Alkali-metal vibrations in bcc, fcc, hcp, and 9R structures: Implications for the energetics of Li and Na martensitic phases
We present an embedded-atom-method (EAM) model that is specifically designed to accurately describe vibrations in bcc alkali metals. Using this model, we study bulk vibrational structure of Li, Na, K, and Rb when configured in bcc and the closed-packed (cp) fcc, hcp, and 9$R$ phases. From the vibrational density of states for each phase we thence find the corresponding vibrational contribution $A_{\rm vib}(T)$ to the Helmholtz free energy $A(T)$. Utilizing (i) differences in $A_{\rm vib}(T)$ between the bcc and cp structures and (ii) experimentally inferred thermodynamic transition temperatures for Li and Na (which martensitically transform from bcc to cp phases upon cooling), we extract values for zero-temperature energy differences between the bcc and relevant cp phases. We also put constraints on zero-temperature cp-bcc energy differences for K and Rb, which do not exhibit temperature induced transitions.