Electronic-Entropy-Driven Solid-Solid Phase Transitions in Elemental Metals

TL;DR

Under strong electronic excitation, the relative stability of $hcp$, $fcc$, and $bcc$ phases in elemental metals can be governed by electronic entropy rather than lattice heating. The authors compute finite-temperature Helmholtz free energies $F(T,V)$ using Mermin-DFT (Quantum ESPRESSO) for 17 metals across $hcp/fcc/bcc$ up to $T=7$ eV, extracting $oldsymbol{ riangle F}$ and transition temperatures. They find that electronic entropy generally lowers $oldsymbol{ riangle F}$ and drives one or two solid–solid transitions, with density and magnetic effects mediating the sequences and with Zr showing an anomalous, density-opposing stabilization linked to its $d$-band DOS. The work identifies electronic thermal pressure as a unifying mechanism for entropy-driven phase transitions and provides a benchmark for finite-$T$ DFT in ultrafast regimes, with proposed pump–probe XRD tests to observe transient structural rearrangements.

Abstract

We compute the thermodynamic phase diagram of seventeen elemental metals with hexagonal close-packed (hcp), face-centered cubic (fcc), and body-centered cubic (bcc) crystal structures using finite-temperature density functional theory. Helmholtz free-energy differences between competing hcp, fcc, and bcc phases are evaluated as functions of electronic temperature up to 7 eV, allowing us to identify solid-solid phase transitions driven by electronic entropy. The systems studied include Zr, Ti, Cd, Zn, Co, and Mg (hcp), Ni, Cu, Ag, Al, Pt, and Pb (fcc), and Cr, W, V, Nb, and Mo (bcc) in their ground-state structures. From the free-energy crossings, we extract the transition electronic temperatures and analyze systematic trends across the metallic systems. We found that all the studied systems go through one or two solid-solid phase transition caused purely by electronic entropy except Mg and Pb. Our results establish electronic entropy as a key factor governing structural stability in metals under strong electronic excitation.

Figures (5)

• Figure 1: Helmholtz free-energy differences $\Delta F$ between the fcc, bcc, and hcp phases as functions of electronic temperature. Vertical lines indicate the phase transition temperatures. The phase diagram of Co was obtained using spin-polarized DFT and the inset shows the temperature dependence of the absolute magnetization per atom. The vanishing magnetization and the condition $\Delta F<10$ meV/atom occur at the same temperature region, as highlighted.
• Figure 2: Helmholtz free-energy differences between the bcc, hcp, and fcc phases as functions of electronic temperature. Vertical lines indicate the phase transition temperatures. The phase diagram of Ni was obtained using spin-polarized DFT and the inset shows the temperature dependence of the absolute magnetization per atom. The vanishing magnetization and the condition $\Delta F<10$ meV/atom occur at the same temperature region, as highlighted.
• Figure 3: Helmholtz free-energy differences between the fcc, hcp, and bcc phases as functions of electronic temperature. Vertical lines indicate the phase transition temperatures.
• Figure 4: (a) The behavior of density of fcc and bcc phases with respect to hcp for hcp-group elements. (b) The behavior of density of hcp and bcc phases with respect to fcc for fcc-group elements. (c) The behavior of density of hcp and fcc phases with respect to bcc for bcc-group elements.
• Figure 5: The internal energy E (a), and electronic entropy term -TS (b) of fcc and bcc phases of Zr with respect to hcp. (c) Thermal pressure of fcc and bcc phases of Zr with respect to hcp versus temperature. (d) Projected electronic density of states of d-band (pDOS$_d$) of hcp, fcc and bcc phases near the Fermi energy. The vertical line shows the Fermi energy. (e) Chemical potential $\mu(T)$ of of fcc and bcc phases of Zr with respect to hcp as a function of T.