V. I. Dubinko, A. A. Turkin, D. I. Vainshtein and H. W. den Hartog
Modeling of the radiation-induced microstructural evolution in ionic crystals
Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, Volume 153, Issues 1-4, June 1999, Pages 163-166
Corresponding author. Tel.: +380-572-351020; fax: +380-572-353731

Abstract
Results of experimental and theoretical investigations are presented on heavily irradiated natural and synthetic NaCl crystals in the temperature range where anion defects are mobile. They give a strong evidence for the formation of vacancy voids, which cannot be explained by the Jain-Lidiard model used up to date for description of metal colloids and dislocation loops formed in ionic crystals during earlier stages of irradiation.

We consider an additional set of reactions between experimentally observed extended defects (metal colloids, gas bubbles and voids) and point defects.

• The latter include F and H centers that are the primary defects produced by irradiation, and
• cation vacancies (with a trapped hole) that are secondary defects, produced in the process of dislocation climb due to absorption of extra H centers.

We show that

1. highly overpressurized bubbles of fluid halogen are strongly biased for absorption of H centers, which makes them grow via punching out interstitial dislocation loops.
2. The loops grow and produce cation vacancies that are subsequently trapped at the incoherent colloids together with extra F centers giving rise to the colloid-void transition.
3. Elastic interaction between extended defects and point defects is shown to play a major role, since it determines the bias factors of extended defects, which is a major driving force of the microstructural evolution under irradiation.

A quantitative comparison of the new model for radiation damage in NaCl with experimental data is presented. Mean sizes and volume fractions of all types of observed defects are calculated.

It is shown that voids formed due to agglomeration of F centers and cation vacancies can grow to the dimensions exceeding the mean distance between colloids and bubbles, eventually absorbing them, hence, bringing the halogen gas and metal to a back reaction.

Impurities play a major role in the void development with increasing irradiation dose, which strongly affects the radiation stability of NaCl.

Abstract
Experimental and theoretical results are presented on formation of colloids, halogen bubbles and large vacancy voids in heavily irradiated NaCl crystals leading to their explosive decomposition into small pieces under further irradiation or subsequent heating.

The dependence of the radiation stability of material with increasing irradiation dose on the void evolution is analyzed. It is shown that

• voids can grow very fast as compared to colloids and bubbles.
• For doses higher than 100 Grad, the void dimensions can exceed the mean distance, first, between bubbles and then between colloids resulting in their collisions with voids.
• Collisions with bubbles fill the voids with gas, and subsequent collisions with colloids (during further irradiation or heating) bring the halogen gas and metal to a back reaction inside the voids.
• Such a sudden release of stored energy can be shown to result in a temperature spike (above 10⁴ K) and instantaneous gas pressure rise up to 1 GPa within the voids, which may transform voids into penny-shaped cracks along the cleavage planes of the matrix.
• A subsequent growth of the cracks results in fracture of the material.

Dependence of the critical amount of stored energy required for the void-crack transition on the mean size of the voids is estimated and compared with experimental data.

Article Outline

1. Introduction
2. Explosion driven void-crack transition
3. Summary

Abstract
A kinetic model is formulated for the chemical reaction between radiolytic sodium colloids and gas bubbles, which are brought into contact with each other during the exposure to ionising radiation by the growing voids.

• The reaction starts with the evaporation of Na atoms into the void due to the localized heat release caused by reactions between chlorine molecules colliding with the colloid surface.
• It is shown that this exothermic and autocatalytic reaction leads to a sudden temperature increase inside the void, which gives rise to thermoelastic stresses in the surrounding matrix.
• Tangential stresses might exceed the threshold stress required for localized cleavage of the matrix resulting in crack formation and mechanical instability of NaCl under high dose irradiation.

Article Outline

1. Introduction
2. Back reaction model
3. Results of calculations
4. Conclusions

Abstract
The dependencies of void formation and radiolytic sodium accumulation on the irradiation dose, dose rate, temperature and impurity content are analyzed within a framework of a theoretical model, which is based on a new mechanism of dislocation climb.

1. The mechanism involves the production of V_F centers (self-trapped hole neighboring a cation vacancy) as a result of the absorption of excess H centers at dislocation lines.
2. Voids are shown to arise due to the reaction between F and V_F centers at the surface of halogen bubbles.

• All reactions involved in the evolution of extended defects are controlled by the difference between the absorption of H centers and F centers.
• This difference is determined by the material specific parameters responsible for the bias factors of extended defects and by the mean concentration of point defects.
• The latter depends on the temperature and dose rate as described in the present paper.
• Impurities can facilitate or suppress radiation damage formation depending on their effect on the nucleation of extended defects under irradiation.

This is demonstrated by comparing theoretical results obtained for dose dependence of colloid volume fraction at different dislocation densities with experimental data obtained in crystals doped with different impurities.

Article Outline

1. Experimental results
2. Theory
   1. New mechanism of dislocation climb
   2. Radiation-induced evolution of extended defects
   3. Temperature/dose rate dependence of the colloid production
3. Comparison of experimental results with theory

Abstract
Rock salt might be a promising geological medium for a radioactive waste repository. However, we have observed that even a basically stable compound such as NaCl may become unstable after heavy irradiation. As a result of the irradiation, dislocations, Na and Cl₂ precipitates and large voids are produced followed ultimately by sudden explosion-driven fracture of the material.

We present a new concept of the radiation-induced micro-structural evolution, which explains the phenomena observed in heavily irradiated NaCl samples. This concept can be a prototype of a more general assessment of radiation effects in crystalline radwaste and repository materials, which is necessary for the evaluation of critical effects and maximization of the safety of repositories.

Zitierte Literatur: [14] V.I. Dubinko, A.A. Turkin, D.I. Vainshtein, H.W. den Hartog, J. Nucl. Mater. 289 (2001) 86. click on figure to enlarge

Zitierte Literatur: [16] A.A. Turkin, V.I. Dubinko, D.I. Vainshtein, H.W. den Hartog, Nucl. Instr. and Meth. B 191 (2002) 83. click on figure to enlarge

Article Outline Introduction Void formation in irradiated NaCl Explosive fracture of rock salt due to back reactions between radiolytic products Summary and outstanding problems Acknowledgements References

Abstract
We propose a mechanism of void growth in di-atomic ionic crystals due to agglomeration of divacancies produced by interactions between dislocations and excitons. An exciton can cause movement of nearby dislocation jogs, resulting in the creation of equal numbers of anion and cation vacancies (Schottky defects). Owing to the heat generated locally during the exciton annihilation, the jog can be displaced while a divacancy arises in the lattice. Subsequent diffusion and agglomeration of divacancies can result in void formation and growth. We evaluate the void nucleation and growth rates in electron irradiated NaCl.

Abstract
Recent results on heavily irradiated natural and synthetic NaCl crystals give evidence for the formation of large vacancy voids, which were not addressed by the conventional Jain-Lidiard model of radiation damage in alkali halides. This model was constructed to describe metal colloids and dislocation loops formed in alkali halides during earlier stages of irradiation.

We present a theory based on a new mechanism of dislocation climb, which involves the production of V_F centers (self-trapped hole neighboring a cation vacancy) as a result of the absorption of excess H centers.

• Voids are shown to arise due to the reaction between F and V_F centers at the surface of halogen bubbles.
• Critical parameters associated with the bubble-to-void transition are evaluated.
• Voids can grow to sizes exceeding the mean distance between colloids and bubbles, eventually absorbing them, and, hence, igniting a back reaction between the halogen gas and metal.
• The amount of radiation damage in alkali halides should be evaluated with account of void formation, which strongly affects the radiation stability of material.

Article Outline

1. Introduction
2. Model of dislocation climb
3. Bias of spherical inclusions due to elastic interaction difference (EID)
   1. Colloid bias
   2. The bias of halogen bubbles and vacancy voids
4. Rate equations for point defects
5. Nucleation and growth of extended defects (ED)
   1. Colloids
   2. Bubbles
   3. Critical parameters controlling bubble-void transition
   4. Vacancy voids
6. Simultaneous evolution of ED at high dose irradiation
7. Temperature dependence of the damage production
8. Discussion of the results and comparison with experimental data
9. Summary

Abstract
In many ceramic solids, the number of primary displaced ions is different for different sublattice components, either because the ion masses and displacement energies differ in simple binary collisions (like in alumina) or because radiolytic displacements occur on a single sublattice (like in halides). However, irradiation produces not only metal colloids or gas precipitates, but stoichiometric dislocation loops, and voids as well. We propose a secondary displacement mechanism of vacancy production at a dislocation as a result of its interaction with a primary interstitial ion in another sublattice which explains the observed phenomena.

Article Outline

1. Introduction
2. Biases of extended defects for absorption of point defects
3. Void formation in NaCl due to a back reaction between sodium and chlorine colloids
4. Evolution of bubbles, colloids and voids in NaCl under electron irradiation
5. Void and aluminum colloid formation in electron irradiated alpha-Al₂O₃
6. Summary

Abstract
The kinetics of nucleation and coarsening of vacancy clusters in irradiated crystals are considered with account of their elastic interaction with point defects resulting in the biased absorption of vacancies and interstitial atoms. It is shown that in the technologically important range of high dose rate (or low temperature) irradiation, the nucleation rate and the final number density of clusters are determined by the bias parameters rather than by irradiation conditions. The model is applied to the evolution of sodium colloids and chlorine bubbles in NaCl resulting in the formation of voids followed by a sudden fracture of the material, which presents a potential problem in rock salt nuclear waste repositories. The number densities and mean sizes of colloids, bubbles and voids are evaluated and compared with experimental data.

Article Outline

1. Introduction
2. Nucleation model
1. Rate equations
2. Classical nucleation theory
3. Nucleation under irradiation
3. Nucleation and growth of metallic colloids and halogen bubbles
1. Colloids
2. Bubbles
3. Simultaneous evolution of colloids and bubbles
4. Void formation and growth in irradiated NaCl
5. Discussion and conclusions