Solid state chemistry

1. SOLID STATE
CHEMISTRY

2. COnTEnTS
•Introduction
•Types of solids
•Crystal Structures
•Elements of Symmetry
•Bragg’s equation
•Allotropes of carbon: Diamond, graphite &
Fullerene

3. InTRODUCTIOn
Three phases of matter:
Gas
 Liquid
 Solid

4. Gas
molecules
4

5. Liquid
molecules
5

6. Solid
molecules
6

7. WHAT IS SOLID?
•Definite shape.
• Definite volume.
• Highly incompressible.
• Rigid.
• Constituent particles held closely by strong
intermolecular forces.
• Fixed position of constituents.

8. TYPES OF SOLIDS
Two types (based upon atomic arrangement,
binding energy, physical & chemical
properties):
1.Crystalline
2. Amorphous

9. CRYSTALLInE SOLIDS
• The building constituents arrange themselves in regular
manner throughout the entire three dimensional network.
• Existence of crystalline lattice.
• A crystalline lattice is a solid figure which has a definite
geometrical shape, with flat faces and sharp edges.
• Incompressible orderly arranged units.
• Definite sharp melting point.
• Anisotropy.
• Definite geometry.
• Give x-ray diffraction bands.
• Examples: NaCl, CsCl, etc.

10. AMORPHOUS SOLIDS
•Derived from Greek word ‘Omorphe’ meaning
shapeless.
•No regular but haphazard arrangement of atoms or
molecules.
• Also considered as non-crystalline solids or super-
cooled liquids.
• No sharp m.p.
• Isotropic.
• No definite geometrical shape.
• Do not give x-ray diffraction bands.
• Examples: glass, rubber, plastics.

11. TYPES OF CRYSTAL STRUCTURES
• Ionic crystals
• Covalent crystals
• Molecular crystals
• Metallic crystals

12. IOnIC CRYSTALS

• Lattice points are occupied by positive and negative ions.
•Hard and brittle solids.
• High m.p. due to very strong electrostatic forces of
attraction.
• Poor conductors of electricity in solid state but good in
molten state.
• Packing of spheres depends upon:
 presence of charged species present.
 difference in the size of anions and cations.
•Two types:
 AB types.
 AB
2
types.

13. COvALEnT CRYSTALS

• Lattice points are occupied by neutral atoms.
• Atoms are held together by covalent bonds
•Hard solids.
• High m.p.
• Poor conductors of electricity.
• Two common examples: diamond & graphite.

14. MOLECULAR CRYSTALS
•Lattice points are occupied by neutral molecules.
•The molecules are held together by vander
Waal’s forces.
•Very soft solids.
• Low m.p.
• Poor conductors of electricity.

15. METALLIC CRYSTALS
•Lattice points are occupied by positive metal ions
surrounded by a sea of mobile e
-
.
•Soft to very hard.
• Metals have high tensile strength.
• Good conductors of electricity.
• Malleable and ductile.
• Bonding electrons in metals remain delocalized over
the entire crystal.
• High density.

16. LAWS OF SYMMETRY

•Plane of symmetry
•Centre of symmetry
• Axis of symmetry.

17. ELEMEnTS OF SYMMETRY
In CUbIC CRYSTAL
• Rectangular planes of symmetry: 3
• Diagonal planes of symmetry: 6
• Axes of four-fold symmetry: 3
• Axes of three-fold symmetry: 4
• Axes of two-fold symmetry: 6
• Centre of symmetry: 1
Total symmetry elements: 23

18. Planes of symmetry
Rectangular plane of
symmetry: 3
Diagonal plane of
symmetry: 6

19. axis of symmetry
Four-fold axis of
symmetry: 3
Three-fold axis of
symmetry: 4

20. axis & centre of
symmetry
Two-fold axis of
symmetry: 6
Centre of symmetry: 1

21. tyPes of cubic crystals
Four types:
1.Simple or primitive type
2. Body-centered
3. Face-centered
4. End face-centered

22. Simple or primitive type (sc)Body-centered cell (bcc)

23. Face-centered cell (fcc) End face-centered cell

24. number of atoms Per unit
cell in a cubic lattice

•Simple cubic cell: 1atom/unit cell of sc
• Body-centered cell: 2 atoms/unit cell of bcc
• Face-centered cell: 4 atoms/unit cell of fcc
• End face-centered cell: 2 atoms/unit cell

25. No of atoms per unit cell= 8 x 1/8 = 1

26. No of atoms per unit cell= 8 x 1/8 = 1

27. e.g.Polonium
52% of the space is occupied by the atoms

28. No of atoms present per unit cell
= (8 x 1/8 ) + (1 x 1) = 2

29. No of atoms per unit cell= (8 x 1/8) +1 = 2

30. e.g. CsCl, CsBr
68% of the space is occupied by the atoms

31. No of atoms present per unit cell

= (8 x 1/8 ) + (6 x 1/2) = 4

32. e.g. NaCl, NaF, KBr, MgO
74% of the space is occupied by the atoms

33. No of atoms present per unit cell

= (8 x 1/8 ) + (2 x 1/2) = 2

34. atomic radius of a cubic lattice

•Simple cubic cell:
r = a/2
• Face-centered cubic cell:
r = a/√8
• Body-centered cubic cell:
r = √3a/4

(where a → length of cube)

35. Radius Ratio Rule
• Relation between the radius, co-ordination
number and the structural arrangement of the
molecule.
Radius ratio =
• Greater the radius ratio, larger the size of the
cation and hence the co-ordination number.
• density = (z*Ma)/Na*a^3 Ma=mass no.,
Na=avogadro, a= side length, z=no. of atoms

36. stRuctuRal analysis by
Radius Ratio Rule
S.NO. RADIUS
RATIO
CO-ORDINATION
NUMBER
SHAPE EXAMPLE
1. 0.0 – 0.155 2 Linear HF
-
2. 0.155–0.225 3 Triangular
planar
B
2
O
3
, BN
3. 0.225– 0.414 4 Tetrahedral ZnS, SiO
4
-4
4. 0.414– 0.732 6 Octahedral NaCl
5. 0.732 – 1.0 8 Body-centered
cubic
CsCl

37. bRaVais lattices
• Unit cell parameters:
Lengths a, b & c.
 Angles α, β & γ.
• Total crystal lattices: 7
• Total Bravais lattices: 14

38. cRystal systems with unit
cell paRameteRs
S.No.System Cell
Dimensions
Crystal
Angles
Bravais
Lattices
Min. Sym.
Elements
1. Cubic a = b = cα=β=γ=90ْsc, fcc,
bcc = 3
3-fold axes: 4
4-fold axes: 3
2. Orthorhombica ≠ b ≠ cα=β=γ=90ْsc, fcc,
bcc, efcc
= 4
2-fold axes: 3
3. Tetragonal a = b ≠ cα=β=γ=90ْsc, bcc= 24-fold axis: 1

39. S.No. System Cell
Dimensions
Crystal
Angles
Bravais
Lattices
Min. Sym.
Elements
4. Monoclinic a ≠ b ≠ cα = γ = 90ْ
β ≠ 90ْ
sc, efcc = 22-fold axis: 1
5. Triclinic a ≠ b ≠ cα≠β≠γ≠ 90ْsc = 11-fold axis: 1
6. Hexagonal a = b ≠ cα = β = 90ْ
γ = 120ْ
sc = 16-fold axis: 1
7.Rhombohedral
or Trigonal
a = b = cα=β=γ≠ 90ْsc = 13-fold axis: 1

40. examples of diffeRent
cRystal systems
S.No.System Example
1. Cubic NaCl, KCl, CaF
2
, Cu, ZnS, CsCl, Cu
2
O
2. Orthorhombic BaSO
4
, KNO
3
, MgSiO
3
, K
2
SO
4
, CdSO
4
,
AgBr
3. Tetragonal SnO
2
, TiO
2
, ZrSiO
4

4. Monoclinic CaSO
4
.2H
2
O, monoclinic S
5. Triclinic CuSO
4
.5H
2
O, NaHSO
4
, H
3
PO
3
6. Hexagonal PbI
2
, Mg, Cd, Zn, ZnO, BN, SiO
2
, HgS,
CdS
7. Rhombohedral or TrigonalGraphite, ICl, Al
2
O
3
, calcite (CaCO
3
), As,
Sb, Bi

41. Cubic lattice

42. Orthorhombic lattice

43. Tetragonal lattices

44. Monoclinic lattice

45. Triclinic lattice

46. Hexagonal lattice

47. Rhombohedral (Trigonal) lattice

48. stRuctuRes of impoRtant
ionic compounds
1.AB type: NaCl (rock salt)
CsCl
ZnS (zinc blende / sphalerite)
2. AB
2
type: CaF
2
(fluorite)

TiO
2
(rutile)

SiO
2


3. A
2
B type: K
2
O (antifluorite)

49. • FCC type.
• Co-ordination number 6:6.
• Calculation of no. of atoms of NaCl/unit
cell:
Cl at corners: (8 ´ 1/8) = 1
Cl at face centres (6 ´ 1/2) = 3
Na at edge centres (12 ´ 1/4) = 3
Na at body centre = 1
Unit cell contents are 4(Na
+
Cl
-
)
i.e. per each unit cell, 4 NaCl
units will be present.

Structure of NaCl (Rock salt)

50. stRuctuRe of sodium
choRide
Cubic unit cell:
smallest repeatable unit

51. Structure of CsCl
•bcc type.
• Co-ordination number 8:8.
• Number of atoms/unit cell:1

52. Structure of ZnS

•fcc type.
• Co-ordination number

4:4.
• Calculation of no. of
atoms/unit cell:
Total S = 8x1/8 + 6x1/2 = 4
Total Zn = 4
Hence, total ZnS = 4

53. Structure of CaF
2
•fcc type.
• Co-ordination number: 8:4
(8 for cation, 4 for anion)
*Note: All the compounds of AB
2
type follow the same pattern.


F-
Ca
+

54. Structure of K
2
O

•fcc type.
•Co-ordination number: 4:8
4 for cation
8 for anion

Na
+
O
-2

55. Structure of important
covalent compoundS
1.Diamond
2. Graphite

56. Diamond

57. Structure of diamond
•fcc type.
•Tetrahedral
•C-C bond length = 1.34A
•Refractive index = 2.4
•High dispersive power of light
•Non-conductor of electricity
•3d network
• Hardest substance ever known.
• Used as abrasive.

58. 3d- structure of diamond

59. Graphite

60. Structure of Graphite
•One of the softest substances ever known.
•2-d hexagonal layer structure
•C-C bond length = 1.45A
•Inter layer distance = 3.54A
•Sliding nature
•sp
2
hybridisation with one electron left over.
•Specific gravity 2.2
•Electrical conductor
•Metallic lustre
•Used as good lubricant.

61. 2d- structure of graphite

62. fullureneS

63. Important points about Fullurenes
• Discovered in 1985 as C
60
.
• Consists of spherical, ellipsoid or cylindrical
arrangement of dozens of C-atoms.
• 3 types:
 Spherical: Also called ‘bucky balls’. Molecule
of the year 1991 by Science magazine.
 Cylindrical: C nanotubes or buckytubes.
 Planar.

64. Structure of fullurenes
•60 C-atoms arranged in pentagons and hexagons.
• 7Å in diameter.
• Soccer-ball shaped molecule with 20 six-membered & 12
five-membered rings.
•Each pentagon is surrounded by five hexagons.
• No two pentagons are adjecent.
• Each carbon is sp
2
-hybridized.
•Used:
 as photoresistant.
in the preparation of super-conductors.
 in optical devices.
 in batteries as charge carriers.

65. BraGG’S eQuation
X
Y
Z
d
Incident radiation “Reflected” radiation
Transmitted radiation
q q
1
2
X-ray
Tube Detector
Beam 2 lags beam 1 by XYZ = 2d sin q
so 2d sin q = nl Bragg’s Law