  In this paper, we developed a thermodynamically consistent approach to
account for the Gibbs energy of pure metallic element with thermal vacancy over
wide temperature range. Taking body centered cubic (bcc) W for a demonstration,
the strong nonlinear increase for temperature dependence of heat capacities at
high temperatures and a nonlinear Arrhenius plots of vacancy concentration in
bcc W can be nicely reproduced by the obtained Gibbs energy. The successful
description of thermal vacancy on abnormal thermodynamic behaviors in bcc W
indicates that the presently proposed thermodynamically consistent approach is
a universal one, and applicable to the other metals.
