Long-Range Order and Short-Range Order inPd3V: Breakdown of the Mean-Field Theory

1987 ◽  
Vol 58 (21) ◽  
pp. 2245-2248 ◽  
Author(s):  
F. Solal ◽  
R. Caudron ◽  
F. Ducastelle ◽  
A. Finel ◽  
A. Loiseau
Keyword(s):  
Field Theory ◽  
Long Range ◽  
Short Range ◽  
Short Range Order ◽  
Mean Field Theory ◽  
Mean Field ◽  
Range Order ◽  
Long Range Order ◽  
The Mean

Onset of long-range order in superlattices: Mean-field theory

1992 ◽  
Vol 46 (18) ◽  
pp. 11681-11687 ◽  
Author(s):  
R. W. Wang ◽  
D. L. Mills
Keyword(s):  
Field Theory ◽  
Long Range ◽  
Mean Field Theory ◽  
Mean Field ◽  
Range Order ◽  
Long Range Order

scholarly journals Evidence of exactness of the mean-field theory in the nonextensive regime of long-range classical spin models

2000 ◽  
Vol 61 (17) ◽  
pp. 11521-11528 ◽  
Author(s):  
Sergio A. Cannas ◽  
A. C. N. de Magalhães ◽  
Francisco A. Tamarit
Keyword(s):  
Field Theory ◽  
Long Range ◽  
Mean Field Theory ◽  
Mean Field ◽  
Spin Models ◽  
Classical Spin ◽  
The Mean ◽  
Classical Spin Models

Pb()O3-type Perovskites: Part I. Pair-correlation Theory of Order-disorder Phase Transition

1997 ◽  
Vol 12 (8) ◽  
pp. 2117-2126 ◽  
Author(s):  
Hyun M. Jang ◽  
Su-Chan Kim
Keyword(s):  
Long Range ◽  
Order Parameter ◽  
Short Range ◽  
Short Range Order ◽  
Pair Correlation ◽  
Range Order ◽  
Statistical Thermodynamic ◽  
Range Order Parameter ◽  
Long Range Order ◽  
Short Range Order Parameter

The limitation of the long-range order parameter and the necessity of the short-range order parameter for the thermodynamic description of Pb()O3-type perovskites are discussed. Based on the discussion, a statistical thermodynamic model that takes into account the configuration of the neighboring B-site ions (B′ and B″ cations) was developed. A pair-correlation approximation was used in the calculation of the configurational entropy and the long-range coulombic interaction energy between the nearest B-site ions. The theoretical calculations using Pb(Sc1/2Ta1/2)O3 (PST) and Pb(Sc1/2Nb1/2)O3 (PSN) systems indicate that the short-range order parameter persists over a wide range of temperatures examined (0–1800 K) and that there possibly occur consecutive long-range order-disorder transitions in the configuration of B-site cations. The possibility of the existence of short-range ordering above the long-range order-disorder transition temperature was also examined using the annealed PSN specimen as a typical example of Pb()O3-type perovskites.

Short range order and its transformation to long range order in Ni4Mo

1998 ◽  
Vol 46 (3) ◽  
pp. 881-892 ◽  
Author(s):  
Satoshi Hata ◽  
Syo Matsumura ◽  
Noriyuki Kuwano ◽  
Kensuke Oki
Keyword(s):  
Long Range ◽  
Short Range ◽  
Short Range Order ◽  
Range Order ◽  
Long Range Order
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