The physics of heat conduction in layered, anisotropic crystals is probed by measurements of the cross-plane elastic constant $C_{33}$ and thermal conductivity $\Lambda$ of muscovite mica as a function of hydrostatic pressure. Picosecond interferometry and time-domain thermoreflectance provide high-precision measurements of $C_{33}$ and $\Lambda$, respectively, of micron-sized samples within a diamond-anvil cell; $\Lambda$ changes from the anomalously low value of $0.46\text{W}{\text{m}}^{-1}{\text{K}}^{-1}$ at ambient pressure to a value more typical of oxides crystals with large unit cells, $6.6\text{W}{\text{m}}^{-1}{\text{K}}^{-1}$, at $P=24\text{GPa}$. Most of the pressure dependence of $\Lambda$ can be accounted for by the pressure dependence of the cross-plane sound velocities.

Significance: Seismic studies revealed that shear wave ( S wave) travels through the inner core at an anomalously low speed, thus challenging the notion of its solidity. Here we show that for the candidate inner core component Fe ₇ C ₃ , shear softening associated with a pressure-induced spin-pairing transition leads to exceptionally low S -wave velocity ( v _S ) in its low-spin and nonmagnetic phase. An Fe ₇ C ₃ -dominant inner core would match seismic observations and imply a major carbon reservoir in Earth’s deepest interior.

The Leibfried-Schlömann (LS) equation, a commonly assumed model for the pressure dependence of thermal conductivity $\Lambda$, is tested by measurements on compressed ${\mathrm{H}}_2$O using a combination of the time-domain thermoreflectance method with the diamond anvil cell technique. The thermal conductivity of ice VII increases by an order of magnitude between 2 and 22 GPa, reaching $\Lambda \approx 25$ W m${}^{-1}$ K${}^{-1}$. Over a large compression range of $\approx$4%–33%, the LS equation describes the pressure dependence of $\Lambda$ of ice VII to better than 20%.