基于吉布斯热力学曲面理论的镁橄榄石熔融计算研究

赵轩; 尹坤

doi:10.11858/gywlxb.20251130

基于吉布斯热力学曲面理论的镁橄榄石熔融计算研究

doi: 10.11858/gywlxb.20251130

赵轩^1,,
尹坤^{1, 2,*, ,}

1.
成都理工大学地球与行星科学学院, 四川成都　610059
2.
成都理工大学地质灾害防治与地质环境保护全国重点实验室, 四川成都　610059

基金项目: 国家自然科学基金（41972036）；国家重点研发计划（2024YFF0807500）

详细信息

作者简介:
赵　轩（2000－），男，硕士研究生，主要从事计算矿物物理研究. E-mail：zhaoxuane@outlook.com

通讯作者:
尹　坤（1982－），男，博士，副研究员，主要从事计算矿物物理研究. E-mail：yinkun@cdut.edu.cn

中图分类号: O521.2; P311.9
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出版历程
- 收稿日期: 2025-07-15
- 修回日期: 2025-07-23
- 网络出版日期: 2025-07-28
- 刊出日期: 2025-10-05

A Gibbs Thermodynamic Surface Approach to Modeling the Melting of Forsterite

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

摘要

摘要: 熔融过程在地球与其他行星的演化中发挥着重要作用。由于行星内部普遍处于高压环境，研究物质在高压条件下的熔融行为对于理解其组成及内部动力学过程至关重要。为此，在吉布斯热力学曲面理论及前人工作的基础上，结合第一性原理分子动力学模拟，通过构建几何模型，获得了镁橄榄石在0～16 GPa压力范围内的熔融数据。该方法能够在有限的计算资源下高效且准确地获取特定压力范围内任意点的熔融数据，包括固相和熔体相各自的吉布斯自由能、亥姆霍兹自由能、焓、内能、熵和体积。同时，使用该方法确定了镁橄榄石和瓦兹利石在1200～2500 K内的相变边界。所有计算结果均与已有实验及计算数据高度一致，验证了该方法在计算高压下物质的熔化行为的可靠性和准确性。该方法突破了现有方法在有限计算资源下难以高效获取完整高压熔融数据的瓶颈。
- 熔化曲线 /
- 吉布斯热力学曲面 /
- 高压 /
- 分子动力学模拟 /
- 镁橄榄石
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

HTML全文

图 1 吉布斯热力学曲面示意图

Figure 1. Schematic diagram of Gibbs thermodynamic surface

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图 2 橄榄石单胞

Figure 2. Unit cell of olivine

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图 3 镁橄榄石在不同温度下的径向分布函数（V/V₀=1.0）

Figure 3. Radial distribution functions of forsterite at various temperatures (V/V₀=1.0)

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图 4 2.0～10.0 GPa压力范围内镁橄榄石的4种热力学势相图

Figure 4. Projection diagrams of four thermodynamic potentials in the range of 2.0 to 12.0 GPa for forsterite

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图 5 镁橄榄石的熔化曲线

Figure 5. Melting curves of forsterite

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图 6 镁橄榄石和瓦兹利石的相变边界

Figure 6. Phase boundary between forsterite and wadsleyite

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表 1 镁橄榄石的熔融数据

Table 1. Melting data of forsterite

p/GPa	T_m/K	Phase	V/(Å³/atom)	G/(eV/atom)	A/(eV/atom)	H/(eV/atom)	U/(eV/atom)	S/(μeV·K⁻¹/atom)
0.5	2195	Solid	11.357	−6.597	−6.633	−6.538	−6.574	27
0.5	2195	Liquid	12.540	−6.583	−6.622	−6.373	−6.412	102
1.0	2232	Solid	11.310	−6.563	−6.634	−6.496	−6.567	30
1.0	2232	Liquid	12.365	−6.550	−6.627	−6.318	−6.395	110
2.0	2295	Solid	11.214	−6.495	−6.635	−6.416	−6.556	34
2.0	2295	Liquid	12.109	−6.487	−6.638	−6.210	−6.361	124
3.0	2363	Solid	11.125	−6.428	−6.636	−6.335	−6.543	39
3.0	2363	Liquid	11.908	−6.425	−6.648	−6.111	−6.334	135
4.0	2411	Solid	11.125	−6.428	−6.636	−6.335	−6.543	39
4.0	2411	Liquid	11.908	−6.425	−6.648	−6.111	−6.334	135
6.0	2469	Solid	10.834	−6.226	−6.632	−6.122	−6.528	42
6.0	2469	Liquid	11.377	−6.225	−6.651	−5.876	−6.302	142
8.0	2529	Solid	10.657	−6.095	−6.627	−5.985	−6.517	43
8.0	2529	Liquid	11.088	−6.094	−6.647	−5.731	−6.285	143
9.0	2555	Solid	10.573	−6.030	−6.623	−5.918	−6.512	44
9.0	2555	Liquid	10.957	−6.029	−6.644	−5.662	−6.277	144
10.0	2579	Solid	10.492	−5.965	−6.620	−5.852	−6.507	44
10.0	2579	Liquid	10.834	−5.964	−6.641	−5.593	−6.270	144
11.0	2630	Solid	10.424	−5.902	−6.618	−5.779	−6.494	47
11.0	2630	Liquid	10.731	−5.905	−6.641	−5.517	−6.254	148
13.0	2634	Solid	10.261	−5.773	−6.606	−5.660	−6.493	43
13.0	2634	Liquid	10.503	−5.773	−6.625	−5.397	−6.249	143
14.0	2649	Solid	10.189	−5.710	−6.600	−5.598	−6.488	42
14.0	2649	Liquid	10.404	−5.710	−6.619	−5.333	−6.242	142
16.0	2672	Solid	10.051	−5.585	−6.588	−5.475	−6.479	41
16.0	2672	Liquid	10.219	−5.585	−6.605	−5.209	−6.230	140

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表 2 镁橄榄石-瓦兹利石相变边界热力学数据

Table 2. Data for phase boundary between forsterite and wadsleyite

p/GPa	T/K	Phase	V/（Å³/atom）	G/(eV/atom)	A/(eV/atom)	H/(eV/atom)	U/(eV/atom)	S/(μeV·K⁻¹/atom)
13.84	1200	Fo	9.850	−5.800	−6.651	−6.010	−6.861	−178
13.84	1200	Wd	9.259	−5.800	−6.600	−6.024	−6.824	−186
13.92	1300	Fo	9.860	−5.778	−6.635	−5.978	−6.834	−156
13.92	1300	Wd	9.277	−5.778	−6.584	−5.992	−6.798	−164
14.01	1400	Fo	9.870	−5.757	−6.621	−5.945	−6.808	−135
14.01	1400	Wd	9.296	−5.757	−6.570	−5.959	−6.772	−144
14.12	1500	Fo	9.882	−5.738	−6.608	−5.911	−6.781	−116
14.12	1500	Wd	9.315	−5.738	−6.558	−5.926	−6.747	−125
14.25	1600	Fo	9.893	−5.718	−6.598	−5.875	−6.755	−98
14.25	1600	Wd	9.333	−5.718	−6.549	−5.891	−6.721	−108
14.41	1700	Fo	9.904	−5.699	−6.590	−5.838	−6.729	−82
14.41	1700	Wd	9.352	−5.699	−6.540	−5.854	−6.695	−91
14.60	1800	Fo	9.913	−5.680	−6.583	−5.799	−6.702	−66
14.60	1800	Wd	9.368	−5.680	−6.534	−5.816	−6.670	−76
14.83	1900	Fo	9.922	−5.660	−6.578	−5.757	−6.676	−51
14.83	1900	Wd	9.383	−5.660	−6.528	−5.776	−6.644	−61
15.09	2000	Fo	9.930	−5.639	−6.574	−5.714	−6.650	−38
15.09	2000	Wd	9.395	−5.639	−6.524	−5.733	−6.618	−47
15.36	2100	Fo	9.937	−5.619	−6.572	−5.670	−6.623	−24
15.36	2100	Wd	9.405	−5.619	−6.521	−5.690	−6.592	−34
15.65	2200	Fo	9.944	−5.599	−6.571	−5.626	−6.597	−12
15.65	2200	Wd	9.413	−5.599	−6.519	−5.647	−6.566	−21
15.94	2300	Fo	9.951	−5.581	−6.571	−5.582	−6.571	0
15.94	2300	Wd	9.419	−5.581	−6.518	−5.603	−6.540	−10
16.21	2400	Fo	9.960	−5.564	−6.572	−5.538	−6.546	11
16.21	2400	Wd	9.425	−5.564	−6.518	−5.560	−6.513	2
16.47	2500	Fo	9.970	−5.550	−6.575	−5.496	−6.520	22
16.47	2500	Wd	9.429	−5.550	−6.519	−5.518	−6.487	13

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