Direct Measurement of Hydrogen Dislocation Pipe Diffusion in Deformed Polycrystalline Pd Using Quasielastic Neutron Scattering

The temperature-dependent diffusivity $D(T)$ of hydrogen solute atoms trapped at dislocations—dislocation pipe diffusion of hydrogen—in deformed polycrystalline ${\mathrm{PdH}}_x$ ($x\sim {10}^{-3}[\mathrm{H}]/[\mathrm{Pd}]$) has been quantified with quasielastic neutron scattering between 150 and 400 K. We observe diffusion coefficients for trapped hydrogen elevated by one to two orders of magnitude above bulk diffusion. Arrhenius diffusion behavior has been observed for dislocation pipe diffusion and regular bulk diffusion, the latter in well-annealed polycrystalline Pd. For regular bulk diffusion of hydrogen in Pd we find $D(T)=D_0\text{exp}(-E_a/\mathrm{k}T)=0.005\text{exp}(-0.23\mathrm{eV}/\mathrm{k}T){\mathrm{cm}}^2/\mathrm{s}$, in agreement with the known diffusivity of hydrogen in Pd. For hydrogen dislocation pipe diffusion we find $D(T)\simeq {10}^{-5}\text{exp}(-E_a/\mathrm{k}T){\mathrm{cm}}^2/\mathrm{s}$, where $E_a=0.042$ and 0.083 eV for concentrations of $0.52\times {10}^{-3}$ and $1.13\times {10}^{-3}[\mathrm{H}]/[\mathrm{Pd}]$, respectively. Ab initio computations provide a physical basis for the pipe diffusion pathway and confirm the reduced barrier height.

Figure 1

Fits to intensity versus energy transfer in the QENS region (the $Q=0.9{\mathrm{\AA }}^{-1}$ bin) for Def-1 at 200 and 400 K, as explained in the text. The 20-K measurement quantifies the instrumental resolution, which is sample dependent [18], since all motions are assumed to be frozen. The 200-and 400-K plotting symbols are the $\pm 1\sigma$ error bars associated with each data point. The decrease in elastic intensity is shown in the inset (linear intensity scale) and corresponds to an increase in the QENS response.

Figure 2

Fits of the Chudley-Elliot model [Eq. (4)] to the Def-1 sample Lorentzian widths $E_L$ for all temperatures. Widths $E_L$ are shown on a log scale to highlight the significant variation in Lorentzian widths versus $T$. The experimental uncertainties in all $E_L$ values are approximately 10% fractional error.

Figure 3

Arrhenius plot of the hydrogen diffusivities derived from QENS analysis. Blue lines are best fits to the samples analyzed in this work; Def-1 (open circles), Def-2 (open boxes), Ann-1 (open triangles), and Ann-2 (solid triangles). $E_a$ and $D_0$ values for these fits are listed in Table 1. The thick black line is the expected bulk regular diffusivity of hydrogen in well-annealed Pd from Ref. [29].

Figure 4

Ab initio results of site and activation energies (in meV) for hydrogen diffusion in the near partial dislocation core environment in Pd, relative to the bulk octahedral interstitial site, $E_{oct}=0$. $\mathrm{\Delta }E$ accounts for the slight reduction of the O-T trapping network, as discussed in the text. Vertical arrows indicate diffusion activation energy barriers. The site in the partial core is meta-stable with respect to the preferred trap site that resides just below the partial dislocation [33]. Solute hopping along core sites is associated with DPD, and core sites can only be accessed via the preferred trap sites.