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The axial vector R is selected as the order parameter of the antiferroelectric phase transition of Lead Zirconate. This order parameter can adequately reflect the symmetry change of the paraelectric-antiferroelectric (PE-AFE) phase transition of PbZrO3 by using Curie principle. The axial vector R of the single-crystal PbZrO3 is calculated. R = 1.09× 10- 9k(C/m). [ABSTRACT FROM AUTHOR]

The relationship between the slowness curved surface and the softening of the acoustic mode is discussed. The acoustic mode softening of hexagonal system corresponds to the maximum slowness. The eigenvector of soft mode corresponds to the polarization of acoustic mode. By solving the Christoffel equation, the maximum slowness and the polarization of the acoustic mode can be obtained. The symmetry change of proper ferroelastic phase transition can be determined by analyzing the solutions of the Christoffel equation and by using Curie principle. [ABSTRACT FROM AUTHOR]

The Hg2CuTi-type structure is found to be preferable energy wise than the Cu2MnAl-type structure for full-Heusler Cr2MnAl and exhibits half-metallic ferromagnetism based on first principles. The calculations for the mixed compounds with disorder between B and D sublattices reveal that the case of exchanging one atom maintains the half-metallicity while the case of exchanging two atoms loses it. The electronic structures of the atoms at sites A or C are affected mainly by the nearest-neighboring coordination while that of the atoms at site B are determined by the next-nearest-neighboring coordination. [ABSTRACT FROM AUTHOR]