The Chemistry of Solids

1. Chapter 11 The Chemistry of Solids

2. Band Theory As the half-filled 4s orbitals of an increasing number of Cu atoms overlap, their energies are split into a half-filled valence band. Electrons can move from the filled half (purple) to the slightly higher energy upper half (red), where they are free to migrate from one empty orbital to another.

3. Metallic Bonds Band theory is an extension of molecular orbital theory that describes bonding in solids. Bands of orbitals that are filled or partially filled by valence electrons are called valence bands. Higher-energy unoccupied bands in which electrons are free to migrate are called conduction bands.

4. Band Gap The energy gap between the valence and conduction bands is called the band gap. A semiconductor is a substance whose conductivity can be made to vary over several orders of magnitude by altering its chemical composition. A n-type semiconductor contains excess electrons contributed by electron-rich dopant atoms. A p-type semiconductor contains electron-poor dopant atoms.

5. Band Theory

6. Band Theory

11. Examples of Unit Cells

15. Unit Cells A body-centered cubic (bcc) unit cell has atoms at the 8 corners of a cube and at the center of the cell A simple cubic unit cell has atoms only at the 8 corners of a cube.

16. Number Atoms in a Unit Cell In the simple cubic cell there are only the 8 atoms at the corners. 1/8 x 8 = 1 atom in cell In bcc, 8 atoms at the corners and 1 in center. 1/8 x 8 + 1 x 1 = 2 atoms in the cell

18. Example Problem: Polonium metal crystallizes in a simple cubic structure. Calculate the density of the polonium metal if the atom radius is 176 pm. [Based on a literature density of 9.196 g cm-3, what is the radius of Po? (167 pm)]

20. Problem The radius of the copper atom is 127.8 pm, and its’ density is 8.95 g/cm3. Which unit cell is consistent with these data: sc, bcc, or fcc?

26. Metallic Crystalscan be thought to form via an efficient packing scheme…

27. Stacking Patterns A crystalline solid is made of an ordered array of atoms, ions, or molecules. Hexagonal closest-packed (hcp) describes a crystal structure in which the layers of atoms or ions in hexagonal unit cell have an a-b-a-b-a-b stacking pattern. Cubic closest packed (ccp) describes a crystal structure in which the layers of atoms, ions, or molecules in face-centered cubic unit cells have an a-b-c-a-b-c-a-b-c stacking pattern.

31. Summary of Crystal Structures

34. Example Problem: What is the packing efficiency in the simple cubic cell of CsCl? What is the percentage of empty space in the unit cell? The chloride ions are at the corners with the cesium in the middle of the unit cell. rCl- = 181 pm; rCs+ = 169 pm

42. Example Problem What is the packing efficiency of NaCl? What is the percentage of empty space in the NaCl unit cell? ) rCl- = 181 pm; rNa+ = 98 pm; edge dist.NaCl = 562.8 pm

49. Alloys An alloy is a blend of a host metal and one or more other elements which are added to change the properties of the host metal. In a substitutional alloy the atoms of one metal replace atom in the crystal lattice. Interstitial alloys are formed when hetero atoms occupy interstitial octahedral and tetrahedral holes of the host metal lattice.

50. Bronze is substitutional allow

51. Carbon Steel is an interstitial alloy

53. Network Solids Covalent network solids are made of a rigid, three-dimensional array of covalently bonded atoms. Crystals of molecular solids are formed by neutral covalently bonded molecules held together by intermolecular attractive forces.

55. Crystalline Versus Amorphous

56. Allotropes of Carbon

57. Allotropes of Phosphorus

58. Other Ionic Crystals

60. Other forms of Silica

62. Superconductors A superconductor is a material that has zero resistance to the flow of electric current. The critical temperature (Tc) is the temperature below which a material becomes a superconductor. Current superconductors, like Nb3Sn, have to be cooled to 20 K to remain superconducting.

63. High Temperature Superconductors YBa2Cu3O7 ceramic is superconducting at 77K (just above liquid nitrogen’s boiling point). The ceramic is structure is called a perovskite unit cell.

64. Yttrium-barium-copper Oxides These and related materials behave as superconductors because of the formation of electron pairs called Cooper pairs.

65. X-ray Diffraction X-ray diffraction (XRD) is a technique for determining the arrangement of atoms or ion in a crystal by analyzing the pattern that results when X-rays are scattered after bombarding the crystal. The Bragg equation relates the angle of diffraction (2?) of X-rays to the spacing (d) between the layers of ions or atoms in a crystal: n????2dsin?.

68. Problem (text) Cobalt(II) oxide is used as a pigment in pottery. It has the same type of crystal structure as NaCl. When exposed to X-rays (l=153 pm) reflections were observed at 42.38°, 65.68°, and 92.60°. Determine the values of n to which these reflections correspond, and calculate the spacing between the crystal layers. n?? = 2?d?sin ?