Parametric Rietveld refinement for the evaluation of powder diffraction patterns collected as a function of pressure

Under the assumption that the structural parameters of a crystalline phase change `smoothly' with increasing pressure, the evolution of the parameters can be parameterized as a function of pressure using continuous monotonic functions. Four different approaches to determine the structural evolution of As₂O₅ with increasing pressure from a set of powder diffraction patterns collected over the pressure range from 2.5 to 19.5 GPa have been investigated. Approach (A) was the common sequential refinement of atomic coordinates with restraints on the geometry and was compared with three parameterization approaches. Approach (B) used direct parameterization by low-order polynomials of each crystallographically distinct atomic coordinate, (C) described the atoms of the asymmetric unit as a rigid body and allowed the internal degrees of freedom of the rigid body to vary with the change in pressure using rigid unit modes, and (D) described the crystal structure as a distortion of the higher-symmetry structure of As₂O₅ (which is here also a high-temperature phase) by using symmetry-adapted distortion modes. Approach (D) offers the possibility to directly introduce an order parameter into Rietveld refinement through an empirical power law derived from Landau theory and thus to obtain the value of the critical exponent. In contrast, the rigid-body approach did not fit the data as well. All parameterizations greatly reduce the number of required parameters.