SOLID STATE CHEMISTRY

1. SOLID STATE CHEMISTRY By Shirinaz I.Khan

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

5. Liquid molecules

6. Solid molecules

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): • Crystalline • 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 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: • Simple or primitive type • Body-centered • Face-centered • End face-centered

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

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

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

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

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

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

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

33. End face-centered cubic lattice 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

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

40. Examples of different crystal systems

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

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