TT-SCHA for Thermodynamics of Binary Alloys

Abstract

The free energy of a crystal is an integral over the positions of all its atoms, in 3N dimensions. We evaluate it without random sampling for the ordered alloys B2 NiAl and gamma-TiAl with embedded-atom potentials, using a self-consistent harmonic approximation (SCHA) corrected to third order in temperature, calculated via thermal averages of tensor-train (TT) integrals built from one atom and its neighbors, which we call TT-SCHA. The result is for an infinite crystal without sampling error; its numerical error is set by the starting pivots of the interpolation (up to 9 MPa in the pressure, reduced by averaging three runs; SM Table S26). Against the molecular dynamics of 65,536 atoms (Frenkel-Ladd free energy at 600 K, integrated energy above), TT-SCHA free energy agrees to 0.13 meV per atom at 600-1000 K, using 420-500 times fewer core-seconds for one run. At zero pressure, results agree with published calculations that use the same embedded-atom potential: the published elastic constants of gamma-TiAl (to 1 GPa, by a static lattice calculation) and its thermal expansion from Monte Carlo sampling (to 0.012 percentage points).

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BibTeX RIS

BibTeX

@misc{alexandrov2026ttscha,
  title = {{TT-SCHA for Thermodynamics of Binary Alloys}},
  author = {Boian S. Alexandrov and Dimiter Petsev},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.04402},
  eprint = {2611.04402},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.04402},
}

RIS

TY  - UNPB
TI  - TT-SCHA for Thermodynamics of Binary Alloys
AU  - Boian S. Alexandrov
AU  - Dimiter Petsev
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.04402
UR  - https://arxiv.org/abs/2611.04402
AB  - The free energy of a crystal is an integral over the positions of all its atoms, in 3N dimensions. We evaluate it without random sampling for the ordered alloys B2 NiAl and gamma-TiAl with embedded-atom potentials, using a self-consistent harmonic approximation (SCHA) corrected to third order in temperature, calculated via thermal averages of tensor-train (TT) integrals built from one atom and its neighbors, which we call TT-SCHA. The result is for an infinite crystal without sampling error; its numerical error is set by the starting pivots of the interpolation (up to 9 MPa in the pressure, reduced by averaging three runs; SM Table S26). Against the molecular dynamics of 65,536 atoms (Frenkel-Ladd free energy at 600 K, integrated energy above), TT-SCHA free energy agrees to 0.13 meV per atom at 600-1000 K, using 420-500 times fewer core-seconds for one run. At zero pressure, results agree with published calculations that use the same embedded-atom potential: the published elastic constants of gamma-TiAl (to 1 GPa, by a static lattice calculation) and its thermal expansion from Monte Carlo sampling (to 0.012 percentage points).
ER  -

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