1

Ionic Conductivity and Solid Electrolytes

Ceramic insulators

•The primary function of insulation in electrical circuits is physical separation of conductors and regulation or prevention of current flow between them.

•Other functions are to provide mechanical support, heat dissipation, and environmental protection for conductors.

•Ceramic materials which in use these functions are classified as ceramic insulators.

•They include most glasses, porcelains, and oxide and nitride materials.

•The advantage of ceramics as insulators is their capability for high-temperature operation.

Insulation Resistance

•Conductivity

= d/(R A) and 1/ = = (R A)/d

•Or in terms of the material parameters

= nq

where is the electrical resistivity (m), R () the sample

resistance, A is area (m2), and d thickness (m).

•If more than one type of charge carrier being present, the

resultant conductivity can be defined as the sum of component

conductivities (I) as follows:

= i ni (ez)i i = i i

Insulation Resistance

•Depending on which charge carriers predominate, the solid may be classified as primarily an

–electronic (n or p type) or

–ionic conductor.

•However, mixed conduction is

= electronic + ionic

Insulation Resistance

•For an ionic solid, mobility is related to the diffusion coefficient D (cm2/sec) by the Einstein relationship

= ezD/kT

•Diffusion and conductivity are related by the Nernst-Einstein equation:

= n(ez)2D/kT

•Since both diffusion and N (number of defects generated) are activated processes, where

N = n exp(-w/2kT)

Insulation Resistance

D = Do exp(- /kT) Then = o exp(-E/kT) •and E = w/2 +

•Where w and are activation energies for defect generation and migration.

•For extrinsic conduction w=0 and E=; that is, the ionic mobility becomes the controlling factor in the conduction.

2

Ionic Conduction

What is an ion? •An ion is a positive or negative loaded atom caused by electron deficiency or electron excess.

•This electron deficiency/excess arises at the reaction of two atoms (ionic connection).

•Positive loaded ions are called cations and negative loaded ions are called anions.

•In ionic crystal, the individual lattice atoms transfer electron between each other to form positively charged cations and negatively charged anions.

Ionic Conduction

•The binding forces between ions are electrostatic in nature and thus very strong.

•The RT conductivity of ionic crystals is much lower than the conductivity of typical metallic conductors.

•The large difference in conductivity can be understood by realizing that the wide bandgap in insulators allows only extremely few electrons to become excited from the valence band into the conduction band.

Ionic Conduction

•Ionic conduction is caused by the movement of some negatively (or positively) charged ions which “hop” from lattice site to lattice site under the influence of an electric field.

•This ionic conductivity: (1)

–Nion is the number of ions per unit volume that can change their position under the influence of an electric field

–ion is the mobility of these ions.

ionionion eN

Ionic Conduction

•In order for ions to move through a crystalline solid, they must have sufficient energy to pass over an “energy barrier” (see schematic).

•Thus, Nion in eq.(1) depends on the vacancy concentration in the crystal (i.e., on the number of Schottky defects).

Ionic Conduction

d

Q

E

distance

(a) E

distance

(b)

Figure: Schematic representation of a potential barrier, which an ion ( )

has to overcome to exchange its site with a vacancy ( ).

(a) Without an external electric field, (b) with an external electric field. d =

distance between two adjacent, equivalent lattice sites, Q = activation

energy.

Ionic Conduction

•The D varies with temperature; this dependence is commonly expressed by an Arrhenius equation:

(2)

•Where Q is the activation energy , Do is a pre-exponential factor that depends on the vibrational frequency of the atoms and some structural parameters.

Tk

QDD

B

o exp

3

Ionic Conduction

•Combining (1) through (2) yields,

(3)

•Equation (3) is shortened by combining the pre-exponential constant:

(4)

•Taking the natural logarithm yields:

• (5)

Tk

Q

Tk

DeN

BB

oion

ion exp

2

Tk

Q

B

oion exp

Tk

Q

B

oion

1lnln

Ionic Conduction

If plotted ln ion vs. 1/T,

a straight line with a

negative slope would

result. (See figure).

The slopes in Arrhenius

plots are utilized to

calculate the activation

energy, Q or Ea.

Tk

Q

B

oion

1lnln

Ionic Conduction

Slope = - Q/k

For SiO2 from graph:

Slope = (ln 10-7 – ln 10-14)/(1.5x10-3 – 2.55x10-3)

= [ln (10-7/10-14)]/(-1x10-3)

= ln 107/(-1x10-3) = - 1.612x104

From Slope = - Q/k

Q = (1.612x104)x(1.3806x10-23) = 2.225x10-19 J

Q = 1.39 eV (1 eV = 1.6x10-19 J)

Ionic Conduction

800 600 400

ln

1/T

T(oC)

Sometimes,

ln vs. 1/T plot will

give us two (2) line regions representating of two different Q values. Figure: Schematic representation of ln

versus 1/T for Na+ ions in NaCl.

(Arrhenius plot).

Ionic Conduction

•At low T, the Q is small, the thermal energy is just sufficient to allow the hopping of ions into already existing vacancy sites. This T range is commonly called the “extrinsic region”.非本征区域

•At high T, the thermal energy is large enough to create additional vacancies.

•The related Q is thus the sum of the Q for vacancy creation and ion movement. This T range is called the “intrinsic region”.本征区域

High Conducting Ceramics

•Ceramics are generally classified as electronic conductors, ionic conductors, mixed (electronic/ionic) conductors, and insulators.

•The electronic conductors include superconductors, and semiconductors.

•Ionic conductors generally exhibit conductivities in the range 10-1 to 100 S m-1 that increase exponentially with temperature.

•Insulators such as high-purity alumina are at the lower extreme of the conductivity of 10 -13 S m-1.

4

Temperature Sensitive Resistor

•Some ceramic resistors exhibit high value of the temperature coefficient of resistance (TCR) and they may be negative (NTC) or positive (PTC).

Temperature Sensitive Resistor

•In a ceramic a large temperature coefficient of resistivity can arise from 3 causes:

The intrinsic characteristic.

A structure transition which accomponied by a change in the conduction mechanism from semiconducting to metallic.

A rapid change in dielectric properties in certain ceramics which affects the electronic properties in the intergranular region to give rise to a large increase in resistivity with temperature over small temperature range.

•The 3rd Mechanism has led to important TCR devices.

Typical resistance-temperature response for various sensor materials

NTC Thermistor

•The TCR of a semiconductor is expected to be negative. •In each case the resistivity depends on temperature according to

•where is approximately independent of T and B is a constant related to the energy required to active the electron to conduct.

•Differentiating this equation leads to TCR value R:

T

BT exp)(

2

1

T

B

dT

dR

NTC Thermistor

•The most NTC materials are based on solid solutions of oxides with spinel structure, e.g. Fe3O4-ZnCr2O4 and Fe3O4-MgCr2O4.

•A series that gives favorable combinations of low resistivity and high coefficients is based on Mn3O4 with a partial replacement of Mn by Ni, Co and

Cu.

PTC Thermistor

•PTC thermistors exhibit an increase in resistance at a specified temperature.

•PTC resistor could be classified as critical temperature resistors because, in the case of the most widely used type

•The positive coefficient is associated with the ferroelectric Curie point.

5

PTC Thermistor

•Most PTC has the negative resistivity-temperature characteristic up to about 100oC and above about 200oC.

•While between these temperatures there is an increase of several orders of magnitude in resistivity.

•The PTC effect is exhibited by specially doped and processed (eg. BaTiO3).

Application of PTC Thermistor

•The are two main groups:

–Applications such as temperature measurement, temperature control, temperature compensation and over-temperature protection.

–The second group includes applications such as over-current protection, liquid level detection and time delay.

Voltage-dependent Resistors (Varistors)

•There are a number of situations in which it is valuable to have a resistor which offers a high resistance at low voltages and a low resistance at high voltages.

•Such a devices can be used to protect a circuit from high-voltage transients by providing a path across the power supply that

–takes only a small current under normal conditions but takes large current if the voltage rises abnormally,

–thus preventing high-voltage pulses from reaching the circuit.

•Schematic use of a VDR to protect a circuit against transients,

VDR Circuit to be protected Source

Varistors-VDR

•Ceramics based on SiC and ZnO are two materials in everyday use for VDR.

•The VDR behaviour in ZnO varistors for example is governed by electron states that are formed on the surfaces of crystals as a consequence of the discontinuity.

•These surface states act as acceptors for electrons from the n-type semiconductor.

•Electrons will be withdrawn from region near the surface and replaced by a positive space charge.

•Oppositely oriented Schottky barrier will be created at surface of neihbouring crystals so that a high resistance will be offered to electron flow in either direction.

Illustrations of actual microstructure of a varistor

6

Basic principles of Varistors-VDR

•At low applied fields small thermally activated currents pass over the reverse biased junction.

•At high fields tunneling through the junction will occur, accounting for the low resistance.

•The behavior is similar in some respects to Zener diodes.

•From varistor I-V characteristic, the linear part can be represented by the relation,

•Where kI is a constant and falls off at low voltages.

•If I1 and I2 are currents at voltages that differ by factor of 10,

UkI I

21

2

110 ,log II

I

I

Basic principles of Varistors-VDR

•Alternatively,

•where

•The resistance at a given voltage is

•Power dissipated is

•with = 25, a 10 % increase in voltage would increase the power dissipation by a factor about 2.5.

IkU V

/1/1 IV kkand

)1(1 1 Uk

IkRI

V

1 UkIUP I

Solid Electrolytes

Electrolyte - A substance that conducts electricity through the movement of ions.

Most electrolytes are solutions or molten salts, but some electrolytes are solids and some of those are crystalline solids. Different names are given to such materials:

–Solid Electrolyte

–Fast Ion Conductor

–Superionic Conductor

we will be looking at materials which behave as solid

electrolytes, their properties and applications.

Ionic vs. Electronic Conductivity

Let’s begin by comparing the properties of ionic conductors with the conventional electronic conductivity of metals.

Metals –Conductivity Range = 10 S/cm < s < 105 S/cm

–Electrons carry the current

–Conductivity Increases linearly as temperature decreases (phonon scattering decreases as T )

Solid Electrolytes –Conductivity Range = 10-3 S/cm < s < 10 S/cm

–Ions carry the current

–Conductivity decreases exponentially as temperature decreases (activated transport)

Defects In order for an ion to move through a crystal it must hop from an occupied site to a vacant site. Thus ionic conductivity can only occur if defects are present. The two simplest types of point defects are Schottky and Frenkel defects.

Schottky Defect (i.e. NaCl) Na+ + Cl- Vna + VCl

Frenkel Defect (i.e. AgCl) Ag+ VAg+ Ag+

interstitial

Chem 754 - Solid State Chemistry

Ion Migration (Schottky Defects) Consider the movement of Na+ ions in NaCl via vacancies originating from Schottky defects. Note that the Na+ ion must squeeze through the lattice, inducing significant local distortion/relaxation. This is one factor that limits the mobility of ions. A second factor that contributes is the relatively high probability that the ion will jump back to it’s

original position, leading to no net ionic migration.

To get across the unit cell into the vacancy the Na+ ion must hop through the center of the cube where it squeezes by 4 Cl- and 2 Na+. The energy of this “transition state” will determine the ease of migration.

Na

Na

Na

Cl

Cl

Cl

Cl

E

7

Ion Migration (Frenkel Defects) The Frenkel defects in AgCl can migrate via two mechanisms.

Ag

Ag

Ag

Cl

Cl

Cl

Cl

Ag2

Ag1

Ag

Ag

Cl

Cl

Ag

Ag

Ag

Cl

Cl

Cl

Cl

Ag2

Ag1

Ag

Ag

Cl

Cl

Ag

Ag

Ag

Cl

Cl

Cl

Cl

Ag1

Ag2

Ag

Ag

Cl

Cl

Ag

Ag

Ag

Cl

Cl

Cl

Cl

Ag2

Ag1

Ag

Ag

Cl

Cl

Direct Interstitial Jump

Interstitialcy Mechanism

由于离子的可移动性比电子要小得多，用霍尔效应测定载流子为何种离子是不大可能的

Conductivity 1.31 Ω-1·cm-1

Applications of Ionic Conductors

There are numerous practical applications, all based on electrochemical cells, where ionic conductivity is needed and it is advantageous/necessary to use solids for all components.

–Batteries

–Fuel Cells

–Gas Sensors

In such cells ionic conductors are needed for either the electrodes, the electrolyte or both.

–Electrolyte (Material needs to be an electrical insulator to prevent short circuit)

–Electrode (Mixed ionic and electronic conductivity is needed to avoid open circuit)

Electrolyte

Anode Cathode

Useful Power

e-

sOe2gO 2

221

e2)g(OH2H)s(O2 22

2

Schematic of a Solid Oxide Fuel Cell

http://www.cas.cn/ky/kyjz/201304/t

20130428_3829169.shtml 上海硅酸盐所固体氧化物燃料电池研究取得进展

燃料电池电池工作原理 氢燃料电池 甲醇等小分子燃料电池

燃料电池分类

8

• 质子交换膜燃料电池（PEMFC）简介

• 质子交换膜燃料电池(proton exchange membrane fuel cell，英文简称PEMFC)是一种燃料电池，在原理上相当于水电解的“逆”装置。其单电池由阳极、阴极和质子交换膜组成，阳极为氢燃料发生氧化的场所，阴极为氧化剂还原的场所，两极都含有加速电极电化学反应的催化剂，质子交换膜作为电解质。工作时相当于一直流电源，其阳极即电源负极，阴极为电源正极。

• 两电极的反应分别为：

• 阳极(负极)：2H2-4e=4H+

• 阴极(正极)：O2+4e+4H+=2H2O

• 碱性燃料电池（AFC）简介

• 使用的电解质为水溶液或稳定的氢氧化钾基质，且电化学反应也与羟基（-OH）从阴极移动到阳极与氢反应生成水和电子略有不同。这些电子是用来为外部电路提供能量，然后才回到阴极与氧和水反应生成更多的羟基离子。

• 负极反应：2H2 + 4OH- → 4 H2O + 4e-

• 正极反应：O2 + 2H2O + 4 e- → 4OH-

质子交换膜燃料电池优点： •其发电过程不涉及氢氧燃烧，因而不受卡诺循环的限制，能量转换率高； •发电时不产生污染，发电单元模块化，可靠性高，组装和维修都很方便，工作时也没有噪音。所以，质子交换膜燃料电池电源是一种清洁、高效的绿色环保电源。 •质子交换膜燃料电池工作温度低、启动快、比功率高、结构简单、操作方便等 碱性电池的优点： •效率高，因为氧在碱性介质中的还原反应比其他酸性介质高； •因为是碱性介质，可以用非铂催化剂，廉价。 •因工作温度低，碱性介质，所以可以采用镍板做双极板。

Schematic of Rechargeable Li Battery

Taken from A. Manthiram & J. Kim – “Low Temperature Synthesis of Insertion Oxides for Lithium Batteries”, Chem. Mater. 10, 2895-2909 (1998).

Solid Electrolyte Materials

•Ag+ Ion Conductors

–AgI & RbAg4I5

•Na+ Ion Conductors

–Sodium -Alumina (i.e. NaAl11O17, Na2Al16O25)

–NASICON (Na3Zr2PSi2O12)

•Li+ Ion Conductors

–LiCoO2, LiNiO2

–LiMnO2

•O2- Ion Conductors

–Cubic stabilized ZrO2 (YxZr1-xO2-x/2, CaxZr1-xO2-x)

– -Bi2O3

–Defect Perovskites (Ba2In2O5, La1-xCaxMnO3-y, …)

•F- Ion Conductors

–PbF2 & AF2 (A = Ba, Sr, Ca)

Chem 754 - Solid State Chemistry

-AgI & RbAg4I5 have ionic conductivities comparable to conc. H2SO4

Stabilized ZrO2 is not a good ionic conductor at low temperature.

Taken from “Solid State Chemistry and its Applications” by Anthony West

General Characteristics: Solid Electrolytes 1. A large number of the ions of one species should be mobile. This

requires a large number of empty sites, either vacancies or accessible interstitial sites.

– Empty sites are needed for ions to move through the lattice.

2. The empty and occupied sites should have similar potential energies with a low activation energy barrier for jumping between neighboring sites.

– High activation energy decreases carrier mobility, very stable sites (deep potential energy wells) lead to carrier localization.

3. The structure should have solid framework, preferable 3D, permeated by open channels.

– The migrating ion lattice should be “molten”, so that a solid framework of the other ions is needed in order to prevent the entire material from melting.

4. The framework ions (usually anions) should be highly polarizable.

– Such ions can deform to stabilize transition state geometries of the migrating ion through covalent interactions.

9

Ag+ Ion Conductors

-AgI • Stable below 146 ºC

• Wurtzite Structure (tetrahedral coordination)

• s = 0.001 S/cm – 0.0001 S/cm

-AgI • Stable above 146 ºC

• BCC Arrangement of I-, molten/ disordered Ag+

• s ~ 1 S/cm, EA=0.05 eV

• Conductivity decreases on melting

RbAg4I5

• Highest known conductivity at room temperature

• BCC Arrangement of I-, molten/disordered Ag+

• s ~ 0.25 S/cm (25 ºC), EA=0.07 eV

Chem 754 - Solid State Chemistry

Na+ Ion Conductors NaAl7O11 (Na2O.nAl2O3) • FCC like packing of oxygen

• Every fifth layer ¾ of the O2- ions are missing, Na+ ions present. These layers are sandwiched between spinel blocks.

• 2D ionic conductor

Na3Zr2PSi2O12 (NASICON) • Framework of corner sharing ZrO6

octhahedra and PO4/SiO4 tetrahedra

• Na+ ions occupy trigonal prismatic and octahedral sites, ¼ of the Na+ sites are empty

• EA ~ 0.3 eV

Chem 754 - Solid State Chemistry

Favored Materials (SOFC)

Cathode (Air Electrode)

–(La1-xCax)MnO3 (Perovskite)

•(La1-xSrx)(Co1-xFex)O3 (Perovskite)

•(Sm1-xSrx)CoO3 (Perovskite)

•(Pr1-xSrx)(Co1-xMnx)O3 (Perovskite)

Anode (H2/CO Electrode)

–Ni/Zr1-xYxO2 Composites

Electrolyte (Air Electrode)

–Zr1-xYxO2 (Fluorite)

•Ce1-xRxO2 , R = Rare Earth Ion (Fluorite)

•Bi2-xRxO3 , R = Rare Earth Ion (Defect Fluorite)

•Gd1.9Ca0.1Ti2O6.95 (Pyrochlore)

•(La,Nd)0.8Sr0.2Ga0.8Mg0.2O2.8 (Perovskite)

Interconnect (between Cathode and Anode)

–La1-xSrxCrO3 (Perovskite)

O2 Gas Sensor

The partial pressure of oxygen in the sample gas, PO2(sample), can be determined from the measured potential, V, via the Nernst equation.

Because of the low ionic conductivity at low temperatures, the sensor is only useful above 650 ºC.

See http://www.cambridge-sensotec.co.uk/sensors_explained.htm for details

V = (RT/4F) ln[{(PO2(ref.)}/{(PO2(sample)}]

• Example: Oxygen sensor ZrO2 • Principle: Make diffusion of ions

fast for rapid response.

Application: Sensors

A Ca 2+ impurity

removes a Zr 4+ and a

O 2 - ion.

Ca 2+

• Approach: Add Ca impurity to ZrO2: -- increases O2- vacancies

-- increases O2- diffusion rate

reference gas at fixed oxygen content

O 2-

diffusion

gas with an unknown, higher Oxyge n content

- + voltage difference produced!

sensor • Operation: -- voltage difference

produced when O2- ions diffuse from the external surface of the sensor to the reference gas.

Design Principles: O2- Conductors

•High concentration of anion vacancies

–necessary for O2- hopping to occur

•High Symmetry

–provides equivalent potentials between occupied and vacant sites

•High Specific Free Volume (Free Volume/Total Volume)

–void space/vacancies provide diffusion pathways for O2- ions

•Polarizable cations (including cations with stereoactive lone pairs)

–polarizable cations can deform during hopping, which lowers the activation energy

•Favorable chemical stability, cost and thermal expansion characteristics

–for commercial applications

10

Phase Transitions in ZrO2

Room Temperature Monoclinic (P21/c)

7 coordinate Zr 4 coord. + 3 coord. O2-

High Temperature(2500oC） Cubic (Fm3m)

cubic coordination for Zr tetrahedral coord. for O2-

Effect of Dopants: ZrO2, CeO2

•Doping ZrO2 (Zr1-xYxO2-x/2, Zr1-xCaxO2-x) fulfills two purposes

–Introduces anion vacancies (lower valent cation needed)

–Stabilizes the high symmetry cubic structure (larger cations are most effective)

•We can also consider replacing Zr with a larger cation (i.e. Ce4+) in order to stabilize the cubic fluorite structure, or with a lower valent cation (i.e. Bi3+) to increase the vacancy concentration.

Compound r4+ Specific Free Conductivity

(Angstroms) Volume @ 800ºC

Zr0.8Y0.2O1.9 0.86 0.31 0.03 S/cm

Ce0.8Gd0.2O1.9 1.01 0.38 0.15 S/cm

-Bi2O3 1.17 0.50 1.0 S/cm (730ºC)

Bi2O3 is only cubic from 730ºC to it’s melting point of 830ºC. Doping is necessary to

stabilize the cubic structure to lower temps.

Gd2Ti2O7 Pyrochlore烧绿石

The pyrochlore structure can be derived from fluorite, by removing 1/8 of the oxygens, ordering the two cations and ordering the oxygen vacancies.

By replacing some of the Gd3+ with Ca2+

oxygen vacancies in the A2O network are created, significantly increasing the ionic conductivity (at 1000ºC):

Gd2Ti2O7

s = 1 10-4 S/cm, EA = 0.94 eV

Gd1.8Ca0.2Ti2O6.95

s = 5 10-2 S/cm, EA = 0.63 eV

There is an opportunity to obtain mixed electronic-ionic conductivity in the pyrochlore structure.

M2O6 Network A2O Network

Ba2In2O5 Brownmillerite钙铁石

The brownmillerite structure can be derived from perovskite, by removing 1/6 of the oxygens and ordering the vacancies so that 50% of the smaller cations are in distorted tetrahedral coordination.

In Ba2In2O5 at 800 ºC the oxygen vacancies disorder throughout the tetrahedral layer, and the ionic conductivity jumps from 10-3 S/cm to 10-1 S/cm.

BaZrO3-Ba2In2O5 solid solutions absorb water to fill oxygen vacancies and become good proton conductors over the temperature range 300-700 ºC.

Tetrahedral Layer

Octahedral Layer

Aurivillius and BIMEVOX phases

Bi2WO6 is a member of the Aurivilius structure family. The structure contains 2D perovskite-like sheets made up of corner sharing octahedra, stacked with Bi2O2

2+ layers.

Bi4V2O11 is a defect Aurivillius phase, better written as (Bi2O2)VO3.5, where 1/8 of the oxygen sites in the perovskite layer are vacant. Conductivity at 600 ºC is the highest ever reported for an O2- conductor ~ 0.2 S/cm.

Only the perovskite oxygens are mobile.

Normally Bi4V2O11 undergoes phase transitions upon cooling that lower it’s ionic conductivity, but doping onto the V site stabilizes the HT phase. These phases are generally called BIMEVOX phases. (Bi2O2)V0.9Cu0.1O3.35 has a conductivity of 0.01 S/cm at 350 ºC !!

Summary O2- Conductors

•It is generally true that dopants have to be added either to introduce vacancies, or to stabilize the high temperature/high symmetry phase

•Among fluorite based O2- conductors both doped CeO2 and Bi2O3 have higher conductivities than stabilized ZrO2, but both are less chemically stable. In particular they are prone to reduction. This limits their use.

•Brownmillerite钙铁石conductors show high conductivity, but are prone to become electrically conducting under mildly reducing conditions. They show promise as proton conductors.

•Ionic conductors based on Bi4V2O11 (BIMEVOX) show very high conductivity for low temperature applications.