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Title: Single-Crystal Elasticity of Zoisite, Ca2Al3Si3O12(OH) , by Brillouin Scattering

Abstract

The single-crystal elastic constants of zoisite Ca{sub 2}Al{sub 3}Si{sub 3}O{sub 12}(OH) were determined by Brillouin scattering at ambient conditions. The elastic tensor was obtained by an inversion of acoustic velocity data for three different crystal planes. The aggregate bulk modulus, shear modulus, and Poisson's ratio are K{sub S0} = 125.3(4) GPa, G{sub 0} = 72.9(2) GPa, and {sigma}{sub 0} = 0.26(1) for the VRH (Voigt-Reuss-Hill) average, respectively. The maximum azimuthal anisotropy of zoisite is 22% for compressional velocity and 33% for shear velocity. The maximum shear splitting is 21% along the [001] direction. Our results resolve the discrepancies in bulk modulus and axial compressibilities reported from static compression studies, and provide the first experimental constraints on the shear modulus. Trends in the elastic moduli of minerals in the CaO-Al{sub 2}O{sub 3}-SiO{sub 2}-H{sub 2}O (CASH) system are evaluated.

Authors:
; ;
Publication Date:
Research Org.:
Brookhaven National Laboratory (BNL) National Synchrotron Light Source
Sponsoring Org.:
Doe - Office Of Science
OSTI Identifier:
930427
Report Number(s):
BNL-81168-2008-JA
Journal ID: ISSN 0003-004X; AMMIAY; TRN: US200904%%704
DOE Contract Number:
DE-AC02-98CH10886
Resource Type:
Journal Article
Resource Relation:
Journal Name: American Mineralogist; Journal Volume: 92
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; ACOUSTICS; ANISOTROPY; BRILLOUIN EFFECT; COMPRESSIBILITY; COMPRESSION; CRYSTAL STRUCTURE; ELASTICITY; EPIDOTES; MONOCRYSTALS; SHEAR; VELOCITY; national synchrotron light source

Citation Formats

Mao,Z., Jiang, F., and Duffy, T. Single-Crystal Elasticity of Zoisite, Ca2Al3Si3O12(OH) , by Brillouin Scattering. United States: N. p., 2007. Web. doi:10.2138/am.2007.2329.
Mao,Z., Jiang, F., & Duffy, T. Single-Crystal Elasticity of Zoisite, Ca2Al3Si3O12(OH) , by Brillouin Scattering. United States. doi:10.2138/am.2007.2329.
Mao,Z., Jiang, F., and Duffy, T. Mon . "Single-Crystal Elasticity of Zoisite, Ca2Al3Si3O12(OH) , by Brillouin Scattering". United States. doi:10.2138/am.2007.2329.
@article{osti_930427,
title = {Single-Crystal Elasticity of Zoisite, Ca2Al3Si3O12(OH) , by Brillouin Scattering},
author = {Mao,Z. and Jiang, F. and Duffy, T.},
abstractNote = {The single-crystal elastic constants of zoisite Ca{sub 2}Al{sub 3}Si{sub 3}O{sub 12}(OH) were determined by Brillouin scattering at ambient conditions. The elastic tensor was obtained by an inversion of acoustic velocity data for three different crystal planes. The aggregate bulk modulus, shear modulus, and Poisson's ratio are K{sub S0} = 125.3(4) GPa, G{sub 0} = 72.9(2) GPa, and {sigma}{sub 0} = 0.26(1) for the VRH (Voigt-Reuss-Hill) average, respectively. The maximum azimuthal anisotropy of zoisite is 22% for compressional velocity and 33% for shear velocity. The maximum shear splitting is 21% along the [001] direction. Our results resolve the discrepancies in bulk modulus and axial compressibilities reported from static compression studies, and provide the first experimental constraints on the shear modulus. Trends in the elastic moduli of minerals in the CaO-Al{sub 2}O{sub 3}-SiO{sub 2}-H{sub 2}O (CASH) system are evaluated.},
doi = {10.2138/am.2007.2329},
journal = {American Mineralogist},
number = ,
volume = 92,
place = {United States},
year = {Mon Jan 01 00:00:00 EST 2007},
month = {Mon Jan 01 00:00:00 EST 2007}
}
  • The second-order elastic constants of brucite were determined by Brillouin scattering to 15 GPa in a diamond anvil cell. The experiments were carried out using a 4:1 methanol-ethanol mixture as pressure medium, and ruby as a pressure standard. Two planes, one perpendicular to the c axis (basal plane) and the other containing the c axis (meridian plane), were measured at room pressure and 10 elevated pressures. Individual elastic stiffnesses, aggregate moduli, and their pressure derivatives were obtained by fitting the data to Eulerian finite strain equations. The inversion yields individual elastic constants of C{sub 11} = 154.0(14) GPa, C{sub 33}more » = 49.7(7) GPa, C{sub 12} = 42.1(17) GPa, C{sub 13} = 7.8(25) GPa, C{sub 14} = 1.3(10) GPa, C{sub 44} = 21.3(4) GPa, and their pressure derivatives of ({delta} C{sub 11}/{delta} P){sub 0} = 9.0(2), ({delta} C{sub 33}/{delta} P){sub 0} = 14.0(5), ({delta} C{sub 12}/{delta} P){sub 0} = 3.2(2), ({delta} C{sub 13}/{delta} P){sub 0} = 5.0(1), ({delta} C{sub 14}/{delta} P){sub 0} = 0.9(1), ({delta} C{sub 44}/{delta} P){sub 0} = 3.9(1). Aggregate moduli and their pressure derivatives are K{sub S0} = 36.4(9) GPa, G{sub 0} = 31.3(2) GPa, ({delta} K{sub S}/{delta} P){sub T0} = 8.9(4), ({delta} G/{delta} P){sub 0} = 4.3(1) for the Reuss bound, and K{sub S0} = 43.8(8) GPa, G{sub 0} = 35.2(3) GPa, ({delta} K{sub S}/{delta} P){sub T0} = 6.8(2), ({delta} G/P){sub 0} = 3.4(1) for the Voigt-Reuss-Hill average. The ratio of the linear compressibility along the c and a axes decreased from 4.7 to 1.3 over the examined pressure range. The shear anisotropy (C{sub 66}/C{sub 44}) decreased from 2.6(1) at ambient condition to 1.3(1) with increase of pressure to 12 GPa. Axial compressibilities and a compression curve constructed from our Brillouin data are in good agreement with previous X-ray diffraction data. The increased interlayer interactions and hydrogen repulsion that occurs as brucite is compressed produce a continuous variation of elastic properties rather than any abrupt discontinuities.« less
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  • The longitudinal (LA) and transverse (TA) Brillouin spectra along [001] phonon direction have been measured as a function of temperature (50--475 K) in single-crystal PbMg{sub 1/3}Nb{sub 2/3}O{sub 3} with scattering angles {theta}{sub {ital s}}=180{degree} and 32.5{plus_minus}0.2{degree}. The Brillouin frequency shift with decreasing temperature shows a broad softening anomaly for both LA and TA phonon modes. For {theta}{sub {ital s}}=180{degree}, a gradual growth in damping with maximum near 270 K is observed and is attributed to order parameter fluctuations. An additional Landau--Khalatnikov maximum is also observed at {ital T}{sub {ital c}}{similar_to}212 K. This anomaly implies a rapid growth of ferroelectric orderingmore » near {ital T}{sub {ital c}} and is consistent with the earlier linear birefringence results reported by Westphal {ital et} {ital al}. The elastic stiffness and compliance constants, {ital C}{sup {ital E}}{sub 11}, {ital C}{sup {ital E}}{sub 44}, and {ital s}{sup {ital E}}{sub 44} are also determined between 200 and 370 K. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.« less