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American Mineralogist

Journal of Earth and Planetary Materials

Ed. by Baker, Don / Xu, Hongwu / Swainson, Ian

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Volume 102, Issue 1


Solved: The enigma of labradorite feldspar with incommensurately modulated structure

Shiyun Jin
  • NASA Astrobiology Institute, Department of Geoscience, University of Wisconsin–Madison, Madison, Wisconsin 53706, U.S.A
  • Other articles by this author:
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/ Huifang Xu
  • Corresponding author
  • NASA Astrobiology Institute, Department of Geoscience, University of Wisconsin–Madison, Madison, Wisconsin 53706, U.S.A
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  • Other articles by this author:
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Published Online: 2017-01-03 | DOI: https://doi.org/10.2138/am-2017-5807


Intermediate plagioclase feldspars are the most abundant minerals in the Earth’s crust. Their incommensurately modulated structure has puzzled geologists and crystallographers for decades since the phenomenon in a labradorite was reported in 1940. Solving the structure is a necessary step toward mapping the complex subsolidus phase relations of plagioclase solid solution. The structure of a homogeneous labradorite (An51) single crystal from a metamorphic rock is solved and refined from single-crystal X-ray diffraction. The result structure can be simplified as alternating I1-like lamellae domains related by inversion twins. The inversion boundary shows an anorthite-like structure with I1¯ symmetry and is richer in Ca than the neighboring domains with opposite polarity. No albite-like subunits appear in the e-plagioclase structure. The modulated structure displays a unique Al-Si ordering pattern. A density modulation with a variation of 17 mol% in composition is also observed and can be properly described only by applying second-order harmonic waves for the atomic modulation functions. The modulated structure reveals details that cannot be observed from refinement with only main reflections and may be used to assess the ordering state and cooling rate of its host rock. The homogeneity of the crystal indicates the closure of the solvus for Bøggild intergrowth at low temperature. The highly ordered modulation supports the thermodynamic stability of e-plagioclase. Both Al-Si ordering and Ca-Na ordering are the driving force for formation of the incommensurately modulated structure.

Keywords: Intermediate plagioclase; incommensurate; modulated structure; density modulation; single-crystal XRD; e-plagioclase; labradorite; aperiodic crystal; Invited Centennial article

References cited

  • Angel, R.J., Carpenter, M.A., and Finger, L.W. (1990) Structural variation associated with compositional variation and order-disorder behavior in anorthite-rich feldspars. American Mineralogist, 75, 150–162.Google Scholar

  • Angel, R.J., Gatta, G.D., Ballaran, T.B., and Carpenter, M.A. (2008) The mechanism of coupling in the modulated structure of nepheline. Canadian Mineralogist, 46, 1465–1476.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.Google Scholar

  • Bagautdinov, B., Hagiya, K., Noguchi, S., Ohmasa, M., Ikeda, N., Kusaka, K., and Iishi, K. (2002) Low-temperature studies on the two-dimensional modulations in akermanite-type crystals: Ca2MgSi2O7 and Ca2ZnSi2O2. Physics and Chemistry of Minerals, 29, 346–350.Google Scholar

  • Bindi, L., Bonazzi, P., Dusek, M., Petricek, V., and Chapuis, G. (2001) Five-dimensional structure refinement of natural melilite, (Ca1.89Sr0.01 Na0.08K0.02)(Mg0.92Al0.08) (Si1.98Al0.02)O7. Acta Crystallographica, B57, 739–746.Google Scholar

  • Bown, M.G., and Gay, P. (1959) The reciprocal lattice geometry of the plagioclase felspar structures. Zeitschrift für Kristallographie, 111, 1–14.Google Scholar

  • Boysen, H., and Kek, S. (2015) The modulated structure of labradorite. Zeitschrift für Kristallographie, 230, 23–36.Google Scholar

  • Carpenter, M.A. (1994) Subsolidus phase relations of the plagioclase feldspar solid solution. In I. Parsons, Ed., Feldspars and Their Reactions, 421, p. 221–269. Kluwer, Dordrecht.Google Scholar

  • Carpenter, M.A., McConnell, J.D.C., and Navrotsky, A. (1985) Enthalpies of ordering in the plagioclase feldspar solid-solution. Geochimica et Cosmochimica Acta, 49, 947–966.Google Scholar

  • Chao, S.H., and Taylor, W.H. (1940) Isomorphous replacement and superlattice structures in the plagioclase felspars. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 176, 76–87.Google Scholar

  • Cinnamon, C.G., and Bailey, S.W. (1971) Antiphase domain structure of intermediate composition plagioclase feldspars. American Mineralogist, 56, 1180–1198.Google Scholar

  • Dam, B., Janner, A., and Donnay, J.D.H. (1985) Incommensurate morphology of calaverite (AuTe2) crystals. Physical Review Letters, 55, 2301–2304.Google Scholar

  • Donnay, J.D.H. (1935) Alternating axes and symmetry symbols in crystallography. Journal of the Washington Academy of Sciences, 25, 476–488.Google Scholar

  • Ferry, J.M. (1980) A case study of the amount and distribution of heat and fluid during metamorphism. Contributions to Mineralogy and Petrology, 71, 373–385.Google Scholar

  • Fitz Gerald, J.D., Parise, J.B., and Mackinnon, I.D.R. (1986) Average structure of an An48 plagioclase from the Hogarth Ranges. American Mineralogist, 71, 1399–1408.Google Scholar

  • Friese, K., Grzechnik, A., Petricek, V., Schonleber, A., van Smaalen, S., and Morgenroth, W. (2011) Modulated structure of nepheline. Acta Crystallographica, B67, 18–29.Google Scholar

  • Grove, T.L. (1977) A periodic antiphase structure model for the intermediate plagioclases (An33 to An75). American Mineralogist, 62, 932–941.Google Scholar

  • Grove, T.L., Ferry, J.M., and Spear, F.S. (1983) Phase-transitions and decomposition relations in calcic plagioclase. American Mineralogist, 68, 41–59.Google Scholar

  • Horst, W., Tagai, T., Korekawa, M., and Jagodzinski, H. (1981) Modulated structure of a plagioclase An52: Theory and structure determination. Zeitschrift für Kristallographie 157, 233–250.Google Scholar

  • Janner, A., and Janssen, T. (2015) From crystal morphology to molecular and scale crystallography. Physica Scripta, 90, 23.Google Scholar

  • Kirkpatrick, R.J., Carpenter, M.A., Yang, W.-H., and Montez, B. (1987) 29Si magic-angle NMR spectroscopy of low-temperature ordered plagioclase feldspars.Nature, 325, 236–238.Google Scholar

  • Kitamura, M., and Morimoto, N. (1975) The superstructure of intermediate plagioclase. Proceedings of the Japan Academy, 51, 419–424.Google Scholar

  • ———(1977) The superstructure of plagioclase feldspars. Physics and Chemistry of Minerals, 1, 199–212.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. Mineralogical Society of America, Chantilly, Virginia.Google Scholar

  • Kumao, A., Hashimoto, H., Nissen, H.U., and Endoh, H. (1981) Ca and Na positions in labradorite feldspar as derived from high-resolution electron-microscopy and optical diffraction. Acta Crystallographica, A37, 229–238.Google Scholar

  • Li, L., Wölfel, A., Schönleber, A., Mondal, S., Schreurs, A.M.M., Kroon-Batenbuig, L.M.J., and van Smaalen, S. (2011) Modulated anharmonic ADPs are intrinsic to aperiodic crystals: a case study on incommensurate Rb2ZnCl4. Acta Crystallographica, B67, 205–217.Google Scholar

  • McConnell, J.D.C. (1974) Analysis of the time-temperature-transformation behaviour of the plagioclase feldspars. In W.S. MacKenzie and J. Zussman, Eds., The Feldspars, pp. 460–477. Manchester University Press, New York.Google Scholar

  • ———(2008) The origin and characteristics of the incommensurate structures in the plagioclase feldspars. Canadian Mineralogist, 46(6), 1389–1400.Google Scholar

  • McConnell, J.D.C., and Fleet, S.G. (1963) Direct electron-optical resolution of anti-phase domains in a silicate. Nature, 199, 586.Google Scholar

  • Megaw, H.D. (1960a) Order and disorder. I. Theory of stacking faults and diffraction maxima. The Proceedings of the Royal Society of London, 259, 59–78.Google Scholar

  • ———(1960b) Order and disorder. II. Theory of diffraction effects in the intermediate plagioclase feldspars. The Proceedings of the Royal Society of London, 259, 159–183.Google Scholar

  • ———(1960c) Order and disorder. III. The structure of the intermediate plagioclase feldspars. The Proceedings of the Royal Society of London, 259, 184–202.Google Scholar

  • ———(1974) Tilts and tetrahedra in feldspars. In W.S. MacKenzie and J. Zussman, Eds., The Feldspars, pp. 87–113. Manchester University Press, U.K.Google Scholar

  • Momma, K., and Izumi, F. (2011) VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. Journal of Applied Crystallography, 44(6), 1272–1276.Google Scholar

  • Nakajima, Y., Morimoto, N., and Kitamura, M. (1977) The superstructure of plagioclase feldspars. Physics and Chemistry of Minerals, 1, 213–225.Google Scholar

  • Oszlanyi, G., and Suto, A. (2004) Ab initio structure solution by charge flipping. Acta Crystallographica, A60, 134–141.Google Scholar

  • ———(2005) Ab initio structure solution by charge flipping. II. Use of weak reflections. Acta Crystallographica, A61, 147–152.Google Scholar

  • Palatinus, L., and Chapuis, G. (2007) SUPERFLIP—a computer program for the solution of crystal structures by charge flipping in arbitrary dimensions. Journal of Applied Crystallography, 40, 786–790.Google Scholar

  • Petříček, V., Dušek, M., and Palatinus, L. (2014) Crystallographic Computing System JANA2006: General Features. Zeitschrift für Kristallographie, 229, 345–352.Google Scholar

  • Ribbe, P.H. (1983) Aluminum-silicon order in feldspars: Domain textures and dif-fraction. In P.H. Ribbe, Ed., Feldspar Mineralogy, 2nd ed., 2, p. 21–55. Reviews in Mineralogy, Mineralogical Society of American, Chantilly, Virginia.Google Scholar

  • Rusakov, D.A., Abakumov, A.M., Yamaura, K., Belik, A.A., van Tendeloo, G., and Takayama-Muromachi, E. (2011) Structural evolution of the BiFeO3-LaFeO3 system. Chemistry of Materials, 23, 285–292.Google Scholar

  • Slimming, E.H. (1976) An electron diffraction study of some intermediate plagioclases. American Mineralogist, 61, 54–59.Google Scholar

  • Smith, J.V. and Brown, W.L. (1988) Feldspar Minerals. Springer-Verlag.Google Scholar

  • Smith, J.V. and Ribbe, P.H. (1969) Atomic movements in plagioclase feldspars: Kinetic interpretation. Contributions to Mineralogy and Petrology, 21, 157–202.Google Scholar

  • Smith, J.V., and Wenk, H.-R. (1983) Reinterpretation of a Verzasca plagioclase—a correction. American Mineralogist, 68, 742–743.Google Scholar

  • Steurer, W., and Jagodzinski, H. (1988) The incommensurately modulated structure of an andesine (An38). Acta Crystallographica, B44, 344–351.Google Scholar

  • Stokes, H.T., Campbell, B.J., and van Smaalen, S. (2011) Generation of (3 + d)-dimensional superspace groups for describing the symmetry of modulated crystalline structures. Acta Crystallographica, A67, 45–55.Google Scholar

  • Toman, K., and Frueh, A. (1973) On the centrosymmetry of intermediate plagioclase. Zeitschrift für Kristallographie, 138, 337–342.Google Scholar

  • (1976a) Modulated structure of an intermediate plagioclase. I. Model and computation. Acta Crystallographica, B32, 521–525.Google Scholar

  • ———(1976b) Modulated structure of an intermediate plagioclase. II. Numerical results and discussion. Acta Crystallographica, B32, 526–538.Google Scholar

  • van Smaalen, S. (2007) Incommensurate Crystallography. Oxford University Press.Google Scholar

  • Wagner, T., and Schoenleber, A. (2009) A non-mathematical introduction to the superspace description of modulated structures. Acta Crystallographica, B65, 249–268.Google Scholar

  • Wei, F.X., Baikie, T., An, T., Kloc, C., Wei, J., and White, T. (2012) Crystal chemistry of melilite [CaLa]2[Ga]2[Ga2O7]2: A five dimensional solid electrolyte. Inorganic Chemistry, 51, 5941–5949.Google Scholar

  • Wenk, H.-R. (1979) Albite-anorthite assemblage in low-grade amphibolite facies rocks. American Mineralogist, 64, 1294–1299.Google Scholar

  • Wenk, H.-R., and Nakajima, Y. (1980) Structure, formation, and decomposition of APB’s in calcic plagioclase. Physics and Chemistry of Minerals, 6, 169–186.Google Scholar

  • Wenk, H.-R., Joswig, W., Tagai, T., Korekawa, M., and Smith, B.K. (1980) Average structure of an 62-66 labradorite. American Mineralogist, 65, 81–95.Google Scholar

  • Xu, H. (2015) Direct observation of Ca-Na ordering and structure polarity in Ca-rich intermediate plagioclase feldspar with incommensurate modulated structure. American Mineralogist, 100, 510–515.Google Scholar

  • Xu, H., Buseck, P.R., and Carpenter, M.A. (1997) Twinning in synthetic anorthite: A transmission electron microscopy investigation. American Mineralogist, 82, 125–130.Google Scholar

  • Yamamoto, A., Nakazawa, H., Kitamura, M., and Morimoto, N. (1984) The modulated structure of intermediate plagioclase feldspar CaxNa1−xAl1+xSi3−xO8. Acta Crystallographica, B40, 228–237.Google Scholar

About the article

Received: 2016-04-12

Accepted: 2016-06-21

Published Online: 2017-01-03

Published in Print: 2017-01-01

Citation Information: American Mineralogist, Volume 102, Issue 1, Pages 21–32, ISSN (Online) 1945-3027, ISSN (Print) 0003-004X, DOI: https://doi.org/10.2138/am-2017-5807.

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© 2017 by Walter de Gruyter Berlin/Boston.

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