On the sink concentration dependence of reaction constants for point defect trapping

Fastenau, R. H. J.; Baal, C. M. van; Penning, Paul; Veen, A. van

doi:10.1002/pssa.2210520226

Cited by 15 publications

(4 citation statements)

References 12 publications

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“…For the random arrangement 27 sinks were randomly introduced in the crystallite, which were rearranged after each 50 starts of a random walker. Earlier work [9] has shown that increasing the number of sinks does not give significant changes in the results. The set of lifetimes] of random walkers obtained in this way determines the capture survival probability p,,.…”

Section: Monte Carlo Simulationsmentioning

confidence: 80%

On the point defect – dislocation interaction in rate theory

Fastenau

Penning

1981

Phys. Stat. Sol. (a)

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The rate of the reaction of point defects and dislocations is studied for periodic and random arrangements of the sinks. Models based on diffusion and on random walk theory are used. The latter model is based on the number of distinct lattice sites visited by a random walking cloud of lattice points. An equation approximating this quantity is given. Cood agreement between the various models for the periodic and for the random arrangement is obtained. Only in the second case deviations from first-order kinetics are found. Consequences of this effect on the theoretical models of swelling caused by irradiation and models dealing with the annealing of point defects by capture by dislocations will be discussed. Die Reaktionsrate von Punktdefekten und Versetzungen wird fiir periodische und statistische Anordnungen von Senken untersucht. Es werden Modelle verwendet, die sich auf die Diffusion und die Theorie zufalliger Bewegungen griinden. Das letztere Modell basiert aufder Zahl getrennter Gitterplatze, die von einer statistisch sich bewegenden Wolke von Gitterpliitzen beriihrt werden. Es wird eine Gleichung aufgestellt, die diese GroBe approximativ angibt. Zwischen den verschiedenen Modellen fiir die periodische und die statistische Anordnung wird gute vbereinstimmung erzielt. Nur im zweiten Fall werden Abweichungen von der Kinetik zweiter Ordnung gefunden. Konsequenzen dieses Effekts auf das theoretische Modell des durch Bestrahlung verurmchten Anschwellens sowie auf Modelle, die das Ausheilen von Punktdefekten infolge Einfang durch Versetzungen betrachten, werden diskutiert.

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Section: Monte Carlo Simulationsmentioning

confidence: 80%

On the point defect – dislocation interaction in rate theory

Fastenau

Penning

1981

Phys. Stat. Sol. (a)

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“…He atoms leaving the box are entering it at the opposite side of the box, so that the box is equivalent with periodically arranged traps, see also refs. [13,15]. For sinks three different trapping radii were taken, in accordance with the calculations in sect.…”

Section: Pe~~~~ally Arranged Trapsmentioning

confidence: 99%

Effects of vacancies near substitutional implants on trapping and desorption of helium — a simulation

Kolk

Veen

Hosson

et al. 1985

Nuclear Instruments and Methods in Physics Research Section B:

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Trapping of He by vacancies and drainage of He from substitutional implants (Ag and Kr in W) to nearby vacancies are investigated using static lattice calculations. The calculations indicate that drainage of He will occur to vacancies within a radius of 2.5 lattice units from the implant. Furthermore the trapping probability of substitutional and interstitial random walkers on a bee lattice by substitutional traps or vacancies is calculated. When implantation-produced vacancies are present in the vicinity of the observed trap a shielding effect occurs. Trapping constants are calculated with two random walk models for both the unshielded and the shielded defect. For the latter several configurations were taken. The results show that shielding of a defect by one vacancy at a distance of three lattice units leads already to a reduction of He trapping by that defect of 30% to 40%.

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“…Rosenstock (2, 3) suggested approximating the term ((1 -c)S) by (1-c) (Sn) and then evaluating the series in Eq. 1 by using the asymptotic form for (Sn ) derived by several authors (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13). It is the purpose of this note to point out that in three dimensions Jain and Pruitt (14) have derived an asymptotic form for p(Sn), the probability density for S.", allowing us to find a more accurate expression for (n) than that yielded by the Rosenstock approximation.…”

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confidence: 95%

“…There has been considerable recent interest in the problem of random walks on lattices with randomly distributed trapping sites (1)(2)(3)(4)(5)(6). The original motivation for studying this problem was to model the trapping of mobile defects in crystals with point sinks (1, 2, 7), but many further applications have been found for this model.…”

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confidence: 99%

Asymptotic form for random walk survival probabilities on three-dimensional lattices with traps

Weiss

1980

Proc. Natl. Acad. Sci. U.S.A.

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The problem of calculating statistics of timeto-trapping of a random walker on a trapfilled lattice is of interest in solid state physics. Several authors have suggested approximate methods for calculating the average survival probabilities. Here, an exact asymptotic form for the probability that an n step random walk visits S. distinct sites is used to ascertain the validity of a simple approximation suggested by Rosenstock. For trap concentrations below 0.05, the relative error in using Rosenstock's approximation is less than 10%.There has been considerable recent interest in the problem of random walks on lattices with randomly distributed trapping sites (1-6). The original motivation for studying this problem was to model the trapping of mobile defects in crystals with point sinks (1, 2, 7), but many further applications have been found for this model. Rosenstock (2) studied the trapping model in analyzing kinetic experiments on luminescent organic materials, and Montroll (8, 9) considered the same model in connection with the kinetics of the conversion of light energy to oxygen in photosynthesis. Klafter and Silbey (6) give a good set of references to various applications of the random walk trapping model. Shuler et al. (10) have also dealt with the relationship between the expected number of distinct sites visited in a random walk and the mean time to trapping, in the context of the Montroll (8, 9) model in which there is one trapping site per unit cell. The present treatment is more general in the sense that it starts from the exact asymptotic distribution of the number of distinct sites visited in an n-step random walk rather than from its expected value.If the random walk takes place on a regular lattice and the probability that a given site is a trapping point is equal to c, then the probability that trapping occurs after step n is (1 -c)Sn where S. is the number of distinct sites visited during the course of an n-step random walk. Hence the expected time to trapping is (n ) = E (1-CM J=1

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On the sink concentration dependence of reaction constants for point defect trapping

Cited by 15 publications

References 12 publications

On the point defect – dislocation interaction in rate theory

On the point defect – dislocation interaction in rate theory

Effects of vacancies near substitutional implants on trapping and desorption of helium — a simulation

Asymptotic form for random walk survival probabilities on three-dimensional lattices with traps

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