Structure and Packing Density of Liquid Metals
نویسندگان
چکیده
The diffraction pattern of molten metals shows several intensity-maxima, which can be interpreted in a similar way as the Debye-Scherrer pattern of crystalline powders. For this purpose, however, it is necessary to introduce liquid-like distortions. Such an approach has been given by the concept of paracrystallinity [1] , which contains the well known equations of crystallography [2] as limiting case. Kratky [3, 4] was the first who tried to construct the pair correlation function by randomly oriented distorted mierodomains. Satisfying results have recently been obtained in the case of feeand bccmolten metals by means of convolution polynomials [5, 6 ] . In a paracrystal, the positions of atoms are labeled by integers i, k, I and p, q, r, corresponding to positions on lines, rows, and columns. The p, q, r are the relative coordinates of an ideal lattice site. However, contrary to the crystalline state, the distance statistics of pairs (i, k, I) and (i + p, k + q, l + r), averaged over all i, k, I, become broader with increasing ( | p j , j ^ j , | r | ) . The average over many paracrystals with arbitrary orientations results in spherical shells. Apart from some well known factors and additive terms these result in the pair correlation function. Instead of simply averaging over all i, k, I, one can first rotate the different paracrystals until they are aligned in parallel to each other and then average over all these oriented (i, k, I) environments. The resulting correlation function is no longer spherically symmetric, but is splitted into individual density humps Wpqr{x) whose centers form a threedimensional lattice. In some (i, k, I) environments a site (p, q, r) may be vacant, in others doubly occupied. Thus J WPQr Or) &x_ is not necessarily unity.
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