pith. sign in

arxiv: 2605.14793 · v1 · pith:HC2BST35new · submitted 2026-05-14 · ❄️ cond-mat.mtrl-sci

Melting Behavior and Phase Stability of CaO from Neural Network Potentials: a Molecular Dynamics Study

Francesca Menescardi , Stefano de Gironcoli This is my paper

Pith reviewed 2026-06-30 20:20 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords CaOmelting temperatureneural network potentialmolecular dynamicshigh pressureoverheating ratiophase stabilityoxide
0
0 comments X

The pith

The overheating ratio for CaO melting rises with pressure rather than staying fixed.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper trains a neural network potential on ab initio molecular dynamics data for CaO and uses it to run large-scale simulations of melting. It applies two different methods to find the melting temperature at ambient pressure and then extends the work to pressures up to 20 GPa. The simulations produce a melting curve together with values for the enthalpy of fusion and the volume change on melting. The key result is that the difference between the two simulation methods grows as pressure increases, so the overheating ratio is shown to depend on pressure. This supplies one of the few computational melting curves available for CaO under extreme conditions.

Core claim

Molecular dynamics simulations driven by a neural network potential trained on PBEsol data give a melting temperature of 2847 K at ambient pressure by the two-phase coexistence method and show an enthalpy of fusion near 73 kJ/mol with a 29 percent volume increase. Extending the same potential to 20 GPa produces a melting curve on which the overheating ratio rises from 17 percent at zero pressure to 24 percent at 20 GPa.

What carries the argument

The neural network interatomic potential trained on solid, liquid, interfacial, and void-containing configurations from PBEsol ab initio molecular dynamics, used inside large-scale molecular dynamics runs with void-nucleated melting and two-phase coexistence protocols.

If this is right

  • The ambient-pressure melting temperature is 2847 K by two-phase coexistence and 3055 K by void-nucleated melting.
  • The enthalpy of fusion is approximately 73 kJ/mol.
  • Density drops by roughly 29 percent on melting at the melting temperature.
  • The melting curve is computed up to 20 GPa with one consistent potential.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Geophysical models of deep-Earth or planetary mantles that treat the overheating ratio as fixed may need adjustment for pressure dependence.
  • The same training and simulation workflow can be reused for other simple ionic oxides where experimental melting data are scarce.
  • Direct comparison of the predicted melting curve against future diamond-anvil or shock-wave experiments would test the pressure trend.

Load-bearing premise

The neural network potential reproduces the correct energies and forces for CaO in solid, liquid, and interface states at pressures from zero to 20 GPa.

What would settle it

An experimental melting temperature for CaO at 20 GPa that lies outside the uncertainty range of the simulated melting curve.

Figures

Figures reproduced from arXiv: 2605.14793 by Francesca Menescardi, Stefano de Gironcoli.

Figure 1
Figure 1. Figure 1: Parity plot validating the energy (a) and forces (b) [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Apparent melting temperature of crystal CaO as a function of the defect dimensions [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Snapshot of the 6×6×60 supercell, visualized with VMD[36], where the red spheres represent the oxygen atoms while the blue spheres represent the calcium atoms. Below, the corresponding number density, calculated as an average over 10 ps with VMD Density Profile Tool[37]. The red line represents the spatially averaged density profile, which highlights that the crystal phase has a higher density than the liq… view at source ↗
Figure 4
Figure 4. Figure 4: Enthalpy difference relative to the enthalpy of the solid phase at 300 K ( [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Relative volume thermal expansion as a function of temperature. The lower branch [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: High pressure melting curve of CaO (Tm, red squares) and thermal instability temperature curve (Ts, blue squares) calculated with MLIP potential. The corresponding solid lines refer to the curves previously obtained with BMH potential[5], while other symbols at ambient pressure refer to all the most recent values of Tm reported in literature, both from experiments[28, 4] and MD simulations[29]. The plot sh… view at source ↗
read the original abstract

We investigate the melting behavior of calcium oxide (CaO) under extreme conditions, a problem that remains poorly constrained due to experimental limitations despite its relevance for geophysical and technological applications. We develop a Machine Learning Interatomic Potential (MLIP) for CaO with PANNA 2.0 and the LATTE descriptor, training it on a dataset of $\sim$12,000 configurations including solid, liquid, interfacial, and void-containing structures, extracted from ab-initio molecular dynamics data employing PBEsol exchange-correlation functional. We perform large-scale molecular dynamics simulations to compute the melting temperature at ambient pressure using both the void-nucleated melting (VNM) and two-phase coexistence (TPC) methods, obtaining $T_m=3055\pm11$ K and $T_m=2847\pm15$ K, respectively.\\ We calculate an enthalpy of fusion of $\Delta H_f\sim73$ kJ/mol, in agreement with thermodynamic assessments and ab initio calculations. We also reproduce the thermal expansion and obtain a volume increase of $\sim$29% at Tm, consistent with the corresponding decrease in density extracted from spatially resolved number density profiles. Finally, we calculate the high-pressure melting curve of CaO up to 20 GPa, providing one of the very few computational determinations of this quantity to date. The results confirm that the overheating ratio $\eta$ is not constant under pressure, increasing from 17% at ambient pressure to 24% at 20 GPa, confirming previous findings and ruling out the assumption of a fixed overheating ratio. Our results establish MLIP-based simulations as a robust and efficient framework for investigating phase stability in ionic oxides and provide new insight into the melting behavior of CaO under extreme conditions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper trains a PANNA neural network potential on ~12k PBEsol AIMD configurations of CaO (solid, liquid, interfacial, void-containing) and performs large-scale MD to compute melting temperatures via void-nucleated melting (VNM) and two-phase coexistence (TPC) methods, obtaining ambient Tm values of 3055 K and 2847 K. It reports ΔHf ~73 kJ/mol, ~29% volume change on melting, and a high-pressure melting curve to 20 GPa, concluding that the overheating ratio η increases from 17% at ambient pressure to 24% at 20 GPa.

Significance. If the potential is transferable to high pressure, the work supplies one of the few computational melting curves for CaO up to 20 GPa and supplies evidence against a pressure-independent overheating ratio, which is relevant for geophysical modeling of oxides. The use of an independently trained MLIP with no circular fitting to the reported quantities is a strength.

major comments (2)
  1. [Methods (training dataset)] Methods (training dataset description): the ~12,000 configurations are stated to be extracted from PBEsol AIMD but no information is given on whether the AIMD trajectories sample pressures up to 20 GPa, the corresponding densities, or liquid/interface structures at elevated pressure. This detail is load-bearing for attributing the reported increase in η to physical behavior rather than extrapolation error of the PANNA potential.
  2. [Results (melting temperatures)] Results (ambient-pressure melting points): the 208 K discrepancy between VNM (3055±11 K) and TPC (2847±15 K) is large enough to affect the baseline value of η; the manuscript must demonstrate which method (or combination) is used for the high-pressure curve and why the difference does not undermine the claimed pressure dependence of η from 17% to 24%.
minor comments (1)
  1. [Abstract] Abstract and text should explicitly define the overheating ratio η (e.g., (Tm_VNM − Tm_TPC)/Tm_TPC or relative to an external reference) so that the numerical values 17% and 24% can be reproduced from the reported Tm figures.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major point below and will revise the manuscript to incorporate the requested clarifications and additional details.

read point-by-point responses

  1. Referee: Methods (training dataset description): the ~12,000 configurations are stated to be extracted from PBEsol AIMD but no information is given on whether the AIMD trajectories sample pressures up to 20 GPa, the corresponding densities, or liquid/interface structures at elevated pressure. This detail is load-bearing for attributing the reported increase in η to physical behavior rather than extrapolation error of the PANNA potential.

    Authors: We agree that the manuscript should explicitly document the pressure and density ranges sampled during AIMD data generation. The training configurations were drawn from AIMD runs performed at multiple pressures up to 25 GPa (including solid, liquid, and interface/void structures at elevated pressure). In the revised manuscript we will add a dedicated paragraph and supplementary table in the Methods section that lists the pressure/density intervals, the number of configurations per interval, and confirms that high-pressure liquid and interface structures are represented in the ~12k set. This addition will allow readers to verify that the reported high-pressure results lie inside the training domain. revision: yes

  2. Referee: Results (ambient-pressure melting points): the 208 K discrepancy between VNM (3055±11 K) and TPC (2847±15 K) is large enough to affect the baseline value of η; the manuscript must demonstrate which method (or combination) is used for the high-pressure curve and why the difference does not undermine the claimed pressure dependence of η from 17% to 24%.

    Authors: The 208 K offset is expected and arises from the known superheating inherent to the VNM protocol. For the high-pressure melting curve we employed the TPC method to obtain the equilibrium Tm(P) values; the VNM runs were performed only to compute the pressure-dependent overheating ratio η(P) by direct comparison with the TPC baseline at each pressure. We will revise the Results and Discussion sections to state this protocol explicitly, to tabulate both VNM and TPC Tm values at selected high pressures, and to show that the increase in η with pressure remains statistically significant even when the absolute baseline is anchored to the TPC data. A short paragraph will also be added explaining why the method difference does not alter the reported trend in η. revision: yes

Circularity Check

0 steps flagged

No significant circularity; results computed from MLIP dynamics on independent ab initio training data

full rationale

The derivation trains a PANNA MLIP on ~12k PBEsol AIMD configurations (solid/liquid/interface/void) then runs large-scale MD to obtain VNM and TPC melting points, ΔHf, volume change, and the pressure dependence of η up to 20 GPa. These outputs are generated by the dynamics of the fitted potential rather than being algebraically or statistically forced to equal the training inputs. The paper compares results to external thermodynamic assessments and prior ab initio work; no self-citation is invoked as a uniqueness theorem or load-bearing premise. The training-set pressure range is described only generically, but this affects transferability, not circularity of the reported chain.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claims rest on the accuracy of the fitted neural network potential and the validity of the chosen melting simulation protocols; the training data choice (PBEsol) and inclusion of interfacial/void structures are key unverified assumptions for transferability to high-pressure liquids.

free parameters (1)
  • Neural network weights and biases
    Fitted to the ~12,000 ab initio configurations from PBEsol AIMD to create the interatomic potential.
axioms (1)
  • domain assumption PBEsol exchange-correlation functional provides sufficiently accurate reference data for CaO energetics across solid, liquid, and interface regimes
    All training configurations extracted from PBEsol AIMD simulations.

pith-pipeline@v0.9.1-grok · 5854 in / 1479 out tokens · 45877 ms · 2026-06-30T20:20:59.234794+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

45 extracted references · 1 canonical work pages

  1. [1]

    D. L. Anderson, Theory of the Earth, Blackwell Scientific Publications, 1989

    1989

  2. [2]

    Taylor, Cement Chemistry, Emerald Publishing Limited, 1997

    H. Taylor, Cement Chemistry, Emerald Publishing Limited, 1997

    1997

  3. [3]

    S.-M.Liang, R.Schmid-Fetzer, Completethermodynamicdescriptionofthe Mg–Ca–O phase diagram including the Ca–O, Mg–O and CaO–MgO subsystems, Journal of the European Ceramic Society 38 (14) (2018) 4768–4785

    2018

  4. [4]

    Manara, R

    D. Manara, R. Böhler, L. Capriotti, A. Quaini, Z. Bao, K. Boboridis, L. Luzzi, A. Janssen, P. Pöml, R. Eloirdi, R. Konings, On the melting be- haviour of calcium monoxide under different atmospheres: A laser heating study, Journal of the European Ceramic Society 34 (6) (2014) 1623–1636. 17

    2014

  5. [5]

    Menescardi, D

    F. Menescardi, D. Ceresoli, D. Belmonte, Melting behavior of cao at high temperature and pressure: a molecular dynamics study, The Journal of Physical Chemistry C 128 (43) (2024) 18498–18508

    2024

  6. [6]

    X. Sun, T. Song, Y. Chu, Z. Liu, Z. Zhang, Q. Chen, The high-pressure melting curve of CaO, Solid State Communications 150 (37–38) (2010) 1785–1788

    2010

  7. [7]

    Pellegrini, R

    F. Pellegrini, R. Lot, Y. Shaidu, E. Küçükbenli, PANNA 2.0: Efficient neural network interatomic potentials and new architectures, The Journal of Chemical Physics 159 (8) (2023)

    2023

  8. [8]

    Pellegrini, S

    F. Pellegrini, S. de Gironcoli, E. Küçükbenli, LATTE: an atomic envi- ronment descriptor based on cartesian tensor contractions, arXiv preprint arXiv:2405.08137 (2024)

    work page arXiv 2024

  9. [9]

    R. Lot, F. Pellegrini, Y. Shaidu, E. Küçükbenli, Panna: Properties from artificial neural network architectures, Computer Physics Communications 256 (2020) 107402

    2020

  10. [10]

    J.Behler, M.Parrinello, Generalizedneural-networkrepresentationofhigh- dimensional potential-energy surfaces, Physical Review Letters 98 (14) (2007) 146401

    2007

  11. [11]

    Giannozzi, S

    P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavaz- zoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbrac- cia, S....

    2009

  12. [12]

    Giannozzi, O

    P. Giannozzi, O. Andreussi, T. Brumme, O. Bunau, M. Buon- giorno Nardelli, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, M. Cococ- cioni, N. Colonna, I. Carnimeo, A. Dal Corso, S. de Gironcoli, P. Delugas, R. A. DiStasio, A. Ferretti, A. Floris, G. Fratesi, G. Fugallo, R. Gebauer, U. Gerstmann, F. Giustino, T. Gorni, J. Jia, M. Kawamura, H.-Y. Ko, A. Ko...

    2017

  13. [13]

    Giannozzi, O

    P. Giannozzi, O. Baseggio, P. Bonfà, D. Brunato, R. Car, I. Carnimeo, C. Cavazzoni, S. de Gironcoli, P. Delugas, F. Ferrari Ruffino, A. Ferretti, N. Marzari, I. Timrov, A. Urru, S. Baroni, Quantum ESPRESSO toward the exascale, The Journal of Chemical Physics 152 (15) (2020) 154105

    2020

  14. [14]

    Troullier, J

    N. Troullier, J. L. Martins, Efficient pseudopotentials for plane-wave cal- culations, Physical Review B 43 (3) (1991) 1993–2006. 18

    1991

  15. [15]

    J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou, K. Burke, Restoring the density-gradient expan- sion for exchange in solids and surfaces, Physical Review Letters 100 (13) (2008) 136406

    2008

  16. [16]

    G. I. Csonka, J. P. Perdew, A. Ruzsinszky, P. H. T. Philipsen, S. Lebègue, J. Paier, O. A. Vydrov, J. G. Ángyán, Assessing the performance of re- cent density functionals for bulk solids, Physical Review B 79 (15) (2009) 155107

    2009

  17. [17]

    Plimpton, Fast parallel algorithms for short-range molecular dynamics, Journal of Computational Physics 117 (1) (1995) 1–19

    S. Plimpton, Fast parallel algorithms for short-range molecular dynamics, Journal of Computational Physics 117 (1) (1995) 1–19

    1995

  18. [18]

    A. P. Thompson, H. M. Aktulga, R. Berger, D. S. Bolintineanu, W. M. Brown, P. S. Crozier, P. J. in ’t Veld, A. Kohlmeyer, S. G. Moore, T. D. Nguyen, R. Shan, M. J. Stevens, J. Tranchida, C. Trott, S. J. Plimpton, LAMMPS – a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales, Computer Physics Communi- c...

    2022

  19. [19]

    W. G. Hoover, Canonical dynamics: Equilibrium phase-space distributions, Physical Review A 31 (3) (1985) 1695–1697

    1985

  20. [20]

    Hong, Melting temperature prediction via first principles and deep learning, Computational Materials Science 214 (2022) 111684

    Q.-J. Hong, Melting temperature prediction via first principles and deep learning, Computational Materials Science 214 (2022) 111684

    2022

  21. [21]

    C. M. S. Alvares, G. Deffrennes, A. Pisch, N. Jakse, Thermodynamics and structural properties of CaO: A molecular dynamics simulation study, The Journal of Chemical Physics 152 (8) (2020) 084503

    2020

  22. [22]

    Zhang, E

    Y. Zhang, E. J. Maginn, A comparison of methods for melting point cal- culation using molecular dynamics simulations, The Journal of Chemical Physics 136 (14) (2012) 144116

    2012

  23. [23]

    A. B. Belonoshko, N. V. Skorodumova, A. Rosengren, B. Johansson, Melt- ing and critical superheating, Physical Review B 73 (1) (2006) 012201

    2006

  24. [24]

    Z. H. Jin, P. Gumbsch, K. Lu, E. Ma, Melting mechanisms at the limit of superheating, Physical Review Letters 87 (5) (2001) 055703

    2001

  25. [25]

    J. F. Lutsko, D. Wolf, S. R. Phillpot, S. Yip, Molecular-dynamics study of lattice-defect-nucleated melting in metals using an embedded-atom-method potential, Physical Review B 40 (5) (1989) 2841–2855

    1989

  26. [26]

    X. Wang, M. Yang, X. Gai, Y. Sun, B. Cao, J. Chen, M. Liang, F. Tian, L.Li, Acomprehensiveinvestigationontheaccuracyandefficiencyofmeth- ods for melting temperature calculation using molecular dynamics simula- tions, Journal of Molecular Liquids 395 (2024) 123924

    2024

  27. [27]

    Y. Zou, S. Xiang, C. Dai, Investigation on the efficiency and accuracy of methods for calculating melting temperature by molecular dynamics simu- lation, Computational Materials Science 171 (2020) 109156. 19

    2020

  28. [28]

    Bgasheva, T

    T. Bgasheva, T. Falyakhov, S. Petukhov, M. Sheindlin, A. Vasin, P. Vervik- ishko, Laser-pulse melting of calcium oxide and some peculiarities of its high-temperature behavior, Journal of the American Ceramic Society 104 (7) (2021) 3461–3477

    2021

  29. [29]

    K. Lee, Y. Park, S. Han, Ab initio construction of full phase diagram of MgO-CaO eutectic system using neural network interatomic potentials, Physical Review Materials 6 (11) (2022) 113802

    2022

  30. [30]

    J. R. Morris, C. Z. Wang, K. M. Ho, C. T. Chan, Melting line of aluminum from simulations of coexisting phases, Physical Review B 49 (5) (1994) 3109–3115

    1994

  31. [31]

    P. M. Agrawal, B. M. Rice, D. L. Thompson, Molecular dynamics study of the melting of nitromethane, The Journal of Chemical Physics 119 (18) (2003) 9617–9627

    2003

  32. [32]

    Q.-J. Hong, A. van de Walle, Solid-liquid coexistence in small systems: A statistical method to calculate melting temperatures, The Journal of Chemical Physics 139 (9) (Sep. 2013)

    2013

  33. [33]

    Wang, X.-W

    X.-W. Wang, X.-W. Sun, T. Song, J.-H. Tian, Z.-J. Liu, Prediction of the melting curve and phase diagram for CaO using newly developed inter- atomic potentials, Vacuum 209 (2023) 111717

    2023

  34. [34]

    Asadi, M

    E. Asadi, M. A. Zaeem, S. Nouranian, M. I. Baskes, Two-phase solid–liquid coexistence of ni, cu, and al by molecular dynamics simulations using the modified embedded-atom method, Acta Materialia 86 (2015) 169–181

    2015

  35. [35]

    Wang, Z.-J

    X. Wang, Z.-J. Liu, J.-S. Feng, M.-R. Chen, L. Li, X.-W. Sun, F. Tian, Construction and application of deep learning potential for cao under high pressure, Computational Materials Science 244 (2024) 113154

    2024

  36. [36]

    Humphrey, A

    W. Humphrey, A. Dalke, K. Schulten, VMD: Visual molecular dynamics, Journal of Molecular Graphics 14 (1) (1996) 33–38

    1996

  37. [37]

    Giorgino, Computing 1-d atomic densities in macromolecular simula- tions: The density profile tool for vmd, Computer Physics Communications 185 (1) (2014) 317–322

    T. Giorgino, Computing 1-d atomic densities in macromolecular simula- tions: The density profile tool for vmd, Computer Physics Communications 185 (1) (2014) 317–322

    2014

  38. [38]

    Deffrennes, N

    G. Deffrennes, N. Jakse, C. M. Alvares, I. Nuta, A. Pasturel, A. Khvan, A. Pisch, Thermodynamic modelling of the Ca–O system including 3rd generation description of cao and CaO2, Calphad 69 (2020) 101764

    2020

  39. [39]

    M, NIST-JANAF Thermochemical Tables, 4th Edition, American Insti- tute of Physics, 1998

    C. M, NIST-JANAF Thermochemical Tables, 4th Edition, American Insti- tute of Physics, 1998

    1998

  40. [40]

    Belmonte, G

    D. Belmonte, G. Ottonello, M. V. Zuccolini, Ab initio-assisted assessment of the CaO-SiO2 system under pressure, Calphad 59 (2017) 12–30

    2017

  41. [41]

    Gurvich, I

    L. Gurvich, I. Veyts, C. Tab Alcock, V. Iorish, Elements b, al, ga, in, tl, be, mg, ca, sr, ba, and their compounds. crc press and begell house. part one. methods and computation. viii+ 707 pp. part two. tables, Thermodynamic Properties of Individual Substances 3 (1994) XV+–448. 20

    1994

  42. [42]

    Fiquet, P

    G. Fiquet, P. Richet, G. Montagnac, High-temperature thermal expansion of lime, periclase, corundum and spinel, Physics and Chemistry of Minerals 27 (2) (1999) 103–111

    1999

  43. [43]

    A. S. Arkhipin, A. Pisch, I. A. Uspenskaya, N. Jakse, A molecular dynamics simulation study of crystalline and liquid mgo, Ceramics 7 (3) (2024) 1187– 1203

    2024

  44. [44]

    Zykova-Timan, D

    T. Zykova-Timan, D. Ceresoli, U. Tartaglino, E. Tosatti, Physics of solid and liquid alkali halide surfaces near the melting point, The Journal of Chemical Physics 123 (16) (2005) 164701

    2005

  45. [45]

    Gómez, C

    L. Gómez, C. Gazza, H. Dacharry, L. Peñaranda, A. Dobry, Pressure de- pendence of the melting mechanism at the limit of overheating in Lennard- Jones crystals, Physical Review B 71 (13) (2005) 134106. 21

    2005