A Triangular Scheme For Crystal Morphology

Abstract

It is possible to relate the seven permissible crystal forms in any crystal class by means of an equilateral triangle. Three of the forms, with fixed Miller indices (fundamental forms), are assigned to vertices of the triangle. Three of the remaining forms with variable indices have two indices equal, or a third equal to zero. These forms, designated univariant, are assigned to legs of the triangle. The seventh form is the general form for the class and is assigned to the area within the triangle. The forms may be numbered from one to seven in such a way that the sum of the numbers for any fundamental form and the opposite univariant form will be equal to the number of the general form, which is taken as seven. The sum of the numbers of any two fundamental forms will then equal the number of the related univariant form. For any three numerically related forms, the sum of the Miller indices for the two forms with lower numbers in the triplet will give simplest indices for the third form. If the poles of re...