Pressure-Dependent hcp-to-fcc Phase Transition Path Derived from Exact Lattice Summations over Inverse Power Law Potentials
Abstract
We investigate the phase transition between hexagonal close-packed (hcp) and face-centered cubic (fcc) structures along the Burgers-Bain transformation path at pressures up to several hundred gigapascals. We consider a hierarchy of interatomic potentials, from (n,m)-Lennard-Jones potentials to extended Lennard-Jones two-body interactions in terms of inverse-power expansions and the Axilrod-Teller-Muto three-body term, alongside density functional theory (DFT) calculations for solid argon. For inverse-power potentials, free energies are evaluated through exact lattice sums and efficient integral representations based on generalizations of the Epstein zeta function to anisotropic interaction kernels, followed by lattice-parameter optimization. This methodology enables an accurate determination of the pressure-dependent Burgers-Bain minimum-energy path and the associated activation barrier for the phase transition. The transformation exhibits pronounced symmetry breaking connecting the Burgers and Bain paths, a feature confirmed by DFT calculations. At high pressure, the hcp-to-fcc activation barrier increases approximately linearly with pressure, owing to the dominant pressure-volume contribution. Including entropy and anharmonic effects yields excellent agreement with experimental temperature-dependent volumes up to the melting point. DFT results also highlight the increasing importance of many-body interactions under compression. Whereas two-body potentials predict that the path passes through the body-centered cubic (bcc) structure only at very high pressures, DFT generally predicts a pathway that bypasses bcc. The Axilrod-Teller-Muto term slightly reduces this discrepancy. Furthermore, DFT performs better at high pressures, where dispersion forces become less important.
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BibTeX
@misc{maltby2026pressuredependent,
title = {{Pressure-Dependent hcp-to-fcc Phase Transition Path Derived from Exact Lattice Summations over Inverse Power Law Potentials}},
author = {Tage W. Maltby and Andres Robles-Navarro and Jonathan K. Hartlaub and Andreas A. Buchheit and Øivind Wilhelmsen and Morten Hammer and Peter Schwerdtfeger},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22855},
eprint = {2610.22855},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22855},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Pressure-Dependent hcp-to-fcc Phase Transition Path Derived from Exact Lattice Summations over Inverse Power Law Potentials
AU - Tage W. Maltby
AU - Andres Robles-Navarro
AU - Jonathan K. Hartlaub
AU - Andreas A. Buchheit
AU - Øivind Wilhelmsen
AU - Morten Hammer
AU - Peter Schwerdtfeger
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.22855
UR - https://arxiv.org/abs/2610.22855
AB - We investigate the phase transition between hexagonal close-packed (hcp) and face-centered cubic (fcc) structures along the Burgers-Bain transformation path at pressures up to several hundred gigapascals. We consider a hierarchy of interatomic potentials, from (n,m)-Lennard-Jones potentials to extended Lennard-Jones two-body interactions in terms of inverse-power expansions and the Axilrod-Teller-Muto three-body term, alongside density functional theory (DFT) calculations for solid argon. For inverse-power potentials, free energies are evaluated through exact lattice sums and efficient integral representations based on generalizations of the Epstein zeta function to anisotropic interaction kernels, followed by lattice-parameter optimization. This methodology enables an accurate determination of the pressure-dependent Burgers-Bain minimum-energy path and the associated activation barrier for the phase transition. The transformation exhibits pronounced symmetry breaking connecting the Burgers and Bain paths, a feature confirmed by DFT calculations. At high pressure, the hcp-to-fcc activation barrier increases approximately linearly with pressure, owing to the dominant pressure-volume contribution. Including entropy and anharmonic effects yields excellent agreement with experimental temperature-dependent volumes up to the melting point. DFT results also highlight the increasing importance of many-body interactions under compression. Whereas two-body potentials predict that the path passes through the body-centered cubic (bcc) structure only at very high pressures, DFT generally predicts a pathway that bypasses bcc. The Axilrod-Teller-Muto term slightly reduces this discrepancy. Furthermore, DFT performs better at high pressures, where dispersion forces become less important.
ER -