2' Defect Structure and Transport

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.)

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2. Introduction

• The total electrical conductivity (sT) in an
  electrolyte
• niConcentration of the material (i) with charge
• ZiValency of the material (i) with charge
• µiMobility of the material (i) with charge
• eElectronic charge

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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.

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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.

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2.1 Types of Point Defects

• Schottky defects
• A cation vacancyan anion vacancy (VmVx).
  These are the predominant defects in alkali
  halides.
• Frenkel Defects
• A cation vacancy an interstitial cation
  (VmMi). Silver halides generally have Frenkel
  Defect.
• an anion vacancy an interstitial
  anion (VxXi)
• Anti-Frenckel defects. ( occur in ThO2 and
  CaF2)

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2.1 Types of Point Defects

• 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 solutionTwo kinds of
  solute and solvent crysyal can be mutual
  dissolved with any unlimited proportion.
• Limited solid solutionThe 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

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2.1 Types of Point Defects

• The valency of the impurity cation is higher
  than that of the host cation
• impurity cation interstitial anion,
  LmXi
• impurity cation cation vacancy, LmVm
• The valency of the impurity cation is less than
  that of the host cation
• impurity cation anion vacancy
• 
  
• impurity cation cation interstitial
• 
  (1800oC??,CaOlt10)

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2.1 Types of Point Defects

• 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

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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.

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2.1 Types of Point Defects

• Electronic Defects
• Free electron (e)
• Electron hole (h)
• Pure ionic solids contain very few electronic
  defects and have wide forbidden energy gaps
  generallygt0.3 eV.
• At high temperature

Intrinsic defect
Extrinsic defect
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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.