Crystallography Overview

Crystallography

• Crystallography pertains to the study of crystals, their structure, properties, and formation.
• Matter exists in three states: gas, liquid, and solid (crystal).
• Gases expand to fill their containers and have weak intermolecular forces.
• Liquids have constant volume but take the shape of their container with stronger intermolecular forces than gasses.
• Crystals (solids) have a fixed shape and volume, made of atoms, ions, or molecules arranged in an ordered, 3D pattern.

Introduction

• All matter is composed of atoms, ions, or molecules.
• In a gas, particles move rapidly, have high kinetic energy, and are widely separated with weak attractions.
• In a liquid, particles touch but move past each other, have medium kinetic energy, and experience moderate attractive forces.
• In a crystal (solid), particles are strongly attracted to each other, have low kinetic energy, and form an ordered 3-D framework.

Crystallization

• Crystallization is the process where a solid forms with atoms or molecules arranged in an organized pattern, known as a crystal.
• Crystalline solids have regular geometric shapes.
• Crystallization happens through precipitation from solutions, freezing, or deposition from gasses.
• A crystal has a specific chemical structure and arrangement.

Crystal Growth

• Crystals form through two steps: nucleation and growth.
• Nucleation involves the coming together of a few atoms/molecules to form a nucleus, which is the initial small crystal structure.
• Growth involves the addition of more atoms/molecules onto the faces of the nucleus to form a larger crystal with a repeating 3D pattern.
• Factors like temperature, pressure, and saturation affect the speed of crystal growth.
• Single crystals grow from a single nucleus, while polycrystals arise from multiple nuclei that grow together.

Atomic Arrangement

• Crystalline solids have a periodic arrangement of atoms, meaning they repeat in a regular pattern.
• Amorphous solids (e.g., glass) have a random arrangement of atoms without a repeating pattern.
• The ordered arrangement of atoms in crystalline solids can be described by a network of points in space called a lattice.

The Crystalline State

• Crystals can have a wide variety of appearances and colors.
• Some crystals have distinctive cleavage patterns (splitting into smaller pieces with smooth faces) that are unique to them.
• Crystals can exhibit pleochroism, which means they absorb different colors depending on the direction the light travels through the crystal.
• The hardness of a crystal reflects its resistance to scratching.

Fundamentals of Morphology

• Morphology is the study of the external shape and form of crystals.
• The faces and edges of a crystal are the external surfaces defined by the arrangement of atoms.
• The habit describes the relative sizes of different faces of a crystal.
• Types of crystal habits include equant, planar/tabular, and prismatic/acicular.

Crystal Structure

• A space lattice is a 3D arrangement of points, each with identical surroundings.
• Crystals are formed by filling this 3D lattice of points with atoms, ions, or molecules.
• A unit cell is the smallest repeating unit within a crystal's lattice; the arrangement of the atoms within a unit cell is called the basis.
• Crystal structure forms through a combination of the lattice and the basis.

The Unit Cell

• The unit cell is the smallest repeating unit of a crystal lattice.
• Types of unit cells include primitive (simple), body-centered, and face-centered which depend on the arrangement of the atoms within the cell.

The Lattice and its Properties

-Lattice points are identical and have identical surroundings. -The periodicity along a line is defined as an inter-atomic distance.

• Generating a line, plane, and eventually, space lattice occurs with repeating operations.

Classification of Lattices

• There are seven crystal systems that identify the unique combinations of angles and lengths of lattice unit cells
• Each type of system has a defined arrangement of its lattice unit cells.
• 14 Bravais lattices describe the 14 possible ways to arrange points in a crystal structure.

Crystal Systems

• There are seven crystal systems, each defined by the angles and lengths of the unit cell axes.
• Examples: cubic, tetragonal, rhombohedral, hexagonal, orthorhombic, monoclinic, triclinic

Point and Space Groups

• Point groups describe the symmetry operations that leave a point unchanged when applied to the crystal.
• Space groups describe all symmetry operations in a crystal structure, including translations.

Point Coordinates

• The position of any point within a unit cell in a crystal can be described by coordinates (u, v, w) relative to the unit cell axes.
• Coordinates are expressed in terms of the lattice vectors.

Crystal Directions

• Crystal directions are specified by unit vectors.
• Direction indices ([uvw]) represent directions within a crystal lattice.

Crystal Planes

• Crystal planes are defined by intercepts on the crystal axes.
• Miller indices (hkl) are used to uniquely identify a plane within a crystal.

Family of planes

• A family of planes are planes that are equivalent in their shape and features, but not necessarily in the same location within the crystal structure.