地球物质科学的基本原理: 固体地球科学中的热力学研究历史与展望

王超; 渠淼; 喻慧阳

doi:10.19509/j.cnki.dzkq.tb20230210

地球物质科学的基本原理: 固体地球科学中的热力学研究历史与展望

doi: 10.19509/j.cnki.dzkq.tb20230210

王超^{a, b, ,},
渠淼^{a, b},
喻慧阳^c

a.
西北大学大陆动力学国家重点实验室, 西安 710069
b.
西北大学地质学系, 西安 710069
c.
西北大学马克思主义学院, 西安 710069

基金项目:

国家自然科学基金项目 42272054

国家自然科学基金项目 42030307

大陆动力学国家重点实验室(西北大学)团队重点项目

详细信息

通讯作者:
王超, E-mail: chaowang@nwu.edu.cn

中图分类号: P5
计量
- 文章访问数: 245
- PDF下载量: 93
- 被引次数: 0
出版历程
- 收稿日期: 2023-04-19
- 录用日期: 2023-07-05
- 修回日期: 2023-06-09

Principle of Earth materials: A historical perspective of thermodynamics of the Earth

WANG Chao^{a, b
, ,},
QU Miao^{a, b},
YU Huiyang^c

a.
State Key Laboratory of Continental Dynamics, Northwest University, Xi'an 710069, China
b.
Department of Geology, Northwest University, Xi'an 710069, China
c.
School of Marxism, Northwest University, Xi'an 710069, China

More Information

Corresponding author: WANG Chao, E-mail: chaowang@nwu.edu.cn

摘要

摘要:
地球是一种物质和能量结合的存在形式。地球及其他行星的形成和运作过程实际上是物质和能量状态的演化历史。研究物质的科学是物理和化学, 描述物质自然规律的语言是数学, 这属于热力学的研究范畴。从19世纪中叶开尔文利用热力学理论计算地球年龄开始, 热力学在地球科学领域的应用已有100多年历史, 它在阐释地球和行星演化过程的基本逻辑与规律方面发挥了核心作用, 引起了固体地球科学发展史中的许多重要变革。近20年来, 随着物理、化学和计算机科学的不断发展, 经典热力学和非平衡热力学在地球物质科学中的应用进一步发展, 成为地球物质研究的基本原理体系。通过研究地球物质的形成与演化条件来揭示地球结构、动力学和演化过程的地球热力学学科已经形成。未来地球热力学的发展需要与地球物理、地球化学理论和实验相结合, 在热力学数据库发展的基础上, 建立合适的热力学模型来解决实际的地球科学问题。另外, 地球热力学的进一步发展需要与相应的课程教学相结合、加强热力学在地球科学中的课程建设是当前的一项重要任务。热力学是地球物理、地球化学、地质学等多学科交叉研究的纽带和桥梁。如何从热力学的视角认识地球及其演变过程将会是一个永恒课题。
- 地球物质科学 /
- 热力学 /
- 非平衡热力学 /
- 地球系统科学
Abstract: <p>Earth is a combination of material and energy. The evolution of Earth and planets is a history of the transfer of matter and energy. Materials science is codified into physics and chemistry, while mathematics is the language that describes the law of nature, which belongs to the field of thermodynamics.</p></sec><sec><title>Significance
Thus, thermodynamics, consisting of physics, chemistry and mathematics, can unravel the principles of earth materials. Since the middle of the 19th century, Kelvin used thermodynamic theory to calculate the age of the Earth, and thermodynamics has been applied in the field of earth science for more than 100 years, which has provided a vital theoretical framework for understanding the planet's formation and evolution. Its application revolutionized the development of earth science.
Progress
In the past 20 years, with the development of physics, chemistry and computer science, the application and development of classical thermodynamics and nonequilibrium thermodynamics in earth matter science have further improved and become the fundamental principal system of earth material research. The thermodynamics of earth have been studied to determine the structure, dynamics and evolution of earth by studying the formation and evolution of earth materials. Thermodynamics links geophysics, geochemistry and geology. However, new thermodynamic models, databases, and methods for teaching and learning about thermodynamics in earth science need to be developed.
Conclusions and Prospects
It is foreseeable that understanding the earth and its evolution from the perspective of thermodynamics will be a permanent issue. Thermodynamics will exert its power in unknown fields such as planetary science, earth's internal evolution as well as earth systems science, driving people to make new observations and theories about nature.
- Earth materials /
- thermodynamics /
- non-equilibrium thermodynamics /
- Earth system
注释:

所有作者声明不存在利益冲突。

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图 1 地球系统中的热力学示意图(其指示不同体系之间的能量转化关系(左侧实线)和效应(右侧虚线)(据文献[1]修改))

Figure 1. A planetary thermodynamic view of the Earth system, with its cascades of energy conversion(left, solid lines) and its effects(right, dashed lines)

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图 2 KFMASH体系P-T视剖面图(据文献[15]修改)

chl.绿泥石; bi.黑云母; st.十字石; g.石榴石; ky.蓝晶石; sill.夕线石

Figure 2. P-T pseudosection in KFMASH(+mu+q+H₂O) for a "common" pelite composition: Al₂O₃=41.89, MgO=18.19, FeO=27.29, and K₂O=12.63(in mol%).Water activity=1

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图 3 岩浆储库中不同过程MCS模拟的岩浆主量元素变化图解(详见文献[20])

FC.分离结晶; AFC.部分混染分离结晶; R₂FC.补给分离结晶; S₂FC.同化混染分离结晶; R₂AFC.补给混染分离结晶

Figure 3. Results of MCS simulations for five cases(FC, AFC, R₂FC, S₂FC, and R₂AFC) shown in SiO₂(%) magma melt versus TiO₂(a), Al₂O₃(b), Fe₂O₃(c), FeO(d), MgO(e), and CaO(f)

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图 4 地幔矿物的热容(C_P)^[22]

capv.立方CaSiO₃钙钛矿; ri.林伍德石; ak.阿基墨石; hpcpx.高压单斜辉石; ol.橄榄石; opx.斜方辉石; cpx.单斜辉石; sp.尖晶石; gt.石榴石; fp.铁方镁石; wa.瓦兹利石; st.斯石英; nal.新型六方铝相; bg.布里奇曼石

Figure 4. Heat capacity C_P. The lines representing phase transitions are suppressed so as not to obscure the properties of narrow phase transitions.HeFESTo was computed on a regular pressure-temperature grid with spacings of 0.01 GPa and 1 K

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图 5 地球科学中的主要热力学数据库和模拟软件(修改自文献[45])

Figure 5. Map showing the principal thermodynamic databases and modelling tools in earth science

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图 6 石榴石生长理论模型^[66]

a.石榴石开始在相互连接且流体充填的空间平衡生长，允许一定的连续元素通量(左图)。稀土元素通过分数平衡结晶进入石榴石(中图)。石榴石中的REE浓度遵循右图中的粗体黑线；b.岩石的渗透性下降，导致孔隙空间的封闭和反应岩石区域的隔离(左图)。此阶段的石榴石生长导致石榴石(中图)中的REE快速减少，这导致HREE谷(右图)的发展；c.由于岩石发生脱水反应，岩石渗透性增加(左图)。渗透性的增加重新发生流体渗透，从而补充可用于石榴石生长的稀土元素(中图)。石榴石中的稀土含量返回到初始连续背景元素通量(右图)；d.上述步骤的重复以及钛铁矿-金红石的转变导致样品中观察到的复杂REE环带和REE分配模式

Figure 6. Conceptual model of garnet growth

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参考文献(82)

[1]	KLEIDON A. Thermodynamic foundations of the Earth system[M]. Cambridge: Cambridge University Press, 2007.
[2]	KLEIN C, PHILPOTTS A R. Earth materials: Introduction to mineralogy and petrology[M]. Second Edition. Cambridge: Cambridge University Press, 2016.
[3]	谢鸿森, 侯渭. 地球物质科学: 一个新的综合性边缘学科[J]. 地球科学进展, 1989, 4(1): 15-21. https://www.cnki.com.cn/Article/CJFDTOTAL-DXJZ406.003.htm XIE H S, HOU W. Earth materials science: A new comprehensive edge discipline[J]. Advances in Earth Science, 1989, 4(1): 15-21. (in Chinese with English abstract) https://www.cnki.com.cn/Article/CJFDTOTAL-DXJZ406.003.htm
[4]	NAVROTSKY A. Physics andchemistry of Earth materials: Cambridge Topics in Mineral Physics and Chemistry[M]. 6th ed. Cambridge: Cambridge University Press, 1994.
[5]	KLEIDON A. Thermodynamic foundations of the Earth system[M]. 1st Edition. Cambridge: Cambridge University Press, 2007.
[6]	吉巴米卡·甘古利. 地球与行星科学中的热力学[M]. 程伟基译. 合肥: 中国科学技术大学出版社. 2016. GANGULY J. Thermodynamics in Earth and planetary sciences[M]. CHENG W J, Translate. Hefei: University of Science and Technology of China Press, 2016. (in Chinese with English abstract)
[7]	GIBBS J W. On the equilibrium of heterogeneous substances[J]. American Journal of Science, 1878, 16(96): 441-458.
[8]	BOWEN N L. The evolution of the igneous rocks[M]. Princeton: Princeton University Press, 1928.
[9]	GOLDSCHMIDT V M, MUIR A. Geochemistry[M]. Oxford: Clarendon Press, 1954.
[10]	LEVIN E M, ROBBINS C R, MCMURDIE H F. Phase diagrams for ceramists[M]. Second Edition. Columbus, Ohio: American Ceramic Society, 1964.
[11]	FERRY J M, SPEAR F S. Experimental calibration of the partitioning of Fe and Mg between biotite and garnet[J]. Contributions to Mineralogy and Petrology, 1978, 66(2): 113-117. doi: 10.1007/BF00372150
[12]	GHENT E. Plagioclase-garnet-Al₂SiO₅-quartz: A potential geobarometer-geothermometer[J]. American Mineralogist, 1976, 61(7/8): 710-714.
[13]	HOLLAND T J B, POWELL R. An enlarged and updated internally consistent thermodynamic dataset with uncertainties and correlations: The system K₂O-Na₂O-CaO-MgO-MnO-FeO-Fe₂O₃-Al₂O₃-TiO₂-SiO₂-C-H₂-O₂[J]. Journal of Metamorphic Geology, 1990, 8(1): 89-124. doi: 10.1111/j.1525-1314.1990.tb00458.x
[14]	POWELL R, HOLLAND T. On thermobarometry[J]. Journal of Metamorphic Geology, 2008, 26: 155-179. doi: 10.1111/j.1525-1314.2007.00756.x
[15]	PHILPOTTS A R, AGUE J J. Principles of igneous and metamorphic petrology[M]. 2nd Ed. Cambridge: Cambridge University Press, 2009.
[16]	RICHET P, OTTONELLO G. Thermodynamics of phase equilibria in magma[J]. Elements, 2010, 6(5): 315-320. doi: 10.2113/gselements.6.5.315
[17]	GANGULY J. Thermodynamics in Earth and planetary sciences[M]. 2nd Edition. Berlin: Springer Cham, 2020.
[18]	GHIORSO M S, SACK R O. Chemical mass transfer in magmatic processes: Ⅳ. A revised and internally consistent thermodynamic model for the interpolation and extrapolation of liquid-solid equilibria in magmatic systems at elevated temperatures and pressures[J]. Contributions to Mineralogy and Petrology, 1995, 119: 197-212. doi: 10.1007/BF00307281
[19]	BOHRSON W A, SPERA F J, GHIORSO M S, et al. Thermodynamic model for energy-constrained open-system evolution of crustal magma bodies undergoing simultaneous recharge, assimilation and crystallization: The magma chamber simulator[J]. Journal of Petrology, 2014, 55: 1685-1717. doi: 10.1093/petrology/egu036
[20]	BOHRSON W A, SPERA F J, HEINONEN J S, et al. Diagnosing open-system magmatic processes using the Magma Chamber Simulator (MCS). Part Ⅰ: Major elements and phase equilibria[J]. Contributions to Mineralogy and Petrology, 2020, 175: 104. doi: 10.1007/s00410-020-01722-z
[21]	廖一帆, 孙宁宇, 毛竹. 地球下地幔矿物结构和热力学参数的研究进展与展望[J]. 地球科学进展, 2017, 32(5): 465-480. https://www.cnki.com.cn/Article/CJFDTOTAL-DXJZ201705002.htm LIAO Y F, SUN N Y, MAO Z. Recent advance and prospects in the structure and thermal elastic properties of lower mantle minerals[J]. Advances in Earth Science, 2017, 32(5): 465-480. (in Chinese with English abstract) https://www.cnki.com.cn/Article/CJFDTOTAL-DXJZ201705002.htm
[22]	STIXRUDE L, LITHGOW-BERTELLONI C. Thermal expansivity, heat capacity and bulk modulus of the mantle[J]. Geophysical Journal International, 2021, 228(2): 1119-1149. doi: 10.1093/gji/ggab394
[23]	SCHUBERT G, YUEN D A, TURCOTTE D L. Role of phase-transitions in a dynamic mantle[J]. Geophysical Journal International, 1975, 42(2): 705-735.
[24]	LI L, WEIDNER D J. Effect of phase transitions on compressional-wave velocities in the Earth's mantle[J]. Nature, 2008, 454: 984-986. doi: 10.1038/nature07230
[25]	DURAND S, CHAMBAT F, MATAS J, et al. Constraining the kinetics of mantle phase changes with seismic data[J]. Geophysical Journal International, 2012, 189(3): 1557-1564. doi: 10.1111/j.1365-246X.2012.05417.x
[26]	MOGK. Complex physical, chemical, biological and anthropogenic interactions in the Earth system. https://serc.carleton.edu/NAGTWorkshops/complexsystems/workshop2010/participants/mogk.html.
[27]	GARRELS R M. Mineral equilibria: At low temperature and pressure[M]. [S. l.]: Harper, 1960.
[28]	KERN R, WEISBROD A. Thermodynamique de base pour minéralogistes, pétrographes et géologues[M]. [S. l.]: Masson, 1964.
[29]	GANGULY J. Thermodynamics in earth and planetary sciences[M]. Berlin: Springer, 2008.
[30]	ANDERSON G M. Thermodynamics of natural systems[M]. New York: John Wiley, 1996.
[31]	ANDERSON G M. Thermodynamics of natural systems[M]. 2nd Edition. Cambridge: Cambridge University Press, 2005.
[32]	穆克敏, 李树勋. 结晶岩岩石物理化学[M]. 北京: 地质出版社, 1988. MU K M, LI S X. Physical Chemical of Crystalline rock[M]. Beijing: Geological Publishing House, 1988. (in Chinese)
[33]	周珣若, 王方正. 岩石物理化学[M]. 郑州: 河南科学技术出版社, 1987. ZHOU X R, WANG F Z. Physical chemistry in petrology[M]. Zhengzhou: Henan Science and Technology Press, 1987. (in Chinese)
[34]	赵容端. 岩石矿物的物理化学基础[M]. 北京: 地质出版社, 1980. ZHAO R D. The Physical chemistry foundations of rocks and minerals[M]. Beijing: Geological Publishing House, 1980. (in Chinese)
[35]	李佩兰, 余行祯. 地质化学热力学: 原理、计算、应用[M]. 长沙: 中南工业大学出版社, 1989. LI P L, YU X Z. Geochemical thermodynamics: Principle, calculation and application[M]. Changsha: Central South University of Technology Press, 1989. (in Chinese)
[36]	江培谟. 地质热力学基础[M]. 北京: 科学出版社, 1989. JIANG P M. Thermodynamics in geology[M]. Beijing: Science Press, 1989. (in Chinese)
[37]	马鸿文. 结晶岩热力学概论[M]. 北京: 地质出版社, 1993. MA H W. Introduction to thermodynamics in crystalline petrology[M]. Beijing: Geological Publishing House, 1993. (in Chinese)
[38]	马鸿文. 结晶岩热力学概论[M]. 2版. 北京: 高等教育出版社, 2001. MA H W. Introduction to thermodynamics in crystalline petrology[M]. 2nd Edition. Beijing: High Education Press, 2001. (in Chinese)
[39]	张有学. 地球化学动力学[M]. 倪怀玮, 王皓越, 刘洋, 等. 译. 北京: 高等教育出版社, 2010. ZHANG Y X. Geochemical kinetics[M]. Ni H W, Wang H Y, Liu Y, et al, Translate. Beijing: High Education Press, 2010. (in Chinese)
[40]	FABRICHNAYA O B, SAXENA S K, RICHET P, et al. Thermodynamic data, models, and phase diagrams in multicomponent oxide systems: An assessment for materials and planetary scientists based on calorimetric, volumetric, and phase equilibrium data[M]. Berlin: Springer, 2004.
[41]	STIXRUDE L, LITHGOW-BERTELLONI C. Thermodynamics of mantle minerals: Ⅱ. Phase equilibria[J]. Geophysical Journal International, 2011, 184: 1180-1213. doi: 10.1111/j.1365-246X.2010.04890.x
[42]	WHITE R W, POWELL R, HOLLAND T J B, et al. New mineral activity-composition relations for thermodynamic calculations in metapelitic systems[J]. Journal of Metamorphic Geology, 2014, 32: 261-286. doi: 10.1111/jmg.12071
[43]	GREEN E C R, WHITE R W, DIENER J F A, et al. Activity-composition relations for the calculation of partial melting equilibria in metabasic rocks[J]. Journal of Metamorphic Geology, 2016, 34: 845-869. doi: 10.1111/jmg.12211
[44]	HOLLAND T J B, GREEN E C R, POWELL R. Melting of peridotites through to granites: A simple thermodynamic model in the system KNCFMASHTOCr[J]. Journal of Petrology, 2018, 59(5): 881-900. doi: 10.1093/petrology/egy048
[45]	LANARI P, DUESTERHOEFT E, HERMANN J. Mapping equilibrium relationships in metamorphic rocks: Petrological modeling beyond equilibrium phase diagrams[C]//Anon. [S. l.]: [s. n.], MSG-meeting, 2021.
[46]	WU C M. Revised empirical garnet-biotite-muscovite-plagioclase geobarmeter in metapelites[J]. Journal of Metamorphic Geology, 2015, 33: 167-176. doi: 10.1111/jmg.12115
[47]	WU C M. Calibration of the biotite-muscovite geobarometer for metapelitic assemblages devoid of garnet or plagioclase[J]. Lithos, 2020, 372/373: 105668. doi: 10.1016/j.lithos.2020.105668
[48]	WU C M, CHEN H X. Calibration of a Ti-in-muscovite geothermometer for ilmenite-and Al₂SiO₅-bearing metapelites[J]. Lithos, 2015, 212/215: 122-127. doi: 10.1016/j.lithos.2014.11.008
[49]	Wu C M, CHEN H X. Revised Ti-in-biotite geothermometer for ilmenite-or rutile-bearing crustal metapelites[J]. Science Bulletin, 2015, 60: 116-121. doi: 10.1007/s11434-014-0674-y
[50]	WEI C J, POWELL R. Calculated phase relations in the system NCKFMASH (Na₂O-CaO-K₂O-FeO-MgO-Al₂O₃-SiO₂-H₂O) for high-pressure metapelites[J]. Journal of Petrology, 2006, 47(2): 385-408. doi: 10.1093/petrology/egi079
[51]	WEI C J, CLARKE G L. Calculated phase equilibria for MORB compositions: A reappraisal of metamorphic evolution of lawsonite eclogite[J]. Journal of Metamorphic Geology, 2011, 29: 939-952. doi: 10.1111/j.1525-1314.2011.00948.x
[52]	XIANG H, CONNOLLY J A D. GeoPS: An interactive visual computing tool for thermodynamic modelling of phase equilibria[J]. Journal of Metamorphic Geology, 2022, 40: 243-255. doi: 10.1111/jmg.12626
[53]	章军锋, 倪怀玮, 杨晓志, 等. 中国实验地球科学研究进展与展望(2011-2020)[J]. 矿物岩石地球化学通报, 2021, 40(3): 597-609. https://www.cnki.com.cn/Article/CJFDTOTAL-KYDH202103005.htm ZHANG J F, NI H W, YANG X Z, et al. Progress and perspective of experimental geoscience in China (2011-2020)[J]. Acta Metallurgica Sinica, 2021, 40(3): 597-609. (in Chinese with English abstract) https://www.cnki.com.cn/Article/CJFDTOTAL-KYDH202103005.htm
[54]	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. https://www.cnki.com.cn/Article/CJFDTOTAL-GYWL201706001.htm 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. (in Chinese with English abstract) https://www.cnki.com.cn/Article/CJFDTOTAL-GYWL201706001.htm
[55]	张宝华, 毛竹, 刘锦, 等. 实验矿物物理的发展现状与趋势: 1. 相变和状态方程、电导率、热导率[J]. 地球科学, 2022, 47(8): 2714-2728. https://www.cnki.com.cn/Article/CJFDTOTAL-DQKX202208005.htm ZHANG B H, MAO Z, LIU J, et al. Recent progress and perspective of experimental mineral physics: 1. Phase transition and equation of state, electrical conductivity and thermal conductivity[J]. Earth Science, 2022, 47(8): 2714-2728. (in Chinese with English abstract) https://www.cnki.com.cn/Article/CJFDTOTAL-DQKX202208005.htm
[56]	许文良, 任建国, 章军锋. 实验地球科学的前沿与发展战略[J]. 地球科学, 2022, 47(8): 2667-2678. https://www.cnki.com.cn/Article/CJFDTOTAL-DQKX202208001.htm XU W L, REN J G, ZHANG J F. Frontiers and development strategies of experimental geoscience[J]. Earth Science, 2022, 47(8): 2667-2678(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-DQKX202208001.htm
[57]	倪怀玮, 王沁霞, 王春光, 等. 实验岩石学发展现状与趋势[J]. 地球科学, 2022, 47(8): 2691-2700. https://www.cnki.com.cn/Article/CJFDTOTAL-DQKX202208003.htm NI H W, WANG Q X, WANG C G, et al. Experimental petrology: Status quo and prospect[J]. Earth Science, 2022, 47(8): 2691-2700. (in Chinese with English abstract) https://www.cnki.com.cn/Article/CJFDTOTAL-DQKX202208003.htm
[58]	陈伟林, 肖凡. 成矿动力学数值计算模拟研究进展: 理论、方法与技术[J]. 地质科技通报, 2023, 42(3): 234-249. doi: 10.19509/j.cnki.dzkq.2022.0125 CHEN W L, XIAO F. Advances in numerical modeling of metallogenic dynamics: A review of theories, methods and technologies[J]. Bulletin of Geological Science and Technology, 2023, 42(3): 234-249. (in Chinese with English abstract) doi: 10.19509/j.cnki.dzkq.2022.0125
[59]	李献华, 李扬, 李秋立, 等. 同位素地质年代学新进展与发展趋势[J]. 地质学报, 2022, 96(1): 104-122. https://www.cnki.com.cn/Article/CJFDTOTAL-DZXE202201007.htm LI X H, LI Y, LI Q L, et al. Progress and prospects of radiometric geochronology[J]. Acta Geologica Sinica, 2022, 96(1): 104-122. (in Chinese with English abstract) https://www.cnki.com.cn/Article/CJFDTOTAL-DZXE202201007.htm
[60]	COSTA F, SHEA T, UBIDE T. Diffusion chronometry and the timescales of magmatic processes[J]. Nature Reviews Earth & Environment, 2020, 1: 201-214.
[61]	COOPER K M, KENT A J R. Rapid remobilization of magmatic crystals kept in cold storage[J]. Nature, 2014, 506: 480-483. doi: 10.1038/nature12991
[62]	LI Y, ALLEN M B, LI X H. Millennial pulses of ore formation and an extra-high Tibetan Plateau[J]. Geology, 2022, 50(6): 665-669. doi: 10.1130/G49911.1
[63]	LI Y, PAN J Y, WU L G, et al. Transient tin mineralization from cooling of magmatic fluids in a long-lived system[J]. Geology, 2023, 51(3): 305-309. doi: 10.1130/G50781.1
[64]	RUBATTO D, BURGER M, LANARI P, et al. Identification of growth mechanisms in metamorphic garnet by high-resolution trace element mapping with LA-ICP-TOFMS[J]. Contributions to Mineralogy and Petrology, 2020, 175(7): 61. doi: 10.1007/s00410-020-01700-5
[65]	LANARI P, ENGI M. Loal bulk compositional effects on metamorphic mineral assemblages[J]. Rev. Mineral Geochem., 2017, 83: 55-102. doi: 10.2138/rmg.2017.83.3
[66]	KONRAD-SCHMOLKE M, HALAMA R, CHEW D, et al. Discrimination of thermodynamic and kinetic contributions to the heavy rare earth element patterns in metamorphic garnet[J]. Journal of Metamorphic Geology, 2022, 41(2).
[67]	WU L G, LI Y, JOLLANDS M C, et al. Diffuser: A user-friendly program for diffusion chronometry with robust uncertainty estimation[J]. Computers & Geosciences, 2022, 163: 105108.
[68]	陈祖兴, 曾志刚, 王晓媛, 等. 岩浆房持续的时间: 矿物内元素扩散年代学研究进展及展望[J]. 地球科学进展, 2020, 35(12): 1232-1242. doi: 10.11867/j.issn.1001-8166.2020.098 CHEN Z X, ZENG Z G, WANG X Y, et al. Duration of magma chamber: Progress and prospect of element diffusion chronometry of minerals[J]. Advances in Earth Science, 2020, 35(12): 1232-1242. (in Chinese with English abstract) doi: 10.11867/j.issn.1001-8166.2020.098
[69]	陈厚彬, 纪伟强, 张少华. 扩散年代学原理及其在岩浆体系研究中的应用[J]. 岩石学报, 2022, 38(5): 1499-1511. https://www.cnki.com.cn/Article/CJFDTOTAL-YSXB202205014.htm CHEN H B, JI W Q, ZHANG S H. The principles of diffusion chronometry and applications in magmatic systems[J]. Acta Petrologica Sinica, 2022, 38(5): 1499-1511. (in Chinese with English abstract) https://www.cnki.com.cn/Article/CJFDTOTAL-YSXB202205014.htm
[70]	邹屹, 陈俊行, 吴佳林, 等. 变质地质学中的扩散: 原理、前沿应用和问题[J]. 岩石学报, 2022, 38(10): 2949-2970. https://www.cnki.com.cn/Article/CJFDTOTAL-YSXB202210004.htm ZOU Y, CHEN J X, WU J L, et al. Diffusion in metamorphic geology: Principles, applications, and problems[J]. Acta Petrologica Sinica, 2022, 38(10): 2949-2970. (in Chinese with English abstract) https://www.cnki.com.cn/Article/CJFDTOTAL-YSXB202210004.htm
[71]	AFONSO J C, FULLEA J, GRIFFIN W L, et al. 3-D multi-observable probabilistic inversion for the compositional and thermal structure of the lithosphere and upper mantle: Ⅰ. A priori petrological information and geophysical observables[J]. Journal of Geophysical Research: Solid Earth, 2013, 118(5): 2586-2617. doi: 10.1002/jgrb.50124
[72]	SAMMON L G, GAO C, MCDONOUGH W F. Lower crustal composition in the southwestern United States[J]. Journal of Geophysical Research: Solid Earth, 2020, 125(3): e2019JB019011. doi: 10.1029/2019JB019011
[73]	SAMMON L G, MCDONOUGH W F, MOONEY W D. Compositional attributes of the deep continental crust inferred from geochemical and geophysical data[J]. Journal of Geophysical Research: Solid Earth, 2022, 127(8): e2022JB024041. doi: 10.1029/2022JB024041
[74]	李琴, 罗洋, 叶信宇, 等. 第一性原理计算在相图计算中的应用研究进展[J]. 有色金属科学与工程, 2015, 6(6): 37-46. https://www.cnki.com.cn/Article/CJFDTOTAL-JXYS201506009.htm LI Q, LUO Y, YE X Y, et al. Application progress of first-principles calculations in CALPHAD technology[J]. Nonferrous Metals Science and Engineering, 2015, 6(6): 37-46. (in Chinese with English abstract) https://www.cnki.com.cn/Article/CJFDTOTAL-JXYS201506009.htm
[75]	COOPER R F. On being a student of thermodynamics: Trust your eyes, Use your imagination[J]. Elements, 2010, 6(5): 282-283.
[76]	BOTT A. Thermodynamic processes in the moist atmosphere[J]. Elements, 2010, 6(5): 293-298. doi: 10.2113/gselements.6.5.293
[77]	MILLERO F J, DITROLIO B R. Use of thermodynamics in examining the effects of ocean acidification[J]. Elements, 2010, 6: 299-303. doi: 10.2113/gselements.6.5.299
[78]	WALD R M. The thermodynamics of black holes[J]. Living Rev Relativ, 2001, 4(1): 6. doi: 10.12942/lrr-2001-6
[79]	LONGHI J. Petrogenesis of picritic mare magmas: Constraints on the extent of early lunar differentation[J]. Geochimica et Cosmochimica Acta, 2006, 70: 5919-5934. doi: 10.1016/j.gca.2006.09.023
[80]	鞠东阳, 庞润连, 李瑞, 等. 热力学计算模拟对初始月幔结构的约束[J]. 岩石学报, 2022, 38(4): 1025-1042. https://www.cnki.com.cn/Article/CJFDTOTAL-YSXB202204005.htm JU D Y, PANG R L, LI R, et al. The initial lunar mantle structure constrained by thermodynamic simulation[J]. Acta Petrologica Sinica, 2022, 38(4): 1025-1042. (in Chinese with English abstract) https://www.cnki.com.cn/Article/CJFDTOTAL-YSXB202204005.htm
[81]	FEGLEY B J. Thermodynamic models of the chemistry of lunar volcanic gases[J]. Geophysical Research Letters, 1991, 18: 2073-2076. doi: 10.1029/91GL02624
[82]	LU Y, MANTHA D, REDDY R G. Thermodynamic analysis on lunar soil reduced by hydrogen[J]. Metallurgical and Materials Transactions B, 2010, 41: 1321-1327.