Introduction to Crystallography

Crystallography

• Matter exists in three states: gas, liquid, and crystal
• Gases have high kinetic energy, adopt both volume and shape of container, and have weak attractive forces between molecules
• Liquids have constant volume, adopt shape of container, and molecules have weaker kinetic energy than gases; attractive forces allow molecules to touch, but not maintain fixed positions.
• Crystals maintain their shape and volume regardless of container. When the temperature falls below freezing, kinetic energy is low, molecules are permanently bonded, and a three-dimensional framework of attractive forces forms resulting in a regular ordered structure.

Introduction

• All matter is composed of atoms, ions, or molecules
• Crystals have a specific arrangement of atoms
• Morphology studies the external shape of a crystal (faces and edges)
• Crystal structure is the internal structure of a crystal.
• Crystallography studies the laws governing the crystalline state of solid materials, atomic arrangements in crystals, and physical/chemical properties, synthesis, and crystal growth.

Crystallization

• Crystallization is the process by which a solid forms, where atoms or molecules are highly organized into a crystal structure
• Ways crystals form include precipitating from a solution, freezing, and deposition from a gas

Crystal Growth

• Crystals grow from supersaturated solutions, supercooled melts, or vapors
• Nucleation: atoms come together to form a three-dimensional periodic array of atoms (nucleus), attracting more atoms forming more planes
• Growth: existing lattice planes continue to grow, slow growth rates are larger, and rapid growth rates are smaller, crystallisation rates are affected by temperature/pressure/saturation degree of the solution.
• Single crystal: a nucleus forms, growing into a single crystal
• Polycrystal results: many nuclei form simultaneously.

Atomic Arrangement

• Crystalline: atoms arranged in a repeating periodic pattern
• Amorphous: random arrangement of atoms; no repeating pattern
• Crystalline solids can be described as a network of points called a lattice.

Crystalline State

• Crystal appearance is variable
• Properties: smooth faces, regular geometric shapes, cleavage (similar fragments with similar shapes), color (dependent on optical absorption), and hardness.

Fundamentals of Morphology

• Morphology studies the external shape or habit of a crystal.
• Form: collection of faces that characterize a crystal
• Habit describes the relative size of faces (equant, planar/tabular, prismatic/acicular).

Crystal Structure

• A lattice is a three-dimensional array of points with identical surroundings to form a crystal.
• Identical objects occupy lattice points in a repeating pattern
• The basis is the arrangement of atoms in a unit cell
• Lattice + Basis = Crystal Structure

The Unit Cell

• The smallest repeating unit in a crystal structure
• Types of unit cells: primitive/simple, body-centered, and face-centered.

The Lattice and Its Properties

• Points in a 3-D lattice have identical surroundings.
• Line, plane, and space lattices are formed, from a lattice point
• Translation is the operation used to create a lattice.
• Lattice translation: a line lattice is generated and written as [uvw] (some times called vectors).

Classification of Lattice

• Seven crystal systems
• Fourteen Bravais lattices

Crystal Systems

• Cubic, tetragonal, rhombohedral, hexagonal, orthorhombic, monoclinic, and triclinic
• Specific relationships between the cell dimensions (a, b, c) and angles (α, β, γ)

Point Groups

• Groups of point symmetry operations which leave at least one point fixed.

Space Groups

• Generated when translations are applied to point groups
• 230 unique shapes

Point Coordinates

• Coordinates define the position of points in unit cells using lattice vectors a, b, and c.
• Coordinates are expressed as fractions from the origin

Crystal Directions

• Directions described by coordinates of a point on the vector, passing through the origin (u, v, w), expressed in brackets [uvw]
• Equivalent directions are those that have the same direction indices which are called a family or form, and enclosed in angle brackets <>

Crystal Planes

• Intercepts of a plane on the crystallographic axes give rise to indices hkl. This is reciprocated and reduced to the smallest integers and enclosed in parentheses (hkl)
• Equivalent planes are those with the same Miller indices and are denoted as {hkl}

Explore the fascinating world of crystallography, where matter is studied in its crystalline state. This quiz covers the states of matter, the structure of crystals, and the properties that distinguish solids from liquids and gases. Test your knowledge on the arrangement of atoms and the morphology of crystals.