Finite-Size Effects: Hydrogen in $\mathrm{Fe}/\mathrm{V}$(001) Superlattices

We investigate the effect of finite size on phase boundaries of hydride formation in ultrathin metallic films, using $\mathrm{Fe}/\mathrm{V}$(001) superlattices as a model system. The critical temperature is determined to scale linearly with the inverse thickness of the V layers. The decrease of the ordering temperature with decreasing layer thickness arises from the missing H neighbors at the interfaces, analogous to observed finite-size effects in magnetic layers and nanosized ice crystals.

Figure 1

Sketch of the sample design. 25 bilayers of $\mathrm{Fe}/\mathrm{V}$(001) are grown as a single crystal on a MgO substrate, with a Pd capping protecting against oxidation and catalyzing the hydrogen uptake. The panels on the right-hand side show two types of interstitial sites that hydrogen (red spheres) can occupy: $O_z$ (octahedral $z$ site) and $T_z$ (tetrahedral $z$ site). Light blue and dark blue spheres symbolize the V atoms and the Fe atoms, respectively.

Figure 2

Pressure-composition isotherms of hydrogen in the V layers for the ${\mathrm{Fe}}_3/{\mathrm{V}}_{16}$ sample. The concentration is in units of atomic ratio.

Figure 3

Representative changes in the chemical potential as a function of temperature for the ${\mathrm{Fe}}_1/{\mathrm{V}}_7$ sample.

Figure 4

Changes in the chemical potential with respect to hydrogen concentration as a function of temperature and concentration are shown as a color map. The solid lines are isolines of the second derivative of the chemical potential with respect to concentration. The yellow circles follow from the Curie-Weiss analysis and mark the spinodal temperature. Note that $\mathrm{\Delta }\mu$ below 320 K is extracted based on an extrapolation of the linear fit of the van’t Hoff plot. The solid line represents a fit to the spinodal line. The insets in the figures depict the Curie Weiss analysis. Note that all phase diagrams were measured at the same strain values in the vanadium layers.

Figure 5

The figure illustrates the inverse thickness dependence of the ordering temperature for hydrogen in ultrathin biaxially strained V lattices [$\mathrm{Fe}/\mathrm{V}$(001) superlattices (present work)], thin V layers, and the magnetic ordering temperature of Ni on Cu(001) and Cu(111) [1]. The dashed lines are fits using Eq. (2). $n$ is the number of atomic layers.