• journal_title：The Canadian Mineralogist
• Contributor：J. Desmond C. McConnell
• Publisher：Mineralogical Association of Canada
• Date：2008-
• Format：text/html
• Language：en
• Identifier：10.3749/canmin.46.6.1389
• journal_abbrev：Can Mineral
• issn：0008-4476
• volume：46
• issue：6
• firstpage：1389
• section：Articles

The true nature of the incommensurate structures of the plagioclase feldspars has remained an enigma for a very long period of time. The present analysis of these structures is novel in that it uses a group-theoretical approach in association with relevant thermodynamic criteria. As the plagioclase feldspars are triclinic, modulation behavior, of necessity, involves only the translation group of the crystal, here shown to be isomorphic to the Dihedral group D_n, and, in the case of order–disorder, to the related group D_2n. Both groups are non-Abelian, and the relevant two-dimensional representation matrices may be used to define translational invariance with respect to the Gibbs free energy in terms of the local variation of order–disorder parameters in the component structures in the modulation. In the incommensurate structure e₂ (in plagioclases with anorthite content between 25 and 50%), the main criterion for the appearance of the modulated structure is the high energy associated with Al non-avoidance, circa 40 kJ/mol, and the modulation achieves this avoidance locally in an otherwise disordered structure. In the e₁ incommensurate phase (in plagioclases with more than 50% anorthite), the body-centered anorthite structure, which exists above 800°C, orders Na and Ca ions below this temperature to create the second component structure in the modulation. A phase diagram for the plagioclase feldspars is presented, and this is used to predict the development of spinodal Bøggild intergrowths.