Crystallography: Solid State Structures

Crystallography

• Crystallography studies the arrangement of atoms, ions, or molecules in crystalline solids.
• Matter exists in three states: gas, liquid, and solid (crystal).
• Gases have no fixed volume or shape. Molecules move rapidly with weak attractive forces.
• Liquids have fixed volume but adopt the shape of their container. Molecules touch, but have no fixed position.
• Crystals have a fixed shape and volume, regardless of the container. Attractive forces lock molecules into a fixed, regular arrangement.

Introduction

• All matter is made up of atoms, ions, or molecules.
• In a crystal, there is a three-dimensional framework of attractive interactions among molecules.
• The molecules are regularly ordered.

Crystalline VS Amorphous Solids

• Crystalline solids have an ordered internal structure. Regularly arranged atoms. Create flat faces and symmetrical shapes.
• Amorphous solids don't have a long-range ordered structure. Random arrangement of atoms. No defined shape.

Crystallization

• Crystallization is the process where atoms or molecules organize into a crystalline structure.
• Ways crystals form: precipitation from solutions, freezing, or deposition from gases.
• A crystal is a solid substance with a specific chemical structure.

Crystal Growth

• Crystals grow in two steps: Nucleation (atoms gather to form a nucleus) and growth of nucleus to crystal (atoms add to the nucleus).
• Crystal growth rate depends on temperature, pressure, and saturation level.
• Single crystals grow from individual nuclei. Polycrystals are formed from multiple nuclei that grow together.

Atomic Arrangement

• Crystalline solids have a periodic arrangement of atoms.
• Non-crystalline (or amorphous) solids have a random arrangement.
• Crystalline solid structure can be described by a network of points in space called a lattice.

The Crystalline State

• Crystals may have varying appearances.
• Some properties characteristic of crystals:
  • Smooth faces
  • Regular geometric shapes
  • Cleavage (when broken, fragments maintain similar shape)
  • Color (due to absorption of light) - pleochroism (different colors in different directions)
  • Hardness
• Crystals have different properties, including hardness, and color related to light absorption.

Morphology

• Morphology studies the external form or shape of crystals.
• Form is the totality of faces that characterize a crystal.
• Habit describes the relative size of crystal faces. (Habit types like equant, planar, tabular, prismatic, or acicular).
• Morphology of a crystal is characterized by its collection of faces.

Crystal Structure

• To form a crystal, a lattice must be occupied by atoms/ions/molecules.
• The points in a lattice are all identical.
• The arrangement of atoms in a unit cell is known as the basis.
• Lattice translations reproduce parts of the structure throughout the entire lattice.

The Unit Cell

• The smallest repeating unit in a crystal lattice.
• The arrangement of atoms within the unit cell is called the basis.
• Primitive / Simple, Body-Centered, and Face-Centered are types of unit cells.

The Lattice and its Properties

• A space lattice is a 3D array of points with repeating surroundings.
• A point in the lattice can be specified using coordinates (uvw) or vector components.
• Lattice translations reproduce atoms throughout the lattice.

Classification of Lattices

• There are 7 crystal systems with varying internal arrangements.
• Each system has a specific set of characteristics like a=b=c (cubic) and a=b≠c (tetragonal), et cetera.
• The 14 Bravais lattices are different types of unit cells within a crystalline system that can be used to describe a crystal structure.

Crystal Systems

• Seven crystal systems based on the relationships between a, b, and c (lattice parameters) and the angles between them (α, β, γ).

Crystal Directions

• Crystallographic directions are indicated by giving values of u, v, and w following the [uvw] notation. Fractions are converted to integers and reduced to the lowest terms.
• A family of directions are enclosed in angle brackets
• Use the coordinates of two points to determine the direction vector.

Crystal Planes

• Crystallographic planes are represented by (hkl) Miller indices, with h, k, and l being integers.
• Miller indices are calculated from the reciprocals of the intercepts on the crystallographic axes in terms of the unit cell parameters.

Family of Planes

• Planes with similar indices are grouped into a family, which is represented using curly braces {hkl}.

This quiz covers the fundamental concepts of crystallography, including the arrangement of atoms in crystalline solids versus amorphous solids. Explore the properties and differences of various states of matter, focusing on how molecular arrangements create distinct shapes and volumes. Test your understanding of the three-dimensional frameworks that define crystalline structures.