Structures of Solids

1. Structures of Solids • Solids have maximum intermolecular forces. • Molecular crystals are formed by close packing of the molecules (model by packing spheres). • We rationalize maximum intermolecular force in a crystal by the close packing of spheres. • When spheres are packed as closely as possible, there are small spaces between adjacent spheres. • The spaces are called interstitial holes.

2. Structures of Solids

3. Structures of Solids • A crystal is built up by placing close packed layers of spheres on top of each other. • There is only one place for the second layer of spheres. • There are two choices for the third layer of spheres: • Third layer eclipses the first (ABAB arrangement). This is called hexagonal close packing (hcp); • Third layer is in a different position relative to the first (ABCABC arrangement). This is called cubic close packing (ccp).

4. Structures of Solids

5. Structures of Solids Close Packing of Spheres • Each sphere is surrounded by 12 other spheres (6 in one plane, 3 above and 3 below). • Coordination number: the number of spheres directly surrounding a central sphere. • Hexagonal and cubic close packing are different from the cubic unit cells. • If unequally sized spheres are used, the smaller spheres are placed in the interstitial holes.

6. Structures of Solids X-Ray Diffraction • When waves are passed through a narrow slit they are diffracted. • When waves are passed through a diffraction grating (many narrow slits in parallel) they interact to form a diffraction pattern (areas of light and dark bands). • Efficient diffraction occurs when the wavelength of light is close to the size of the slits. • The spacing between layers in a crystal is 2 - 20 Å, which is the wavelength range for X-rays.

7. Structures of Solids X-ray diffraction (X-ray crystallography): • X-rays are passed through the crystal and are detected on a photographic plate. • The photographic plate has one bright spot at the center (incident beam) as well as a diffraction pattern. • Each close packing arrangement produces a different diffraction pattern. • Knowing the diffraction pattern, we can calculate the positions of the atoms required to produce that pattern. • We calculate the crystal structure based on a knowledge of the diffraction pattern.

8. X-Ray Diffraction

9. Structures of Solids Unit Cells • Crystalline solid: well-ordered, definite arrangements of molecules, atoms or ions. • Crystals have an ordered, repeated structure. • The smallest repeating unit in a crystal is a unit cell. • Unit cell is the smallest unit with all the symmetry of the entire crystal. • Three-dimensional stacking of unit cells is the crystal lattice.

10. Structures of Solids Unit Cells

11. Structures of Solids

12. Structures of Solids • Three common types of unit cell. • Primitive cubic, atoms at the corners of a simple cube, • each atom shared by 8 unit cells; • Body-centered cubic (bcc), atoms at the corners of a cube plus one in the center of the body of the cube, • corner atoms shared by 8 unit cells, center atom completely enclosed in one unit cell; • Face-centered cubic (fcc), atoms at the corners of a cube plus one atom in the center of each face of the cube, • corner atoms shared by 8 unit cells, face atoms shared by 2 unit cells.

13. Structure of Crystals • Simple cubic

14. Structure of Crystals • Simple cubic • each particle at a corner is shared by 8 unit cells • 1 unit cell contains 8(1/8) = 1 particle

15. Structure of Crystals • Body centered cubic (bcc) • 8 corners + 1 particle in center of cell • 1 unit cell contains 8(1/8) + 1 = 2 particles

16. Structure of Crystals • Face centered cubic (fcc)

17. Structure of Crystals • Face centered cubic (fcc) • 8 corners + 6 faces • 1 unit cell contains 8(1/8) + 6(1/2) = 4 particles

18. Bonding in Solids Molecular (formed from molecules) - usually soft with low melting points and poor conductivity. Covalent network (formed from atoms) - very hard with very high melting points and poor conductivity. Ions (formed form ions) - hard, brittle, high melting points and poor conductivity. Metallic (formed from metal atoms) - soft or hard, high melting points, good conductivity, malleable and ductile.

19. Bonding in Solids

20. Molecular Solids • Intermolecular forces: dipole-dipole, London dispersion and H-bonds. • Weak intermolecular forces give rise to low melting points. • Room temperature gases and liquids usually form molecular solids and low temperature. • Efficient packing of molecules is important (since they are not regular spheres).

21. Molecular Solids • molecules occupy unit cells • low melting points,volatile & insulators • examples: • water, sugar, carbon dioxide, benzene

22. Covalently Bonded Solids • Intermolecular forces: dipole-dipole, London dispersion and H-bonds. • Atoms held together in large networks. • Examples: diamond, graphite, quartz (SiO2), silicon carbide (SiC), and boron nitride (BN). • In diamond: • each C atom has a coordination number of 4; • each C atom is tetrahedral; • there is a three-dimensional array of atoms. • Diamond is hard, and has a high melting point (3550 C).

23. Covalent Network Solids

24. Covalently Bonded Solids In graphite • each C atom is arranged in a planar hexagonal ring; • layers of interconnected rings are placed on top of each other; • the distance between C atoms is close to benzene (1.42 Å vs. 1.395 Å in benzene); • the distance between layers is large (3.41 Å); • electrons move in delocalized orbitals (good conductor).

25. Ionic Solids • Ions (spherical) held together by electrostatic forces of attraction: • The higher the charge (Q) and smaller the distance (d) between ions, the stronger the ionic bond. • There are some simple classifications for ionic lattice types:

26. Ionic Solids

27. Ionic Solids NaCl Structure • Each ion has a coordination number of 6. • Face-centered cubic lattice. • Cation to anion ratio is 1:1. • Examples: LiF, KCl, AgCl and CaO. CsCl Structure • Cs+ has a coordination number of 8. • Different from the NaCl structure (Cs+ is larger than Na+). • Cation to anion ratio is 1:1.

28. Crystal Structure of Sodium Chloride • Face-centered cubic lattice. • Two equivalent ways of defining unit cell: • Cl- (larger) ions at the corners of the cell, or • Na+ (smaller) ions at the corners of the cell. • The cation to anion ratio in a unit cell is the same for the crystal. In NaCl each unit cell contains same number of Na+ and Cl- ions. • Note the unit cell for CaCl2 needs twice as many Cl- ions as Ca2+ ions.

29. Crystal Structure of Sodium Chloride

30. Metallic Solids • Metallic solids have metal atoms in hcp, fcc or bcc arrangements. • Coordination number for each atom is either 8 or 12. • Problem: the bonding is too strong for London dispersion and there are not enough electrons for covalent bonds.

31. Metallic Solids • Resolution: the metal nuclei float in a sea of electrons. • Metals conduct because the electrons are delocalized and are mobile. • positively charged nuclei surrounded by a sea of electrons • positive ions occupy lattice positions • examples: • Na, Li, Au, Ag, ……..

32. Metallic Solids

33. Bonding in Solids • Variations in Melting Points • Molecular Solids Compound Melting Point (oC) ice 0 ammonia -77.7 benzene, C6H6 5.5 napthalene, C10H8 80.6 benzoic acid, C6H5CO2H 122.4

34. Covalent Solids Substance sand, SiO2 carborundum, SiC diamond graphite Melting Point (oC) 1713 ~2700 >3550 3652-3697 Bonding in Solids

35. Ionic Solids Compound LiF LiCl LiBr LiI CaF2 CaCl2 CaBr2 CaI2 Melting Point (oC) 842 614 547 450 1360 772 730 740 Bonding in Solids

36. Metallic Solids Metal Na Pb Al Cu Fe W Melting Point (oC) 98 328 660 1083 1535 3410 Bonding in Solids

37. Band Theory of Metals • Na’s 3s orbitals can interact to produce overlapping orbitals

38. Band Theory of Metals • Can also overlap with unfilled 3p orbitals

39. Band Theory of Metals • Insulators have a large gap - forbidden zone • Semiconductors have a small gap