Migration of He in Fe has been studied using

ab initio134 and EAM MD/MS methods.159,160 Inter­stitial Hei diffusion is almost athermal, with very low migration energy, Em « 0.06 eV134 to 0.08 eV.159,160 Hes diffuses by either (a) a classical vacancy exchange (Hes-V) mechanism; or (b) by dissociation mecha­nism that involves a Hes! Hei + V reaction, fol­lowed by the diffusion of Hei. The activation energy (Ea) for the dissociation mechanism is estimated

1.0

(b) VgbA (nm)

=——— 1 8 fl*—8S—8—■———————— ■——— =

0 2 4 6 8 10 12

(c) Distance from cluster (A)

Figure 39 (a) Substitutional He atom binding energies to edge and screw dislocations along with the excess volume as a function of the distance from the core. (b) Maximum binding energy of interstitial and substitution He atoms as a function of the excess volume per unit GB area. (c) Binding energies of vacancies and substitutional He to a 2-nm coherent Cu precipitate as a function of the distance.

Table 4 Binding energies of He atoms to various micro­structural features

Feature Maximum

binding energy (eV)

Hei Hes

to be «2.4 to 3.70 eV based on and EAM MD/MS methods, respectively.134’159 The vacancy exchange mechanism is similar to that for any substitutional solute, except that there is an unusually high binding energy for HesV complex. In bcc crystals Hes dif­fuses by a sequence of an initial Hes-V exchange, followed by a jump of the vacancy from the first nearest neighbor (NN) to a second NN position. Thus, Hes diffusion then requires that a (the same or another) vacancy jump back to a different NN position than the one involved in the initial exchange. The rates of exchange, including jumps to a third NN position, are needed to model the Hes diffusion coefficient,

DHes. Indeed, a minimum of five jump frequencies must be considered in modeling any substitutional solute diffusion coefficient in a bcc lattice, in this case Hes (DHes).276 The analytical five-frequency model provides both the correlation coefficient and net migration energy (Em) for Hes diffusion expressed in terms of the individual vacancy exchange activa­tion energies. The activation energies for the various exchanges have been evaluated by both MD159,160 simulations and ab initio calculations.134 These activa­tion energies have been used in the five-frequency model to estimate DHe as well as in direct KLMC simulations. The KLMC model yields:

DHes = 2.8 x 10~4exp(—2.35/kT)(m2s~1) [20]

He atoms also diffuse quasi one dimensionally along a dislocation core. The detailed mechanisms and acti­vation energies have been studied by MD and Dimer method.136 For example, interstitial Hei trapped on an a/2(111){110}edge dislocation in a-Fe is in a (111) crowdion configuration. Thus, He atoms can migrate along the dislocation line by jumping as a crowdion to an adjacent close-packed row with the migration energy of «0.4-0.5 eV.273 Hei also migrates along a a/2 (111) screw dislocation within or near the core with a similar migration energy of «0.4 eV, in this case via exchanges between octahedral interstitial sites. Hes migrates near the core of the screw dislocations by vacancy mechanism. The migration energy of 1.1 eV is associated with vacancy jumps from NN to second NN positions.274 Thus, the Em for Hei is higher on dislocations than in the matrix and lower for Hes.

Diffusion of He atoms on two symmetric tilt GBs, S3{112}, S 11{323}, was also studied using MD and Dimer methods.277-279 Hei diffusion was found to be one to three dimensional depending on the boundary characteristics. Hei diffuses one dimensionally along <1-13> direction in the S11{323} GBs at tempera­tures from 600 to 1200 K. In the S3{112} GBs, Hei diffuses two or three dimensionally at lower and higher temperatures, respectively.278 The mean square displacement in a long-term MD simulation indicated in Em = 0.28 (eV) for interstitial He migra­tion on S3{112} boundary and Em = 0.34 (eV) for migration on S11{323} boundary. Both of these GBs Em are higher than the value 0.087 eV in a-Fe lattice. The preexponential coefficient was found to be 4.35 x 10-8 (m2s—*) in both cases.

Dimer saddle point searches of possible migration paths of the Hei yield somewhat different Em but rationalize the slightly different results for the two

GBs. Possible migration paths of vacancies and Hes — vacancy complexes have also been studied using Dimer method. An important observation is that both tend to migrate one dimensionally, especially at low temperatures.279 These results depend on the EAM potentials and cannot be considered to be quantitative. However, the trends provide considerable insight, and it is notable that the estimated grain boundary vacancy and Hes-vacancy Em are lower in the GBs than bulk Fe matrix, while the Hei Em is higher. These Em are summarized in Table 5.