- dimmers at pyrophosphate composition (Na4P2O7), and monomer
PO43- at orthophosphate (Na3PO4) composition. This Na+ contributes to the ionic
conductivity at high temperature. These materials which partly modify the glass network
are called network modifiers. Some oxides such as Al2O3, which themselves never form
glass but are incorporated in the network when added to the glass formers are called
intermediate compounds. Addition of the modifiers change the glass structure especially
the concentration of the NBO, which strongly affect the mechanical, thermodynamic and
ionic transport properties of oxide glasses due to the break down of the framework
structure and trapping the cation around the NBO [105]. The mixing of different network
formers and modifiers often results in the ionic conductivity enhancement and is called
mixed anion effect or mixed former effect [106]. It is mainly due to the change in the
binding energy between the oxide and mobile cation caused by the network structure
modifications.
14
1.7 Present work
Understanding of the ion conduction and relaxation mechanisms in fast ion
conductors is a challenging one. The most commonly used technique to characterize the
dynamics of diffusing ions in glasses, melts and crystals is the electrical relaxation.
Among the various types of glasses investigated, the NASICON type phosphate glasses
have shown interesting features, such as remarkable structure, glass forming ability, good
chemical stability and easy fabrication of various shapes, electrical and optical properties,
and a promising material for solid electrolyte. In these views the chapters are arranged as
follows
The second chapter comprises of two parts:
(1) The synthesis of NASICON phosphate glasses of various compositions.
(2) Characterization, physical, thermal and electrical studies of the prepared glasses.
In part one, a complete solid state reaction technique of synthesis of NASICON
phosphate glasses is provided. In the second part, different experimental tool used to
characterize the materials are broadly outlined.
Chapter III is directed towards the dynamics of different cations in the NASICON
based glass matrix with Ti4+ and Nb5+ as transition metal oxide in various compositions
A5TiP3O12 (where A=Li, Na, Ag), A4NbP3O12 (where A= Li, Na, Ag) and A(4+x)TixNb(1-
x)P3O12, (where A=Li, Na and x=0.0, 0.25, 0.50, 0.75, 1.0). This involves insight in both
the local structures of the host network and cation coordinated within these systems. The
ac conductivity measurements for these samples are carried out with variation in
frequency at different temperatures and the results are discussed. The scaling in ac
conductivity and electric modulus are also investigated and results are reported. Silver
based NASICON polycrystalline have been reported earlier but silver based glasses with
NASICON framework have not be reported in the literature yet to our knowledge.
L4NbP3O12 glass systems show high thermal stability and glass forming ability compare
to other system investigated.
Chapter IV deals with mixed alkali effect in NASICON type glasses with
composition changes in cations, e.g. (LixNa1-x)4NbP3O12 and (LixNa1-x)5TiP3O12. The
study of mixed alkali effect related to the ionic transport is important for the purposes of
understanding the diffusion mechanism of alkali ions and these mechanistic insights are
15
vital to the development of new solid/rubbery electrolytes for battery applications with
potentially widespread technological application. The influence of mixed alkali effect on
the physical, thermal and structural properties has been interpreted using density, DSC
and FTIR studies. The effect in electrical properties has been discussed using various
tools of ac regimes followed by the scaling behavior in NASICON glass.
Chapter V, electrical relaxation and ion dynamics are studied with inclusion of
metal oxide in B site substitution of the NASICON glasses with variation in composition.
As NASICON glasses are binary phosphate glasses with transition metal oxide as glass
modifier, the charge carrier concentration of these glasses also depend on the transition
metal oxide. Their physical, thermal and structure properties changed significantly when
transition metal oxide are replaced by the other. The effect of divalent ions in the
electrical conductivities is studied in composition A2NbMP3O12, where A=Li, Na and
M=Cu, Zn, Cd, Pb. Since zinc based materials have higher conducting compared to the
other divalent ions, a new composition of A4Nb(1-x)Zn5xP3O12, where A=Li, Na, x=0.1,
0.2, 0.3, 0.4 glasses are prepared and the relative electrical measurement data are
analyzed using various formalism to study the effect of insertion of divalent ion (zinc) in
NASICON glasses in ion dynamics and its relaxation. The salient features of the thesis
are summarized in chapter VI.
The part of work done in this thesis have been published in internationally peer
reviewed journals like Solid State Ionics, Material Chemistry and Physics and Solid State
Sciences [107-109] and one of the published paper has been cited in the recent published
work of C.M. Chu et al., [110].
16
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21
Chapter-II
EXPERIMENTAL TECHNIQUES The present investigation comprises the following two parts:
(1) The synthesis of NASICON phosphate glasses of various compositions.
(2) Characterization, physical, thermal and electrical studies of the prepared glasses.
2.1 Preparation of glasses
In principle any substance can be made into a glass provided it is cooled from its
liquid state fast enough to prevent crystallization [1, 2]. In actual practice, glass formation
has been achieved with relatively limited number of substances. There are at least a
dozen of different techniques used to prepare materials in an amorphous state. Three
commonly used methods are: (i) melt quenching, (ii) thermal evaporation, and (iii) sol-
gel process. The first method speeds up the rate of cooling from the liquid state by
employing the different sophisticated techniques, with a quenching rate of 109K/s [3,4].
The second method involves the condensation of the vapor phase to the glassy thin films.
In the third method glass materials are obtained by sol-gel process [5]. In this, melt
quenching is the oldest method of producing an amorphous solid in which the molten
form of the material is cooled quickly to stop the crystal growth [6]. There are several
techniques that can be used to prepare glassy materials using melt quenching method. Out
of these, five are commonly used to prepare most of the non-crystalline materials for
commercial or academic. Quenching rates play a significant role in the preparation of
glassy solids. Different quenching rates are categorized by:
a. Slow quenching (cooling rate ~10K/s)
b. Moderate quenching (cooling rate ~102K/s)
c. Rapid splat quenching (cooling rate ~105K/s)
d. Condensation from vapor (cooling rate ~108K/s)
22
Fig. 2.1: Different methods of glass preparation: (a) Twin roller quenching (b) melt
spinning (c) Slow cooling of the melt, (d) Quenching of the melt in liquid nitrogen
and (e) Thermal evaporation.
23
Different methods of preparation of glassy solids are schematical shown in
Fig. 2.1. For materials with very high glass forming tendency like SiO2, the melt can be
allowed to cool slowly at the rate of 10-4 to 10-1K/s by simply turning off the furnace or
by bringing down its temperature in a programmed manner. For example, 1K/s is being
used to form an amorphous solid of glass formers such as SiO2, B2O3 or P2O5. Some
materials require faster cooling rates and these materials are prepared by quenching the
melt in air or in water, in this case the rate of cooling would be in the range of 101-
102K/s. Metallic glasses require a very high cooling rate ~ 105 to 106 K/s which can be
obtained by splat-quencing method in which a material in its molten form is poured into
the gap between two mutating rollers [7, 8]. Another method to obtain an amorphous
solid is by by-passing the liquid state completely using vacuum thermal evaporation,
sputtering decomposition of gaseous compound by r-f discharge, or deposition from salt
solution by electrolysis [9].
In the present investigation vitreous samples of NASICON phosphate with
various compositions were synthesized by melting the mixture of stochiometic quantities
of raw materials and they are shown in Table 2.1. The overall reaction for the formation
of Na5TiP3O12 , Li5Nb1-xZn2.5xP3O12 (where 0≤x≤0.4) and Ag4NbP3O12 are given by:
2.5Na2CO3+TiO2+3NH4H2PO4 Na5TiP3O12+3NH3+9/2H2O+2CO2
5/2Li2CO3+x/2Nb2O5+(5x/2)ZnO+3NH4H2PO4 Li5Nb1-xZn2.5xP3O12+3NH3 +
9/2H2O+5/2CO2
4AgNO3+½ Nb2O5+3NH4H2PO4 Ag4NbP3O12+4NO2+3NH3+9/2H2O+O2
Similar reaction condition was followed for the preparation of other samples. The
synthetic procedure was optimized by varying the choice of reagents, heating temperature
and duration of reaction. The following is the typical procedure for the preparation of
samples:
24
Step 1: The calculated amounts of the starting materials were weighed and ground in an
agate mortar for 45 min.
Step 2: The mixture was placed in silica crucible and slowly heated in an electrical
furnace up to 573 K for 6 hours in order to ensure the total decomposition of
the reagents. For silver based samples the mixture was maintained at 443 K for
48 hours for the decomposition of the reagents.
Step 3: After cooling to room temperature, the mixture was again ground for 45 min in
agate mortar and heated in a silica crucible for 14-16 hours at temperature
673-1073 K depending upon the composition without melting the mixtures.
Step 4: The samples were heated further to melting and stirred for 5-10 min to ensure
homogeneity.
Step 5: Finally, the melts were poured into stainless steel plate and quenched by
pressing with another stainless steel plate at room temperature. Stainless steel
plates were preheated before quenching for some of the samples to get a
brittle less glass.
Step 6: Soon after the glass preparation, the glass samples are kept for annealing well
below the glass transition temperature in order to avoid internal mechanical
stresses developed during solidification of liquid phase to glassy phase.
Table 2.1: Glass Compounds prepared and the starting materials used
S. No Glass Compound Starting materials
1. A4NbP3O12 (A = Na, Li, Ag),
A5TiP3O12 (A = Na, Li, Ag),
A(4+x)TixNb(1-x)P3O12, where A=Li,
Na (0.0≤x≤1.0).
Na2CO3, Li2CO3, AgNO3, TiO2,
Nb2O5, NH4H2PO4.
2. (LixNa1-x)4NbP3O12
(LixNa1-x)5TiP3O12.
Na2CO3, Li2CO3, TiO2, Nb2O5,
NH4H2PO4.
3. A2NbMP3O12, where A=Li, Na and
M=Cu, Zn, Cd, Pb
A4Nb(1-x)Zn5xP3O12.
Na2CO3, Li2CO3, Nb2O5,
NH4H2PO4, CuO, ZnO, CdO
and PbO
25
2.2 Physical Characterization
2.2.1. X-Ray Diffraction
X-Ray diffraction (XRD) technique has been an indispensable tool for structural
studies of solids [10]. It gives a complete description of the structure such as the crystal
system, space group, unit cell dimension, atomic coordinates and electron density
distribution around them [11]. There are three standard methods of X-ray diffraction
analysis for the crystal structure determination:
(1) Laue method
(2) Rotating crystal method
(3) Powder method
Fig. 2.2: XRD pattern of Li(4+x)TixNb(1-x)P3O12 (LNTPx) where 0≤x≤1 with no
characteristic peaks.
In the present study the powder method has been used, in which the incident
monochromatic radiation are allowed to fall on a finely powdered specimen. The
diffracted rays leave individual crystallites satisfying the Bragg’s equation, 2dsinθ=nλ,
where λ is the wavelength of the monochromatic X-ray, n is the order of the diffraction, d
is the perpendicular distance between the parallel planes in the crystal and θ is the angle
of diffraction. The XRD measurements usually yields structure less peaks for amorphous
materials due to its disorder. In the present study X'Pert PANalytical X-ray diffractometer
26
with monochromatic CuKα radiation (λ=1.5418 Å) was employed to record on powder
glass samples at room temperature. The scanning was made at the rate of 2o/min at the
glancing angles between 5 and 75o. Fig. 2.2 shows the XRD pattern of Li(4+x)TixNb(1-x)P3O12
(LNTPx), where 0≤x≤1. It didn’t show any characteristic peak intimating the amorphous
nature of the sample. The similar nature was observed for all the samples prepared.
2.2.2 Density Measurement
Density of the freshly synthesized bulk glassy samples can be used to characterize
glasses. The relation between density and composition is very important because of its
association with the structural details of the glass. Density changes may occur in a glass
by changing the composition of the glass formers or the glass modifiers. Minami and
Tanka [12] have calculated the molar volume and ion concentration in silver ion
conducting glasses from the measured density. Calvo and Jordan [13] reviewed the
observed density and proposed a structural model to explain the variation of density with
composition. The density measurements were also used to find the oxygen packing
density in oxide glasses [14]. In the present study density of the glasses were determined
by Archimede’s method using glass fragments free from bubbles. High purity xylene was
used as buoyancy liquid and a single pan electrical balance of 10-4g sensitivity was used
to measure the weight of the liquid and the glass samples. The density is obtained from
the relation:
ρ=Waρ1/(Wa-W1), (2.1)
where ρ is the density of the sample, Wa is the weight of the sample in air, W1 is the
weight of the sample fully immersed in liquid and ρ1 is the density of the liquid used.
These measurements were carried out at room temperature with an accuracy of
±0.03g/cm. The molar volume Vm was calculated from density using formula Vm=M/ρ,
where M is the corresponding molecular weight of the samples.
2.2.3 Thermal Analysis
Measurement of physical and chemical properties of the materials as a function of
temperature is called the thermal analysis. Thermal analysis techniques are useful to
determine the glass transition temperature, chemical decompositions, phase transition
27
temperature, crystallization kinetics of glass and polymers, coefficient of thermal
expansion and heat capacity, etc. The differential scanning calorimetry (DSC) is a
versatile technique to study phase transitions such as glass transition temperature Tg,
onset of the crystallization temperature Ts, crystallization temperature Tc, and melting
temperature Tm of the glass. In this technique, the sample and the reference material are
maintained at the same temperature during the heating process. The extra heat input
required to maintain the temperature during the event in the sample is measured and
plotted against temperature or time. During the thermal event, the sample temperature
either lags behind or leads the temperature of the reference depending on the change
whether it is endothermic or exothermic.
200 400 600 800-50
-45
-40
-35
-30
-25
-20
-15
-10
Tm
Tc
Ts
Tg
Heat Flow [mW]
Temperature [oC]
Fig 2.2: DSC thermogram of Li5TiP3O12 glass sample in N2 flow at 10oC/min heating
rate showing Tg is glass transition temperature, Ts is onset crystalline temperature,
Tc is crystalline temperature and Tm is melting temperature.
28
The thermal stability ∆T parameter is usually employed to estimate the glass
stability [15] which is defined by:
∆T=Ts-Tg (2.2)
According to Saad and Poulin [16] the thermal stability parameter S which reflects the
resistance for devitrification of glass and it is defined by:
S=(Tc-Ts) (Tc-Tg)/Tg (2.3)
The term (Tc-Ts) is the rate of devitrification transformation of glassy phase. The glass
forming ability parameter Kgl known as Hruby’s parameter for the different glass is given
by [17]:
Kgl = (Tc-Tg)/(Tm-Tc) (2.4)
The value of ∆T, S and Kgl calculated from Eqs. (2.2), (2.3) & (2.4) respectively and
these are used later and the results are discussed subsequently. According to Hruby,
higher the value of Kgl greater its stability against crystallization and supposedly the
higher the vitrification ability. The DSC studies were carried out using thermal analyzer
TA-SDT-Q600 in temperature range 313–1173K and Metteler Toledo 821e in the
temperature range 313–773K instruments under N2 atmosphere at a heating rate of 10 K
min−1 on the as-quenched glass-plate. Fig 2.2 shows the DSC thermogram of Li5TiP3O12
glass sample showing glass transition temperature Tg, onset crystalline temperature Ts,
crystalline temperature Tc and melting temperature Tm.
2.3.4 Fourier Transform Infrared Spectroscopy Studies
Since the diffraction techniques are not advantageous position in amorphous
materials due to the absence of long-range order, the elucidation of the information on the
structural elements and symmetry in amorphous materials is a result of the experiments
involving the transmission, reflection, refraction and scattering of light in the range of
400-4000cm-1. Raman and infrared spectroscopy techniques are the direct probes for such
studies. The vibrational spectra provide essential information about the structural
arrangement of the glassy network, such as the degree of polymerization of the network
forming polyhedra. FTIR transmittance spectra for the samples in the wave number
region 1600-400cm-1 were recorded with a resolution of 8 cm-1 and with a data
accumulation of 40 cycles using a Shimadzu FTIR-8700 Fourier transform infrared
29
1600 1400 1200 1000 800 600 400
8
1- P-O-P Stretching
2- O-P-O Bending
3- P-O-P Stretching
4 P-O-P Bending
5- PO4
3- Ionic
6- PO4
3- Ionic
7- (P-O)(-) ionic vibration
8- P2O7
4- vibration
76 5 4
3
1
2 1
Na4NbP
3O12
Na5TiP
3O12
Transmittance [A. U.]
Wavenumber [cm-1]
spectrophotometer. The measurements were made using spectral grade potassium
bromide (KBr) pellets containing 1wt% of powdered glass. Sample and KBr powder
were mixed in 1:20 weight ratio and the mixture was ground into a fine powder in a clean
agate mortar. The powder was pressed to form transparent thin pellets by using a KBr
press and they were used to record the FTIR spectra at room temperature.
Fig 2.3: FTIR spectrum of NASICON glass.
Table 2.2: FTIR bands for some of the NASICON type glasses
Sample FTIR band positions (cm-1
)
Li5TiP3O12 1153, 1055, 750, 635, 565, 471
Na5TiP3O12 1150, 1080, 976, 906, 729, 625, 555, 486, 444
Ag5TiP3O12 1159, 1023, 917, 740, 622, 534.
Li4NbP3O12 1175, 1070, 997, 916, 750, 642, 544, 471
Na4NbP3O12 1200, 1080, 984, 902, 741, 633, 536, 444
Ag4NbP3O12 1162, 1026, 914, 740, 623, 525
Na2NbCdP3O12 1169, 1010, 914, 745, 625, 528
Na2NbZnP3O12 1169, 1022, 918, 745, 624, 536
Na2NbCuP3O12 1180, 1015, 922, 756, 632, 536
Na2NbPbP3O12 1153, 1022, 906, 740, 605, 532
30
Li5-xNbxTi1-xP3O12 FTIR band position in cm-1
x=0 1153, 1055, 993, 750, 635, 565, 471
x=0.25 1155, 1059, 997, 748, 642, 563, 471
x=0.50 1151, 1059, 999, 759, 642, 563, 465
x=0.75 1159, 1070, 993, 752, 642, 559, 471
x=1.0 1175, 1070, 997, 916, 750, 642, 544, 471
Na5-xNbxTi1-xP3O12 FTIR band position in cm-1
x=0 1150, 1080, 976, 906, 729, 625, 555, 486, 444
x=0.25 1159, 1082, 976, 903, 727, 624, 550, 471, 434
x=0.50 1167, 1082, 978, 891, 731, 629, 542, 484, 438
x=0.75 1176, 1082, 980, 897, 733, 629, 540, 474, 446
x=1.0 1200, 1080, 984, 902, 741, 633, 536, 444
(Li1-xNax )4NbP3O12 FTIR band position in cm-1
x=0 1175, 1070, 997, 916, 750, 642, 544, 471
x=0.20 1180, 1076, 987, 918, 748, 628, 552, 481, 451
x=0.40 1192, 1080, 991, 906, 748, 628, 567, 552, 447
x=0.60 1192, 1080, 987, 918, 741, 632, 552, 471
x=0.80 1199, 1080, 984, 903, 741, 633, 536, 447
x=1.0 1200, 1080, 984, 902, 741, 633, 536, 444
(Li1-xNax )5TiP3O12 FTIR band position in cm-1
x=0 1153, 1055, 750, 635, 565, 471
x=0.20 1130, 1049, 976, 926, 744, 629, 571, 463, 432
x=0.40 1138, 1053, 984, 922, 741, 632, 567, 474, 444
x=0.60 1145, 1050, 972, 918, 736, 628, 571, 478,
x=0.80 1149, 1084, 972, 914, 733, 626, 555, 450
x=1.0 1150, 1080, 976, 906, 729, 625, 555, 486, 444
31
Na4Nb(1-x)Zn5x/2 P3O12 FTIR band position in cm-1
x=0 1150, 1080, 976, 906, 729, 625, 555, 486, 444
x=0.1 1085, 984, 907, 724, 632, 545, 482
x=0.2 1082, 986, 909, 730, 634, 547, 480
x=0.3 1082, 991, 909, 737, 635, 550, 481
x=0.4 1086, 991, 917, 736, 638, 551, 478
Li4Nb(1-x)Zn5x/2 P3O12 FTIR band position in cm-1
x=0 1175, 1070, 997, 916, 750, 642, 544, 471
x=0.1 1176, 1080, 995, 922, 752, 636, 552, 467, 436
x=0.2 1174, 1083, 996, 924, 750, 641, 562, 465
x=0.3 1090, 999, 926, 748, 644, 571, 463
x=0.4 1082, 998, 928, 750, 640, 576, 462
The FTIR spectra of two different glasses are shown in Fig. 2.3. These bands are
assigned to the various vibrational contributions of the basic phosphates. The spectra
endorse that the sample are fully vitrified as there are no traces of initial precursors
(absence of carbonate IR peaks in the region 1500-1400cm−1). Table 2.2 lists the
assignments of FTIR bands based on the standard literature references [18-23]. The
origin of the bands at lower wave numbers, namely, below 600cm1, is not quite clear. It
is usually assumed that in this range bands originate from vibrations of large groups of
atoms, like 3,4-member rings or short chains. The continuous spectrum observed in the
region between 1200cm-1 to 890cm-1 assign to the symmetric and asymmetric stretching
modes. In this region the superposing of band vibrations of structural forms, mentioned
above, as well as the bending vibrations of P-O-P. The peak at ~540cm-1 and the weak
shoulder peak at ~640cm-1 together constitute a band. The position of this band
corresponds to the asymmetric bending modes of the PO4 ion in the spectra [24]. An
absorption band present in this region 500–650cm–1 in all glasses is attributable to O–P–
O bending modes [24, 25]. The weak band at ~460cm–1 is also assigned to bending mode
of the PO4 tetrahedra [24-26]. Superposing of bands due to vibrations of structural forms,
32
mentioned above, as well as the bending vibrations of P–O–P and P–O–Nb bridges give
continuous spectrum usually observed in this region [23]. The vibration band at 1175cm-1
is due to the P2O74 pyrophosphate contribution present in the glass [16, 27]. In Ti
containing glass the band 750cm–1 is assigned to [TiO6] entities. Particularly strong
vibration bands at 565cm-1 can be taken as indication of octahedrally coordinated Ti [27].
In niobium containing glasses the bands of P-O-P and O-Nb-O are similar [27]. The
strong vibration peak present at ~900cm-1 may be due to the contribution of [NbO6]
vibrations [29].
2.3 Electrical properties
When an external electric field is applied to any material medium, a finite amount
of charge transport by either electrons or ions takes place resulting in a direct current, Io
and polarization displacement current, Ip. The magnitudes of Io and Ip may vary in wide
limits according to the nature of the material medium. The materials medium is said to be
insulator if the magnitude of Io is found to be very small in comparison to Ip and in such
materials the phenomena of polarization and relaxation dominate. If Io dominates, the
medium is said to be a conductor of electricity. Basically when a dielectric material is
subjected to an electric field the polarization takes place due to induced dipole moment or
due to rotation of permanent electric dipoles present in the materials. In dielectric
materials, the possible polarizations are the electronic, ionic and orientation polarization.
In this mechanism the charges are locally bound in atoms, in molecules or in the structure
of solids. Electronic polarization occurs due to the shift in the electronic charge cloud of
the atom with respect to the positive nucleus, which induces dipole moment under the
influence of local electric field. In ionic polarization, the net induced dipole moment is
due to the displacement of positive and negative ions from the net equilibrium position.
In orientation polarization, the orientation of molecular dipoles contributes to the total
polarizability. Some mobile charges either electrons or ions can also be found in
dielectrics and may move by hopping between localized sites. If the hopping is continued
only to limited paths it does not produce dc conduction which requires transfer of charge
from one electrode to the other. The macroscopic behavior of a dielectric can be
understood by considering the dielectric in between a parallel plate capacitor.
33
2.3.1. Impedance spectroscopy
Generally the electrical conductivity and relaxation process in fast ion conducting
glasses play an important role and these are often the deciding factors about the
suitability of the material for a particular solid state ionic device. Therefore, the
extraction of true or intrinsic nature of ion conduction mechanism is essential for a
material. Impedance spectroscopy is a powerful method for electrical characterization of
various ion conducting solids. It is capable of determining the contributions of individual
ion conductivity and or electrode process [30, 31]. Electrical response of a system can be
determined by several single processes in solid state ion conductors. The vital property of
impedance spectroscopy is its exclusive capability to distinguish the different steps in an
ion conducting process including the detailed information about the surface and bulk
properties. In contrast to dc measurements, frequency dependent complex impedance
measurements generally give more detailed information on the electrical properties of a
system. Impedance measurements are performed by applying small sinusoidal potential
or current to the sample and measuring its current or potential response over a wide range
of frequencies. Individual resistive processes can usually be distinguished via varying the
frequencies by several orders of magnitude. In 1969, Bauerle was the first researcher
applied the technique for ion conducting materials to differentiate between the bulk, grain
boundary and electrode resistances [32]. Since then impedance spectroscopy become the
most powerful tool to investigate a wide range of ionic conductors such as polymers,
ceramics and glasses.
The graphical representation are commonly applied for the complex function, Z,
in order to analyze the impedance measurements is the Nyquist plot, where the real and
imaginary parts of impedance are plotted on linear axis against one another in one plane
as shown in the Fig. 2.4. The lower frequency data are represented on higher values of
impedance in x axis of the Nyquist plot. This representation is widely used for the
interpretation of the ion conducting materials. According to the impedance spectra an
electrical network representation called equivalent circuit can be constructed which
interprets various contributions to the electrical circuit. Optimization of impedance
analysis via equivalent circuit simulation has the basis to regard the measured
impedances as network impedance elements[33, 34]. This network model has to
34
approximate the measured impedance well over the whole frequency range and it can
consist of resistors (R), capacitors (C), inductors (L), Warburg impedance (W) and
constant phase element (CPE). Each of these elements can be characterized in Nyquist as
well as in Bode plots. Serial or parallel combinations of these elements produce the
impedance plots. When modeling an ionic process, an ideal capacitor assumes that the
surface under investigation is homogeneous. Irregular electrode surface, which is usually
due to surface roughness or non-uniformly distributed properties, leads to a dispersion of
the parameters [35].
Fig. 2.4: Impedance plot for a depressed circular arc showing definition of
quantities.
The depression of the semicircles is always encountered in real systems, and thus
the non-ideal behavior is exhibited to some degree. Hence, commonly observed non-ideal
capacitance can be simulated mathematically very well by introducing so-called the
constant phase element, CPE [37, 38]. Thus, by replacing the capacitor in the RC element
with CPE, one can deal with the frequently observed depressed semicircles. The circuits
containing CPE are widely used to explain the behavior of solid ionic conductors and
solid-solid interfaces. The impedance of a CPE element is expressed as:
CPE
1Z
( )nQ iω= (2.5)
35
where n is an empirical constant having values between 0 and 1 [39]. When n=1, CPE
acts as an ideal capacitor where Q=C and when n=0, CPE is treated as an ideal resistance
where Q=R. The parameter n is a measure for the degree of depression in Nyquist plot.
Parallel connection of R and C circuit is a semicircular in Nyquist plot. It is perfect
semicircle for n=1 and depressed semicircle for n<1. The semicircle has an intercept on
the Z' axis at low frequency and the Z'' has maximum where ωRC=1. The imaginary part
of the impedance reaches maximum at a frequency, ωimp=1/RC and it is time constant
τimp=1/ωimp and treated as a hopping charge relaxation time.
When two RC elements are present in the systems, each parallel RC element gives
rise to a semicircle in the complex impedance plane. Two well separated semicircles in
the complex impedance plane are represented by constructing two serial RC elements as
exemplified in Fig. 2.5. For example, in real polycrystalline systems two semicircles can
be observed due to bulk and grain boundary phenomena. This could be encountered when
there is a difference in magnitude as shown in Table. 2.3 for the capacitances of the
observed processes. Therefore, the capacitance can be calculated for each process and its
magnitude gives strong information on the physical origin of the semicircles.
Table 2.3: Typical order of magnitude of some common capacitance.
Capacitance [F] Responsible Phenomenon
10-12 Bulk
10-11 Minor, second phase
10-11-10-8 Grain boundary
10-7-10-5 Sample-electrode interface
10-4 Electrochemical reaction
36
Fig. 2.5: Impedance spectra with two semicircles, insert shows equivalent circuit for
two serial connected RC elements.
2.3.2. AC response and conductivity
The conductivity process is visualized as a series of consecutive and independent
hops of ions over the barriers along the direction of an electric field. The measurement of
conductivity is perhaps the most widespread application of impedance spectroscopy and
numerous examples can be found in which the conductivity is indeed essentially
independent of frequency over many decades. However, there are also examples in
which, even after correct treatment of experimental data, considerable dispersion of the
conductivity remains. In many non-metallic ionic conductors dc or ac electrical
conductivity is the result of diffusion of ions through the conductors. The process of ions
through fast ionic conductors, enter into a wide range of other phenomena of concern to
solid state physics, chemistry, metallurgy and material science. The diffusion of ions
which follows on the existence of gradients in chemical or isotropic composition i.e.,
solid state diffusion is basic to these interests. The electrical conductivity of ionic
material, particularly in the amorphous state, has been much studied in the past few
37
decades. Hopping conductivity is no longer expected to be independent of frequency in
the presence of many-body (long-range) interactions. Following the work of Jonscher
[38, 40], who showed that a large number of dive, the presence of interactions has been
invoked by Almond et al., [41-43] to explain the observation of frequency dispersion in
the conductivity of a number of solid electrolytes. These authors expressed the ionic
conductivity of a number of materials by the following expression:
σ'(ω)=σdc+Aωn (2.6)
where σdc and A are the scales of dc and ac conductivities, respectively, and n is related
to the nature of physical process controlling the conduction of ions and the second term is
of the CPE type. Using Jonscher's empirical equation, this expression was rewritten in the
form:
σ'(ω)=Kωp+ Kωp1-n ωn (2.7)
where K is the dc pre-exponent, which depends on the concentration of carriers, and ωp is
the hopping frequency of the ions. Combining these two equations allows the calculation
of the hopping rate:
ωp=(σdc /A)1/n. (2.8)
The high temperature limiting vale of ωp is equal to the attempt frequency, which is
independently accessible by infrared measurements. With this ωp, it is possible to
estimate the carrier concentrations. According to Jonscher, the source of power-law
behavior in hopping conductors is relaxation of the ionic atmosphere after the movement
of a particle. A quantitative model based on a similar idea has been developed by Funke
[44]. It is assumed that immediately after an ion hops to a new site (new minimum in
lattice potential energy), it is still displaced from the true minimum in potential energy,
which includes contributions from other mobile defects. At longer times the ion may
either hop back to its initial site or the other defects will relax so as to move the true
minimum closer to, and eventually coincident with, the new lattice site. The dynamics of
this model have been developed, and apparently they predict upper and lower frequency-
limiting conductivities and, in between, a region of power law dependency of the type
expressed by the CPE. Unlike simple CPE response, the complex plane arcs approach the
real axes vertically, corresponding to upper and lower limits to the relaxation time of the
system. Depending on the frequency of the measurement, the processes of diffusion of
38
ions with different jump probabilities will contribute different amounts to the total
conductivity. At a frequency corresponding to each transition rate, a new conductivity
process with higher activation energy will begin to contribute to the total. It is evident
that the overlap of several different processes will lead to dispersion over a wide
frequency range.
An alternate approach of complex electric modulus formalism was adopted in the
field solid state ionics because it discriminated against electrode polarization and other
interfacial effects. That is the impedance and conductivity formalism might emphasize
inter-granular conduction process whilst the electric modulus would be dominated by
bulk effects. This has been introduced by Macedo et al. called electric modulus, M*=1/ε*,
where ε* is the complex permittivity, which tend to emphasize bulk properties at the
expense of interfacial polarization [45,46]. Typical features of M*(ω) include a broad,
asymmetric peak in the imaginary part and a sigmoidal step in the real part. Proponents of
the modulus approach interpret the broad, asymmetric Gaussian-like shape of M*(ω) as
indicative of a non-exponential decay of the electric field in response to an applied
displacement field [45, 47]. This decay is reasonably well described by a stretched
exponential defined by Kohlrausch William-Watts forms [48, 49] as:
ϕ(t)=exp [–(t/τ)β], (2.9)
which is related to M*(ω) as:
( )
−=∞ dt
d-L1
ε
1ωM* φ
(2.10)
where L(x) is the Laplace transform of x the stretching parameter β is approximately
equal to 1/W, where W is the full width at half maximum (FWHM) of M''(ω) normalized
to that of Debye process. The smallness of the exponent β characterizes the degree of
non-Debye behavior. This particular decay function is also used to describe dipolar
reorientation in super cooled liquids [50, 51] and is found in a variety of other relaxation
phenomena in amorphous materials including mechanical, volumetric, nuclear magnetic
resonance, and magnetic relaxation. The shapes of the Williams-Watts derived M'' plots
lie between the symmetric plots expected from log-normal and Cole-Cole forms and the
highly asymmetric Cole-Davidson form. Here the parameter β was found to be largely
independent of temperature.
39
2.3.3. Electrical measurements
The electrical measurements were performed with impedance analyzer (Alpha-A
4.2 Analyzer, Novo Control, Hundsangen, Germany) which was combined with the ZG 4
impedance interface in a two probe method. This system is comprised of the Novocontrol
alpha dielectric analyser, the automated liquid nitrogen (LN2) quatro temperature control
system, and the two-wire ZGS active sample cell. Silver paste was applied on opposite
faces of the pellets as electrodes. Measurements and data recording were performed with
WinDeta data analysis program by the central computer assisted controlling of all
components. The equipment was designed to measure very high impedance values over a
wide range of frequencies varying from 0.01Hz to 10MHz. The set up for impedance
spectroscopy cell is schematically shown in Fig. 2.6. For some of the samples both faces
of the samples were polished by using silicon carbide sheet and silicon carbide powder
(mesh size 800) with water as free lubricant. Then the glass samples were washed with
flowing water so that no impurity left in the surface. The washed samples were slowly
heated up to 423 K and were held at this temperature for 1 h to remove the water from the
surfaces. Silver paint was pasted on parallel faces of the polished sample, and the sample
was fixed in a spring loaded sample holder.
Fig. 2.6: Schematic representation of the set up for impedance measurements.
40
The polished glass samples whose diameters were 1cm and thickness in the range
of 0.9mm to 1.2mm were squeezed between the electrodes are mounted over two outer
platinum electrodes, which established the connection to the impedance analyzer through
the platinum wires. The electrodes were made tight enough with the help of a steel spring
load in order to keep the sample in contact with the electrodes. The cell was then covered
with a stainless steel which is connected to the liquid nitrogen cell in order to allow the
measurements to be performed under inert conditions. The temperature of the cells is
attained by heating the N2 gas and the cell does not have the contact with the outer
atmosphere since vacuum is produced between the cell and the atmosphere. The
measurements were performed with variation of 10K with the error of ±0.1K min-1.
For the some of the samples the electrical measurements were performed by
placing the cell in a horizontal tube furnace and the temperature was controlled by a
thermocouple in close vicinity of the sample. Parallel conductance and capacitance were
measured using a Hioki 3532-50 LCR Hitester in the frequency range 100 Hz to 1 MHz
for various temperatures [52, 53]. Before starting the electrical conductivity
measurements, the samples were heated at 393K in the sample holder for stabilization of
the electrodes. The real part, Z'(ω) and imaginary part, Z''(ω) of complex impedance, real
part of ac conductivity σ'(ω), real part, M'(ω) and imaginary part, M''(ω) of electric
modulus are calculated using:
( )222 CωG
GωZ
+=′ (2.11)
( )222 CωG
CωωZ
+=′′ (2.12)
( )A
Gdωσ =′ (2.13)
( )d
ZAωωM 0
′′=′
ε (2.14)
( )d
ZAωωM 0
′=′′
ε (2.15)
where G and C are the measured parallel conductance and capacitance and ω=2πf, f
being the frequency in Hz, A is the electrode area, d is the thickness of the sample,
ε0=8.856x10-14F/cm is the permittivity of the free space. The experimental results derived
41
from different formalism are interpreted using the theories of hopping conduction in
addition to the microscopic features of glasses in the forthcoming chapters.
42
References
[1] G. O. Jones, Glass, (Methuen, London, 1956).
[2] S. R. Elliott, Physics of Amorphous Materials, (Longman, London, 1984).
[3] M. Tatsumisago, A. Hamada, T. Minami, M. Tanaka, J. Am. Ceram, Soc. 66 (1985) 890; Glasstech. Ber. 56 (1983) 943.
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45
Chapter III
IONIC CONDUCTIVITY IN TITANIUM AND NIOBIUM
BASED NASICON GLASSES
3.1 Preview
The concept of energy storage in a sodium-sulphur cell initiated the search of new
high sodium ion conduction as potential candidate for the application as solid
electrolytes. In the case of ceramic materials, an important effort has been made with β
alumina [1, 2] and NASICON [3-5]. However, polycrystalline solid electrolytes generally
imply the danger of grain boundary fatigue creating an inhomogeneous current density
within the ceramic materials favoring the degradation. Phosphate glasses are of great
scientific and technical interest on account of their various properties such as simple
composition with strong glass forming character, low transition temperature, high thermal
expansion coefficient, low melting and softening temperature, high electrical
conductivity, ultraviolet and far-infrared transmission and other optical
characteristics [6-8].
Alkali ion containing glasses with wide range of ionic conductivities are found to
form in binary phosphates with NASICON type compositions, AxByP3O12, which has the
capability of accommodating a wide range of compositional variation, thereby offering
flexibility of physical and electrical properties [11-15]. The structure of these glasses
appear to be built of [POOm/2Ok]k- tetrahedra and [BOl/2]
n- polyhedra randomly
interconnected through bridging oxygens, (where m and k are the numbers of the bridging
and non-bridging ions connected to the phosphorous atom, l is the coordination number
of B, and n=l- the valency of B). A is alkali ions which are surrounded by both bridging
and non-bridging oxygen in local close packing geometry and the molar volumes of the
glasses are affected by the size of the A ions [11,12]. Glasses therefore enable variation
of concentration of A ions and also its lattice binding through the variation of B ions
whose valences can vary from 3 to 5. Susman et al., have achieved a best conductivity in
zirconia based silicate glass which was derived form the composition of NASICON series
[16] since then number of glasses with NASICON framework have been synthesized.
Lejeune et al., demonstrated the aptitude of NASICON-analogous compositions for
46
optimized ion transport in glasses [17]. Thus NASICON glasses provide a good system to
perform a systematic investigation of the ionic conductivities. A survey of literature has
shown that though many NASICON based phosphate glasses are known and have been
investigate in detail, Na5TiP3O12 and Na4NbP3O12 glasses are quite interesting because of
the glass forming ability and the high ionic conductivity observed in ambient temperature
compare to that of the crystalline counterpart [11,12, 18, 19]. Both these materials are
expected to have potential electrochemical application.
Glasses and ceramic ionic conductors based on LiTi2(PO4)3 structure is analogous
to NaZr2P3O12 NASICON type structure [20], and these are among the most promising
group of oxide-based lithium ion conductors investigated in recent years. The
NASICON-type materials have fascinated much awareness recently, as they facilitate a
large scope for preparing number of materials with variation in their constituent metal
ions and composition. Various attempts have been made to enhance the ionic
conductivity and chemical durability of these NASICON glasses, which include the
addition of another glass former and glass modifier oxide [21-25]. The conductivity is
observed to be higher in this system with alkali ion present in a mixed anion environment
[26, 27] There are also many reports in the preparation and physical properties of LiNbO3
and NaNbO3 embedded in glass matrix [28-31] after the discovery of amorphous LiNbO3
and LiTaO3 by Glass et al., [28, 29] which possessed extraordinarily high dielectric
constant and high Li+ ion conductivity.
The aim of the present work is to explore the glass with high ionic conductivity in
NASICON framework and its variation with composition and temperature. The role of A
site mobile charge carriers such as Na+, Li+ and Ag+ and the role of B site cations such as
Ti4+ and Nb5+ in NASICON glassy media are investigated. Electrical properties of
different A site and B site substituted glasses such as Na5TiP3O12 (NTP), Na4NbP3O12
(NNP), Li5TiP3O12 (LTP), Li4NbP3O12 (LNP), Ag5TiP3O12 (ATP) and Ag4NbP3O12
(ANP), and different composition dependent Li(4+x)TixNb1-xP3O12 (LNTPx) where x=0,
0.25, 0.50, 0.75, 1.0 and Na(4+x)TixNb1-xP3O12 (NTNPx), where x=0, 0.25, 0.50, 0.75, 1.0,
are systematically investigated and the results were compared in addition to the basic
characterization such as XRD, FTIR and DSC.
47
3.2 Results and discussions
3.2.1 Characterization
The amorphous nature of the samples was confirmed by X-ray powder diffraction
studies. The FTIR spectra bands are assigned to the various vibrational contributions of
the basic phosphates as discussed in Chapter II. The densities of the samples are given in
Table 3.1 & 3.2. It clearly shows the trend that lithium based samples has less density
compared to sodium and silver based sample. The reduced density might be due to the
low molecular weight of the lithium glass compare to sodium and silver. Density of the
composition Li(4+x)TixNb1-xP3O12 and Na(4+x)TixNb1-xP3O12, x=0, 0.25, 0.50, 0.75, 1.0,
glasses exhibit insignificant decrease in density with the increase in x which may be
attributed to the introduction of the lithium in the glasses and also due to the replacement
of lesser molecular weight titanium with respect to niobium.
The glassy nature was confirmed by the observation of the glass transition
temperature in DSC for all the samples. The glass transition temperature Tg, the onset of
the crystallization temperature Ts, the peak crystallization temperature Tc, and melting
temperature Tm, were determined and listed in Tables 3.1 & 3.2. The Tg is high for LTP
and it decreases as titanium is replaced by niobium, whereas, the peak crystallization
temperature is high for LNP and it decreases as niobium is replaced by titanium. It is
known that the Tg decreases with decreasing bond strength and cross-linking in phosphate
glasses. The significant difference that exists between the glass transition, Tg and the
onset of the crystallization temperature Ts accounts the thermal stability of the glasses.
The value of ∆T, S and Kgl calculated from Eqs. (2.2)-(2.4) respectively are given in
Tables 3.1 & 3.2. According to Hruby, higher the value of Kgl greater its stability against
crystallization and supposedly the higher the vitrification ability [32]. These data reveals
that the LNP sample have high thermal stability and good glass forming ability than
sodium and silver based glasses. Similarly, niobium based glass have higher glass
forming ability and thermal stability compared to that of titanium based glasses. The
value of Kgl is less for Ti based glasses because the titanium ions prefer to occupy the
network modifying position rather than the network formation. This is an identification of
higher disorder for titanium based glasses compare to niobium based glasses [33].
48
Table 3.1: Glass transition temperature Tg, onset of crystallization temperature Ts,
crystallization peak temperature Tc, melting temperature Tm, thermal stability
parameters (∆T, S), Hruby parameter Kgl for NASICON series sample of different
cations.
Sample Tg (K)
Ts (K)
Tc (K)
Tm (K)
∆T (K)
S Kgl ρ
±0.02 (g/cm3)
Li4NbP3O12 703 914 933 1034 210 5.97 2.33 2.83 Na4NbP3O12 680 783 800 - 103 4.06 - 2.91 Ag4NbP3O12 636 - - - - - - 5.60 Li5Ti P3O12 736 818 832 1104 82 1.67 0.35 2.64
Na5TiP3O12 699 774 842, 791 1057 75 2.50 0.34 2.73
Ag5TiP3O12 611 740 761 - 29 1.87 - 5.23
Table 3.2: Glass transition temperature Tg, onset of crystallization temperature Ts,
crystallization peak temperature Tc, melting temperature Tm, thermal stability
parameters (∆T, S), Hruby parameter Kgl for LTNPx and NTNPx glass samples.
Sample Tg
(K) Ts
(K) Tc1
(K) Tc2
(K) Tm
(K) ∆T (K)
S Kgl ρ ±0.0
2 gcm-3
Li4NbP3O12 703 914 933 - 1034 210 5.97 2.33 2.83 Li4.25Ti0.25Nb0.75P3O12 729 836 866 914 1070 107 4.40 0.87 2.81 Li4.5Ti0.5Nb0.5P3O12 727 835 872 913 1075 108 5.50 0.89 2.72 Li4.75Ti0.75Nb0.25P3O12 729 823 840 891 1094 94 2.19 0.55 2.68 Li5Ti P3O12 736 818 832 - 1104 82 1.67 0.35 2.64 Na4NbP3O12 680 783 800 - - 103 4.06 - 2.91 Na4.25Ti0.25Nb0.75P3O12 709 830 843 - 1018 120 3.58 0.77 2.89 Na4.5Ti0.5Nb0.5P3O12 698 850 864 - - 152 5.01 - 2.86 Na4.75Ti0.75Nb0.25P3O12 689 802 841 - 1013 113 1.59 0.88 2.79 Na5Ti P3O12 700 772 842,
791 - 1056 72 2.19 0.71 2.73
3.2.2 Impedance spectroscopy studies
It is well known that the conductivity of glass materials is frequency dependent,
so the diffusivity of the mobile ions is not only characterized by resistance but also the
capacitance. An impedance measurement is a versatile tool that is often used to
characterize the response of ionic conductors [34]. When an ac electric field is applied
49
across a solid electrolyte, the processes like, ion movement through bulk of the
electrolyte, charge transfer across the electrode–electrolyte interface, etc., takes place.
Each process has different relaxation times and hence they respond in different frequency
ranges to the applied ac electric field. Experimental complex impedance data may well be
approximated by the impedance of an equivalent circuit consists of resistors, capacitors
and possibly various distributed circuit elements. These equivalent circuits can be
physically interpreted and assigned to appropriate process consisting the resistance (R),
and the constant phase element (CPE) represented as Q of the samples, combine in serial
and parallel. The complex impedance analysis was carried out over wide range of
frequencies on the samples at different temperature. The Z'(ω) and Z''(ω) were used in the
electrochemical impedance software equivalent circuit (EC) version 4.62 [35]. The
sample parameters such as bulk resistance Rb, bulk CPE Q=Qo(iω)(1-α), where Qo in units
of ohm-1 and the CPE exponent α, electrode resistance and electrode CPE, Qe are
extracted.
The typical impedance plots for the ion conducting sample NTP and LTP are
shown in Fig. 3.1 and Fig. 3.2 respectively for various temperature ranges. The
impedance spectrum shows depressed semi-circle or part of depressed semi-circle
corresponds to bulk contribution at high frequency region. The bulk resistance (Rb) for
given temperature is the intercept of the real axis of the zero-phase angle extrapolation of
the lowest-frequency curve. The centers of the depressed semi-circle lie below abscissa
and therefore Q have been used in equivalent circuit model. In the equivalent circuit, the
depressed semi-circle was interpreted as a parallel (RQ) element. At high temperatures,
two depressed semi-circles were observed at both low and high frequency regions which
are interpreted in equivalent circuit as two parallel (RQ) elements connected in series.
But at high temperature only one semi-circle can be visualized in the complex impedance
plot, the bulk properties semi-circle curve get depressed by high capacitance electrode
effect, this is clearly shown for LNP in Fig. 3.3 with inset showing the high frequency
data. At intermediate temperature, there is a depressed semi-circle in addition to a spike
or part of depressed semi-circle at low frequency region which is interpreted as addition
constant phase element.
50
Fig. 3.1: Complex impedance plot for Na5TiP3O12 systems at various temperatures.
0 5 10 15
0
5
10
-Z''(
ω)x106 [
Ω]
Z'(ω)x106 [Ω]
303K
313K
323K
0 3 6
0
3
6
-Z''(
ω)x 107 [
Ω]
Z'(ω) x 107 [Ω]
273K
283K
293K
0 5 10
0
2
4
-Z''(
ω)x105
[Ω]
Z'(ω)x105 [Ω]
383K
393K
403K
51
Fig. 3.2: Complex impedance plot of Li5TiP3O12 at various temperatures.
0 5 10 15 20 25 300
5
10
15
20
25
30
273K
-Z''(
ω) x 105 [
Ω]
Z'(ω) x 105 [Ω]
0 2 4 6 8 100
1
2
3
4
5
6
Z'(ω) x 105 [Ω]
Z'(ω) x 105 [Ω]
-Z''(
ω) x 105 [
Ω] 293K
0 1 2 3 4
0
1
2
3
4
-Z''(
ω) x 105 [
Ω]
313K
0 3 6 9
0
3
6
-Z''(
ω) x 104 [
Ω]
Z'(ω) x 104 [Ω]
343K
0 2 4 60
2
4
6
Z'(ω) x 104 [Ω]
-Z''(
ω) x 104 [
Ω]
353K
0 3 6 9 12 150
3
6
9
12
15
Z'(ω) x 103 [Ω]
-Z''(
ω) x 103 [
Ω]
373K
0 2 4 60
2
4
6
Z'(ω) x 103 [Ω]Z'(ω) x 10
3 [Ω]
-Z''(
ω) x 103 [
Ω] 413K
0 1 2 3
1
2
-Z''(
ω) x 103 [
Ω]
433K
52
0 1 2 30
1
2
3
B
EI
(RbQb)(R
IQI)Q
e
Z'(ω)x103 [Ω]
-Z''(
ω)x103 [
Ω]
333K
343k
353k
363K
Fig. 3.3: Complex impedance plot of Li4NbP3O12 at high temperatures, inset shows
the high frequency data for the respective temperature range.
Fig. 3.4: Complex impedance plot of Ag5TiP3O12 at various temperatures.
0 1 2 3 4 5 60
1
2
3
4
5
6
0.0 0.1 0.2 0.30.0
0.1
0.2
0.3
Li4NbP
3O12
-Z''(
ω) x 104 [
Ω]
Z'(ω) x 104 [Ω]
413K
423K
433K
Boukamp Fit
0 1 20
1
2
Z'(ω)x104 [Ω]
-Z''(
ω)x104 [
Ω]
293K
303K
313K
323K
53
The capacitance values for the high frequency semi-circles determined at different
temperature (C~10-12F) corresponds to the typical values for the bulk capacitance of the
samples. The impedance spectra having spike or depressed semi-circle in low frequency
region is due to the charge transfer barrier between ion blocking electrode and the sample
and it is represented as electrode polarization effect. This happens due to the multiple
point contacts resulting, spreading in resistance and air-gap capacitance at the electrodes
[36]. In the silver based glasses the impedance plot shows two depressed semi-circle at
low temperature itself, this is clearly shown in Fig. 3.4. As temperature increases, the
supplementary interfacial region introduces third complex impedance in the series
combination. The three regions are noted as B, I and E in the impedance plot in Fig. 3.4
for 333K. This additional interfacial region may be due to the existence of two different
conducting areas if the sample has an inhomogeneous microstructure [37].
The impedance data for typical samples has been analyzed using Boukamp’s
equivalent circuit software [35]. As explained earlier the circuit description code (CDC)
can be assigned for each impedance plot. If the impedance plot shows two depressed
semi-circles combined each other in the low frequency region i.e., the electrode sample
interface dispersion has to be considered for the first step in the analysis. Three points in
the low frequency regions are selected to fit the semi-circle by the program. This gives
approximate interface resistance and the corresponding constant phase element. Using
these partial values of non-linear least square fit (NLLS) is done for the particular semi-
circle and partially fitted data set is obtained. The same step is followed for the high
frequency semi-circle to get sample resistance and the corresponding CPE value for the
final fitting procedure. The partially fitted data sets saved separately in the notepad was
used for the final partial NLLS fit by selecting the entire data values to get a combined
equivalent circuit. The final NLLS fit has been done with partial NLLS fit data in various
frequency ranges to obtain final fitted data with minimum percentage of error. The
frequencies dispersion based on the final parameters is compared with the total measured
dispersion in the fit quality plot using the dispersion simulation program [35]. Similar
procedure was followed for different compositions of the sample at different temperature.
The CDC is observed to be (RbQb) for low temperature and as the temperature increases
CDC is observed to be (RbQb)Qe and (RbQb)(ReQe) respectively for NTP, NNP, LTP and
54
NTP. For ATP and ANP, the CDC is observed to be (RbQb)(RIQI)Qe at high temperature,
where RI and QI are the resistance and capacitance of interfacial region respectively. For
the complex impedance plot at 403 K the interfacial capacitance of 35 nF is obtained.
103
104
105
106
107
0.00
0.01
0.02
Modulus
313K
323K
333K
343K
ω [rad s-1]
M''(
ω)
0
1
Impedance
313K
323K
333K
343K
Z''(
ω)/Z'' max(ω)
Fig. 3.5: Normalized impedance and electric modulus spectroscopy plot for
Na4NbP3O12.
As temperature increases, the radius of the arc corresponding to the bulk
resistance of the sample decreases indicating an activated conduction mechanism. Also,
the presence of CPE in the circuit exemplifies the existence of distributed elements in the
sample and sample-electrode system. This illustrates that the relaxation time is not a
single value but it is distributed continuously or discretely around a mean relaxation time.
This is also confirmed from the spectroscopy plots of Z″ and the electric modulus M″
versus angular frequency that the Z″max and M″max do not occur in the same frequency
[33, 38-42]. The normalized impedance and electric modulus spectroscopy plots is shown
in Fig. 3.5. It shows that the Z″ spectra broaden in the low frequency side and the M″
spectra broaden in the higher frequency side. The large rise in Z″ at low frequencies is
due to the electrode polarization. The maxima of both the curves are close to each other
55
0 5 10
0
5
10
15
(c)
Z'(ω) x 105 [Ω]
-Z''(
ω) x 105 [
Ω]
253K
263K
273K
Ri(R
bQb)(R
eQe)
indicating that the impedance peak associated with the bulk RC element is responsible for
the modulus peak and the dielectric response of the sample is the result of non-localized
conduction [33].
Fig. 3.6 (a)-(d): Impedance plot of Na4.75Ti0.75Nb0.25P3O12 for various temperatures,
line represents the respective equivalent circuits. Insert shows the enlarged high
frequency data and their fitting.
Similarly the electrical properties of the composition Li(4+x)TixNb1-xP3O12 and
Na(4+x)TixNb1-xP3O12 were determined using impedance spectroscopy. The resistance and
the capacitance associated with the glass have been estimated using impedance
0 2 4 6
0
2
4
6 (d)
0.0 2.0x1044.0x10
40.0
2.0x104
4.0x104
-Z''(
ω) x 105 [
Ω]
Z'(ω) x 105 [Ω]
393 K
403 K
413 K
Ri(R
bQb)(R
eQe)
0 2 4 60
2
4
6
(a)
-Z''(
ω) x 107 [
Ω]
Z'(ω) x 107 [Ω]
273K
283K
293K
303K
Ri(R
bQb)
0 1 2 3 4
0
1
2
3
4
(b)
Z'(ω) x 106 [Ω]-Z''(
ω) x 106 [
Ω]
313K
323K
333K
343K
Ri(R
bQb)Q
e
56
spectroscopy. Fig. 3.6 shows a typical complex impedance plane plots and the
corresponding equivalent circuits of NTNP0.75 glass for various temperature. The plot
shows the typical spectrum of the ionic conductors consist of high frequency arc (or its
part) and the low frequency tail. A deeper insight into the electrical properties of the
NASICON type glasses is obtained from the complex impedance plane plot analysis with
Boukamp equivalent circuit package [35]. The value of bulk resistance Rb was
determined from the intersection of the arc with the real axis of the impedance Z′.
3.2.3 Dc conductivity analysis
Direct measurement of dc conductivity of the samples is not possible because of
the polarization effects at the sample-electrode interface and practical difficulties in
finding suitable electrode. The impedance spectroscopy technique can overcome these
difficulties by analyzing the ac impedance data. The bulk resistance Rb obtained from the
equivalent circuit analysis at different temperatures for all the samples are used to find
the magnitude of dc conductivity σdc as:
σdc=(d/RbA) (3.1)
where d is the thickness of the sample in cm and A is area of cross section of the sample
in cm2. Fig 3.7 shows the dc conductivity of the samples as a function of the inverse of
temperature. The σdc of all the six glasses calculated from impedance spectroscopy
increases with increase in temperature and obey Arrhenius behavior:
σdcT=σ0exp(-Edc/kBT) (3.2)
where σ0 is the pre-exponential factor, Edc is the activation energy for the dc conduction,
kB is Boltzmann’s constant and T is the absolute temperature. The increase in dc
conductivity with temperature is due to the increase in the thermal activated drift mobility
of ions according to hopping conduction mechanism. The dc conductivity activation
energy Edc was calculated from the slopes of the straight line plot of log(σdcT) against
reciprocal temperature 1000/T. The correlation coefficients R for the fit was higher than
0.99 for each samples. The magnitude of σdc at 303K and 403K, and the respective
equivalent circuit model for the different glasses are listed in Table 3.3.
57
Table 3.3: DC conductivity and equivalent circuit model for NASICON glasses
calculated from impedance measurement.
Sample σdc(S/cm)
at 303K σdc(S/cm)
at 403K Equivalent Circuit Model
Na5TiP3O12 4.12 × 10-8 1.01 × 10-5 (RbQb); (RbQb)Qe; (RbQb)(ReQe)
Na4NbP3O12 2.29 × 10-8 6.09 × 10-6 (RbQb); (RbQb)Qe; (RbQb)(ReQe)
Li5TiP3O12 8.70 × 10-7 1.48 × 10-4 (RbQb)Qe; (RbQb)(ReQe)
Li4NbP3O12 3.23 × 10-7 7.35 × 10-5 (RbQb)Qe; (RbQb)(ReQe)
Ag5TiP3O12 4.99 × 10-5 2.16 × 10-3 (RbQb)(RIQI); (RbQb)(RIQI)Qe
Ag4NbP3O12 6.68 × 10-6 3.53 × 10-4 (RbQb)(RIQI); (RbQb)(RIQI)Qe
Fig. 3.7: Temperature dependent of dc conductivity observed from impedance
spectroscopy for different mobile ion A in ATP and ANP glassy systems.
Fig. 3.7 clearly shows that the magnitudes of the Ag+ ion based glasses have
higher conductivity compared to the Li+ and Na+ based glasses. In general, as a whole
these glasses have high conductivity not only due to the higher concentration of mobile
ions but also due to the environment of the mobile ions in the glasses. In the present
glasses, the structure of the glass is suggested to be as (APO3)(1-x)(Nb2O5)x/(TiO2)x, where
A=Li, Na, Ag. In an alkali metal phosphate glasses, the structure is built up of long
2.0 2.5 3.0 3.5 4.0-8
-6
-4
-2
0
log(σ
dcT) [S cm-1 K]
1000/T [K-1]
ATP
ANP
LTP
LNP
NTP
NNP
Linear Fit
58
chains of O=PO2/2O- units. When Nb2O5 or TiO2 is introduced in the glass matrix, the
niobium and titanium atom prefer the octahedral sites of type [TiO6/2] and [NbO6/2]
respectively [29, 43]. These units can act as building blocks in the structure of these
glasses, along with [POO3/2] types of tetrahedral units. The glass structure has been
pictured in Fig. 3.8. Further every Nb5+ and Ti4+ atom will convert the non-bridging
oxygen in the phosphate glass network into bridging oxygen [33]. This dislocates the
negative charges of non-bridging oxygen towards [NbO6/2] or [TiO6/2] octahedral;
consequently the mobility of the cations is higher and an optimized conductivity achieved
as observed. The magnitude of the σdc follows the trend of Ag+ >Li+ >Na+ ion based
glasses.
Fig. 3.8: The microscopic picture of NNP glass which shows the dislocation bridging and
non-bridging oxygen.
In the composition variation NASICON glass samples, the glasses have high dc
conductivity at ambient temperature as the incorporation of displacement type
ferroelectric material in glass matrix, which will assist the cationic conduction [28]. The
dc conductivity for the glass compositions LNTPx and NNTPx is shown in Fig. 3.9 as a
function of inverse temperature. The lithium based materials have higher conductivity
compared to the sodium based materials. It is factual that both the compositions do not
show any drastic change in conductivity for the composition variation. This is because
the mobile ion, lithium and sodium, content is very high (~40-50mol%) in the
composition range of investigation which constrains major structural transformation,
consequently the conductivity for these glasses were less composition dependent [29-31].
O P O- O
- P O
Na+
Na+
+ Nb2O5
Na+
O O
Na+
O- P O Nb O P O Nb O
-
O O
O O
O O
O O
O O
59
2.1 2.4 2.7 3.0 3.3 3.6 3.9
-7
-6
-5
-4
-3
-2
-1 LTP
LNTP75
LNTP50
LNTP25
LNP
NTP
NNTP75
NNTP50
NNTP25
NNP
Linear Fitlog(σdcT) [S cm-1K]
1000/T
Fig. 3.9: Temperature dependent of dc conductivity observed from impedance
spectroscopy for composition variation of Li(4+x)TixNb1-xP3O12 &Na(4+x)TixNb1-xP3O12.
In the present glass composition niobium and titanium oxide used as glass
modifier and these atom prefer the octahedral sites of the glass matrix. Both anions will
convert the non-bridging oxygen in the phosphate glass network into bridging oxygen
and so there was no characteristic change observed in the structure due to these anions.
The small increase in dc conductivity with temperature is due to the increase in the
thermally activated drift mobility of ions according to hopping conduction mechanism.
As temperature increases, the radius of the arc corresponding to the bulk resistance of the
sample decreases, indicating an activated conduction mechanism. The linearity of the dc
conductivity data with inverse in temperature indicates thermally activated hopping
conductivity and the corresponding activation energy was obtained from the least-square
straight line fits of the data and is given in Table 3.3. The magnitudes of dc conductivity
σdc and their activation energy Eσ for the different composition are listed in Table 3.4. In
each case the magnitude of Li+ ion conductivity is remarkable at higher temperature.
60
Table 3.4: Dc conductivity at 373K, activation energies for dc conductivity (Eσ),
impedance peak (Eimp), hopping frequency (Eω) and conductivity relaxation time
(Eττττ) and modulus stretching parameter β for the different NASICON type glasses.
Eσ Eimp Eω Eτ Sample σdc± 0.04%
(S/cm) at 373 K ±0.02 eV
β ±0.03
Li4NbP3O12 1.78 x 10-5 0.61 0.59 0.60 0.58 0.61 Li4.25Ti0.25Nb0.75P3O12 1.81 x 10-5 0.60 0.59 0.55 0.60 0.60 Li4.5Ti0.5Nb0.5P3O12 3.11 x 10-5 0.58 0.62 0.53 0.61 0.59 Li4.75Ti0.75Nb0.25P3O12 2.96 x 10-5 0.59 0.61 0.54 0.60 0.60 Li5Ti P3O12 2.83 x 10-5 0.57 0.58 0.54 0.54 0.60 Na4NbP3O12 1.22 x 10-6 0.62 0.59 0.59 0.58 0.58 Na4.25Ti0.25Nb0.75P3O12 1.74 x 10-6 0.62 0.61 0.57 0.60 0.58 Na4.5Ti0.5Nb0.5P3O12 9.64 x 10-7 0.61 0.61 0.59 0.58 0.59 Na4.75Ti0.75Nb0.25P3O12 1.74 x 10-6 0.60 0.58 0.56 0.57 0.61 Na5Ti P3O12 1.49 x 10-6 0.56 0.57 0.57 0.55 0.60 Ag4NbP3O12 1.18 x 10-4 0.45 0.45 0.45 0.43 0.61 Ag5Ti P3O12 8.69 x 10-4 0.45 0.46 0.47 0.46 0.64
3.2.4 Ac conductivity analysis
In the past few decades there have been considerable efforts to explore the ionic
conductivity and relaxation mechanisms in ion conducting glasses. The understanding of
the conductivity mechanism is still not clear because of the difficulty of separating the
contribution of ionic concentration and mobility of the ions from the total measured
conductivity [44-48]. Many models have been proposed to relate the dispersive behavior
of the ionic conducting glasses to the microscopic features [49-53]. Similarly the
contribution of the ionic concentration on the relaxation mechanism also remains
unsolved. The dynamics of mobile ion in FIC glasses were interpreted in terms of ac
conductivity. The conductivity representation is a most prominent representation to relate
the macroscopic measurement to the microscopic movement of the ions.
The frequency dependence of real part of the conductivity σ'(ω) at various
temperatures for the present investigating glasses are shown in Figs. 3.10-3.12 for NNP,
LNP and ANP respectively. The conductivity exhibits the typical behavior of ionic
materials, i.e. the dc plateau at low frequency region and the frequency dependent at high
frequency region described as power law behavior. Such behavior is known as the
“universal dynamic response” which is widely observed in highly disordered materials
61
[54,55]. The physical origin for this behavior is not yet completely understood, but the
dispersion clearly reflects the non-random or correlated kind of motion of mobile ions
through the host matrix of the ionic glasses [44-55]. At low frequencies, the diffusion of
hopping charge carriers takes place through activated hopping of ions over the random
distribution of free energy barriers that separates adjacent sites, giving raise to a
frequency independent conductivity. The observed conductivity relaxation at high
frequencies is due to the probability of the correlated forward–backward hopping
together with the relaxation of the ions. The power law regime of the ac conductivity is
least temperature dependent than the dc conductivity, i.e. the activation energy of dc
conductivity is greater than that of activation energy observed at different frequencies. It
is also observed that higher the frequency lower the activation energy.
102
103
104
105
106
107
1E-9
1E-8
1E-7
1E-6
1E-5
1E-4
1234567891011121314151617
1819
2021
222324252627282930313233
ABCDEFGHIJKLMNOP
QR
ST
UVWXYZAAABACADAEAFAG
273K
283K
293K
303K
313K
323K
333K
343K
353K
363K
373K
383K
393K
403K
413K1 423KA 433K
AWF Fit
σ'(
ω)[S cm-1]
ω [rad s-1]
Fig. 3.10: Ac conductivity of NNP at different temperature.
62
Fig. 3.11 Ac conductivity of LNP at different temperature.
Fig. 3.12 Ac conductivity of ANP at different temperature.
1000 10000 100000 1000000
1E-6
1E-5
1E-4
ω [rad s-1]
σ'(
ω)[S cm-1]
273K
283K
293K
303K
313K
323K
333K
343K
353K
363K
373K
383K
AWM Fit
103
104
105
106
1E-7
1E-6
1E-5
σ'(
ω) [S cm-1]
ω [rad s-1]
273K
283K
293K
303K
313K
323K
333K
343K
353K
363K
373K
383K
AWM Fit
63
Starting at low frequencies at higher temperature, there is a large decrease in
conductivity. This phenomenon results from the presence of blocking electrodes that do
not permit the mobile ions to transfer into the external measuring circuit. This leads to the
pile up of ions near one electrode leaving a depletion layer near the opposite electrode.
This normally results to the drop of conduction and it is said to be electrode polarization
effects [56]. The electrode contribution in low frequencies at higher temperature region is
evident in complex impedance plots analysis and corresponding capacitance or constant
phase element values obtained in the order of magnitude 10−7 to 10−9 F. This electrode
polarization effect is a non-equilibrium process which depends upon the nature of the
electrode interface and the thickness of the specimen [56-57].
Almond et al. [58-60] has analyzed the ac behavior of glasses and other solid
electrolytes in the light of Jonsher’s general treatment of dielectrics loss. These
investigators have applied Jonsher’s universal power law relation to account for the
conductivity in the plateau and the dispersion regions of some glassy electrolytes and it is
given by
σ'(ω)=σdc+A ωn, 0<n<1, (3.3)
where σdc is the frequency independent dc conductivity, A is pre-factor depends on
temperature and n is the frequency exponent. All the samples at different temperatures
exhibit the high frequency dispersion, which has a inseparable part of frequency
independent conductivity at low frequencies. The switch over from the frequency
independent region to frequency dependent regions signals the onset of conductivity
relaxation or hopping frequency ωp, which shifts towards higher frequencies as the
temperature increases. Almond have related hopping frequency and dc conductivity as
[58],
A=σdc/ωpn (3.4)
Substituting Eq. (3.4) into Eq. (3.5) provides an expression for the frequency dependent
conductivity which is called as Almond and West conductivity formalism.
σ'(ω)=σdc[1+(ω/ωp)n] (3.5)
The ac conductivity data was fitted using non-linear least square fit procedure of
Levenberg-Marquardt [61, 62] for all the samples at different temperature with Eq. (3.5)
64
and the parameters σdc, ωp, and n are extracted. The dc conductivity and the hopping
frequency are temperature dependent indicating that both are originating from the ion
migration. These two parameters namely σdc and ωp are used to scale the conductivity
spectra and it will be discussed later. In a glass matrix, there exists number of distributed
free energy barriers, the dc conductivity activation energy Edc correspond to the hardest
hop of the mobile ions in the easiest pathways. Generally the covalent bonds between the
glass network formers act as the energy barriers to the mobile ions. So the glass structure
plays the major role for the dc conductivity of the glass. However, at higher frequencies,
in addition to the long-range transport, short range displacements of the mobile ions play
the major role for the increase in conductivity. In the host matrix of the glass, the mobile
ions have inter-ionic interaction resulting short-range hopping. This short range hopping
is high correlated motion in which the ions perform number of recurred forward-
backward hops before completion of successful forward displacement at frequency down
to the hopping frequency ωp. Hence, the dispersion portion of σ'(ω)∝Aωn, exists lower
activation energy than that of the dc conductivity. The value of n lies in the range of 0.5-
0.7 for all the samples. The fit parameters are shown in Table 3.5 (a)-(f) for the six
samples.
The statement is modified as “In higher temperature, the low frequency
conductivity data is influenced by polarization effect. In the above fitting procedure,
inclusion of low frequency data will decrease the perfection of the fitting and hence the
error in each parameter will be high. For the better fitting of the conductivity data the low
frequency data has been eliminated at high temperatures. Similar procedure is followed
for other ionic conducting glasses. It is found that the conductivity increases as the size of
the mobile ions decreases, i.e. it follows the trend as Ag+>Li+>Na+. In the presently
investigated glasses with various mobile ions, it is found that the titanium based glasses
have higher magnitude of conductivity compared to the niobium based glasses and also
the difference in magnitude increases as the size of the mobile ions decreases. Figure 3.13
shows the dc conductivity and the hopping frequency as function of inverse of
temperature. The temperature dependent dc conductivity and activation energy of the
NTP, NNP and LTP glasses are already reported in the literature [11, 18, 19, 29] and
agree with present results well within experimental error.
65
Table 3.5 (a)-(f): Parameters obtained from the fits of ac conductivity data by using
Eq. (3.5) for different NASICON type glasses.
(a) NTP
T (K) σσσσdc (S/cm) ωωωωp (rad/s) n
273 3.09±0.04 x 10-9 9.45±0.04 x 103 0.62 283 7.17±0.02 x 10-9 1.94±0.03 x 103 0.62 293 1.51±0.03 x 10-8 3.67±0.03 x 104 0.61 303 2.73±0.02 x 10-8 6.07±0.03 x 104 0.59 313 5.06±0.02 x 10-8 1.02±0.03 x 105 0.57 323 9.42±0.02 x 10-8 1.79±0.02 x 105 0.56 333 1.74±0.02 x 10-7 3.27±0.03 x 105 0.55 343 3.06±0.03 x 10-7 5.56±0.03 x 105 0.54 353 5.10±0.04 x 10-7 9.31±0.03 x 105 0.54 363 9.14±0.03 x 10-7 1.91±0.04 x 106 0.55 373 1.49±0.04 x 10-6 2.96±0.03 x 106 0.55 383 2.75±0.03 x 10-6 6.75±0.03 x 106 0.54 393 4.00±0.03 x 10-6 9.30±0.03 x 106 0.54
(b) NNP
T (K) σσσσdc (S/cm) ωωωωp (rad/s) n
273 1.94±0.04 x 10-9 8.72±0.04 x 103 0.64 283 4.11±0.03 x 10-9 1.35±0.03 x 103 0.63 293 9.76±0.03 x 10-9 2.88±0.03 x 104 0.63 303 2.01±0.03 x 10-8 4.62±0.03 x 104 0.59 313 3.94±0.02 x 10-8 8.62±0.03 x 104 0.58 323 7.44±0.03 x 10-8 1.65±0.04 x 105 0.57 333 1.50±0.03 x 10-7 3.59±0.03 x 105 0.58 343 2.70±0.03 x 10-7 6.27±0.03 x 105 0.59 353 4.64±0.04 x 10-7 9.96±0.04 x 105 0.58 363 7.69±0.03 x 10-7 1.56±0.04 x 106 0.55 373 1.22±0.02 x 10-6 2.11±0.03 x 106 0.54 383 2.04±0.02 x 10-6 3.85±0.04 x 106 0.53 393 3.23±0.03 x 10-6 5.93±0.03 x 106 0.53 403 5.04±0.02 x 10-6 7.82±0.03 x 106 0.54 413 7.62±0.02 x 10-6 1.20±0.03 x 107 0.54 423 1.11±0.02 x 10-5 1.55±0.03 x 107 0.55
66
(c) LTP
T (K) σσσσdc (S/cm) ωωωωp (rad/s) n
273 5.86±0.04 x 10-8 9.75±0.04 x 104 0.58 283 1.47±0.02 x 10-7 2.22±0.04 x 105 0.55 293 3.22±0.03 x 10-7 4.98±0.03 x 105 0.55 303 7.10±0.03 x 10-7 1.39±0.03 x 106 0.55 313 1.31±0.04 x 10-6 2.30±0.03 x 106 0.55 323 2.31±0.02 x 10-6 3.51±0.03 x 106 0.55 333 4.17±0.04 x 10-6 6.70±0.04 x 106 0.55 343 7.11±0.04 x 10-6 1.14±0.03 x 107 0.53 353 1.16±0.04 x 10-5 1.87±0.03 x 107 0.53 363 1.90±0.03 x 10-5 3.15±0.04 x 107 0.55 373 2.83±0.03 x 10-5 4.22±0.03 x 107 0.55
(d) LNP
T (K) σσσσdc (S/cm) ωωωωp (rad/s) n
273 2.33±0.04 x 10-8 7.27±0.04 x 104 0.64 283 5.97±0.02 x 10-8 1.53±0.04 x 105 0.63 293 1.36±0.02x 10-7 3.11±0.03 x 105 0.61 303 2.83±0.02 x 10-7 6.33±0.03 x 105 0.60 313 5.68±0.04 x 10-7 1.27±0.03 x 106 0.59 323 1.10±0.02 x 10-6 2.57±0.03 x 106 0.60 333 2.09±0.02x 10-6 5.06±0.04 x 106 0.60 343 3.76±0.04 x 10-6 9.57±0.04 x 106 0.61 353 6.54±0.04 x 10-6 1.80±0.04 x 107 0.62 363 1.12±0.02 x 10-5 4.70±0.04 x 107 0.62 373 1.78±0.03 x 10-5 6.78±0.03 x 107 0.63
(e) ATP
T (K) σσσσdc (S/cm) ωωωωp (rad/s) n
273 6.08±0.04 x 10-6 1.49±0.04 x 107 0.68 283 1.27±0.04 x 10-5 2.97±0.04 x 107 0.67 293 2.31±0.03 x 10-5 4.81±0.03 x 107 0.65 303 4.04±0.03 x 10-5 9.79±0.03 x 107 0.64 313 6.66±0.04 x 10-5 1.49±0.03 x 108 0.62 323 1.06±0.02 x 10-4 2.69±0.04 x 108 0.62 333 1.61±0.02 x 10-4 5.32±0.04 x 108 0.60 343 2.37±0.02 x 10-4 9.93±0.03 x 108 0.59
67
(f) ANP
T (K) σσσσdc (S/cm) ωωωωp (rad/s) n
273 9.45±0.04 x 10-7 1.34±0.04 x 106 0.57 283 1.79±0.03 x 10-6 2.72±0.04 x 106 0.58 293 3.32±0.02 x 10-6 5.47±0.03 x 106 0.60 303 5.77±0.03 x 10-6 9.87±0.04 x 106 0.61 313 9.58±0.04 x 10-6 1.68±0.03 x 107 0.60 323 1.58±0.04x 10-5 2.97±0.04 x 107 0.59 333 2.48±0.03 x 10-5 4.76±0.04 x 107 0.58 343 3.83±0.02 x 10-5 8.42±0.03 x 107 0.57 353 5.65±0.03 x 10-5 9.99±0.03 x 107 0.60 363 8.48±0.03 x 10-5 1.71±0.04 x 108 0.61 373 1.18±0.03 x 10-4 2.34±0.05 x 108 0.62
2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0-8
-6
-4
-2
0
2
4
1000/T [K-1]
log(σdcT) [S cm-1K]
ATP
ANP
LTP
LNP
NNP
NNP
Linear Fit
-4
-2
0
2
4
6
8
10
log(ωp) [rad s-1]
Fig. 3.13: Arrhenius plots of ln(σσσσdcT) and hopping frequency ωp versus 1000/T for
different NASICON type glasses. The solid lines represent the Arrhenius fits.
The variance in conductivity and hopping frequency with respect to anions clearly
illustrates the effect of anions. The dc conductivity, σdc, and hopping frequency, ωp,
obtained from UPL are temperature dependent and they are found to obey the Arrhenius
equations similar to Eq. (3.2) and it is given by:
68
σdcT=σexp(-Eσ/kT), (3.6)
ωp=ω0exp(-Ep/kT), (3.7)
where σ0 is the dc conductivity pre-exponential factor, Eσ is the dc conductivity
activation energy for mobile ions, ω0 is the pre-exponential of hopping frequency, and
Ep, is the activation energy for hopping frequency. The activation energy, Ep, of the
hopping frequency is in agreement to the activation energy, Eσ, for the dc conductivity
which is shown in Table. 3.4. The variation falls within the experimental error. This
indicates that the charge carriers have to overcome the same energy barrier while
conducting as well as relaxing.
The dc conductivity and the hopping frequency of the ionic glasses are
temperature dependent and their activation energy is almost same. This initiates many of
the research in the field of solid state ionic to find the relation and the constant of
proportionality between ωp and σdc, which is almost universal, vary weakly with
temperature. Barton [63], Nakajima [64], and Namikawa [65] (BNN), carried out a closer
analysis of the proportionality and arrived at the following equation to be valid for most
of the ion conducting materials:
σdc=pε0εωp, (3.8)
where p is a numerical constant order of 1, ε0 is the free space permittivity, ε=εs-ε∞ is
the permittivity change from the unrelaxed baseline ε∞ to fully relaxed level εs. This
permittivity change is a direct consequence of the relaxation of hopping cations.
The BNN relationship conveys the important relation between ac and dc
conduction, which are closely correlated to each other and are having the same
mechanism. The plot of ln(σdc) versus ln(ωp) is shown in Fig. 3.14 for different cation
NASICON series glasses and Fig. 3.15 for composition variation NASICON glasses. The
values of σdc and ωp were obtained from the best fits of Eq. (3.8). The dashed lines are
the least-square straight-line fits. The slopes are found to be almost equal to unity for
present investigated glasses. The σdc versus ωp fall within the lower and upper dashed
lines as shown in Figs. 3.14 & 3.15 and this band is due to the material dependent
variation of ∆ε. The slopes imply that the dc and ac conductions are correlated with each
other and the BNN relation is obeyed for the present glass samples.
69
2 4 6 8-10
-8
-6
-4
log(ωp) [rad s
-1]
log(σdc) [S cm-1]
Fig. 3.14: log(σσσσdc) versus log(ωωωωp) plots for the different cation NASICON type
glasses
Fig. 3.15: log(σσσσdc) versus log(ωωωωp) plots for the composition variation of
A(4+x)TixNb1-xP3O12 (where A=Li, Na) NASICON glasses.
3 4 5 6 7 8 9-10
-9
-8
-7
-6
-5
-4
-3
ATP
ANP
LTP
LNP
NTP
NNP
linear fit
log(σdc) S cm-1
log(ωp) rad s
-1
70
3.2.5 Electrical modulus behavior
Electrical relaxation in ion conducting materials have been extensively studied
and analyzed in terms of electrical modulus formalism. The advantage of representing the
electrical relaxation in modulus formalism is that the electrode polarization effects are
suppressed in this representation. This is primarily because of the insensitiveness of the
frequency dependence of the imaginary part of the modulus M"(ω) to the polarization
processes, provided these are characterized by capacitances which are much larger than
the bulk capacitance. The conductivity relaxation model, in which a dielectric modulus
M*(ω) is defined as the reciprocal of complex dielectric permittivity ε∗(ω), can be used to
define in absence of a well-defined dielectric loss peak [66]. The real and imaginary parts
of the electrical modulus as a function of frequency are shown in Fig. 3.16 and Fig. 3.17
respectively. As shown in Fig.3.16 M'(ω) rises its low-frequency value from minimum
value toward a high-frequency limit, M∞, and the dispersion region moves to high
frequencies as the temperature increases. At low frequencies M'(ω) tends to zero
suggesting negligible or absence of electrode polarization.
103
104
105
106
107
0.00
0.02
0.04
0.06
M'(
ω)
ω[rad s-1]
273K
283K
293K
303K
313K
323K
333K
343K
353K
363K
373K
Fig. 3.16: Real part of electric modulus M'(ω) for NNP glass.
Solid lines are fit to KWW fit.
71
100 1000 10000 100000 1000000 1E7
0.000
0.005
0.010
0.015
0.020
ω [rad s-1]
M''(
ω)
273K
283K
293K
303K
313K
323K
333K
343K
353K
363K
373K
Fig. 3.17: Imaginary part of electric modulus M"(ω) for NNP glass.
Solid lines are fit to KWW fit.
The M″(ω) shows a slight asymmetric peak at each temperature as shown in
Fig. 3.17. The low frequency wing of the peak represents the range of frequencies in
which the ions can move over long distances, i.e. ions can perform successful hopping
from one site to the neighboring site. On the other hand, corresponding to the high
frequency wing of the M″(ω) peak, the ions are spatially confined to their potential wells
and the ions can make only localized motion within the well. The peak of M″(ω) is
positioned at around the center of the M'(ω)dispersion. The reciprocal of the peak
frequency of the M''(ω) spectra represents the time scale of the transition from the long-
range to short range mobility and is defined as the characteristic relaxation time τm. The
peak frequency shifts towards higher frequencies with temperature according to the
Arrhenius relation. Similar features are observed for the remaining glasses. The electric
modulus could be expressed as the Fourier transform of a relaxation function φ(t) [67]:
M*(ω) =
− ∫∞
∞
0
tjω tddt
de1M
ϕ, (3.9)
where the function φ(t) is the time evolution of the electric field within the materials and
is usually taken as the Kohlrausch–Williams–Watts (KWW) function [68-70]
72
β
mφ(t)=exp[-(t/τ ) ] , (3.10)
where τm is the characteristic relaxation time and the exponent β indicates the deviation
from Debye type relaxation. The modulus fitting for each composition is performed using
the procedure of Moynihan et al., [71, 72]. The least squares iterative routine software
package developed by Baskaran [73] in C++ has been used to fit the experimental data
with Eqs. (3.9) & (3.10). The initial values of the free parameters for the fitting, M∞, τ
and β were taken from the high-frequency limit of M'(ω), inverse of the peak frequency
and the magnitude of full width at half maximum (FWHM) of the M''(ω) curve
respectively. The continuous line in Figs. 3.16 and 3.17 denotes the fitted values of M*,
whereas the symbols correspond to the experimental data of NNP. The stretched
exponential parameter β obtained from the fitting is listed in Table 3.4. The shape of the
M'' curves for various glass compositions at 303K temperature is shown in Fig. 3.18. The
curves look alike and differ only in its peak height and FWHM. All spectra show a
relaxation behavior typical of the glassy state relaxation and the peak frequency in the
M''(ω) spectra corresponds to the relaxation frequency ωm. This relaxation time
associated with the above process can be determined from the plot of M''(ω) versus
frequency. The activation energy involved in the relaxation process of ions could be
obtained from the temperature dependent relaxation time τm.
τm=τ0exp (Em/kBT) (3.11)
where Em is the activation energy associated with relaxation process, τ0 is the pre-
exponential factor, kB is the Boltzmann constant, and T is the absolute temperature.
Generally the experimental data of the relaxation in time domain is defined by the KWW
equation. It is to be noted that with KWW function, Fourier transform from time domain
to frequency domain can be performed only through the numerical method, since there is
no analytical Fourier transform of the KWW function. A series expansion has been used
to facilitate the time frequency conversion. However, Bergman [74] has found an
approximate frequency representation of the KWW function, which allows fitting directly
in the frequency domain. The imaginary part of the M''(ω) in frequency domain due to
KWW decay function could be defined for β≥0.4 as:
73
M″() = max
βmax max
Mβ
1-β+ [β(ω /ω)+(ω/ω ) ]1+β
′′, (3.12)
where M″max is peak maximum of imaginary part of modulus, and ωmax is the peak
frequency of imaginary part of modulus. Eq. (3.12) could effectively be described for β ≥
0.4. Theoretical fits of Eq. (3.12) to the experimental data are illustrated in Fig. 3.18 and
Fig. 3.19 as the solid lines. The experimental data are well fitted to this model except in
the high frequency regime. From Bergman’s fitting of M''(ω) versus frequency plots, the
value of M″max, ωmax and β are determined. It is clear that Bergman has assigned
appropriate relations to define the frequency domain parameters to time domain KWW
parameters and it is given by
m
max
1 1τ =
ω 1 1Γ
β β
(3.13)
This relaxation time matches the relaxation time calculate through the KWW fit. The
activation energy involved in the relaxation process is also determined from the
temperature dependent relaxation time defined by Eq. (3.11).
103
104
105
106
107
0.000
0.004
0.008
0.012
0.016
0.020 NNP
NTP
LNP
LTP
ANP
ATP
Bergman Fit
M''(
ω)
ω [rad s-1]
Fig. 3.18: Imaginary part of electric modulus M"(ω) for NASICON glass at 303K.
Solid lines are fit to Bergman equation.
74
1000 10000 100000 1000000 1E70.000
0.007
0.014
0.021
M''(
ω)
ω [rad s-1]
293K
303K
313K
323K
Bergman Fit
KWW Fit
Fig. 3.19: Imaginary part of electric modulus M"(ω) for LNP glass. Solid lines are
fit to KWW fit and doted lines are fit to Bergman equation.
2.4 2.7 3.0 3.3 3.6 3.9
-7
-6
-5
-4
-3
τ [s
-1
]
1000/T [K-1]
NNP
NTP
LNP
LTP
ANP
ATP
Linear Fit
Fig. 3.20: The temperature dependent of relaxation time for the NASICON glasses.
75
2.0 2.5 3.0 3.5 4.0-8
-6
-4
-2
log(σdcT) [S cm-1]
1000/T [K-1]
AW σdc
Impedance σdc
Modulus σdc
Linear Fit
Fig. 3.21: Arrhenius Plot of dc conductivity obtained for NNP sample from different
formalism.
Fig. 3.20 shows the temperature dependent of relaxation time of the different
cation NASICON glass samples. The activation energy calculated is almost equal to that
of the dc conductivity activation energy (Table. 3.4) for all the samples of the NASICON
glasses. The dc conductivity of the glass for various temperatures can be estimated from
the modulus representation also. The electric modulus M*(ω) provides information about
the dynamics aspects of ions for an ionic conductors in terms of the time decay of the
electric charges on opposite sides of the sample. This variation of the charge is described
by the time variation of the electric field E(t)=E(0)φ(t), where E(0) is the initial electric
field imposed at time t=0 and φ(t) the electric field relaxation function. The φ(t) was in
turn assumed to be expressible in terms of a distribution of electric field relaxation times,
τ given in Eq. (3.10).
The real part of conductivity σ' is related to the imaginary part of complex
permittivity ε"(ω) by σ'(ω)=ε0ε"(ω), where ε0 is the permittivity of free space. Since
ε*(ω)=1/M*(ω), the frequency dependence ac conductivity is related as
σ'(ω)= ε0ε"(ω)=ε0[M"/[(M')2+(M")2] (3.14)
The dc conductivity σdc is related to the average relaxation time <τ> by the relation:
76
0dc
ω 0
εσ = limσ(ω)=
M <τ>→∞
(3.15)
The average relaxation time <τ> is given by
0
<τ>= φ(t)dt∞
∫ (3.16)
For KWW relaxation function φ(t) given by Eq. (3.10), the average relaxation time is
found to be:
( )1
β
mβ
Γ<τ>=τ (3.17)
Substituting Eq. (3.17), in Eq. (3.15) provides the conductivity expression:
( )
Γ=
∞ β/1
β
)T(M m
odc τ
εσ (3.18)
Eq. (3.18) is used to extract dc conductivity from the electric modulus data [75]. Fig. 3.21
shows the dc conductivity data obtained from the above expression at various
temperatures with the dc conductivity obtained from the impedance and Almond West
relation. It is clearly seen that the dc conductivity matches well from all the formalism
and it is evident that all the formalism are related to each other and valid for the ion
dynamics and its relaxation. Scaling and universality are important concepts that arise in many circumstances
in our physical world [76, 77]. It is an important feature in any data evaluation program.
The ability to scale different data sets so as to collapse all to one common curve indicates
that the process can be separated into a common physical mechanism modified only by
thermodynamic scales [78]. In these instances, scaling and universality serve to reduce
the process to simpler parts so that a deeper understanding could be achieved [79].
However, the high degree of universality suggests that the ac conductivity contains only
little information on microscopic details of the conduction process [80].
Recently, renewed interest has developed regarding the scaling observed in the
frequency dependent conductivity of ion containing glasses. For the ion conducting
77
materials, a remarkable feature is their response to an applied electric field. At low
frequencies, random diffusion of the ionic charge carriers via activated hopping gives rise
to a frequency independent conductivity. At higher frequencies, however σ'(ω) exhibits
dispersion, increasing roughly in a power law fashion and eventually becoming almost
linear at even higher frequencies. Interestingly, polaron conductors, both crystalline and
glassy, display a behavior that is quite similar to the ionic ones. The physical origins are
not yet completely understood, but the dispersion clearly reflects a nonrandom or
correlated kind of motion of the ions occurring on relatively short time scales.
Taylor analyzed the dielectric properties of ionic glasses in accordance with the
Debye equation with a spread of relaxation times [81]. He showed that the dielectric loss
for all glass fell on a single plot against scaled frequency. In 1961, Isard relabeled
Taylor’s axis by plotting dielectric loss against log of the product of frequency and
resistivity [82]. Since then this Taylor-Isard scaling, has been used for several ionic as
well as electronic conducting disordered solids to construct ac conductivity master curves
from measurements at different temperatures. Disordered solids have ac electrical
properties remarkably in common. In the electrical relaxation investigation, the electrical
measured data are represented as ac conductivity or as electric modulus formalism that
explains the ion dynamics and its relaxation process in the glasses. When a time
dependent electrical field is applied to the ion conducting glasses, the field produces
corresponding time dependent conductivity or polarization. This conductivity arises from
a variety of mechanisms in which charge is displaced from the equilibrium [83]. Even
then, the temperature dependence of conductivity σ'(ω) is “quasi-universal”. That is the
minimalist’s approach of comparing spectra against each other shows the common
features.
In recent publications, different workers have made scaling in ac response of the
ionic materials by considering the scaling frequency in different forms. Generally, the
frequency dependent ac conductivity of the ionic glasses is exclusively determined by the
hopping motion of the ions. The dynamical process in disordered materials below few
MHz, exhibit similar behavior at different temperature and it is usually possible to scale
the ac data at different temperatures for one compound into one single curve. This master
curve gives the dimensionless ac conductivity as a function of dimensionless frequency.
78
The existence of such a master curve is referred to as time-temperature superposition
principle (TTSP) [84]. Roling et al. [85] have taken σdcT as the scaling frequency for
different temperatures and σdcT/x for different compositions, where x is the mole fraction
of alkali ions forNa2O)x (B2O31-x glasses in the composition range 0.1≤x≤ 0.3 and T is
the absolute temperature. They have also made use of the Barton-Nakajima-Namikawa
(BNN) relation [65] while defining the crossover frequency from dc behavior to the
dispersive conductivity. Sidebottom [86] has extended the above scaling approach to the
case where the alkali content is very low by making use of the fact that the ion hopping
length changes with the alkali content. This author has used σdc/ε0∆ε) as the scaling
frequency, where ε0 is the free space permittivity and ∆ε=ε0-ε∞ is the permittivity change
from the unrelaxed baseline ε∞ to the fully relaxed level ε0. This scaling frequency is
again equivalent to some numerical factor times the crossover or hopping frequency
according to the BNN relation [65].
Ghosh et al., [87] have considered the hopping frequency as a more appropriate
parameter for the scaling of the conductivity spectra for the glasses, where on dielectric
loss peaks or static dielectric constant value can be obtained. This proposed scaling
automatically takes into account the permittivity change implicitly. The advantage of
using hopping frequency as the scaling frequency is that it is not specifically delimitated
by the composition range or the type of glass. This appears quite justified as the change
in hopping length with composition is manifested in the change in the hopping frequency
which takes into account the correlation effects between successive hops through the
Haven ratio [88]. So to construct the ac master curve, frequency must be divided by ωp.
Because the dielectric loss strength ∆ε is only weakly temperature dependent, while σdc
and ωp are both Arrhenius, the BNN relation implies ωp~σdc. These different approaches
have been suggested providing rules for the superposition of individual conductivity
spectra. Thus the existence of a master curve is conveniently summarized as:
σ(ω)/σdc=F1(ω/ωs), (3.15)
where F1 is a temperature independent function and ωs is temperature dependent scaling
parameter. In the present chapter a scaling approach have been applied for different
NASICON type glasses by choosing ωs in Eq. (3.15) as (i) ωp, Ghosh scaling and (ii)
σdcT, Summerfield scaling for a given glass at different temperatures at an arbitrary
79
temperature. Scaling in modulus for different NASICON type glasses is also studied by
choosing ωmax and M"max as the scaling parameter in the x- axis and y-axis respectively.
3.2.6 (a) Ac conductivity scaling
The scaled conductivity spectra are shown in Fig. 3.22 for different NASICON
type glasses, where the conductivity axis is scaled by σdc and the frequency axis by ωp at
different temperature. A perfectly superposed master curve for the conductivity spectra is
obtained for each composition for the five NASICON type glasses. Thus the relaxation
mechanism is found to be temperature independent under conductivity formalism.
Obviously, the TTSP is fulfilled, suggesting that the conductivity relaxation mechanism
is independent of temperature in the conductivity formalism. For all samples, the scaled
conductivity plateau spectra are deviated at low frequency due to electrode polarization
and are clearly seen in Fig. 3.22.
10-5
10-3
10-1
101
103
101
102
103
104
105
106
107
ANP
LTP
LNP
NTP
NNP
σ'(
ω)/
σdc
ω/ωp
273K
283K
293K
303K
313K
323K
343K
353K
363K
373K
Fig. 3.22: Scaling plots for the conductivity spectra of different NASICON type
glasses. To separate the curves, the coordinate of the LTP, LNP, NTP and NNP
glasses are shifted respectively by one unit in the log scale of conductivity axis.
80
1E-3 0.01 0.1 1 10 100
1
10
Electrode Effect
ω/ωp
σ(ω)/
σdc
ANP
LTP
LNP
NTP
NNP
Fig. 3.23: Scaling plots for the conductivity spectra of different NASICON type
glasses at 293K.
In the NTP and NNP system, the electrode polarization process is almost
independent of temperature. However, in the case of LTP, LNP and ANP systems
electrode polarization process depends on temperature, i.e., it is scattered in low
frequency. In ATP sample the ac conductivity data are mostly affected by electrode effect
so it is difficult to collapse to a single master curve. Fig. 3.23 shows the scaling approach
of hopping frequency with respect to various compositions at a particular temperature. It
has been found that the five NASICON samples collapse into single master curve, this
simply means the compositional independence of the electrical relaxation mechanism,
and also that, when hopping frequency is taken as scaling frequency it automatically
takes into account the permittivity change implicitly. The change in hopping length with
composition is manifested in the change in the hopping frequency which takes into
account the correlation effects between successive hops through the Haven ratio [88]
given by:
R
p0
dcH 4π
∆εωεσ = (3.16)
81
where HR is the Haven ratio, ε0 is the permittivity of free space and ∆ε is the permittivity
change.
A universal scaling of the conductivity with respect to composition can be
achieved only for a limited composition range, where the structure does not change
drastically. So the single master curve of different composition with variance in mobile
ions implies that the ions do not change the structure of the composition, which is
confirmed in the FTIR result. A simple possibility to produce master curves of the real
part of the conductivity without using arbitrary scaling parameters is to plot log(σ'(ω)/σdc)
vs log(ω/(σdcT)). In 1985, Summerfield proposed the following scaling law for the ac
conductivity spectra of amorphous semiconductors [89]. Summerfield scaling method has
an advantage since it uses the directly accessible quantities such as dc conductivity and
temperature. Fig. 3.27 shows Summerfield scaling for different NASICON type glasses
where the conductivity axis is scaled by σdc, and the frequency axis by σdcT at different
temperatures. Here again for the samples scaled conductivity plateau spectra deviates at
low frequencies due to electrode polarization; these are presented in Fig. 3.24.
The scaled material response of the ac conductivity data collapsed into a single
curve for various NASICON type glasses as shown in Figs. 3.24. Generally the diffusion
of cations through the glass matrix occurs by random hopping between charge-
compensating anionic sites located throughout the lattice. The conduction can be related
to this diffusion through the Nernst-Einstein relation given by
2 2
dc H
B R
γNq dσ
6k THf= (3.17)
where N is the cation density, γ is the fraction of cations which are mobile, q is the charge
of the cation, d is the distance traversed in a single hop, and fH is the rate at which these
hops occur. HR is the Haven ratio which accounts for possible correlations between the
hopping movements of different mobile ions. In Fig. 3.25, a Summerfield master curve
has been obtained for the NASICON glass at 393K. The master curve does not show the
superimposing of different NASICON type glasses into single curve. The inset shows
clearly the separation of curves of various glasses. The master curve shift in frequency
axis is due to the variation in the ion hopping distance and the carrier concentration.
82
10610
710
810
910
1010
1110
1210
13
100
101
102
103
104
105
106
NNP
NTP
LNP
LTP
ANP
ω/(σdcT) [rad s
-1/(S cm
-1K)]
σ'(
ω)/
σdc
Fig. 3.24: Summerfield scaling for the conductivity spectra of different NASICON
type glasses. To separate the curves, the ordinate of the LTP, LNP, NTP and NNP
glasses are shifted respectively by one unit in the log scale of conductivity axis.
107
108
109
1010
1011
1012
1
10
109
1010
1011
1
10
ω/(σdcT) [rad s
-1/(S cm
-1K)]
σ(ω)/
σdc
NNP
NTP
LNP
LTP
ANP
Fig. 3.25: Summerfield scaling plots for the conductivity spectra of
different NASICON type glasses at 293K.
83
3.2.6 (b) Electric modulus scaling
10-410
-310
-210
-110
010
110
210
3
0.0
0.2
0.4
0.6
0.8
1.0
M''(
ω)/M'' max
ω/ωmax
Fig. 3.26: Electric modulus scaling plots for NTP Glass.
Our aim is to try to scale all the electric modulus data in such a manner that it can
be fitted into a single curve. Since the peak of imaginary part of the electric modulus shift
to higher frequency as temperature increases, the frequency axis was scaled by ωmax. In
order for the peaks to have the same height the imaginary part of the electrical modulus
was scaled by M"max. The master curve of electric modulus for NNP glass is shown in
Fig. 3.26 for different temperature. From Fig. 3.26 it is observed that the M" spectra
superimposed into a single master curve insisting that the conductivity relaxation process
is temperature independent. Here the data points for different temperature are top of each
other very well; this is because the β does not vary very much as the temperature is
increased in the NNP glass. Similar behavior is observed for all other samples.
84
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[89] S. Summerfield, Philos. Mag. B 52 (1985) 9.
88
Chapter IV
MIXED ALKALI EFFECT IN NASICON GLASSES
4.1 Introduction
The majority of the known methods for calculating the particular properties of
oxide glasses from composition are based on additive formulae that represent the
calculated property as a linear function of oxide concentrations. The evolution of the
glass structure according to the composition provides an overview of the behavior of each
species. However the physical properties of oxide glasses cannot generally be related to
the composition accurately by means of linear functions of the amounts of each
component. Linear factors may be used, to a first approximation, and many such sets of
aspects have been invoked for the guidance of glass technologists in developing or
modifying glass compositions to meet particular specifications [1]. One of the important
exceptions to this approximate linearity is the effect of changing the relative proportions
of the alkali oxides in glasses containing more than one alkali. When one alkali is
progressively substituted for another, the variation of physical properties with the amount
substituted is often so non-linear that the initial trend is later reversed, giving rise to a
maximum or a minimum. This extreme departure from linearity is called the mixed alkali
effect (MAE) [2-5].
The use of mixed alkalis has been exploited in many commercial compositions to
give glasses having superior combinations of properties that could be obtained with the
incorporation of any one alkali alone. This effect has a significant application [6-8] and
makes the mixed alkali glasses of special interest, for instance, low dielectric loss glasses
can easily be obtained by incorporating two different alkali. The challenge of the mixed
alkali effect arises from its universal occurrence and from the systematic way in which it
increases with the difference in sizes of the alkali ions. An adequate theory must be
applicable to any oxide glass, simple or complex, and must relate the effect only to the
ionic sizes. Many authors has put forward theories to explain the effect as far as a
particular property is concerned, more especially the electrical conductivity, but the
mixed alkali effect is noticeable on the majority of properties and it is essential for the
success of a theory that it agrees, at least qualitatively, with all the experimental facts.
89
The MAE in glasses gives rise to large changes in many dynamic properties,
particularly those related to ionic transport such as electrical conductivity, ionic diffusion,
dielectric relaxation and internal friction, when a fraction of the mobile ions is substituted
by another type of mobile ions [1, 2, 5, 9]. Macroscopic properties such as molar volume
and density, refractive index, thermal expansion coefficient, and elastic moduli usually
change linearly or only slowly with composition. Properties related to structural
relaxation, such as viscosity and glass transition temperature, usually exhibit similar
deviations from linearity as other mixed glass-forming systems which do not contain any
cations [2-4]. The reduced diffusivity in mixed alkali glasses as compared to single alkali
glasses cannot be explained by any major structural alteration upon the mixing of alkali
ions. Rather, experimental results show [10-13] that the alkali ions tend to preserve their
local structural environment regardless of the glass composition. Furthermore, the two
types of alkali ions are randomly mixed in the glass [13-15]. Similar conclusions have
been drawn from computer simulations of mixed alkali glasses [16-18].
Based on the experimental findings, a few theoretical models have also been
developed to understand the MAE [19-24]. These models consider either based upon
structural features e.g., conduction pathways [19, 21, 22] or based upon differing cation
interactions resulting from differences in the mass and/or size of the cation [23, 24].
However, these models are more or less unverified assumptions, such as site relaxation, a
selective hopping mechanism, or a crucial role of Coulomb interactions between the
mobile ions. The promising model which takes into account the two features of the MAE
is the dynamic structure model (DSM) reported by Bunde et al., and Maass et al., [19,
22]. In these models the reduced ion diffusivity in mixed alkali glasses has been
explained in terms of a site relaxation and memory effect, where each type of mobile
cation is able to adapt the glassy nature according to its spatial and chemical
requirements. Swenson et al., have predicted MAE and its relevant alkali conduction
pathways for the mixed alkali glass (LixRb1-xPO3) through reverse Monte Carlo structural
models by bonds valence model [12]. While all these models yield a qualitative
composition dependence of the ionic diffusivity, none of them is able to account for the
mixed alkali effect in the frequency response of the ionic conductivity. This present study
explores the conductivity and relaxation mechanism in mixed alkali NASICON glasses in
90
the system (LixNa(1-x))5TiP3O12 and (LixNa(1-x))4NbP3O12) in order to understand the
dynamics of charge carriers in such oxide systems. The ac conductivity and relaxation
mechanisms have been analyzed in the framework of the conductivity and the modulus
formalism. In the present work it has been shown that the conductivity formalism
accounts for the same qualitative variation of relaxation parameters with composition as
the modulus formalism. In this chapter the electrical properties of the glasses have been
studied for NASICON glasses with varying compositions in (LixNa(1-x))5TiP3O12
(LNTPx) and (Lix Na(1-x))4NbP3O12 (LNNbPx).
4.2 Synthesis and Characterization
The mixed alkali NASICON glasses were synthesized by the conventional melt
quenching method. Stoichiometric amount of analytical grade Li2CO3, Na2CO3, Nb2O5,
TiO2 and NH4H2PO4 were used as starting materials. All the compositions form glasses
when cast onto a steel mould; these glasses were subjected to X-ray diffraction studies
and no crystalline phases were detected. FTIR spectrum shows similar six main peaks at
~1200 , 1080, 983, 900, 741, 544 cm-1 for Niobium based glasses and five main peaks at
~ 1150, 1050, 920, 741, 571 for titanium based glasses. The assigns of these bands are
mostly from the contribution of various phosphate vibration and very few from Nb and Ti
vibration which has been discussed in chapter II. There is no deviation in vibration
frequency when alkali atom is replaced, which insists that there is no structural changes
in the glasses due to MAE.
The density (ρ) and the molar volume (V) for these glasses are shown in
Table 4.1. When Li2O is replaced by Na2O, it can be noted that the measured density as
well as the molar volume increases. These variation shapes are similar to those of mixed
Li2O and Na2O alkalis in the Li2O–Na2O–MoO3–P2O5 system [25]. Since the values of
the density and the molar volume are consistent with the ionic size, atomic weight of
lithium and sodium elements and their amount in these glasses, there is no MAE in these
parameters. Glassy nature was confirmed in DSC for all the samples. The glass transition
temperature Tg, the onset of the crystallization temperature Ts, the peak crystallization
temperature Tc, and melting temperature Tm, and the thermal stability parameters (∆T,S)
[26, 27] and Hurby’s parameter, Kgl [28] were determined and listed in Table 4.1. All the
91
critical temperature is low for x=0.6 insisting MAE in thermal properties of the sample.
The strength of the MAE in the composition for the glass transition temperature is
defined as,
∆Tg=Tg,lin – Tg (4.1)
where Tg,lin is the linear interpolation between the experimentally determined Tg values of
the two end members (the single alkali NASICON glasses) at the composition which
corresponds to Tg. The ∆Tg,min for (NaxLi(1-x))5TiP3O12 and (NaxLi(1-x))4NbP3O12 is 47
and 44 respectively.
Table 4.1: Glass transition temperature Tg in K, onset of crystalline temperature Ts
in K, crystalline temperature Tc in K, melting temperature Tm in K, thermal
stability parameters (∆T, S), Hruby parameter Kgl and strength of MAE ∆Tg for NASICON glasses.
Sample Tg Ts Tc1 Tc2 Tm ∆T S Kgl ∆Tg ρ Vm
Na5TiP3O12 699 774 791 842 1057 75 2.24 0.34 - 2.83 158.24
Na4Li1Ti P3O12 672 781 793 833 883 109 2.16 1.34 34 2.76 156.44
Na3Li2Ti P3O12 667*
737* 747* 775* 868* 70 1.20 0.66 47 2.73 152.31
Na2Li3Ti P3O12 676 801 806 852 970 125 0.96 0.79 44 2.71 147.54
Na1Li4Ti P3O12 680 790 803 845 1079 110 2.35. 0.44 48 2.69 142.51
Li5Ti P3O12 736 818 832 - 1104 82 1.82 0.35 - 2.61 140.83
Na4NbP3O12 693 - - - 1034 - - - - 2.91 161.44
Na3.2Li0.8Nb P3O12 664 784 799 - - - - - 30 2.9 157.56
Na2.4Li1.6Nb P3O12 652* 744* 792* - - - - - 44 2.87 154.74
Na1.6Li2.4Nb P3O12 664 754 804 - - - - - 33 2.85 151.32
Na0.8Li3.2Nb P3O12 669 786 838 - - - - - 29 2.83 147.85
Li4NbP3O12 701 914 933 - - - - - - 2.82 143.82 *denotes the minimum value
4.3 Impedance spectroscopy and dc conductivity analysis
Typical complex impedance plots for the glass at various temperature are shown
in Fig. 4.1. At low temperature, glasses show only one arc representing the bulk
properties and at high temperature, two arcs are found which represents the bulk and the
92
sample electrode interface effects. The impedance data are fitted using Boukamp
equivalent circuit and corresponding bulk resistance for particular temperature has been
calculated. The dc conductivity for each temperature was obtained from the bulk
resistances which follow Arrhenius behavior. The temperature dependence of the dc
conductivity obtained from the complex impedance plots are shown in Fig. 4.2 for
(NaxLi(1-x))5TiP3O12 glass compositions. It is noted that the variation of the conductivity
with temperature obeys Arrhenius equation σdcT=σ0exp(−Eσ/kBT), where σ0 is a
conductivity pre-factor and Eσ is the activation energy.
0 4 8 120
4
8
12
-Z''(
ω)x108 [
Ω]
Z'(ω)x108[Ω]
293K
303K
313K
323K
Boukamp fit
Fig. 4.1: Complex impedance plot for Na2Li3TiP3O12 systems at various
temperature.
2.0 2.4 2.8 3.2 3.6 4.0
-8
-6
-4
-2 (a)
log(σdcT) [S cm-1K]
1000/T [K-1]
NTP
NLTP0.8
NLTP0.6
NLTP0.4
NLTP0.2
LTP
Linear fit
2.0 2.4 2.8 3.2 3.6 4.0
-10
-8
-6
-4
-2
0
(b)
NNbP
NLNbP0.8
NLNbP0.6
NLNbP0.4
NLNbP0.2
LNP
Linear Fit
1000/T [K-1]
log(σdcT) [S cm-1K]
Fig. 4.2: Temperature dependent of dc conductivity observed from impedance
spectroscopy for composition variation of mixed alkali in (a) (NaxLi(1-x))5TiP3O12 and
(b) (NaxLi(1-x))4NbP3O12 glasses.
93
0.0 0.2 0.4 0.6 0.8 1.010
-14
10-12
1x10-10
1x10-8
1x10-6
1x10-4
273K
323K
373K
423K
x [Li/Na]
σdc [S cm-1]
0.5
0.6
0.7
0.8
0.9
1.0
Eσ
Fig. 4.3: Composition variation of dc conductivity and its respective activation
energy for (NaxLi(1-x))5TiP3O12.
0.0 0.2 0.4 0.6 0.8 1.0
10-11
1x10-10
1x10-9
1x10-8
1x10-7
1x10-6
1x10-5 273K
323K
373K
x [Li/Na]
σdc [Scm-1]
0.60
0.65
0.70
0.75
0.80
0.85
0.90
Eσ
Fig. 4.4: Composition variation of dc conductivity and its respective activation
energy for (LixNa(1-x))4NbP3O12.
The values of the activation energy Eσ were obtained from the least-squares
straight-line fits. The dependence of the conductivity at selected temperature (273K,
323K, 373K and 423K) and its corresponding activation energy on the relative
composition of NLTPx and NLNbPx NASICON glasses are shown in Figs. 4.3 and 4.4,
respectively. The 273K dc conductivity data for x=0.4, 0.6 and 0.8 of NLTPx has been
obtained from the extrapolated data of Arrhenius equation. These plots show a minimum
94
near x=0.6. It is worth to notice that this minimum is usually observed in mixed-alkali
glasses. This could be attributed to the maximum of the activation energy. Such behavior
is compatible with mixed-alkali effect. Similar trend associated with the glass transition
temperature. The conductivity and the glass transition temperature are expected to behave
in a similar manner since both properties are associated with the dynamics of the glass
system. The drop in conductivity related to the mixed-alkali effect is about five orders of
magnitude at 273K and four orders of magnitude at 323K compared to the original Li and
Na analogue glasses. Indeed, deep minimum in isotherm of the conductivity increases
with decreasing temperature as shown in Fig. 4.3 & 4.4. The magnitude of MAE in dc
conductivity at a particular temperature can be determined:
∆log(σdc)=log(σdc,lin)-log(σdc,min) (4.2)
where log(σdc,min) represents the minimum experimental value of log(σdc). The value of
log(σdc,lin) is obtained from the linear interpolation between the experimentally
determined logarithmic conductivity of the end members, at the composition which
corresponds to log(σdc,min). The calculated value of ∆log(σdc) by Eq. (4.2) at 323K, 373K
and 423K are 3.87, 3.23 and 2.69 for NLTPx and 1.73, 1.68 and 1.50 for NLNbPx
samples respectively. Both results show that the MAE becomes less pronounced as the
temperature increased. The disappearance of MAE with increase in temperature was
predicted by Hunt by applying the theory of percolation transport [29]. The MAE
strength in the dc conductivity of the two samples interpret that NLTPx shows stronger
MAE strength compare to the NLNbPx samples. Similar to the dc conductivity, the
strength of MAE in the activation energy is defined as:
∆Ea= Ea,max-Ea,lin, (4.3)
where Ea,max gives the maximum value of activation energy at x=0.6 composition and
Ea,lin is the activation energy corresponding to Ea,max obtained from the linear
interpolation between the activation energy of the two single alkali glasses. The
calculated values of ∆Ea by Eq. (4.3) are 0.37eV and 0.28eV for NLTPx and NLNbPx
samples respectively. The mixed alkali effect in the activation energy for mixed alkali
NLTPx glass system is stronger than NLNbPx glass systems.
The MAE observed in the NASICON glasses can be understood on the basis of
dynamic structure model (DSM) reported by Bunde et al., and Maass et al., [19,22], the
95
observed minimum of the conductivity in the glasses could be attributed to the distinctly
different local environment of the two alkali ions, which are preserved in the mixed
glasses. The pathway network is extended for the Li based glass than for Na based
glasses, explaining the higher conductivity of the former glass. In mixed alkali glasses Li
and Na ions have distinctly different conduction pathways and the pathway volume for
the Li ions is considerably larger than for the Na ions, which implies that Na conduction
gives only a minor contribution to the total conductivity. The argument is that the atomic
characteristics of Li and Na are very different and each cation may reside in a site formed
by a local environment in the single glasses as well as in the mixed-alkali compositions.
Generally in oxide glasses, lithium and sodium cations are normally connected with non-
bridging oxygen anions to satisfy the charge neutrality conditions. Since the activation
energy associated with Na-glass is larger than that of single Li-glass, one can predict that
the magnitude of the interactions and the polarization effects related to the alkali-
environment are different.
In a single alkali glass, an alkali ion moves into a site previously occupied by the
same type alkali, a sort of structural memory effect [19] favors its migration. However, in
the mixed alkali compositions the hopping dynamics of Li and Na cations are intimately
coupled with the structural relaxations of the glass network. For instance, to
accommodate the jump of Li cation into a site previously occupied by a sodium cation,
the latter must undergo a local relaxation, after which the cation can continue to migrate
through the matrix. As a matter of fact, the alkali cations have different local
environments; they occupy specialized sites with the possibility to retain the memory of
their original position before changing the site due to the conductivity. Since Li+ and Na+
ions are distinguishable, these sites form clusters of various sizes which are intertwined.
Note that any vacant site may become occupied by a cation of different nature. When that
happened the concerned cation becomes effectively trapped until site relaxation is
reconfigured to the newly occupying ion. This trapping mechanism causes a reduction in
the overall ionic diffusion, as a consequence of such trapping, a decrease in dc
conductivity is observed.
Statistically, it can be noted that a minimum may be pronounced for a
composition corresponding to a maximum disorder of alkali elements. Accordingly, the
96
conductivity decreases when substituting lithium by sodium and vice versa. In addition to
ionic conductivity, the glass transition temperature, Tg, which is not directly dependent
on ionic transport, shows a pronounced departure from linearity at intermediate mixed-
alkali ion compositions. It is also observed that the glass transition temperature is lower
for mixed glasses than for the original compositions (x=0, 1). Such behavior could also
be associated to the ’structural disorder’ imposed by the presence of two kinds of cations.
This kind of Tg variation was also reported for other vitreous mixed alkali glasses.
4.4 Ac conductivity analysis
The conductivity isotherm is investigated as a function of the frequency for all the
compositions and Fig. 4.5 shows the plot for Na2.4Li1.6NbP3O12. The dynamic
conductivity related to the real part of the complex conductivity showed a typical
behaviour: a frequency-independent plateau for low frequency range and a power-law
increase at high frequencies. The conductivity spectra have also been analyzed in the
framework of the Almond–West formalism. To get a clear picture of ac response of the
conductivity, frequency dependent conductivity for all the composition at 323K is shown
in Figs. 4.6 & 4.7. The conductivity plateau region is much lower in the mixed alkali
glasses than in the single alkali glasses. As the frequency increases the conductivity rises
above its plateau value featuring a dispersive behavior. At low temperature the plateau
features is not observed for the composition x=0.4 and 0.6. The rapid fall of the
conductivity at low frequencies for compositions x=0 and 1.0 is the well-known electrode
polarization phenomenon.
The movement of dissociated cations in the glass matrix can be described in the
conductivity representation framework by Jonsher’s universal power law relation
represented by Eq. (3.3). The temperature dependence of dc conductivity for various
composition obtained from the ac conductivity analysis is similar to that of the dc
conductivity of impedance spectroscopic studies. The hopping frequency obtained from
the Eq. (3.5) shows the trend similar to the dc conductivity. The ac conduction takes
place on the mixed alkali glass with complex subset of diffusion cluster or fat percolation
cluster. These clusters consist of two types of alkali glasses which are randomly mixed
and tend to attain the same local structure environment as in single alkali glasses with
97
different low dimensional conduction pathways. This results in a large energy mismatch
between the local potential of site Li+ and Na+ which reflects as high activation energy
for the ions to jump into the dissimilar energy sites.
102
103
104
105
106
107
10-12
10-11
1x10-10
1x10-9
1x10-8
1x10-7
1x10-6
ω[rad s-1]
σ'(
ω) [S cm-1]
273 K
283 K
293 K
303 K
313 K
323 K
333 K
343 K
353 K
363 K
373 K
383 K
393 K
403 K
AWM Fit
Fig. 4.5: Ac conductivity of Na2.4Li1.6NbP3O12 at different temperature. Solid lines
are fit to Almond West model.
102
103
104
105
106
107
1E-10
1E-9
1E-8
1E-7
1E-6
1E-5
σ'(
ω) [S cm-1]
ω[rad s-1]
NTP
N4L1TP
N3L2TP
N2L3TP
N1L4TP
LTP
Fig. 4.6: Ac conductivity plot of composition (NaxLi(1-x))5TiP3O12 at 323K. Solid lines
are fit to Almond West model.
98
2.1 2.4 2.7 3.0 3.3 3.6 3.9
2
3
4
5
6
7
8
9
1000/T [K-1]
log(ωp) [rad s-1]
NNP
N32NP
N24NP
N16NP
N8NP
LNP
Linear Fit2.1 2.4 2.7 3.0 3.3 3.6 3.9
1
2
3
4
5
6
7
8
log(ωp) [rad s-1]
1000/T [K-1]
LTP
N1L4TP
N2L3TP
N3L2TP
N4L1TP
NTP
Linear Fit
100 1000 10000 100000 1000000 1E7
1E-10
1E-9
1E-8
1E-7
1E-6
σ'(
ω) [S cm-1]
ω[rad s-1]
LNP
LNNP0.8
LNNP0.6
LNNP0.4
LNNP0.2
NNP
AWM fit
Fig. 4.7: Ac conductivity plot of composition (NaxLi(1-x))4NbP3O12 at 323K. Solid
lines are fit to Almond West model.
(a) (b)
Fig. 4.8: The temperature dependence of the cross-over frequency ωp for
composition variation of mixed alkali (a) (NaxLi(1-x))5TiP3O12 and (b)
(NaxLi(1-x))4NbP3O12 glasses.
99
Arrhenius behaviour of the cross-over frequency ωp obtained from the best fits for
all glass compositions is shown in Fig. 4.8. The values of the activation energy Eω for
cross-over frequency of charge carriers are obtained from the least-squares fits of data in
Fig 4.8 and are displayed in Table 4.2 .The dependence of the cross-over frequency at
various temperature (323 K, 373 K and 423 K) and its corresponding activation energy
for various samples with composition (NaxLi(1-x))5TiP3O12 is shown in Fig 4.9. It is
observed that cross-over frequency shows a minimum and the activation energy of the
cross-over frequency shows a maximum at a value of x=0.6, which strongly supports the
existence of the mixed alkali effect in the present NASICON glass compositions. But it is
to be noted from the Fig.4.9 that as the temperature increases, the strength of the hopping
frequency decreases between the single and the mixed alkali glasses.
0.0 0.2 0.4 0.6 0.8 1.010
0
102
104
106
108
log(ω
p)
323K
373K
423K
x (Li/Li+Na)
0.5
0.6
0.7
0.8
0.9
1.0
Eω [eV]
Fig. 4.9: Composition variation of hopping frequency at three different temperature
and its respective activation energy for (NaxLi(1-x))5TiP3O12.
100
0.0 0.2 0.4 0.6 0.8 1.01E-11
1E-10
1E-9
1E-8
1E-7
1E-6
σac[S cm-1]
σdc
1x105Hz
1x106Hz
x(Li/Li+Na)
Fig. 4.10: Variation of the dc conductivity at 323K and the ac conductivity, at 105
and 106Hz for (NaxLi(1-x))5TiP3O12 with lithium cation mole fraction.
0.0 0.2 0.4 0.6 0.8 1.0
1E-8
1E-7
1E-6
σ' [S cm-1]
σdc at 323K
σac at 10
5 Hz 323K
σacat 10
5 Hz 373K
x(Li/Li+Na)
Fig. 4.11: Composition dependence of dc conductivity at 373K and ac conductivity
at 323K and 373K with fixed frequency of 105
Hz for (NaxLi(1-x))5TiP3O12 glasses.
101
Fig. 4.10 shows the variation of the dc conductivity (473K) and the ac
conductivity, at 105 and 106Hz after subtracting the dc conductivity with the lithium-
cation mole fraction. It is interesting to note that the ac conductivity also goes through a
minimum at the same composition and in the same manner as in the dc conductivity.
Although, the magnitude of the effect seems to decrease with frequency, it is nevertheless
significant and indeed the ac conductivity exhibits MAE. This is a decisive result in
observing MAE in the ac conductivity. It is also evident from Fig. 4.11 that the MAE in
the ac conductivity is present at different frequencies at a fixed temperature and also at a
fixed frequency (105Hz) and two different temperature with significant depth. In both
cases, the depth decreases with increasing temperature or frequencies.
4.5 Electric modulus
An alternate method to analyze the ac electric response from the sample is electric
modulus. A typical modulus spectrum for one of the compositions is shown in Fig. 4.12
at different temperature. It may be noted that the spectrum is slightly asymmetric
suggesting a stretching behavior for the mixed alkali composition. In order to get a proper
description of the relaxation, data are fitted with Bergman’s approach which is an
approximate frequency representation of the KWW function, allowing direct fitting in the
frequency domain. The solid line curves in Fig. 4.12 are the fits to this equation and the
parameters M"max, ωmax and β are extracted from the fit. The modulus peak gets shifted to
higher frequency as the temperature is increased. An interesting feature observed in this
modulus representation is the relaxation peaks appear in lower frequency for mixed alkali
glasses compared to the single alkali glasses. This is due to the increase in relaxation time
when the single alkali glass is replaced by second alkali gradually, which is associated to
mixed alkali effect and indicates slowing down of the ionic motions both on local and
long ranges [25].
The width of the modulus peak can be quantified by the stretching parameter β.
During the fitting procedure it was noticed that β depends on the frequency interval
chosen for fitting. This introduces uncertainties in the determinations of β. Although high
frequency points were excluded in the fitting procedure, β of the same glass varied
slightly for different temperature. The error limits in Table. 4.2 are estimated from this
102
variation of β. The modulus peak width decreases and hence the stretching parameter β
increases, as the alkali concentration decreases in single alkali glasses. This increase in β
parameter in mixed alkali glasses is because the mixed alkali glass LixNa1-xG behaves as
two diluted glass LixG and Na1-xG, where G is the glass matrix and the conduction takes
place in distinctly different pathways for the Li and Na. According to the coupling model,
the coupling or degree of cooperation is reflected in the coupling parameter n=1-β,
between ions when the concentration decreases [21, 30, 31]. Therefore the increase in the
concentration of second alkali will decline the cooperation between two ions and the
corresponding increase in β observed in mixed alkali glasses. The typical cation jump
distance tends to increase in mixed composition which is proposed to be the main reason
for the MAE in glasses. The temperature dependent relaxation time dependence is shown
in Fig. 4.13 for NLTPx samples, which clearly shows the relaxation features in mixed
alkali glass. The activation energy extracted from the linear regression is given in
Table. 4.2
10110
210
310
410
510
610
7
0.000
0.008
0.016
M''(
ω)
ω [rad s-1]
323K
333K
343K
353K
363K
373K
383K
393K
403K
413K
423K
433K
Bergman Fit
103
Table 4.2: Activation energies of dc conductivity (Eσ), impedance peak (Eimp),
hopping frequency (Eω) and conductivity relaxation time (Eττττ), dc conductivity at 323
K and modulus stretching parameter β for the different NASICON type glasses.
Eσ Eω Eτ Samples
±0.02eV
(σdc± 0.04%) Scm-1 at 323K
β ±0.03
Na5TiP3O12 0.58 0.54 0.55 9.42 x10-8 0.60
Na4Li1Ti P3O12 0.84 0.83 0.82 4.46 x10-10 0.65
Na3Li2Ti P3O12 0.94 0.96 0.95 4.59 x10-11 0.68
Na2Li3Ti P3O12 0.91 0.89 0.89 1.85 x10-10 0.63
Na1Li4Ti P3O12 0.80 0.78 0.79 1.45 x10-8 0.62
Li5Ti P3O12 0.56 0.50 0.52 2.31 x10-6 0.60
Na4NbP3O12 0.61 0.58 0.58 7.51 x10-8 0.58
Na3.2Li0.8Nb P3O12 0.83 0.77 0.78 4.73 x10-10 0.60
Na2.4Li1.6Nb P3O12 0.89 0.86 0.87 9.16 x10-11 0.63
Na1.6Li2.4Nb P3O12 0.84 0.82 0.81 3.86 x10-10 0.63
Na0.8Li3.2Nb P3O12 0.79 0.78 0.77 6.79 x10-9 0.61
Li4NbP3O12 0.61 0.58 0.57 1.09 x10-6 0.61
2.1 2.4 2.7 3.0 3.3 3.6 3.9
-7
-6
-5
-4
-3
-2
-1
τ [s]
1000/T [K-1]
NTP
N4LTP
N3L2TP
N2L3TP
N1L4TP
LTP
Linear Fit
104
4.6 Scaling
4.6.1 Ac conductivity scaling
The ability to scale different conductivity isotherms so as to collapse all to one
common curve indicates that the process can be separated into a common physical
mechanism modified only by temperature scales. In this chapter scaling studies have been
performed in mixed alkali glasses in ac conductivity and electric modulus and the results
are discussed. In order to compare the shape of the conductivity response the scaling
technique proposed by Ghosh et al., and Summerfield are adopted which is explained in
chapter III. The ac conductivity curve for particular composition of NASICON glasses
collapse into a single master curve for different temperature. This is proved in both the
method of scaling insisting that the shape of the conductivity dispersion does not depend
on temperature. In this chapter both the methods are adopted to scale the ac conductivity
for varying composition.
Fig. 4.14 shows the results of Ghosh scaling procedure for the mixed alkali
glasses. In this, the conductivity axes of each conductivity isotherm for a particular glass
composition at different temperature has been scaled by the dc conductivity σdc and the
frequency axis by the crossover frequency ωp obtained from the fitting of conductivity
isotherms. Surprisingly, it has been found that the mixed alkali NASICON samples
collapse into single master curve, this simply means that the compositional independence
of the electrical relaxation mechanism. As the conductivity isotherms superpose on a
single master curve, this may imply that the relaxation mechanism is not only
independent of temperature but also independent of concentration and type (i.e.
concentration of Na+, Li+) of the ionic charge carriers. Therefore, the advantage of using
hopping frequency as the scaling frequency is that it is not specifically delimitated by the
composition range or the type of glass. The change in hopping length with composition is
manifested in the change in the hopping frequency which takes into account the
correlation effects between successive hops through the Haven ratio. Generally it is
observed that, Haven ratio increases when there is a decrease in mobile ion concentration
in single alkali glasses [33]. Since the mixed alkali glasses is similar to the dilute single
alkali glasses the Haven ratio takes into account of the mixed alkali glasses as one alkali
is replaced by the second. This insisted that the mobile ion concentration is not
105
necessarily need to be proportional to the cation concentration and so variation in mobile
ions (single and diluted single alkali glasses) can scale into single master curve in Ghosh
scaling approach.
1E-3 0.01 0.1 1 10 100 1000
1
10
100
α
α
αα
αα
αα
αα
αα
αα
αα
ααααααααα
β
β
ββ
ββ
ββ
ββ
ββ
ββ
βββββββββββ
Χ
Χ
ΧΧ
ΧΧ
ΧΧ
ΧΧ
ΧΧ
ΧΧΧΧΧΧΧΧΧΧΧΧΧ
ΓΓ
ΓΓ
ΓΓ
ΓΓ
ΓΓ
ΓΓΓΓΓΓΓΓΓΓΓΓΓΓΓΓΓ
ΩΩ
ΩΩ
ΩΩ
ΩΩΩΩΩΩΩΩΩΩΩΩΩΩΩΩΩΩΩΩ
Ω
QQQQQQQQQQQQQQQQQQQQQ
QQQQQ
Q
BBBBBBBBBBBBBBBBBBBBBBBBBBBBB
BB
CCCCCCCCCCCCCCCCCCCCCCCCCCCCC
CC
DDDDDDDDDDDDDDDDDDDDDDDDDD
DDDD
E
EEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
FFFFFFFFFFFFFFFFFFFFFFFFFFFFF
FF
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
ΟΟΟ
ΟΟ
ΟΟ
ΟΟ
ΟΟ
ΟΟ
ΟΟ
ΟΟ
ΟΟ
ΟΟΟΟΟΟΟΟΟΟΟΟΟΟΟΟΟΟΟΟΟΟ
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
σ(ω
)/σdc
ω/ωp
Fig. 4.14: Scaling plots for the conductivity spectra of different mixed alkali
(NaxLi(1-x))5TiP3O12 NASICON type glasses at different temperature.
106
108
1010
1012
1014
1016
10-1
100
101
102
103
ω/(σdcT) [rad s
-1/ S cm
-1K]
σ'(
ω)/
σdc
x= 0, 1
Fig. 4.15: Summerfield scaling plots for the conductivity spectra of mixed alkali
(NaxLi(1-x))5TiP3O12 NASICON type glasses.
106
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.750.1
0.2
0.3
0.4
0.5
∆ log[σ'(
ω)]-∆ log(ω)
log(σ'(ω)/σdc)
Li5TiP
3O12
Na2Li3TiP
3O12
Na5TiP
3O12
Fig. 4.16: Approximate slope of the conductivity dispersion σ'(ω) in
(NaxLi(1-x))5TiP3O12 glasses as a function of the scaled conductivity σ(ω)/σdc.
103
104
105
106
107
108
0.2
0.4
0.6
∆ log[σ'(
ω)]/∆ log(ω)
ω [rad s-1]
Li5TiP
3O12
Na2Li3TiP
3O12
Na5TiP
3O12
Fig. 4.17: Frequency dependence of the approximate slope of conductivity for
single and mixed alkali (NaxLi(1-x))5TiP3O12 glasses.
107
Fig. 4.15 shows the results of Summerfield scaling procedure for the mixed alkali
glass samples. In this the conductivity data for different composition were plotted as
log(σ(ω)/σdc) vs. log(ω/σdcT). All the conductivity data collapse to single curve for
different temperature but when the conductivity of different composition is take into
account, the single alkali glasses are closely similar, whereas the mixed alkali glass
shows a different behavior. The conductivity σ'(ω) of the mixed alkali glass increases
slowly compare to the single alkali glasses as the frequency increases. The shape of the
ac conductivity σ'(ω) in the dispersive region can be analyzed using the slope of the
conductivity curve in a plot of logσ'(ω) against log(ω). In order to enhance the difference
in shape between the conductivity dispersion data of the different glasses the slope of the
conductivity curve was plotted against σ'(ω)/σdc as shown in Fig.4.16. This approach was
introduced by Schroder and Dyre [34, 35]. The approximate value of the slope
∆[log σ(ω)]/∆[log(ω)] at each frequency was estimated using the forward incremental
ratio [log(σ(ωi+1))-logσ(ωi)]/[log(ωi+1)-log(ωi)]. Fig. 4.16 shows that the mixed alkali
glass behaves differently from the single alkali glasses at the onset of the dispersive
region, whereas differences between single alkali glasses become relevant only at higher
frequencies/shorter timescales. Fig. 4.17 shows the behavior of the slope
∆[log(σ(ω))]/∆[log(ω)] as a function of frequency, hence excluding any scaling
parameter. It can be observed that in single alkali glasses the slope of conductivity curve
increases almost abruptly above the low frequency plateau while in the mixed alkali glass
the onset of dispersion is less marked and the increase of the slope is gradual. Fig. 4.17
insisted that the transition from the conductivity plateau to the dispersive region is more
gradual in the glasses with lower alkali content [36]. Compared to the present
investigation, these results would suggest that, with respect to the conductivity, mixed
alkali glasses behaves as diluted single alkali glasses. This is in agreement with the
conclusions drawn from an electrical modulus [37].
4.6.2 Electric modulus scaling
In order to compare the shape of the modulus curves, the data points can be
superimposed on each other by rescaling the axes with M"(ω) by M"max and the
frequency axis by ωmax. Fig. 4.18 shows the normalized modulus curves for all the
108
compositions. It is clearly seen that the lower frequency wing of the normalized modulus
curve superimpose into single curve but it does not happen in high frequency wing. This
is because that the mixed alkali glass have narrow curve compared to the single alkali
glass. This makes the stretching parameter β low for mixed glass. The result of modulus
scaling insist that the long range conduction process are same for various compositions,
whereas the relaxation process vary with composition, this makes the high frequency
curve not to collapse to single curve
10-4
10-2
100
102
104
0.0
0.3
0.6
0.9
1.2
x= 0.2,0.4, 0.6
x= 0, 1
M''(
ω)/M'' max
ω/ωmax
Fig. 4.18: Electric modulus scaling plots for mixed alkali (NaxLi(1-x))5TiP3O12 glass
systems.
The scaling for modulus described earlier clearly shows that KWW function can
not describe the relaxation process in the whole frequency and temperature range
particularly in the high frequency range. This is because that the full wave half maximum
width W varies significantly as single alkali is replaced by the other. Dixon et al., [38,
39] studied the universality by scaling the dielectric response of different glass formers
and shown the dielectric master curve. This scaling approach has been extended for
electric modulus and studied scaling for various oxide glasses.
109
-4 -2 0 2 4 6-6
-4
-2
0
W-1log(ω
pM''/
∆M
ω)
W-1(1+W
-1)log(ω/ω
p)
433K
443K
453K
463K
473K
483K
493K
Fig. 4.19 Dixon scaling plot of electrical modulus data for Na3Li2TiP3O12 glass at
different temperature
-4 -2 0 2 4 6-5
-4
-3
-2
-1
0
1
W-1log(ωpM''/
∆M
ω)
W-1(1+W
-1)log(ω/ω
p)
LTP
N1L4TP
N2L3TP
N3L2TP
N4L1TP
NTP
Fig. 4.20 Dixon scaling plot of electrical modulus data for mixed alkali
(NaxLi(1-x))5TiP3O12 glass systems.
110
In order to obtain a single curve that superimposes all the modulus, plots has been
constructed between W-1log(M''ωp/∆Mω) and W-1(1+ W-1) log(ω/ωp) where W is the
width of the modulus peak normalized to a Debye relaxation, ∆M is the modulus
relaxation strength, and ωp is the peak frequency for the maximum observed in M''. The
results are shown in Fig. 4.19, where the Dixon scaling approach is quite successful in
collapsing M'' for a range of temperature over which W changes substantially from 1.1 to
1.6 decades. Furthermore, the scaling curve obtained has exactly the same form as that
reported for other types of relaxation processes in structural glasses. It is also interesting
to see from Fig. 4.20 that the modulus scaling is successful for the mixed alkali glasses in
the composition variation which clearly indicates that Dixon scaling is excellent when
compare to the power law scaling which is also reported earlier [40]. It also reveals that
there are no intrinsic changes occurring in the ion motion and relaxation in the mixed
alkali glass [41].
111
References
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[2] D. E. Day, J. Non-Cryst. Solids 21 (1976) 343.
[3] A. H. Dietzel, Phys. Chem. Glasses 24 (1983) 172.
[4] M. Ingram, Glastech. Ber. 67 (1994) 151.
[5] J. F. Stebbins, Solid State Ionics 112 (1998) 137.
[6] R. M. Hakim and D.R. Uhlmann, Phys. Chem. Glasses 8 (1967) 174.
[7] R. M. Hakim and D.R. Uhlmann, Phys. Chem. Glasses 12 (1967) 132.
[8] O. L. Anderson and D. A. Stuart, J. Amer. Ceram. Soc. 37 (1954) 573.
[9] T. Uchino, T. Yoko, J. Phys. Chem. B 103 (1999) 1854.
[10] B. Rouse, P. J. Miller, and W. M. Risen, J. Non-Cryst. Solids 28 (1978) 193.
[11] A. C. Hannon, B. Vessal, and J. M. Parke, J. Non-Cryst. Solids 150 (1992) 97.
[12] J. Swenson, A. Matic, A. Brodin, L. Börjesson and W.S. Howells, Phys. Rev. B 58 (1998) 11331.
[13] J. Swenson, A. Matic, C. Karlsson, L. Borjesson, C. Meneghini, and W. S. Howells, Phys. Rev. B 63 (2001) 132202.
[14] B. Gee and H. Eckert, J. Phys. Chem. 100 (1996) 3705.
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[16] T. Uchino, T. Sib, Y. Ogata, M. J. Iwasaki, J. Non-Cryst. Solids 146 (1992) 26.
[17] S. Balasubramanian and K. J. Rao, J. Non-Cryst. Solids 181 (1995) 157.
[18] J. Habasaki, I. Okada and Y. Hiwatari, J. Non-Cryst. Solids 208 (1996) 181.
[19] P. Maass, A. Bunde and M. D. Ingram, Phys. Rev. Lett. 68 (1992) 3064.
[20] P. Maass, J. Non-Cryst. Solids 255 (1999) 35.
[21] G. N. Greaves and K. L. Ngai, Phys. Rev. B 52 (1995) 6358.
[22] A. Bunde, M.D. Ingram, P. Maass, K.L. Ngai, J. Phys. A 24 (1991) 2881.
[23] R. Kirchheim, J. Non-Cryst. Solids 272 (2000) 85.
[24] D. P. Button, R. P. Tandon, C. King, M. H. Velez, H. L. Tuller, D. R. Uhlmann, J. NonCryst. Solids 49 (1982) 129.
[25] L. Abbas, L. Bih, A. Nadiri, Y. El Amraoui, D. Mezzane, B. Elouadi, Journal of Molecular Structure 876 (2008) 194.
[26] S. Mahadevan, A. Giridhar, A.K. Singh, J. Non-Cryst. Solids 88 (1986) 11.
[27] M. Saad, M. Poulin, Mater. Sci. Forum. 19&20 (1987) 11.
[28] A. Hurby, Czech. J. Phys. B 22 (1972) 1187.
112
[29] A. Hunt, J. Non-Cryst. Solids 220/1 (1997) 1.
[30] K. L. Nagi, J. Non-Cryst. Solids 203 (1996) 232.
[31] K. L. Ngai, G. N. Greaves and C. T. Moynihan, Phys. Rev. Lett. 80(1998) 1018.
[32] H. Aono, E. Sugimoto, Y. Sadaoka, N. Imanaka, G. Adachi, J. Electrochem. Soc. 136 (1989) 590.
[33] J. E. Kelly III, J.F. Cordaro, M. Tomozawa, J. Non-Cryst. Solids 41 (1980) 47.
[34] T. B. Schroder, J. C. Dyre, Phys. Rev. Lett. 84 (2000) 310.
[35] J. C. Dyre, T.B. Schroder, Rev. Mod. Phys. 72 (2000) 873.
[36] B. Roling, C. Martiny, Phys. Rev. Lett. 85 (2000) 1274.
[37] S. Vinoth Rathan, G. Govindaraj, Solid State Ionics (to be submitted)
[38] P. K. Dixon, L. Wu, S. R. Nagel, B. D. Williams, J. P. Carini, Phys. Rev. Lett. 65 (1990) 1108.
[39] P. K. Dixon, L. Wu, S. R. Nagel, B. D. Williams, J. P. Carini, Phys. Rev. Lett 66 (1991) 959.
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113
Chapter V
INVESTIGATIONS ON DIVALENT ION SUBSTITUTED
NASICON GLASSES
5. 1 Addition of divalent ions in NASICON glasses
5.1.1 Introduction
Phosphate glasses are both scientifically and technologically important materials
because of their structural versatility to accept several cation and/or anion exchanges.
These features allow the reengineering of glass formulation, which leads to advances in
their physical properties [1] and for commercial exploitation purposes. Thus, an
investigation on the relationship between the composition and properties of these
materials was seen to be important. Generally the properties of any glass and the
chemical durability can be changed by addition of halides or oxides of alkaline earth or
transition metal ions into the glass matrix. In the NASICON framework (AxByP3O12)
materials both crystalline and glassy materials have the advantage that a complete
substitution of ions is possible at both A and B sites and various monovalent and
transition metal ions can be introduced at A and B sites respectively [2]. In fact, A sites
can be substituted by divalent ions and B sites by several tetravalent and trivalent
elements or even the alkali ions. Therefore this work has been undertaken with an aim of
arriving at a new class of fast ion conducting material by adding appropriate amount of
divalent ions into the NASICON glass matrix.
In this chapter four different divalent ions such as Zn, Cu, Cd and Pb have been
used to study the change in the electrical properties. Addition of ZnO significantly
modifies the glasses as a network modifier. Such glasses with transition metal ions have
several potential applications [3–6]. Similarly, PbO is a conditional glass former and so
with this oxides in the glass matrix, a low rate of crystallization, moisture resistance,
stable and transparent glasses have been achieved because of the dual role played by PbO
as a glass former if Pb–O is ionic and glass modifier if Pb–O is covalent [7, 8]. Whereas,
copper can exist on different valence state such as a monovalent (Cu+) and divalent
(Cu2+) ions [9] and both was found to be stable and sensitive to the glass environment. It
has been reported earlier that the valence state of copper not only modifies the chemical
114
and physical properties, but also the glass forming ability [10]. In general divalent doped
alkali phosphate glasses were shown to be a good compromise between a low glass
transition and a good chemical durability [12-14]. In this chapter different NASICON
type glasses with divalent ions are prepared and their electrical properties have been
studied in addition to the characterization of samples using XRD, DSC and FTIR.
5.1.2 Synthesis and Characterization
The glass composition of A2NbMP3O12 (where A =Li and Na; M= Cd, Zn, Pb and
Cu) were prepared as explained in chapter II. The final heating temperature in this case
was above 1200oC. The lack of any sharp peaks for all the samples in XRD spectra
indicates the amorphous nature of the samples. From FTIR studies it is obvious that there
are four main peaks at ~1170, ~1010, ~910 and ~530 cm-1 in addition to two weak bands
at ~741 and 617 cm-1. These bands are assigned to the various vibrational contributions
of the basic phosphates group [15-21]. The glassy natures of the samples were further
confirmed by the observation of the glass transition temperature through DSC
measurements. The Tg values for all samples were reported in Table 5.1. Also, the density
and the molar volume of the four glass samples were given in Table 5.1.
5.1.3 Impedance spectroscopic studies
Conductivity measurements was made at different temperature using a Hioki
3532-50 LCR Hitester in the frequency range 100 Hz to 1 MHz as explained in
Chapter II. Figures 5.1(a)-(d) show a typical complex impedance plane plots and the
corresponding equivalent circuits of the Na2NbZnP3O12 glasses for various temperature.
The impedance spectrum shows depressed semicircle or part of depressed semicircle
corresponds to bulk contribution at low temperature. The bulk resistance (Rb) relative to
each experimental temperature is the intercept of the real axis of the zero-phase angle
extrapolation of the lowest-frequency curve. The centers of the depressed semicircle lie
below abscissa and therefore constant phase elements (Q) have been used in equivalent
circuit model. At high temperature, two depressed semicircles were observed at both low
and high frequency region. In intermediate temperature, there is a depressed semicircle in
addition to a spike or part of depressed semicircle at low frequency region. The
115
impedance spectra having spike or depressed semicircle in low frequency region are due
to the surface related artifacts between the electrode and the sample and it is represented
as electrode polarization effect [22].
As temperature increases, the radius of the arc corresponding to the bulk
resistance of the sample decreases indicating an activated conduction mechanism. Similar
results were observed for other glasses. A deeper insight into the electrical properties of
the NASICON type glasses is obtained from the complex impedance plane analysis with
Boukamp equivalent circuit package [23] as shown in the inset of Figs. 5.1 (a)-(d). The
increase of dc conductivity with temperature is represented by Arrhenius relation. This is
due to the increase in the thermally activated drift mobility of ions according to hopping
conduction mechanism. The activation energy Ea for the conduction process extracted
from the slope of the straight line plot of log(σdcT) against reciprocal temperature 1000/T
is provided in Table 5.1.
0 3 6
0
3
6
(a)
Qb
Rb
-ZII (
ω)X 106 [
Ω]
-ZII(ω) X 107 [
Ω]
ZI (ω) X 10
7 [Ω ]
363K
373K
383K
NLLS Fit
0 3 6
0
3
6 (b)
Qb
Rb
ZI(ω) X 10
6 [Ω ]
403K
413K
423K
0 3 6 90
3
6
(c)
Qe
Qb
Rb
ZI (ω)X 10
5 [Ω ]
-ZII (
ω)X 105 [
Ω]
443K
453K
463K
0 4 8 12 160
4
8
12 (d)
Qe
Qb
ReR
b
ZI(ω) X 10
4 [Ω ]
-ZII(ω) X 104 [
Ω]
483K
493K
503K
Fig. 5.1: (a)-(d): Complex impedance plot of NNZP glass at different temperature.
The continuous curves are fits to the equivalent circuit elements shown in inset.
116
Fig. 5.2 shows the variation of imaginary part of impedance with frequency at
different temperature for NNZP. The curves are broader than Debye curve and
asymmetric. These features indicate that the relaxation time τ is not a single valued but it
is distributed continuously or discretely around a mean, τm=1/ωm [24]. As temperature
increases the magnitude of Z'' peak maxima decreases and the peak frequency shifts to
the higher values. The inset of Fig. 5.2 shows the variation of peak frequency, ωpeak,
as a function of temperature for NNZP glass and it follows Arrhenius relation
ωpeak=ωoexp(-Eimp/kBT). The activation energy corresponding to the non-Debye type of
relaxation is obtained and it is almost equal to the value of activation energy Eσ as shown
in Table 5.1
103
104
105
106
107
0
2
4
6
8
2.0 2.4 2.8
3
4
5
6
log(ω
max)[rad s-1]
1000/T [K-1]
0.80eV
ZIIx105 [
Ω]
log (ω) [rad s-1]
423K
433K
443K
453K
NLLS Fit
Fig. 5.2: Variation of imaginary part of impedance Z″″″″ with frequency at different
temperature of NNZP. Inset: Arrhenius plot of the peak frequency ωωωωmax for NNZP
sample.
5.1.4 Ac conductivity studies
The frequency dependence of real part of the conductivity σ'(ω) at various
temperature exhibits the typical behaviour of ionic materials, i.e. the dc plateau at low
frequency region and the frequency dependent at high frequency region. The dc plateau
region is frequency independent and it is caused by translational diffusion of the mobile
117
ions. However, with the increase in frequency, it shows dispersion, i.e, around the
hopping frequency, ωp the ac conductivity sets in, which shifts to higher frequencies with
increasing temperature and for frequency greater than hopping frequency, the σ′(ω) is
close to a frequency power law with exponent <1 and it characterizes the non-Debye
feature [24]. The observed conductivity relaxation at high frequencies is due to the
probability of the correlated forward–backward hopping together with the relaxation of
the ions. The power law regime of the ac conductivity is much less temperature
dependent than the dc conductivity. At high temperature, the conductivity data shows
dispersion at low frequencies due to electrode polarization. The electrode contribution in
low frequencies at higher temperature region is evident in complex impedance plots
analysis and corresponding capacitance or constant phase element values obtained in the
order of magnitude 10-6 to 10-8 Ssn.
Table 5.1: Molar volume (Vm), glass transition temperature (Tg), dc conductivity
activation energy (Eσ ) from impedance, impedance peak activation energy Eimp, conductivity relaxation time activation energy (Eττττ), dielectric relaxation time
activation energy (W) for the different NASICON type glasses.
Sample ρ ± 0.02 g/cm3
Vm (cm3)
Tg
(K) Ea (eV)
± 0.02 Eimp (eV) ± 0.02
W (eV) ± 0.02
Eτ (eV) ± 0.02
NNZP NNCP NNCuP NNPP
2.96 3.21 3.27 3.56
152.04 163.98
136.89 159.59
728 744 720 824
0.82 0.87 0.97 0.98
0.80 0.88 0.94 0.93
0.83 0.87 0.97 1.01
0.81 0.85 0.94 0.96
The increase in conductivity with the frequency at high frequency region for
different temperature is described through Jonscher’s universal power law [25] and fitted
with Eq. (3.5). The dc conductivity extracted from the impedance spectrum and ac
conductivity show a general trend of NNP>NNZP>NNCP>NNCuP>NNPP for sodium
based glasses and the temperature dependence of dc conductivity follows the Arrhenius
behavior which is shown in Fig. 5.3(a). In this series of glass investigated, the addition of
divalent ions decreases the dc conductivity compared to the host glass NNP. Similar
trends in Ti based NASICON type glasses with Cd and Zn as bivalent elements as
reported by C. R. Marriappan et al., [26]. This decrease is not only due to the decrease in
118
mobile ions but also the block in the conduction paths of alkali ions due to divalent ions
[27]. The blocking becomes much higher as the size of divalent ion increase. The divalent
and alkali ions form a coordination complex with mutual oxygen ions, thus maximizing
the local charge distribution in the glass [28]. The coordination complex has higher
activation energy barrier to migration, consequently the ionic conductivity decreases.
Though the divalent ion size of copper is small compared to that of the Zn2+ and Cd2+ ion,
the glass containing Cu2+ has low conductivity compared to the latter. It is well known
that the presence of transition metals such as copper tends to increase the electrical
conductivity of the glass, but the electrical conduction process is characterized by a high
activation energy which is mainly governed by electronic hopping between Cu+ and Cu2+
ions [9, 29]. Hence a mixed polaron-ionic conductivity mechanism or ion-polaron
interaction and breaking of percolation paths takes place in copper-containing glass and
this strongly affects the electrical conduction mechanism in lower temperature.
1.8 2.1 2.4 2.7 3.0 3.3 3.6 3.9
-8
-6
-4
-2
log(σdcT) [S cm-1 K)]
1000/T [K-1]
NNP
NNZnP
NNCdP
NNCuP
NNPbP
Linear Fit
1.8 2.1 2.4 2.7 3.0
-7
-6
-5
-4
-3
-2
σdc
σac(ω)
σtotal(ω)
Linear Fit
100kHz
10kHz
1kHz
1MHz
log(σ
(ω)) [Scm-1]
1000/T [K-1]
Fig. 5.3(a): Temperature dependence of the dc conductivity of various NASICON
glasses (b) Temperature dependence of dc, ac (filled template) and total conductivity
(unfilled template) for NNZP glass at different frequencies.
The dependence of the σac(ω), σdc, σtotal(ω) upon reciprocal temperature for NNCP
glass is shown in Fig.5.3 (b), where the σac(ω) values were derived by subtracting σdc
from the total measured conductivity σ'(ω). The activation energy Eac of σac(ω)
conductivity for selected frequency was determined from the slope of log σac(ω) against
1000/T and these values are listed in Table 5.2. The activation energy for the ac
conductivity Eac is lower than the Eσ. From Table 5.2, it is observed that the Eac for all
119
the glasse,s decreases with increasing frequency. So these composition variations are
taking part in ion transport mechanism and ac conductivity relaxation.
Table 5.2: Activation energy Eac at different frequencies for NNZP, NNCP, NNCuP
and NNPP.
Sample Eac(eV) at 1kHz ± 0.02
Eac (eV) at 10kHz ± 0.02
Eac (eV)
at 100kHz ± 0.02
Eac (eV) at 1MHz ± 0.02
NNZP NNCP NNCuP NNPP
0.36 - 0.34 0.35
0.34 0.33 0.33 0.34
0.32 0.33 0.31 0.31
0.31 0.32 0.29 0.28
Full analysis of this ac response of the materials not only requires accurate data,
but also needs appropriate model to represent the response. In the literature, several
theoretical models have been proposed to explain the observed dispersive behavior in a.c.
conductivity [30-33], and in these, there is number of theoretical models based on the
anomalous diffusion [34-37], which is one of the traditional model that concentrate on the
random walk on a fractal. In the present work Jonscher’s UPT and ADM of Sidebottom
et al., [37] are considered for ac conductivity and permittivity analysis and these models
are compared.
Generally anomalous diffusion is described as a random walk on a fractal lattice
but Maass and Coworkers [38-39] suggested that such diffusion can arise from coulombic
interactions in a disordered medium. Thus the actual presence of fractal structures does
not appear to be a requirement. The model appears to be of some general validity and has
been successful in describing the dynamics of amorphous systems such as gels at the
large length scales probed by light scattering and polymers at short length scales. The ac
part of the conductivity remains an enigma. As the power law feature is most prominent
at high frequencies, it presumably must represent short time motion that occurs prior to
the hopping of the ion past its barrier; i.e., motion of the ion within its potential well or
possibly reiterative pair wise hopping between adjacent sites.
Empirically, the ac part can be obtained by describing the response of the electric
displacement, De, at short times by a Curie-von Schweidler current [40]:
j(t) = dDe/dt ≈t-n. (5.1)
120
Currently, two basic views exist on how this Curie-von Schweidler current arises.
According to the first view, the high frequency power law is assumed to represent the
high frequency wing of a relaxation process whose low frequency wing is covered by dc
conductivity [41]. This relaxation is presumed to result from hopping of ions over local
energy barriers at high frequencies and long-range excursions over multiple barriers at
low frequencies.
The second view interprets the frequency dependence of the conductivity as
simply the result of changes in the manner in which the ions diffuse [42]. At long time
(low frequency) the mean-square displacement of a diffusing ion is linear in time,
reflecting a constant coefficient of diffusion and hence also constant conductivity σdc. At
shorter times, the ion is strongly influenced by the local environment, including
interactions with other neighboring ions, and exhibits a mean-square displacement, which
increases more slowly.
Number of models have been proposed based upon anomalous diffusion to
account for the ac part of the conductivity [43-46]. Numerical simulations for the mean-
square displacement, <r2>, of an ion performing a random walk on a fractal lattice
indicate
1-n2 t , 0 n 1; r
<r >t; r
ξξ
< < <∝
> . (5.2)
The real part of dielectric permittivity ε′(ω) and conductivity σ′(ω) are derived from Eq.
(5.2) by Sidebottom et al., [37] are given by
ε′(ω) = 1dc 0
c
(σ /ε ε ) n(1 g(n)sin )
ω 2n
c
πε −∞
∞ + Ω
, (5.3)
σ′(ω) =n
(1 g(n)cos )2
n
dc c
πσ + Ω
, (5.4)
where Ωc =ω/ωc, 2
2 ,6
edc c
B
e nK K
k Tσ ξ ω= = (5.5)
and ne is the number density of charge carriers.
Further, Eqs. (5.3) and (5.4) can be simplified by invoking Maxwell relation
namely, ωσ =σdc/ε∞ and hence Eqs. (5.3) and (5.4) become:
121
( )1
( ) 1 sin2
n
nh n
σ
π ωε ω ε
ω
−
∞
′ = + (5.6)
( ) ( )1 cos2
n
dc
nh n
σ
π ωσ ω σ
ω
′ = + (5.7)
with h(n) = fng(n), ωσ=fωc, g(n) is a gamma function defined as g(n)=(1-n)Γ(1-n)=Γ(2-n)
and ωσ = fωc or ωσ = σdc/ε∞ε0, where σdc is the dc conductivity, ωσ is the conductivity
relaxation frequency, ε∞ is the high-frequency dielectric permittivity, ε0 is the permittivity
of free space, ξ is cross over length, n the frequency exponent (0<n<1), ωc the crossover
frequency, e is electronic charge, and ne is the number density of charge carrier.
Eqs. (3.5) & (5.7) are used to fit the real part of the conductivity and the
parameters σdc, A, n and ωc are extracted. At high temperature, low frequency σ′(ω) data
are omitted in the fitting process since these data contains electrode polarization
contributions and this will influence in the fitting parameter. Both equations fits well with
the experimental data as shown in Fig. 5.4 and 5.5. The parameters evaluated from the
above fitting are represented in Table 5.3. The dc conductivity obtained from both the
approach is almost equal and it increases with increase in temperature and obey
Arrhenius behavior given in Eq. (3. 12).
A similar fitting procedure is followed for the other samples. The
magnitude of the observed dc conductivity and activation energy for the NASICON
glasses is given in Table 5.3. The physically relevant length and time scales involved in
the diffusion process were obtained by using Eq. (5.5). The charge carrier density ncρ was
calculated using ρNav/M, where ρ is density, Nav is Avogadro’s number and M is
molecular weight of the compound. The cross over length ξ is calculated and it is
averaged over the temperature range of investigation and results are shown in Table 5.3.
The crossover length parameter involved in the diffusion process is increasing as the size
of divalent ion size increase.
122
103
104
105
106
10-10
10-9
10-8
10-7
10-6
1 2 3 45 6 7 8 9101112131415161718192021 222324252627282930
3132333435 36
373839404142
43444546
47484950
515253545556
A B CDE FG H I J KLMNOPQRS T U VWXYZAAABACADAEAFAGAHAI
AJAKALAMANAOAP
AQARASATAU
AVAWAXAY
AZBABBBCBD
ω [rad s-1]
σ'(
ω) [S cm-1]
373K
383K
393K
403K
413K
423K
433K
443K
453K
463K
473K
483K
493K
503K1 513KA 523K
JPL
Fig. 5.4: Ac conductivity plot of NNPP at various temperature,
Solid lines are fits to AWM of Eq. (3.5).
103
104
105
106
107
1E-9
1E-8
1E-7
1E-6
1E-5
353K 363K 373K 383K 393K 403K 413K 423K 433K 443K 453K 463K 473K 483K 493K 503K 513K 523K ADM Fit
ω [rad s-1]
σ'(
ω) [S cm-1]
Fig. 5.5: Ac conductivity plot of NNZP at various temperature,
Solid lines are fits to ADM of Eq. (5.7).
123
Table. 5.3: Density (ρ), number density of charge carrier (ncρ), crossover length
parameter (ξ), dc conductivity σdc, activation energy for dc conductivity (Eσσσσ) and
relaxation frequency (Eωωωω), ), ), ), exponent (n) and Kohlrausch parameter (β) for different
glasses
Sample ρ g/cm3 ncρ cm-3
ξ Å
σdc at 423K
Scm-1 Eσ eV ± 0.02
Eω eV ± 0.02
n at 423K ±0.02
β ±0.02
NNP NNZP NNCP NNCuP NNPP
2.96 3.21 3.27 3.56 3.95
3.81 x 1021 3.95 x 1021 4.15 x 1021
4.84 x 1021 4.14 x 1021
1.32 1.93 1.97 1.66 2.15
1.15x 10-5 7.19 x 10-8
2.46 x 10-8
1.57 x 10-8 1.89 x 10-8
0.61 0.82 0.87 0.97 0.98
0.58 0.81 0.85 0.94 0.99
0.61 0.65 0.65 0.65 0.68
0.62 0.53 0.58 0.58 0.59
5.1.5 Dielectric properties
5.1.5(a) Permittivity studies
Figure 5.6 shows the frequency dependence of real part ε'(ω) of complex
permittivity ε* respectively for the composition. The observed variation in ε'(ω) with
frequency is ascribed to the formation of a space charge region at the electrode/sample
interface. As the vitreous substances are disordered at molecular level, one would expect
a variation in the free energy barriers from site to site in the quasi lattice unlike the case
of materials with a long range lattice structure. The observed dispersion in ε'(ω) can be
explained in terms of the ion diffusion and polarization model [47]. The glassy materials
have free energy barriers of varying height with random spacing because of the macro-
level disorder of these materials. The dispersion in ε* is attributed to the lack of
translational invariance in the free energy barriers for ion diffusion. In the low frequency
region, the ions jump in the field direction and pile up at sites with high free energy
barrier in the field direction after successfully hopping sites with low free energy barrier.
This piling of charges leads to a net polarization of the ionic medium and hence a large
contribution to the low frequency value of ε'(ω). At high frequencies the periodic reversal
of the field takes place so rapidly that there are no excess ion jumps in the field direction.
The ε'(ω) remains nearly constant at the high frequency which is probably the result of
rapid polarization process with no ionic movement contribution. At this frequency the
ions can only oscillate without reaching the sample electrode interface [48].
124
103
104
105
106
107
102
103
104
ε'(ω)
ω [rad s-1]
393K
403K
423K
433K
443K
453K
463K
473K
483K
493K
503K
513K
523K
533K
AW Fit
Fig. 5.6(a): Variation of ε'(ω) with ω at various temperature for NNCP, solid
lines are best fits of Eq. (5.8).
103
104
105
106
107
101
102
ε'(ω)
ω [rad s-1]
403 K
413 K
423 K
433 K
443 K
453 K
463 K
473 K
483 K
493 K
503 K
513 K
523 K
ADM Fit
Fig. 5.6(b): Variation of ε'(ω) with ω at various temperature for NNPP, Solid
Lines are best fits to Eq. (5.6).
125
The real part of the complex dielectric permittivity in the fixed frequency window
is obtained from Eq. 5.6 and it is given by:
( ) n)(1
0
ω2
nπtan
ε
Aεωε −−
∞
+=′ (5.8)
Where, A is the pre exponential factor defined as A=(σdc/ωpn), ε∞ is the background
contribution to ε' arising from unrelated process at high-frequency and ε0 the permittivity
of free space.
The real part of dielectric, ε'(ω) for different temperature have been fitted to Eqs.
(5.6) and (5.8) and the parameters ε∞, A, h(n), n, and ωσ are extracted respectively. The
low frequency ε′(ω) data are omitted in the fitting process. Both equations fit well with
the experimental data shown in Fig. 5.6(a) and (b). The ωσ is strongly temperature
dependent and obey the Arrhenius relation:
ωσ=ω0 exp(-Eω/kBT) (5.9)
where ω0 is the pre-exponential of the conductivity relaxation frequency, and Eω is the
activation energy for the conductivity relaxation frequency. The activation energies Eσ
and Eω were determined using Eqs. (3.8) & (5.9) and are shown in Table 5.3. The close
match between Eω and Eσ indicates that the charge carriers have to overcome the same
energy barrier in both conduction and relaxation processes.
The imaginary part of the complex permittivity, ε''(ω) do not show any loss peak
in the frequency range 10Hz to 1Mz. The ionic conducting glasses do not possess well-
defined dielectric loss peaks, and as a consequence the values of the static dielectric
constant could not be obtained from the frequency dependence of dielectric data, which
normally appears in the low frequency region. An upward trend in ε''(ω) at low
frequencies (lower than 10kHz) is attributed to dc conductivity with electrode
polarization, i.e., the conduction losses is predominate and hence at all temperature the
ε''(ω) shows the 1/ω dependence on the frequency.
126
103
104
105
106
107
100
101
102
103
104
ε''(
ω)
ω [rad s-1]
383K
393K
403K
413K
423K
433K
443K
453K
463K
473K
483K
493K
503K
513K
523K
1.8 2.0 2.2 2.4 2.6 2.82
3
4
5
6
7
log(ω
m) [rad s-1]
1000/T [K-1]
NNZP
NNCP
NNCuP
NNPP
Liner Fit
Fig. 5.7: Variation of ε''(ω) with ω at various Fig. 5.8: Variation of characteristic
frequency,temperature for NNPP. ωm with inverse temperature.
The ε''(ω) is found to increase with increase in temperature and dielectric loss
peak has not been observed at any temperature. Hence the determination of characteristic
frequency ωm for the dielectric loss is not possible however according to Hunt’s model
[49] Arrhenius law is valid for both below and above the characteristic frequency ωm,
which can be expressed as
m m0
B
W-
k Tω =ω exp
(5.10)
where W is the activation energy for dielectric loss and kB and T have usual meaning.
From Fig. 5.7 the frequency values corresponding to ε''=10 at different temperature have
been determined. Figure 5.8 shows the variation of characteristic frequency, ωm, as a
function of temperature for all the glass of composition and it follows the Arrhenius
relation as per Eq. (5.10). The activation energy, W of dielectric loss was calculated from
the slopes of the least square fit of the data and are given in Table 5.1 and it is
comparable to dc activation energy. The correlation coefficient R for the least square fit
is above 0.99.
5.1.5 (b) Electric modulus analysis
The dielectric response of the materials can be analyzed in terms of complex
electric modulus. In modulus representation, the electrode polarization contribution is
suppressed [50, 51]. Recently, several researchers have presented the advantages and
127
qualitative appraisal of the electric modulus analysis [52-54] and also some criticized the
misleading behavior of the frequency dependence of electric modulus [55-57]. In spite of
these criticisms in the modulus analysis; it is still being used in the literature [58-61] for
the characterization of ion dynamics. In this section a comparison has been made between
the electric modulus fitting by KWW and Sidebottom’s ADM and the results are
discussed. Figs. 5.9 and 5.10 represents the real and imaginary part M'(ω) of the electric
modulus respectively at different temperature for NNZP glass. The M'(ω) attains a
constant value at high frequencies for all temperature and tends to zero at low
frequencies, indicating negligible electrode polarization [62]. The M"(ω) spectra in Fig.
5.10 shows asymmetric peak and the peaks are broader than the Debye peak. The M"(ω)
asymmetry in glass has usually been regarded as an indication of a distribution of
relaxation times in the conduction process. According to Hasz et al., [63] the distribution
of relaxation time is connected with a distribution of free energy barriers for ionic jumps,
in which the distribution increases with increasing disorder, whereas, Grant et al., [64]
attributed the distribution of relaxation times is not due to the disordered structure of
glasses but is assumed to be the consequence of the cooperative nature of the conduction
process, as required by the existence of strong repulsive interactions among the mobile
cations.
103
104
105
106
0.00
0.04
0.08
393K
403K
413K
423K
433K
443K
453K
463K
473K
483K
493K
503K
ADM Fit
ω [rad s-1]
M'(
ω)
Fig. 5.9: Real part of electric modulus spectra M'(ω) for NNZP at several
temperature
128
103
104
105
106
107
0.00
0.01
0.02
0.03
393K
403K
413K
423K
433K
443K
453K
463K
473K
493K
513K
523K
KWW Fit
ADM Fit
M''(
ω)
ω [rad s-1]
Fig. 5.10: Imaginary part of electric modulus spectra M''(ω) for NNZP at several
temperature. The dashed line is fits to KWW equation. The solid curves are fits to
ADM.
The M" peak heights for the different temperature are almost constant which
shifts towards higher frequencies as temperature increases. This suggests the invariance
of dielectric constant, but relaxation times get distributed with temperature [30]. The
modulus plot is non-symmetric and can be expressed in non exponential decay function.
The stretched exponential function is defined empirically by Kohlrausch–Williams–Watts
(KWW) function φ(t)=exp[-(t/τ)β], where τ is the characteristic relaxation time and β is
the well-known Kohlrausch parameter which is less than one for most practical solid
electrolyte [65, 66]. Generally, β characterizes the degree of non-Debye behavior and it
decreases with an increase in the relaxation time distribution. The experimental data are
analyzed using Bergman’s formula which is a modified KWW function [67]. The
β values obtained for different samples are shown in Table 5.3 and they vary from 0.5 to
0.6. The KWW approach reproduce the usual features of M'' upto 104 Hz but at high
frequency it underrate the data which is clearly shown in Fig. 5.12 for real and imaginary
part of electric modulus for the sample Na2NbCdP3O12 for two selected temperature. The
obtained relaxation frequency is temperature dependent and follows the Arrhenius
129
relation Eq. (3.12). The activation energy Em for the conductivity relaxation time is
obtained from the least square straight line fits for all glass compositions.
103
104
105
106
107
0.00
0.02
0.04
0.06
0.08
0.10 M''-423K
M'-423K
M''443K
M'-443K
ADM Fit
KWW Fit
M'(
ω)/M''(
ω)
ω [rad s-1]
Fig 5.11: Electric modulus spectra for NNCP for selected temperature. The dashed
line is fits to KWW equation. The solid curves are fits to ADM.
Fig. 5.12: Temperature dependence of conductivity relaxation frequency for various
glasses. The solid lines are the fits to Eq. (5.9).
130
As an alternate approach, ADM has been used for modulus representation to
eradicate the uncertainty in the high frequency data fitting. The data generate by Eqs.
(5.6) & (5.7) are used in:
M′(ω)=ε'(ω)/( ε'2(ω)+ (σ'(ω)/ω)
2), (5.11)
M″(ω)=(σ'(ω)/ω)/(ε'2(ω)+ (σ'(ω)/ω)2), (5.12)
and fitted the real and imaginary parts of measured modulus data. The fitted results are
shown in Figs. (5.9) and (5.10) for NNZP glass. Though ADM fails to depict ε'(ω) and
σ'(ω) at low frequencies dominant by electrode effect and high frequencies dominant by
constant loss phenomena, they provide best fitting to the experimental data at the range of
frequencies of present interest where M''(ω) peak occurs. It is clear from Fig. 5.11 that
the ADM are particularly successful at describing the high frequency wing of M'(ω) and
M''(ω) where it has been widely acknowledged that fits using KWW typically miss this
wing and underestimate the actual data at these frequencies. The KWW fitting ωmax
values and ADM fitting ωσ values are equal and they are shown in Fig. 5.11. The KWW
and ADM fitting approaches provide the same quantitative information regarding the
conductivity relaxation frequency i.e., steady state ion transport process. However, the
ADM fitting is better than KWW fitting as the high frequency wing of M″(ω) has
superior fitting. Fig. 5.12 clearly illustrates that the relaxation frequency decreases as
divalent ions is replaced to alkali ions
5.1.6 Scaling studies in ac conductivity and electrical modulus
The study of the conductivity spectra of several glasses at different
temperature leads to a scaling law, which results in a time-temperature superposition
(TTSP) principle [68]. The validity of the TTSP suggests that the basic microscopic
mechanisms of the dynamic processes do not depend on temperature, although the
frequency window of these processes exhibits generally strong temperature dependence.
In recent publications [69-72], the scaling behaviour in ac conductivity data has been
studied by the directly measurable quantities such as temperature, dc conductivity,
131
10-2
100
102
0.0
0.2
0.4
0.6
0.8
1.0(a)NNCP
MII(ω)/MII
max
(ω/ωmax)
1E-3 0.1 10 1000
0.0
0.3
0.6
0.9
1.2
(b)NNZP
(ω/ωmax)
MII(ω)/MII
max
concentration, dielectric strength, maximum magnitude of dielectric loss and hopping
frequency ωp.
10-3
10-1
101
103
100
102
104
106
12 345 67 8 91011121314151617181920212223242526272829303132333435363738394041424344
454647484950515253
545556
ω/ωp
σ(ω
)/σdc
NNPP
NNCuP
NNZP
NNCP
Fig. 5.13: Scaling plots for the NNCP, NNZP, NNCuP and NNPP conductivity
spectra. The coordinate of the NNZP, NNCuP and NNPP samples are shifted by one
unit in the log scale.
Fig. 5.14: The scaled imaginary part of electric modulus M''/M''max versus ωωωω/ωωωωmax
for (a) NNCP (b) NNZP glass.
132
In the present work, we have scaled the conductivity spectra by a scaling process
[73] reported by Ghosh et al. In this scaling process, the ac conductivity is scaled by σdc,
while the frequency axis is scaled by the crossover frequency ωp, which is expected to be
more appropriate for scaling the conductivity spectra of ionic conductors, as it takes into
account the dependence of the conductivity spectra on structure and the possible changes
of the hopping distance experienced by the mobile ions. From Fig. 5.13, it is observed
that the conductivity curves are superimposed into single master curve. Obviously, the
TTSP is fulfilled and suggest that the conductivity relaxation mechanism is independent
of temperature. The imaginary part of the electrical modulus is scaled by M''max and the
frequency axis is scaled by ωmax for NNCP and NNZP glasses as shown in
Fig. 5.14(a) & (b) at different temperature. It is observed that the M'' spectra
superimposed in to a single master curve. Similar behavior was observed for all other
samples.
5.2 Effects of ZnO on electrical conductivity of NASICON type glasses
5.2.1 Introduction
In the previous series of the divalent doped NASICON based glasses, dc
conductivity and cross over frequency shows almost two orders of decrease compared to
that of the host materials. In this composition, the divalent ions substitution with various
sizes was replaced to the mobile ions, so the decrease in conductivity may be mainly due
to the decrease in the concentration of mobile ions. To get a clear picture on insertion of
divalent ions in conductivity, the detailed composition dependence with temperature and
frequencies are need. As Zn substituted glasses have higher conductivity compared to the
other divalent ion based glasses, the conductivity and relaxation studies of lithium and
sodium ion glasses were investigated with various composition of ZnO. Here the cation
concentration has been maintained constant over the whole range of composition to find
the influence of the divalent ions in the mobility and ionic conductivity in glass. In view
of above, the objective of the present work is to study the correlation between the
structural modification of glass network and their electrical properties as a function of
composition by employing FTIR, DSC and impedance spectroscopy.
133
5.2.2 Preparation and Characterization
The glass composition of A4Nb1-xZn5/2xP3O12 0≤x≤0.5 (where A=Li and Na) were
obtained by quenching of a melt containing analytical grade lithium carbonate or sodium
carbonate, Nb2O5, ZnO and NH4HPO4 in stoichiometric proportions. The mixture of
purified reagents was melted at 8000C for 2h in alumina crucibles and then quenched in
stainless steel moulds. A test to detect the possible existence of crystalline patterns was
carried out using the X-ray diffraction technique on a powdered sample. The glass
transition temperature of the material was determined by differential scanning
calorimetry. The XRD and DSC studies confirm the glassy nature of the sample.
Table 5.4: Density(ρ), Molecular weight, Molar volume (Vm), number density and
glass transition temperature (Tg)
Compound name ρ ±0.03
(gcm-3)
Molecular Weight,M
(g)
Vm (cm3)
Number density
(ncρ) cm-3
Tg (K)
LNP 2.92 408.45 138.16 4.32 x1021 703
LNZ25P 2.94 412.62 140.26 4.29 x1021 668
LNZ50P 2.95 419.68 142.13 4.24 x1021 663
LNZ75P 2.98 426.73 143.07 4.21 x1021 657
LNZ100P 2.99 433.79 144.75 4.16 x1021 653
NNP 2.96 469.76 158.56 3.81 x1021 680
NNZ25P 2.99 476.83 159.47 3.78 x1021 673
NNZ50P 3.02 483.83 160.06 3.76 x1021 669
NNZ75P 3.03 490.89 161.49 3.72 x1021 662
NNZ100P 3.05 497.95 162.84 3.69x1021 657
The FTIR studies reveal that the bands are assigned to the various vibrational
contributions of the basic phosphates group with NASICON framework [15-20]. The
Nb–O–Nb vibration bands are also clearly absorbed in the FTIR spectrum and rather it is
observed that the glass network is not significantly modified by substituting Zn in the
glassy system except a small band appeared approximately at 445 cm−1 which is
attributed to the vibration of Zn2+ ions in the network vacancies [74]. The glass transition
134
temperature Tg decreases as Zn2+ substitution increases. It is known that the Tg decreases
with decreasing bond strength and cross-linking in phosphate glasses i.e. Tg is directly
correlated to the strength and number of bonds that are destroyed within a glassy network
in order to allow it to rearrange itself into a thermodynamically stable phase. From the
thermal analysis data, it is noticed that Tg decreases as the amount of Nb is substituted by
Zn. The reason for that is Nb–O–P and Nb–O–Nb linkages are stronger than the Zn–O–P
bond, requiring lower temperature for relaxation. The density, molar volume and the
number density was calculated as discussed earlier. These parameters follow the same
trend in both the series of composition, i.e. both the parameters increase as increasing
content of Zn in the NASICON glass. The density and number density are used to
calculate the mobility of the mobile ions in the glasses, which would be discussed later in
this chapter.
5.2.3 Impedance spectroscopic studies
Conductivity measurement was made for different temperature using a Novo-
control impedance analyzer in the frequency range 100 Hz to 1 MHz as explained in
Chapter II. The electrical conductivity of the ZnO substituted glasses have been
characterized using different formalism. Fig. 5.15(a)-(d) shows a typical complex
impedance plane plots and the corresponding equivalent circuits of the NNZ25P glasses
for various temperature. The impedance plot follows the same trend with two relaxations,
one is with the bulk properties and the other with the electrode polarization at low
frequencies and high temperature as discussed earlier. The equivalent circuit
corresponding to the samplesis shown in Table 5.5
The temperature dependence of the dc conductivity obtained from the complex
impedance plots are shown in Fig. 5.16 for the lithium and sodium based glasses with
different composition of ZnO. It is noted that the variation of the conductivity with
temperature obeys Arrhenius equation σdcT=σ0exp(−Eσ/kT), where σ0 is a conductivity
prefactor and Eσ is the activation energy. The values of the activation energy Eσ were
obtained from the least-squares straight-line fits. The dc conductivity at 303K and the dc
conductivity activation energy Eσ is given in Table. 5.5. It clearly shows that the dc
conductivity decreases as ZnO is substituted to Nb2O5.
135
0 1 2 30
1
2
3
(a)-Z''(
ω)x108[Ω]
Z'(ω)x108[Ω]
273K
283K
293K
0 3 6 90
3
6
9
(b)
Z'(ω)x106[Ω]
-Z''(
ω)x106[Ω]
323K
333K
343K
0 5 10 150
5
10
15
(c)
Z'(ω)x105[Ω]
-Z''(
ω)x105[Ω]
353K
363K
373K
0 3 60
2
4(d)
Z'(ω)x105[Ω]
-Z''(
ω)x105[Ω]
383K
393K
403K
Fig. 5. 15: Impedance Plot for NNZ25P glass.
2.4 2.8 3.2 3.6 4.0-9
-8
-7
-6
-5
-4
-3
-2
log(σ
dcT) [Scm
-1K]
1000/T [K-1]
NNP
NNZn25P
NNZn50P
NNZn75P
NNZn100P
Linear Fit
2.5 3.0 3.5 4.0
-8
-7
-6
-5
-4
-3
-2
-1
LNP
LNZn25P
LNZn50P
LNZn75P
LNZn100P
Linear Fit
log(σ
dcT) [Scm
-1K]
1000/T [K-1]
Fig. 5.16: Temperature dependence of dc conductivity for composition
A4Nb1-xZn5/2xP3O12 0≤x≤0.5 (where A=Li and Na).
136
Table 5.5: Name of the composition, their electrical circuit elements and their
combinations, dc conductivity σ(0) at corresponding temperature and dc
conductivity activation Energy Eσ.
Sample Equivalent circuit elements and their combinations for different temperature
σdc (S/cm) at 303K
Eσ ± 0.03 (eV)
Eτ ± 0.03 (eV)
β ± 0.02
NNP Ri(RbQb); Ri(RbQb)Qe;
Ri(RbQb)(ReQe) 2.29 x10-8 0.66 0.58 0.58
NNZ25P Ri(RbQb); Ri(RbQb)Qe; Ri(RbQb)(ReQe)
6.86 x10-9 0.64 0.62 0.56
NNZ50P Ri(RbQb); Ri(RbQb)Qe ;Ri(RbQb)(ReQe)
2.27 x10-9 0.65 0.64 0.60
NNZ75P Ri(RbQb); Ri(RbQb)Qe ;Ri(RbQb)(ReQe)
1.11 x10-9 0.65 0.67 0.65
NNZ100P Ri(RbQb); Ri(RbQb)Qe; Ri(RbQb)(ReQe)
3.75 x10-10 0.68 0.69 0.68
LNP Ri(RbQb)Qe; Ri(RbQb)(ReQe) 2.83 x10-7 0.61 0.58 0.61
LNZ25P Ri(RbQb); Ri(RbQb)Qe; Ri(RbQb)(ReQe)
1.74 x10-8 0.64 0.66 0.60
LNZ50P Ri(RbQb); Ri(RbQb)Qe ;Ri(RbQb)(ReQe)
1.29 x10-8 0.68 0.69 0.63
LNZ75P Ri(RbQb); Ri(RbQb)Qe ;Ri(RbQb)(ReQe)
2.83 x10-9 0.70 0.72 0.65
LNZ100P Ri(RbQb); Ri(RbQb)Qe; Ri(RbQb)(ReQe)
7.99 x10-9 0.73 0.74 0.69
5.2.4 Composition dependence of dc conductivity
Many phenomenological models have been proposed for describing the
conduction process in fast ionic conducting glasses [75-78]. In these models the changes
in conductivity and in activation energies accompanying the variation of glass
composition been dealt differently. The basic conductivity relation is given by
σ=neµ (5.13)
where n is the concentration of mobile ion, e is the charge and µ is the mobility of the ion.
Any changes in conductivity may either due to change in n or µ values. The proposed
models treat these factors distinctly to explain the conduction process in fast ionic
conducting glasses.
The bulk resistance for all the samples is obtained from the impedance plots at
each temperature and dc conductivity is calculated as usual. From the Arrhenius plot one
137
can clearly see that the variation of conductivity when Nb is replaced by Zn. The highest
conductivity was obtained only for the host composition for both the series. The
activation energy calculated from Arrhenius plot is given in Table 5.5. The activation
energy is found to be less for composition x=0.1 for both the composition series. The
observed variation of conductivity can be explained as follows. The cation concentration
for the both the composition is calculated from the chemical composition using the
relation
n=Nvρnf/M (5.14)
where Nv is the Avagadro number, ρ is the density, nf is the number of moles of
conducting species and M is the molecular weight. While adding the ZnO the mobile ion
concentration is maintained constant for both the series but the dc conductivity decreases.
This suggest that all the mobile ions presented in the glass can not be treated as potential
carriers as required by the random site model. Further, the change in the activation energy
with the ZnO concentration is not linear and does not show any definite indication for the
mobility dependence of conductivity changes.
According to the weak electrolyte model [79], a fraction of total ions contribute to
the conduction and the remaining are immobile [80, 81]. Since the mobile ion
concentration are maintained constant in the present glasses as compared to the host
glasses, the decrease in conductivity is not due to mobile ions, it clearly suggest that not
all the mobile ions are potential carriers for the present system of glasses. The ion
fraction is decided by the dissociated part and the immobile ions by the associated part of
the ions. Thus the change in conductivity with composition is controlled by the change in
the carrier concentration. The concentration of mobile ions and their mobility in these
glasses are calculated from Eq. (5.13) and (5.14). Fig. 5.17 shows the plot of mobility
against the concentration of Zn. The mobility of the mobile ions decreases as the Zn2+
substitution increases; this reveals that mobile ions in a particular anionic environment
are responsible for such conductivity changes. The decrease in mobility is high in the
initial change of composition. i.e., the mobility decreases drastically (about an order)
when Zn is added to the host materials. These suggestions conclude that the change in
conductivity is not due to the total mobile ion concentration, but it is due to the change in
the environment of the particular mobile ions.
138
The A5Nb1-xZn5/2xP3O12 (where A=Li, Na) glasses have a complex composition of
network formers, intermediates and modifiers which are being differentiated and
classified according to the value of electronegativity and bond strength. As the ZnO
concentration is increased in the host system there is relatively a small depolymerization
of bridging oxygen (BO) bonds between adjacent PO4 tetrehedra and NbO6 octahedra
takes place and thus induces more non-bridging oxygen (NBO) sites. Relatively, the
average chain length of the phosphate network decreases and reduces the average
interatomic spacing. In other words, the compactness of the glass network has increased
as evidenced in the increase in density as ZnO content increases. Meanwhile, such Zn2+
ions is more likely located in the interstitial position as network modifiers within the
glass matrix rather than participating in the network in order to balance the net columbic
charges of the structure [82] and acts as blocking effect as well. This is to be expected
because the ZnO bond is more covalent than Li2O and Na2O bond and Zn2+ ions are more
tightly bonded to the network than alkali ions [82]. A similar behaviour was reported by
Rao et al., [83] for Na2O–ZnO–P2O5 glasses and Stevel [84] for other divalent cations in
sodium silicate glasses. Generally, with the highly disordered structures resulting in a
broad distribution of both the trap sites and the migration of barriers with the deepest
traps likely to control the conduction [85]. Therefore, the relatively free mobile ions (Li+,
Na+) experience impeding effects along the conduction path and hence σdc decreases.
0.00 0.25 0.50 0.75 1.00
1E-14
1E-13
1E-12
1E-11
1E-10
Mobility (
µ) [cm2/V s]
x (ZnO)
Na based glass
Li based glass
Fig. 5.17: Mobility of mobile ions with various compositions
A4Nb1-xZn5/2xP3O12 0≤x≤0.5 (where A=Li and Na).
139
5.2.5 Ac electric response studies
The study of frequency dependent conductivity spectra is a well established
method for characterizing the hopping dynamics of ions. The angular frequency
dependence of the conductivity σ′(ω) at different temperature for LNZ25P and NNZ75P
are shown in Fig. 5.18 and Fig 5.19 respectively. It is evident that at low frequencies the
conductivity is found to be independent of frequency and at higher frequencies, σ′(ω)
exhibits frequency dispersion and is correlated to the short-time ion dynamics which is
characterized by back-and-forth motion over limited ranges and said to be sub diffusive
dynamics, whereas the long-time dynamics is characterized by random walks resulting in
long range ion transport, and called to be ‘diffusive’ dynamics. The back-and-forth
motion leads to dispersive conductivity at high frequencies, while the long-range
transport leads to the low-frequency plateau marking the dc conductivity. There is
experimental evidence that in materials with high ion concentration, on short time scales
only part of the ions are actively involved in back-and-forth motion. Similar results are
obtained for other samples as well. Levenberg-Marquardt method of NLLS fitting is used
to fit the ac conductivity data with Eq. 3.5. The dc conductivity, σdc, and hopping
frequency, ωp, obtained from UPL are temperature dependent and they are found to obey
Arrhenius equations. Activation energies, Eσ, Ep, and pre-exponential factors A0, ω0 are
determined using Arrhenius equation by linear regression. The activation energy, Ep, of
the hopping frequency is in agreement to the activation energy, Eσ, for the dc
conductivity. The variation falls within the experimental error. This indicates that the
charge carrier have to overcome the same energy barrier while conducting as well as
relaxing.
140
103
104
105
106
107
10-9
10-8
10-7
10-6
1x10-5
σ'(ω
) [S cm
-1]
ω [rad s-1]
273K
283K
293K
303K
313K
323K
333K
343K
353K
363K
373K
383K
393K
403K
413K
423K
433K
AWM Fit
Fig. 5.18: Ac conductivity plot of LNZ25P at different temperature. Solid lines are
the fits to Eq. (3.5).
Fig. 5.19: Ac conductivity plot of NNZ75P at different temperature. Solid lines are
the fits to Eq. (3.5).
103
104
105
106
107
10-10
10-9
10-8
10-7
10-6
(a) NNZ75P
273K
283K
293K
303K
313K
323K
333K
343K
353K
363K
373K
383K
393K
403K
413K
423K
AWF
Fit
σ'(
ω) [S cm-1]
ω [rad s-1]
141
103
104
105
106
107
0.00
0.01
0.02
M"(
ω)
ω [rad s-1]
303K
313K
323K
333K
343K
353K
363K
373K
383K
393K
403K
413K
Bergman Fit
5.20: Imaginary part of electric modulus for LNZ100P glasses.
The ac response of these glasses can also be explained using electric modulus
data. This formalism discriminates against electrode polarization and other interfacial
effects in solid electrolytes. Fig. 5.20 shows the plot of imaginary part of complex
electrical modulus versus frequency for different NASICON glasses. It is related to the
energy dissipation factor in the irreversible conduction process. It is also seen that M"(ω)
spectrum has a asymmetric peak with broadening wing in high frequency side which are
spatially confined to their potential wells with ions making localized motion within the
well. On the other hand the low frequency wing of the peak represents the range of
frequency at which the ions can move long range distances, i.e., ions can perform
successful hopping to the neighboring site. In the present two series of the sample the
frequency range for successful hopping decreases as ZnO is substituted to Nb2O5, i.e.,
peak frequency get shifted as ZnO is substituted for a particular temperature.
142
2.1 2.4 2.7 3.0 3.3 3.6 3.9
-7
-6
-5
-4
-3
-2(a)
τ [s]
1000/T [K-1]
LNP
LNZ25P
LNZ50P
LNZ75P
LNZ100P
Linear Fit
2.1 2.4 2.7 3.0 3.3 3.6 3.9
-6
-5
-4
-3
-2
(b)
τ [s]
1000/T [K-1]
NNP
NNZ25P
NNZ50P
NNZ75P
NNZ100P
Linear Fit
Fig. 5. 21: Temperature dependence of relaxation time for (a) Li4Nb1-xZn5/2xP3O12
0≤x≤0.5 and (b) Na4Nb1-xZn5/2xP3O12 0≤x≤0.5. The solid lines are the fits to
Eq. (3.11).
The shape of the M" (ω) curves for various glass compositions are similar but
differs in their peak height M"peak and stretching parameters β. The M"peak, β and ωmax
value obtained by fitting the Bergman’s equation to the M" (ω) curves. The relaxation
time calculated from these peaks are plotted as function of inverse temperature in Fig.
5.21 for NNZP and LNZP series. Fig. 5.21 clearly illustrate that when the Nb is replaced
by Zn in the glass matrix the relaxation time for the hopping of ions increases which
indicates slowing down of the ionic motions both on local and long ranges The relaxation
time activation energy and β obtained from the plots is given in Table. 5.5.
5.2.6 Ac conductivity scaling studies
Both the ac conductivity scaling, Ghosh scaling and Summerfield scaling have
been used which can be made as discussed earlier. The scaling plots of both the method
show a single master curve for various temperature and they are shown in Fig. (5.22) &
(5.23). The other series of samples also shows the similar behavior.
143
Fig.5.22: Scaling plot for the conductivity spectra of different NASICON type
glasses. The conductivity and frequency axis are scaled by the dc conductivity and
hopping frequency respectively. To separate the curves, the coordinate of the
NNZ75P, NNZ50P and NNZ25P are shifted respectively by one unit in the log scale
of conductivity axis.
105
107
109
1011
1013
1015
10-1
100
101
102
103
104
105
LNZ100P
LNZ75P
LNZ50P
LNZ25P
σ'(
ω)/
σ) dc
ω/σdcT [(rad/s)/(S/cm)K]
Fig.5.23: Summerfield scaling plot for the conductivity spectra of different
NASICON type glasses. To separate the curves, the coordinate of the LNZ50P,
LNZ75P and LNZ100P glasses are shifted respectively by one unit in the log scale of
conductivity axis.
10-5
10-3
10-1
101
103
105
100
101
102
103
104
105
NNZ100P
NNZ75P
NNZ50P
NNZ25P
σ'(ω)/
σdc
ω /ωp
144
The scaling matches pretty well for the composition change when the frequency is
scaled by hopping frequency. This scaling series with composition change also proves the
compatibility of Ghosh scaling in which the hopping frequency take the account of the
hopping distance and the permittivity change in the glass sample as compared to the
Summerfield scaling.
145
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149
Chapter VI
Summary
Many physical properties of the glasses depends significantly on the composition
of the constituents. In this thesis, the microscopic ion dynamics in titanium and niobium
based NASICON glasses have been investigated by varying the mobile ion and glass
modifier in various compositions. From the XRD, FTIR and DSC results, all the samples
are confirmed to be glasses with phosphate network.
The present investigation reveals that the mobile ions play a major role in the ion
dynamics and its relaxation. As an example, the ion dynamics for the six glassy systems,
(i) Na5TiP3O12 (NTP), (ii) Na4NbP3O12 (NNP), (iii) Li5TiP3O12 (LTP),
(iv) Li4NbP3O12 (LNP), (v) Ag5TiP3O12 (ATP), and (vi) Ag4NbP3O12 (ANP);
have been investigated by impedance spectroscopy. For samples NTP, NNP and LTP
conductivity and activation energy were found to be in agreement with the literature.
Later three samples LNP, ATP and ANP were not reported in literature and attempts
were made to synthesize these new glasses with NASICON framework and were
successfully vitrified. In these samples prepared, ATP has higher conductivity
(5×10-5Scm-1) at room temperature, which is the highest conductivity in NASICON
framework glasses reported in the literature. In general, these glasses have optimized
conductivity due to the higher concentration of mobile ions and also due to the local
structure of this NASICON framework glasses in which, the [TiO6/2] and [NbO6/2]
octahedral units act as building blocks along with [POO3/2] types of tetrahedral units. The
thermal studies reveals that the LNP sample have high thermal stability and good glass
forming ability.
Niobium and titanium as a modifier play the major role in modifying the
structure of the glass in the present NASICON glassy system. The NASICON systems
(i) Li(4+x)TixNb1-xP3O12 (x=0, 0.25, 0.50, 0.75, 1) (LNTPx) and
(ii) Na(4+x)TixNb1-xP3O12 (x=0, 0.25, 0.50, 0.75, 1) (NNTPx)
have been prepared by melt quenching method and the effect of glass modifier in these
compositions were studied. This involves insight in both the local structures of the host
network and cation coordinated within LNTPx and NNTPx systems. Thermal studies
150
elucidate that niobium based glass have higher glass forming ability and thermal stability
compared to that of titanium based glasses, this is because the titanium ions prefer to
occupy the network modifying position rather than the network formation. The LNTPx
and NNTPx compositions do not show any drastic change in conductivity since there is
no major structural transformation due to the high content of mobile ions in the
composition range. The BNN relation was found to be valid for the present NASICON
type glasses. The scaling of ac conductivity and electric modulus into a single master
curve insist that their respective process is independent of temperature and composition.
Interesting feature of the conductivity and relaxation mechanism has been found
for mixed alkali NASICON glasses:
(i) (NaxLi(1-x))5TiP3O12 and (ii) (NaxLi(1-x))4NbP3O12).
The physical properties such as density and the molar volume not accomplished in mixed
alkali glasses. The dc conductivity and hopping frequency estimated from conductivity
measurements shows minimum for x=0.6, which is attributed to the maximum of
activation energy. The mixed alkali effect is found in the conductivity and its activation
energy, crossover frequency and conductivity relaxation frequency and their activation
energy and also in glass transition temperature. The minimum in glass transition
temperature is associated to be the ‘structural disorder’ imposed by the presence of two
kinds of cations. The strength of mixed alkali effect in glass transition temperature
∆Tg,min for NLTPx and NLNbPx is 47 and 44 respectively. The temperature dependent of
MAE is explained by dynamic structure model and structural memory effect which
clearly explain the decrease in conductivity for mixed alkali glasses when compared to
the single alkali glasses. The MAE strength in the dc conductivity of the two samples
interpret that NLTPx shows stronger MAE strength compare to the NLNbPx samples. It
also shows that the MAE strength in the dc conductivity decreases as temperature
increases.
The hopping frequency extracted from JPL fit and the conductivity relaxation
time from KWW fit clearly follows the Arrhenius relation and obviously shows MAE.
The parameters M"max, ωmax and β extracted from the Bergman’s approach explain the
features of MAE. The shift in modulus peak to the lower frequency was observed as the
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alkali ion composition changes from the single alkali glass to mixed alkali glasses. This is
attributed to the increase in relaxation time when the single alkali glass is replaced by
mixed alkali. The scaling approach introduced by Schroder and Dyre perceptibly
differentiate the single alkali and the mixed alkali glasses and suggest that, with respect
to the conductivity, mixed alkali glasses behaves as diluted single alkali glasses. This is
in agreement with the conclusions drawn from electrical modulus analysis. The high
frequency curve of electric modulus that does not collapse into single master curve in
modulus scaling was eradicated in Dixon scaling, which includes the full width at half
maximum as a scaling parameter in addition to modulus strength and peak frequency.
A new class of glassy system Na2NbMP3O12 (where M=Cd, Zn, Pb and Cu) was
prepared by replacing partial amount of alkali by appropriate amount of divalent ions into
the NASICON glass matrix Na4NbP3O12. The dc conductivity extracted from the
impedance spectrum and ac conductivity show a general trend of
NNP>NNZP>NNCP>NNCuP>NNPP and the temperature dependence of dc conductivity
follows the Arrhenius behavior. The dc conductivity of the divalent substituted
NASICON glasses is lower compare to the host glass NNP. This decrease in conductivity
is due to the decrease in mobile ions and the block of alkali ions by divalent ions in the
conduction paths. The divalent and alkali ions form a coordination complex with mutual
oxygen ions, thus maximizing the local charge distribution in the glass. This coordination
complex has higher activation energy barrier to migration, consequently the ionic
conductivity decreases. The blocking becomes much higher as divalent ion size increase.
Uncertainty in fitting M″(ω) in the high frequency wing has been eliminated by using the
ADM. The crossover length parameter ξ involved in the diffusion process calculated
from the ADM shows an increasing trend as the size of divalent ion increase and hence
the conductivity decreases.
To get a clear picture on insertion of divalent ions in conductivity with
temperature and frequencies, the exhaustive composition dependence studies have been
carried out for the new glassy systems A4Nb1-xZn5/2xP3O12 0≤x≤0.5 (where A=Li and Na).
Here, the cation concentration has been maintained even over the whole range of
composition to find the influence of the divalent ions in the mobility and ionic
conductivity in glass. The mobility of the mobile ions and hence the conductivity
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decreases as the Zn2+ substitution increases. This reveals that mobile ions in a particular
anionic environment are responsible for such conductivity changes. The decrease in
mobility is high in the initial change of composition. i.e. the mobility decreases
drastically (about an order) when Zn is added to the host materials. These predictions
conclude that the change in conductivity is due to the change in the environment of the
particular mobile ions. The various scaling methods, collapse the electric response data
into single master curve elucidates the temperature and composition independent
conductivity and electric modulus.
The materials investigated under the present thesis may find application in gas
sensors and electrode materials. There is an ample scope for further work based on this
thesis work. In present thesis, silver based NASICON with high ionic conductivity has
been identified and there is a need to initiate further thorough work on silver incorporated
NASICON glasses and their characterization. The crystallization of the lithium based
NASICON glass will produce the glass ceramic with dispersed isotropic lithium ion
conductive crystal in glass matrix. This may be used as a solid electrolyte for elemental
Li/Air batteries and Li/seawater batteries which will contribute to the advancement of
higher capacity and more innovative energy storage beyond present lithium ion batteries.
The lithium based glass ceramics have an immense advantage to conventional powder
sintered ceramic. These LISICON ceramic may have great potential in the preparation as
a catalyst for oxygen reduction.
List of Publications
Papers published in peer reviewed research journals 1. Preparation, characterization, ac conductivity and permittivity studies on vitreous M4AlCdP3O12 (M = Li, Na, K) system C.R. Mariappan, G. Govindaraj , S. Vinoth Rathan, G. Vijaya Prakash Materials Science and Engineering B 121 (2005) 2–8 2. Vitrification of K3M2P3O12 (M =B, Al, Bi) NASICON-type materials and electrical relaxation studies C.R. Mariappan, G. Govindaraj , S. Vinoth Rathan, G. Vijaya Prakash Materials Science and Engineering B 123 (2005) 63–68 3. Electrical relaxation studies on Na2NbMP3O12 (M= Zn, Cd, Pb and Cu) phosphate glasses S. Vinoth Rathan, G. Govindaraj Materials Chemistry and Physics 120 (2010) 255–262 4. Dispersive conductivity and dielectric behavior in niobium based NASICON glasses and analysis using anomalous diffusion model S. Vinoth Rathan, G. Govindaraj, Solid State Ionics 181 (2010) 504–509 5. Thermal and electrical relaxation studies in Li(4+x)TixNb1-xP3O12 (0.0 ≤ x ≤ 1.0) phosphate glasses S. Vinoth Rathan, G. Govindaraj, Solid State Sciences 12 (2010) 730-735 6. Mixed alkali effect in NASICON glasses S. Vinoth Rathan, G. Govindaraj, Solid State Ionics (To be communicated) 7. Effect of Zn2+ substitution in electrical relaxation on vitrified Li5Nb1-xZn5/2xP3O12
materials S. Vinoth Rathan, G. Govindaraj Materials Chemistry and Physics (To be communicated)
8. Impedance spectroscopy studies on silver phosphate glasses S. Vinoth Rathan, G. Govindaraj J. Non-Crystalline Solids (To be communicated)
Paper published in proceedings of the Conference / Symposium 1. Synthesis, Characterization and Electrical properties of Li1+xTi2-xBixP3O12 Solid
Solution, S. Vinoth Rathan, G. Govindaraj
Solid State Physics - Proceedings of the DAE Solid State Physics Symposium 52 (2007) 899- 900.
2. Sodium ion conduction and relaxation studies on A2NbCdP3O12 (A=Li, K, Na)
glasses S. Vinoth Rathan, G. Govindaraj
Proceeding Asian Conference on Solid State Ionics 11 (2008) 509-515. 3. Electrical relaxation studies in Na2MNbP3O12 (M=Zn, Cd, Pb)
S. Vinoth Rathan, G. Govindaraj Solid State Physics - Proceedings of the DAE Solid State Physics Symposium 53
(2008) 1005-1006 4. Sodium ion conduction and relaxation studies on Na(4+X)TiXNb1-XP3O12 where (0.0 ≤ X ≤ 1.0) glasses S. Vinoth Rathan, G. Govindaraj Proceeding of Asian Conference on Solid State Ionics 12 (2010) 206-212 5. Ac conductivity and electrical relaxation in ion conducting Li4Nb1-x Zn2.5xP3O12 glasses S. Vinoth Rathan, Aashaq Hussain Shah, G. Govindaraj Solid State Physics - Proceeding of the DAE Solid State Physics Symposium:
Volume 55 (2010); ISBN 978-0-7354-0905-7.