UPSC MainsGEOLOGY-PAPER-II201910 Marks
Q13.

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

How to Approach

This question requires a detailed understanding of the tetragonal crystal system and its various crystal forms. The answer should begin with a brief explanation of the tetragonal system's characteristics. Then, it should systematically describe the common crystal forms – prism, pyramid, dipyramid, scalenohedron, and pedion – using projection diagrams. Emphasis should be on illustrating the symmetry elements and the resulting forms. A clear, labelled diagram for each form is crucial. The answer should demonstrate a strong grasp of crystallography and mineralogy.

Model Answer

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Introduction

The tetragonal crystal system is one of the seven crystal systems, characterized by two equal axes at right angles to each other and a third axis, also at right angles, which is of a different length. This results in a rectangular prism shape as the basic building block. The tetragonal system is relatively common in mineralogy, hosting important minerals like zircon, rutile, and cassiterite. Understanding the crystal forms developed within this system is fundamental to mineral identification and understanding their physical properties. This answer will describe the various crystal forms developed in the normal class of the tetragonal system, accompanied by illustrative projection diagrams.

Tetragonal Crystal System – Normal Class

The normal class of the tetragonal system (also known as the holohedral class) possesses a four-fold rotation axis, a two-fold rotation axis, a mirror plane perpendicular to the four-fold axis, and a mirror plane bisecting the angle between the two-fold axes. This symmetry dictates the possible crystal forms that can develop.

Crystal Forms and Projection Diagrams

1. Tetragonal Prism {010}

The tetragonal prism is the most basic form in this system. It is formed by faces parallel to the c-axis. The projection diagram shows a rectangular prism. The symmetry elements present are the four-fold rotation axis (c-axis) and the mirror plane perpendicular to it.

Tetragonal Prism

2. Tetragonal Pyramid {110}

The tetragonal pyramid is formed by faces intersecting the c-axis at an angle of 45 degrees. The projection diagram shows a pyramid with a square base. The symmetry elements include the four-fold rotation axis and the two mirror planes.

Tetragonal Pyramid

3. Tetragonal Dipyramid {110} and {11-1}

The tetragonal dipyramid is formed by two tetragonal pyramids joined base to base. It exhibits higher symmetry than the single pyramid. The projection diagram shows two pyramids sharing a square base. The symmetry elements are the four-fold rotation axis and the four mirror planes.

Tetragonal Dipyramid

4. Tetragonal Scalenohedron {120}

The tetragonal scalenohedron is a more complex form with faces that are not parallel to the crystallographic axes. It is formed by faces intersecting all three axes. The projection diagram shows a more complex polyhedron. The symmetry elements include the four-fold rotation axis and mirror planes.

Tetragonal Scalenohedron

5. Tetragonal Pedion {001}

The tetragonal pedion represents the basal pinacoid, which is a flat face perpendicular to the c-axis. It is essentially the top and bottom faces of the tetragonal prism. The projection diagram shows a simple rectangular face.

Tetragonal Pedion

Combinations of Forms

Minerals often exhibit combinations of these basic forms, leading to more complex crystal habits. For example, a mineral might display a prism with pyramidal terminations, or a dipyramid with scalenohedral faces. The specific combination of forms depends on the growth conditions and the relative development of different faces.

Conclusion

In conclusion, the tetragonal crystal system exhibits a variety of crystal forms due to its unique symmetry elements. The tetragonal prism, pyramid, dipyramid, scalenohedron, and pedion represent the fundamental building blocks of tetragonal crystals. Understanding these forms and their projection diagrams is crucial for mineral identification and interpreting the crystallographic properties of minerals within this system. The combination of these forms leads to a diverse range of crystal habits observed in nature.

Answer Length

This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.

Additional Resources

Key Definitions

Crystal Form
A crystal form is a set of symmetrically equivalent faces of a crystal. It represents a specific geometric shape that is characteristic of a particular crystal structure.
Holohedral Class
A holohedral class is a crystal class that possesses all the symmetry elements characteristic of its crystal system. The normal class of the tetragonal system is holohedral.

Key Statistics

Approximately 25% of known minerals crystallize in the tetragonal system (data as of 2020, based on Mindat.org).

Source: Mindat.org

The tetragonal system is the 4th most common crystal system, following cubic, hexagonal, and orthorhombic (based on data from the International Mineralogical Association).

Source: International Mineralogical Association (IMA)

Examples

Zircon

Zircon (ZrSiO4) is a common tetragonal mineral found in igneous and metamorphic rocks. It often exhibits a combination of prism and pyramidal forms, resulting in characteristic tetragonal crystals.

Frequently Asked Questions

What is the difference between a crystal form and a crystal habit?

A crystal form refers to the geometric shape of a set of symmetrically equivalent faces, while crystal habit describes the overall external appearance of a crystal, which can be influenced by growth conditions and may not always reflect the underlying crystal form.

Topics Covered

GeologyMineralogyCrystallographyCrystal SystemsMineral IdentificationSymmetry