# Saddle-point equilibrium lines between fcc and bcc phases in Al and Ca from first principles

## Abstract

Phase equilibrium lines (denoted ph-eq lines) of face-centered-cubic (fcc) and body-centeredcubic (bcc) phases, as well as saddle-point equilibrium lines (denoted sp-eq lines) in Al and Ca are studied by first-principles total-energy calculations. For a non-vibrating crystal of Al we determine the transition pressure pt = 2.62 Mbar from fcc to bcc phase. The sp-eq line lies between the two ph-eq lines, merges with the bcc-eq line at V = 61 au3/atom (p = 1.64 Mbar) and with the fcc-eq line at V = 42.4 au3/atom (p = 5.50 Mbar), gives the Gibbs free energy barrier δG = 0.64 mRy/atom at pt. The bcc phase is unstable below 1.64 Mbar, while the fcc phase is unstable above 5.50 Mbar. In a non-vibrating crystal of Ca two sp-eq lines (denoted sp1-eq line and sp2-eq line, respectively) are found corresponding to two phase transitions: one is from fcc to bcc at pt1 = 89.6 kbar, the other is from bcc to fcc at pt2 = 787 kbar. The sp1-eq line merges with the bcc-eq line at V = 231 au3/atom (p = 50 kbar) and with the fcc-eq line at V = 183 au 3/atom (p = 174 kbar), gives a barrier of δG1 = 0.62 mRy/atom at pt1. The sp2-eq line merges with the bcc-eq line at V = 90 au 3/atom (p = 981 kbar) and with the fcc-eq line at V = 110 au 3/atom (p = 624 kbar), gives a barrier of δG2 = 1.1 mRy/atom at pt2. The bcc phase is stable in the range from 50 kbar to 981 kbar but unstable outside this range, while the fcc phase is unstable in the range from 174 to 624 kbar but stable outside this range. This work confirms all the features of the sp-eq line described in our recent work [S.L. Qiu, P.M. Marcus, J. Phys.: Condens. Matter 24, 225501 (2012)] and finds two additional features: (1) there are two sp-eq lines corresponding to the two phase transitions between fcc and bcc phases in Ca; (2) fcc phase of Ca is unstable between the two merge points on the fcc-eq line but stable beyond them, while bcc phase of Ca is stable between the two merge points on the bcc-eq line but unstable beyond them.© EDP Sciences Società Italiana di Fisica Springer-Verlag 2013.