Electronic Temperature-Driven Phase Stability and Structural Evolution of Iron at High Pressure

TL;DR

The paper addresses how electronic temperature affects iron's solid-state phase stability under extreme pressures, a regime where electronic entropy can influence structural transitions. Using finite-temperature DFT and DFPT within Quantum Espresso, the authors compute $G=G_{el}+G_{lat}$ for the bcc, fcc, and hcp phases up to $P=300\,\mathrm{GPa}$ and $T_{el}=3\,\mathrm{eV}$, isolating electronic contributions by fixing ionic temperature. A key finding is that increasing $T_{el}$ drives a transition toward higher-entropy phases (fcc and, with phonons, bcc) and that phonon free energy is essential for predicting the bcc stabilization at elevated $T_{el}$, with a maximum around $T_{el}\approx1.4\ \mathrm{eV}$ and near-degeneracy beyond $\sim2\ \mathrm{eV}$. These results reveal nonmonotonic density and lattice-parameter trends and highlight the importance of including both electronic and vibrational free energies when modeling iron under ultra-high-pressure, high-temperature conditions relevant to planetary interiors and high-energy-density experiments.

Abstract

We present Gibbs free-energy phase diagrams for compressed iron within a pressure range of 20 to 300 GPa and electronic temperature up to 3 eV obtained using finite-temperature density functional and density functional perturbation theories. Our results for bcc, fcc, and hcp phases predict solid-solid phase transitions in iron driven purely by electronic entropy and temperature. We found a phase transition from hcp to bcc at pressures above 200 GPa, which depends on the electronic temperature. An experimental observation of the stability of the bcc phase above 200 GPa by X-ray Free Electron Laser has recently been reported.

Figures (5)

• Figure 1: The Gibbs free energy difference between fcc and hcp phases. 1600 finite-temperature DFT simulations were performed (800 for each phase), where the lattice parameters of the hcp phase (both a and c) and the fcc phase were fully optimised to satisfy the input T$_{el}$ and P conditions.
• Figure 2: (Left panel) Evolution of $c/a$ parameter of hcp phase as a function of pressure obtained at different electronic temperature T$_{el}$. The experimental data are obtained using X ray diffraction experiments with the diamond anvil cellMao1990. (Right panel) Non-linear increasing of $c/a$ as a function of electronic temperature.
• Figure 3: The Gibbs free energy difference between hcp and bcc phases. The color map shows the electronic Gibbs free energy difference. The data points on the map show the full (electronic and lattice dynamic) Gibbs free energy difference.
• Figure 4: Thermodynamic Gibbs free energy of Fe-bcc with respect to Fe-hcp as a function of electronic temperature. Free energies are calculated at pressures 150, 200, 250, and 300 GPa.
• Figure 5: Density of hcp, fcc, and bcc phases of iron in $g/cm^3$ as a function of pressure and electronic temperature. The above panel show the whole studied temperature and pressure range, while the second panel only focuses on high-pressure range. The axes in all plots are the same.