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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 that 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 aid 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(Vc) Room Temperature, 25 C Melting Temperature, 1083 C fr Q slope R = - ( 29 exp exp 1 ln fr v t fr v fr v Q N N RT Q C RT 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 v cat v an Q C C 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 v i Q C C 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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Coordination Number and Atomic Radius Coordination Number 12 8 6 4 Modified Radius 1 0.97 0.96 0.88 Interatomic distance Temperature γ α 910ºC
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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 J D 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 D D RT = - 1 ln( ) ln( ) o Q D D R T  = -   y b mx = + 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 D D RT Q D D RT = - = - 1 1 2 2 exp exp o o Q D RT D D Q D RT - = - 1 2 1 2 1 1 exp
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