The Mathematical Analysis of Diffusion in Dislocations

Claire, A.D. Le; Rabinovitch, A.

doi:10.1016/b978-0-12-522662-2.50010-8

Cited by 35 publications

(43 citation statements)

References 41 publications

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“…Therefore, if an equal value of dln C/dX is obtained for different diffusion times, the deeper region can be attributed to the dislocation pipe diffusion. If the tail slope in the deeper region is caused by the grain boundary diffusion, dln C/dX 6/5 is linear and it depends on diffusion time [17,18].…”

Section: Resultsmentioning

confidence: 99%

Volume and dislocation diffusion of iron, chromium and cobalt in CVD ß-SiC

Takano

Nitta

Seto

et al. 2001

Science and Technology of Advanced Materials

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Impurity tracer diffusion of 59 Fe, 51 Cr and 57 Co in CVD b-SiC has been studied in the temperature range between 973 and 1873 K. The temperature dependence of the volume diffusion coef®cients of iron and chromium can be expressed by linear Arrhenius equations. The preexponential factor and the activation energy are estimated to be 8.7 £ 10 215 m 2 s 21 and 111 kJ mol 21 for iron, respectively, and 9.5 £ 10 215 m 2 s 21 and 81 kJ mol 21 for chromium, respectively. The diffusion coef®cients of iron and chromium are much higher than those of the self-diffusion in b-SiC. Furthermore, the activation energies for the diffusion of iron and chromium are about one-tenth of those for carbon and silicon in b-SiC. Therefore, it seems that an interstitial mechanism is predominant for the diffusion of iron and chromium in b-SiC. On the other hand, the diffusion coef®cient of cobalt above 1673 K is higher than that of iron, while at lower temperatures it is much lower than that of iron. The difference in the diffusion coef®cients at 1173 K is more than three orders of magnitude. Thus, the temperature dependence of the diffusion coef®cients of cobalt shows a strongly curved Arrhenius relation. This suggests that cobalt atoms diffuse by an interstitial mechanism at higher temperatures and by a substitutional mechanism at lower temperatures. From the deeper regions of the penetration pro®les of iron, chromium and cobalt the dislocation diffusion coef®cients of them have been estimated. q

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Section: Resultsmentioning

confidence: 99%

Volume and dislocation diffusion of iron, chromium and cobalt in CVD ß-SiC

Takano

Nitta

Seto

et al. 2001

Science and Technology of Advanced Materials

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“…The error function and the tail regions can be ascribed to the result of lattice diffusion and the fast diffusion of 180 along high diffusivi ty paths, such as dislocations at the crystal sur face, respectively (Le Claire and Rabinovitch, 1984). By the same reasons as and Sakaguchi et al (1992) we recognized that the tail can be ascribed to the fast diffusion of 180 along dislocations introduced into the sur face region of the crystal by mechanical treat ment.…”

Section: Measurement Of Concentration Gradientsmentioning

confidence: 75%

Oxygen self-diffusion along high diffusivity paths in forsterite.

1992

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Diffusion profiles of 180 tracer in single crystals of forsterite following anneals at 1100° and 1200°C have been determined by a depth profiling technique using secondary ion mass spectrometry. The diffu sion penetration profiles showed error function forms -with developed tails. The profiles were analyzed in terms of diffusion in the forsterite lattice together with a contribution from dislocation. The present results of lattice diffusion lie in the range of the extrapolation of lines on Arrhenius plots reported previously for intracrystalline diffusion in forsterite. The dislocation diffusion coefficients are about 104 times faster than the lattice diffusion at the same temperature.Diffusion along the dislocations takes place within a pipe with radius of about 0.1 nm surrounding the dislocation line. Based on the above results, 0 diffusion along high diffusivity paths, such as dislocations and grain boundaries, play an im portant role on the diffusional creep in olivine under laboratory condition.

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“…Using periodic models, additive formulas [6,7] for diffusion in Harrison's A-type regime [8] can probably be refined and extended to different kinds of structure and diffusant-defect interaction.…”

Section: Discussionmentioning

confidence: 99%

“…This leads to vanishing first and second terms on the left-hand side of (10) and therefore averaging these equations gives (11) These relations determine the values of Dij which ensure that (10) are solvable for yij Thus, with functions y k and yij as determined according to (7) to (11) the initial equation…”

Section: Technique For the Effective Diffusivity Calculationmentioning

confidence: 98%

On effective diffusivity of periodic non‐homogeneous solid media

Mishin

1992

Physica Status Solidi (b)

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Diffusion in a non-homogeneous medium with periodic spatial variations of diffusivity and driving force is analyzed in detail. After a time t $ 7 (z being time to attain local quasi-stationarity) diffusicn proceeds like in a homogeneous medium with an effective diffusivity D i j Correct procedure of Qi calculation includes solution of a stationary diffusion problem in a pzriodic unit cell with special boundary conditions. Methods of exact calculation and estimation of D, are discussed, some simple estimates are presented. Possible applications of the theory are sketched.

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The Mathematical Analysis of Diffusion in Dislocations

Cited by 35 publications

References 41 publications

Volume and dislocation diffusion of iron, chromium and cobalt in CVD ß-SiC

Volume and dislocation diffusion of iron, chromium and cobalt in CVD ß-SiC

Oxygen self-diffusion along high diffusivity paths in forsterite.

On effective diffusivity of periodic non‐homogeneous solid media

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