# Enhanced high-pressure superconductivity and local structure of the Ba8 Si46 clathrate

F. Morales, M. Núñez-Regueiro, Pierre Toulemonde, D. Machon, S. Le Floch, V. Pischedda, P. Lagarde, A. Flank, J. Itié, A. San-Miguel

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F. Morales, M. Núñez-Regueiro, Pierre Toulemonde, D. Machon, S. Le Floch, et al., Enhanced high-pressure superconductivity and local structure of the Ba8 Si46 clathrate. Physical Review B, 2016, 94 (10), pp.104507. 10.1103/PhysRevB.94.104507. [hal-01692100]

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Enhanced high-pressure superconductivity and local structure of the Ba<sub>8</sub>Si<sub>46</sub> clathrate

F. Morales,¹ M. Núñez-Regueiro,²,³ P. Toulemonde,²,³ D. Machon,⁴,⁵ S. Le Floch,⁴,⁵ V. Pischedda,⁴,⁵ P. Lagarde,⁶
A.-M. Flank,⁶ J. P. Itié,⁶ and A. San-Miguel⁴,⁵

¹Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, México, D.F. 04510, México

²CNRS, Institut Néel, F-38000 Grenoble, France

³Université Grenoble Alpes, Institut Néel, F-38000 Grenoble, France

⁴Université de Lyon, F-69000 Lyon, France

⁵Institut Lumière Matière, CNRS, UMR 5306, Université Lyon 1, F-69622 Villeurbanne, France

⁶Synchrotron SOLEIL, L'Orme des Merisiers Saint-Aubin, BP 48, 91192 Gif sur Yvette Cedex, France

(Received 14 June 2016; revised manuscript received 23 August 2016; published 13 September 2016)

The high-pressure superconducting properties and the local structure of the Ba<sub>8</sub>Si<sub>46</sub> clathrate have been studied using electrical resistance and x-ray absorption spectroscopy measurements up to more than 20 GPa. At pressures above 10–13 GPa, corresponding to a well-known volume collapse phase transformation, a sudden increase in the critical temperature leads to a maximum value of the superconducting critical temperature T<sub>c</sub> of ~8.5–9 K at 20 GPa. In the low-pressure clathrate phase, the superconducting critical temperature decreases as pressure is applied with an electron-phonon coupling constant λ = 1.1 derived from the temperature evolution of the electrical resistance at different pressures. A progressive disorder in the Ba-Si correlations in the Ba@Si<sub>24</sub> cages of the structure is observed for pressures beyond ~5 GPa. These observations exclude a structural homothecy at the volume collapse transition. The high-pressure collapsed phase of Ba<sub>8</sub>Si<sub>46</sub> is then associated with local structural changes and shows enhanced superconducting properties.

DOI: 10.1103/PhysRevB.94.104507

# I. INTRODUCTION

Group-IV clathrate compounds are nanocage sp³-based structures allowing for endohedral guest atom intercalation. They attract high interest due to their superconductivity [1,2], as potential ultrahard materials [3,4], or as a prototype for ternary compounds currently investigated for thermoelectrical properties [5-7]. In the clathrate structures the host lattice-phonon structure is highly decoupled from the guest lattice which from its side can provide the charge carriers. Such type of structural arrangement appears to strongly favor superconductivity as has been shown not only in silicon clathrates [8] but also in recent calculations on hydride clathrate structures such as CaH₆ [9] or YH₆ [10] with predictions of high-pressure superconducting critical temperatures beyond 260 K. Understanding how superconductivity properties evolve in clathrate structures at high pressures appears then as an important ingredient in the quest of higher critical temperature superconductors. Silicon clathrates crystallize in different structures which are differentiated into types, of which type-I and type-II are the most studied [11,12]. The type-I compounds can be viewed as composed of two Si₂₀ and six Si₂₄ nanocages per unit cell, while the type-II are composed by eight Si₂₀ and sixteen Si₂₈ nanocages [13]. Other clathrate related structures of type I exist [14,15]. In all these clathrate structures the Si atoms are interlinked through tetrahedral sp³ covalent bonds leading to nanocages assembled through sharing faces. These cagelike compounds have an adequate topology for hosting other elements. In particular, silicon clathrates hosting alkaline or earth-alkaline elements in all the nanocages form compounds with ideal formula M<sub>8</sub>Si<sub>46</sub> for the type-I clathrates and M<sub>24</sub>Si<sub>136</sub> for the type-II compounds, where M is the guest element. The presence of guest atoms modifies the electronic properties. For example, Na and Ba hosting in type-I clathrates leads to superconductivity below 4 K [1]. When only Ba is intercalated the superconducting critical temperature increases

to about 8 K [16] having a BCS character with multigap signatures [17–19]. Superconductivity has also been measured with lower critical temperatures in (Ba₁-xSrx)₈Si₄₆ [20] or in the type-III clathrate Ba₂₄Si₁₀₀ [21]. It is noteworthy that silicon is not a superconducting material under normal conditions in its diamond tetrahedral sp³ structure, but it transits to a superconducting state when subjected to high pressure [22] as well as through high boron doping [23]. Silicon in the β-Sn structure, i.e., above 11.5 GPa, is superconducting with T_c ≃ 6.3 K at 12 GPa. At pressures above 14 GPa there is a new structural transition from the β-Sn phase to a simple hexagonal phase; this transition occurs at room temperature. At low temperatures, silicon in the simple hexagonal structure is superconducting at pressures above 13.5 GPa, reaching its highest T_c of 8.2 K under a pressure of 15.2 GPa [22].

The high-pressure structural evolution of silicon clathrates is strongly influenced by the nature of the guest atoms. The Na-filled type-I silicon clathrate under high pressure decomposes from 14 GPa and the hexagonal phase of silicon is observed [3,24]. The situation is totally different for heavier guest atoms [25] as in Ba<sub>8</sub>Si<sub>46</sub> [24,26–30], K<sub>8</sub>Si<sub>46</sub> [31,32], I<sub>8</sub>Si<sub>44</sub>I<sub>2</sub>, or Rb<sub>8</sub>Si<sub>46</sub> [33]. Their high-pressure evolution is first characterized by the preservation of the tetrahedral silicon clathrate structure for pressures up to more than 4 times the stability domain of the diamond phase and, second, by a progressive volume collapse in a rather narrow pressure domain [25]. In Ba<sub>8</sub>Si<sub>46</sub> the collapse transition is observed at 14–16 GPa [24]. A first transition at about 5–7 GPa precedes this one as evidenced by crystallographic structural measurements by x-ray diffraction and x-ray absorption spectroscopy [27] as well as Raman spectroscopy [26]. This transition has been discussed as due to displacements of the Ba atoms within the Si₂₄ cages [28] preserving the host-atom type-I clathrate structure. The second transition at about 15 GPa has been first described as a homothetic volume collapse
[24,27] and is also observed in type-III silicon clathrates [34]. To explain this second transition other mechanisms have been proposed as an electron topological transition related to an extensive rehybridization of the Si atoms leading to a transfer of valence electrons from the bonding to the interstitial region inside the cages [30]. Finally, the diffusion of some of the silicon atoms in the (6c) Wyckoff positions of the cages [35] has been proposed to explain the lower bulk modulus of the high-pressure phase. Whatever the case, the importance of the role of the (6c) Si positions seems to be confirmed by the high-pressure Raman spectroscopy comparison of different chemical substituted compounds based on Ba₈Si₄₆ [36].

Superconducting transition temperatures, as a function of pressure, have been reported in Ba₈Si₄₆ by resistance versus temperature measurements up to 1.8 GPa [8]. In this pressure range $T_c$ decreases as the pressure increases, going from a $T_c$ of 8 K at ambient pressure to ≈6.8 K at 1.8 GPa. In another study [30] the electrical resistance of Ba₈Si₄₆ was measured up to pressures of 20 GPa but in a temperature domain between 80 and 280 K which did not allow exploring the superconducting properties.

In this work we have studied both the pressure evolution of the electronic transport properties at low temperatures of the Ba₈Si₄₆ clathrate and the evolution of the local structure of its guest atoms (Ba) up to pressures beyond 20 GPa, i.e., beyond the volume collapse pressure. The superconducting critical temperature $T_c$ decreases as the pressure increases up to 14 GPa reaching a $T_c$ ~ 3 K; however, at higher pressures $T_c$ increases reaching $T_c$ ~ 8.5–9 K at 20 GPa, showing that the high-pressure collapsed phase is also superconducting. The local structure studied by XAS shows a clear evolution from 5 GPa. The correlation between the two studies allows one to obtain better insight on the electron-phonon coupling mechanism driving the superconducting properties of Si clathrates, to discuss the possible role of Ba substoichiometry on the first high-pressure transition at 5–7 GPa, and to restrict the scenario on the nature of the collapse transition.

## II. EXPERIMENTAL

Ba₈Si₄₆ powder samples were prepared following the high-pressure route in a belt apparatus following Refs. [25,37]. Starting from the BaSi₂ Zintl phase mixed with silicon powder and placed in an h-BN cell, the synthesis occurs at 1000 K under high pressure (1–5 GPa). The sample is quenched at room temperature before the pressure is slowly released. The powder samples were finely ground to obtain homogeneous powders.

The high-pressure electrical resistivity measurements were performed in a sintered diamond Bridgman anvil apparatus using a pyrophyllite gasket and two steatite disks as the pressure medium. The Cu-Be device that locked the anvils can be temperature cycled between 1.2 K and 300 K inside a sealed Dewar. Pressure was calibrated against the various phase transitions of Bi under pressure at room temperature, and with a superconducting Pb manometer at lower temperatures. The overall uncertainty in the quasihydrostatic pressure is estimated to be ±15%. The pressure spread across the sintered diamond anvils was previously determined on Pb manometers within 1.5–2 GPa depending on the applied pressure. The temperature was determined using a calibrated

<figure><img src="image_2.png" /><figcaption>FIG. 1. Electrical resistance as function of temperature at different pressures in Ba₈Si₄₆. Symbols do not denote measured points but just serve to identify curves.</figcaption></figure>

Cernox thermometer with a maximum uncertainty (due mainly to temperature gradients across the Cu-Be clamp) of 0.5 K. Four-probe electrical resistivity dc measurements were carried out through platinum wires in contact with the sample, using a Keithley 182 nanovoltmeter combined with a Keithley 238 current source. Two samples, of the same batch, were measured giving similar behavior.

X-ray absorption experiments at the Ba $L_{III}$ edge (5248 eV) and $L_{II}$ edge (5624 eV) under high pressure were performed at the LUCIA beamline [38] at the SLS synchrotron source. The sample was loaded in a perforated double diamond anvil cell in order to reduce the x-ray absorption from the diamond anvils. Silicon oil was used as a pressure-transmitting medium and pressure was calibrated using the *in situ* ruby luminescence method [39]. Spectra were taken up to a maximum pressure of 20.5 GPa. X-ray absorption data were analyzed on the Ba $L_{III}$ edge spectra by combining the extended x-ray absorption fine structure (EXAFS) data extraction using the CDXAS code [40] and the FEFF [41] and FEFFIT [42] ones for EXAFS fitting.

## III. ELECTRICAL RESISTANCE UNDER HIGH PRESSURE

In Fig. 1 we show the temperature dependence of the electrical resistance of one sample as a function of pressure. The smooth variation of our curves contrasts with the measurements of Ref. [30]. This can be explained by the difficulties of the diamond anvil cell experiments and by the use in that work of MgO as a pressure-transmitting medium. In our case, the use of larger sample sizes and the use of a more hydrostatic pressure-transmitting medium (steatite) would explain the better data quality. At the lowest pressure the electrical resistance temperature dependence has an S shape characteristic of a bad but superconducting metal.
It also shows a very small residual resistance ratio (RRR) ~1.3, defined as the ratio of resistance at room temperature to the extrapolated resistance at 0 K. This ratio gives a measure of the relevance of the electron scattering by impurities and defects. The small value for RRR implies a large number of defects, which may correspond to numerous ion vacancies due to barium substoichiometry. In fact, the nominal Ba<sub>8</sub>Si<sub>46</sub> clathrate is usually obtained in high-pressure synthesis in the substoichiometry form, Ba<sub>8-x</sub>Si<sub>46</sub>, with values 0.24 ≤ x ≤ 0.39 [16] or even higher [43]. As a function of pressure, the resistance of our samples decreases monotonically, though more slowly for pressures larger than 10 GPa.

It is interesting to analyze the low-temperature dependence trying to determine the dominating carrier scattering above the superconducting transition. We have found that within the range of 20 to 40 K the dependence is clearly quadratic in temperature, as shown in Fig. 2(a), where we plot the low-temperature resistance as a function of the square of the temperature.

Quadratic temperature dependencies can be due to numerous reasons [44], and have been observed and thoroughly studied in superconductors [45]. Taking into account that we have a very strong impurity scattering, the most favorite candidate to explain the observed quadratic behavior is inelastic scattering against impurities [46] or Koshino-Taylor (K-T) scattering. If K-T scattering is the main reason for the quadratic temperature term, then the coefficient of the quadratic term should be directly proportional to the residual resistance [47], R₀ (RRR), with a slope around ~10⁻⁵ K⁻². We show in Fig. 2(b) that this is indeed the case, with a slope of 2 × 10⁻⁵ K⁻². So, the impurities not only generate a strong elastic scattering, measured by the RRR, but also produce a strong inelastic scattering yielding an unusually large quadratic temperature term, A. Nevertheless, as T_c also scales with A, we can attempt the Fermi liquid fit [48], $T_c = \theta e^{-\zeta/\sqrt{A}}$, where θ and ζ are adjustable parameters, which allow us to estimate the electron-phonon coupling constant of Ba<sub>8</sub>Si<sub>46</sub>, $\lambda = \sqrt{A/\zeta}$. As the slope that we obtain for A/R₀ = 2 × 10⁻⁵, i.e., the double of the expected one [45], we have corrected the measured value of A, subtracting the K-T term, A'(P) = A(P) - 10⁻⁵ R₀(P), and performed the fit with A'. Figure 3 shows the relation between T_c and the square root of A'. We obtain at ambient pressure λ = 1.1, in good agreement with the one calculated in Ref. [8], λ = 1.05. Our result shows that even if the K-T is present, it does not dominate all the T² scattering and a quite good estimate of the coupling parameter can be obtained by the Fermi liquid fit.

We now discuss the superconducting transition and its evolution with pressure, shown in Fig. 4. The superconducting transition temperature first decreases gradually and then, beyond ~15 GPa, increases with pressure. Between 12 and 17 GPa, the transition seems double (there are two maxima in the temperature derivative of the resistance curve), as if there were a coexistence of two different phases. This coexistence region seemingly corresponds to the volume collapse transition observed in combined x-ray diffraction and x-ray absorption spectroscopy experiments [24,27,30].

The pressure dependence of the superconducting transition temperature is shown in Fig. 5(a). The decrease followed by the increase of T_c is clear, as it is also the existence of two

<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /><figcaption>FIG. 2. (a) Low-temperature electrical resistances, within the range of 20 K to 40 K, of Ba<sub>8</sub>Si<sub>46</sub> as a function of the square of the temperature. It shows a defined dependence. Symbols are the same as those of Fig. 1. (b) Correlation between A, the coefficient of the quadratic temperature term, and the residual resistivity. It is clearly linear with a slope of 2.18 × 10<sup>-5</sup> K<sup>-2</sup>. It shows that this term is due to inelastic scattering of carriers against impurities.</figcaption></figure>

different transition onsets in the coexistence region between the volume-collapsed and the noncollapsed phase. This is further evidenced in Fig. 5(b) by plotting the width of the transition zone taken as the temperature domain between the onset of the transition and the zero resistivity. We distinguish clearly three regimes, with the intermediate one between ~12 and 17 GPa corresponding to a phase mixing.

The T_c pressure decrease was previously measured below 1.8 GPa and its pressure dependence calculated theoretically [8]. Our data for the low-pressure phase follow nicely the
<figure><img src="image_5.png" /><figcaption>FIG. 3. Fermi liquid fit $T_c = \theta e^{-\xi/\sqrt{A}}$ on the corrected coefficient $A'(P) = A(P) - 10^{-5}R_0$. We obtain an ambient pressure $\lambda = 1.1$, in very good agreement with the calculations of Ref. [8], which give $\lambda = 1.05$.</figcaption></figure>

calculated dependence as shown by the dashed-point curve of Fig. 5(a). Thus, the behavior of superconductivity with pressure for the clathrate low-pressure phase seems well understood. However, the data for the high-pressure phase, i.e., above the volume collapse starting at 13–15 GPa, are more difficult to grasp. In the high-pressure phase, the higher $T_c$ could be ascribed to an enhancement of the hybridization of the barium orbitals by volume reduction. This appears as

<figure><img src="image_6.png" /><figcaption>FIG. 4. Superconducting transition in Ba$_8$Si$_{46}$ at high pressure. We observe a decrease of $T_c$ with pressure, followed by an increase beyond 14 GPa.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>FIG. 5. (a) Dependence of the superconducting transition temperature, $T_c$, on pressure. We observe a decrease followed by an increase above 14 GPa. The decrease follows the previously calculated pressure dependence of $T_c$ (dashed curve, from Ref. [8]). In the region of coexistence we can determine two different onsets, which seem to be associated with the two different phases. (b) Dependence of the temperature width of the superconducting transition as observed in Fig. 4. The line is a guide for the eye.</figcaption></figure>

contradictory with the observed evolution in the low-pressure phase (before the volume collapse). This result, then, does not support the idea of a homothetic volume collapse but of a change of structure implying new schemes of hybridization as suggested in Refs. [29,35]. On the other hand, due to the proximity of the $T_c$ values to the ones of the simple hexagonal high-pressure phase of silicon [22], we may be tempted to speculate that some portion of the clathrate sample may be dissociated and lead to microcrystalline silicon even if the $T_c$ evolution with pressure for pure silicon does not correspond to the one measured here for $P > 13$ GPa.
In order to test that hypothesis, we cycled Ba₈Si₄₆ up to 17 GPa using a Paris-Edinburgh press with sintered diamond anvils [49]. We did not use a pressure-transmitting medium to better mimic the experimental conditions in our electric transport measurements and compared the x-ray diffraction pattern before and after the pressure cycle. The diffraction pattern was clearly reversible and it was not possible to distinguish any trace of silicon in its diamond form within the experimental resolution of the diffractometer. There was no trace of presence of the characteristic diffraction peaks from other silicon metastable phases obtained after pressure cycling as BC8 [50]. The zero resistivity observed beyond 13–15 GPa would imply at least one third of the sample in the superconducting state. This clearly excludes the idea of a high-pressure segregation and supports the idea that the superconducting behavior at P > 15 GPa does correspond to the high-pressure phase of Ba₈Si₄₆ with a modified structure.

We then use x-ray absorption spectroscopy as a comple-
mentary technique to x-ray diffraction or Raman spectroscopy
to obtain insight on the high-pressure local effects [51] on the
properties of Ba<sub>8</sub>Si<sub>46</sub>.

IV. X-RAY ABSORPTION SPECTROSCOPY

X-ray absorption spectroscopy allows us to extract local
structural and electronic property information from selected
atomic species in condensed matter systems [52,53]. Figure 6
shows the x-ray absorption near edge structure (XANES)
evolution at the Ba *L*<sub>III</sub> edge during compression. The Ba *L*<sub>II</sub>
edge XANES signal is shown in Fig. S1 of the Supplemental
Material [54], but we will concentrate our discussion on the
Ba *L*<sub>III</sub> edge data which had a better signal to noise ratio. The

<figure><img src="image_8.png" /><figcaption>FIG. 6. Evolution of the Ba *L*<sub>III</sub> XANES signal in Ba<sub>8</sub>Si<sub>46</sub> as a function of pressure. The spectra have been vertically shifted for clarity. Pressure is indicated at the right side. In red are the spectra corresponding to the collapsed phase.</figcaption></figure>

here obtained data quality contrasts with the XANES data
from Ref. [27] in which essentially only the edge position
and the white line could be measured (in that work two XAS
studies were included: one at the Ba *L*<sub>III</sub> edge in energy
dispersive mode up to 20 GPa and another at the Ba *K* edge in
XAS scanning mode up to 14.4 GPa). Here we observe a clear
modification of the XANES resonances for pressures beyond
13.0 GPa in correspondence with the collapse pressure domain
in Ba<sub>8</sub>Si<sub>46</sub>. This change can be described in particular by an
important modification of the intensity ratio of the two first
XANES resonances after the white line (the first prominent
XANES peak just after the absorption edge). Homothetic
compression associated with the volume reduction could be
in principle at the origin of intensity ratio modifications of
XANES resonances [55]. Nevertheless, the stability of the two
XANES profiles below and beyond 13.0 GPa (with similar
volume changes in the two pressure domains) points to a
clear evolution of the local structure at the volume collapse
transition.

The pressure evolution of the absorption edge energy
can provide information on the evolution of the symmetry-
projected local electronic structure of the absorbing atoms.
The obtained evolution is shown in Fig. S2 of the Supple-
mental Material [54] and compared with the already reported
evolution in Ref. [27] using an energy-dispersive XAS optics
[56]. Both data are in good agreement showing a down-shift
of the edge position of about 0.5 eV at 3–5 GPa. The edge
position remains then constant until the collapse transition
where the Ba *L*<sub>III</sub> position starts to decrease steadily at a rate
of –60 meV GPa<sup>–1</sup>. The onset of the collapse transition can be
set between 10 and 13 GPa in the present experiment in good
agreement with Ref. [27], where it was found to lie between
11.5 and 14 GPa.

The extracted EXAFS signal is shown in Fig. 7. The
proximity of the *L*<sub>II</sub> edge limits the maximum energy domain

<figure><img src="image_9.png" /><figcaption>FIG. 7. Evolution of the Ba *L*<sub>III</sub> EXAFS signal in Ba<sub>8</sub>Si<sub>46</sub> as a function of pressure. The spectra have been shifted vertically for clarity. The different colors correspond to the spectra before the collapse transition (black) and after the collapse transition (red). The spectrum at 13.0 in magenta is intermediate. In the inset the spectra have been superimposed allowing us to better distinguish the differences between the spectra before and after the collapse transition.</figcaption></figure>
available after the *L*<sub>III</sub> edge to 380 eV. In spite of this
limitation, we observe a clear change in the oscillation scheme
for pressures beyond 13.0 GPa. This change is rather strong
and difficult to justify by the only volume reduction associated
with the smooth volume collapse. Then, a modification in
the local structure around the Ba atom after the pressure
collapse appears as a clear plausible hypothesis in agreement
with our XANES data and other studies [29]. We would
like to underline that in previous works [27] EXAFS data
were only obtained for pressures below the collapse pressure.
Due to the limited *k* range allowed for the EXAFS fitting
available in our experiment (Fig. 7), several fitting schemes
were tested. All of them included the *k*-space fitting of the
Fourier-transformed filtered signal within the type-I clathrate
model using the *ab initio* calculation of the atomic scattering
amplitude and phase shift for each scattering path using the
FEFF code [41] and the fit within that structural model using
FEFFIT [42].

In our fitting model, only the local cage environment
around each Ba atom made of Si<sub>20</sub> and Si<sub>24</sub> cages was
fitted. This was done by filtering the Fourier-transformed
signal obtained from a *k* domain between 3 and 7 Å<sup>-1</sup> (see
Fig. S3 of the Supplemental Material [54]). We observe clearly
in the Fourier transform that the signal is dominated by a
double peak at phase-shift-uncorrected distances below 3.2 Å,
which correspond to the cage shell. The *R*-space filtered
signal corresponding to that doublet was inverse Fourier
transformed and fitted within the type-I clathrate model. Best
fits were obtained by considering as input fitting parameters
the high-pressure cell parameters obtained by x-ray diffraction
[27] at each pressure point and only considering as free
variables the pseudo-Debye temperatures associated to the
Ba-Si scattering paths in each one of the two cages and the
cell parameters themselves. The pseudo-Debye Waller factor
is a measurement of the static (disorder) or dynamic (thermal
agitation) loss of coherence projected in the EXAFS scattering
paths [57], i.e., the Ba-Si distances in the cages in our case. It
is frequent to use the associated Debye temperature of a pure
dynamic and harmonic pseudo-Debye Waller to characterize
it [57]. In the absence of static disorder the pseudo-Debye
temperature will then increase with pressure as a result of the
bond strengthening in correspondence with the increase of the
Debye temperature of the material. Figure 8 shows the obtained
results for the pressure evolution of the relative pseudo-Debye
temperature associated with the Ba-Si paths in the Si<sub>20</sub> and Si<sub>24</sub>
cages. The obtained cell parameters in the compression cycle
were in excellent agreement with the ones obtained by x-ray
diffraction in previous works (see Fig. S4 of the Supplemental
Material [54]). The relative evolution of the pseudo-Debye
temperature associated with the Ba-Si scattering paths in the
Si<sub>20</sub> and Si<sub>24</sub> cages shows a continuous but totally opposite
evolution with pressure. This qualitative evolution is also well
reproduced by the other EXAFS models which we tested in
our work.

We were able to improve the fit quality for the three data
points between 4.5 and 10 GPa by displacing the Ba atoms by
0.1 Å in the Si₂₄ cages in the (100) direction which corresponds
to the direction towards the center of the hexagons in the
Si₂₄ chains (see Fig. S5 of the Supplemental Material [54]).
It is difficult from our EXAFS signal to conclude that this

<figure><img src="image_10.png" /><figcaption>FIG. 8. Relative pressure evolution of the Ba-Si pseudo-Debye temperature in Ba₈Si₄₆ in the two different local environments, i.e., the Ba@Si₂₀ and Ba@Si₂₄ cages.</figcaption></figure>

Ba displacement is what is really taking place as many other
hypothesis would need to be verified. In fact, using a higher
*k* domain EXAFS signal, but for pressures below the volume
collapse, the main conclusion in Ref. [27] was that the barium
atoms remained at the center of the cages up to pressures of
14 GPa, with an incertitude of 0.3 Å. We should note that
in Raman studies [26], the presence of a phase transition
at 7 GPa was proposed which was attributed to the random
displacement of the Ba position inside the Si₂₄ cage leading to
a cage distortion of the Si host frame and hence a relaxation
of the Raman selection rules.

In our experiments, for pressures in the 5–12 GPa range, the Debye temperature associated with the Ba-Si Ba@Si₂₄ scattering paths strongly decreases with respect to the one of the Ba@Si₂₀ cage. This indicates that from that pressure, there is an important static disorder developing in the Ba@Si₂₄ cages. We have to conclude then that there is a progressive static (structural) disorder associated with the Ba-Si scattering paths in the Ba@Si₂₄ cage from pressures situated between 5 and 10 GPa.

The EXAFS fits beyond 13 GPa became essentially inde-
pendent of the model used for the Si24 cage, as its contribution
to the EXAFS signal appeared as negligible with respect to
the one of the Si20 cage. Fits became more difficult, with one
of the spectra (18.1 GPa) giving larger uncertainties for the
pseudo-Debye temperature than the obtained values (we have
not then included this point in the graph). The uncertainties of
the Ba@Si20 pseudo-Debye temperature could not be obtained
as shown in Fig. 8. We conclude that for pressures beyond
13 GPa, the local structure model of the low-pressure phase
does not apply. This is confirmed by the last point of the
Ba@Si20 pseudo-Debye temperature in Fig. 8 whose value
decreases, which could point to a possible distortion in this
cage. In our EXAFS fits, we tried to verify the hypothesis
of Iitaka [35] which proposes that the collapse is related to
the diffusion of the Si(6c) atoms of the hexagons by fitting
occupancy numbers for all the scattering paths involving these
atoms. Unfortunately, the accuracy with which this occupancy number was obtained was insufficient to discriminate this hypothesis. In fact, the Si(6c) major contribution to the EXAFS signal is related to the Si₂₄ cages through the Ba − Si(6c) scattering paths, but as stated before, after the collapse the contribution of the Si₂₄ scattering paths to the EXAFS signal becomes negligible. Examples of EXAFS fits are provided in Fig. S6 of the Supplemental Material [54].

V. DISCUSSION

The EXAFS results show that there is a significant differ-
ence between the pressure evolution of the structure and/or
dynamics in the two types of cages. The Ba@Si<sub>20</sub> is the
cage keeping the higher spatial/dynamical coherence. The
difference between the behavior of the two cages becomes
significant from pressures above 5 GPa, which corresponds to
the first observed transition of Ba<sub>8</sub>Si<sub>46</sub> at 5–7 GPa [26,27].
The differences between the behavior of the two cages is
amplified with pressure up to the volume collapse transition
at 10–13 GPa (see Fig. 8). All these changes do not affect
the observed pressure evolution of the superconducting T<sub>c</sub>
(Fig. 5) which progressively decreases down to values of
~3 K at 14 GPa, in rather good agreement with predictions
based on a perfect clathrate crystal [8]. Then, the contribution
of the Ba-Si associated phonon modes in the Si<sub>24</sub> cages to
the electron-phonon coupling needs to be discarded. The
low energy of the Ba-associated dynamics [6,19] and the
importance of the Si sp<sup>3</sup> character on the electron-phonon
coupling [8] support the idea that the guest atom dynamics
does not participate in the electron-phonon coupling driving
the clathrate superconducting character.

At the volume collapse we observe a positive jump of the
superconducting critical pressure which increases up to values
of ~8.5-9 K at 20 GPa (Fig. 5) which tends to exclude the
possibility of a homothetic volume collapse: a modification of
the nanocages' local structure is needed to explain the T_c jump,
which could favor in principle either the electron topological
transition scenario for the high-pressure phase [30] or the
diffusion of some of the silicon atoms [35]. Nevertheless the
absence of crystalline silicon diffraction peaks on samples
recovered from 17 GPa does not support this last hypothesis.
The contribution of the Si_24 cage to the EXAFS signal
vanishes in the high-pressure phase, but it is not possible to
establish whether this has been due to a progressive or sudden
evolution of the structure or dynamics of the nanocage. Data
acquisition in a larger *k* domain (possible at the Ba *K* edge)
would allow us to apply more advanced EXAFS modeling
which coupled with statistical structural simulations [58]
should allow us to study eventual local order/disorder effects
which could contribute in the high-pressure phase or establish
local distortions in the nanocages.

Our work shows that the superconducting character of
the clathrate structure can be preserved and even enhanced
despite local changes which may affect both the host and the

guest structures. This robustness in the superconductivity of
the clathrate structure could be related also to the observed
superconductivity of Ag₆O₈AgHF₂ [59]. In fact, this is the
only silver-containing compound in which superconductivity
has been observed and its structure is clathrate based.

One of the remaining questions is the possible impact of
the Ba vacancies on the observed transition at 5–7 GPa. The
very small residual electrical resistance ratio found in our
experiments clearly points to a high concentration of defects,
which finds as most a possible origin of the Ba deficiency
in the Si₂₄ cages [43]. In fact, it has been observed in the
case of Na-intercalated type-II clathrates an important shift of
the Na atoms from the center of the Si₂₈ cages [60] which
can be interpreted in terms of a Peierls distortion [61] or in
terms of particular dynamics [62]. In the case of the type-I
structure, the presence of Ba vacancies in certain Si₂₄ cages
introduces a local symmetry breaking as has also been found in
mixed Ba₈(Si,Ge)₄₆ clathrates [63]. Such symmetry breaking
would affect the Ba-Ba interactions and could be at the origin
of the observed incoherence of the EXAFS signal observed
in our experiments in the larger cages at pressures beyond 5
GPa when Ba-Ba lattice mediated interactions [19] become
more important. XAS and Raman experiments point in fact
to a correlation between this lower-pressure transition and
Ba displacement from the center of the Si₂₄ cages in type-I
clathrates. This suggests that this transition could disappear
for perfectly stoichiometric Ba₈Si₄₆ crystals.

VI. CONCLUSIONS

We have shown that through the Landau theory of a Fermi
liquid treatment, the superconducting critical temperature T_c
scales with the quadratic term of the resistance dependence
with temperature [48]. This allows us to obtain the electron-
phonon coupling constant λ = 1.1 for the low-pressure phase,
in very good agreement with published calculations [8].
T_c decreases with pressure monotonically until the volume
collapse transition at 10–13 GPa. This evolution is not affected
by the strong difference between the local structure evolution
with pressure of the two types of nanocages composing
the structure Ba@Si<sub>20</sub> and Ba@Si<sub>24</sub> which is observed for
pressures beyond ~5 GPa. The evolution of the nanocages’
local structure evidences the progression of a structural loss
of coherence in the Ba@Si<sub>24</sub> cages. At pressures above
~10–13 GPa, corresponding to the volume collapse phase
transformation, we observe a sudden increase in the critical
temperature with a maximum T_c of ~8.5–9 K at 20 GPa:
the collapsed structure of Ba<sub>8</sub>Si<sub>46</sub> is then superconducting
with an enhanced superconductivity. The collapse transition
is concomitant with local structure modifications around the
Ba atoms evidenced by the near-edge XAS sudden changes.
These observations exclude a structural homothecy in the
volume collapse transition. The measured superconductivity
in the high-pressure collapsed phase of Ba<sub>8</sub>Si<sub>46</sub> points out the
robustness of superconductivity in clathrate structures.

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