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

Liquid molecules

Solid molecules

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): Crystalline 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 symmetry: 3 Diagonal plane of symmetry: 6

Axis of symmetry Four-fold axis of symmetry: 3 Three-fold axis of symmetry: 4

Axis & centre of symmetry Two-fold axis of symmetry: 6

Types of cubic crystals Four types: Simple or primitive type Body-centered Face-centered End face-centered

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

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

Simple cube No of atoms per unit cell= 8 x 1/8 = 1

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

Simple cubic arrangement e.g.Polonium 52% of the space is occupied by the atoms

Body centered cubic lattice 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

Body centered cubic lattice e.g. CsCl, CsBr 68% of the space is occupied by the atoms

Face-centered cubic lattice No of atoms present per unit cell = (8 x 1/8 ) + (6 x 1/2) = 4

Face-centered cubic lattice e.g. NaCl, NaF, KBr, MgO 74% of the space is occupied by the atoms

End face-centered cubic lattice No 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 RATIO CO-ORDINATION NUMBER SHAPE EXAMPLE 1. 0.0 – 0.155 2 Linear HF- 2. 0.155–0.225 3 Triangular planar B2O3, BN 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 cubic CsCl

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 Dimensions Crystal Angles Bravais Lattices Min. Sym. Elements 1. Cubic a = b = c α=β=γ=90ْ sc, fcc, bcc = 3 3-fold axes: 4 4-fold axes: 3 2. Orthorhombic a ≠ b ≠ c sc, fcc, bcc, efcc = 4 2-fold axes: 3 3. Tetragonal a = b ≠ c sc, bcc= 2 4-fold axis: 1

Rhombohedral or Trigonal S.No. System Cell Dimensions Crystal Angles Bravais Lattices Min. Sym. Elements 4. Monoclinic a ≠ b ≠ c α = γ = 90ْ β ≠ 90ْ sc, efcc = 2 2-fold axis: 1 5. Triclinic α≠β≠γ≠ 90ْ sc = 1 1-fold axis: 1 6. Hexagonal a = b ≠ c α = β = 90ْ γ = 120ْ 6-fold axis: 1 7. Rhombohedral or Trigonal a = b = c α=β=γ≠ 90ْ 3-fold axis: 1

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 AB type: NaCl (rock salt) CsCl ZnS (zinc blende / sphalerite) AB2 type: CaF2 (fluorite) TiO2 (rutile) SiO2 A2B type: K2O (antifluorite)

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 fcc type. Co-ordination number: 8:4 (8 for cation, 4 for anion) *Note: All the compounds of AB2 type follow the same pattern. Ca+ F-

Structure of K2O fcc type. Co-ordination number: 4:8 4 for cation 8 for anion O -2 Na+

Structure of important covalent compounds Diamond 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 Beam 2 lags beam 1 by XYZ = 2d sin  so 2d sin  = n Bragg’s Law