  In this study, we conduct atomistic-level molecular dynamics simulations on
fixed-sized silicon-germanium (Si$_{1-x}$Ge$_{x}$) crystals to elucidate the
effects of dopant concentration and temperature on the crystalline inter-planar
distances. Our calculations consider a range of Ge dopant concentrations
between pure Si (0%) and 15%, and for both the optimised system state and a
temperature of 300 K. We observe a linear relationship between Ge concentration
and inter-planar distance and lattice constant, in line with the approximation
of Vegard's Law, and other experimental and computational results. These
findings will be employed in conjunction with future studies to establish
precise tolerances for use in crystal growth, crucial for the manufacture of
crystals intended for emerging gamma-ray crystal-based light source
technologies.
