Quantitative assessment of hydrogen diffusion by activated hopping and quantum tunneling in ordered intermetallics

Diffusion of hydrogen in metals is a fundamental process in hydrogen storage in metal hydrides, hydrogen purification by metal membranes, and in hydrogen embrittlement. Quantitative applications of existing models for hydrogen diffusion by activated hopping and quantum tunneling require large scale first principles calculations that are not well suited to metal alloys containing many structurally distinct interstitial sites. We applied a semiclassically corrected version of harmonic transition state theory in conjunction with plane wave density functional theory to examine hydrogen diffusion in multiple C15 Laves phase $A{B}_2$ compounds and in bcc CuPd. Comparison with experimental data shows that this theory correctly captures the characteristics of hydrogen diffusion in these materials over a wide range of temperatures. This method is well suited to application in complex alloys.

Figure 1

The net self-diffusion rate for H in $\mathrm{Zr}{\mathrm{Cr}}_2$ as predicted by harmonic transition state theory (HTST), semiclassically corrected harmonic transition state theory (SC-HTST), and as measured experimentally by Renz et al. (Ref. 33). The fits to the experimental data in the low and high temperature regime reported by Majer (Ref. 36) are also shown.

Figure 2

The relative diffusion rates of H and $D$ in $\mathrm{Zr}{\mathrm{Cr}}_2$ as predicted by harmonic transition state theory (HTST) and semiclassically corrected harmonic transition state theory (SC-HTST).

Figure 3

The net self-diffusivities of H in six different C15 $A{B}_2$ intermetallics as predicted by semiclassically corrected harmonic transition state theory. Experimental data for $\mathrm{Zr}{\mathrm{V}}_2$ from Majer et al. (Ref. 31) and $\mathrm{Hf}{\mathrm{Ti}}_2$ from Eberle et al. (Ref. 26) are also shown.

Figure 4

The hopping rate for the rate-determining step of H diffusion in bcc CuPd as predicted by harmonic transition state theory (HTST) and semiclassically corrected harmonic transition state theory (SC-HTST).

Figure 5

The temperature dependent effective activation energy defined in Eq. (3) for the hopping rate of H and $D$ in bcc CuPd.