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Anion Disorder in KBHB H and Its Effect on Cation Mobility Yolanda Sadikin, Roman V. Skoryunov, Olga A. Babanova, Alexei V. Soloninin, Zbigniew #odziana, Matteo Brighi, Alexander V. Skripov, and Radovan #erný J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b00364 • Publication Date (Web): 22 Feb 2017 Downloaded from http://pubs.acs.org on February 24, 2017

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The Journal of Physical Chemistry

Anion Disorder in K3BH4B12H12 and its Effect on Cation Mobility

Yolanda Sadikin1, Roman V. Skoryunov2, Olga A. Babanova2, Alexei V. Soloninin2, Zbigniew Lodziana3, Matteo Brighi1, Alexander V. Skripov2 and Radovan Černý1,*

1

Department of Quantum Matter Physics, Laboratory of Crystallography, University of

Geneva, Quai Ernest-Ansermet 24, CH-1211 Geneva, Switzerland 2

Institute of Metal Physics, Ural Division of the Russian Academy of Sciences, S.

Kovalevskoi 18, Ekaterinburg 620990, Russia 3

Polish Academy of Sciences, Institute of Nuclear Physics, ul. Radzikowskiego 152, 31-342

Kraków, Poland

E-mail: [email protected]

Abstract Mixed anion borohydride – closo-borane of potassium, K3BH4B12H12, has been synthesized using mechanochemistry and characterized by combination of temperature dependent Synchrotron Radiation X-ray Powder Diffraction, solid state Nuclear Magnetic Resonance, Thermal Analysis, Electrochemical Impedance Spectroscopy, Topology Analysis and ab initio solid state calculations. At RT the compound crystallizes in the monoclinic superstructure (P2/c) of the cubic anti-perovskite prototype. At 565 K it transforms by first order phase transition into a rhombohedral (R-3m) deformation of the cubic prototype, which further transforms at 680 K by a second order phase transition into a cubic (P23) anti-perovskite structure. While the monoclinic polymorph is observed for the first time among mixed anion salts, the rhombohedral and cubic polymorphs are known among other alkali metal and

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ammonium halides (or borohydrides) – closo-boranes. The first phase transition is related to the repulsive homopolar H-H contacts between BH4- and B12H122- anions which are released at bigger cell volumes, and the orientation of BH4- anion becomes disordered. The second phase transition is related to orientational disorder of the B12H122- anion at bigger cell volumes. The parameters of reorientational motion (activation energies and jump rates) for both BH4– and B12H122– anions in the monoclinic phase were found from the nuclear spin-lattice relaxation measurements. The effect of orientation disorder of both anions on mobility of cations was studied as a case example for the whole family of complex hydrides based on borohydride or closo-borane anions, important solid state electrolytes. While the dynamics of smaller BH4anion does not have any measurable effect on K+ mobility, the dynamics and orientation disorder of bigger B12H122- is promoting the K+ mobility which would otherwise be limited by small radius of conducting channels even in the cubic anti-perovskite structure.

Introduction Many materials which can potentially be used as solid state electrolytes in Li or Na batteries can be rationally designed from lithium or sodium salts containing dynamically disordered complex anions. The structure typically contains polyanions AByn- with covalent A-B bonds (e.g.: PO43-, SO42- and NO2-), where the rotational motion of AByn- promotes cationic conductivity, decreasing the associated activation energy via the so-called "paddle-wheel" mechanism.1 Several superionic metal borohydrides based on the complex anion BH4- were reported,2-4 and a possible “paddle-wheel” mechanism was discussed in these compounds.5-7 This concept was later extended to higher boranes such as B12H122- or B10H102- in Na-based compounds.8,9 It was shown by solid state NMR and quasi-elastic neutron scattering,10,11 that the high rotational mobility promotes superionicity in the respective materials, whose conductivity increases by several orders of magnitude upon polymorphic order-disorder


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transitions into the superionic high temperature (HT) phases, 0.1 S cm-1 (above 480 K) and 0.01 S cm-1 (above 360 K), respectively, however, transforming reversibly to the nonconducting phase upon temperature decrease. Currently, therefore, efforts are being invested to stabilize superionic conduction in such materials at room temperature (RT). One approach is mixing the cations as in (Li,Na)2B12H12 which resulted in nearly hysteresis-free transition at 488

K,12,13

the

other

approach

used

anion

mixing

in

Na3BH4B12H12

and

(Li0.7Na0.3)3BH4B12H12 resulting in superionic conductivity values close to the order of 10-3 S cm-1 at RT in the former.14 The attention of the researchers turned latter to carborane anions CB11H12- and CB9H10- resulting in conductivities of 0.1 S cm-1 (above 380 K) and 0.05 S cm-1 (above 323 K) for sodium and of 0.1 S cm-1 (above 400 K) and 0.04 S cm-1 (above 357 K) for lithium, respectively.15-17 Mixing the carborane anions led to the increase of conductivity close to RT up to 0.07 S cm-1 at 300 K for Sodium.18 In all studies the dynamic behaviour of the complex anions was proposed as the effect switching on the superionic conductivity either by phase transition to a HT phase with high symmetry packing of rotating anions or by the "paddle-wheel" mechanism. The exception is Na3BH4B12H12 where the RT phase is already a superionic conductor and no phase transition occurs till the compound melting. We present here a systematic study of anions dynamics in K3BH4B12H12, a member of a broader family of mixed anion hydroborates A3BH4B12H12, (A=Li, Na, K, Rb, Cs) with anti-perovskite or related structure types.14,19,20 We will show that successive orientation disordering of the two complex anions results in three distinct crystallographic phases, and we discuss the interaction between the anions and its possible effect on cation mobility.

Experimental methods Synthesis: All sample handling was done in a glovebox under argon atmosphere. KBH4 (99.9 %) was purchased from Sigma-Aldrich, K2B12H12 (>99.5%) from Katchem. The reactants



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were mixed in nominal composition 1:1, and milled at 400 rpm in a Fritsch Pulverisette 7 premium line planetary ball mill in a two-step milling process of 30 repetitions where milling intervals of 2 min are followed by breaks of 2 min to avoid overheating of the sample in the grinding bowl. The powder-to-ball mass ratio was approximately 1:50. One sample has been prepared by solvent-free milling while another sample was prepared by water assisted milling. For water assisted milling, water was added to improve the reactivity of the reactants. Reactants (1 mmol) were dissolved in 5 mL of water and milled for total milling time of 10 minutes. All reactants are easily dissolved in the water. After milling, there was neither precipitation, nor a change of the color. KBH4 is stable in water for complete reaction. After milling, the aqueous solution was dried at 373 K under dynamic vacuum until water was removed). Samples synthesized with water-assisted milling were better crystallized compared to solvent-free milled samples. Therefore, for further characterization, the water-assisted milled samples were used. Synchrotron Radiation X-Ray Powder Diffraction (SR-XPD): The data used for crystal structure solution and refinements were collected at the Swiss-Norwegian Beamlines of ESRF (European Synchrotron Radiation Facility, Grenoble, France). Data were recorded on a Dectris Pilatus M2 detector at a wavelength of 0.8198 Å. The temperature was controlled with a hot air blower and 2D images were integrated and treated with the locally written program Bubble. For all measurements, the samples were sealed into borosilicate capillaries of diameter 0.5mm (under Argon atmosphere), which were spun during data acquisition. The wavelengths were calibrated using NIST SRM640c Si standard. The crystal structures presented herein were solved ab-initio using the software Fox21 and refined with the Rietveld method using TOPAS.22 Both complex anions, BH4- and B12H122-, have been modelled as rigid bodies with ideal tetrahedral and icosahedral shapes, respectively, and with


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corresponding B-H and B-B distances. Temperature dependent SR-XPD data were refined sequentially using FullProf.23 Solid state NMR: For NMR experiments, the sample was flame-sealed in a glass tube under vacuum. NMR measurements were performed on a pulse spectrometer with quadrature phase detection at the frequencies ω/2π = 14 and 28 MHz for 1H and 28 MHz for 11B. The magnetic field was provided by a 2.1 T iron-core Bruker magnet. A home-built multinuclear continuous-wave NMR magnetometer working in the range 0.32 – 2.15 T was used for field stabilization. For rf pulse generation, we used a home-built computer-controlled pulse programmer, the PTS frequency synthesizer (Programmed Test Sources, Inc.), and a 1 kW Kalmus wideband pulse amplifier. Typical values of the π/2 pulse length were 2 – 3 µs for all nuclei studied. For the measurements at T < 450 K, a probe head with the sample was placed into an Oxford Instruments CF1200 continuous-flow cryostat using helium or nitrogen as a cooling agent. The sample temperature, monitored by a chromel-(Au-Fe) thermocouple, was stable to ±0.1 K. Measurements at T ≥ 450 K were performed using a furnace probe head; for this setup, the sample temperature, monitored by a copper – constantan thermocouple, was stable to ±0.5 K. The nuclear spin-lattice relaxation rates were measured using the saturation – recovery method. NMR spectra were recorded by Fourier transforming the solid echo signals (pulse sequence π/2x – t – π/2y). Thermal Analysis: Differential Scanning Calorimetry (DSC) measurements were carried out on Netzsch STA449 F3 Jupiter at a ramping rate of 5 K min-1 using sealed Aluminium pans as sample holder. Conductivity measurements by Electrochemical Impedance Spectroscopy (EIS): K-ionic conductivity was measured with an HP 4192A LF impedance analyser, in a frequency range 5 Hz - 10 MHz with a signal amplitude of 50 mV; sample was compressed to a pellet with a nominal dimension of 3.175 mm diameter and a thickness of 0.76 mm using a manual axial



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hand press (Parr Pellet Press) and placed in a BDS 1200 Novocontrol sample cell for air sensitive materials, under inert argon atmosphere, between two gold ion-blocking electrodes. The pellet compaction achieved was above 95%, owed to the mechano-chemistry treatment. Conduction path analysis: The possible conduction paths accessible to mobile K-species were determined by using Voronoi-Dirichlet Polyhedra (VDP) analysis implemented in the program package TOPOS.24 In this study, which is a geometrical approximation, BH4 is represented by a single sphere while B12H12 group by 12 spheres of the same radius. The possible hop was constructed by connecting void/interstitial sites available in the anionic sublattice. The hop is characterized by Rad or radius of channel which is the narrowest window in the channel with certain dimensionality (1D, 2D or 3D). The structures with larger characteristic Rad have higher probability for cation hopping. The threshold radius of the conducting channel is treated as Rad > 2.9 Å (89% of cation-anion distance) and the radius of mobile cation RK = 1.37 Å. Ab initio calculations: The calculations are performed within density functional theory (DFT) formalism, and the generalized gradient approximation (GGA) for the exchange correlation functional.25 We used a plane-wave basis set and the valence configurations 1s1 for H; 2s22p1 for B; 3p64s1 for K were represented by projector-augmented wave (PAW) potentials26,27 as implemented in the Vienna Ab initio Simulation Package (VASP).28-30 The plane wave cutoff was 450 eV for all static calculations, and the k-points samplings assuring total energy convergence within 1 meV per formula unit for static calculations of the ground state. The ground state electronic density was determined by iterative diagonalization of the Kohn-Sham Hamiltonian and Gaussian smearing 0.05 eV was applied. For all calculations parametrized dispersion correction was used.31 Atomic position were optimized with conjugated gradient algorithm. Nudged Elastic Band (NEB) calculations were performed on the supercells with three or six formula units, only Γ point was used for k-point sampling. Five images were


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created for each path considered for anion rotation. Ab initio Molecular Dynamics (MD) was performed on the same supercells as NEB calculations. For MD energy cutoff was 350 eV, the time step 0.6 fs was used for integration of equations for atomic motion to assure accurate description of fast B-H stretching modes. Total sampling time was 3 ps, and temperatures 250 K, 350 K, 450 K were considered. At each temperature systems were equilibrated for 2 ps. Nose-Hoover thermostat32 was used. This setup was also used for simulated annealing performed on single unit cell. For this case 2×2×2 k-point sampling was applied.

Results and discussion Formation and stability of K3BH4B12H12 from SR-XPD and DSC: The K3BH4B12H12 forms in 1:1 mixture of KBH4 and K2B12H12 according to addition reaction: KBH4 + K2B12H12 → K3(BH4)(B12H12)

(1)

In both samples (solvent-free and water assisted) unreacted crystalline K2B12H12 has been observed while the diffraction peaks of KBH4 have disappeared. The complete reaction can be obtained by using 10 mol. % excess of KBH4. In tested reactions of various combinations of borohydrides and closo-boranes of K with those of Li and Na the K3BH4B12H12 forms as a secondary phase only in 1:1 mixture of NaBH4 and K2B12H12 in addition to a double cation (Na,K)2B12H12. Variable temperature in situ SR-XPD (Figure 1) and DSC (Figure 2) reveal three crystalline polymorphs of K3BH4B12H12: A monoclinic (P2/c) polymorph is observed in as milled sample. On heating (4 K/min,) it transforms at 565 K into a rhombohedral (R-3m) polymorph (first transition), isostructural to RT phase of Cs3BH4B12H12, which transforms at 680 K into a cubic (P23) polymorph (second transition), also known as HT phase of Cs3BH4B12H12.19,20 The cubic polymorph is stable at least up to 773 K, the highest temperature in our experiment.



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While on cooling (10 K/min) the first transition shows a small hysteresis of 6 K, no hysteresis was observed for the second transition within the precision of our measurement.

Figure 1: Variable temperature SR-XPD data (T-ramp) of the water assisted ball milled KBH4:K2B12H12 mixture. Heating (4 K/min) between RT and 773 K (left), cooling (10 K/min) from 773 K down to RT (right).

Figure 2: DSC data obtained on the water assisted ball milled KBH4:K2B12H12 mixture in sealed crucible with heating/cooling rate of 5 K/min.

Crystal structures of three K3BH4B12H12 polymorphs, and order/disorder transition:


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The space group symmetry and lattice parameters of the three K3BH4B12H12 polymorphs at the temperature used for crystal structure refinement are given in the Table 1. The monoclinic structure was originally solved in the space group Pc, and the DFT optimization of the ordered crystal structure corrected the space group to P2/c. This involves a small orientation correction of both anions to follow the site symmetry. The Rietveld plots are given in Supporting Information (Figures S1-S3), the structural data as refined by Rietveld method and for monoclinic phase also as optimized by DFT with fixed lattice and constrained symmetry are included in CIF files.

Polymorph

SG

V [Å3]

a [Å]

b [Å]

c [Å]

β [°]

6.9917(2)

13.4192(3)

94.508(1)

m-K3BH4B12H12

P2/c

659.37(2)

7.0497(2)

r-K3BH4B12H12

R-3m

1074.23(6)

10.2464(4)

c-K3BH4B12H12

P23

368.47(1)

7.1692(4)

11.8147(5)

T [K] 300 673 773

Table 1: Space group symmetry (SG) and lattice parameters from Rietveld refinements at given temperature of three K3BH4B12H12 polymorphs. The meaning of the prefix in the compound name: m- for monoclinic, r- for rhombohedral and c- for cubic.

The cubic c-K3BH4B12H12 crystallizes in anti-perovskite structure type ABO3 with B12H122- on the A-position, BH4- on the B-position and potassium cations on the positions of the oxide, and is isostructural to HT polymorphs of A3BH4B12H12 (A=Rb, Cs).33,34 The structure of rK3BH4B12H12 is a rhombohedral deformation of the anti-perovskite type, found also for the RT polymorph of Cs3BH4B12H12.20 The rhombohedral structure is of the same type as in multiferroic BiFeO3, and it is found also for several halide analogous A3HaB12H12 (A=NH4, Na, K, Rb, Cs; Ha=Cl, Br, I).20,35-37 The m-K3BH4B12H12 is a monoclinic deformation and a two-fold superstructure of the cubic anti-perovskite type which is found for a first time among perovskites. The structural relation between the three polymorphs is shown in the Figure 3.



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(a)

(b)

(c)

Figure 3: Crystal structure of monoclinic (a), rhombohedral (b) and cubic (c) polymorphs of K3BH4B12H12. The relation of the rhombohedral unit cell (black) to the cubic one (magenta) is shown in (b). B, H and K atoms in red, grey and green, respectively.

The evolution of the volume/f.u. and lattice parameters with the temperature presented in the Figure 4 shows a step changes for the first transition while the second transition has continuous character. In agreement with unobserved hysteresis for the latter transition and shape of its DSC signal (Figure 2) the second transition is of 2nd order while the first transition is of the 1st order. Both transitions are accompanied by disordering of anions as concluded


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from the refined crystal structures and confirmed by DFT optimization of the ordered mpolymorph: The orientational disordering of BH4- accompanies the first transition and orientational disordering of B12H122- the second transition. The two phase transitions in K3BH4B12H12 resembles those in Na2B12H12, both in the closo-borane disordering and in the type of the transition.38

Figure 4: Variation of volume/f.u. (top left), lattice parameters (top right) and monoclinic angle β and rhombohedral angle α (bottom) with temperature for K3BH4B12H12 showing the two order/disorder phase transitions.

We will now discus the orientational disordering of B12H122- in more details. There are two sites with two different orientations for the closo-borane in the m-polymorph related by a cglide plane. Their relative orientation may be compared to the two orientations found in mNa2B12H12 and c1-Na2B12H12 where they are related by the n-glide plane of the s.g. P21/n and Pm-3n, resp.38,39 We have performed an analysis of all known crystal structures of alkali



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metal closo-boranes and found that these two orientations of the anion occur in all ordered structures and they are related by the rotation by ~45° around the C3 axis which is not a symmetry element of the icosahedral closo-borane. The two orientations therefore do not correspond to the reorientation dynamics conserving the crystal symmetry existing in alkali metal closo-boranes.10,11,40 When the c-glide plane disappears in K3BH4B12H12 during the first phase transition, the two closo-boranes reorient, become equivalent by lattice translation and the monoclinic superstructure disappears. We may find also BH4 in the structure of mK3BH4B12H12 in two orientations related by the c-glide plane. They correspond to the two orientations found in the disordered BH4 in both HT polymorphs. Potassium cations are located in all three polymorphs in a half of the available octahedral voids of bcc packing formed by both anions, small BH4- and big B12H122-, ignoring the difference between them (Figure S4). The octahedral (O) and tetrahedral (T) voids in bcc packing interpenetrate each other, and the cations of suitable size move easily from the Osites to neighbouring T-sites, which is at the origin of the positional disorder of K+ in both rand c-K3BH4B12H12 (Figure S4 b and c). This will be discussed in more details in the following chapter on the formability of anti-perovskites.

Formability of alkali metal halides/borohydrides closo-boranes - anti-perovskites: The formability of a perovskite structure is usually described by two parameters, the Goldschmidt tolerance factor t and the ionic radii ratio, i.e. the radii ratio rc/ra of the octahedral cation and of the anion (first Pauling rule).41,42 The same parameters may be used to validate also the anti-perovskite structures. While the tolerance factor is a pure geometrical consideration and does not depend on the charge of the ions, the first Pauling rule is defined for packing of anions with cations filling the interstitial sites. It means that when constructing the formability graph for anti-perovskite structures, such one which we are presenting for


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alkali metal (X) halides/borohydrides (B) closo-boranes (A) X3BA in the Figure 5, the ionic radii ratio must be calculated for cation X which is coordinated by octahedron (BH4)2(B12H12)4. As Pauling has not considered the case of mixed anion compounds, we have approximated the anion radius in our case as a weighted averaged of the radii of the two anions, i.e. borohydride and closo-borane.

Figure 5. Formability of closo-borane antiperovskites[14,33-35] as a function of Goldschmidt tolerance factor t and ratio of cation/anions ionic radii.43,44 Ionic radii of mono-atomic ions from ref. [44], radius of 2.03 Å for BH4- from [45] and 3.23 Å for B12H122- from [43].

The tolerance factor t for all formed anti-perovskite structures in the Figure 5 falls exactly between 0.9 – 1.0 where the ideal cubic structure is expected43, but the structures are rhombohedrally deformed which happens when t < 0.9, and is usually explained by too small A ion. In the case of closo-borane anion on the A site it was argued that this is due to the fact that the closo-borane is not spherical but icosahedral.43 Indeed at higher temperatures when the orientation of the closo-borane is disordered all structures become cubic.



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Concerning the ionic radii ratio the situation is similar. The octahedral coordination is expected for rc/ra between 0.414 and 0.592.42 Indeed our anti-perovskite structures fall within this limits with the exception of Na3IB12H12 where Na+ cations are disordered and are expected to be highly mobile.14 The K disorder in here presented K3BH4B12H12 is therefore unexpected and its origin is certainly in the non-spherical shape of the BH4- anion which plays a role when the cations are small. The two BH4- containing structures outside the octahedral limits contain Na+ and Li+, and crystalize with other structure types where the cation is located in tetrahedral voids (Figure 5) in agreement with the first Pauling rule. Both structures, Na3BH4B12H12 and (Li,Na)3BH4B12H12 contain also two orientations of closoborane and borohydride related by a glide plane as discussed above.14 The two structures are related to the anti-perovskite: Their anionic packing can be derived from the anionic bcc packing in anti-perovskite borohydrides closo-boranes by a crystallographic shear (Figure S5). In the following section we will discuss the results of solid state NMR study and dynamics in the structures of the monoclinic and rhombohedral polymorphs of K3BH4B12H12. The cubic polymorph is stable only at temperatures inaccessible to the NMR experiment.

NMR studies of anion dynamics: The results of the proton spin-lattice relaxation measurements are presented in Figure 6. This figure shows the 1H spin-lattice relaxation rates R1H measured at two resonance frequencies ω/2π as functions of the inverse temperature. As can be seen from this figure, R1H (T ) exhibits two frequency-dependent peaks (near 200 K and 390 K). Each of the peaks is typical of the spin-lattice relaxation due to motionmodulated dipole-dipole interaction between nuclear spins.46 Generally, a proton relaxation rate maximum is expected to occur at the temperature, at which the H jump rate τ -1(T)


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becomes nearly equal to ω. The observation of two R1H (T ) maxima indicates a coexistence of two types of H jump motion with different characteristic rates. For the faster process, the corresponding R1H (T ) peak occurs at the lower temperature. As typical of complex hydrides47, the two peaks can be attributed to different types of reorientation motion of complex anions. It should be noted that the positions of the relaxation rate peaks for K3(BH4)(B12H12) differ from the peak positions for both KBH4 and K2B12H12. In fact, the

R1H (T ) peak for KBH4 is observed near 120 K,48 and that for K2B12H12 is observed near 490 K.10 Thus, the mixed-anion compound K3(BH4)(B12H12) exhibits its own dynamics; this is consistent with the idea that the parameters of reorientation motion strongly depend on the local environment of the corresponding complex anions.49 Comparison with the results of the 11

B spin-lattice relaxation measurements (to be discussed below) suggests that the low-T

proton relaxation rate peak in K3(BH4)(B12H12) originates from reorientation motion of BH4 groups, and the high-T peak can be attributed to reorientations of B12H12 groups.



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Figure 6. Proton spin-lattice relaxation rates measured at 14 and 28 MHz for K3(BH4)(B12H12) as functions of the inverse temperature. The solid curves show the simultaneous fit of the two-peak model with Gaussian distributions of the activation energies to the data in the temperature range 160 – 548 K.

For parametrization of the proton spin-lattice relaxation data with two R1H (T ) peaks, we have used the model based on two coexisting motional processes with the H jump rates τ i−1 (i = 1, 2) assuming that i = 1 corresponds to the faster process (i.e., the one giving rise to the R1H peak at lower T). According to the standard theory of nuclear spin-lattice relaxation due to atomic motion, for each of the processes, in the limit of slow motion (ωτi >> 1), the relaxation rate R1Hi should be proportional to ω −2τ i−1 , and in the limit of fast motion (ωτi 350 K, the data points represent the results of a single-exponential approximation of the

11

B longitudinal relaxation, and at T < 350 K, they

represent the faster component of the two-exponential relaxation.

In order to distinguish between reorientations of the BH4 and B12H12 groups in the mixedanion compound, we may use measurements of the

11

B spin-lattice relaxation rate R1B . As

noted previously, the amplitude of the R1B (T ) peak due to B12H12 reorientations is dominated by strong fluctuations of the electric quadrupole interaction of

11

B nuclei;10 this amplitude

should be considerably higher than the amplitude of the R1B (T ) peak due to BH4 reorientations, since for the latter the quadrupole interaction is relatively unimportant. The



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results of our

11

B spin-lattice relaxation measurements for K3(BH4)(B12H12) are shown in

Figure 7. It should be noted that at T < 350 K, the recovery of the 11B nuclear magnetization deviates from a single-exponential behavior. The reasons for such a non-exponential relaxation may be related to non-zero electric quadrupole moment of

11

B nuclei and to the presence of several

well-separated inequivalent 11B nuclei relaxing with different rates.46 The relaxation curves at T < 350 K can be well approximated by sums of two exponential components. In the hightemperature region (T > 350 K), the observed exponential. The

11

11

B relaxation becomes nearly single-

B spin-lattice relaxation rates shown in Figure 7 correspond to the faster

exponential component at T < 350 K and to the single exponent at T > 350 K. Comparison of Figures 6 and 7 shows that the

11

B relaxation peaks are observed at nearly the same

temperatures as the corresponding 1H relaxation peaks. Thus, the low-temperature and hightemperature R1B (T ) peaks originate from the same fast and slow reorientation processes as the corresponding R1H (T ) peaks. The large amplitude of the high-temperature R1B (T ) peak clearly indicates that this peak originates from reorientations of [B12H12]2– anions. The minor low-temperature R1B (T ) peak can thus be attributed to reorientations of [BH4]– anions. The evolution of the 1H NMR spectrum measured at 28 MHz with temperature is shown in Figure S6. With increasing temperature, the width of the spectrum decreases; such a behavior reflects the motional narrowing.46 Indeed, at low temperatures, the 1H NMR line width ∆ωR is usually determined by static dipole-dipole interactions between nuclear spins. With increasing temperature, the atomic motion leads to averaging of the dipole-dipole interactions, and this ‘rigid-lattice’ line width starts to decrease when the H jump rate τ -1(T) becomes nearly equal to ∆ωR.46 For typical hydrides, this narrowing occurs at the temperature, at which τ -1(T) reaches values of ~105 s-1. In our case, there are at least two coexisting motional processes with different rates; therefore, some of the spectra look like superposition of two lines with


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different widths (see Figure S6). The temperature dependence of the full width at halfmaximum, ∆H, of the 1H NMR spectrum is shown in Figure 8. Although for complex shapes of the NMR spectra the value of ∆H does not provide a full description of the data, its temperature dependence reveals a number of interesting features.

50

K3(BH4)(B12H12)

40

∆H (kHz)

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30 20 10 0

0

100

200

300

400

T (K)

Figure 8. Temperature dependence of the width (full width at half-maximum) of the 1H NMR spectrum measured at 28 MHz for K3(BH4)(B12H12).

As can be seen from Figure 8, the temperature dependence of ∆H exhibits two large ‘steps’, near 80 K and near 250 K. Each of the ‘steps’ can be attributed to a certain type of H jump motion. It should be noted that, for a particular type of motion, the ∆H(T) ‘step’ should be observed at a considerably lower temperature than the appropriate R1H (T ) peak, since the former corresponds to the jump rate scale of ~105 s-1, and the latter corresponds to the scale of 108 s-1. Having this in mind, the low-temperature ∆H(T) ‘step’ can be attributed to the faster jump process (BH4 reorientations), and the high-temperature one should be associated with the slower process (B12H12 reorientations). The minor ∆H(T) ‘step’ near 320 K (see Figure 8)



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may be related to the residual K2B12H12 phase, since for this phase the line narrowing was found to occur in the same temperature range.10 It should also be noted that heating the sample above 600 K results in the appearance of the very narrow component in the 1H NMR spectrum; this narrow component is found to remain after cooling the sample to room temperature. As in the case of Li2B12H12, such a behavior may indicate the onset of slow decomposition.38 Because of this irreversibility, we have not performed any systematic NMR measurements above 595 K.

Anion dynamics and cation mobility: The mobility of K+ cation in all three polymorphs has been characterized by measuring the ionic conductivity and was modelled by topology analysis of conduction paths. K3BH4B12H12 is a fast ionic conductor only at higher temperatures, and especially in its cubic modification. However, the existence of three polymorphs distinguished by increasing degree of orientation disorder of two different complex anions allows us to discuss the effect of anion dynamics on cation mobility. The conductivity (Figure 9) of as milled sample is measurable by EIS starting from ~380 K where it reaches the value of 2.10-6 S cm-1. The conductivity follows the Arrhenius temperature dependence with smaller slope and higher conductivity on heating than on cooling of the first cycle. This is certainly an effect of the microstructure of the ball milled sample as it was demonstrated for various closo-boranes.52 When K3BH4B12H12 transforms from the monoclinic to the rhombohedral polymorph the orientation of the BH4- anion becomes disordered, and its dynamics increases. The B12H122- anion stays ordered as seen by SR-XPD. On the basis of the available NMR data, we cannot exclude a possibility that the transition from the monoclinic to the rhombohedral polymorph is also accompanied by a certain increase in the reorientational jump rate of B12H12 groups, although B12H122– anions


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remain ordered. However, any numerical estimates of the jump rates for each of the reorientational processes in the rhombohedral phase are hardly possible, since in this temperature range both τ1-1 and τ2-1 are much higher than the resonance frequency ω.

Figure 9: Variation of K-ionic conductivity with temperature for K3BH4B12H12 showing the first cycle of heating and cooling.

As no particular change of the conductivity behaviour is observed we may conclude that the disordering and increased dynamics of BH4- anion does not promote K+ mobility. On further heating the conductivity starts to gain in value much faster than what should follow from the Arrhenius behaviour, and this increase is understood as due to increasing orientation disorder of B12H122- anion. In the same time the rhombohedral distortion of the cubic anti-perovskite structure is decreasing with temperature till it is unmeasurable by SR-XPD above 680 K and the crystal becomes cubic. During cooling down from this temperature, the conductivity vs. T has more regular form than that measured on heating, and corresponds to Arrhenius dependency without microstructure effect, because the sample is now annealed. Very close to 680 K the slope of the dependency is smaller and corresponds to lower energy barriers of K+



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jumps in the cubic phase. When the cubic phase deforms rhombohedraly the disorder of B12H122- anion is decreasing and the slope is increasing without any visible change at the transition to the monoclinic phase triggered by the ordering of BH4- anion. The topology analysis of the conduction paths confirms the existence of channels formed by T-T hops which percolate creating so 3D conduction pathways. The radius of the T-T channels increases from 2.57 Å and 2.45 Å in the m- and r-polymorphs, respectively, to the value of 2.72 Å in the c-polymorph which is, however, still lower than the threshold radius of conducting channel 2.90 Å. The increase of ionic conductivity in c-K3BH4B12H12 must be therefore seen in the increased dynamics of B12H122- anion. However, we cannot speak about the “paddle-wheel mechanism” which refers to the situation when each elementary reorientational anion jump gives rise to a cation jump. This implies that the anion and cation jump rates should be close to each other. Such a situation has been observed in LiLa(BH4)3Cl.7 For K3(BH4)(B12H12), as well as for various closo-boranes, the reorientational anion jump rates are much higher than the cation jump rates leading to translational diffusion. Therefore, we can state that the fast rotational anion motion facilitates cation diffusion, but without direct reference to the “paddle-wheel” mechanism. The dynamics of BH4- anion has no effect on the K+ mobility which is similar to the mobility of Na+ in o-Na3BH4B12H12 where the cation is mobile only in the pathways containing B12H122- anions with the radius greater than the threshold radius of 2.66 Å.14 Contrary to K3BH4B12H12 the closo-anion stays ordered in Na3BH4B12H12 as seen by SR-XPD. We cannot comment on the reorientation motion of the closo-anion in Na3BH4B12H12 as neither experimental data nor calculation results are currently available.

Computational studies:


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Further insight into the factors promoting ionic mobility in the mixed anion boranes were obtained by a number of ab-initio calculations in the framework of density functional theory (DFT). In particular, this allowed us to investigate (i) the factors stabilizing the three polymorphs derived from the anti-perovskite structure, and (ii) the role of homo-polar H-H contacts. In order to trace the first phase transition, we have optimized atomic positions and monoclinic unit cell parameters for series of increasing unit cell volumes. The symmetry was constrained during these calculations. The volume dependence of lattice parameters of the monoclinic structure is shown in the left panel of Figure S7. With increasing volume/f.u., the lattice parameter a0 has the lowest slope. At volume 330 Å3 it equals to b0. Above 350 Å3 per formula unit monoclinic structure becomes unstable. With increasing volume, the monoclinic angle β decreases toward 90°. When the symmetry is relaxed both the lattice parameters and unit cell angles deviate from monotonous change observed for the symmetry constrained calculations. While such result does not provide direct insight into the first phase transition it indicates that the monoclinic – rhombohedral structural change is related to the cation sublattice distortion primarily occurring in the octahedral coordination of BH4- anion. This distortion is related to non-spherical anion reorientation as already discussed above. The optimized structure of the monoclinic polymorphs at volume/f.u. of 330 Å3 (experimental volume at 293 K) with fixed symmetry contains the shortest homo-polar H-H contacts concentrated around 2.1 Å, known as Switendick limit53. These contacts connect both anions into a 3D framework shown in the Figure S8. Two types of contact are present: BH4 – B12H12 and B12H12 – B12H12, and two factors are related to H-H separation: distortion of cation sublattice and orientation of anions within potassium coordination polyhedra. With increasing volume, the separation between two different anions increases faster than between two B12H122- anions. In the symmetry constrained calculations the orientation of anions is fixed by



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the symmetry, however relaxation of the symmetry constraints shows abrupt change in anion – anion separation: BH4 – B12H12 separation increases abruptly and shortest H-H distance in B12H12 – B12H12 separation returns to 2.15 Å. This is related to change of BH4 and B12H12 orientation. In the cubic phase shortest H-H distance remains above 2.25 Å, and occur in BH4 – B12H12 separation. In order to gain insight into anion dynamics, barriers for BH4- and B12H122- anions rotation were calculated with Nudged Elastic Band method. Only two polymorphs were considered: LT monoclinic and HT cubic phases. For the later a static structure based on anti-perovskite was used with the unit cell constrained to one of possible configuration minima with frozen anion orientation. For BH4- anion rotations around C2 and C3 axes were selected, for B12H122anion four independent axes related to 5-fold symmetry were considered; only the lowest barrier is reported. In the monoclinic phase and the volume/f.u. of 280.8 Å3 corresponding to the ground state these barriers are as high as 500 meV (BH4) and 1600 meV (B12H12), see Figure 10. This indicates that anions are practically immobile at low temperatures. In the monoclinic phase at volume/f.u. of 320 Å3 (200 K) the rotation of BH4 is related to a barrier of 250 meV, while in the cubic phase with volume/f.u. of 350 Å3 (550 K) this barrier is only 100 meV. At volume close to the experimental rhombohedral-cubic transition at 680 K the local rotation axes of BH4 are not representative for rotation pathway, and the corrugation of the potential for BH4 flipping is 25 meV. Rotation barriers for B12H122- anion in the cubic phase also strongly depend on the volume, see Figure 10. At volume/f.u. corresponding to the experimental stability limit of the cubic phase this barrier is 240 meV, while it increases to 400 meV at the stability limit of the rhombohedral phase. In the monoclinic phase flipping of B12H12 requires overcoming barrier larger than 1600 meV that excludes rotational motion of this anion. The rotational barriers for


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B12H122- stays at all temperatures approx. 2.5 times higher than those for BH4-, in agreement with NMR results.

Figure 10: Top: Barriers for B12H12 rotation as a function of volume/f.u. The insert presents the barrier height with respect to volume/f.u. Bottom: Barriers for BH4 rotation around C3 (left), and C2 (right) axes. Dashed lines are for LT monoclinic phase, solid lines are for HT cubic phase.



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The calculated barriers are in reasonable agreement with NMR data for volumes corresponding to monoclinic/rhombohedral phases (240 meV vs 236 meV for BH4 rotation or 400meV vs 594 meV for B12H12 anion). In the cubic phase the model does not account for the cation disorder that might be a reason for overestimation of rotation barriers in this phase. The static calculations were complemented with molecular dynamics calculations. This approach allows to trace anion dynamics on the time-scale ~3ps without any assumptions with respect to rotation pathways. In the monoclinic phase there is no anion dynamics observed, except for the case of expanded structure with volume/ f.u. of 320 Å3, where disorder/rotation of BH4- anion is present (Figure 11). No B12H122- anion flipping is observed on the time scale of 3 ps. On this time scale orientation of BH4- in the expanded lattice does correspond to C2 axis of rotation, and is at the origin of the cation sub-lattice expansion along rotation axis. In the cubic phase BH4- anion is disordered and the orientation disorder of this anion is accompanied by large vibration of central boron atom, see Figure 11. The amplitude of potassium vibrations is significantly larger than for monoclinic phase which is experimentally observed as disorder of potassium position in rhombohedral and cubic phases. In the cubic phase also B12H122- anion is rotationally mobile as it is indicated by the low energy barrier calculated for this anion rotation. Disorder on cation sites and anion reorientation promoted by lattice expansion have been recently confirmed by molecular dynamics calculations as critical for high ionic conduction. 54,55


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Figure 11: Snapshots of atomic positions in K3BH4B12H12 from MD calculations collected for 3 ps. The snapshots present superimposed positions of single anions and the nearest cations. Green spheres are for potassium, red for boron and grey ones are for hydrogen. Top: coordination of BH4- anion in the monoclinic phase is shown in the left, that in the monoclinic phase expanded to the volume/f.u. of 320 Å3 in the center, and that in the cubic phase is shown on the right. Bottom: coordination of the B12H122- anion in the monoclinic (left), expanded monoclinic (middle) and cubic (right) phase.

Conclusions Combined X-ray powder diffraction, solid state NMR, ab initio calculations and Electrochemical Impedance Spectroscopy analyses confirm the increasing orientational



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disorder of two complex anions, BH4- and B12H122-, in K3BH4B12H12. First the reorientational jump rate of the borohydride anion increases, which is related to the cation sub-lattice distortion, and this anion becomes disordered at 565 K which leads to the 1st order phase transition and an increase of the crystal symmetry from monoclinic to rhombohedral. This process is related to expansion of the crystal lattice. Further lattice expansion frees the closoborane anion, and the rhombohedral distortion is continuously disappearing leading to the 2nd order phase transition into a cubic anti-perovskite phase at 680 K. The first phase transition is related to the repulsive homopolar H-H contacts between BH4and B12H122- anions which are released at bigger cell volumes, and the orientation of BH4anion becomes disordered. The second phase transition is related to the increasing dynamics and orientation disorder of the B12H122- anion at bigger cell volumes. While the dynamics of smaller BH4- anion does not have any measurable effect on K+ mobility, the dynamics and orientation disorder of bigger B12H122- is promoting the K+ mobility.

Supporting Information Rietveld plots, additional structural drawings, 1H NMR spectra, calculated lattice expansion

Acknowledgements This work was supported by the Swiss National Science Foundation, and in part by the Russian Federal Agency of Scientific Organizations under Program “Spin” No. 01201463330 and the Russian Foundation for Basic Research under Grant No. 15-03-01114. Support by NCN project 2015/17/B/ST3/02478, Poland and CPU allocation at PL-Grid are kindly acknowledged. The authors acknowledge the Swiss-Norwegian Beamlines of ESRF and the Materials Science beamline of the SLS for the allocation of beamtime and excellent support


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with the data collection. The authors thank Prof. Hans Hagemann for access to DSC equipment



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ToC Graphics


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Figure 1 left 249x200mm (150 x 150 DPI)



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Figure 1 right 257x197mm (150 x 150 DPI)


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Figure 2 634x327mm (149 x 149 DPI)



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Figure 3 a 437x374mm (96 x 96 DPI)


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Figure 3 b 437x374mm (96 x 96 DPI)



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Figure 3 c 374x374mm (96 x 96 DPI)


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Figure 4 bottom 55x39mm (300 x 300 DPI)



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Figure 4 top left 55x39mm (300 x 300 DPI)


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Figure 4 top right 55x39mm (300 x 300 DPI)



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Figure 5 88x61mm (300 x 300 DPI)


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Figure 6 281x217mm (149 x 149 DPI)



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Figure 7 281x217mm (149 x 149 DPI)


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Figure 8 61x47mm (300 x 300 DPI)



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Figure 9 277x273mm (150 x 150 DPI)


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Figure 10 bottom left 56x40mm (300 x 300 DPI)



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Figure 10 bottom right 56x40mm (300 x 300 DPI)


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Figure 10 top 42x22mm (300 x 300 DPI)



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Figure 10 top insert 28x20mm (300 x 300 DPI)


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Figure 11 top left 83x86mm (300 x 300 DPI)



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Figure 11 top middle 119x177mm (300 x 300 DPI)


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Figure 11 top right 88x98mm (300 x 300 DPI)



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Figure 11 bottom left 80x81mm (300 x 300 DPI)


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Figure 11 bottom right 80x80mm (300 x 300 DPI)


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Anion Disorder in K - ACS Publications - American Chemical

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