3METALLIC AND IONIC SOLIDS 13.4 Table 13.6, gives a brief over view of various types of solids and the forces holding the unit together.This table is a very good summary.We will now consider crystal lattice solids.
9Crystal Lattices and Unit Cells of Metal Atoms The crystal lattice is made up of unit cells, the smallest repeating unit of the solid structure.There are many different types of unit cells, but we will consider only the cubic unit cells.Figure 13.27the seven crystal system unit cells.
11Crystal LatticesRegular 3-D arrangements of equivalent LATTICE POINTS in space.The lattice points define UNIT CELLS, the smallest repeating internal unit that has the symmetry characteristic of the solid.There are 7 basic crystal systems, but we are only concerned with CUBIC.
12Cubic Unit CellsAll sidesequal lengthAll anglesare 90 degrees
13Unit Cells of Metal Atoms The three important cubic unit cells are:simple cubic (sc)body-centered cubic (bcc)face-centered cubic (fcc).
14Cubic Unit Cells Figure 13.28 Metals have unit cells that are• simple cubic (SC)• body centered cubic (BCC)• face centered cubic (FCC) or CCP
24Crystal Lattices—Packing of Atoms or Ions Assume atoms are hard spheres and that crystals are built by PACKING of these spheres as efficiently as possible.FCC is more efficient than either BCC or SC.
26Crystal Lattices—Packing of Atoms or Ions Packing of C60 molecules.They are arranged at the lattice points of a FCC lattice.
27Unit Cells of Metal Atoms Be sure to study Examples 13.6 and 13.7, and try Exercise 13.7 to develop skills in solving problems involving unit cells, density, atomic mass, and atomic radii.Remember that in metallic solids the atoms touch along and edge or diagonal depending on the unit cell.
28Finding the Lattice Type To find out if a metal is SC, BCC or FCC, use the known radius and density of an atom to calculate number of atoms per unit cell.PROBLEM Al has density = g/cm3 and Al radius = 143 pm. Verify that Al is FCC.
29Finding the Lattice Type SOLUTION1. Calculate unit cell volume (FCC)V = (cell edge)3Edge distance comes from face diagonal.Diagonal distance = √2 • edge(Diagonal)2= 2 (edge)Diag =Ö2 • (edge)Therefore,
30Finding the Lattice Type PROBLEM Al has density = g/cm3 and Al radius = 143 pm. What is Al’s lattice type?SOLUTIONHere diagonal = 4 • radius of Al = 572 pmTherefore, edge = 572 pm / Ö2 = 404 pmIn centimeters, edge = 4.04 x 10-8 cmSo, V of unit cell = (4.04 x 10-8 cm)3V = x cm3
31Finding the Lattice Type PROBLEM Al has density = g/cm3 and Al radius = 143 pm. Verify that Al is FCC.SOLUTION2. Use V and density to calculate mass of unit cell from DENSITY = MASS / VOLMass = density • volume= (6.62 x cm3)(2.699 g/cm3)= x g/unit cell
32Finding the Lattice Type PROBLEM Al has density = g/cm3 and Al radius = 143 pm. Verify that Al is FCC.SOLUTION3. Calculate number of Al per unit cell from mass of unit cell.Mass1 Al atom=26.98 gmol•1 mol6.022 x 1023atoms1 atom = x g, so1.79 x 10-22gunit cell•1 atom4.480 x 10-23=3.99 Al atoms/unit cell32
33Number of Atoms per Unit Cell In the previous problem we calculated 4 Al atoms per unit cell. What does the cell look like?1. Each corner Al is 1/8 inside the unit cell.8 corners (1/8 Al per corner) = 1 net Al2. Each face Al is 1/2 inside the cell6 faces (1/2 per face) = 3 net Al’s
34Number of Atoms per Unit Cell In the previous problem we calculated 4 Alatoms per unit cell. What does the cell look like?RepeatingunitFCC
35Number of Atoms per Unit Cell How many atoms in a SC, BCC or FCC?
38Number of Atoms per Unit Cell Unit Cell Type Net Number AtomsSCBCC 2FCC 4
39Structures and Formulas of Ionic Solids Sodium chloride and cesium chloride are two common type ionic solids.The sodium chloride structure is FCC in Cl- with the sodium ions in the octahedral holes.The cesium chloride structure is simple cubic (SC) in Cl- with the cesium ion in the center hole.Remember, the anion/cation ratio is determined by the chemical formula.
40Simple Ionic Compounds Lattices of many simple ionic solids are built by taking a SC or FCC lattice of ions of one type and placing ions of opposite charge in the holes in the lattice.EXAMPLE: CsCl has a SC lattice of Cs+ ions with Cl- in the center.
41Simple Ionic Compounds CsCl has a SC lattice of Cs+ ions with Cl- in the center.1 unit cell has 1 Cl- ion plus(8 corners)(1/8 Cs+ per corner)= 1 net Cs+ ion.
43Simple Ionic Compounds Salts with formula MX can have SC structure — but not salts with formula MX2 or M2X.
44Simple Ionic Compounds Many common salts have FCC arrangements of anions with cations in OCTAHEDRAL HOLES — e.g., salts such as CA = NaCl• FCC lattice of anions ----> 4 A-/unit cell• C+ in octahedral holes ---> 1 C+ at center+ [12 edges • 1/4 C+ per edge]= 4 C+ per unit cell44
48The Sodium Chloride Lattice Na+ ions are in OCTAHEDRAL holes in a face-centered cubic lattice of Cl- ions.
49Comparing NaCl and CsCl 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.
50Common Ionic Solids Titanium dioxide, TiO2 There are 2 net Ti4+ ions and 4 net O2- ions per unit cell.
51Find the density of MgO Given: The structure is FCC in O2- with Mg2+ in the octahedral holesMg2+ radius = 86 pmO2- radius 126 pm
55Structures and Formulas of Ionic Solids See Examp &13.9, Exer & 13.9O.H. # 97 to det. the formula of perovskite.Additional packing structures are given on page The structure labeled CCP is just another name for FCC.O.H. B , #70p, and # 71p.For ionic unit cells, the ions of opposite charge (usually) touch along an edge or diagonal.See pages 621 for problem-solving tips.
58Common Ionic Solids Zinc sulfide, ZnS The S2- ions are in TETRAHEDRAL holes in the Zn2+ FCC lattice.This gives 4 net Zn2+ ions and 4 net S2- ions.
59Common Ionic Solids Fluorite or CaF2 FCC lattice of Ca2+ ions This gives 4 net Ca2+ ions.F- ions in all 8 tetrahedral holes.This gives 8 net F- ions.
6013.5 MOLECULAR AND NETWORK SOLIDS Molecular solids are held together by relatively weak intermolecular forces.The molecules themselves may be made up of only a few atoms or up to 50 or 60 atoms.The bonds between the atoms within the molecules are always covalent.
61MOLECULAR AND NETWORK SOLIDS Network solids (Macromolecular) are made up of huge molecules having 105or more atoms.Often the chunk we are looking at is one giant molecule!!Diamond and graphite are examples of this type of solid.O.H. # 56 & # 75 and 3D models.
6213.6 THE PHYSICAL PROPERTIES OF SOLIDS Some common properties of solids are:melting pointheat of fusionsublimation pointThe melting point is the temperature when the solid is in equilibrium with the liquid, normally at a pressure of 1 atm.
63PHYSICAL PROPERTIES OF SOLIDS Heat of fusion or enthalpy of fusion, is the energy required to change one mole ( molar enthalpy of fusion) of the solid into the liquid.The magnitudes of these properties can be linked to the intermolecular forces involved.
64PHYSICAL PROPERTIES OF SOLIDS Sublimation is the direct change from solid to vapor without passing through the liquid state. For certain solids at room temperature and pressure, this is the normal transition.The enthalpy of sublimation corresponds to this process.
65PHYSICAL PROPERTIES OF SOLIDS The lattice energy is the energy required to convert the ionic solid to gaseous ions.Trends in lattice energies can be predicted using intermolecular forces.O.H. Figure “13.39” and Table 13.7.
6713.7 CHANGES IN STRUCTURE AND PHASE Phase diagrams can be used to illustrate the changes in phase that result from changes in temperature and pressure.These diagrams contain the following 6 points of interest:triple pointnormal boiling pointmelting pointnormal sublimation pointcritical pointcritical temperature
68TRANSITIONS BETWEEN PHASES See the phase diagram for water, FigureLines connect all conditions of T and P where EQUILIBRIUM exists between the phases on either side of the line.(At equilibrium particles move from liquid to gas as fast as they move from gas to liquid, for example.)
69Phase DiagramsThere are three phases, and equilibrium exists between any two phases at the phase boundary.There are two major classes of diagrams (1) Water and (2) carbon dioxide are most commonly used.In water the normal boiling point is present, the normal sublimation point is because the triple point is in front of the normal sublimation point
71TRANSITIONS BETWEEN PHASES As P and T increase, you finally reach the CRITICAL T and PPcriticalNote that linegoes straight up.Above critical T no liquid exists no matter how high the pressure.(TC,PC)LIQUIDHigh PressureTcriticalGASHigh Temperature
79Phase Diagram for Water Animation of equilibrium between solid and gas phases.
80Phase Diagram for Water Animation of triple point.At the TRIPLE POINT all three phases are in equilibrium.
81Phases Diagrams— Important Points for Water T(°C) P(mmHg)Normal boil pointNormal freeze pointTriple point
82TRANSITIONS BETWEEN PHASES As P and T increase, you finally reach the CRITICAL T and PPcriticalNote that linegoes straight up.Above critical T no liquid exists no matter how high the pressure.(TC,PC)LIQUIDHigh PressureTcriticalGASHigh Temperature
83Critical T and PCOMPD Tc(oC) Pc(atm)H2OCOCHFreon (CCl2F2)Notice that Tc and Pc depend on intermolecular forces.
84Solid-Liquid Equilibria In any system, if you increase P the DENSITY will go up.Therefore — as P goes up, equilibrium favors phase with the larger density (or SMALLER volume/gram).Liquid H2O Solid H2ODensity g/cm g/cm3cm3/gram
86Solid-Liquid Equilbria Raising the pressure at constant T causes water to melt.The NEGATIVE SLOPE of the S/L line is unique to H2O. Almost everything else has positive slope.SolidH2OLiquid760mmHg0 ° CNormalpointPfreezingT
87Solid-Liquid Equilbria The behavior of water under pressure is an example ofLE CHATELIER’S PRINCIPLEAt Solid/Liquid equilibrium, raising P squeezes the solid.It responds by going to phase with greater density, i.e., the liquid phase.Solid-Liquid EquilbriaSolidH2OLiquidPT760mmHg0 ° CNormalfreezingpoint
88Solid-Vapor Equilibrium At P < 4.58 mmHg and T < ° Csolid H2O can go directly to vapor.This process is called SUBLIMATIONThis is how a frost-free refrigerator works.
89In a closed system…Questions Can we change the equilibrium in this system?Is there any reason for wanting to change the equilibrium in this system?
90Frost-free freezersAir in the freezer is warmed then dried. The vapor pressure of ice is torr. Warm, desiccated air can remove water vapor.