B. A. Hasan, N. H. Tariq, H. R. N. Shahid, F. Ali


The order/disorder phenomenon is important in many branches of science especially metallurgy and solid state physics because the transformation is accompanied by changes in many physical properties. In the last several decades many mathematical models of Order-Parameters have been proposed by the scientific community that could better describe the phenomenon. However, due to the subtle but important differences in the definition of an ‘Order Parameter’, as adopted by physicists, metallurgists, chemists, thermo-dynamists, and computer scientists an odd-complexity and abstraction has unintentionally crept in. A brief review is hereby presented of the several prevailing definitions of ‘Order Parameters’ to highlight the use of this term as it is used in materials modeling. The work of the authors is presented that is related with predicting the pair correlations for qausi-chemical treatment of binary alloy systems. The mathematical models chosen cover the range from random to ordered solid solution.

Full Text:



J.P. Sethna, Statistical Mechanics, Entropy,

Order Parameters and Complexity, First Ed.

United States: Oxford University Press


C. Whiston, X-ray Methods, First Ed. Great

Britain: John Wiley & Sons (1987).

J.M. Cowley, Phy. Rev. 77 (1950) 669.

R.W. Ross, C.T. Sims, Nickel-Base Alloys,

in: C.T. Sims, N.S. Stoloff and W.C. Hagel

(Eds.), Superalloys-II. New York: John Ross

Wiley & Sons (1987).

J.M. Cowley, Phy. Rev. 120 (1960) 1648.

B.D. Cullity, Elements of X-ray Diffraction,

Second Ed. United States of America:

Addison-Wesley Publishing Company (1978).

D.A. Porter, K.E. Easterling and M.Y. Sherif,

Third Ed. United Kingdom: Taylor & Francis

Group (2009).

N. Saunder and A.P. Miodownik. CALPHAD,

First Ed. UK: Pergamon (1998).

Pfeiler. Alloy Physics, First Ed. Wiley,

Germany (2007).

G. Bonny, P. Erhart, A. Caro, R.C. Pasianot,

L. Malerba and M. Caro, Modelling Simul.

Mater. Sci. Eng. 17 (2009)1.

E. Esteves-Rams and R.Z. González-Férez

Kristallogr. 224 (2009) 179.

T.B. Massalski Structure and Stability of

Alloys, in R.W. Cahn and P. Haasen (Eds.).

Physical Metallurgy. Netherlands: NorthHolland (1996).

R.A. Swalin, Thermodynamics of Solids, First

Ed., United States of America: John Wiley &

Sons (1962).

E.S. Machlin, An Introduction to Aspects of

Thermodynamics and Kinetics Relevant to

Materials Science, Third Ed. New

York:Elsevier (2007).

M. Hillert, Phase Equilibria, Phase Diagrams

and Phase Transformations, Second Ed.

United States of America: Cambridge

University Press (2008).

A.I. Gusev, A.A. Rempel and A.A. Magerl.

Disorder and Order in Strongly Nonstoichiometric Compounds, First Ed.,

Springer, Germany (2001

J.M. Cowley, Phy. Rev. 138 (1965) A1384.

O. Zhong-Can, L. Ji-Xing and X. Yu-Zhang.

Geometric Methods in the Elastic Theory of

Membranes in Liquid Crystal Phases, First

Ed. Singapore: World Scientific Publishing

Company (1999).

L. Pohl and U. Finkenzeller, Physical

Properties of Liquid Crystals, in Bahadur B

(Ed.). Liquid Crystals. Singapore: World

Scientific Publishing Company (1995).

M.R. Fisch, Liquid Crystals, Laptops and Life,

First Ed. Singapore, World Scientific

Publishing Company (2007).

H. Meyer, Simulation of Structure Formation

in Supercooled Polymer Melts, in J.U.

Sommer and G. Reiter (Eds.), Polymer

Crystallization, Germany: Springer (2003).

G.S. Rohrer, Structure and Bonding in

Crystalline Materials, First Ed. UK,

Cambridge (2004).


  • There are currently no refbacks.