Warren-Cowley parameters

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 ... 

If the coordination numbers of two types of molecules are the same in the solution (z = z b), then the two Warren-Cowley order parameters are also... 

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.

The quantities of interest to follow the global evolution of precipitation during the simulation are Warren-Cowley short range order (SRO) parameters [5]. SRO parameters for first-nearest neighbors evolve too quickly to give any really significant information on precipitation state. During simulation first steps, Zr atoms surround themselves... 

Dividing by leads to the well-known Warren-Cowley SRO parameter... 

For a quantitative description of the SRO, it is common to calculate the so-caUed Warren-Cowley coefficients a r) [11, 75-77). The most intuitive definition of these parameters is... 

Figure 12.24 Comparison of the Warren-Cowley SRO parameters determined from experimental data (o) and from MC simulations (x) at different compositions of the...

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

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. 

It is also of interest to obtain information on changes of short-range order (SRO) during irradiation as well as of long-range order (LRO). The state of SRO is usually given by the Cowley-Warren parameters a, that describe the conditional probability (P ba) finding B (A) atoms on the successive coordination shells around A (B) atoms, and which have the form... 

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