Introduction to Crystallography

Crystallography

• Crystallography studies the arrangement of atoms in solids, specifically crystals.
• Matter exists as solids, liquids, and gases.
• Gases occupy the volume and shape of their container; molecules move quickly and have high kinetic energy; forces between molecules are weak.
• Liquids have constant volume but adapt the shape of their container; molecules are in contact, but not fixed; temperature decrease converts gas to liquid, decreasing kinetic energy.
• Crystals maintain both shape and volume; molecules are rigidly bonded in a three-dimensional structure; interactions are strong; permanent interactions create a regular ordered arrangement; and temperature below freezing point makes kinetic energy small enough for molecules to become permanently attached to each other.

Introduction

• All matter is composed of atoms, ions, or molecules.
• The state of matter depends on the kinetic energy of particles and the attractive forces between them.

Crystallization

• The process where a solid forms; atoms/molecules are highly organized into a crystal structure.
• Ways a crystal forms: precipitation from solution, freezing, and deposition directly from gas.
• A crystal has a fixed chemical structure and specific crystal arrangement.

Crystal Growth

• Two-step process:
  • Nucleation: Atoms/molecules initially aggregate to form a small nucleus.
  • Growth: Nucleus draws in additional particles; lattice planes form with periodicity.
• Crystal growth rates affected by temp, pressure, and degree of saturation.
• Single crystal: A single nucleus or few grow separately, forming large single crystal.
• Polycrystal: Multiple nuclei grow together, disturbing crystal faces and forms, resulting in a polycrystalline material.

Atomic Arrangement

• Crystalline solids: atoms arranged with a definite repetitive pattern.
• Amorphous solids: atoms arranged randomly.
• The arrangement of atoms in crystalline solids characterized by a network of points in space called lattice.

The Crystalline State

• Crystals vary in appearance; properties include:
  • Regular geometric shapes; smooth faces.
  • Cleavage: If split, fragments have similar shapes with smooth faces.
  • Color: Color perceived depends on the crystal's optical absorption in different directions (pleochroism).
  • Hardness: Crystals can be scratched to make a deep hollow.

Fundamentals of Morphology

• Morphology: the study of the external shape and form of a crystal.
• Crystal form: total collection of faces that characterize a particular crystal
• Habit: relative sizes of crystal faces (equant, planar, tabular, prismatic, acicular).

Crystal Structure

• Lattice points occupied by atoms/ions/molecules.
• Basis: Arrangement of atoms within a unit cell.
• Lattice translations: reproduce the arrangement throughout the entire lattice, creating the crystal structure.
• Lattice+Basis=Crystal structure

The Unit Cell

• Smallest repeating unit of a crystal structure.
• Types of unit cells:
  • Primitive/simple: atoms only at corners.
  • Body-centered: atoms at corners and center.
  • Face-centered: atoms at corners and faces center.

The Lattice and Its Properties

• Space lattice: three-dimensional array of points with identical surroundings.
• Line lattice: develop lattice concepts based on points from a line.
• Plane lattice: develop concepts based on the points in a plane.
• Space lattice: 3-dimensional array of points, each has identical surroundings.
• Vectors define positions of points in space with translation.
• Vectors notation: [uvw] = miller indices.

Crystal Systems

• Seven fundamental crystal systems based on shape and relationships between axes.
• Cubic, Tetragonal, Rhombohedral or Trigonal, Hexagonal, Orthorhombic, Monoclinic, Triclinic

Bravais Lattices

• Fourteen distinct lattice arrangements (Bravais lattices) that can occur in the seven crystal systems.

Point and Space Groups

• Point group: set of symmetry operations that leave at least one point in a structure unchanged; symmetries of external form of crystal.
• Space group: combining point group symmetries with translation symmetries; symmetries of internal structure of crystals.
• Relationship between point and space groups: point groups describe possible forms, space groups describe complete structure.

Point Coordinates

• Position of a point in a unit cell using coordinate distances (from x, y, and z axes) in terms of lattice vectors a, b, and c.

Crystal Directions

• Directions in a crystal described by vector components (u, v, w).
• Indices enclosed in brackets [uvw]
• Directions [uvw] are crystallographically equivalent

Crystal Planes

• Planes in a crystal described by Miller indices (hkl). Reciprocal of intercepts of plane on crystal axes.
• Indices defined by smallest integer multiples
• Family of planes: set of equivalent planes sharing similar Miller indices {hkl}

Explore the fascinating study of crystallography, which examines how atoms are arranged in solids, particularly in crystals. Understand the characteristics of different states of matter—solids, liquids, and gases—and how kinetic energy influences their behavior. This quiz will challenge your knowledge on the fundamentals of matter and crystallization.