Determination of the full elastic tensor of single crystals using shear wave velocities by Brillouin spectroscopy
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Dawei Fan
,
Zhu Mao
Abstract
Single-crystal elasticity of candidate minerals in the Earth’s mantle, such as that of ferropericlase and bridgmanite, etc., is very important for understanding the seismic observations, geodynamic flow patterns, and testing geochemical and mineralogical models of the planet’s deep interior. Determination of the full elastic tensor typically requires measuring both compressional and shear wave velocities (vP and vS) of the candidate single crystal as a function of crystallographic orientations at high pressures, but it has been a huge technical challenge obtaining vP at pressures above 25 GPa using Brillouin light scattering coupled with in a diamond-anvil cell due to the spectral overlap of the sample vP with the vS of the diamond window. In this study, we present a new method to derive the full elastic tensor (Cij) of single crystals using only measured vS of a given crystal platelet as a function of the azimuthal angle. Experimentally determined vP and vS results from Brillouin measurements for cubic periclase (MgO) and spinel (MgAl2O4), tetragonal stishovite (SiO2), and orthorhombic zoisite [Ca2Al3Si3O12(OH)] at ambient conditions are used as examples to demonstrate the application of our approach from theoretical analyses and experimental prospective. For high-symmetry cubic minerals, such as cubic MgO and spinel, a suitable crystallographic plane with small tradeoffs between any two Cij in vS is required for the method to work well such that the obtained Cij using measured vS velocities alone can be within 3% of the values derived from using both vS and vP. Our analyses show that the (-1,0.5,0.2) platelet for periclase and the (1,1,0) platelet for spinel are respective optimal orientations for applying our method. For lower symmetry minerals, such as tetragonal stishovite and orthorhombic zoisite, three crystallographic planes, that are orthogonal to each other and are tilted at least 20° from the principal crystallographic planes, can be used to provide reliable constraints on Cij using measured vS alone. We have extended this method to derive Cij of the (-1,0.5,0.2) platelet for periclase at pressures of 5.8 and 11.3 GPa, in a high-pressure diamond-anvil cell to demonstrate the usefulness of the approach in studying the elasticity of Earth’s mantle minerals at relevant pressure-temperature conditions. Our proposed approach can be extended to all other crystal systems at high pressures to overcome the constant lack of experimental vP velocities at above 25 GPa, potentially providing new experimental and theoretical approaches in constraining the elastic tensor of the materials in the Earth’s deep interior, which will be an effective strategy to solve one of the most relevant difficulties involved in the experimental study of the elastic properties (especially elastic anisotropy) of minerals of the lower mantle.
© 2015 by Walter de Gruyter Berlin/Boston
Articles in the same Issue
- On understanding the structure and composition of crystals
- Stable and metastable silicate liquid immiscibility in ferrobasalts
- When was the Earth’s conveyor belt set in motion?
- Trace element partitioning into sulfide: How lithophile elements become chalcophile and vice versa
- Petrology on Mars
- Hf and Nd isotope systematics of early Archean komatiites from surface sampling and ICDP drilling in the Barberton Greenstone Belt, South Africa
- Quasicrystals at extreme conditions: The role of pressure in stabilizing icosahedral Al63Cu24Fe13 at high temperature
- Tracking the thermal decomposition of plasma-sprayed hydroxylapatite
- Experimental constraints on bubble formation and growth during magma ascent: A review
- Ankerite grains with dolomite cores: A diffusion chronometer for low- to medium-grade regionally metamorphosed clastic sediments
- Crystal structure, high-pressure, and high-temperature behavior of carbonates in the K2Mg(CO3)2–Na2Mg(CO3)2 join
- Temperature micro-mapping in oscillatory-zoned chlorite: Application to study of a green-schist facies fault zone in the Pyrenean Axial Zone (Spain)
- Micro- and nano-characterization of Zn-clays in nonsulfide supergene ores of southern Peru
- Mineralogical characterization of individual growth structures of Mn-nodules with different Ni+Cu content from the central Pacific Ocean
- The magma plumbing system of the Emeishan large igneous province and its role in basaltic magma differentiation in a continental setting
- Weathering of the Ethiopian volcanic province: A new weathering index to characterize and compare soils
- Recommended mineral-melt partition coefficients for FRTEs (Cu), Ga, and Ge during mantle melting
- Tetrahedral plot diagram: A geometrical solution for quaternary systems
- Investigations on alunogen under Mars-relevant temperature conditions: An example for a single-crystal-to-single-crystal phase transition
- Crystallization of calcium oxalate hydrates by interaction of calcite marble with fungus Aspergillus niger
- Direct and indirect evidence for free oxygen (O2–) in MO-silicate glasses and melts (M = Mg, Ca, Pb)
- Effect of fluid composition on growth rate of monazite in quartzite at 1.0 GPa and 1000 °C
- Determination of the full elastic tensor of single crystals using shear wave velocities by Brillouin spectroscopy
- Temperature dependence of the velocity-density relation for liquid metals under high pressure: Implications for the Earth’s outer core
- Thermal, compositional, and compressional demagnetization of cementite
- The MnCO3-II high-pressure polymorph of rhodocrosite
- Lanthanide tetrads in normalized rare element patterns of zircon from the Koktokay No. 3 granitic pegmatite, Altay, NW China
- Hydrogrossular, Ca3Al2(SiO4)3–x(H4O4)x: An ab initio investigation of its structural and energetic properties
- High-pressure synthesis of skiagite-majorite garnet and investigation of its crystal structure
- Mineralogical evolution of Fe–Si-rich layers at the olivine-water interface during carbonation reactions
- High-pressure spectroscopic study of siderite (FeCO3) with a focus on spin crossover
- Exploring the potential of Raman spectroscopy for crystallochemical analyses of complex hydrous silicates: I. Amphiboles
- Apexite, NaMg(PO4)·9H2O, a new struvite-type phase with a heteropolyhedral cluster
- The mechanism of infiltration of metamorphic fluids recorded by hydration and carbonation of epidote-amphibolite facies metabasaltic sills in the SW Scottish Highlands
- The axial ratio of hcp Fe and Fe–Ni–Si alloys to the conditions of Earth’s inner core
- Shock-induced mobilization of metal and sulfide in planetesimals: Evidence from the Buck Mountains 005 (L6 S4) dike-bearing chondrite
- The accretion and differentiation of Earth under oxidizing conditions
- Dislocation microstructures in simple-shear-deformed wadsleyite at transition-zone conditions: Weak-beam dark-field TEM characterization of dislocations on the (010) plane
- Chemical composition and crystal structure of merrillite from the Suizhou meteorite
Articles in the same Issue
- On understanding the structure and composition of crystals
- Stable and metastable silicate liquid immiscibility in ferrobasalts
- When was the Earth’s conveyor belt set in motion?
- Trace element partitioning into sulfide: How lithophile elements become chalcophile and vice versa
- Petrology on Mars
- Hf and Nd isotope systematics of early Archean komatiites from surface sampling and ICDP drilling in the Barberton Greenstone Belt, South Africa
- Quasicrystals at extreme conditions: The role of pressure in stabilizing icosahedral Al63Cu24Fe13 at high temperature
- Tracking the thermal decomposition of plasma-sprayed hydroxylapatite
- Experimental constraints on bubble formation and growth during magma ascent: A review
- Ankerite grains with dolomite cores: A diffusion chronometer for low- to medium-grade regionally metamorphosed clastic sediments
- Crystal structure, high-pressure, and high-temperature behavior of carbonates in the K2Mg(CO3)2–Na2Mg(CO3)2 join
- Temperature micro-mapping in oscillatory-zoned chlorite: Application to study of a green-schist facies fault zone in the Pyrenean Axial Zone (Spain)
- Micro- and nano-characterization of Zn-clays in nonsulfide supergene ores of southern Peru
- Mineralogical characterization of individual growth structures of Mn-nodules with different Ni+Cu content from the central Pacific Ocean
- The magma plumbing system of the Emeishan large igneous province and its role in basaltic magma differentiation in a continental setting
- Weathering of the Ethiopian volcanic province: A new weathering index to characterize and compare soils
- Recommended mineral-melt partition coefficients for FRTEs (Cu), Ga, and Ge during mantle melting
- Tetrahedral plot diagram: A geometrical solution for quaternary systems
- Investigations on alunogen under Mars-relevant temperature conditions: An example for a single-crystal-to-single-crystal phase transition
- Crystallization of calcium oxalate hydrates by interaction of calcite marble with fungus Aspergillus niger
- Direct and indirect evidence for free oxygen (O2–) in MO-silicate glasses and melts (M = Mg, Ca, Pb)
- Effect of fluid composition on growth rate of monazite in quartzite at 1.0 GPa and 1000 °C
- Determination of the full elastic tensor of single crystals using shear wave velocities by Brillouin spectroscopy
- Temperature dependence of the velocity-density relation for liquid metals under high pressure: Implications for the Earth’s outer core
- Thermal, compositional, and compressional demagnetization of cementite
- The MnCO3-II high-pressure polymorph of rhodocrosite
- Lanthanide tetrads in normalized rare element patterns of zircon from the Koktokay No. 3 granitic pegmatite, Altay, NW China
- Hydrogrossular, Ca3Al2(SiO4)3–x(H4O4)x: An ab initio investigation of its structural and energetic properties
- High-pressure synthesis of skiagite-majorite garnet and investigation of its crystal structure
- Mineralogical evolution of Fe–Si-rich layers at the olivine-water interface during carbonation reactions
- High-pressure spectroscopic study of siderite (FeCO3) with a focus on spin crossover
- Exploring the potential of Raman spectroscopy for crystallochemical analyses of complex hydrous silicates: I. Amphiboles
- Apexite, NaMg(PO4)·9H2O, a new struvite-type phase with a heteropolyhedral cluster
- The mechanism of infiltration of metamorphic fluids recorded by hydration and carbonation of epidote-amphibolite facies metabasaltic sills in the SW Scottish Highlands
- The axial ratio of hcp Fe and Fe–Ni–Si alloys to the conditions of Earth’s inner core
- Shock-induced mobilization of metal and sulfide in planetesimals: Evidence from the Buck Mountains 005 (L6 S4) dike-bearing chondrite
- The accretion and differentiation of Earth under oxidizing conditions
- Dislocation microstructures in simple-shear-deformed wadsleyite at transition-zone conditions: Weak-beam dark-field TEM characterization of dislocations on the (010) plane
- Chemical composition and crystal structure of merrillite from the Suizhou meteorite
