Crystal Notation and Parameters

Crystal faces are described according to their relations to the crystallographic axes. A series of numbers which indicate the relative distances by which a face intersects the different axes are called its parameters. A face which cuts all three axes at distances from the point of their intersection which are relatively the same as the unit lengths of the axes is said to have the following parameters: 1a, 1b, 1c. A face which cuts the two horizontal axes at distances which are relatively to each other as the unit lengths of those axes but is parallel to the vertical axis would have for parameters 1a, 1b, c. If a face cuts the two horizontal axes at distances proportional to their unit lengths and cuts the vertical axis at a distance twice its relative unit length. It will have for parameters 1a, 1b, 2c. It is to be emphasized that these parameters are strictly relative in their values and do not indicate any actual cutting lengths. To further illustrate this, consider Fig. 11, which represents a possible sulfur crystal. The forms present upon it are two pyramids of different slope but each intersecting all three of the crystal axes when properly extended. The lower pyramid intersects the two horizontal axes at distances which are proportional to their unit lengths and if it was extended as shown by the dotted liner would also cut the vertical axis at a distance proportional to its unit length. The parameters of the face of this form which cuts the positive ends of the three axes would be 1a, 1b, 1c. The upper pyramid would cut the two horizontal axes, as shown by the dotted lines, also at distances which, although greater than in the case of the lower pyramid, are still proportional to their unit lengths. It cuts the vertical axis, however, at a distance which, when considered in respect to its intersections whit the horizontal axes, is proportional the one half of the unit length of c. the parameters of a face of this form would therefore be 1a, 1b, 1/2c. Form this example it will be seen that the parameters 1a, 1b, do not in the two cases represent the same actual cutting distances but express only relative values. The parameters of a face do not in any way determine its size, for a face may be moved parallel to itself for any distance without changing the relative values of its intersections with the crystallographic axes.