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Study Notes

Crystallography

Crystallography is the study of the arrangement of atoms, ions, or molecules in crystalline solids.
Matter can exist in three states: gas, liquid, and solid (crystal).
Gases adopt both volume and shape of their container, have high kinetic energy, and weak attractive forces.
Liquids have constant volume but adopt the shape of their container; attractive forces cause molecules to touch, but they don't maintain fixed positions.
Crystals have both fixed volume and shape, regardless of their container. Atoms become permanently attached below the freezing point; this forms a three-dimensional framework of attractive interactions resulting in a regularly ordered structure.
Materials can be either crystalline or amorphous:
- Crystalline materials have an ordered arrangement of atoms and exhibit regular geometric shapes.
- Amorphous materials have a random arrangement of atoms and don't form regular shapes.
Crystallization is the process where atoms or molecules organize into a crystal structure.
- Methods of crystallization include precipitation from solutions, freezing, and deposition from gas.
Crystallography is concerned with the laws governing the crystalline state of solid materials, the arrangement of atoms in crystals, and their physical and chemical properties, as well as their synthesis and growth.
Crystal growth happens in two stages:
- Nucleation: a few atoms come together to form a three-dimensional periodic array (a nucleus).
- Growth: the nucleus attracts further atoms, building new lattice planes. Rates are affected by temperature, pressure, and saturation.

Atomic Arrangement

Crystalline solids have a periodic arrangement of atoms/ions/molecules (definite repeating patterns).
Non-crystalline (amorphous) solids have a random arrangement of atoms/ions/molecules.
The periodicity of atoms in crystalline materials can be represented by a network of points in space called a lattice.

The Crystalline State

Crystals exhibit a wide range of appearances.
Characteristic properties:
- Smooth faces and geometric shapes (resulting from ideal growth conditions).
- Cleavage: breaking into fragments with similar shapes (typical of crystals).
- Color variations due to optical absorption (pleochroism).
- Hardness varies from crystal to crystal.

Fundamentals of Morphology

Morphology studies the external crystal boundary (faces and edges).
Form: the overall collection of faces characterizing a crystal.
Habit: the relative sizes of the crystal faces. Types include equant, planar/tabular, prismatic, and acicular.

Crystal Structure

Lattice: a three-dimensional array of points with identical surroundings.
Basis: the arrangement of atoms/ions/molecules at those lattice points.
Crystal structure: lattice + basis
The unit cell is the smallest repeating unit in a crystal structure. Types: primitive, body-centered, face-centered.

The Lattice and Its Properties

Periodicity along a line is written (uvw).
A crystal is formed via lattice translations.
Lattice planes, lines, and points are infinitely many in crystal structures.
A vector notation gives an atom's position as: vector ruvw = ua + vb + wc. where u, v, w are integers.

Classification of Lattice

There are 7 crystal systems. The fundamental variations of the basic unit cell were explored, and 14 Bravais lattices that can describe all possible lattice networks were found.

Crystal Systems

Cubic, tetragonal, rhombohedral, hexagonal, orthorhombic, monoclinic, and triclinic.
Different systems have specific relationships between the lengths (a, b, c) and angles (α, β, γ) of the unit cell.

Crystal Directions

Crystal directions are specified by coordinates (u, v, w) of a point on a vector. These directions can be represented using square brackets, like direction [uvw].
Directions with similar indices but in different orientations are called a '' family (e.g., <100> family includes 100, 010, and 001 directions).

Crystal Planes

Crystallographic planes are represented using Miller indices (hkl).
Miller indices are reciprocals of intercepts of a plane with the crystallographic axes.
Planes with similar indices form a family {hkl}.