In-situ X-ray diffraction study of hydrogen absorption and desorption processes in Pd thin films: Hydrogen composition dependent anisotropic expansion and its quantitative description

The hydrogen absorption/desorption processes of (111)-textured and normal palladium (Pd) thin films of thickness ranging from 8 to 48 nm are investigated using X-ray diffractometry. The one-dimensional expansion of Pd lattice due to the substrate clamping is observed at the low hydrogen composition phase while both out-of-plane and in-plane expansions are detected at the high hydrogen composition phase. Accordingly, using a biaxial Poisson’s ratio, an anisotropic expansion factor is proposed for describing such phenomenon quantitatively and the hydrogen composition dependence on this factor is investigated.


I. INTRODUCTION
In recent years, palladium (Pd) has attracted a growing amount of research due to its hydrogenrelated catalytic and hydrogen storage properties. It is well-known that there are two phases, namely α-and β-phases, in the Pd-H system at room temperature. 1 The α-phase is the low hydrogen composition phase (up to ∼2 at.% H in the case of bulk) while the β-phase is the high hydrogen composition phase (more than ∼37.6 at.% H). In both α-and β-phases, their lattices are based on face-centered cubic (fcc) Pd and hydrogen atoms are incorporated randomly into the interstitial octahedral sites of fcc Pd.
Many studies have already been conducted on this α-to-β phase transformation using bulk Pd (nano-)particles, for instance, in the narrowing of the miscibility gap in Pd nanoparticles. 2 Baldi et al. 3 have in-situ observed on the hydrogen absorption and desorption processes in Pd nanoparticles using electron energy-loss spectroscopy. The avalanching strain and the effect of the surface structure have been revealed using diffractometry. [4][5][6] Reviews concerning the size effect can be found in Refs. 7 and 8. In the case of Pd films, the α-to-β phase transformation is much more complex. In general, thin Pd films (thickness less than a few tens of nm) are resistant against hydride formation. 9,10 Also, thin epitaxial Pd films tend to exhibit reversible and coherent phase transition compared to thick Pd films. [11][12][13] These unique characteristics are considered to be derived from substrate clamping, or substrate constraint. 11,[14][15][16][17][18] The main effect of substrate clamping is the suppression of in-plane expansion. Thus, when the in-plane expansion is suppressed completely, one-dimensional expansion along the out-of-plane (or the substrate normal) direction can be observed during hydrogen absorption. [19][20][21][22][23] Such anisotropic expansion is accompanied by large in-plane compressive stress, and, according to resent study, such stress affects the thermodynamic properties of hydrogen Two types of Pd films -highly (111)-textured and normal -were prepared using sputtering deposition. An AlN(20 nm)/Pd(8 nm)/AlN(20 nm) three-layered underlayer (hereafter, denoted as APA-underlayer) was employed for preparing highly (111)-textured Pd films of thicknesses 8, 16, 24 and 48 nm. Although the APA-underlayer improves the (111) fiber-texture of Pd films deposited onto it, the diffraction intensity of the APA-underlayer is relatively small compared to the textureimproved Pd film as shown later (section III.A). The Pd/APA-underlayer film has been fabricated using a continuous sputter deposition process which improves the film texture. 26,27 In brief, using two direct current magnetron sputtering guns equipped with metallic platinum (Pd) and aluminum (Al) targets, the three-layered APA-underlayer and Pd films were deposited on a synthetic fused silica substrate. Because the two guns are discharged at the same gas conditions, the deposition is uninterrupted and incorporation of contaminants, such as oxygen atoms, into the interfaces is suppressed. The pressure before gas introduction was better than 5 × 10 -5 Pa. Other details of deposition conditions are shown in Table I. The Pd film (thickness: 48 nm) without the APA-underlayer was also prepared by depositing it directly onto a synthetic fused silica substrate (denoted as Pd (48 nm)/substrate or normal Pd film). As shown in later, this film has weak (111) and (200) textures. Note that the deposition conditions are the same as those for fabricating (111)-textured Pd films.
The structure of the prepared film was confirmed using a transmission electron microscope (TEM) (JEM-3010; JEOL) operated at 300 kV. For cross-sectional observation, silicon (Si) (100) wafers with native oxide were also employed as a substrate. The cross-sectional specimen for TEM was prepared by argon ion milling. The texture of the film was measured using a normal X-ray diffractometer (radiation: CuKα, wavelength: 0.15418 nm). Figure 1 shows the experimental setup for the in-situ XRD measurements. A Bruker D8 Discover diffractometer was employed to measure (111) lattice spacings of α-and β-phases at the tilt-angles psi (ψ) = 0°and 70.5°(d 111 ψ=0 • and d 111 ψ=70.5 • ). Note that since the angle-difference between {111} is 70.5°, the (111)-textured film exhibits strong diffraction intensity not only at ψ = 0°but also at ψ = 70.5°. The diffractometer consists of a rotating copper anode generator, a Montel-P mirror, a laboratory-designed gas cell and a two-dimensional (2D) position sensitive Vantec-500 detector. The X-ray was generated at 50 kV, 22 mA and paralleled using the Montel-P mirror, which consists of two multilayered mirrors. The divergence of the paralleled beam is less than 0.04°in horizontal and vertical directions. The Montel-P mirror also works as a monochromator for CuKα, and cuts out other wavelengths such as CuKβ X-ray. The specimen film was irradiated by a paralleled CuKα X-ray beam collimated through a pinhole (diameter: 0.1 mm). It was placed at the center of the goniometer and the atmosphere around the specimen film was controlled using two mass flow controllers for hydrogen and nitrogen gases. Diffracted X-rays were collected using the Vantec-500 detector placed at 199.8 mm from the specimen. The frame size of the detector was 2048 × 2048 pixels and the size of each pixel was 68 × 68 µm 2 . The data acquisition steps are shown in Fig. 2. One set of measurements consisted of 136 cycles and took about six and a half hours for each film. During the XRD measurement, 0%, 2%, 0%, 4%, 0%, 6%, 0%, 8%, 0%, 10% and 0% H 2 gases mixed with pure-N 2 were introduced sequentially. The H 2 gas profile over time is shown later (Sec. III C). All measurements were conducted at room temperature (∼293 K) and atmospheric pressure.

B. In-situ XRD measurements
After the measurement, line profiles were extracted from the two-dimensional frames. The backgrounds of each profile were subtracted using the profiles of the APA-underlayer or the synthetic fused silica substrate measured in the same manner. In other words, the profiles employed for profile fitting were derived only from the Pd films on the APA-underlayer or on the substrate. The peak intensity, peak position and the full width at half maximum (FWHM, or 2w) were determined by fitting the peak with a pseudo-Voigt profile. Since the incident beam contained CuKα 1 and CuKα 2 , the fitting was conducted under the assumption that the peak consisted of two peaks corresponding  to Kα 1 and Kα 2 . All profile fittings were conducted using Mathematica (Version 9; Wolfram, Champaign, IL, USA). Note that the accuracy of the diffraction angle (2θ) and the amount of instrumental broadening of the diffractometer were confirmed using NIST SRM 640c silicon powder. The 640c powder was installed to the gas cell similarly to the in-situ measurement of the films. The diffraction profiles were acquired at ψ = 0°and 70.5°and the accuracy of 2θ was better than 0.04°for all ψ.
The sum of this 0.04°error and the standard error of peak position during the profile fitting was adopted as a possible total error, and indicated by error bars in figures after consideration of error propagation.

C. Analyses of measured results
The measured results were first analyzed using rhombohedral distortion analysis, which can calculate the in-plane lattice strain from measured lattice spacings without any elastic constants. Thereafter, the same measured results were analyzed using diffraction stress analysis, in which inplane stress and the strain-free lattice parameter were estimated. In addition, the hydrogen composition was calculated from the strain-free lattice parameter. Note that all analyses were conducted under the assumption that there was no stress gradient in the Pd films. This assumption is widely employed for the case of thin films. 28

Rhombohedral distortion analysis
The rhombohedral distortion analysis method is based on the primitive rhombohedral cell of fcc. 29 This method can be used for films with (111) fiber-texture and stress with rotational symmetry (i.e. σ 11 = σ 22 = σ || where σ 11 and σ 22 are in-plane stresses). The parameters inferred from the analysis are the angle (γ r ) and the lattice parameter (l r ) of the rhombohedral cell. These two parameters can be calculated from the measured lattice spacings of (111) planes at two different ψ angles, 0°a nd 70.5°(d 111 Since the in-plane lattice spacing of (110) can be written as 29 the in-plane (||) strain referenced from (110) lattice spacing of bulk Pd (d 110 bulk Pd ) is described as The out-of-plane ( ⊥ ) strain referenced from (111) (Important note: In this paper, there are two-types of strains; one-type is defined using the strain-free lattice parameter and another-type is defined using the lattice spacing of bulk Pd. To distinguish between these two strains, the strains of the latter-type are indicated using the degree symbol "°" as the above equations.) Since Eqs. (4) and (5) contain no constants except for the lattice spacings of bulk Pd, both out-of-plane and in-plane strains can be calculated without any elastic coefficients. Note that since this rhombohedral distortion analysis method is applicable only to (111)-textured film, the in-plane strain of normal film was estimated using diffraction stress analysis instead.
where d 111 ψ is the (111) lattice spacing at ψ and a sf is a strain-free lattice parameter. When two (111) lattice spacings at ψ = 0°and 70.5°(d 111 ψ=0 • and d 111 ψ=70.5 • ) are measured, the strain-free lattice parameter and the in-plane stress can be calculated from Eq. (6) as Note that the approximation of sin 2 70.5°= 8/9 is employed. The constants S 111 1 and 1 2 S 111 2 are diffraction elastic constants for 111 reflection and have texture dependence. Table II  for normal film are calculated by solving equations in Ref. 39. Since the hydrogen composition dependence on the elastic compliances could not be found in literature, the assumption that the diffraction elastic constants of α-and β-phases are the same as pure-Pd and PdH 0.66 , respectively, was applied in the following.
Employing the strain-free lattice parameter calculated from Eq. (7), the hydrogen composition (x H ), defined as the H/Pd atomic ratio, is estimated using the following equation 18,41 a sf − a bulk Pd where α H is a (linear) expansion coefficient due to hydrogen incorporation. The value of 0.061 is the average of 0.063 in the literature 18,41 and 0.059, which is estimated from Vegard law between pure-Pd and PdH 0.603 . 1 Note that this equation is valid at both α-and β-phases. Also, since the strain-free lattice parameter is the lattice parameter at the stress-free state, the hydrogen composition can be estimated without the influences of the stress, its relaxation and the grain boundaries. The a bulk Pd denotes the bulk lattice parameter of pure-Pd (0.389019 nm 42 ).

A. Film structure
The texture of the prepared films was confirmed using normal θ-2θ XRD measurements (Fig. 3). It is clear that the Pd(48 nm)/substrate has weak (111) and (200) textures, as both 111 Pd and 200 Pd peaks were detected. In contrast, the Pd film on the APA-underlayer is highly (111)-textured, since a strong 111 Pd peak was observed. Note that the APA-underlayer exhibits no peak at around 111 Pd and therefore does not affect measurements on the 111 Pd peak of the texture improved Pd(x nm) film deposited on it. Figure S1 in the supplementary material shows 111 pole figures of prepared films. It is clear that Pd films on the APA-underlayer are almost full (111) fiber-texture with the rotational symmetry, since the strong 111 pole is observed at the center and the ring at ψ = ∼70°. Table S1 summarizes the pole widths at the center and they were ∼2°at half-width at half maximum. According to Ref.  The rotational symmetry in the in-plane stress was investigated using the in-plane rotation angle (φ) dependence on the (111) lattice spacing at ψ = 70.5° (Fig. S2 in the supplementary material). Since the deviation is less than the error range, the validity of the assumption "σ 11 = σ 22 = σ || " is confirmed.
In the case of Pd films deposited on the APA underlayer, the layer structure was further investigated using cross-sectional TEM. The bright-field (BF) image of the Pd(8 nm)/APAunderlayer/substrate is shown in Fig. 4(a). The designed film structure consisting of the Pd film and APA-underlayer was confirmed. The thicknesses of each layer measured from TEM images, Pd(7.9 nm)/AlN(17.8 nm)/Pd(7.8 nm)/AlN(19.1 nm)/SiO x (0.7 nm)/Si wafer, were in good agreements with the designed thicknesses. The dark-field (DF) image and the selected area electron diffraction (SAED) pattern demonstrated that the Pd film on the APA-underlayer had (111) texture and the upper AlN in the APA-underlayer was in c-axis preferred orientation while other layers were polycrystalline (Figs. 4(b) and (c)). It should be noted that although all layers are served for acquiring SAED, the diffraction rings of bottom two layers are submerged in background due to the strong 111 Pd and 002 AlN spots derived from the upper two layers. The high-resolution TEM (HRTEM) image further confirmed (111) texture of the Pd film on the APA-underlayer (Fig. 4(d)) and no texture of the Pd layer in the APA-underlayer (Fig. 4(e)). According to the (111) lattice image of Fig. 4(d), the crystal size along the substrate normal, or the vertical grain size, of Pd is almost equal to the thickness of the Pd film (8 nm). The roughnesses of the interfaces between Pd and AlN layers are around 2 nm. Since the lattice fringes of Pd were connected to that of AlN in some parts, local-epitaxial growth at the interface took place.  In summary, the Pd film on the APA-underlayer was highly (111) fiber-textured, while the Pd film deposited directly on the substrate had weak (111) and (200) textures. The APA-underlayer is an ideal underlayer from the viewpoint of diffractometry since there is no intensity around the 111 Pd peak position in the diffraction profile. Based on these results, we used the prepared highly (111)textured Pd films deposited on the APA-underlayer and the normal Pd film to conduct the in-situ XRD investigation.

B. In-situ XRD measurements
Typical in-situ XRD profiles, shown in Fig. 5, indicate the formation of β-phase in the emergence of a new peak at around 38.5°when ψ = 0°, and 39°when ψ = 70.5°(Note: the peak position difference is related to the in-plane stress and discussed in the next section).
It is clear that the hydrogen concentration for the β-phase formation exhibits thickness dependence: the thicker film tends to form β-phase while the thinner film has a resistance against hydride formation (Figs. 5(a)-(d)). For example, in the case of 8% H 2 , the 48 nm-thick Pd film is almost entirely in β-phase, the 24 and 16 nm-thick Pd films are a composite of α-and β-phases, and the 8 nm-thick Pd film is mainly in α-phase. This result is in agreement with the literature that thinner Pd films exhibit less resistivity change while thicker Pd films show large change due to β-phase formation. 10 Also, in comparison with the normal Pd(48 nm)/substrate, it can be concluded that (111)-texture also suppresses the formation of β-phase (Figs. 5(d) and (e)). In the case of 4% H 2 , the main phase of (111)-textured film remains in α-phase while the normal film has already transformed into β-phase. These thickness and texture dependences can be explained by substrate clamping. 11,15-18 Figure 6 shows a typical reciprocal space map during hydrogen introduction. The observed spots at the center are 111 reflections of α-and β-phases. The intensity distributions of both α-and β-phases were in spots rather than rings and follow the line of q y = 0, indicating that the (111) texture is retained during α-to-β phase transformation. In addition, since the spot width along the q y direction of β-phase is almost equal to one of α-phase, we see that the in-plane crystal size is also retained. Similar retainment was also observed in β-to-α transformation (not shown). Thus, in the case of textured film, the formation of hydride phase and subsequent recovery of metallic phase took place while retaining both the film texture and the in-plane crystal size. This may be related to the coherent phase transition, 11,13,16 however, the details are still under investigation.

C. Anisotropic lattice expansion due to substrate clamping
To further investigate the process, the center positions, FWHM and peak intensities of α-and β-phases were estimated using peak profile fitting. The calculated peak profiles are shown as red lines in Fig. 5 and show good agreement with the measured profiles. The fitting and the analysis results are summarized in Fig. 7 (in the supplementary material, the undivided version of this figure can be found).
The peak intensities (peak heights) of α-and β-phases clearly demonstrated that the hydride formability has the thickness and texture dependences discussed in the previous section (first row of Fig. 7). For example, the (111)-textured 8 nm-thick Pd film diffraction pattern exhibits no β-phase intensity at up to 6% H 2 while that of the (111)-textured 48 nm-thick Pd film shows β-phase intensity from 4% H 2 . In addition, since the XRD intensity of the final hydrogen lading stage is slightly larger than that of the initial loading stage, the crystallinity and/or the texture of the film should be improved by hydrogen absorption and subsequent desorption. Since hydrogen absorption/desorption cycles are known to result in crystallinity degradation, this intensity increase could be explained by the texture improvement. Similar texture improvement has been already reported by Gremaud et al. 16 The FWHM of the peak at ψ = 0°corresponds to crystal size along the out-of-plane direction (or the vertical grain size) and non-uniform strain (second row of Fig. 7). Although it is difficult to treat these two effects separately, the following is clear: when the film is in a single-phase of α-or β-phase, the vertical grain size is large and the non-uniform strain is small because the FWHM is small. When the film is in a mixture of α-and β-phases, the vertical grain size is small and/or the non-uniform strain is large since the FWHM is larger than the single-phase case. Hence, it can be concluded that, during the β-phase formation, the film is non-uniformly strained and the vertical grain size is decreased. However, once α-phase transforms to β-phase completely, the non-uniform strain in the film disappears and the vertical grain size returns to the initial one.
According to strain along out-of-plane and in-plane directions (third and fourth rows of Fig. 7), the strain before hydrogen introduction was almost equal to 1 for any direction and thickness, indicating that stress in the films was almost zero and lattices consisted of Pd with a lattice parameter equal to the bulk one. After the hydrogen introduction, lattice expansion occurred, dividable into two stages: an initial stage before β-phase formation and second one during β-phase formation.
During the initial stage of hydrogen absorption, the lattice expansion occurred mainly along the out-of-plane direction (up to 1% expansion) with almost zero expansion/shrinkage along the in-plane direction (compare third row to fourth row of Fig. 7). This anisotropic expansion was observed in all films. This clearly demonstrates that the lattice expansion in the initial stage was one-dimensional. After replacing the 2% hydrogen gas with 100% nitrogen gas, the lattice expansion was halted and the strain returned to 1. Thus, within this initial stage, the lattice expansion and shrinkage can be considered to be a one-dimensional reversible process and no plastic deformation takes place.
At the start of second stage, the film is a combination of hydride β-phase and metallic α-phase, before finally transforming into β-phase completely. The formation of β-phase was observed as the lattice expanded in both out-of-plane and in-plane directions, indicating the decrease of the out-ofplane anisotropy in β-phase. The measured 34% expansion was reasonable from the viewpoint of hydride formation, since the lattice constant difference between bulk Pd and PdH 0.6 is known at 3.5%. 1,41 In detail, the observed out-of-plane expansion was ∼4% and slightly larger than for inplane (∼3%). This can be explained by the in-plane compressive stress which is discussed in the next section. In the α-phase, in addition to the lattice expansion along the out-of-plane direction, the lattice shrinkage along the in-plane direction was observed in this second stage. This observation is different from the initial stage (i.e. no expansion/shrinkage along in-plane direction). This lattice shrinkage in the α-phase is considered to be derived from the formation of the β-phase of which in-plane expansion is relatively large (∼2-3%). The observed large in-plane stress supports this consideration. Once β-phase forms, the hydrogen absorption-desorption reaction becomes irreversible. The strain after hydrogen desorption cannot return to zero, indicating that the plastic deformation, such as an introduction of misfit dislocations at the film/(substrate or underlayer) interface, 11,13,16 takes place during the β-phase formation. In fact, the out-of-plane strain after recovering α-phase reached negative 0.51%, while the in-plane strain was positive. This strain could be considered to be an elastic deformation due to the in-plane tensile residual stress deriving from the plastic deformation during α-to-β transformation and the subsequent large shrinkage during β-to-α transformation. According to these observations, we conclude the following: in the initial stage, the reversible lattice expansion/shrinkage occurred only along the out-of-plane direction, while there was no expansion/shrinkage along the in-plane direction. This anisotropic lattice expansion, or one-dimensional expansion, indicates that no plastic deformation took place at this initial stage. During the second stage, the formation of β-phase was observed through large expansions around 34% along both out-of-plane and in-plane directions resulting in irreversibility. During the formation of β-phase, plastic deformation occurred and it results in the decrease of the out-of-plane anisotropy. This indicates that the anisotropic expansion has a hydrogen composition dependence. After returning to its metallic lattice (α-phase), there was large in-plane tensile residual stress derived from the plastic deformation during α-to-β transformation and the subsequent lattice shrinkage during β-to-α transformation. first row), FWHM (2w) of the peak at ψ = 0°(second), out-of-plane strain (ε⊥) (third), in-plane strain (ε ) (fourth), in-plane stress (σ ) (fifth), strain-free lattice parameter (a sf ) (sixth), and hydrogen gas concentration introduced to the cell (seventh) are plotted against time. Note that the strain-free lattice parameter is normalized using the bulk lattice parameter of pure-Pd (a bulk Pd ), even in the case of β-phase. In the supplementary material, the undivided version of this figure can be found.