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9026

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Potassium-rich antiperovskites K3HTe and K3FTe
and their structural relation to lithium and sodium
counterparts†
Koji Okada, a Susumu Fujii, b,c Cédric Tassel,*a Shenghan Gao,aHiroki Ubukata, a Wenli Pan,d Kentaro Yamamoto, d,e Yoshiharu Uchimoto,
Akihide Kuwabara *b and Hiroshi Kageyama *adUnlike perovskite oxides, antiperovskites M3HCh and M3FCh (M = Li, Na; Ch = S, Se, Te) mostly retain theirideal cubic structure over a wide range of compositions owing to anionic size ﬂexibility and low-energy
phonon modes that promote their ionic conductivity. In this study, we show the synthesis of potassiumbased antiperovskites K3HTe and K3FTe and discuss the structural features in comparison with lithium andsodium analogues. It is shown experimentally and theoretically that both compounds maintain a cubic
symmetry and can be prepared at ambient pressure, in contrast to most of the reported M3HCh and
M3FCh which require high pressure synthesis. A systematic comparison of a series of cubic M3HTe andReceived 5th April 2023,
Accepted 25th May 2023

M3FTe (M = Li, Na, K) revealed that telluride anions contract in the order of K, Na, Li, with a pronounced

DOI: 10.1039/d3dt01039b

contraction in the Li system. This result can be understood in terms of the diﬀerence in charge density ofalkali metal ions as well as the size ﬂexibility of Ch anions, contributing to the stability of the cubic

rsc.li/daltonsymmetry.

Introduction
Antiperovskites, represented by the chemical formula X3BA (A,B: anions, X: cations), exhibit diverse physical and chemical
properties owing to a versatile array of chemical compositions(Fig. 1).1–9 For example, lithium- and sodium-rich antiperovskites such as M3O(Cl1−xBrx) (M = Li, Na) exhibit excellent
lithium/sodium ion conductivity that could be used in solid
electrolytes for high energy density batteries.1–3 Recently, we
have synthesized antiperovskites M3HCh (M = Li, Na; Ch = S,
Se, Te) with H anions at the B-site using high pressure reactions, and observed that the size flexibility of the H− anionaDepartment of Energy and Hydrocarbon Chemistry, Graduate School of Engineering,
Kyoto University, Nishikyo-ku, Kyoto 615-8510, Japanb
Nanostructures Research Laboratory, Japan Fine Ceramics Center,
Nagoya 456-8587, Japanc
Division of Materials and Manufacturing Science, Graduate School of Engineering,Osaka University, Osaka 565-0871, Japand
Graduate School of Human and Environment Studies, Kyoto University, Sakyo-ku,
Kyoto 606-8501, Japane
Faculty of Engineering, Nara Women’s University, Kitauoyanishimachi,
Nara 630-8506, Japan† Electronic supplementary information (ESI) available: Laboratory X-ray diﬀraction patterns of K3HTe and K3FTe, size-flexibility of soft anions in other compounds, migration barriers in K3HTe and K3FTe, and measured ionic conductionof pristine and iodine substituted K3HTe (PDF). See DOI: https://doi.org/10.1039/
d3dt01039b

9026 | Dalton Trans., 2023, 52, 9026–9031

ˉm) over a wide comstabilizes the ideal cubic structure (Pm−3positional space, with the exception of Na3HS.10 These compounds show a high ionic conductivity, which can be attributed to the low energy phonon modes associated with therotation of HM6 octahedra, lowering the migration barrier for
lithium and sodium cations.10
Subsequently, antiperovskites M3FCh (M = Li, Na; Ch = S,
Se, Te) were synthesized mainly using the high pressure technique.11 Despite the use of the hard F anion instead of the soft
H anion, M3FCh also adopts the cubic structure with theFig. 1 Crystal structure of alkali metal rich antiperovskite M3BTe (M =Li, Na, K; B = H, F). The newly synthesized K3HTe and K3FTe adopt the
cubic symmetry (Pm−3̄m). The B-site anion (H or F) (blue) occupies theoctahedral center formed by K cations (green) and the A-site telluride
anion (yellow) occupies the cuboctahedral site.

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Dalton Transactions
exception of Na3FS, and thus comparable ionic conduction is
obtained due to the associated low energy FM6 octahedral
rotation modes. These results, together with first-principles
calculations, imply that highly polarizable Ch anions play amajor role in stabilizing the cubic symmetry. Furthermore, we
found a correlation between the soft phonon modes, the tolerance factor,12 and the activation energy for the mobile cations.
This work aims to expand the available compositional
space of M3HCh and M3FCh by including potassium insteadof Li and Na. We have successfully synthesized K3HTe andK3FTe under both high pressure and ambient pressure conditions. The preparation of a series of alkali metal-rich antiperovskites allows us to compare them systematically together
with first-principles calculations. It is found that in M3BCh (M= Li, Na, K; B = H, F; Ch = S, Se, Te), not only the size-flexibilityof the Ch-site anions but also the charge density of the M-site
cations has an impact on their structures.

Experimental
Polycrystalline samples of K3HTe and K3FTe were initially synthesized by a solid-state reaction under high pressure using
washed KH (Sigma-Aldrich, 30 wt% dispersion mineral oil)with hexane and K2Te (Kojundo, 99%), and KF (Wako, 99.0%)
and K2Te as precursors, respectively. K3FTe was obtained witha stoichiometric ratio (i.e., KF : K2Te = 1 : 1), while the synthesisof K3HTe requires a hydrogen-rich ratio of KH : K2Te = 2 : 1, asis the case with other oxyhydrides synthesized under pressure
including SrCrO2H,13 BaScO2H,14 BaVO3−xHx (0.3 ≤ x ≤ 0.8)15
and LaSrMnO3.3H0.7.16 The starting materials were thoroughly
ground and pressed into a pellet, which was inserted into aboron nitride (BN) sleeve and sealed at both ends with BN
caps. The assembly was then loaded into a graphite tube
heater and sealed in a pyrophyllite cube, serving as a pressure
medium. All the above procedures were conducted in a glovebox filled with N2 (mBRAUN, Unilab-2000) due to the instability of the precursors and the products towards air and humidity. The cubic cells were pressed under 5 GPa, and then heatedat 400 °C for 10 min for K3HTe and at 750 °C for 10 min for
K3FTe. After maintaining the temperature for 1 hour, thesamples were cooled to room temperature in 5 min before thepressure was released. The recovered cells were placed back in
the glovebox and the obtained polycrystalline samples werecollected. We also attempted to synthesize both compounds
under ambient pressure; pellets of the mixture of starting
materials were vacuum sealed into Pyrex tubes and heated at
330 °C for 14 hours for K3HTe and at 450 °C for 14 hours for
K3FTe. Iodine-substituted K3HTe was synthesized using a
mixture of KH, K2Te and KI with a hydrogen-rich ratio of
2 : 0.9 : 0.1 under the same conditions as those for pristine
K3HTe.
High-resolution synchrotron X-ray diﬀraction (SXRD)
measurements were carried out at room temperature with awavelength of λ = 0.42 Å at the BL02B2 beamline in SPring-8(Japan), equipped with MYTHEN solid-state detectors. The

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K3HTe and K3FTe powder samples were sealed in borosilicate
capillaries. Le Bail and Rietveld analyses of SXRD data werecarried out using JANA2006 software,17 while the crystal structures were visualized using VESTA.18
Ionic conductivities of cold-pressed pellets of K3HTe andI-substituted K3HTe were measured by electrochemical impedance spectroscopy (EIS) with a constant voltage of 10 mV in
the frequency range from 1 MHz to 0.1 Hz using an ECS
ModuLab potentiostat/galvanostat. Around 0.2 g of the powder
specimen was placed between two stainless-steel rods as an
ion-blocking electrode in a custom-made Swagelok cell andpressed into a 10 mm diameter pellet using a hydraulic press
at 360 MPa (thickness: 1–1.5 mm). The temperature was varied
from 25 °C to 100 °C. Data at each temperature were collected
after being held for 115 min to ensure temperature stabilization.
Ab initio calculations on K3HTe, K3FTe, KH, KF and K2Te
were performed under 0 and 5 GPa using the plane-wave basis
projector augmented wave (PAW) method19 implemented inthe Vienna Ab initio Simulation Package (VASP).20,21 The generalized gradient approximation in the form of PBEsol22 was
employed. The valence configurations in the PAW potentials
used in this study are as follows: [3s2 3p6 4s1] for K, [1s1] for H,[2s2 2p5] for F, and [5s2 5p4] for Te. The remaining electrons
were treated as frozen core electrons. The plane-wave energy
cutoﬀ was set to 650 eV. The first Brillouin zone was sampledusing Γ-centered k-point grids with a spacing of 0.2 Å−1. The
total energy convergence was set to 1.0 × 10−6 eV per atom,
and atomic positions and lattice constants were relaxed until
the residual forces of atoms were less than 1.0 × 10−3 eV Å−1.
Phonon band structures and vibrational free energies underharmonic approximation were calculated using the finite displacement method23 implemented in Phonopy.24 The displacement of atoms from their stationary positions to obtainsecond-order force constants was set to 0.01 Å. A 2 × 2 × 2
supercell with respect to the conventional unit cell was used to
avoid the self-interaction between the displaced atoms. Nonanalytical term correction25 was adopted using the Borneﬀective charge tensors and dielectric constants calculatedusing density functional perturbation theory implemented in
VASP.20,21
The nudged elastic band (NEB) method26 was used to calculate the energy barriers of K+ migration via vacancies and interstitial defects (dumbbell) in K3HTe and K3FTe. Charged supercells with the dimensions of 3 × 3 × 3 were used. The first
Brillouin zone was sampled with one k-point (0.25, 0.25, 0.25)
due to the large size of supercells. For NEB calculations, thetotal energy and force convergence were set to 1.0 × 10−6 eV
per cell and 2.0 × 10−2 eV Å−1, respectively. Note that all thecomputational conditions employed here are consistent with
our previous studies.10,11

Results and discussion
As shown in Fig. S1a,† the XRD pattern of K3HTe synthesized
at 400 °C under 5 GPa is similar to that of the ideal antiperovs-

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Paperˉm).10 Several additional reflections werekite Na3HTe (Pm−3assigned to unreacted KH, while the remaining small peaks
could not be assigned to any known phases, nor to a superstructure as found in Na3HS and Na3FS with coherent octahedral rotations.10,11 The lattice parameter of K3HTe, a =5.35927(2) Å, is longer than that of Na3HTe (a = 4.76349(2)Å),10 reflecting the diﬀerence in ionic radius between Na and K(Na+: 1.02 Å vs. K+: 1.38 Å).27 Similarly, the XRD pattern of
K3FTe was indexed in the ideal cubic structure, along with KF
and unknown impurities (Fig. S1b†). The lattice constant a =5.25451(1) Å is longer than that of the Na counterpart (a =4.70315(1) Å).11
Rietveld refinement of the SXRD data for K3HTe assumingˉm) readily converged
the cubic antiperovskite structure (Pm−3to GOF = 3.94, Rp = 5.44% and Rwp = 7.56% (Fig. 2a), withreasonable isotropic atomic displacement parameter, Uiso,
values of 0.0385(2) Å2 and 0.0239(1) Å2 for K and Te, respectively. Refining occupancy factors, g, at K resulted in 0.988(1).
Note that the Uiso of H and g of H and Te are not refined.
Likewise, the Rietveld analysis of K3FTe converged successfully, yielding GOF = 5.52, Rp = 5.33% and Rwp = 7.31%, Uiso of

Fig. 2 Rietveld reﬁnement of SXRD data of (a) K3HTe and (b) K3FTe. The
red circles, the green solid line, and the blue solid line represent theobserved, calculated, and diﬀerence intensities, respectively. The upper
ticks indicate the calculated Bragg reﬂections for (a) K3HTe and (b)K3FTe, while the lower ticks for (a) KH and (b) KF. The unknown peaks
are removed from the reﬁnement.

9028 | Dalton Trans., 2023, 52, 9026–9031

Dalton Transactions
0.0235(2) Å2 for K, 0.0155(9) Å2 for F and 0.0165(1) Å2 for Te(Fig. 2b), and the occupancy of 0.990(1) for K and 0.960(5) for
F. Thus, unless otherwise stated, we hereafter use the stoichiometric compositions of K3HTe and K3FTe.
Most of the alkali metal rich antiperovskites M3HCh and
M3FCh (M = Li, Na) reported so far have been synthesized athigh pressure,10,11 with the exception of Na3HTe and Na3FTe(unpublished data). First-principles calculations showed thatthe ideal cubic structure is dynamically stable at high pressure
for most Na- and Li-based compounds, but at ambientpressure, many of them showed imaginary phonon modes
appearing at the M and R points relevant to octahedral
rotation. Here, we calculated the phonon band structures of
K3HTe and K3FTe using the cubic structure at 0 and 5 GPa andfound no imaginary phonon modes even under ambientpressure (Fig. 3a and b). The atom projected phonon densityof states (DOS) for K3HTe indicates that the light H ion is
responsible for high frequencies, whereas the heavy K and Te
ions are for low frequencies. In K3FTe, this tendency is lesspronounced. In addition, both compounds are lower in energy
at ambient pressure than the starting materials K2Te and KH/
KF, suggesting that they are thermodynamically stable phases(Fig. 3c and d). These results led us to synthesize K3HTe andK3FTe under ambient pressure, and we indeed obtained the
XRD patterns with identical lattice constants for both cases(Fig. S2 and S3†).
The discovery of K3HTe and K3FTe oﬀers an opportunity tosystematically compare the impact of the cations on stabiliz-

Fig. 3 Phonon band structures and partial phonon DOS of each ion of
the cubic antiperovskites (a) K3HTe and (b) K3FTe at 0 GPa. The absenceof imaginary phonon frequencies at the M and R points related to octahedral tilting, as found in, e.g., Na3HS and Na3FS,10,11 means that bothcompounds are dynamically stable. The Gibbs free energy ΔG (ΔG =ΔUinternal + PΔV − ΔFphonon, ΔFphonon = ΔEZPE − TΔSphonon) of (c) K3HTe
relative to that of KH + K2Te and (d) K3FTe relative to that of KF + K2Te at
0 GPa, all calculated at ambient pressure.

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ation in the two sets of cubic antiperovskites, M3HTe and
M3FTe (M = Li, Na, K). Fig. 4a shows the lattice parameters of
cubic M3HTe and M3FTe as a function of Shannon ionic radiiof the alkali metal cations, rM.27 In both systems, the lattice
expands linearly with increasing rM, but the slope is obviously
diﬀerent, with a larger value for M3HTe, which suggests that
this phenomenon is related to the size flexibility of hydride
anions (vs. F−).10,28 To obtain further insights into the structural features, the obtained lattice constants were used to estimate the ionic radius of H− anions, rH, where rH = a/2 − rM (rLi
= 0.76 Å, rNa = 1.02 Å, rK = 1.38 Å), as employed previously(Fig. 4b).10 The expanded H− anion in Na3HTe compared tothat in K3HTe looks reasonable because the smaller ionicradius of Na+ (vs. K+) is compensated by the larger H− anion.
Following this trend, the H− radius of Li3HTe is expected to belarger than that of Na3HTe. However, the opposite result, inwhich H− contracts, was obtained, which implies that thehydride anion is not solely responsible for stabilizing andmaintaining the cubic structure.
We hence took a theoretical approach to address this issue.
We estimated the Bader volume29 for each ion using therelaxed structures at ambient pressure by first-principles calculations. In terms of the H− volume, its M dependence with acontraction at Li3HTe appears to be reproduced, as shown in
Fig. 5. However, similar dependence is also found in the F−
volume both qualitatively and quantitatively, with a smaller F−
volume in Li3FTe than in Na3FTe. Instead, a more pronounced
M-dependence is seen in the tellurium anion, where the Teanion decreases its size in the order of K, Na, and Li.
The large variation in the size of the Te anion as a functionof the alkali metal cations or unexpected contractions of the
B-site anions in Li systems is likely related to the surface
charge density of the alkali metal which, when increasingfrom K to Na and Li, leads to stiﬀer anions. We have noticed
similar behaviour in lattice constants or anionic sizes inbinary compounds, such as rock-salt MH30–35 and antifluorite
M2Te36–39 (Fig. S4†). Thus, the charge density of the M-site
cation seems to predominantly modify the size of the Te anion
to compensate for the size mismatch and preserve the cubic

Fig. 4 (a) The lattice parameters of (blue) M3HTe and (red) M3FTe (M =Li, Na, K).10,11 (b) The ionic radius of H− and F−, rH and rF, determinedfrom the lattice constant, where rH = (a − 2rM)/2 and rF = (a − 2rM)/2.
The ﬁxed ionic radii of 0.76 Å, 1.02 Å and 1.38 Å were used for Li, Na andK, respectively.27 Error bars are within the circles in both ﬁgures.

This journal is © The Royal Society of Chemistry 2023

Paper

Fig. 5 The Bader volume of the alkali metal cation (green), H−/F− anion(blue), and Te2− anion (yellow) in M3HTe (circles) and M3FTe (triangles).

symmetry. Bearing in mind that Te has a high compressibility,
the exceptionally small Te anion in Li3HTe is consistent withthe fact that it can only be synthesized under high pressure.
Since M3HCh and M3FCh (M = Li, Na; Ch = S, Se, Te)exhibit excellent lithium or sodium ion conductivity,10,11 we
performed nudged elastic band (NEB) calculations to estimate
the migration energy barriers of K+ transport in K3HTe andK3FTe. As seen in Fig. 6, their energy barriers are comparable
to those of Li-rich and Na-rich antiperovskites, as low as
265 meV and 352 meV, respectively, for the vacancy mechanism, and 76 meV and 102 meV for the interstitial dumbbell
mechanism. The low migration energy barriers in K-rich antiperovskites indicate their potential as ionic conductors, once
vacancies or interstitial defects are introduced by the aliovalent
substitution approach, for example. K3HTe has a lower energy
barrier than K3FTe, which is partly due to the softer phonon

Fig. 6 Migration energy barriers of (circles) M3HTe and (triangles)
M3FTe (where M = Li, Na, K). The results of vacancy and interstitial
dumbbell mechanisms are shown in red and blue, respectively. The
schematics on the right side show the migration pathways of M+ ionsaround the HM6/FM6 octahedron. The migration energy barriers of Liand Na-rich antiperovskites are taken from ref. 10 and 11.

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mode relevant to HK6 octahedral rotation (Fig. S5†). Attempts
to measure the K+ ion conductivity of pristine and I-doped
K3HTe resulted in high resistances (at least >106 Ω), which precluded proper estimation of bulk conductivities and activationenergies (Fig. S6†). The large resistances may be attributed tothe extremely high sensitivity of the sample surface to trace
amounts of oxygen and water; thus, there is considerable room
to adjust synthetic conditions in the future.

Conclusions
We prepared two potassium-rich cubic K3HTe and K3FTe
under ambient conditions, unlike the reported sodium- andlithium-rich antiperovskites M3HCh and M3FCh (M = Li, Na;
Ch = S, Se, Te) stabilized under high pressure conditions. The
systematic comparison of the two sets of M3HTe and M3FTecompounds, using first-principles calculations, revealed theunexpected contraction of B-site anions in Li systems andalkali metal-dependent size variation in Te anions. In perovskite oxides, the crystal structure is mainly controlled by octahedral rotations in order to compensate for the size mismatch
between A, B, and O ions; thus, the cubic phase is stable only
in a narrow compositional space, which could be a problem
for some applications such as ionic conductivity. In contrast,
the cubic structure is stable over a wide compositional spacein M3HCh and M3FCh. Depending on the surface charge
density of the M-site cations, the Ch-site anions flexibly
change their size to compensate for the size mismatch
between the BM6 octahedra and the Ch-site anion to maintainthe cubic symmetry. The alkali metal-dependent size eﬀects ofother ions obtained in this study provide a new dimension in
structural control, and thus control of physical and chemical
properties, not limited to antiperovskites.

Author contributions
K. O. and S. F. contributed equally to this work. K. O. carriedout all the synthetic work and was helped by S. G. K. O.,
H. U. and C. T. contributed to the refinement of XRD
data. S. F. and A. K. performed theoretical calculations. P. W.,
K. Y. and Y. U. measured the ionic conductivities. H. K.
designed and coordinated this study, and contributed to allmeasurements and analyses.

Conﬂicts of interest
There are no conflicts to declare.

Acknowledgements
This work was supported by a Grant-in-Aid for Scientific
Research on Innovative Areas “Mixed Anion” (JP16H06438,
JP16H06439, and JP16H06440), a Grant-in-Aid for Specially

9030 | Dalton Trans., 2023, 52, 9026–9031

Dalton Transactions
Promoted Research “Hydrogen Ion Ceramics” (JP22H04914), a
Grant-in-Aid for Scientific Research (JP22H01777, andJP23K13544), and JSPS Core-to-Core Program (A) Advanced
Research Networks (JPJSCCA20200004).

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