scholarly journals Order-Parameter Expansion of Free Energy and Its Application to Some Models with First and Second Order Phase Transitions

1977 ◽  
Vol 58 (6) ◽  
pp. 1679-1691 ◽  
Author(s):  
S. Naya ◽  
S. Nambu
Keyword(s):  
Free Energy ◽  
Phase Transitions ◽  
Order Parameter ◽  
Second Order ◽  
Parameter Expansion

SECOND ORDER HIGH DENSITY EXPANSION FOR FREE ENERGY AND ORDER PARAMETER

1991 ◽  
Vol 05 (18) ◽  
pp. 2935-2949
Author(s):  
M. BARTKOWIAK ◽  
K.A. CHAO
Keyword(s):  
Free Energy ◽  
Order Parameter ◽  
Order Approximation ◽  
Local Approximation ◽  
Second Order ◽  
High Density ◽  
First Order ◽  
First Order Approximation ◽  
Consistent Equation ◽  
Density Expansion

The self-consistently renormalized high-density expansion (SHDE) is first used to determine temperature dependence of order parameter. Free energy and magnetization of the Ising model has been calculated to the second order. It is shown that the unphysical discontinuity of the order parameter as a function of temperature, which appears in the first-order approximation, still remains in the second-order calculation. Based on the 1/d expansion, we then construct a method to select (1/z)i contributions from the high density expansion terms. This method is applied to the first and second-order self-consistent equation for magnetization. Selection of the first order in 1/z contributions within the first order of the SHDE leads to considerable improvement of the behavior of magnetization as a function of temperature, and application of the local approximation to the second order of the SHDE term gives an acceptable single-value behavior of the order parameter.

scholarly journals Landau theoretical analyses of phase transitions and ferroelec-tricity in antiferroelectric ferroics

2017 ◽  
Vol 6 (3) ◽  
pp. 51
Author(s):  
Egidius Rutatizibwa Rwenyagila
Keyword(s):  
Phase Transitions ◽  
Order Parameter ◽  
Energy Functional ◽  
Second Order ◽  
Theoretical Interpretation ◽  
Additional Energy ◽  
Polarization Gradient ◽  
Theoretical Analyses ◽  
Parameter Profile ◽  
Second Order Phase Transition

This paper presents Landau theoretical interpretation of phase transitions in Antiferroelectrics (AFEs) materials. The results show that the phase transitions occurring in AFEs have prominently first and second order properties. Landau theories of first and second order phase transition have been appropriately analyzed in order to explain some of desirable phenomenological behaviors occurring in AFE materials. The spatial order parameter profile of AFE domain wall was derived and tested for possibilities of having ferroelectricity (FE) in accordance with Landau type energy functional. It was found that FE may appear but with additional system instability because of additional energy as a result of polarization gradient.

Phase Diagrams for Incommensurate Systems

1982 ◽  
Vol 21 ◽  
Author(s):  
P. Toledano
Keyword(s):  
Free Energy ◽  
Phase Transitions ◽  
Energy Density ◽  
Phase Diagrams ◽  
Order Parameter ◽  
Landau Theory ◽  
Free Energy Density ◽  
Lock In

ABSTRACTPhase diagrams, for systems undergoing one or several incommensurate and lock-in transitions, are discussed in the framework of the Landau theory of phase transitions. It is shown that their essential features can be deduced from the explicit forms of the free-energy density ø and the k-dispersion of the coefficient α(→k)of the quadratic contribution of the order-parameter components in ø. Two families of phase diagrams are distinguished depending on symmetry considerations.

Symmetry rules and strain/order-parameter relationships for coupling between octahedral tilting and cooperative Jahn–Teller transitions in ABX 3 perovskites. II. Application

2009 ◽  
Vol 65 (2) ◽  
pp. 147-159 ◽  
Author(s):  
Michael A. Carpenter ◽  
Christopher J. Howard
Keyword(s):  
Phase Transitions ◽  
Order Parameter ◽  
Formal Analysis ◽  
Local Strain ◽  
Second Order ◽  
Order Transition ◽  
First Order ◽  
Jahn Teller ◽  
Octahedral Tilting ◽  
Parameter Coupling

The structural evolution of selected perovskites containing Jahn–Teller cations has been investigated in the light of a formal analysis of symmetry hierarchies for phase transitions driven by octahedral tilting and Jahn–Teller cooperative distortions. General expressions derived from the strain/order-parameter coupling relationships allowed by symmetry are combined with observed changes in lattice parameters to reveal details of order-parameter evolution and coupling. LuVO3, YbVO3, YVO3 and CeVO3 are representative of systems which develop Jahn–Teller ordering schemes associated with irreducible representations M^+_2 and R^+_3 of the space group Pm\bar 3m. Tilting of their octahedra is associated with M^+_3 and R^+_4. The Pnma (M^+_3+R^+_4 tilting) ↔ P21/a (M^+_3+R^+_4 tilting, R^+_3 Jahn–Teller order) transition below room temperature is close to second order in character. Shear strains which depend primarily on tilt angles show little variation, implying that there is only weak coupling between the tilting and Jahn–Teller order parameters. The subsequent P21/a ↔ Pnma (M^+_3+R^+_4 tilting, M^+_2 Jahn–Teller order) is first order in character, and involves either a reduction in the R^+_4 tilt angle or a change in the strength of tilt/Jahn–Teller order-parameter coupling. In LaMnO3, the isosymmetric Pnma (M^+_3+R^+_4 tilting) ↔ Pnma (M^+_3+R^+_4 tilting, M^+_2 Jahn–Teller order) transition can be described in terms of a classical first-order transition conforming to a 246 Landau expansion with negative fourth-order coefficients. Strain evolution in Ba-doped samples suggests that the transition becomes second order in character and reveals a new strain relaxation mechanism in LaMnO3 which might be understood in terms of local strain heterogeneities due to the disordering of distorted MnO6 octahedra. Transitions in PrAlO3 and La0.5Ba0.5CoO3 illustrate the transformation behaviour of systems in which the Jahn–Teller ordering scheme is associated with the irreducible representation \Gamma^+_3. Overall, coupled tilting + Jahn–Teller phase transitions in perovskites conform to mean-field behaviour, consistent with the underlying role of strain in promoting long interaction lengths.

scholarly journals Fluctuation effects in metastable states near first-order phase transitions

2016 ◽  
Vol 30 (21) ◽  
pp. 1650149
Author(s):  
Dimo I. Uzunov
Keyword(s):  
Free Energy ◽  
Perturbation Theory ◽  
Phase Transitions ◽  
Internal Energy ◽  
Order Parameter ◽  
First Order ◽  
Pressure Concentration ◽  
Fluctuation Effects ◽  
First Order Phase ◽  
Temperature Factors

Fluctuation effects at first-order phase transitions driven by changes of other-than-temperature factors like pressure, concentration or external fields are investigated by perturbation theory. The results for the fluctuation contributions to the order parameter, the internal energy and the free energy at pre-transitional states near spinodal points of first-order phase transitions are presented to the first-nonvanishing order of the expansion parameters of the theory.

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