By Marko V. Jaric, Denis Gratias
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I defer edge and vertex connection to later discussion, and take up here icosahedra of the same orientations connected at faces. Because we have in mind that the connected icosahedra represent clusters of a t o m s , an important criterion is that the units cannot overlap. We do not specify the precise nature of the cluster, and so it is not possible to specify a priori the excluded volume a r o u n d each unit. However, it is reasonable to expect, and experience bears out, that the shape of the excluded volume affects the diffraction patterns relatively weakly.
Schaefer, R. , and Bendersky, L. A. In Aperiodicity and Order, Vol. 1, Intro duction to Quasicrystals, Ed. by Μ. V. Jaric (Academic Press, Boston, 1988). Stephens, P. , and Goldman, A. I. (1986). Phys. Rev. Lett. 56, 1168. Henley, C. L. (1986). Phys. Rev. B34, 797. , and Steinhardt, P. J. (1986). Phys. Rev. B34, 596. Yu-Zhang, K. (1987). Materials Science Forum 22-24, 627. Nissen, Η. , Beeli, C , and Csanady, A. (1988). Phil. Mag. B57, 587. Cahn, J. , and Gratias, D. (1986). J. Mater. Res. 1, 13.
Magnitude of phason momentum | G | for a first-fit icosahedral glass. The wave vector scales are appropriate for Al-Li-Cu. Small dots are results for model II discussed in Sec. 1. The experimental data points are taken from Heiney et al. (1987). X Over the range of G plotted in Fig. 5 and - 4 . 8 power of | G | , respectively. By way of contrast, the fitted intensity and width are independent of G". For suffi ciently small | G | , the peak width is limited by the finite sample size, and the intensity is on the order of TV , as discussed above.
Extended Icosahedral Structures by Marko V. Jaric, Denis Gratias