Renormalization-group classification of continuous structural phase transitions induced by six-component order parameters

1986 ◽  
Vol 33 (9) ◽  
pp. 6196-6209 ◽  
Author(s):  
Dorian M. Hatch ◽  
Jai Sam Kim ◽  
Harold T. Stokes ◽  
Jeffrey W. Felix
Keyword(s):  
Renormalization Group ◽  
Phase Transitions ◽  
Structural Phase ◽  
Group Classification ◽  
Order Parameters ◽  
Structural Phase Transitions ◽  
Component Order

Neutron-diffraction study of the structural phase transitions in the antifluorite K2PtBr6

1985 ◽  
Vol 63 (7) ◽  
pp. 988-996 ◽  
Author(s):  
Robin L. Armstrong ◽  
Rose M. Morra ◽  
Brian M. Powell
Keyword(s):  
Phase Transitions ◽  
Nuclear Quadrupole Resonance ◽  
Goodness Of Fit ◽  
Structural Phase ◽  
Spectral Characteristics ◽  
Neutron Diffraction Study ◽  
Structural Phase Transitions ◽  
Quadrupole Resonance ◽  
Nuclear Quadrupole

Neutron-powder-diffraction profiles are reported for the antifluorite K2PtBr6 at temperatures of 296, 160, 141, and 120 K. Bromine nuclear-quadrupole-resonance measurements have shown that each of these temperatures corresponds to a different crystal structure and have provided information on the most probable structures. A variety of structural models with symmetries obtained from a group theoretical classification of structural phase transitions are fitted to the diffraction data. A comparison of goodness-of-fit parameters for the models considered at each temperature allows the space group of each phase to be identified. The results provide (i) a definitive test of the validity of a classification scheme proposed for nuclear-quadrupole-resonance spectral characteristics, and (ii) support for the proposition that the allowable, continuous distortions of a crystal are given by the nondisruptive criterion rather than the more restrictive group–subgroup criterion.

Probabilistic model of structural phase transition in perovskites

2021 ◽  
pp. 2150211
Author(s):  
S. H. Jabarov ◽  
R. T. Aliyev ◽  
N. A. Ismayilova
Keyword(s):  
Mathematical Model ◽  
Phase Transitions ◽  
Crystal Structures ◽  
Structural Phase ◽  
Random Variable ◽  
Structural Phase Transitions ◽  
The Moment ◽  
The Mathematical Model ◽  
First Time

In this work, the crystal structures and phase transitions of compounds with perovskite structure were investigated. The classification of structural phase transitions in perovskites was carried out, the most common crystal structures and structural phase transitions were shown. A mathematical model was constructed, a theorem was given and proved for the probability of a possible transition. The formulas [Formula: see text] and [Formula: see text] are given for the mathematical expectation and variance of random variable [Formula: see text], which is the moment when the stochastic process [Formula: see text] deviation from the boundary [0, [Formula: see text]] interval for the first time. According to the mathematical model, one of the trajectories of random processes corresponding to the phase transitions that occur in perovskites is constructed.

Renormalization-group study of the fixed points and of their stability for phase transitions with four-component order parameters

1985 ◽  
Vol 31 (11) ◽  
pp. 7171-7196 ◽  
Author(s):  
Jean-Claude Toledano ◽  
Louis Michel ◽  
Pierre Toledano ◽  
Edouard Brezin
Keyword(s):  
Renormalization Group ◽  
Phase Transitions ◽  
Fixed Points ◽  
Order Parameters ◽  
Component Order
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