Weiss parameters

Paramètres de Weiss (Fr). Weiss-Parameter (Ge). Parámetros de Weiss (Sp). Параметры Вайс (Ru). Parametri di Weiss (It). ワイスパラメーター (Ja).

The Weiss parameters, introduced by Christian Samuel Weiss in 1817, are the ancestors of the Miller indices. They give an approximate indication of a face orientation with respect to the crystallographic axes, and were used as a symbol for the face.

Weiss parameters are the reciprocal of Miller indices, each followed by the corresponding axis symbols.

Example. Weiss parameters 2a:3b:1c indicate that a face intercepts the a axis at twice the a_o units and the b axis at three times b_o units as it cuts the c axis in c_o units. The first plane of the family to which this face belongs has intercepts at 1/3, 1/2 and 1/6 on a, b, and c respectively, so that the corresponding Miller indices are (326).

Reference

Weiss, C. S. (1817). Abhandlungen der Königlichen Akademie der Wissenschaften in Berlin, 286-336. Ueber eine verbesserte Methode für die Bezeichung der verschiedenen Flächen eines Krystallisationssystemes; nebst Bemerkungen über den Zustand von Polarisierung der Seiten in den Linien der krystallinischen Structur (digitized version available online)