Derivation of a formula for calculating the faces of the initial belt using the zonal calculation system
Abstract
The geometric constants, even for a triclinic crystal, are five angles, the values of which can be easily determined by direct measurement on a universal goniometer, and then no preliminary calculations are needed; using these same five angular values with the help of a fundamental formula, the determination of any face, not only measured, but any possible one, given by the indices of the symbol, is produced, as mentioned, by simple additions and subtractions, but with the exception of the faces located in the original belt itself, that is, the belt of faces a and b. And in the textbook (“A Brief Course in Crystallography”) no formula is provided for calculating the angles between the faces in this belt. Here I will present the derivation of this remarkable and extremely simple formula.
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