Role of the lattice in the two-step evolution of $\gamma$-cerium under pressure

We report here highly accurate ultrasonic measurements on ultrapure polycrystalline cerium up to 1 GPa. By simultaneously fitting the complete measured data set, bulk and shear moduli have been deduced without any independent input. We observe a maximum in the pressure evolution of the bulk modulus and show that this peculiar behavior can be qualitatively interpreted by taking into account the pressure-induced effects on electron-electron interaction and the anharmonicity of bonding in the $\gamma$ phase. The vibrational contribution to the total entropy change across the $\gamma$ to $\alpha$ transition is estimated to be on the order of 15%, highlighting the need to consider the lattice dynamics for an accurate description of the phase transition.

Figure 1

(Color online) Pressure dependence of longitudinal modulus $\rho v_L^2$ in polycrystalline Ce. The uncertainties in pressure and modulus are within the symbol size. Inset: zoom of the low-pressure region, where the longitudinal modulus reaches a maximum.

Figure 2

(Color online) Pressure dependence of shear modulus $\rho v_T^2$ in polycrystalline Ce. The uncertainties in pressure and modulus are within the symbol size.

Figure 3

(Color online) Pressure dependence of the bulk modulus $B$ in polycrystalline Ce. Inset: equation of state $V\left(p\right)$ of Ce at 300 K deduced from the $B\left(p\right)$ ultrasonics data.

Figure 4

(Color online) Bulk modulus $B=-V\frac{{\partial }^{2}E}{\partial V^2}$ as a function of volume from the model of Ref. 19 with a Murnaghan equation of state for $F_0\left(V\right)$. The thermodynamical ideal transition pressure, computed with the double tangent construction on the free energy, is shown on the pressure axis by vertical lines. The corresponding volumes are indicated by arrows: the area of transition is between these two volumes. Inset: corresponding free energies as a function of volume.