Abstract
The full elastic tensors of two K-rich monoclinic alkali feldspars, Or83Ab15 sanidine and Or93Ab7 orthoclase, have been determined by using the Impulse Stimulated Light Scattering technique to measure surface acoustic wave velocities. The new data confirm that alkali feldspars exhibit extreme elastic anisotropy, so the bounds of their isotropic average properties span a wide range. The measured adiabatic moduli are, for Or83Ab15 and Or93Ab7, respectively, KReuss = 54.7(7), 54.5(5) GPa; KVoigt = 62.9(1.1), 64.4(0.6) GPa; GReuss = 24.1(1), 24.5(1) GPa; and GVoigt = 36.1(5), 36.1(7) GPa. The small differences in moduli between the samples suggests that variations in composition and in state of Al, Si order only have minor effects on the average elastic properties of K-rich feldspars. The new measurements confirm that the earliest determinations of elastic wave velocities of alkali feldspars, widely used to calculate wave velocities in rocks, resulted in velocities systematically and significantly too slow by 10% or more.
Acknowledgments
This work was supported by grants from the National Science Foundation to J.M.B. (EAR 0711591) and N.L.R. and R.J.A. (EAR-1118691). The samples were kindly provided from the Mineralogical Museum of the University of Hamburg by curator Jochen Schlüter.
References cited
Abramson, E.H., Brown, J.M., and Slutsky, L.J. (1999) Applications of impulsive stimulated scattering in the earth and planetary sciences. Annual Review of Physical Chemistry, 50, 279–313.10.1146/annurev.physchem.50.1.279Search in Google Scholar
Angel, R.J. (1994) Feldspars at high pressure. In I. Parsons, Ed., Feldspars and Their Reactions, p. 271–312. Kluwer, Dordrecht.10.1007/978-94-011-1106-5_7Search in Google Scholar
Angel, R.J. (2004) Equations of state of plagioclase feldspars. Contributions to Mineralogy and Petrology, 146, 506–512.10.1007/s00410-003-0515-5Search in Google Scholar
Angel, R.J., Sochalski-Kolbus, L.M., and Tribaudino, M. (2012) Tilts and tetrahedra: The origin of the anisotropy of feldspars. American Mineralogist, 97, 765–778.10.2138/am.2012.4011Search in Google Scholar
Angel, R.J., Ross, N.L., Zhao, J., Sochalski-Kolbus, L., Krüger, H., and Schmidt, B.U. (2013) Structural controls on the anisotropy of tetrahedral frameworks: the example of monoclinic feldspars. European Journal of Mineralogy, 25, 597–614.10.1127/0935-1221/2013/0025-2323Search in Google Scholar
Avellaneda, M., and Milton, G.W. (1989) Optimal bounds on the effective bulk modulus of polycrystals. SIAM Journal on Applied Mathematics, 49, 824–837.10.1137/0149048Search in Google Scholar
Avellaneda, M., Cherkaev, A.V., Gibiansky, L.V., Milton, G.W., and Rudelson, M. (1996) A complete characterization of the possible bulk and shear moduli of planar polycrystals. Journal of the Mechanics and Physics of Solids, 44, 1179–1218.10.1016/0022-5096(96)00018-XSearch in Google Scholar
Brown, J.M. (2015) Determination of Hashin–Shtrikman bounds on the isotropic effective elastic moduli of polycrystals of any symmetry. Computers & Geosciences, 80, 95–99.10.1016/j.cageo.2015.03.009Search in Google Scholar
Brown, J.M., Abramson, E.H., and Angel, R.J. (2006) Triclinic elastic constants for low albite. Physics and Chemistry of Minerals, 33, 256–265.10.1007/s00269-006-0074-1Search in Google Scholar
Carpenter, M.A., and Salje, E.K.H. (1994) Thermodynamics of nonconvergent cation ordering in minerals: III. Order parameter coupling in potassium feldspar. American Mineralogist, 79, 1084–1098.Search in Google Scholar
Carpenter, M.A., and Salje, E.K.H. (1998) Elastic anomalies in minerals due to structural phase transitions. European Journal of Mineralogy, 10, 693–812.10.1127/ejm/10/4/0693Search in Google Scholar
Christensen, N.I. (1966) Compressional wave velocities in single crystals of alkali feldspar at pressures to 10 kilobars. Journal of Geophysical Research, 71, 3113–3116.10.1029/JZ071i012p03113Search in Google Scholar
Hacker, B.R. (2003) Subduction factory 1. Theoretical mineralogy, densities, seismic wave speeds, and H2O contents. Journal of Geophysical Research, 108, 1–26.10.1029/2001JB001127Search in Google Scholar
Haussühl, S. (1993) Thermoelastic properties of beryl, topaz, diaspore, sanidine and periclase. Zeitschrift für Kristallographie, 204, 67–76.10.1524/zkri.1993.204.Part-1.67Search in Google Scholar
Isaak, D.G., Ohno, I., and Lee, P.C. (2006) The elastic constants of monoclinic single-crystal chrome-diopside to 1,300 K. Physics and Chemistry of Minerals, 32, 691–699.10.1007/s00269-005-0047-9Search in Google Scholar
Kroll, H., and Ribbe, P.H. (1983) Lattice parameters, composition, and Al/Si order in alkali feldspars. In P.H. Ribbe, Ed., Feldspar Mineralogy, 2, p. 57–100. Reviews in Mineralogy, Mineralogical Society of America, Chantilly, Virginia.10.1515/9781501508547-008Search in Google Scholar
McNeil, L.E., and Grimsditch, M. (1993) Elastic moduli of muscovite mica. Journal of Physics: Condensed Matter, 5, 1681–1690.10.1088/0953-8984/5/11/008Search in Google Scholar
Newnham, R.E. (2005) Properties of Materials, 378 p. Oxford University Press, U.K.Search in Google Scholar
Pleger, S. (1996) Diffuse X-ray scattering of homogeneous potassium-rich low- and high-temperature sanidines. Zeitschrift für Kristallographie, 211, 293–298.10.1524/zkri.1996.211.5.293Search in Google Scholar
Ryzhova, T.V., and Aleksandrov, K.S. (1965) The elastic properties of potassiun-sodium feldspars. Izvestiya of the Academy of Sciences, USSR, 89-102, Earth Physics Series, Physics of the Soldid Earth (English translation), 1, 53–56.Search in Google Scholar
Salje, E.K.H. (2015) Tweed, twins, and holes. American Mineralogist, 100, 343–351.10.2138/am-2015-5085Search in Google Scholar
Sanchez-Munoz, L., Nistor, L., Van Tendeloo, G., and Sanz, J. (1998) Modulated structures in KAlSi3O8: a study by high resolution electron microscopy and 29Si MAS-NMR spectroscopy. Journal of Electron Microscopy, 47, 17–28.10.1093/oxfordjournals.jmicro.a023555Search in Google Scholar
Schäffer, A.-K., Jäpel, T., Zaefferer, S., Abart, R., and Rhede, D. (2014) Lattice strain across Na-K interdiffusion fronts in alkali feldspar: an electron back-scatter diffraction study. Physics and Chemistry of Minerals, 41, 795–804.10.1007/s00269-014-0692-ySearch in Google Scholar PubMed PubMed Central
Simmons, G. (1964) Velocity of compressional waves in various minerals at pressures to 10 kilobars. Journal of Geophysical Research, 69, 1117.10.1029/JZ069i006p01117Search in Google Scholar
Speziale, S., Reichmann, H.J., Schilling, F.R., Wenk, H.R., and Monteiro, P.J.M. (2008) Determination of the elastic constants of portlandite by Brillouin spectroscopy. Cement and Concrete Research, 38, 1148–1153.10.1016/j.cemconres.2008.05.006Search in Google Scholar
Tribaudino, M., Bruno, M., Nestola, F., Pasqual, D., and Angel, R.J. (2011) Thermoelastic and thermodynamic properties of plagioclase feldspars from thermal expansion measurements. American Mineralogist, 96, 992–1002.10.2138/am.2011.3722Search in Google Scholar
Williame, C., and Brown, W.L. (1974) A coherent elastic model for the determination of the orientation of exsolution boundaries: Application to the feldspars. Acta Crystallographica, A30, 316–331.10.1107/S0567739474010783Search in Google Scholar
© 2016 by Walter de Gruyter Berlin/Boston
