Elasticity of phase‐X at high pressure

Using a plane‐wave pseudopotential method, we calculate the equation of state and elasticity of phase‐X [(K,Na) 2 Mg 2 Si 2 O 7 ] up to 30 GPa, which encompasses its experimentally observed stability field. We find that the pressure‐volume results for anhydrous phase‐X are well represented by a third order Birch‐Murnaghan formulation, with K 0 = 132 GPa, K ′ 0 = 4.4 and V 0 = 284.6 Å 3 for the potassium (K) end member and K 0 = 128 GPa, K ′ 0 = 4.0 and V 0 = 265.9 Å 3 for the sodium (Na) end member. The full elastic constant tensor reveals significantly larger stiffness along the [001] direction than in the (100) plane. We attribute such stiffness to the 180 0 angle of Si‐O‐Si units and their orientation parallel to the [001] direction. Assuming ideal behavior between Na and K phase‐X, the shear modulus softens with sodium content as G = [84 − 0.14 × Na ( wt %)] GPa.