Effect of Spin-Orbit Interaction on the Lattice Properties of Solids: Sb and Bi

We present measurements of the specific heat ($C)$ vs. $T $for Bi and Sb and vs. isotopic mass for Sb. The measurements are compared with \textit{ab-initio }calculations performed with the ABINIT code, including spin-orbit (S-O) interaction. It is shown that the S-O interaction softens the lattice and thus increases the value of $C $at the low $T $maximum ($T_{m}$ \textit{$\sim $}8K for Bi, $T_{m}$ \textit{$\sim $}14K for Sb), improving agreement between theory and experiment. The effect of S-O interaction on other thermodynamic properties, such as the lattice parameter, $a_{0}$, and the cohesive energy, $E_{c}$, is also calculated. It is shown that this interaction decreases $E_{c}$ and, correspondingly, increases $a_{0}$. These effects are proportional to $c_{2}$\textit{$\lambda $} $^{2}+c_{3}$\textit{$\lambda $}$^{3}$, where \textit{$\lambda $ }is the S-O coupling constant, about twice as large for Bi as for Sb.