Crystal Structures

Arrangement of Atoms

Consider how atoms are arranged; atomic arrangement impacts properties

Atomic Bonds and Positioning

How many bonds per atom? How are atoms positioned with respect to each other?

Crystal

Collection of atoms or molecules that arrange themselves in a long-range ordered and periodic manner; can be crystalline or amorphous

Crystalline

Molecular structure has a repeating pattern (e.g., Quartz); usually metals (steel, brass), often ceramics (alumina), never polymers

Amorphous

No real pattern in molecular structure (e.g., Glass); rarely metals (metallic glass), often ceramics (soda glass), usually polymers (polyethylene)

Mixed Crystalline and Amorphous

Contains both crystalline and amorphous structures; never metal, often ceramic (silicon nitride), sometimes polymers (nylon)

Unit Cell

Basic structural unit of a crystal; crystals are made up of repeated unit cells; unit cells are 3D

Crystal Unit Cells

Different types include Simple Cubic, Body-Centered Cubic (BCC), Face-Centered Cubic (FCC), and Hexagonal Close-Packed (HCP)

Crystal Unit Cell Parameters

Includes Number of Atoms per Unit Cell, Coordination Number, and Atomic Packing Factor

Coordination Number

Number of nearest-neighbour atoms; based on the center atom

Atomic Packing Factor

Volume of atoms divided by unit cell volume; assumes atoms are spheres

Simple Cubic

Atoms at every corner of a cube; 1 atom per unit cell, coordination number 6, atomic packing factor 0.52, cube edge length = 2R

Body-Centered Cubic (BCC)

Atoms at all eight corners + one in the center; 2 atoms per unit cell, coordination number 8, atomic packing factor 0.68, cube edge length = 4R/√3

Face-Centered Cubic (FCC)

Atoms at all corners + 1 at each face of the cube; 4 atoms per unit cell, coordination number 12, atomic packing factor 0.74, cube edge length = r * 2 * √2

Hexagonal Close-Packed (HCP)

Atoms at corners of top/bottom faces, 2 face atoms, 3 interior atoms; 6 atoms per unit cell, coordination number 12, atomic packing factor 0.74, a = 2√(2R), c = 1.63a