Experimental and theoretical study of deviations from Vegard's law in the Sn_xGe_1-x system

First principles density functional theory is used to study the compositional dependence of the structural, elastic, electronic, and bonding properties of newly prepared Sn_xGe_1-x alloys and compounds. The calculated variation of lattice constant a(x) with composition for tin content (% Sn, x < 0.20) exhibits a small and systematic positive deviation of the lattice constants from ideal Vegard behavior, in agreement with our measurements on Sn_xGe_1-x alloys synthesized in this range. Over this range the compressibility also exhibits a concomitant increase relative to the Vegard average. To elucidate this structural behavior, we treat Si_xGe_1-x, Ge_xC_1-x, and Si_xC_1-x using the same computational procedure and find the expected negative deviations in a(x) from Vegard's Law behavior in all of these cases. Calculations on molecular analogues, consisting of tetrahedral A(XH₃)₄ clusters with {A,X} = {Sn,Ge}, {Si,Ge} {Si,C}, and {Ge,C} reveal that both the sign and magnitude of the deviations from ideal behavior are also present at the molecular level. The calculated bond lengths in all of these clusters agree well with available molecular structure data for these systems.