Hydrogen-induced defects in bulk niobium

Our aim in the present work was to investigate changes of the defect structure of bulk niobium induced by hydrogen loading. The evolution of the microstructure with increasing hydrogen concentration was studied by x-ray diffraction and two complementary techniques of positron annihilation spectroscopy (PAS), namely positron lifetime spectroscopy and slow positron implantation spectroscopy with the measurement of Doppler broadening, in defect-free Nb $\left(99.9\%\right)$ and Nb containing a remarkable number of dislocations. These samples were electrochemically loaded with hydrogen up to $x_{\mathrm{H}}=0.06\left[\mathrm{H}∕\text{Nb}\right]$, i.e., in the $\alpha$-phase region, and it was found that the defect density increases with hydrogen concentration in both Nb samples. This means that hydrogen-induced defects are created in the Nb samples. A comparison of PAS results with theoretical calculations revealed that vacancy-hydrogen complexes are introduced into the samples due to hydrogen loading. Most probably these are vacancies surrounded by 4 hydrogen atoms.

Figure 1

The inter-plane distance $d$ of the (310) planes as a function of ${\sin }^2\Psi$. The tilting angle $\Psi$ represents the angle between the scattering vector and normal to the surface of the sample. The dependence of $d$ on ${\sin }^2\Psi$ is plotted by open circles for the as-received Nb sample and by full circles for the Nb sample annealed at $1000°\mathrm{C}$. A linear fit of the experimental points is shown by the solid lines.

Figure 2

The relative lattice expansion $\Delta a∕a_0$, $\Delta a=a-a_0$, as a function of the hydrogen concentration $x_{\mathrm{H}}$. $a_0$ and $a$ denote the lattice constant for a virgin sample and a sample with a hydrogen concentration $x_{\mathrm{H}}$, respectively. The relative lattice expansion for the as-received sample is plotted by full circles. Open triangles are used to show the relative lattice expansion for the Nb sample annealed at $850°\mathrm{C}$, and the relative lattice expansion for the Nb sample annealed at $1000°\mathrm{C}$ is plotted by open circles. A linear fit of the experimental data is shown by the solid lines.

Figure 3

(a) The lifetimes ${\tau }_1$ and ${\tau }_2$ of the exponential components resolved in PL spectra for the Nb sample annealed at $1000°\mathrm{C}$ as a function of hydrogen concentration $x_{\mathrm{H}}$. (b) Dependence of the relative intensity $I_2$ on hydrogen concentration for the Nb sample annealed at $1000°\mathrm{C}$.

Figure 4

(a) The lifetimes ${\tau }_1$ and ${\tau }_2$ of the exponential components resolved in the PL spectra for the Nb sample annealed at $850°\mathrm{C}$ as a function of the hydrogen concentration $x_{\mathrm{H}}$. (b) Dependence of the relative intensity $I_2$ on the hydrogen concentration for the Nb sample annealed at $850°\mathrm{C}$.

Figure 5

$S\left(E\right)$ curves for the Nb sample annealed at $1000°\mathrm{C}$ as a function of hydrogen concentration $x_{\mathrm{H}}$. The solid lines show fits of the corresponding $S\left(E\right)$ dependencies by VEPFIT.

Figure 6

$S$ parameter (full circles) and positron diffusion length $L_{+}$ (open circles) for bulk Nb as a function of hydrogen concentration $x_{\mathrm{H}}$. $S$ and $L_{+}$ were obtained from fits of the $S\left(E\right)$ curves measured on the Nb sample annealed at $1000°\mathrm{C}$.

Figure 7

The binding energy $\Delta E_{\text{eff}}^{\text{hom}}$ in the (001) plane for hydrogen in perfect, defect-free Nb, calculated using the effective medium theory. For details of calculations see the text. Note that a constant factor of $2.0\text{eV}$ was added to all calculated binding energies in order to shift them to positive numbers to scale the contours in the logarithmic scale, i.e., the contours are equally separated in the logarithmic scale. It was done only to present graphically the calculted results in a convenient form. The coordinates in the $x$ and $y$ axis are given in fractions of the Nb lattice parameter $a=3.3033\mathrm{\AA }$.

Figure 8

The binding energy $\Delta E_{\text{eff}}^{\text{hom}}$ in the (001) plane for hydrogen in Nb with vacancy in the 1,1,0 position (indicated schematically by an open square). $\Delta E_{\text{eff}}^{\text{hom}}$ was calculated using the effective medium theory. For details of the calculations see the text. A constant factor of $2.5\text{eV}$ was added to all calculated binding energies in order to shift them to positive values and to plot the contours in logarithmic scale. It was done only to present graphically the calculted results in a convenient form. The positions with low energy $\Delta E_{\text{eff}}^{\text{hom}}$ are situated in a ring surrounding the vacancy. The position of the ring is indicated by arrows. The coordinates in the $x$ and $y$ axis are given in fractions of the Nb lattice parameter $a=3.3033\mathrm{\AA }$.

Figure 9

A schematic diagram of position of hydrogen atom bound to a vacancy calculated using the efective medium theory. The hydrogen atom is denoted by an open circle, while Nb atoms are plotted by filled circles. The vacancy depicted by an open square is placed at the 1,1,0 position. The hydrogen atom bound to the vacancy is displaced $0.46\mathrm{\AA }$ from the nearest neighbor octahedral interstitial position (denoted by an arrow) towards the vacancy.

Figure 10

The calculated positron density in (001) plane for Nb with a vacancy associated with a single hydrogen atom. Four unit cells are shown in the figure. The cell boundaries are shown by the dotted lines. The vacancy is situated at the 1,1,0 position. The hydrogen atom is placed at the 0.64,1,0 position calculated using the effective medium theory. The coordinates are given in fractions of the Nb lattice parameter $a=3.3033\mathrm{\AA }$.

Figure 11

Calculated lifetime $\tau$ and binding energy $E_b$ of positrons trapped in a Nb vacancy as a function of the number of hydrogen atoms surrounding the vacancy. The Nb bulk lifetime is plotted by the dashed line.

Figure 12

The concentration of hydrogen-induced vacancy–hydrogen complexes in the Nb sample annealed at $1000°\mathrm{C}$ estimated from experimental data using Eq. (3) is shown by filled circles connected by a dotted line. The estimated equilibrium concentration of vacancy–4H complexes calculated using Eq. (6), with the probability $p$ given by Eq. (7) for $x_{\mathrm{H}}<0.025$ and $p=1$ for $x_{\mathrm{H}}⩾0.025$ is plotted by a solid line.