Thermodynamics of the $\alpha \text{−}\gamma$ transition in cerium studied by an LDA + Gutzwiller method

Utilizing the local-density approximation (LDA) + Gutzwiller method, we have studied the $\alpha \text{−}\gamma$ transition in cerium. Our results indicate that the volume collapse transition between $\alpha$ and $\gamma$ phases is present at zero temperature with negative pressure. By further providing a newly finite temperature generalization of the LDA + Gutzwiller method (using the mean-field potential approach), the entropy contributed by both electronic quasiparticles and lattice vibration included, we obtain the Gibbs free energy at a given volume and temperature, from which we get the $\alpha \text{−}\gamma$ transition at finite temperature and pressure. Our results indicate that the electronic entropy and lattice vibrational entropy both play important roles in the $\alpha \text{−}\gamma$ transition. We also calculated the equation of state and phase diagram of cerium, finding good agreement with the experiments.

Figure 1

Calculated cold energy for different $U$ (upper left panel) and free energy for different temperatures (upper right panel) as a function of atomic volume, with quasiparticle renormalization weights of the 7/2 and 5/$2f$ electrons (lower left panel) and 7/2 and 5/2 orbital populations (lower right panel).

Figure 2

Energy related term across the $\alpha \text{−}\gamma$ transition, where the upper panel denotes experimental data $(◯$ [13], $\square$ [13], $▵$ [3]) and the lower panel denotes present data $(△$, electronic entropy; $▽$, entropy of phonon), with entropy terms $T\Delta S$ (solid symbols) and $P\Delta V$ (open symbols) and internal energy $\Delta E$ (open symbols overlapped with plus symbol).

Figure 3

Equation of state of fcc Ce. The solid line and open symbols denote results of $\text{LDA}+\mathrm{G}$ calculations, where the open symbols denote the region of thermodynamic instability, i.e., the $\alpha \text{−}\gamma$ transition. The solid symbols denote previous experimental data [2].

Figure 4

Pressure vs temperature phase diagram of fcc Ce. Open and closed circles denote present $\text{LDA}+\mathrm{G}$ data. The other symbols denote previous experimental data $(\diamond$ [1], $▵$ [2], $\square$ [2], $▾$ [3], $★$ [46]).