06-SolidState

8/12/2019 06-SolidState

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Solid State

This is one more important chapter. More weightage questions such as passages, matching etc wereasked every year

Most important area is the ‘Unit Cell parameters and Crystal Defects’ Understanding of arrangement of atoms in cubic and hexagonal unit cell helps. Questions are expected from ‘Defects’

Seven crystal systems: The seven crystal systems are given below:

Crystal System Bravais Lattices Parameters of Unit CellIntercepts Crystal angle

1. Cubic Primitive, Face Centered, BodyCentered = 3

a = b = c α = β = γ = 90o

2. Orthorhombic Primitive, Face Centered, BodyCentered, End Centered = 4

a ≠ b ≠ c α = β = γ = 90o

3. Tetragonal Primitive, Body Centered =2 a = b ≠ c α = β = γ = 90o

4. Monoclinic Primitive, End Centered = 2 a ≠ b ≠ c α = γ = 90o, β ≠ 90o

5. Triclinic Primitive = 1 a ≠ b ≠ c α ≠ β ≠ γ ≠ 900

6. Hexagonal Primitive = 1 a = b

≠ c

α =

β = 90

0

,γ = 120o

7. Rhombohedral Primitive = 1 a = b = c α = γ = β ≠ 90o

Total = 14

Packing Fraction:

It is defined as ratio of the volume of the unit cell that is occupied by the spheres of a unit cell to the

volume of the unit cell.

i) Primitive Cubic Unit Cell:

Atoms are present at the corners of the cube. Each of the eight atoms present at the eight corners isshared amongst eight unit cells. Hence,

Number of atoms per unit cell = 8 18

1=

Atoms touch each other along edges. Hence,r = a/2

Therefore, PF = 52.0)r2(

r3

4

3

3

≈

π

.

ii) Body-Centred Cubic Unit Cell :

Besides atoms present at the corners of the cube, there is one atom in the centre of cube which belongsexclusively to this unit cell. Hence,

Number of atoms per unit cell = 8 218

1=+

Atoms touch each other along the cross diagonal of the cube. Hence

a4

3r

=



The packing fraction in this case is = 68.0

)3

r4(

r3

42

3

3

≈π×

iii) Face-Centred Cubic Unit Cell:

Besides atoms present at the corners of the cube, there are atoms at the centres of six faces, each of which is shared between two unit cells. Hence

Number of atoms per unit cell = 4

Atoms touch each other along the face diagonal. Hence a4

2r

= 74.0

)2

r4(

r3

44

fractionpacking3

3

≈

π×

=

Hexagonal Primitive Unit Cell:

Each corner atom would be common to 6 other unit cells; therefore their contribution to one unit cell would be

1/6. Therefore, the total number of atoms present per unit cell effectively is 6. The height of the unit cell 'c' is

3 / 2r4 and the lenght of the unit cell 'a' is 2r. Therefore the area of the base is equal to the area of six

equilateral triangles, = 2)r2()43(6× . The volume of the unit cell = 3 / 2r4)r2()43(6 2×× . P.F.

=

3

2r4)r2(

4

36

r3

46

2

3

××

π×

≈ 0.74

Density of Cubic Crystals: ρ =Na

Mz3 ×

×

Where z is the number of molecules (or atoms) per unit cell, 'a' is the edge length of the unit cell, M is themolar mass of the substance, and NA is Avogadro’s constant.

Crystalstructure Brief description and examples C.N

No. of formula

units per u.c

1. Rock salt(NaCl-type)

Cl− ions in CCP, Na+ ions occupy all theoctahedral voids (or vice versa)Examples Halides of Li, Na, K and Rb, AgCl,AgBr, NH4Cl etc.

Na+ - 6Cl− - 6

4

2. CsCl – type Cl− ions at the corners of a cube and Cs+ ionsin the cubic void (or vice-versa)Examples: CsCl, CsBr, CsI etc.

Cs+ - 8Cl− - 8

1

3. Zinc-blende(ZnS - type)

S2− ions in CCP, Zn+2 ions occupy alternatetetrahedral voids. i.e. only half of the totalnumber of tetrahedral voids are occupied.

Examples: ZnS, CuCl, CuBr, CuI, AgI etc.

Zn+2-4S2− - 4 4

4. Fluoritestructure

(CaF2-type)

Ca+2 ions in CCP and F− ions in all thetetrahedral voidsExamples: CaF2, SrF2, BaF2, BaCl2 etc.

Ca+2-8F− - 4

4

5. Antifluoritestructure

Negative ions in CCP and positive ions in allthe tetrahedral voidsExamples Na2O

Na+ - 4O2 - 8

4

Tetrahedral Voids And Octahedral Voids:

These voids are only found in either FCC or Hexagonal primitive unit cells.



1. On calculation, it can be found out that FCC unit cell has four octahedral voids effectively. Thenumber of octahedral voids of a unit cell is equal to the effective no. of atoms of that unit cell.

2. As there are eight corners, there are eight tetrahedral voids in a FCC unit cell, therefore the no. of tetrahedral voids is double the no. of octahedral void.

Radius Ratio:

The ratio of radii of cation and that of anion in ionic crystal is called as radius ratio .

Limiting radius ratio xr

r

=−

+ Co –

ordinationnumber Shape Examplex < 0.155 2 Linear BeF2

0.155 ≤ x < 0.225 3 Planar Triangle AlCl3

0.225 ≤ x < 0.414 4 Tetrahedron ZnS0.414 ≤ x < 0.732 4 Square planar PtCl4

2- 0.414 ≤ x < 0.732 6 Octahedron NaCl

0.732 ≤ x < 0.999 8 Body centered cubic CsCl

Point defects: When some ions are missing from ionic crystals from their theoretical latticepoint, the crystal has defected structure.

Defect due to missing of ions from theoretical lattice point is called point defect.Characteristic of point defect:

Point defect increases with increase in temperature. At absolute zero temperature, ionic crystalmay not have any defect.

n = no. of defect per unit volume = N.e–W/Rt

W = work done to produce one mole defectR = Gas constantN = No. of sites (lattice points) per cc of crystal.Point defects are of two types:

(i) Stoichiometric defect: Defects due to which overall formula of ionic compound do not change iscalled stoichiometric defect.

(ii) Non- Stoichometric defects are those due to which overall formula of compound changes.

Stoichiometric defect:

Schottky :-This defect is common in ionic compounds with high coordination number. As temperatureis increased, some vacancies are always created in crystal lattice.Ex. of crystals showing schottky defect: NaCl, KCl, NaBr etc.

Frenkel defect : This type of defect very common in compounds in which there is large differencebetween size of cation and anion. e.g.ZnS ; AgBr; etcConsequence of defects:Due to schottky defect density of crystal decreasesCrystal can conduct electricity to a small extent.Due to these defects dielectric constants of crystals may increases.

Non-stoichiometric defects:

Non stoichiometric compounds are those in which the ratio of positive and negative ions present in thecompounds differ from that indicated by their chemical formula. eg. Fe0.95O, Cu197S, etc.These non-stoichiometric compounds have defect's in addition to normal thermodynamic defects.These defects arise due to excess of metal or non-metal atoms

Model Questions



1. In the zinc blende structure, zinc ions occupy alternate tetrahedral voids and S–2 ions exist as ccp.The radii of Zn+2 and S–2 ions are 0.83Å and 1 .74 Å respectively. The distance between the two S2– ions which are on the same body diagonal is(A) 11.48 Å (B) 9.94 Å (C) 10.28 Å (D) 13.44 Å

1 C

2. A metal crystallizes into two cubic faces (FCC) and (BCC) whose unit cell lengths are 3.5 0

A and 3.00

A respectively. The ratio of densities of FCC and BCC will be(A) 1.26 (B) 3.14 (C) 2.18 (D) 4.26

2 A3. Select the correct statement(s)(A) Schottky defect is shown by CsCl (B) Frenkel defects shown by Zns(C) hcp and ccp structures have the same coordination number 12(D) On increasing pressure, coordination number of CsCl decreases to that of NaCl

3 A, B, C

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