Imperfections in Solids

• Perfect crystals do not exist; even the best crystals have 1ppb defects.– Defects are imperfections in the regular repeating

pattern and may be classified in terms of their dimensionality (Point vs. Extended).

– Classification is given by; 1. Point Defects 2. Line Defects

1. Point Defects The irregularities or deviations from ideal arrangement

around a point or an atom in a crystalline substance.2. Line defects  The irregularities or deviations from ideal arrangement

in entire rows of lattice points.

1. Point DefectsPoint defects can be classified into three types :(i)   Stoichiometric Defects (E.g. Vacancy Defect,

Interstitial Defect)(ii)  Impurity Defects(iii) Non-Stoichiometric Defects (E.g. Metal Excess

Defect, Metal Deficiency Defect )

(i) Stoichiometric Defects

a) Vacancy Defect

– given a perfect crystal (e.g. of Cu), an atom can be placed on the outside of the cell to produce a vacancy (≡ □); remember atom migration.

– e.g. TiO has 1:1 stoichiometry and NaCl structure, but has 15% vacancies on the Ti sites and 15% vacancies on the O sites. Both sets of vacancies are disordered.

b) Interstitial Defect When some constituent particles (atoms or molecules)

occupy an interstitial site, the crystal is said to have interstitial defect. This defect increases the density of the substance.

*Ionic Crystals shows the following Defects

– in pure metal compounds, don’t need to worry about electroneutrality.

– in an ionic crystal, the interior and surface must remain ≈ neutral.

c) Schottky Defect– take anions and cations and place them on surface

in equal numbers.– stoichiometric effect: equal numbers of anion and

cation vacancies.– may be randomly distributed, but tend to cluster

because of- oppositely charged vacancies.– most important with alkali halides.– at room temp, ~1 in 1015 pairs vacant in NaCl, so 1mg sample has ~10,000 Schottky Defects.– This defect causes the decrease in density of- the substance

b) Frenkel Defect– take cation out of position and

cram it into an interstitial site (void between normal atomic position).

– Ag+ surrounded by 4Cl- stabilizes this defect.

– tendency for vacancy and interstitial to form nearby pair.

– also a stoichiometric deffect (vacancies = interstitials).

(ii)Impurity Defect

Due to Impurities and Doping• Impurities are elements present in the material

that are different from those in the compound formula.

• Dopants are intentionally added impurities (to make alloys or affect changes in properties). Alloy formation most likely when dopant anions and cations are close in size to original material.

• Isovalent dopants: substitution species have the same charge.NaCl:AgCl → Na1-xAgxCl (alloy on cation site)

AgBr:AgCl → AgBr1-xClx (alloy on anion site)

• Aleovalent dopant: substitution species has different charge.NaCl:SrCl2 could be either Na1-2xSrx□xCl or Na1-

xSrxClClxi

– either could happen; experimentally, first is found.

Figure shows the impurity defect in NaCl by Sr2+ ion

*Additional Information about The Impurity Defect

Due to Vacancy: Missing atom from an atomic site Atoms around the vacancy displaced Tensile stress field produced in the vicinity

Tensile StressFields ?

Impurity

Interstitial

Substitutional

SUBSTITUTIONAL IMPURITY Foreign atom replacing the parent atom in the crystal E.g. Cu sitting in the lattice site of FCC-Ni

INTERSTITIAL IMPURITY Foreign atom sitting in the void of a crystal E.g. C sitting in the octahedral void in HT FCC-Fe

Compressive stress fields

Tensile StressFields

Compressive StressFields

Relativesize

Due to Interstitial Atom: