Chapter 4
The Structures of Simple Solids
Dr. Lihua Wang
Two Major Classifications of Solid
Materials
 Crystals
 Amorphous
Crystalline Solids have atoms, ions, or
molecules packed in regular geometric
arrays.
Classifying Crystalline Solids
 Molecular solids are solids whose composite
particles are molecules
 Ionic solids are solids whose composite
particles are ions
 Atomic solids are solids whose composite
particles are atoms
◦ nonbonding atomic solids are held together by dispersion
forces
◦ metallic atomic solids are held together by metallic bonds
◦ network covalent atomic solids are held together by
covalent bonds
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Unit Cell: Definition
 The smallest repeating unit in a crystalline
solid is an unit cell.
 Unit Cell: is a structural unit that when
repeated in all directions, results in a
macroscopic crystal.
Seven Crystalline Classes
Atoms (Ions) in a Unit Cell
 The atoms on the corners, edges, or
faces of the unit cell are shared with
other unit cells.
 The positions of atoms are described in
lattice points, expressed as fractions
of the unit cell dimensions.
Cubic Unit Cells
 All 90° angles between corners of the unit cell
 The length of all the edges are equal
 If the unit cell is made of spherical particles
◦ ⅛ of each corner particle is within the cube
◦ ½ of each particle on a face is within the cube
◦ ¼ of each particle on an edge is within the cube
c
b
a
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Cubic Unit Cells Simple Cubic (Primitive Cubic)
 Eight particles, one at each corner
of a cube
 1/8th of each particle lies in the
unit cell
◦ each particle : part of eight cells
◦ total = one particle in each unit
cell
 8 corners x 1/8
 Edge of unit cell = twice the radius
 Coordination number of 6
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2r
9
Simple Cubic
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Cubic Unit Cells Body-Centered Cubic
 Nine particles, one at each corner
of a cube + one in center
 1/8th of each corner particle lies in
the unit cell
◦ two particles in each unit cell
 8 corners x 1/8
 + 1 center
 Edge of unit cell = (4/ 3) times
the radius of the particle
 Coordination number of 8
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4r
3
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Body-Centered Cubic
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Cubic Unit Cells Face-Centered Cubic
 14 particles, one at each corner of
a cube + one in center of each face
 1/8th of each corner particle + 1/2
of face particle lies in the unit cell
◦ 4 particles in each unit cell
2r 2
 8 corners x 1/8
 + 6 faces x 1/2
 Edge of unit cell = 2 2 times the
radius of the particle
 Coordination number of 12
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Face-Centered Cubic
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Close-Packed Structures
 Many metallic and ionic solids can be
described as composed of atoms and ions
represented as hard spheres.
◦ And there is no directional covalent bonding,
◦ These spheres pack as closely as possible.
◦ Leading to Close-packed Structures.
Closest-Packed Structures
First Layer
 With spheres, it is more efficient to offset each
row in the gaps of the previous row than to line
up rows and columns
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Closest-Packed Structures
Second Layer
 The second layer sits over the holes in the
first layer – called an AB pattern
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Closest-Packed Structures
Third Layer
 The third layer atoms can align directly over the
atoms in the first layer– called an ABA pattern
• Or the third layer can sit over the uncovered
holes in the first layer– called an ABC pattern
Cubic Closest-Packed
Hexagonal
Closest-Packed
Face-Centered Cubic
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Hexagonal Closest-Packed Structures
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The Unit Cell of Hexagonal Close
Packing
 Hexagon unit cell:
◦ a = b = 2r, c = 2.83 r
◦ α = β = 90o, γ= 120o
 Two atoms in each
unit cell at lattice
points:
◦ (0, 0, 0)
◦ (1/3, 2/3, ½)

Cubic Closest-Packed Structures
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The Unit Cell of Cubic Closest-Packed
Structures
 Face-Centered Cube
 Four atoms in the unit cell at lattice points:
◦ (0,0,0)
◦ (0,1/2,1/2)
◦ (1/2,0, ½)
◦ (1/2, ½, 0)
The close-packed structure
 The coordination number (CN) of a
sphere in a close-packed structure is 12.
 The occupied space in a close-packed
structure is 74%.
 The remaining 26% of space between the
close-packed spheres are known as
“holes”.
◦ Alloys and ionic compounds: an expanded close-packed
arrangement of atoms or ions in which additional atoms or ions
occupy all or some of the holes.
Lattice Holes
Tetrahedral
Hole
Octahedral
Hole
Simple Cubic
Hole
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Octahedral and Tetrahedral Holes
Octahedral Holes
Tetrahedral Holes
Lattice Holes
 For a close-packed structure of N particles, there
are N Oh holes and 2N Td holes
= Octahedral
= Tetrahedral
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Solids with Close-Packed Structures
 Many metals
 Noble gas solids
 Almost spherical molecules e.g. C60
 Small molecules that can rotate around its
center in the solid state and appear spherical
◦ Such as H2, F2
 Metal Alloys and Some ionic compounds:
◦ An expanded close-packed arrangement of
atoms or ions in which additional atoms or ions
occupy all or some of the holes.
Solid Fullerene
C60
Structures of Metallic Crystals at
Room Temperature
Blank: more complex
structure
1/3: Body-centered cubic (bcc)
 1/3: Cubic close-packed (ccp)
 1/3: Hexagonal close-packed (hcp)
 Polymorphism: Changes with temperature and pressure

Alloys
 An alloy is a blend of metallic elements
prepared by mixing the molten
components and then cooling the
mixture.
Substitutional
Interstitial
Solid Solution
Intermetallic Compound
Three requirements for
substitutional solid solutions
 The atomic radii of the elements are
within about 15% of each other.
 The crystal structures of the two pure
metals are the same
 The electropositive characters of the two
components are the same.
Interstitial Solid Solutions
 Interstitial solid solutions are formed
when additional small atoms occupy the
holes of the lattice of the original metal
structure.
◦ Small atoms such as C, B, N occupy the Oh or
Td holes of a metal (C steels)
Ionic Crystals
 Lattice sites occupied by ions
 Held together by attractions between oppositely charged ions
◦ nondirectional
◦ therefore every cation attracts all anions around it, and vice-versa
 The coordination number represents the number of close cation–
anion interactions in the crystal
◦ The higher the coordination number, the more stable the solid
◦ lowers the potential energy of the solid
 The coordination number depends on the relative sizes of the
cations and anions that maintains charge balance
◦ generally, anions are larger than cations
◦ the number of anions that can surround the cation is limited by the size of the
cation
◦ the closer in size the ions are, the higher the coordination number is
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Cesium Chloride Structures
 ⅛ of each Cl─ (184 pm) inside
the unit cell
 Whole Cs+ (167 pm) inside the
unit cell
◦ cubic hole = hole in simple cubic
arrangement of Cl─ ions
 Cs:Cl = 1: (8 x ⅛), therefore the
formula is CsCl
 Coordination number = 8
 CsBr, CsI, etc have this structure.
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Another Example of CsCl Structure:
NH4Cl
NaCl (Rock-Salt) Structures
 Face centered cubes of Cl─ ions (181 pm)
with Na+ (97 pm) in all the Oh holes
 Na:Cl = (¼ x 12) + 1: (⅛ x 8) + (½ x 6) =
4:4 = 1:1,
 Therefore the formula is NaCl
 Coordination number = 6 for both Cl- and
Na+
 Many alkali halides and other cations :
anions =1:1 ionic compounds have this
structure
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Zinc Blende Structures
 The most common zinc ore
 Coordination number = 4
 Zn2+ (74 pm) and S2─ (184 pm) ions
each in a face-centered cubic
arrangement
 Each ion is in a tetrahedral hole of
the other lattice (1/2 of the
tetrahedral holes are filled)
 Zn:S = (4 x 1) : (⅛ x 8) + (½ x 6) = 4:4
= 1:1,
 Therefore the formula is ZnS
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Diamond
 Has the same
structure as Zinc
Blende with all
atoms replaced by
C.
NiAs
 Ni atoms occupy all
the octahedral holes
of a hexagonal closepacked arsenic lattice.
 Many MX compounds
have this structure. M:
transition metals, X:
group IVA,VA,VIA
elements
Fluorite Structures
 Ca2+ ions (99 pm) in a face-centered
cubic arrangement with eight F─ (133
pm) in all the tetrahedral holes between
Ca2+
 Ca:F = (⅛ x 8) + (½ x 6): (8 x 1) = 4:8
= 1:2,
 Therefore the formula is CaF2
 Coordination number = 8 for Ca
and 4 for F-
 Antifluorite structure when the
cation:anion ratio is 2:1:
◦ Oxides and sulfides of Li, K, Na, Rb
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Rutile, TiO2
 Distorted TiO6 octahedra that form
columns by sharing edges.
 Coordination number = 6 for Ti and
3 for O.
 Unit cell:
◦ Ti at the corners and the center;
◦ 2 O’s at in the opposite quadrants
of the bottom face and 2 O’s in
the top face.
◦ 2 O’s in the plane with the Ti.
 SnO2, MgF2 and ZnF2 also have this
structure.

Applications of Ti2O?? (24.17 a 24.18)
The Perovskite Structure
Named after the mineral perovskite:
CaTiO3
 Many ABX3 solids, particularly oxides have
this type of structure.
 A is usually a larger cation of lower charge
than B.
 Cubic with each A cation surrounded by 12
X and each B surrounded by 6 X
 Materials having the perovskite structure
often show interesting and useful electrical
properties such as piezoelectricity,
ferroelectricity, and high-temp.
superconductivity.
 New Perovskite semiconducting materials
for photovoltaic cells: Box 14.4 MAPI
(Methylammonium Lead Iodide)

Cubic Unit Cell
(outlined in Blue)
Pervoskite Solar Cells:
Introduction:
https://news.energysage.com/perovskite-solar-cells/
Make the solar Cell:
https://www.youtube.com/watch?v=oQ2bz6jlbz0
MAPI for Solar Cells
The Spinel Structure
 Spinel: MgAl2O4
 Oxide Spinel: AB2O4
 ccp of O2-; A cations in 1/8 of
Td holes; B cations in ½ of Oh
holes.
 B is usually the smaller and
higher-charged ion than A
 A and B can be the same
element of different charges
e.g. Fe3O4 ,Magnetite.
Applications ??
O2A cations
B cations
Radius Ratio
 Coordination numbers in different crystals depend on
the sizes and shapes of the ions or atoms, their
electronic structures, and temperature and pressure
under which they were formed.
 A simple way to approximately predict the coordination
number is to use the radius ratio= r+/r-.
Defects and Nonstoichiometry
 Defects: imperfection of structures and composition
 Defects influence properties such as mechanical
strength, electrical conductivity, and chemical reactivity.
 Intrinsic Defects: Defects occur in the pure substance
 Extrinsic Defects: Defects due to the presence of
impurities
 Point Defects: Occurs at single sites
 Extended Defects: Involving various irregularities in the
stacking of the planes of atoms
Intrinsic Point Defects
 Schottky defect:
◦ A point defect in which an atom or
ion is missing from its normal site in
the structure
◦ Stoichiometry unchanged
 Frenkel defect:
Schottky Defect
◦ A point defect in which an atom or
ion has been displaced onto an
interstitial site.
◦ Stoichiometry unchanged
 Atom-interchange (Anti-site
defect:
◦ Consists of an interchanged pair
of atoms or ions
◦ Occurs in alloys or in ternary or
more complex ionic compounds
Frenkel Defect
Extrinsic Point Defects:
 Defects introduced into a solid as a result
of doping with an impurity atom.
◦ Commonly seen in naturally occurring
minerals. (e.g. gemstones)
◦ Can be introduced intentionally by doping
one material with another.
◦ Examples:
 As replace Si
 Ca2+ replace Zr4+ in ZrO2
Applications Ca doped Zirconia
Y3+ doped Zirconia (24.4 b. Box 24.1)
Calcium Doped ZrO2 Used in
Oxygen Sensor (Section 24.4)
Yttrium Stabilized Zirconia (YSZ) as
a Solid O2- Electrolyte in Solid State
Fuel Cells (Box 24.1)
Nonstoichiometry Compound and
Solid Solutions
 Many defects result in a compound being nonstoichiometric. Such defects often occur in crystalline
solids of d-block metal compounds when the metal
exhibits variable oxidation states.
◦ Example: Fe1-xS
 Solid Solutions: A solid solution occurs where there is a
continuous variation in compound stoichiometry w/o a
change in structure.
◦ Example: Cu/Zn brasses Cu1-xZnx (0<x<0.38)
The electronic Structures of Solids
 The properties of solids such as electric
conductivity, magnetism, and many optical
effects are determined by the electronic
structures of solids.
◦ Need to understand the interactions of
electrons with each other and the extended
arrays of atoms and ions.
Band Theory
 A solid is regarded as a single
huge molecule and the
interaction of many atomic
orbitals leads to the formation of
a large # of molecular orbitals
Density of States and Band Width
 The band width
depends on the
strength of the
interaction between
neighboring atoms.
◦ Strong interactions
lead to wider band
 The density of states
is highest in the
middle of the band
Metallic Conductors and Insulators

Metallic conductor: partially
filled band
Metallic Conductor

Insulator: has a large band
gap
Insulator
Fermi level: The highest energy level in a solid at T = 0 when electrons
occupy the lowest energy orbitals available.
Semiconductors
 A semiconductor is a solid whose
electrical conductivity increases with
increasing temperature.
 Semiconductors have smaller band gap
than insulators.
Intrinsic and Extrinsic
Semiconductors
 Intrinsic
semiconductor
 Extrinsic semiconductor: A
substance that is a semiconductor
due to the presence of intentionally
added impurities.
n-type
p-type
Principles of LED (Light Emitting
Diode): p-n Junction and
Group13/15 Semiconductor
 Group 13/15
Semiconductors:
◦ GaAs, GaP, etc.
◦ Different combinations
produce different color
◦ Respond more rapidly to
electrical signals than
those based on Si.
Sections 24.19, 24.20
Homework
 5– 8, 11 -12, 15, 17 – 20, 22, 25, 47, 51
Reference
“Inorganic Chemistry”, 7th Ed. By Weller,
Overton, Rourke, Armstrong, Oxford
University Press, New York, NY 10016