2M1 phlogopite–muscovite series minerals at increasing pressure to 9 GPa. I Atomic volumes and compressibilities

Muscovite (Ms) and phlogopite (Phl) series mineral is studied in the 2M₁ polytype and modeled by the substitution of three Mg²⁺ cations in the three octahedral sites of Phl [KMg₃(Si₃Al)O₁₀(OH)₂] by two Al³⁺ and one vacancy, increasing the substitution up to reach the Ms [KAl₂□(Si₃Al)O₁₀(OH)₂]. The series was computationally examined at DFT using Quantum ESPRESSO, as a function of pressure from − 3 to 9 GPa. Crystal structure is calculated, and cell parameters, and geometry of atomic groups agree with experimental values. OH in the Mg²⁺ octahedrons are approximately perpendicular to the (001) plane, meanwhile when they are in Al³⁺, octahedral groups are approximately parallel to this plane. From Quantum Theory of Atoms in Molecules, the atomic basins are calculated as a function of the pressure, K⁺ and basal O show the largest volumes. The bulk excess volume (Vxs) and the excess atomic volumes are analyzed as a function of the composition and the pressure. K⁺, basal and apical O Vxs show a behavior similar to the bulk Vxs as a function of the composition, keeping qualitatively this behavior as a function of pressure; substituent atoms do not show a Vxs behavior similar to the bulk and their effect consequently is mostly translated to atoms in the interlayer space. Atomic compressibilities are also calculated. Atomic compressibilities are separated in the different sheets of the crystal cell. Atomic moduli of K and basal O are the lowest and the ones behaving as the bulk modulus of the series. The atomic bulk modulus of the H’s is different depending of their position with respect to the (001) plane.