Crystal Structure of Materials

Metals and ceramics are composed of aggregations of small grains, each of which is an individual crystal. In contrast, glasses have an amorphous or non-crystalline structure. Polymers are composed of chainlike molecules, which are sometimes arranged in regular arrays in a crystalline manner.

Basic Crystal Structure of Materials

The arrangement of atoms (or ions) in crystals can be described in terms of the smallest grouping that can be considered to be a building block for a perfect crystal. Such a grouping, called a unit cell, can be classified according to the lengths and angles involved. There are seven basic types of unit cell, three of which are shown in Fig. 1.

Fig. 1.

If all three angles are 90 and all distances are the same, the crystal is classed as cubic. But if one distance is not equal to the other two, the crystal is tetragonal.

If, in addition, one angle is 120 while the other two remain at 90, the crystal is hexagonal. The four additional types are orthorhombic, rhombohedral, monoclinic, and triclinic.

For a given type of unit cell, various arrangements of atoms are possible; each such arrangement is called a crystal structure. Three crystal structures having a cubic unit cell are the primitive cubic (PC), body-centered cubic (BCC), and face-centered cubic (FCC) structures. These are illustrated in Fig. 2.

Fig. 2.

Note that the PC structure has atoms only at the corners of the cube, whereas the BCC structure also has one in the center of the cube. The FCC structure has atoms at the cube corners and in the center of each surface. The PC structure occurs only rarely, but the BCC structure is found in a number of common metals, such as chromium, iron, molybdenum, sodium, and tungsten. Similarly, the FCC structure is common for metals, as in silver, aluminum, lead, copper, and nickel.

The hexagonal close-packed (HCP) crystal structure is also common in metals. Although the unit cell is the one shown in Fig. 1, it is useful to illustrate this structure by using a larger grouping that forms a hexagonal prism, as shown in Fig. 2.

Two parallel planes, called basal planes, have atoms at the corners and center of a hexagon, and there are three additional atoms halfway between these planes, as shown. Some common metals having this structure are beryllium, magnesium, titanium, and zinc.

A given metal or other material may change its crystal structure with temperature or pressure, or with the addition of alloying elements. For example, the BCC structure of iron changes to FCC above 910C, and back to BCC above 1390C.

These phases are often called, respectively, alpha iron, gamma iron, and delta iron, denoted α-Fe, γ -Fe, and δ-Fe. Also, the addition of about 10% nickel or manganese changes the crystal structure to FCC, even at room temperature.

Similarly, HCP titanium is called α-Ti, whereas β-Ti has a BCC structure and occurs above 885◦C, although it can also exist at room temperature as a result of alloying and processing.

More Complex Crystal Structure of Materials

Compounds formed by ionic or covalent bonding, such as ionic salts and ceramics, have more complex crystal structures than elemental materials. This is due to the necessity of accommodating more than one type of atom and to the directional aspect of even partially covalent bonds.

However, the structure can often be thought of as an elaboration of one of the basic crystal structures. For example, NaCl is an FCC arrangement of Cl ions with Na+ ions at intermediate positions, so these also form an FCC structure that is merged with the one for the Cl ions. Many important ionic salts and ceramics have this structure, including oxides such as MgO and FeO, and carbides such as TiC and ZrC.

In the diamond cubic structure of carbon, half of the atoms form an FCC structure, and the other half lie at intermediate positions, as required by the tetragonal bonding geometry, also forming an FCC structure.

Another solid with a diamond cubic structure is SiC, in which Si and C atoms occupy alternate sites in the same structure. The ceramic Al2O3 has a crystal structure with a hexagonal unit cell, with aluminum atoms occurring in two-thirds of the spaces available between the oxygen atoms. Many ceramics have even more complex crystal structures than these examples.

Intermetallic compounds also have crystal structures that range from fairly simple to quite complex. An example of one of the simpler ones is Ni3Al, which has an FCC structure, with aluminum atoms at the cube corners and nickel atoms at the face centers.

Polymers may be amorphous, in that the structure is an irregular tangle of chain molecules. Alternatively, portions or even most of the material may have the chains arranged in a regular manner under the influence of the secondary bonds between the chains. Such regions are said to have a crystalline structure. This is illustrated in Fig. 3.

Fig. 3

Defects in Crystals

Ceramics and metals in the form used for engineering applications are composed of crystalline grains that are separated by grain boundaries. This is shown for a metal in Fig. 4. Materials with such a structure are said to be polycrystalline materials. Grain sizes vary widely, from as small as 1μm to as large as 10 mm, depending on the material and its processing.

Fig. 4

Even within grains, the crystals are not perfect, with defects occurring that can be classed as point defects, line defects, or surface defects. Both grain boundaries and crystal defects within grains can have large effects on mechanical behavior.

In discussing these, it is useful to use the term lattice plane to describe the regular parallel planes of atoms in a perfect crystal, and the term lattice site to describe the position of one atom. Some types of point defects are illustrated in Fig. 5.

Fig. 5

A substitutional impurity occupies a normal lattice site, but is an atom of a different element than the bulk material. A vacancy is the absence of an atom at a normally occupied lattice site, and an interstitial is an atom occupying a position between normal lattice sites.

If the interstitial is of the same type as the bulk material, it is called a self interstitial; and if it is of another kind, it is called an interstitial impurity. Relatively small impurity atoms often occupy interstitial sites in materials with larger atoms.

An example is carbon in solid solution in iron. If the impurity atoms are of similar size to those of the bulk material, they are more likely to appear as substitutional impurities.

This is the normal situation where two metals are alloyed—that is, melted together. An example is the addition of 10 to 20% chromium to iron (and in some cases also of 10 to 20% nickel) to make stainless steel.

Line defects are called dislocations and are the edges of surfaces where there is a relative displacement of lattice planes. One type is an edge dislocation, and the other is a screw dislocation, both of which are illustrated in Fig. 6.

Fig. 6

The edge dislocation can be thought of as the border of an extra plane of atoms, as shown in (a). The dislocation line shown identifies the edge of the extra plane, and the special symbol indicated is sometimes used. The screw dislocation can be explained by assuming that a perfect crystal is cut as shown in Fig. 6(b). The crystal is then displaced parallel to the cut and finally reconnected into the configuration shown. The dislocation line is the edge of the cut and hence also the border of the displaced region.

Dislocations in solids generally have a combined edge and screw character and form curves and loops. Where many are present, complex tangles of dislocation lines may form. Grain boundaries can be thought of as a class of surface defect where the lattice planes change orientation by a large angle. Within a grain, there may also be low-angle boundaries. An array of edge dislocations can form such a boundary, as shown in Fig. 7.

crystal structure of materials
Fig. 7

Several low-angle boundaries may exist within a grain, separating regions of slightly different lattice orientation, which are called subgrains. There are additional types of surface defects.

A twin boundary separates two regions of a crystal where the lattice planes are a mirror image of one another. If the lattice planes are not in the proper sequence for a perfect crystal, a stacking fault is said to exist.

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