Thermodynamics of the insulator-metal transition in dense liquid deuterium

Recent dynamic compression experiments [M. D. Knudson et al., Science 348, 1455 (2015); P. M. Celliers et al., Science 361, 677 (2018)] have observed the insulator-metal transition in dense liquid deuterium, but with an approximately 95-GPa difference in the quoted pressures for the transition at comparable estimated temperatures. It was claimed in the latter of these two papers that a very large latent heat effect on the temperature was overlooked in the first, requiring correction of those temperatures downward by a factor of 2, thereby putting both experiments on the same theoretical phase boundary and reconciling the pressure discrepancy. We have performed extensive path-integral molecular dynamics calculations with density functional theory to directly calculate the isentropic temperature drop due to latent heat in the insulator-metal transition for dense liquid deuterium and show that this large temperature drop is not consistent with the underlying thermodynamics.

Figure 1

Notional schematic of the $PT$ phase diagram for deuterium around the insulator-metal transition with representative isentropes. The black dashed line represents the phase boundary and terminates at the critical point. The isentropes are depicted with slight $-dT/dP$ near the phase boundary, resulting from a negative Grüneisen $\gamma$, in accordance with first-principles calculations. The red arrow suggests a convenient integration path from $S+\mathrm{\Delta }{S}_1$ back to $S$.

Figure 2

Energy versus temperature in the vicinity of the insulator-metal transition at specific volumes of 1.80 Å${}^3$/atom (green circles, dotted fit) and 1.78 Å${}^3$/atom (black circles, solid fit). $C_V$ is given by the slope.

Figure 3

Pressure times volume versus energy in the vicinity of the insulator-metal transition at specific volumes of 1.80 Å${}^3$/atom (green circles, dotted fit) and 1.78 Å${}^3$/atom (black circles, solid fit). The Grüneisen $\gamma$ is given by the slope.

Figure 4

Pressure versus temperature for several specific volumes. Labels for each fit indicate the specific volume (in Å${}^3$/atom).

Figure 5

Pressure versus specific volume at 1345 K.