chapter-3-1 chemistry 281, winter 2015 la tech cth 277 10:00-11:15 am instructor: dr. upali...
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Chapter-3-1Chemistry 281, Winter 2015 LA Tech
CTH 277 10:00-11:15 am
Instructor: Dr. Upali Siriwardane
E-mail: [email protected]
Office: 311 Carson Taylor Hall ; Phone: 318-257-4941;
Office Hours: MTW 8:00 am - 10:00 am;
Th,F 8:30 - 9:30 am & 1:00-2:00 pm.
January 13, 2015 Test 1 (Chapters 1&,2),
February 3, 2015 Test 2 (Chapters 2 & 3)
February 26, 2015, Test 3 (Chapters 4 & 5),
Comprehensive Final Make Up Exam: March 3
Chemistry 281(01) Winter 2015
Chapter-3-2Chemistry 281, Winter 2015 LA Tech
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.
Chapter-3-3Chemistry 281, Winter 2015 LA Tech
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
Network: atoms bonded together covalently throughout the solid (also known as covalent crystal or covalent network).
Covalent or Molecular: collections of individual molecules; each lattice point in the crystal is a molecule
Chapter-3-4Chemistry 281, Winter 2015 LA Tech
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
Chapter-3-5Chemistry 281, Winter 2015 LA Tech
Packing and GeometryClose 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
CCPHCP
Chapter-3-6Chemistry 281, Winter 2015 LA Tech
Loose packing
Simple cube SC
Body-centered cubic BCC
Packing and Geometry
Chapter-3-7Chemistry 281, Winter 2015 LA Tech
The Unit CellThe basic repeat unit that build up the whole solid
Chapter-3-8Chemistry 281, Winter 2015 LA Tech
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 c b a
Chapter-3-9Chemistry 281, Winter 2015 LA Tech
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.
Chapter-3-10Chemistry 281, Winter 2015 LA Tech
Fourteen Bravias Unit Cells
Chapter-3-11Chemistry 281, Winter 2015 LA Tech
Seven Crystal Systems
Chapter-3-12Chemistry 281, Winter 2015 LA Tech
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) Face-1/2
Coner- 1/8Edge - 1/4Body- 1
Chapter-3-13Chemistry 281, Winter 2015 LA Tech
Close Pack Unit Cells
CCP HCP
FCC = 4 ( 8 coners, 6 faces)
Chapter-3-14Chemistry 281, Winter 2015 LA Tech
Simple cube SC Body-centered cubic BCC
Unit Cells from Loose Packing
SC = 1 (8 coners) BCC = 2 (8 coners, 1 body)
Chapter-3-15Chemistry 281, Winter 2015 LA Tech
Coordination NumberThe 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
Chapter-3-16Chemistry 281, Winter 2015 LA Tech
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
Chapter-3-17Chemistry 281, Winter 2015 LA Tech
Holes in SC Unit Cells
Cubic Hole
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Octahedral Hole in FCC
Octahedral Hole
Chapter-3-19Chemistry 281, Winter 2015 LA Tech
Tetrahedral Hole in FCC
Tetrahedral Hole
Chapter-3-20Chemistry 281, Winter 2015 LA Tech
Structure of MetalsCrystal 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.
Chapter-3-21Chemistry 281, Winter 2015 LA Tech
PolymorphismMetals 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.
Chapter-3-22Chemistry 281, Winter 2015 LA Tech
AlloysSubstitutional
Second metal replaces the metal atoms in the lattice
Interstitial
Second metal occupies interstitial space (holes) in the lattice
Chapter-3-23Chemistry 281, Winter 2015 LA Tech
Properties of AlloysAlloying 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.
Chapter-3-24Chemistry 281, Winter 2015 LA Tech
Structure of Ionic SolidsCrystal 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
Chapter-3-25Chemistry 281, Winter 2015 LA Tech
Basic Ionic Crystal Unit Cells
Chapter-3-26Chemistry 281, Winter 2015 LA Tech
Cesium Chloride Structure (CsCl)
Chapter-3-27Chemistry 281, Winter 2015 LA Tech
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.
Chapter-3-28Chemistry 281, Winter 2015 LA Tech
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
Chapter-3-29Chemistry 281, Winter 2015 LA Tech
Rock Salt (NaCl)
© 1995 by the Division of Chemical Education, Inc., American Chemical Society.
Reproduced with permission from Soli-State Resources.
Chapter-3-30Chemistry 281, Winter 2015 LA Tech
Sodium Chloride Lattice (NaCl)
0,0,1 0,0,2
1,1,12,2,2
Chapter-3-31Chemistry 281, Winter 2015 LA Tech
CaF2
0,0,1 0,0,4 0,0,2 0,0,4
0,0,20,0,2 0,0,4
Chapter-3-32Chemistry 281, Winter 2015 LA Tech
Calcium Fluoride
© 1995 by the Division of Chemical Education, Inc., American Chemical Society.
Reproduced with permission from Solid-State Resources.
Chapter-3-33Chemistry 281, Winter 2015 LA Tech
Zinc Blende Structure (ZnS)
0,0,1 0,0,4 0,0,40,0,2
Chapter-3-34Chemistry 281, Winter 2015 LA Tech
Lead Sulfide
© 1995 by the Division of Chemical Education, Inc., American Chemical Society.
Reproduced with permission from Solid-State Resources.
Chapter-3-35Chemistry 281, Winter 2015 LA Tech
Wurtzite Structure (ZnS)
Chapter-3-36Chemistry 281, Winter 2015 LA Tech
Antifluorite Structure
Chapter-3-37Chemistry 281, Winter 2015 LA Tech
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:
ρ = r+
r−
Radius ratio rule
Chapter-3-38Chemistry 281, Winter 2015 LA Tech
Radius Ratio Rules
r+/r- Coordination Holes in Which
Ratio Number Positive Ions Pack
0.225 - 0.414 4 tetrahedral holes FCC
0.414 - 0.732 6 octahedral holes FCC
0.732 - 1 8 cubic holes BCC
Chapter-3-39Chemistry 281, Winter 2015 LA Tech
Radius Ratio AppplicationsSuggest 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
Chapter-3-40Chemistry 281, Winter 2015 LA Tech
Radius Ratio Appplicationsa) 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
• 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
r+/r- Coordination Holes in Which
Ratio Number Positive Ions Pack
0.225 - 0.414 4 tetrahedral holes FCC
0.414 - 0.732 6 octahedral holes FCC
0.732 - 1 8 cubic holes BCC
Chapter-3-41Chemistry 281, Winter 2015 LA Tech
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
Chapter-3-42Chemistry 281, Winter 2015 LA Tech
Unit Cells dimensions and radius
a = 2r or r = a/2
Chapter-3-43Chemistry 281, Winter 2015 LA Tech
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
Chapter-3-44Chemistry 281, Winter 2015 LA Tech
Density CalculationsAluminum 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