Assessing the importance of cation size in the tetragonal-cubic phase transition in lithium garnet electrolytes

Lithium garnets are promising solid-state electrolytes for next generation lithium-ion batteries. These materials have high ionic conductivity, a wide electrochemical window and stability with Li metal. However, lithium garnets have a maximum limit of 7 lithium atoms per formula unit (e.g. La3Zr2Li7O12), before the system transitions from a cubic to a tetragonal phase with poor ionic mobility. This arises from full occupation of the Li sites. Hence, the most conductive lithium garnets have Li between 6-6.55 Li per formula unit, which maintains the cubic symmetry and the disordered Li sub-lattice. The tetragonal phase, however, forms the highly conducting cubic phase at higher temperatures, thought to arise from increased cell volume and entropic stabilisation permitting Li disorder. However, little work has been undertaken in understanding the controlling factors of this phase transition, which could enable enhanced dopant strategies to maintain room temperature cubic garnet at higher Li contents. Here, a series of nine tetragonal garnets were synthesised and analysed via variable temperature XRD to understand the dependence of site substitution on the phase transition temperature. Interestingly the octahedral site cation radius was identified as the key parameter for the transition temperature with larger or smaller dopants altering the transition temperature noticeably. A site substitution was, however, found to make little difference irrespective of significant changes to cell volume.


Introduction
High-energy density, portable and safe energy storage remains one of the most prevalent issues in modern society. Lithium-ion batteries (LIB) are amongst the most promising options but are far from achieving their theoretical performance 1-3 . Maximal energy density of lithium batteries can only be achieved by use of Li metal anodes, which enable the highest theoretical capacity (3860 mA h g −1 ) and the lowest electrochemical potential (−3.04 V vs. the standard hydrogen electrode) of all anode materials 1, 2 . However, current LIB electrolytes (usually LiPF6 dissolved in a ethylene carbonate/dimethyl carbonate 22 ) are incompatible with Li metal, present with safety concerns and an inability to accommodate high V cathode materials. Hence, electrolyte optimisation, or replacement, is paramount 1, 2, 4-8 .
All solid-state batteries (ASSBs) are natural successors to current LIBs, as they could enable Li metal anodes, wider electrochemical windows and improved safety 9 . However, the development of a suitable solid-state electrolyte (SSE) has proved troublesome. To date many oxide and sulphide SSEs have been studied, but often have a high ionic conductivity or a wide electrochemical window, but rarely both 6,[9][10][11][12][13][14][15] . Finding a suitable SSE is, therefore, a key challenge to enable the next generation of energy storage 9 .
Lithium garnets have emerged as contenders for use as an SSE, owing to a wide electrochemical window (0-6V vs Li/Li + ), chemical stability with Li metal and (in recent years) high ionic conductivity (> 0.1 mS cm -1 )  . These materials, however, form a poorly conductive tetragonal phase at high Li content (as outlined below) and suffer from atmospheric H + /Li + exchange (which ultimately forms insulating Li2CO3 passivating layers due to instability of the Li dopant in high concentrations) [41][42][43][44] . This is in addition to the common SSE problems of high interfacial resistance and time-consuming synthesis.
An ideal garnet has the formula; A3B2X3O12, where A, B and X are eight, six and four coordinated cation sites, respectively, which crystallise in a face-centred cubic structure (e.g. A = Mg, Fe, B = Al, Cr, Fe, and X = Si, Fe, Al, Ga) 26,45,46 . This structure comprises BO6 octahedra and XO4 tetrahedra, arranged in a 3D framework wherein larger A cations occupy dodecahedral positions in the interstices 57,59 . Lithium ions fully occupy the tetrahedra 24d site, with 3 Li per formula unit (pfu). Alteration of A and B sites dopants, such as in La3Zr2Li7O12 (LLZO), enables up to 7 Li pfu (the upper maximum). However, at this point the system changes from a highly conductive cubic phase (Ia3 ̅ d or I43 ̅ d, Li content ~6.2-6.55 pfu), with vacant interstitial sites for ionic mobility, to a system whereby Li sites are fully occupied and have thus ordered (to reduce short Li-Li distances) [47][48][49] . This gives a reduction in symmetry from a cubic to a tetragonal cell (I41/acd) with ordered lithium occupying the tetrahedral (8a) and distorted octahedral (16f/32g) sites 32, 46-48, 50, 51 .
However, these tetragonal Li garnets, such as La3Zr2Li7O12, La3Hf2Li7O12 and Nd3Zr2Li7O12 , undergo a high temperature tetragonal-cubic phase transition (~700°C), believed to arise from increased unit cell size and entropy factors 52,53 . It would therefore be of great interest if this transition temperature could be lowered to room temperature, thus forming a cubic Li7 phase, which should further optimise the conductivity of Li garnets. This requires a greater understanding of the factors which influence the temperature of this phase transition, which is somewhat limited in the literature. Some studies initially thought this transition occurred ~100-200°C in LLZO but this was determined to arise from hydration, due to either the direct insertion of water molecules or through a H + /Li + exchange mechanism 54 . Therefore, the characteristic, reversible tetragonal -cubic phase transition in LLZO is believed to be 620 -650°C 13,26,54 , while the smaller cell volume La3Sn2Li7O12 (LLSnO) exhibits a phase transition ~750 -800°C 47,51,53 . This suggests that the cell volume is potentially key to dictating the phase transition. doping was predicted to give octahedral site Li-ion vacancies which weakened the 'blocking' effect of the tetragonal (16f) sites, allowing for lithium-ion redistribution and thus, lowering the transition temperature 53 . These data indicate B site substitution could play an important role in the transition temperature, and that the direct relation to cell volume is perhaps too simplistic. Outside of these reports, work on the tetragonal to cubic phase transition is somewhat limited.
Herein nine tetragonal lithium garnets were synthesised; A3B2Li7O12 (A =La, Pr, Nd) (B = Zr, Hf), La3Zr1.75Ce0.25Li7O12 and LaSr2B2 Li7O12 (B = Nb, Ta). Both A and B site doping was undertaken to assess the relative importance of each site on the transition temperature. These materials were studied by variable temperature XRD analysis to ascertain if any new insights could be gained regarding the phase transition. Interestingly, we determine that, irrespective of A site substitution it is the B site which is the predominant factor in determining the phase transition temperature. It is shown that a direct relation solely to cell volume is too simplistic, rather it is suggested the sites which dictate the degree of tetragonality, which correspond to the framework polyhedra, are of higher importance than A site cations which reside within. Furthermore, the transition temperatures identified enabled regression analysis to predict the ideal octahedral B site radius for a room temperature stable cubic Li7 phase.
Post sintering, pellets were sanded to remove any Al contamination from the Al crucible.

Characterisation
All samples were stored in an argon glove box to prevent proton-Li exchange in the garnet. Phase analysis was performed by X-ray diffraction (XRD) using a Bruker D8 diffractometer with Cu source from 15 -80 2θ with a step size of 0.018°. Variable temperature measurements were conducted in a similar manner on a Bruker D8 instrument equipped with an Anton Parr heating stage from 50°C up to a maximum of 1000°C.

Rietveld Refinement
For each garnet synthesised, Rietveld refinements were performed in GSAS-II 55 using room temperature powder X-ray diffraction (XRD) patterns and variable temperature X-ray diffraction (VTXRD) patterns (50°C to 1000°C, 50°C increments). All structural models were obtained from ISCD 48,49 and atoms altered where required to give an analogous crystal structure. For Ce-doped LLZO, fractional occupancies were set to the intended ratio.

X-ray diffraction
All nine Li7 garnets were first analysed for phase purity at room temperature, and all were indexed on a tetragonal garnet cell (I41/acd). Variable temperature X-Ray diffraction (VTXRD) data were subsequently collected for these garnets up to 1000°C. This is beyond the common phase transition temperature (~700°C) but was required to reach the phase transition temperature for the Nb/Ta tetragonal phases. This caused some degradation for some systems; hence the complete reversal of the phase transition was not observed.
The tetragonal to cubic phase transition is readily noticeable in the VT-XRD patterns via the coalescence of the split peaks into sharp, singular peaks. Data were collected in 50°C increments (50°C -1000°C), but were plotted every 100°C for clarity, see figure 1. Near the phase change temperature patterns were commonly biphasic (cubic and tetragonal phases present) and not used for structure refinements. Rietveld refinements were performed for all other XRD patterns with cell volume, cell parameters and A/B site bond lengths studied. An exemplar refinement (with tabulated data at each temperature) for LLZO is shown in figure 2 and table 1. Although these data were collected for all nine Li7 phases, only LLZO is shown in detail, whereas table 2 shows the relevant data for the other eight phases only at room temperature and the transition temperature. Table 3     This was a little surprising given the significant reduction in cell volume across the series from La -Pr- Overall the results were in contradiction with the common consensus; that the primary phase transition driving factor is the cell volume alone, as B site substitutions alter the cell volume considerably less than the A site substitutions yet give substantial differences in transition temperature, see figure 3 26,53 . B site substitution in LaSr2B2Li7O12 also corresponds to larger increases in tetragonality. This indicates the B site plays a more key structural role in determining tetragonal distortion than the A site 26,51 . This is logical given the garnet framework polyhedra of corner linked BO6 and XO4 units, as these sites would structurally define the cell more than the interstitial A site.     In terms of future work, a further factor that could be examined to alter the transition temperature is the oxygen site. This determination of the phase transition temperature via O site substitution has yet to be explored, although has been considered as potential room temperature cubic phase stabilisation prior 107 . However, assessment via Cl or F substitution with O on the phase transition temperature is complex, as high temperatures can easily remove the halogen dopant forming more thermodynamically stable by-products. Further correlative evidence could be found by investigating the transition temperature by changing the XO4 sites, this may yield further confirmation of the controlling factors, but would not necessarily aid in cubic Li7 phase formation

Conclusions
To conclude, it is suggested that the primary factor in the determination of the temperature of the tetragonal -cubic phase transition in the Li7-garnet systems is the B site, which is suspected to arise from the fact that this cation helps to dictate the garnet framework structure, in contrast to the A site, which occupies the cavities within the framework of corner linked octahedra and tetrahedra. This is illustrated by the fact that octahedral site doping showed significant changes to the transition temperature, whereas negligible changes were observed for A site doping. Changes can be correlated to the degree of tetragonality which appears to be dependent on B site dopant size, rather than the cell volume. This work shows that as the degree of tetragonality of the garnet increases, the transition temperature increases too. Therefore, it is hypothesized that the octahedral site is instrumental in determining the tetragonality of the phase, and hence doping at this site with larger cations is the best method in lowering the transition temperature. A similar affect could also be the case for doping in the XO4 tetrahedra (which are also part of the garnet framework) and may help to explain the stability of Li site doping by Ga/Al and subsequent formation of the cubic phase.
Further work by neutron diffraction is required to clarify this relationship more accurately, however, once this phase transition is fully understood, it is hoped that Li7 phases could be cubic at room temperature, thus enabling a higher conductivity SSE.