Thermal expansion and atomic displacement parameters of cubic KMgF₃perovskite determined by high-resolution neutron powder diffraction

Abstract

The structure of KMgF 3 has been determined by high-resolution neutron powder diffraction at 4.2 K, room temperature and at 10 K intervals from 373 K to 1223 K. The material remains cubic at all temperatures. The average volumetric coefficient of thermal expansion in the range 373–1223 K was found to be 7.11 (3) × 10 −5 K −1 . For temperatures between 4.2 and 1223 K, a second-order Grüneisen approximation to the zero-pressure equation of state, with the internal energy calculated via a Debye model, was found to fit well, with the following parameters: θ D = 536 (9) K, V o = 62.876 (6) Å 3 , K_{o}^{\,\prime} = 6.5 (1) and ( V o K o /γ′) = 3.40 (2) × 10 −18 J, where θ D is the Debye temperature, V o is the volume at T = 0, K_{o}^{\,\prime} is the first derivative with respect to pressure of the incompressibility ( K o ) and γ′ is a Grüneisen parameter. The atomic displacement parameters were found to increase smoothly with T and could be fitted using Debye models with θ D in the range 305–581 K. At 1223 K, the displacement of the F ions was found to be much less anisotropic than that in NaMgF 3 at this temperature.