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## Creator

Jie Chen, [Alexei A. Belik](https://orcid.org/0000-0001-9031-2355), [Kazunari Yamaura](https://orcid.org/0000-0003-0390-8244), Jianshi Zhou

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This document is the Accepted Manuscript version of a Published Work that appeared in final form in Chemistry of Materials, copyright © 2024 American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see https://doi.org/10.1021/acs.chemmater.4c00568.[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

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[New Structural Distortions in Osmate Perovskite Na1–xKxOsO3 Synthesized under High Pressure](https://mdr.nims.go.jp/datasets/45840ef2-d481-4542-8e49-1652223cf74a)

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New structural distortions in the osmate perovskite Na1-xKxOsO3 synthesized under high pressureJie Chen1, Alexei A. Belik2, Kazunari Yamaura,2,3, and J.-S. Zhou 1*1 Materials Science and Engineering Program, Department of  Mechanical Engineering, University of Texas at Austin, Austin, Texas 78712, USA2 Research Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan3 Graduate School of Chemical Sciences and Engineering, Hokkaido University, North 10 West 8, Kita-ku, Sapporo, Hokkaido 060-0810, JapanAbstract Most ABO3 oxides crystalize in the perovskite structure. In responding to the degree of bonding mismatch of A-O versus B-O in the structure, the perovskite can adopt a total of 15 tilting systems of BO6 octahedra. Depending on the charge configurations, i.e. A3+B3+O3, A2+B4+O3, and A1+B5+O3, these complex oxides undergo distinct pathways within the tilting systems as the bond-length mismatch is changed by either the chemical substitution, or temperature or pressure. The report of orthorhombic NaOsO3 and the newly synthesized nearly cubic KOsO3 lead to an opportunity for studying the structural distortions in A1+B5+O3 which has only been studied in the d0 systems of AMO3 (A = alkaline, M = Nb, Ta). Here we report the new structural sequence from a cubic perovskite phase to distorted phases as temperature decreases in the solid solution of Na1-xKxOsO3 by synchrotron X-ray powder diffraction; these distorted phases do not belong to the 15 tilting systems. In comparison with the distorted perovskite phases found in the d0 systems of A1+B5+O3 perovskites, the phase transitions with decreasing temperature found in Na1-xKxOsO3 are likely caused by the instabilities of their electronic structures.  I. Introduction Over the past decade, the intriguing physical properties of the ternary osmate oxides with the A1+Os5+O3 configuration have garnered significant attention. LiOsO3, which adopts a rhombohedral LiNbO3-type structure, undergoes a nonpolar (R-3c) to polar (R3c) phase transition at 130 K, while remaining metallic down to the lowest temperature 1. It is commonly referred a ferroelectric metal or polar metal 2. Due to the smaller Li+ occupying the A-site in A1+Os5+O3, the geometric tolerance factor t (= (A-O)/(B-O)2) of LiOsO3 (t = 0.86) is too small to adopt a perovskite structure. NaOsO3 (t = 0.98) synthesized under a pressure of 6 GPa crystallizes in an orthorhombic perovskite structure 3. A metal-insulator-transition (MIT) accompanied by a G-type antiferromagnetic ordering, was observed in NaOsO3 at TMI = 410 K. The MIT has been attributed to a Slater transition since there is no abrupt structural change at the transition 4. In the recent years, both experimental and theoretical studies suggest that the MIT in NaOsO3 is closely associated with a Mott transition 5, 6. Like other perovskite systems with t <1, it is normal for NaOsO3 to adopt the orthorhombic Pbnm phase for a t = 0.98. The observation that the metal-insulator transition temperature is not sensitive to hydrostatic pressure motivated a study of structural determination under pressure by single crystal diffraction with synchrotron X-ray radiation 7. The Pbnm structure remains stable to 40 GPa, the highest pressure in the study. Significant octahedral-site rotations induced under pressure occur in NaOsO3, which contributes to the majority of compressibility in the oxide whereas OsO6 octahedra are less compressible. Increasing the bending angle Os-O-Os, which corresponds to a reduction of the electron bandwidth and compensates the effect of shortening the Os-O bond length under pressure, appears to be responsible for a smaller pressure effect on TMI. The recent successful synthesis of perovskite KOsO3 (t = 1) under a high pressure of 14 GPa 8 presents new opportunities to investigate the structural distortions corresponding to the bonding mismatch in the A1+B5+O3 perovskite with occupied d orbitals where the t factor calculated based on the tabulated ionic radius can be progressively reduced by the chemical substitution in Na1-xKxOsO3. The perovskite KOsO3 crystallizes into a cubic perovskite structure (Pm-3m) at 500 K and transforms to a tetragonal perovskite structure (P4/mmm) at 320 K followed by a second transition to a rhombohedral phase(R-3m) at 230 K. In sharp contrast to other d0 A1+B5+O3 where the tilting systems are developed with decreasing t factor, the bond angles Os-O-Os in these structures maintained at 180° through these structural transitions in perovskite KOsO3. In this paper, we report a thorough crystal structural study of Na1-xKxOsO3 in the phase diagram of the chemical substitution and temperature and compare the new structural distortions with those established for other perovskite compounds.II. ExperimentSample synthesisThe polycrystalline solid-solution samples Na1-xKxOsO3 (x = 0.1, 0.6, 0.65, 0.75 and 1) were synthesized by solid-state reaction under high-pressure and high-temperature conditions. The starting materials KO2 (O2-45.6 %, Sigma-Aldrich), Na2O2 (97%, Sigma-Aldrich), OsO2 (Os-84.0%, Alfa Aesar) were thoroughly mixed in a stoichiometric ratio with 15 mol% excessive KO2 and Na2O2 for reducing the impurities of OsO2 and Os in the final products. The total mass of starting materials for each sample is around 50 mg. The process of mixing and grinding were conducted in an Ar-filled glove box; the mixture was sealed in a Pt crucible before taking out from the glove box. The TEL/EL = 6/12 (TEL = truncated edge length on the cubic anvil, EL = edge length of the pressure-medium octahedron) sample assembly was used in the high-pressure synthesis with a Walker-type-multi-anvil module (Rockland Research Co.). Under 14 GPa, the samples were heated to the target temperature of 1100°C and held there for 30 min followed by a temperature quench to room temperature before releasing the pressure. The temperature quench was achieved by cutting the power supply, and the sample reached room temperature within one minute. To mitigate the risk of potential exposure to the highly toxic OsO4, we conducted the preparation of starting materials and opened the sample crucible within an Ar-filled glove box and a venting hood.Powder diffraction and refinement Each polycrystalline sample was initially checked by X-ray powder diffraction (XRD) with the in-house diffractometer RIGAKU-MiniFlex 600 with Cu-Kα radiation at room temperature. The synchrotron X-ray diffraction (SXRD) measurement was performed on powder samples Na1-xKxOsO3 (x = 0.1, 0.6, 0.65, 0.75 and 1) at room temperature at BL02B2 beamline of SPring-8 with the wavelength λ = 0.61928 Å. The temperature-dependent SXRD data of Na1-xKxOsO3 (x = 0.65, 0.75, 1) was collected from 100 to 400 K at BL02B2 beamline of SPring-8 with the wavelength λ = 0.61974 Å. The Rietveld refinement for powder X-ray diffraction patterns was conducted by RIETAN-FP and VESTA software 9, 10.Measurements of physical propertiesThe magnetic properties of the Na1-xKxOsO3 samples were measured in a magnetic property measurement system (MPMS, Quantum Design, Inc.). The polycrystalline samples were encased in a copper foil in the measurement. The contribution of the copper capsule was subtracted from the raw data.The thermoelectric power for the powder sample was measured in a home-made device fitting to the thermal transport option (TTO) in a physical property measurement system (PPMS, Quantum Design, Inc.). The powder sample from grinding the as-grown sample, was placed into a 0.7 mm diameter hole within a hard-plastic die. To verify the reliability of the thermoelectric powder measured on a powder form of a sample, the single crystal sample NaOsO3 and the powder sample made by crushing the single crystal sample were checked and nearly identical results of the thermoelectric power were obtained.Differential scanning calorimetry (DSC) measurement was conducted on polycrystalline samples using a Mettler Toledo DSC1 STARe system. The samples, 5.57 mg for x = 0.65 and 3.34 mg for x = 0.75, were enclosed within aluminum capsules, respectively. The samples underwent several rounds of DSC measurements to validate its reproducibility.III. ResultsStructural characterizationsFig.1 summarizes the room-temperature results about the phases and their lattice parameters of Na1-xKxOsO3 obtained by refining the SXRD patterns. The lattice parameters of the orthorhombic phase for the Na-rich compositions are converted into values in the primary cell. The two-phase coexistence (the tetragonal and the orthorhombic phases) is found in the compositions x= 0.1 and 0.6. A negligible change in lattice parameters in both phases as a function of the nominal concentration x indicates that almost all Na stay in the orthorhombic phase and almost all K stay in the tetragonal phase regardless of the nominal composition. The single phase of tetragonal structure T (P4/mmm) is found in the compositions of x > 0.60. The Na substitution reduces slightly the lattice parameter in the cubic phase (at 400 K). All SXRD patterns at room temperature and the refinement results are shown in Fig.2. Results of the phase analysis and lattice parameters are listed in Table 1. We have also refined the patterns with another tetragonal structure model (I4/mcm) reported in perovskite oxides such as SrTiO3 11, in which there is an antiphase octahedral-site titling along the c axis. Despite adopting a larger unit cell in the I4/mcm structure model in comparison with P4/mmm, no significant improvement in R values is obtained, and no superstructure reflections were observed.We have chosen the nominal compositions of x = 0.65 and 0.75 with a single phase of the tetragonal structure (at room temperature) for the structural study at different temperatures from 100 to 400 K. The chemical compositions x = 0.573(6) and 0.77(1) for these two samples were determined based on the SXRD patterns collected at 100 K, which are close to their nominal compositions. It is noted that the occupancy of A-site for the same sample is fixed at the same value during the refinement of SXRD data collected at 120- 400 K. The occupancies for the oxygen sites were attempted to refine, and the values of 1.12 and 1.05 are obtained, indicating that these samples are close to oxygen stoichiometric. Thus, the oxygen occupancies were fixed to 1 in the final refinement. We have identified three phases, a cubic phase C (Pm-3m), T, and a rhombohedral phase R (R-3m) in the temperature range. Typical SXRD patterns and the Rietveld refinement results are present in Fig. 3 and the data are listed in Table 2-4. Fig. 4 shows the evolution of crystal structures and their lattice parameters as a function of temperature. The same structural consequence in KOsO3 at low temperatures is found in the Na1-xKxOsO3 (x>0.6).  The Na substitution in these perovskites lowers the R-T and T-C phase transitions by ~ 20 K. It should be noted that the R-T and T-C phase transitions in Na1-xKxOsO3 (x = 0.75) show slight increase compared to Na1-xKxOsO3 (x = 0.65), as indicated by the DSC measurements, as shown in Fig. 5. From the DSC curves, it is observed that the temperatures of the R-T and T-C transitions in sample x = 0.65 are 220 K and 308 K, respectively, while in sample x = 0.75, they are 222 K and 312 K. This small difference is not discernible in SXRD measurement because of a larger temperature interval between sampling points. The structural distortion in R phase reflects in a slight deviation from 90° in the unit cell. The temperature dependence of the rhombohedral  is shown in inset of Fig. 4. Physical propertiesAll the samples of Na1-xKxOsO3 synthesized under 14 GPa come as powder with grain size in the range 20-500 m after opening the Pt crucible. The standard four-probe and the Hall bar patterns were created on the surface of rectangular crystal fabricated by the focused ion beam (FIB). Unfortunately, the surface quality is deteriorated severely after FIB; results of the resistivity measurement no longer reflect the bulk property. Instead, we measured the temperature dependence of thermoelectric power S(T) of the cold-pressed the samples of Na1-xKxOsO3 for monitoring the evolution of electronic state in these phases as a function of x and temperature. In the insulator phase of the parent compound NaOsO3, the gap opening at the Fermi energy does not lead to the typical behavior for a semiconductor or an insulator. Instead, S(T) in Fig. 6 manifests a broad hump in the magnitude near 200 K. Without a sound model to fit the S(T) in the insulator phase, we use it as the benchmark for the insulator phase in the study of electronic state evolution in Na1-xKxOsO3 series. Although there is no reliable indication of any K substitution in the sample of x = 0.10 from the structural study, the K substitution reduces the maximum value of |S(T)| near 200 K. In the two-phase coexistence, the thermoelectric power is weighted by conductivity of individual components, S = (1S1 + 2S2)/(1 + 2). The magnitude reduction of S(T) in the x = 0.10 sample is more likely dominated by the contribution from a small and temperature independent S(T) in a more conducting tetragonal phase from the structural study. A similar situation also happens in the x = 0.6 sample where even larger phase volume of the tetragonal phase is found. As a result, S(T) in this sample is dominated by that as seen in the single-phase samples of x = 0.65 and 0.75. The S(T) for the x = 0.65 sample is typical for the tetragonal phase Na1-xKxOsO3. The magnitude of S(T) in this sample is small, consisting with a metallic phase. More importantly, there are clear anomalies at the phase transitions from R to T and T to C phase. The magnetic susceptibility (T) of the x = 0.65 and 0.75 samples are featureless as shown in Fig. 7. The kink around 50 K is due to the contribution from a minor infiltration of oxygen into the sample space in the MPMS. However, the non-linear M-H curves of the x = 0.65 and 0.75 samples indicate a weak ferromagnetism in a magnetic ordered phase with the Curie temperature Tc above room temperature. There are still tiny impurity phases like Os metal and OsO2 in the samples. As confirmed by separate measurements, these materials are not magnetic to 4 K.IV. DiscussionThe geometric tolerance factor t = (A-O)/(B-O)2 reflects the bond-length mismatch in the perovskite structure. A cubic perovskite is always found for t value close to 1. The octahedral-site tilting systems are developed to accommodate the bond length mismatch created in perovskites with t < 1. There are 15 tilting systems which can be organized through groups and their subgroups based on their structural symmetries 12, 13. Depending on the charge configurations, i.e. A1+B5+O3, A2+B4+O3, A3+B3+O3, varying t factor through either the chemical substitution and changing temperature leads to the structural distortions through a particular pathway in the tilting systems. It should be noted that all the ferroelectric phases with breaking the inversion symmetry in perovskite BaTiO3 with t >1 are not within the 15 tilting systems. There are examples of perovskite systems exhibiting the complete structural evolution between orthorhombic and cubic perovskite phases as t =1 is approached from t <1. For instance, Ca1-xSrxFeO3 14,  Sr1-xBaxRuO3 15, and (Ca, Sr, Ba)OsO3 16 represent 3d-, 4d-, and 5d- perovskite oxides, respectively. Through larger-atom substitution in the A-site, all the series undergo a subsequent phase transition from orthorhombic to cubic perovskite structure. The cubic perovskite structure (Pm-3m) is observed in Ca1-xSrxFeO3 (x ≥ 0.8), whereas the structure of Sr1-xBaxRuO3 changes from the Pbnm phase to Pm-3m phase (x ≥ 0.4) with an intermediate phase Imma phase (x = 0.2-0.3). It is common in the A2+B4+O3 perovskites that the tilting system changes from a0a0a0 of the Pm-3m phase to a-a-c+ of the Pbnm phase with intermediate phases a0b-b- of the Imma phase and a0a0c- of the I4/mcm phases between them 17. The success in high-pressure synthesis of KOsO3 perovskite has enabled the demonstration of the complete evolution from the orthorhombic perovskite NaOsO3 to the cubic phase of the perovskite KOsO3 at T > 320 K. Unfortunately, a complete solid-state solution can only be found in the cubic phase with x > 0.6 in Na1-xKxOsO3. The two-phase coexistence is found in the substitution range 0 < x ≤ 0.6. The lattice parameters in these two phases are nearly independent to x, which implies that there is a negligible K doping in the orthorhombic phase and a negligible Na doping in comparison with x = 0.65 sample in the tetragonal phase. Lacking the intermediate phases found in other perovskite systems could be attributed to a substantially large size variance in Na1-xKxOsO3 due to a large difference of ionic size between Na1+ and K1+. The calculation based on bond lengths from experiments shown in Fig.8 gives a t =1.000 at room temperature, and 0.9999 at 100 K for x=0.65, 0.75 in Na1-xKxOsO3. On the other hand, the calculation based on tabulated ionic size via SPuDs 18 gives a t =1.0423 and a t =1.072 for x=0.5 and 0.75, respectively. Therefore, the (Na, K)-O bonds must be under compression whereas the Os-O bonds are under tension in the products of high-pressure synthesis. It is understandable that the average (Na, K)-O bond length reduces as x decreases because of the reduction of the mean ionic size at the A site of the perovskite structure, which also releases somehow the tension stress on the Os-O bonds. The variation of the tension stress on the Os-O bond as a function of x in the cubic phase is also reflected in the bond valance sum (BVS). There is no Os(5) in the SpuDs software 18. The BVS for Os in Na1-xKxOsO3, shown in Fig. 8, are calculated by , where , N is the coordination number, l is the bond length, B = 0.37 19, and R0(Os5+) = 1.867 20. A BVS = 4.83 indicates that Os-O in KOsO3 is in underbonding due to the tension stress. It is gradually improved to a BVS=4.91 for the x = 0.65 sample. The underbonding M-O can also be found in all perovskites with a 180  M-O-M bond angle, which are synthesized under high pressure, a BVS = 3.85 in BaIrO3,21 3.77 in BaRuO3,22 and 3.477 in BaOsO3 16. An entire evolution from the overbonding to underbonding can be found in Ca1-xSrxMnO3 and Sr1-yBayMnO3, a BVS= 4.14 for Ca0.8Sr0.2, 4.04 for Ca0.9Sr0.1, 4.0056 for Sr, 3.935 for Sr0.9Ba0.1, 3.867 for Sr0.8Ba0.2 23. The two-step synthesis route appears to play a significant role to make the Mn-O bonds under a tension stress in these manganites. In contrast, the compressive stress on the M-O array in the orthorhombic RMO3 is released by the octahedral-site rotations. In these cases, a BVS, which is extremely close to their formal valence value, is obtained, for example, a BVS=3.0±0.09 in RFeO3, and 3.0±0.04 in RCrO3. All the M-O bond lengths used are from the reference 24. It remains puzzling to understand the underbonding Os-O in the orthorhombic NaOsO3In the perovskite ABO3, the competition for the bonding covalency with oxygen 2p between A-O and B-O bonds is correlated with the charge configuration. The structural evolution found in ATaO3 perovskites provides a good template for us to study the structures in AOsO3, A = alkaline. At room temperature, KTaO3 crystallizes into a cubic perovskite structure 25, whereas NaTaO3 has been identified as exhibiting phase coexistence of two orthorhombic structures with Pbnm and Cmcm (a0b+c-) space groups, respectively 26. The Na1-xKxTaO3 samples maintain the cubic structure until x = 0.28, with the tetragonal structure P4/mmm appearing when x = 0.16 27. The author pointed out in the paper that crystal growth encountered difficulties when attempting to grow Na1-xKxTaO3 crystal samples with 0.16 < x < 0.26. This challenge may be attributed to a miscibility gap existing within the range between the cubic and tetragonal phases, potentially impeding crystal growth. An almost linear relationship between lattice parameter of Na1-xKxTaO3 (x > 0.28) and x is observed, similar to what is seen in Na1-x K xOsO3 (x = 0.65, 0.75, 1). The lattice parameter undergoes a significant decrease from cubic phase to orthorhombic phase in Na1-xKxTaO3, resembling the behavior observed in the case of Na1-xKxOsO3. In a structural study as a function of temperature, Darlington and Knight have shown the change of the tilting system from a0a0a0 (Pm-3m) to a0b0c+ (P4/mbm), to a0b-c+ (Cmcm), to a-a-c+ (Pbnm) as temperature decreases from 1050 to 750 K in NaNbO3 and NaTaO3 28. Lacking the solid solution for x < 0.65 in Na1-xKxOsO3 prevents us from studying the tilting systems that may develop between the orthorhombic phase and the cubic phase. The ideal perovskite structure is cubic in space group Pm-3m, which belongs to point group Oh. According to the existing perovskite compounds, three possible types of distortion can lead to distorted perovskite structures: octahedral-site distortions, displacement of B cation including ferroelectric and antiferroelectric displacements, and octahedral-site tilting 29. These distortions are also accompanied by A-site cation dislocation. The majority of distorted perovskites derived from the parent cubic perovskite structure can be obtained through the tilting of octahedra. Howard and Stokes conducted a thorough group-theoretical analysis, focusing on octahedral tilting, resulting in 14 subgroups from the cubic perovskite structure 13. Since the Os-O bonds are under a tension stress in Na1-xKxOsO3 (x > 0.6), any structural distortions can be only made without the octahedral-site rotations. As shown in Table 5 and Fig. 9, the Os-O-Os remains at 180° in the three phases throughout the entire temperature range from 100 to 400 K. The T (P4/mmm) and R (R-3m) perovskite structures do not belong to the subgroup derived from octahedral tilting. The unit cell volume decreases smoothly through the phase transition from C to T and T to R in perovskites Na1-xKxOsO3 (x ≥ 0.65) as temperature decreases, as shown in Fig. 4. Within the space group Oh1, there are 32 subgroups with unchanged unit cells, encompassing P4/mmm (D3d5) and R-3m (D4h1) 30. Additionally, the coordinates of the A-site and B-site atoms in perovskite Na1-xKxOsO3 (x ≥0.65) remain unchanged in the distorted phases, with the symmetry alteration attributed solely to the deformation of the unit cell. In the T (P4/mmm) phase, the deformation of unit cell is reflected in the presence of two shorter Os-O along the c axis and four longer Os-O in the ab plane. In the R (R-3m) phase, it results in O-Os-O angles deviating slightly from 90°.A sharp difference between the d0 A1+B5+O3 perovskites and the Na1-xKxOsO3 (x ≥0.65) in terms of subgroup structures deviated from the cubic phase as temperature decreases makes it unlikely that saving the elastic energy is the driving force behind the phase transitions in the latter. With the t2g3eg0 configuration in Na1-xKxOsO3, the orbital angular momentum L is quenched in the L-S coupling. However, the spin-orbit coupling (SOC) is to play an important role in the j-j coupling in these 5d perovskites. In NaOsO3, the anomaly of lattice parameters on crossing the metal-insulator transition can be well simulated only if the SOC is considered 6. The subtle local structural distortions in the T and R phase in Na1-xKxOsO3 (x > 0.6) may manifest the higher-order instabilities of electronic structure. The transition temperatures of C to T and T to R phase transitions shift to lower temperature by ~20 K from the perovskite x=1 to x=0.75 and 0.65. In perovskite RAlO3 where the phase transitions are triggered for saving the lattice elastic energy, however, the transition temperature increases for the phase transition from a lower symmetry phase to a higher symmetry phase as t factor decreases.31 This observation aligns with the hypothesis that the phase transitions in Na1-xKxOsO3 (x ≥ 0.65) have an electronic origin. V. ConclusionThe osmate perovskite Na1-xKxOsO3 was synthesized for the first time under high-pressure and high-temperature conditions. The solid-solution of Na1-xKxOsO3 in the tetragonal phase at room temperature can only be found for x ≥ 0.65. The two-phase coexistence (Pbnm and P4/mmm) is found in the samples with 0 < x < 0.65. The structural determination of the samples of Na1-xKxOsO3 with x ≥ 0.65 over 100-400 K reveals the phase transitions from the cubic phase (Pm-3m) to the tetragonal phase (P4/mmm) at ~320 K and subsequently to the rhombohedral phase (R-3m) at ~230 K. The phase diagram of osmate perovskite Na1-xKxOsO3 is shown in Fig. 10. In sharp contrast to the tilting systems developed due to the bond-length mismatch in the d0 A1+B5+O3 perovskites, the distortions in the low symmetry P4/mmm and R-3m phases are characterized by slightly change of local bond lengths and a slightly deviation of the angle in the unit cell from 90 º. These distorted structures in the perovskite Na1-xKxOsO3 (x ≥ 0.65) do not belong to the tilting systems in perovskites reported.  The structural comparison between the phases found in Na1-xKxOsO3 with x ≥ 0.65 and those in the d0 A1+B5+O3 perovskites and the structural analysis based on BVS imply the driving force for the phase transitions is likely from the electron structural instability. The perovskites Na1-xKxOsO3 (x ≥ 0.6) appear to be metallic at least up to 400 K in the cubic, tetragonal, and rhombohedral phases and magnetic at least up to 300 K.Fig. 1 Lattice parameters of Na1-xKxOsO3 obtained by refining the SXRD patterns collected at room temperature.Fig. 2 Patterns of synchrotron XRD collected at room temperature and the results of Rietveld refinement for the Na1-xKxOsO3 (x = 0.1, 0.6, 0.65, and 0.75). The crosses and solid lines show the observed and calculated patterns, respectively, with their differences shown at the bottom. The expected Bragg reflections are marked by ticks for (a-c) the P4/mmm structure, and (d) Pbnm structure (top); (a-b) OsO2, (c) Pbnm structure, and (d) P4/mmm structure (bottom). Fig. 3 Patterns of synchrotron XRD collected at 100 K and 400 K and the results of Rietveld refinement for the Na1-xKxOsO3 (x = 0.75). The crosses and solid lines show the observed and calculated patterns, respectively, with their differences shown at the bottom. (a) The expected Bragg reflections are marked by ticks for the R-3m structure (top) and OsO2 (bottom). (b) The expected Bragg reflections are marked by ticks for the Pm-3m structure (top) and OsO2 (bottom). The similar synchrotron XRD profiles (T = 100 K and 400 K) and the refinement results have been obtained for Na1-xKxOsO3 (x = 0.65).Fig. 4 Lattice parameters (upper) and cell volumes (bottom) versus temperature for the Na1-xKxOsO3 (x = 0.65, 0.75, 1). The α angles of rhombohedral phase versus temperature are shown in inset.Fig. 5 Results of differential scanning calorimetry of Na1-xKxOsO3 (a) x = 0.65 and (b) x = 0.75. Fig. 6 Temperature dependences of the thermoelectric power (S) of Na1-xKxOsO3 (x = 0, 0.1, 0.65, and 0.75).Fig. 7 Field dependences of the magnetization of Na1-xKxOsO3 (a) x = 0.65, (b) x = 0.75; temperature dependences of the magnetization of (c) x = 0.65, (d) x = 0.75.Fig. 8 Room-temperature bond length of (a) A-O, (b) Os-O and BVS for Os, and (c) calculated tolerance factor (t) for Na1-xKxOsO3 (x = 0, 0.65, 0.75, and 1).Fig. 9 Structure models for Na1-xKxOsO3 (x = 0.65 and 0.75) at different temperatures. The tetragonal (P4/mmm) and rhombohedral (R-3m) structures contain multiple unit cells.Fig. 10 Phase diagram of Na1-xKxOsO3.Table 1 Summary of the room-temperature phases and the lattice parameters of Na1-xKxOsO3 obtained by refining the SXRD patterns x 0.1 0.6 0.65 0.75 Phases of Na1-xKxOsO3 P4/mmm (2 wt %); Pbnm (98 wt %) P4/mmm (82 wt %); Pbnm (18 wt %) P4/mmm P4/mmm Lattice parameters of tetragonal phase  a = 3.88536(7) Åc = 3.8803(1) Å a = 3.88621(1) Å c = 3.88397(2) Å a = 3.88235(2) Åc = 3.88016(4) Å a = 3.88446(2) Åc = 3.88351(5) Å Lattice parameters of orthorhombic phase a = 5.33435(2) Åb = 5.38713(1) Åc = 7.58684(2) Å a = 5.33066(3) Åb = 5.38543(3) Åc = 7.58256(6) Å  Table 2 Rietveld refinement results for Na1-xKxOsO3 (x = 0.65 and 0.75) as measured by synchrotron X-ray diffraction at room temperature x 0.65 0.75 Space group P4/mmm P4/mmm a (Å) 3.88235(2) 3.88446(2) c (Å) 3.88016(4) 3.88351(5) V (Å3) 58.4844(7) 58.5985(9) Occupancy of potassium at A-site 0.573 0.77 dcal (g/cm3) 7.679 7.754 Uij of A site (10-3 Å2) U11 = 2.5(7)U33 = 13(2) U11 = 9(1)U33 = 10(2) Uij or Uiso of Os site (10-3 Å2) Uiso = 3.77(4) U11 = 7.6(3)U33 = 3(4) Uiso of oxygen site (10-3 Å2) Uiso (O1) = 6(4)Uiso (O2) = 6(2) Uiso (O1) = 10(6)Uiso (O2) = 8(3) Final R values (%) Rwp = 8.004Rp = 5.789RB = 3.225RF = 1.292 Rwp = 7.521Rp = 5.607RB = 1.898RF = 1.184General atomic positions for P4/mmm (no. 123): A 1a (0, 0, 0), Os 1d (0.5, 0.5, 0.5), O1 1c (0.5, 0.5, 0), O2 2e (0.5, 0, 0.5). Anisotropic displacement parameters (Uij, 10-3 Å2) for 1a and 1d: U11 = U22, U12 = U13 = U23 = 0. Isotropic displacement parameter is represented by Uiso.Table 3 Rietveld refinement results for Na1-xKxOsO3 (x = 0.65 and 0.75) as measured by synchrotron X-ray diffraction at 100 K x 0.65 0.75 Space group R-3m R-3m a (Å) 5.48901(2) 5.49213(2) c (Å) 6.71015(3) 6.71427(2) V (Å3) 175.086(1) 175.393(1) Occupancy of potassium at A-site 0.573(6) 0.77(1) dcal (g/cm3) 7.695 7.770 Uij of A site (10-3 Å2) U11 = 0.8(3)U33 = 3.8(6) U11 = 4.2(3)U33 = 8.3(6) Uij of Os site (10-3 Å2) U11 = 2.57 (6)U33 = 2.4(1) U11 = 3.54(7)U33 = 4.0(1) Uiso of oxygen site (10-3 Å2) 3.8(3) 6.0(3) Final R values (%) Rwp = 7.192Rp = 5.022RB = 3.411RF = 1.088 Rwp = 7.244Rp = 5.389RB = 1.747RF = 0.960General atomic positions for R-3m (no. 166): A 3b (0, 0, 0.5), Os 3a (0, 0, 0), O 9d (0.5, 0, 0.5). Anisotropic displacement parameters (Uij, 10-3 Å2) for 3b and 3a: U11 = U22 = 2 × U12, U13 = U23 = 0. Isotropic displacement parameter is represented by Uiso.Table 4 Rietveld refinement results for Na1-xKxOsO3 (x = 0.65 and 0.75) as measured by synchrotron X-ray diffraction at 400 K x 0.65 0.75 Space group Pm-3m Pm-3m a (Å) 3.88426(1) 3.88661(1) V (Å3) 58.6038(2) 58.7101(2) Occupancy of potassium at A-site 0.573 0.77 dcal (g/cm3) 7.663 7.739 Uij of A site (10-3 Å2) U11 = 7.6(3) U11 = 11.7(2) Uij of Os site (10-3 Å2) U11 = 4.60(4) U11 = 5.92(5) Uii of oxygen site (10-3 Å2) U11 = 7(1)U22 = 8.0(8) U11 = 3(1)U22 = 15.2(9) Final R values (%) Rwp = 8.722Rp = 6.196RB = 3.558RF = 1.433 Rwp = 8.208Rp = 6.245RB = 1.947RF = 1.147General atomic positions for Pm-3m (no. 221): A 1a (0, 0, 0), Os 1b (0.5, 0.5, 0.5), O 3c (0, 0.5, 0.5). Anisotropic displacement parameters (Uij, 10-3 Å2) for 1a and 1b: U11 = U22 = U33, U12 = U13 = U23 = 0. For 3c, the parameters are U22 = U33, U12 = U13 = U23 = 0.Table 5 Comparison of the room-temperature structural parameters of Na1-xKxOsO3 perovskite oxides x 1 0.75 0.65 0 Pressure of synthesis 14 GPa 14 GPa 14 GPa 6 GPa Space group P4/mmm P4/mmm P4/mmm Pbnm a (Å) 3.89488(1) 3.88446(2) 3.88235(2) 5.32817(1) b (Å)    5.38420(1) c (Å) 3.89243(1) 3.88351(5) 3.88016(4) 7.58038(1) V/Z (Å3) 59.0486(3) 58.5985(9) 58.4844(7) 54.3664(3) <A-O> (Å) 2.7535(1) Ⅻ 2.7465(1) Ⅻ 2.7447(1) Ⅻ 2.492(5) Ⅷ;2.701(5) Ⅻ Os-O1 (Å) 1.94622(1) × 2 1.94176(3) × 2 1.94008(3) × 2 1.945(1) × 2 Os-O2 (Å) 1.94744(1) × 4 1.94223(1) × 4 1.94117(1) × 4 1.940(3) × 21.939(3) × 2 <Os-O> (Å) 1.9470(1) 1.9421(2) 1.9408(2) 1.941(2) Volume of OsO6 (Å3) 9.8414 9.7664 9.7474 9.7516 Tolerance factor 1.000 Ⅻ 1.000 Ⅻ 1.000 Ⅻ 0.908 Ⅷ; 0.984 Ⅻ Os-O1-Os (°) 180 180 180 153.9(3) Os-O2-Os (°) 180 180 180 155.2(2) <Os-O-Os> (°) 180 180 180 154.6(3)Tolerance factors are calculated by t = <A-O>/<B-O>/2, where <A-O> and <B-O> represent the average bond lengths obtained from structure refinement. The structural parameters of NaOsO3 are used from reference 3.*jszhou@mail.utexas.eduACKNOWLEDGMENTSThis research was primarily supported by the National Science Foundation through the Center for Dynamics and Control of Materials: an NSF MRSEC under Cooperative Agreement No. DMR-2308817. This work was partially supported by a Grant-in-Aid for Scientific Research (No. JP22H04601) from the Japan Society for the Promotion of Science and the Kazuchika Okura Memorial Foundation (No. 2022-11). Synchrotron radiation was used at the powder diffraction beamline BL02B2 at SPring-8, with permission from the Japan Synchrotron Radiation Research Institute (Proposal Numbers: 2023A1496, 2023A2361, and 2023B1676). MANA is supported by World Premier International Research Center Initiative (WPI), MEXT, Japan.Reference1. Shi, Y.;  Guo, Y.;  Wang, X.;  Princep, A. 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