Applicability of Vegard's Law to the PbxSn1−xTe Alloy System

The relationship between lattice constant a0, alloy fraction x, and stoichiometry has been studied for the PbxSn1−xTe alloy system. Using the hole concentration p as a measure of the deviation from stoichiometry, it is shown that a0 for SnTe varies with p according to a0(SnTe)=−1.7×10−23 p+6.327, where a0 is measured in Å, and p in cm−3. For small deviations from stoichiometry it is shown that the alloys obey Vegard's law. Evidence is presented that Vegard's law holds in general providing fixed deviations from stoichiometry are considered. The functional relationship between a0, x, and p may be expressed as a0(alloy)=0.133x+a0(SnTe), where a0(SnTe) is given by the expression presented above. On the basis of this equation it is shown that previously reported deviations from Vegard's law arise in a natural way from the varying deviations from stoichiometry which characterize these alloys.