Cowley parameter

Those Warren-Cowley parameters have been determined in situ above the order-disorder transition temperature by diffuse neutron scattering. From these experimentally determined static correlations, the first nine effective pair interactions have been deduced using inverse Monte Carlo simulations. 

The Warren-Cowley parameters provide more detailed information about the mutual correlation of impurities they also CeUi be directly used in calculations of transport and magnetic properties. 

The results for the Warren-Cowley parameters, summarized in Tab. 2, show that Mnl atoms have always a tendency to attract each other, while Mn atoms of opposite orientation of spin repel each other. In the first coordination sphere all impurities repel each other with the exception of Mn -Mn and Mn -As pairs. The attraction of Mn -Mnl and As-As priirs in the second and third coordination spheres is remarkable. 

Table 2. Warren-Cowley parameters of ordered structures in their perfectly ordered states.

The ordering processes in the Ni-Mo and Ni-V alloys reproduced by Monte Carlo simulation are discussed based on the pairwise interaction model. Table 2 shows Warren-Cowley parameters a(w) of the ordered structures in their perfectly ordered states. The parameter a(n) is defined by ... 

The Cowley SRO parameter is defined in this case as O = 1---—, where is the... 

Equations of the form of Equation (4) form the basis of the analysis of strain and elasticity reviewed in this chapter. The issues to be addressed are (a) the geometry of strain, leading to standard equations for strain components in terms of lattice parameters, (b) the relationship between strain and the driving order parameter, and (c) the elastic anomalies which can be predicted on the basis of the resulting free energy functions. The overall approach is presented as a series of examples. For more details of Landau theory and an introduction to the wider literature, readers are referred to reviews by Bruce and Cowley (1981), Wadhawan (1982), Toledano et al. (1983), Bulou et al. (1992), Salje (1992a,b 1993), Redfern (1995), Carpenter et al. (1998a), Carpenter and Salje (1998). 

The relation between W and Ws, the domain wall widths in the bulk and at the surface, can be seen in Figure 8. The effect of the surface relaxation is clearly visible as the order parameter at the surface Qs never reaches the bulk value Qo- The distribution of the square of the order parameter at the surface shows the structure that some of the related experimental works have been reported (Tsunekawa et al. 1995, Tung Hsu and Cowley 1994), namely a groove centred at the twin domain wall with two ridges, one on each side. 

Cowley RA (1964) The theory of Raman scattering from crystals. Proc Phys Soc 84 281-296 Ghose S, Ito Y, Hatch DM (1991) Paraelectric-antrferroelectric phase transition in titanite, CaTiSiOs. I. A high temperature X-ray diffraction study of the order parameter and transition mechansim. Phys Chem Miner 17 591-603... 

For a solution containing molecules i and j, Warren and Cowley defined an order parameter 77 as ... 

In a substitutional solid solution with a single type of site, the coordination indices of the two t5rpes of molecules are the same in the solution (z = z g), so the two Warren and Cowley order parameters are also equal... 

Let us calculate Warren and Cowley s parameter for the quasichemical model. 

Figure 2.12 shows the variations in Warren and Cowley s order parameter for the quasi-chemical model, with the following values of the parameters T = 800 K, NsWab = 30 kJ and z = 12. The result obtained respects the symmetry of the model, with a minimum for the composition Xa = Xb = 0.5. 

Table 2. Warren-Cowley short-range order parameters for impurities in the (Gao.9325MnJ 04O625M o-oo9375- o.oi75)As alloy at T = 1400 K.

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