Diffusion

Claire, A.D. Le

doi:10.1007/978-1-4684-8082-5_1

Cited by 14 publications

(9 citation statements)

References 39 publications

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“…The effective or bulk diffusion coefficient in this case will be Claire 1976) where D, Dp are, respectively, the volume and pipe diffusion coefficients and x ~ CpUp/CU iS the mole ratio of the amount of the diffusing species in the cores to that in the matrix, Cp and c being the respective molar concentrations in cores and matrix and Vp and v the respective volumes occupied by cores and matrix. If we take the effective pipe diameter of the dislocation to be of the order of 1 nm, then vp/v --~ 10 18p where p is the dislocation density in m -e and, for predominance of pipe diffusion, (1) leads to D c p >> lft ~s --_ Dp Cp…”

Section: Kinetics Of Equilibration With Respect To Water Effectsmentioning

confidence: 99%

Quartzite rheology under geological conditions

1990

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The problems associated with extrapolating laboratory measurements on quartzite rheotogy to geological conditions are discussed, with special reference to the question of equilibration with respect to the effect of water. Some new results on synthetic specimens crystallized from wet amorphous silica are presented in the expectation that water equilibration is more closely attained in these than in natural quartz specimens. These results and earlier ones from the literature are collated and used to arrive at limits on quartzite flow strength under geological conditions.

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Section: Kinetics Of Equilibration With Respect To Water Effectsmentioning

confidence: 99%

Quartzite rheology under geological conditions

1990

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“…Most solid state transformations are properly described by an Arrhenius dependence of the rate constant20–22: where E A is the activation energy and R is the universal gas constant ( E A is temperature‐independent). With this particular temperature dependence and supposing that thetransformation rate at T 0 is negligible, Eq.…”

Section: Introductionmentioning

confidence: 99%

Simple approximate analytical solution for nonisothermal single‐step transformations: Kinetic analysis

Farjas

Roura

2008

AIChE Journal

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In this paper, we develop a method for obtaining the approximate solution for the evolution of single-step transformations under non-isothermal conditions. We have applied it to many reaction models and obtained very simple analytical expressions for the shape of the corresponding transformation rate peaks. These analytical solutions represent a significant simplification of the system's description allowing easy curve fitting to experiment. A remarkable property is that the evolutions of the transformed fraction obtained at different heating rates are identical when time is scaled by a time constant. The accuracy achieved with our method is checked against several reaction models and different temperature dependencies of the transformation rate constant. It is shown that its accuracy is closely related with that of the Kissinger method.

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“…1 has been verified when there is at least twofold symmetry around the individual jump vectors (Compaan and Haven 1956, 1958, Le Claire and Lidiard 1956 or, alternatively, when all tracer jumps are 'equivalent' (Mullen 1961, Howard 1966, and when 'direct' correlation exists only over consecutive jumps (Kutner 1985). Analysis of its validity in particular circumstances seems especially useful.…”

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confidence: 97%

“…Analysis of its validity in particular circumstances seems especially useful. Le Claire (1970) has demonstrated that eqn. (1) is valid for self-diffusion and impurity diffusion with a vanishingly small concentration of vacancies; de Bruin, Bakker and van der Mey (1977) have shown that eqn.…”

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confidence: 98%

“…(1) it is possible to explore the correlation effect through the correlation between consecutive jumps with the result that most analytical work has been based on this equation. For example, it is essential for calculations of the tracer correlation factor using the 'matrix method' (Le Claire and Lidiard 1956, Mullen 1961, Howard 1966, andit is built into theManning (1968,1971) theory of tracer diffusion in the random alloy.…”

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confidence: 99%

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