The Muppet’s Guide to:

1. The Muppet’s Guide to: The Structure and Dynamics of Solids 2. Simple Crystal Structures

2. Bonding or EA is bonding dependent Already looked at vdW and ionic Figure adapted from Callister, Materials science and engineering, 7th Ed.

3. Covalent Bond Short range interaction between pairs of atoms Highly directional in space Number of bonds proportional to number of valence electrons Conduction band (semi-conductors or insulators) Valence band Figure adapted from Callister, Materials science and engineering, 7th Ed.

4. Covalent Bond Relies on orbital overlap (hybridisation) Total wavefunction must be anti-symmetric s - bond p - bond Bonding orbital formed from overlap of symmetric wavefunctions, Electrons must be anti-symmetric Figure adapted from hyperphysics

5. Hybridisation

6. Covalent Structures Graphite and Graphene– sp2 Methane – sp3 Diamond, Si, Ge – sp3

7. Covalent Materials Si, Ge, Diamond, Organic molecules and Polymers, SiH4, CH4, H2O, HNO3, HF.. Diamond – >3550°C Bismuth – 270°C Range of bond energies Strong angular preference of bonds due to overlap sp2 hybridisation – trigonal planar structure sp3 hybridisation – tetragonal tetrahedra Low density materials Open structures, polymorphs Large lattice parameters

8. Metallic Bonds Complex bonding mechanism between the degenerate electrons and the ion cores but also between electrons. Not all electrons involved in bonding – good electrical and thermal conductors Tungsten: 3410°C Mercury: -39°C Range of bond energies Figure adapted from Callister, Materials science and engineering, 7th Ed.

9. Crystal Structures How do atoms pack given their bonding? Figures adapted from Callister, Materials science and engineering, 7th Ed.

10. Packing Fraction Nature453, 629-632 (29 May 2008), Physics World The secrets of random packing May 29, 2008

11. Dense Packed Structures Atoms modelled as incompressible spheres In 2 D, each atom has 6 nearest neighbours

12. Unit Cell, Lattice and Basis A crystal is a parallelepiped that is made up of a regular repeat of some representative unit, called the unit cell. Unit Cell: A volume of space bounded by lattice points which describe the symmetry. It is defined in terms of their axial lengths (a,b,c) and the inter-axial angles (,,). TRANSLATIONAL SYMMETRY maps the unit cells across the entire volume of the crystal

13. Crystal Structure Convolution of Basis and lattice

14. 2D Bravais Lattices A lattice is an infinite periodic set of points defined by the three basis vectors, a,b and c. In 2D total of 5 distinct lattices T Lattice vector:

15. Bravais Lattices – 14 possible in 3D F I P I P P F I C P P R C T T – trigonal R- rhombohedral All lattices have translational symmetry

16. Simple Metals W W BASIS BCC LATTICE

17. Molecular crystals BASIS FCC LATTICE

18. Lattice and Basis The basis can be convolved with the lattice in different ways due to the symmetry of the basis and lattice

19. SiF4 BASIS LATTICE NB: The point symmetries of the basis and lattice MUST be compatible! CRYSTAL

20. Dense Packed Structures Atoms modelled as incompressible spheres In 2 D, each atom has 6 nearest neighbours Extend to three dimensions by layering sheets on top of each other Repeat Patterns: ABABAB…. Hexagonal close packed ABCABCABC… Face centred cubic

21. Simple Centred Cubic AAAAAAAAAA Stacked symmetry is cubic P Polonium Centre of 4 unit cells is an octahedral site Packing Fraction=52.4% No. of Neighbours=6 Figure adapted from Callister, Materials science and engineering, 7th Ed.

22. Hexagonal Close Packed ABABABABAB Cd, Mg, Zn Co P The second layer (B) is translated with respect to the first (A) such that the atoms in layer B sit in the dimples between the atoms in layer A Packing Fraction=74% No. of Neighbours=12 c/a=1.663 Figure adapted from Callister, Materials science and engineering, 7th Ed.

23. Face Centred Cubic Noble Gases Cu, Ag, Au, Ni, Al, Pb ABCABCABCABC [111] F Initial stacking is the same as hcp. Then the third layer (C) is translated with respect to both the first and second such that the atoms in layer C sit in the dimples between the atoms in layer B. Packing Fraction=74% No. of Neighbours=12 Figure adapted from Callister, Materials science and engineering, 7th Ed.

24. [111] FCC (111)

25. Body Centred Cubic Cr Fe W ABABABABAB Stacked symmetry is cubic not hexagonal I Packing Fraction=68% No. of Neighbours=8

26. Tetragonal Distortions In such cases the structure is usually written as bct or fct Figure adapted from Callister, Materials science and engineering, 7th Ed.

27. Covalent Elements - Diamond Group VI elements such as C, Si and Ge sp3 hybridisation - tetrahedra 2 FCC lattices Packing Fraction=37% Number of neighbours=12 http://cwx.prenhall.com http://www.ipap.jp/jpsj/news/jpsj-nc_17-fig1.gif

28. Diatomic, AX type structures • The three most common AX type structures are cubic and named after the representative examples: • Rocksalt – NaCl • Caesium Chloride – CsCl • Zinc blende or sphalerite - ZnS Ionic Covalent

29. Diatomic, AX type structures • The three most common AX type structures are cubic and named after the representative examples: • Rocksalt – NaCl • Caesium Chloride – CsCl • Zinc blende or sphalerite - ZnS Ionic Covalent

30. The Rocksalt Structure Structure adopted for materials with strong ionic bonds MgO, MnS, LiF, FeO, Alkali halides and hydrides and II-VI compounds fcc lattice Each cation/anion is surrounded by 6 neighbours of the opposite kind in a perfect octahedral arrangement. Figure adapted from Callister, Materials science and engineering, 7th Ed.

31. Caesium Chloride Resembles bcc lattice but it is not because the atom at the centre is different and so it is not a lattice point. Primitive lattice Each cation/anion is surrounded by 8 neighbours of the opposite kind. Figure adapted from Callister, Materials science and engineering, 7th Ed.

32. Zinc Blende III-V and I-VII as well as ZnS (l=18%), SiC (l=12%), CdTe, ZnTe, MnTe A structure that resembles the Diamond structure. Common in materials which exhibit low ionic character and thus favour sp3 hybridised bonds and tetragonal bond angles No. of Neighbours=12 Figure adapted from Callister, Materials science and engineering, 7th Ed.