Crystallography: Understanding Crystal Structures and Symmetry

Crystalline and Amorphous Bodies

Crystalline body: Atoms and molecules are in perfect order, obeying physical laws.

Amorphous body: Atoms and molecules are in disorder and do not obey any law.

Crystallography Fundamentals

Crystallography: The science that studies crystals as geometric polyhedra.

Types of Crystal Definitions

• Euhedral: Completely defined edges and faces.
• Subhedral: Partially defined edges and faces.
• Anhedral: No defined edges or faces.

Crystal Size Classifications

• Microcrystalline: Tiny crystals, visible only under a microscope.
• Cryptocrystalline: Crystals only visible with X-rays.

Objectives of Crystallography

1. Study of crystals.
2. Study of crystal systems.
3. Study of mineral aggregates (twins).

Crystal Symmetry Elements

• Center of Symmetry: The center of the crystal, equidistant from all points on the crystal's surface.
• Axis of Symmetry: An imaginary axis passing through the crystal's center, around which the crystal can be rotated 360° to repeat its appearance.
• Plane of Symmetry: An imaginary plane passing through the center of symmetry that divides the crystal into two equal, mirror-image parts.

Crystal Symmetry Rules

1. A q-fold axis of symmetry passing through the center of symmetry determines an axis perpendicular to it.
2. If n q-fold axes are located in the same plane, a higher-order axis perpendicular to that plane and those axes is determined.

Morphological Relations of Crystals

Includes concepts like:

• Euler's theorem.
• Space lattices.
• Crystalline Forms:
  • Pedion
  • Pinacoid
  • Sphenoid
  • Domo
  • Prisms
  • Pyramids
  • Trapezohedra
  • Rhombohedra
  • Scalenohedra
  • Dipyramids

Crystallographic Values

Crystallographic Planes

A plane passing through two crystallographic axes that divides space into 8 or 12 parts. When a plane coincides with a crystallographic plane of symmetry, it is called a diametral or diagonal plane.

Crystallographic Axes

A coordinate system used to determine the position of crystal faces relative to the crystallographic space.

Angles

The angles formed by each pair of crystallographic axes.

Parameters

The intersection points a face makes with respect to the crystallographic axes.

Types of Faces

• Pinacoidal: A face that intersects only one crystallographic axis.
• Prismatic: Faces parallel to one crystallographic axis and intersecting the other two.
• Pyramidal: Faces that cut all three crystallographic axes.

Crystallographic Notations

Analytical representations of crystal faces with reference to the crystallographic axes.

Zone Indices

The set of parallel faces oriented in the same direction.

Zone Axis

An imaginary axis passing through the crystal's center of symmetry, parallel to the faces within a zone.

Zone Map

A plane perpendicular to the zone axis.

Glass Properties

Glass is a three-dimensional geometric polyhedron with internal order. It transitions from solid to liquid or gaseous states under specific temperature, pressure, and time conditions.