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

2 Structures of Solids

3 n A crystal is built up by placing close packed layers of spheres on top of each other. n There is only one place for the second layer of spheres. n 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 Close Packing of Spheres n Each sphere is surrounded by 12 other spheres (6 in one plane, 3 above and 3 below). n Coordination number: the number of spheres directly surrounding a central sphere. n Hexagonal and cubic close packing are different from the cubic unit cells. n If unequally sized spheres are used, the smaller spheres are placed in the interstitial holes.

6 Structures of Solids X-Ray Diffraction n When waves are passed through a narrow slit they are diffracted. n 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). n Efficient diffraction occurs when the wavelength of light is close to the size of the slits. n The spacing between layers in a crystal is 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 n Crystalline solid: well-ordered, definite arrangements of molecules, atoms or ions. n Crystals have an ordered, repeated structure. n The smallest repeating unit in a crystal is a unit cell. n Unit cell is the smallest unit with all the symmetry of the entire crystal. n Three-dimensional stacking of unit cells is the crystal lattice.

10 Structures of Solids Unit Cells

11 Structures of Solids

12 Structures of Solids n Three common types of unit cell. – Primitive cubic, atoms at the corners of a simple cube, n 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, n 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, n corner atoms shared by 8 unit cells, face atoms shared by 2 unit cells.

13 Structure of Crystals n Simple cubic

14 Structure of Crystals n 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 n 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 n Face centered cubic (fcc)

17 Structure of Crystals n 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 n Intermolecular forces: dipole-dipole, London dispersion and H-bonds. n Weak intermolecular forces give rise to low melting points. n Room temperature gases and liquids usually form molecular solids and low temperature. n 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: n water, sugar, carbon dioxide, benzene

22 Covalently Bonded Solids n Intermolecular forces: dipole-dipole, London dispersion and H-bonds. n Atoms held together in large networks. n Examples: diamond, graphite, quartz (SiO 2 ), silicon carbide (SiC), and boron nitride (BN). n 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 Å in benzene); – the distance between layers is large (3.41 Å); – electrons move in delocalized orbitals (good conductor).

25 Ionic Solids n 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. n There are some simple classifications for ionic lattice types:

26 Ionic Solids

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

28 Crystal Structure of Sodium Chloride n Face-centered cubic lattice. n 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. n 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. n Note the unit cell for CaCl 2 needs twice as many Cl - ions as Ca 2+ ions.

29 Crystal Structure of Sodium Chloride

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

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

32 Metallic Solids

33 Bonding in Solids n Variations in Melting Points n Molecular Solids CompoundMelting Point ( o C) ice 0 ammonia-77.7 benzene, C 6 H napthalene, C 10 H benzoic acid, C 6 H 5 CO 2 H122.4

34 Bonding in Solids n Covalent Solids Substance sand, SiO 2 carborundum, SiC diamond graphite Melting Point ( o C) 1713 ~2700 >

35 Bonding in Solids n Ionic Solids Compound LiF LiCl LiBr LiI CaF 2 CaCl 2 CaBr 2 CaI 2 Melting Point ( o C)

36 Bonding in Solids n Metallic Solids Metal Na Pb Al Cu Fe W Melting Point ( o C)

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

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

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