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Transcript of Introduction To Materials Science, Chapter 4, Imperfections in solids University of Virginia, Dept....
Introduction To Materials Science, Chapter 4, Imperfections in solids
University of Virginia, Dept. of Materials Science and Engineering 1
“Crystals are like people, it is the defects in them which tend to make them interesting!” - Colin Humphreys.
• Defects in Solids
0D, Point defects vacancies interstitials impurities, weight and atomic composition
1D, Dislocations edge screw
2D, Grain boundaries tilt twist
3D, Bulk or Volume defects
Atomic vibrations
4.9 - 4.11 Microscopy & Grain size determination –
Not Covered / Not Tested
Chapter Outline
Introduction To Materials Science, Chapter 4, Imperfections in solids
University of Virginia, Dept. of Materials Science and Engineering 2
Real crystals are never perfect, there are always defects
Schematic drawing of a poly-crystal with many defects by Helmut Föll, University of Kiel, Germany.
Defects – Introduction (I)
Introduction To Materials Science, Chapter 4, Imperfections in solids
University of Virginia, Dept. of Materials Science and Engineering 3
Defects – Introduction (II)
Defects have a profound impact on the macroscopic properties of materials
Bonding
+
Structure
+
Defects
Properties
Introduction To Materials Science, Chapter 4, Imperfections in solids
University of Virginia, Dept. of Materials Science and Engineering 4
Composition
Bonding Crystal Structure
ThermomechanicalProcessing
Microstructure
Defects – Introduction (III)
Processing determines the defects
defect introduction and manipulation
Introduction To Materials Science, Chapter 4, Imperfections in solids
University of Virginia, Dept. of Materials Science and Engineering 5
Types of Defects
Four categories depending on their dimension
0D, Point defects: atoms missing or in irregular places in the lattice (vacancies, interstitials, impurities)
1D, Linear defects: groups of atoms in irregular positions (e.g. screw and edge dislocations)
2D, Planar defects: interfaces between homogeneous regions of the material (grain boundaries, external surfaces)
3D, Volume defects: extended defects (pores, cracks)
Introduction To Materials Science, Chapter 4, Imperfections in solids
University of Virginia, Dept. of Materials Science and Engineering 6
Point defects: vacancies &interstitials
Self-interstitials
Vacancy
Vacancy - lattice position that is vacant because atom is missing.
Interstitial - atom that occupies a place outside the normal lattice position. May be same type of atom (self interstitial) or an impurity interstitial.
Introduction To Materials Science, Chapter 4, Imperfections in solids
University of Virginia, Dept. of Materials Science and Engineering 7
Equilibrium number of vacancies is due to thermal vibrations
How many vacancies?
Ns = number of regular lattice sites
kB = Boltzmann constant
Qv = energy to form a vacant lattice site in a
perfect crystal T = temperature in Kelvin (note, not in oC or oF).
Room temperature in copper: one vacancy per 1015 atoms.Just below the melting point: one vacancy for every 10,000 atoms.Above lower bound to number of vacancies. Additional (non-equilibrium) vacancies introduced in growth process or treatment
(plastic deformation, quenching, etc.)
Tk
QexpNNB
vsv
Introduction To Materials Science, Chapter 4, Imperfections in solids
University of Virginia, Dept. of Materials Science and Engineering 8
Estimate number of vacancies in Cu at room T
kB = 1.38 10-23 J/atom-K = 8.62 10-5 eV/atom-K
T = 27o C + 273 = 300 K. kBT = 300 K 8.62 10-5 eV/K = 0.026 eV
Qv = 0.9 eV/atom
Ns = NA/Acu
NA = 6.023 1023 atoms/mol
= 8.4 g/cm3
Acu = 63.5 g/mol
Tk
QexpNNB
vsv
3
223
23
s cmatoms108
molg5.63
cmg4.8mol
atoms10023.6N
atomeV026.0
atomeV9.0expcm
atoms108N
322
v
37 cmvacancies104.7
Introduction To Materials Science, Chapter 4, Imperfections in solids
University of Virginia, Dept. of Materials Science and Engineering 9
Large distortions in surrounding lattice Energy of self-interstitial formation is ~ 3 x larger than for vacancies (Qi ~ 3Qv) equilibrium concentration of self-interstitials is very low(< 1/ cm3 at 300K)
Self-interstitials
1
2
3
4
5
Point defects: self-interstitials, impurities
(1) vacancies(2) self-interstitial(3)interstitial impurity(4,5)substitutional impurities
Arrows local stress introduced by defect
Introduction To Materials Science, Chapter 4, Imperfections in solids
University of Virginia, Dept. of Materials Science and Engineering 10
Impurities
Impurities atoms which differ from host
All real solids are impure. Very pure metals 99.9999%
- one impurity per 106 atoms May be intentional or unintentional
Carbon in small amounts in iron makes steel. It is stronger.
Boron in silicon change its electrical properties.
Alloys - deliberate mixtures of metalsSterling silver is 92.5% silver – 7.5% copper alloy.
Stronger than pure silver.
Introduction To Materials Science, Chapter 4, Imperfections in solids
University of Virginia, Dept. of Materials Science and Engineering 11
How Are Impurities Contained in Alloy?Solid solutions
Host (Solvent or Matrix) dissolves minor component (Solute). Ability to dissolve is called Solubility. Solvent: element in greater amount Solute: element present in lesser amount Solid Solution:
homogeneous maintain crystal structure randomly dispersed impurities
(substitutional or interstitial)
Second Phase As solute atoms added: new compounds or structures form or solute forms local precipitates
Whether addition of impurities results in a solid solution or second phase depends nature of impurities, concentration, temperature and pressure
Introduction To Materials Science, Chapter 4, Imperfections in solids
University of Virginia, Dept. of Materials Science and Engineering 12
Substitutional Solid Solutions
Factors for high solubility(Solubility limit maximum that can dissolve)
Atomic size: need to “fit” solute and solvent atomic radii should be within ~ 15%
Crystal structure: solute and solvent the same
Electronegativities: should be comparable (otherwise new inter-metallic phases favored)
Valency: If solute has higher valency than solvent, generally more goes into solution
Ni
Cu
Introduction To Materials Science, Chapter 4, Imperfections in solids
University of Virginia, Dept. of Materials Science and Engineering 13
Interstitial Solid Solutions
Factors for high solubility:
FCC, BCC, HCP: void space between host (matrix) atoms relatively small atomic radius of solute should be significantly less than solvent
Max. concentration 10%, (2% for C-Fe)
Carbon interstitial atom in BCC iron
Interstitial solid solution of C in BCC Fe ( phase). C small enough to fit (some strain in BCC lattice).
Introduction To Materials Science, Chapter 4, Imperfections in solids
University of Virginia, Dept. of Materials Science and Engineering 14
Composition / Concentration
atom percent (at %): useful in understanding material at atomic level
Number of moles (atoms) of one element relative to total number of moles (atoms) in alloy.
2 component: concentration of element 1 in at. %:
Weight Percent (wt %)
Weight of one element relative to total alloy weight
2 components: concentration of element 1 in wt. %
100mm
mC
21
11
100nn
nC
21
1
mm
m'1
nm1= number density = m’1/A1 (m’1 = weight in
grams of 1, A1 is atomic weight of element 1)
Introduction To Materials Science, Chapter 4, Imperfections in solids
University of Virginia, Dept. of Materials Science and Engineering 15
Composition Conversions
Weight % to Atomic %:
100ACAC
ACC
2'21
'1
1'1
1
Atomic % to Weight %:
100ACAC
ACC
2'21
'1
2'2
2
100ACAC
ACC
1221
21'1
100ACAC
ACC
1221
12'2
Textbook, pp. 71-74
Introduction To Materials Science, Chapter 4, Imperfections in solids
University of Virginia, Dept. of Materials Science and Engineering 16
Dislocations = Linear Defects
Interatomic bonds significantly distorted in immediate vicinity of dislocation line
(Creates small elastic deformations of lattice at large distances.)
Dislocations affect mechanical properties Discovery in 1934 by Taylor, Orowan and Polyani marked beginning of our understanding of mechanical properties of materials
Introduction To Materials Science, Chapter 4, Imperfections in solids
University of Virginia, Dept. of Materials Science and Engineering 17
Describe Dislocations Burgers Vector
Burgers vector, b, describes size + direction of lattice distortion by a dislocation. Make a circuit around dislocation: go from atom to atom counting the same number of atomic distances in both directions.
Vector needed to close loop is bb
Burgers vector above directed perpendicular to dislocation line. These are called edge dislocations.
Introduction To Materials Science, Chapter 4, Imperfections in solids
University of Virginia, Dept. of Materials Science and Engineering 18
Screw dislocations
Screw dislocation: parallel to the direction in which the crystal is being displaced Burgers vector parallel to dislocation line
Edge dislocation: Burgers vector perpendicular to dislocation line.
Find the Burgers vector of a screw dislocation. How did it get its name?
Introduction To Materials Science, Chapter 4, Imperfections in solids
University of Virginia, Dept. of Materials Science and Engineering 19
Interfacial DefectsExternal SurfacesSurface atoms unsatisfied bonds higher energies than bulk atoms Surface energy, (J/m2)
• Surface areas try to minimize (e.g. liquid drop)
• Solid surfaces can “reconstruct” to satisfy atomic bonds at surfaces.
Grain BoundariesPolycrystalline: many small crystals or grains. Grains have different crystallographic orientation. Mismatches where grains meet.
1. Surfaces and interfaces are reactive
2. Impurities tend to segregate there.
3. Extra energy associated with interfaces
larger grains tend to grow by diffusion of atoms at expense of smaller grains, minimizing energy.
Introduction To Materials Science, Chapter 4, Imperfections in solids
University of Virginia, Dept. of Materials Science and Engineering 20
High and Low Angle Grain Boundaries
Misalignments of atomic planes between grains Distinguish low and high angle grain boundaries
Introduction To Materials Science, Chapter 4, Imperfections in solids
University of Virginia, Dept. of Materials Science and Engineering 21
Tilt and Twist Grain Boundaries
Tilt boundary Low angle grain boundary: an array of aligned edge dislocations (like joining two wedges)
Twist boundary - boundary region consisting of arrays of screw dislocations (like joining two halves of a cube and twist an angle around the cross section normal)
Transmission electron microscope image of a small angle tilt boundary in Si. The red lines mark the edge dislocations, the blue lines indicate the tilt angle
Introduction To Materials Science, Chapter 4, Imperfections in solids
University of Virginia, Dept. of Materials Science and Engineering 22
Bulk or Volume Defects
Pores: affect optical, thermal, mechanical properties
Cracks: affect mechanical properties Foreign inclusions: affect electrical,
mechanical, optical properties
Cluster of microcracks in a melanin granule irradiated by a short laser pulse. Computer simulation by L. V. Zhigilei and B. J. Garrison.
Introduction To Materials Science, Chapter 4, Imperfections in solids
University of Virginia, Dept. of Materials Science and Engineering 23
Atomic Vibrations
Heat causes atoms to vibrate
Vibration amplitude increases with temperature
Melting occurs when vibrations are sufficient to rupture bonds
Vibrational frequency ~ 1013 Hz
Average atomic energy due to thermal excitation is of order kT
Introduction To Materials Science, Chapter 4, Imperfections in solids
University of Virginia, Dept. of Materials Science and Engineering 24
Summary
Alloy Atom percent Atomic vibration Boltzmann’s constant Burgers vector Composition Dislocation line Edge dislocation Grain size Imperfection Interstitial solid solution Microstructure Point defect Screw dislocation Self-Interstitial Solid solution Solubility limit Solute Solvent Substitutional solid solution Vacancy Weight percent
Understand language and concepts: