Ashcroft-Langreth

Figure 9.1 shows the simulated total neutron scattering functions obtained from both the compressed and quenched configurations and compared to those obtained from high pressure neutron scattering experiments [67]. The (Ashcroft-Langreth) structure factors are calculated directly from the atom positions via =... 

Ashcroft-Langreth functions may be converted easily into the Faber-Ziman form [68]. The simulated total scattering functions are obtained directly from the weighted combination of the Faber-Ziman partial structure factors. 

SOURCES of values Most were chosen such that = 0 at the same q as in the model potential due to Animalu and Heine (1965) and Animalu (1966). Values of q at the first crossing of the horizontal axis were taken from Cohen and Heine (1970, p. 235). The exceptions are O, S, and Cl, which were obtained from fitted pseiidopotentials (Cohen and Heine, 1970), and Rb and Cs, from Ashcroft and Langreth (1967). 

The theoretical form of (3—x)/a was also calculated using interference functions derived from a hard-sphere alloy in the Percus-Yevick approximation (Ashcroft and Langreth, (1967), Enderby and North, (1968)). The results are given in curve (b) of Figure 7.27 and it is clear that the model fails to predict the sharp peak in the experimental data discussed above. The reason for this is that the hard sphere model predicts that should fall roughly midway between n-Sn Cu-Cu complementary effect of the concentration dependence of a. and cu-Sn which occurs in evaluation F(2kp) will be absent for hard spheres. 

It is necessary to determine the volume dependence of each of the terms in Eq. (3.29). This can be done with quite high accuracy for most of the terms. The exception is the term Aq. If the volume is an important variable, the usual pseudopotential approach must be modified (Ashcroft and Langreth, 1967 Hasegawa and Young, 1981) to obtain Aq. Up to now, unfortunately, this has been done only by simply adopting empirical expressions with parameters fitted to the data at specific reference points. 

At least in the case of liquid simple metals, a knowledge of the effective pan-potentials describing the interaction between the ions in the liquid metal can also be utilized to calculate g(r) and A K). The most common such method involves the assumption of a hard-sphere potential in the Percus-Yevick (PY) equation its solution provides the hard-sphere structure factor, /4hs( C). (See Ashcroft and Lekner 1966.) The two parameters that must be provided for a calculation of Ahs( ) are the hard-sphere diameter, a, and the packing fraction, x. It is found that j = 0.45 for most liquid metals at temperatures just above their melting points. A hard-sphere solution of the PY equation has also been obtained for binary liquid metal alloys, and provides estimates of the three partial structure factors describing the alloy structure (Ashcroft and Langreth 1967). To the extent that the hard-sphere approximation appears to be valid for the liquid R s, pair potentials should dominate these metals also, at least at short distances. 

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