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Calcite (CaCO 3 , trigonal crystal system, space group    $$R\overline{3}c$$  R 3 ¯ c ) is a ubiquitous carbonate phase commonly found on the Earth’s crust that finds many useful applications in both scientific (mineralogy, petrology, geology) and technological fields (optics, sensors, materials technology) because of its peculiar anisotropic physical properties. Among them, photoelasticity, i.e., the variation of the optical properties of the mineral (including birefringence) with the applied stress, could find usefulness in determining the stress state of a rock sample containing calcite by employing simple optical measurements. However, the photoelastic tensor is not easily available from experiments, and affected by high uncertainties. Here we present a theoretical Density Functional Theory approach to obtain both elastic and photoelastic properties of calcite, considering realistic experimental conditions (298 K, 1 atm). The results were compared with those available in literature, further extending the knowledge of the photoelasticity of calcite, and clarifying an experimental discrepancy in the sign of the  p  41  photoelastic tensor component measured in past investigations. The methods here described and applied to a well-known crystalline material can be used to obtain the photoelastic properties of other minerals and/or materials at desired pressure and temperature conditions.

Study of the variation of the optical properties of calcite with applied stress, useful for specific rock and material mechanics