The incommensurately modulated structure of an andesine (An<sub>38</sub>)

Steurer, Walter; Jagodziñski, H.

doi:10.1107/s0108768188001806

Cited by 20 publications

(7 citation statements)

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“…The study on Na-rich plagioclase is challenging because the satellite reflections are much weaker and more diffuse compared with the Ca-rich plagioclase, which makes the characterization of the modulated structure difficult. This might be the reason why there was only one reported structure refinement on Na-rich e-plagioclase with the e2 structure (Steurer & Jagodzinski, 1988). However, with modern X-ray diffractometers with stronger beam intensity and more sensitive detectors, we are able to collect high-quality data with enough satellite intensities for structure refinement, even for the samples with very weak modulation.…”

Section: Introductionmentioning

confidence: 99%

Investigations of the phase relations amonge1,e2 andC{\bar {\bf 1}} structures of Na-rich plagioclase feldspars: a single-crystal X-ray diffraction study

Jin

2017

Acta Crystallogr B Struct Sci Cryst Eng Mater

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The subsolidus phase relations of plagioclase feldspar solid solution have been puzzling mineralogists and petrologists for decades, mainly due to the complicated structures of intermediate plagioclase at low temperature. The crystal structures of 12 Na-rich plagioclase samples are investigated by single-crystal X-ray diffraction analyses. The samples studied cover a compositional range from An to An (An is anorthite, CaAlSiO), as well as a wide variety of origins, from extremely slow-cooled gabbroic rocks to pegmatite and metamorphic rocks. The structures fall into three different types: C{\bar 1}, e2 and e1, with an obviously increasing trend in the ordering states of the structures. The phase transitions from C{\bar 1} to e2 and e2 to e1 are both continuous in nature, as no abrupt structure change is required for the transformation. However, the structural difference between C\bar 1 and e1 is large enough to create a miscibility gap causing the Bøggild intergrowth. As the plagioclase structure becomes more and more ordered, Al-Si reorganization in the framework would occur before the ordering of Ca and Na in M sites. Dramatic variations of Na occupancy would only appear in e1 structure with density modulation. This result confirms that Al-Si ordering is the major driving force of the formation of e-plagioclase structure. The composition of the lower end of the Bøggild intergrowth is precisely constrained to An-An, based on the structural differences between two samples from the same pegmatite crystal. The modulation periods and directions of e-plagioclase are dependent on the conditions at which e-ordering starts to happen, other than the composition of the plagioclase. However, the three components (δh, δk and δl) of the q vector show strong linear correlations among one another, indicating some crystallographic constraint on the modulation direction which might be independent from the composition. The detailed subsolidus phase relations among e1, e2 and C{\bar 1} are illustrated with a local phase diagram, and schematic free energy curves at different temperatures are provided.

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Section: Introductionmentioning

confidence: 99%

Investigations of the phase relations amonge1,e2 andC{\bar {\bf 1}} structures of Na-rich plagioclase feldspars: a single-crystal X-ray diffraction study

Jin

2017

Acta Crystallogr B Struct Sci Cryst Eng Mater

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“…The higher-dimensional PF has been used successfully in the analysis of incommensurately modulated structures (Steurer, 1987;Steurer & Jagodzinski, 1988) and can be applied to the analysis of quasicrystalline structures in an analogous manner (Cahn, Gratias & Mozer, 1988). Geometrically, the Patterson function is defined as the map of all possible weighted vectors between the atoms of a crystal structure.…”

Section: Higher-dimensional Patterson Functions (Pf's) the Principlesmentioning

confidence: 99%

Five-dimensional Patterson analysis of the decagonal phase of the system Al-Mn

Steurer¹

1989

Acta Crystallogr Sect B

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534COMMENSURATELY MODULATED STRUCTURE OF TaTe4 refinement for low-symmetry SSG pe4~ with harmonic displacive modulations and with 44 positional parameters was performed. It yielded an R factor of 0.054. Results of all these refinements are collected in Table 4. For the last two refinements corresponding atomic positional coordinates in the superstructure are not exactly related by the inversion centre (the discrepancy exceeds a few standard deviations). However, taking into account the number of structural parameters and the minor differences in R values obtained by different models, it can be concluded that the SSG description of the TaTe4 structure at room temperature with DPa/ncc -~r~ as well as the corresponding centrosymmetric SG P4/ncc, represent very good approximations. ConclusionsIt is shown that the room-temperature TaTe4 superstructure (2a x 2a x 3c) can be described as a commensurately modulated basic structure (2a x 2a x c) with q = (00~). The SSG pe4/~ describes not only the structural symmetry and relations between coordinates of groups of atoms but also predicts extinction rules which are, together with additional conditions on reflections, in agreement with experiment. The origin of these additional limitations is also explained. Analysis of different 'real' sections through the supercrystal gives a more general insight into the problem of centro-or noncentrosymmetricity of the room-temperature TaTe4 modulated structure. The refinements show that the choice of SG P4/ncc (Bronsema et al., 1987) is justified on basis of a reduced number of parameters needed for the structure description. It is also shown that this reduction does not, at least significantly, increase the discrepancy factor R. VAN (1985). PhD Thesis, Univ. of Groningen, The Netherlands. SMAALEN, S. VAN (1987) A37, 625--636. YAMnMOTO, A. (1982). Acta Cryst. B38, 1446-1451, 1451-1456. YAMnMOTO, A. & NAKAZAWA, H. (1982. Acta Cryst. A38, 79-86. Acta Cryst. (1989

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“…. , where the symbols An and An* represent plagioclase lamellar domains with an anorthite-like structure in anti-phase relationships (Cinnamon & Bailey, 1971;McConnell & Fleet, 1963;Wenk & Nakajima, 1980;Horst et al, 1981;Steurer & Jagodzinski, 1988). Another stacking model using anorthite (I " 1 1) and albite (C " 1 1Þ like structures was also suggested: An .…”

Section: Introductionmentioning

confidence: 99%

Communication between cation environments in aluminosilicate frameworks: incommensurately modulated crystal structure of ane-plagioclase

Fredrickson

2016

Acta Crystallogr Sect B

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Despite being one of the most common minerals in the earth's crust the crystal structure of intermediate e-plagioclase remains only partially understood, due in a large part to its complex diffraction patterns including satellite reflections. In this article we present a detailed analysis of the structure of e-plagioclase (An) using single-crystal X-ray diffraction measured at ambient and low temperature (T = 100 K), in which the full modulated structure is successfully refined. As in earlier studies, the diffraction pattern exhibits strong main a-reflections and weak e-satellite reflections. The average structure could be solved in terms of an albite-like basic cell with the triclinic centrosymmetric and non-centrosymmetric space groups P \bar 1 and P1 (treated in its C \bar 1 and C1 setting, respectively, to follow conventions in the literature), while the incommensurately modulated structure was modeled in (3 + 1)D superspace, employing both the centro- and non-centrosymmetric superspace groups X \bar 1(αβγ)0 and X1(αβγ)0, where X refers to a special (3 + 1)D lattice centering with centering vectors (0 0 ½ ½), (½ ½ 0 ½), and (½ ½ ½ 0). Individual positional and occupational modulations for Ca/Na were refined with deeper insights being revealed in the non-centrosymmetric structure model. Through the structural details emerging from this model, the origin of the modulation can be traced to the communication between Ca/Na site positions through their bridging aluminosilicate (Si/Al)O tetrahedra.

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The incommensurately modulated structure of an andesine (An₃₈)

Cited by 20 publications

References 9 publications

Investigations of the phase relations amonge1,e2 andC{\bar {\bf 1}} structures of Na-rich plagioclase feldspars: a single-crystal X-ray diffraction study

Investigations of the phase relations amonge1,e2 andC{\bar {\bf 1}} structures of Na-rich plagioclase feldspars: a single-crystal X-ray diffraction study

Five-dimensional Patterson analysis of the decagonal phase of the system Al-Mn

Communication between cation environments in aluminosilicate frameworks: incommensurately modulated crystal structure of ane-plagioclase

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The incommensurately modulated structure of an andesine (An38)

Cited by 20 publications

References 9 publications

Investigations of the phase relations amonge1,e2 andC{\bar {\bf 1}} structures of Na-rich plagioclase feldspars: a single-crystal X-ray diffraction study

Investigations of the phase relations amonge1,e2 andC{\bar {\bf 1}} structures of Na-rich plagioclase feldspars: a single-crystal X-ray diffraction study

Five-dimensional Patterson analysis of the decagonal phase of the system Al-Mn

Communication between cation environments in aluminosilicate frameworks: incommensurately modulated crystal structure of ane-plagioclase

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The incommensurately modulated structure of an andesine (An₃₈)