1 Metallic & Ionic Solids Chapter 13 The Chemistry of Solids Jeffrey Mack California State University, Sacramento Crystal Lattices Properties of Solids Regular 3-D arrangements of equivalent LATTICE POINTS in space. Lattice points define UNIT CELLS Unit cells are the smallest repeating internal unit that has the symmetry characteristic of the solid. 1. Molecules, atoms or ions locked into a CRYSTAL LATTICE. 2. Particles are CLOSE together. 3. These exhibit strong intermolecular forces 4. Highly ordered, rigid, incompressible ZnS, zinc sulfide Types of Solids Network Solids Type: Examples: Forces: Ionic Compounds NaCl, BaCl 2, ZnS Ion-Ion (ionic bonding) Diamond Metals Fr, Al Metallic Molecular Ice, I 2, C 12 H 22 O 11 Dipole-Dipole ot Induced Dipoles Network Amorphous Diamond, Graphite Glass, Coal Extended Covalent bonds Covalent; directional electron-pair bonds Graphite
2 Cubic Unit Cells Cubic Unit Cells There are 7 basic crystal systems, but we will only be concerned with CUBIC form here. All angles are 90 degrees All sides equal length 1/8 of each atom on a corner is within the cube 1/2 of each atom on a face is within the cube 1/4 of each atom on a side is within the cube Primitive cubic (PC) Bodycentered cubic (BCC) Facecentered cubic (FCC) Cubic Unit Cells Unit Cells for Metals Simple Cubic Unit Cell Atom Packing in Unit Cells Assumes atoms are hard spheres and that crystals are built by PACKING these spheres as efficiently as possible. Each atom is at a corner of a unit cell and is shared among 8 unit cells. Each edge is shared with 4 cells Each face is part of two cells.
Atom Packing in Unit Cells Crystal Lattices Packing of Atoms or Ions 3 FCC is more efficient than either BC or PC. Leads to layers of atoms. Crystal Lattices Packing of Atoms or Ions Atomic Radii Packing of C 60 molecules. They are arranged at the lattice points of a FCC lattice. Calcium metal crystallizes in a face-centered cubic unit cell. The density of the solid is 1.54 g/cm 3. What is the radius of a calcium atom? Calcium metal crystallizes in a face-centered cubic unit cell. The density of the solid is 1.54 g/cm 3. What is the radius of a calcium atom? Unit cell volume: 40.08 g 1 cm 3 1 mol Ca 23 4 Ca atoms = 1.73 10 22 cm 3 1 mol Ca 1.54 g 6.022 10 atoms unit cell
4 Calcium metal crystallizes in a face-centered cubic unit cell. The density of the solid is 1.54 g/cm 3. What is the radius of a calcium atom? Unit cell volume: 40.08 g 1 cm 3 1 mol Ca 23 4 Ca atoms = 1.73 10 22 cm 3 1 mol Ca 1.54 g 6.022 10 atoms unit cell Unit cell edge length: 22 V = 1.73 10 3 3 cm = (edge length) Calcium metal crystallizes in a face-centered cubic unit cell. The density of the solid is 1.54 g/cm 3. What is the radius of a calcium atom? Unit cell volume: 40.08 g 1 cm 3 1 mol Ca 23 4 Ca atoms = 1.73 10 22 cm 3 1 mol Ca 1.54 g 6.022 10 atoms unit cell Unit cell edge length: 22 V = 1.73 10 3 3 cm = (edge length) 3 22 edge length = 1.73 10 3 8 cm = 5.57 10 cm 3 22 edge length = 1.73 10 3 8 cm = 5.57 10 cm face diagonal = 4 radius = 2 edge length radius = 8 2 (5.57 10 cm) 8 = 1.97 10 cm = 197 pm 4 Number of Atoms Per Unit Cell Unit Cell Type PC 1 BCC 2 FCC 4 Net Number Atoms Atom Sharing at Cube Faces & Corners There is 1/8 th of an atom shared in corner. There is 1/2 shared at each face Two Views of CsCl Lattice can be Primitive Cubic lattice of Cl - with Cs + in hole OR a Primitive Cubic of Cs + with Cl - in hole Either arrangement leads to formula of 1 Cs + and 1 Cl - per unit cell Rutile, TiO 2, crystallizes in a structure characteristic of many other ionic compounds. How many formula units of TiO 2 are in the unit cell illustrated here? (The oxide ions marked by an x are wholly within the cell; the others are in the cell faces.) 8 corner Ti 1/8 = 1 Ti 4 face O ½ = 2 O 1 internal Ti = 1 Ti 2 internal O = 2 O = 2 Ti total = 4 O total There are two TiO 2 units per unit cell.
5 Common Ionic Solids Titanium dioxide, TiO 2 There are 2 net Ti 4+ ions and 4 net O 2- ions per unit cell. Structure & Formulas of Ionic Compounds Salts with formula MX can have Primitive Cubic structure. Salts with formula MX 2 or M 2 X cannot. The Sodium Chloride Lattice NaCl Construction Many common salts have Face Centered Cubic arrangements of anions with cations in octahedral holes. Example: NaCl FCC lattice of anions: 4 Cl per unit cell Na + in octahedral hole: 1 Na + at center 1 Na + (center) + (12 edges 1/4 Na + per edge) = 4 Na + per unit cell FCC lattice of Cl - with Na + in holes Na + in octahedral holes Octahedral Holes FCC Lattice The Sodium Chloride Lattice Na + ions are in OCTAHEDRAL holes in a face-centered cubic lattice of Cl ions.
6 Comparing NaCl with CsCl Common Ionic Solids Even though their formulas have one cation and one anion, the lattices of CsCl and NaCl are different. The different lattices arise from the fact that a Cs + ion is much larger than a Na + ion. Zinc sulfide, ZnS The S 2 ions are in facecentered cubic (FCC) structure. 1/8 of each corner S 2- ½ of each face S 2- Each Zn 2+ is in a hole between S 2-. The holes are tetrahedral 1 atom in ½ of the holes. Zn = (4 1) = 4 S = (1/8 8) + (½ 6) = 4 Zn:S = 4:4 = 1:1 Therefore the formula is ZnS Common Ionic Compounds Fluorite or CaF 2 FCC lattice of Ca 2+ ions This gives 4 net Ca 2+ ions. F ions in all 8 tetrahedral holes. This gives 8 net F ions. Bonding in Metals & Semiconductors Molecular orbital (MO) theory was introduced in Chapter 9 to rationalize covalent bonding in molecules MO theory can also be used to describe metallic bonding. Metals can be thought of as a supermolecule. Metallic bonding is described as delocalized: The electrons are associated with all the atoms in the crystal and not with specific bonded atoms. This theory of metallic bonding is called band theory. Bonding in Metals & Semiconductors Band Theory An energy-level diagram shows the bonding and antibonding molecular orbitals blending together into a band of molecular orbitals. Molecular orbitals are constructed from the valence orbitals on each atom and are delocalized over all the atoms. When sufficient energy is added, electrons are excited to the conduction band. (Thermal energy provides this for metals)
7 Band Theory Classifications of Solids Solids can be classified on the basis of the bonds that hold the atoms or molecules together. This approach categorizes solids as either: Molecular orbitals are constructed from the valence orbitals on each atom and are delocalized over all the atoms. When sufficient energy is added, electrons are excited to the conduction band. (Thermal energy provides this for metals) molecular Network (covalent) ionic metallic Molecular Solids Molecular solids are characterized by relatively strong intramolecular bonds between the atoms that form the molecules The intermolecular forces between these molecules are much weaker than the bonds. Because the intermolecular forces are relatively weak, molecular solids are often soft substances with low melting points. Examples: I 2 (s), sugar (C 12 H 22 O 11 ) and Dry Ice, CO 2 (s) Network (Covalent) Solids In Network solids, conventional chemical bonds hold the chemical subunits together. The bonding between chemical subunits is identical to that within the subunits resulting in a continuous network of chemical bonds. Two common examples of network solids are diamond (a form of pure carbon) and quartz (silicon dioxide). In quartz one cannot detect discrete SiO 2 molecules. Instead the solid is an extended threedimensional network of...-si-o-si-o-... bonding. Ionic Solids Ionic solids are salts, such as NaCl, that are held together by the strong force of attraction between ions of opposite charge. q( + ) q( -) F» 2 r Because this force of attraction depends on the square of the distance between the positive and negative charges, the strength of an ionic bond depends on the radii of the ions that form the solid. As these ions become larger, the bond becomes weaker. Metallic Solids In Molecular, ionic, and covalent solids the electrons in these are localized within the bonding atoms. Metal atoms however don't have enough electrons to fill their valence shells by sharing electrons with their immediate neighbors. Electrons in the valence shell are therefore shared by many atoms, instead of just two. In effect, the valence electrons are delocalized over many metal atoms. Because these electrons aren't tightly bound to individual atoms, they are free to migrate through the metal. As a result, metals are good conductors of electricity.
8 Bonding in Ionic Compounds: Lattice Energy The energy of an ion pair (cation/anion) is described by Coulombs law: U ion pair ( n + e - )( n - e + ) = C d n + = cation charge, n = anion charge d = distance between ion centers lattice U is the energy of formation of one mole of the solid crystaline compound from its ions in the gas phase. + - M ( g) + X ( g) MX( s) The Lattice Energy of a salt is dependant upon the charge and size of the ions. U ion pair Lattice Energy ( n + e - )( n - e + ) = C d Lattice Energy Calculation of lattice energy via the Born Haber cycle, an application of Hess s law. Solution: Approach this problem using Hess s Law. You need to find the enthalpy for the reaction: Start by drawing the Born-Haber cycle for the reaction: Li(s) + ½ F 2 (g) LiF(s)
9 Start by drawing the Born-Haber cycle for the reaction: Li + (g) Li(g) IE sub H + EA D o F (g) F(g) Li(s) + ½ F 2 (g) LiF(s) Using Hess s Law, the enthalpy of formation is found by: Li + (g) + F (g) Li(g) IE sub H EA D o F(g) Li(s) + ½ F 2 (g) LiF(s) f H o = sub H + I 1 + D o + EA + lattice U f H o = sub H + IE + D o + EA + lattice U Li(s) Li(g) sub H = +159.37 kj/mol Li(g) Li + (g) + e IE = +520. kj/mol ½ F 2 (g) F(g) D o = +78.99 kj/mol F(g) + e F (g) EA = 328.0 kj/mol Li + (g) + F (g) LiF(s) lattice U = 1037 kj/mol f H = = 607 kj/mol Phase Changes Involving Solids Melting: Conversion of Solid into Liquid The melting point of a solid is the temperature at which the lattice collapses into a liquid. Like any phase change, melting requires energy, called the enthalpy of fusion. Energy absorbed as heat on melting = enthalpy of fusion fusion H (kj/mol) Energy evolved as heat on freezing = enthalpy of crystallization fusion H (kj/mol) Enthalpies of fusion can range from just a few thousand joules per mole to many thousands of joules per mole. Enthalpies of Fusion Are a Function of Intermolecular Forces Phase Changes Involving Solids Sublimation: Conversion of Solid into Vapor Molecules can escape directly from the solid to the gas phase by sublimation Solid Gas Energy required as heat = sublimation H Sublimation, like fusion and evaporation, is an endothermic process. The energy required as heat is called the enthalpy of sublimation.
10 Sublimation Sublimation entails the conversion of a solid directly to its vapor. Here, iodine (I 2 ) sublimes when warmed. Transitions Between Phases: Phase Diagrams Phase diagrams are used to illustrate the relationship between phases of matter and the pressure and temperature. Phase Diagram for Water Phase Equilibria Water Liquid phase Solid-liquid Gas-Liquid Solid phase Gas phase Gas-Solid Triple Point Water Phases Diagrams: Water At the TRIPLE POINT all three phases are in equilibrium. T( C) P(mmHg) Normal boil point (at 1atm): 100 760 Normal freeze point (at 1atm): 0 760 Triple point: 0.0098 4.58
11 Phases Diagrams: Water Water has its maximum density at 4 C, in the liquid phase. Most substances have a maximum density in the solid phase. Hydrogen bonding accounts for water s deviation from normal behavior. Phases Diagram: Water At constant temp, an increase in pressure can bring about a phase change from solid to liquid! Phases Diagrams: Water At constant temp, an increase in pressure can bring about a phase change from solid to liquid! This occurs when the blade of an ice skate runs on the ice. Ice skaters actually ride on a film of water, not the ice! CO 2 Phase Diagram Notice the CO 2 has a forward slope of the solid/liquid boundary. This is seen because CO 2 does not exhibit hydrogen bonding. CO 2 Phases Separate phases Increasing pressure More pressure Supercritical CO 2