W.G. Wolfer

Surface melting and evaporation during disruptions in magnetic fusion reactors

Abstract Disruptions in tokamaks lead to high energy deposition for short times on in-vessel components. Melting and evaporation may then occur. A comprehensive model to evaluate the extent and duration of melting, the amount of evaporation, and the time for resolidification is presented. This model entails the solution of a heat conduction problem with two moving boundaries, the liquid surface and the melt—solid interface with a surface boundary condition determined by the dynamics of evaporation. Extensive numerical results are presented for in-vessel components made of stainless steel, molybdenum, or graphite. The effects of vapor shielding, pulse shape, and pulse duration are also investigated.

Conditions for dislocation loop punching by helium bubbles

Abstract Under continuous helium but insufficient vacancy supply, bubbles in metals grow by pressure-driven athermal processes such as metal interstitial emission and dislocaton loop punching. To discuss the energetic conditions for these processes, the formation and interaction energies of bubbles and interstitial type metal defects are analyzed. The only condition which has been considered to date is that the decrease in the free energy of a bubble associated with the emission of an interstitial type metal defect must be equal to or larger than the formation free energy of the latter defect. Consideration of the elastic interaction energies result in additional conditions controlling loop punching for bubbles with radii larger than about 10 Burgers vectors. Possible modes for the loop punching process are discussed.

Correlation of radiation creep theory with experimental evidence

Abstract A review is presented of theoretical models related to irradiation creep and to the evolution of the dislocation structure in irradiated stainless steels. The results of detailed analysis for stress-induced loop alignment and stress-induced preferential absorption (SIPA) of point defects at dislocations is presented. Stress-induced rotation of tri-interstitials is shown to be too small to account for the observed variations in loop densities on different crystallographic planes. However, it is possible to predict large variations with the SIPA mechanism. Predictions of irradiation creep by the SIPA mechanism are in agreement with measured data at intermediate fluences. At low fluences, additional contributions to irradiation creep must come from dislocation glide. The evolution of the dislocation structure can be explained by the continuous formation of interstitial type loops and by the radiation-induced recovery of the dislocation network.

The effect of solute additions on void nucleation

Abstract In 316 stainless steel and other alloys, nickel and silicon appear to be major determinants of the radiation-induced swelling behavior. In this study it has been shown that the fast-diffusing species concept proposed by Venker and Ehrlich appears to be a viable mechanism for suppression of void nucleation by silicon atoms. While the role of silicon can be ascribed at least partially to the fast-diffusion effect, the role of nickel cannot, and its influence appears to lie in the operation of other physical mechanisms. The enhanced diffusivity of the alloy which results from the addition of silicon leads to a substantial increase in the free energy barrier to void nucleation, particularly at higher temperatures. The fast-diffusion mechanism operates in addition to the interstitial-solute binding effect, and the combined fast-diffusion/interstitial binding model dispenses with the requirement of unrealistically large interstitial-solute binding energies needed for the solute-binding concept to suppress swelling. Solute binding may account for most of the observed silicon segregation behavior while fast-diffusion accounts for the void suppression. The addition of slow-diffusing elements has an opposite but less pronounced effect on void nucleation.

Advances in void swelling and helium bubble physics

Abstract The extensive experimental data base on irradiated austenitic alloys reveals that swelling as a function of dose can be divided into an initial transient period of low swelling rate, followed eventually by a rate of about 1%/dpa. Whereas the transient depends strongly on microstructure, temperature, and composition, the final rate of swelling is nearly independent of these variables. Models of void nucleation and growth are reviewed to demonstrate that they provide theoretical results which are in general agreement with the basic features of the observed swelling behavior. According to these models, the transient period comprises two regimes, one period of nucleation to obtain the void number density at a given irradiation temperature plus a period to reach parity between the dislocation and the void sink strength. The universal swelling rate eventually achieved is characterized by a state of sink parity.

On melt layer stability following a plasma disruption

Abstract When hard plasma disruptions produce melting of a surface layer on first wall components, the melt layer is in general also subject to various forces. Among these, the forces produced by eddy currents and the magnetic fields are the most severe, and they may cause the removal of the melt layer. It appears that one of the most effective mechanisms for removal is by a Rayleigh-Taylor instability. Numerical results are presented for both the most critical wavenumber and its amplification exponent as a function of two parameters which account for the effect of viscosity and surface tension. The results given for the critical amplification exponent allow an easy assessment of the stability of a melt layer when the forces are known. Examples of such an assessment are given, and it is found that within the range of estimated eddy-current forces, the melt layer may or may not be stable. Hydrodynamic instabilities induced by flow and tangential forces appear to be less severe than the Rayleigh-Taylor instability.

The role of gas pressure and lateral stress on blistering

Abstract Both gas pressure in bubbles and lateral stress have been suggested as primary causes of blistering. An analysis of both mechanisms is presented, and the conditions for blistering are examined. To realistically predict the gas pressure in bubbles, a recently derived high-density equation of state for helium is utilized. It is shown that the formation of overpressurized gas bubbles leads to a state of stress in the surface layer which is a superposition of a tensile microstress surrounding the bubbles and a lateral compressive macrostress across the bombarded layer. When the microstress reaches a value of 0.003 μ for fcc metals or 0.009 μ for bcc metals, interbubble fracture occurs. These critical values are reached for an implanted helium concentration between 20 to 40%. The exact value depends to some degree on the bubble density, the temperature, and the helium to vacancy ratio. The lateral stress is shown to saturate prior to the onset of blistering, but it remains the driving force for blister dome formation once a sufficiently large area of the bombarded layer is detached.

The capture efficiency of coated voids

Abstract Segregation of impurities and alloying elements to voids produces a shell of different composition which significantly affects the mechanical interaction with point defects. This interaction determines the capture efficiency for interstitials and vacancies, and contains several contributions. Two contributions, namely the change of the relaxation energy of the point defect, and the interaction with coherency strains, have not previously been considered. The former arises when composition affects the local shear modulus, and the latter, when it causes a change in lattice parameter. Both contributions are added to two considered in previous works, the image interaction and the stress-induced interaction. The total mechanical interaction is evaluated for voids coated with a shell of material with properties different from those of the matrix, and an expression is derived for the capture efficiency. It is found that shells with a shear modulus only a few per cent larger than in the matrix make voids strongly biased against interstitials. This strong effect is due mainly to the change in relaxation energy rather than to the image interaction. Therefore, shells with diffuse or sharp interfaces are equally effective. However, shells with lower shear modulus are ineffective unless they possess a larger lattice parameter.

Suppression of void nucleation by injected interstitials during heavy ion bombardment

Abstract In a heavy ion irradiation the injected ions come to rest at the end of range as interstitials without a vacancy partner. These extra interstitials perturb the delicate balance of vacancy and interstitial flux to voids. It is shown that the void nucleation rate is drastically reduced by the injected interstitials whenever recombination is an important process. As a result, void nucleation is suppressed in ion-bombardment experiments below a characteristic threshold temperature in the region of the ion deposition. This leads to a void free zone near the end of range in low temperature ion-bombardment experiments. The results obtained are in qualitative agreement with earlier experimental observations.

Drift forces on vacancies and interstitials in alloys with radiation-induced segregation

Abstract Radiation-induced segregation in alloys leads to compositional gradients around point defect sinks such as voids and dislocations. These compositional gradients in turn affect the drift forces on both interstitials and vacancies and thereby modify the bias. Linear irreversible thermodynamics is employed to derive the total drift force on interstitials and vacancies in substitutional binary alloys. The obtained results are evaluated for binary Fe-Ni alloys. It is shown that radiation-induced segregation produces new drift forces which can be of the same order of magnitude as the stress-induced drift force produced by edge dislocations in an alloy with uniform composition. Hence, segregation results in a significant modification of the bias for void nucleation and swelling. The additional drift forces on interstitials and vacancies are due to the compositional dependence of the formation and migration energies; due to the dependence of the point defects strain energy on the local elastic properties; due to a coherency strain field caused by lattice parameter variations; and finally due to the Kirkendall force produced by the difference in tracer mobilities. Estimates of these forces given for Fe-Ni alloys indicate that the Kirkendall force is small compared to the other segregation-induced forces on interstitials. In contrast, the Kirkendall force seems to be the dominant one for vacancies.