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Symbols and Approximate Angles

symmetry, axis, plane and crystal


Finding the System of a Crystal.—The following rules quickly determine the of a crystal, without the need of a complete determination of symmetry or any consideration of axes.

Approximate measurements are usually needed.

Essestiol Cowelition Systetst More than one axis of three-fold Isometric.


One axis of fottr-fold symmetry. or Tetragonal.

composite symmetry and one only.

One axis of three-fold symmetry, Hexagonal.

and one only Rhombohedral divi' sion.

One axis of six-fold symmetry. Hexagonal division.

More than one axis of two-fold sym- Orthorhombic metry but 120 axis of higher sym metry (or one axis and two planes symmetry).

One axis of two-fold symmetry only, Monoclinic.

or one plane of symmetry only or both.

Withottt axes or plane of symmetry. Triclinic..

An axis of symmetry in a crystal is a direc tion rather than a line throuFh specific points.

through the centre of the drawing, and in Fig. 2 a similarly placed four-fold axis.

A plane of symmetry holds a definite angular re lation to a crystal rather than a fix ed position in the crystal, and with respect to it the Fin. 2. crystal faces are in pairs, the angle between each pair be ing bisected by the plane of symmetry. Thus, in the crystals shown in Figs. I and 2 there are

planes of symmetry parallel to each of the dot and dash lines and each perpendicular to the plane of the paper.

The system may be also determined from the relations between co-ordinate axes chosen in the following order: First, axes of symmetry.

Second, lines perpendicular to planes of symmetry.

Third, lines in a plane of symmetry parallel to edges or faces.

Fourth, lines parallel or equally inclined to several faces of the crystal.

The six systems may then be defined in terms of axes, each including all crystals which are by the given rules, referred to a particular set of axes: more repetitions, that is, positions at which all the faces are parallel to the previous positions of other faces.

According to _r the number repetitions during a complete revolution the axis is known as two-fold, three-fold, four fold or six-fold. No other varieties exist.

In Fig. 1 there is an axis of three-fold geo metric symmetry perpendicular to the plane of the 11,7,70 and at 1.SIV C1111.11C t.tys tal is revolved (or assumed to revolve) about this direction there must be one or