Crystal Structure and Mechanical Properties

Crystal Structure

• Atoms, ions, or molecules are spatially arranged in a crystal structure.
• Crystal structure can be 2D or 3D.

2D Crystalline Structure

• Adjacent atoms form a unit cell.
• Example of 2D crystalline structure is shown.

3D Crystalline Structures

Simple (Primitive) Cubic (SC)

• Consists of one lattice point on each corner of the cube.
• Each atom at a lattice point is shared equally between eight adjacent cubes.
• Unit cell contains one atom (1/8 × 8).
• Coordination number (nearest neighbor) is 6.

Body-Centred Cubic (BCC)

• Has one lattice point in the centre of the unit cell in addition to the eight corner points.
• Net total of 2 lattice points per unit cell (1/8 × 8 + 1).
• Examples: Cr, α-Fe, Mo.
• Cube edge length, a = 4R/√3, R = a√3/4.
• Atomic packing factor (APF) = 0.68.

Face-Centred Cubic (FCC)

• Examples: Cu, Al, Ag, Au.

Interatomic Interaction

• Repulsion between atoms is related to the Pauli principle.
• Energy of the system increases abruptly when electronic clouds surrounding atoms start to overlap.
• Attractive part of the potential energy curve dominates at large distances.

Potential Energy of Interatomic Interaction

• Can be calculated from the potential energy curve.
• Depends only on the distance between the two atoms, U(r12).

Energy Units

• Electron volt (eV) is a convenient unit for atomic bonding.
• Defined as the energy lost or gained by an electron when taken through a potential difference of one volt.
• 1 eV = 1.6 × 10^-19 J.