structural analysis of hexaferrite materials yazan maswadeh

STRUCTURAL ANALYSIS OF HEXAFERRITE MATERIALS

By

Yazan Osama Maswadeh

Supervisor

Prof. Sami Husain Mahmood

This Thesis was Submitted in Partial Fulfillment of the Requirements for the

Master’s Degree of Physics

Faculty of Graduate Studies

The University of Jordan

August 2014

IV

AKNOWLEDGEMENT

I would like to express my deep gratitude to Professor Sami Mahmood, my research supervisor, for his patient guidance, enthusiastic encouragement and useful critiques of this research work. I would also like to warmly thank my friend Dr. Ahmad Awadallah, for his advice and assistance in keeping my progress on schedule. Also my special thanks to my friend Dr. Feres Ben Jemaa for his assistance and guidance and patience in the refinement. As well, my thanks to Ms. Aynoor Oqaily for her assistance in the labs.

I would also like to extend my thanks to Mr. Yousef Abu Salha the technician of the XRD and XRF laboratory in the geology department for his help in offering me the XRD data.

Finally, I wish to thank my parents for their support and encouragement throughout my study.

V

List of Contents

Page Subject

ii Committee Decision

iii Thesis Publishing

iv Acknowledgement

v List of Contents

vii List of Tables

ix List of Figures

xv Abstract (English

1 Chapter 1 - Introduction

2 - 1.1 Magnetic material

2 - 1.2 Hexagonal Ferrites

3 - 1.3 Building blocks of hexagonal ferrites

6 - 1.4 The M-type hexaferrites

9 - 1.5 Our study

10 - 1.6 X-ray crystallography

11 - 1.7 Powder Diffraction

11 - 1.8 Rietveld Fitting

14 - 1.9 Literature Review

18 Chapter 2 - Methodology

19 - 2.1 Preparation of non-stoichiometric Barium hexaferrite samples

19 - 2.2 Structural and characterization

27 - 2.3 Preparation of non-stoichiometric Barium hexaferrite samples

with iron to barium ratio = 9 and 7

VI

28 Chapter 3 – Result

29 - Result of non-stoichiometric barium hexaferrite Samples

Iron to barium ratio (Fe+3 : Ba+2) ≥ 11.5

37 - XRD Data Refinement Result of Non-Stoichiometric Barium Hexaferrite

Samples with Iron to Barium ratio = 9

52 - XRD Data Refinement Result of Non-Stoichiometric Barium Hexaferrite


67 Chapter 4 – Analysis and Discussion

68 - Non-stoichiometric barium hexaferrite samples

with Fe:Ba ratio ≥ 11.5


with Fe:Ba ratio = 9



90 Chapter 5 – Conclusions and Recommendations

91 - Conclusions

92 - Recommendations for Future Work

93

100

REFERANCES

Abstract (Arabic)

VII

PAGE TABLE CAPTION NUMBER

6 Table 1.1: Types of Compositions and building blocks of barium

hexaferrites. 1

9 Table 1.2: Metallic sub-lattices of M-type hexaferrite 2

19 Table (2.1) the iron to barium ratio for each sample. 3

26 Table (2.2) outputs compatibility between Rietveld and Profile

matching methode. 4

42

Table (3.1) Structural phases existing in the samples with Fe:Ba =

9 sintered at different temperatures

5

56 Table (3.2) Structural phases existing in the samples with Fe:Ba =

7 sintered at different temperatures 6

70

Table (4.1) The integrated intensity of all structural peaks of BaM

(IBaM) and of α-Fe2O3 (Iα), and the ratio (Iα/IBaM) for the samples

with different Fe:Ba ratio. 7

71

Table (4.2) The integrated intensities of the main peaks of BaM

(IMB), α-Fe2O3 (IMα), and the peak ratios of the two phases for all

samples. 8

73

Table (4.3) α-Fe2O3 α-Fe2O3 wt% determined from Rietveld

refinement of the diffraction patterns and the corresponding

relative main peak integrated intensity.

9

80

Table (4.4) the calculated ratios for each phase according to the

sintering temperature.

10

81

Table (4.5) the total sites multiplicity and the unit cell volume of

each phase at 1000° C sintering temperature.

11

83 Table (4.6) the unit cell volume at each sintering degree. 12

87 Table (4.7) the calculated ratios for each phase according to the

sintering temperature. 13

VIII

PAGE FIGURE CAPTION NUMBER

4 Figure (1.1) a close-packed layer of spheres occupying positions A. 1

5 Figure (1.2) a two close-packed layers of spheres stacking on

each other occupying positions A and B. 2

5

Figure (1.3) a three close-packed layers of spheres stacking on each

other occupying positions A, B and C with the two stacking form

(ABAB.., ABCABC..).

3

5 Figure (1.4) a three dimensional modeling for the (ABAB..,

ABCABC..) stacking 4

7

Figure (1.5) S block structure in barium hexaferrite, (a) Top oxygen

R layer viewed from above to determine the unit cell shape. (b) The

two S block layers with their oxygen ions and cations and the top R

layer.

5

8 Figure (1.6) R block structure in barium hexaferrite with the ions and

cations sites. 6

9 Figure (1.7) T block structure in barium hexaferrite with the ions and

cations sites. 7

10 Figure (1.8) Constructive Interference of reflected waves following

Bragg law terms. 8

20 Figure (2.1) XRD pattern of barium hexaferrite sample with Fe:Ba

ratio = 11.5 9

IX

21

Figure (2.2) XRD pattern matching for the sample with Fe:Ba ratio

of 11.5.

10

22 Figure (2.3) XRD pattern matching for the sample with Fe:Ba ratio

of 16.16. 11

24 Figure (2.4) The fitted XRD pattern using profile matching method

for the sample with Fe:Ba ratio of 11.5. 12

24 Figure (2.5) The fitted XRD pattern using profile matching method

for the sample with Fe:Ba ratio of 16.16. 13

30 Figure (3.1) Fitted XRD pattern using Rietveld method for the

sample with Fe:Ba ratio = 11.5. 14




sample with Fe:Ba ratio = 13.05 16







38 Figure (3.7) XRD pattern for the sample with Fe:Ba = 9 sintered at

1200° C. 20

X


1100° C. 21


1000° C. 22

40 Figure (3.10) XRD pattern for the sample with Fe:Ba = 9 sintered

at 900° C. 23

41 Figure (3.11) XRD pattern for the sample with Fe:Ba = 9 sintered

at 800° C. 24

45 Figure (3.12) FullProf fitted pattern of the sample with Fe:Ba = 9 sintered at 1200° C

25


26


27


28


29

52 Figure (3.17) XRD pattern for the sample with Fe:Ba = 7 sintered at 1200° C.

30

53 18) XRD pattern for the sample with Fe:Ba = 7 sintered at 1100° C. 31

53 19) XRD pattern for the sample with Fe:Ba = 7 sintered at 1000° C. 32


33


34


35


36


37


38

XI


39

69

Figure (4.1) XRD patterns of all samples added with different

amounts of α-Fe2O3. The main structural peaks of iron oxide phase

are shaded in yellow

40

70 Figure (4.2) A plot of Iα/IBaM (%) vs Fe:Ba ratio for all samples 41

72 Figure (4.3) A plot of IMα/IMB (%) vs Fe:Ba ratio for all samples 43

73 Figure (4.4) A plot of IMα/IMB (%) as a function of α-Fe2O3

wt% evaluated from the refinement of the patterns of all samples 44

74 Figure (4.5) Linear fit of Fe:Ba ratio vs α-Fe2O3 wt% obtained from the refinement of the diffraction patterns.

45

75 Figure (4.6) the calculated XRD stick pattern for BaFe12O19 phase

compared with other standard patterns in ICDD library. 46

76 Figure (4.7) the crystal structure of BaFe12O19 unit cell in 3D. 47

76 Figure (4.8) the crystal structure of Fe2O3 unit cell in a 3D. 48

77 Figure (4.9) Compression of tow barium hexaferrite structures,

samples zero and twenty-five percent. 49

79

Figure (4.10) XRD patterns samples with Fe:Ba of 9 sintered at

different temperatures. α-Fe2O3 was highlighted in yellow, the

barium spinel (BaFe2O4) in blue, and the barium iron oxide

(Ba3Fe2O6) in green.

50

81

Figure (4.11) a schematic representation for each phase calculated

ratios according to the sintering temperature, Fe:Ba ratio =9.

51

XII

82 Figure (4.12) the XRD stick pattern of barium iron oxide

(Ba3Fe2O6) phase. 52

82 Figure (4.13) the calculated XRD stick pattern for Ba3Fe2O6 phase

compared with other standard pattern in ICDD library. 53

83 Figure (4.14) the calculated XRD stick pattern for BaFe2O4

phase compared with other standard patterns in ICDD library. 54

84 Figure (4.15) the crystal structure of Ba3Fe2O6 unit cell in 3D. 55

84 Figure (4.16) the crystal structure of BaFe2O4 unit cell in 3D. 56

85 Figure (4.17) Compression of tow barium hexaferrite structures sintered at 800° & 1200° C.

57

86

Figure (4.18) XRD patterns samples with Fe:Ba of 7 sintered at

different temperatures. α-Fe2O3 was highlighted in yellow, the

barium spinel (BaFe2O4) in blue, and the barium iron oxide

(Ba3Fe2O6) in green.

58

88 Figure (4.19) a schematic representation for each phase calculated

ratios according to the sintering temperature, Fe:Ba ratio = 7. 59

XIII

Structural Analysis of Hexaferrite Materials

By

Yazan Maswadeh

Supervisor

Prof. Sami Mahmood

ABSTRACT

The main essence of this study is about the structural analysis of barium hexaferrite

material, based on XRD pattern fitting using Rietveld refinement. Our methodology start by

preparing a samples of barium iron oxide materials, with different stoichiometric ratios, under

different laboratory conditions. In an attempt to understand the formation of barium hexaferrite

phases, in order to synthesis a pure phase of M-type barium hexaferrite (BaFe12O19). As well

as to understand the effect of temperature and impurities on the resulted phases.

In the beginning, a precursor material was prepared in order to obtain M-type barium

hexaferrite (BaFe12O19) samples, and modifying the proportion of Fe:Ba ratio in each sample

ascending from (11.5) to (16:16), for five samples and synthesizing them under the same

laboratory conditions. The analysis of these samples shows that the M-type barium hexa ferrite

was not affected structurally or quantitatively, and the increase of the iron oxide quantity in the

precursor material, appeared as separate phase (impurity) in each sample, which increases with

increasing the Fe:Ba ratio in the precursor material. According to these results, a reference

scheme measures the weight ratio of iron oxide to the M-type barium hexaferrite was created,

depending on the main peaks ratio for each phase.

XIV

To study these samples in a wider range according to the barium to iron ratio in the

precursor material, we prepared samples with barium to iron ratio of (1:9) and (1:7), and five

samples of each proportion were sintered at different temperatures (800, 900, 1000, 1100,

1200° C).

The analysis results showed the formation of four phases in different proportions at each

sintering temperature. A scheme representing the phases evolution according to sintering

temperature was plotted depending on the analysis results. The XRD stick pattern for each

phase was obtained, in addition to building a three-dimensional model of each crystalline

structure with an indication to the structural differences that have occurred depending on the

variation of sintering temperature.

1

CHAPTER 1

Introduction

1.1 Magnetic materials

1.2 Hexagonal Ferrites

1.3 Building blocks of hexagonal ferrites

1.4 The M-type hexaferrites

1.5 Our study

1.6 X-ray crystallography

1.7 Powder Diffraction

1.8 Rietveld Fitting

1.9 Literature Review

2

1.1 Magnetic materials

Magnetic materials are widely used in our everyday life, covering the range from

being employed in components of electronic devices and equipment to refrigerator

stickers and parts of children toys. Ferrites are magnetic ceramics based on iron oxides,

and form a class of important magnetic materials due to their desirable magnetic and

electrical properties, chemical stability, and low cost of production. Ferrites exist in

different forms such as cubic ferrites, hexagonal ferrites, orthoferrites and garnets [1 – 3].

These materials play an important role in the technological and industrial progress, and

the evolution of new applications, where for example they were efficiently used in

telecommunication and radar technologies, digital storage devices, and motor industry.

The demand for low-cost novel magnetic materials with properties required to satisfy the

specific needs of the various technological and industrial applications had therefore

generated a great interest in the synthesis and characterization of hexagonal ferrites due

to their improved and tunable properties [4 – 7].

1.2 Hexagonal Ferrites

These ferrites with hexagonal structure (also known as hexaferrites) were first

discovered in the 1950s, and the barium-based hexaferrites are composed of special

stacking sequence of close-packed oxygen layers with barium ions partially substituting

oxygen ions at specific positions in the unit cell, and the small metallic ions occupying

interstitial positions [1 – 3]. Owing to their interesting properties and wide range of

applications, hexagonal ferrites had attracted special interest which grew exponentially

until they become probably the most important magnetic materials today [7]. The

3

properties of the hexaferrites were found to depend crucially on the method of preparation

and experimental conditions as well as on the cationic substitution for iron ions [8 – 16].

Further, the substitution of Ba2+ ions by other ions such as Sr2+, Pb2+ and Ca2+ was also

found to influence the properties of the hexaferrites [16 – 20].

1.3 Building blocks of hexagonal ferrites

Visualizing the ion in the crystal structure of the hexaferrite as a hard sphere, the

large oxygen ions are closely packed in hexagonal layers as illustrated by figure (1.1). If

the ions in the first layer occupy positions labelled by (A), close packing of an over-layer

can be achieved by placing oxygen ions at any of the two positions labelled by (B) and

(C). If the second layer is at position (B), a third layer can then be placed on top of the

second layer either at position A (forming an ABA stacking) or C (forming an ABC

stacking) as illustrated by Figure (1.2) [21]. An infinite stacking of the type (ABABAB…)

then reproduces the hexagonal close-packed structure, whereas an infinite stacking of the

type (ABCABC…) reproduces the face-centered cubic (fcc) structure as explained by

general undergraduate solid state text books, see Figure (1.3 - 4). These two types of

stacking are the simplest special cases. An infinite number of stacking sequences can,

however, be produced by variations of the positions of the over-layers.

The crystal structure of the different types of hexagonal ferrites is based on the

sequential stacking of three main blocks of close-packed oxygen layers (with Ba partially

substituting oxygen in some of these layers) as demonstrated by Figure (1.5). The spinel

(S) block consists of two oxygen layers with ABCABC… stacking sequence. The

hexagonal (R) consists of three oxygen layers (ABAB… stacking) with one Ba ion

substituting an oxygen in the middle layer [22], Figure (1.6). On the other hand, the

4

hexagonal (T) block consists of four oxygen layers with one barium ion substituting an

oxygen ion in each of the two middle layers, Figure (1.7) [7]. The metal ions (primarily

Fe3+) occupy the interstitial positions in these blocks, and in the interface between the

different blocks in the hexaferrite structure. Table (1.1) summarizes the stacking

sequences of the blocks of the six known types of hexaferrites, where the starred block is

rotated by 180° about the c-axis, and the primed and double primed block is rotated by

120° [23].

Figure (1.1) a close-packed layer of spheres occupying positions A.

5

Figure (1.2) a two close-packed layers of spheres stacking on each other occupying

positions A and B.

Figure (1.3) a three close-packed layers of spheres stacking on each other occupying

positions A, B and C with the two stacking form (ABAB.., ABCABC..).

Figure (1.4) a three dimensional modeling for the (ABAB.., ABCABC..) stacking.

6

Table 1.1: Types of Compositions and building blocks of barium hexaferrites.

Hexaferrite Combination Chemical formula Stacking

M M BaFe12O19 RSR*S*

Y Y Ba2Me2Fe12O22 TST’S’T”S”

W MS BaMe2Fe16O27 SSRS*S*R*

X M2S Ba2Me2Fe28O46 3(SRS*S*R*)

Z MY Ba3Me2Fe24O41 STSRS*T*S*R*

U M2Y Ba4Me2Fe36O60 SRS*R*S*T

1.5 The M-type hexaferrites

The M-type barium hexaferrite (also known as Ferroxdure or BaM) is a

ferrimagnetic material with chemical formula BaFe12O19, melting point of 1390° C, and

theoretical density of 5.3 g/cm3 [7]. The unit cell consists of the sequence RSR*S* and

contains two molecules. BaM hexaferrite is the most important hexaferrite in terms of

production (more than 50% of the total market share of the magnetic materials [7]). The

symmetry of the barium hexaferrite crystal structure is characterized by the space group

(P63/mmc) with lattice parameter a = b = 5.89Å, c = 23.17 Å, β = α = 90°, γ = 120° [7].

The unit cell of M-type barium hexaferrite is built by stacking S and R blocks along

the hexagonal c-axis, the S block consisting of two close-packed plans have eight oxygen

ions, four ions in each, one iron cation at (2a) octahedral site, two iron cations at (4f1)

tetrahedral sites and three iron cations at (12k) octahedral sites, following the stacking

(A, B, C) where the (C) here belongs to the next R block. As a result, the S block has the

chemical formula Fe6O8, see Figure (1.5) [23].

The R block consists of three close-packed layers in an hcp stacking sequence as

shown above. The chemical formula for this block is BaFe6O11, containing one iron cation

at the (2b) trigonal site, two iron cations at the (4f2) octahedral sites and three iron cations

7

at (12k) octahedral sites. Table (1.2) summarizes the M-type barium hexaferrite

(BaFe12O19) structure and the iron ions sites at the sublattices coordinations.

Figure (1.5) S block structure in barium hexaferrite, (a) Top oxygen R layer viewed

from above to determine the unit cell shape. (b) The two S block layers with their

oxygen ions and cations and the top R layer.

The unit cell of M-type barium hexaferrite contains two BaFe12O19 molecules, one

in SR blocks and the other in the S*R* blocks rotated by 180° about the c-axis.

8

Figure (1.6) R block structure in barium hexaferrite with the ions and cations sites.

Figure (1.7) T block structure in barium hexaferrite with the ions and cations sites.

9

Table 1.2: Metallic sub-lattices of M-type hexaferrite

Block Sublattice Formula Coordination Cations / Site Spin

S 4f1

2(Fe3O4) Tetrahedral 2 2 ↓

2a Octahedral 1 1 ↑

R 4f2

BaFe6O11 Octahedral 2 2 ↓

2b Bi-pyramidal 1 1 ↑

(S-R) (R-S*) 12k SHARED Octahedral 6 (3↑) (3↑)

S* 4f1

2(Fe3O4) Tetrahedral 2 2 ↓

2a Octahedral 1 1 ↑

R* 4f2

BaFe6O11 Octahedral 2 2 ↓

2b Bi-pyramidal 1 1 ↑

(S*-R*) (R*-S) 12k SHARED Octahedral 6 (3↑) (3↑)

1.5 Our study

Our study is mainly concerned with the identification and the structural analyses of

the phases evolving in the process of synthesizing barium hexaferrite samples using

different Fe:Ba ratios. Further, the weight ratios of the different coexisting phases were

determined as a function of Fe:Ba ratio in the precursor powder. Extrapolation of the

weight ratio of the impurity phases in samples with Fe:Ba ≥ 11.5 was used to determine

the optimal ratio necessary to produce single M-type barium hexaferrite phase.

Another objective of this study was to identify and analyze the phases evolving in

samples prepared from precursors with Fe:Ba ratios of 9 and 7. The effect of sintering

temperature on the development of phases was investigated, and a phase diagram was

obtained.

1.6 X-ray crystallography

X-ray diffraction (XRD) is a non-destructive technique that is often used for the

structural analyses of solids owing to its availability, accessibility, and low cost of

operation. Regular arrays of atoms in a crystal diffract the x-ray beam into certain

directions determined by the angular positions of the diffraction peaks in a given pattern.

10

Analysis of the diffracted beam intensities into different angular positions gives

information on the atomic arrangement in a crystalline material, and allows the

construction of a three-dimensional image of the unit cell. This analysis gives full

structural information including the local atomic positions in the crystal structure,

chemical bond lengths and angles, cell deformation, and atomic order-disorder

phenomena.

When directing the x-rays to the crystalline material, the electrons of the atoms

scatter the x-rays in all directions forming a secondary spherical wave in a process similar

to the rebound of water waves after hitting a barrier. The scattered x-ray waves usually

cancel each other in most directions via destructive interference, and in some directions

(Fig. 1.8) they add up constructively, giving peaks in the intensity profile at angular

positions given by Bragg’s law [24]:

𝓃 λ = 2 𝒹 sinθ (1)

Here (λ) is the incident beam wavelength, θ the angle between the direction of the x-ray

beam and the surface of the sample, and n is an integer [25].

Figure (1.8) Constructive Interference of reflected waves following Bragg law terms.

11

1.7 Powder Diffraction

XRD is considered as one of the most common techniques to identify and analyze

the crystalline phases in a given material. A small amount of the material is required for

such analysis, and the time taken in this analysis is relatively short.

The diffraction pattern involving the peak positions and diffracted intensity profile

of a given crystalline phase is unique. Therefore, XRD provides the means to identify the

components of the study sample without pre-knowledge of the chemical elements that

constitute the sample. The d-spacing between parallel planes responsible for a given

diffraction peak (dhkl) is readily determined from the position by using Bragg’s law. This

parameter is a function of Miller indices (hkl) of the parallel reflecting planes, the unit

cell dimensions, and the type of the crystal structure of the phase [24]. Further, the

intensity of a diffraction peak is dependent on the types and positions of atoms in the

crystal, the crystal structure, the angular position of the peak, and the multiplicity of the

reflecting atomic planes [24].

The XRD sample should be made of fine powder of the material, so that the particles

are randomly oriented over the sample surface and every possible crystalline orientation

will be quite equally represented in the powder sample. Accordingly, XRD pattern with

relative intensity ratios representative of a powder sample is obtained.

1.8 Rietveld Fitting

Although crystal structure determination from powder diffraction data is simple in

theory, it is highly challenging in the case of multi-phase analysis due to overlapped

12

reflections. Rietveld method, which is also known as full pattern analysis technique, is

used to refine the crystal structure of a material and obtain accurate structural parameters

of the different phases in the sample under investigation.

Rietveld method uses the least squares minimization technique to fit the observed

XRD pattern with a theoretical pattern, which is generated using the crystal structure

information along with the microstructural and instrumental information. Other

specialized techniques to determine unknown structures from powder data are also

available [26].

Even though there are many primary terms that are frequently used in the pattern

refinement field, we will only address and interpret the most important ones as outlined

by Rodriguez [27]:

(I) The Chi squared value (𝜒2) represents the goodness of the fit. This value is given

by [28-29]:

𝜒2 = ∑(𝒪 − ℰ)2

ℰ (2)

Where 𝒪 is the observed value and ℰ is the calculated value. Therefore, low values

of 𝜒2 indicate that the proposed theoretical model represents the crystal structure

satisfactorily, while higher values indicate the model should not be accepted as

representative of the structure of the crystalline phase.

(II) Pearson's chi-squared test (Person’s r) is a statistical test applied to sets of

categorical data to evaluate how likely it is that any observed difference between the sets

arose by chance. It is suitable for unpaired data from large samples [30].

Pearson's correlation is computed by dividing the sum of the 𝓍𝓎 column by the

square root of the product of the sum of the 𝓍2 and 𝓎2, following the formula [31]:

𝓇 =∑𝓍𝓎

√(∑𝓍2∑𝓎2) (3)

13

(III) RF-factor (ℛℱ) , which is also known as Crystallographic RF-Factor, is a

measure of the agreement between the crystallographic model and the experimental X-

ray diffraction data. In other words, it is a measure of how well the refined structure

predicts the observed data. RF -factor is given by [32]:

ℛℱ = 100∑ |′ℱobs,𝑘′ − ℱcalc,ℎ|

ℎ

∑ |′ℱobs,ℎ′|ℎ

(4)

Where ℱ is the structure factor.

(IV) Bragg R-factor (ℛℬ) is a measure of the agreement between the reflected

intensities calculated from a crystallographic model and those measured experimentally.

This is given by [33]:

ℛℬ = 100∑ |′ℐobs,ℎ′ − ℐcalc,ℎ|

ℎ

∑ |′ℐobs,ℎ′|ℎ

(5)

Here ℐ is the integrated intensity.

(V) PSEUDOVOIGT peak shape, (pVx) function is a linear combination of a

Lorentzian (ℒ′) and a Gaussian (𝒢′) of the same FWHM.

𝒱(𝓍) = ℒ(𝓍) ⨂ 𝒢(𝓍) = ∫ −∞

+∞

ℒ(𝓍 − 𝓊)𝒢(𝓊)𝒹𝓊 (6)

(VI) Biso or isotropic Debye-Waller factors, is used to describe the attenuation of x-

ray scattering caused by thermal motion.

(VII) Occ, Occupation number i.e. (chemical occupancy × site multiplicity) can be

normalized to the multiplicity of the general position of the group.

(VIII) Wyckoff position of a space group G consists of all points X for which the

site-symmetry groups are conjugate subgroups of G, the Wyckoff positions tell us where

the atoms in a crystal can be found.[34].

14

(IIX) The lattice constant, or lattice parameter, refers to the physical dimension of

unit cells in a crystal lattice. Lattices in three dimensions generally have three lattice

constants, referred to as a, b, and c.[35].

(IX) In quantitative analysis, noting that in a mixture of N crystalline phases, the

weight fraction Wj of phase j is given by:

Wj ={ Sj Zj Mj Vj / tj} / Sum(i)[Si Zi Mi Vi /ti] (7)

Where Sj is the scale factor of phase j, Zj is the number of formula units per unit

cell for phase j, Mj is the mass of the formula unit, Vj is the unit cell volume and tj is the

Brindley particle absorption contrast factor for phase j.

The 𝒜𝒯𝒵 coefficient, which is used to calculate the phase weight percent, depends

on several parameters, and is given by:

𝒜𝒯𝒵 = 𝒵 ℳ𝒲 f 2/𝓉 (8)

Here 𝒵 is the number of formula units per unit cell, ℳ𝒲 the molecular weight, and 𝓉 is

the Brindley coefficient.For a stoichiometric phase f = 1 if these multiplicities are

calculated by dividing the Wyckoff multiplicity 𝓂 of the site by the general

multiplicity ℳ. Otherwise

f = 𝒪𝒸𝒸. ℳ 𝓂⁄ (9)

where 𝒪𝒸𝒸 is the occupation number, lastly.

1.9 Literature Review

The existence of impurity phases in barium hexaferrite sample, mainly α-Fe2O3 and

barium spinel (BaFe2O4) phases were reported by several investigators [36 - 40]. These

phases affect the properties of the prepared hexaferrites samples negatively. The presence

15

of such phases was shown to depend on the method of fabrication and the experimental

conditions, such as the heat treatment.

Sözeri et al. [37] synthesized BaFe12O19 particles by citrate sol–gel combustion

route with a sintering temperature ranging from 800 to 1200° C. The Fe:Ba ratio in this

study was varied from 2 to 12. They observed that the sample with Fe:Ba ratio of 12

sintered at 800° C contains a Ba-hexaferrite phase with a minor α-Fe2O3 impurity phase.

The sintering temperature of 900° C was high enough to crystallize barium hexaferrite

phase in the sol–gel route. They also observed that the annealing temperature up to 1100°

C would increase both the specific saturation magnetization and coercivity, where a

transition from single to multi domain structure occurs. Furthermore, they reported the

appearance of two peaks at about two-theta of 37° and 44°, in the sample sintered at 1200°

C, which they claimed to be associated with BaM phase. The peaks were reported to

become narrower with increasing the temperature, which they associated with increasing

the crystallite size.

Suastiyant, et al. [38] used the sol gel auto combustion method to synthesis barium

hexaferrite powder, then investigating the powder crystallite and grain size, crystal

structure and magnetic properties. They found that the Fe:Ba ratio in the precursor

material has an important influence on the diffraction pattern, magnetic properties and

crystallite size. They reported that the ratio 11.5 is the best ratio which gives the well-

crystalline powder with the smallest crystallite size 22 nm as they found. Nevertheless,

they did not use an accurate fitting method for the structural study and phase

identification.

Wang and Zhang [39] studied the Ba:Fe ratio effect on synthesizing a barium

hexaferrite powder using the citrate–EDTA complexing method. Powders with Fe:Ba

16

ratios of 6.5, 7,11, 11.5, and 12, calcined at 1000° C for five hours were synthesized. They

reported that the Fe:Ba ratio value is very important in developing the BaFe12O19 phase.

They claimed that they obtained pure barium hexaferrite phase with Fe:Ba ratios of 11

and 11.5. For other ratios, BaFe2O4 and Fe2O3 were observed, in addition to the hexagonal

barium ferrite major phase. However, they did not investigate the phase purity of the

samples treated at higher temperatures. Also their results showed that the calcination

temperature for samples with Fe:Ba ratio of 11.5 is lower than for other ratios.

Topal et al. [40] investigated the structural and magnetic properties of BaFe12O19

prepared by the ammonium nitrate melt technique (ANMT) with tuning the Fe:Ba ratio

from 2 to 13, and treated them at different temperatures from 800° C to 1200° C. They

reported that the BaFe2O4 impurity phase is formed at low Fe:Ba ratios (Fe:Ba = 2–6), in

addition to BaFe12O19 phase, and Fe2O3 is the only impurity phase that appears at high

Fe:Ba ratios (Fe:Ba = 8–13). They also claimed to obtain a high-quality single crystalline

BaFe12O19 successfully using ANMT, while keeping the Fe:Ba ratio between 2 and 6, and

washing the samples with diluted HCl after the heat treatment in order to get rid of the

BaFe2O4 impurity.

Other researchers used mixing and physical milling technique to prepare the barium

hexaferrite powder. Zlatkov, et al. [41] investigated the barium hexaferrite permanent

magnets prepared using the powder injection molding. The starting barium hexaferrite

powder was prepared by calcination followed by milling.

Suarez et al. [42] studied the magnetization for barium ferrite powders with

increasing the heating temperature from 1000° C to 1200° C with Fe:Ba ratios varying

from 7 to 15 and. They found that increasing the heating temperature was effective in

increasing the magnetization of the powders for the ratios larger than 10. For lower ratios,

17

the magnetization increased initially and then decreased with increasing temperature

“presumably due to the formation of BaFe2O4” as they predicted. Furthermore, they

investigated the effect of the milling time on the magnetic properties and powder

characteristics and found that forty hours of milling was enough to obtain samples with

less volume fraction of other phases.

Janasi, et al. [43] prepared MnZn ferrites using co-precipitation and solid state

reaction. They investigated the effect of the calcination temperature on the magnetic

properties of the ferrites.

Campbell, et al. [44] investigated the effects of dry-milling BaM in air on the

particle properties using X-ray diffraction. They reported that the sizes of the particles

decrease, and a partial decomposition of BaFe12O19 to α-Fe2O3 was found to take place

upon extended milling for 1000 h.

Using the XRD pattern refinement technique, Ashima, et al. [45] used the Rietveld

refinement of X-ray powder diffraction data of Ca–Sr substituted barium hexaferrites and

found that the samples possess single hexagonal phase with space group consistent that

for BaM phase having the composition BaFe12O19. On the other hand, Brando, et al. [46]

used X-ray data to determine the cation distributions Ir-Co and Ir-Zn on the various Fe

sites of the substituted BaM-hexaferrites. They used their XRD results concerning the

preferred sites and multiplicity of the different cations to explain the magnetization data.

Also, Suminar Pratapa, [47] analyzed the phase composition of ceramic powder using

Rietveld refinement method.

18

CHAPTER 2

Methodology

2.1 Preparation of non-stoichiometric Barium hexaferrite samples

With high iron to barium ratio (11.5 – 16.16)

2.2 Structural characterization

2.3 Preparation of non-stoichiometric Barium hexaferrite samples with iron to

barium ratio = 9 and 7

19

2.1 Preparation of non-stoichiometric Barium hexaferrite samples

With high iron to barium ratio (11.5 – 16.16)

About 10 g of a mixture of the of high purity (≥ 99%) BaCO3 and α-Fe2O3 powders

with Fe:Ba molar ratio of 11.5 was prepared using high energy ball milling. Appropriate

amounts of the powder precursors were weighed accurately (to five decimal places) and

mixed in two zirconia cups and milled for 16 hours in an acetone bath using a (Fritsch

Pulverisette 7) ball mill. Seven zirconia balls were used for the milling with a ball-to-

powder ratio of 14. The rotational speed was 250 rpm. The milled powder was left to dry

at room temperature. This powder was used to synthesize six different barium hexaferrite

samples with Fe to Ba ratio ranging from 11.5 to 16.16. About one gram of the dry powder

was pressed into 1.3 mm diameter disc under a 50 kN force, and sintered at 1100° C for 2

hours. This sample is labled (0%) as shown in Table 2.1. Then five different samples with

different Fe:Ba ratios were prepared by mixing portions of the original powder with

different weight ratios of α-Fe2O3 (from 5% to 25%) for about an hour using an agate

mortar and pestle, pressing into discs and sintering at 1100° C (Table 2.1).

Table (2.1) the iron to barium ratio for each sample.

Sample name 25% 20% 15% 10% 5% 0%

Fe:Ba Ratio 16.158 14.993 13.699 13.053 12.236 11.500

2.2 Structural characterization

The structure of the samples was investigated by θ-2θ x-ray diffraction (XRD) using

Shimadzu X-ray Diffraction Instrument, with Cu-Kα ray (λα1 = 1.540560 Å and λα2 =

1.544390 Å). The XRD scan configuration was, (2θ = 20° – 70°) for the scan range, with

step time of 1.2 s and 0.01° sampling pitch. A divergence slit of width DF = 2.4 mm, a

scattering slits of width SS = 1.25 mm, and a receiving slit of width RS = 0.9 mm were

used for the data collection.

20

XRD patterns of the samples were initially analyzed beginning with Panalytical

X'Pert Highscore plus software based on PDF-2 ICDD library. This analysis revealed the

phases in each sample by matching the observed pattern with those included in the library.

It was found that the sample with Fe:Ba ratio of 11.5 consisted of a single phase of

M-type barium hexaferrite (Fig 2.1). However, all samples added with α-Fe2O3 consisted

of two phases; the M-type barium hexaferraite, and the iron oxide (α-Fe2O3). Figures (2.2)

and (2.3) show the patterns of the samples 0% (Fe:Ba = 11.5) and 25% (Fe:Ba = 16.16)

analyzed using the X’pert software.

Figure (2.1) XRD pattern of barium hexaferrite sample with Fe:Ba ratio = 11.5

21

Figure (2.2) XRD pattern matching for the sample with Fe:Ba ratio of 11.5.

22

Figure (2.3) XRD pattern matching for the sample with Fe:Ba ratio of 16.16.

23

The process of determining the phases in a pattern using X'Pert Highscore plus

software begins by matching two things, first by matching the peak positions of the XRD

pattern, secondly by matching the height of these peaks with reference patterns in the

software database. It should be noted that the software cannot determine the phases

automatically; it needs a user's hand and eye to match those profiles.

The second step of the analysis begins by fitting these data to a theoretical pattern

of the structure, based on the space group, cell dimension, and other parameters that play

a role in the fitting routine. Initially, the patterns were fitted using the whole-pattern

decomposition (Profile Matching) procedure in FullProf software (this procedure is also

known as Lebail Fitting) [48]. It has been used in Profile Matching with the constant scale

factor technique. This technique makes data entry much easier and significantly expands

the scope of the powder pattern profile refinement. However, the restriction applicable to

the refinement is much less severe than the Rietveld refinement, and the Profile Matching

is therefore more prone to instability, but it is a very useful initial step in the refinement

process, due to the speed and the ease of the refinement, and the validity confirmation of

the input information. Furthermore, the output of this process is excellent.

The five samples were fitted using the Profile Matching refinement routine. The

difference in the impurity phase’s integrated intensities between the samples was obvious,

and the fitting came up with a very good chi square value, the Bragg R-factor and RF-

factor were rather low, indicating the reliability of the fit. The goodness of fit can be

concluded directly by observing the difference pattern between the observed and the

theoretical patterns (Yobs - Ycal) as shown in Figures (2.4) and (2.5).

24

Figure (2.4) The fitted XRD pattern using profile matching method for the sample with

Fe:Ba ratio of 11.5.

Figure (2.5) The fitted XRD pattern using profile matching method for the sample with

Fe:Ba ratio of 16.16.

25

The first fitted pattern for the sample of Fe:Ba ratio of 11.5 in figure (2.4) has a Chi

squared value = 1.24, (BaFe12O19) Brag R-factor= 0.442 and RF-factor= 0.601. The

second pattern for the sample of Fe:Ba ratio of 16.16 in figure (2.5) has a Chi squared

value = 1.344. The BaFe12O19 Brag RB-factor = 0.434 and RF-factor = 0.523, while the α-

Fe2O3 Brag RB-factor = 0.523 and RF-factor = 0.517.

The output parameters of the previous operation include the cell parameters (a, b,

c) and some other important parameters necessary for the next fitting step. Rietveld

refinement process is then performed using the previous output. Several other parameters

were necessary for the process, Wyckoff positions being the most important.

Although the Rietveld profile refinement is rather simple in theory, it requires some

expertise and good scientific background in crystallography to be implemented properly.

Many characteristics of this refinement technique make it a tough starting refinement

method and may lead to incorrect starting steps. The correlation between the structure

parameters in this refinement may readily cause a premature divergence, and the least-

squares minimization algorithm often falls into fake minima. In order to avoid these

weaknesses, a particular procedure should be followed, using the cell parameters obtained

from the previous refinement method (Profile Matching). In addition, this procedure

shortens the time required for the development of the cell refinement prototype, and ends

up with a good pattern fit.

Shift relaxation factors, which include the instrumental zero-shift, displacement and

transparency, pattern background information and parameters, are all picked from the

outputs of the previous refinement technique (Profile Matching). The cell parameters,

angles and the FWHM (Full width at half maximum) parameters for each phase are also

being taken from the previous outputs. Next, the atomic positions and related parameters

represented by the element, the Wyckoff positions, the occupancy and the isotropic

26

temperature parameter (Debye–Waller factor) for each site are used in the structural

refinement.

In the absence of sufficient crystallographic information regarding the structure, the

atomic positions are manually calculated to approximate numbers depending on the

theoretical reference of each space group, by taking the Wyckoff sites and their

multiplicities and coordinates. In addition, the normalized occupancies are manually

calculated. Initially the isotropic temperature parameters for all atoms are given the same

value, and then the refinement procedure leads to the final accurate refined values.

Table (2.2) shows the compatibility of the parameters after refinement by Profile

Matching method and Rietveld method. The word helpful means it helps in the fitting

process if it is used as an initial value.

Table (2.2) outputs compatibility between Rietveld and Profile matching method.

Parameters Compatibility Parameters Compatibility

Cell Parameters (a,b,c) 99.90% FWHM (U,V,W) peaks

parameters

Helpful, Don’t

match

Cell Angles, Space

group 100%, no change Scale Factor Unmatched

Pattern Background Helpful , 70% Preferred orientation Unmatched

Zero-shift,

displacement,

Transparency.

95%

Eta0, X

Unmatched (Additional shape parameters,

Lorentzian isotropic strain)

In all refinement methods, it is important to plot and compare the changes in the

fitted pattern. The difference between the fitted patterns after each refinement step is an

efficient and fast way to detect the fault-fitting step, and modify the refinement procedure

to obtain the best sequence and most reliable results.

27

2.3 Preparation of non-stoichiometric Barium hexaferrite samples with iron to

barium ratio = 9 and 7

Precursor powders with Fe:Ba ratios of 9 and 7 (significantly lower than the

stoichiometric ratio of 12) were prepared following the same procedure for preparing the

sample with Fe:Ba = 11.5 as outlined in section 2.1. The sample with Fe:Ba ratio of 7 has

the stoichiometry of Fe2-Y barium hexaferrite (Ba2Fe2Fe12O22) [7]. Therefore, the choice

of these two compositions was motivated by the fact that they extend between the

stoichiometries of the Y-type and the M-type hexaferrites. The effect of the sintering

temperature on the evolution of the structural phases in these samples was investigated

by analyzing the structure of different portions of the powder sintered at different

temperatures (800, 900, 1000, 1100 and 1200° C).

28

CHAPTER 3

Results

3.1 Result of non-stoichiometric barium hexaferrite Samples, Iron to barium

ratio (Fe+3 : Ba+2) ≥ 11.5

3.2 XRD Data Refinement Result of Non-Stoichiometric Barium Hexaferrite




29

3.1 Result of non-stoichiometric barium hexaferrite Samples.

Iron to barium ratio (Fe+3 : Ba+2) ≥ 11.5

This section is concerned with the structural refinement of barium iron oxide sample

with Fe:Ba = 11.5. Rietveld profile refinement was performed using some of the fitting

parameters reported elsewhere [50 - 53]. A reliable fit was obtained Figure (3.1) with a

rather low Chi-Squared value, and the corresponding main structural output parameters

are listed below. The atomic positions obtained in this refinement process are in good

agreement with previously reported results [50-51].

Phase data Chi2 = 1.254

Space-group P 63/m m c (194) - hexagonal

Cell

a=5.8909 Å c=23.2087 Å

c/a=3.9398

V=697.50 Å3

Atomic parameters

Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]

Ba +2 2d -6m2 0.66667 0.33333 0.25000 0.00850

Fe +3 2a -3m. 1.02874 0.00000 0.00000 0.00000 0.00640

Fe +3 2b -6m2 0.95243 0.00000 0.00000 0.25027 0.00860

Fe +3 4f 3m. 0.97621 0.33333 0.66667 0.02660 0.00240

Fe +3 4f 3m. 0.99455 0.33333 0.66667 0.19027 0.00970

Fe +3 12k .m. 0.99554 0.16930 0.33856 0.89165 0.00590

O -2 4e 3m. 1.04014 0.00000 0.00000 0.15157 0.01460

O -2 4f 3m. 1.05451 0.33333 0.66667 0.94388 0.00020

O -2 6h mm2 0.97985 0.17590 0.35188 0.25000 0.00830

O -2 12k .m. 1.06558 0.15414 0.30820 0.05200 0.00790

O -2 12k .m. 1.04840 0.50185 1.00368 0.14928 0.00490

As it appears, there is no such difference between the figures (2.4) and (3.1), the two

fitted figures for the same sample (Zero Percent) done by the two different refinement

methods, the Profile Matching and Rietveld Refinement.

Sample Zero Percent (0%)

30

Figure (3.1) Fitted XRD pattern using Rietveld method for the sample with Fe:Ba ratio

= 11.5.

In what follows we show the fitted patterns and present the main structural results

of the two phase appearing in the patterns of the samples added with different weight

ratios of α-Fe2O3.

Sample Five Percent (5%)

Current global Chi2 (Bragg contrib.) = 1.312

Phase: 1 - BaFe12O19

Bragg R-factor : 2.64 Vol: 698.311 Fract(%): 95.35

Rf-factor : 2.51 ATZ: 47.727 Brindley: 1

Phase data


Cell

a=5.8928 Å c=23.2207 Å

c/a=3.9405

V=698.31 Å3

Atomic parameters


Ba +2 2d -6m2 0.66667 0.33333 0.25000 -0.00450

Fe +3 2a -3m. 1.03856 0.00000 0.00000 0.00000 -0.00330

Fe +3 2b -6m2 0.89774 0.00000 0.00000 0.25027 -0.00180

Fe +3 4f 3m. 0.95977 0.33333 0.66667 0.02722 -0.01350

Fe +3 4f 3m. 1.09681 0.33333 0.66667 0.19067 0.01280

Fe +3 12k .m. 1.01411 0.16838 0.33653 0.89167 0.00050

31

O -2 4e 3m. 0.98114 0.00000 0.00000 0.14998 -0.02330

O -2 4f 3m. 1.13034 0.33333 0.66667 0.94643 0.03240

O -2 6h mm2 1.10925 0.18134 0.36263 0.25000 0.00610

O -2 12k .m. 1.18231 0.15705 0.31385 0.05151 0.01520

O -2 12k .m. 1.19880 0.50313 1.00634 0.14946 0.01820

Phase: 2 - Fe2O3


Rf-factor : 4.06 ATZ: 30.8 Brindley: 0.75

Phase data

Space-group R -3 c (167) - trigonal

Cell

a=4.9908 Å c=13.8549 Å

c/a=2.7761

V=298.86 Å3

Atomic parameters


Fe +3 12c 3.0 0.00000 0.00000 0.37484 0.00810

O -2 18e 0.2 1.04882 0.45368 0.00000 0.25000 0.01200


= 12.24.

32


= 13.05

Sample Ten Percent (10%)





Phase data


Cell

a=5.8933 Å c=23.2186 Å

c/a=3.9398

V=698.36 Å3

Atomic parameters


Ba +2 2d -6m2 0.66667 0.33333 0.00000 -0.00290

Fe +3 2a -3m. 1.02491 0.00000 0.00000 0.00000 -0.00880

Fe +3 2b -6m2 0.90808 0.00000 0.00000 0.25027 -0.00300

Fe +3 4f 3m. 0.96735 0.33333 0.66667 0.02734 -0.00800

Fe +3 4f 3m. 1.08892 0.33333 0.66667 0.19063 0.01590

Fe +3 12k .m. 1.01904 0.16928 0.33841 0.89179 -0.00040

O -2 4e 3m. 0.97380 0.00000 0.00000 0.15076 -0.01660

O -2 4f 3m. 1.15979 0.33333 0.66667 0.94475 0.04390

O -2 6h mm2 1.13459 0.17995 0.35989 0.25000 0.01810

O -2 12k .m. 1.18657 0.15524 0.31029 0.05176 0.02230

O -2 12k .m. 1.21664 0.50398 1.00803 0.14867 0.02910

33

Phase: 2 - Fe2O3



Phase data


Cell

a=5.0357 Å c=13.7488 Å

c/a=2.7303

V=301.93 Å3

Atomic parameters


Fe +3 12c 3.0 0.00000 0.00000 0.35501 -0.00330

O -2 18e 0.2 1.54843 0.32240 0.00000 0.25000 0.10040

Sample Fifteen Percent (15%)





Phase data


Cell

a=5.8946 Å c=23.2242 Å

c/a=3.9399

V=698.84 Å3

Atomic parameters


Ba +2 2d -6m2 0.66667 0.33333 0.25000 -0.00270

Fe +3 2a -3m. 0.99057 0.00000 0.00000 0.00000 -0.01150

Fe +3 2b -6m2 0.93310 0.00000 0.00000 0.25027 -0.00210

Fe +3 4f 3m. 0.96784 0.33333 0.66667 0.02788 -0.01280

Fe +3 4f 3m. 1.08877 0.33333 0.66667 0.19012 0.00920

Fe +3 12k .m. 0.96598 0.16914 0.33816 0.89180 -0.00970

O -2 4e 3m. 1.03173 0.00000 0.00000 0.14939 0.00990

O -2 4f 3m. 1.09777 0.33333 0.66667 0.94525 0.01800

O -2 6h mm2 1.23928 0.18519 0.37042 0.25000 0.02850

O -2 12k .m. 1.09248 0.15492 0.30968 0.05153 -0.00090

O -2 12k .m. 1.24943 0.50201 1.00404 0.14796 0.02910

Phase: 2 - Fe2O3



Phase data


Cell

a=5.0363 Å c=13.7528 Å

c/a=2.7307

V=302.10 Å3

Atomic parameters


Fe +3 12c 3.0 0.00000 0.00000 0.35517 -0.00910

O -2 18e 0.2 1.23563 0.31597 0.00000 0.25000 0.04070

34


= 13.97.


= 14.99.

35

Sample Twenty Percent (20%)





Phase data


Cell

a=5.8926 Å c=23.2151 Å

c/a=3.9397

V=698.09 Å3

Atomic parameters


Ba +2 2d -6m2 0.66667 0.33333 0.25000 -0.00170

Fe +3 2a -3m. 1.06749 0.00000 0.00000 0.00000 -0.00190

Fe +3 2b -6m2 0.94403 0.00000 0.00000 0.25027 -0.00700

Fe +3 4f 3m. 0.92099 0.33333 0.66667 0.02696 -0.02320

Fe +3 4f 3m. 1.05597 0.33333 0.66667 0.18997 0.00750

Fe +3 12k .m. 1.01166 0.16919 0.33822 0.89195 -0.00500

O -2 4e 3m. 1.26872 0.00000 0.00000 0.15181 0.05130

O -2 4f 3m. 1.24897 0.33333 0.66667 0.94445 0.03290

O -2 6h mm2 1.10809 0.18162 0.36332 0.25000 0.00730

O -2 12k .m. 1.26145 0.15671 0.31334 0.05194 0.03990

O -2 12k .m. 1.23018 0.50476 1.00954 0.14930 0.02110

Phase: 2 - Fe2O3



Phase data


Cell

a=5.0348 Å c=13.7483 Å

c/a=2.7306

V=301.82 Å3

Atomic parameters


Fe +3 12c 3.0 0.00000 0.00000 0.35555 -0.00260

O -2 18e 0.2 1.13611 0.31775 0.00000 0.25000 0.01650

36

Sample Twenty Five Percent (25%)





Phase data


Cell

a=5.8934 Å c=23.2183 Å

c/a=3.9397

V=698.37 Å3

Atomic parameters


Ba +2 2d -6m2 0.66667 0.33333 0.25 0.0023

Fe +3 2a -3m. 1.11471 0 0 0 0.0107

Fe +3 2b -6m2 1.02743 0 0 0.25027 0.0284

Fe +3 4f 3m. 0.92394 0.33333 0.66667 0.02739 -0.0171

Fe +3 4f 3m. 0.97091 0.33333 0.66667 0.19008 -0.0093

Fe +3 12k .m. 0.98351 0.1675 0.33489 0.89174 -0.0063

O -2 4e 3m. 1.31214 0 0 0.15056 0.0729

O -2 4f 3m. 0.84414 0.33333 0.66667 0.94507 -0.0529

O -2 6h mm2 1.02605 0.17826 0.35665 0.25 0.0002

O -2 12k .m. 1.33195 0.15185 0.30357 0.05105 0.0467

O -2 12k .m. 1.0859 0.50385 1.00771 0.15112 0.0059

Phase: 2 - Fe2O3



Phase data


Cell

a=5.0354 Å c=13.7483 Å

c/a=2.7303

V=301.89 Å3

Atomic parameters


Fe +3 12c 3.0 0.00000 0.00000 0.35608 0.00110

O -2 18e 0.2 0.88372 0.31022 0.00000 0.25000 -0.03920

37


= 16.16.

3.2 XRD Data Refinement Result of Non-Stoichiometric Barium

Hexaferrite Samples with Fe:Ba Ratio = 9

This section presents the Rietveld refinement results of barium iron oxide samples

with Fe:Ba ratio of 9. The structural characteristics for (BaFe2O4 & Ba3Fe2O6) reported

elsewhere [53, 54] were used at the initial stages of the fitting process in order to

shorten the processing time and ease the job.

The patterns of the samples sintered at different temperatures were initially analyzed

using X’Pert High Score Plus software (Figures 3.7-3.11). These figures indicate that the

patterns of the samples sintered at temperatures below 1000° C consisted of BaM

hexaferrite phase in addition to two minor phases, namely, BaFe2O4 barium spinel and α-

Fe2O3. At higher sintering temperatures these phases diminish with increasing sintering

temperature, and a new (Ba3Fe2O6) phase evolves. Table (3.1) shows the phases co-

existing in the patterns of the samples sintered at different temperatures.

38

Figure (3.7) XRD pattern for the sample with Fe:Ba = 9 sintered at 1200° C.


39


40


41


42

Table (3.1) Structural phases existing in the samples with Fe:Ba = 9 sintered at different

temperatures

Sample's Phases in the sample

Cent. Tem. Phase #1 Phase #2 Phase #3

1200° C Ba Fe12 O19 Ba3 Fe2 O6

1100° C Ba Fe12 O19 Ba3 Fe2 O6 Ba Fe2 O4


900° C Ba Fe12 O19 Ba Fe2 O4 Fe2 O3


The main structural information for the various phases in all samples were

obtained from Rietveld refinement of the diffraction patterns. Specifically, the types of

phases, their structural parameters and relative proportion (as weight ratio) in each

sample are presented below.

Sample Sintered at (1200° C)





Phase data


Cell

a=5.9002 Å c=23.2864 Å

c/a=3.9467

V=702.06 Å3

Atomic parameters


Ba +2 2d -6m2 0.66667 0.33333 0.25000 0.00930

Fe +3 2a -3m. 1.01784 0.00000 0.00000 0.00000 0.00840

Fe +3 2b -6m2 0.87766 0.00000 0.00000 0.25027 0.00520

Fe +3 4f 3m. 0.96304 0.33333 0.66667 0.02757 0.00320

Fe +3 4f 3m. 1.06839 0.33333 0.66667 0.19068 0.00760

Fe +3 12k .m. 1.02251 0.16758 0.33501 0.89240 0.00610

O -2 4e 3m. 0.98003 0.00000 0.00000 0.14883 0.00600

O -2 4f 3m. 0.93670 0.33333 0.66667 0.94346 0.00680

O -2 6h mm2 1.02407 0.17994 0.35994 0.25000 0.00560

O -2 12k .m. 1.19088 0.14689 0.29360 0.04970 0.00630

O -2 12k .m. 1.09544 0.50402 1.00812 0.14942 0.00600

Phase: 2 - Ba3Fe2O6



Phase data

Space-group P a -3 (205) - cubic

43

Cell a=16.7507 Å

V=4700.00 Å3

Atomic parameters


Ba 4a .-3. 0.00000 0.00000 0.00000 0.01270

Ba 4b .-3. 0.73916 0.50000 0.00000 0.00000 0.01270

Ba 8c .3. 1.00129 0.25226 0.25226 0.25226 0.01270

Ba 8c .3. 0.76440 0.37500 0.37500 0.37500 0.01270

Ba 24d 1 0.84110 0.12964 0.37744 0.11673 0.01270

Ba 24d 1 0.83700 0.37372 0.38000 0.11977 0.01270

Fe 24d 1 2.58565 0.26620 -0.00217 0.01797 0.01270

Fe 24d 1 2.83225 0.24765 0.23832 -0.00329 0.01270

O 24d 1 1.69547 0.28115 0.11895 0.01386 0.01270

O 24d 1 1.92632 0.48167 0.12288 0.25036 0.01270

O 24d 1 1.22244 0.24696 0.30480 0.10193 0.01270

O 24d 1 0.21458 0.41001 0.29516 0.01270

O 24d 1 1.96656 0.36943 -0.00574 0.01734 0.01270

O 24d 1 4.63592 0.15068 -0.01144 -0.02054 0.01270






Phase data


Cell

a=5.8962 Å c=23.2481 Å

c/a=3.9429

V=699.95 Å3

Atomic parameters


Ba +2 2d -6m2 0.66667 0.33333 0.25000 0.00930

Fe +3 2a -3m. 0.96584 0.00000 0.00000 0.00000 0.00840

Fe +3 2b -6m2 0.98036 0.00000 0.00000 0.25027 0.00520

Fe +3 4f 3m. 1.04398 0.33333 0.66667 0.02795 0.00320

Fe +3 4f 3m. 1.13920 0.33333 0.66667 0.19125 0.00760

Fe +3 12k .m. 1.04256 0.16737 0.33459 0.89182 0.00610

O -2 4e 3m. 1.04825 0.00000 0.00000 0.15556 0.00600

O -2 4f 3m. 1.11187 0.33333 0.66667 0.94346 0.00680

O -2 6h mm2 1.35753 0.18147 0.36294 0.25000 0.00560

O -2 12k .m. 1.13123 0.16429 0.32834 0.05167 0.00630

O -2 12k .m. 1.33276 0.50224 1.00454 0.14769 0.00600

44

Phase: 2 - Ba3Fe2O6



Phase data


Cell a=16.7506 Å

V=4699.89 Å3

Atomic parameters


Ba 4a .-3. 0.00000 0.00000 0.00000 0.01270

Ba 4b .-3. 0.69485 0.50000 0.00000 0.00000 0.01270

Ba 8c .3. 0.53613 0.25126 0.25126 0.25126 0.01270

Ba 8c .3. 0.99923 0.37543 0.37543 0.37543 0.01270

Ba 24d 1 1.09877 0.12767 0.37353 0.12316 0.01270

Ba 24d 1 0.94081 0.37121 0.37647 0.12617 0.01270

Fe 24d 1 1.25109 0.25225 -0.00517 -0.00019 0.01270

Fe 24d 1 1.66013 0.24902 0.24418 -0.00322 0.01270

O 24d 1 1.71791 0.27413 0.11091 0.01235 0.01270

O 24d 1 2.46861 0.48665 0.12833 0.25334 0.01270

O 24d 1 0.61991 0.23381 0.33620 0.13170 0.01270

O 24d 1 0.22811 0.43551 0.28525 0.01270

O 24d 1 2.93889 0.35669 -0.00251 0.01393 0.01270

O 24d 1 2.51819 0.13222 -0.01231 -0.01094 0.01270

Phase: 3 - BaFe2O4



Phase data

Space-group B b 21 m (36) - orthorhombic

Cell

a=19.3033 Å b=5.4285 Å c=8.4462 Å

a/b=3.5559 b/c=0.6427 c/a=0.4376

V=885.06 Å3

Atomic parameters


Ba 4 0.13070 0.25000 0.00000 0.01270

Ba 4 0.61730 0.22700 0.00000 0.01270

Fe 8 0.50000 0.04240 0.73200 0.27760 0.01270

Fe 8 0.50000 0.20840 0.77400 0.29130 0.01270

O 8 0.50000 0.03700 0.40300 0.24300 0.01270

O 8 0.50000 0.12300 0.91700 0.22500 0.01270

O 8 0.50000 0.20900 0.41700 0.28100 0.01270

O 4 0.45300 0.22600 0.00000 0.01270

O 4 0.28000 0.22600 0.00000 0.01270

45

Figure (3.12) FullProf fitted pattern of the sample with Fe:Ba = 9 sintered at 1200° C


46






Phase data


Cell

a=5.8916 Å c=23.2140 Å

c/a=3.9402

V=697.83 Å3

Atomic parameters


Ba +2 2d -6m2 0.66667 0.33333 0.25000 0.00930

Fe +3 2a -3m. 0.96584 0.00000 0.00000 0.00000 0.00840

Fe +3 2b -6m2 0.98036 0.00000 0.00000 0.25027 0.00520

Fe +3 4f 3m. 1.04398 0.33333 0.66667 0.02744 0.00320

Fe +3 4f 3m. 1.13920 0.33333 0.66667 0.19146 0.00760

Fe +3 12k .m. 1.04256 0.16667 0.33241 0.89153 0.00610

O -2 4e 3m. 1.04825 0.00000 0.00000 0.15584 0.00600

O -2 4f 3m. 1.11187 0.33333 0.66667 0.94336 0.00680

O -2 6h mm2 1.35753 0.17698 0.35395 0.25000 0.00560

O -2 12k .m. 1.13123 0.15578 0.31132 0.05096 0.00630

O -2 12k .m. 1.33276 0.49863 0.99731 0.14760 0.00600

Phase: 2 - Ba3Fe2O6



Phase data


Cell a=16.7298 Å

V=4682.43 Å3

Atomic parameters


Ba 4a .-3. 0.00000 0.00000 0.00000 0.01270

Ba 4b .-3. 0.73111 0.50000 0.00000 0.00000 0.01270

Ba 8c .3. 0.52897 0.25126 0.25126 0.25126 0.01270

Ba 8c .3. 0.82462 0.37543 0.37543 0.37543 0.01270

Ba 24d 1 0.89095 0.12767 0.37353 0.12316 0.01270

Ba 24d 1 0.78915 0.37121 0.37647 0.12617 0.01270

Fe 24d 1 0.89987 0.25225 -0.00517 -0.00019 0.01270

Fe 24d 1 1.27131 0.24902 0.24418 -0.00322 0.01270

O 24d 1 1.29670 0.27413 0.11091 0.01235 0.01270

O 24d 1 2.05405 0.48665 0.12833 0.25334 0.01270

O 24d 1 0.74370 0.23381 0.33620 0.13170 0.01270

O 24d 1 0.22811 0.43551 0.28525 0.01270

47

O 24d 1 2.06623 0.35669 -0.00251 0.01393 0.01270

O 24d 1 2.26942 0.13222 -0.01231 -0.01094 0.01270

Phase: 3 - BaFe2O4



Phase data


Cell

a=19.2787 Å b=5.4314 Å c=8.4396 Å

a/b=3.5495 b/c=0.6436 c/a=0.4378

V=883.72 Å3

Atomic parameters


Ba 4 0.13070 0.25000 0.00000 0.01270

Ba 4 0.61730 0.22700 0.00000 0.01270

Fe 8 0.50000 0.04240 0.73200 0.27760 0.01270

Fe 8 0.50000 0.20840 0.77400 0.29130 0.01270

O 8 0.50000 0.03700 0.40300 0.24300 0.01270

O 8 0.50000 0.12300 0.91700 0.22500 0.01270

O 8 0.50000 0.20900 0.41700 0.28100 0.01270

O 4 0.45300 0.22600 0.00000 0.01270

O 4 0.28000 0.22600 0.00000 0.01270


48

Sample Sintered at #4 (900° C)





Phase data


Cell

a=5.8927 Å c=23.2097 Å

c/a=3.9388

V=697.95 Å3

Atomic parameters


Ba +2 2d -6m2 0.66667 0.33333 0.25000 0.00930

Fe +3 2a -3m. 1.13704 0.00000 0.00000 0.00000 0.00840

Fe +3 2b -6m2 0.94186 0.00000 0.00000 0.25027 0.00520

Fe +3 4f 3m. 1.01744 0.33333 0.66667 0.02868 0.00320

Fe +3 4f 3m. 1.16653 0.33333 0.66667 0.19152 0.00760

Fe +3 12k .m. 0.93037 0.16877 0.33730 0.89164 0.00610

O -2 4e 3m. 1.17982 0.00000 0.00000 0.15225 0.00600

O -2 4f 3m. 1.01163 0.33333 0.66667 0.94275 0.00680

O -2 6h mm2 1.40670 0.18357 0.36716 0.25000 0.00560

O -2 12k .m. 0.96110 0.16475 0.32925 0.05035 0.00630

O -2 12k .m. 1.06271 0.49655 0.99298 0.14611 0.00600

Phase: 2 - BaFe2O4



Phase data


Cell

a=19.0096 Å b=5.3973 Å c=8.4821 Å

a/b=3.5221 b/c=0.6363 c/a=0.4462

V=870.27 Å3

Atomic parameters


Ba1 4 0.13070 0.25000 0.00000 0.03590

Ba2 4 1.30716 0.61730 0.22700 0.00000 0.03930

Fe1 8 1.96763 0.04240 0.73200 0.27760 0.09300

Fe2 8 1.31198 0.20840 0.77400 0.29130 0.04200

O1 8 1.85124 0.03700 0.40300 0.24300 0.00130

O2 8 0.68871 0.12300 0.91700 0.22500 0.00130

O3 8 1.25689 0.20900 0.41700 0.28100 0.00130

O4 4 0.31543 0.45300 0.22600 0.00000 0.02440

O5 4 3.39807 0.28000 0.22600 0.00000 0.05480

49

Phase: 3 - Fe2O3

Bragg R-factor : 7.15 Vol: 295.448 Fract(%): 1


Phase data


Cell

a=4.9776(1) Å c=13.7694(0) Å

c/a=2.7663

V=295.45(1) Å3

Atomic parameters


Fe +3 12c 3.0 0.00000 0.00000 0.35530 0.00110

O -2 18e 0.2 0.81256 0.33032 0.00000 0.25000 -0.03920


50

Sample Sintered at #5 (800° C)





Phase data


Cell

a=5.8906 Å c=23.2093 Å

c/a=3.9401

V=697.44 Å3

Atomic parameters


Ba +2 2d -6m2 0.66667 0.33333 0.25000 0.00930

Fe +3 2a -3m. 1.09325 0.00000 0.00000 0.00000 0.00840

Fe +3 2b -6m2 1.17956 0.00000 0.00000 0.25027 0.00520

Fe +3 4f 3m. 1.12302 0.33333 0.66667 0.02872 0.00320

Fe +3 4f 3m. 1.25546 0.33333 0.66667 0.19257 0.00760

Fe +3 12k .m. 1.02133 0.16313 0.32604 0.89065 0.00610

O -2 4e 3m. 1.42708 0.00000 0.00000 0.15777 0.00600

O -2 4f 3m. 1.08383 0.33333 0.66667 0.94588 0.00680

O -2 6h mm2 1.63757 0.18002 0.36003 0.25000 0.00560

O -2 12k .m. 1.00876 0.15616 0.31204 0.04811 0.00630

O -2 12k .m. 1.16204 0.47897 0.95788 0.14526 0.00600

Phase: 2 - BaFe2O4



Phase data


Cell

a=19.0160 Å b=5.3845 Å c=8.4579 Å

a/b=3.5316 b/c=0.6366 c/a=0.4448

V=866.02 Å3

Atomic parameters


Ba1 4 0.13070 0.25000 0.00000 0.03590

Ba2 4 1.60329 0.61730 0.22700 0.00000 0.03930

Fe1 8 1.48709 0.04240 0.73200 0.27760 0.09300

Fe2 8 1.08157 0.20840 0.77400 0.29130 0.04200

O1 8 0.55106 0.03700 0.40300 0.24300 0.00130

O2 8 1.09566 0.12300 0.91700 0.22500 0.00130

O3 8 1.52934 0.20900 0.41700 0.28100 0.00130

O4 4 0.20305 0.45300 0.22600 0.00000 0.02440

O5 4 3.23005 0.28000 0.22600 0.00000 0.05480

51

Phase: 3 - Fe2O3



Phase data


Cell

a=5.0353 Å c=13.7445 Å

c/a=2.7296

V=301.79 Å3

Atomic parameters


Fe +3 12c 3.0 0.00000 0.00000 0.35530 0.00110

O -2 18e 0.2 0.81256 0.33032 0.00000 0.25000 -0.03920


52



This section presents the Rietveld refinement results of barium iron oxide samples

with Fe:Ba = 7 Refinement method. XRD patterns of the samples sintered at different

temperatures (3.17 – 3.21) indicated the existence of the phases observed in the patterns

of the sample with Fe:Ba = 9, which evolve with increasing the sintering temperature in

a similar fashion. Although the stoichiometry of this sample is identical to that oy the T-

type hexaferrite, the Y-type phase was not observed in the range of sintering temperature

up to 1200° C. Table (3.2) summarizes the phases that were formed in the samples

sintered at different temperaturess.


53



54


55


56

Table (3.2) Structural phases existing in the samples with Fe:Ba = 7 sintered at different

temperatures

Sample's Phases in the sample

Cent. Tem. Phase #1 Phase #2 Phase #3 Phase #4

1200° C Ba Fe12 O19 Ba3 Fe2 O6



900° C Ba Fe12 O19 Ba3 Fe2 O6 Ba Fe2 O4 Fe2 O3


The main structural information for the various phases in all samples were

obtained from Rietveld refinement of the diffraction patterns. Specifically, the types of

phases, their structural parameters and relative proportion (as weight ratio) in each

sample are presented below.






Phase data


Cell

a=5.9044(0) Å c=23.3217 Å

c/a=3.9499

V=704.12(0) Å3

Atomic parameters


Ba +2 2d -6m2 0.66667 0.33333 0.25000 0.00930

Fe +3 2a -3m. 0.92928 0.00000 0.00000 0.00000 0.00840

Fe +3 2b -6m2 0.88158 0.00000 0.00000 0.25027 0.00520

Fe +3 4f 3m. 0.96875 0.33333 0.66667 0.02743 0.00320

Fe +3 4f 3m. 1.15666 0.33333 0.66667 0.19039 0.00760

Fe +3 12k .m. 0.99753 0.16744 0.33475 0.89260 0.00610

O -2 4e 3m. 1.02056 0.00000 0.00000 0.15183 0.00600

O -2 4f 3m. 1.02097 0.33333 0.66667 0.94413 0.00680

O -2 6h mm2 1.18503 0.17905 0.35813 0.25000 0.00560

O -2 12k .m. 1.15159 0.14913 0.29810 0.04955 0.00630

O -2 12k .m. 1.16886 0.50535 1.01076 0.14843 0.00600

Phase: 2 - Ba3Fe2O6


57


Phase data


Cell a=16.7549 Å

V=4703.59 Å3

Atomic parameters


Ba 4a .-3. 0.00000 0.00000 0.00000 0.01270

Ba 4b .-3. 1.33436 0.50000 0.00000 0.00000 0.01270

Ba 8c .3. 0.86081 0.25126 0.25126 0.25126 0.01270

Ba 8c .3. 0.87730 0.37543 0.37543 0.37543 0.01270

Ba 24d 1 1.06391 0.12767 0.37353 0.12316 0.01270

Ba 24d 1 0.81046 0.37121 0.37647 0.12617 0.01270

Fe 24d 1 1.60953 0.25225 -0.00517 -0.00019 0.01270

Fe 24d 1 1.93737 0.24902 0.24418 -0.00322 0.01270

O 24d 1 1.51483 0.27413 0.11091 0.01235 0.01270

O 24d 1 2.74642 0.48665 0.12833 0.25334 0.01270

O 24d 1 1.53847 0.23381 0.33620 0.13170 0.01270

O 24d 1 0.22811 0.43551 0.28525 0.01270

O 24d 1 2.81339 0.35669 -0.00251 0.01393 0.01270

O 24d 1 2.86388 0.13222 -0.01231 -0.01094 0.01270






Phase data


Cell

a=5.9020 Å c=23.2905 Å

c/a=3.9462

V=702.60 Å3

Atomic parameters


Ba +2 2d -6m2 0.66667 0.33333 0.25000 0.00850

Fe +3 2a -3m. 0.94418 0.00000 0.00000 0.00000 0.00640

Fe +3 2b -6m2 0.94797 0.00000 0.00000 0.25027 0.00860

Fe +3 4f 3m. 0.91769 0.33333 0.66667 0.02648 0.00240

Fe +3 4f 3m. 1.03832 0.33333 0.66667 0.18970 0.00970

Fe +3 12k .m. 0.99495 0.17061 0.34131 0.89239 0.00590

O -2 4e 3m. 0.83207 0.00000 0.00000 0.15348 0.01460

O -2 4f 3m. 0.80416 0.33333 0.66667 0.94427 0.00020

O -2 6h mm2 0.99748 0.17085 0.34180 0.25000 0.00830

58

O -2 12k .m. 1.07742 0.15136 0.30269 0.05053 0.00790

O -2 12k .m. 1.04494 0.50146 1.00287 0.15073 0.00490

Phase: 2 - Ba3Fe2O6



Phase data


Cell a=16.7554 Å

V=4704.01 Å3

Atomic parameters


Ba 4a .-3. 0.00000 0.00000 0.00000 0.01270

Ba 4b .-3. 1.20223 0.50000 0.00000 0.00000 0.01270

Ba 8c .3. 0.85908 0.25126 0.25126 0.25126 0.01270

Ba 8c .3. 0.91162 0.37543 0.37543 0.37543 0.01270

Ba 24d 1 1.08585 0.12767 0.37353 0.12316 0.01270

Ba 24d 1 0.80188 0.37121 0.37647 0.12617 0.01270

Fe 24d 1 1.59528 0.25225 -0.00517 -0.00019 0.01270

Fe 24d 1 2.05427 0.24902 0.24418 -0.00322 0.01270

O 24d 1 1.48222 0.27413 0.11091 0.01235 0.01270

O 24d 1 2.52070 0.48665 0.12833 0.25334 0.01270

O 24d 1 1.35894 0.23381 0.33620 0.13170 0.01270

O 24d 1 0.22811 0.43551 0.28525 0.01270

O 24d 1 2.87102 0.35669 -0.00251 0.01393 0.01270

O 24d 1 3.08094 0.13222 -0.01231 -0.01094 0.01270

Phase: 3 - BaFe2O4



Phase data


Cell

a=18.8592 Å b=5.3793 Å c=8.5524 Å

a/b=3.5059 b/c=0.6290 c/a=0.4535

V=867.64 Å3

Atomic parameters


Ba1 4 0.13070 0.25000 0.00000 0.03590

Ba2 4 1.61333 0.61730 0.22700 0.00000 0.03930

Fe1 8 1.53576 0.04240 0.73200 0.27760 0.09300

Fe2 8 1.11697 0.20840 0.77400 0.29130 0.04200

O1 8 0.56909 0.03700 0.40300 0.24300 0.00130

O2 8 1.13152 0.12300 0.91700 0.22500 0.00130

O3 8 1.57939 0.20900 0.41700 0.28100 0.00130

O4 4 0.20970 0.45300 0.22600 0.00000 0.02440

O5 4 3.33576 0.28000 0.22600 0.00000 0.05480

59



60






Phase data


Cell

a=5.8974 Å c=23.2364 Å

c/a=3.9401

V=699.87 Å3

Atomic parameters


Ba +2 2d -6m2 0.66667 0.33333 0.25000 0.00850

Fe +3 2a -3m. 1.03977 0.00000 0.00000 0.00000 0.00640

Fe +3 2b -6m2 1.05044 0.00000 0.00000 0.25027 0.00860

Fe +3 4f 3m. 0.91562 0.33333 0.66667 0.02689 0.00240

Fe +3 4f 3m. 1.02764 0.33333 0.66667 0.18981 0.00970

Fe +3 12k .m. 0.98561 0.17127 0.34262 0.89152 0.00590

O -2 4e 3m. 0.93744 0.00000 0.00000 0.15949 0.01460

O -2 4f 3m. 0.89282 0.33333 0.66667 0.94268 0.00020

O -2 6h mm2 1.01164 0.16905 0.33817 0.25000 0.00830

O -2 12k .m. 0.98173 0.14337 0.28669 0.05051 0.00790

O -2 12k .m. 0.88862 0.50519 1.01028 0.14927 0.00490

Phase: 2 - Ba3Fe2O6



Phase data


Cell a=16.7484 Å

V=4698.07 Å3

Atomic parameters


Ba 4a .-3. 0.00000 0.00000 0.00000 0.01270

Ba 4b .-3. 1.27461 0.50000 0.00000 0.00000 0.01270

Ba 8c .3. 0.96526 0.25126 0.25126 0.25126 0.01270

Ba 8c .3. 0.90447 0.37543 0.37543 0.37543 0.01270

Ba 24d 1 1.13565 0.12767 0.37353 0.12316 0.01270

Ba 24d 1 0.87055 0.37121 0.37647 0.12617 0.01270

Fe 24d 1 1.50400 0.25225 -0.00517 -0.00019 0.01270

Fe 24d 1 2.28632 0.24902 0.24418 -0.00322 0.01270

O 24d 1 1.66998 0.27413 0.11091 0.01235 0.01270

O 24d 1 2.25407 0.48665 0.12833 0.25334 0.01270

O 24d 1 1.34105 0.23381 0.33620 0.13170 0.01270

61

O 24d 1 0.22811 0.43551 0.28525 0.01270

O 24d 1 3.29267 0.35669 -0.00251 0.01393 0.01270

O 24d 1 3.68900 0.13222 -0.01231 -0.01094 0.01270

Phase: 3 - BaFe2O4



Phase data


Cell

a=18.8825 Å b=5.3663 Å c=8.5631 Å

a/b=3.5187 b/c=0.6267 c/a=0.4535

V=867.68 Å3

Atomic parameters


Ba1 4 0.13070 0.25000 0.00000 0.03590

Ba2 4 1.61333 0.61730 0.22700 0.00000 0.03930

Fe1 8 1.53576 0.04240 0.73200 0.27760 0.09300

Fe2 8 1.11697 0.20840 0.77400 0.29130 0.04200

O1 8 0.56909 0.03700 0.40300 0.24300 0.00130

O2 8 1.13152 0.12300 0.91700 0.22500 0.00130

O3 8 1.57939 0.20900 0.41700 0.28100 0.00130

O4 4 0.20970 0.45300 0.22600 0.00000 0.02440

O5 4 3.33576 0.28000 0.22600 0.00000 0.05480


62






Phase data


Cell

a=5.8941 Å c=23.2194 Å

c/a=3.9394

V=698.58 Å3

Atomic parameters


Ba +2 2d -6m2 0.66667 0.33333 0.25000 0.00850

Fe +3 2a -3m. 1.12500 0.00000 0.00000 0.00000 0.00640

Fe +3 2b -6m2 1.04400 0.00000 0.00000 0.25030 0.00860

Fe +3 4f 3m. 0.93400 0.33333 0.66667 0.02740 0.00240

Fe +3 4f 3m. 1.10600 0.33333 0.66667 0.19010 0.00970

Fe +3 12k .m. 1.03700 0.16880 0.33770 0.89250 0.00590

O -2 4e 3m. 0.96100 0.00000 0.00000 0.16340 0.01460

O -2 4f 3m. 1.10700 0.33333 0.66667 0.94390 0.00020

O -2 6h mm2 0.99900 0.17910 0.35820 0.25000 0.00830

O -2 12k .m. 1.01000 0.15750 0.31510 0.04650 0.00790

O -2 12k .m. 0.93900 0.51240 1.02460 0.14730 0.00490

Phase: 2 - Ba3Fe2O6



Phase data


Cell a=16.6794 Å

V=4640.25 Å3

Atomic parameters


Ba 4a .-3. 0.00000 0.00000 0.00000 0.01270

Ba 4b .-3. 2.26600 0.50000 0.00000 0.00000 0.01270

Ba 8c .3. 1.07500 0.25370 0.25370 0.25370 0.01270

Ba 8c .3. 1.07300 0.37700 0.37700 0.37700 0.01270

Ba 24d 1 1.08900 0.12770 0.37350 0.12320 0.01270

Ba 24d 1 1.24000 0.37120 0.37650 0.12620 0.01270

Fe 24d 1 1.60200 0.25220 -0.00520 -0.00020 0.01270

Fe 24d 1 2.77600 0.24900 0.24420 -0.00320 0.01270

O 24d 1 1.09200 0.27410 0.11090 0.01240 0.01270

O 24d 1 1.48700 0.48660 0.12830 0.25330 0.01270

O 24d 1 1.58400 0.23380 0.33620 0.13170 0.01270

63

O 24d 1 0.22810 0.43550 0.28530 0.01270

O 24d 1 3.30300 0.35670 -0.00250 0.01390 0.01270

O 24d 1 4.80100 0.13220 -0.01230 -0.01090 0.01270

Phase: 3 - BaFe2O4



Phase data


Cell

a=18.9739 Å b=5.3879 Å c=8.4986 Å

a/b=3.5216 b/c=0.6340 c/a=0.4479

V=868.81 Å3

Atomic parameters


Ba1 4 0.13070 0.25000 0.00000 0.03590

Ba2 4 1.58200 0.61730 0.22700 0.00000 0.03930

Fe1 8 1.94700 0.04240 0.73200 0.27760 0.09300

Fe2 8 1.18800 0.20840 0.77400 0.29130 0.04200

O1 8 0.08400 0.03700 0.40300 0.24300 0.00130

O2 8 1.47700 0.12300 0.91700 0.22500 0.00130

O3 8 1.28000 0.20900 0.41700 0.28100 0.00130

O4 4 0.62100 0.45300 0.22600 0.00000 0.02440

O5 4 3.33900 0.28000 0.22600 0.00000 0.05480

Phase: 4 - Fe2O3



Phase data


Cell

a=4.9790 Å c=13.8068 Å

c/a=2.7730

V=296.42 Å3

Atomic parameters


Fe +3 12c 3.0 0.00000 0.00000 0.35530 0.00110

O -2 18e 0.2 0.81300 0.33030 0.00000 0.25000 -0.03920

64



65






Phase data


Cell

a=5.8889 Å c=23.1999 Å

c/a=3.9396

V=696.76 Å3

Atomic parameters


Ba +2 2d -6m2 0.66667 0.33333 0.25000 0.00930

Fe +3 2a -3m. 1.20140 0.00000 0.00000 0.00000 0.00840

Fe +3 2b -6m2 1.29113 0.00000 0.00000 0.25027 0.00520

Fe +3 4f 3m. 1.15354 0.33333 0.66667 0.03134 0.00320

Fe +3 4f 3m. 1.25823 0.33333 0.66667 0.19511 0.00760

Fe +3 12k .m. 1.01496 0.16420 0.32819 0.89023 0.00610

O -2 4e 3m. 2.15753 0.00000 0.00000 0.15834 0.00600

O -2 4f 3m. 0.93868 0.33333 0.66667 0.95571 0.00680

O -2 6h mm2 1.86075 0.14504 0.29004 0.25000 0.00560

O -2 12k .m. 1.17398 0.14676 0.29331 0.04655 0.00630

O -2 12k .m. 1.12895 0.46730 0.93449 0.13989 0.00600

Phase: 2 - BaFe2O4



Phase data


Cell

a=19.008(2) Å b=5.3822(8) Å c=8.4532(9) Å

a/b=3.5316 b/c=0.6367 c/a=0.4447

V=864.80(18) Å3

Atomic parameters


Ba1 4 0.13070 0.25000 0.00000 0.03590

Ba2 4 1.40000 0.61730 0.22700 0.00000 0.03930

Fe1 8 1.33838 0.04240 0.73200 0.27760 0.09300

Fe2 8 1.08378 0.20840 0.77400 0.29130 0.04200

O1 8 0.96162 0.03700 0.40300 0.24300 0.00130

O2 8 0.41405 0.12300 0.91700 0.22500 0.00130

O3 8 1.40000 0.20900 0.41700 0.28100 0.00130

O4 4 0.45300 0.22600 0.00000 0.02440

O5 4 3.11000 0.28000 0.22600 0.00000 0.05480

66

Phase: 3 - Fe2O3



Phase data


Cell

a=5.0336 Å c=13.7384 Å

c/a=2.7293

V=301.46 Å3

Atomic parameters


Fe +3 12c 3.0 0.00000 0.00000 0.35714 0.00110

O -2 18e 0.2 0.84102 0.33333 0.00000 0.25000 -0.03920

67

CHAPTER 4

Analysis and

Discussion

4.1 Non-stoichiometric barium hexaferrite samples

with Fe:Ba ratio ≥ 11.5





68

4.1 Non-stoichiometric barium hexaferrite samples with Fe:Ba ratio

≥ 11.5

In this section the results of the structural refinement for the system with Fe:Ba ratio

ranging from 11.5 – 16.16 are discussed. The relative diffracted intensity for the evolving

α-Fe2O3 (hematite) phase with increasing (Fe:Ba) ratio was used to determine the weight

ratio of the secondary hematite phase in the sample. In addition, a relation between the

weight ratio of the hematite phase and the starting Fe:Ba ratio was established, from

which the optimal ratio required for the synthesis of a pure hexaferrite phase was

determined. A summary of crystallographic information is also included, and the unit cell

of each crystallographic phase is constructed from the refined crystallographic

parameters.

As it has been shown in the previous chapter, the process of Rietveld refinement

revealed full structural information and the relative proportions of iron oxide (α-Fe2O3)

and BaM phases in each sample. Figure (4.1) shows the diffraction patterns of all samples

added with different amounts of α-Fe2O3. The figure demonstrates the evolution of the

structural peaks corresponding to α-Fe2O3 (shaded in yellow) as a function of the weight

ratio of hematite added to the original powder (Fe:Ba = 11.5). The integrated intensities

Iα and IBaM of all structural peaks of α-Fe2O3 and BaFe12O19 phases, respectively, and the

ratio of these intensities for each sample are summarized in Table (4.1).

69

Figure (4.1) XRD patterns of all samples added with different amounts of α-Fe2O3. The

main structural peaks of iron oxide phase are shaded in yellow.

70

Table (4.1) The integrated intensity of all structural peaks of BaM (IBaM) and of

α-Fe2O3 (Iα), and the ratio (Iα/IBaM) for the samples with different Fe:Ba ratio.

The percentage ratio associated with the Fe:Ba ratio represents the wt% of α-

Fe2O3 added to the original powder

Fe:Ba => 16.158

(25%)

14.993

(20%)

13.966

(15%)

13.053

(10%)

12.236

(5%)

11.500

(0%)

IBaM 1234.7 1368.9 1408.9 1727.3 1626.3 1661.8

Iα 265.8 209.2 146 80.7 37.1 0

Iα/IBaM (%) 21.53 15.28 10.36 4.67 2.28 0

Figure (4.2) A plot of Iα/IBaM (%) vs Fe:Ba ratio for all samples

Figure 4.2 demonstrates a linear variation of the relative integrated intensity of α-Fe2O3

with increasing Fe:Ba ratio. The linear fit to the data gave a slope of 5.208 and an

intercept of 62.701. These values can be used to determine an approximate value (based

on integrated intensity) of the optimal Fe:Ba ratio for fabricating single BaM phase with

71

no additional iron oxide phase. The results indicates that the optimal value of Fe:Ba ratio

is 12.039.

The ratio of the secondary iron oxide phase in each sample can also be determined by

investigating the integrated intensities of the main peaks of the phases. Table (4.2) shows

the integrated intensity of the main peak of BaM at 34.1° (IMB) and that of α-Fe2O3 located

at 33.15° (IMα), as well as the ratio of the intensities of these peaks. Figure 4.3 shows the

relative intensity of the main peak of α-Fe2O3 as a function of Fe:Ba ratio. Linear fit to

the data gave a slope of 9.0535 and an intercept of 109.565. From these values the optimal

Fe:Ba ratio for a single BaM phase was found to be 12.102. This value is close to that

obtained from the whole-pattern integrated intensity analysis, and to the stoichiometric

composition of 12.0 for M-type hexaferrite. Further, Figure 4.3 can be used to determine

the weight ratio of α-Fe2O3 phase in any hexaferrite sample by evaluating the relative

intensity of the main peak and determining the corresponding Fe:Ba ratio, which can be

subsequently converted into wt% of the α-Fe2O3 phase using the molecular weights of the

phases and standard calculations.

Table (4.2) The integrated intensities of the main peaks of BaM (IMB), α-Fe2O3 (IMα), and

the peak ratios of the two phases for all samples. The percentage ratio associated with the

Fe:Ba ratio represents the wt% of α-Fe2O3 added to the original powder

angle

Fe:Ba ratio

16.158 14.993 13.966 13.053 12.236 11.5

-25% -20% -15% -10% -5% 0%

IMB 34.1 187.1 208.9 212 266.2 248.6 267.9

IMα 33.15 69.2 53.5 37.1 21 4 0

IMα/ IMB (%) 37 25.6 17.5 7.9 1.6 0

72

Figure (4.3) A plot of IMα/IMB (%) vs Fe:Ba ratio for all samples

The weight ratios of the different structural phases in a given sample can be

evaluated using Reitveld fitting of the corresponding diffraction pattern. The wt% of α-

Fe2O3 phase for each sample as determined by the fitting routine is listed in Table 4.3.

These values are generally lower than the wt% of α-Fe2O3 added to the original powder

(with Fe:Ba = 11.5), which indicates that the Fe:Ba ratio required for the synthesis of a

single BaM phase is higer than 11.5, a result consistent with the optimal ratio determined

by the analyses associated with Figure 4.2. Figure 4.4 shows the variation of the relative

main peak intensity of α-Fe2O3 with the weight ratio of this phase in each sample as

determined from Reitveld refinement of the corresponding diffraction pattern. The wt%

of α-Fe2O3

73

Table (4.3) α-Fe2O3 α-Fe2O3 wt% determined from Rietveld refinement of the

diffraction patterns and the corresponding relative main peak integrated intensity.

Sample 25% 20% 15% 10% 5% 0%

α-Fe2O3 wt% 25.01 19.53 14.59 7.50 3.53 0.00

IMα/ IMB (%) 37.00 25.60 17.50 7.90 1.60 0.00

The quantitative analysis parameters belonging to the impurity α-Fe2O3 phase were left

to be generated automatically in the refinement process of the sample added with 5 wt%

α-Fe2O3 to get better results. This is because the phase peaks are weak, approaching the

background fluctuations, so that the X-Ray absorption contrast cannot play a proper role

in this calculation. J. Berar [55] and R. Hill [56] for Standard deviations multiplication

factor (correlated residuals) during the fitting process.

Figure (4.4) A plot of IMα/IMB (%) as a function of α-Fe2O3 wt% evaluated from

the refinement of the patterns of all samples

74

The optimum ratio for synthesizing pure sample of barium hexaferrite (BaFe12O19)

can be obtained from the experimental result by linearly fitting the Fe:Ba ratio of the

prepared samples with the α-Fe2O3 wt% obtained from Rietveld refinement (Figure 4.6).

The best straight line representing the data intercepts the Fe:Ba ratio axis at 11.6, which

is the refined optimum ratio for a single barium hexaferrite phase. This value is somewhat

higher than 11.5 as predicted in the above discussion, but is lower than the value obtaind

from analysis of the integrated intensities.

Figure (4.5) Linear fit of Fe:Ba ratio vs α-Fe2O3 wt% obtained from the refinement of

the diffraction patterns.

Our refined patterns with rather low Chi-squared values gave valuable information

on the crystal structure and relative proportions of α-Fe2O3 α-Fe2O3 secondary phase.

Figure (4.6) shows the calculated pattern of our hexaferrite sample with Fe:Ba = 11.5,

together with standard patterns available in the ICDD library [57 , 58].

75

Figure (4.6) the calculated XRD stick pattern for BaFe12O19 phase compared with other

standard patterns in ICDD library.

All the data needed to build up the structural model of the unit cell is now available.

Since there is no difference in the crystallographic structure of the phases in samples

prepared with different stoichiometries as can be clearly seen from the results of the

refinement, the structural data of the sample with Fe:Ba = 11.5 was used to construct the

unit cell. Figures 4.7 and 4.8 show the unit cell from different angles as can be noted from

the direction of the unit cell vectors in each snapshot.

76

Figure (4.7) the crystal structure of BaFe12O19 unit cell in 3D.

Figure (4.8) the crystal structure of Fe2O3 unit cell in a 3D.

77

Figure (4.9) shows a two-dimensional cross-section of the barium hexaferrite unit

cell of the samples with Fe:Ba = 11.5 and 16.158 (in yellow and red colors), overlapped

over each other to check if there are structural differences in the two extreme samples. It

is obvious from this figure that no structure structural differences are apparent in the two

samples.

Figure (4.9) Compression of tow barium hexaferrite structures, samples zero and

twenty-five percent.

The chemical composition for our barium hexaferrite phase was determined by

XRD quantitative analysis using Rietveld refinement, and was found to be

BaFe11.896O19.812 which is very close to the theoretical composition. In addition, our

refined composition is in good agreement with the formula BaFe11.80O19.46 reported by

Sozeriet et al. [37].

78

4.2 Non-stoichiometric barium hexaferrite samples with Fe:Ba ratio

= 9

This section is concerned with the results of the structural analysis of samples of non-

stoichiometric ferrites with Fe:Ba 9 sintered at different temperatures. The phases

present in each sample were identified, and their evolution with temperature was

investigated. The crystallographic information derived from the structural refinement

was used to construct the unit cell for each phase.

A preliminary look at the XRD patterns of the samples of this system indicated the

evolution trends of the impurity phases with sintering temperature. Barium spinel

(BaFe2O4) and α-Fe2O3 were observed at T ≤ 900°C. At higher temperatures, these phases

disappear almost completely, and a new high-temperature phase (Ba3Fe2O6) evolves. The

appearance of barium spinel phase was expected in barium rich sample [36], and the

coexistence of this phase with α-Fe2O3 phase at low sintering temperatures indicated that

these are intermediate phases resulting from incomplete reaction at such low

temperatures. Figure 4.10 shows a highlight of the main peaks for each phase and their

evolution with the sintering temperature. In this figure the main peaks of each phase were

highlighted in a unique color, the iron oxide (α-Fe2O3) was highlighted in yellow, the

barium spinel (BaFe2O4) in blue, and the barium iron oxide (Ba3Fe2O6) in green.

79

Figure (4.10) XRD patterns samples with Fe:Ba of 9 sintered at different temperatures.

α-Fe2O3 was highlighted in yellow, the barium spinel (BaFe2O4) in blue, and the barium

iron oxide (Ba3Fe2O6) in green.

80

Quantitative analysis of the patterns of the samples sintered at different

temperatures was performed to obtain the relative proportions of the different phases in

each sample, and to establish some sort of a phase diagram for barium iron oxide with

Fe:Ba = 9. Table (4.4) shows the wt% of each phase in each sample, and the Figure (4.11)

shows the phases and their relative proportions as a function of sintering temperature.

This figure demonstrates that the barium iron oxide phase (Ba3Fe2O6) is a high-

temperature phase, which appears in barium rich samples (Fe:Ba < 12). On the other hand,

the barium spinel (BaFe2O4) is a low-temperature phase. This phase appears in large

quantities in samples sintered at temperatures below 900° C, and diminishes with

increasing sintering temperature until it disappears completely at 1200° C. Our results

indicate that the reaction of α-Fe2O3 to form other barium-iron oxides is completed at

sintering temperature of 1000° C, beyond which the relative abundances of BaFe12O19

and Ba3Fe2O6 seem to stabilize. The unit cell and other structural information on each

phase are summarized in Table 4.5.

Table (4.4) the calculated ratios for each phase according to the sintering temperature.

Ba:Fe ratio = 1:9

Sintering T° BaFe12O19 BaFe2O4 Ba3Fe2O6 α-Fe2O3

1200 C° 93.79% 0.00% 6.21% 0.00%

1100 C° 92.35% 1.52% 6.13% 0.00%

1000 C° 92.35% 1.53% 6.12% 0.00%

900 C° 90.43% 9.57% 0.00% 1.00%

800 C° 55.59% 28.39% 0.00% 16.02%

81

Figure (4.11) a schematic representation for each phase calculated ratios according to

the sintering temperature, Fe:Ba ratio =9.

Table (4.5) the total sites multiplicity and the unit cell volume of each phase at 1000° C

sintering temperature.

Unit Cell Number

Phase volume (Å3) tot. mult. of Sites

BaFe12O19 698.6 64 11

BaFe2O4 868.8 56 9

Ba3Fe2O6 4640.2 272 14

α-Fe2O3 296.4 30 2

Figure (4.12) shows the calculated pattern of the barium iron oxide (Ba3Fe2O6)

phase which appeared. Also Figure (4.13) shows the comparison between this pattern and

another one indexed in the ICDD library [59]. Figure (4.2.5) also shows the calculated

barium spinel pattern compared to other indexed ICDD patterns [60 – 61].

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

70.00%

80.00%

90.00%

100.00%

800 900 1000 1100 1200

System 2 – Ba:Fe ratio = 1:9

BaFe12O19 BaFe2O4 Ba3Fe2O6 α-Fe2O3

82

Figure (4.12) the XRD stick pattern of barium iron oxide (Ba3Fe2O6) phase.

Figure (4.13) the calculated XRD stick pattern for Ba3Fe2O6 phase compared with other

standard pattern in ICDD library.

That the barium iron oxide (Ba3Fe2O6) is a complicated structure as it became clear

during the data refinement. Refinement of this pattern is time-consuming, where a

refinement step for this structure takes about five seconds of calculation, whereas the rest

of the phases combined take about just one second of calculation in each step.

The data also show that the unit cell volume is temperature dependent, where in

general, increasing the sintering temperature leads to an increase in the unit cell volume.

Table (4.6) shows the cell volume of the barium hexaferrite and barium iron oxide

(Ba3Fe2O6) at different sintering temperatures.

83

Figure (4.14) the calculated XRD stick pattern for BaFe2O4 phase compared with

other standard patterns in ICDD library.

Table (4.6) the unit cell volume at each sintering degree.

Sintering Temp. => 1200 C° 1100 C° 1000 C° 900 C° 800 C°

BaFe12O19 volume (Å3) 702.056 699.947 697.834 697.946 697.436

Ba3Fe2O6 volume (Å3) 4699.908 4699.897 4682.433 4640.244

From Table (4.9), the barium hexaferrite formed at low temperature with unit cell

volume about (697 Å3). Increasing the sintering temperature above 1000° C seems to

result in an increase of the unit cell volume. On the other hand, the unit cell volume of

Ba3Fe2O6 seems to stabilize at the maximum value of 4699 Å3 in samples sintered at

temperatures T ≥ 1100° C. This value is only about 0.1% higher than that (4694.37 Å3)

reported by Montorsi et al. [59]. At lower sintering temperatures, the cell volume is

smaller, and seems to decrease with decreasing sintering temperature.

Figure (4.15) and (4.16) shows he barium spinel (BaFe2O4) and the barium iron

oxide (Ba3Fe2O6),derived from the refinement output.

84

Figure (4.15) the crystal structure of Ba3Fe2O6 unit cell in 3D.

Figure (4.16) the crystal structure of BaFe2O4 unit cell in 3D.

It was hard to notice significant difference between the atomic positions in the

barium hexaferrite lattice of samples sintered at different temperatures. However, there is

a slight noticeable difference (a slight cell deformation) when comparing the samples

sintered at 800° C and 1200° C. Figure (4.17) shows overlapped cross sections of the

barium hexaferrite unit cell for the samples sintered at 800° C (yellow) and 1200° C

(green).

85

Figure (4.17) Compression of tow barium hexaferrite structures sintered at 800° &

1200° C.

4.3 Non-stoichiometric barium hexaferrite samples samples with

Fe:Ba ratio = 7

This section is concerned with the results of the structural analysis of samples of

non-stoichiometric ferrites with iron to barium ratio of 7 sintered at different

temperatures. The phases present in each sample were identified, and their evolution with

temperature was investigated.

Five discs of the powder sample were prepared and sintered at different

temperatures ranging from 800° to 1200° C. The XRD paterns (Figure 4.18) show the

presence of the phases observed in the previous sample with Fe:Ba = 9. The main peaks

for each phase were highlighted in diffirent color, the iron oxide (α-Fe2O3) in yellow, the

barium spinel (BaFe2O4) in blue and the barium iron oxide (Ba3Fe2O6) in green. The phase

evolution with temperature is similar to that observed in the previous sample. However,

the high-temperature equilibrium ratio of the BaM phase is lower than that observed in

the previous sampe due to the the lower concentration of Fe in this sample. This is obvious

86

since by noticing the Fe:Ba ratio in the two phases, where it is clear that while the

formation of the BaM phase require a high Fe:Ba ratio ( of 12), the formation of the

Ba3Fe2O6 requires a ratio as low as 0.67. Table (4.7) summarizes the wt% of the different

phases in samples sinterd at different temperatures. Also, Figure (4.19) illestrates the

evolution of the different phases with increasing sintering temperature.

Figure (4.18) XRD patterns samples with Fe:Ba of 7 sintered at different temperatures.

α-Fe2O3 was highlighted in yellow, the barium spinel (BaFe2O4) in blue, and the barium

iron oxide (Ba3Fe2O6) in green.

87

Table (4.7) the calculated ratios for each phase according to the sintering temperature.

Ba:Fe ratio = 1:7

Sintering T° BaFe12O19 BaFe2O4 Ba3Fe2O6 α-Fe2O3

1200° C 87.57% 0.00% 12.43% 0.00%

1100° C 87.31% 1.10% 11.59% 0.00%

1000° C 87.29% 1.09% 11.62% 0.00%

900° C 70.14% 24.69% 4.32% 0.85%

800° C 51.52% 39.06% 0.00% 9.42%

Due to the increease of barium relative concentration in the sample with Fe:Ba = 7,

the Ba3Fe2O6 wt% was found to be 12.4% (at 1200° C), to be compared with 6.2%

observed in the sample of Fe:Ba ratio of 9. The extra barium ratio gives the opportunity

to form more barium iron oxide (Ba3Fe2O6) phase which requires more barium than BaM

phase.

88

Figure (4.19) a schematic representation for each phase calculated ratios according to

the sintering temperature, Fe:Ba ratio = 7.

The barium spinel (BaFe2O4) and the iron oxide (α-Fe2O3) phases, almost

disapeared at 1000° C, and the barium iron oxide (Ba3Fe2O6) phase was formed at 900°

C. Also, the proportions of the different phases changed with the increase in barium to

iron ratio. The data show an increase of barium spinel weight ratio, which reached (39%)

compared with (28.4%) observed in the previous sample with Fe:Ba = 9 sintered at 800°

C. This can also be directly attributed to the additional quantity of barium in the sample

with Fe:Ba = 7, since barium spinel phase requires more relative Ba content thanbaM

phase.

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

70.00%

80.00%

90.00%

100.00%

800 900 1000 1100 1200

System 3 - Ba:Fe ratio = (1:7)

BaFe12O19 BaFe2O4 Ba3Fe2O6 α-Fe2O3

89

The previous study shows that the sintering temperature of (1000° C), is the

transformational sintering tempreture, below which the high tempreture phases will tend

to disapear, and above it the intermediate phases will do the same.

In conclusion, the use of low Fe:Ba ratio (lower than 11.5) in preparing M-type

barium hexaferrites results in the development of barium spinel intermediate phase, and

the presence of unreacted α-Fe2O3 at low sintering temperatures. Our results are in good

agreement with the experimental results of Topal et al. [40] who reported the presence of

the intermediate phases in samples with low Fe/Ba ratio.

The barium hexaferrite phase (BaFe12O19) prepared from powders with different

Fe:Ba ratios ranging from 7 to 16.16) was found to have the same structural

characteristics, which are not affected by the presence of other phases in the sample. This

result is in disagreement with the results of Suastiyant et al. who reported a shift in phase

peak positions (and a cchnage in cell parameters) due to the different Fe:Ba ratio that was

used for preparing the precursor material. The only parameter which seems to affect the

charactristics of the structural phases is the sintering temperature, a result which is in full

agreement with the results of Guo et al. [62].

http://www.ncbi.nlm.nih.gov/pubmed?term=Guo%20L%5BAuthor%5D&cauthor=true&cauthor_uid=15348403

90

CHAPTER 5

Conclusions and

Recommendations

91

Conclusions

The structural analysis of the samples consisting of a mixture of M-type barium

hexaferrit (with Fe/Ba ratio of 11.5) and α-Fe2O3 iron oxide revealed the presnece of pure

M-type phase and α-Fe2O3 phase, with no other secondary phases. Also, the structural

properties of the M-type barium hexaferrite phase were found to be independent of the α-

Fe2O3 mass ratio in the mixture. The quantitative analysis using Rietveld refinement for

these samples had shown that the optimum iron-to-barium ratio require to prepare a pure

M-type barium hexaferrite phase is in the range of 11.6 – 12. This work established a

reference scheme for the determination of the mass ratio of iron oxide (α-Fe2O3) impurity

phase in non-stoichiometric hexaferrite compounds.

The structural analyses of non-stoiciometric hexaferrites with Fe:Ba ratio of 9 and

7 prepared by sintering at temperatures ranging between 800° to 1200° C revealed the

presence of different phases, the proportion of which was found to depend critically on

the sintering temperature. Specifically, barium spinel phase (BaFe2O4) and α-Fe2O3

phases were detected at sintering temperatures ≤ 900° C due to incomplete reaction

between these intermediate phases in this temperature regime. At higher temperatures,

these intermediate phases disappear as they fully react, resulting in the appearance of a

new barium ferrite phase (Ba3Fe2O6) due to the excessive amounts of Ba in the samples.

It was shown that the M-type barium hexaferrite structure differed slightly with the

temperature variation. The structural deformation was however slight when the structural

parameters of samples sintered at 800° C and 1200° C were compared. Also, the unit cell

volume of Ba3Fe2O6 Ba3Fe2O6 was found to increase with increasing the sintering

temperature.

92

The particle absorption contrast factor represented by Brindley's coefficient, was

determined for each phase in the barium hexaferrite samples. The refined powder

diffraction pattern for each phase was calculated and the relative abundance of each

structural phase in each sampe was determined.

The structural characteristics of the barium iron oxide (Ba3Fe2O6) phase appearing

in the samples with Fe:Ba = 7 and 9 were fully investigated using Rietveld refinement,

and its whole crystalline information was determined; the cell parameter, Wyckoff

positions, space group, atomic sites, multiplicity...etc. Up to our knowledge, these

structural charcteristics were not previously reported in the literature.

Recommendations for Future Work

In order to determine the exact temperature required for the complete reaction of

intermediate spinel and iron oxide phases and appearance of the new barium ferrite phase

(Ba3Fe2O6), we suggest the preparation and careful structural characterization of samples

with iron to barium ratio of 9 and sintering temperatures in the range 900° C – 1000° C.

Further, the present approach of the structural analyses of non-stoichiometric

barium hexaferrites can be applied to other systems with different impurity phases and

structural properties. The impurity phases and their relative abundances can be

determined quantitatively by following the steps developed in this thesis.

93

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100

تحليل التركيب البلوري لمركبات الفرايت السداسي

إعداد

يزن مسودة

المشرف

األستاذ الدكتور سامي محمود

ملخــــــــص

الجوهر الرئيسيييييه للدر ال ياضييييي لتحيييييلب اه التركيا اللحدئه للردلدي الر ل السييييي اضيييييي

بحدًء عكى مالئل أنلدط حيود االشيييييس السييييييحي وبدألخص مردلدي الر ل السييييي اضيييييي م اللديلو

بدضييييت ا رييييلا يلتنيك ومب و دياضيييي وجركيا الحتدئل اللحيول لكلردلدي الته جو جرحيييييرهد اه

ظروف م لرل م تكن اه مردول لنلو ديني جشيييييها هدر اللردلدي وأاحيييييا الهر، لت يييييحيسلد

بحي هدر اللردلدي.بدإلضدا الى جأ ير ديج الرراية والشوائب عكى

م 19O12BaFeب ال ً جو جرحيييييير مواد جللي ل للردب الر ل السييييي اضيييييه مب نو

1.11.11 وحتى 1.11.1مراعدة جس لا نسييييييل اللديلو الى الر ل اه هدر السيحدي ابت اًء مب

مردب دي انبدلت يلل عكى خلس عيحدي وجرت ننس الظروف الل لرل . جليب مب جركيا هدر السيح

الر ل السييييي اضيييييه مب نو لو لتأ ر بحدئيد او دليد وددنت الملددة اه دلي أدسيييييي الر ل جظلر

دلرحك شييدئل محن ييك اه هدر السيحدي جمداد دليتلد بدددلدد نسييل الر ل الى اللديلو اه اللواد

نسيييل لهلي مردلدي الر ل التللي ل وجو علا م هط مرجسه لليدس دلي شيييوائب أدسيييي الر ل

الس اضي م اللديلو جلسد لحسل مسدح الللو الرئيسي بيب اللردليب.

101

ول ياض هدر السيحدي بدختالف نسل اللديلو الى الر ل اه اللواد التللي ل عكى م ى أوض

دا نسيييل وجكلي خلس عيحدي مب1.1 و 1.1جو جرحيييير مواد جللي ل بحسيييل بديلو الى ح ل

ديج مئول .1088 1188 1888 188 088دا عكى ديج حراية م تكن

جليب مب جركيا السيحدي السيييدبل جشيييها أيب مردلدي م تكن جتراوس اه نسيييللد جلسد الختالف

ديج حراية التكل وجو وض م هط لليب جهوي جشها اللراحا اه هدر السيحدي جلسد الددلدد ديج

حسييييدط نلط لليب حلو حيود االشييييس السيييييحي اللبدله لها مردب ويضييييو نلو ال ه الرراية و

االبسدد لها مردب م بيدن االختالادي الته طرأي عكى الليها اللحيوي لها مردب جلسد الختالف

ديج حراية التكل .

FullProf output file. Example: sample (10%),

Full pattern refinement. Number of phases = 2. Chi squared value = 1.135

**********************************************************

** PROGRAM FullProf.2k (Version 4.60 - Mar2009-ILL JRC) **

**********************************************************

M U L T I -- P A T T E R N

Rietveld, Profile Matching & Integrated Intensity

Refinement of X-ray and/or Neutron Data

Date: 12/08/2013 Time: 18:42:46.759

=> PCR file code: 10 per

=> DAT file code: 10 per.dat -> Relative contribution: 1.0000

==> CONDITIONS OF THIS RUN FOR PATTERN No.: 1

=> Global Refinement of X-ray powder diffraction data

=> Global Refinement of X-ray powder diffraction data

Bragg-Brentano or Debye-Scherrer geometry

=> Title: 10 per

=> Number of phases: 2

=> Number of excluded regions: 0

=> Number of scattering factors supplied: 0

=> Conventional weights: w=1.0/Variance(yobs)

=> Asymmetry correction as in J.Appl.Cryst. 26,128(1993)

=> Background linearly interpolated between the 52 points given

=> The 5th default profile function was selected

=> Pseudo-Voigt function (ETA variable)

X-parameter correspond to: ETA=ETA0+X*2theta

pV(x)= ETA*L(x)+(1-ETA)*G(x)

==> INPUT/OUTPUT OPTIONS:

=> Generate file *.PRF for plot

=> Output Integrated Intensities

=> Generate new input file *.PCR

=> Data supplied in free format for pattern: 1

=> Plot pattern at each cycle

=> Wavelengths: 1.54056 1.54439

=> Alpha2/Alpha1 ratio: 0.5000

=> Cos(Monochromator angle)= 0.9100

=> Asymmetry correction for angles lower than 0.000 degrees

=> Absorption correction (AC), muR-eff = 0.0000

=> Base of peaks: 2.0*HW* 8.00

=> Number of cycles: 1

=> Relaxation factors ==> for coordinates: 1.00

=> for anisotropic temperature factors: 1.00

=> for halfwidth/strain/size parameters: 1.00

=> for lattice constants and propagation vectors: 1.00

=> EPS-value for convergence: 0.1

=> Background ==>

Position Intensity

20.32 28.91 0.00

20.87 26.14 0.00

21.48 26.65 0.00

22.30 26.16 0.00

23.56 21.90 0.00

23.72 21.47 0.00

24.72 21.57 0.00

25.63 22.54 0.00

26.54 21.21 0.00

27.34 22.87 0.00

28.71 22.32 0.00

30.08 15.49 0.00

31.73 7.97 0.00

32.84 0.44 0.00

32.96 8.40 0.00

33.62 6.83 0.00

34.90 6.62 0.00

36.36 17.12 0.00

36.56 12.72 0.00

38.12 14.61 0.00

38.88 17.99 0.00

39.63 14.09 0.00

41.42 13.65 0.00

41.66 14.41 0.00

42.15 16.77 0.00

43.38 13.69 0.00

44.47 17.94 0.00

45.12 16.08 0.00

47.02 16.30 0.00

48.23 14.23 0.00

49.05 15.65 0.00

49.34 15.43 0.00

51.64 17.56 0.00

52.67 18.50 0.00

52.87 19.05 0.00

53.74 19.52 0.00

55.71 17.75 0.00

55.92 18.50 0.00

57.11 17.55 0.00

58.14 19.83 0.00

59.59 17.93 0.00

60.60 18.69 0.00

60.86 18.09 0.00

61.75 18.27 0.00

62.15 17.51 0.00

63.96 19.47 0.00

65.08 19.17 0.00

66.43 15.60 0.00

67.84 20.76 0.00

68.53 11.46 0.00

69.00 16.97 0.00

69.62 16.47 0.00

=> Number of Least-Squares parameters varied: 0

=>--------------------------->

=>-------> PATTERN number: 1

=>--------------------------->

=> Global parameters and codes ==>

=> Zero-point: 0.1368 0.0000

=> Displacement peak-shift parameter and code: 0.00 0.00

=> Transparency peak-shift parameter and code: 0.01 0.00

=> Reading Intensity data =>>

==> Angular range, step and number of points:

2Thmin: 20.000000 2Thmax: 70.000000 Step: 0.010000 No. of points: 5001

--------------------------------------------------------------------------------

=> Phase No. 1

BaFe12O19

--------------------------------------------------------------------------------

=>-------> Pattern# 1

=> Crystal Structure Refinement

=> Preferred orientation vector: 0.0000 0.0000 1.0000

=>-------> Data for PHASE: 1

=> Number of atoms: 11

=> Number of distance constraints: 0

=> Number of angle constraints: 0

=> Symmetry information on space group: P 63/M M C

-> The multiplicity of the general position is: 24

-> The space group is Centric (-1 at origin)

-> Lattice type P: { 000 }

-> Reduced set of symmetry operators:

No. IT Symmetry symbol Rotation part Associated Translation

1: ( 1) 1 --> ( x , y, z) + { 0.0000 0.0000 0.0000}

2: ( 6) 6+ ( 0, 0, z) --> ( x-y, x , z) + { 0.0000 0.0000 0.5000}

3: ( 2) 3+ ( 0, 0, z) --> ( -y, x-y, z) + { 0.0000 0.0000 0.0000}

4: ( 4) 2 ( 0, 0, z) --> (-x , -y, z) + { 0.0000 0.0000 0.5000}

5: ( 3) 3- ( 0, 0, z) --> (-x+y,-x , z) + { 0.0000 0.0000 0.0000}

6: ( 5) 6- ( 0, 0, z) --> ( y,-x+y, z) + { 0.0000 0.0000 0.5000}

7: ( 7) 2 ( x, x, 0) --> ( y, x ,-z) + { 0.0000 0.0000 0.0000}

8: (12) 2 (2x, x, 0) --> ( x , x-y,-z) + { 0.0000 0.0000 0.5000}

9: ( 8) 2 ( x, 0, 0) --> ( x-y, -y,-z) + { 0.0000 0.0000 0.0000}

10: (10) 2 ( x,-x, 0) --> ( -y,-x ,-z) + { 0.0000 0.0000 0.5000}

11: ( 9) 2 ( 0, y, 0) --> (-x ,-x+y,-z) + { 0.0000 0.0000 0.0000}

12: (11) 2 ( x,2x, 0) --> (-x+y, y,-z) + { 0.0000 0.0000 0.5000}

Information on Space Group:

---------------------------

=> Number of Space group: 194

=> Hermann-Mauguin Symbol: P 63/m m c

=> Hall Symbol: -P 6c 2c

=> Table Setting Choice:

=> Setting Type: IT (Generated from Hermann-Mauguin symbol)

=> Crystal System: Hexagonal

=> Laue Class: 6/mmm

=> Point Group: 6/mmm

=> Bravais Lattice: P

=> Lattice Symbol: hP

=> Reduced Number of S.O.: 12

=> General multiplicity: 24

=> Centrosymmetry: Centric (-1 at origin)

=> Generators (exc. -1&L): 2

=> Asymmetric unit: 0.000 <= x <= 0.667

0.000 <= y <= 0.667

0.000 <= z <= 0.250

=> List of S.O. without inversion and lattice centring translations

=> SYMM( 1): x,y,z => SYMM( 2): x-y,x,z+1/2

=> SYMM( 3): -y,x-y,z => SYMM( 4): -x,-y,z+1/2

=> SYMM( 5): -x+y,-x,z => SYMM( 6): y,-x+y,z+1/2

=> SYMM( 7): -y,-x,z => SYMM( 8): -x,-x+y,z+1/2

=> SYMM( 9): -x+y,y,z => SYMM(10): y,x,z+1/2

=> SYMM(11): x,x-y,z => SYMM(12): x-y,-y,z+1/2

=> Initial parameters ==>

Atom Ntyp X Y Z B occ. in fin Spc Mult

B11 B22 B33 B12 B13 B23

Ba Ba 0.66667 0.33333 0.25000 -0.22808 0.01164 0 0 0 2

Codes: 0.00000 0.00000 0.00000 0.00000 0.00000

Fe Fe 0.00000 0.00000 0.00000 -0.69165 0.01193 0 0 0 2

Codes: 0.00000 0.00000 0.00000 0.00000 0.00000

Fe Fe 0.00000 0.00000 0.25027 -0.24119 0.01057 0 0 0 2

Codes: 0.00000 0.00000 0.00000 0.00000 0.00000

Fe Fe 0.33333 0.66666 0.02734 -0.63383 0.02252 0 0 0 4

Codes: 0.00000 0.00000 0.00000 0.00000 0.00000

Fe Fe 0.33333 0.66666 0.19063 1.25653 0.02535 0 0 0 4

Codes: 0.00000 0.00000 0.00000 0.00000 0.00000

Fe Fe 0.16928 0.33841 0.89179 -0.03360 0.07117 0 0 0 12

Codes: 0.00000 0.00000 0.00000 0.00000 0.00000

O O 0.00000 0.00000 0.15076 -1.30999 0.02267 0 0 0 4

Codes: 0.00000 0.00000 0.00000 0.00000 0.00000

O O 0.33333 0.66667 0.94475 3.46959 0.02700 0 0 0 4

Codes: 0.00000 0.00000 0.00000 0.00000 0.00000

O O 0.17995 0.35989 0.25000 1.43085 0.03962 0 0 0 6

Codes: 0.00000 0.00000 0.00000 0.00000 0.00000

O O 0.15524 0.31029 0.05176 1.76383 0.08287 0 0 0 12

Codes: 0.00000 0.00000 0.00000 0.00000 0.00000

O O 0.50398 1.00803 0.14867 2.30019 0.08497 0 0 0 12

Codes: 0.00000 0.00000 0.00000 0.00000 0.00000

=> IT IS ASSUMED THAT THE FIRST GIVEN SITE IS FULLY OCCUPIED

(If this is not the case, change the order of atoms to obtain correct values for the content of the unit cell)

The phase contains sites partially occupied

-> Atom: Ba , Chemical element: BA Atomic Mass: 137.3400

-> Atom: Fe , Chemical element: FE Atomic Mass: 55.8470





-> Atom: O , Chemical element: O Atomic Mass: 15.9994





=> The given value of ATZ is 45.65 the program has calculated: 45.65

The value of ATZ given in the input PCR file will be used for quantitative analysis

=> The chemical content of the unit cell is:

2.0000 Ba + 2.0498 Fe + 1.8162 Fe + 3.8694 Fe + 4.3557 Fe + 12.2285 Fe + 3.8952 O + 4.6392 O + 6.8076 O + 14.2388 O +

14.5997 O

=> The normalized site occupation numbers in % are:

100.0000 Ba : 102.4914 Fe : 90.8076 Fe : 96.7354 Fe : 108.8917 Fe : 101.9044 Fe : 97.3797 O : 115.9794 O : 113.4593 O : 118.6569 O :

121.6638 O

=>-------> PROFILE PARAMETERS FOR PATTERN: 1

=> Overall scale factor: 0.133890E-02

=> ETA (p-Voigt) OR M (Pearson VII): 0.5868

=> Overall temperature factor: 0.00000

=> Halfwidth U,V,W: 0.02994 -0.03141 0.04166

=> X and Y parameters: 0.0014 0.0000

=> Direct cell parameters: 5.8933 5.8933 23.2186 90.0000 90.0000 120.0000

=> Preferred orientation parameters: 0.0186 0.0000

=> Asymmetry parameters : 0.00000 0.00000 0.00000 0.00000

=> Strain parameters : 0.00000 0.00000 0.00000

=> Size parameters : 0.00000 0.00000

==> CODEWORDS FOR PROFILE PARAMETERS of PATTERN# 1

=> Overall scale factor: 0.000



=> Halfwidth U,V,W: 0.000 0.000 0.000






=> Size parameters : 0.000 0.000

=> Cell constraints according to Laue symmetry: 6/mmm

Metric information:

-------------------

=> Direct cell parameters:

a = 5.8933 b = 5.8933 c = 23.2186

alpha = 90.000 beta = 90.000 gamma = 120.000

Direct Cell Volume = 698.3628

=> Reciprocal cell parameters:

a*= 0.195935 b*= 0.195935 c*= 0.043069

alpha*= 90.000 beta*= 90.000 gamma*= 60.000

Reciprocal Cell Volume = 0.00143192

=> Direct and Reciprocal Metric Tensors:

GD GR

34.7308 -17.3654 0.0000 0.038391 0.019195 0.000000

-17.3654 34.7308 0.0000 0.019195 0.038391 0.000000

0.0000 0.0000 539.1033 0.000000 0.000000 0.001855

=> Cartesian frame: x // a; y is in the ab-plane; z is x ^ y

Crystal_to_Orthonormal_Matrix Orthonormal_to_Crystal Matrix

Cr_Orth_cel Orth_Cr_cel

5.8933 -2.9466 0.0000 0.169685 0.097968 0.000000

0.0000 5.1037 0.0000 0.000000 0.195935 0.000000

0.0000 0.0000 23.2186 0.000000 0.000000 0.043069

=> Number of propagation vectors [K] = 0

=> Laue symmetry 6/mmm will be used to generate HKL for pattern# 1

=> Reflections generated between S(1/d)min: 0.2249 A-1 and S(1/d)max: 0.7721 A-1

=> dmax: 4.4469 A and dmin: 1.2952 A

=> The number of reflections generated is: 85

=> The max. scatt. variable (gen.ref.) is: 72.9821

=> Scattering coefficients from internal table

=> X-ray scattering coeff. (A1, B1, A2,...C, f(0), Z, Dfp,Dfpp)

BA 20.3361 3.2160 19.2970 0.2756 10.8880 20.2073 2.6959 167.2020 2.7731 55.9901 56.0000 -1.3340 8.4600

FE 11.7695 4.7611 7.3573 0.3072 3.5222 15.3535 2.3045 76.8805 1.0369 25.9904 26.0000 -1.1790 3.2040

O 3.0485 13.2771 2.2868 5.7011 1.5463 0.3239 0.8670 32.9089 0.2508 7.9994 8.0000 0.0470 0.0320

--------------------------------------------------------------------------------

=> Phase No. 2

Fe2O3

--------------------------------------------------------------------------------

=>-------> Pattern# 1

=> Crystal Structure Refinement

=> Preferred orientation vector: 0.0000 0.0000 1.0000

=>-------> Data for PHASE: 2

=> Number of atoms: 2

=> Number of distance constraints: 0

=> Number of angle constraints: 0

=> Symmetry information on space group: R -3 c

-> The multiplicity of the general position is: 36

-> The space group is Centric (-1 at origin)

-> Lattice type R: { 000; 2/3 1/3 1/3; 1/3 2/3 2/3 }+

-> Reduced set of symmetry operators:

No. IT Symmetry symbol Rotation part Associated Translation

1: ( 1) 1 --> ( x , y, z) + { 0.0000 0.0000 0.0000}

2: ( 2) 3+ ( 0, 0, z) --> ( -y, x-y, z) + { 0.0000 0.0000 0.0000}

3: ( 3) 3- ( 0, 0, z) --> (-x+y,-x , z) + { 0.0000 0.0000 0.0000}

4: ( 7) 2 ( x, x, 0) --> ( y, x ,-z) + { 0.0000 0.0000 0.5000}

5: ( 8) 2 ( x, 0, 0) --> ( x-y, -y,-z) + { 0.0000 0.0000 0.5000}

6: ( 9) 2 ( 0, y, 0) --> (-x ,-x+y,-z) + { 0.0000 0.0000 0.5000}

Information on Space Group:

---------------------------

=> Number of Space group: 167

=> Hermann-Mauguin Symbol: R -3 c

=> Hall Symbol: -R 3 2"c

=> Table Setting Choice: H

=> Setting Type: IT (Generated from Hermann-Mauguin symbol)

=> Crystal System: Rhombohedral

=> Laue Class: -3m1

=> Point Group: -3m

=> Bravais Lattice: R

=> Lattice Symbol: hR

=> Reduced Number of S.O.: 6

=> General multiplicity: 36

=> Centrosymmetry: Centric (-1 at origin)

=> Generators (exc. -1&L): 2

=> Asymmetric unit: 0.000 <= x <= 0.667

0.000 <= y <= 0.667

0.000 <= z <= 0.083

=> List of S.O. without inversion and lattice centring translations

=> SYMM( 1): x,y,z => SYMM( 2): -y,x-y,z

=> SYMM( 3): -x+y,-x,z => SYMM( 4): -y,-x,z+1/2

=> SYMM( 5): -x+y,y,z+1/2 => SYMM( 6): x,x-y,z+1/2

=> Initial parameters ==>

Atom Ntyp X Y Z B occ. in fin Spc Mult

B11 B22 B33 B12 B13 B23

Fe Fe 0.00000 0.00000 0.35571 0.01865 0.02352 0 0 0 12

Codes: 0.00000 0.00000 0.00000 0.00000 0.00000

O O 0.31546 0.00000 0.25000 4.90012 0.04681 0 0 0 18

Codes: 0.00000 0.00000 0.00000 0.00000 0.00000

=> IT IS ASSUMED THAT THE FIRST GIVEN SITE IS FULLY OCCUPIED

(If this is not the case, change the order of atoms to obtain correct values for the content of the unit cell)

The phase contains sites partially occupied



=> The given value of ATZ is 5.24 the program has calculated: 5.24

The value of ATZ given in the input PCR file will be used for quantitative analysis

=> The chemical content of the unit cell is:

12.0000 Fe + 23.8827 O

=> The normalized site occupation numbers in % are:

100.0000 Fe : 132.6814 O

=>-------> PROFILE PARAMETERS FOR PATTERN: 1

=> Overall scale factor: 0.167490E-02



=> Halfwidth U,V,W: -0.31472 0.25684 -0.01466

=> X and Y parameters: -0.0078 0.0000





=> Size parameters : 0.00000 0.00000

==> CODEWORDS FOR PROFILE PARAMETERS of PATTERN# 1

=> Overall scale factor: 0.000



=> Halfwidth U,V,W: 0.000 0.000 0.000






=> Size parameters : 0.000 0.000

=> Cell constraints according to Laue symmetry: -3m1

Metric information:

-------------------

=> Direct cell parameters:

a = 5.0357 b = 5.0357 c = 13.7488

alpha = 90.000 beta = 90.000 gamma = 120.000

Direct Cell Volume = 301.9332

=> Reciprocal cell parameters:

a*= 0.229304 b*= 0.229304 c*= 0.072734

alpha*= 90.000 beta*= 90.000 gamma*= 60.000

Reciprocal Cell Volume = 0.00331199

=> Direct and Reciprocal Metric Tensors:

GD GR

25.3581 -12.6790 0.0000 0.052580 0.026290 0.000000

-12.6790 25.3581 0.0000 0.026290 0.052580 0.000000

0.0000 0.0000 189.0288 0.000000 0.000000 0.005290

=> Cartesian frame: x // a; y is in the ab-plane; z is x ^ y

Crystal_to_Orthonormal_Matrix Orthonormal_to_Crystal Matrix

Cr_Orth_cel Orth_Cr_cel

5.0357 -2.5178 0.0000 0.198583 0.114652 0.000000

0.0000 4.3610 0.0000 0.000000 0.229304 0.000000

0.0000 0.0000 13.7488 0.000000 0.000000 0.072734

=> Number of propagation vectors [K] = 0

=> Laue symmetry -3m1 will be used to generate HKL for pattern# 1

=> Reflections generated between S(1/d)min: 0.2249 A-1 and S(1/d)max: 0.7722 A-1

=> dmax: 4.4469 A and dmin: 1.2951 A

=> The number of reflections generated is: 17

=> The max. scatt. variable (gen.ref.) is: 72.9950

=> Scattering coefficients from internal table

=> X-ray scattering coeff. (A1, B1, A2,...C, f(0), Z, Dfp,Dfpp)

=> No optimization for routine tasks

Standard deviations have to be multiplied by: 1.2583

(correlated residuals) See references:

-J.F.Berar & P.Lelann, J. Appl. Cryst. 24, 1-5 (1991)

-J.F.Berar, Acc. in Pow. Diff. II,NIST Sp.Pub. 846, 63(1992)

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

=> CYCLE No.: 1

---------------------------------------------------------------------------------------

=> Phase 1 Name: BaFe12O19

---------------------------------------------------------------------------------------

=> New parameters, shifts, and standard deviations

Atom x dx sx y dy sy z dz sz B dB sB occ. docc. socc.

Ba 0.66667 0.00000 0.00000 0.33333 0.00000 0.00000 0.25000 0.00000 0.00000 -0.22808 0.00000 0.00000 0.01164 0.00000 0.00000

Fe 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 -0.69165 0.00000 0.00000 0.01193 0.00000 0.00000

Fe 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.25027 0.00000 0.00000 -0.24119 0.00000 0.00000 0.01057 0.00000 0.00000

Fe 0.33333 0.00000 0.00000 0.66666 0.00000 0.00000 0.02734 0.00000 0.00000 -0.63383 0.00000 0.00000 0.02252 0.00000 0.00000

Fe 0.33333 0.00000 0.00000 0.66666 0.00000 0.00000 0.19063 0.00000 0.00000 1.25653 0.00000 0.00000 0.02535 0.00000 0.00000

Fe 0.16928 0.00000 0.00000 0.33841 0.00000 0.00000 0.89179 0.00000 0.00000 -0.03360 0.00000 0.00000 0.07117 0.00000 0.00000

O 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.15076 0.00000 0.00000 -1.30999 0.00000 0.00000 0.02267 0.00000 0.00000

O 0.33333 0.00000 0.00000 0.66667 0.00000 0.00000 0.94475 0.00000 0.00000 3.46959 0.00000 0.00000 0.02700 0.00000 0.00000

O 0.17995 0.00000 0.00000 0.35989 0.00000 0.00000 0.25000 0.00000 0.00000 1.43085 0.00000 0.00000 0.03962 0.00000 0.00000

O 0.15524 0.00000 0.00000 0.31029 0.00000 0.00000 0.05176 0.00000 0.00000 1.76383 0.00000 0.00000 0.08287 0.00000 0.00000

O 0.50398 0.00000 0.00000 1.00803 0.00000 0.00000 0.14867 0.00000 0.00000 2.30019 0.00000 0.00000 0.08497 0.00000 0.00000

==> PROFILE PARAMETERS FOR PATTERN# 1

=> Overall scale factor: 0.001338900 0.000000000 0.000000000

=> Eta(p-Voigt) or m(Pearson VII): 0.586780 0.000000 0.000000

=> Overall tem. factor: 0.000000 0.000000 0.000000

=> Halfwidth parameters:

0.029938 0.000000 0.000000

-0.031407 0.000000 0.000000

0.041664 0.000000 0.000000

=> Cell parameters:

5.893282 0.000000 0.000000

5.893282 0.000000 0.000000

23.218599 0.000000 0.000000

90.000000 0.000000 0.000000

90.000000 0.000000 0.000000

120.000000 0.000000 0.000000

=> Preferred orientation:

0.018610 0.000000 0.000000

0.000000 0.000000 0.000000

=> Asymmetry parameters:

0.000000 0.000000 0.000000

0.000000 0.000000 0.000000

0.000000 0.000000 0.000000

0.000000 0.000000 0.000000

=> X and Y parameters:

0.001372 0.000000 0.000000

0.000000 0.000000 0.000000

=> Strain parameters:

0.000000 0.000000 0.000000

0.000000 0.000000 0.000000

0.000000 0.000000 0.000000

=> Size parameters (G,L):

0.000000 0.000000 0.000000

0.000000 0.000000 0.000000

---------------------------------------------------------------------------------------

=> Phase 2 Name: Fe2O3

---------------------------------------------------------------------------------------



Fe 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.35571 0.00000 0.00000 0.01865 0.00000 0.00000 0.02352 0.00000 0.00000

O 0.31546 0.00000 0.00000 0.00000 0.00000 0.00000 0.25000 0.00000 0.00000 4.90012 0.00000 0.00000 0.04681 0.00000 0.00000






-0.314717 0.000000 0.000000

0.256845 0.000000 0.000000

-0.014657 0.000000 0.000000

=> Cell parameters:

5.035680 0.000000 0.000000

5.035680 0.000000 0.000000

13.748774 0.000000 0.000000

90.000000 0.000000 0.000000

90.000000 0.000000 0.000000

120.000000 0.000000 0.000000


0.045350 0.000000 0.000000

0.000000 0.000000 0.000000


0.000000 0.000000 0.000000

0.000000 0.000000 0.000000

0.000000 0.000000 0.000000

0.000000 0.000000 0.000000


-0.007842 0.000000 0.000000

0.000000 0.000000 0.000000


0.000000 0.000000 0.000000

0.000000 0.000000 0.000000

0.000000 0.000000 0.000000


0.000000 0.000000 0.000000

0.000000 0.000000 0.000000

==> GLOBAL PARAMETERS FOR PATTERN# 1

=> Zero-point: 0.1368 0.0000 0.0000

=> Cos( theta)-shift parameter : -0.0005 0.0000 0.0000

=> Sin(2theta)-shift parameter : 0.0126 0.0000 0.0000

==> RELIABILITY FACTORS WITH ALL NON-EXCLUDED POINTS FOR PATTERN: 1

=> R-Factors: 8.42 12.5 Chi2: 1.13 DW-Stat.: 1.9223 Patt#: 1

=> Expected : 11.8 1.9122

=> Deviance :0.571E+04 Dev*: 1.136

=> GoF-index: 1.1 Sqrt(Residual/N)

=> N-P+C: 5001

=> SumYdif SumYobs SumYcal SumwYobsSQ Residual Condition

0.3046E+05 0.3616E+06 0.3563E+06 0.3616E+06 5675. 0.000

=> Conventional Rietveld Rp,Rwp,Re and Chi2: 11.0 15.2 14.3 1.135

=> (Values obtained using Ynet, but true sigma(y))

=> SumYnet, Sum(w Ynet**2): 0.2760E+06 0.2441E+06

=> N-sigma of the GoF: 6.740

==> RELIABILITY FACTORS FOR POINTS WITH BRAGG CONTRIBUTIONS FOR PATTERN: 1

=> R-Factors: 8.42 12.5 Chi2: 1.13 DW-Stat.: 1.9223 Patt#:

=> Expected : 11.8 1.9122

=> Deviance :0.571E+04 Dev*: 1.136


=> N-P+C: 5001


0.3046E+05 0.3616E+06 0.3563E+06 0.3616E+06 5675. 0.000





=> Global user-weigthed Chi2 (Bragg contrib.): 1.13

=> ---------> Pattern# 1

=> Phase: 1

=> Bragg R-factor: 1.65

=> RF-factor : 1.87

=> Phase: 2


=> RF-factor : 3.02

Standard deviations have to be multiplied by: 1.2583

(correlated residuals) See references:

-J.F.Berar & P.Lelann, J. Appl. Cryst. 24, 1-5 (1991)

-J.F.Berar, Acc. in Pow. Diff. II,NIST Sp.Pub. 846, 63(1992)

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

=> CYCLE No.: 1

=> Convergence reached at this CYCLE !!!!

=> Parameter shifts set to zero

---------------------------------------------------------------------------------------

=> Phase 1 Name: BaFe12O19

---------------------------------------------------------------------------------------



Ba 0.66667 0.00000 0.00000 0.33333 0.00000 0.00000 0.25000 0.00000 0.00000 -0.22808 0.00000 0.00000 0.01164 0.00000 0.00000

Fe 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 -0.69165 0.00000 0.00000 0.01193 0.00000 0.00000

Fe 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.25027 0.00000 0.00000 -0.24119 0.00000 0.00000 0.01057 0.00000 0.00000

Fe 0.33333 0.00000 0.00000 0.66666 0.00000 0.00000 0.02734 0.00000 0.00000 -0.63383 0.00000 0.00000 0.02252 0.00000 0.00000

Fe 0.33333 0.00000 0.00000 0.66666 0.00000 0.00000 0.19063 0.00000 0.00000 1.25653 0.00000 0.00000 0.02535 0.00000 0.00000

Fe 0.16928 0.00000 0.00000 0.33841 0.00000 0.00000 0.89179 0.00000 0.00000 -0.03360 0.00000 0.00000 0.07117 0.00000 0.00000

O 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.15076 0.00000 0.00000 -1.30999 0.00000 0.00000 0.02267 0.00000 0.00000

O 0.33333 0.00000 0.00000 0.66667 0.00000 0.00000 0.94475 0.00000 0.00000 3.46959 0.00000 0.00000 0.02700 0.00000 0.00000

O 0.17995 0.00000 0.00000 0.35989 0.00000 0.00000 0.25000 0.00000 0.00000 1.43085 0.00000 0.00000 0.03962 0.00000 0.00000

O 0.15524 0.00000 0.00000 0.31029 0.00000 0.00000 0.05176 0.00000 0.00000 1.76383 0.00000 0.00000 0.08287 0.00000 0.00000

O 0.50398 0.00000 0.00000 1.00803 0.00000 0.00000 0.14867 0.00000 0.00000 2.30019 0.00000 0.00000 0.08497 0.00000 0.00000






0.029938 0.000000 0.000000

-0.031407 0.000000 0.000000

0.041664 0.000000 0.000000

=> Cell parameters:

5.893282 0.000000 0.000000

5.893282 0.000000 0.000000

23.218599 0.000000 0.000000

90.000000 0.000000 0.000000

90.000000 0.000000 0.000000

120.000000 0.000000 0.000000


0.018610 0.000000 0.000000

0.000000 0.000000 0.000000


0.000000 0.000000 0.000000

0.000000 0.000000 0.000000

0.000000 0.000000 0.000000

0.000000 0.000000 0.000000


0.001372 0.000000 0.000000

0.000000 0.000000 0.000000


0.000000 0.000000 0.000000

0.000000 0.000000 0.000000

0.000000 0.000000 0.000000


0.000000 0.000000 0.000000

0.000000 0.000000 0.000000

---------------------------------------------------------------------------------------

=> Phase 2 Name: Fe2O3

---------------------------------------------------------------------------------------



Fe 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.35571 0.00000 0.00000 0.01865 0.00000 0.00000 0.02352 0.00000 0.00000

O 0.31546 0.00000 0.00000 0.00000 0.00000 0.00000 0.25000 0.00000 0.00000 4.90012 0.00000 0.00000 0.04681 0.00000 0.00000






-0.314717 0.000000 0.000000

0.256845 0.000000 0.000000

-0.014657 0.000000 0.000000

=> Cell parameters:

5.035680 0.000000 0.000000

5.035680 0.000000 0.000000

13.748774 0.000000 0.000000

90.000000 0.000000 0.000000

90.000000 0.000000 0.000000

120.000000 0.000000 0.000000


0.045350 0.000000 0.000000

0.000000 0.000000 0.000000


0.000000 0.000000 0.000000

0.000000 0.000000 0.000000

0.000000 0.000000 0.000000

0.000000 0.000000 0.000000


-0.007842 0.000000 0.000000

0.000000 0.000000 0.000000


0.000000 0.000000 0.000000

0.000000 0.000000 0.000000

0.000000 0.000000 0.000000


0.000000 0.000000 0.000000

0.000000 0.000000 0.000000

==> GLOBAL PARAMETERS FOR PATTERN# 1

=> Zero-point: 0.1368 0.0000 0.0000

=> Cos( theta)-shift parameter : -0.0005 0.0000 0.0000

=> Sin(2theta)-shift parameter : 0.0126 0.0000 0.0000

==> RELIABILITY FACTORS WITH ALL NON-EXCLUDED POINTS FOR PATTERN: 1

=> R-Factors: 8.42 12.5 Chi2: 1.13 DW-Stat.: 1.9223 Patt#: 1

=> Expected : 11.8 1.9122

=> Deviance :0.571E+04 Dev*: 1.136


=> N-P+C: 5001


0.3046E+05 0.3616E+06 0.3563E+06 0.3616E+06 5675. 0.000





==> RELIABILITY FACTORS FOR POINTS WITH BRAGG CONTRIBUTIONS FOR PATTERN: 1

=> R-Factors: 8.42 12.5 Chi2: 1.13 DW-Stat.: 1.9223 Patt#:

=> Expected : 11.8 1.9122

=> Deviance :0.571E+04 Dev*: 1.136


=> N-P+C: 5001


0.3046E+05 0.3616E+06 0.3563E+06 0.3616E+06 5675. 0.000





=> Global user-weigthed Chi2 (Bragg contrib.): 1.13

=> ---------> Pattern# 1

=> Phase: 1


=> RF-factor : 1.87

=> Phase: 2


=> RF-factor : 3.02

--------------------------------------------------------------------------------------------------------------

Pattern# 1 Phase No: 1 Phase name: BaFe12O19

--------------------------------------------------------------------------------------------------------------

No. Code H K L Mult Hw ETA/M 2theta/TOF Icalc Iobs Sigma StrFactor^2 d-hkl CORR

1 1 1 0 3 12 0.192100 0.615360 20.831 0.6 0.8 0.473 1.2943 4.260726 1.018325

2 1 0 0 6 2 0.191102 0.618285 22.963 24.8 26.7 2.090 416.6114 3.869767 1.000000

3 1 1 0 4 12 0.190999 0.618593 23.187 4.4 4.6 0.307 12.3454 3.832868 1.013523

4 1 1 0 5 12 0.189794 0.622341 25.919 1.5 2.1 1.007 5.2692 3.434747 1.010194

5 1 1 0 6 12 0.188558 0.626474 28.931 2.3 2.5 0.370 10.5098 3.083600 1.007863

6 1 1 1 0 6 0.188027 0.628362 30.307 115.2 116.5 1.582 1103.9879 2.946641 1.046989

7 1 0 0 8 2 0.187849 0.629012 30.782 39.1 39.1 0.471 1216.9846 2.902325 1.000000

8 1 1 1 2 12 0.187659 0.629714 31.293 23.9 24.3 0.530 124.4419 2.856078 1.033071

9 1 1 0 7 12 0.187346 0.630901 32.158 239.7 240.7 1.586 1357.1069 2.781190 1.006200

10 1 1 1 4 12 0.186677 0.633558 34.095 266.2 267.2 1.661 1681.4869 2.627483 1.022818

11 1 2 0 0 6 0.186336 0.634989 35.137 26.0 26.2 0.431 342.3931 2.551866 1.046989

12 1 2 0 1 12 0.186266 0.635288 35.356 13.9 14.0 0.237 93.3158 2.536592 1.040542

13 1 1 0 8 12 0.186204 0.635560 35.554 17.8 17.8 0.239 125.5349 2.522919 1.004988

14 1 2 0 2 12 0.186063 0.636178 36.005 2.8 3.0 0.257 19.7391 2.492364 1.034729

15 1 2 0 3 12 0.185742 0.637632 37.064 125.7 127.6 2.104 945.6779 2.423528 1.029615

16 1 1 1 6 12 0.185368 0.639415 38.364 7.9 8.1 0.386 64.6778 2.344363 1.015876

17 1 2 0 4 12 0.185329 0.639609 38.505 0.6 0.7 0.059 5.2376 2.336085 1.025208

18 1 0 0 10 2 0.185261 0.639945 38.750 1.3 1.4 0.195 64.3379 2.321860 1.000000

19 1 1 0 9 12 0.185168 0.640413 39.091 6.0 6.4 0.444 52.2035 2.302412 1.004085

20 1 2 0 5 12 0.184854 0.642062 40.293 84.1 85.4 1.537 765.9689 2.236429 1.021467

21 1 2 0 6 12 0.184355 0.644944 42.394 56.3 56.9 0.968 575.4030 2.130363 1.018325

22 1 1 0 10 12 0.184276 0.645433 42.750 3.3 3.4 0.210 34.4981 2.113434 1.003398

23 1 1 1 8 12 0.184067 0.646795 43.742 2.5 2.7 0.299 28.0185 2.067744 1.011323

24 1 2 0 7 12 0.183867 0.648207 44.772 1.4 1.9 0.619 16.5458 2.022561 1.015704

25 1 1 0 11 12 0.183563 0.650605 46.520 14.9 15.8 1.000 190.6987 1.950547 1.002866

26 1 0 0 12 2 0.183501 0.651153 46.919 0.3 0.4 0.071 24.8150 1.934883 1.000000

27 1 2 1 0 12 0.183478 0.651360 47.070 0.0 0.0 0.006 0.2195 1.929029 1.046989

28 1 2 1 1 24 0.183452 0.651596 47.242 2.9 3.2 0.316 18.6834 1.922406 1.042060

29 1 2 0 8 12 0.183429 0.651810 47.398 1.5 1.6 0.203 19.1567 1.916434 1.013523

30 1 2 1 2 24 0.183378 0.652300 47.755 2.8 2.9 0.252 18.4861 1.902938 1.037482

31 1 2 1 3 24 0.183266 0.653461 48.601 2.0 2.5 0.653 13.9138 1.871766 1.033290

32 1 2 1 4 24 0.183132 0.655062 49.768 2.8 2.9 0.170 20.5378 1.830591 1.029503

33 1 1 1 10 12 0.183111 0.655336 49.968 8.3 8.6 0.392 124.0588 1.823722 1.008323

34 1 2 0 9 12 0.183083 0.655719 50.247 21.4 22.4 1.076 322.3138 1.814253 1.011708

35 1 1 0 12 12 0.183069 0.655924 50.396 2.1 2.2 0.119 31.5208 1.809230 1.002447

36 1 2 1 5 24 0.182996 0.657080 51.239 1.0 1.3 0.385 7.7858 1.781439 1.026120

37 1 2 1 6 24 0.182886 0.659491 52.997 0.9 1.2 0.440 7.2142 1.726420 1.023125

38 1 2 0 10 12 0.182873 0.659905 53.298 8.7 8.8 0.384 148.6288 1.717373 1.010194

39 1 3 0 0 6 0.182853 0.660654 53.844 22.0 22.1 0.483 744.5333 1.701244 1.046989

40 1 3 0 1 12 0.182849 0.660868 54.000 0.0 0.0 0.000 0.0451 1.696696 1.042625

41 1 1 0 13 12 0.182840 0.661386 54.377 1.6 1.5 0.058 28.1489 1.685801 1.002111

42 1 3 0 2 12 0.182838 0.661507 54.466 4.9 5.2 0.351 85.8677 1.683266 1.038529

43 1 2 1 7 24 0.182832 0.662272 55.023 104.8 105.9 1.412 956.2604 1.667534 1.020492

44 1 3 0 3 12 0.182831 0.662565 55.237 0.9 0.9 0.010 16.5028 1.661576 1.034729

45 1 0 0 14 2 0.182830 0.662719 55.349 17.5 17.4 0.301 1985.9094 1.658471 1.000000

46 1 3 0 4 12 0.182840 0.664030 56.305 60.5 61.6 1.200 1150.8531 1.632571 1.031241

47 1 2 0 11 12 0.182845 0.664346 56.535 121.1 121.7 1.029 2373.4250 1.626481 1.008928

48 1 1 1 12 12 0.182854 0.664823 56.882 12.9 13.3 0.389 257.7462 1.617365 1.006302

49 1 2 1 8 24 0.182869 0.665397 57.301 14.8 15.2 0.598 147.6992 1.606543 1.018190

50 1 3 0 5 12 0.182885 0.665888 57.659 0.1 0.1 0.004 1.0948 1.597419 1.028069

51 1 1 0 14 12 0.182931 0.666995 58.465 2.2 3.3 1.675 47.2806 1.577285 1.001839

52 1 3 0 6 12 0.182993 0.668121 59.286 1.8 2.0 0.324 39.6205 1.557390 1.025208

53 1 2 1 9 24 0.183040 0.668845 59.814 3.2 3.6 0.498 35.5924 1.544904 1.016182

54 1 2 0 12 12 0.183053 0.669027 59.947 8.2 8.6 0.560 182.3922 1.541800 1.007863

55 1 3 0 7 12 0.183193 0.670712 61.175 0.0 0.0 0.026 0.4430 1.513751 1.022643

56 1 2 1 10 24 0.183392 0.672598 62.549 4.2 4.2 0.110 51.0758 1.483760 1.014435

57 1 1 0 15 12 0.183411 0.672758 62.666 5.5 5.6 0.171 136.8466 1.481278 1.001615

58 1 2 2 0 6 0.183475 0.673275 63.043 126.1 126.7 1.168 6049.6938 1.473320 1.046989

59 1 3 0 8 12 0.183523 0.673646 63.313 1.7 1.7 0.030 41.1813 1.467686 1.020357

60 1 2 0 13 12 0.183562 0.673939 63.527 6.7 6.9 0.298 169.3220 1.463256 1.006964


61 1 2 2 2 12 0.183577 0.674050 63.608 0.1 0.1 0.006 2.3224 1.461597 1.039599

62 1 0 0 16 2 0.183677 0.674752 64.119 1.6 1.6 0.074 253.7202 1.451162 1.000000

63 1 1 1 14 12 0.183737 0.675153 64.412 3.7 3.6 0.231 96.2901 1.445276 1.004903

64 1 2 2 4 12 0.183930 0.676351 65.285 0.1 0.1 0.030 1.7636 1.428039 1.033071

65 1 2 1 11 24 0.183979 0.676640 65.496 11.7 12.8 1.274 157.6939 1.423957 1.012914

66 1 3 0 9 12 0.184026 0.676905 65.689 0.1 0.1 0.006 1.6466 1.420242 1.018325

67 1 3 1 0 12 0.184087 0.677244 65.936 0.0 0.0 0.002 0.1181 1.415521 1.046989

68 1 3 1 1 24 0.184121 0.677433 66.074 2.4 2.8 0.480 32.3982 1.412897 1.043340

69 1 3 1 2 24 0.184229 0.678000 66.487 2.2 2.2 0.206 29.6998 1.405114 1.039873

70 1 1 0 16 12 0.184365 0.678686 66.987 0.3 0.3 0.065 7.1565 1.395835 1.001429

71 1 3 1 3 24 0.184417 0.678941 67.173 0.3 0.4 0.036 4.8257 1.392423 1.036605

72 1 2 0 14 12 0.184446 0.679078 67.273 32.4 33.9 1.654 927.2337 1.390595 1.006200

73 1 2 2 6 12 0.184673 0.680121 68.033 7.0 7.2 0.373 199.7649 1.376904 1.027484

74 1 3 1 4 24 0.184702 0.680251 68.127 1.0 1.0 0.061 14.1806 1.375221 1.033549

75 1 3 0 10 12 0.184754 0.680477 68.292 3.9 4.0 0.194 112.5767 1.372301 1.016525

76 1 2 1 12 24 0.184868 0.680962 68.646 2.4 3.0 0.682 36.0887 1.366095 1.011591

77 1 3 1 5 24 0.185105 0.681922 69.345 0.5 1.0 1.039 6.9699 1.354012 1.030711

--------------------------------------------------------------------------------------------------------------

Pattern# 1 Phase No: 2 Phase name: Fe2O3

--------------------------------------------------------------------------------------------------------------


1 1 0 1 2 6 0.160883 0.660264 24.148 5.3 5.9 0.725 25.3785 3.682522 1.046915

2 1 1 0 4 6 0.184160 0.589602 33.158 21.0 20.9 0.389 200.2004 2.699516 1.020410

3 1 1 1 0 6 0.188095 0.570234 35.628 15.2 15.2 0.218 153.7020 2.517840 1.118397

4 1 0 0 6 2 0.192156 0.541555 39.285 0.3 0.3 0.049 12.7175 2.291462 1.000000

5 1 1 1 3 12 0.193258 0.529210 40.860 4.7 5.0 0.300 34.3266 2.206734 1.053131

6 1 2 0 2 6 0.194219 0.508461 43.505 0.5 0.7 0.278 8.1953 2.078460 1.075101

7 1 0 2 4 6 0.192037 0.461764 49.460 7.8 8.2 0.509 173.9207 1.841261 1.046915

8 1 1 1 6 12 0.185629 0.425625 54.068 9.2 9.6 0.441 126.9143 1.694701 1.025032

9 1 2 1 1 12 0.181106 0.409268 56.154 0.0 0.0 0.001 0.5522 1.636594 1.100256

10 1 1 2 2 12 0.177721 0.399154 57.444 0.6 0.6 0.019 8.7935 1.602880 1.084241

11 1 0 1 8 6 0.177280 0.397934 57.600 1.8 1.9 0.122 59.0510 1.598920 1.006411

12 1 2 1 4 12 0.159419 0.360034 62.433 6.9 7.1 0.330 125.9719 1.486252 1.058928

13 1 3 0 0 6 0.151527 0.347779 63.995 6.6 6.5 0.306 241.3243 1.453676 1.118397

14 1 1 2 5 12 0.139147 0.331840 66.028 0.0 0.0 0.004 0.2995 1.413766 1.049365

15 1 2 0 8 6 0.108820 0.303863 69.595 0.8 0.8 0.208 39.3914 1.349758 1.020410

-----------------------------------------------------

BRAGG R-Factors and weight fractions for Pattern # 1

-----------------------------------------------------

=> Phase: 1

=> Bragg R-factor: 1.65 Vol: 698.363( 0.000) Fract(%): 92.36( 0.00)

=> Rf-factor= 1.87 ATZ: 45.649 Brindley: 1.0000

=> Phase: 2

=> Bragg R-factor: 3.19 Vol: 301.933( 0.000) Fract(%): 7.64( 0.00)

=> Rf-factor= 3.02 ATZ: 5.239 Brindley: 0.7500

-----------------------------------------------------------------

SYMBOLIC NAMES AND FINAL VALUES AND SIGMA OF REFINED PARAMETERS:

-----------------------------------------------------------------

------------------------------------------------------------------

=> Dimensions of dynamic allocated arrays in this run of FullProf:

------------------------------------------------------------------

=> Total approximate array memory (dynamic + static): 22050920 bytes

MaxPOINT= 60000 Max.num. of points(+int. Inten.)/diffraction pattern

MaxREFLT= 20000 Max.num. of reflections/diffraction pattern

MaxPARAM= 300 Max.num. of refinable parameters

MaxOVERL= 2096 Max.num. of overlapping reflections

----------------------------------------------------------

=> Dimensions of fixed arrays in this release of FullProf:

----------------------------------------------------------

NPATT = 50 Max.num. of powder diffraction patterns

NATS = 830 Max.num. of atoms (all kind) in asymmetric unit

MPAR = 350 Max.num. of non atomic parameters/phase

IEXCL = 30 Max.num. of excluded regions

IBACP = 200 Max.num. of background points for interpolation

NPHT = 16 Max.num. of phases

NMAGM = 8 Max.num. of rotation-matrices sets for magnetic structure

NBASIS = 12 Max.num. of basis functions associated to a single atom

NIREPS = 9 Max.num. of irreducible representations to be combined

N_EQ = 48 Max.num. of user-supplied symmetry operators/propagation vectors

NGL = 222 Max.num. of global parameters/diffraction pattern

N_LINC = 30 Max.num. of global linear restraints

NAT_P = 64 Max.num. of atomic parameters per atom

NCONST = 500 Max.num. of slack constraints per phase

N_SPE = 16 Max.num. of different chemical species

N_FORM = 60 Max.num. of scattering factor values in a table

NPR = 150 Max.num. of points defining a numerical profile

INPR = 25 Max.num. of different numerical peak shapes

NPRC = 150 Max.num. of terms in the table for correcting intensities

NSOL = 10 Max.num. of solutions to be stored in Montecarlo searchs

CPU Time: 0.858 seconds

0.014 minutes

=> Run finished at: Date: 12/08/2013 Time: 18:42:47.670

structural analysis of hexaferrite materials yazan maswadeh

Science

barium ratio fe

ba ratio

ratio iibam

different fe

blocks of barium hexaferrites

fitted xrd pattern

rietveld refinement

structural phases