2. Defect Structure and Transport

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1 2. Defect Structure and Transport
Introduction point defects------electrical conduction in solid electrolytes Ionic solids contains these defects at all temperatures above O K. (thermal defect, intrinsic defects) Aliovalent impurities also introduce excess defects whose concentration is fixed mainly by composition and is often independent of temperature. (impurity defect, extrinsic defects) Ionic defects-----ionic conductivity Electronic defects-----electronic conductivity (which is undesirable in a solid electrolyte) For a solid electrolyte to be useful, the ratio of ionic to electronic conductivity should be 100 or greater. (otherwise, it will cause short circuit.) 本章要点：点缺陷数量的统计计算；点缺陷的表示方式 (Kroger-Vink符号)；晶体点缺陷的电荷平衡 ；点缺陷的生成反应 重点强调：具有较多缺陷的离子型固体(several percent),而不是仅有几个ppm数量级缺陷的固体。 讨论：缺陷形成的机理 表征固体电解质缺陷结构和传输行为的试验技术。 回顾：几类重要的固体电解质材料的性能。 总结：快离子导体产生的条件和准则。

2 2. Introduction 电导率的表征公式，影响电导率的物理因素 The total electrical conductivity (σT) in an electrolyte: ni—Concentration of the material (i) with charge Zi—Valency of the material (i) with charge μi—Mobility of the material (i) with charge e—Electronic charge

3 2. Defect Structure Kröger-Vink notation: The different kinds of ionic and electronic defects which may be present in an ionic solid are conveniently presented using Kröger-Vink notation, which specifies the nature, location, and effective charge of a defect. The nature of point defects and their concentration in any solid are determined by the consideration of chemical equilibrium between the various species. Clustering of defects and lattice disorder take place at relatively higher defect concentrations. Kröger-Vink记号：离子型固体中所出现的不同种类的离子和电子缺陷通常用该记号来表示。它详细规定了缺陷种类、位置和有效电荷的表示方法。 在任何固体中，点缺陷的种类和他们的浓度可以通过考虑不同物种之间的化学平衡来得到。 在缺陷浓度较高的固体中，经常会发生缺陷的聚集和晶格的扭曲现象。

4 2.1 Types of Point Defects The various kinds of point imperfections possible in an ionic crystal MX(M and X are monovalent), taking into account the requirement of charge neutrality. These are follows. Vacancies A mising M+ ion in a pure binary compound MX from its normal site is depicted as VM’. Similarly a vacant anion site is represented as Vx·.Here, V0 stands for a vacancy, the subscript for the missing species, and the superscript for the charge, prime for effective negative charge and dot for effective positive charge. Interstitials When an ion M+(or X-) occur in an interstitial site, then the defect is Mi· or Xi’. Misplaced Atoms When the atom M occupies a normal X site or vice versa, one has Mx or XM. 缺陷反应方程式的三个规则： 位置关系：在化合物MaXb中M位置数和X的位置数总是保持a：b。例如TiO2中Ti的位置数和O的位置数总是保持1:2。但这并不影响TiO2可以成为非化学计量化合物，因为位置的比例并不一定要和化学物质之间的比例一致。 质量平衡：缺陷方程的两边必须保持质量平衡。 电中性：晶体即使出现了各种微观缺陷也应保持电中性。这要求缺陷反应两边具有相同数目的有效电荷。

5 2.1 Types of Point Defects Frenkel Defects
Schottky defects A cation vacancy+an anion vacancy (Vm’Vx·). These are the predominant defects in alkali halides. Frenkel Defects A cation vacancy + an interstitial cation (Vm’Mi·). Silver halides generally have Frenkel Defect. an anion vacancy + an interstitial anion (Vx·Xi’) —Anti-Frenckel defects. ( occur in ThO2 and CaF2) 考虑到材料的电中性，在离子晶体MX(M,X是单价元素）中可能的几种点缺陷： 空位、间隙离子、错位原子、肖特基缺陷、 弗仑克尔缺陷。

6 2.1 Types of Point Defects Impurities
杂质：缺陷原子或离子有可能取代正常格位的原子或离子（取代杂质）或进入间隙位置。如果杂质与所取代的离子具有相同的电价，则由此产生的缺陷便没有有效电荷。另一方面，异价杂质的掺杂则会引起不同的缺陷。 对于任何一种掺杂，实际上都是形成了固溶体。固溶体分为有限固溶体和无限固溶体。 无限固溶体：溶质和溶剂二种晶体可以按任意比例无限制地相互溶解。 有限固溶体：杂质原子在固溶体中的溶解度是有限的，存在一个溶解度极限。 形成无限固溶体还是有限固溶体取决于溶质和溶剂两种晶体中的离子（或原子）半径的大小、晶体结构的型式、键的性质以及电价的大小。 Impurities Impurity atoms or ions may replace an atom or an ion in a normal lattice site (substitutional impurities) or enter interstitial sites.If the impurity has the same valency as the original ion, there is no effective charge associated with the defect. On the other hand, aliovalent impurities give rise to the following pairs of defects. In fact, all kinds of doping materials are formed solid solution which can be divided into limited solid solution and unlimited solid solution. Unlimited solid solution：Two kinds of solute and solvent crysyal can be mutual dissolved with any unlimited proportion. Limited solid solution：The solubility of impurity atoms in solid solution is limited and have a solubility limit. The formation of an unlimited or limited solid solution depends on the size of ions (or atomic) in the solute and solvent crystals, the type of crystal structure, the nature of chemical bond and the valency. Simple substitute ：Equivalent replacement is exchanged between the same valency ions. charge compensation substitute：

7 2.1 Types of Point Defects 掌握低价掺杂和高价掺杂时，缺陷化学方程式的两种不同写法。 The valency of the impurity cation is higher than that of the host cation impurity cation + interstitial anion, Lm·Xi’ impurity cation + cation vacancy, Lm·Vm’ The valency of the impurity cation is less than that of the host cation impurity cation + anion vacancy impurity cation + cation interstitial （1800oC以上，CaO<10%)

8 2.1 Types of Point Defects 异价杂质的取代还包括阴离子的取代，以及阴阳离子的同时取代。他们原则上是可能的，但其相关的研究还不够深入。由此产生的缺陷与阳离子的取代所产生的缺陷是一样的。 杂质离子的大小决定了它可能产生的缺陷形式，如取代、间隙。由于离子型固体通常被认为是阴离子组成紧密堆积结构，而阳离子占据某些空隙位置，所以阴离子间隙型的缺陷形式一般是很少有的。 但是对于具有开放结构的晶体，如CaF2，间隙阴离子的存在也是可能的。另外，提高温度，也可以松弛物质的结构，从而使以间隙离子为模型的缺陷得以存在。 Aliovalent impurities involving replacement of anions of one valency by those of another, as well as simultaneous substitution of both cations and anions by appropriate ions, are in principle possible but have not been investigated much so far. The resulting defects, however, are covered by the ones listed above. The size of the impurity ions relative to that of an available site (substitutional or interstitial) is important in determining the kind of defects which are favored. Since most ionic solids can be considered as composed of a close packing of the anions with the cations occupying some of the interstitial sites, defects types based on interstitial anions are generally less probable. However, if the structure is a relatively open one, such as CaF2, interstitial ions can indeed be accommodated. Further, increased temperature tends to loosen a structure, making a defect model based on interstitial ions sometimes possible at elevated temperatures

9 2.1 Types of Point Defects While many types of defects may coexist, energy considerations generally favor only one type of defect under a given set of conditions of temperature, pressure, type of impurity, and crystal structure. 不管是高电价取代还是低电价取代，都有产生缺陷的两种机理，但对于实际某一种材料来讲，只有一种机理是稳定存在的。 判断到底是哪一种机理在起作用，一般是通过测量纯物质和含杂质物质的真密度来判断。 空位机制一般密度减少，而间隙机制一般密度增加。 但这也不一定，对于低密度杂质的掺杂，无论哪种机制，其密度的变化都是减少的，但减少的速度或趋势是不同的。

10 2.1 Types of Point Defects Electronic Defects
了解电子缺陷的种类。 Electronic Defects Free electron (e’) Electron hole (h·) Pure ionic solids contain very few electronic defects and have wide forbidden energy gaps generally>0.3 eV. At high temperature Conduction band Valence band Forbidden energy gap Intrinsic defect Extrinsic defect

11 2.1 Types of Point Defects In the presence of impurities or in a nonstoichiometric solid, free electrons or electron holes are produced as a result of “charge compensation” to neutralize the effect of charged ionic defects 。 e.g. The effective negative charge of a metal vacancy may be neutralized by the presence of an electron hole in the crystal. It may be emphasized that at a given temperature, atmosphere, and composition, the concentration of either an ionic or electronic defect predominates. 在杂质存在的情况下，或在非化学计量比的固体中，为了中和带电离子缺陷所引起的电荷不平衡，便会产生自由电子或电子空穴。 如：金属离子空位所产生的有效负电荷可以由电子空穴来平衡。 需要重复强调的是：在给定温度、气氛和组成下，不管是离子缺陷的浓度还是电子缺陷的浓度，都是一定的。