Brief notes on the Normal Class of Tetragonal System

Crystals belonging to tetragonal system are referred to three crystallographic axes, which are perpendicular to each other.

Out of the three axes, two are horizontal, lie in the horizontal plane, equal in length and thus, are mutually interchangeable. They are designated as and a₂. Axis a, runs from front to back, positive on observer side and negative in the back; a, axis runs from right to left, positive on right hand side and negative on the left hand side.

The third axis is vertical;] perpendicular to the plane containing a, and a₂ axes and is different in length, either shorter as in case of zircon or longer as in case of octahedrite. It is designated as ‘c’. The: c values in case of zircon and octahedrite are 1:0.901 and 1:1.777 respectively.

There are seven classes grouped under this system. These are ditetragonal dipyramidal, tetragonal scalenohedral, ditetragonal pyramidal, tetragonal trapezohedral, tetragonal dipyramidal, tetragonal disphenoidal and tetragonal pyramidal.

The ditetragonal dipyramidal class is known as the normal class of tetragonal system as it shows the maximum symmetry among all the classes belonging to tetragonal system and zircon type after the characteristic mineral zircon that crystallizes in this class.

Symmetry elements:

The vertical crystallographic axis ‘c’ is the axis of 4-fold rotational symmetry. In addition, there are four axes of 2-fold symmetry, two of which are coincident with the horizontal crystallographic axes and other two are diagonal and bisect the angle between the horizontal crystallographic axes.

There are five mirror planes (planes of symmetry), three are axial (one horizontal and two vertical) each containing two of the crystallographic axes and other two are vertically diagonal bisecting the angles between the vertical axial planes mentioned above. Centre of symmetry is present.

Forms:

Different forms belonging to this class are basal pinewood, three types of prisms and corresponding three types of pyramids. These are given in Table 3.2.

Table 3.2 Forms of normal class of tetragonal system

Shape of fact in simple form

Tetragonal prism of second order

Tetragonal dipyramid of second order

(i) Basal pinewood (001)₂:

The basal pinewood is an open form composed of two horizontal faces, which remain parallel with the horizontal axes and intersect the vertical crystallographic axis equal lengths. The form symbol is (001)₂ and the symbols of two faces are 001 and 00As it forms the base of the crystal, it is know; as basal pinewood.

(ii) Tetragonal prism of first order (110)₄:

It is an open form that consists of four rectangular faces, each of which intersects the horizontal crystallographic axes at equal lengths and remains parallel with the vertical crystallographic axis. The form symbol is (110)₄ and the four faces are 110, 110, 110 and 1 1O.

(iii) Tetragonal prism of second order (100)₄:

It is an open form that consists of four rectangular faces, each of which intersects one horizontal crystallographic axis and remains parallel with the other two crystallographic axes. The form symbol is (100)₄ and the four faces are 100, 010, 100 and 010.

(iv) Ditetragonal prism (hk0)₈:

The ditetragonal prism is an open form that consists of eight rectangular faces, each of which intersects both the horizontal crystallographic axes at different lengths. The form symbol is (hk0)₈.

This prism can be thought of as derived from the tetragonal prism of first order by development of two faces on each face of the tetragonal prism of first order. Depending upon the different intercepts made on the horizontal crystallographic axes a number of ditetragonal prisms exist but the most common one is (120).

Tetragonal dipyramid of first order (hhl) ₈: It is a closed from having eight isosceles triangular faces, each of which intersects both the horizontal crystallographic axes at equal lengths and the vertical crystallographic axis at a different length.

The form symbol is (hhl) _g. If a face of this dipyramid cuts the horizontal and the vertical crystallographic axes in the same ratio as the axial ratio i.e. h: l = a: c, the form is called unit or fundamental form and the symbol becomes (111)₈. Though the unit dipyramid is most common, dipyramids with symbols (221) _g, (331) _g, (112) _g, (113) _g etc also exist.

(vi) Tetragonal dipyramid of second order (0kl) ₈:

It is a closed from having eight isosceles triangular faces, each of which intersects the vertical crystallographic axis and one of the horizontal crystallographic axis at different lengths remaining parallel to the other horizontal crystallographic axis. The form symbol is (Okl) _g. The unit dipyramid (011) g is most common, but dipyramids with symbols (021) _g, (031) _g, (012) _g, (013) _g etc also exist.

(vii) Ditetragonal dipyramid (hkl) ₁₆:

The ditetragonal dipyramid is a solid bounded by sixteen scalene triangular faces each of which intersects all the three crystallographic axes at unequal lengths. The form symbol is dipyramid (hkl) _h. There are various ditetragonal dipyramids depending upon the different intersections on the crystallographic axes.

Different forms of the normal class of tetragonal system also occur in combinations with each other. Combination forms of tetragonal dipyramid of first order and tetragonal prism of first order as well as tetragonal dipyramid of first order and tetragonal prism of second order are shown in and 3.29 respectively.

Important minerals crystallizing in this class are zircon, rutile, anatase, cassiterite, idocrase, apophyllite, octahedrite etc.