The behavior of the f-electrons in the lanthanides and actinides governs important macroscopic properties but their pressure and temperature dependence is not fully explored. Cerium with nominally just one 4f electron offers a case study with its iso-structural volume collapse from the γ-phase to the α-phase ending in a critical point (p _C, V _C, T _C), unique among the elements, whose mechanism remains controversial. Here, we present longitudinal (c _L) and transverse sound speeds (c _T) versus pressure from higher than room temperature to T _C for the first time. While c _L experiences a non-linear dip at the volume collapse, c _T shows a step-like change. This produces very peculiar macroscopic properties: the minimum in the bulk modulus becomes more pronounced, the step-like increase of the shear modulus diminishes and the Poisson's ratio becomes negative-meaning that cerium becomes auxetic. At the critical point itself cerium lacks any compressive strength but offers resistance to shear.

It is qualitatively well known that kinetics related to nucleation and growth can shift apparent phase boundaries from their equilibrium value. In this work, we have measured this effect in Bi using time-resolved X-ray diffraction with unprecedented 0.25 ms time resolution, accurately determining phase transition pressures at compression rates spanning five orders of magnitude (10^-2-10³ GPa/s) using the dynamic diamond anvil cell. An over-pressurization of the Bi-III/Bi-V phase boundary is observed at fast compression rates for different sample types and stress states, and the largest over-pressurization that is observed is ΔP = 2.5 GPa. The work presented here paves the way for future studies of transition kinetics at previously inaccessible compression rates.