The study of geometry and structure of solids is a science known as crystallography. X-rays and microscopes have substantially contributed to this area.

The atoms and molecules are held together by chemical bonds in the solids. The orientation, periodicity, and symmetries of atoms and molecules vary widely.

The arrangement of atoms may be regular as in metals or irregular as in rubber; closely packed as in metals or loosely packed as in non-metals. In this way, the solids may be grouped as under:

1. Crystalline solids
2. Non-crystalline or amorphous solids.

Structure of metals is generally crystalline. Non-metals such as plastics, rubber, ceramic, wood, organic fibers and glass etc. have amorphous structure in normal conditions.

A metal may behave as amorphous, and a non-metal can exhibit crystalline nature under specific conditions.

Silica, a non-metal, takes on the crystalline form as quartz and amorphous form such as silica glass. The high density polyethylene (HDPE), another non-metal, is almost crystalline due to its long aligned molecular chains.

Quartz, single crystal Ti, single crystal garnet and single crystal Si are examples of some mono-crystalline materials.

Steel, iron, nickel, copper, magnesium, zinc, tungsten, and gold are examples of some mono-crystalline materials.

Crystalline and Amorphous Structures

Crystalline form of solid has periodically repeated arrangement of atoms. But the solids in amorphous form do not have long range periodic repetition. However, in both of the above forms, the coordination number is almost the same.

Formation of amorphous structure is characterized by several factors enumerated as below:

1. Non-formation of three-dimensional primary bond.
2. Formation of one-dimensional chain molecule.
3. Formation of two-dimensional sheet molecule.
4. Absence of primary bonds in all the directions.
5. Weak secondary bond.
6. Non-parallel, entangled chain configuration.
7. Open network of the atomic packing.

Several factors responsible in the formation of amorphous state are:

Poor secondary bonding force: It does not allow formation of straight and parallel molecular chain during solidification of the solid from molten state.

Larger free energy: Amorphous solids possess larger free energy than crystalline solids due to which they do not crystallize. Fast rate of cooling prevents re-crystallization.

Softening with increase in temperature: Amorphous solids soften with an increase in temperature. Consequently, the crystalline and the amorphous states of solids exhibit different behavior.

Comparison  of Crystalline and Amorphous Solids

A crystalline solid

• possesses long range periodicity,
• has higher density due to closed packing of atoms,
• presents sharp diffraction pattern,
• exhibits pin-pointed melting point,
• has well-defined crystal structure and geometries.

Whereas an amorphous solid

• possesses entangled chain without periodicity,
• has lower density as the packing of atoms is zigzag,
• does not show sharpness of diffraction pattern,
• melts over a range of temperatures,
• has varying structure and geometries.

Mono-crystalline and Poly-crystalline Crystal Structures

 Materials, on the basis of their structure, may be classified into two groups viz.

1. Crystalline, and
2. Amorphous or Non-crystalline

Generally metals are crystalline, and non-metals are amorphous. But this is not a rule. Plastics a non-metal may be obtained in almost crystalline form.

Crystalline solids have periodically repeating arrangement of atoms. Such solids can be further sub-classified as follows:

1. Mono-crystalline
2. Polycrystalline

Most of the materials in engineering applications are polycrystalline.

A mono-crystalline material has a single crystal. It finds use in specific applications. As an example, a single crystal quartz is employed in generating ultrasonic waves. We are concerned here with the geometry of crystalline materials only. The amorphous materials will be taken up in later articles.

The smallest visible part of a material is made up of large number of crystals. These crystals may be of different shapes and sizes. They generally have random orientation.

Each crystal is further composed of basic structural item called unit cell. Unit cells are of different types. These unit cells contain atoms arranged in a very systematic pattern.

Space Lattice

A space lattice is defined as an infinite array of points in three-dimensional space in which each point is identically located with respect to the other.

Concept of space lattice is helpful in understanding the crystal structure of existing materials, and also those materials which are likely to be developed in future.

Figures (i) and (ii) depict two-dimensional lattice. A two-dimensional lattice may have a square array or a rectangular array.

In above Figures, a and b are the fundamental translation vectors, and c is generated vector. If points are located such that a = b, the arrangement will be known as square lattice.

If location of the points is such that a ≠ b then the arrangement will be called rectangular lattice.

Figure (iii) shows an array on the front plane, right side and top planes. These may be called square or rectangular array on the basis of geometry whether a = b or a ≠b.

Repeated translation of three non-coplanar vectors results into a three-dimensional space lattice. A three-dimensional space lattice may then have either a

• cubic array when a = b = c, or
• non-cubic array

The smallest unit formed by joining these identically spaced points is referred to as a unit cell. One such unit cell, shown in above figure, may be cubical or non-cubical depending on the dimensions of translation vectors.

 A unit cell may be conceived from its geometrical vectors a, b and c, or as marked by A in Figure (iii).

Basis

The way of filling-up of points in a space lattice by the atoms is known as Basis.

Each point may be occupied by one, two or many atoms in different solids. The space lattice when combines with the basis generates a unit cell.

Thus, space lattice + basis = unit cell

The unit cell will be called mono-atomic if one atom occupies a lattice point. When two atoms occupy a lattice point, it will make a diatomic unit cell.

Similarly the unit cell will be known as multi-atomic when too many atoms occupy a lattice point. These types of unit cells are shown in following Figures.

Here the atoms are shown separated from each other for clarity, which in actual materials are not separated. In diatomic and multi-atomic unit cells, the center of larger atom coincides with the lattice point.

The basis for some materials are given as follows:

 

Material: Polonium

Symbol: Po

Basis: 1 atom per lattice point

 

Material: Aluminum

Symbol: Al

Basis: 1 atom per lattice point

 

Material: Chromium

Symbol: Cr

Basis: 1 atom per lattice point

 

Material: Manganese

Symbol: Mn

Basis: 29 atoms per lattice point

 

Material: Protein (combination of amino acids)

Symbol:

Basis: thousands of atoms per lattice point.