How to enhance the applicability of Murnaghan equation of state
Abstract
The paper presents the brief overview of known isothermal equations of state for solids and of theoretical background to construct them, focusing on widely used Murnaghan equation. Since the latter has a limited range of application, failing to reproduce reliably both near-equilibrium and high-pressure regions simultaneously, the paper proposes simple, but rather efficient way to improve it. The suggested modification favors its applicability at high pressures, allowing to expand considerably the region of reliable reproducing of experimental or computational data. The proposed improved equation has been tested in fitting of U(V) data, obtained within ab initio computations, as well as of experimental V-P data for a representative selection of solids. In comparison with ordinary Murnaghan equation, it has found significant advantages, extending the range, where the computational data may be reproduced trustworthy (from the equilibrium state to the pressures, appreciably higher, the ordinary equation could). As for the fitting of experimental data, the proposed improved Murnaghan equation reproduces them, in the presented examples, at least not worse than other well-known equations (Vinet, Birch-Murnaghan, Mao) do. Some aspects of fitting process, as well as some alternative approaches to obtain the proposed equation of state in various forms are also discussed.
Versions
Related
- NJL-Chiral Soliton and the Nucleon Equation of State at supra-saturation density: Impact of Chiral Symmetry Restoration
- Hot and dense QCD equation of state from the complex Langevin equation
- Equation of state of hot and dense QCD using the complex Langevin equation
- Vectorial lattice Boltzmann solver for compressible inviscid flows with generic equation of state
- Guaranteed wave-speed bounds for the compressible Euler equations with a composite equation of state
BibTeX
@misc{bannikov2026enhance,
title = {{How to enhance the applicability of Murnaghan equation of state}},
author = {V. V. Bannikov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07400},
eprint = {2609.07400},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07400},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - How to enhance the applicability of Murnaghan equation of state
AU - V. V. Bannikov
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.07400
UR - https://arxiv.org/abs/2609.07400
AB - The paper presents the brief overview of known isothermal equations of state for solids and of theoretical background to construct them, focusing on widely used Murnaghan equation. Since the latter has a limited range of application, failing to reproduce reliably both near-equilibrium and high-pressure regions simultaneously, the paper proposes simple, but rather efficient way to improve it. The suggested modification favors its applicability at high pressures, allowing to expand considerably the region of reliable reproducing of experimental or computational data. The proposed improved equation has been tested in fitting of U(V) data, obtained within ab initio computations, as well as of experimental V-P data for a representative selection of solids. In comparison with ordinary Murnaghan equation, it has found significant advantages, extending the range, where the computational data may be reproduced trustworthy (from the equilibrium state to the pressures, appreciably higher, the ordinary equation could). As for the fitting of experimental data, the proposed improved Murnaghan equation reproduces them, in the presented examples, at least not worse than other well-known equations (Vinet, Birch-Murnaghan, Mao) do. Some aspects of fitting process, as well as some alternative approaches to obtain the proposed equation of state in various forms are also discussed.
ER -