solid state

Solid State

Solid state:

1. Crystalline: - Particles arranged in a different geometric pattern in 3D in short as well as long range order. (True Solid)

2. Amorphous: - No regular arrangement of particles and only short range exists. (Pseudo Solid)

Classification of Crystalline Solids:

1. Ionic - Constituent particles are ions (cations or anions). Due to electrostatic forces of attraction they are tightly held together, example: NaCl,

2. Molecular: - Molecules are the constituent particles. Exist in three different forms: -

a. non polar molecular solids: - constituent particles are polar molecules like H2, Cl2, I2,

b. polar molecular solids: - constituent particles are polar molecules like HCl, SO2

c. Hydrogen-bonded molecular solids: - constituent particles are the molecules which contain hydrogen atom linked to a highly electronegative atom small in size such as F,O and N. Example: - H2O, NH3,

3. Covalent or Network Solids: - Constituent particles are non metal atoms example: SiC, Diamond, Graphite

4. Metallic Solids: - constituent particles are positively charged metal ions and free electrons.

Space Lattice/ Crystal Lattice/ Unit Cell

Crystal lattice: - Regular arrangement of constituent particles (atoms, ions or molecules) of a crystal in a 3D dimensional space.

Unit Cell: Smallest 3D portion of a complete space lattice which when repeated over and again in different directions produces the complete space lattice.

Unit cell is of two types

1. Primitive (simple unit cell): - The unit cells in which the constituent particles are present only at the corners

2. Non-primitive: - The unit cells in which the constituent particles are present not only at the corners of the unit cells but also at some other positions are called non-primitive unit cells or centred unit cells. It is of three types: -

a. Face centred: corners and at each face

b. End Centred: - corners and at opposite face

c. Body Centred: - corners and at the centre of the unit.

Cubic is most symmetrical while triclinic is the most unsymmetrical system.

Coordination No. : number of its nearest neighbours.

Calculation of no. of particles per unit cell of a cubic crystal system

Simple cubic unit cell: - total no. of spheres = 8,

every sphere shares its 1/8th portion into the cube.

Hence total no. of spheres inside the cube = 1/8 x 8 = 1 sphere

Face Centred Cubic: - total no. of spheres = 8 corner + 6 faces.

Contribution by atoms on the corners = 1/8 x 8 =1

Contribution by atoms on the faces = 1/2 x 6 = 3

Number of atoms present in the unit cell= 1+3 = 4

Body Centred: total no. of spheres = 8 corner + 1 body centre

Contribution by 8 atoms present on the corners = 1/8 x 8 = 1

Contribution by the atom present within the body = 1

Number of atoms present in the unit cell = 1+1=2

Closed packing in crystals

1. close packing in one dimension:- OOOOOOOOOOOOOOOOOO

2. closed packing in two dimension: -

it is two types: -

a. AAAAAA: - Square close packing

b. ABABAB: - Hexagonal close packing

3. closed packing in 3D:-

a. 3D close packing from two dimensional square close packed layers

b. 3D close packing from two dimensional hexagonal close packed layers

Square close packing in 3D

hexagonal close packing in 3D

Tetrahedral void: void surrounded by four spheres:

(Radius of tetrahedral void= 0.225R) = cation occupying tetrahedral void r+ = 0.225 r-

Octahedral void: void surrounded by six spheres.

(Radius of Octahedral void = 0.414R) = cation occupying the octahedral void r+ = 0.414 r-

No. of octahedral voids = total no. of spheres in the unit cell

No. of tetrahedral voids = 2 x total no. of spheres in the unit cell

cubic close packing means face centred packing means hexagonal close packing = total no. of spheres are 4 = octahedral voids will be 4= tetrahedral voids will be 8.

Packing efficiency

simple cubic = 52.4% (Relation of Edge and Radius a=2r or r = 0.5 a)

Face centred = 74% (Relation of Edge and Radius √2a=4r or simply we can write a = 2√2 r or r = 0.3535a)

body Centred = 68% (Relation of Edge and Radius a = 4r/√3 or r = 0.433a)

Simple Cubic

face centred efficiency

body centred

Imperfections or Defects

1. Point Defect: Deviation is from a point or an atom in the lattice.

a. Stoichiometric defects: - also called intrinsic defect or thermodynamic defect

i. Vacancy Defect: - Decrease in density.

ii. interstitial defect: - constituent particles present in interstitial sites. Non-ionic solids show this type of defect

iii. Schottky defect - I. High Coordination No. II. small difference in the size of cation and anion. Example NaCl, KCl, AgBr, CsCl. (Density decreases)

iv. Frenkel Defect: - Dislocation defect. Ion missing from its site and occupies interstitial position. Low Coordination no. and large difference in size of cation and anion. Example AgCl, AgBr, AgI, ZnS. Density remains same.

b. Non-Stoichiometric Defects:

i. Metal excess: I. anion vacancies II. presence of extra cations in the interstitial sites.

ii. Metal deficiency: FeO, FeS

c. Impurity Defects: Foreign atom occupies lattice site. (Doping)

2. Line Defect: Deviation is in the entire row of the lattice points.

Q. The energy gaps in the energy band diagrams of a conductor, semiconductor and insulator are E1, E2, and E3. Arrange them increasing order.

Ans. The energy gap in a conductor is zero, in a semiconductor is ≈1eV and in an insulator is ≥3eV .

∴ E1=0,E2=1eV,E3≥3eV

∴ E1<E2<E3

MCQs