Thermal Signatures of the Kondo Volume Collapse in Cerium

X-ray diffraction measurements of cerium in the vicinity of the isostructural $\gamma \mathrm{\text{−}}\alpha$ transition have been performed with high precision and accuracy from room temperature to almost 800 K. The disputed location of the critical point has been found to occur at $1.5\pm 0.1\mathrm{GPa}$ and $480\pm 10\mathrm{K}$. The data are well fit by the Kondo volume collapse model plus a quasiharmonic representation of the phonons. The resultant free energy is validated against data for the thermodynamic Grüneisen parameter and, beyond the dominant spin-fluctuation contribution, indicates a dramatic change in the lattice Grüneisen parameter across the transition.

Figure 1

Pressure-volume isotherms shifted by 0, 0.2, 0.4, …, 1.4 GPa from lowest to highest for visual clarity. Pressures were determined using the NaCl equation of state [31]. The points are the present data, while the curves are functional forms of the KVC model (see text). The inset shows the unshifted results at large volume. Atomic volumes are accurate to about $0.05{\AA }^3$, pressure uncertainty is estimated to be $<0.05–0.1\mathrm{GPa}$ for data recorded using the same setup and x-ray calibration.

Figure 2

Angle dispersive diffraction patterns at RT in the vicinity of the VC showing the transition.

Figure 3

Room-temperature thermodynamic $\gamma =V(\partial P/\partial E{)}_V$ (${\gamma }_1$, ${\gamma }_2$) and lattice ${\gamma }_{\mathrm{lat}}$ (${\gamma }_{1,\mathrm{lat}}$, ${\gamma }_{2,\mathrm{lat}}$) Grüneisen parameters as obtained from Eq. (1) in two fits to the pressures (see text). The open circles [32], filled squares [33] and filled triangles (present $V(\partial P/\partial T{)}_V$ divided by $C_V$ [33]) are experimental results for $\gamma$.

Figure 4

Ce phase diagram. Solid black symbols denote present (gray symbols previous [12 ▪, 13 ●, 18 ▾, 23 ◂, 24 ▸, 25 ▴]) VC data. The open black circles are bulk modulus $B_T$ minima obtained from the inset showing $B_T(p)$ for $T=481$, 500, 577, 692, and 775 K. The solid (VC) and dashed ($B_T$ minima) lines are from the two models as labeled.