Volume 33 Issue 6
Nov 2019
Turn off MathJax
Article Contents
YANG Longxing, LIU Lei, LIU Hong, YI Li, GU Xiaoyu. Structure and Elasticity of Garnet under High Pressure by First-Principles Simulation[J]. Chinese Journal of High Pressure Physics, 2019, 33(6): 060104. doi: 10.11858/gywlxb.20190785
Citation: YANG Longxing, LIU Lei, LIU Hong, YI Li, GU Xiaoyu. Structure and Elasticity of Garnet under High Pressure by First-Principles Simulation[J]. Chinese Journal of High Pressure Physics, 2019, 33(6): 060104. doi: 10.11858/gywlxb.20190785

Structure and Elasticity of Garnet under High Pressure by First-Principles Simulation

doi: 10.11858/gywlxb.20190785
  • Received Date: 28 May 2019
  • Rev Recd Date: 12 Jun 2019
  • Issue Publish Date: 25 Sep 2019
  • Garnet is an important component of the upper mantle and mantle transition zone, and its properties under high temperature and pressure are of great significance to understand the composition, structure and dynamic process of mantle. Therefore, the crystal structure and elastic properties of pyrope, almandine, spessartite, uvarovite, grossular and andradite under 0–16 GPa, the six most common garnet in the Earth, were calculated by first principle method. The results show the unit cell volume of pyralaspite (pyrope, almandine, spessartite) is smaller than that of ugrandite (uvarovite, grossular and andradite), and the density of pyralaspite is higher than that of ugrandite except for pyrope. During structural compression, the volume change of polyhedron is from large to small as [XO8] dodecahedron, [YO6] octahedron and [SiO4] tetrahedron, and their ratio is close to 3∶2∶1, indicating that the compression mechanism of garnet is mainly controlled by the dodecahedron. The variation of bond angle shows that tetrahedron and octahedron of the ugrandite would be more regular under high pressure; while the tetrahedron of pyralaspite becomes more irregular under high pressure. The bulk modulus of garnet increases with the increase of almandine, and decreases with the increase of uvarovite and grossular; while the shear modulus of garnet increases with the increase of grossular, and decreases with the increase of almandine and uvarovite. The wave velocity of pyralaspite is smaller than that of ugrandite except for pyrope. Calculation results show that the wave velocities of garnet intersect with the typical wave velocity model of the Earth near 410 km, proving that garnet is an important component of the mantle, and the existence of garnet and its solid solution with different compositions may have an important influence on the wave velocity structure of the Earth’s mantle.

     

  • loading
  • [1]
    PALKE A C, STEBBINS J F, GEIGER C A, et al. Cation order-disorder in Fe-bearing pyrope and grossular garnets: a 27Al and 29Si MAS NMR and 57Fe Mossbauer spectroscopy study [J]. American Mineralogist, 2015, 100(2/3): 536–547.
    [2]
    范大伟, 李博, 陈伟, 等. 石榴子石族矿物状态方程研究进展 [J]. 高压物理学报, 2018, 32(1): 010101. doi: 10.11858/gywlxb.20170597

    FAN D W, LI B, CHEN W, et al. Research progress of the equation of state for garnet minerals [J]. Chinese Journal of High Pressure Physics, 2018, 32(1): 010101. doi: 10.11858/gywlxb.20170597
    [3]
    FEI Y, BERTKA C M. Phase transitions in the Earth’s mantle and mantle mineralogy [J]. Mantle Petrology: Field Observations and High Pressure Experimentation, 1999, 6: 189–207.
    [4]
    RINGWOOD A E. Phase transformations and their bearing on the constitution and dynamics of the mantle [J]. Geochimica et Cosmochimica Acta, 1991, 55(8): 2083–2110. doi: 10.1016/0016-7037(91)90090-R
    [5]
    IRIFUNE T, RINGWOOD A E. Phase transformations in subducted oceanic crust and buoyancy relationships at depths of 600–800 km in the mantle [J]. Earth and Planetary Science Letters, 1993, 117(1/2): 101–110.
    [6]
    WANG Z, JI S. Elasticity of six polycrystalline silicate garnets at pressure up to 3.0 GPa [J]. American Mineralogist, 2001, 86(10): 1209–1218. doi: 10.2138/am-2001-1009
    [7]
    CONRAD P G, ZHA C S, MAO H K, et al. The high-pressure, single-crystal elasticity of pyrope, grossular, and andradite [J]. American Mineralogist, 1999, 84(3): 374–383. doi: 10.2138/am-1999-0321
    [8]
    BABUŠKA V, FIALA J, KUMAZAWA M, et al. Elastic properties of garnet solid-solution series [J]. Physics of the Earth and Planetary Interiors, 1978, 16(2): 157–176. doi: 10.1016/0031-9201(78)90086-9
    [9]
    ANDERSON O L, NAFE J E. The bulk modulus-volume relationship for oxide compounds and related geophysical problems [J]. Journal of Geophysical Research, 1965, 70(16): 3951–3963. doi: 10.1029/JZ070i016p03951
    [10]
    ANDERSON D L, ANDERSON O L. The bulk modulus-volume relationship for oxides [J]. Journal of Geophysical Research, 1970, 75(26): 3494–3500.
    [11]
    HAZEN R M. Crystal structures and compressibilities of pyrope and grossular to 60 kbar [J]. American Mineralogist, 1978, 63(3/4): 297–303.
    [12]
    LEGER J M, REDON A M, CHATEAU C. Compressions of synthetic pyrope, spessartine and uvarovite garnets up to 25 GPa [J]. Physics and Chemistry of Minerals, 1990, 17(2): 161–167.
    [13]
    ZHANG L, AHSBAHS H, KUTOGLU A, et al. Single-crystal hydrostatic compression of synthetic pyrope, almandine, spessartine, grossular and andradite garnets at high pressures [J]. Physics and Chemistry of Minerals, 1999, 27(1): 52–58. doi: 10.1007/s002690050240
    [14]
    TAKAHASHI T, LIU L G. Compression of ferromagnesian garnets and the effect of solid solutions on the bulk modulus [J]. Journal of Geophysical Research, 1970, 75(29): 5757–5766. doi: 10.1029/JB075i029p05757
    [15]
    HUANG S, CHEN J. Equation of state of pyrope–almandine solid solution measured using a diamond anvil cell and in situ synchrotron X-ray diffraction [J]. Physics of the Earth and Planetary Interiors, 2014, 228: 88–91. doi: 10.1016/j.pepi.2014.01.014
    [16]
    MILANI S, NESTOLA F, ALVARO M, et al. Diamond-garnet geobarometry: the role of garnet compressibility and expansivity [J]. Lithos, 2015, 227: 140–147. doi: 10.1016/j.lithos.2015.03.017
    [17]
    FAN D, XU J, MA M, et al. P-V-T equation of state of spessartine-almandine solid solution measured using a diamond anvil cell and in situ synchrotron X-ray diffraction [J]. Physics and Chemistry of Minerals, 2015, 42(1): 63–72. doi: 10.1007/s00269-014-0700-2
    [18]
    MURAKAMI M, SINOGEIKIN S V, LITASOV K, et al. Single-crystal elasticity of iron-bearing majorite to 26 GPa: implications for seismic velocity structure of the mantle transition zone [J]. Earth and Planetary Science Letters, 2008, 274(3/4): 339–345.
    [19]
    FAN D W, WEI S Y, LIU J, et al. High pressure X-ray diffraction study of a grossular-andradite solid solution and the bulk modulus variation along this solid solution [J]. Chinese Physics Letters, 2011, 28(7): 076101. doi: 10.1088/0256-307X/28/7/076101
    [20]
    FAN D W, KUANG Y, XU J, et al. Thermoelastic properties of grossular-andradite solid solution at high pressures and temperatures [J]. Physics and Chemistry of Minerals, 2017, 44(2): 137–147. doi: 10.1007/s00269-016-0843-4
    [21]
    DU W, CLARK S M, WALKER D. Thermo-compression of pyrope-grossular garnet solid solutions: non-linear compositional dependence [J]. American Mineralogist, 2014, 100(1): 215–222.
    [22]
    GILLAN M J, ALFÈD, BRODHOLT J, et al. First-principles modelling of Earth and planetary materials at high pressures and temperatures [J]. Reports on Progress in Physics, 2006, 69(8): 2365–2441. doi: 10.1088/0034-4885/69/8/R03
    [23]
    PERDEW J P, ZUNGER A. Self-interaction correction to density-functional approximations for many-body systems [J]. Physical Review B, 1981, 23(10): 5048–5079. doi: 10.1103/PhysRevB.23.5048
    [24]
    WENTZCOVITCH R M, MARTINS J L, PRICE G D. Ab initio molecular dynamics with variable cell shape: application to MgSiO3 [J]. Physical Review Letters, 1993, 70(25): 3947–3950. doi: 10.1103/PhysRevLett.70.3947
    [25]
    DA SILVA C, STIXRUDE L, WENTZCOVITCH R M. Elastic constants and anisotropy of forsterite at high pressure [J]. Geophysical Research Letters, 1997, 24(15): 1963–1966. doi: 10.1029/97GL01756
    [26]
    KARKI B B, STIXRUDE L, WENTZCOVITCH R M. High-pressure elastic properties of major materials of Earth’s mantle from first principles [J]. Reviews of Geophysics, 2015, 39(4): 507–534.
    [27]
    LIU L, DU J G, ZHAO J, et al. Elastic properties of hydrous forsterites under high pressure: first-principle calculations [J]. Physics of the Earth and Planetary Interiors, 2009, 176(1): 89–97.
    [28]
    LIU L, DU J, LIU W, et al. Elastic behavior of (Mg xFe1- x)2SiO4 olivine at high pressure from first-principles simulations [J]. Journal of Physics and Chemistry of Solids, 2010, 71(8): 1094–1097. doi: 10.1016/j.jpcs.2010.03.013
    [29]
    LIU L, DU J G, LIU H, et al. Differential stress effect on the structural and elastic properties of forsterite by first-principles simulation [J]. Physics of the Earth and Planetary Interiors, 2014, 233: 95–102. doi: 10.1016/j.pepi.2014.06.010
    [30]
    LIU L, LV C J, ZHUANG C Q, et al. Effects of differential stress on the structure and Raman spectra of calcite from first-principles calculations [J]. American Mineralogist, 2016, 101(8): 1892–1897. doi: 10.2138/am-2016-5558
    [31]
    CEPERLEY D M, ALDER B J. Ground state of the electron gas by a stochastic method [J]. Physical Review Letters, 1980, 45(7): 566–569. doi: 10.1103/PhysRevLett.45.566
    [32]
    NIELSEN O H, MARTIN, RICHARD M. First-principles calculation of stress [J]. Physical Review Letters, 1983, 50(9): 697–700. doi: 10.1103/PhysRevLett.50.697
    [33]
    VANDERBILT D. Soft self-consistent pseudopotentials in a generalized eigenvalue formalism [J]. Physical Review B, 1990, 41(11): 7892–7895. doi: 10.1103/PhysRevB.41.7892
    [34]
    NIELSEN O H, MARTIN R M. Quantum-mechanical theory of stress and force [J]. Physical Review B, 1985, 32(6): 3780–3791. doi: 10.1103/PhysRevB.32.3780
    [35]
    马艳梅, 彭刚, 李敏. 镁铝石榴子石的高压X射线衍射研究 [J]. 高压物理学报, 2008, 22(3): 305–308. doi: 10.3969/j.issn.1000-5773.2008.03.014

    MA Y M, PENG G, LI M. X-ray diffraction investigation of pyrope under pressure [J]. Chinese Journal of High Pressure Physics, 2008, 22(3): 305–308. doi: 10.3969/j.issn.1000-5773.2008.03.014
    [36]
    WEBB S L. The elasticity of the upper mantle orthosilicates olivine and garnet to 3 GPa [J]. Physics and Chemistry of Minerals, 1989, 16(7): 684–692.
    [37]
    ZOU Y, GRÉAUX S, IRIFUNE T, et al. Thermal equation of state of Mg3Al2Si3O12 pyrope garnet up to 19 GPa and 1700 K [J]. Physics and Chemistry of Minerals, 2012, 39(7): 589–598. doi: 10.1007/s00269-012-0514-z
    [38]
    HAZEN R M, DOWNS R T, CONRAD P G, et al. Comparative compressibilities of majorite-type garnets [J]. Physics and Chemistry of Minerals, 1994, 21(5): 344–349.
    [39]
    BASS J D. Elasticity of uvarovite and andradite garnets [J]. Journal of Geophysical Research: Solid Earth, 1986, 91(B7): 7505–7516. doi: 10.1029/JB091iB07p07505
    [40]
    BASS J D. Elasticity of grossular and spessartite garnets by Brillouin spectroscopy [J]. Journal of Geophysical Research, 1989, 94(B6): 7621–7628. doi: 10.1029/JB094iB06p07621
    [41]
    O’NEILL B, BASS J, R. SMYTH J, et al Elasticity of a grossular-pyrope-almandine garnet [J]. Journal of Geophysical Research Solid Earth, 1989, 94(B12): 17819–17824. doi: 10.1029/JB094iB12p17819
    [42]
    SATO Y, AKAOGI M, AKIMOTO S I. Hydrostatic compression of the synthetic garnets pyrope and almandine [J]. Journal of Geophysical Research, 1978, 83(B1): 335–338. doi: 10.1029/JB083iB01p00335
    [43]
    徐光宪, 王祥云. 物质结构[M]. 2版. 北京: 高等教育出版社, 1987: 621–622.

    XU G X, WANG X Y. Material structure [M]. 2nd ed. Beijing: Higher Education Press, 1987: 621–622.
    [44]
    LI L, WEIDNER D J, BRODHOLT J, et al. Ab initio molecular dynamic simulation on the elasticity of Mg3Al2Si3O12 pyrope [J]. Journal of Earth Science, 2011, 22(2): 169–175. doi: 10.1007/s12583-011-0169-6
  • 加载中

Catalog

    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

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(7)  / Tables(2)

    Article Metrics

    Article views(9713) PDF downloads(58) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return