11.7 Structures of Solids
Unit Cells
The Crystal Structure of Sodium Chloride
Close Packing of Spheres
Cara Barskey, Brendan Degnan, Courtney Gregor
Crystalline Solids
Atoms, ions, or molecules are ordered in welldefined arrangements
Amorphous Solids
Greek – “without form”, particles
have no orderly structure
Quartz
When melted, converted from crystalline  amorphous
Unit Cell
Repeating unit of a solid, the crystalline “brick”
Shows symmetry characteristic of entire pattern (2dimensional)
Described by lengths of edges and angles
Crystal lattice
- represented by 3-D array of points
Types of Unit Cells
7 basic types - simplest is cubic unit cell
3 types of cubic unit cell
Primitive: lattice points at CORNERS ONLY
Body-centered: at corners and at center of unit cell
Face-centered: lattice points at corners and at center
of each face
Simple crystal structures
Cubic unit cells with only ONE ATOM centered at each
lattice point – as seen in metals
3-D Solids
Nickel atom on each of the eight corners of the cell

Simple cubic structure:
8 corners x 1/8 = 1 atom
Body-centered cubic structure = two atoms per unit cell

Body-centered cubic structure:
(8 corners x 1/8) + 1 body = 2 atoms
Six atoms on the faces of the unit cell = three nickel atoms, for a
total of four atoms per unit cell

Face-centered cubic structure:
(8 corners x 1/8) + (6 faces x 1/2) = 4 atoms
Crystal Structure of Sodium Chloride
Particles at corners, edges, and faces are shared
by other unit cells (fractions)
Total cation : anion ratio must be SAME for entire
crystal
Equal number of Na+ ions
and Cl- ions
Ex: Unit cell of CaCl2
1 Ca+2 for every 2 Cl-
Fraction of an atom that
occupies a unit cell
Position in Unit Cell
Center
Fraction in Unit Cell
1
Face
1/2
Edge
1/4
Corner
1/8
Practice
Plan : Find total number of ions of each type
Solve : There is 1/4 of an Na+ on each edge, a
whole Na+ in the center, 1/8 of a Cl- on each
corner, and 1/2 of a Cl- on each face.
Close Packing of Spheres
Close contact, maximize forces
Most efficient arrangement 
equal-sized spheres
Each sphere has six others in layer
Possible to have second and third layer
Two Depression Types of
rd
3
Layer
Hexagonal Close Packing
3rd layer spheres are placed
in line with 1st layer

1,3 & 2,4 repeat = ABAB
Cubic Close Packing
3rd layer spheres are placed
as staggered in relation to
1st layer


1,4 repeat = ABCA
Face-centered cubic
Coordination Number
Each sphere  12 equidistant neighbors
Coordination number = 12
Number of particles immediately surrounding a particle in the
crystal structure
Body-centered has coordination number of 8
Simple cubic-centered has coordination number of 6
Unequal-sized spheres: large particles take closepacked arrangements, small particles occupy cavities
between larger spheres
Section Questions
How does an amorphous solid differ from a
crystalline one? Give an example of an
amorphous solid
In a crystalline solid, particles are arranged in a
regularly repeating pattern. An amorphous solid is
one whose particles show no such order. An
example of an amorphous solid is rubber or glass.
Amorphous silica has a density of about 2.2
g/cm3, whereas the density of crystalline quartz
is 2.65 g/cm3. Account for this difference in
densities
Something has an effect on something that causes
one thing to be more dense than the other thing
What is a unit cell? What properties does it
have?
The unit cell is the smallest part of the crystal than
can reproduce the three-dimensional structure,
which can also be represented by its crystal lattice.
The simplest unit cells are cubic; these cubic unit
cells can be primitive, body-centered, or facecentered.
Perovskite, a mineral composed of Ca, O, and Ti
has the cubic unit cell shown in the drawing.
What is the chemical formula of this mineral?
TiCa8O6
The elements xenon and gold both have solid-state structures
consisting of cubic close-packed arrangements of atoms. Yet Xe
melts at -112 °C and gold melts at 1064 °C. Account for these
greatly different melting points.
It requires more kinetic energy to overcome the delocalized metallic
bonding in gold than to overcome the relatively weak London dispersion
forces in xenon.
Rutile is a mineral compound of Ti and O. It’s unit cell, shown in
the drawing, contains Ti atoms at each corner and a Ti atom at
the center of the cell. Four O atoms are on the opposite face of
the cell, and two are entirely with-in the cell. A.) What is the
chemical formula. B.) What is the nature of the bonding that
holds the solid together?
Ti3O2
Electrostatic attractions because its ionic bonding (see Table 11.7 on page
435)
Iridium crystallizes in a face-centered cubic unit
cell that has an edge length of 3.833 Angstroms.
The atom in the center of the face is in contact
with the corner atoms, as shown in the drawing.
A.) Calculate the atomic radius of an iridium
atom. B.) Calculate the density of the iridium
metal.
4(192.2 amu)=768.8 amu
768.8 amu
(3.833 Å)3
22.7 g/cm3
1g
6.02 x 1023 amu
(1 Å)3
(10^-8 cm)3
Aluminum metal crystallizes in a cubic close-packed
structure (face-centered cubic cell, Figure 11.34). A.)
How many aluminum atoms are in a unit cell? B.) What
is the coordination number of each aluminum atom? C.)
Assume that the aluminum atoms can be represented
as spheres, as shown in the drawing fro Exercise 11.59.
If each Al atom has a radius of 1.43 Å, what is the
length of a side of the unit cell? D.) Calculate the
density of aluminum metal.
½(6)+1/8(8)=4 atoms of Al
12, it’s a face-centered cubic cell unit
1.43 Å x 4=5.72 Å
2x2=5.72
4(27.0) amu
1g
(1 Å)3
x=1.69 Å
(1.69 Å)3
6.02x1023 amu (10^-8 cm)3
37.2 g/cm3