2019 Fall
Introduction to Materials Science and Engineering
09. 17. 2019 Eun Soo Park
Office: 33‐313 Telephone: 880‐7221 Email: [email protected] Office hours: by appointment 1 Contents for previous class
Atomic Bonding in Solids : an attempt to fill electron shells a. Primary bonding (1) Ionic bonds (2) Covalent bonds (3) Metallic bonds b. Secondary bonding (1) Van der Waals (2) Hydrogen bonding
c. Properties From Bonding
If Eo is larger,
Tm (melting temp.→brokenBroken Bonds bonds),
E (elastic modulus), ((possibly)) Yield strength is larger, but is smaller. (thermal expansion coefficient)2 Contents for previous class Materials-Bonding Classification
< 실제 많은 재료는 2개 혹은 그 이상의 결합에 혼합 > 3 Contents for previous class Summary: Properties from Bonds Ceramics Large bond energy (Ionic & covalent bonding): large Tm large E small Metals Variable bond energy (Metallic bonding): moderate Tm moderate E moderate
Polymers Directional Properties (Covalent & Secondary): Secondary bonding dominates small Tm small E large
4 Materials Science and Engineering
Processing •Sintering • Heat treatment • Thin Film Structure • Melt process • Mechanical •Atomic • Crystal • Microstructure • Macrostructure Properties • Mechanical • Electrical • Magnetic Theory & • Thermal
Design • Optical 5 Contents for today’s class CHAPTER 3: Fundamentals of Crystallography I. Crystal Structures
- Lattice, Unit Cells, Crystal system
II. Crystallographic Points, Directions, and Planes
- Point coordinates, Crystallographic directions, Crystallographic planes
III. Crystalline and Noncrystalline Materials
- Single crystals, Polycrystalline materials, Anisotropy,
Noncrystalline solids 6 Stacking of atoms in solid Finding stable position
2 1
• Minimize energy configuration – Related to the bonding nature
7 Materials and Packing
Crystalline materials... • atoms pack in periodic, 3D arrays • typical of: -metals -many ceramics
-some polymers crystalline SiO2 Adapted from Fig. 3.22(a), Callister 7e. Quasicrystalline materials... Si Oxygen Noncrystalline materials... • atoms have no periodic packing • occurs for: -complex structures -rapid cooling "Amorphous" = Noncrystalline noncrystalline SiO2
Adapted from Callister 7e. 8 atomic arrangement in the solid state
Solid materials are classified according to the regularity with which atoms and ions are arranged with respect to one another.
So, how are they arranged ?
(a) periodically – having long range order in 3-D Crystal
(b) quasi-periodically Quasicrystal
(c) randomly – having short range order with the characteristics of bonding type but losing the long range order
Crystal: Perfection → Imperfection Amorphous 9 Chapter 3.2 I. Crystal structures • How can we stack metal atoms to minimize empty space? 2-dimensions
vs.
Now stack these 2-D layers to make 3-D structures
10 Crystalline materials - three-dimensional periodic arrangement of atoms, ions, or molecules- translational periodicity
Crystal – related topics
– Periodicity (주기성) – Symmetry (대칭성) – Anisotropy (비등방성) – Directions and Planes (방향과 면) – Interplanar spacing & angles (면간거리와 각도) – Diffraction (회절) 11 I. Crystal structure
(1) Lattice : 결정 공간상에서 점들의 규칙적인 기하학적 배열 – 3D point array in space, such that each point has identical surroundings. These points may or may not coincide with atom positions. – Simplest case : each atom its center of gravity point or space lattice pure mathematical concept
example: sodium (Na) ; body centered cubic
Hard‐sphere unit cell Reduced sphere unit cell Aggregate of many atoms Chapter 3.3 (2) Unit cell : smallest repetitive volume which contains the complete lattice pattern of a crystal Chapter 3.4 Crystal systems Unit cell (3) Lattice parameter
length: a, b, c angle: α, β, γ
14 (4) 7 crystal systems Unit cell
15 (4) 7 crystal systems (continued) Unit cell
16 Unit cell
F • P, I, F, C C P : Primitive
I : Body centered P F : Face centered I
C : Base centered
P 17 Unit cell
(5) 14 Bravais Lattice - Only 14 different types of unit cells are required to describe all lattices using symmetry
rhombohedral cubic hexagonal tetragonal orthorhombic monoclinic triclinic (trigonal)
P
I
F
C
18 II. Crystallographic points, directions and planes
Chapter 3.5 Point coordinates • position: fractional multiples of the unit cell edge lengths – ex) P: q,r,s
cubic unit cell 19 Chapter 3.5 Point coordinates
z 111 Point coordinates for unit cell c center are a/2, b/2, c/2 ½½½ y a 000 b x Point coordinates for unit cell corner are 111 z 2c Translation: integer multiple of lattice constants b y identical position in another unit cell b
20 Chapter 3.6 Crystallographic Directions
z Algorithm 1. Vector repositioned (if necessary) to pass through origin. 2. Read off projections in terms of unit cell dimensions a, b, and c y 3. Adjust to smallest integer values 4. Enclose in square brackets, no commas x [uvw]
ex: 1, 0, ½ => 2, 0, 1 => [201] -1, 1, 1 => [ 111 ] where overbar represents a negative index families of directions
22 Impose index coordination k
j i 23 Directional indices
< ij k> : permutation of [ ij k] 24 Lattice Parameter
length: a, b, c angle: α, β, γ
25 26 27 14 Bravais Lattice
• Only 14 different types of unit cells are required to describe all lattices using symmetry • simple (1), body-centered (2), base-centered (2) face-centered
(4 atoms/unit cell) 28 Crystal view -Silicon
29 Crystallographic planes
30 Chapter 3.7 Crystallographic Planes Lattice plane (Miller indices) z p m00, 0n0, 00p: define lattice plane m, n, ∞ : no intercepts with axes c Intercepts @ 213 n y (mnp) a b Reciprocals ½ 1 1/3 Miller indicies 3 6 2 m (362) plane x Plane (hkl) Family of planes {hkl}
Miller indicies ; defined as the (362) smallest integral multiples of the reciprocals of the plane intercepts on the axes 31 Crystallographic Planes
A B C D
E F 32 Crystallographic Planes
33 {110} Family
34 {110} Family
35 Directions, Planes, and Family
• line, direction – [111] square bracket – <111> angular bracket - family
•Plane – (111) round bracket (Parentheses) – {111} braces - family
36 HCP Crystallographic Directions • Hexagonal Crystals – 4 parameter Miller-Bravais lattice coordinates are related to the direction indices (i.e., u'v'w') as follows. z [u'v 'w '] [uvtw ] 1 u (2u'-v') 3 a 2 1 v (2 v'-u') - 3 a 3 t -(u +v) a 1 w w ' Fig. 3.8(a), Callister 7e.
37 𝑐⃗
𝑎
𝑎
𝑎
38 Miller index 100 Miller-Bravais index 1 2 i=-(h+k) u (2u'v') u 3 3 1 1 v v (2v'u') 3 𝑐⃗ 3 w 0 w w' h k i l
𝑎
𝑐⃗ 𝑎 𝑎 𝑎 𝑎 𝑎
39 Miller index 101 Miller-Bravais index 1 2 u (2u'v') u 3 3 1 1 v v (2v'u') 3 3 w 1 w w'
𝑐⃗ 𝑎 𝑎 𝑐⃗ 𝑎
𝑎
𝑎
𝑎 Miller index Miller-Bravais index
𝑐⃗ 𝑎 𝑎 𝑎 001
100
Miller index Miller-Bravais index
𝑐⃗ 𝑎 𝑎 𝑎 001 u' u t 2u v v' v t 2v u w' w
100 Miller index
42 Miller index Miller-Bravais index
𝑐⃗ 𝑎 𝑎 𝑎 001 u' u t 2u v 101 0 v' v t 2v u 1 w' w u (2u'v') 3 100 1 v (2v'u') 3 w w' 43 Miller-Bravais vs. Miller index system Directions in Hexagonal system
Conversion of 4 index system (Miller-Bravais) to 3 index (Miller) t u'a v'a w'c ua va ta wc Ex. M [100] 1 2 1 2 3 u=(1/3)(2*1-0)=2/3 v=(1/3)(2*0-1)=-1/3 Miller-Bravais to Miller Miller to Miller-Bravais w=0 4 to 3 axis 3axis to 4 axis system => 1/3[2 -1 -1 0] 1 u' u t 2u v u (2u'v') 3 Ex. M-B [1 0 -1 0] u’=2*1+0=2 v' v t 2v u 1 v (2v'u') v’=2*0+1=1 w' w 3 w’=0 => [2 1 0] w w' 44 Hexagonal Crystal
• Miller-Bravais scheme
[]uvtw ()hkil tuv () ihk ()
45 Crystallographic Planes (HCP) • In hexagonal unit cells the same idea is used z
example a1 a2 a3 c 1. Intercepts 1 -1 1 2. Reciprocals 1 1/ -1 1 a 1 0 -1 1 2 3. Reduction 1 0 -1 1
a3
4. Miller-Bravais Indices (1011) a1
Adapted from Fig. 3.8(a), Callister 7e.
46 Crystallographic Planes (HCP) • In hexagonal unit cells the same idea is used z
example a1 a2 a3 c 1. Intercepts 1 -1 1 2. Reciprocals 1 1/ -1 1 a 1 0 -1 1 2 3. Reduction 1 0 -1 1
a3
4. Miller-Bravais Indices (1011) a1
Adapted from Fig. 3.8(a), Callister 7e.
47 Miller-Bravais index Miller index 𝑐⃗ 𝑐⃗
𝑎 𝑎
𝑎 𝑎
𝑎 𝑎
Inverse of 1 =1 Inverse of 1 =1 Position at 𝑎 =1 Position at 𝑐⃗ =1
Does not Meet with 𝑎 48 Miller index Miller-Bravais index
𝑎 𝑎 𝑎 𝑐⃗ 001
100 Miller index
49 𝑐⃗
𝑎
𝑎
𝑎
50 Schematic view of planes
1 Take c Reciprocal
𝟏
𝟐 b
𝟏 1 𝟏a Inter-planar spacing 51 Schematic view of (111) plane c
b
a 52 Inter-planar distance (면간거리) d
(hkl) plane
Interplanar spacing of the (hkl) plane The value of d which characterizes the distance between adjacent planes in the set of planes with Miller indices (hkl) is given by the following relations. The cell edges and the angles are a, b, c and α, β ,γ.
1 h2 k 2 l 2 Cubic : d 2 a 2 . 1 h2 k 2 l 2 Tetragonal : d 2 a 2 c 2 . 1 h2 k 2 l 2 Orthorhombic : d 2 a 2 b2 c 2 . 1 4 h2 hk k 2 l 2 Hexagonal : 2 2 2 d 3 a c . 1 1 h2 k 2 sin 2 l 2 2hl cos Rhombohedral : 2 2 2 2 2 d sin a b c ac . 1 (h2 k 2 l 2 )sin 2 2(hk kl hl)(cos2 cos ) Monoclinic : d 2 a 2 (1 3cos2 2cos3 ) . 1 1 2 2 2 Triclinic : (S11h S22k S33l 2S12hk 2S23kl 2S31hl) d 2 V 2 2 2 2 S11 b c sin S a 2c 2 sin 2 Where : 2 2 2 3 2 2 2 22 V a b c (1 cos cos cos 2cos cos cos ) 2 2 2 S33 a b sin S abc2 (cos cos cos ) 12 S a 2bc(cos cos cos ) 23 2 S31 ab c(cos cos cos ) 54 III. Crystalline and Noncrystalline Materials
CRYSTALS AS BUILDING BLOCKS • Some engineering applications require single crystals: --diamond single crystals --turbine blades Natural and artificial Fig. 8.30(c), Callister 6e. (Fig. 8.30(c) courtesy of Pratt and Whitney).
(Courtesy Martin Deakins, GE Superabrasives, Worthington, OH. Used with permission.)
• Crystal properties reveal features of atomic structure. --Ex: Certain crystal planes in quartz fracture more easily than others. (Courtesy P.M. Anderson) 55 Single vs Polycrystals
• Single Crystals E (diagonal) = 273 GPa Data from Table 3.3, -Properties vary with Callister 7e. (Source of data is R.W. direction: anisotropic. Hertzberg, Deformation and Fracture Mechanics of -Example: the modulus Engineering Materials, 3rd ed., John Wiley and Sons, of elasticity (E) in BCC iron: 1989.)
E (edge) = 125 GPa • Polycrystals -Properties may/may not 200 m Adapted from Fig. 4.14(b), Callister 7e. vary with direction. (Fig. 4.14(b) is courtesy of L.C. Smith and C. Brady, -If grains are randomly the National Bureau of Standards, Washington, oriented: isotropic. DC [now the National Institute of Standards and (Epoly iron = 210 GPa) Technology, Gaithersburg, -If grains are textured, MD].) anisotropic. 56 Grain Boundaries
57 Polycrystals Anisotropic • Most engineering materials are polycrystals.
Adapted from Fig. K, color inset pages of Callister 5e. (Fig. K is courtesy of Paul E. Danielson, Teledyne Wah Chang Albany)
1 mm
• Nb-Hf-W plate with an electron beam weld. Isotropic • Each "grain" is a single crystal. • If grains are randomly oriented, overall component properties are not directional. • Grain sizes typ. range from 1 nm to 2 cm (i.e., from a few to millions of atomic layers). 58 Polymorphism
• Two or more distinct crystal structures for the same material (allotropy/polymorphism) iron system titanium liquid , -Ti 1538ºC -Fe carbon BCC diamond, graphite 1394ºC FCC -Fe 912ºC BCC -Fe
59 DEMO: HEATING AND COOLING OF AN IRON WIRE
The same atoms can • Demonstrates "polymorphism" have more than one Temperature, C crystal structure. Liquid 1536 BCC Stable 1391
longer heat up FCC Stable shorter! 914 BCC Stable longer! cool down Tc 768 magnet falls off shorter
60