Introduction to Crystallography

Crystallography

• Crystallography studies the arrangement of atoms, ions, or molecules in solids, specifically crystals.
• All matter (gas, liquid, or crystal) is composed of atoms, ions, or molecules.
• Gases fill their container and have a high kinetic energy; their attractive forces are weak.
• Liquids have constant volume but assume the shape of their container; their molecules touch but don't maintain fixed positions as temperature decreases.
• Crystals retain their shape and volume, regardless of their container. At temperatures below freezing, their attractive forces become significant, molecules become rigidly attached to each other, and a three-dimensional framework forms.
• The arrangements in crystals are regularly ordered.

Introduction to Crystallization

• Crystallization is the process of forming a solid where atoms or molecules become highly organized into a crystal structure.
• Crystallization can occur through precipitation from a solution, freezing, or deposition from a gas.
• Crystals are naturally occurring solids with distinct chemical structures and arrangements.
• Crystallography examines the laws governing the crystalline state of materials, the arrangement of atoms within crystals, and their physical and chemical properties, synthesis, and growth.

Crystal Growth

• Crystals form through nucleation and growth.
• Nucleation involves few atoms aggregating to form a basic three-dimensional structure (nucleus).
• Lattice planes form as the nucleus attracts more atoms, following the established periodicity.
• Crystal growth rate depends on temperature, pressure, and saturation level.
• Single crystals grow from a single nucleus; multiple nuclei forming crystals can intermingle and create polycrystalline structures.

Atomic Arrangement

• Crystalline solids display a repeating, ordered pattern of atoms.
• The structure of crystalline solids is defined by the lattice, a network of points defining the arrangement of atoms in a repeating pattern.
• Amorphous solids have a disordered arrangement of atoms.

The Crystalline State

• Crystals exhibit varied appearances. Common characteristics include:
  • Smooth faces and regular geometric shapes under ideal growth conditions.
  • Cleavage: when some split crystals maintain similar shapes after division.
  • Colors associated with optical absorption properties from specific directions. Plceochroism - variation in color depending on the viewing direction of the crystal.
  • Hardness: A crystal's resistance to scratching.

Fundamentals of Morphology

• Morphology studies the external characteristics of a crystal.
• Crystal form includes the total collection of faces characterizing the crystal.
• Habit refers to the relative sizes of the faces of a crystal. There are three different habits: equant ,planer or tabular and prismatic or acicular.

Crystal Structure

• To form a crystal from a lattice structure, the points of the lattice need to be occupied by atoms, ions, or molecules, all identical.
• The unit cell is the smallest repeating unit of a crystal lattice structure containing a particular pattern of atoms.

Unit Cell

• Unit cells have vectors (a,b,c) and interaxial angles (α,β,γ).
• Different types of unit cells include primitive/simple, body-centered, and face-centered.

The Lattice and Its Properties

• A lattice is a three-dimensional array of points with identical surrounding environments.
• Lattice points can be represented with indices (uvw) or [uvw].
• Lattice translations produce identical points.

Classification of Lattices

• Seven crystal systems (triclinic, monoclinic, orthorhombic, tetragonal, hexagonal, trigonal, cubic) are based on the relationships of lattice vectors.
• The 14 Bravais lattices describe the arrangement of atoms in unit cells for each crystal system.

Crystal Directions

• Directions in a crystal are represented as [uvw] indices, the components of the vector along the crystallographic axes.
• Equivalent directions share the same indices, represented using .

Crystal Planes

• Planes in crystals are identified using Miller indices (hkl), the reciprocals of the intercepts of a plane on the crystallographic axes.
• Equivalent planes share the same indices, represented using {hkl}.