Chapter4 - Chapter 4 Point Defects and Diffusion...

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• Introduction • Point Defects • Impurities • Solid State Diffusion Chapter 4 Point Defects and Diffusion
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Introduction- Defects and Impurities • Considering the number of atoms in a cm 3 of crystalline material ( 8.5X10 22 ) it should not be surprising that some atoms will be missing from the lattice. • The presence of the missing atoms aids in the atomic transport process in the solid state. • Trace elements, impurities, can have a dramatic effect on the properties of a material.
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Point Defects Vacancies and interstitials in a crystalline material
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Point Defects
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Point Defects Vacant lattice site G = H - T S
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The Effect of Temperature on the Vacancy Concentration of Nickel -40 -35 -30 -25 -20 -15 -10 -5 0 0 0.001 0.002 0.003 0.004 1/T, 1/K ln(Cv) Room Temperature, 25 C Melting Temperature, 1083 C fr Q slope R ⎛⎞ =− ⎜⎟ ⎝⎠ () exp 1 ln fr vt fr v fr v Q NN RT Q C Q C R T
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1E-15 1E-13 1E-11 1E-09 1E-07 1E-05 0.001 0.1 0 0.001 0.002 0.003 0.004 1/T Cv The Effect of Temperature on the Vacancy Concentration of Nickel T RT T m
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Point Defects Schottky defect 2V Cl and 1V Mg - 2+ Schottky defect 1V Cl and 1V Na - + Cation-anion pair Schottky defect ,, exp 2 fvc vca t van Q CC RT ⎛⎞ == ⎜⎟ ⎝⎠
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Point Defects The defect involves a cation The defect involves an anion The cation defect is more common because of the size of the cation compared to the size of the anion. Vacancy-Interstitial Pair Frenkel defect in AgCl exp 2 fvi vi Q CC RT ⎛⎞ == ⎜⎟ ⎝⎠
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Impurities Interstitial Solid Solution Solvent Solute
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Impurities Substitutional Solid Solution Solvent Solute
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Hume-Rothery Rules Guidelines for Solubility • The size difference between the solute and solvent must be no greater than ~15%. • The electronegativities of the two atomic species must be comparable. • The valence of the two species must be similar. • The crystal structures of the two species must be the same. This is required if the alloy are to form a continuous series of solid solutions. Examples would be Cu-Ni and Si-Ge.
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Propylene mer in a polyethylene chain Ethylene mer in a polypropylene chain Second mer Impurities in a Polymer Chain
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Impurities in Ionic Crystals
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A atoms B atoms Fick’s First Law • Factors affecting atomic transport: dc JD dx =− • Leads to: J = D(C 1 –C 2 )/ x Concentration gradient Jump distance, x Temperature Structure
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Temperature Dependence of Diffusivity exp o Q DD RT ⎛⎞ =− ⎜⎟ ⎝⎠ 1 ln( ) ln( ) o Q R T yb m x =+ lnD o lnD 1/T, K -1 Increasing T Decreasing T Q slope R 0.
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Temperature Dependence of Diffusivity lnD o lnD 1/T, K -1 Increasing T Decreasing T 1 1 2 2 exp exp o o Q DD RT Q RT ⎛⎞ =− ⎜⎟ ⎝⎠ 1 1 2 2 exp exp o o Q D RT D D Q D RT = 1 21 2 11 exp DQ DR T T ⎡⎤ ⎢⎥ ⎣⎦ 1 2 ln T T 1 2 12 1 ln QD RD TT ⎧⎫ ⎪⎪ −= ⎨⎬ ⎩⎭ Q slope R + + + 0.
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Tracer (Self) Diffusion Diffusion of a radioactive isotope
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Melting Point Diffusivity 1E-55 1E-45 1E-35 1E-25 1E-15 1E-05 0 0.001 0.002 0.003 0.004 1/T D Al Cu Ni Pt Melting point diffusivities
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Chapter4 - Chapter 4 Point Defects and Diffusion...

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