Quantum-Mechanical Interatomic Potentials with Electron Temperature for Strong-Coupling Transition Metals

In narrow $d$-band transition metals, electron temperature $T_{\mathrm{el}}$ can impact the underlying electronic structure for temperatures near and above melt, strongly coupling the ion- and electron-thermal degrees of freedom and producing $T_{\mathrm{el}}$-dependent interatomic forces. Starting from the Mermin formulation of density functional theory, we have extended first-principles generalized pseudopotential theory to finite electron temperature and then developed efficient $T_{\mathrm{el}}$-dependent model generalized pseudopotential theory interatomic potentials for a Mo prototype. Unlike potentials based on the $T_{\mathrm{el}}=0$ electronic structure, the $T_{\mathrm{el}}$-dependent model generalized pseudopotential theory potentials yield a high-pressure Mo melt curve consistent with density functional theory quantum simulations, as well as with dynamic experiments, and also support a rich polymorphism in the high-$(T,P)$ phase diagram.

Figure 1

Strong dependence of the electronic density of states on temperature in bcc Mo, as obtained by the present DFT quantum simulations with $T_{\mathrm{el}}=T_{\mathrm{ion}}$ at an atomic volume of 92.99 a.u. The result at 5000 K with the smoothed solid curve represents conditions near melt.

Figure 2

Dependence of the of the shear modulus $C^{\prime }$ on electron temperature $T_{\mathrm{el}}$ in Mo, as determined from first-principles DFT calculations performed in the static bcc lattice with $T_{\mathrm{ion}}=0$, and as used here to constrain $T_{\mathrm{el}}$-dependent MGPT potentials.

Figure 3

Large positive impact of noncanonical $d$ bands on the $T_{\mathrm{el}}$-dependent MGPT calculation of the anomalous $H$-point phonon frequency and its volume dependence in bcc Mo at an electron temperature of 5000 K.

Figure 4

High-pressure melt curve for Mo, as obtained from MD simulations with $T_{\mathrm{el}}=0$ and $T_{\mathrm{el}}$-dependent MGPT potentials, using canonical (c) and noncanonical (nc) $d$ bands, and from the present and previous (Ref. 7) QMD simulations, and as compared to experimental isobaric (Ref. 10) and shock (Ref. 21) data.