All steps of sample preparation and recovery were performed in a glove box under argon atmosphere. Powdered NaH (Sigma-Aldrich, 90%) and powdered Si [325 mesh, 99.999% (metals basis), Thermo Scientific] were mixed at a molar ratio of 1:1 and 2:1 (NaH:Si) and compressed into pellets with an outer diameter (OD) of 2 mm. Ammonia borane (BH₃NH₃, Sigma-Aldrich, 90%) served as a hydrogen source since it has a well-defined decomposition behavior at high pressures and produces chemically inert BN as a residue (Nylén et al., 2009). The amount of BH₃NH₃ used for each sample corresponded to an approx. 4× molar excess of H₂ with respect to Si. NaH/Si sample pellets were sandwiched between pelletized BH₃NH₃ and sealed inside NaCl capsules with 3.0 mm OD.

In situ synchrotron diffraction high-pressure experiments were performed at beamline ID06-LVP at the ESRF and employed 14/7 multi-anvil assemblies, which are described in detail elsewhere (Vekilova et al., 2023). Amorphous SiBCN rods and either MgO or amorphous BCN epoxy were used as X-ray windows in the octahedra and gaskets, respectively, along the beam direction. Assemblies were compressed to target pressures ≈5 and ≈9 GPa and heated in a Voggenreiter-built modified-cubic press (Guignard and Crichton, 2015). Pressure was estimated in situ from PXRD diffraction patterns using the equation of state of NaCl by Matsui et al. (2012). The temperature was evaluated from power–T calibration curves. Angle-dispersive powder X-ray diffraction patterns were collected in the 1.27°–15.26° 2θ range at a constant wavelength (λ = 0.233933 Å). Data were acquired using the Pilatus3X-900 kW CdTe high-resolution 2D detector. The in situ data were integrated, visualized, and manipulated using Fit2D software (Hammersley, 2016). Indexing of the powder patterns was performed using DICVOL and TAUP algorithms within the CRYSFIRE package (Shirley, 2004). Le Bail fitting (Le Bail et al., 1988) and Rietveld refinement (Rietveld, 1969) against the in situ data were performed in Jana 2006 (Petříček et al., 2014). A detailed description of the high-pressure experiments and data analysis is given in Supplementary Material.

The Na–Si–H system was studied with a crystal structure prediction methodology using Ab initio random structure searching implemented in the code AIRSS (Pickard and Needs, 2006; Pickard and Needs, 2011) and an evolutionary algorithm implemented in the Universal Structure Predictor: Evolutionary Xtallography (USPEX) code (Oganov and Glass, 2006; Oganov et al., 2011; Lyakhov et al., 2013), both coupled with the Vienna Ab Initio Simulation Package (VASP) (Kresse and Hafner, 1993; Kresse and Furthmüller, 1996). VASP calculations were based on a first-principles projector-augmented wave (PAW) method (Blöchl, 1994) within the density functional theory (DFT) (Hohenberg and Kohn, 1964; Kohn and Sham, 1965). The generalized gradient approximation for exchange and correlation potential and energy was used in its Perdew–Burke–Erzernhof (PBE) (Perdew et al., 1996; Perdew et al., 1997) flavor. H at zero pressure was calculated as a molecule (H₂) and at higher pressures as a solid with an I4/mmm structure (according to the work of Pickard and Needs (2007)).

All Na_mSiH_(4+m) (m = 1, 2, 3) model structures were fully relaxed; i.e., volume, shape, and internal atomic positions were adjusted to get nearly zero forces and stresses (stress components of order 0.1 GPa and forces of order 0.01 eV/Å maximum). The considered pressures were 0, 10, and 20 GPa. The Monkhorst–Pack (Monkhorst and Pack, 1976) k-point density for integrations over the Brillouin zone was set with 0.2. The energy cutoff for plane waves was set to 320 eV. All the static calculations were conducted at temperature T = 0 K.

Phonons were calculated from the force constants in real space obtained by VASP using density functional perturbation theory (DFPT) used as an input for the PHONOPY program (Togo and Tanaka, 2015). A plane-wave energy cutoff of 500 eV was used in all the corresponding calculations. A 2 × 2 × 2 supercell of each structure was used. To investigate the dynamical stability of P4/mbm Na₃SiH₇ at experimentally relevant temperature of 600 K and pressure 10 GPa, ab initio molecular dynamics (AIMD) calculations, as implemented in VASP, were conducted and then post-processed by the temperature-dependent effective potential method (TDEP) (Hellman et al., 2011; Hellman et al., 2013). TDEP maps the AIMD data onto a model Hamiltonian and provides the best harmonic fit to the system of anharmonic vibrating atoms at a particular temperature. Therefore, effective temperature-dependent phonon dispersions are obtained, and in particular, dynamical stability due to anharmonic vibrations can be studied. AIMD simulation were performed in 2 × 2 × 2 supercells (176 atoms) for P4/mbm Na₃SiH₇, with 2 × 2 × 2 k points, and 500 eV energy cutoff for the plane waves, with the same PAW potentials and exchange-correlation as in the static calculations. The canonical NVT ensemble using a Nosé–Hoover thermostat with the default Nosé mass as set by VASP and a 0.5 fs time step was applied. The data from 600 time steps after equilibration were used for the extraction of temperature-dependent force constants.

A recent exploration of the Na–Si–H system for stable ternary high-pressure phases yielded only one compound, trigonal P¯3m1 Na₂SiH₆, up to 50 GPa (Liang et al., 2021). At pressures below 3 GPa, the proposed Na₂SiH₆ is not dynamically stable, i.e., its phonon dispersion has branches with imaginary frequencies. This indicates lattice instability, and as a consequence, there should be a more stable structure with this composition, or decomposition into a different composition. We re-examined structure predictions (and also introduced a number of trial structures from chemical intuition) allowing for Z = 4 (Z = number of formula units) and focused on the low-pressure region up to 20 GPa which would be accessible in LVP hydrogenations. The dominant feature of SiH₆ ²⁻ octahedral units in low-pressure structures, as established from previous A–Si–H structure prediction work (Liang et al., 2020; Liang et al., 2021; Zhang et al., 2020; Wu et al., 2022; Xie et al., 2022), together with chemical reasoning, suggested that compositions Na_mSiH_(4+m) (m = 1, 2, 3) are most plausible, and we restricted our search to these compositions. Phase diagrams were established for 0, 10, and 20 GPa. Compared to earlier work, a radically different picture evolved.

Figure 1 shows the phase diagrams for ambient pressure and 10 GPa (the phase diagram for 20 GPa is virtually identical to that for 10 GPa). In Supplementary Figure S5, phonon dispersions of some of the predicted structures are depicted. At ambient pressure (Figure 1A), a compound Na₃SiH₇ with an orthorhombic Pbam structure appeared to be stable with respect to decomposition into NaH, NaSi, Si, and H₂ but was not dynamically stable. This suggests that the composition Na₃SiH₇ is stable at ambient pressure but should occur in a different, most likely more complex, structure. As a matter of fact, identifying Na₃SiH₇ as a potential stable composition at ambient pressure was rather inferred from the experimental results than initially obtained from computational structure prediction. We will discuss the structures for Na₃SiH₇ and their stability in detail later. Furthermore, at ambient pressure, we found a hexagonal form of Na₂SiH₆ with P6₃ mc symmetry slightly (by ≈0.05 eV/Z) more stable than P¯3m1-Na₂SiH₆. However, the enthalpy of Na₂SiH₆ is still above the convex hull, and both polymorphs are not dynamically stable at ambient pressure (cf. Supplementary Figures 5D, E). The Na₂SiH₆ structures are depicted in Figure 2.

At 10 GPa, we find that the complete sequence of compositions Na_mSiH_(4+m) (m = 1, 2, 3) is stable, both thermodynamically and dynamically. Pbam-Na₃SiH₇, which was found only enthalpically stable at ambient pressure, is now also dynamically stable. With pressure, the trigonal Na₂SiH₆ polymorph stabilizes over the hexagonal one and also becomes dynamically stable. NaSiH₅ structures are not expected to realize separated SiH₆ ²⁻ octahedral units but chains of corner-condensed or dimers of edge-condensed octahedra, [SiH₄H_2/2 ⁻]_∞ and Si₂H₁₀ ²⁻, respectively. Indeed, Pbcm-NaSiH₅, which is isostructural to BaAlH₅ (Figure 2) (Zhang et al., 2002), was found on the convex hull. At the same time, a different octahedral chain structure, Pna2₁-NaSiH₅ [isostructural to SrAlH₅ (Sato et al., 2018)], is only about 0.15 eV/Z less stable (Figure 2). It can be speculated that the composition NaSiH₅ gives rise to a manifold of enthalpically close-lying polymorphic structures (Weidenthaler et al., 2006; Shlyapnikov et al., 2018) and that, most likely, the most stable one has yet to be identified. Supplementary Tables S3–S5 in Supplementary Material list the parameters of some Na_mSiH_(4+m) structures. It is also easy to understand that computational structure prediction meets severe difficulties when tackling ternary compositions with complex structural features (Kvashnin et al., 2020).

Reactions m NaH + Si + 4 H₂ (m = 1, 2), targeting originally proposed Na₂SiH₆, were performed at around 5 and 9 GPa. After compressing to target pressure, the reaction mixtures were initially heated to a temperature around 400°C at which the H-source BH₃NH₃ is expected to be completely decomposed into h-BN and hydrogen fluid (Nylén et al., 2009). The samples were then equilibrated for about 15–20 min. The reaction mixtures behaved very similar, independent of starting composition (m = 1 or 2) or pressure (5 or 9 GPa). In the following, reported results refer to m = 2 (2NaH:1Si) mixtures.

Figure 3 shows the evolution of diffraction patterns for the p ≈ 9 GPa run. In this experiment, one can recognize the growth of an intermediate phase above ≈380°C, which manifests as broad low-intensity diffraction peaks. The peaks could be indexed to a hexagonal unit cell (a ≈ 4.75 Å, c ≈ 7.65 Å), yet this phase remains uncharacterized due to the diffuse character and poor intensity of its reflections. Above ≈560°C, the peaks of the intermediate phase are superseded by another set of reflections, which were indexed to a primitive tetragonal unit cell with a ≈ 6.59 and c ≈ 4.78 Å (at ≈7.2 GPa and 770°C, as observed in the p ≈ 5 GPa run). P4/mbm was derived as the highest applicable space group from the extinction symbol P–b–. The symmetry and lattice parameter ratio (c/a ≈ 0.725) suggested an isostructural relation to K₃SiF₇ (c/a = 0.719 at ambient pressure) (Deadmore and Bradley, 1962; Hofmann and Hoppe, 1979) and, thus, a composition Na₃SiH₇. Calculated reflection intensities for K₃SiF₇-type Na₃SiH₇ matched closely with the experiment. Furthermore, with the knowledge of composition and formula units, P4/mbm-Na₃SiH₇ could be obtained as a low-enthalpy phase from the computational structure prediction methodology. The DFT optimized structure (Supplementary Tables S5D, E) was then used in Rietveld analysis of the in situ PXRD data (≈7.2 GPa, 770°C), yielding a reasonable fit (R _obs≈5.5%) despite the low phase fraction of Na₃SiH₇ (Supplementary Figure S3). Details of the refinement process as well as the corresponding plot and extracted structural data are provided in Supplementary Material (Supplementary Tables S1, S2).

The formation of P4/mbm-Na₃SiH₇ during hydrogenations of NaH–Si mixtures requires pressures above 5 GPa (cf. Supplementary Figures S2, S4). In the p ≈ 5 GPa hydrogenation experiment, the intermediate hexagonal phase was not seen. Diffraction peaks from P4/mbm-Na₃SiH₇ become noticeable above ≈490°C. Irrespective of pressure, the P4/mbm-Na₃SiH₇ phase grows very sluggishly even when raising temperatures up to 850°C. This indicates a rather high thermal stability of P4/mbm-Na₃SiH₇ at high-pressure conditions and shows at the same time that elemental Si represents a rather unreactive precursor.

Upon cooling from (high) synthesis temperatures to below 120°C, the tetragonal diffraction pattern showed a clear splitting into an orthorhombic one, which appeared continuous and was accompanied with a doubling of unit cell (a _o ≈ b _o = √2a _t, c _o ≈ c _t). For the p ≈ 9 GPa run, this feature is included in Figure 3. For the p ≈ 5 GPa experiment, this tetragonal-to-orthorhombic transition is shown in Figure 4. The reflections were indexed to a unit cell a ≈ 9.23 Å, b ≈ 9.36 Å, and c ≈ 4.76 Å (at p ≈ 5.2 GPa, ≈RT). Again, suspecting analogy with fluorides, the (NH₄)₃GeF₇ structure (Pbam space group symmetry, Z = 4) (Mel’nikova et al., 2016; Mel’nikova et al., 2017; Bogdanov et al., 2019) was assigned to the orthorhombic phase.

In both 5 and 9 GPa runs, a further transition was noticeable upon decompression below ≈4.5 GPa, see again Figure 4 (and Supplementary Material for details). Indexing of the diffraction peaks arising at ≈4 GPa suggested as best-fitting candidates two primitive tetragonal unit cells (parameters are given relative to the initial tetragonal phase): a) a ≈ √2a _t, c ≈ 2c _t (a ≈ 9.42 Å, c ≈ 9.61 Å, Z = 8); b) a ≈ a _t, c ≈ 2c _t (a ≈ 6.66 Å, c ≈ 9.61 Å, Z = 4). The structure was difficult to resolve due to peak overlap as well as the occurrence of sudden pressure drops during decompression which obscured analysis. Further structure prediction work would be required to establish the structure and corresponding space group. Also, it remains unclear whether Na₃SiH₇ is recoverable to ambient pressure. The ex situ analysis of the only partially reacted run products was inconclusive.

Figure 5 shows the structures of polymorphic Na₃SiH₇ along with the p, T conditions for the observed phases. As mentioned, Na₃SiH₇ represents a double salt Na₃[SiH₆]H containing both octahedral SiH₆ ²⁻ moieties and hydridic H. Hydridic H is octahedrally coordinated by six Na atoms, and HNa₆ octahedra build up a corner-connected framework similar to the BO₃ framework in perovskites ABO₃. SiH₆ ²⁻ octahedra are located in the voids accommodating the (larger-sized) A constituent of perovskites. Thus, the Na₃SiH₇ structures may be considered as an anti-perovskite arrangement (SiH₆ ²⁻)[HNa₃]²⁺, and as for perovskites, there is inherent structural flexibility from rotations and tilts of octahedra. Pbam is a subgroup of P4/mbm. The group-subgroup relationship is indicated in Figure 5. Analogous and also more extended sequences of phase transitions have been reported for fluorosilicate and fluorogermanate double salts [e.g., (NH₄)₃SiF₇ and (NH₄)₃GeF₇] as a function of temperature (Mel’nikova et al., 2014; Molokeev et al., 2014; Pogoreltsev et al., 2014; Mel’nikova et al., 2016; Mel’nikova et al., 2017; Bogdanov et al., 2019). These may potentially also include the yet unknown Na₃SiH₇ structure at room temperature and low pressures.

As previously mentioned, Pbam-Na₃SiH₇ was found enthalpically stable but dynamically unstable at ambient pressure. According to total energy calculations, this polymorph is by 0.4 eV/Z more stable than the P4/mbm structure. At 10 GPa, Pbam-Na₃SiH₇ is by about 0.24 eV more stable than the tetragonal form and dynamical stable, whereas P4/mbm-Na₃SiH₇ appears to be dynamically unstable at all pressures (cf. Supplementary Figures S5G, H).

To investigate the dynamical stability of the P4/mbm-Na₃SiH₇ phase at experimentally relevant conditions, phonon dispersions were calculated in the framework of the TDEP method (Hellman et al., 2011; Hellman et al., 2013) at 10 GPa and 600 K. Figures 6A, B compare the phonon dispersions for 10 GPa at zero and 600 K. Si–H stretching and bending modes of the entities SiH₆ ²⁻ (i.e., internal modes) and the (translational) modes of the hydridic H within Na₆ octahedra are above around 500 cm⁻¹, whereas SiH₆ ²⁻ libration modes (i.e., rotation of octahedral units against each other) and optic translation modes of Na⁺ and SiH₆ ²⁻ units (i.e., external modes) are below 500 cm⁻¹.

At 0 K, P4/mbm-Na₃SiH₇ has two imaginary branches (Figure 6A). These originate from libration and acoustic modes which, according to the atom-decomposed phonon density of states (shown in Supplementary Figure S6), involve Na1 atoms (which are situated on the 4-fold axes 0,0,z and ½,½,z, cf. Figure 5) and the H atoms being part of SiH₆ octahedra. The imaginary modes stabilize with temperature, which is attributed to the anharmonicity of atomic vibrations, causing renormalizing of the phonon modes due to phonon–phonon interaction (Figure 6B). Thus, P4/mbm-Na₃SiH₇ is stable at high-pressure and high-temperature conditions. Conversely, lowering temperature introduces dynamical instability, driving the distortion to the orthorhombic Pbam structure (a _o ≈ √2a _t, b _o ≈ √2a _t) which is dynamically stable at 10 GPa (Figure 6D). Reducing pressure to about 5 GPa introduces dynamical instability for the Pbam polymorph (Figure 6C), indicating a transition to yet another polymorph.

Thus, total energy and phonon calculations support the experimental findings described in the previous section. The structural chemistry and polymorphism of Na₃SiH₇ reminds of fluorosilicates and germanates A₃Si/GeF₇ (A = K, Rb, Cs, NH₄). These materials have wide band gaps in the UV region (≈6 eV) in combination with interesting birefringent optical properties (Mel’nikova et al., 2016; Huang et al., 2020). In contrast, the calculated band structure of Na₃SiH₇ (Supplementary Figure S7) suggests a semiconductor with a direct band gap of around 2 eV. An interesting aspect, which has not been investigated in the course of this work, is a potentially superionic behavior of Na₃SiH₇. Superionicity of H⁻ was proposed in (yet) hypothetical Na₂SiH₆ where extraordinary diffusive H seems to be promoted by the hypervalent nature of SiH₆ ²⁻ units (Liang et al., 2021). Against this background, it appears worthwhile to study the dynamical properties of Na₃SiH₇ over a wider temperature range by dedicated AIMD simulations.