The incommensurately modulated structures of low-temperature labradorite feldspars: a single-crystal X-ray and neutron diffraction study.

Labradorite feldspars of the plagioclase solid solution series have been known for their complicated subsolidus phase relations and enigmatic incommensurately modulated structures. Characterized by the irrationally indexed e-reflections in the diffraction pattern, e-labradorite shows the largest variation in the incommensurate ordering states among the e-plagioclase structures. The strongly ordered low-temperature e-labradorite is one of the last missing pieces of the e-plagioclase puzzle. Nine plutonic and metamorphic labradorite feldspar samples from Canada, Ukraine, Minnesota (USA), Tanzania and Greenland with compositions ranging from An52.5 to An68 were studied with single-crystal X-ray diffraction. Two crystals from Labrador, Canada, and Duluth, MN, USA, with wide enough twin lamellae were analyzed with single-crystal neutron diffraction. The incommensurately modulated structures of e-plagioclase are refined for the first time with neutron diffraction data, which confirmed that the T-O distance modulation in the low-temperature e-plagioclase results from the Al-Si ordering in the framework. Detailed configurations of the M site are also observed in the structures refined from neutron diffraction data, which were not possible to see with X-ray diffraction data. The relation between the q-vectors and the mole% An composition is revealed for the entire compositional range of e-plagioclase, from An25 to An75. The previously proposed two-trend relation depending on the cooling rate and phase transition path is confirmed. A new classification of e-plagioclase (eα, eβ and eγ) is proposed based on the q-vector of the structure, which makes it an independent character from the presence/absence of density modulation. New parameters are proposed to quantify the ordering states of these complicated aperiodic structures of e-plagioclases, such as the difference between 〈T1o-O〉 and 〈T1m-O〉 at phase t = 0.2 or the normalized intensity of the (071\bar 1) reflection.

[1]  J. Pouwelse,et al.  ConTrib: Universal and Decentralized Accounting in Shared-Resource Systems , 2020, DICG@Middleware.

[2]  D. Morgan,et al.  The incommensurately modulated structures of volcanic plagioclase: displacement, ordering and phase transition. , 2019, Acta crystallographica Section B, Structural science, crystal engineering and materials.

[3]  Huifang Xu,et al.  Revisiting the I{\overline {\bf 1}} structures of high-temperature Ca-rich plagioclase feldspar - a single-crystal neutron and X-ray diffraction study. , 2018, Acta crystallographica Section B, Structural science, crystal engineering and materials.

[4]  Huifang Xu,et al.  Investigations of the phase relations among e1, e2 and C{\bar {\bf 1}} structures of Na-rich plagioclase feldspars: a single-crystal X-ray diffraction study. , 2017, Acta crystallographica Section B, Structural science, crystal engineering and materials.

[5]  Huifang Xu,et al.  Study on structure variations of incommensurately modulated labradorite feldspars with different cooling histories , 2017 .

[6]  Huifang Xu,et al.  Solved: The enigma of labradorite feldspar with incommensurately modulated structure , 2017 .

[7]  Huifang Xu,et al.  Incommensurate density modulation in a Na-rich plagioclase feldspar: Z-contrast imaging and single-crystal X-ray diffraction study. , 2016, Acta crystallographica Section B, Structural science, crystal engineering and materials.

[8]  Huifang Xu.  Direct observation of Ca-Na ordering and structure polarity in Ca-rich intermediate plagioclase feldspar with incommensurate modulated structure , 2015 .

[9]  P. F. Peterson,et al.  Mantid - Data Analysis and Visualization Package for Neutron Scattering and $μ SR$ Experiments , 2014, 1407.5860.

[10]  P. F. Peterson,et al.  Integration of neutron time-of-flight single-crystal Bragg peaks in reciprocal space , 2014 .

[11]  V. Petříček,et al.  Crystallographic Computing System JANA2006: General features , 2014 .

[12]  S. Kek,et al.  The modulated structure of labradorite , 2014 .

[13]  Fujio Izumi,et al.  VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data , 2011 .

[14]  Matthew J. Frost,et al.  CrystalPlan: an experiment-planning tool for crystallography , 2011 .

[15]  V. Petříček,et al.  A modulated crystal structure in Rb2ZnX4 (X = Cl, Br)—a neutron time-of-flight single-crystal study , 2008 .

[16]  M. Holness,et al.  A Textural Record of Solidification and Cooling in the Skaergaard Intrusion, East Greenland. , 2007 .

[17]  I. Pashkevich,et al.  The 1.80-1.74-Ga gabbro-anorthosite-rapakivi Korosten Pluton in the Ukrainian Shield: a 3-D geophysical reconstruction of deep structure , 2004 .

[18]  Mohsen Harakeh,et al.  Proceedings of a NATO Advanced Study Institute , 1997 .

[19]  J. Ganguly,et al.  Cation ordering of orthopyroxenes from the Skaergaard Intrusion: implications for the subsolidus cooling rates and permeabilities , 1996 .

[20]  Their Reactions,et al.  Feldspars and their reactions , 1994 .

[21]  J. D. Miller,et al.  Anorthositic Rocks of the Duluth Complex: Examples of Rocks Formed from Plagioclase Crystal Mush , 1990 .

[22]  R. Angel,et al.  Structural variation associated with compositional variation and order-disorder behavior in anorthite-rich feldspars , 1990 .

[23]  M. Carpenter.  Experimental delineation of the “e” ⇌ I $$\bar 1$$ and “e” ⇌ C $$\bar 1$$ transformations in intermediate plagioclase feldspars , 1986 .

[24]  A. Navrotsky,et al.  Enthalpies of ordering in the plagioclase feldspar solid solution , 1985 .

[25]  T. Grove,et al.  Coupled CaAl-NaSi diffusion in plagioclase feldspar: Experiments and applications to cooling rate speedometry , 1984 .

[26]  A. Yamamoto,et al.  The modulated structure of intermediate plagioclase feldspar CaxNa1−xAl1+xSi3−xO8 , 1984 .

[27]  M. Carpenter,et al.  Experimental delineation of the Cl Il transformation in intermediate plagioclase feldspars , 1984 .

[28]  C. Lukehart,et al.  Single-crystal, time-of-flight, neutron-diffraction structure of hydrogen cis-diacetyltetracarbonylrhenate, [cis-(OC)4Re(CH3CO)2]H: a metallaacetylacetone molecule , 1984 .

[29]  W. Brown.  Feldspars and Feldspathoids , 1984 .

[30]  T. Grove.  Use of exsolution lamellae in lunar clinopyroxenes as cooling rate speedometers; an experimental calibration , 1982 .

[31]  H. Jagodzinski,et al.  Modulated structure of a plagioclase An52: Theory and structure determination , 1981 .

[32]  K. Toman,et al.  Modulated structure of an intermediate plagioclase. II. Numerical results and discussion , 1976 .

[33]  K. Toman,et al.  Modulated structure of an intermediate plagioclase. I. Model and computation , 1976 .

[34]  J. Zussman,et al.  The feldspars;: Proceedings of a NATO Advanced Study Institute, Manchester, 11-21 July 1972 , 1974 .

[35]  K. Toman,et al.  Patterson function of plagioclase satellites , 1973 .

[36]  K. Toman,et al.  The intensities and Fourier transforms of difference reflections , 1973 .

[37]  A. Frueh,et al.  On the centrosymmetry of intermediate plagioclases , 1973 .

[38]  K. Toman,et al.  Intensity averages of plagioclase satellites: distribution in reciprocal space , 1972 .

[39]  A. J. Frueh,et al.  On the origin of plagioclase satellite reflections , 1971 .