Pure orthorhombic (o-LiBH₄, Pnma space group) and hexagonal (h-LiBH₄, P6₃mc space group) structures of LiBH₄ were optimized at the DFT-Perdew-Burke-Ernzerhof (DFT-PBE) level of theory, starting from the experimental coordinates [21].The optimized unit cell structures are shown in Figure 1, whereas the most important structural parameters are summarized in Table 1 in comparison with experimental data.

For the orthorhombic crystal, a systematic overestimation of the B-H bond length is observed, as already pointed out in literature [2,19], which however does not significantly affect the unit cell volume.

The hexagonal phase is stable at high temperature (T ≥ 381 K) [12]. Therefore, without inclusion of temperature effects, full geometry optimization starting from the experimental structure dramatically distorts the internal geometry and the cell volume, as reported in Table 1. Indeed, for the unit cell of h-LiBH₄, frequency calculation at Gamma point on the optimized structure reveals six imaginary frequencies, showing the instability of this phase when temperature is not taken into account. Maintaining the cell parameters fixed at the experimental values does not remove the structural instability, as the internal atomic displacements are still very large, as shown also by Miwa et al. [22],due to the dynamic disorder of BH₄⁻ units [23]. In order to overcome these difficulties and, moreover, to simulate solid solutions, a supercell approach was adopted in the case of h-LiBH₄, considering a larger and more representative scenario (for the original cell Z = 2 → 12 atoms, while in the supercell Z = 16 → 96 atoms). In this operation of doubling each cell vector, symmetry is completely lost and borohydride tetrahedra are free to rotate, so removing the phonon instability found in the single unit cell. Indeed, when computing frequency values for the hexagonal supercell, only one imaginary mode is found at −20 cm⁻¹. In the following, to avoid numerical problems due to the variable number of imaginary frequencies for the structures, we have used the whole set of frequencies by considering also the imaginary values (by using their absolute value in the statistical thermodynamic formulae) for the calculation of the zero point energy (ZPE) and enthalpy corrections, as described below.

The relative energy stabilities calculated for the two phases favor the orthorhombic structure with respect to the hexagonal, as expected, but their enthalpy difference (^{ORTHO − HEX}ΔH = 10 kJ∙mol⁻¹ per formula unit) overestimates experimental measurements [24,25], due to the instability of the hexagonal model.

Even if the stable LiCl polymorph at room temperature is cubic, corresponding structures were obtained for both the orthorhombic and hexagonal phases as the full substitution of BH₄^- with chlorine. The difference in enthalpy for the three phases of LiCl was calculated for the phase diagram calculation, giving ^{CUBIC − ORTHO}ΔH = 21.8 kJ∙mol⁻¹ and ^{CUBIC − HEX}ΔH = 15.1 kJ∙mol⁻¹.

The simulation of orthorhombic solid solution o-Li(BH₄)_1−xCl_x, where four borohydride units are present in the o-LiBH₄ unary cell, was performed, considering three compositions with molar fraction of chlorine, x, equal to 0.25, 0.50 and 0.75. The corresponding unary cells are reported in Figure 1. For x = 0.5, three non-equivalent configurations were computed, namely C1, C2 and C3, as shown in Figure 1. Among them, C3 structure turned out to be the most stable, because of the largest Cl-Cl distance. Conversely, for the hexagonal solid solution h-Li(BH₄)_1−xCl_x, due to the large size of the supercell, only three compositions have been considered, that are Li(BH₄)_0.94Cl_0.06, Li(BH₄)_0.5Cl_0.5, and Li(BH₄)_0.06Cl_0.94.

For the orthorhombic solid solutions, the unit cell volume decreases with the increase of Cl substitution, as expected, with a maximum variation of about 10% for the highest chlorine content (x = 0.75). For the hexagonal structures, the volume decreases as a function of Cl content, with a maximum variation of about 13% for x = 0.94. It can be mentioned here that the calculated cell volume reduction for the Cl-substituted o-LiBH₄ and h-LiBH₄ correlates well with the experimentally observed values [12].

Thermal entropy was calculated for each composition using classical statistical thermodynamic formulae. As it was computed using the harmonic set of frequencies, the hindered BH₄⁻ rotation is included, as well as the frustrated translation of the substituting Cl. It turned out that the hindered BH₄⁻ soft rotational motion is compensated by the frustrated translation of the substituting Cl ion, so that the thermal entropy contribution is very small, well below the contribution due to the ideal configurational entropy.

The enthalpy of mixing was computed at room temperature for the models shown in Figure 1. The obtained results are shown in Figure 2 as a function of the increasing LiCl mole fraction. According to simulations, o-LiBH₄ is slightly destabilized by the substitution of chloride inside the lattice, since computed enthalpy of mixing (ΔH_mix) values are positive and small (less than 2 kJ mol⁻¹ per formula unit). On the contrary, in the hexagonal phase, the enthalpy of mixing shows slightly negative values, less than −1 kJ mol⁻¹ per formula unit, so that the h-LiBH₄ is, to some extent, stabilized by LiCl. As stated above, the thermal entropy contribution is very small, so ideal entropy of mixing (ΔS_mix) has been considered for free energy calculations. When ΔH_mix and −TΔS_mix terms are summed up at room temperature, the free energy of mixing (ΔG_mix) becomes close to zero for the orthorhombic phase and slightly negative for the hexagonal phase for all compositions.

In order to describe thermodynamic behavior of the LiBH₄-LiCl system, the CALPHAD approach [26] was used. Due to the lack of thermodynamic data for the LiBH₄-LiCl liquid mixture, the phase diagram was evaluated, neglecting the liquid phase, and it is considered only below the melting temperature of LiBH₄.The presence of an attractive interaction in the liquid state could induce a stabilization of the liquid phase below the melting temperatures of pure components, as found experimentally by in situ X-ray diffraction [12].

On the basis of the evaluated thermodynamic parameters, the pseudo binary phase diagram for the LiBH₄-LiCl system has been calculated and the results shown in Figure 3. The calculated solubility of Cl into o-LiBH₄ is rather low and it reaches a value x = 0.1 at about 500 K for the h-LiBH₄ phase. A eutectoid phase transition is calculated at 372 K and x = 0.04. The phase diagram behavior is very sensitive to both lattice stabilities (i.e., free energy difference between different phases of the pure components) as well as to the free energy of mixing. The very strong instability, predicted for the metastable o-LiCl (^{CUBIC − ORTHO}ΔH = 21.8 kJ∙mol⁻¹), and the calculated nearly zero ΔG_mix , prevent any relevant solubility of Cl inside the orthorhombic phase. The negative ΔG_mix for the hexagonal solid solution and a more stable h-LiCl, if compared to the orthorhombic one (^{HEX − ORTHO}ΔH = 6.7 kJ∙mol⁻¹), allow for the stabilization of the hexagonal phase with respect to the orthorhombic one when Cl is added. Of course, a lower value of ^{HEX − ORTHO}ΔH and a more negative enthalpy of mixing for the hexagonal phase would promote a higher solubility of Cl in h-LiBH₄ phase.

Ab initio calculations based on DFT GGA Hamiltonian (PBE) were carried out with the periodic CRYSTAL09 code and localized basis set functions of polarized double-ζ quality. In detail: Li cation was described with a 5–11G(d) basis set (α_sp = 0.479 bohr⁻² for the most diffuse shell exponent and α_pol = 0.600 bohr⁻² for polarization), while for boron a 6–21G(d) was adopted (α_sp = 0.124 bohr⁻² for the most diffuse shell exponent and α_pol = 0.800 bohr⁻² for polarization). For hydrogen, a 31G(p) (α_sp = 0.1613 bohr⁻² for the most diffuse shell exponent and α_pol = 1.1 bohr⁻² for polarization) was considered; for chlorine, a 86–311G basis set was used (α_sp = 0.125 bohr⁻² for the most diffuse shell exponent).

Phonons at Γ point in the harmonic approximation were computed to derive the thermodynamic functions by diagonalizing the associated mass-weighted Hessian matrix (for details on the computational procedure see references [31,32]). Grimme’s correction to the electronic energy was computed to take dispersion forces into account for all calculations, following the D* approach described in the literature [33,34]. The enthalpy data were obtained as the electronic energy, including the zero-point energy correction (ZPE), and the thermal factor at the desired temperature.

Unary phases (i.e., pure elements) have been described according to the SGTE database [35]. The cubic phase was considered as stoichiometric LiCl, neglecting the possible solubility of LiBH₄ in this structure. The thermodynamic parameters for this compound (^CUBICG(LiCl)) were taken from the Substance SGTE database [36].

LiBH₄-LiCl solid solutions with orthorhombic and hexagonal structures were modeled using two sublattices, the first occupied by Li⁺ and the second occupied by Cl⁻ or by a BH₄⁻ unit.

As usual, the Gibbs free energy of these solutions can be expressed as [26]: where φ represents the phase (orthorhombic or hexagonal), x represents the mole fraction of LiCl, T is the temperature, and G^ref, S^id, G^exc are the reference Gibbs energy, the ideal entropy contribution and the excess contribution to the free energy, respectively.

^ORTHOG(LiBH₄) was taken from the Substance database. On the basis of ab initio calculations, the free energy of orthorhombic LiCl was evaluated as ^ORTHOG(LiCl) = ^CUBICG(LiCl) + A − BT, where ^CUBICG(LiCl) was taken from the Substance database and A = 21.8 kJ·mol⁻¹ and B = 7.2 J·K⁻¹·mol⁻¹. As shown in Figure 2, since the ab initio calculated enthalpy of mixing is slightly positive and nearly symmetric, the excess Gibbs energy was modeled as a regular solution, giving with Ω = 5.940 kJ·mol⁻¹.

Because the thermodynamic function for LiBH₄ reported in the Substance database does not take into account the phase transition [25] from orthorhombic to hexagonal phases occurring at 383 °K, new thermodynamic parameters for the hexagonal LiBH₄ have been evaluated. According to the enthalpy and temperature of transition measured by Price et al. [25], the Gibbs free energy of h-LiBH₄ has been described as ^HEXG(LiBH₄) = ^ORTHOG(LiBH₄) + A − BT, where A = 4.4 kJ·mol⁻¹ and B = 11.4 J·K⁻¹·mol⁻¹. Since no experimental data are available for the hexagonal LiCl, ^HEXG(LiCl) was evaluated on the basis of ab initio calculations as ^HEXG(LiCl) = ^CUBICG(LiCl) + A − BT, where A = 15.1 kJ·mol⁻¹ and B = 2.3 J·K⁻¹·mol⁻¹. According to the results of ab initio calculations the excess Gibbs energy of the hexagonal solid solution was modeled as a regular solution, giving with Ω = −4.827 kJ·mol⁻¹kJ·mol⁻¹.