Diffusion Solids Fundamentals Diffusion Controlled Solid State Episode 2 Part 2 pot

... ϕ: ∂C ∂t = D r 2  ∂ ∂r  r 2 ∂C ∂r  + 1 sin Θ ∂ ∂Θ  sin Θ ∂C ∂Θ  + 1 sin 2 Θ ∂ 2 C ∂ 2 ϕ  = D  ∂ 2 C ∂r 2 + 2 r ∂C ∂r + 1 r 2 sin 2 Θ ∂ 2 C ∂ϕ 2 + 1 r 2 ∂ 2 C ∂Θ 2 + 1 r 2 cot Θ ∂C ∂Θ  . (2. 9) Experimental ... diffusion coefficient for that direction, D(α 1 ,α 2 ,α 3 ), can be written as D(α 1 ,α 2 ,α 3 )=α 2 1 D 1 + α 2 2 D 2 + α 2 3 D 3 . (2....

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... with x-projection d x ), Eq. (4 .21 ) re- duces to  R 2 random  =  n  d 2 ,  X 2 random  =  n  d 2 x . (4 .22 ) Here n denotes the average number of jumps of a particle. It is useful to introduce ... Perfect Solids, W. Shockley (Ed.), Wiley, New York, 19 52, p. 26 2 9. C. Wert, Phys. Rev. 79, 601 (1950) 10. G. Vineyard, J. Phys. Chem. Sol. 3, 121 (1957) 11. W.M. Franklin,...

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... formation: V F SP 1.63 for KBr 2. 04 for NaCl 1 .23 for KBr 1.37 for NaBr Yoon and Lazarus [22 ] Cation migration: V M V C 0 .21 for KCl 0 .26 for NaCl 0 .25 for KBr 0 .25 for NaBr Yoon and Lazarus [22 ] Intrinsic conduction: V M V C + ... probability F 3 (α)= 2. 76 + 4.93α +2. 05α 2 2.76 + 6.33α +4. 52 2 + α 3 (7.43) is a function of the ratio α = ω 4 /ω 5 . For self-diffusion, all freq...

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... Publishing, 1983, p.1139 21 . R.M. Emrick, Phys. Rev. 122 , 1 720 –1733 (1961) 22 . D.N. Yoon, D. Lazarus, Phys. Rev. B 5, 4935 (19 72) 23 . B.E. Mellander, Phys. Rev. B 26 , 5886 (19 82) 24 . A.M. Brown, M.F. ... Andrew, Inc., 20 05, p. 69 26 . N.L. Peterson, Solid State Physics 22 , 481 (1968) 27 . J.A.M. van Liempt, Z. Physik 96, 534 (1935) 28 . O.D. Sherby, M.T. Simnad, Tran...

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... York, 1985 12. A.Einstein,Z.f.Elektrochemie17, 23 5 (1908) 13. C.A. Angell, J. Non-Cryst. Solids 1 02, 20 5 (1988) 14. A.W. Imre, S. Voss, H. Mehrer, Defect and Diffusion Forum 23 7 24 0, 370 (20 05) 15. ... Non-Cryst. Sol. 351, 3816 (20 05) 29 . A.W. Imre, S. Voss, H. Mehrer, Phys. Chem. Chem. Phys. 4, 321 9 (20 02) 30. S. Voss, F. Berkemeier, A.W. Imre, H. Mehrer, Z. Phys. Chem. 2...

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... β)= c 0 √ Dt L 2 √ π ∆  1  η 2 σ − 2  exp(−η 2 /4σ) σ 3 /2  ∆ − σ ∆ − 1  1 /2  exp(−Y 2 ) √ π − Y erfcY  dσ. ( 32. 28) The factor 1/L in Eqs. ( 32. 26) and ( 32. 28) is important. For a bicrystal ... diffusivities we have: ∂c ∂t = D  ∂ 2 c ∂y 2 + ∂ 2 c ∂z 2  for | y |≥ δ /2 , ∂c gb ∂t = D gb  ∂ 2 c gb ∂y 2 + ∂ 2 c gb ∂z 2  for | y |<δ /2 . ( 32. 3) I...

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... BibliographyofSolid-StateDiffusion 18 Part I Fundamentals of Diffusion 2 Continuum Theory of Diffusion 27 2. 1 Fick’sLawsinIsotropicMedia 27 2. 1.1 Fick’sFirstLaw 28 2. 1 .2 EquationofContinuity 29 2. 1.3 Fick’s Second Law ... ProfileAnalysisbySerialSectioning 21 7 13.3 .2 ResidualActivityMethod 22 2 13.4 IsotopicallyControlledHeterostructures 22 3 13.5 SecondaryIonMassSpectrom...

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... t)= 4C 0 π ∞  j=0 1 2j +1 sin  (2j +1)π L x  exp  − (2j +1) 2 π 2 D L 2 t  , (3.50) where for convenience 2j + 1 was substituted for n so that j takes values 0, 1, 2, . Each term in Eq. ... is R 2 = n  i=1 r 2 i +2 n−1  i=1 n  j=i+1 r i r j , X 2 = n  i=1 x 2 i +2 n−1  i=1 n  j=i+1 x i x j . (4.19) If we perform an average over an ensemble of particles, we get Fi...

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... 125 , 8 62 (19 62) 23 . R.O. Simmons, R.W. Balluffi, Phys. Rev. 125 , 8 62 (19 62) 24 . A. Seeger, J. Phys. F. Metal Phys. 3, 24 8 1973) 25 . R.O. Simmons, R.W. Balluffi, Phys. Rev. 117, 52 (1960) 26 . G. Bianchi, ... planar 1 ∞ diamond 0.4 423 1.7 929 imple cubic 0.3405 1.5164 bcc 0 .28 22 1.39 32 fcc 0 .25 36 1.3447 bcc, octahedral interstices 0. 428 7 1.7504 bcc, tetrahedral interst...

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... (20 01) 24 . I.V. Belova, G.E. Murch, Philos. Mag, A78, 1085–10 92 (1998) 25 . I.V. Belova, G.E. Murch, Philos. Mag, A79, 193 20 2 (1999) 26 . I.V. Belova, G.E. Murch, J. Phys. Chem. Sol. 60, 20 23 20 29 ... Mater. 52, 623 (20 04) 35. A. Paul, A.A. Kodentsov, F.J.J. van Loo, Defect and Diffusion Forum 23 7– 24 0, 813 (20 05) 10.5 Microstructural Stability of the Kirkendall Plane 175 s...

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