research papers\(\def\hfill{\hskip 5em}\def\hfil{\hskip 3em}\def\eqno#1{\hfil {#1}}\)

IUCrJ
Volume 7| Part 4| July 2020| Pages 656-662
ISSN: 2052-2525

Crystal structure and magnetism in the S = 1/2 spin dimer compound NaCu2VP2O10

aDivision of Advanced Ceramics, Nagoya Institute of Technology, Nagoya 466-8555, Japan, and bFrontier Research Institute for Materials Science, Nagoya Institute of Technology, Nagoya 466-8555, Japan
*Correspondence e-mail: urushihara.daisuke@nitech.ac.jp

Edited by A. Fitch, ESRF, France (Received 3 February 2020; accepted 22 April 2020; online 27 May 2020)

The crystal structure of the spin dimer magnet NaCu2VP2O10 was determined using single-crystal X-ray diffraction and electron diffraction. NaCu2VP2O10 displayed a non-centrosymmetric orthorhombic C2221 structure with a = 6.13860 (10) Å, b = 14.4846 (3) Å and c = 8.2392 (2) Å. The layered structure comprised CuO4 plaquettes, VO6 octahedra and PO4 tetrahedra. A pair of CuO4 plaquettes formed Cu2O6 structural dimers through edge sharing. The Cu–Cu network formed a distorted puckered-layer structure with pseudo-one-dimensional characteristics. Maximum magnetic susceptibility was observed at ∼60 K and NaCu2VP2O10 became non-magnetic upon further cooling. The spin gap between the spin-singlet non-magnetic ground state and triplet excited state was estimated to be 43.4 K. Thus, NaCu2VP2O10 was assumed to be an alternating chain system with a singlet ground state of dimer origin. The V5+ ions in the VO6 octahedra showed large off-centre displacements along the [110] direction in the primitive perovskite structure, which were attributed to the pseudo-Jahn–Teller distortion of d0 transition metals.

1. Introduction

Quantum-spin systems have attracted considerable attention since the discovery of characteristic quantum phenomena such as superconductivity and quantum-spin liquids (Lee, 2008[Lee, P. A. (2008). Rep. Prog. Phys. 71, 012501.]; Balents, 2010[Balents, L. (2010). Nature, 464, 199-208.]). Spin dimer systems are representative materials that exhibit quantum-spin fluctuations. In such systems, magnetic ions are often coupled with antiferromagnetic exchange interactions, resulting in the formation of spin dimers. Dimers are coupled with neighbouring dimers via weak exchange interactions. With increasing interactions between dimers in low-dimensional systems, spin dimer compounds can be considered as an alternating chain system. Dimerized quantum magnets usually display an energy gap between spin-singlet non-magnetic ground and triplet excited states; furthermore, the inter- and intra-dimer interactions caused by the arrangement of magnetic ions affect the energy gap.

In the spin dimer system of Cu2+ (S = 1/2), dimerized Cu2+ often shows characteristic atomic arrangements; Cu2+, which possesses a 3d9 configuration, exhibits Jahn–Teller distortion owing to the occupied d3z2–r2 orbital and sometimes forms a CuO4 plaquette or distorted CuO6 octahedron. A CuO4 plaquette is two-dimensional because its ligands prefer planar coordination. Thus, Cu2O6 dimers formed by edge-sharing CuO4 plaquettes show various arrangements which are related to interactions between Cu ions. These Cu2O6 dimers have been identified in compounds such as SrCu2(BO3)2 (Smith & Keszler, 1991[Smith, R. W. & Keszler, D. A. (1991). J. Solid State Chem. 93, 430-435.]; Kageyama et al., 1999[Kageyama, H., Yoshimura, K., Stern, R., Mushnikov, N. V., Onizuka, K., Kato, M., Kosuge, K., Slichter, C. P., Goto, T. & Ueda, Y. (1999). Phys. Rev. Lett. 82, 3168-3171.]), Cu2P2O7 (Effenberger, 1990[Effenberger, H. (1990). Acta Cryst. C46, 691-692.]; Janson et al., 2011[Janson, O., Tsirlin, A. A., Sichelschmidt, J., Skourski, Y., Weickert, F. & Rosner, H. (2011). Phys. Rev. B, 83, 094435.]) and BaCu2V2O8 (Vogt & Müller-Buschbaum, 1990[Vogt, R. & Müller-Buschbaum, H. (1990). Z. Anorg. Allg. Chem. 591, 167-173.]; Klyushina et al., 2016[Klyushina, E. S., Tiegel, A. C., Fauseweh, B., Islam, A. T. M. N., Park, J. T., Klemke, B., Honecker, A., Uhrig, G. S., Manmana, S. R. & Lake, B. (2016). Phys. Rev. B, 93, 241109.]). SrCu2(BO3)2 represents a typical two-dimensional orthogonal dimer system. In SrCu2(BO3)2, Cu2O6 dimers are located orthogonally along the [110] direction in a tetragonal system and connected through BO3 triangles. In Cu2P2O7, Cu2O6 dimers are located parallel to the b axis in the monoclinic system. The Cu–Cu network in Cu2P2O7 has a distorted two-dimensional honeycomb structure. In contrast, BaCu2V2O8 has three-dimensional arrangements of Cu2O6 dimers and its Cu–Cu network adopts pseudo-one-dimensional screw chains along the c axis. Both arrangements of Cu2O6 dimers and Cu–Cu networks strongly affect quantum states. Thus, it is important to discover other examples of spin dimer systems with a finite spin gap to an excited state.

In this study, we synthesize the spin dimer compound NaCu2VP2O10, the crystal structure of which was determined using single-crystal X-ray diffraction (XRD) and electron diffraction. The obtained crystal structure is layered, and it comprises corner-sharing Cu2O6 dimers, VO6 octahedra and PO4 tetrahedra. Magnetic susceptibility measurements of NaCu2VP2O10 reveal that it exhibits a non-magnetic ground state and a spin gap between the ground and excited states. We clarify that NaCu2VP2O10 is an alternating chain system and discuss the relationship between its crystal structure and magnetic properties.

2. Experimental section

2.1. Synthesis

Polycrystalline samples were synthesized by a solid-state reaction. A mixture of equal amounts of NaVO3 and Cu2P2O7 was sintered at 823 K for 20 h and then 923 K for 10 h. To grow single crystals, the sintered sample was heated at 1023 K for 2 h and then cooled to 923 K at a rate of 1 K/ h. The obtained crystals had a columnar shape with a diameter of ∼50 µm.

2.2. Electron-probe microanalysis

The chemical composition of the polycrystalline materials was measured using an electron-probe microanalyzer (JXA-8230, JEOL). The prepared samples were polished to form flat surfaces. The normalized Na:Cu:V:P ratio for the three grains was determined to be 0.87 (12):2.014 (7):1.094 (3):2.022 (9), which is close to the stoichiometric chemical composition (Na:Cu:V:P ratio of 1:2:1:2).

2.3. Powder X-ray diffraction

To determine the phase purity and estimate the basic structure of the synthesized compounds, we collected powder XRD patterns using a powder X-ray diffractometer (X'Pert Pro Alpha-1, Panalytial) equipped with a high-speed detector and Cu Kα1 X-ray source (45 kV, 40 mA). The scanning range of diffraction angles (2θ) was 5–145°, which was adequate for indexing the diffraction peaks. We confirmed that the samples did not contain any impurity phases by comparing the measured powder XRD patterns with a simulated pattern of the refined structure model of NaCu2VP2O10 (see Fig. S1 in the Supporting information).

2.4. Electron diffraction

Selected-area electron diffraction (SAED) measurements were performed using a transmission electron microscope (JEM-ARM200F, JEOL) operated at 200 kV. The specimen was prepared by crushing the polycrystals; the particles were deposited on a copper grid with a holey carbon support film. We determined the space group by testing the extinction rules of the sample using SAED.

2.5. Single-crystal X-ray diffraction

Diffraction data were collected using a single-crystal X-ray diffractometer (D8 VENTURE, Bruker) equipped with a complementary metal oxide semiconductor detector and Mo Kα X-ray source (50 kV, 1 mA). A single crystal with a diameter of ∼50 µm was mounted on a borosilicate glass needle using an adhesive. Lattice constants were determined using the SAINT program (Bruker, 2015[Bruker (2015). APEX3, SAINT and SADABS. Bruker AXS Inc., Madison, Wisconsin, USA.]) and multi-scan absorption correction was carried out using the SADABS program (Bruker, 2015[Bruker (2015). APEX3, SAINT and SADABS. Bruker AXS Inc., Madison, Wisconsin, USA.]). The initial structure model was calculated using the SUPERFLIP program based on the charge-flipping algorithm (Palatinus & Chapuis, 2007[Palatinus, L. & Chapuis, G. (2007). J. Appl. Cryst. 40, 786-790.]). Crystal structure analysis was carried out using the JANA2006 program package (Petricek et al., 2014[Petricek, V., Dusek, M. & Palatinus, L. (2014). Z. Kristallogr. 229, 345-352.]) and the analysed crystal structure was visualized using the VESTA program (Momma & Izumi, 2011[Momma, K. & Izumi, F. (2011). J. Appl. Cryst. 44, 1272-1276.]).

2.6. Magnetic susceptibility

The magnetic susceptibility of the polycrystalline materials was measured using a superconducting quantum-interference device magnetometer (MPMS, Quantum Design). Magnetization was obtained at 2–400 K in an applied field of 1 T.

2.7. Thermal analysis

The heat capacity of the polycrystalline materials was measured using a physical property measurement system (PPMS, Quantum Design). The temperature dependence of the heat capacity was measured at 2–300 K using a thermal-relaxation method. No thermal anomalies were observed in the investigated temperature range.

3. Results

3.1. Space group determination

We measured the powder XRD pattern of NaCu2VP2O10, which could be indexed to an orthorhombic unit cell. According to the indices obtained from the powder XRD patterns, the zone axes of the incident electron beams were identified in the SAED patterns. Fig. 1[link] shows the SAED patterns collected under several electron beams with different incidences. In the [100] and [010] zone axis SAED patterns [Figs. 1[link](a) and 1[link](b)], only diffraction spots with indices of k = 2n and h = 2n were observed. The [001] zone axis SAED pattern [Fig. 1[link](c)] shows an extinction rule of h + k = 2n, which contains both k = 2n and h = 2n in the [100] and [010] zone axis SAED patterns. Such extinction rules indicate the C lattice symmetry (hkl: h + k = 2n) of the orthorhombic system. We then observed the diffraction spots of the 00l condition by tilting the specimen to remove the multiple reflections at forbidden reflection positions, which may appear in a crystal structure with screws or grid planes [Fig. 1[link](d)]. The reflections in the 00l condition were indexed as l = 2n, which represents a twofold screw parallel to the c axis (00l: l = 2n). The extinction rule was identical to that determined from the single-crystal XRD data, which was based on the kinematical theory of diffraction [Figs. S2(a)–S2(c)]. Analysis of the SAED patterns revealed that the space group of NaCu2VP2O10 was C2221 and non-centrosymmetric.

[Figure 1]
Figure 1
(a) [100] zone axis, (b) [010] zone axis and (c) [001] zone axis SAED patterns of NaCu2VP2O10. (d) 00l systematic reflections of NaCu2VP2O10.

3.2. Crystal structure determination from XRD data

Single-crystal XRD data obtained for NaCu2VP2O10 were indexed to an orthorhombic cell, consistent with the SAED patterns. The determined unit-cell dimensions of NaCu2VP2O10 were a = 6.13860 (10) Å, b = 14.4846 (3) Å and c = 8.2392 (2) Å. The initial structure model was determined using the charge-flipping method. This model represents nine independent sites in the unit cell. The Na site was at the Wyckoff position 4b (Na), the Cu site was at 8c (Cu), the V site was at 4b (V), the P site was at 8c (P) and the O sites were at 8c (O1–O5). We successfully refined all site-coordination and anisotropic atomic displacement parameters (U). The reliability indices were R = 2.33% and wR = 7.62%. The U values were adequate at all sites. The refined crystal structure model is shown in Fig. 2[link]; the crystal data, structural parameters and atomic distances are summarized in Tables 1[link], 2[link] and 3[link], respectively.

Table 1
Crystal data and XRD conditions for NaCu2VP2O10

Chemical formula NaCu2VP2O10
Space group C2221 (No. 20)
a (Å) 6.13860 (10)
b (Å) 14.4846 (3)
c (Å) 8.2392 (2)
V (Å)3 733.58 (3)
Z 4
Dx (Mg m−3) 3.84
   
2θ range <60.94
Observed reflection 13034
Unique reflection 1110
Rint 0.0254
Collection range −8 ≤ h ≤ 8
  −20 ≤ k ≤ 20
  −11 ≤ l ≤ 11
R (F2 > 3σ) 0.0233
wR (F2) 0.0762

Table 2
Structural parameters and atomic displacement parameters of NaCu2VP2O10

Site Wyckoff position g x y z Ueq2)
Na 4b 1 0 0.46651 (11) 1/4 0.0198 (5)
Cu 8c 1 0.15209 (6) 0.11957(3) 0.10586 (4) 0.01583 (12)
V 4b 1 0 0.86680 (4) 1/4 0.0072 (2)
P 8c 1 0.34633 (11) 0.16200 (4) 0.45456 (7) 0.0066 (2)
O1 8c 1 0.0438 (4) 0.39928 (14) 0.5749 (2) 0.0119 (5)
O2 8c 1 0.1072 (3) 0.06005 (13) 0.8811 (2) 0.0107 (5)
O3 8c 1 0.1107 (4) 0.2370 (2) 0.9171 (2) 0.0153 (6)
O4 8c 1 0.2228 (3) 0.34868 (13) 0.1330 (2) 0.0104 (5)
O5 8c 1 0.3418 (3) 0.37507 (14) 0.8450 (2) 0.0117 (5)
             
Site U11 U22 U33 U12 U13 U23
Na 0.0207 (9) 0.0159 (7) 0.0229 (9) 0 0.0051 (8) 0
Cu 0.0051 (2) 0.0363 (2) 0.0061 (2) 0.00172 (14) 0.00042 (13) 0.00126 (13)
V 0.0071 (3) 0.0092 (3) 0.0051 (3) 0 −0.0001 (2) 0
P 0.0046 (3) 0.0099 (3) 0.0054 (3) −0.0002 (2) 0.0007 (2) 0.0002 (2)
O1 0.0042 (9) 0.0168 (8) 0.0146 (10) −0.0010 (6) −0.0016 (7) −0.0029 (7)
O2 0.0124 (9) 0.0109 (8) 0.0088 (8) −0.0002 (6) −0.0005 (7) 0.0009 (7)
O3 0.0162 (10) 0.0167 (9) 0.0131 (10) −0.0043 (7) 0.0024 (8) −0.0056 (7)
O4 0.0076 (9) 0.0191 (8) 0.0046 (8) −0.0006 (7) −0.0020 (6) 0.0000 (6)
O5 0.0053 (9) 0.0244 (9) 0.0054 (8) −0.0026 (8) 0.0008 (7) 0.0006 (6)

Table 3
Atomic distances (Å) in NaCu2VP2O10

Na–O1 2.861 (2) (×2)   V–O2 1.649 (2) (×2)
Na–O1 2.434 (2) (×2)   V–O3 2.147 (2) (×2)
Na–O2 2.670 (2) (×2)   V–O4 1.973 (2) (×2)
Na–O4 2.388 (2) (×2)   〈V–O〉 1.9230  
〈Na–O〉 2.5883          
        P–O1 1.522 (2)  
Cu–O1 1.904 (2)     P–O3 1.516 (3)  
Cu–O2 2.060 (2)     P–O4 1.538 (2)  
Cu–O5 1.949 (2)     P–O5 1.561 (2)  
Cu–O5 1.972 (2)     〈P–O〉 1.5343  
〈Cu–O〉 1.9713          
[Figure 2]
Figure 2
Crystal structure model of NaCu2VP2O10. Atom colours: Na (green), Cu (blue), V (yellow), P (pink) and O (red). Ellipsoids are set at a 90% probability level.

The average bond distances of 〈Na–O〉, 〈Cu–O〉, 〈V–O〉 and 〈P–O〉 in the crystal structure of NaCu2VP2O10 were 2.5883, 1.9713, 1.9230 and 1.5343 Å, respectively, which are in good agreement with the bond distances estimated by combinations of the effective ionic radii of the respective ions of 2.58, 1.97, 1.94 and 1.57 Å (Shannon, 1976[Shannon, R. D. (1976). Acta Cryst. A32, 751-767.]). The valence of each site was estimated using the bond valence sum (BVS) method, which is used to calculate valence from experimental parameters and bond distances (Brese & O'Keeffe, 1991[Brese, N. E. & O'Keeffe, M. (1991). Acta Cryst. B47, 192-197.]). The calculated BVS values of the Na, Cu, V and P sites were 1.07, 1.84, 5.08 and 4.84, respectively. The average bond distances and BVS values were appropriate, which suggests that the structure analysis was successfully performed. As shown in Fig. 2[link], Cu ions display characteristic highly anisotropic ellipsoids along the b direction. In general, Cu ions in CuO4 plaquettes prefer the anisotropic displacement perpendicular to the CuO4 plane because there are no apical oxygen ions (Effenberger, 1990[Effenberger, H. (1990). Acta Cryst. C46, 691-692.]; Smith & Keszler, 1991[Smith, R. W. & Keszler, D. A. (1991). J. Solid State Chem. 93, 430-435.]). Furthermore, NaCu2VP2O10 has enough space for Cu ions to fluctuate along the b direction. The anisotropic ellipsoids of the Cu ions can be interpreted from crystallographic considerations. The Flack parameter, which is an index of the ratio of inversion structure, was determined to be 0.018 (14) (Flack & Bernardinelli, 1999[Flack, H. D. & Bernardinelli, G. (1999). Acta Cryst. A55, 908-915.]). Therefore, the measured single crystal is regarded as a monodomain crystal with respect to the inversion twin.

3.3. Magnetic susceptibility

Fig. 3[link] shows the temperature dependence of the magnetic susceptibility measured at 1 T using a single-phase polycrystalline NaCu2VP2O10 sample. The maximum magnetic susceptibility was observed at ∼60 K and the magnetic susceptibility became close to zero upon further cooling. The Curie–Weiss fitting using χ(T) = C/(T − θ) + χ0 for the high-temperature region (>200 K) represents the Weiss temperature of θ = −41.9 K and Curie constant of C = 4.04 × 10−1 emu K/ mol Cu. The inset in Fig. 3[link] shows the temperature dependence of 1/χ, which represents a straight line owing to Curie paramagnetism in the high-temperature region. Both the effective magnetic moment of μeff = 1.80μB and the g factor of 2.07 are decent values for Cu2+ (S = 1/2) compounds. Fitting for the magnetic susceptibility using the isolated spin dimer model (Bleaney & Bowers, 1952[Bleaney, B. & Bowers, K. D. (1952). Proc. R. Soc. A, 214, 451-465.]) resulted in failure (Fig. S3). Alternatively, the data can be fitted in the full range using an alternating Heisenberg chain model (Johnston et al., 2000[Johnston, D. C., Kremer, R. K., Troyer, M., Wang, X., Klümper, A., Bud'ko, S. L., Panchula, A. F. & Canfield, P. C. (2000). Phys. Rev. B, 61, 9558-9606.]) using the expression χ(T) = NAg2μB2/kBJ × χ*(α, T) + Cimp/(T − θimp) + χ0. Here, NA, μB and kB are Avogadro number, Bohr magneton and Boltzmann constant, respectively. The exchange parameter J, alternation parameter α ( = J′/J), Cimp, θimp, and χ0 are the fitting parameters. When α = 0 and α = 1, the function represents the isolated spin dimer and the uniform chain models, respectively. A small impurity Curie–Weiss contribution, which appeared because of magnetic impurities or defects of Cu2+ in NaCu2VP2O10, was observed below ∼5 K. We obtained a Weiss temperature of θimp = −2.38 K and Curie constant of Cimp = 3.72 × 10−3 emu K/ mol Cu, corresponding to 0.99% of nearly free S = 1/2 impurities; χ0 represents the temperature-independent term of −2.35 × 10−5 emu/ mol Cu. We obtained J = 99.3 K, α = 0.72 and a g factor of 2.12 in the S = 1/2 alternating chain model. This α value indicates that there are non-negligible interactions between the dimers. Using the relationship ΔJ(1 − α)3/4(1 + α)1/4, we estimated that the spin gap Δ was 43.4 K. In the thermal analysis, the heat capacity indicated that there were no anomalies below 100 K (Fig. S4). This result suggests that the long-range magnetic order did not evolve and that changes in the magnetic susceptibility were not related to a conventional phase transition. The crystal structure and magnetic susceptibility of NaCu2VP2O10 indicated that it is a spin-gap system.

[Figure 3]
Figure 3
Temperature dependence of the magnetic susceptibility χ of NaCu2VP2O10. Red open symbols represent raw data. The blue solid and black dashed lines show the fitting curves of the alternating chain and Curie–Weiss models. The inset shows the temperature dependence of 1/χ.

4. Discussion

Fig. 4[link](a) shows the crystal structure model of NaCu2VP2O10. The layered structure consisted of Cu2O6 dimers, VO6 octahedra and PO4 tetrahedra, which were connected through corner sharing. The Na ions were located between the polyhedral layers. As shown in Figs. 1[link](a) and 1[link](c), the weak diffuse streak scattering along the [010] direction indicates the presence of stacking faults in the layered structure. The Cu2O6 dimers were almost parallel to the ac plane in each layer. Fig. 4[link](b) depicts the partial structure of one polyhedral layer viewed from the [010] direction. These layers were composed of two-layer units [Figs. 4[link](c) and 4[link](d)]. The two-layer units were related to the twofold screw parallel to the c axis, which was constrained by the symmetry of the crystal structure. Each layer unit was connected by corner-sharing VO6 octahedra and PO4 tetrahedra. Fig. 4[link](c) displays one of the polyhedral layer units, in which the Cu2O6 dimers were connected to two VO6 octahedra and four PO4 tetrahedra. The Cu2O6 dimers lay in a line approximately parallel to the [101] direction. The PO4–VO6–PO4 polyhedral clusters alternated with Cu2O6 dimers to fill the space. In the other polyhedral layer unit, Cu2O6 dimers lay in a line almost along the [10 [{\overline 1}]] direction [Fig. 4[link](d)].

[Figure 4]
Figure 4
Crystal structure models of (a) NaCu2VP2O10 viewed from the a axis, (b) the local structure of a single layered structure, (c) the upper layer unit and (d) the lower layer unit.

Fig. 5[link](a) displays the VO6 octahedron in NaCu2VP2O10. The VO6 octahedron showed anisotropic V–O bond distances. In particular, the V–O2 bond distance of 1.649 Å was shorter than that of the other bonds in the VO6 octahedron. Furthermore, the V–O2 bond distance was not in good agreement with the effective ionic radius of V5+ in sixfold coordination {r[V5+(6)] + r[O2−(6)]} of 1.94 Å (Shannon, 1976[Shannon, R. D. (1976). Acta Cryst. A32, 751-767.]); this bond distance suggests that hybridization occurred between V5+ and O2−. Fig. 5[link](b) also shows anisotropic bond distances, which indicate the large off-centre displacement of V ions. The pseudo-Jahn–Teller effect occurs in the d0 transition-metal octahedra when the empty d orbitals of the metal form hybrid orbitals with the filled p orbitals of the ligands (Bersuker, 2013[Bersuker, I. B. (2013). Chem. Rev. 113, 1351-1390.]; Kunz & Brown, 1995[Kunz, M. & Brown, I. D. (1995). J. Solid State Chem. 115, 395-406.]; Halasyamani & Poeppelmeier, 1998[Halasyamani, P. S. & Poeppelmeier, K. R. (1998). Chem. Mater. 10, 2753-2769.]; Urushihara et al., 2019[Urushihara, D., Asaka, T., Fukuda, K. & Sakurai, H. (2019). Phys. Rev. B, 99, 094104.]). Therefore, V5+ ions with a d0 configuration can display the pseudo-Jahn–Teller effect. It has been reported that in some vanadium oxides, V5+ ions in VO6 octahedra show off-centre displacements in the [110] or [100] direction in simple cubic perovskites (Zavalij & Whittingham, 1999[Zavalij, P. Y. & Whittingham, M. S. (1999). Acta Cryst. B55, 627-663.]; Halasyamani, 2004[Halasyamani, P. S. (2004). Chem. Mater. 16, 3586-3592.]). In NaCu2VP2O10, V5+ ions in the VO6 octahedra also exhibit an off-centre displacement in the [110] direction in the simple cubic perovskite notation. Here, we defined that the direction of the V—O4 bonds is the [001] direction in the simple cubic perovskite. V5+ moves toward the edge of O2 ions connected to the Cu2O6 dimer, as shown in Fig. 5[link](b). The off-centre displacement would arise from the Coulomb repulsion between the higher valence V5+ and P5+ ions and pseudo-Jahn–Teller distortion. In potassium vanadium selenite K(VO2)3(SeO3)2, V5+ ions also represent an off-centre displacement along the [110] direction in the simple cubic perovskite notation (Harrison et al., 1995[Harrison, W. T. A., Dussack, L. L. & Jacobson, A. J. (1995). Acta Cryst. C51, 2473-2476.]). Two of the six V–O bond distances in the VO6 octahedron are much shorter than those expected based on the effective ionic radius. These shorter V—O bonds could be owing to the off-centre displacement towards the octahedral edge, which is accompanied by hybridization between V5+ and O2−, as with NaCu2VP2O10 compounds.

[Figure 5]
Figure 5
Local structure models of (a) a VO6 octahedron, (b) a corner-sharing octahedron and (c) a Cu2O6 dimer of NaCu2VP2O10.

Fig. 5[link](c) shows the local structure around the Cu2O6 dimer. The Cu–O2 bond distance was slightly longer than the other Cu–O bond distances. The green and red dashed lines represent ∠O5—Cu—O2 and ∠O5—Cu—O1 bond angles, which were determined to be 156.4° and 172.7°, respectively. The O2 ions are offset from the prescribed position of the planar CuO4 plaquette. This also suggests that O2 ions strongly connect with V5+, and the bonding state is different from that of other O ions connected to P5+. Thus, NaCu2VP2O10 is expected to exhibit complicated interactions between Cu ions because of Cu—O—V—O—Cu superexchange interactions.

Fig. 6[link] shows the Cu–Cu networks, which are arrangements of magnetic ions. The Cu ions form a puckered-layer structure, which has also been observed in other two-dimensional materials such as black phospho­rus (Brown & Rundqvist, 1965[Brown, A. & Rundqvist, S. (1965). Acta Cryst. 19, 684-685.]; Liu et al., 2014[Liu, H., Neal, A. T., Zhu, Z., Luo, Z., Xu, X., Tománek, D. & Ye, P. D. (2014). ACS Nano, 8, 4033-4041.]). As shown in Figs. 6[link](a) and 6[link](b), the first-nearest-neighbour connection is the Cu pairs in Cu2O6 dimers, which have a distance of 3.021 Å. The dimer bridging angle ∠Cu—O5—Cu is 100.8° [Fig. 5[link](c)]; therefore, it is reasonable to suppose that the intradimer exchange interaction is antiferromagnetic (Crawford et al., 1976[Crawford, V. H., Richardson, H. W., Wasson, J. R., Hodgson, D. J. & Hatfield, W. E. (1976). Inorg. Chem. 15, 2107-2110.]). The second-nearest-neighbour Cu–Cu connection distance was 3.874 Å and the third-nearest-neighbour connection distance was 4.887 Å. Figs. 6[link](c)–6[link](e) display the single layer Cu–Cu network viewed from different directions. The armchair and zigzag directions are along the c and a axes, respectively. For a prototypical puckered-layer structure, such as that of black phospho­rus, two connections in the layer have the same distances. In contrast, the connections in NaCu2VP2O10 have different distances, which correspond to the first- and third-nearest-neighbour connections. Therefore, the Cu–Cu network displays a highly distorted puckered-layer structure. As a result, the Cu–Cu network can be regarded as a pseudo-one-dimensional system; that is, the Cu–Cu chains along the armchair direction correlate with each other. Thus, NaCu2VP2O10 represents a new type of spin dimer compound with a pseudo-one-dimensional system.

[Figure 6]
Figure 6
(a) Crystal structure model of NaCu2VP2O10. Na ions are omitted. (b) Cu–Cu network and local structures of a single layer of the Cu–Cu network along the (c) [010], (d) [100] and (e) [001] directions. Large and small Cu ions represent the atomic positions at the front and back, respectively. The red, green and blue dashed lines indicate the first-, second- and third-nearest-neighbour Cu–Cu bond distances, respectively.

5. Conclusions

In this study, we synthesized the spin dimer compound NaCu2VP2O10. Using selected-area electron diffraction, the space group of NaCu2VP2O10 was revealed to be C2221. The crystal structure of NaCu2VP2O10 consisted of a layered structure containing Cu2O6 dimers, VO6 octahedra and PO4 tetrahedra. Furthermore, temperature-dependent magnetic susceptibility measurements revealed that NaCu2VP2O10 has a non-magnetic ground state and spin gap. V5+ in the VO6 octahedra exhibited off-centre distortion caused by the pseudo-Jahn–Teller effect. The hybridization between V and O2 led to complicated interactions via the Cu—O—V—O—Cu path. The crystal structure and magnetic susceptibility results suggest that NaCu2VP2O10 is a new quantum-spin system owing to dimerized Cu2+.

Supporting information


Computing details top

Data collection: APEX2 (Bruker, 2015); cell refinement: SAINT (Bruker, 2015); data reduction: SAINT (Bruker, 2015); program(s) used to solve structure: SUPERFLIP (Palatinus & Chapuis, 2007); program(s) used to refine structure: JANA2006 (Petříček et al., 2014); molecular graphics: VESTA (Momma & Izumi, 2011).

(I) top
Crystal data top
Cu2NaO10P2VF(000) = 808
Mr = 423Dx = 3.840 Mg m3
Orthorhombic, C2221Mo Kα radiation, λ = 0.71073 Å
Hall symbol: C 2c 2Cell parameters from 13034 reflections
a = 6.1386 (1) Åθ = 2.8–30.5°
b = 14.4646 (3) ŵ = 7.56 mm1
c = 8.2392 (2) ÅT = 298 K
V = 731.58 (3) Å3Block, yellow
Z = 40.06 × 0.06 × 0.03 mm
Data collection top
Bruker CCD
diffractometer
1122 independent reflections
Radiation source: X-ray tube1110 reflections with I > 3σ(I)
Graphite monochromatorRint = 0.025
φ and ω scansθmax = 30.5°, θmin = 2.8°
Absorption correction: multi-scan
SADABS v2014/5 (Bruker, 2014)
h = 88
Tmin = 0.462, Tmax = 0.593k = 2020
13034 measured reflectionsl = 1111
Refinement top
Refinement on F2Weighting scheme based on measured s.u.'s w = 1/(σ2(I) + 0.0016I2)
R[F > 3σ(F)] = 0.023(Δ/σ)max = 0.015
wR(F) = 0.076Δρmax = 1.66 e Å3
S = 1.74Δρmin = 0.87 e Å3
1122 reflectionsExtinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
76 parametersExtinction coefficient: 100 (200)
0 restraintsAbsolute structure: 462 of Friedel pairs used in the refinement
0 constraintsAbsolute structure parameter: 0.018 (14)
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Na00.46651 (11)0.250.0198 (5)
Cu0.15209 (6)0.11957 (3)0.10586 (4)0.01583 (12)
V00.86680 (4)0.250.00715 (16)
P0.34633 (11)0.16200 (4)0.45456 (7)0.00661 (16)
O10.0438 (4)0.39928 (14)0.5749 (2)0.0119 (5)
O20.1072 (3)0.06005 (13)0.8811 (2)0.0107 (5)
O30.1107 (4)0.23698 (15)0.9171 (2)0.0153 (6)
O40.2228 (3)0.34868 (13)0.1330 (2)0.0104 (5)
O50.3418 (3)0.37507 (14)0.8450 (2)0.0117 (5)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Na0.0207 (9)0.0159 (7)0.0229 (9)00.0051 (8)0
Cu0.00505 (19)0.0363 (2)0.00610 (19)0.00172 (14)0.00042 (13)0.00126 (13)
V0.0071 (3)0.0092 (3)0.0051 (3)00.0001 (2)0
P0.0046 (3)0.0099 (3)0.0054 (3)0.0002 (2)0.0007 (2)0.00014 (19)
O10.0042 (9)0.0168 (8)0.0146 (10)0.0010 (6)0.0016 (7)0.0029 (7)
O20.0124 (9)0.0109 (8)0.0088 (8)0.0002 (6)0.0005 (7)0.0009 (7)
O30.0162 (10)0.0167 (9)0.0131 (10)0.0043 (7)0.0024 (8)0.0056 (7)
O40.0076 (9)0.0191 (8)0.0046 (8)0.0006 (7)0.0020 (6)0.0000 (6)
O50.0053 (9)0.0244 (9)0.0054 (8)0.0026 (8)0.0008 (7)0.0006 (6)
Geometric parameters (Å, º) top
Na—Nai4.2321 (5)Cu—Vi3.0834 (4)
Na—Naii4.2321 (5)Cu—O1vii1.904 (2)
Na—Cuiii3.2975 (11)Cu—O2xi2.0604 (17)
Na—Cuiv3.2975 (11)Cu—O3xi2.317 (2)
Na—Vv3.3912 (7)Cu—O5vii1.9722 (17)
Na—Vvi3.3912 (7)Cu—O5viii1.9488 (19)
Na—Piii3.4245 (13)V—O2i1.6486 (16)
Na—Pvii3.2047 (10)V—O2ix1.6486 (16)
Na—Piv3.4245 (13)V—O3i2.147 (2)
Na—Pviii3.2047 (10)V—O3ix2.147 (2)
Na—O1i2.4335 (19)V—O4iii1.9732 (18)
Na—O1ix2.4335 (19)V—O4iv1.9732 (18)
Na—O2vii2.6700 (18)P—O1xii1.522 (2)
Na—O2viii2.6700 (18)P—O3vii1.516 (3)
Na—O42.3881 (19)P—O4xiii1.5380 (18)
Na—O4x2.3881 (19)P—O5vii1.5608 (18)
Cu—Cux3.0213 (5)
Nai—Na—Naii153.52 (5)O1ix—Na—O4138.18 (7)
Nai—Na—Cuiii59.713 (17)O1ix—Na—O4x113.15 (6)
Nai—Na—Cuiv101.35 (3)O2vii—Na—O2viii163.43 (8)
Nai—Na—Vv95.588 (9)O2vii—Na—O462.82 (6)
Nai—Na—Vvi95.588 (9)O2vii—Na—O4x104.54 (6)
Nai—Na—Piii106.86 (4)O2viii—Na—O4104.54 (6)
Nai—Na—Pvii52.66 (2)O2viii—Na—O4x62.82 (6)
Nai—Na—Piv48.07 (2)O4—Na—O4x88.96 (7)
Nai—Na—Pviii150.71 (4)Navi—Cu—Cux96.727 (13)
Nai—Na—O1i40.56 (4)Navi—Cu—Vi125.557 (18)
Nai—Na—O1ix113.23 (6)Navi—Cu—O1vii46.92 (5)
Nai—Na—O2vii115.26 (4)Navi—Cu—O2xi97.47 (5)
Nai—Na—O2viii68.85 (4)Navi—Cu—O3xi143.61 (6)
Nai—Na—O476.73 (4)Navi—Cu—O5vii69.76 (5)
Nai—Na—O4x123.80 (5)Navi—Cu—O5viii125.79 (5)
Naii—Na—Cuiii101.35 (3)Cux—Cu—Vi124.085 (14)
Naii—Na—Cuiv59.713 (17)Cux—Cu—O1vii135.34 (5)
Naii—Na—Vv95.588 (9)Cux—Cu—O2xi128.60 (5)
Naii—Na—Vvi95.588 (9)Cux—Cu—O3xi117.38 (6)
Naii—Na—Piii48.07 (2)Cux—Cu—O5vii39.32 (5)
Naii—Na—Pvii150.71 (4)Cux—Cu—O5viii39.88 (5)
Naii—Na—Piv106.86 (4)Vi—Cu—O1vii100.29 (5)
Naii—Na—Pviii52.66 (2)Vi—Cu—O2xi29.72 (4)
Naii—Na—O1i113.23 (6)Vi—Cu—O3xi44.08 (6)
Naii—Na—O1ix40.56 (4)Vi—Cu—O5vii162.41 (6)
Naii—Na—O2vii68.85 (4)Vi—Cu—O5viii84.21 (5)
Naii—Na—O2viii115.26 (4)O1vii—Cu—O2xi87.18 (7)
Naii—Na—O4123.80 (5)O1vii—Cu—O3xi97.05 (8)
Naii—Na—O4x76.73 (4)O1vii—Cu—O5vii96.94 (7)
Cuiii—Na—Cuiv95.64 (4)O1vii—Cu—O5viii172.70 (7)
Cuiii—Na—Vv72.503 (11)O2xi—Cu—O3xi71.83 (7)
Cuiii—Na—Vvi150.66 (2)O2xi—Cu—O5vii156.46 (6)
Cuiii—Na—Piii56.25 (2)O2xi—Cu—O5viii94.16 (7)
Cuiii—Na—Pvii107.851 (13)O3xi—Cu—O5vii130.09 (7)
Cuiii—Na—Piv56.41 (2)O3xi—Cu—O5viii90.19 (8)
Cuiii—Na—Pviii118.184 (13)O5vii—Cu—O5viii79.02 (7)
Cuiii—Na—O1i34.85 (6)Naiii—V—Naxiv129.67 (4)
Cuiii—Na—O1ix75.49 (6)Naiii—V—Cuii72.468 (8)
Cuiii—Na—O2vii145.83 (6)Naiii—V—Cuxv104.292 (11)
Cuiii—Na—O2viii50.67 (3)Naiii—V—O2i50.65 (6)
Cuiii—Na—O4134.80 (4)Naiii—V—O2ix95.08 (7)
Cuiii—Na—O4x104.69 (4)Naiii—V—O3i90.63 (7)
Cuiv—Na—Vv150.66 (2)Naiii—V—O3ix125.71 (6)
Cuiv—Na—Vvi72.503 (11)Naiii—V—O4iii43.61 (5)
Cuiv—Na—Piii56.41 (2)Naiii—V—O4iv146.82 (5)
Cuiv—Na—Pvii118.184 (13)Naxiv—V—Cuii104.292 (11)
Cuiv—Na—Piv56.25 (2)Naxiv—V—Cuxv72.468 (8)
Cuiv—Na—Pviii107.851 (13)Naxiv—V—O2i95.08 (7)
Cuiv—Na—O1i75.49 (6)Naxiv—V—O2ix50.65 (6)
Cuiv—Na—O1ix34.85 (6)Naxiv—V—O3i125.71 (6)
Cuiv—Na—O2vii50.67 (3)Naxiv—V—O3ix90.63 (7)
Cuiv—Na—O2viii145.83 (6)Naxiv—V—O4iii146.82 (5)
Cuiv—Na—O4104.69 (4)Naxiv—V—O4iv43.61 (5)
Cuiv—Na—O4x134.80 (4)Cuii—V—Cuxv172.67 (2)
Vv—Na—Vvi129.67 (5)Cuii—V—O2i38.29 (5)
Vv—Na—Piii95.843 (17)Cuii—V—O2ix134.66 (6)
Vv—Na—Pvii91.14 (3)Cuii—V—O3i48.64 (6)
Vv—Na—Piv126.91 (2)Cuii—V—O3ix138.60 (7)
Vv—Na—Pviii59.129 (18)Cuii—V—O4iii102.24 (5)
Vv—Na—O1i103.84 (6)Cuii—V—O4iv78.76 (5)
Vv—Na—O1ix116.05 (6)Cuxv—V—O2i134.66 (6)
Vv—Na—O2vii139.12 (5)Cuxv—V—O2ix38.29 (5)
Vv—Na—O2viii28.52 (4)Cuxv—V—O3i138.60 (7)
Vv—Na—O4102.41 (6)Cuxv—V—O3ix48.64 (6)
Vv—Na—O4x34.74 (4)Cuxv—V—O4iii78.76 (5)
Vvi—Na—Piii126.91 (2)Cuxv—V—O4iv102.24 (5)
Vvi—Na—Pvii59.129 (18)O2i—V—O2ix100.21 (8)
Vvi—Na—Piv95.843 (17)O2i—V—O3i84.38 (9)
Vvi—Na—Pviii91.14 (3)O2i—V—O3ix174.16 (9)
Vvi—Na—O1i116.05 (6)O2i—V—O4iii93.50 (8)
Vvi—Na—O1ix103.84 (6)O2i—V—O4iv96.27 (8)
Vvi—Na—O2vii28.52 (4)O2ix—V—O3i174.16 (9)
Vvi—Na—O2viii139.12 (5)O2ix—V—O3ix84.38 (9)
Vvi—Na—O434.74 (4)O2ix—V—O4iii96.27 (8)
Vvi—Na—O4x102.41 (6)O2ix—V—O4iv93.50 (8)
Piii—Na—Pvii159.05 (4)O3i—V—O3ix91.28 (9)
Piii—Na—Piv68.67 (3)O3i—V—O4iii86.99 (8)
Piii—Na—Pviii91.375 (16)O3i—V—O4iv82.35 (8)
Piii—Na—O1i66.59 (5)O3ix—V—O4iii82.35 (8)
Piii—Na—O1ix23.07 (6)O3ix—V—O4iv86.99 (8)
Piii—Na—O2vii99.71 (4)O4iii—V—O4iv164.75 (7)
Piii—Na—O2viii93.97 (4)Navi—P—Naxiii79.27 (3)
Piii—Na—O4161.02 (5)Navi—P—O1xii38.81 (7)
Piii—Na—O4x103.46 (4)Navi—P—O3vii130.35 (8)
Pvii—Na—Piv91.375 (16)Navi—P—O4xiii117.60 (6)
Pvii—Na—Pviii109.10 (4)Navi—P—O5vii68.61 (6)
Pvii—Na—O1i92.57 (4)Naxiii—P—O1xii63.17 (7)
Pvii—Na—O1ix151.69 (6)Naxiii—P—O3vii131.46 (8)
Pvii—Na—O2vii87.58 (4)Naxiii—P—O4xiii45.31 (6)
Pvii—Na—O2viii82.82 (4)Naxiii—P—O5vii117.24 (6)
Pvii—Na—O427.25 (4)O1xii—P—O3vii112.97 (12)
Pvii—Na—O4x93.52 (6)O1xii—P—O4xiii108.28 (9)
Piv—Na—Pviii159.05 (4)O1xii—P—O5vii107.27 (10)
Piv—Na—O1i23.07 (6)O3vii—P—O4xiii109.85 (9)
Piv—Na—O1ix66.59 (5)O3vii—P—O5vii110.02 (10)
Piv—Na—O2vii93.97 (4)O4xiii—P—O5vii108.31 (10)
Piv—Na—O2viii99.71 (4)Naii—O1—Cuxiii98.24 (8)
Piv—Na—O4103.46 (4)Naii—O1—Pviii118.13 (12)
Piv—Na—O4x161.02 (5)Cuxiii—O1—Pviii135.99 (10)
Pviii—Na—O1i151.69 (6)Naxiii—O2—Cuxvi107.64 (7)
Pviii—Na—O1ix92.57 (4)Naxiii—O2—Vii100.83 (8)
Pviii—Na—O2vii82.82 (4)Cuxvi—O2—Vii111.99 (8)
Pviii—Na—O2viii87.58 (4)Cuxvi—O3—Vii87.28 (10)
Pviii—Na—O493.52 (6)Cuxvi—O3—Pxiii123.41 (10)
Pviii—Na—O4x27.25 (4)Vii—O3—Pxiii149.23 (13)
O1i—Na—O1ix74.18 (7)Na—O4—Vvi101.65 (7)
O1i—Na—O2vii117.04 (7)Na—O4—Pvii107.44 (9)
O1i—Na—O2viii77.02 (7)Vvi—O4—Pvii135.91 (11)
O1i—Na—O4113.15 (6)Cuxiii—O5—Cuxii100.80 (8)
O1i—Na—O4x138.18 (7)Cuxiii—O5—Pxiii127.25 (11)
O1ix—Na—O2vii77.02 (7)Cuxii—O5—Pxiii128.06 (10)
O1ix—Na—O2viii117.04 (7)
Symmetry codes: (i) x, y+1, z1/2; (ii) x, y+1, z+1/2; (iii) x1/2, y+1/2, z; (iv) x+1/2, y+1/2, z+1/2; (v) x1/2, y1/2, z; (vi) x+1/2, y1/2, z; (vii) x+1/2, y+1/2, z1/2; (viii) x1/2, y+1/2, z+1; (ix) x, y+1, z+1; (x) x, y, z+1/2; (xi) x, y, z1; (xii) x+1/2, y+1/2, z+1; (xiii) x+1/2, y+1/2, z+1/2; (xiv) x+1/2, y+1/2, z; (xv) x, y+1, z; (xvi) x, y, z+1.
 

Acknowledgements

We thank A. Iwasaka for assistance with electron-probe microanalysis and T. Kimura, K. Kimura, M. Tokunaga, A. Miyake and K. Kindo for helpful discussions.

Funding information

This work was partly supported by the Nanotechnology Platform Program (Molecule and Material Synthesis) of the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.

References

First citationBalents, L. (2010). Nature, 464, 199–208.  Web of Science CrossRef CAS PubMed Google Scholar
First citationBersuker, I. B. (2013). Chem. Rev. 113, 1351–1390.  Web of Science CrossRef CAS PubMed Google Scholar
First citationBleaney, B. & Bowers, K. D. (1952). Proc. R. Soc. A, 214, 451–465.  CAS Google Scholar
First citationBrese, N. E. & O'Keeffe, M. (1991). Acta Cryst. B47, 192–197.  CrossRef CAS Web of Science IUCr Journals Google Scholar
First citationBrown, A. & Rundqvist, S. (1965). Acta Cryst. 19, 684–685.  CrossRef ICSD IUCr Journals Web of Science Google Scholar
First citationBruker (2015). APEX3, SAINT and SADABS. Bruker AXS Inc., Madison, Wisconsin, USA.  Google Scholar
First citationCrawford, V. H., Richardson, H. W., Wasson, J. R., Hodgson, D. J. & Hatfield, W. E. (1976). Inorg. Chem. 15, 2107–2110.  CrossRef CAS Web of Science Google Scholar
First citationEffenberger, H. (1990). Acta Cryst. C46, 691–692.  CrossRef ICSD CAS Web of Science IUCr Journals Google Scholar
First citationFlack, H. D. & Bernardinelli, G. (1999). Acta Cryst. A55, 908–915.  Web of Science CrossRef CAS IUCr Journals Google Scholar
First citationHalasyamani, P. S. (2004). Chem. Mater. 16, 3586–3592.  Web of Science CrossRef CAS Google Scholar
First citationHalasyamani, P. S. & Poeppelmeier, K. R. (1998). Chem. Mater. 10, 2753–2769.  Web of Science CrossRef CAS Google Scholar
First citationHarrison, W. T. A., Dussack, L. L. & Jacobson, A. J. (1995). Acta Cryst. C51, 2473–2476.  CrossRef ICSD CAS Web of Science IUCr Journals Google Scholar
First citationJanson, O., Tsirlin, A. A., Sichelschmidt, J., Skourski, Y., Weickert, F. & Rosner, H. (2011). Phys. Rev. B, 83, 094435.  Web of Science CrossRef Google Scholar
First citationJohnston, D. C., Kremer, R. K., Troyer, M., Wang, X., Klümper, A., Bud'ko, S. L., Panchula, A. F. & Canfield, P. C. (2000). Phys. Rev. B, 61, 9558–9606.  Web of Science CrossRef CAS Google Scholar
First citationKageyama, H., Yoshimura, K., Stern, R., Mushnikov, N. V., Onizuka, K., Kato, M., Kosuge, K., Slichter, C. P., Goto, T. & Ueda, Y. (1999). Phys. Rev. Lett. 82, 3168–3171.  Web of Science CrossRef CAS Google Scholar
First citationKlyushina, E. S., Tiegel, A. C., Fauseweh, B., Islam, A. T. M. N., Park, J. T., Klemke, B., Honecker, A., Uhrig, G. S., Manmana, S. R. & Lake, B. (2016). Phys. Rev. B, 93, 241109.  Web of Science CrossRef Google Scholar
First citationKunz, M. & Brown, I. D. (1995). J. Solid State Chem. 115, 395–406.  CrossRef CAS Web of Science Google Scholar
First citationLee, P. A. (2008). Rep. Prog. Phys. 71, 012501.  Web of Science CrossRef Google Scholar
First citationLiu, H., Neal, A. T., Zhu, Z., Luo, Z., Xu, X., Tománek, D. & Ye, P. D. (2014). ACS Nano, 8, 4033–4041.  Web of Science CrossRef CAS PubMed Google Scholar
First citationMomma, K. & Izumi, F. (2011). J. Appl. Cryst. 44, 1272–1276.  Web of Science CrossRef CAS IUCr Journals Google Scholar
First citationPalatinus, L. & Chapuis, G. (2007). J. Appl. Cryst. 40, 786–790.  Web of Science CrossRef CAS IUCr Journals Google Scholar
First citationPetricek, V., Dusek, M. & Palatinus, L. (2014). Z. Kristallogr. 229, 345–352.  CAS Google Scholar
First citationShannon, R. D. (1976). Acta Cryst. A32, 751–767.  CrossRef CAS IUCr Journals Web of Science Google Scholar
First citationSmith, R. W. & Keszler, D. A. (1991). J. Solid State Chem. 93, 430–435.  CrossRef ICSD CAS Web of Science Google Scholar
First citationUrushihara, D., Asaka, T., Fukuda, K. & Sakurai, H. (2019). Phys. Rev. B, 99, 094104.  Web of Science CrossRef Google Scholar
First citationVogt, R. & Müller-Buschbaum, H. (1990). Z. Anorg. Allg. Chem. 591, 167–173.  CrossRef ICSD CAS Web of Science Google Scholar
First citationZavalij, P. Y. & Whittingham, M. S. (1999). Acta Cryst. B55, 627–663.  Web of Science CrossRef CAS IUCr Journals Google Scholar

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Volume 7| Part 4| July 2020| Pages 656-662
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