Chapter 1 - Solid state

Chapter 1 SOLID STATE

1. The following are the characteristic properties of the solid state:

(i) They have definite mass, volume and shape.

(ii) Intermolecular distances are short.

(iii) Intermolecular forces are strong.

(iv) Their constituent particles (atoms, molecules or ions) have fixed positions and can only

oscillate about their mean positions.

(v) They are incompressible and rigid.

2. Solids can be classified as crystalline or amorphous on the basis of the

nature of order present in the arrangement of their constituent particles.

Distinction between Crystalline and Amorphous Solids

Property	Crystalline	Amorphous
Shape	Definite characteristic geometrical shape	Irregular shape
Anisotropy	Anisotropic in nature	Isotropic in nature
Order in arrangement of constituent particles	Long range order	Only short range order.
Melting point	Melt at a sharp and characteristic temperature	Gradually soften over a range of temperature

3. Classification of Crystalline Solids

Molecular Solids : Molecules are the constituent particles of molecular solids. These are further sub divided into the following categories:

Non polar Molecular Solids: They comprise of either atoms, for example, argon and helium or the molecules formed by non polar covalent bonds for example H2, Cl2 and I2. In these solids, the atoms or molecules are held by weak dispersion forces or London forces. These solids are soft and non-conductors of electricity.

Polar Molecular Solids: The molecules of substances like HCl, SO2, etc. are formed by polar covalent bonds. The molecules in such solids are held together by relatively stronger dipole-dipole interactions. These solids are soft and non-conductors of electricity.

Hydrogen Bonded Molecular Solids: The molecules of such solids contain polar covalent bonds between H and F, O or N atoms. Strong hydrogen bonding binds molecules of such solids like H2O (ice). They are non-conductors of electricity.

Ionic Solids :

Ions are the constituent particles of ionic solids. Such solids are formed by the three dimensional arrangements of cations and anions bound by strong coulombic (electrostatic) forces. Since the ions are not free to move about, they are electrical insulators. However, in the molten state or when dissolved in water, the ions become free to move about and they conduct electricity.

Metallic Solids

Metals are orderly collection of positive ions surrounded by and held together by a sea of free electrons. These electrons are mobile and are evenly spread out throughout the crystal. These free and mobile electrons are responsible for high electrical and thermal conductivity of metals. Metals are highly malleable and ductile.

Covalent or Network Solids

Covalent bonds are strong and directional in nature, therefore atoms are held very strongly

at their positions. Such solids are very hard and brittle. They are insulators and do not conduct electricity. Diamond and silicon carbide are typical examples of such solids. Graphite is soft and a conductor of electricity.

4. Crystal Lattices and Unit Cells

A regular three dimensional arrangement of points in space is called a crystal lattice. There are only 14 possible three dimensional lattices. These are Bravais lattices.

Unit cell is the smallest portion of a crystal lattice which,when repeated in different directions, generates the entire lattice.

5. Primitive and Centred Unit Cells

Unit cells can be broadly divided into two categories, primitive and centred unit cells.

(a) Primitive Unit Cells

When constituent particles are present only on the corner positions of a unit cell, it is called as primitive unit cell.

(b) Centred Unit Cells

When a unit cell contains one or more constituent particles present at positions other than corners in addition to those at corners, it is called a centred unit cell. Centred unit cells are of three types:

(i) Body-Centred Unit Cells: Such a unit cell contains one constituent particle (atom, molecule or ion) at its body-centre besides the ones that are at its corners.

(ii) Face-Centred Unit Cells: Such a unit cell contains one constituent particle present at the centre of each face, besides the ones that are at its corners.

(iii).End-Centred Unit Cells: In such a unit cell, one constituent particle is present at the centre of any two opposite faces besides the ones present at its corners.

6. Number of Atoms in a Unit Cell

a. Simple unit cell :Each cubic unit cell has 8 atoms on its corners, the total number of atoms in one unit cell is 8X 1/8 = 1atom.

b. Body-Centred Cubic Unit Cell : A body-centred cubic (bcc) unit cell has an atom at each of its corners and also one atom at its body centre.

The total number of atoms in one unit cell is 8X 1/8 ! = 2 atoms.

c. A face-centred cubic (fcc) unit cell contains atoms at all the corners and at the centre of all the faces of the cube.

The total number of atoms in one unit cell is 8X 1/8 + 6X 1/2 = 4 atoms.

7. Voids

The vacant sites or empty space in close packed structures are called interstitial voids.The voids surrounded by sixspheres in octahedral positions is called an octahedral void.

Tetrahedral voids are formed when the centres of four spheres are joined.

Let the number of close packed spheres be N, then:

The number of octahedral voids generated = N

The number of tetrahedral voids generated = 2N

8. Calculations Involving Unit Cell Dimensions

Suppose, edge length of a unit cell of a cubic crystal determined by X-ray diffraction is a, d the density of the solid substance and M the molar mass. In case of cubic crystal:

Volume of a unit cell = a3

Mass of the unit cell = number of atoms in unit cell × mass of each atom = z × m

(Here z is the number of atoms present in one unit cell and m

is the mass of a single atom)

Mass of an atom present in the unit cell:m = M/ N A(M is molar mass)

Therefore, density of the unit cell = mass of unit cell / volume of unit cell

= zM /a³ N_A

9. Imperfections in Solids

Any departure from perfectly ordered arrangement of atoms or ions in crystal is called a defect or imperfection.

Defects are of two types – point defects and line defects.

Point defects are the deviations from ideal arrangement around a point in a crystalline substance.

Line defects are the deviations from ideal arrangement in entire row of lattice points.

Types of Point Defects

Point defects can be classified into three types : (i) stoichiometric defects (ii) impurity defects and (iii) non-stoichiometric defects.

(a) Stoichiometric Defects

These are the point defects that do not disturb the stoichiometry of the solid. They are also called intrinsic or thermodynamic defects. Basically these are of two types, vacancy defects and interstitial defects.

i. Vacancy Defect: When some of the lattice sites are vacant, the crystal is said to have vacancy defect. This results in decrease in density of the substance.

(ii) Interstitial Defect: When some constituent particles (atoms or molecules) occupy an interstitial site, the crystal is said to have interstitial defect. This defect increases the density of the substance.

(iii) Frenkel Defect: This defect is shown by ionic solids. The smaller ion (usually cation) is dislocated from its normal site to an interstitial site.

Frenkel defect is also called dislocation defect.It does not change the density of the solid. Frenkel defect is shown by ionic substance in which there is a large difference in the size of ions, for example, ZnS, AgCl, AgBr and AgI due to small size of Zn2+ and Ag+ ions.

(iv) Schottky Defect: It is basically a vacancy defect in ionic solids. In order to maintain electrical neutrality, the number of missing cations and anions are equal. Schottky defect decreases the density of the substance.

Schottky defect is shown by ionic substances in which the cation and anion are of almost similar sizes.

For example, NaCl, KCl, CsCl and AgBr. It may be noted that AgBr shows both, Frenkel as well as Schottky defects.

(b) Impurity Defects

Foreign atoms can occupy interstitial sites in a crystal. If the impurity ions have different valence state than that of the host ions, vacancies are created. Example : AgCl crystals can be doped with. CdCl₂.

(c) Non-Stoichiometric Defects

Defects which produce non stoichiometry in compounds are called non stoichiometric defects.

These defects are of two types: (i) metal excess defect and (ii) metal deficiency defect.

1. Metal Excess Defect : Metal excess defect due to anionic vacancies:

The defect arises due to the missing of some anions from their lattice sites leaving holes which are occupied by electrons. The anion sites occupied by electrons are called F – centres. All F- centre compounds ae coloured.

(ii)Metal excess defect due to the presence of extra cations at interstitial sites: Extra positive ions occupy interstitial positions in the lattice. Equivalent number of electrons are also accommodated in the neighbourhod interstitial positions to maintain electrical neutrality. Example are ZnO, CdO and Fe₂O₃.

(ii) Metal Deficiency Defect

There are many solids which are difficult to prepare in the stoichiometric composition and contain less amount of the metal as compared to the stoichiometric proportion. In crystals of FeO some Fe2+ cations are missing and the loss of positive charge is made up by the presence of required number of Fe3+ ions.

10. Electrical Properties

Solids can be classified into three types on the basis of their conductivities.

1. Conductors: The solids with conductivities ranging between 104 to 107 ohm–1m–1 are called conductors. Metals have conductivities in the order of 107 ohm–1m–1 are good conductors.

2. Insulators : These are the solids with very low conductivities ranging between 10–20 to 10–10 ohm–1m–1.

3. Semiconductors : These are the solids with conductivities in the intermediate range from 10–6 to 104 ohm–1m–1.

11. Conduction of Electricity in Metals

A conductor may conduct electricity through movement of electrons or ions.

The conductivity of metals depend upon the number of valence electrons available per atom.

Conduction of Electricity in Semiconductors

In case of semiconductors, the gap between the valence band and conduction band is small. Therefore, some electrons may jump to conduction band and show some conductivity. Electrical conductivity of semiconductors increases with rise in temperature, since more electrons can jump to the conduction band. Substances like silicon and germanium show this type of behaviour and are called intrinsic semiconductors.

The conductivity is increased by adding an appropriate amount of suitable impurity. This process is called doping. Doping can be done with an impurity which is electron rich or electron deficient as compared to the intrinsic semiconductor silicon or germanium. Such impurities introduce electronic defects in them.

1. Electron – rich impurities

Doping of Si or Ge with a group 15 element like P or As containing 5 electrons in outermost shell introduce one extra electron per impurity atom into the structure. This will enhances the semi conductivity. These are called n – type semiconductors.

2. Electron – deficit impurities

Doping of Si orGe with a group 13 element like Ga or In containing only 3 electrons in outermost shell produce a positive hole into the structure. These are called p – type semiconductors.

12. Magnetic Properties

On the basis of their magnetic properties, substances can be classified into five categories: (i) paramagnetic (ii) diamagnetic (iii) ferromagnetic (iv) antiferromagnetic and (v) ferrimagnetic.

1. Paramagnetism: Paramagnetic substances are weakly attracted by a magnetic field. They are magnetised in a magnetic field in the same direction. They lose their magnetism in the absence of magnetic field. Paramagnetism is due to presence of one or more unpaired electrons which are attracted by the magnetic field. O2, Cu2+, Fe3+, Cr3+ are some examples of such substances.
2. Diamagnetism: Diamagnetic substances are weakly repelled by a magnetic field. H2O, NaCl and C6H6 are some examples of such substances. They are weakly magnetised in a magnetic field in opposite direction.

(iii) Ferromagnetism: A few substances like iron, cobalt, nickel,gadolinium and CrO2 are attracted very strongly by a magnetic field. Such substances are called ferromagnetic substances.Besides strong attractions, these substances can be permanently magnetised.

3. Antiferromagnetism: Substances like MnO showing antiferromagnetism have domain structure similar to ferromagnetic substance, but their domains are oppositely oriented and cancel out each other's magnetic moment.

(v) Ferrimagnetism: Ferrimagnetism is observed when the magnetic moments of the domains in the substance are aligned in parallel and anti-parallel directions in unequal numbers (Fig. 1.32 c). They are weakly attracted by magnetic field as compared to ferromagnetic substances.