Unit 1: Crystallography Practicals

Introduction to Practical Crystallography

This practical unit focuses on understanding the external 3D geometry of crystals. The core concept is that a crystal's internal atomic arrangement is expressed externally through its faces and symmetry. Your goal is to be able to identify the symmetry elements in a crystal model and represent its 3D form in 2D using stereographic projection. This practical is based on the theory from GEL-DSC-102.

Study of Crystal Symmetry Elements

Symmetry elements are imaginary geometric operations that describe the regularity of a crystal's form. In the lab, you will use wooden or plastic crystal models to find these elements.

The Three Main Symmetry Elements

1. Axis of Symmetry (Rotation Axis):
   • What it is: An imaginary line through the crystal's center. When the crystal is rotated around this axis, it appears identical more than once in a 360° turn.
   • Types:
     • 2-fold (Diad): Looks the same every 180° (2 times).
     • 3-fold (Triad): Looks the same every 120° (3 times).
     • 4-fold (Tetrad): Looks the same every 90° (4 times).
     • 6-fold (Hexad): Looks the same every 60° (6 times).
   • How to find it: Hold the model between your fingers (at opposite faces, edges, or corners) and rotate it to see how many times it repeats.
2. Plane of Symmetry (Mirror Plane):
   • What it is: An imaginary flat plane that divides the crystal into two identical halves, where one half is the mirror image of the other.
   • How to find it: Imagine slicing the crystal with a "mirror." If the half on one side reflects perfectly onto the half on the other, you've found a plane.
3. Center of Symmetry (Inversion Center):
   • What it is: An imaginary point in the center of the crystal. Any line drawn from a face or corner through the center will emerge at an identical point on the opposite side.
   • How to find it: Check if every face has an identical, inverted, parallel face on the opposite side of the crystal. A cube has a center; a tetrahedron does not.

Crystal Systems, Normal Classes, and Forms

A Form is a set of identical crystal faces that are related by symmetry (e.g., the 6 identical faces of a cube). The Normal Class (or Holohedral Class) of each system is the class with the highest possible symmetry.

Summary of Normal Classes and Common Forms

Stereographic Projection

This is the main practical exercise. A stereographic projection is a 2D map that accurately represents the 3D angular relationships of crystal faces and symmetry elements.

Practical Objective

To plot the poles (imaginary lines perpendicular to each crystal face) onto a 2D circle (the stereogram). This allows you to visualize all crystal faces and their symmetry on a single diagram.

Tools Needed

• A Wulff Net: A circular grid of latitude and longitude lines.
• Tracing paper and a thumb tack.
• A protractor and ruler.

Step-by-Step Guide (General)

1. Setup: Place the tracing paper over the Wulff Net, secured at the center with the tack. Draw the basic circle (called the primitive circle).
2. Orient the Crystal: Imagine the crystal at the center of a sphere. The vertical c-axis exits at the top (North Pole) and the a/b axes are on the horizontal (Equator) plane.
3. Plotting Faces (Poles):
   • A face on the top of the crystal (e.g., (001)) plots as a dot (•) at the center.
   • A face on the bottom (e.g., (00-1)) plots as a small circle (○) at the center.
   • Faces on the horizontal/vertical sides (e.g., (100), (010)) plot on the outer primitive circle.
   • Inclined faces plot inside the circle. You'll measure their angles (rho, phi) and use the Wulff net to find their precise location.
4. Plotting Symmetry:
   • Symmetry axes are marked at their exit points with symbols (■ for 4-fold, ▲ for 3-fold, etc.).
   • Symmetry planes are drawn as bold lines (either straight diameters or curved great circles).