مکانیزم های نفوذ در جامدات

صفحه 1:
Correlation in Solid-State Diffusion 

صفحه 2:
Random walk of a atom on a lattice © © © © © © © © © © Einstein(alsoEinstein- Smoluchowski) relation: relates the mean square displacement to the diffusion coefficient D and time t 

صفحه 3:
2 tracer correlation factor =—SN The tracer correlation factor can be expressed in terms of the cosine of the angle between the ‘first’ Jump and all given ‘atom (the tracer). is the tracer correlation factor 

صفحه 4:
The tracer correlation factor 10 0 < 9و > 1+2 -۲ m=1 Example of the convergence of the cosine between the first tracer A jump and the m’th tracer A jump 

صفحه 5:
cer correlation factors depend on: * the type of lattice. * the diffusion mechanism. ۰ the type of diffusing atom in the matrix. ¢ the degree of local order of the atomic components. 

صفحه 6:
كي - ‎mechani‏ ی solutes Small solutes 9 2 6 such © ۳ ۳ ; > : At low concentrations all jump directions as H, C, N, and eee 5 ‏يج‎ | are equally probable > no correlation Oin bec and fcc s$s 9 se metals are dissolved in 96 65666 octahedral © Matrix atom © = Interstitial solute a. 7 ‏تست‎ Ue 

صفحه 7:
(0056) <0 mal alt reo For self-diffusion in cubic lattices, the correlation factors for vacancy- assisted diffusion are just numbers, often called geometric correlation factors f0: ‘fec:-f0-=-0.781- bec: FO =0.727 6 sc: f0O —0.653 diamond: fo= Vacancy mechanism After a vacancy- tracer exchange a reverse tracer jump is more likely, simply because the vacancy is still available on the neighbour site. © © © © 01019 © © © © © © © © dominates self- and solute diffusio in metals, crvstals. © © © © © © © © © © © © © © © Matrix atom Tracer atom Vacancy © ۰ لا 

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Vacancy mechanism of self-diffusion - Rule of Thumb” > 1-7 | Spatial and Temporal Correlation ۳ Mossbauer spectroscopy (MBS) ۳ ic techni i = 7 icroscopic techniques 1 ۳ 500 9۳ ‏با‎ nuclear magnetic relaxation (NMR) 7 

صفحه 9:
Calculation of Correlation Factors 1 .=— = €08180° - ممرظ ند (6۵۵0) This equation is similar to the ‘rule of thumb’ 

صفحه 10:
Exact values of f for self-diffusion in various lattices id chain vacancy 0 honeycomb vacancy 1/3 2d-square vacancy 0.467 2d hexagonal vacancy 0.56006 diamond vacancy 1/2 simple cubic vacancy 0.6531 bee cubic vacancy 0.7272, (0.72149) fee eubie vacancy 0.7815 fee eubie divacaney 0.4579 bee cubic divacancy 0.335 to 0.469 fec cubic (100) dumb-bell interstitial 0.4395, any lattice direct interstital 1 diamond colinear interstitialey 0.727 CaP. (F) non-colinear interstitialcy 0.9855 CaF2(Ca) _colinear interstitialcy 4/5 CaF2(Ca) _non-colinear interstitialcy 1 

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۳ Between ۳ = estimates of correlation factors and exact values exact values ‘Rule of Thu: Lattice 7 1-2 Correlation factor fee 12 0.833 0.781 bec 8 0.750 0.727 simple cubic 6 0.667, 0.653. diamond 4 0.500 0.500 honeycomb, 3 1/3 1/3 2d square 4 0.5, 0.467 6 2d hexagonal 2/3 0.56006 10 

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Vacancy-mediated Solute Diffusion olvent diffusion dilute fcc alloys ive-frequency-model’ 3 11 

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Face-Centered Cubic Solvents wy: solute-vacancy exchange rate wy: rotation rate of the solute-vacancy pair wy: dissociation rate of the solute-vacancy pair ‘Five-frequency model’ Ye 8 wy: association rate of the solute-vacancy pair ‘Energy 8 8 8 ۱۶ ٩ ‏9ه‎ @, landscape’ w: vacancy-atom exchange rate in the solvent © mB, 2 © © “oe 5 CLT ‏ورس‎ © Ww 0 ‏مح لله ونه‎ The correlation factor f2 is a function of all vacancy- © Matrix atom @ Soluteatom 1 Vacancy atom exchange 12 

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رس several special cases vacancy-solute exchanges occur much faster than vacancy-solvent vacancy-solute exchange is much slower than vacancy-solvent exc tT ‏ونا‎ >> W1,W3,..., ۱ 13 

صفحه 15:
Thanks for attention