Resonant enhancement of grazing incidence neutron scattering for the characterization of thin films

We use signal enhancement in a quantum resonator for the characterization of a thin layer of vanadium hydride using neutron reflectometry and demonstrate that pressure-concentration isotherms and expansion coefficients can be extracted from the measurement of totally externally reflected neutrons only. Moreover, a consistent data analysis of the attenuation cross section allows us to detect and quantify off-specular and small angle scattering. As our experiments are effective direct beam measurements, combined with resonant signal enhancement, counting times become considerably reduced. This allows us to overcome the challenges resulting from the comparatively low brilliance of neutron beams for grazing incidence scattering experiments. Further, we discuss the potential of resonant enhancement to increase any scattering, which is of particular interest for grazing incidence small angle neutron scattering and spectroscopy.

Figure 1

(a) Scheme of the structure of the vanadium hydride resonator thin film. (b) Spin up (red line) and spin down (blue dashed line) scattering length density (SLD) profiles of the sample. Dimensions are not to scale.

Figure 2

Position of the first four resonances, $m=1$–4, in $Q_z$ depending on (a) the SLD with respect to vacuum and (b) the thickness of the resonator.

Figure 3

(a) Color map of the spin up intensity measured on the PSD at $T=473$ K for the lowest pressure data. The ROIs of integration are marked by black rectangles: [A] specular ROI, and [B] nonspecular ROI. The positions of the resonances are marked by vertical dashed lines. (b) Integrated spin up intensities: (black line) specular ROI for lowest pressure data, (blue line) nonspecular ROI for lowest pressure data, (red line) specular ROI for $P\approx 200$ mbar data, (orange) nonspecular ROI for $P\approx 200$ mbar data. The positions of the resonances for the lowest pressure data and for the $P\approx 200$ mbar data are marked by vertical dashed lines and vertical dotted lines, respectively. The order of the resonances is also indicated.

Figure 4

Reflected intensity of (a) spin up and (b) spin down polarized neutrons at $T=473$ K and at different hydrogen pressures. The count rate is normalized to monitor and the data for different pressures are vertically offset by 0.05 for clarity. The critical edge $Q_c$ at $Q_z\le 0.017{\AA }^{-1}$, which is the upper limit of the total external reflection region, is shown as a black vertical line. The resonances, marked $m=1$–4, are indicated by black dashed lines. Fits over the extended region are marked by black lines.

Figure 5

Coherent SLD (line) plotted versus hydrogen content according to Eq. (13). The experimental values of the SLD from the fit of the extended region are indicated by markers. The dashed line shows SLD values if the volume expansion is neglected.

Figure 6

Cross sections plotted versus hydrogen content: incoherent ${\mathrm{\Sigma }}_{\text{inc}}$ (red line), absorption ${\mathrm{\Sigma }}_{\text{abs}}$ (green line), $x$-independent low-$Q$ scattering ${\mathrm{\Sigma }}_{\text{lowQ,0}}$ (blue line), $x$-dependent low-$Q$ scattering with ${\mathrm{\Sigma }}_{\text{lowQ,x}}=2.75{\mathrm{cm}}^{-1}$ (dashed blue line), and the sum of these four cross sections ${\mathrm{\Sigma }}_{\text{t}}$ (black line). The experimental values of the attenuation cross section from the fit of the extended region ${\mathrm{\Sigma }}_{\text{t,eff}}$ are indicated by black markers.

Figure 7

Relative change in volume $\mathrm{\Delta }V/V$ of the ${\mathrm{VH}}_x$ layer plotted as a function of hydrogen content $x$, extracted from the fits of the (a) extended and (b) pre-edge regions. The black line is the fit to the data assuming a linear expansion.

Figure 8

Isotherm of ${\mathrm{VH}}_x$ based on the hydrogen concentrations determined from the fit of ${\mathrm{SLD}}_{\text{coh}}$ for the extended region (black diamonds), pre-edge region (red circles), and from the analysis of ${\mathrm{\Sigma }}_{\text{t}}$ for the extended region (blue squares). The pressure axis is in log scale, and the lowest pressure point for which $x\approx 0$ is not represented. Note that the error bars of two isotherm profiles are omitted for clarity. The black circles and lines represent the isotherm at 473 K reproduced and adapted from Schober et al. [65].