A Gibbs Thermodynamic Surface Approach to Modeling the Melting of Forsterite

ZHAO Xuan; YIN Kun

doi:10.11858/gywlxb.20251130

Volume 39 Issue 10

Oct 2025

Turn off MathJax

Article Contents

Chinese Journal of High Pressure Physics > 2025 > 39(10): 100101.

ZHAO Xuan, YIN Kun. A Gibbs Thermodynamic Surface Approach to Modeling the Melting of Forsterite[J]. Chinese Journal of High Pressure Physics, 2025, 39(10): 100101. doi: 10.11858/gywlxb.20251130

Citation:

ZHAO Xuan, YIN Kun. A Gibbs Thermodynamic Surface Approach to Modeling the Melting of Forsterite[J]. Chinese Journal of High Pressure Physics, 2025, 39(10): 100101. doi: 10.11858/gywlxb.20251130

ZHAO Xuan, YIN Kun. A Gibbs Thermodynamic Surface Approach to Modeling the Melting of Forsterite[J]. Chinese Journal of High Pressure Physics, 2025, 39(10): 100101. doi: 10.11858/gywlxb.20251130

Citation:

ZHAO Xuan, YIN Kun. A Gibbs Thermodynamic Surface Approach to Modeling the Melting of Forsterite[J]. Chinese Journal of High Pressure Physics, 2025, 39(10): 100101. doi: 10.11858/gywlxb.20251130

PDF( 2297 KB)

A Gibbs Thermodynamic Surface Approach to Modeling the Melting of Forsterite

doi: 10.11858/gywlxb.20251130

ZHAO Xuan^1
,,
YIN Kun^{1, 2,*
,
,}

1.
College of Earth and Planetary Sciences, Chengdu University of Technology, Chengdu 610059, Sichuan, China
2.
State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology, Chengdu 610059, Sichuan, China

Received Date: 15 Jul 2025
Rev Recd Date: 23 Jul 2025

Available Online: 28 Jul 2025

Issue Publish Date: 05 Oct 2025

Abstract

Abstract

The process of melting is widespread in nature and plays a crucial role in the evolution of magma oceans on Earth and other planetary bodies. Given that planetary interiors are generally subjected to high-pressure conditions, the study of melting behavior under high-pressure conditions is essential for understanding the composition and dynamic evolution of planetary interiors. Based on the theory of the Gibbs thermodynamic surface and previous research, this study employs ab initio molecular dynamics simulation combined with a geometric model to obtain the melting data of forsterite (Mg₂SiO₄) within the pressure range of 0 to 16 GPa. Under limited computational resources, this method enables the efficient and accurate acquisition of melting-related properties at any point within a given pressure range, including the Gibbs free energy, Helmholtz free energy, enthalpy, internal energy, entropy, and volume of solid and liquid phases. This approach is also used to determine the phase boundary between forsterite and wadsleyite within the temperature range of 1200 to 1500 K. The calculated results show high consistency with existing experimental and computational data, validating the reliability and accuracy of this method for obtaining melting data under high pressure. This approach overcomes the bottleneck of existing methods in efficiently obtaining complete high-pressure melting data with limited computational resources.
- melting curve,
- Gibbs thermodynamic surface,
- high pressure,
- molecular dynamics simulation,
- forsterite

FullText(HTML)

References(44)

References

[1]	MAO H K, CHEN X J, DING Y, et al. Solids, liquids, and gases under high pressure [J]. Reviews of Modern Physics, 2018, 90(1): 015007. doi: 10.1103/RevModPhys.90.015007
[2]	XU M L, LI Y W, MA Y M. Materials by design at high pressures [J]. Chemical Science, 2022, 13(2): 329–344. doi: 10.1039/D1SC04239D
[3]	SAKAIRI T, OHTANI E, KAMADA S, et al. Melting relations in the Fe-S-Si system at high pressure and temperature: implications for the planetary core [J]. Progress in Earth and Planetary Science, 2017, 4(1): 10. doi: 10.1186/s40645-017-0125-x
[4]	HU J P, SHARP T G. Formation, preservation and extinction of high-pressure minerals in meteorites: temperature effects in shock metamorphism and shock classification [J]. Progress in Earth and Planetary Science, 2022, 9(1): 6. doi: 10.1186/s40645-021-00463-2
[5]	贺芝宇, 黄秀光, 舒桦, 等. 冰巨行星内部深处物理与化学过程研究进展 [J]. 高压物理学报, 2023, 37(5): 050105. doi: 10.11858/gywlxb.20230721 HE Z Y, HUANG X G, SHU H, et al. Progress on physical and chemical processes deep inside ice giants [J]. Chinese Journal of High Pressure Physics, 2023, 37(5): 050105. doi: 10.11858/gywlxb.20230721
[6]	YIN K, BELONOSHKO A B, LI Y H, et al. Davemaoite as the mantle mineral with the highest melting temperature [J]. Science Advances, 2023, 9(49): eadj2660. doi: 10.1126/sciadv.adj2660
[7]	KATSURA T. Phase relations of bridgmanite, the most abundant mineral in the Earth’s lower mantle [J]. Communications Chemistry, 2025, 8(1): 28. doi: 10.1038/s42004-024-01389-8
[8]	LI J, WU Q, LI J B, et al. Shock melting curve of iron: a consensus on the temperature at the Earth’s inner core boundary [J]. Geophysical Research Letters, 2020, 47(15): e2020GL087758. doi: 10.1029/2020GL087758
[9]	王宝云, 肖万生, 宋茂双. δ-(Al, Fe)OOH的高压相变 [J]. 高压物理学报, 2021, 35(6): 061201. doi: 10.11858/gywlxb.20210765 WANG B Y, XIAO W S, SONG M S. Pressure-induced phase transitions in δ-(Al, Fe)OOH [J]. Chinese Journal of High Pressure Physics, 2021, 35(6): 061201. doi: 10.11858/gywlxb.20210765
[10]	姜昌国, 谭大勇, 谢亚飞, 等. 高压剪切作用下三水铝石的结构稳定性 [J]. 高压物理学报, 2022, 36(1): 011202. doi: 10.11858/gywlxb.20210766 JIANG C G, TAN D Y, XIE Y F, et al. Investigation on structural stability of γ-Al(OH)₃ under high pressure and shear stress [J]. Chinese Journal of High Pressure Physics, 2022, 36(1): 011202. doi: 10.11858/gywlxb.20210766
[11]	陈炜珊, 谭毅, 谭大勇, 等. NaPO₃高压结构行为的第一性原理理论研究 [J]. 高压物理学报, 2024, 38(5): 050106. doi: 10.11858/gywlxb.20240755 CHEN W S, TAN Y, TAN D Y, et al. First-principles theoretical study on the structure behaviors of NaPO₃ under compression [J]. Chinese Journal of High Pressure Physics, 2024, 38(5): 050106. doi: 10.11858/gywlxb.20240755
[12]	何宇, 孙士川, 李和平. 地球内核超离子态铁合金及其效应 [J]. 高压物理学报, 2024, 38(3): 030202. doi: 10.11858/gywlxb.20240707 HE Y, SUN S C, LI H P. Superionic iron alloys in Earth’s inner core and their effects [J]. Chinese Journal of High Pressure Physics, 2024, 38(3): 030202. doi: 10.11858/gywlxb.20240707
[13]	吴忠庆, 王文忠. 矿物高温高压下弹性的第一性原理计算研究进展 [J]. 中国科学: 地球科学, 2016, 46(5): 582–617. WU Z Q, WANG W Z. First-principles calculations of elasticity of minerals at high temperature and pressure [J]. Science China Earth Sciences, 2016, 59(6): 1107–1137.
[14]	甘波, 李俊, 蒋刚, 等. Fe高压熔化线的实验研究进展 [J]. 高压物理学报, 2021, 35(6): 060101. doi: 10.11858/gywlxb.20210859 GAN B, LI J, JIANG G, et al. A review of the experimental determination of the melting curve of iron at ultrahigh pressures [J]. Chinese Journal of High Pressure Physics, 2021, 35(6): 060101. doi: 10.11858/gywlxb.20210859
[15]	LUO S N, STRACHAN A, SWIFT D C. Nonequilibrium melting and crystallization of a model Lennard-Jones system [J]. The Journal of Chemical Physics, 2004, 120(24): 11640–11649. doi: 10.1063/1.1755655
[16]	BELONOSHKO A B. Molecular dynamics of MgSiO₃ perovskite at high pressures: equation of state, structure, and melting transition [J]. Geochimica et Cosmochimica Acta, 1994, 58(19): 4039–4047. doi: 10.1016/0016-7037(94)90265-8
[17]	BELONOSHKO A B, SKORODUMOVA N V, ROSENGREN A, et al. Melting and critical superheating [J]. Physical Review B, 2006, 73(1): 012201. doi: 10.1103/PhysRevB.73.012201
[18]	SIMON F, GLATZEL G. Bemerkungen zur schmelzdruckkurve [J]. Zeitschrift für Anorganische und Allgemeine Chemie, 1929, 178(1): 309–316. doi: 10.1002/zaac.19291780123
[19]	KECHIN V V. Melting curve equations at high pressure [J]. Physical Review B, 2001, 65(5): 052102. doi: 10.1103/PhysRevB.65.052102
[20]	GIBBS J W. Graphical methods in the thermodynamics of fluids [J]. Transactions of the Connecticut Academy of Arts and Sciences, 1873, 2: 309–342.
[21]	GIBBS J W. A method of geometrical representation of the thermodynamic properties of substances by means of surfaces [J]. Transactions of the Connecticut Academy of Arts and Sciences, 1873, 2: 382–404.
[22]	GIBBS J W. On the equilibrium of heterogeneous substances [J]. Transactions of the Connecticut Academy of Arts and Sciences, 1876, 3: 108–248.
[23]	YIN K, LU X C, ZHOU H Q, et al. Thermodynamic stability limit of the crystalline state from the Gibbs perspective [J]. Physical Review B, 2018, 98(14): 144113. doi: 10.1103/PhysRevB.98.144113
[24]	KATSURA T, YAMADA H, NISHIKAWA O, et al. Olivine-wadsleyite transition in the system (Mg, Fe)₂SiO₄ [J]. Journal of Geophysical Research: Solid Earth, 2004, 109(B2): B02209. doi: 10.1029/2003JB002438
[25]	刘曦, 代立东, 邓力维, 等. 近十年我国在地球内部物质高压物性实验研究方面的主要进展 [J]. 高压物理学报, 2017, 31(6): 657–681. doi: 10.11858/gywlxb.2017.06.001 LIU X, DAI L D, DENG L W, et al. Recent progresses in some fields of high-pressure physics relevant to Earth sciences achieved by Chinese scientists [J]. Chinese Journal of High Pressure Physics, 2017, 31(6): 657–681. doi: 10.11858/gywlxb.2017.06.001
[26]	BOSTROEM D. Single-crystal X-ray diffraction studies of synthetic Ni-Mg olivine solid solutions [J]. American Mineralogist, 1987, 72(9/10): 965–972.
[27]	KRESSE G, FURTHMÜLLER J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set [J]. Physical Review B, 1996, 54(16): 11169–11186. doi: 10.1103/PhysRevB.54.11169
[28]	PERDEW J P, RUZSINSZKY A, CSONKA G I, et al. Restoring the density-gradient expansion for exchange in solids and surfaces [J]. Physical Review Letters, 2008, 100(13): 136406. doi: 10.1103/PhysRevLett.100.136406
[29]	NOSÉ S. A unified formulation of the constant temperature molecular dynamics methods [J]. The Journal of Chemical Physics, 1984, 81(1): 511–519. doi: 10.1063/1.447334
[30]	HOOVER W G. Canonical dynamics: equilibrium phase-space distributions [J]. Physical Review A, 1985, 31(3): 1695–1697. doi: 10.1103/PhysRevA.31.1695
[31]	OHTANI E, KUMAZAWA M. Melting of forsterite Mg₂SiO₄ up to 15 GPa [J]. Physics of the Earth and Planetary Interiors, 1981, 27(1): 32–38. doi: 10.1016/0031-9201(81)90084-4
[32]	DAVIS B T C, ENGLAND J L. The melting of forsterite up to 50 kilobars [J]. Journal of Geophysical Research, 1964, 69(6): 1113–1116. doi: 10.1029/JZ069i006p01113
[33]	PRESNALL D C, WALTER M J. Melting of forsterite, Mg₂SiO₄, from 9.7 to 16.5 GPa [J]. Journal of Geophysical Research: Solid Earth, 1993, 98(B11): 19777–19783. doi: 10.1029/93JB01007
[34]	BOYD F R, ENGLAND J L. The quartz-coesite transition [J]. Journal of Geophysical Research, 1960, 65(2): 749–756. doi: 10.1029/JZ065i002p00749
[35]	BOWEN N L, ANDERSEN O. The binary system MgO-SiO₂ [J]. American Journal of Science, 1914, s4-37(222): 487–500.
[36]	DE KOKER N P, STIXRUDE L, KARKI B B. Thermodynamics, structure, dynamics, and freezing of Mg₂SiO₄ liquid at high pressure [J]. Geochimica et Cosmochimica Acta, 2008, 72(5): 1427–1441. doi: 10.1016/j.gca.2007.12.019
[37]	HORIUCHI H, SAWAMOTO H. β-Mg₂SiO₄: single-crystal X-ray diffraction study [J]. American Mineralogist, 1981, 66(5/6): 568–575.
[38]	AKAOGI M, ITO E, NAVROTSKY A. Olivine-modified spinel-spinel transitions in the system Mg₂SiO₄-Fe₂SiO₄: calorimetric measurements, thermochemical calculation, and geophysical application [J]. Journal of Geophysical Research: Solid Earth, 1989, 94(B11): 15671–15685. doi: 10.1029/JB094iB11p15671
[39]	KATSURA T, ITO E. The system Mg₂SiO₄-Fe₂SiO₄ at high pressures and temperatures: precise determination of stabilities of olivine, modified spinel, and spinel [J]. Journal of Geophysical Research: Solid Earth, 1989, 94(B11): 15663–15670. doi: 10.1029/JB094iB11p15663
[40]	MORISHIMA H, KATO T, SUTO M, et al. The phase boundary between α- and β-Mg₂SiO₄ determined by in situ X-ray observation [J]. Science, 1994, 265(5176): 1202–1203. doi: 10.1126/science.265.5176.1202
[41]	YU Y G, WU Z Q, WENTZCOVITCH R M. α-β-γ transformations in Mg₂SiO₄ in Earth’s transition zone [J]. Earth and Planetary Science Letters, 2008, 273(1/2): 115–122. doi: 10.1016/j.jpgl.2008.06.023
[42]	GASPARIK T. Phase relations in the transition zone [J]. Journal of Geophysical Research: Solid Earth, 1990, 95(B10): 15751–15769. doi: 10.1029/JB095iB10p15751
[43]	PERDEW J P, ZUNGER A. Self-interaction correction to density-functional approximations for many-electron systems [J]. Physical Review B, 1981, 23(10): 5048–5079. doi: 10.1103/PhysRevB.23.5048
[44]	PERDEW J P, BURKE K, ERNZERHOF M. Generalized gradient approximation made simple [J]. Physical Review Letters, 1996, 77(18): 3865–3868. doi: 10.1103/PhysRevLett.77.3865

Relative Articles

Supplements(0)

Cited By

Proportional views

Proportional views

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Figures(6) / Tables(2)

Get Citation

PDF

XML

Article Metrics

Article views(382) PDF downloads(57)

A Gibbs Thermodynamic Surface Approach to Modeling the Melting of Forsterite

doi: 10.11858/gywlxb.20251130

Abstract

References

Proportional views

Catalog

通讯作者: 陈斌, bchen63@163.com

Article Metrics

Proportional views

Related

A Gibbs Thermodynamic Surface Approach to Modeling the Melting of Forsterite

doi: 10.11858/gywlxb.20251130

Abstract

References

Proportional views

Catalog

通讯作者: 陈斌, bchen63@163.com

Article Metrics

Proportional views

Related

Export File

Citation

Format

Content