Diffusion of a low-soluble impurity in a solid matrix

Gladkov, V. P.; Kashcheev, V. A.; Петров, Н. В.; Rumyantsev, I. M.

doi:10.1134/1.1688411

Cited by 2 publications

(7 citation statements)

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“…(9) leads to a slight distortion of the resulting curves for the flux ϕ(τ) and the impurity-concentration profile c(x, t), whereas the shape of the curve is invariant and the results obtained are consistent with the physical meaning of the processes initially incorporated in the mathematical model (1), (7). Equation (10) represents the linear integral Volterra equation with its kernel in the form of a convolution.…”

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confidence: 53%

“…In [6], an analysis has been made of the process of diffusion of the impurity from a thin layer into a solid matrix, in which the finite time of dissociation of the layer α −1 was taken into account and the time dependence of the diffusion-source strength and an expression for the concentration profile of the impurity in the sample c(x, t) were obtained. In [7], consideration has been given to the process of diffusion on condition of a constantly acting source but under the assumption that the content of the impurity in the matrix is limited by the solubility limit c * .…”

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confidence: 99%

“…The set of expressions (11) and (12) is the solution of problem (1), (7) in the approximation of the linearized equation for the impurity flux (10).…”

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confidence: 99%

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Problem on Diffusion of a Partially Soluble Impurity in a Solid Matrix with Allowance for the Depletion of the Diffusant Source with Time

Gladkov

Kashcheev

Петров

et al. 2005

J Eng Phys Thermophys

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An analytical expression for the concentration profile of a diffusing element partially soluble in the material's sample has been obtained on condition that the diffusion source is depleted with time. Examples of the use of the solution obtained for processing of diffusion experiments carried out with a number of impurities in beryllium have been considered. The use of the present model shows a more accurate agreement of the calculated and experimental concentration profiles, which enables one to refine the characteristics of diffusion mobility of the impurities in the materials under study.The stability of the structure of solid materials containing impurities is determined, as a rule, by the redistribution of the impurities between the solid solution and the isolated phases. The mobility of impurities in solid materials is limited by diffusion processes; therefore, the diffusion coefficients D i (i = 1, 2, ..., n) of the impurities, which are found by the corresponding experiments [1], are an important characteristic of any impurity-containing material. To increase the migration rate of the impurities one carries out the experiments at a higher-than-average temperature (homogenizes samples) and then extrapolates the result obtained for D to the region of low * ) temperatures, using the Arrhenius law [2]:Clearly, in extrapolating D(T) to lower temperatures, the error of determination of low-temperature diffusion coefficients increases; therefore, to improve the accuracy of their determination one must organize the processing of diffusion experiments so as to minimize the computational error for D.We recall that, in the course of diffusion experiments, one most often applies a source layer of labeled (radioactive) diffusing atoms to one side of the sample; the sample is annealed isothermally for a certain period; then one successively removes its layers on the source side of the source layer and analyzes the radioactivity of the sample's residue N(x), where x is the distance from the source layer to the sample [3].To simplify the processing of the experiment the layer applied to the sample is made as thin as possible and the geometry of the sample is selected so that the process of diffusion can be considered to be one-dimensional. The diffusion coefficient D is determined by comparison of the dependences N exp (x) obtained in the experiment and a certain reference calculated function N calc (x). The form of the latter depends on conditions that are realized at the boundary of the matrix and the source layer of a diffusing impurity in the process of diffusion. In [4], it has been shown that unreliable data on the boundary conditions reduce the accuracy of determination of the coefficient D several times. Consequently, extrapolating the result for D to low temperatures, one can make a mistake by an order of magnitude or more. In this connection, in processing the experiments, we seek to reconstruct the boundary conditions realized at the source layer-matrix boundary in homogenization of a sample as accurately as p...

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Problem on Diffusion of a Partially Soluble Impurity in a Solid Matrix with Allowance for the Depletion of the Diffusant Source with Time

Gladkov

Kashcheev

Петров

et al. 2005

J Eng Phys Thermophys

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“…When the layer is essentially infinitely thin, the diffusion equation has the solution given in [23] with h → 0 and the amount of Mn atoms in the source (the near-surface layer) is Q = N 0 h. Then Eq. (4) takes the form of a gaussian distribution [23],…”

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confidence: 99%

“…Thus, the low-temperature doping of ZnS with manganese corresponds best to solving the problem of the impurity distribution from a layer of finite thickness (diffusion from a bounded source) into a semi-infinite body. The general solution of Fick's equation [23] is…”

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Diffusional relaxation in ZnS after thermal doping at 800°C

Bacherikov

Optasyuk

2010

J Appl Spectrosc

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Photoluminescence spectra of powdered ZnS thermally doped with MnS are studied. Correlations are demonstrated between variations in the luminescence characteristics of ZnS:Mn, on one hand, and some features of radiation center formation and the diffusion of Mn in ZnS after processing, on the other. It is found that after manganese doping at a temperature (T = 800 o C) lower than the phase transition temperature of ZnS, relaxation processes owing to diffusion of Mn in ZnS take place in the material over times as long as 6⋅10 3 h. It is shown that 6⋅10 3 h after doping the α-MnS phase is essentially completely dissolved in the volume of the ZnS. Diffusion of Mn in powdered ZnS is found to occur via several channels, rapid diffusion along interior boundaries and slow diffusion via interstitial space, which indicates the existence of different activation energies for diffusion of Mn depending on its localization within the ZnS lattice.

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Diffusion of a low-soluble impurity in a solid matrix

Cited by 2 publications

References 3 publications

Problem on Diffusion of a Partially Soluble Impurity in a Solid Matrix with Allowance for the Depletion of the Diffusant Source with Time

Problem on Diffusion of a Partially Soluble Impurity in a Solid Matrix with Allowance for the Depletion of the Diffusant Source with Time

Diffusional relaxation in ZnS after thermal doping at 800°C

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