Describe using projection diagram various crystal-forms developed in the normal class of tetragonal system.

The Tetragonal Crystal System: A Recap

The tetragonal system is defined by three unequal axes, where two axes are of equal length and intersect at right angles, while the third axis is also at right angles to the other two but of a different length. The general formula for the unit cell parameters is a = b ≠ c, and all angles are 90°. The normal class of the tetragonal system exhibits a four-fold rotation axis (C₄), two two-fold rotation axes (C₂), a mirror plane perpendicular to the C₄ axis, and a center of symmetry.

Crystal Forms of the Normal Class

1. Tetragonal Prism {100}

The tetragonal prism is formed by faces perpendicular to the c-axis. It is the simplest form in the tetragonal system. Its projection diagram shows a rectangular prism. The interfacial angle between the prism faces is 90°. It exhibits a four-fold symmetry around the c-axis. The habit is typically prismatic, meaning the crystal tends to elongate along the c-axis.

2. Tetragonal Pyramid {110}

The tetragonal pyramid is formed by faces intersecting the c-axis at an angle. Its projection diagram shows a pyramid with a square base. The interfacial angle between the pyramidal faces is 90°. This form exhibits four-fold symmetry. The habit is typically pyramidal, with the crystal terminating in a pointed apex. The {110} form is commonly observed in minerals like zircon.

3. Tetragonal Pinacoid {001}

The tetragonal pinacoid consists of faces parallel to the c-axis. Its projection diagram shows a flat, plate-like crystal. The interfacial angle is 180°. It exhibits a four-fold symmetry. The habit is typically tabular or platy, with the crystal being thin and flat. Pinacoids are often present as end faces of prismatic crystals.

4. Tetragonal Scalenohedron {120}

The tetragonal scalenohedron is a more complex form, formed by faces that intersect both the c-axis and the a/b axes. Its projection diagram shows a crystal with eight faces. The interfacial angle is not 90°. This form exhibits four-fold symmetry. The habit can vary, but it often results in a more complex crystal shape. The {120} scalenohedron is frequently found in minerals like rutile.

Combinations of Forms

In nature, crystals rarely exhibit a single form in isolation. They often display combinations of these basic forms, leading to more complex crystal shapes. For example, a prism may be terminated by a pyramid, or a pinacoid may be present on the prism faces. These combinations are governed by the relative growth rates of the different faces, which are influenced by the chemical environment and temperature.