Ch03
This document was uploaded by user and they confirmed that they have the permission to share it. If you are author or own the copyright of this book, please report to us by using this DMCA report form. Report DMCA
Overview
Download & View Ch03 as PDF for free.
More details
- Words: 1,206
- Pages: 52
Chapter 3 Structures of Metals and Ceramics
MAE 2321
Crystal Structures
FCC (Face-Centered Cubic)
BCC (Body-Centered Cubic)
HCP (Hexagonal Close-Packed)
MAE 2321
FACE CENTERED CUBIC STRUCTURE (FCC) • Close packed directions are face diagonals. --Note: All atoms are identical; the face-centered atoms are shaded differently only for ease of viewing.
• Coordination # : Nearest-neighbor or touching atoms FCC: 12
MAE 2321
FCC (Face-Centered Cubic)
MAE 2321
BODY CENTERED CUBIC STRUCTURE (BCC)
Unit cell
Reduced-sphere unit cell
MAE 2321
BCC (Body-Centered Cubic)
MAE 2321
BCC (Body-Centered Cubic)
Unit cell for BCC
MAE 2321
HCP (Hexagonal Close-Packed) Structure
Reduced-sphere unit cell MAE 2321
MAE 2321
MAE 2321
MAE 2321
MAE 2321
MAE 2321
Stacking sequence
A
A A B B C A A A A B B B C C A A A B B A
A
A
ABCABC….: FCC
A
A A
B A
A
B A A B A
A B AA
B A B A
A B
A
A A
ABAB…..: HCP (see next slide)
MAE 2321
A A sites B sites
A
B
B C B
C B
B C B
B
C sites
MAE 2321
FCC STACKING SEQUENCE • ABCABC... Stacking Sequence • 2D Projection A B B C A B B B A sites C C B sites B B C sites • FCC Unit Cell
A B C
MAE 2321
HCP
MAE 2321
FCC
MAE 2321
ATOMIC PACKING FACTOR APF =
Volume of atoms in unit cell* Volume of unit cell
*assume hard spheres
a
Unit Cell Unit cellcontains contains: Close-packed directions: 6 x 1/2 + 8 x 1/8 length = 4R = 4 atoms/unit cell = 2a atoms volume 4 π ( 2a/4)3 4 unit cell atom 3 APF = volume a3 unit cell
•
APF for a face-centered cubic structure = 0.74, which is the maximum packing possible for spheres all having the same diameter. MAE 2321
THEORETICAL DENSITY, ρ # atoms/unit cell
ρ= nA VcNA Volume/unit cell (cm3/unit cell)
Atomic weight (g/mol)
Avogadro's number (6.023 x 10 23 atoms/mol)
Example: Copper
Data from Table inside front cover of the textbook: • crystal structure = FCC: 4 atoms/unit cell • atomic weight = 63.55 g/mol (1 amu = 1 g/mol) • atomic radius R = 0.128 nm (1 nm = 10-7cm) Vc = a3 ; For FCC, a = 4R/ 2 ; Vc = 4.75 x 10-23cm3
Result: theoretical ρCu = 8.89 g/cm3 Compare to actual: ρCu = 8.94 g/cm3 MAE 2321
Characteristics of Selected Elements at 20C
At. Weight Element Symbol (amu) Aluminum Al 26.98 Argon Ar 39.95 Barium Ba 137.33 Beryllium Be 9.012 Boron B 10.81 Bromine Br 79.90 Cadmium Cd 112.41 Calcium Ca 40.08 Carbon C 12.011 Cesium Cs 132.91 Chlorine Cl 35.45 Chromium Cr 52.00 Cobalt Co 58.93 Copper Cu 63.55 Flourine F 19.00 Gallium Ga 69.72 Germanium Ge 72.59 Gold Au 196.97 Helium He 4.003 Hydrogen H 1.008
Density (g/cm3) 2.71 -----3.5 1.85 2.34 -----8.65 1.55 2.25 1.87 -----7.19 8.9 8.94 -----5.90 5.32 19.32 -----------
Crystal Structure FCC -----BCC HCP Rhomb -----HCP FCC Hex BCC -----BCC HCP FCC -----Ortho. Dia. cubic FCC -----------
Atomic radius (nm) 0.143 -----0.217 0.114 Adapted from -----Table, "Charac-----teristics of 0.149 Selected 0.197 Elements", inside front 0.071 cover, 0.265 Callister 6e. -----0.125 0.125 0.128 -----0.122 0.122 0.144 ----------12 MAE 2321
DENSITIES OF MATERIAL CLASSES ρmetals ρceramics ρpolymers Why?
30
Ceramics have...
ρ (g/cm3)
Metals have... • close-packing (metallic bonding) • large atomic mass
• less dense packing (covalent bonding) • often lighter elements
Polymers have...
• poor packing (often amorphous) • lighter elements (C,H,O)
Composites have... • intermediate values
Metals/ Alloys
20
Platinum Gold, W Tantalum
10
Silver, Mo Cu,Ni Steels Tin, Zinc
5 4 3 2 1
0.5 0.4 0.3
Titanium Aluminum Magnesium
Graphite/ Ceramics/ Polymers Semicond
Composites/ fibers
Based on data in Table B1, Callister *GFRE, CFRE, & AFRE are Glass, Carbon, & Aramid Fiber-Reinforced Epoxy composites (values based on 60% volume fraction of aligned fibers in an epoxy matrix). Zirconia Al oxide Diamond Si nitride Glass-soda Concrete Silicon Graphite
Glass fibers PTFE Silicone PVC PET PC HDPE, PS PP, LDPE
GFRE* Carbon fibers CFRE* Aramid fibers AFRE*
Wood
Data from Table B1, Callister 6e. 13 MAE 2321
CERAMIC BONDING • Bonding: --Mostly ionic, some covalent. --% ionic character increases with difference in electronegativity.
• Large vs small ionic bond character: H CaF2: large 2.1
He -
C 2.5 Si 1.8
Li 1.0
Be 1.5
Na 0.9 K 0.8 Rb 0.8
Mg 1.2
Ca 1.0 Sr 1.0
I 2.5
Cs 0.7
Ba 0.9
At 2.2
Fr 0.7
Ra 0.9
SiC: small Ti 1.5
Cr 1.6
Fe 1.8
Ni 1.8
Zn 1.8
As 2.0
F 4.0
Ne -
Cl 3.0 Br 2.8
Ar Kr Xe Rn -
Table of Electronegativities
Adapted from Fig. 2.7, Callister 6e. (Fig. 2.7 is adapted from Linus Pauling, The Nature of the Chemical Bond, 3rd edition, Copyright 1939 and 1940, 3rd edition. Copyright 1960 by Cornell University.
MAE 2321
IONIC BONDING & STRUCTURE • Charge Neutrality: --Net charge in the structure should be zero. --General form:
CaF2:
Ca2+ + cation
Fanions F-
AmXp m, p determined by charge neutrality
• Stable structures:
--maximize the # of nearest oppositely charged neighbors.
-
+
-
unstable
-
+
-
stable
-
+
Adapted from Fig. 12.1,
Callister 6e.
-
stable MAE 2321
COORDINATION # AND IONIC RADII rcation • Coordination # increases with r anion Issue: How many anions can you arrange around a cation? rcation ranion
Coord #
< .155
2
.155-.225
3
.225-.414
4
ZnS (zincblende) Adapted from Fig. 12.4,
Callister 6e.
NaCl (sodium chloride)
Adapted from Fig. 12.2,
.414-.732
6
.732-1.0
8
Adapted from Table 12.2, Callister 6e.
Callister 6e.
CsCl (cesium chloride)
Adapted from Fig. 12.3,
Callister 6e.
MAE 2321
MAE 2321
MAE 2321
Rock Salt (NaCl) Structure
FCC
NaCl MAE 2321
Cesium Chloride (CsCl) Structure
MAE 2321
Zinc Blende (ZnS) Structure
Diamond
MAE 2321
AmXp STRUCTURES r cation 0.100 = ≈ 0.8 • Consider CaF2 : 0.133 r anion
• Based on this ratio, coord # = 8 and structure = CsCl. • Result: CsCl structure w/only half the cation sites occupied. • Only half the cation sites are occupied since #Ca2+ ions = 1/2 # F- ions.
Adapted from Fig. 12.5,
Callister 6e.
MAE 2321
Fluorite (CaF2) Structure
MAE 2321
Silicon-oxygen tetrahedron
MAE 2321
Polymorphism and Allotropy Polymorphism: having more than one crystal structure Allotropy: polymorphism for elemental solids
MAE 2321
A Unit Cell
MAE 2321
MAE 2321
Point Coordinates
MAE 2321
Point Coordinates
MAE 2321
Point Coordinates
MAE 2321
Crystallographic Directions
MAE 2321
Crystallographic Planes and Miller Indices
MAE 2321
Crystallographic Planes and Miller Indices
MAE 2321
Crystallographic Planes and Miller Indices
MAE 2321
Atomic Arrangements
MAE 2321
Atomic Arrangements
MAE 2321
• Single Crystals • Polycrystals • Noncrystalline materials (Amorphous materials) • Grain and Grain Boundary (Fig. 3.35)
Si
Oxygen
noncrystalline SiO2 MAE 2321
Grain and Grain Boundary
MAE 2321
Classification of Solid Materials
Single crystals Crystalline polycrystalline Solid materials Noncrystalline
MAE 2321
X-Ray Diffraction and Bragg’s Law
Eq. 3.15 and Eq. 3.16
MAE 2321
X-Ray Diffractometer
MAE 2321
Family of Lattice Planes
d hkl =
a h 2 + k 2 +l 2
a : lattice parameter MAE 2321
X-Ray Diffraction and Bragg’s Law
MAE 2321
MAE 2321
Crystal Structures
FCC (Face-Centered Cubic)
BCC (Body-Centered Cubic)
HCP (Hexagonal Close-Packed)
MAE 2321
FACE CENTERED CUBIC STRUCTURE (FCC) • Close packed directions are face diagonals. --Note: All atoms are identical; the face-centered atoms are shaded differently only for ease of viewing.
• Coordination # : Nearest-neighbor or touching atoms FCC: 12
MAE 2321
FCC (Face-Centered Cubic)
MAE 2321
BODY CENTERED CUBIC STRUCTURE (BCC)
Unit cell
Reduced-sphere unit cell
MAE 2321
BCC (Body-Centered Cubic)
MAE 2321
BCC (Body-Centered Cubic)
Unit cell for BCC
MAE 2321
HCP (Hexagonal Close-Packed) Structure
Reduced-sphere unit cell MAE 2321
MAE 2321
MAE 2321
MAE 2321
MAE 2321
MAE 2321
Stacking sequence
A
A A B B C A A A A B B B C C A A A B B A
A
A
ABCABC….: FCC
A
A A
B A
A
B A A B A
A B AA
B A B A
A B
A
A A
ABAB…..: HCP (see next slide)
MAE 2321
A A sites B sites
A
B
B C B
C B
B C B
B
C sites
MAE 2321
FCC STACKING SEQUENCE • ABCABC... Stacking Sequence • 2D Projection A B B C A B B B A sites C C B sites B B C sites • FCC Unit Cell
A B C
MAE 2321
HCP
MAE 2321
FCC
MAE 2321
ATOMIC PACKING FACTOR APF =
Volume of atoms in unit cell* Volume of unit cell
*assume hard spheres
a
Unit Cell Unit cellcontains contains: Close-packed directions: 6 x 1/2 + 8 x 1/8 length = 4R = 4 atoms/unit cell = 2a atoms volume 4 π ( 2a/4)3 4 unit cell atom 3 APF = volume a3 unit cell
•
APF for a face-centered cubic structure = 0.74, which is the maximum packing possible for spheres all having the same diameter. MAE 2321
THEORETICAL DENSITY, ρ # atoms/unit cell
ρ= nA VcNA Volume/unit cell (cm3/unit cell)
Atomic weight (g/mol)
Avogadro's number (6.023 x 10 23 atoms/mol)
Example: Copper
Data from Table inside front cover of the textbook: • crystal structure = FCC: 4 atoms/unit cell • atomic weight = 63.55 g/mol (1 amu = 1 g/mol) • atomic radius R = 0.128 nm (1 nm = 10-7cm) Vc = a3 ; For FCC, a = 4R/ 2 ; Vc = 4.75 x 10-23cm3
Result: theoretical ρCu = 8.89 g/cm3 Compare to actual: ρCu = 8.94 g/cm3 MAE 2321
Characteristics of Selected Elements at 20C
At. Weight Element Symbol (amu) Aluminum Al 26.98 Argon Ar 39.95 Barium Ba 137.33 Beryllium Be 9.012 Boron B 10.81 Bromine Br 79.90 Cadmium Cd 112.41 Calcium Ca 40.08 Carbon C 12.011 Cesium Cs 132.91 Chlorine Cl 35.45 Chromium Cr 52.00 Cobalt Co 58.93 Copper Cu 63.55 Flourine F 19.00 Gallium Ga 69.72 Germanium Ge 72.59 Gold Au 196.97 Helium He 4.003 Hydrogen H 1.008
Density (g/cm3) 2.71 -----3.5 1.85 2.34 -----8.65 1.55 2.25 1.87 -----7.19 8.9 8.94 -----5.90 5.32 19.32 -----------
Crystal Structure FCC -----BCC HCP Rhomb -----HCP FCC Hex BCC -----BCC HCP FCC -----Ortho. Dia. cubic FCC -----------
Atomic radius (nm) 0.143 -----0.217 0.114 Adapted from -----Table, "Charac-----teristics of 0.149 Selected 0.197 Elements", inside front 0.071 cover, 0.265 Callister 6e. -----0.125 0.125 0.128 -----0.122 0.122 0.144 ----------12 MAE 2321
DENSITIES OF MATERIAL CLASSES ρmetals ρceramics ρpolymers Why?
30
Ceramics have...
ρ (g/cm3)
Metals have... • close-packing (metallic bonding) • large atomic mass
• less dense packing (covalent bonding) • often lighter elements
Polymers have...
• poor packing (often amorphous) • lighter elements (C,H,O)
Composites have... • intermediate values
Metals/ Alloys
20
Platinum Gold, W Tantalum
10
Silver, Mo Cu,Ni Steels Tin, Zinc
5 4 3 2 1
0.5 0.4 0.3
Titanium Aluminum Magnesium
Graphite/ Ceramics/ Polymers Semicond
Composites/ fibers
Based on data in Table B1, Callister *GFRE, CFRE, & AFRE are Glass, Carbon, & Aramid Fiber-Reinforced Epoxy composites (values based on 60% volume fraction of aligned fibers in an epoxy matrix). Zirconia Al oxide Diamond Si nitride Glass-soda Concrete Silicon Graphite
Glass fibers PTFE Silicone PVC PET PC HDPE, PS PP, LDPE
GFRE* Carbon fibers CFRE* Aramid fibers AFRE*
Wood
Data from Table B1, Callister 6e. 13 MAE 2321
CERAMIC BONDING • Bonding: --Mostly ionic, some covalent. --% ionic character increases with difference in electronegativity.
• Large vs small ionic bond character: H CaF2: large 2.1
He -
C 2.5 Si 1.8
Li 1.0
Be 1.5
Na 0.9 K 0.8 Rb 0.8
Mg 1.2
Ca 1.0 Sr 1.0
I 2.5
Cs 0.7
Ba 0.9
At 2.2
Fr 0.7
Ra 0.9
SiC: small Ti 1.5
Cr 1.6
Fe 1.8
Ni 1.8
Zn 1.8
As 2.0
F 4.0
Ne -
Cl 3.0 Br 2.8
Ar Kr Xe Rn -
Table of Electronegativities
Adapted from Fig. 2.7, Callister 6e. (Fig. 2.7 is adapted from Linus Pauling, The Nature of the Chemical Bond, 3rd edition, Copyright 1939 and 1940, 3rd edition. Copyright 1960 by Cornell University.
MAE 2321
IONIC BONDING & STRUCTURE • Charge Neutrality: --Net charge in the structure should be zero. --General form:
CaF2:
Ca2+ + cation
Fanions F-
AmXp m, p determined by charge neutrality
• Stable structures:
--maximize the # of nearest oppositely charged neighbors.
-
+
-
unstable
-
+
-
stable
-
+
Adapted from Fig. 12.1,
Callister 6e.
-
stable MAE 2321
COORDINATION # AND IONIC RADII rcation • Coordination # increases with r anion Issue: How many anions can you arrange around a cation? rcation ranion
Coord #
< .155
2
.155-.225
3
.225-.414
4
ZnS (zincblende) Adapted from Fig. 12.4,
Callister 6e.
NaCl (sodium chloride)
Adapted from Fig. 12.2,
.414-.732
6
.732-1.0
8
Adapted from Table 12.2, Callister 6e.
Callister 6e.
CsCl (cesium chloride)
Adapted from Fig. 12.3,
Callister 6e.
MAE 2321
MAE 2321
MAE 2321
Rock Salt (NaCl) Structure
FCC
NaCl MAE 2321
Cesium Chloride (CsCl) Structure
MAE 2321
Zinc Blende (ZnS) Structure
Diamond
MAE 2321
AmXp STRUCTURES r cation 0.100 = ≈ 0.8 • Consider CaF2 : 0.133 r anion
• Based on this ratio, coord # = 8 and structure = CsCl. • Result: CsCl structure w/only half the cation sites occupied. • Only half the cation sites are occupied since #Ca2+ ions = 1/2 # F- ions.
Adapted from Fig. 12.5,
Callister 6e.
MAE 2321
Fluorite (CaF2) Structure
MAE 2321
Silicon-oxygen tetrahedron
MAE 2321
Polymorphism and Allotropy Polymorphism: having more than one crystal structure Allotropy: polymorphism for elemental solids
MAE 2321
A Unit Cell
MAE 2321
MAE 2321
Point Coordinates
MAE 2321
Point Coordinates
MAE 2321
Point Coordinates
MAE 2321
Crystallographic Directions
MAE 2321
Crystallographic Planes and Miller Indices
MAE 2321
Crystallographic Planes and Miller Indices
MAE 2321
Crystallographic Planes and Miller Indices
MAE 2321
Atomic Arrangements
MAE 2321
Atomic Arrangements
MAE 2321
• Single Crystals • Polycrystals • Noncrystalline materials (Amorphous materials) • Grain and Grain Boundary (Fig. 3.35)
Si
Oxygen
noncrystalline SiO2 MAE 2321
Grain and Grain Boundary
MAE 2321
Classification of Solid Materials
Single crystals Crystalline polycrystalline Solid materials Noncrystalline
MAE 2321
X-Ray Diffraction and Bragg’s Law
Eq. 3.15 and Eq. 3.16
MAE 2321
X-Ray Diffractometer
MAE 2321
Family of Lattice Planes
d hkl =
a h 2 + k 2 +l 2
a : lattice parameter MAE 2321
X-Ray Diffraction and Bragg’s Law
MAE 2321
