Introduction to Crystallography

Crystallography Introduction

• Matter exists in three states: gases, liquids, and crystals.
• Gases have no fixed volume or shape, liquids have a fixed volume but not a fixed shape while crystals have both a fixed volume and shape.
• Gases have high kinetic energy and weak intermolecular forces, liquids have lower kinetic energy and stronger intermolecular forces, and crystals have very low kinetic energy and strong permanent intermolecular interactions, resulting in a highly ordered structure.

Crystallization or Crystallisation

• Crystallization is the process of forming a solid where atoms or molecules become highly organized into a crystal structure.
• Methods for crystal formation include precipitation from solution, freezing, and deposition from a gas.
• A crystal has a fixed chemical structure and a specific crystal arrangement.

Crystallography

• Crystallography studies the crystalline state of solid materials.
• It investigates the arrangement of atoms in crystals and their physical and chemical properties.
• It includes topics on crystal synthesis and growth.

Crystal Growth

• Crystals grow from supersaturated solutions, supercooled melts, and vapors.
• The growth process is typically divided into two steps: Nucleation and Growth.
• Nucleation involves atoms coming together to form a nuclei with a periodic 3-dimensional array and growth involves the accretion of atoms to the existing crystal faces.
• Factors influencing crystal growth rate include temperature, pressure, and saturation degree.
• Crystals may be single crystals or aggregates (polycrystals).
• Single crystal growth occurs when only one nucleus is formed, while polycrystalline growth occurs from multiple nuclei in a random fashion.

Atomic Arrangement

• Crystalline solids have a periodic arrangement of atoms with a definite repetitive pattern.
• Non-crystalline or amorphous solids have a random arrangement of atoms.
• The periodicity of atoms in crystalline solids is described via a lattice.

The Crystalline State

• Crystals' outward appearance can vary widely.
• Many crystals exhibit smooth faces and regular geometric shapes if growth conditions are ideal.
• Cleavage is a phenomenon where crystal fragments have similar shapes with smooth faces, typical for crystals such as salt (NaCl).
• Crystals display specific colors depending on direction due to optical absorption; this is called pleochroism.
• The hardness is a characteristic feature of crystals, determined using materials like steel needles.

Fundamentals of Morphology

• Morphology studies the external shape of crystals.
• Morphology is related to the crystal structure, where crystal faces are parallel to sets of lattice planes and edges are parallel to lattice lines.
• The habit describes the relative sizes of the crystal faces.
• Habit classifications include: equant, planar, tabular, prismatic, and acicular.

Crystal Structure

• To form a crystal from a lattice, the lattice points must be occupied by atoms, ions, or molecules which must also be identical.
• The arrangement of these atoms within a unit cell forms the basis, which repeated through translational operations forms the entire crystal lattice.

The Unit Cell

• The unit cell is the smallest repeating unit in a crystal structure.
• Unit cell types include primitive, body-centered, and face-centered.

The Lattice and Its Properties

• A space lattice is a 3-dimensional array of points with identical surroundings.
• Lattice points can be connected through vectors (written as [uvw]) indicating the periodicity in each direction.

Classification of Lattice

• Seven crystal systems exist with varying relationships between lattice parameters (a, b, c) and interaxial angles (α, β, γ).
• Within these systems, there are 14 possible ways to arrange lattice points within a unit cell, called Bravais lattices.

Crystal Systems

• Crystal systems are based on the relationship between the lattice parameters (a, b, c) and the interaxial angles (α, β, γ).
• Seven different crystal systems exist, which define and standardize the unit cells in crystal structures.

Crystal Directions

• Crystal directions are described using a notation, [uvw] (where u, v, and w are integers).
• Direction indices are obtained from the differences in the coordinate components of parallel vectors in a crystal structure.

Crystal Planes

• Crystal planes are denoted using Miller indices (hkl), derived from the reciprocals of the plane's intercepts on the crystal axes
• Planes with similar indices are grouped into a family, denoted with curly brackets {hkl}, recognizing crystallographic equivalence.