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

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 An_52.5 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 (e_α, e_β and e_γ) 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.