Chapter 3: Structures of Metals

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Chapter 3 Structures of Metals Ceramics
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Structures

• The properties of some materials are directly
  related to their crystal structures.
• Significant property differences exist between
  crystalline and noncrystalline materials having
  the same composition.

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Energy and Packing
Non dense, random packing
Dense, ordered packed structures tend to have
lower energies.
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Materials and Packing
Crystalline materials...
atoms pack in periodic, 3D arrays
typical of
-metals -many ceramics -some polymers
crystalline SiO2
Si
Oxygen
Noncrystalline materials...
atoms have no periodic packing
occurs for
-complex structures -rapid cooling
noncrystalline SiO2
"Amorphous" Noncrystalline
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 Metallic Crystal Structures

• How can we stack metal atoms to minimize empty
  space?
• 2-dimensions

vs.
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Metallic Crystal Structures
Tend to be densely packed.
Reasons for dense packing

• Typically, only one element is present, so all
  atomic radii are the same.
• - Metallic bonding is not directional.
• - Nearest neighbor distances tend to be small in
• order to lower bond energy.
• - The electron cloud shields cores from each
  other

They have the simplest crystal structures.
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Simple Cubic Structure (SC)
Rare due to low packing density (only Po has
this structure) Close-packed directions are
cube edges.
Coordination 6 ( nearest neighbors)
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Atomic Packing Factor (APF)
Volume of atoms in unit cell
APF
Volume of unit cell
assume hard spheres
APF for a simple cubic structure 0.52
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APF
3
a
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Body Centered Cubic Structure (BCC)
Atoms touch each other along cube diagonals.
All atoms are identical.
ex Cr, W, Fe (?), Tantalum, Molybdenum
Coordination 8
2 atoms/unit cell 1 center 8 corners x 1/8
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Atomic Packing Factor BCC
APF for a body-centered cubic structure 0.68
a
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Face Centered Cubic Structure (FCC)
Atoms touch each other along face diagonals.
--Note All atoms are identical the
face-centered atoms are shaded differently
only for ease of viewing.
ex Al, Cu, Au, Pb, Ni, Pt, Ag
Coordination 12
4 atoms/unit cell 6 face x 1/2 8 corners x 1/8
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c03prob
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Atomic Packing Factor FCC
APF for a face-centered cubic structure 0.74
maximum achievable APF
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Hexagonal Close-Packed Structure (HCP another
view)
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Hexagonal Close-Packed Structure (HCP)
ABAB... Stacking Sequence
3D Projection
2D Projection
6 atoms/unit cell
Coordination 12
ex Cd, Mg, Ti, Zn
APF 0.74
c/a 1.633
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c03f30
ABAB... Stacking Sequence
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X-Ray Diffraction
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X-Ray Diffractometer
sample
d distance between the same atomic
planes ? monochromatic wavelength ?
angle of diffracto- meter
Braggs Equation d ?/2 sin?
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c03tf01
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Theoretical Density, r
Density ?
where n number of atoms/unit cell
A atomic weight VC Volume of unit
cell a3 for cubic NA Avogadros
number 6.022 x 1023 atoms/mol
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Theoretical Density, r

• Ex Cr (BCC)
• A (atomic weight) 52.00 g/mol
• n 2 atoms/unit cell
• R 0.125 nm

a 4R/ 3 0.2887 nm
?theoretical
7.18 g/cm3
ractual
7.19 g/cm3
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Factors that Determine Crystal Structure
1. Relative sizes of ions Formation of stable
structures --maximize the of oppositely
charged ion neighbors.
stable
stable
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Atomic Bonding in Ceramics
Bonding -- Can be ionic and/or covalent
in character. -- ionic character increases
with difference in electronegativity of
atoms.
Degree of ionic character may be large or
small
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Coordination and Ionic Radii
Coordination increases with
To form a stable structure, how many anions can
surround a cation?
Coord
linear
2
lt 0.155
triangular
0.155 - 0.225
3
tetrahedral
0.225 - 0.414
4
octahedral
0.414 - 0.732
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cubic
0.732 - 1.0
8
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c03tf03
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Computation of Minimum Cation-Anion Radius Ratio

• Determine minimum rcation/ranion for an
  octahedral site (C.N. 6)

a
Measure the radii (blue and yellow spheres)
a 2ranion
Substitute for a in the above equation
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Example Problem Predicting the Crystal
Structure of FeO
On the basis of ionic radii, what crystal
structure would you predict for FeO?
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Rock Salt Structure

• Same concepts can be applied to ionic solids in
  general.
• Example NaCl (rock salt) structure

rNa 0.102 nm
rCl 0.181 nm

• rNa/rCl 0.564
• cations (Na) prefer octahedral sites

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MgO and FeO
MgO and FeO also have the NaCl structure
O2- rO 0.140 nm Mg2 rMg 0.072 nm

• rMg/rO 0.514
• cations prefer octahedral sites

So each Mg2 (or Fe2) has 6 neighbor oxygen atoms
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AX Crystal Structures
AXType Crystal Structures include NaCl, CsCl,
and zinc blende
Cesium Chloride structure
? Since 0.732 lt 0.939 lt 1.0, cubic sites
preferred
So each Cs has 8 neighbor Cl-
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AX2 Crystal Structures
Fluorite structure

• Calcium Fluorite (CaF2)
• Cations in cubic sites
• UO2, ThO2, ZrO2, CeO2
• Antifluorite structure
• positions of cations and anions
  reversed

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ABX3 Crystal Structures

• Perovskite structure
• Ex complex oxide
• BaTiO3

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SUMMARY
Atoms may assemble into crystalline or
amorphous structures.
Common metallic crystal structures are FCC,
BCC and HCP. Coordination number and atomic
packing factor are the same for both FCC
and HCP crystal structures.
We can predict the density of a material,
provided we know the atomic weight, atomic
radius, and crystal geometry (e.g., FCC,
BCC, HCP).
Interatomic bonding in ceramics is ionic
and/or covalent.
Ceramic crystal structures are based on
-- maintaining charge neutrality --
cation-anion radii ratios.