Methods for pseudosymmetry evaluation: a comparison between the atomic displacements and electron density approaches

Abstract

Abstract Structural pseudosymmetry is a fundamental property to be considered when trying to predict structural phase transitions at high temperatures. In the present work, two methods for detecting and characterizing pseudosymmetry, the here-called atomic displacements and electron density methods are briefly introduced, analyzed and compared. Conceptually both approaches are similar: the pseudosymmetry check is carried out with respect to a supergroup of the crystal space group. However, due to the different way of estimating the deviations between the initial and the possible high-symmetry structure, the two approaches study distinct and, to a certain extent, complementary aspects of the pseudosymmetry problem. This conclusion is also confirmed by the lack of functional relationship between the corresponding quantitative parameters used to estimate the structural pseudosymmetry. Several examples illustrate the main features of the two methods. The temperature dependences of the two parameters and their empirical relations with the transition temperature in ferroelectric transitions are discussed. Algorithmic procedures based on the two approaches have been implemented in two computer programs. They form part of the Bilbao Crystallographic Server as free web tools.