cp-frenkel defect.pptx

8/18/2019 cp-Frenkel defect.pptx

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Frenkel defect

Derivation of equilibrium

number of Frenkel defectspresent in elemental solids ormonatomic solids


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Frenkel defect: derivation

• Frenkel defect = Vacancy +interstitial atoms

• Interstitial atoms are the extra atomsthat are squeezed in beteen normalatom sites!

• "tom from a re#ular lattice site isremoved and placed it at theinterstitial position!

• $here by vacancy and interstitial is

simultaneously created% knon as


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• &imilar to previous derivations in the caseof &chottky defect

•'alculate the number of Frenkel defects inequilibrium at a temperature $

• (et

)i = the ener#y required to displace an

atom from re#ular lattice site to aninterstitial position *activation ener#y tocreate Frenkel defect

,= $otal number of atoms in the crystal,i = $otal number of interstitial sites

present in the crystal


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$otal number of ays in hich n Frenkel defects can be formed by


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and is% therefore% termed as ionic conductivity! $he above fact of ion motion #ivin# rise toconductivity is easily at hand if a potentialdi-erence is applied beteen to oppositefaces of an ionic crystal and the current ismeasured! $hese currents are too lar#e to be

explained in terms of the motion of electronsbecause the number of electrons in theconduction band at the temperatures involvedill be much too small! 'onsequently% the

currents must be a result of the mi#ration ofions under the in.uence of the electric /eld!Further% for the mi#ration of ions 0di-usion1 thelattice must have some vacant sites to #ive

place to mi#rated ions! $his implies that


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Question:

Derive the equation forequilibrium number ofFrenkel defects for

ionic solids

cp-frenkel defect.pptx

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