Atomic displacements at and order of all phase transitions in multiferroic YMnO3 and BaTiO3

Coordinate analysis of the multiple phase transitions in hexagonal YMnO(3) leads to the prediction of a previously unknown aristotype phase, with the resulting phase-transition sequence: P6(3)'cm'(e.g.) <--> P6(3)cm <--> P6(3)/mcm <--> P6(3)/mmc <--> P6/mmm. Below the Néel temperature T(N) approximately = 75 K, the structure is antiferromagnetic with the magnetic symmetry not yet determined. Above T(N) the P6(3)cm phase is ferroelectric with Curie temperature T(C) approximately = 1105 K. The nonpolar paramagnetic phase stable between T(C) and approximately 1360 K transforms to a second nonpolar paramagnetic phase stable to approximately 1600 K, with unit-cell volume one-third that below 1360 K. The predicted aristotype phase at the highest temperature is nonpolar and paramagnetic, with unit-cell volume reduced by a further factor of 2. Coordinate analysis of the three well known phase transitions undergone by tetragonal BaTiO(3), with space-group sequence R3m <--> Amm2 <--> P4mm <--> Pm3m, provides a basis for deriving the aristotype phase in YMnO(3). Landau theory allows the I <--> II, III <--> IV and IV <--> V phase transitions in YMnO(3), and also the I <--> II phase transition in BaTiO(3), to be continuous; all four, however, unambiguously exhibit first-order characteristics. The origin of phase transitions, permitted by theory to be second order, that are first order instead have not yet been thoroughly investigated; several possibilities are briefly considered.