Abstract
The thermal annealing of radiation-induced interstitial clusters is analysed, taking into account the nonlinear feedback between the defect density, the rate of annealing, and the temperature (thermal-concentration feedback). The discussion covers isothermal and isochronous annealing regimes, a change in cluster size distribution during the annealing, and the travelling wave of annealing. It is shown that the thermal-concentration feedback leads to a stronger than exponential dependence of the number of annealed defects on time, and is the mechanism of the self-sustained annealing and its propagation. Furthermore, the travelling wave of annealing can be unstable with respect to oscillations of the propagation rate and the temperature profile. The reason for this instability is the preheating of an as yet un-annealed area of metal.
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Notes
- 1.
In a real life situation the temperature of the material is positive and the radiation-damaged crystal is not in a stationary state, since the lifetime of the defects is finite.
- 2.
The assumption of a sharp dependence of the annealing rate on temperature for the Arrhenius function (24) means a greater value of the activation energy \(E_{\mathrm {a}}\) .
- 3.
The temperature difference is small in the annealing zone since, due to the strong dependence of the annealing rate on temperature, the bulk of defects are annealed at a maximum temperature \(T_{\infty }\) [21].
- 4.
In principle the same zero flux condition across the borders holds for the density of defects. But this condition is satisfied automatically because we consider a problem in which the diffusion of defects is negligibly small.
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Selyshchev, P.A., Bokov, P.M. (2018). Kinetics of Annealing: Basic Relationships and Nonlinear Effects. In: Archilla, J., Palmero, F., Lemos, M., Sánchez-Rey, B., Casado-Pascual, J. (eds) Nonlinear Systems, Vol. 2. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-72218-4_12
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