# Introduction to Cubic Crystal Lattice Structures

The outstanding macroscopic properties of crystalline solids are rigidity, incompressibility and characteristic shape. All crystalline solids are composed of orderly arrangements of atoms, ions, or molecules. The macroscopic result of the microscopic arrangements of the atoms, ions or molecules is exhibited in the symmetrical shapes of the crystalline solids.

Solids are either amorphous, without form, or crystalline. In crystalline solid s the array of particles are well ordered. Crystalline solids have definite, rigid shapes with clearly defined faces. The arrangement of the atoms, ions or molecules are very ordered and repeat in 3-dimensions. Small, 3-dimensional, repeating units called unit cells are responsible for the order found in crystalline solids.

The unit cell can be thought of as a box which when stacked together in 3-dimensions produces the crystal lattice. There are a limited number of unit cells which can be repeated in an orderly pattern in three dimensions. We will explore the cubic system in detail to understand the structure of most metals and a wide range of ionic compounds.

In the cubic crystal system three types of arrangements are found;

Perhaps the simplest cubic system is the simple cubic structure. The unit cell for the simple cubic structure contains one-eighth portions of eight corner atoms to make one complete atom, molecule or ion in each unit cell. Given the radius of the atom or ion the edge length is just; edge length (a) = 2r where r is the radius of the atom or ion.

The body-centered cubic structure is built up of body-centered cubic unit cell containing two atoms in each unit cell, one atom from the eight, one-eighth portions of the eight corner atoms and one from the atom located in the center of the unit cell. In this structure the relationship between the edge length and the radius of the atom is more complicated. edge length (a) = 4r/SQRT(3)

The last unit cell is the face-centered cubic cell. This cell contains 4 atoms per unit cell. Three atoms from the six faces, one-half of each face atom is contained in a particular unit cell, and one atom from the eight, one-eighth portions of the eight corner atoms. The relationship of the edge length to the atoms radius is; edge length (a) = 2*SQRT(2)r

Ionic crystals are composed of charged species and the ions of the compound have different sizes. There are several ionic structures which you should be familiar.

The NaCl structure which is common to LiCl, KBr, RbI, MgO, CaO and AgCl. This structure can be viewed two different ways: face-centered cubic in chloride ions with sodium ions in every octahedral hole, or as two interpenetrating face-centered cubic structures.

The CsCl structure has a simple cubic arrangement of chlorides ions with the cesium ion in the body-centered hole (cubic hole).

ZnS, or zinc blende, has a face-centered cubic arrangement of sulfide ions with zinc ions in every other tetrahedral hole.

Calcium fluoride has a face-centered structure of calcium ions with fluoride ions in every tetrahedral hole.

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