Entropy and free energy at the hcp-bcc transformation temperature in metals and alloys

Abstract

It has been shown that a plot of the Φ function, defined by -(G_tr - G_o)/T_tr where G_tr and G_o are respectively the Gibb’s free energies at the hcp → bcc allotropie transformation temperature(T_tr ) and at absolute zero, vs the entropy (S_tr) of the hcp phase at T_tr is linear. This concept of the Φ function and its relation to S_tr can be extended to alloys with the aid of the 'central atoms' solution model. Its use has been demonstrated with respect to the Ti-Zr system where the estimated transformation temperatures are shown to be within the (hcp + bcc) phase field.