Tetragonal System, Crystallographic Axes and Normal Class

Crystallographic Axes: The crystallographic axes of the Tetragonal System are three in number and make right angles with each other. The two horizontal axes are equal in length and interchangeable, but the vertical axis is of some different length which varies with each tetragonal mineral. The length of the horizontal axes is taken as unity, and the relative length of the vertical axis is expressed in terms of the horizontal. This length has to be determined for each tetragonal mineral by measuring the interfacial angles on a crystal and making the proper calculations. For zircon the length of the vertical axis is expressed as c= 0.640. the proper orientation of the crystallographic axes and the method of their notation is like that of the Isometric System.

Normal Class: Symmetry and Forms. The symmetry of the Normal Class of the Tetragonal System I a flows: The vertical crystallographic axis is an axis of tetragonal symmetry. The vertical crystallographic axis is an axis of tetragonal symmetry. There are four horizontal axes of binary symmetry, two of which are coincident with the crystallographic axes, while the other two bisect the angles between these. Fig. 80 shows the axes of symmetry. There are four vertical and one horizontal planes of symmetry. Each vertical plane of symmetry passes through one of the horizontal axes of symmetry.

The forms of the Normal Class, Tetragonal System, are as follows:

1. Prism of First Order
The prism of the first order consists of four rectangular vertical faces, each of which intersect the two horizontal crystallographic axes equally. Its symbol is 110).

2. Prism of Second Order
The prism of the second order consists of four rectangular vertical faces, each of which intersects one horizontal crystallographic axis and is parallel to the other two axes. Its symbol is (100). The form is represented in Fig. 83. The prism of the first and second order are identical forms, except for their orientation. They can be converted into each other by a revolution about the vertical axis of 45°. Since both may occur together upon the same crystal it is necessary to recognize the two forms.

3. Ditetragonal Prism
The ditetragonal prism is a form consisting of eight rectangular vertical faces, each of which intersects the two horizontal crystallographic axes unequally. There are various ditetragonal prism, depending upon their differing relations to the horizontal axes. The symbol of a common form is (210).

4. Pyramid of First Order
The pyramid of the first order is a form consisting of eight isosceles triangular faces, each of which intersects all three crystallographic axes, the intercepts upon the two horizontal axes being equal. There are various pyramids of the first order, depending upon the inclination of their faces. The unit pyramid which intersectws all the axes at their unit lengths is the most common, its symbol being (111). Symbols for other pyramids of the first order are (221), (331), (112), (113), etc. fig. 85 represents the unit pyramid on zircon.

5. Pyramid of Second Order
The pyramid of the second order is a form composed of eight isosceles triangular faces, each of which intersects one horizontal axis and the vertical axis and is parallel to the second horizontal axis. There are various pyramids of the second order, with different intersections upon the vertical    axis. The most common form is the unit pyramid, which has (101) for its symbol. Other pyramids of the second order would have the symbols (201), (301), (102), (103), etc. fig. 86 represents a unit pyramid of the second order upon zircon. The same relationship exists between the pyramids of the first and second order as in the case of the corresponding prisms; see above.

6. Ditetragonal Pyramid
The ditetragonal pyramid is a form composed of sixteen isosceles triangular faces, each of which intersects all three of the crystallographic axes, cutting the two horizontal axes at different lengths. There are various ditetragonal pyramids, depending upon the different axial intersections possible. One of the most common is the pyramid having /311) for its symbol.

7.Basal Pinacoid
The basal pinacoid, basal plane, or base, as it is variously called, is a form composed of two horizontal faces. Its symbol is (001).

Tetragonal Combinations. The different pyramids are the only tetragonal forms that can occur alone, and even they are ordinarily found in combination with other forms.