# Ionic Conductivity and Solid Electrolytes

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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 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 (m ), 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 n i (ez) i i = i i 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 Insulation Resistance For an ionic solid, mobility is related to the diffusion coefficient D (cm /sec) by the Einstein relationship = ezd/kt Diffusion and conductivity are related by the Nernst- Einstein equation: = n(ez) D/kT Since both diffusion and N (number of defects generated) are activated processes, where N = n exp(-w/kt) Then and D = D o exp(- /kt) = o exp(-e/kt) E = w/ + 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. 1

2 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. 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 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: ion Nion eion (1) In order for ions to move through a crystalline solid, they must have sufficient energy to pass over an energy barrier (see schematic). Thus, N ion in eq.(1) depends on the vacancy concentration in the crystal (i.e., on the number of Schottky defects). N ion 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. E d (a) Q distance E (b) distance 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. The D varies with temperature; this dependence is commonly expressed by an Arrhenius equation: Q D Do exp kbt () Where Q is the activation energy, D o is a preexponential factor that depends on the vibrational frequency of the atoms and some structural parameters.

3 Combining (1) through () yields, Nion e Do Q ion exp kbt kbt (3) Equation (3) is shortened by combining the preexponential constant: Q ion o exp kbt (4) 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. Taking the natural logarithm yields: Q 1 ln ion ln o (5) kb T ln ion Q 1 ln o kb T Slope = - Q/k For SiO from graph: Slope = (ln 10-7 ln )/(1.5x x10-3 ) = [ln (10-7 /10-14 )]/(-1x10-3) = ln 10 7 /(-1x10-3 ) = x10 4 From Slope = - Q/k Q = (1.61x10 4 )x(1.3806x10-3 ) =.5x10-19 J Q = 1.39 ev (1 ev = 1.6x10-19 J) Sometimes, ln vs. 1/T plot will give us two () line regions representating of two different Q values. ln T( o C) 1/T Figure: Schematic representation of ln versus 1/T for Na + ions in Na. (Arrhenius plot). 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 S m -1. 3

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 3 rd Mechanism has led to important TCR devices. NTC Thermistor The TCR of a semiconductor is expected to be negative. In each case the resistivity depends on temperature according to B ( T) exp T 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 : Typical resistance-temperature response for various sensor materials 1 d B R dt T NTC Thermistor The most NTC materials are based on solid solutions of oxides with spinel structure, e.g. Fe 3 O 4 -ZnCr O 4 and Fe 3 O 4 -MgCr O 4. A series that gives favorable combinations of low resistivity and high coefficients is based on Mn 3 O 4 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. 4

5 PTC Thermistor Most PTC has the negative resistivity-temperature characteristic up to about 100 o C and above about 00 o C. 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. BaTiO 3). Application of PTC Thermistor The are two main groups: Applications such as temperature measurement, temperature control, temperature compensation and overtemperature 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, Source VDR Circuit to be protected 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 5

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, I kiu Where k I is a constant and falls off at low voltages. If I 1 and I are currents at voltages that differ by factor of 10, log I 1 10, I I I 1 Basic principles of Varistors-VDR Alternatively, where U k The resistance at a given voltage is R kv I Power dissipated is V 1/ and k V k with = 5, a 10 % increase in voltage would increase the power dissipation by a factor about.5. I P IU k U I 1 1/ I U k 1 1 ( 1) 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 < 10 5 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. Ion Migration (Schottky Defects) Consider the movement of Na + ions in Na 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. Na Na E Schottky Defect (i.e. Na) Na V na + V Frenkel Defect (i.e. ) + V + + interstitial Na 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 - and Na +. The energy of this transition state will determine the ease of migration. Chem Solid State Chemistry 6

7 Ion Migration (Frenkel Defects) The Frenkel defects in can migrate via two mechanisms. 1 1 Direct Interstitial Jump 1 1 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 e - Useful Power Electrolyte Anode Cathode 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) Schematic of a Solid Oxide Fuel Cell g 1 O e O O (s) H H O(g) e s _ 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 7

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 ):H -4e=4H + 阴极 ( 正极 ):O +4e+4H+=H O 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 :H + 4OH - 4 H O + 4e - 正极反应 :O + H O + 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, (1998). Solid Electrolyte Materials + Ion Conductors I & Rb 4 I 5 Na + Ion Conductors Sodium -Alumina (i.e. NaAl 11 O 17, Na Al 16 O 5 ) NASICON (Na 3 Zr PSi O 1 ) Li + Ion Conductors LiCoO, LiNiO LiMnO O - Ion Conductors Cubic stabilized ZrO (Y x Zr 1-x O -x/, Ca x Zr 1-x O -x ) -Bi O 3 Defect Perovskites (Ba In O 5, La 1-x Ca x MnO 3-y, ) F - Ion Conductors PbF & AF (A = Ba, Sr, Ca) Stabilized ZrO is not a good ionic conductor at low temperature. -I & Rb 4 I 5 have ionic conductivities comparable to conc. H SO 4 Chem Solid State Chemistry 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.. 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. 8

9 + Ion Conductors -I Stable below 146 ºC Wurtzite Structure (tetrahedral coordination) s = S/cm S/cm -I Stable above 146 ºC BCC Arrangement of I -, molten/ disordered + s ~ 1 S/cm, E A =0.05 ev Conductivity decreases on melting Rb 4 I 5 Highest known conductivity at room temperature BCC Arrangement of I -, molten/disordered + s ~ 0.5 S/cm (5 ºC), E A =0.07 ev Na + Ion Conductors Na 3 Zr PSi O 1 (NASICON) Framework of corner sharing ZrO 6 octhahedra and PO 4 /SiO 4 tetrahedra Na + ions occupy trigonal prismatic and octahedral sites, ¼ of the Na + sites are empty E A ~ 0.3 ev NaAl 7 O 11 (Na O. nal O 3 ) FCC like packing of oxygen Every fifth layer ¾ of the O - ions are missing, Na + ions present. These layers are sandwiched between spinel blocks. D ionic conductor Chem Solid State Chemistry Favored Materials (SOFC) Cathode (Air Electrode) (La 1-x Ca x )MnO 3 (Perovskite) (La 1-x Sr x )(Co 1-x Fe x )O 3 (Perovskite) (Sm 1-x Sr x )CoO 3 (Perovskite) (Pr 1-x Sr x )(Co 1-x Mn x )O 3 (Perovskite) Anode (H /CO Electrode) Ni/Zr 1-x Y x O Composites Electrolyte (Air Electrode) Zr 1-x Y x O (Fluorite) Ce 1-x R x O, R = Rare Earth Ion (Fluorite) Bi -x R x O 3, R = Rare Earth Ion (Defect Fluorite) Gd 1.9 Ca 0.1 Ti O 6.95 (Pyrochlore) (La,Nd) 0.8 Sr 0. Ga 0.8 Mg 0. O.8 (Perovskite) Interconnect (between Cathode and Anode) La 1-x Sr x CrO 3 (Perovskite) Chem Solid State Chemistry The partial pressure of oxygen in the sample gas, P O (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. O Gas Sensor V = (RT/4F) ln[{(p O (ref.)}/{(p O (sample)}] See for details Application: Sensors Example: Oxygen sensor ZrO Principle: Make diffusion of ions fast for rapid response. Approach: Add Ca impurity to ZrO: -- increases O - vacancies -- increases O - diffusion rate Operation: -- voltage difference produced when O - ions diffuse from the external surface of the sensor to the reference gas. Ca + gas with an unknown, higher Oxyge n content A Ca + impurity removes a Zr 4+ and a O - ion. sensor reference gas at fixed O - oxygen content diffusion + voltage difference produced! - Design Principles: O - Conductors High concentration of anion vacancies necessary for O - 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 O - 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 9

10 Phase Transitions in ZrO Room Temperature Monoclinic (P 1 /c) 7 coordinate Zr 4 coord. + 3 coord. O - High Temperature(500 o C) Cubic (Fm3m) cubic coordination for Zr tetrahedral coord. for O - Effect of Dopants: ZrO, CeO Doping ZrO (Zr 1-x Y x O -x/, Zr 1-x Ca x O -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. Ce 4+ ) in order to stabilize the cubic fluorite structure, or with a lower valent cation (i.e. Bi 3+ ) to increase the vacancy concentration. Compound r 4+ Specific Free Conductivity (Angstroms) 800ºC Zr 0.8 Y 0. O S/cm Ce 0.8 Gd 0. O S/cm -Bi O S/cm (730ºC) Bi O 3 is only cubic from 730ºC to it s melting point of 830ºC. Doping is necessary to stabilize the cubic structure to lower temps. Gd Ti O 7 Pyrochlore 烧绿石 Ba In O 5 Brownmillerite 钙铁石 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 Gd 3+ with Ca + oxygen vacancies in the A O network are created, significantly increasing the ionic conductivity (at 1000ºC): Gd Ti O 7 s = S/cm, E A = 0.94 ev Gd 1.8 Ca 0. Ti O 6.95 s = S/cm, E A = 0.63 ev There is an opportunity to obtain mixed electronic-ionic conductivity in the pyrochlore structure. M O 6 Network A O Network 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 Ba In O 5 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. BaZrO 3 -Ba In O 5 solid solutions absorb water to fill oxygen vacancies and become good proton conductors over the temperature range ºC. Tetrahedral Layer Octahedral Layer Aurivillius and BIMEVOX phases Bi WO 6 is a member of the Aurivilius structure family. The structure contains D perovskite-like sheets made up of corner sharing octahedra, stacked with Bi O + layers. Bi 4 V O 11 is a defect Aurivillius phase, better written as (Bi O )VO 3.5, where 1/8 of the oxygen sites in the perovskite layer are vacant. Conductivity at 600 ºC is the highest ever reported for an O - conductor ~ 0. S/cm. Only the perovskite oxygens are mobile. Normally Bi 4 V O 11 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. (Bi O )V 0.9 Cu 0.1 O 3.35 has a conductivity of 0.01 S/cm at 350 ºC!! Summary O - 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 O - conductors both doped CeO and Bi O 3 have higher conductivities than stabilized ZrO, 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 Bi 4 V O 11 (BIMEVOX) show very high conductivity for low temperature applications. 10

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