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University Engineering

Notes by Category University Engineering

Mechanics & Stress Analysis*
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Crystal Structures

In this notes sheet:

  1. The Hard Sphere Model

  2. Packing in Two Dimensions

  3. Packing in Three Dimensions

  4. Simple Cubic

  5. Body-Centred Cubic (BCC)

  6. Face-Centred Cubic (FCC)

  7. Hexagonal Close-Packed (HCP)

  8. Atomic Density

Understanding the molecular structure of a material is crucial in understanding how that material behaves. Many of its physical properties are directly caused and explained by its crystalline structure (known as a lattice). We define this as:

A crystalline lattice is a regular repeating pattern of atoms or molecules.

An amorphous material is one that does not display a crystalline structure. Instead, the structure is random – examples include some polymers and ceramics.

  • Some other polymers are known as semi-crystalline

The Hard Sphere Model

The Hard Sphere Model allows us to model atoms or molecules as, you guessed it, hard spheres. There are a number of conditions for this to apply:

  1. The outer electron shell must be full

  2. The remaining electrons must be distributed rotationally symmetrically

  3. Electron clouds of neighbouring atoms do not overlap much or at all

For the outer shell of electrons to be full, metals must lose electrons, while non-metals must gain electrons. This means they are actually ions.

Packing in Two Dimensions

It is impossible to arrange circles in such a way that there are no unfilled spaces between them:

Squares, rectangles, triangles, and hexagons, however, can be arranged into a complete lattice:

  • The primitive unit cell is the smallest cell that can be regularly repeated throughout the str