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SOLID STATE
 CHEMISTRY
COnTEnTS
•   Introduction
•   Types of solids
•   Crystal Structures
•   Elements of Symmetry
•   Bragg’s equation
•   Allotropes of carbon: Diamond, graphite &
    Fullerene
InTRODUCTIOn

Three phases of matter:
 Gas
 Liquid
 Solid
Gas
molecules




            4
Liquid
molecules




            5
Solid
molecules




            6
WHAT IS SOLID?
 • Definite shape.
 •  Definite volume.
 •  Highly incompressible.
 •  Rigid.
 •  Constituent particles held closely by strong
   intermolecular forces.
 • Fixed position of constituents.
TYPES OF SOLIDS
  Two types (based upon atomic arrangement,
  binding energy, physical & chemical
  properties):
1.Crystalline
2. Amorphous
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.
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.
TYPES OF CRYSTAL STRUCTURES
    •   Ionic crystals
    •   Covalent crystals
    •   Molecular crystals
    •   Metallic crystals
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.
   AB2 types.
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.
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.
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.
LAWS OF SYMMETRY

• Plane of symmetry
• Centre of symmetry
• Axis of symmetry.
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
Planes of symmetry
Rectangular plane of   Diagonal plane of
symmetry: 3            symmetry: 6
axis of symmetry
Four-fold axis of   Three-fold axis of
symmetry: 3         symmetry: 4
axis & centre of
              symmetry
Two-fold axis of   Centre of symmetry: 1
symmetry: 6
tyPes of cubic crystals
  Four types:
  1.Simple or primitive type
  2. Body-centered
  3. Face-centered
  4. End face-centered
Simple or primitive type (sc)   Body-centered cell (bcc)
Face-centered cell (fcc)   End face-centered cell
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
No of atoms per unit cell= 8 x 1/8 = 1
No of atoms per unit cell= 8 x 1/8 = 1
e.g.Polonium
52% of the space is occupied by the atoms
No of atoms present per unit cell
                 = (8 x 1/8 ) + (1 x 1) = 2
No of atoms per unit cell= (8 x 1/8) +1 = 2
e.g. CsCl, CsBr
68% of the space is occupied by the atoms
No of atoms present per unit cell

               = (8 x 1/8 ) + (6 x 1/2) = 4
e.g. NaCl, NaF, KBr, MgO
74% of the space is occupied by the atoms
of atoms present per unit cell

                   = (8 x 1/8 ) + (2 x 1/2) = 2
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)
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
stRuctuRal analysis by
   Radius Ratio Rule
S.NO.     RADIUS       CO-ORDINATION      SHAPE        EXAMPLE
          RATIO           NUMBER
 1.     0.0 – 0.155          2         Linear          HF-
 2.     0.155–0.225          3         Triangular      B2O3, BN
                                       planar
 3.     0.225– 0.414         4         Tetrahedral     ZnS, SiO4-4
 4.     0.414– 0.732         6         Octahedral      NaCl
 5.     0.732 – 1.0          8         Body-centered   CsCl
                                       cubic
bRaVais lattices

• Unit cell parameters:
 Lengths a, b & c.
 Angles α, β & γ.

• Total crystal lattices: 7

• Total Bravais lattices: 14
cRystal systems with unit
    cell paRameteRs
S.No.   System         Cell         Crystal     Bravais     Min. Sym.
                       Dimensions   Angles      Lattices    Elements

1.      Cubic          a=b=c        α=β=γ=90ْ   sc, fcc,    3-fold axes: 4
                                                bcc = 3     4-fold axes: 3




2.      Orthorhombic   a≠b≠c        α=β=γ=90ْ   sc, fcc,    2-fold axes: 3
                                                bcc, efcc
                                                =4


3.      Tetragonal     a=b≠c        α=β=γ=90ْ   sc, bcc= 2 4-fold axis: 1
S.No.     System          Cell       Crystal       Bravais        Min. Sym.
                       Dimensions    Angles        Lattices       Elements

 4.      Monoclinic     a≠b≠c       α = γ = 90ْ   sc, efcc = 2   2-fold axis: 1
                                      β ≠ 90ْ

 5.       Triclinic     a≠b≠c       α≠β≠γ≠ 90ْ      sc = 1       1-fold axis: 1



 6.      Hexagonal      a=b≠c       α = β = 90ْ     sc = 1       6-fold axis: 1
                                     γ = 120ْ

 7.     Rhombohedral    a=b=c       α=β=γ≠ 90ْ      sc = 1       3-fold axis: 1
         or Trigonal
examples of diffeRent
       cRystal systems
S.No.   System                     Example
1.      Cubic                      NaCl, KCl, CaF2, Cu, ZnS, CsCl, Cu2O
2.      Orthorhombic               BaSO4, KNO3, MgSiO3, K2SO4, CdSO4,
                                   AgBr
3.      Tetragonal                 SnO2, TiO2, ZrSiO4
4.      Monoclinic                 CaSO4.2H2O, monoclinic S
5.      Triclinic                  CuSO4.5H2O, NaHSO4, H3PO3
6.      Hexagonal                  PbI2, Mg, Cd, Zn, ZnO, BN, SiO2, HgS,
                                   CdS
7.      Rhombohedral or Trigonal   Graphite, ICl, Al2O3, calcite (CaCO3), As,
                                   Sb, Bi
Cubic lattice
Orthorhombic lattice
Tetragonal lattices
Monoclinic lattice
Triclinic lattice
Hexagonal lattice
Rhombohedral (Trigonal) lattice
stRuctuRes of impoRtant
    ionic compounds
  1. AB type: NaCl (rock salt)
              CsCl
              ZnS (zinc blende / sphalerite)

  2.   AB2 type: CaF2 (fluorite)

                   TiO2 (rutile)

                   SiO2
Structure of NaCl (Rock salt)
• 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 sodium
                        choRide
Cubic unit cell:
smallest repeatable unit
Structure of CsCl




• bcc type.
• Co-ordination number 8:8.
• Number of atoms/unit cell:1
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
Structure of CaF2
                 Ca+

            F-




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

*Note: All the compounds of AB2 type follow the same pattern.
Structure of K2O
                       O -2
                 Na+




• fcc type.
• Co-ordination number: 4:8
  4 for cation
  8 for anion
Structure of important
  covalent compoundS
 1.Diamond
 2. Graphite
Diamond
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.
3d- structure of diamond
Graphite
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
•   sp2 hybridisation with one electron left over.
•   Specific gravity 2.2
•   Electrical conductor
•   Metallic lustre
•   Used as good lubricant.
2d- structure of graphite
fullureneS
Important points about Fullurenes
  • Discovered in 1985 as C60.
  • 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.
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 sp2-hybridized.
• Used:
 as photoresistant.
 in the preparation of super-conductors.
 in optical devices.
 in batteries as charge carriers.
BraGG’S eQuation
X-ray
Tube                                                                Detector
             Incident radiation             “Reflected” radiation         1

                                                                          2


                            θ                θ

                                X       Z
                                    Y
              d



                                                  Transmitted radiation
   Beam 2 lags beam 1 by XYZ = 2d sin θ

   so                 2d sin θ = nλ                         Bragg’s Law

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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
  • 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.  AB2 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 Diagonal plane of symmetry: 3 symmetry: 6
  • 19. axis of symmetry Four-fold axis of Three-fold axis of symmetry: 3 symmetry: 4
  • 20. axis & centre of symmetry Two-fold axis of Centre of symmetry: 1 symmetry: 6
  • 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. 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 CO-ORDINATION SHAPE EXAMPLE RATIO NUMBER 1. 0.0 – 0.155 2 Linear HF- 2. 0.155–0.225 3 Triangular B2O3, BN planar 3. 0.225– 0.414 4 Tetrahedral ZnS, SiO4-4 4. 0.414– 0.732 6 Octahedral NaCl 5. 0.732 – 1.0 8 Body-centered CsCl cubic
  • 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 Crystal Bravais Min. Sym. Dimensions Angles Lattices Elements 1. Cubic a=b=c α=β=γ=90ْ sc, fcc, 3-fold axes: 4 bcc = 3 4-fold axes: 3 2. Orthorhombic a≠b≠c α=β=γ=90ْ sc, fcc, 2-fold axes: 3 bcc, efcc =4 3. Tetragonal a=b≠c α=β=γ=90ْ sc, bcc= 2 4-fold axis: 1
  • 39. S.No. System Cell Crystal Bravais Min. Sym. Dimensions Angles Lattices Elements 4. Monoclinic a≠b≠c α = γ = 90ْ sc, efcc = 2 2-fold axis: 1 β ≠ 90ْ 5. Triclinic a≠b≠c α≠β≠γ≠ 90ْ sc = 1 1-fold axis: 1 6. Hexagonal a=b≠c α = β = 90ْ sc = 1 6-fold axis: 1 γ = 120ْ 7. Rhombohedral a=b=c α=β=γ≠ 90ْ sc = 1 3-fold axis: 1 or Trigonal
  • 40. examples of diffeRent cRystal systems S.No. System Example 1. Cubic NaCl, KCl, CaF2, Cu, ZnS, CsCl, Cu2O 2. Orthorhombic BaSO4, KNO3, MgSiO3, K2SO4, CdSO4, AgBr 3. Tetragonal SnO2, TiO2, ZrSiO4 4. Monoclinic CaSO4.2H2O, monoclinic S 5. Triclinic CuSO4.5H2O, NaHSO4, H3PO3 6. Hexagonal PbI2, Mg, Cd, Zn, ZnO, BN, SiO2, HgS, CdS 7. Rhombohedral or Trigonal Graphite, ICl, Al2O3, calcite (CaCO3), As, Sb, Bi
  • 48. stRuctuRes of impoRtant ionic compounds 1. AB type: NaCl (rock salt) CsCl ZnS (zinc blende / sphalerite) 2. AB2 type: CaF2 (fluorite) TiO2 (rutile) SiO2
  • 49. Structure of NaCl (Rock salt) • 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.
  • 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 CaF2 Ca+ F- • fcc type. • Co-ordination number: 8:4 (8 for cation, 4 for anion) *Note: All the compounds of AB2 type follow the same pattern.
  • 54. Structure of K2O O -2 Na+ • fcc type. • Co-ordination number: 4:8 4 for cation 8 for anion
  • 55. Structure of important covalent compoundS 1.Diamond 2. Graphite
  • 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
  • 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 • sp2 hybridisation with one electron left over. • Specific gravity 2.2 • Electrical conductor • Metallic lustre • Used as good lubricant.
  • 61. 2d- structure of graphite
  • 63. Important points about Fullurenes • Discovered in 1985 as C60. • 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 sp2-hybridized. • Used:  as photoresistant.  in the preparation of super-conductors.  in optical devices.  in batteries as charge carriers.
  • 65. BraGG’S eQuation X-ray Tube Detector Incident radiation “Reflected” radiation 1 2 θ θ X Z Y d Transmitted radiation Beam 2 lags beam 1 by XYZ = 2d sin θ so 2d sin θ = nλ Bragg’s Law