Complex structural materials, such as FMS and NFA, are composed of a wide range of types, morphologies, size scales, and associations of various microstuctural features. A general master model approach to treating He transport, fate, and consequences in such alloys is shown in Figure 3. He transport and clustering reac­tions within the matrix and in various microstructural regions are treated. In this framework, RT models, or KMC simulations, are used to transport and partition He to the various microstructural regions, such as dislocations, grain and subgrain boundaries, and het­erophase interfaces. He is further transported within a region to and from internal subregions. For exam­ple, dislocations are regions, and precipitates and jogs on dislocations constitute subregions. He can recycle within or between regions. The accumulation of He in the various sites results in the formation of He bubbles (and in some cases voids).

Preliminary development of a master model code to implement this framework is underway.178 In its current RT formulation, He is generated by transmu­tations as both Hei and Hes at relative fractions that can be based on a physically motivated parameter that needs to be established. These interstitial and substitutional forms can switch by interaction with vacancies and SIA, respectively. The Hei rapidly dif­fuses to the various regions where it is trapped or captured by a matrix vacancy to form Hes. Hes dif­fuses more slowly to the various regions or is dis­placed by a SIA to form Hei. The differences in the diffusion rate are reflected in the steady-state matrix concentrations of Hei (very low) and Hes (higher).

A CD model (see Section 1.06.3) is used to track the fate of He and bubble evolution by reactions He + Hem! Hem +1 in the various regions and subregions. Although the framework of the CD mod­els allows the disassociation ofclusters by He emission, this is not implemented in the results described below. That is, a He2 cluster is taken as a stable nucleus for the formation and evolution of larger bubbles. A further assumption is that the HemVn clusters grow with He addition as equilibrium bubbles (m/n < 1), along the lowest free-energy path, with a real gas equation of state p = 2g/rb, as described in Section 1.06.3. This approximation is valid at low damage rates and vacancy-rich environments associated with neutron irradiations. The current implementation focuses on bubble evolution, and since the dislocation bias is set to B = 0, the model does not directly treat void formation and swelling. However, this capability will be implemented in future versions of the code.

Helium atoms trapped at precipitates, disloca­tions, and GBs may either be emitted back to the matrix, at a rate determined by their binding ener­gies, or diffuse to be captured by deeper subregion traps. The He + He! He2 reactions form a bubble nucleus in all regions and subregions, either hetero­geneously with other trapped He or homogeneously with reactions between two freely diffusing He atoms. Nucleation of bubbles on dislocations is a very impor­tant process. Dislocations are modeled as a size distri­bution of segments bounded by deeper traps than the dislocation itself, such as junctions, jogs, and attached precipitates. The initial distribution of dislocation seg­ments is resegmented (split) as bubbles homogeneously nucleate on them.

The master model contains many parameters. Where possible, microstructural observations were used to provide microstructural parameters for grain sizes, dislocation densities, and precipitates, as summar­ized in Table 6. In general, the binding and activation energies were obtained from the models described in Section 1.06.5. Details are presented elsewhere.178

Figure 41 shows an example of the master model predictions of bubble radii (a, c) and number densi­ties (b, d) compared with the ISHI data described previously in this section for 40 appm He/dpa at 500 °C up to 10 dpa for the FMS F82H (a, b) and NFA MA957 (c, d) microstructure variables shown in Table 6. The data are shown for F82H in both as tempered (AT) and 20% CW conditions. The over­all agreement is quite good. The model predicts that almost all of the bubbles form on dislocations in F82H and on dislocations and dislocation associated NF in MA957, broadly consistent with observations. The model predicts a smaller number of larger

	(b) dPa
(c) dpa	(d) dpa

Figure 41 Model predictions corresponding in situ He-implanter data for the (a) average bubble radius; (b) number density in F82H; (c) average bubble radius; and (d) number density in MA957also show the observations in experiments.

bubbles than observed in the F82H in the AT condi­tion. The agreement is better for MA957, and the model predictions are consistent with the observation that a higher number density of smaller bubbles form in this case. The MA957 model predicts that there is a lower number of smaller bubbles in the matrix and especially on GBs. Note that the models do not yet contain lath boundaries that are observed to contain a high concentration of bubbles in F82H. The predicted size distribution of bubbles is shown in Figure 42. The agreement with the experimental results is again quite good and reflects the significant differences that are observed in the two alloys.