# Metallic and Ionic Solids Section 13.4

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Metallic and Ionic Solids Section 13.4

METALLIC 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.

Network Solids Diamond Graphite

Network Solids A comparison of diamond (pure carbon) with silicon.

Properties of Solids 1. Molecules, atoms or ions locked into a CRYSTAL LATTICE 2. Particles are CLOSE together 3. STRONG IM forces 4. Highly ordered, rigid, incompressible ZnS, zinc sulfide

Figure 13.25 2-D model

Crystal 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.

Figure 13.27

Crystal Lattices Regular 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.

Cubic Unit Cells All sides equal length All angles are 90 degrees

Unit Cells of Metal Atoms
The three important cubic unit cells are: simple cubic (sc) body-centered cubic (bcc) face-centered cubic (fcc).

Cubic Unit Cells Figure 13.28
Metals have unit cells that are • simple cubic (SC) • body centered cubic (BCC) • face centered cubic (FCC) or CCP

Figure 13.28

Figure 13.29 Face Atom Corner Atom

Simple Cubic Unit Cell Figure 13.28
Note that each atom is at a corner of a unit cell and is shared among 8 unit cells.

Body-Centered Cubic Unit Cell

Definitions: for a Cube (x=y=z)
g o n l

BCC cell Body Diagonal WHY? Diagonal =4 atom radius = 3 edge

c e l l e d g e c e l l d i a g o n a l f a c e d i a g o n a l

Face Centered Cubic Unit Cell
Atom at each cube corner plus atom in each cube face. NOTE: FCC = CCP

Face diagonal ?

Crystal 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.

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Crystal Lattices—Packing of Atoms or Ions
Packing of C60 molecules. They are arranged at the lattice points of a FCC lattice.

Unit 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.

Finding 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.

Finding the Lattice Type
SOLUTION 1. Calculate unit cell volume (FCC) V = (cell edge)3 Edge distance comes from face diagonal. Diagonal distance = √2 • edge (Diagonal) 2 = 2 (edge) Diag = Ö 2 • (edge) Therefore,

Finding the Lattice Type
PROBLEM Al has density = g/cm3 and Al radius = 143 pm. What is Al’s lattice type? SOLUTION Here diagonal = 4 • radius of Al = 572 pm Therefore, edge = 572 pm / Ö2 = 404 pm In centimeters, edge = 4.04 x 10-8 cm So, V of unit cell = (4.04 x 10-8 cm)3 V = x cm3

Finding the Lattice Type
PROBLEM Al has density = g/cm3 and Al radius = 143 pm. Verify that Al is FCC. SOLUTION 2. Use V and density to calculate mass of unit cell from DENSITY = MASS / VOL Mass = density • volume = (6.62 x cm3)(2.699 g/cm3) = x g/unit cell

Finding the Lattice Type
PROBLEM Al has density = g/cm3 and Al radius = 143 pm. Verify that Al is FCC. SOLUTION 3. Calculate number of Al per unit cell from mass of unit cell. Mass 1 Al atom = 26.98 g mol 1 mol 6.022 x 10 23 atoms 1 atom = x g, so 1.79 x 10 -22 g unit cell 1 atom 4.480 x 10 -23 = 3.99 Al atoms/unit cell 32

Number 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 Al 2. Each face Al is 1/2 inside the cell 6 faces (1/2 per face) = 3 net Al’s

Number of Atoms per Unit Cell
In the previous problem we calculated 4 Al atoms per unit cell. What does the cell look like? Repeating unit FCC

Number of Atoms per Unit Cell
How many atoms in a SC, BCC or FCC?

SC Repeating unit

BCC Repeating unit

Number of Atoms per Unit Cell
Unit Cell Type Net Number Atoms SC BCC 2 FCC 4

Structures 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.

Simple 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.

Simple 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.

Figure 13.30

Simple Ionic Compounds
Salts with formula MX can have SC structure — but not salts with formula MX2 or M2X.

Simple 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 cell 44

Figure 13.31

46

Ionic Lattice Page 620 47

The Sodium Chloride Lattice
Na+ ions are in OCTAHEDRAL holes in a face-centered cubic lattice of Cl- ions.

Comparing 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.

Common Ionic Solids Titanium dioxide, TiO2
There are 2 net Ti4+ ions and 4 net O2- ions per unit cell.

Find the density of MgO Given:
The structure is FCC in O2- with Mg2+ in the octahedral holes Mg2+ radius = 86 pm O2- radius 126 pm

CD

BCC

BCC

Structures and Formulas of Ionic Solids
See Examp &13.9, Exer & 13.9 O.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.

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Common 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.

Common 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.

13.5 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.

MOLECULAR 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.

13.6 THE PHYSICAL PROPERTIES OF SOLIDS
Some common properties of solids are: melting point heat of fusion sublimation point The melting point is the temperature when the solid is in equilibrium with the liquid, normally at a pressure of 1 atm.

PHYSICAL 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.

PHYSICAL 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.

PHYSICAL 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.

Figure 13.35 Enthalpies of Fusion

13.7 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 point normal boiling point melting point normal sublimation point critical point critical temperature

TRANSITIONS BETWEEN PHASES
See the phase diagram for water, Figure Lines 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.)

Phase Diagrams There 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

H2O

TRANSITIONS BETWEEN PHASES
As P and T increase, you finally reach the CRITICAL T and P P critical Note that line goes straight up . Above critical T no liquid exists no matter how high the pressure. (TC,PC) LIQUID High Pressure T critical GAS High Temperature

Tc, Pc CO2 T3 Tos

Water Carbon dioxide

Phase Diagram for Water
Animation of solid phase.

Phase Diagram for Water
Animation of equilibrium between solid and liquid phases.

Phase Diagram for Water
Animation of liquid phase.

Phase Diagram for Water
Animation of equilibrium between liquid and gas phases.

Phase Diagram for Water
Animation of gas phase.

Phase Diagram for Water
Animation of equilibrium between solid and gas phases.

Phase Diagram for Water
Animation of triple point. At the TRIPLE POINT all three phases are in equilibrium.

Phases Diagrams— Important Points for Water
T(°C) P(mmHg) Normal boil point Normal freeze point Triple point

TRANSITIONS BETWEEN PHASES
As P and T increase, you finally reach the CRITICAL T and P P critical Note that line goes straight up . Above critical T no liquid exists no matter how high the pressure. (TC,PC) LIQUID High Pressure T critical GAS High Temperature

Critical T and P COMPD Tc(oC) Pc(atm) H2O CO CH Freon (CCl2F2) Notice that Tc and Pc depend on intermolecular forces.

Solid-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 H2O Density g/cm g/cm3 cm3/gram

Solid-Liquid Equilibria
LIQUID H 2 O ICE favored at low P high P Solid H 2 O Liquid P T 760 mmHg 0 °C Normal freezing point

Solid-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. Solid H 2 O Liquid 760 mmHg 0 ° C Normal point P freezing T

Solid-Liquid Equilbria
The behavior of water under pressure is an example of LE CHATELIER’S PRINCIPLE At Solid/Liquid equilibrium, raising P squeezes the solid. It responds by going to phase with greater density, i.e., the liquid phase. Solid-Liquid Equilbria Solid H 2 O Liquid P T 760 mmHg 0 ° C Normal freezing point

Solid-Vapor Equilibrium
At P < 4.58 mmHg and T < ° C solid H2O can go directly to vapor. This process is called SUBLIMATION This is how a frost-free refrigerator works.

In 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?

Frost-free freezers Air in the freezer is warmed then dried. The vapor pressure of ice is torr. Warm, desiccated air can remove water vapor.

WATER PRESSURE