imperfections in solids week 3 1. 2 solidification - result of casting of molten material –2 steps...
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IMPERFECTIONS IN SOLIDS
Week 3
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• Solidification- result of casting of molten material– 2 steps
• Nuclei form
• Nuclei grow to form crystals – grain structure
• Start with a molten material – all liquid
Imperfections in Solids
• Crystals grow until they meet each other
nuclei crystals growing grain structureliquid
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Polycrystalline Materials
Grain Boundaries• regions between crystals• transition from lattice of one
region to that of the other• slightly disordered• low density in grain
boundaries– high mobility– high diffusivity– high chemical reactivity
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Solidification
Columnar in area with less undercooling
Shell of equiaxed grains due to rapid cooling (greater T) near wall
Grain Refiner - added to make smaller, more uniform, equiaxed grains.
heat
flow
Grains can be - equiaxed (roughly same size in all directions)
- columnar (elongated grains)~ 8 cm
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Imperfections in Solids
There is no such thing as a perfect crystal.
• What are these imperfections?
• Why are they important?
Many of the important properties of materials are due to the presence of imperfections.
Crystalline defect -> a lattice irregularity having one or more of its dimensions on the order of an atomic diameter
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• Vacancy atoms• Interstitial atoms• Substitutional atoms
Point defects
Types of Imperfections
• Dislocations Line defects
• Grain Boundaries Area defects
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• Vacancies:-vacant atomic sites in a structure.
• Self-Interstitials:-"extra" atoms positioned between atomic sites.
Point Defects
Vacancydistortion of planes
self-interstitial
distortion of planes
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Boltzmann's constant
(1.38 x 10 -23 J/atom-K)
(8.62 x 10-5 eV/atom-K)
Nv
Nexp
Qv
kT
No. of defects
No. of potential defect sites.
Activation energy
Temperature
Each lattice site is a potential vacancy site
• Equilibrium concentration varies with temperature!
Equilibrium Concentration:Point Defects
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• We can get Qv from an experiment.
Nv
N= exp
Qv
kT
Measuring Activation Energy
• Measure this...
Nv
N
T
exponential dependence!
defect concentration
• Replot it...
1/T
N
Nvln
-Qv /k
slope
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EXAMPLE PROBLEM 4.1
Calculate the equilibrium number of vacancies per cubic meter for copper at 1000C. The energy for vacancy formation is 0.9 eV/atom; the atomic weight and density (at 1000C) for copper are 63.5g/mol and 8.4g/cm3, respectively
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Find the equil. # of vacancies in 1m3 of Cu at 1000C.• Given:
ACu = 63.5 g/mol = 8.4 g/cm3
Qv = 0.9 eV/atom NA = 6.02 x 1023 atoms/mol
Estimating Vacancy Concentration
For 1 m3 , N =NAACu
x x 1 m3 = 8.0 x 1028 sites8.62 x 10-5 eV/atom-K
0.9 eV/atom
1273K
Nv
Nexp
Qv
kT
= 2.7 x 10-4
• Answer:
Nv = (2.7 x 10-4)(8.0 x 1028) sites = 2.2 x 1025 vacancies
=N.Acu/V.NA
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• Low energy electron microscope view of a (110) surface of NiAl.• Increasing T causes surface island of atoms to grow.• Why? The equil. vacancy conc. increases via atom motion from the crystal to the surface, where they join the island.
Observing Equilibrium Vacancy Concentration.
Island grows/shrinks to maintain equil. vancancy conc. in the bulk.
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IMPURITIES IN SOLIDS• Impurity or foreign atoms will always be
present, and some will exist as crystalline point defects
• Alloys -> impurity atoms have been added intentionally to impart specific characteristics to the material
• Alloying with copper significantly enhances the mechanical strength without depreciating the corrosion resistance appreciably
• The addition of impurity atoms to a metal will result in the formation of a solid solution
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Two outcomes if impurity (B) added to host (A):• Solid solution of B in A (i.e., random distribution of point defects)
• Solid solution of B in A plus particles of a new phase (usually for a larger amount of B)
OR
Substitutional solid soln.(e.g., Cu in Ni)
Interstitial solid soln.(e.g., C in Fe)
Second phase particle--different composition--often different structure.
Point Defects in Alloys
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Imperfections in Solids
Conditions for substitutional solid solution (S.S.)• W. Hume – Rothery rule
– 1. r (atomic radius) < 15%– 2. Proximity in periodic table
• i.e., similar electronegativities
– 3. Same crystal structure for pure metals– 4. Valency
• All else being equal, a metal will have a greater tendency to dissolve a metal of higher valency than one of lower valency
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Substitutional Solid Solution – Cu-Ni
• The atomic radii for copper and nickel are 0.128 and 0.125nm, respectively
• Both have the FCC crystal structure
• Their electronegativities are 1.9 and 1.8
• Valencies for Cu and Ni are +2
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Imperfections in SolidsApplication of Hume–Rothery rules – Solid
Solutions
1. Would you predictmore Al or Ag to dissolve in Zn?
2. More Zn or Al
in Cu?
Element Atomic Crystal Electro- ValenceRadius Structure nega-
(nm) tivity
Cu 0.1278 FCC 1.9 +2C 0.071H 0.046O 0.060Ag 0.1445 FCC 1.9 +1Al 0.1431 FCC 1.5 +3Co 0.1253 HCP 1.8 +2Cr 0.1249 BCC 1.6 +3Fe 0.1241 BCC 1.8 +2Ni 0.1246 FCC 1.8 +2Pd 0.1376 FCC 2.2 +2Zn 0.1332 HCP 1.6 +2
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Conditions for Interstitial Impurity
• The atomic diameter of an interstitial impurity must be substantially smaller than that of the host atoms
• The maximum allowable concentration of interstitial impurity atoms is low
• Even very small impurity atoms are ordinarily larger than the interstitial sites, and as a consequence they introduce some lattice strains on the adjacent host atoms
• Different crystal structures can fill interstitials
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Specification of Composition
– weight percent100x
21
11 mm
mC
m1 = mass of component 1
100x 21
1'1
mm
m
nn
nC
nm1 = number of moles of component 1
– atom percent
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• are line defects,• slip between crystal planes result when dislocations move,• produce permanent (plastic) deformation.
Dislocations:
Schematic of Zinc (HCP):• before deformation • after tensile elongation
slip steps
Dislocations - Line Defects
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Imperfections in Solids
Linear Defects (Dislocations)– Are one-dimensional defects around which atoms are misalignedBurgers vector (b) represents the magnitude and direction of the
distortion of dislocation in a crystal lattice
Dislocation Line -> A curve running along the center of a dislocation.
• Edge dislocation:– extra half-plane of atoms inserted in a crystal structure– b to dislocation line
• Screw dislocation:– spiral planar ramp resulting from shear deformation– b to dislocation line
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Imperfections in Solids
Edge Dislocation
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• Dislocation motion requires the successive bumping of a half plane of atoms (from left to right here).• Bonds across the slipping planes are broken and remade in succession.
Atomic view of edgedislocation motion fromleft to right as a crystalis sheared.
Motion of Edge Dislocation
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Imperfections in Solids
Screw Dislocation
Burgers vector b
Dislocationline
b
(a)(b)
Screw Dislocation
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Edge, Screw, and Mixed Dislocations
Edge
Screw
Mixed
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Imperfections in Solids
Dislocations are visible in electron micrographs
51,450 magnified
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Planar Defects in Solids• One case is a twin boundary (plane)
– Essentially a reflection of atom positions across the twin plane.
• A twin boundary is a special type of grain boundary across which there is a specific mirror lattice symmetry
• Annealing twins are typically found in metals that have the FCC crystal structure, while mechanical twins are observed in BCC and HCP metals
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Planar Defects in Solids
• Stack Fault are found in FCC metals when there is an interruption in the ABCABCABC . . . stacking sequence of close-packed planes
• Phase boundaries exist in multiphase materials across which there is a sudden change in physical and/or chemical characteristics
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Bulk or Volume Defects
• Other defects exist in all solid materials that are much larger than those discussed
• These include pores, cracks, foreign inclusions, and other phases
• They are normally introduced during processing and fabrication steps.
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Numerical Problems
• Problems 4.1 to 4.5 and 4.7 to 4.25
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