Theoretical and Experimental Study of LiBH4-LiBr Phase Diagram

Because substitutions of BH4- anion with Br can stabilize the hexagonal structure of the LiBH4 at room temperature, leading to a high Li-ion conductivity, its thermodynamic stability has been investigated in this work. The binary LiBH4-LiBr system has been explored by means of X-ray diffraction and differential scanning calorimetry, combined with an assessment of thermodynamic properties. The monophasic zone of the hexagonal Li(BH4)1-x(Br)x solid solution has been defined from x=0.30 to x=0.55 at room temperature. Solubility limits have been determined by in-situ X-ray diffraction at various temperatures. For the formation of the h-Li(BH4)0.6(Br)0.4 solid solution, a value of the enthalpy of mixing has been determined experimentally equal to 1.0 kJ/mol. In addition, the enthalpy of melting has been measured for various compositions. Lattice stabilities of LiBH4 and LiBr have been determined by ab initio calculations, using CRYSTAL and VASP codes. Combining results of experiments and theoretical calculations, the LiBH4-LiBr phase diagram has been determined in all composition and temperature range by the CALPHAD method.


Introduction
Due to its high gravimetric and volumetric density of hydrogen, LiBH4 has been largely studied as a solid-state hydrogen storage material. 1 It shows a polymorphic transition from an orthorhombic structure at room temperature (RT), space group (s.g.) Pnma, to a hexagonal structure, s.g. P63mc, 2 above 110 ± 2 °C, 3 with an enthalpy change equal to 5.0 ± 0.9 kJ/mol. 3 In 2007, Matsuo et al. 4 reported a drastic increase of the Li-ion conductivity of LiBH4 above the phase transition temperature, suggesting it as a solid-state electrolyte. Despite the hexagonal polymorph (h-LiBH4) shows a remarkable ionic conductivity (~10 −3 S cm -1 at 120 °C), the orthorhombic room temperature phase (o-LiBH4) is much less conductive, showing a Li-ion conductivity of 9.5 × 10 −9 ± 2 × 10 −9 S cm -1 at 30 °C, 5 making a room temperature battery target unviable. 4 Different approaches have been used to increase the Li-ion conductivity of LiBH4 at RT, such as by mixing it with oxides or by means of nanoconfinement. [6][7][8][9] Differently, many studies showed that substitution of BH4anion with halides (e.g. I -, Brand Cl -) can make the hexagonal structure thermodynamically stable, providing a high ionic conductivity at RT. 10-12 For instance, a LiBH4-LiI hexagonal solid solution with 25 mol.% of LiI showed a Li-ion conductivity of about 10 −4 S cm -1 at 30 °C. The h-Li(BH4)1-α(I)α solid solutions have been reported to be stable at RT in the range of 0.18 ≤ α ≤ 0.50. 13 Fast Li-ion conductivity at RT is also observed in h-Li(BH4)1-α(Br)α hexagonal solid solutions (e.g. ~10 −5 S cm -1 for h-Li(BH4)0.7(Br)0. 3) 12 , although it is reduced as the bromide content increases above x = 0.29. 12,14 A full evaluation of thermodynamic properties of borohydrides and their mixtures is fundamental for a further improvements and insight on complex hydrides, aimed to tailor their properties as hydrogen storage materials and solid-state electrolytes. This goal can be reached with the CALPHAD method, which is based on a parametric description of the Gibbs free energy as a function of temperature and composition, by the combination of ab initio calculations and experimental evidences. 15 Starting from experimental data as input, the CALPHAD method allows the assessment of parameters describing the Gibbs free energy of all phases, in order to find the most reliable description of the phase diagram. Ab initio calculations are required to establish the Gibbs free energy of compounds with crystal structures that are not stable in the investigated ranges of temperature and pressure. The use of the CALPHAD approach allowed the determination of different thermodynamic properties of borohydrides, e.g. isobaric heat capacity, Cp, 3 and the definition of phase diagrams as a function of temperature and composition. 16,17 For the LiBH4-LiBr phase diagram, only few experimental data and no thermodynamic assessment are present in the literature. Recently, the hexagonal solid solution h-Li(BH4) x has been demonstrated to be stable at RT in the range 0.29 ≤ x ≤ 0.50, 12,14 while a small solubilisation of the LiBr into o-LiBH4 has been reported (i.e. o-Li(BH4) x where x is ≤0.09) 14 . In addition, the LiBH4 seems to be insoluble in the cubic LiBr at RT. 12,14 Rude et al. 18 reported a temperature of melting of 377.9 °C for the h-Li(BH4)0.5(Br)0.5 solid solution. Therefore, in the present study, we explore the LiBH4-LiBr system, combining experimental and theoretical approaches, in order to determine its thermodynamics and phase diagram. Literature, experimental and ab initio data have been evaluated for an assessment of the system thermodynamics using the CALPHAD approach. The assessment allowed establishing phase stabilities and limits of solubility in the full composition range and in a wide temperature range, i.e. from RT up to the liquid phase.

Synthesis
All manipulations were performed in an argon-filled glovebox (MBraun Lab Star Glove Box supplied with pure 5.5 grade Argon, <1 ppm O2, <1 ppm H2O). LiBH4 (purity >95% from Sigma-Aldrich) and LiBr (purity >99% from Sigma-Aldrich), were mixed in different ratios and by different methods, as reported in Table 1

Attenuated Total Reflection Infrared Spectroscopy (ATR-IR)
Infrared spectra were collected in ATR-IR mode with a Bruker Alpha-P spectrometer, equipped with a diamond crystal. The instrument is placed inside a nitrogen filled glove box. All spectra were recorded in the 5000−400 cm −1 range with a resolution of 2 cm -1 , and are reported as the average of 50 scans.

Powder X-ray diffraction (PXD)
Samples in powder form were characterised by PXD at RT (ex situ) using a Panalytical X-pert Pro MPD (Cu Kα1 = 1.54059 Å, Kα2 = 1.54446 Å) in Debye-Scherer geometry. Patterns were collected in the 2θ range (from 10° to 70°), with a time step of 60 s, for a total of about 30 min per scan. 0.5 mm glass capillaries were used as sample holder and they were filled and sealed under Ar atmosphere.

In situ time-resolved synchrotron radiation powder X-ray diffraction (SR-PXD)
SR-PXD in situ measurements were performed at the diffraction beamline P02, in the Petra III

Rietveld Analysis
The Rietveld refinement of diffraction patterns has been performed using the MAUD (Materials Analysis Using Diffraction) software. 19 The instrumental function was determined using pure Si, for the ex situ measurements and LaB6 for the in situ one. The peak broadening was described using the Caglioti formula, 19 and the peak shape was fitted with a pseudo-Voigt function. Parameters were also refined to consider possible instrument misalignments. Reliability parameters Rwp, Rexp and χ 2 , were used to evaluate the quality of the fitted patterns with selected structural and microstructural (i.e. crystallites size and micro-strain) parameters. The background was described through a polynomial function with 3 or 4 parameters. The following sequence was applied for the refinement of parameters: (1) scale factor (2) background parameters (3) lattice constants (4) crystallites size (5) micro-strain. In some cases, also the occupancy and the position of the 2b site in the hexagonal structure were refined.

Ab initio CRYSTAL
The adopted level of theory for the computational study is in the framework of density functional theory (DFT) with the generalized gradient approximation (GGA) PBE functional. 20 The calculations were performed using the periodic quantum-mechanical software CRYSTAL17, 21

CALPHAD
The Gibbs free energy of single phases was described according to the CALPHAD approach: 15

S id = -R[xln(x) + (1-x)ln(1-x)]
where φ is the considered phase (i.e. CUB: cubic, ORTHO: orthorhombic, HEX: hexagonal, LIQ: liquid), x is the molar fraction of LiBH4, T is the temperature and G ref , -TS id and G exc are the reference, ideal and the excess contributions to the Gibbs energy, respectively. Excess Gibbs energy was modelled with Redlich-Kister expansion series 37 truncated to the first contribution, since the agreement with thermodynamic data was satisfactory: where a and b are optimized parameters. When b=0, a corresponds to the interaction parameter,

Structural characterization
The hexagonal h-Li(BH4) x solid solution has been reported to be stable in the range 0.29 ≤ x ≤ 0.50 12,14 and a small solubilisation of the LiBr into o-LiBH4 has been reported (i.e. o- 14 . In addition, the LiBH4 seems to be insoluble in the cubic LiBr at RT. 12,14 In order to confirm the limit of solubility of LiBr into Li(BH4), samples s1 and s2 (see Table   1) have been analysed by PXD, and results are shown in Figure S1. The formation of a single hexagonal solid solution is confirmed for sample s2 (i.e. Li(BH4)0.5(Br)0.5), whereas a two-phase mixture has been observed for sample s1. To define the composition limits of the bromide rich biphasic (i.e., hexagonal and cubic) zone as a function of temperature, in situ SR-PXD measurement was performed on sample s1 (Figure 1).  confirming obtained results of the refinement. The bromide and boron thermal displacement parameters (Uiso) were bounded to the same value. 14 The Rietveld refinement output parameters are reported in Table S1.
It is possible to exclude any solubilisation of BH4inside the cubic structure of LiBr, since the cell parameter of the cubic phase (a = 5.5082 Å) is equal to that of pure LiBr, as obtained by a Rietveld refinement of the starting material. For this reason, the temperature has been calibrated considering LiBr as internal standard, using the volumetric expansion coefficients reported by Rapp et al. 38 .
The lattice parameters of the hexagonal solid solution at 30 °C, obtained from the Rietveld refinement (Figure 1b), are a = 4.1853 Å and c = 6.6915 Å, in agreement with the lattice parameters obtained from the ex situ pattern at RT (i.e. a = 4.1861 Å, c = 6.6940 Å, Figure S1). In addition, a Li(BH4)0.45(Br)0.55 composition has been obtained from the 2b site occupancy, which is present with a molar phase fraction equal to 0.88, together with pure LiBr.
After the refinement, a molar balance has been applied, according to: shows that the molar fractions of LiBr is nearly the same than that obtained at 370 °C, i.e. 0.24, confirming the occurrence of irreversible transformations during heating. These results suggest that data obtained at temperatures higher than 230 °C cannot be used for further analyses, so that only reliable data have been summarized in Table S1. can be explained considering the lower ionic radius of the Brand Clwith respect to BH4 -, which is responsible for an increase of the bond strength that promotes the formation of a solid solution. 41 Since the bromide-rich biphasic zone has been defined as a function of temperature, samples s3 and s4 (see Table 1) have been synthetized in order to verify the hexagonal solid solution monophasic zone. Figure S9a shows PXD patterns of the samples s3 and s4, together with s2, after the synthesis (ball milling followed by a thermal treatment). In all the patterns, only the high temperature hexagonal phase of LiBH4 is present, confirming that it is stabilized at room temperature for all mixtures. Figure   S10 shows To study the changes in the vibrational properties of lithium borohydride, due to the stabilization of the hexagonal phase by halide additions, IR-ATR spectroscopy was performed on samples s2, s3 and s4 and results are shown in Figure S9b, where the IR-ATR spectrum for pure o-LiBH4 is also reported for comparison. As already reported, 18

Enthalpy of Mixing
To assess the LiBH4-LiBr phase diagram, a value of the enthalpy of mixing for hexagonal solid solutions is needed. For this reason, sample s5 (0.4LiBr-0.6LiBH4 molar fractions) has been prepared by hand mixing (HM) in an agate mortar for about 5 min, in order to intimately put in contact the two components, but avoiding the formation of the hexagonal solid solutions. In fact, Rude et al. 18 reported that a small amount of h-Li(BH4)1-x(Br)x was already stabilized at RT, after 15 min of HM.
Samples s5 was later analysed using DSC under 2 bar of H2. The program temperature provided: a) a 2.5 h isotherm at 60 °C, in order to; b) a fast heating ramp (20 °C/min), in order to limit the temperature range in which the thermal activated mixing process could occurs, and c) a 2.5 h isotherm, at the maximum temperature reached during the heating ramp (250 ÷ 350 °C), to ensure that the possible activated thermal process could be completed and to equilibrate again the DSC signal. The same temperature program was repeated twice on the same sample, in order to have a DSC ramp to be used as baseline for the signal integration.
In all the calorimetric analyses of sample s5 (Figure S11), during the heating ramp, the endothermic peak due to the phase transition of the LiBH4 at 110 °C was detected. At higher temperatures, a broad exothermic DSC signal was observed, which has been associated to the formation of the hexagonal solid solution. So, from its integration, a value of the enthalpy of mixing can be obtained, as described below. It is worth noting that, during the second ramp, the endothermic peak due to the phase transition of the LiBH4 is not present anymore, suggesting that the formation of the h-Li(BH4)1-x(Br)x, is completed after the first ramp. The cooling ramps, from the high temperature isotherms down to 60 °C, were also collected, but they have not been reported, since no thermal events were detected, confirming the formation of the solid solution during the first ramp.
The measurement performed with a maximum temperature up to 350 °C ( Figure S11d) shows that an additional endothermic peak is present at high temperatures. This can indicate that, in this temperature range, the sample starts to melt. The higher stability of the sample obtained in the DSC measurement on sample s5 ( Figure S11d) with respect to that observed in the SR-PXD measurement in sample s1 (Figure 1.) can be explained considering that the overpressure of H2 (2 bar) present during calorimetric analysis suppress possible decompositions. 3 Figure S12 shows that the difference between the first and the second DSC ramp is composed by an endothermic signal, followed by an exothermic signal at higher temperatures. The peak and onset temperatures of these peaks, as well as the corresponding enthalpies changes, are reported in Table   2 for the different calorimetric analysis.
The endothermic peak (∆HEndo) is characterised by two components (Figure S12). The main contribution (∆HTrs) can be assigned to the transition for the orthorhombic to the hexagonal phase of the pure LiBH4, which is present in the hand mixed sample s5. The observed signal has been normalized for its content (∆HTrs/Normalized) and results indicate that, before and during the phase transition, no significant solubilisation occurs. In fact, these values are comparable to that of the pure LiBH4 (i.e. ∆HTrs = 4.89 kJ/mol, see Figure S13). The second contribution to the endothermic event is observed before the phase transition, in the temperature range from 60 °C to 120 °C. This signal (∆HCp) can be explained considering that the molar heat capacity (Cp) of the orthorhombic phase is higher with respect to that of the hexagonal phase. 45 In fact, during the first heating, LiBH4 is still in the orthorhombic phase, while during the second one, LiBH4 have been stabilized in its hexagonal phase, forming the solid solution.   Since the s5 sample was annealed with the same temperature program used during the first ramp of the DSC analysis, it is possible to correlate the reaction coordinate obtained by Rietveld refinement of PXD patterns (Figure S14) with the ∆HExo values reported in Table 2, as shown in  The reaction coordinate in Figure 4 corresponds to the fraction of the LiBr solubilized in the hexagonal solid solution and it has been calculated using the molar fraction of residual cubic LiBr obtained by the Rietveld refinement of PXD patterns. The exothermal peak corresponding to the pattern collected after the heating at 120 °C (the offset temperature of the phase transition peak) has been considered equal to zero. However, a small amount of the hexagonal solid solution was already observed (see Figure S14), suggesting that the reaction might be already initiated during the heating up to the LiBH4 phase transition, but the enthalpy contribution cannot be determined due to sensitivity limitation of the DSC analysis. By a linear fit (95 % of confidence, equation determined: y = 1032x Li(BH4)0.6(Br)0.4 solid solution has been estimated equal to -900 J/mol (Figure 4). Taking into account the intercept of the linear fitting, which represents the missed contribution to the heat of mixing reaction, the measured values of ∆HExo should be corrected by adding 132 J/molmixture. As a conclusion, using a confidence interval of 95 %, the value for the enthalpy of mixing for sample s5 can be considered with an error of ± 160 J/mol, i.e. equal to -1.0 ±0.2 kJ/mol.

Ab initio
Lattice stabilities for LiBH4 have been taken from the literature. 16 In order to determine the relative stability of metastable LiBr structures and to support the assessment of related CALPHAD endmembers energies, different theoretical approaches and computer codes (VASP, CRYSTAL and Quantum Espresso) were used. Energy results are reported in Table 3  LiBr. According to this investigation, the most stable structure is either the cubic or hexagonal one, depending on the computational approaches and settings used (including DFT with B3LYP functional and Hartree-Fock). The lattice parameters calculated with different approaches are reported in Table 4

Assessment of the Phase Diagram
Assessed parameters of thermodynamic functions for different solution phases (hexagonal, cubic, orthorhombic and liquid) have been determined in the present study, in order to explore and characterize the LiBH4-LiBr phase diagrams. In addition, pure components end-members have been also assessed. In both cases, the assessment procedure was based on results of experiments (Table 5) and of ab initio calculations ( Table 3).
The literature reports only a single report supporting the solubility of LiBr into o-LiBH4 up to 0.09 molar fraction. 14 However, this experimental result has been briefly describe in ref. 14  to be HEX Ω = -4167 J/mol. In a first step, the liquid phase has been considered ideal and then it has been assessed based on liquidus and solidus temperatures taken from the literature 18 and obtained by DSC analysis in this work, as reported in Figure S15 and   Starting from results obtained from ab initio calculations, the orthorhombic and hexagonal LiBr end-members have been also assessed. In order to take into account the results of the in-situ XRD analysis as a function of temperature, the LiBr hexagonal end-member has been described introducing a temperature dependent parameter ( Table 6). This was necessary to obtain a limited Brsolubility at high temperature, which turns out as high as x(LiBr) = 0.58 at 207 °C (compared to the experimental result equal to 0.55 at 207 °C, see Figure S4).   Corresponding calculated data are reported in Table 5. would be taken into account, a ORTHO Ω = -1000 J/mol should be considered. In this case, the solubility limit of the hexagonal phase with the orthorhombic solid solution at room temperature would increase accordingly (Figure S15), deviating from experimental findings. So, as stated above, the experimental point at XLiBr = 0.09 has not been considered for the assessment. On the other hand, the calculated solvus line of the hexagonal phase in the center of the diagram shows a slight deviation at high temperatures, compared to present experimental investigation, which essentially establishes a straight line as a function of temperature. The formation of a peritectic reaction at 380 °C and 0.60

Figure 5. Lines
LiBr molar fraction has been evidenced. The assessment provided a solubility up to 0.02 molar fraction of LiBr into o-LiBH4 ( Table 5). The calculated CALPHAD values of the liquidus temperature for samples s2, s3 and s4 ( Figure S16) result in good agreement with respect to the experimental values (Table 5), as well as for melting enthalpy values upon heating ( Table 5 and Table S2). The average melting enthalpy for s4 is lower with respect to s2, s3, and the calculated value, which could be related to a possible incipient decomposition of the sample due to the high temperatures reached in order to observe complete melting. Furthermore, lower experimental enthalpy values are detected during cooling, possibly because of a larger temperature range in which the crystallisation takes place hence causing an underestimation of the enthalpy related to the transformation while integrating the DSC peaks.

Conclusions
The LiBH4-LiBr phase diagram has been explored experimentally by means of PXD, in situ SR-

Supplementary Information
RT PXD, IR-ATR and in situ SR-PXD patterns for various samples at different temperatures.
Lattice parameters as a function of bromide content. DSC traces and solubilisation reaction followed by PXD. DSC traces and data (∆H and temperatures) collected during the analysis.