FUNDAMENTAL CONCEPTS: UNIT CELLS, METALLIC CRYSTALS, CRYSTAL SYSTEMS

Hexagonal Close-Packed (Hcp);

• a reduced- sphere unit cell for this structure, which is termed

Crystalline

material is one in which the atoms are situated in a repeating or periodic array over large atomic distances;

Crystalline

• That is, long-range order exists, such that upon solidification, the atoms will position them- selves in a repetitive three-dimensional pattern, in which each atom is bonded to its

nearest-neighbor atoms

Crystal Structure

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

Atomic Hard-Sphere

• When describing crystalline structures, atoms (or ions) are thought of as being

solid spheres having well-defined diameters. This is termed the

Lattice

is used in the context of crys- tal structures;

Lattice

• means three-dimensional array of points coinciding with atom positions (or sphere centers).

Unit Cell

• in describing crystal structures, it is often convenient to sub-

divide the structure into small repeat entities called

Unit Cell

• cell is the basic structural unit or building block of the crystal structure and defines the crystal structure by virtue

of its geometry and th

face-Centered cubic (FCC)

• The crystal structure found for many metals has a unit cell of cubic geometry, with atoms located at each of the corners and the centers of all the cube faces. It is aptly

Coordination Number And The Atomic Packing Factor (Apf).

• Two other important characteristics of a crystal structure are the

Atomic Packing

Factor (Apf)

• is the sum of the sphere volumes of all atoms within a unit cell (as-

suming the atomic hard-sphere model) divided by the unit cell volume—that is,

Body-Centered Cubic

(Bcc)

Another 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.

Polymorphism.

• Some metals, as well as nonmetals, may have more than one crystal structure, a phe- nomenon known as

Allotropy.

• When found in elemental solids, the condition is

often termed

Lattice Parameters

• The unit cell geometry is completely defined in terms of six parameters: the three edge lengths a, b, and c, and the three interaxial angles a, b, and g.