Chapter 3 - Structures of Metals and Ceramics
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Basic definitions
Metallic crystal structures
Ceramic crystal structures
Silicate ceramics
Carbon
Crystal positions, directions, planes
Linear and planar densities
FCC vs. HCP crystal structures
Polycrystalline materials
Chapter 3 (continued)
Qualitative Questions
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Compare the BCC, FCC, and HCP crystal structures. Consider the
arrangement of atoms, coordination, and packing density.
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Explain is the structural difference between FCC and HCP
structures.
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Describe the factors which determine the crystal structure of
crystalline ceramic materials.
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Describe the difference in structure between crystalline and
amorphous materials. Which way do metals, ceramics, and
polymers generally behave?
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Chapter 3 (continued)
Qualitative Questions (cont.)
16 Explain the relationship between the atomic structure and
mechanical properties of the 2-dimensional (sheet) and
3-dimensional SiO2 and carbon compounds.
17 How are grain boundaries of a metal caused by the solidification
process? How will changes in the solidification process affect the
grain size?
18 Explain how and why glass composition is varied. You don't have
to remember specific formulations.
Chapter 3 (continued)
Quantitative Questions
1 Be able to calculate the coordination number, lattice constant, and
atomic packing factor for FCC, BCC and HCP.
2 Be able to calculate the packing factor, density, for the cubic ionic
crystal structures given in the text (NaCl structure, CsCl structure,
zinc blende structure, pervoskite structure).
3 Be able to calculate the density of a material based on the crystal
structure, and atomic weight for crystalline metallic and ceramic
structures.
4 Be able to determine the atomic positions, directions and Miller
indices in cubic unit cells.
5 Be able to calculate planar, and linear densities in cubic unit cells.
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Chapter 3 (continued)
Basic Definitions
• crystalline structure -
a structure that has a _________
____________________.
ƒ There are 7 crystal structures
ƒ We’ll focus on the _______ and ___________ systems
• lattice - the geometrical arrangement of points in a crystal
structure
• unit cell - the _________________________ .
Chapter 3 (continued)
Basic Definitions
• lattice constant(s) - the _______________ of the unit cell
ƒ nomenclature a, b, c
ƒ just ‘a’ for a cubic structure
• origin - taken as the __________________ of the unit cell
• coordination number - the number of ________________
for each atom
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Chapter 3 (continued)
Basic Definitions
• packing factor - the fraction of the structure occupied by
atoms.
Chapter 3 (continued)
Rules that apply to all cubic structures
• These relationships are independent of the type of packing and
whether it is a pure solid or a ceramic.
• face diagonal ( fd )
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Chapter 3 (continued)
Rules that apply to all cubic structures
• body diagonal ( bd )
Chapter 3 (continued)
Metallic Crystal Structures
• face-centered cubic
ƒ There is an atom at each corner and one at the center of
each face
ƒ atoms/unit cell
= (1/8 x 8 corners) + (1/2 x 6 face centers)
= ___________________
ƒ coordination number = ____
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Chapter 3 (continued)
Metallic Crystal Structures
• face-centered cubic
(Figure 3.1)
Chapter 3 (continued)
Metallic Crystal Structures
• face-centered cubic
lattice constant
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Chapter 3 (continued)
Metallic Crystal Structures
• face-centered cubic
packing factor
This is as high as you can get. Termed a _______________________
Chapter 3 (continued)
Metallic Crystal Structures
• body-centered cubic
ƒ An atom at each corner and one at the center of each face
ƒ atoms/unit cell = (1/8 x 8 corners) + (1 x 1 unit cell center)
= _______________________
ƒ coordination number = ____
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Chapter 3 (continued)
Metallic Crystal Structures
• body-centered cubic
(Figure 3.2)
Chapter 3 (continued)
Metallic Crystal Structures
• body-centered cubic
lattice constant
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Chapter 3 (continued)
Metallic Crystal Structures
• body-centered cubic
packing factor
Not a closely-packed structure
Chapter 3 (continued)
Metallic Crystal Structures
• hexagonal closest packed
ƒ not a cubic structure
ƒ each layer of the unit cell consists of atoms packed in hexagonal
arrangements
ƒ atoms/unit cell = (1/6 x 12 corners) + (1/2 x 2 for top and
bottom centers) + (1 x 3 from center layer)
= ____________________
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Chapter 3 (continued)
Metallic Crystal Structures
• hexagonal closest packed
(Figure 3.3)
Chapter 3 (continued)
Metallic Crystal Structures
• hexagonal closest packed
ƒ coordination number = _____
ƒ c/a = 1.633
(a closest-packed structure)
c and a are the lattice constants (see Figure)
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Chapter 3 (continued)
Metallic Crystal Structures
• hexagonal-closest packed
⎛ 4πr 3 ⎞
packing factor
6⎜
⎟
⎝ 3 ⎠
= 0.74
packing factor =
⎤
⎡1
. a⎥
1.633a *6⎢ a * 0866
⎦
⎣2
where a = 2r
A ______________________
Chapter 3 (continued)
Density Calculations
• We have the ability to calculate the density (mass/vol) given the
atomic packing and the atomic weight
where
n = the number of atoms per unit cell
Vc = the volume of the unit cell
A = the atomic weight of the element
NA = Avogadro’s number = 6.023x1023 atoms/mol
the ratio A/NA = the atomic weight in g/atom
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Chapter 3 (continued)
• Ceramic Crystal Structures
• more complex then metals
(multiple elements)
• When bond is ________________ the structure consists of
________________
(see inside front cover)
• bonding type
remember Equation 2.10
− 0.25( X A − X B ) ⎫
⎧
% ionic character = ⎨1 − e
⎬ *100
⎩
⎭
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Chapter 3 (continued)
(Table 3.2)
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Chapter 3 (continued)
2 factors affect the crystal structure
(1)
_______________
• ex.
(2)
CaF2
(__________ must be maintained)
(2) F-1 ions per (1) Ca+2 ion per unit cell
________________
• cations are smaller
rc / ra < 1
• Each ____________ will have as many ________
surrounding it as physically fit.
Chapter 3 (continued)
It is stable when the surrounding anions touch the cation
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Chapter 3 (continued)
• definition:
coordination number - the number of nearest neighbors
• this is determined by the value of
______
(ionic radii)
• The structure will pack such that the maximum number of
anions surround the cation.
• (remember charge neutrality)
• CN = ________ are the most common
Chapter 3 (continued)
(Table 3.3)
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Chapter 3 (continued)
Ceramic Crystal Structures
• Organized based on the relative number of cations to anions
AX Type Crystals
• ________________ of cations and anions
• several types - for different _____________________
Chapter 3 (continued)
rock salt structure
• CN = ___ for both
Na+ and Cl• an __________ of Cl• an Na+ in center and one
halfway along each of
12 edges
(Figure 3.5)
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Chapter 3 (continued)
rock salt structure
• contact along _________
_________________
• ___ of each ion per unit cell
• termed octahedral coordination
• really 2 interpenetrating FCC lattices
• exs.
NaCl
MgO
MnS
LiF
FeO
Chapter 3 (continued)
cesium chloride structure
• CN = ___ for
both Cs+ and Cl• This is not a ____________
(different ions)
• a Cl- at each corner
a Cs+ in cell center
(see Figure 3.6)
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Chapter 3 (continued)
cesium chloride structure
• contact along ______________
_______________
• ___ of each ion per unit cell
• really 2 interpenetrating simple cubic lattices
(not considered BCC)
Chapter 3 (continued)
zinc blende structure
• CN = ____ for
both Zn+ and S• S- in an FCC array
• cations sit in 4 of 8 interior
____________ sites
(remember charge neutrality)
• ___ of each ion per unit cell
(Figure 3.7)
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Chapter 3 (continued)
zinc blende structure
• center of S to center of Zn = 1/4 of body diagonal
• primarily _________________
• tetrahedral coordination
• most common in structures exhibiting a higher degree of
covalent bonding
electronegativity difference = 0.2 in ZnS
• exs.
ZnS
ZnTe
SiC
Chapter 3 (continued)
AmXp Structures
• Occurs when ________
___________.
• ex. AX2
as in fluorite CaF2
also UO2, ThO2
(Figure 3.8)
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Chapter 3 (continued)
• ____________
therefore CN = ___
• Ca+2 at cell center
F-1 at corners
• Since you need a 2:1 ratio it’s like CsCl with only half the
sites occupied.
• Actually takes 8 cubes to create a unit cell
Chapter 3 (continued)
AmBnXp Type Crystal Structures
• There are structures with _____
________________
• ex. BaTiO3 perovskite
(Figure 3.9)
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