Chapter #16 – Liquids and Solids
16.1) Intermolecular Forces
16.2) The Liquid State
16.3) An Introduction to Structures and Types of Solids
16.4) Structure and Bonding of Metals
16.5) Carbon and Silicon: Network Atomic Solids
16.6) Molecular Solids
16.7) Ionic Solids
16.8) Structures of Actual Ionic Solids
Sections 1, 2, 10 and
11 are covered first
16.9) Lattice Defects
16.10) Vapor Pressure and Changes of State
16.11) Phase Diagrams
Properties of Crystals
Unit Cell: The smallest repeating unit needed
to describe the complete extended structure of
a crystal (through repetition and translation).
Some Common Crystal Lattices
Figure 16.9
How do we know what crystals look like?
x-ray diffraction
Figure 16.10
Why x-rays?
To satisfy the diffraction conditions, the
wavelength of light needs to be comparable to the
unit cell dimensions
Ångstroms (10-10meters)
Diffraction Conditions
Figure 16.11
From Trigonometry: nl = 2d sinq
3 Types of Crystalline Solids
Atomic
Solids
e.g. all metals, Si,
Carbon (diamond, graphite)
Ionic Solids
e.g. salts like NaCl
Molecular
Solids
e.g. protein crystals, sucrose
Figure 16.12
Physical properties of crystals
Crystal structure
Physical Properties
Bonding forces
(intra- and inter-molecular)
• melting point
• mechanical strength
• electrical properties
Example: Copper and Diamond are both atomic solids, but they
have very different physical properties:
Copper:
very soft, lower melting point (1083°C), excellent conductor
Diamond:
hardest known substance, higher m.p. (3500°C), insulator
Structure and Bonding in Metals
Zumdahl Section 16.4
Metals in solids can be treated as hard spheres that
(usually) pack in a way to minimize the empty space
between spheres. This is called closest packing.
Two distinct structures can be formed by closest
packing of atomsa cubic structure, and a hexagonal structure
Cubic: x = y = z
All unit cell angles = 90°
Hexagonal: x = y " z
some unit cell angles
" 90° (60° or 120° instead)
Cubic Closest Packed Structure
Figure 16.13
Figure 16.15
Face Centered Cubic (fcc)
How many atoms are in the fcc unit cell?
Figure 16.17
6(atoms on faces) + 8(atoms on corners)
= 6(1/2) + 8(1/8)
=3+1
=4
Hexagonal Closest Packed Structure
Figure 16.13
Figure 16.14
Hexagonal Prism (hcp)
Both fcc and hcp have the same number of
nearest neighbor interactions = 12
Figure 16.16
Packing Efficiency
The fraction of the volume (often expressed as %) of the
unit cell that is occupied by atoms, ions, or molecules
PE = fv =
volume of particles
volume of unit cell
Example: the face centered cubic unit cell
PE = fv =
=
(#atoms in unit cell)(volume of atom)
(side of cubic unit cell)3
(4)(4/3 pr3)
a3
Example (cont): the face centered cubic unit cell
a
4r
a
a
a
a2 + a2 = (4r)2
a=r8
So,
(4)(4/3 pr3)
= 0.74
or 74%
a3
for the face centered cubic unit cell
PE = fv =
Body-centered cubic unit cell
Simple cubic unit cell
Figure 16.18
Figure 16.19
Figure 16.9
Cubic Crystal Lattices
PE = 52% 6NN
PE = 68% 8NN
PE = 74% 12NN
Determining Atomic Radius
from a Crystal Structure
Problem: Barium is the largest non-radioactive alkaline earth metal. It
has a body-centered cubic unit cell and a density of 3.62g/cm3. What is
the atomic radius of barium? (Volume of a sphere is V = 4/3 pr3.)
Plan: Since an atom is spherical, we can find its radius from its volume.
(1) From the density (mass/volume) and the molar mass (mass/mole),
we find the molar volume of Ba metal.
(2) Since it crystallizes in the body-centered cubic structure, 68% of this
volume is occupied by Ba atoms, and the rest is empty.
(3) Dividing by Avogadro’s number gives the volume of one Ba atom,
from which we determine the atomic radius.
Solution:
3
1
x M = 1 cm
x 137.3 g Ba
3.62 g Ba 1 mol Ba
density
3
= 37.9 cm /mol Ba
Volume/mole of Ba metal =
Volume/mole of Ba atoms = (volume/mol Ba) * (packing efficiency)
= 37.9 cm3 / mol Ba * 0.68 = 26 cm3/mol Ba atoms
Volume/Ba atom =
26 cm3
1 mol Ba atoms
*
1 mol Ba atoms
6.022 x 1023 Ba atoms
= 4.3 x 10 - 23 cm3/Ba atom
Finding the atomic radius of Ba from the volume of a sphere:
V of Ba atom = 4/3pr3 and r3 =
r=
3
3V
4p
=
3
3(4.3 x 10 - 23cm3)
4 x 3.14
3V
4p
= 2.17 x 10 - 8 cm = 2.17Å
The 14 possible Bravais Lattices: Combining 7 Crystal Classes (cubic,
tetragonal, orthorhombic, hexagonal, monclinic, triclinic, trigonal) with
4 unit cell types (P, I, F, C), symmetry allows for only 14 types of 3-D
lattice.
Combining these 14 Bravais lattices with all possible symmetry elements
(such as rotations, translations, mirrors, glides, etc.) yields 230 different
Space Groups.