Symmetry breaking and long-range order: Ann-component model of a structural phase transition

1994 ◽  
Vol 49 (6) ◽  
pp. 4311-4314 ◽  
Author(s):  
H. Chamati ◽  
N. S. Tonchev
Keyword(s):  
Phase Transition ◽  
Symmetry Breaking ◽  
Long Range ◽  
Structural Phase Transition ◽  
Structural Phase ◽  
Range Order ◽  
Component Model ◽  
Long Range Order

LONG RANGE ORDER IN THE BLUME-EMERY-GRIFFITHS MODEL

1991 ◽  
Vol 05 (23) ◽  
pp. 1583-1590
Author(s):  
M. CORGINI
Keyword(s):  
Phase Transition ◽  
Long Range ◽  
Order Phase Transition ◽  
Range Order ◽  
Long Range Order ◽  
First Order ◽  
First Order Phase Transition ◽  
Infrared Bounds ◽  
First Order Phase

Using the Infrared Bounds method it ws demonstrated that a first order phase transition takes place in the m-dimensional (m≥3) Blume-Emery-Griffiths model.

Study of a model for the main phase transition of lipid bilayers using the Kikuchi cluster method

1984 ◽  
Vol 62 (9) ◽  
pp. 935-942 ◽  
Author(s):  
Alzira M. Stein-Barana ◽  
G. G. Cabrera ◽  
M. J. Zuckermann
Keyword(s):  
Phase Transition ◽  
Lipid Bilayers ◽  
Long Range ◽  
Effective Field ◽  
Order Parameters ◽  
Range Order ◽  
Cluster Method ◽  
Variation Method ◽  
Long Range Order ◽  
Approximate Counting

The statistical mechanics of Doniach's two-state lattice model for the main gel – liquid crystal phase transition of phospholipid bilayers is treated in a similar manner to order–disorder transformations in binary alloys and magnetic systems, using the cluster variation method developed by Kikuchi. Indeed, the analogy holds better for the latter system, since the entropy difference between the two states gives rise to an effective temperature-dependent field. This effective field vanishes at the first-order phase transition, whose latent heat is associated with the discontinuity in the order parameter.We use Kikuchi's approximation with the inclusion of triangle bond correlations, and pair and site probabilities in the expression for free energy. We assume that the lipid chains only interact through nearest neighbour pair potentials and that triangle correlations are important for approximate counting of allowed states. Two long-range order parameters and a short-range order parameter are introduced in the formulation of the theory. Both long-range order parameters are discontinuous at the transition temperature. Numerical results for the physical quantities are presented and discussed with respect to earlier work.

scholarly journals Structural and Energy Characteristics of NiAl Alloys with Deviations from Stoichiometric Composition. Part 2

2020 ◽  
pp. 39-46
Author(s):  
A.I. Potekaev ◽  
A.A. Chaplyginа ◽  
M.D. Starostenkov ◽  
A.A. Klopotov ◽  
V.V. Kulagina
Keyword(s):  
Temperature Dependence ◽  
Long Range ◽  
Structural Phase ◽  
Stoichiometric Composition ◽  
Range Order ◽  
Long Range Order ◽  
Heating And Cooling ◽  
Ordered Phases ◽  
Range Parameter ◽  
The Difference

The analysis of the atomic and phase structure confirmed the difference between the structural-phase states at the heating and cooling stages. Based on the analysis of the influence of the deviation of the atomic composition from the stoichiometric condition of the intermetallic compound during cooling, it is established that the deviation is a significant factor in the area of low-stability pre-transitional structural-phase states before the transformation. The behavior of the long-range parameter temperature dependence curves during the cooling of alloys of non-stoichiometric compositions differs significantly from the behavior of the corresponding alloy curve of a stoichiometric composition alloy. It is shown that in the case of cooling of alloys of non-stoichiometric compositions, a significant supercooling is required to establish a long-range order, and the appearance of ordered phases occurs at significantly lower temperatures. It is found that the temperature dependence curve of the long-range parameter of the Ni45Al55 alloy is significantly lower than the corresponding curve of the Ni55Al45 alloy. This indicates different mechanisms for establishing the long-range order of alloys with non-stoichiometric compositions. It is noted that the deviation of the system composition from the stoichiometric one causes a significant reduction of ordered and disordered regions. This article is a continuation of the work published earlier in the journal Izvestiya AltGU. 2020. №1 (111).

Sign in / Sign up

Export Citation Format

Share Document