**Published:** Jan 1987

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**Source: **STP955-EB

Structural materials for advanced energy sources, such as magnetically and inertially confined thermonuclear reactors, are subjected to a radiation environment that produces high-energy displacement cascades and transmutation products, which includes helium. We address these characteristics and formulate their effect on the microstructural evolution of a material.

We consider that, immediately after a high energy cascade event, a vacancy-rich region exists near the primary event site and that an interstitial-rich zone, formed by collision chains, exists some distance from the primary event site. Transmutation-product helium can diffuse into the vacancy-rich zone and stabilize bubble nuclei that will later grow if sufficient vacancies and helium atoms diffuse to the nucleus. These bubbles are the sinks for excess radiation-produced vacancies. The excess radiation-produced interstitials migrate and bond; if the binding energy is high enough, a di-interstitial is considered to be a stable dislocation-loop nucleus. The loop nuclei grow if they receive more interstitials than vacancies; this represents material swelling since the bubbles do not cause a lattice contraction to offset the dilation caused by the growing dislocation loops.

Consider that the interstitial-loop growth process can be represented by a Langevin equation. If the growth process at time *t* is assumed to be dependent only on the instantaneous interstitial concentration and instantaneous microstructural state (dislocation, cavities, and grain boundaries) and independent of previous history, the growth process can be considered to be a Markov process. Application of an equivalent Fokker-Planck equation allows deduction of an interstitial-loop nucleation and growth equation, the solution of which yields an interstitial-loop distribution function.

Use of appropriate material parameters gives the incubation and growth regimes of swelling and also allows a determination of the maximum swelling temperature. At a vacancy and interstitial production rate of 10^{21} m^{−3} s^{−1}, these results predict a maximum swelling temperature of 117°C for aluminum, 550°C for stainless steel, and 1100°C for molybdenum. These values are in good agreement with experimental results.

Basically, the maximum swelling temperature is found to be a function of only *sυ, ευf/ευm*, (ρ^{N} + ρ^{l}), and *˙Np*. The maximum swelling temperature increases as (ρ^{N} + ρ^{l}), *˙Np*, and ε*υf*/ε*υm* increase and decreases as increase and decreases as *sυ* increases. Here, *sυ* is the vacancy formation entropy, ε*υf* is the vacancy formation energy, ε*υm* is the vacancy mobility energy, ρ^{N} is the network dislocation density, ρ^{l} is the dislocation loop density, and *˙Np* is the production rate of vacancies and interstitials per unit volume under irradiation.

**Keywords:**

swelling, high-energy cascades, microstructural evolution, interstitial dislocation loop nucleation, interstitial loop growth, nonequilibrium statistical theory

**Author Information:**

Yu, J *guest scientistSenior scientist, Eidg. Institute für ReaktorforschungInstitute of Atomic Energy, Schweiz,*

**Committee/Subcommittee:** E10.07

**DOI:** 10.1520/STP33832S