The Structure of Crystalline Solids

illustrating how the spots (i.e., the diffraction pattern) in (a) are produced

a light-weight automobile wheel that is made of magnesium

___ material is one in which the atoms are situated in a repeating or periodic array over large atomic distances—that is, long-range order exists, such that upon solidification, the atoms will position themselves in a repetitive three- dimensional pattern, in which each atom is bonded to its nearest neighbour atoms.

of the material, the manner in which atoms, ions, or molecules are spatially arranged.

constituent particles are arranged in a regular fashion containing short range as well as long range order

crystalline particles are NOT arranged in any regular fashion; they may be at the most some range order

All metals Most Ceramics Some polymers

Rubber Glass Plastics Polymers

___ is used in the context of crystal structures; in this sense ___ means a three-dimensional array of points coinciding with atom positions (or sphere centres)

small repeat entities

Three relatively simple crystal structures are found for most of the common metals

It contains 4 atoms in a unit cell. The atomic packing factor for ___ is 0.74 which means it has 26% void space per unit cell.

a = 2R√2 where: a = atomic lenght weight R = atomic radius

Two other important characteristics of a crystal structure

For metals, each atom has the same number of nearest-neighbour or touching atoms

is the sum of the sphere volumes of all atoms within a unit cell (assuming the atomic hard-sphere model) divided by the unit cell volume

common metallic crystal structure also has a cubic unit cell with atoms located at all eight corners and a single atom at the cube center.

The atomic packing factor for BCC is 0.68 which means it has 32% void space per unit cell. Contain 2 atoms in a unit cell

The equivalent of 6 atoms is contained in each unit cell; one-sixth of each of the 12 top and bottom face corner atoms, one-half of each of the 2 center face atoms, and all 3 midplane interior atoms. The atomic packing factor for HCP is 0.74 which means it has 26% void space per unit cell.

Not all metals have unit cells with cubic symmetry; the final common metallic crystal structure has a unit cell that is hexagonal