Chemistry 281(01) Winter 2016
CTH 277 10:00-11:15 am
Instructor: Dr. Upali Siriwardane
E-mail: upali@latech.edu
Office: 311 Carson Taylor Hall ; Phone: 318-2574941;
Office Hours: MTW 8:00 am - 10:00 am;
TR 8:30 - 9:30 am & 1:00-2:00 pm.
January 12, 2016 Test 1 (Chapters 1&,2),
February 2, 2016 Test 2 (Chapters 3 &4)
February 26, 2016, Test 3 (Chapters 5 & 6),
Comprehensive Final Make Up Exam: March 1, 2016
9:30-10:45 AM, CTH 311.
Chemistry 281, Winter 2016 LA Tech
Chapter-3-1
Chapter 3. Structures of simple solids
Crystalline solids: The atoms, molecules or ions
pack together in an ordered arrangement
Amorphous solids: No ordered structure to the
particles of the solid. No well defined faces, angles
or shapes
Polymeric Solids: Mostly amorphous but some have
local crystiallnity. Examples would include glass
and rubber.
Chemistry 281, Winter 2016 LA Tech
Chapter-3-2
The Fundamental types of Crystals
Metallic: metal cations held together by a sea of
electrons
Ionic: cations and anions held together by
predominantly electrostatic attractions
Covalent or Molecular: collections of individual
molecules; each lattice point in the crystal is a m
Network: atoms bonded together covalently
throughout the solid (also known as covalent
crystal or covalent network).
olecule
Chemistry 281, Winter 2016 LA Tech
Chapter-3-3
Metallic Structures
Metallic Bonding in the Solid State:
Metals the atoms have low electronegativities; therefore the
electrons are delocalized over all the atoms.
We can think of the structure of a metal as an arrangement of
positive atom cores in a sea of electrons. For a more
detailed picture see "Conductivity of Solids".
Metallic: Metal cations held together by a sea of valance
electrons
Chemistry 281, Winter 2016 LA Tech
Chapter-3-4
Packing and Geometry
Close packing
ABC.ABC... cubic close-packed CCP
gives face centered cubic or FCC(74.05% packed)
AB.AB... or AC.AC... (these are equivalent). This is
called hexagonal close-packing HCP
CCP
Chemistry 281, Winter 2016 LA Tech
HCP
Chapter-3-5
Packing and Geometry
Loose packing
Simple cube SC
Body-centered cubic BCC
Chemistry 281, Winter 2016 LA Tech
Chapter-3-6
The Unit Cell
The basic repeat unit that build up the whole solid
Chemistry 281, Winter 2016 LA Tech
Chapter-3-7
Unit Cell Dimensions
The unit cell angles are defined as:
a, the angle formed by the b and c
cell edges
b, the angle formed by the a and c cell
edges g, the angle formed by the a
and b cell edges
a,b,c is x,y,z in right handed cartesian
coordinates
a g b a
Chemistry 281, Winter 2016 LA Tech
c b a
Chapter-3-8
Bravais Lattices & Seven Crystals Systems
In the 1840’s Bravais showed that there are only
fourteen different space lattices.
Taking into account the geometrical properties of
the basis there are 230 different repetitive patterns
in which atomic elements can be arranged to form
crystal structures.
Chemistry 281, Winter 2016 LA Tech
Chapter-3-9
Fourteen Bravias Unit Cells
Chemistry 281, Winter 2016 LA Tech
Chapter-3-10
Seven Crystal Systems
Chemistry 281, Winter 2016 LA Tech
Chapter-3-11
Number of Atoms in the Cubic Unit Cell
•
•
•
•
•
•
•
Coner- 1/8
Edge- 1/4
Body- 1
Face-1/2
FCC = 4 ( 8 coners, 6 faces)
SC = 1 (8 coners)
BCC = 2 (8 coners, 1 body)
Body- 1
Chemistry 281, Winter 2016 LA Tech
Face-1/2
Edge - 1/4
Coner- 1/8
Chapter-3-12
Close Pack Unit Cells
CCP
HCP
FCC = 4 ( 8 coners, 6 faces)
Chemistry 281, Winter 2016 LA Tech
Chapter-3-13
Unit Cells from Loose Packing
Simple cube SC
SC
= 1 (8 coners)
Chemistry 281, Winter 2016 LA Tech
Body-centered cubic BCC
BCC = 2 (8 coners, 1 body)
Chapter-3-14
Coordination Number
The number of nearest particles surrounding a
particle in the crystal structure.
Simple Cube: a particle in the crystal has a
coordination number of 6
Body Centerd Cube: a particle in the crystal has a
coordination number of 8
Hexagonal Close Pack &Cubic Close Pack: a
particle in the crystal has a coordination number
of 12
Chemistry 281, Winter 2016 LA Tech
Chapter-3-15
Holes in FCC Unit Cells
Tetrahedral Hole (8 holes)
Eight holes are inside a face centered cube.
Octahedral Hole (4 holes)
One hole in the middle and 12 holes along
the edges ( contributing 1/4) of the face
centered cube
Chemistry 281, Winter 2016 LA Tech
Chapter-3-16
Holes in SC Unit Cells
Cubic Hole
Chemistry 281, Winter 2016 LA Tech
Chapter-3-17
Octahedral Hole in FCC
Octahedral Hole
Chemistry 281, Winter 2016 LA Tech
Chapter-3-18
Tetrahedral Hole in FCC
Tetrahedral Hole
Chemistry 281, Winter 2016 LA Tech
Chapter-3-19
Structure of Metals
Crystal Lattices
A crystal is a repeating array made out of metals.
In describing this structure we must distinguish
between the pattern of repetition (the lattice type)
and what is repeated (the unit cell) described
above.
Chemistry 281, Winter 2016 LA Tech
Chapter-3-20
Polymorphism
Metals are capable of existing in more than one form at a time
Polymorphism is the property or ability of a metal to exist in
two or more crystalline forms depending upon temperature
and composition. Most metals and metal alloys exhibit this
property.
Uranium is a good example
of a metal that exhibits
polymorphism.
Chemistry 281, Winter 2016 LA Tech
Chapter-3-21
Alloys
Substitutional
Second metal replaces the metal atoms in the lattice
Interstitial
Second metal occupies interstitial space (holes) in the
lattice
Chemistry 281, Winter 2016 LA Tech
Chapter-3-22
Properties of Alloys
Alloying substances are usually metals or metalloids. The
properties of an alloy differ from the properties of the pure
metals or metalloids that make up the alloy and this
difference is what creates the usefulness of alloys. By
combining metals and metalloids, manufacturers can
develop alloys that have the particular properties required
for a given use.
Chemistry 281, Winter 2016 LA Tech
Chapter-3-23
Structure of Ionic Solids
Crystal Lattices
A crystal is a repeating array made out of ions. In
describing this structure we must distinguish between
the pattern of repetition (the lattice type) and what is
repeated (the unit cell) described above.
Cations fit into the holes in the anionic lattice since
anions are lager than cations.
In cases where cations are bigger than anions
lattice is considered to be made up of cationic
lattice with smaller anions filling the holes
Chemistry 281, Winter 2016 LA Tech
Chapter-3-24
Basic Ionic Crystal Unit Cells
Chemistry 281, Winter 2016 LA Tech
Chapter-3-25
Cesium Chloride Structure (CsCl)
Chemistry 281, Winter 2016 LA Tech
Chapter-3-26
Miller Indices
Miller indices are used to specify directions and
planes
• These directions and planes could be in
lattices or in
crystals
• The number of indices will match with the
dimension of the
Lattice or the crystal
• (h, k, l) represents a point on a plane
• To obtain h, k, l of a plane Identify the
intercepts on the a- , b- and c- axes of the unit
cell.
Chemistry 281, Winter 2016 LA Tech
Chapter-3-27
Miller Indices
Eg. intercept on the x-axis is at a, b and c ( at the point (a,0,0) ), but
the surface is parallel to the y- and z-axes - strictly therefore there is
no intercept on these two axes but we shall consider the intercept to
be at infinity ( ∞ ) for the special case where the plane is parallel to
an axis.
The intercepts on the a- , b- and c-axes are thus
Intercepts : 1 , ∞ , ∞
Take the reciprocals of the fractional intercepts: 1/1 , 1/ ∞, 1/ ∞
• (h, k, l) for this plane becomes 1,0,0
Chemistry 281, Winter 2016 LA Tech
Chapter-3-28
Rock Salt (NaCl)
© 1995 by the Division of Chemical Education, Inc., American Chemical Society.
Reproduced with permission from Soli-State Resources.
Chemistry 281, Winter 2016 LA Tech
Chapter-3-29
Sodium Chloride Lattice (NaCl)
0,0,1
1,1,1
Chemistry 281, Winter 2016 LA Tech
0,0,2
2,2,2
Chapter-3-30
CaF2
0,0,1
0,0,2
Chemistry 281, Winter 2016 LA Tech
0,0,4
0,0,2
0,0,2
0,0,4
0,0,4
Chapter-3-31
Calcium Fluoride
© 1995 by the Division of Chemical Education, Inc., American Chemical Society.
Reproduced with permission from Solid-State Resources.
Chemistry 281, Winter 2016 LA Tech
Chapter-3-32
Zinc Blende Structure (ZnS)
0,0,1
Chemistry 281, Winter 2016 LA Tech
0,0,4
0,0,2
0,0,4
Chapter-3-33
Lead Sulfide
© 1995 by the Division of Chemical Education, Inc., American Chemical Society.
Reproduced with permission from Solid-State Resources.
Chemistry 281, Winter 2016 LA Tech
Chapter-3-34
Wurtzite Structure (ZnS)
Chemistry 281, Winter 2016 LA Tech
Chapter-3-35
Antifluorite Structure
Chemistry 281, Winter 2016 LA Tech
Chapter-3-36
Radius ratio rule
Radius ratio rule states
As
the size (ionic radius, r+) of a cation increases,
more anions of a
particular size can pack around it.
Thus, knowing the size of the ions, we should be able to predict
a priori
which type of crystal packing
will be observed.
We can account for the relative size of both ions by using the RATIO of
the ionic radii:
+
r
ρ= −
r
Chemistry 281, Winter 2016 LA Tech
Chapter-3-37
Radius Ratio Rules
r+/rRatio
Coordination
Number
0.225 - 0.414
0.414 - 0.732
0.732 - 1
4
6
8
Chemistry 281, Winter 2016 LA Tech
Holes in Which
Positive Ions Pack
tetrahedral holes
octahedral holes
cubic holes
FCC
FCC
BCC
Chapter-3-38
Radius Ratio Appplications
Suggest the probable crystal structure of (a) barium
fluoride; (b) potassium bromide; (c) magnesium
sulfide. You can use tables to obtain ionic radii.
a) barium fluoride;
Ba2+= 142 pm F- = 131 pm
b) potassium bromide; K+= 138 pm Br- = 196 pm
c) magnesium sulfide; Mg2+= 103 pm S2- = 184 pm
a) Radius ratio(barium fluoride): 142/131 =1.08
b) Radius ratio(potassium bromide): 138/196=0.704
c) Radius ratio(magnesium sulfide): 103/184= 0.559
Chemistry 281, Winter 2016 LA Tech
Chapter-3-39
Radius Ratio Appplications
a) Radius ratio(barium fluoride): 142/131 =1.08
b) Radius ratio(potassium bromide): 138/196=0.704
c) Radius ratio(magnesium sulfide): 103/184= 0.559
r+/rRatio
Coordination
Number
0.225 - 0.414
0.414 - 0.732
0.732 - 1
•
•
•
4
6
8
Holes in Which
Positive Ions Pack
tetrahedral holes
octahedral holes
cubic holes
FCC
FCC
BCC
Barium fluoride: 142/131 =1.08 (0.732-1) CN 8 FCC fluorite
Potassium bromide: 138/196=0.704 (0.414-0.732) CN 6 FCC K+ in
octahedral holes
Magnesium sulfide: 103/184= 0.559 (0.414-0.732) CN 6 FCC
Chemistry 281, Winter 2016 LA Tech
Chapter-3-40
Radius Ratio Applications
•
Barium fluoride: 142/131 =1.08 (0.732-1) CN 8 FCC
•
Potassium bromide: 138/196=0.704 (0.414-0.732) CN 6 FCC K+ in
octahedral holes
•
Magnesium sulfide: 103/184= 0.559 (0.414-0.732) CN 6 FCC
Chemistry 281, Winter 2016 LA Tech
Chapter-3-41
Unit Cells dimensions and radius
a = 2r or r = a/2
Chemistry 281, Winter 2016 LA Tech
Chapter-3-42
Summary of Unit Cells
Volume of a sphere = 4/3pr3
Volume of sphere in SC = 4/3p(½)3
= 0.52
Volume of sphere in BCC = 4/3p((3)½/4)3 = 0.34
Volume of sphere in FCC = 4/3p( 1/(2(2)½))3 = 0.185
Chemistry 281, Winter 2016 LA Tech
Chapter-3-43
Density Calculations
Aluminum has a ccp (fcc) arrangement of atoms. The radius
of Al = 1.423Å ( = 143.2pm). Calculate the lattice parameter
of the unit cell and the density of solid Al (atomic weight =
26.98).
Solution:
4 atoms/cell [8 at corners (each 1/8), 6 in faces (each 1/2)]
Lattice parameter: a/r(Al) = 2(2)1/2
a = 2(2)1/2 (1.432Å) = 4.050Å= 4.050 x 10-8 cm
Density = 2.698 g/cm3
Chemistry 281, Winter 2016 LA Tech
Chapter-3-44