Debye-Waller factor of bcc metals: A comparison of the lattice-dynamics and molecular-dynamics results for Li and Rb

We present a method for the numerical calculation of the anharmonic contributions to the Debye-Waller factor (DWF) for metals involving long-range interactions. The numerical results of DWF obtained by the above method are compared with those of a molecular-dynamics calculation for a sixth-neighbor-interaction model of Li and Rb. It is shown that an excellent agreement is achieved between the results calculated by the two methods for the same model of the crystal potential. For Li and Rb the anharmonic contribution to DWF of $O({\left|\overrightarrow{q}\right|}^2$), where $\overrightarrow{q}$ is the wave vector, is about 10% of the quasiharmonic contribution at $T\sim T_m$ ($T_m$ is the melting temperature). The two other anharmonic contributions of $O({\left|\overrightarrow{q}\right|}^4$) to DWF are found to be negligible in Li and Rb even when $T\sim T_m$.