High-resolution and high-pressure x-ray diffraction
study of ScFe2Hx compounds

S. El Bidaoui, L.V.B. Diop, V. Svitlyk, C. Hennig, O. Isnard

► To cite this version:

S. El Bidaoui, L.V.B. Diop, V. Svitlyk, C. Hennig, O. Isnard. High-resolution and high-pressure x-ray diffraction study of ScFe2Hx compounds. Materials Today Communications, 2025, 46, pp.112542. 10.1016/j.mtcomm.2025.112542. hal-05219817

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# High-resolution and high-pressure x-ray diffraction study of ScFe₂Hₓ compounds

S. El Bidaoui a,*, L.V.B. Diop b, V. Svitlyk c,d, C. Hennig c,d, O. Isnard a

## ARTICLE INFO

### Keywords:

- Laves phases

- Hydride

- High pressure

- Equation of state

- Intermetallic compounds

## ABSTRACT

Using synchrotron-based x-ray diffraction (SXRD) techniques, the evolution of the crystal lattice in ScFe₂Hₓ compounds is investigated at room temperature and under pressures up to 25 GPa. High-resolution SXRD experiments reveal that the C14 hexagonal MgZn₂-type structure of the parent intermetallic compound ScFe₂ is preserved upon H insertion into the crystal structure in spite of the large unit-cell expansion of 21.4 %. The lattice expansion proves to be anisotropic with a larger expansion within the basal plane of the hexagonal structure $Δa/a = 7.1 \%$ against $Δc/c = 5.8 \%$. This huge increase in the cell volume is equivalent to $2.92 Å^3$/inserted hydrogen atom, a value much larger than that reported for several other Fe-rich alloys. Angle-dispersive SXRD measurements under external pressure indicate that the hexagonal symmetry of the crystalline lattice remains unaltered within the studied compression range up to 25 GPa. No signature of a structural phase transformation has been observed at least up to the highest applied pressure. The application of hydrostatic pressure induces a monotonous contraction of the cell dimensions. A bulk modulus of $K_0 = 142$ GPa has been inferred from the pressure-volume relationship for the initial alloy ScFe₂. It is further shown that hydrogen (deuterium) absorption leads to a decrease of the bulk modulus down to $K_0 = 112$ and 92 GPa for ScFe₂H₂.₈ and ScFe₂D₃.₂, respectively.

## 1. Introduction

AB₂-type intermetallic compounds are known as “Laves phases”, in reference to Fritz Laves who first described them [1–3]. This binary system AB₂ forms the most abundant group of intermetallic compounds known to date and the compositions are highly diverse. Generally, the B component stands for a smaller, less electropositive element (mid-to-late d-block atom and, infrequently, p-block atom or metalloid) while the A component is a larger electropositive element (early d-block metal, rare-earth, alkali, and alkaline earth). Laves type intermetallic compounds have long been important in metallurgy due to their high strength and high melting temperatures. Successful utilization of Laves phases as functional materials include coatings resistant to wear and corrosion, efficient electrocatalyst for hydrogen evolution, magnetostriction (e.g., Terfenol employed in magneto-mechanical sensors and actuators), magnetocalorics, superconductors, hydrogen storage, to name but a few [4,5].

Laves phases AB₂ crystallize in three structure types: (1) hexagonal MgZn₂ (space group P6₃/mmc, Pearson symbol hP12, Strukturbericht designation C14), (2) hexagonal MgNi₂ (P6₃/mmc, hP24, C36), and (3) cubic MgCu₂ (Fd-3m, cF24, C15). They belong to the group of Frank-Kasper phase compounds characterized by tetrahedrally close packed atomic arrangements. These compounds have been extensively studied owing to their simple crystal structures as well as their interesting physical properties [4,5]. For instance, it has been reported that the crystal symmetry and magnetic properties of iron-based Laves phases, AFe₂, are highly sensitive to external or chemical pressure [6–11]. High-pressure experiments using nuclear resonant scattering of synchrotron radiation and Mossbauer spectroscopy have been carried out on the Laves phases AFe₂ (A = Sc, Y, Gd, and Lu) for the study of magnetism [8–11]. The interest was focused on the variation of the magnetic ordering temperature and of the Fe band moment in AFe₂ as a function of pressure [8–11].

The insertion of H/D into the cubic structure of YFe₂ often leads to a

<footnote>a Université Grenoble Alpes, Institut Néel, CNRS, BP166X, Grenoble 38042, France</footnote>

<footnote>b Université de Lorraine, CNRS, IJL, Nancy F-54000, France</footnote>

<footnote>c Institute of Resource Ecology, Helmholtz Zentrum Dresden Rossendorf, Bautzner Landstrasse 400, Dresden 01328, Germany</footnote>

<footnote>d The Rossendorf Beamline (BM20), European Synchrotron Radiation Facility, 71 Avenue des Martyrs, Grenoble 38043, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: soufianelbidaoui06@gmail.com (S. El Bidaoui).</footnote>
change in the crystal symmetry of this compound [12]. Related with this
appears pressure-induced structural phase transition, collapse of ferro-
magnetism, and a giant isotopic effect on magnetism as have been re-
ported by Isnard et al. [13] in YFe₂(D,H)₄.₂. The cubic structure of ScFe₂,
ErFe₂, as well as the orthorhombic symmetry of their hydrides YFe₂H₅.₆
and ErFe₂H₅.₆, have been investigated by x-ray diffraction under pres-
sure [14]. It has been demonstrated that hydrostatic pressure induces a
phase transition in the hydrides, whereas the cubic structure of the
parent intermetallics remains unchanged up to 31 GPa [14].

ScFe₂ is a remarkable example of itinerant electron magnetism with a
large interplay between its physical properties and volume/pressure
[15–17]. A unique feature of this compound is its polymorphism, as it
can crystallize in all three Laves phase structures mentioned above.
Additionally, ScFe₂ has the ability to reversibly absorb large quantities
of hydrogen [18,19]. The structural properties of the C15 cubic structure
under pressure have been extensively studied [8,13,14,20], whereas the
hexagonal structure has only been investigated in a few works [21,22].
The aim of this study is to explore the structural properties of the C14
hexagonal phase of ScFe₂ and its hydride under hydrostatic pressure.

In this paper, we present high-resolution synchrotron x-ray diffrac-
tion (SXRD) studies on ScFe₂ and its deuteride ScFe₂D₃.₂ to resolve their
crystal structures and investigate any potential lowering of crystal
symmetry due to hydrogen insertion. Additionally, the structural
changes in ScFe₂, ScFe₂H₂.₈ and ScFe₂D₃.₂ will be studied using SXRD
under pressure. We will examine the evolution of the crystal structure,
the pressure dependence of unit cell parameters, volume, and crystal
symmetry. The influence of the hydrogen (deuterium) insertion on the
crystal lattice under pressure will be discussed by comparing ScFe₂H(D)ₓ
with the parent compound ScFe₂. To our knowledge, the effect of
pressure on hydrides of hexagonal C14 structure has not been experi-
mentally studied before.

## 2. Experimental techniques

The ScFe₂ polycrystalline sample was prepared by electric arc
melting from high-purity elemental Sc and Fe. Details of the synthesis
method are presented in Ref. [15]. A hydrogenation device developed at
Néel Institute was used to insert hydrogen (or deuterium) into the
intermetallic compound. Two compositions, ScFe₂H₂.₈ and ScFe₂D₃.₂,
were prepared. The hydrogenation process has been described in
Ref. [23]. It has been reported that there is no significant H/D isotopic
effect on the magnetic properties of ScFe₂(H,D)ₓ [23].

Two types of synchrotron x-ray diffraction (SXRD) experiments were conducted on ScFe₂(H,D)ₓ intermetallic powder samples at the BM20 (ROBL) beamline [24] at the European Synchrotron Radiation Facility (ESRF) in Grenoble. The first involved high-resolution x-ray diffraction with x-ray energy of 17 keV (wavelength 0.728233 Å) were performed under ambient conditions (23°C) using an EIGER2X 500k (CdTe) detector at the XRD-1 station. The raw data were integrated using a specific algorithm using the pyFAI code [25]. The high-pressure in-situ x-ray diffraction measurements were conducted at 23°C using a Pilatus3 x 2 M (Si) detector with x-ray energy of 30 keV (wavelength 0.413282 Å) at the XRD-2 station.

A series of experiments using the high-resolution mode was carried
out on a diffractometer equipped with a 6-circle goniometer and an
EIGER2X 500k detector. Powder samples, sieved to 32 µm, were loaded
into 300 µm diameter borosilicate glass capillaries. The samples have
been diluted with amorphous SiO₂ in order to lower the high absorption
of iron at the energy used. Diffractograms were collected in Debye-
Scherrer scattering geometry in a 2θ range between 4° and 60°. LaB₆
was used as the calibrant for these measurements. The high-resolution
diffraction data were analyzed by Rietveld's method using Fullprof
software [26]. The agreement factors and refinement method used
correspond to the description given in Ref. [27].

The high-pressure SXRD measurements was performed on ScFe₂,
ScFe₂H₂.₈ and ScFe₂D₃.₂ using membrane-driven symmetric diamond-

anvil cells (DAC) with Boehler-Almax type diamond. Two DACs with
diameters of 600 µm and 500 µm were used to collect diffractograms at
pressures of up to 15 GPa and 25 GPa, respectively. The powder samples
were grounded down to fine particles of size less than 32 µm and then
confined between the opposing diamond culets in a 340 µm diameter
hole of 200 µm thick stainless-steel gasket (Fig. 1). The DACs were
loaded using either neon gas or silicone oil as pressure transmitting
medium. Small chips of ruby Al₂O₃:Cr³⁺ were placed to detect the
pressure with the powder in the DAC. Accurate determination of sample
pressure was made by the ruby fluorescence method [28,29], and it was
measured before and after recording each diffractogram using the hy-
drostatic pressure scale determined by Mao et al. [30]. The sample was
placed at a distance of 21.54 cm from the two-dimensional Pilatus3 x
2 M detector. The DAC was rotated by ± 4° during about two minutes of
acquisition for each SXRD pattern. The diffraction images were inte-
grated with the Dioptas program [31], using LaB₆ data measured under
the same geometrical conditions as a calibrant. High-pressure diffraction
patterns for ScFe₂ were refined using the LeBail method, and the
least-squares method was used to determine the lattice parameters of
ScFe₂H₂.₈ and ScFe₂D₃.₂ compounds, taking into account more than 10
Bragg peaks.

## 3. Results and discussion

### 3.1. *High-resolution x-ray diffraction study*

High-resolution diffraction patterns have been refined using Rietveld
method to solve the crystal structures of ScFe₂ and ScFe₂D₃.₂ com-
pounds. Figs. 2 and 3 present a Rietveld refinement for these in-
termetallics. In Fig. 2, the main phase, constituting 94.6(2) %, is indexed
as having the hexagonal MgZn₂-type crystal structure, while a secondary
phase, representing 5.4(2) % of the total fraction, corresponds to the
polymorphic MgNi₂-type structure. The secondary phase was not
detected using laboratory XRD due to its small amount and the strong x-
ray absorption of the sample by the Mo-Kα₁ source. The ScFe₂D₃.₂
diffraction pattern (Fig. 3) indicates the presence of the deuteride phases
of ScFe₂ with the hexagonal MgZn₂ and MgNi₂-type structures, ac-
counting for 95.7(2) % and 4.3(1) % of the relative phase fractions,
respectively.

The results reveal that both ScFe₂ and ScFe₂D₃.₂ reverently crystal-
lize in the hexagonal MgZn₂-type structure, with *P*6₃/*mmc* space group
symmetry, indicating that the crystal structure is preserved upon
hydrogen insertion. A comparison of Figs. 2 and 3 shows that the Bragg
peaks of ScFe₂D₃.₂ are shifted towards smaller diffraction 2θ angles
compared to those of ScFe₂, indicating an expansion of the crystal lat-
tice. The refinement results for the diffractograms of ScFe₂ and ScFe₂D₃.₂
are presented in Table 1. The lattice parameters for ScFe₂ were refined to
be *a* = 4.97630(6) Å and *c* = 8.1392(1) Å which are in good agreement

<figure><img src="image_2.png" /><figcaption>**Fig. 1.** Illustration of the diamond anvil cell (DAC), and an image of DAC loaded with powder sample immersed in silicone oil. (a) powder sample, (b) silicon oil, (c) stainless-steel gasket.</figcaption></figure>
<figure><img src="image_3.png" /><figcaption>**Fig. 2.** High-resolution SXRD pattern for ScFe₂. The green bars represent the positions of the Bragg peaks for the C14 hexagonal MgZn₂-type structure of ScFe₂ main phase (a = 4.97630(6) Å and c = 8.1392(1) Å), and the orange bars corresponds to the C36 hexagonal MgNi₂-type structure of ScFe₂ of minority phase (a = 4.9759(2) Å and c = 16.2625(9) Å).</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>**Fig. 3.** High-resolution SXRD pattern for ScFe₂D₃.₂. The green bars represent the positions of the Bragg peaks for the C14 hexagonal MgZn₂-type structure of ScFe₂D₃.₂ (a = 5.3299(2) Å and c = 8.6155(4) Å), and the orange bars corresponds to the C36 hexagonal MgNi₂-type structure of ScFe₂ deuteride (a = 5.3194 Å and c = 17.2221 Å).</figcaption></figure>

**Table 1**

Lattice parameters, atomic positions, and confidence factors from Rietveld refinement of high resolution SXRD for ScFe₂, ScFe₂D₃.₂ and ScFe₂H₂.₈. The estimated error bar on the last decimal represents three times the standard deviation. Note that the unit cell contains 4 formula units.

<table><thead><tr><th></th><th>ScFe<sub>2</sub></th><th>ScFe<sub>2</sub>D<sub>3.2</sub></th><th>ScFe<sub>2</sub>H<sub>2.8</sub></th></tr></thead><tbody><tr><td>a (Å)</td><td>4.97630 (6)</td><td>5.3299 (2)</td><td>5.2841 (5)</td></tr><tr><td>c (Å)</td><td>8.1392 (1)</td><td>8.6155 (4)</td><td>8.5399 (9)</td></tr><tr><td>c/a</td><td>1.6355</td><td>1.6164</td><td>1.6161</td></tr><tr><td>V (Å<sup>3</sup>)</td><td>174.552 (3)</td><td>211.96 (2)</td><td>206.51 (4)</td></tr><tr><td>zSc(4 f)</td><td>0.0542 (3)</td><td>0.0542 (3)</td><td>0.0566 (4)</td></tr><tr><td>xFe(6h)</td><td>0.8318 (5)</td><td>0.8373 (5)</td><td>0.8341 (7)</td></tr><tr><td>yFe(6h) = 2 xFe(6h)</td><td>1.6636 (8)</td><td>1.6746 (9)</td><td>1.6682 (9)</td></tr><tr><td>χ<sup>2</sup></td><td>8.6</td><td>4.46</td><td>3.33</td></tr><tr><td>R<sub>p</sub> (%)</td><td>7.68</td><td>6.99</td><td>5.97</td></tr><tr><td>R<sub>wp</sub> (%)</td><td>12.2</td><td>9.91</td><td>8.51</td></tr><tr><td>R<sub>exp</sub> (%)</td><td>4.15</td><td>4.7</td><td>4.66</td></tr></tbody></table>

with previously reported XRD data [15]. From Fig. 4, it can be seen that the variation of the unit cell volume as a function of hydrogen concentration is linear for the investigated ScFe₂(H,D)₃ compositions. The insertion of 3.2H/f.u. into the crystal lattice of ScFe₂ induces a huge expansion in the unit cell volume, with ΔV/V = 21.4 %. Notably, the relative change in lattice parameters upon hydrogen insertion, Δa/a = 7.1 % and Δc/c = 5.8 %, indicates an anisotropic lattice expansion. This anisotropic character can also be seen on the variation of the c/a ratio with hydrogen content (Table 1): the c/a ratio varies from 1.6355 for ScFe₂ to 1.6164 for ScFe₂D₃.₂ deuteride. The ideal c/a value for the hexagonal MgZn₂-type structure is $\sqrt{8}/3 = 1.633$ [32]. The experimentally obtained c/a ratio for the initial compound ScFe₂ is in good agreement with the ideal computed ratio, whereas hydrogen insertion induces a slight reduction in the c/a ratio. Regarding the atomic positions in the hexagonal structure of ScFe₂D₃, the z-coordinate of the Sc (4 f) crystallographic site remains unchanged with the insertion of 3.2 D/f.u. By contrast, the x-coordinate of the Fe(6 h) crystal site is found to increase significantly (Table 1).

The interatomic distances for ScFe₂ and ScFe₂D₃.₂ are summarized in Table 2. A large increase of 10.6 % in Fe(6 h)-Fe(6 h) planar distances is observed upon hydrogen insertion. This is due to the fact that hydrogen insertion induces lattice expansion and change in the fractional atomic coordinate xFe(6h). It is worth to point out that the Fe(6 h)-Fe(6 h) interatomic distance is not only the most sensitive to hydrogen insertion, but it is also the shortest among the Fe-Fe distances in the starting ScFe₂ intermetallic compound. This large expansion of the Fe(6 h)-Fe(6 h) distance also leads to the largest nearest neighbor Fe-Fe distance in ScFe₂D₃.₂: 2.728 Å, compared to about 2.602 Å for the other Fe-Fe distance. Additionally, a comparison between the distances in the basal plane and those along the c-axis reveals a slight difference, which is correlated to the anisotropic expansion noted in the crystal lattice.

**3.2. High-pressure x-ray diffraction study**

LeBail refinements of high-pressure SXRD data for ScFe₂ at 0.23 GPa and 15.5 GPa are presented in Fig. 5. All diffraction peaks are indexed in the hexagonal MgZn₂-type structure with space group P6<sub>3</sub>/mmc. Comparing the two diffractograms, it is evident that the Bragg peaks are shifted towards higher diffraction angles due to the contraction of the lattice upon increasing pressure. No structural phase transition is observed for the ScFe₂ compound, as the hexagonal symmetry of the atomic arrangement remains unaltered within the studied pressure

<figure><img src="image_5.png" /><figcaption>**Fig. 4.** Dependence of the unit-cell volume on the hydrogen content for ScFe₂H(D)₃.</figcaption></figure>
<table><caption>**Table 2**
Interatomic distances from high-resolution SXRD for ScFe₂ and ScFe₂D₃.₂. The estimated error bar on the last decimal represents three times the standard deviation.</caption><thead><tr><th>Atom</th><th>Number of neighbors</th><th>Neighbor</th><th>Distances (Å) ScFe<sub>2</sub></th><th>Distances (Å) ScFe<sub>2</sub>D<sub>3.2</sub></th><th>Δd/d (%)</th></tr></thead><tbody><tr><td rowspan="5">Sc (4 f)</td><td>3</td><td>Sc (4 f)</td><td>3.0052(9)</td><td>3.216(1)</td><td>7</td></tr><tr><td>1</td><td>Sc (4 f)</td><td>3.1881(3)</td><td>3.373(4)</td><td>5.8</td></tr><tr><td>3</td><td>Fe (2a)</td><td>2.9067(3)</td><td>3.1125(3)</td><td>7</td></tr><tr><td>6</td><td>Fe (6 h)</td><td>2.955(2)</td><td>3.154(3)</td><td>6.7</td></tr><tr><td>3</td><td>Fe (6 h)</td><td>2.855(2)</td><td>3.058(3)</td><td>7</td></tr><tr><td rowspan="2">Fe (2a)</td><td>6</td><td>Fe (6 h)</td><td>2.499(1)</td><td>2.626(1)</td><td>5.1</td></tr><tr><td>6</td><td>Sc (4 f)</td><td>2.9067(3)</td><td>3.1125(3)</td><td>7</td></tr><tr><td rowspan="5">Fe (6 h)</td><td>2</td><td>Fe (6 h)</td><td>2.465(2)</td><td>2.728(2)</td><td>10.6</td></tr><tr><td>2</td><td>Fe (6 h)</td><td>2.511(2)</td><td>2.602(2)</td><td>3.6</td></tr><tr><td>2</td><td>Fe (2a)</td><td>2.499(1)</td><td>2.626(1)</td><td>5.1</td></tr><tr><td>2</td><td>Sc (4 f)</td><td>2.855(2)</td><td>3.058(2)</td><td>7</td></tr><tr><td>4</td><td>Sc (4 f)</td><td>2.955(2)</td><td>3.154(3)</td><td>6.7</td></tr></tbody></table>

<figure><img src="image_6.png" /><figcaption>**Fig. 5.** High-pressure SXRD patterns for ScFe₂ at 0.23 GPa (bottom) and 15.5 GPa (top). The green bars indicate the positions of the Bragg peaks for the C14 hexagonal MgZn₂-type structure of ScFe₂, and the pink bars at 0.23 GPa corresponds to the minority cubic α-Fe phase (Im-3m).</figcaption></figure>

range. However, a significant peak broadening is evident as the sample is compressed.

The evolution of unit-cell volume as a function of pressure was fitted using the Birch-Murnaghan equation of state (EoS) [33,34]:

$$P = \frac{3}{2} K_0 \left[ \left( \frac{V_0}{V} \right)^{\frac{7}{3}} - \left( \frac{V_0}{V} \right)^{\frac{5}{3}} \right] \left[ 1 + \frac{3}{4} (K'_0 - 4) \left( \left( \frac{V_0}{V} \right)^{\frac{2}{3}} - 1 \right) \right] \# \quad (1)$$

Where, $V_0$ is the zero-pressure unit-cell volume, $K_0$ is the bulk modulus which represents the inverse of compressibility, and $K'_0$ is pressure derivative of bulk modulus. The $K'_0$ value was fixed at 4 for all the compounds studied. The lattice parameters ($l = a$ or $c$) have been fitted using a modified Birch-Murnaghan EoS [35]:

$$P = \frac{3}{2} K_{10} \left[ \left( \frac{l_0}{l} \right)^7 - \left( \frac{l_0}{l} \right)^5 \right] \left[ 1 + \frac{3}{4} (K'_{10} - 4) \left( \left( \frac{l_0}{l} \right)^2 - 1 \right) \right] \# \quad (2)$$

**Fig. 6** displays the variation of unit cell volume as a function of applied pressure for ScFe₂. Fitting $V(P)$ curve using Eq. (1) yielded a bulk modulus $K_0 = 142(3)$ GPa and a zero-pressure unit-cell volume $V_0 = 176$ (2) Å³ for ScFe₂ compound. Note that the unit cell volume corresponds to 4 formula unit per cell. It should be noted that the inflection in the lattice parameters $a, c$, and volume $V$ around 13 GPa is due to the limit of the hydrostatic regime; pressures above this value are measured in non-hydrostatic conditions, as reported in Ref. [36].

For comparison purposes, the equation of state parameters $V_0, K_0,$

<figure><img src="image_7.png" /><figcaption>**Fig. 6.** Pressure dependence of the cell parameters $a, c$, and $V$ for ScFe₂, ScFe₂H₂.₈, and ScFe₂D₃.₂. The red line represents the fit according to the equation of state (1) for $V(P)$ and (2) for $a, c(P)$. Neon gas has been used as pressure transmitting medium for ScFe₂H₂.₈, and ScFe₂D₃.₂, while silicone oil was used for the ScFe₂ sample.</figcaption></figure>

and $K'_0$ for some Laves phase compounds are listed in Table 3. Gerhard Reiß [22] has determined the EoS parameters for several AFe₂ Laves phases ($A = Sc, Y, Ti, Gd, Tb, Dy, and Ho$) using high-pressure SXRD measurements. It has been shown that for the hexagonal structure of ScFe₂, $K_0 = 153(7)$ GPa, $K'_0 = 3.4(2)$ and $V_0 = 175(2)$ Å³, which agrees well with our results. It is important to emphasize that a significant dispersion in $V_0$ values has been observed previously in Ref. [22]. Six high-pressure SXRD experiments were performed on ScFe₂ intermetallic compound and the results clearly demonstrate that the zero-pressure unit-cell volume $V_0$ significantly differs from one run to another. The bulk modulus of ScFe₂ ($K_0 = 142(3)$ GPa) is smaller than that of TiFe₂ ($K_0$
<caption>**Table 3**</caption>

The $V_0$, $K_0$, and $K'_0$ values for ScFe$_2$H$_x$, Sc, α-Fe and other Laves phase compounds. Numerical values obtained from theoretical calculation are marked with a star. In this work, the value given in parenthesis represents the estimated standard deviation on the last decimal.

<table><thead><tr><th>compound</th><th>structure</th><th>V<sub>0</sub> (Å<sup>3</sup>)</th><th>K<sub>0</sub> (GPa)</th><th>K'<sub>0</sub></th><th>References</th></tr></thead><tbody><tr><td>ScFe<sub>2</sub></td><td>C14</td><td>176(2)</td><td>142(3)</td><td>4</td><td>this work</td></tr><tr><td>ScFe<sub>2</sub>H<sub>2.8</sub></td><td>C14</td><td>207(2)</td><td>112(2)</td><td>4</td><td>this work</td></tr><tr><td>ScFe<sub>2</sub>D<sub>3.2</sub></td><td>C14</td><td>214(2)</td><td>92(2)</td><td>4</td><td>this work</td></tr><tr><td>ScFe<sub>2</sub></td><td>C14</td><td>175(2)</td><td>153(7)</td><td>3.4(2)</td><td>[22]</td></tr><tr><td>ScFe<sub>2</sub></td><td>C14</td><td>167.5 *</td><td>121.92 *</td><td>-</td><td>[16]</td></tr><tr><td>ScFe<sub>2</sub></td><td>C14</td><td>162.4 *</td><td>156 *</td><td>-</td><td>[39]</td></tr><tr><td>ScFe<sub>2</sub>H<sub>2</sub></td><td>C14</td><td>188.4 *</td><td>150 *</td><td>-</td><td>[39]</td></tr><tr><td>Hf<sub>0.86</sub>Ta<sub>0.14</sub>Fe<sub>2</sub></td><td>C14</td><td>171.82</td><td>223</td><td>4</td><td>[37]</td></tr><tr><td>TiFe<sub>2</sub></td><td>C14</td><td>161.8(3)</td><td>201(4)</td><td>4</td><td>[21]</td></tr><tr><td>Sc</td><td>hexagonal</td><td>-</td><td>57</td><td>-</td><td>[40]</td></tr><tr><td>α-Fe</td><td>cubic</td><td>-</td><td>167</td><td>-</td><td>[38]</td></tr></tbody></table>

=201(4) GPa) [21], Hf$_{0.86}$Ta$_{0.14}$Fe$_2$ (K$_0$ =223 GPa) [37] and cubic α-Fe metal (K$_0$ =167 GPa) [38]. While ScFe$_2$ and TiFe$_2$ share the same hexagonal structure, the unit cell volume of ScFe$_2$ (V$_0$ = 176(2) Å$^3$) is larger than that of TiFe$_2$ (V$_0$ = 161.8(3) Å$^3$) [21], which explains the difference in compressibility between these two intermetallics. Similar conclusion can be made from the comparison with Hf$_{0.86}$Ta$_{0.14}$Fe$_2$ which also has smaller unit-cell volume (V$_0$ = 171.82 Å$^3$). From Table 3, the K$_0$ and V$_0$ values for ScFe$_2$ obtained from numerical calculations [16,39] are different from those determined experimentally. This discrepancy arises because the bulk modulus is more difficult to calculate accurately than the equilibrium unit cell volume, as it depends on the difference between two calculated values and is highly sensitive to the volume at which it is computed [40].

The evolution of lattice parameters *a* and *c* as a function of hydrostatic pressure for ScFe$_2$ was fitted according to the Eq. (2), as shown in Fig. 6. The fitting results indicate that the bulk modulus $K_0$ along the *c*-axis ($K_0$ =149(4) GPa) is slightly higher than that along the *a*-axis ($K_0$ = 138(3) GPa). This difference is not significant (8 %) compared to TiFe$_2$ [21], where the relative bulk modulus differs by approximately 40 %. This suggests that the compression of the ScFe$_2$ lattice is closer to isotropic behavior.

Fig. 7 represents selected high-pressure SXRD patterns at different pressures for the ScFe$_2$D$_{3.2}$ compound. The positions of Bragg peaks for the hexagonal MgZn$_2$-type structure are marked with green vertical bars. All peaks are shifted to higher angles as a function of applied

pressure, indicating the compression of the ScFe$_2$D$_{3.2}$ unit cell. Some new peaks appear starting at 5.2 GPa, indicating the crystallization of neon as a result of compression. These neon peaks are marked with red arrows in Fig. 6 and have been indexed and compared with the results of Ref. [41] to confirm the crystallization of Ne.

The variation in lattice parameters and volume as a function of external pressure is shown in Fig. 6 for ScFe$_2$D$_{3.2}$ and ScFe$_2$H$_{2.8}$. The EoS parameters for these compounds are presented in Table 3. Absorption of hydrogen in the ScFe$_2$ compound leads to a reduction of the bulk modulus from 142(3) GPa for ScFe$_2$ to 112(2) GPa for ScFe$_2$H$_{2.8}$ and 92 (2) GPa for ScFe$_2$D$_{3.2}$, which mean an increase in compressibility. This trend has also been observed in numerical calculations of K$_0$ for ScFe$_2$ and ScFe$_2$H$_{2}$ [39], where the insertion of 2H/f.u. induces a slight decrease in the K$_0$ value from 156 GPa to 150 GPa. This behavior is attributed to the volume expansion upon hydrogen insertion, as there is more space to compress the unit cell and the material becomes more compressible.

The lattice parameters *a* and *c* behave differently under pressure for the hydrides (Fig. 6), which can be attributed to the difference in the amount of H and D in ScFe$_2$. For ScFe$_2$H$_{2.8}$, the bulk modulus $K_0$ along the *c*-axis is slightly higher than its value in the *ab*-plane, whereas for ScFe$_2$D$_{3.2}$, the K$_0$ value in the *ab*-plane is greater than that along the *c*-axis. Since the relative variation of K$_0$ between the *c*-axis and the basal plane is negligible, the compressibility of these compounds can be considered to be nearly isotropic. We exemplify in Fig. 8 the evolution of the bulk modulus K$_0$ as a function of the zero-pressure unit-cell volume V$_0$ for ScFe$_2$H(D)$_x$ compounds. K$_0$ decreases with V$_0$, i.e., the bulk modulus diminishes upon increasing H(D) content.

## 4. Conclusions

The structural properties of ScFe$_2$H$_x$ metal hydride materials have been investigated by combining high-resolution and high-pressure SXRD experiments at room temperature. Upon hydrogen insertion into the crystal lattice of ScFe$_2$, the hexagonal symmetry of the atomic arrangement is preserved and the unit-cell expands, but in an anisotropic way with a larger expansion in the basal plane. The increase in unit-cell volume amounts to 21.4 % for ScFe$_2$D$_{3.2}$. The high-pressure SXRD study has revealed that the C14 hexagonal crystal symmetry remains stable at least up to 25 GPa, i.e., no change of lattice symmetry is observed within the investigated compression range. The application of

<figure><img src="image_8.png" /><figcaption>**Fig. 7.** High-pressure SXRD patterns for ScFe$_2$D$_{3.2}$ at different pressures. The green bars indicate the positions of the Bragg peaks for the hexagonal MgZn$_2$-type structure. The red arrows indicate the Bragg peak corresponding to cubic neon appearing at large pressure.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Fig. 8.** Variation of bulk modulus $K_0$ as a function of zero-pressure unit-cell volume V$_0$ for ScFe$_2$H(D)$_x$ compounds. The red dots represent DFT data taken from Ref. [39]. The green triangle corresponds to experimental data taken from Ref. [22].</figcaption></figure>
external pressure leads to a shrinkage of the crystalline lattice; a bulk modulus of $K_0 = 142$ and 92 GPa is obtained for ScFe₂ and ScFe₂D₃.₂, respectively.

### CRediT authorship contribution statement

**El Bidaoui S.:** Writing - Original Draft preparation, Methodology, Investigation, Data curation, Formal analysis, Visualization, Writing - Review & Editing. **Diop L.V.B.:** Conceptualization, Methodology, Resources, Investigation, Data curation, Formal analysis, Project administration, Writing - Original Draft preparation, Supervision, Writing - Review & Editing. **Svitlyk V.:** Investigation, Formal analysis, Writing - Review & Editing. **Hennig C.:** Investigation, Formal analysis, Writing - Review & Editing. **Isnard O.:** Resources, Investigation, Project administration, Writing - Original Draft preparation, Supervision, Writing - Review & Editing.

### Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgements

We are indebted to the European Synchrotron Radiation Facility, Grenoble, France for the allocated beam time.

### Data Availability

Data will be made available on request.

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