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These are the Lecture Slides of Science and Engineering of Materials which includes Point Defects, Types of Defects, Equilibrium Number, Thermal Vibrations, Boltzmann Constant, Regular Lattice Sites, Substitutional Solid Solutions, Composition Conversions etc. Key important points are: Defects in Solids, Point Defects, Types of Defects, Equilibrium Number, Thermal Vibrations, Boltzmann Constant, Regular Lattice Sites, Substitutional Solid Solutions, Composition Conversions
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“Crystals are like people, it is the defects in them which tend to make them interesting!” - Colin Humphreys.
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
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)
Composition
Bonding Crystal Structure
Thermomechanical Processing
Microstructure
Defects – Introduction (III)
Processing determines the defects
defect introduction and manipulation
Types of Defects
Four categories
depending on their dimension
atoms missing or in irregular places in the lattice (vacancies, interstitials, impurities)
groups of atoms in irregular positions (e.g. screw and edge dislocations)
interfaces between homogeneous regions of the material (grain boundaries, external surfaces)
extended defects (pores, cracks)
Equilibrium number of vacancies is
due to thermal vibrations
How many vacancies?
N (^) s = 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 o^ C or o^ F).
Room temperature in copper: one vacancy per 10 15 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.)
B v s v
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 = 27 o^ C + 273 = 300 K. kB T = 300 K × 8.62 × 10 -5^ eV/K = 0.026 eV Qv = 0.9 eV/atom Ns = N (^) Aρ/Acu NA = 6.023 × 10 23 atoms/mol ρ = 8.4 g/cm 3 Acu = 63.5 g/mol
N (^) v = Nsexp −Qv kBT
(^223)
(^233) s 8 10 atomscm mol
cm
^ =
= × −
atoms N (^) v (^810223)
= 7. 4 × 107 vacancies cm^3
Impurities
How Are Impurities Contained in Alloy?
homogeneous maintain crystal structure randomly dispersed impurities (substitutional or interstitial)
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
Interstitial Solid Solutions
Interstitial solid solution of C in BCC Fe (α phase). C small enough to fit (some strain in BCC lattice).
Composition / Concentration
atom percent (at %): useful in understanding material at atomic level
N umber 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. %
1 2
1
1 2
1 m m
' m
n (^) m1 = number density = m’ 1 /A 1 (m’ 1 = weight in
grams of 1, A 1 is atomic weight of element 1)
Dislocations = Linear Defects
(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 Docsity.com
b
Burgers vector above directed perpendicular to dislocation line. These are called edge dislocations.
Interfacial Defects
Surface atoms unsatisfied bonds
higher energies than bulk atoms
Surface energy, γ (J/m 2 )
Polycrystalline: many small crystals or grains. Grains have different crystallographic orientation. Mismatches where grains meet.
larger grains tend to grow by diffusion of atoms at expense of smaller grains, minimizing energy.
Misalignments of atomic planes between grains Distinguish low and high angle grain boundaries
