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C: Physical Processes in Nanomaterials and Nanostructures
Dynamics of Hydrogen in a Thin Gd Film: Evidence of Spinodal Decomposition Yishay Manassen, Henry Realpe, and Danielle Schweke J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b00932 • Publication Date (Web): 17 Apr 2019 Downloaded from http://pubs.acs.org on April 18, 2019
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Dynamics of H in a Thin Gd Film: Evidence of Spinodal Decomposition Y. Manassen1, H. Realpe1 and D. Schweke2* 1 Department of Physics and the Ilse Katz Center of Science and Technology in the nm scale, Ben Gurion University of the Negev, P. O. Box, 653, Beer Sheva, 8410501, Israel 2 Nuclear Research Center Negev, P.O.Box 9001, Beer Sheva, 84190, Israel
ABSTRACT: Gd thin films react at room temperature with hydrogen to form hydride, by nucleation and growth, even for very low H content (H/Gd >0.01). This phase transformation can be destabilized and suppressed in highly stressed films. In the present study, a thin Gd layer was deposited on a W(110) substrate, leading to a highly strained film. Following exposure to hydrogen, the overall strain in the film is further increased. Hydrogen was found to dissolve in the metallic matrix without forming distinct hydride nuclei. However, the lateral distribution of H in the film evolved with time, from a rather homogeneous repartition to an inhomogeneous one, reflecting the process of spinodal decomposition of hydrogen in the film. The spinodal decomposition process was monitored using scanning tunneling microscopy (STM). This process involves principally the diffusion of H in the film, but a slow change in shape of the Gd islands covering the wetting layer was also observed. These changes were used to monitor the evolution of the local strains and hydrogen concentrations with time and to draw strain and composition maps at different times, before and after hydrogenation. Numerical simulations of the process, using the chemical potential of H in the highly strained film and applying the Cahn Hillard equation, were shown to be in good agreement with the experimental observations, in both spatial and temporal scales. The presented study extends recent ones and shows that high tensile strains strongly affects the dynamics of the H distribution and the composition of the H containing phases, opening the route for future studies of M-H systems on the nm scale.
INTRODUCTION The physical properties of Yttrium (Y) and Rare earth metals are strongly affected by the presence of hydrogen. For instance, the optical and conductivity properties of Yttrium and Lanthanum hydrides strongly depend on composition. Remarkable modifications of the optical transmission and resistivity of those hydrides, from metallic and shiny to semiconducting and transparent, were achieved by changing the hydride composition.1,2 The transition between the two states is reversible, which enables the use of those hydrides in optical devices such as switchable mirrors. The latter has found various applications as indicator layers or as components in electrochromic or thermochromic devices.3,4 Recent theoretical and experimental studies have shown that the thermodynamics of HydrogenMetal systems can be considerably affected by applying elastic strain.5,6,7 The critical temperature, above which phase transformation to hydride is suppressed, can be noticeably reduced by applying high strains. In thin films clamped to substrate, the strain can be tuned through the thickness of the film5. High strains were recently achieved by adding small amounts of zirconium (Zr) to Y thin films.8 The equilibrium hydrogen pressure of YH2 – YH3 was thus precisely tuned over four orders of magnitude. This allowed realizing a hydrogen sensor in the eye-visible range, indicating the ambient hydrogen pressure at room temperature. Understanding the interaction of hydrogen with metallic thin films is therefore very important from both fundamental and technological standpoints. In the present study, we explore the thermodynamics of a highly strained Gd film with hydrogen, at moderate hydrogen concentrations (H/Gd ~0.6), at mesoscopic dimensions. At that concentration, metal and di-hydride phases coexist in bulk Gd.9 However, in the highly strained Gd film, the phase transformation is prohibited. However, we show experimental evidence that the
H-Gd solid solution undergoes spinodal decomposition to regions of high and low H concentrations. We monitor in-situ the dynamics of this process by Scanning Tunneling Microscopy (STM) and we analyze quantitatively the results in view of the underlying theory, dictated by the Cahn Hillard equation. The experimental distribution (wavelength of the spatial modulation) and temporal evolution in H concentration are found to be in good agreement with the theory.
METHODS A highly strained film of Gd metal was prepared by depositing Gd on a W(110) substrate at room temperature, using an e-beam evaporator. The experiment was carried out in an Ultra High Vacuum (UHV) system with a base pressure of 2.0·10-10 mbar. Before the Gd deposition, the W crystal substrate was cleaned of contaminants, especially Carbon ones, and checked by Auger Electron Spectroscopy (AES). Following deposition, a Gd film of ~2 ML thickness (measured by a Quartz crystal monitor) was obtained. Due to the misfit between the Gd and W lattices, the Gd film is highly dilated (by ~8%).10,11 The film was annealed at 650 °C for 7 min. The resulting film consisted of an epitaxial Gd layer covered by three-dimensional islands. The formation of those islands is the predominant stress relaxation mode in the highly strained film (Stransky-Krastanov mode).12 The film was subsequently exposed to 1L of hydrogen (achieved by a pressure of 7.8·10-9 mbar in the UHV chamber during 3 min). Sequential constant current STM images were recorded at room temperature, before exposure to hydrogen, and at different times after exposure, to follow the evolution of the hydrogenation process. The images, attained with high lateral resolution, reveal topological features and may also
reflect changes in the electronic configuration of the surface due to adsorbed hydrogen, because of the tunneling current dependence on the local density of states. The STM images obtained were analyzed using a digital image processing software, for determining the average aspect ratio (height to diameter ratio) and volume of each island. The aspect ratio of the islands was used as an indicator of the local elastic strain in the film, underneath the island.13 This relies on the fact that islands with large aspect ratio can decrease to some extent the elastic energy, at the cost of increasing the surface energy. Thus, an island of large aspect ratio implies a highly strained surface underneath, and an island of low aspect ratio –a less strained surface. The area and mean height, as well as the contour metric maps of the islands have been acquired simultaneously, from the same region, in STM images taken at different times. The data sets obtained were analyzed using a scientific data analysis software. Most of the images were taken at tunneling conditions that did not allow to distinguish zones with hydrogen adsorbed from others. However, using the measured aspect ratios and volumes of the different islands covering the film, strain maps were obtained, from which H concentration maps were deduced. The method applied was already described in details13 and is summarized in the Supplementary material. A few images were taken at bias voltage that allowed regions of high H concentration to appear as protrusions. It is important to note that the electronic effect should not change the H distribution observed. This results from the fact that the H concentration at the top of the islands is uniform, regardless of the aspect ratio. Indeed, islands with high aspect ratio have a large H concentration underneath but the decay of the concentration all the way up to the surface is significant, while in islands of low aspect ratio, the H concentration underneath is low and the decay is smaller. The H concentration at the top of the different islands, calculated
following the expressions derived by Kern and Muller14 (see Supplementary material for details), was found to vary by less than 2%.
RESULTS AND DISCUSSION Figure 1a shows the first STM image of the film, taken after annealing, before hydrogenation. The image reveals that the tungsten substrate got uniformly covered by an epitaxial layer of Gd, following the terraces and steps of the underlying W(110) substrate. Gd islands, of height varying between 2 and 6 ML, formed above the Gd wetting layer. The strain maps obtained by analyzing the islands in the area indicated by a rectangle in Figure 1a-1b, are shown in Figure 1c-1d. The strain maps indicate that the strain in the film, before hydrogenation, is roughly homogeneous, though some fluctuations are observed. These fluctuations are probably due to local strain relaxing mechanisms related to the islands14 or to edge dislocations at certain locations in the film. The average strain in Figure 1a is 0.10, in agreement with the strain expected due to the lattice misfit between the film and substrate. 10,11
Figure 1: STM images scanned before (a) and 87 min after (b) hydrogenation (It = 1.4nA, Vbias =0.8V). The yellow arrows point to hydride nuclei; (c) and (d): Strain maps deduced from the areas indicated by frames in the STM images; (e) and (f): Morphological changes of a single Gd island.
The STM image taken 87 min after exposure to hydrogen, and the strain map deduced, are shown in Figures 1b and 1d. Several changes, resulting from H adsorption and penetration, can be discerned. First, the strain distribution (Figure 1d) exhibits larger fluctuations, and the local strain reaches higher values (up to ~0.15 on specific areas and ~0.12 on average). The local H concentrations were calculated from the local strains, based on the fact that the strain increases linearly with hydrogen concentration in the film, according to: ε = αH·xH.6 ε is the additional strain due to the presence of hydrogen, xH is the local H/M ratio and αH =0.033 is the expansion factor in Gd.15 The corresponding H concentrations range from ~0.2 to ~1.3, with an average value of 0.63. The morphological changes in the islands, used to map the strain evolution in the film, are illustrated on a representative island in Figure 1e-1f. These morphological changes are enabled by the enhanced diffusion of the Gd atoms by adsorbed hydrogen.16 The diffusion constant at room temperature, on a similar surface, is in the order of 1Å2/second.16 In the present case, the diffusion of the Gd atoms is driven by the increasing strain caused by H adsorption in the thin film. A few hydride nuclei are also observed in the STM image taken after exposure to H. It is marked by a yellow arrow in Figure 1b. These nuclei appear at a region of high H concentration, as expected. As mentioned previously, much more hydride nuclei would have formed if the film was thicker and less strained. The dramatic increase in the strain fluctuations following hydrogen adsorption are attributed to the process of spinodal decomposition of H occurring in the film. Spinodal decomposition is a process in which a mixture separates into its components when cooled down to the miscibility gap.17,18 It is driven by reducing the free energy of the system and can occur in solid or in liquid mixtures. This process results in domains with relatively uniform high and low concentrations,
with a spatial wavelength. The puzzling element in this process is the diffusion against the concentration gradient. This separation occurs because diffusion actually follows the gradient of the chemical potential and not the gradient of the concentration. Spinodal decomposition occurs when the change of the free energy (given below) is negative.19 ∂ 2G
2κ (∆x)2 2
∆G = ∆Gchem + ∆Ggrad = (∂2xH + λ2 )
The first term in equation (1) (ΔGchem) must be negative and is so if the free energy G(xH) has a concave curvature. The second term is an interface term between the two domains. Δx and λ are the amplitude and wavelength of the composition modulation, assumed to be sinusoidal. The parameter κ is the energetic loss at the interface between the two phases. When the second term becomes larger than the first one (for smaller wavelength), the process of phase separation becomes energetically unfavorable. In spinodal decomposition, the wavelength λ is related to the diffusion constant (D) and the time required for the decomposition () by:
τ= λ2/4π2D (2) In order to evaluate the wavelength of the spatial modulation in the present case, we calculated the spatial correlation function of the concentration distribution deduced from Figure 1d. The strain map and corresponding concentration map are shown in Figure 2a,b and the result of the spatial correlation function is shown in Figure 2c. A clear peak at about 100 nm is observed. It is relatively isotropic, as shown by the correlations in two different directions (in black and red). Thus, the fluctuations are dominated by a sinusoidal modulation of wavelength λ~100 nm. The appearance of such a wavelength is characteristic of spinodal decomposition. Putting in equation (2) the values of λ=100 nm and D =1Å2/s16 gives τ=9 hours, which is in the order of magnitude of the time between the STM measurements. (The somewhat higher τ value obtained by the calculation may result from an under-estimation of the diffusion constant, D).
Figure 2: (a) Strain map deduced from the STM image shown in Figure 1, (b) H concentration map deduced from the strain map, (c) Spatial correlation function of the concentration map, indicating the development of a dominant wavelength at ~100 nm. The parameters that dictate the process of spinodal decomposition are dependent on the concentration of the hydrogen atoms and the strain they introduce. We use the published approximate thermodynamic model for H adsorption in thin film to calculate the chemical potential of H in the Gd film.20,6 According to the model, the dependence of the chemical potential on H concentration and strain follows the expression: XH
μH = kT·ln(r ― XH ) + E0 – EHH·xH - V0·αH·σii (xH). (3) where: σii (xH) = E·ε = E·αH·xH. (4) The relevant parameters are r, the total number of interstitial sites per metal atom EHH, the strength of the H-H interaction, V0 the partial molar volume of sites occupied by an interstitial specie and σii the sum of the axial stresses. In Gd, H occupies tetrahedral interstitials and r= 2.21 The additional parameters were taken as: EHH = 0.07 eV (which is the value for Tb, neighboring Gd in the periodic table)21; V0 =1.3 x 10-5 m3/ mol (which is the value for Er, also close to Gd in the periodic table)22; EGd = 55·109 N/m2. The value of E0 is irrelevant for our analysis, as we
consider the derivative of the chemical potential. Using this expression, the chemical potential μH in the present H-Gd system, and its derivative of as a function of concentration xH, were calculated. The result is shown in the Supplementary material. The derivative of the chemical potential equals 0 for xH=0.36 and xH=1.65. Between those two concentrations, the derivative is negative. This is therefore the concentration region for which spinodal decomposition is thermodynamically expected. The derivative of the chemical potential is also connected to the dynamics of the spinodal decomposition. The observed evolution of the fluctuating compositions obeys the Cahn Hillard equation (1). But in the case of spinodal decomposition, the classical diffusion equation is modified such that the diffusion constant is negative. In that case, the diffusion equation can be written in terms of composition fluctuations (xH):19 x H t
M 2 x H. Na xH
Where M is the mobility, Na is Avogadro’s number, and is the chemical potential. If the initial composition distribution (before hydrogen adsorption) is known, equation (5) can be integrated step by step. For each pixel the fluxes in and out can be summarized to give the expected change in H concentration and the induced strain. This can provide the time evolution of the spatial distrbution of the composition fluctuations expected by the Cahn Hillard equation. In the present case, there were some initial fluctuations in strain already before exposure to hydrogen (attributed to local relaxation mechanisms, see Figure 1a. We therefore used this initial strain distribution as initial condition for integrating the Cahn Hillard equation, rather than using a uniform distribution, as generally. The calculated time evolution of the composition domains thus obtained are shown in Figure 3, compared to the corresponding experimental spatial distribution
of the hydrogen composition domains. A very good qualitative agreement is seen between the simulated and experimental results. The similarity between the experiment and theory clearly validates our analysis for getting the composition fluctuations and confirms spinodal decomposition type dynamics of the composition fluctuations in the Gd-H system. We neglected the gradient energy term (equation 1) in our analysis. is of the same order of magnitude as the minimum of /xH, but it is divided by λ2 (~100 atomic diameters) in equation 1. Therefore, it is negligible compared to the chemical spinodal term.
Figure 3: Experimental spatial distribution of hydrogen at different times, compared with simulated ones, obtained by integrating the Cahn Hillard equation. The area considered was shown in Figure 1. The red circles indicate locations at which protrusions appeared. Hydrogen adsorption in the Gd(0001) film is expected to cause electronic effects. Geltzlaff et al. have shown that the bias voltage strongly affects the appearance of the hydrogen affected areas in thick Gd films on W(110).23 At low positive voltages (U=0.8 V), the contrast between uncovered and hydrogen-affected regions was found to vanish whereas for voltage higher than 0.8 V, the hydrogen covered areas appeared brighter than the other regions.24 At the bias voltage used for acquiring the STM images shown so far (0.8V), the topography of the high H concentration areas slightly differs from that of the low H concentration areas. However, when using a higher bias voltage (2.7 V), several bright regions (protrusions) can be discerned. Figure 4a shows an STM image (taken 195 min after exposure to hydrogen), in which several protrusions, of roughly circular form, are observed. A zoom on two representative ones (in black circles in the STM image) is shown in Figure 4b, along with the same areas taken from the STM image measured at 0.8V bias, 159 min after hydrogenation. Line profiles from the protrusions in both images are shown in Figures 4c. A few locations at which hydride precipitates and protrusions appeared in the area previously considered (disclosed by a rectangle) are indicated by red circles in Figures 3d and 4a.
Figure 4: (a) STM image taken 195 min after exposure to hydrogen, at 2.7 V bias voltage. (b) Zoom on the patterns in black circles in the STM image, taken at conditions: It= 0.5nA , Vbias= 2.7V (Left) and It= 1.4nA , Vbias=0.8V (Right). (c) Line profiles along those patterns. It can be seen from Figure 3d that the protrusions appear at regions of high H concentration. More precisely, they appear at regions of high gradient in H concentration and seem to grow from the islands towards the surroundings, stopping at steps. In fact, several patterns, delimited by steps, can be seen in Figure 4a. The height of the protrusions gradually decreases in the direction of the gradient in H concentration. The presumed reason for the appearance of protrusions, in regions of high H concentration, is that these regions have a lower conductance.1,2 This lower conductance implies partial charging of the region, which is partially electrical floating. As a result, the effective tip-sample bias voltage (V) is reduced, and the tunneling conductance (I/V) is increased, leading to a protrusion in the STM image. The charging is more significant at higher bias voltage (2.7V compared with 0.8V). Similar effects of charging of atoms or molecules on a thin insulator film, deposited on a metal surface, have already been reported.25,26
We recall that the H content in those areas is H/M~0.8 on average, exceeding the solubility limit of H in bulk Gd at room temperature. The observation of high H concentration areas, coherent with the Gd matrix, instead of hydride nuclei, is therefore an additional manifestation of the effect of high tensile stress on the thermodynamics of H in Gd.
CONCLUSIONS To conclude, we have shown that H adsorption in a highly strained Gd film resulted in an inhomogeneous distribution of H, indicating spinodal decomposition between regions of high and low H concentration. The spatial distribution of H in the film was deduced from mapping the strain in the film, using the aspect ratios of the islands. The concentration distribution thus obtained was supported by direct STM imaging of areas of high H concentration (appearing as protrusions). In addition, the observed dynamics were found to be in good agreement with numerical simulations of the spinodal decomposition process, obeying the Cahn Hillard equation, in both spatial and temporal scales. The presented work shows new important aspects of the effect of tensile stress on the thermodynamics of Metal-Hydrogen (M-H) systems. The presented results indicate that, under conditions that inhibit phase transformation to hydride, spinodal decomposition of H in the metal may occur. These results suggest that not only the M-H phase diagram is affected by the strain but also the dynamics of the H distribution and the composition of the H containing phases. The sub-surface hydrogen in the regions of high H concentration is expected to cause electronic perturbations, affecting the adsorption properties and catalytic activity.27 The uneven distribution of H in the film is also expected to affect the local physical and chemical properties (in particular, the optical and magnetic properties, which strongly depend on the H content). The presented study
therefore extends recent ones and opens the route for future studies on the effect of high tensile strains on M-H systems.
SUPPORTING INFORMATION DESCRIPTION: The Supporting Information includes calculation details on the use of islands as nanometric probes for local elastic strain, on the derivation of the free energy in the Gd/W(110) film as a function of H content and on the concentration decay from the interface to the top of the islands. AUTHOR INFORMATION Corresponding Author * [email protected] Funding Sources This work was supported by the PAZY foundation and by the Israeli Ministry of Science and Technology.
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