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7/27/2019 Lecture 3 - Structures of Metals and Ceramics
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Chapter 3STRUCTURES OF METALS AND
CERAMICS
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The Next Level Into the Crystals
Discussed about atoms and how they bond Moving into the arrangements of atoms and how
they form a structure
Crystallinity and Non-Crystallinity
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Crystalline Materials
Crystal: A solid with atomsarranged in a repeating or periodicarray over large atomic distances
Long range order exists
Repetitive 3-D pattern Each atom is bonded to its
nearest-neighbor atoms
Simple arrangement for metals,
extremely complex for polymersand ceramics
Properties depend on the spatialatomic arrangement
Li3N
http://cst-www.nrl.navy.mil/lattice/struk.picts/Li3N.s.pnghttp://cst-www.nrl.navy.mil/lattice/struk.picts/Li3N.s.png7/27/2019 Lecture 3 - Structures of Metals and Ceramics
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Atomic Packing and Crystallinity
Local arrangement of atomsin a solid is usuallypredictable
This may be in long range
repeating structureCrystalline
This may be in shortirregular sections
Amorphous or Glassy
Arrangement depends onbond
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atoms pack in periodic, 3D arrays Crystalline materials
-metals
-many ceramics
-some polymers
atoms have no periodic packing
Non-Crystalline materials
-complex structures-rapid cooling
crystalline SiO2
noncrystalline SiO2"Amorphous" = NoncrystallineAdapted from Fig. 3.41(b),
Callister & Rethwisch 4e.
Adapted from Fig. 3.41(a),
Callister & Rethwisch 4e.
Materials and Packing
Si Oxygen
typical of:
occurs for:
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Terminology
Atomic Hard Sphere Model: Atoms arethought of as hard spheres with well defineddiameters
Spheres representing the nearest neighboratoms touch one another
Stable materials want to stacktogether nicely
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Lattice and Unit Cell
Lattice: 3-D arrayof points coincidingwith the atompositions (spherecenters)
Unit Cell: Thesmallest repeating
entities in a crystalstructure
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Crystal Systems
A vast array of possible crystal structures Convenient to divide them into groups based on
cell configurations or atomic arrangements
Most common based on Unit Cell Geometry
Defining the unit cell geometry in terms of sixparameters3 edge lengths and 3 interaxialangles
Crystals having seven possible combinations ofedge lengths and interaxial angles
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3 Cubic Crystal Types
Simple Cubic Body-Centered
Cubic (BCC)
Face-Centered
Cubic (FCC)
Reduced Sphere Models
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More Terminology
Co-Ordination Number: The number of nearestneighbor, or touching atoms
Atomic Packing Factor (APF): Fraction of solidsphere volume in a unit cell (assuming the atomichard sphere model)
Volume of atoms in unit cell
Total volume of the unit cellAPF
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Simple Cubic Structure
Rare Poor packing
Co-ordination number - 6
APF = 0.52
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Body-Centered Cubic (BCC)
Atoms located at the eightcorners, and one at thecenter of the cube
Equivalent of one atom
from the eight corners,and one atom at thecenter2 atoms in aunit cell
Co-ordination number : 8
Hard-Sphere Model
4 1/8 s ahead4 1/8 s behindTotal 8 neighbors
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Body-Centered Cubic (BCC)
a
a2
a3
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BCC Atomic Packing Factor
aR
Unit cell c ontains:
1 + 8 x 1/8= 2 atoms/unit cell
APF = 0.68
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Face-Centered Cubic (FCC)
Atoms located at the eightcorners, and the centers ofall the cube faces
Corner atom is shared
among eight unit cells, face-centered atoms among twounit cells4 atoms in a unitcell
Co-ordination number : 12
a
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Face-Centered Cubic (FCC)
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FCC Atomic Packing Factor
a
Unit cell c ontains:
6 x 1/2 + 8 x 1/8
= 4 atoms/unit cell
APF = 0.74
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ABCABC... Stacking Sequence
2D Projection
FCC Unit Cell
FCC Stacking Sequence
A sites
B B
B
BB
B B
Csites
C C
CA
B
Bsites B B
B
BB
B B
BsitesC C
CA
C C
CA
AB
C
Hexagonal Close Packed Structure
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Hexagonal Close Packed Structure(HCP)
Atoms located at topand bottom hexagonalfaces, and at center ofthe faces
3 atoms provided by theplane between the twofaces
6 atoms in a unit cell
Ideal c/a ratio 1.633
Co-ordination number :12
APF : 0.74
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Coordination # = 12
ABAB... Stacking Sequence
APF = 0.74
3D Projection 2D Projection
Adapted from Fig. 3.3(a),
Callister & Rethwisch 4e.
Hexagonal Close-Packed Structure(HCP)
6 atoms/unit cellex: Cd, Mg, Ti, Zn
c/a = 1.633
c
a
A sites
Bsites
A sites Bottom layer
Middle layer
Top layer
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Energy and Packing
Interatomic spacing
Inte
rparticle
Energy
r0
Interatomic spacing
Interparticle
Energy
r0
Typical bond length
Typical energy
Typical energy
Dense, regular-packedstructures tend to havelower energy
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Theoretical Density ()
Copper FCC Structure, A = 63.5 g/mol,
r=0.128 nm = 0.128 * 10-7 cm
n=4 (since FCC structure)
atoms/mol)(10*023.6*)cellunit/cm()10*128.0(*216
(g/mol)63.5*cell)atoms/unit(423337
3/89.8 cmg (Compare with 8.94 g/cm3 which is the experimental value)
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Common Densities for Materials
Why suchA change?
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Ceramic Crystal Structures
More complex than metals since two or moreelements present
Bonding can vary from purely ionic to purely
covalent, and many in between If dominantly ionic bonding, crystal structures
have electrically charged ions instead ofatoms
Cations positively charged (lost electrons)
Anions negatively charged (gained electrons)
F t th t D t i
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Factors that Determinethe Ceramic Crystal Structure
1.Relative sizes of ions Formation of stable structures:
--maximize the # of oppositely charged ion neighbors.
Adapted from Fig. 3.4,
Callister & Rethwisch 4e.- -
- -+
unstable
- -
- -+
stable
- -
- -+
stable
2.Maintenance of
Charge Neutrality:--Net charge in ceramic
should be zero.--Reflected in chemical
formula:
CaF2:Ca2+
cation
F-
F-
anions+
AmXp
m, p values to achieve charge neutrality
C di ti b d i i
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Co-ordination number and ion sizeratio
Co-ordination number increases with rcation/ ranion(c/a)
Computation of Minimum
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Computation of MinimumCation-Anion Radius Ratio
Determine minimum rcation/ranion for an octahedral site(C.N. = 6)
a 2ranion
2ranion +2rcation = 2 2ranion
ranion + rcation = 2ranion
rcation = ( 2 - 1)ranion
arr 222 cationanion =+
414.012anion
cation==
r
r
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Bond Hybridization
Bond Hybridization is possible when there is significantcovalent bonding
hybrid electron orbitals form
For example for SiC
XSi
= 1.8 and XC
= 2.5
% ionic character = 100 {1- exp[-0.25(XSi - XC)2]} =11.5%
~ 89% covalent bonding
Both Si and C prefersp3 hybridization
Therefore, for SiC, Si atoms occupy tetrahedral sites
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Common Ceramic Crystal Structures
StructureName
StructureType
AnionPacking
Cationco-ord
#
Anionco-ord
#
Examples
Rock salt(sodiumchloride)
AX FCC 6 6 NaCl, MgO,FeO
Cesiumchloride
AX Simplecubic
8 8 CsCl
Zinc blende AX FCC 4 4 ZnS, SiC
Flourite AX2 Simplecubic
8 4 CaF2, UO2
Perovskite ABX3 FCC 12, 6 6 BaTiO3
Spinel AB2X4 FCC 4,6 4 MgAl2O4
Example Problem: Predicting the Crystal
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On the basis of ionic radii, what crystal structure
would you predict for FeO?
Answer:
5500
1400
0770
anion
cation
.
.
.
r
r
=
=
based on this ratio,
-- coord # = 6 because
0.414 < 0.550 < 0.732
-- crystal structure is NaCl
Data from Table 3.4,
Callister & Rethwisch 4e.
Example Problem: Predicting the CrystalStructure of FeO
Ionic radius (nm)
0.053
0.0770.069
0.100
0.140
0.181
0.133
Cation
Anion
Al3+
Fe2+
Fe3+
Ca2+
O2-
Cl-
F-
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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
rNa/rCl = 0.564
cations (Na+) prefer octahedralsites
Adapted from Fig. 3.5,
Callister & Rethwisch 4e.
rCl = 0.181 nm
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AX Crystal Structures
939.0181.0
170.0
Cl
Cs==
-
+
r
r
Adapted from Fig. 3.6,
Callister & Rethwisch 4e.
Cesium Chloride structure:
Since 0.732 < 0.939 < 1.0,
cubicsites preferred
So each Cs+ has 8 neighbor Cl-
AXType Crystal Structures include NaCl, CsCl, and zinc blende
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ABX3 Crystal Structures
Adapted from Fig. 3.9,
Callister & Rethwisch 4e.
Perovskitestructure
Ex: complex oxide
BaTiO3
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Density computation - Ceramics
Theoretical density of a crystalline ceramic
n= number of formula units (all ions that are included inthe chemical formula) within the unit cell
AC= sum of atomic weights of all cations in the formulaunit
AA= sum of atomic weights of all anions in the formulaunit
Vc = unit cell volume
NA= avogadros number = 6.023 * 1023 formula units/mol
AC
AC
NV
AAn )('
Theoretical density of Sodium
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Theoretical density of Sodiumchloride
Compute theoretical density of NaCl ANa = 22.99 g/mol; ACl = 35.45 g/mol
Ionic radii of Na+ = 0.102 nm, that of Cl- =
0.181 nm a
Na+
Cl-
.See the solution in the text book
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Polymorphism and Allotropy
Polymorphism some metals and non metalshave more than one crystal structure
Prevailing crystal structure depends ontemperature and pressure
Polymorphism in elemental solids is calledAllotropy
Carbon polymorphs as Diamond and Graphite
Pure ion has a BCC crystal structure at roomtemperature and FCC at 912oC