Method for estimating the morphological significance of simple forms of crystals from X-ray data
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Method for Estimating the Morphological Significance of Simple Forms of Crystals from XRay Data E. B. Treіvus St. Petersburg State University, St. Petersburg, 199034 Russia email: [email protected] Received March 30, 2010
Abstract—When developing V.I. Mikheev and I.I. Shafranovskiі’s method for estimating the morphological significance of faces of different simple forms from Xray reflection intensities, a way to approximately eval uate the morphological significance of simple forms on crystals from the structure amplitudes of the corre sponding atomic planes is proposed. The potential for this approach is demonstrated by the examples of mar casite and zircon. DOI: 10.1134/S1063774510050299
One question that traditionally must be answered in crystal morphology studies is the relationship between the appearance and habit of crystals and their structure. There are some wellknown methods aimed at solving this problem. The state of this problem was reviewed by Shafranovskiі [1]; a relatively recent review was published by Bennema et al. [2]. However, this problem is far from being exhausted, as evidenced by [3], where a method for calculating the reticular density of faces was developed to this end. Note that the conventional discussion of the mor phological significance of faces from the point of view of their reticular density, which is known to date back to Bravais (the mid1850s), is not very appropriate. In reality, the morphological significance of faces is determined by the electron density of the atomic layers forming these faces, whereas the reticular density is only a manifestation (not always adequate) of their electron density. Obviously, the higher the electron density (within a specific crystal structure) of the packet of atomic layers forming this face is, the higher the degree of compensation of chemical bonds within this packet is and the smaller the extent to which they are directed outside from this face is. As a result, one would expect a lower growth rate for this face and, therefore, its significant development on the crystal. Mikheev and Shafranovskiі [1, 4] proposed esti mating the morphological significance of faces based on the Xray intensity I from the corresponding atomic nets; this characteristic is known to be approx imately correlated to their electron density. They dem onstrated an approximate correspondence between the morphological observations and their theoretical estimates by a number of examples. However, as far as we know, this method has not been in demand and has not even been discussed. At the same time, the Mikheev–Shafranovskiі method has some attractive
features. Compared with the other approaches, its ele gant simplicity is appealing. Nevertheless, the form in which it was applied by the authors is out of date. They used Xray determinants of minerals [5, 6] in which the I value was indicated based on a subjective visual estimation of Xray intensities (on a tenpoint scale). This appears to be completely obsolete. However, the main drawback of their meth
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