The long-range distortion caused by point defects

Abstract

The long-range distortion field associated with point defects, which is characterized by the elastic dipole tensor G, is discussed. This quantity is commonly calculated using the Kanzaki-Hardy formula, which is based on the harmonic approximation. The formula is known to give erroneous results for Schottky defects in ionic crystals, in spite of the fact that harmonic theory gives a reasonable account of formation energies. The reasons for this are examined. It is pointed out that G can be calculated either directly from the long-range displacements, or indirectly from the strain derivative of the formation energy. Harmonic theory necessarily gives different results by the two methods, and the strain-derivative method is to be preferred because it is correct to higher order in the defect forces. This is illustrated by a re-examination of the case of Schottky defects, where it is noted that the correction term discovered by Lidiard is exactly the electrostrictive contribution proposed by Flynn. It is suggested that in general the Kanzaki-Hardy formula is likely to be unreliable if the use of relaxed rather than unrelaxed defect forces substantially affects the results.