D. B. Sirdeshmukh

Atomistic properties of solids

Introduction.- Crystal growth.- Crystallography.- Diffraction of radiation by crystals.- Crystal structure determination.- Cohesion.- Tensor nature of crystal properties.- Mechanical properties.- Thermal properties.- Lattice vibrations.- Dielectric properties.- Pyro-, Piezo- and ferroelectricity.- Optical properties of insulators.- Defects in crystals: I Point defects.- Defects in crystals: II Dislocations.- The other crystalline states (quasi crystals, nano crystals, polycrystals, thin films, liquid crystals).

Mechanical Properties of Solids

As we proceed along,we will see that the elastic properties of solids have twofold importance. Firstly,they indicate the mechanical strength of the solid. Secondly,they are very important in understanding the nature of the interatomic forces and in the analysis of lattice vibrations.

Diffraction of Radiation by Crystals (Principles and Experimental Methods)

What is the nature of X-rays? Do crystals have a regular internal structure which is responsible for their regular external forms? These questions vexed crystallographers and physicists for many years. Laue’s discovery of X-ray diffraction in 1912 answered both the questions: X-rays are short wavelength electromagnetic waves and crystals have a regular internal structure; further, the wavelength of X-rays and the interatomic spacing in crystals are of the same order. Besides answering these questions, the discovery of X-ray diffraction opened up a new field of crystal structure determination.

Principles of Crystal Structure Determination

The principles and experimental methods of diffraction of radiation by crystals were discussed in the preceding chapter. In this chapter, we shall discuss the application of these principles to the determination of crystal structure. By “structure” we mean (1) the shape of the unit cell, i.e. the crystal system, (2) the size of the unit cell, i.e. the unit cell parameters, (3) the contents of the unit cell, i.e. the number of formula units per unit cell, (4) the symmetry of the internal atomic arrangement, i.e. the space group and (5) the atomic coordinates.

Other Crystalline Forms

Solids, liquids and gases are the three states of matter. Among solids, we have the crystalline solids and the amorphous solids. So far, we have considered the properties of crystalline solids. While Mohanty [1] calls liquid crystals the fourth state of matter, Dhar [2] suggests that even powders may be treated as a state of matter different from solids and fluids. Dhar [2] raised the broad issue of classifying matter in three states and pointed out the difficulties in making a clear-cut distinction. He suggested that any matter whose behaviour differs substantially from solids and fluids may be classified as a separate state of matter.

Defects in Crystals II: Dislocations

It was realised quite early that materials, particularly metals, can undergo permanent deformation (plastic deformation) at low stresses. A study of this intriguing phenomenon led to the discovery of dislocations. It was found that apart from providing an explanation for plastic deformation, dislocations play a role in various other aspects of crystal behaviour like crystal growth, hardness, fracture, thermal properties, etc. The subject of dislocations is thus of considerable importance.

Piezo-, Pyro- and Ferroelectricity

In the preceding chapter, we discussed aspects of dielectric behaviour which are common for all insulators. Some electric properties are displayed only by restricted groups of insulators. These are piezo-, pyro- and ferroelectricity. The common feature in these crystals is that they lack a centre of symmetry. Symmetry aspects of these properties are discussed by Nye [1] and Sirotin and Shaskoslaya [2].

Optical Properties of Insulators

In crystals, the refractive index is direction-dependent. It is isotropic in cubic crystals and anisotropic in crystals of all other symmetries. This anisotropy gives rise to the property of birefringence. Crystals show other interesting properties like photoelasticity (piezo-optic effect), electro-optic effect and optical activity. Lasers provide radiation with intense power. This facilitates observation of nonlinear optical effects, the most important among them being harmonic generation.

Defects in Crystals I (Point Defects)

An ideal crystal is defined as an infinite arrangement of atoms in three dimensions which satisfies certain symmetry conditions; such an array is called a crystal lattice. An essential feature of an ideal crystal lattice is that the environment of an atom in the crystal is identical to the environment of any other equivalent atom. But defects (or imperfections) do occur in crystals. An imperfection is any deviation from a regular lattice. These imperfections may be classified according to their dimensions.

Tensor Nature of Physical Properties

A striking feature of physical properties of crystals is their dependence on direction or anisotropy. Some properties (like the density or specific heat) are independent of direction or isotropic in all crystals. They are called scalar properties. There are a few other properties like thermal conductivity or dielectric constant which are isotropic in only cubic crystals but anisotropic in non-cubic crystals. On the other hand, elastic properties are anisotropic even in cubic crystals. This anisotropy of crystal properties arises out of their tensor nature.1