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Crystal structures and comparisons of potassium rare-earth molybdates KRE(MoO4)2 (RE = Tb, Dy, Ho, Er, Yb, and Lu)

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aPacific Northwest National Laboratory, Richland, WA 99354, USA, and bDepartment of Civil and Environmental Engineering and Earth Sciences, University, of Notre Dame, Notre Dame, IN 46556, USA
*Correspondence e-mail: saehwa.chong@pnnl.gov

Edited by P. Roussel, ENSCL, France (Received 20 July 2020; accepted 20 November 2020; online 27 November 2020)

Six potassium rare-earth molybdates KRE(MoO4)2 (RE = Tb, Dy, Ho, Er, Yb, and Lu) were synthesized by flux-assisted growth in K2Mo3O10. The crystal structures were determined using single-crystal X-ray diffraction data. The synthesized molybdates crystallize with the ortho­rhom­bic Pbcn space group (No. 60). Trendlines for unit-cell parameters were calculated using data from the current study. The unit-cell parameters a and c increase linearly whereas b decreases with larger RE cations, based on crystal radii. The unit-cell volumes increase linearly and the densities decrease linearly with larger RE cations. The average distances between the RE cations and the nearest O atoms increase with larger cations whereas the average distances of Mo—O and K—O do not show specific trends.

1. Chemical context

Rare-earth (RE) molybdates have been studied extensively because of their luminescent, magnetoelectric, and ferroelectric properties (Borchardt & Bierstedt, 1967[Borchardt, H. J. & Bierstedt, P. E. (1967). J. Appl. Phys. 38, 2057-2060.]; Axe et al., 1971[Axe, J., Dorner, B. & Shirane, G. (1971). Phys. Rev. Lett. 26, 519-523.]; Pratap et al., 1987[Pratap, V., Gaur, K. & Lal, H. B. (1987). Mater. Res. Bull. 22, 1381-1393.]; Ponomarev et al., 1994[Ponomarev, B. K., Ivanov, S. A., Popov, Y. F., Negrii, V. D. & Red'Kin, B. S. (1994). Ferroelectrics, 161, 43-48.]; Shi et al., 1996[Shi, F., Meng, J. & Ren, Y. (1996). J. Solid State Chem. 121, 236-239.]; Kut'ko, 2005[Kut'ko, V. I. (2005). Low Temp. Phys. 31, 1-31.]; Wang et al., 2007[Wang, Z., Liang, H., Gong, M. & Su, Q. (2007). J. Alloys Compd. 432, 308-312.]; Ponomarev & Zhukov, 2012[Ponomarev, B. K. & Zhukov, A. (2012). Phys. Res. Int. 2012, 276348-1-27634, 8-22.]). The RE molybdates of ARE(MoO4)2 (A = Li, Na, K, Rb, Cs, Ag) generally crystallize with the tetra­gonal I41/a space group with the scheelite (CaWO4) structure or the ortho­rhom­bic Pbcn space group (Wanklyn & Wondre, 1978[Wanklyn, B. M. & Wondre, F. R. (1978). J. Cryst. Growth, 43, 93-100.]; Hanuza & Fomitsev, 1980[Hanuza, J. & Fomitsev, V. V. (1980). J. Mol. Struct. 66, 1-24.]; Leask et al., 1981[Leask, M. J. M., Tropper, A. C. & Wells, M. R. (1981). J. Phys. C.: Solid State Phys. 14, 3481-3498.]; Hanuza et al., 1994[Hanuza, J., Macalik, L. & Hermanowicz, K. (1994). J. Mol. Struct. 319, 17-30.]; Stedman et al., 1994[Stedman, N. J., Cheetham, A. K. & Battle, P. D. (1994). J. Mater. Chem. 4, 707-711.]; Shi et al., 1996[Shi, F., Meng, J. & Ren, Y. (1996). J. Solid State Chem. 121, 236-239.]; Voron'ko et al., 2004[Voron'ko, Y. K., Zharikov, E. V., Lis, D., Sobol, A. A., Subbotin, K. A., Ushakov, S. N. & Shukshin, V. E. (2004). Laser Optics 2003: Solid State Lasers and Nonlinear Frequency Conversion, pp. 60-68. International Society for Optics and Photonics.]; Kut'ko, 2005[Kut'ko, V. I. (2005). Low Temp. Phys. 31, 1-31.]; Wang et al., 2007[Wang, Z., Liang, H., Gong, M. & Su, Q. (2007). J. Alloys Compd. 432, 308-312.]; Mat'aš et al., 2010[Mat'aš, S., Dudzik, E., Feyerherm, R., Gerischer, S., Klemke, S., Prokeš, K. & Orendáčová, A. (2010). Phys. Rev. B, 82, 184427-1-18442, 7-8.]; Poperezhai et al., 2017[Poperezhai, S., Gogoi, P., Zubenko, N., Kutko, K., Kutko, V. I., Kovalev, A. S. & Kamenskyi, D. (2017). J. Phys. Condens. Matter, 29, 095402-1-09540, 2-6.]). The ARE(MoO4)2 compounds having the I41/a space group have luminescent properties with high thermal and hydrolytic stability (Stedman et al., 1994[Stedman, N. J., Cheetham, A. K. & Battle, P. D. (1994). J. Mater. Chem. 4, 707-711.]; Shi et al., 1996[Shi, F., Meng, J. & Ren, Y. (1996). J. Solid State Chem. 121, 236-239.]; Voron'ko et al., 2004[Voron'ko, Y. K., Zharikov, E. V., Lis, D., Sobol, A. A., Subbotin, K. A., Ushakov, S. N. & Shukshin, V. E. (2004). Laser Optics 2003: Solid State Lasers and Nonlinear Frequency Conversion, pp. 60-68. International Society for Optics and Photonics.]; Wang et al., 2007[Wang, Z., Liang, H., Gong, M. & Su, Q. (2007). J. Alloys Compd. 432, 308-312.]) whereas the compounds with the Pbcn space group are known for the structural phase transition by the Jahn–Teller effect (Kut'ko, 2005[Kut'ko, V. I. (2005). Low Temp. Phys. 31, 1-31.]; Mat'aš et al., 2010[Mat'aš, S., Dudzik, E., Feyerherm, R., Gerischer, S., Klemke, S., Prokeš, K. & Orendáčová, A. (2010). Phys. Rev. B, 82, 184427-1-18442, 7-8.]; Kamenskyi et al., 2014[Kamenskyi, D., Poperezhai, S., Gogoi, P., Engelkamp, H., Maan, J., Wosnitza, J. & Kut'ko, V. (2014). Phys. Rev. B, 89, 014410-1-01441.]; Poperezhai et al., 2017[Poperezhai, S., Gogoi, P., Zubenko, N., Kutko, K., Kutko, V. I., Kovalev, A. S. & Kamenskyi, D. (2017). J. Phys. Condens. Matter, 29, 095402-1-09540, 2-6.]). Other well-known RE molybdates RE2(MoO4)3 (RE = La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy) crystallize with different space groups including P21/c, C2/c, or P2m depending on the RE cations and the synthesis conditions (Brixner et al., 1979[Brixner, L. H., Barkley, J. R. & Jeitschko, W. (1979). Handbook on the Physics and Chemistry of Rare Earths, Vol. 3, pp. 609-654. Berlin, Heidelberg, New York: Springer.]; Jeitschko, 1973[Jeitschko, W. (1973). Acta Cryst. B29, 2074-2081.]; Ponomarev & Zhukov, 2012[Ponomarev, B. K. & Zhukov, A. (2012). Phys. Res. Int. 2012, 276348-1-27634, 8-22.]; Pratap et al., 1987[Pratap, V., Gaur, K. & Lal, H. B. (1987). Mater. Res. Bull. 22, 1381-1393.]); these phases exhibit magnetoelectric and ferroelectric properties (Borchardt & Bierstedt, 1967[Borchardt, H. J. & Bierstedt, P. E. (1967). J. Appl. Phys. 38, 2057-2060.]; Axe et al., 1971[Axe, J., Dorner, B. & Shirane, G. (1971). Phys. Rev. Lett. 26, 519-523.]; Ponomarev et al., 1994[Ponomarev, B. K., Ivanov, S. A., Popov, Y. F., Negrii, V. D. & Red'Kin, B. S. (1994). Ferroelectrics, 161, 43-48.]; Ponomarev & Zhukov, 2012[Ponomarev, B. K. & Zhukov, A. (2012). Phys. Res. Int. 2012, 276348-1-27634, 8-22.]). The RE molybdate compounds are synthesized using flux-assisted or solid-state synthesis methods. Wanklyn & Wondre (1978[Wanklyn, B. M. & Wondre, F. R. (1978). J. Cryst. Growth, 43, 93-100.]) synthesized KRE(MoO4)2 (RE = La, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Lu) compounds by the flux-assisted method using REOx, MoO3, and K2SO4 at 1000°C for 24 h. They reported that crystals containing RE = Tb → Lu crystallized in the Pbcn space group whereas RE = La and Pr crystallized in the I41/a space group and others were not defined (Wanklyn & Wondre, 1978[Wanklyn, B. M. & Wondre, F. R. (1978). J. Cryst. Growth, 43, 93-100.]). Shi et al. (1996[Shi, F., Meng, J. & Ren, Y. (1996). J. Solid State Chem. 121, 236-239.]) synth­esized the AgRE(MoO4)2 (RE = Eu, Gd, Tb) compounds with a tetra­gonal scheelite-type structure by heating the stoichiometric mixtures of REOx, Ag2O, and MoO3 at 800°C for 50 h. Wang et al. (2007[Wang, Z., Liang, H., Gong, M. & Su, Q. (2007). J. Alloys Compd. 432, 308-312.]) synthesized the tetra­gonal AEu(MoO4)2 (A = Li, Na, K) compounds by heating a mixture of REOx, LiCO3, NaHCO3, K2CO3, and (NH4)6Mo7O24·4H2O at 550–750°C for 4 h. The RE2(MoO4)3 compounds were synthesized by heating a mixture of REOx and MoO3 at 900–1000°C (Borchardt & Bierstedt, 1967[Borchardt, H. J. & Bierstedt, P. E. (1967). J. Appl. Phys. 38, 2057-2060.]; Guzmán-Afonso et al., 2013[Guzmán-Afonso, C., González-Silgo, C., Torres, M., Matesanz, E. & Mujica, A. (2013). J. Phys. Condens. Matter, 25, 035902-1-03590, 2-10.]).

2. Structural commentary

The title KRE(MoO4)2 compounds crystallized in the ortho­rhom­bic Pbcn space group and have alternating layers of [RE(MoO4)2] and K+ ions (Fig. 1[link]a). The [RE(MoO4)2] layer contains chains formed by edge-sharing REO8 octa­hedra connected by MoO4 tetra­hedra along the c-axis direction (Fig. 1[link]b). The trendlines of the structural parameters were calculated using data from the current study. The unit-cell parameters of a and c increase while those of b decrease linearly with increasing size of the RE cations (Fig. 2[link]). Although these trends are shown clearly, there are large deviations from the trendlines for some molybdates including Tb and Tm molybdates for unit-cell parameter a, and Tb and Yb for unit-cell parameter b. The unit-cell volume of the Yb compound also shows a large deviation. Compared to the structural parameters from the previous studies (PDF 00-050-1762 and PDF 00-052-1688) on the Yb compound, the cell length b is longer by ∼0.02 Å, and the unit-cell volume is larger by ∼2 Å3. The structural parameters in these previous studies are from powder samples whereas the data in this study are from single-crystal studies. These inconsistencies could be due to possible mixed valences of RE or non-stoich­iometry of RE sites. However, the bond-valence calculations for all the KRE(MoO4)2 compounds show that the bond-valence sums of RE cations are close to 3 (Table 1[link]). The average distances between the RE cations and neighboring O atoms increase with larger RE cations whereas there are no trends for <Mo—O> or <K—O> (Fig. 3[link]). Further investigation should be done in the future to understand these deviations from the law. The unit-cell volumes increase linearly whereas the densities of the phases decrease linearly as the radius of the RE cations increases (Fig. 2[link]).

Table 1
Bond-valence (v.u.) calculations for the title KRE(MoO4)2 compounds

Detailed tables are included in the supporting information.

  KTb(MoO4)2 KDy(MoO4)2 KHo(MoO4)2 KEr(MoO4)2 KYb(MoO4)2 KLu(MoO4)2
RE 3.11 2.97 3.25 3.00 2.97 3.13
Mo 5.66 5.66 5.62 5.65 5.66 5.70
K 1.20 1.21 1.19 1.20 1.10 1.13
O1 1.99 1.97 2.00 1.98 1.98 2.00
O2 1.82 1.80 1.82 1.80 1.79 1.82
O3 1.90 1.92 1.97 1.92 1.91 1.91
O4 2.06 2.07 2.07 2.05 2.03 2.09
[Figure 1]
Figure 1
(a) Crystal structure of KRE(MoO4)2 and (b) [RE(MoO4)2] layer showing the chains composed of REO8 octa­hedra connected by MoO4 tetra­hedra along the c-axis direction.
[Figure 2]
Figure 2
Summary of (a) unit-cell parameter a, (b) unit-cell parameter b, (c) unit-cell parameter c, (d) unit-cell volume (V), and (e) density (ρ) as a function of the average crystal radii of the RE in the crystal structures (coordination number = 8) from Shannon (1976[Shannon, R. D. (1976). Acta Cryst. A32, 751-767.]).
[Figure 3]
Figure 3
Average distances of (a) <K—O>, (b) <RE—O>, and (c) <Mo—O> of KRE(MoO4)2 compounds.

3. Synthesis and crystallization

The single crystals of KRE(MoO4)2 were synthesized using Tb4O7 (Alfa Aesar, 99.9%), Dy2O3 (Alfa Aesar, 99.9%), Ho2O3 (Alfa Aesar, 99.9%), Er2O3 (Alfa Aesar, 99.9%), Yb2O3 (Alfa Aesar, 99.9%), Lu2O3 (Alfa Aesar, 99.9%), K2CO3 (Alfa Aesar, 99%), and MoO3 (Alfa Aesar, 99.5%). All the chemicals were used as received. First, K2Mo3O10 was synthesized using K2CO3 and MoO3 by heating at 520°C for 8 h as described in a previous study (Chong et al., 2020[Chong, S., Riley, B. J., Nelson, Z. J. & Perry, S. N. (2020). Acta Cryst. E76, 339-343.]). The stoichiometric mixture of REOx and K2Mo3O10 was put into a Pt/10%Rh crucible with a lid and placed in a Thermolyne box furnace. The furnace was heated to 1150°C at 5°C min−1, dwelled for 10 h, cooled to 400°C at 5°C h−1 in air, and then shut off. The single crystals were recovered from the solidified flux after washing in an ultrasonic bath with deionized water and using vacuum filtration. In addition to the listed six crystals, KTm(MoO4)2 was synthesized similarly, but it was not reported in this study due to the unresolved residual electron densities during structural refinement. All the KRE(MoO4)2 crystals were plates (Fig. 4[link]) with different colors (Fig. 5[link]).

[Figure 4]
Figure 4
SEM micrographs of KRE(MoO4)2. Artifacts on the surface of several crystals shown resemble residual flux not fully removed during rinsing.
[Figure 5]
Figure 5
Pictures of recovered crystals of KRE(MoO4)2 showing various sizes and colors.

4. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 2[link]. A hemisphere of data was collected on two crystals (RE = Ho, Yb) using a Bruker APEXII Qu­azar diffractometer equipped with a microsource tube emitting monochromated Mo Kα X-ray radiation and collected on a CCD detector. Data were collected for five crystals (RE = Dy, Er, Lu, Tb, Tm) with a Rigaku XtaLab Synergy diffractometer using a single microfocus Mo Kα X-ray radiation source in a sealed tube, equipped with a Hybrid Pixel (HyPix) Array detector and using an Oxford liquid-nitro­gen Cryostream. For the Bruker datasets, APEX3 software (Bruker, 2014[Bruker (2014). APEX3. Bruker AXS Inc., Madison, Wisconsin, USA.]) was used for determining the unit cell and integrating the collected reflection data. Absorption corrections were applied with the SADABS software package (Krause et al., 2015[Krause, L., Herbst-Irmer, R., Sheldrick, G. M. & Stalke, D. (2015). J. Appl. Cryst. 48, 3-10.]). For the Rigaku datasets, the CrysAlis Pro software package was used for unit-cell determination and data integration (Rigaku OD, 2019[Rigaku OD (2019). CrysAlis PRO. Rigaku Oxford Diffraction, Yarnton, England.]). The numerical absorption correction was applied utilizing SCALE3 ABSPACK (Clark & Reid, 1995[Clark, R. C. & Reid, J. S. (1995). Acta Cryst. A51, 887-897.]). All structures were solved by the intrinsic phasing method using SHELXT and refined with SHELXL (Sheldrick, 2015a[Sheldrick, G. M. (2015a). Acta Cryst. A71, 3-8.],b[Sheldrick, G. M. (2015b). Acta Cryst. C71, 3-8.]) within the OLEX2 software package (Dolomanov et al., 2009[Dolomanov, O. V., Bourhis, L. J., Gildea, R. J., Howard, J. A. K. & Puschmann, H. (2009). J. Appl. Cryst. 42, 339-341.]).

Table 2
Experimental details

  KTb(MoO4)2 KDy(MoO4)2 KHo(MoO4)2
Crystal data
Mr 517.90 521.48 523.91
Crystal system, space group Orthorhombic, Pbcn Orthorhombic, Pbcn Orthorhombic, Pbcn
Temperature (K) 100 100 273
a, b, c (Å) 5.0826 (1), 18.1273 (7), 7.9875 (2) 5.0776 (2), 18.1214 (7), 7.9428 (3) 5.0770 (15), 18.161 (5), 7.934 (2)
V3) 735.92 (4) 730.84 (5) 731.5 (4)
Z 4 4 4
Radiation type Mo Kα Mo Kα Mo Kα
μ (mm−1) 13.43 14.07 14.66
Crystal size (mm) 0.36 × 0.20 × 0.04 0.11 × 0.11 × 0.03 0.06 × 0.06 × 0.04
 
Data collection
Diffractometer Rigaku XtaLAB Synergy-S, HyPix Rigaku XtaLAB Synergy-S, HyPix Bruker APEXII CCD
Absorption correction Gaussian (CrysAlis PRO; Rigaku OD, 2019[Rigaku OD (2019). CrysAlis PRO. Rigaku Oxford Diffraction, Yarnton, England.]) Gaussian (CrysAlis PRO; Rigaku OD, 2019[Rigaku OD (2019). CrysAlis PRO. Rigaku Oxford Diffraction, Yarnton, England.]) Multi-scan (SADABS; Krause et al., 2015[Krause, L., Herbst-Irmer, R., Sheldrick, G. M. & Stalke, D. (2015). J. Appl. Cryst. 48, 3-10.])
Tmin, Tmax 0.035, 0.703 0.247, 0.695 0.248, 0.343
No. of measured, independent and observed [I > 2σ(I)] reflections 13792, 1350, 1238 17317, 1388, 1196 7665, 936, 818
Rint 0.069 0.075 0.032
 
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.033, 0.102, 1.08 0.033, 0.088, 1.10 0.027, 0.063, 1.25
No. of reflections 1350 1388 936
No. of parameters 56 56 56
Δρmax, Δρmin (e Å−3) 2.63, −2.78 2.38, −2.65 1.51, −1.37
  KEr(MoO4)2 KYb(MoO4)2 KLu(MoO4)2
Crystal data
Mr 526.24 532.02 533.95
Crystal system, space group Orthorhombic, Pbcn Orthorhombic, Pbcn Orthorhombic, Pbcn
Temperature (K) 100 273 100
a, b, c (Å) 5.0602 (2), 18.1965 (8), 7.8920 (3) 5.0417 (5), 18.3039 (19), 7.8693 (8) 5.0292 (2), 18.2519 (10), 7.8174 (4)
V3) 726.68 (5) 726.20 (13) 717.58 (6)
Z 4 4 4
Radiation type Mo Kα Mo Kα Mo Kα
μ (mm−1) 15.42 16.75 17.68
Crystal size (mm) 0.28 × 0.15 × 0.02 0.06 × 0.06 × 0.04 0.44 × 0.15 × 0.04
 
Data collection
Diffractometer Rigaku XtaLAB Synergy-S, HyPix Bruker APEXII CCD Rigaku XtaLAB Synergy-S, HyPix
Absorption correction Gaussian (CrysAlis PRO; Rigaku OD, 2019[Rigaku OD (2019). CrysAlis PRO. Rigaku Oxford Diffraction, Yarnton, England.]) Multi-scan (SADABS; Krause et al., 2015[Krause, L., Herbst-Irmer, R., Sheldrick, G. M. & Stalke, D. (2015). J. Appl. Cryst. 48, 3-10.]) Multi-scan (CrysAlis PRO; Rigaku OD, 2019[Rigaku OD (2019). CrysAlis PRO. Rigaku Oxford Diffraction, Yarnton, England.])
Tmin, Tmax 0.091, 0.911 0.198, 0.301 0.240, 1.000
No. of measured, independent and observed [I > 2σ(I)] reflections 21246, 1386, 1255 8164, 978, 845 19857, 1105, 1004
Rint 0.072 0.038 0.087
 
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.027, 0.073, 1.06 0.022, 0.063, 1.11 0.027, 0.077, 1.17
No. of reflections 1386 978 1105
No. of parameters 56 56 57
Δρmax, Δρmin (e Å−3) 2.04, −1.62 1.55, −1.14 2.05, −3.03
Computer programs: CrysAlis PRO (Rigaku OD, 2019[Rigaku OD (2019). CrysAlis PRO. Rigaku Oxford Diffraction, Yarnton, England.]), APEX3 (Bruker, 2014[Bruker (2014). APEX3. Bruker AXS Inc., Madison, Wisconsin, USA.]), SHELXT (Sheldrick, 2015a[Sheldrick, G. M. (2015a). Acta Cryst. A71, 3-8.]), SHELXL (Sheldrick, 2015b[Sheldrick, G. M. (2015b). Acta Cryst. C71, 3-8.]), OLEX2 (Dolomanov et al., 2009[Dolomanov, O. V., Bourhis, L. J., Gildea, R. J., Howard, J. A. K. & Puschmann, H. (2009). J. Appl. Cryst. 42, 339-341.]), and publCIF (Westrip, 2010[Westrip, S. P. (2010). J. Appl. Cryst. 43, 920-925.]).

Supporting information


Computing details top

Data collection: CrysAlis PRO (Rigaku OD, 2019) for Tb_Molybdate, Dy_Molybdate, Er_Molybdate, Lu_Molybdate; APEX3 (Bruker, 2014) for Ho_Molybdate, Yb_Molybdate. Cell refinement: CrysAlis PRO (Rigaku OD, 2019) for Tb_Molybdate, Dy_Molybdate, Er_Molybdate, Lu_Molybdate; APEX3 (Bruker, 2014) for Ho_Molybdate, Yb_Molybdate. Data reduction: CrysAlis PRO (Rigaku OD, 2019) for Tb_Molybdate, Dy_Molybdate, Er_Molybdate, Lu_Molybdate; APEX3 (Bruker, 2014) for Ho_Molybdate, Yb_Molybdate. For all structures, program(s) used to solve structure: SHELXT (Sheldrick, 2015a); program(s) used to refine structure: SHELXL (Sheldrick, 2015b); molecular graphics: OLEX2 (Dolomanov et al., 2009); software used to prepare material for publication: publCIF (Westrip, 2010).

Potassium terbium bis(molybdate) (Tb_Molybdate) top
Crystal data top
KTb(MoO4)2F(000) = 928
Mr = 517.90Dx = 4.674 Mg m3
Orthorhombic, PbcnMo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2n 2abCell parameters from 6923 reflections
a = 5.0826 (1) Åθ = 2.3–33.5°
b = 18.1273 (7) ŵ = 13.43 mm1
c = 7.9875 (2) ÅT = 100 K
V = 735.92 (4) Å3Plate, white
Z = 40.36 × 0.20 × 0.04 mm
Data collection top
Rigaku XtaLAB Synergy-S, HyPix
diffractometer
1350 independent reflections
Radiation source: micro-focus sealed X-ray tube1238 reflections with I > 2σ(I)
Mirror monochromatorRint = 0.069
Detector resolution: 10.0000 pixels mm-1θmax = 33.7°, θmin = 2.3°
ω scansh = 76
Absorption correction: gaussian
(CrysAlisPro; Rigaku OD, 2019)
k = 2727
Tmin = 0.035, Tmax = 0.703l = 1212
13792 measured reflections
Refinement top
Refinement on F20 restraints
Least-squares matrix: full0 constraints
R[F2 > 2σ(F2)] = 0.033Primary atom site location: dual
wR(F2) = 0.102 w = 1/[σ2(Fo2) + (0.0705P)2 + 1.3389P]
where P = (Fo2 + 2Fc2)/3
S = 1.08(Δ/σ)max = 0.002
1350 reflectionsΔρmax = 2.63 e Å3
56 parametersΔρmin = 2.78 e Å3
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Refinement. Reflections were merged by SHELXL according to the crystal class for the calculation of statistics and refinement.

_reflns_Friedel_fraction is defined as the number of unique Friedel pairs measured divided by the number that would be possible theoretically, ignoring centric projections and systematic absences.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Tb10.0000000.49384 (2)0.2500000.00653 (12)
Mo10.48012 (7)0.60289 (2)0.48337 (5)0.00701 (12)
K10.5000000.77012 (8)0.7500000.0114 (2)
O20.7489 (5)0.53496 (13)0.5042 (2)0.0089 (4)
O40.6111 (5)0.69028 (13)0.4759 (3)0.0105 (5)
O10.2592 (5)0.59503 (12)0.3093 (3)0.0099 (4)
O30.2716 (5)0.60251 (12)0.6603 (3)0.0102 (4)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Tb10.00409 (18)0.01076 (18)0.00476 (17)0.0000.00033 (5)0.000
Mo10.00425 (19)0.01069 (19)0.00610 (19)0.00024 (8)0.00066 (7)0.00020 (10)
K10.0118 (5)0.0136 (5)0.0089 (5)0.0000.0008 (3)0.000
O20.0056 (12)0.0138 (9)0.0073 (9)0.0017 (9)0.0008 (6)0.0002 (7)
O40.0096 (12)0.0130 (10)0.0089 (10)0.0036 (9)0.0011 (7)0.0007 (8)
O10.0069 (10)0.0143 (10)0.0084 (10)0.0001 (8)0.0021 (8)0.0002 (8)
O30.0089 (10)0.0144 (10)0.0073 (9)0.0003 (8)0.0003 (8)0.0008 (7)
Geometric parameters (Å, º) top
Tb1—Tb1i4.0000 (1)Mo1—O31.767 (2)
Tb1—Tb1ii4.0000 (1)K1—Mo1xi3.8378 (9)
Tb1—K1iii4.2788 (14)K1—Mo1xii3.7062 (11)
Tb1—O2iv2.399 (2)K1—Mo1xiii3.8378 (9)
Tb1—O2v2.399 (2)K1—O42.684 (2)
Tb1—O2vi2.511 (2)K1—O4xiv2.771 (2)
Tb1—O2vii2.511 (2)K1—O4xii2.684 (2)
Tb1—O1viii2.308 (2)K1—O4xv2.771 (2)
Tb1—O12.308 (2)K1—O1xiii2.817 (3)
Tb1—O3ix2.339 (2)K1—O1xi2.817 (3)
Tb1—O3ii2.339 (2)K1—O33.330 (3)
Mo1—K13.7062 (11)K1—O3xii3.330 (3)
Mo1—K1x3.9694 (9)O2—Tb1iv2.399 (2)
Mo1—K1iii3.8378 (9)O2—Tb1xvi2.511 (2)
Mo1—O21.847 (2)O4—K1x2.771 (2)
Mo1—O41.719 (2)O1—K1iii2.817 (3)
Mo1—O11.793 (2)O3—Tb1ii2.339 (2)
Tb1ii—Tb1—Tb1i173.598 (18)Mo1xiii—K1—Mo1xi106.29 (4)
Tb1ii—Tb1—K1iii86.799 (9)Mo1—K1—Mo1xiii103.230 (11)
Tb1i—Tb1—K1iii86.799 (9)Mo1xii—K1—Mo1xiii138.798 (13)
O2iv—Tb1—Tb1i146.02 (5)Mo1—K1—Mo1xii70.24 (3)
O2v—Tb1—Tb1i36.40 (5)Mo1xii—K1—Mo1xi103.230 (11)
O2vi—Tb1—Tb1i34.54 (5)O4xii—K1—Mo191.25 (6)
O2vii—Tb1—Tb1i142.24 (5)O4—K1—Mo1xii91.25 (6)
O2iv—Tb1—Tb1ii36.40 (5)O4xiv—K1—Mo1xi72.98 (5)
O2v—Tb1—Tb1ii146.02 (5)O4xiv—K1—Mo1xii127.27 (6)
O2vi—Tb1—Tb1ii142.24 (5)O4xii—K1—Mo1xi78.09 (5)
O2vii—Tb1—Tb1ii34.54 (5)O4—K1—Mo125.32 (5)
O2vi—Tb1—K1iii72.73 (5)O4xiv—K1—Mo179.53 (5)
O2vii—Tb1—K1iii72.73 (5)O4—K1—Mo1xiii78.09 (5)
O2v—Tb1—K1iii102.57 (6)O4—K1—Mo1xi148.56 (6)
O2iv—Tb1—K1iii102.57 (6)O4xii—K1—Mo1xiii148.57 (6)
O2vii—Tb1—O2vi145.47 (11)O4xv—K1—Mo1xi88.96 (6)
O2iv—Tb1—O2vi117.12 (10)O4xv—K1—Mo1xiii72.98 (5)
O2iv—Tb1—O2vii70.93 (9)O4xii—K1—Mo1xii25.32 (5)
O2v—Tb1—O2vi70.93 (9)O4xiv—K1—Mo1xiii88.96 (6)
O2v—Tb1—O2vii117.12 (10)O4xv—K1—Mo1127.27 (6)
O2v—Tb1—O2iv154.87 (11)O4xv—K1—Mo1xii79.53 (5)
O1—Tb1—Tb1i99.23 (6)O4xii—K1—O4xv76.03 (6)
O1viii—Tb1—Tb1i75.57 (6)O4—K1—O4xv121.38 (3)
O1—Tb1—Tb1ii75.57 (6)O4xv—K1—O4xiv149.97 (11)
O1viii—Tb1—Tb1ii99.23 (6)O4—K1—O4xiv76.03 (6)
O1viii—Tb1—K1iii37.35 (6)O4xii—K1—O4xiv121.38 (3)
O1—Tb1—K1iii37.35 (6)O4—K1—O4xii114.75 (11)
O1viii—Tb1—O2iv130.14 (8)O4xii—K1—O1xi103.44 (7)
O1—Tb1—O2vi68.88 (7)O4—K1—O1xi134.69 (7)
O1viii—Tb1—O2vii68.88 (7)O4—K1—O1xiii103.44 (7)
O1viii—Tb1—O2vi83.59 (8)O4xiv—K1—O1xiii89.97 (8)
O1—Tb1—O2iv72.62 (8)O4xiv—K1—O1xi63.32 (7)
O1—Tb1—O2vii83.59 (8)O4xii—K1—O1xiii134.69 (7)
O1viii—Tb1—O2v72.62 (8)O4xv—K1—O1xiii63.32 (7)
O1—Tb1—O2v130.14 (8)O4xv—K1—O1xi89.97 (8)
O1—Tb1—O1viii74.71 (11)O4xv—K1—O3128.69 (7)
O1viii—Tb1—O3ix150.21 (8)O4xv—K1—O3xii81.24 (7)
O1viii—Tb1—O3ii108.63 (9)O4xii—K1—O367.06 (7)
O1—Tb1—O3ix108.63 (9)O4xiv—K1—O381.24 (7)
O1—Tb1—O3ii150.21 (8)O4xiv—K1—O3xii128.69 (7)
O3ix—Tb1—Tb1i74.69 (5)O4—K1—O3xii67.06 (7)
O3ix—Tb1—Tb1ii110.34 (5)O4—K1—O353.56 (7)
O3ii—Tb1—Tb1ii74.69 (5)O4xii—K1—O3xii53.56 (7)
O3ii—Tb1—Tb1i110.34 (5)O1xiii—K1—Mo1128.75 (5)
O3ii—Tb1—K1iii138.32 (6)O1xiii—K1—Mo1xi81.87 (6)
O3ix—Tb1—K1iii138.32 (6)O1xi—K1—Mo1xii128.75 (5)
O3ix—Tb1—O2vii140.29 (7)O1xi—K1—Mo1142.52 (5)
O3ix—Tb1—O2iv76.95 (8)O1xiii—K1—Mo1xii142.52 (5)
O3ii—Tb1—O2vii70.98 (8)O1xiii—K1—Mo1xiii25.90 (5)
O3ii—Tb1—O2v76.95 (8)O1xi—K1—Mo1xiii81.87 (6)
O3ix—Tb1—O2vi70.98 (8)O1xi—K1—Mo1xi25.90 (5)
O3ii—Tb1—O2vi140.29 (7)O1xiii—K1—O1xi59.61 (10)
O3ii—Tb1—O2iv84.31 (8)O1xiii—K1—O3xii131.66 (6)
O3ix—Tb1—O2v84.31 (8)O1xi—K1—O3131.66 (6)
O3ii—Tb1—O3ix83.37 (11)O1xi—K1—O3xii156.71 (6)
K1—Mo1—K1x77.135 (10)O1xiii—K1—O3156.71 (6)
K1iii—Mo1—K1x81.22 (2)O3—K1—Mo1xiii131.63 (4)
K1—Mo1—K1iii78.802 (10)O3—K1—Mo128.44 (4)
O2—Mo1—K1iii156.08 (6)O3xii—K1—Mo1xi131.63 (4)
O2—Mo1—K1x86.36 (7)O3xii—K1—Mo1xiii115.47 (4)
O2—Mo1—K1118.26 (7)O3xii—K1—Mo152.19 (4)
O4—Mo1—K1iii71.14 (9)O3—K1—Mo1xi115.47 (4)
O4—Mo1—K1x36.07 (8)O3xii—K1—Mo1xii28.44 (4)
O4—Mo1—K141.90 (7)O3—K1—Mo1xii52.19 (4)
O4—Mo1—O2109.34 (11)O3—K1—O3xii48.36 (8)
O4—Mo1—O1106.78 (11)Tb1iv—O2—Tb1xvi109.07 (9)
O4—Mo1—O3105.28 (10)Mo1—O2—Tb1iv127.76 (10)
O1—Mo1—K1121.85 (7)Mo1—O2—Tb1xvi120.07 (9)
O1—Mo1—K1iii43.35 (7)Mo1—O4—K1112.78 (11)
O1—Mo1—K1x95.66 (7)Mo1—O4—K1x122.51 (11)
O1—Mo1—O2118.69 (10)K1—O4—K1x122.78 (9)
O3—Mo1—K163.88 (7)Tb1—O1—K1iii112.84 (9)
O3—Mo1—K1iii90.54 (8)Mo1—O1—Tb1125.44 (11)
O3—Mo1—K1x141.01 (7)Mo1—O1—K1iii110.75 (10)
O3—Mo1—O2111.67 (10)Tb1ii—O3—K1145.20 (9)
O3—Mo1—O1104.16 (12)Mo1—O3—Tb1ii127.02 (11)
Mo1—K1—Mo1xi138.799 (13)Mo1—O3—K187.68 (8)
Symmetry codes: (i) x, y+1, z; (ii) x, y+1, z+1; (iii) x+1/2, y+3/2, z1/2; (iv) x+1, y+1, z+1; (v) x1, y+1, z1/2; (vi) x+1, y, z+1/2; (vii) x1, y, z; (viii) x, y, z+1/2; (ix) x, y+1, z1/2; (x) x+3/2, y+3/2, z1/2; (xi) x+1/2, y+3/2, z+1/2; (xii) x+1, y, z+3/2; (xiii) x+1/2, y+3/2, z+1; (xiv) x1/2, y+3/2, z+1; (xv) x+3/2, y+3/2, z+1/2; (xvi) x+1, y, z.
Potassium dysprosium bis(molybdate) (Dy_Molybdate) top
Crystal data top
KDy(MoO4)2F(000) = 932
Mr = 521.48Dx = 4.739 Mg m3
Orthorhombic, PbcnMo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2n 2abCell parameters from 5121 reflections
a = 5.0776 (2) Åθ = 2.3–33.3°
b = 18.1214 (7) ŵ = 14.07 mm1
c = 7.9428 (3) ÅT = 100 K
V = 730.84 (5) Å3Plate, light yellow
Z = 40.11 × 0.11 × 0.03 mm
Data collection top
Rigaku XtaLAB Synergy-S, HyPix
diffractometer
1388 independent reflections
Radiation source: micro-focus sealed X-ray tube1196 reflections with I > 2σ(I)
Mirror monochromatorRint = 0.075
Detector resolution: 10.0000 pixels mm-1θmax = 34.0°, θmin = 2.3°
ω scansh = 77
Absorption correction: gaussian
(CrysAlisPro; Rigaku OD, 2019)
k = 2727
Tmin = 0.247, Tmax = 0.695l = 1111
17317 measured reflections
Refinement top
Refinement on F20 restraints
Least-squares matrix: full0 constraints
R[F2 > 2σ(F2)] = 0.033Primary atom site location: dual
wR(F2) = 0.088 w = 1/[σ2(Fo2) + (0.0343P)2 + 8.538P]
where P = (Fo2 + 2Fc2)/3
S = 1.10(Δ/σ)max = 0.001
1388 reflectionsΔρmax = 2.38 e Å3
56 parametersΔρmin = 2.65 e Å3
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Refinement. Reflections were merged by SHELXL according to the crystal class for the calculation of statistics and refinement.

_reflns_Friedel_fraction is defined as the number of unique Friedel pairs measured divided by the number that would be possible theoretically, ignoring centric projections and systematic absences.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Dy10.0000000.49408 (2)0.2500000.00749 (11)
Mo10.48037 (7)0.60238 (2)0.48347 (5)0.00769 (11)
K10.5000000.77076 (9)0.7500000.0118 (3)
O40.6101 (7)0.6900 (2)0.4770 (4)0.0121 (6)
O20.7489 (7)0.53449 (19)0.5049 (4)0.0100 (6)
O10.2588 (6)0.59449 (19)0.3083 (4)0.0111 (6)
O30.2709 (6)0.60172 (19)0.6610 (4)0.0109 (6)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Dy10.00510 (15)0.01210 (17)0.00526 (16)0.0000.00001 (8)0.000
Mo10.00512 (18)0.0115 (2)0.00648 (18)0.00032 (12)0.00022 (10)0.00023 (12)
K10.0125 (6)0.0147 (6)0.0083 (6)0.0000.0006 (4)0.000
O40.0098 (15)0.0154 (16)0.0109 (15)0.0020 (12)0.0006 (11)0.0004 (12)
O20.0066 (13)0.0161 (16)0.0072 (14)0.0018 (11)0.0009 (11)0.0015 (11)
O10.0081 (13)0.0178 (16)0.0074 (14)0.0013 (12)0.0010 (11)0.0001 (12)
O30.0073 (13)0.0171 (16)0.0082 (14)0.0003 (12)0.0008 (11)0.0006 (11)
Geometric parameters (Å, º) top
Dy1—Dy1i3.9772 (1)Mo1—O31.766 (3)
Dy1—Dy1ii3.9772 (2)K1—Mo1xi3.8305 (10)
Dy1—K1iii4.2614 (16)K1—Mo1xii3.7150 (13)
Dy1—O2iv2.384 (3)K1—Mo1xiii3.8305 (10)
Dy1—O2v2.384 (3)K1—O42.676 (4)
Dy1—O2vi2.502 (3)K1—O4xiv2.770 (3)
Dy1—O2vii2.502 (3)K1—O4xii2.676 (4)
Dy1—O12.292 (3)K1—O4xv2.770 (3)
Dy1—O1viii2.292 (3)K1—O1xiii2.812 (4)
Dy1—O3ix2.325 (3)K1—O1xi2.812 (4)
Dy1—O3ii2.325 (3)K1—O3xii3.352 (4)
Mo1—K13.7150 (13)K1—O33.352 (4)
Mo1—K1x3.9604 (10)O4—K1x2.770 (3)
Mo1—K1iii3.8305 (10)O2—Dy1xvi2.502 (3)
Mo1—O41.720 (4)O2—Dy1iv2.384 (3)
Mo1—O21.845 (3)O1—K1iii2.812 (4)
Mo1—O11.795 (3)O3—Dy1ii2.325 (3)
Dy1ii—Dy1—Dy1i173.818 (18)Mo1—K1—Mo1xii69.57 (3)
Dy1ii—Dy1—K1iii86.909 (9)Mo1—K1—Mo1xi138.737 (15)
Dy1i—Dy1—K1iii86.909 (9)Mo1xii—K1—Mo1xiii138.737 (15)
O2iv—Dy1—Dy1i145.80 (8)Mo1xiii—K1—Mo1xi106.24 (4)
O2v—Dy1—Dy1i36.52 (8)Mo1xii—K1—Mo1xi103.540 (12)
O2vi—Dy1—Dy1i34.53 (8)O4xv—K1—Mo1xii79.68 (8)
O2vii—Dy1—Dy1i142.40 (8)O4—K1—Mo1xii90.40 (9)
O2iv—Dy1—Dy1ii36.52 (8)O4xiv—K1—Mo1xi72.90 (7)
O2v—Dy1—Dy1ii145.80 (8)O4xii—K1—Mo190.40 (9)
O2vi—Dy1—Dy1ii142.40 (8)O4xii—K1—Mo1xi78.63 (8)
O2vii—Dy1—Dy1ii34.53 (8)O4xv—K1—Mo1126.93 (8)
O2vi—Dy1—K1iii72.98 (8)O4xiv—K1—Mo179.68 (8)
O2vii—Dy1—K1iii72.98 (8)O4—K1—Mo1xiii78.63 (8)
O2v—Dy1—K1iii102.55 (8)O4—K1—Mo1xi148.63 (8)
O2iv—Dy1—K1iii102.55 (8)O4xii—K1—Mo1xiii148.63 (8)
O2vii—Dy1—O2vi145.97 (16)O4xv—K1—Mo1xi89.19 (8)
O2iv—Dy1—O2vi116.87 (14)O4xv—K1—Mo1xiii72.90 (7)
O2iv—Dy1—O2vii71.05 (13)O4—K1—Mo125.09 (8)
O2v—Dy1—O2vi71.05 (13)O4xiv—K1—Mo1xiii89.19 (8)
O2v—Dy1—O2vii116.87 (14)O4xii—K1—Mo1xii25.09 (8)
O2v—Dy1—O2iv154.91 (17)O4xiv—K1—Mo1xii126.93 (8)
O1viii—Dy1—Dy1i75.84 (8)O4xii—K1—O4xv76.26 (9)
O1—Dy1—Dy1i99.15 (8)O4—K1—O4xv121.24 (5)
O1viii—Dy1—Dy1ii99.15 (8)O4xv—K1—O4xiv150.24 (16)
O1—Dy1—Dy1ii75.84 (8)O4—K1—O4xiv76.25 (8)
O1—Dy1—K1iii37.45 (8)O4xii—K1—O4xiv121.24 (5)
O1viii—Dy1—K1iii37.45 (8)O4—K1—O4xii113.67 (16)
O1—Dy1—O2iv72.59 (12)O4xii—K1—O1xi104.12 (10)
O1viii—Dy1—O2vi84.04 (12)O4—K1—O1xi134.94 (11)
O1—Dy1—O2vii84.04 (12)O4—K1—O1xiii104.12 (10)
O1—Dy1—O2vi68.85 (11)O4xiv—K1—O1xiii90.21 (11)
O1viii—Dy1—O2iv130.11 (12)O4xiv—K1—O1xi63.27 (10)
O1viii—Dy1—O2vii68.85 (11)O4xii—K1—O1xiii134.94 (11)
O1—Dy1—O2v130.11 (12)O4xv—K1—O1xiii63.27 (10)
O1viii—Dy1—O2v72.59 (12)O4xv—K1—O1xi90.21 (11)
O1viii—Dy1—O174.89 (17)O4xv—K1—O3xii81.35 (10)
O1—Dy1—O3ix108.36 (12)O4xv—K1—O3128.30 (10)
O1—Dy1—O3ii150.54 (12)O4xii—K1—O3xii53.25 (10)
O1viii—Dy1—O3ix150.54 (12)O4xiv—K1—O3xii128.30 (10)
O1viii—Dy1—O3ii108.36 (12)O4xiv—K1—O381.35 (10)
O3ix—Dy1—Dy1i74.74 (8)O4—K1—O353.25 (10)
O3ix—Dy1—Dy1ii110.11 (8)O4—K1—O3xii66.32 (10)
O3ii—Dy1—Dy1ii74.74 (8)O4xii—K1—O366.32 (10)
O3ii—Dy1—Dy1i110.11 (8)O1xiii—K1—Mo1129.20 (7)
O3ii—Dy1—K1iii138.31 (8)O1xiii—K1—Mo1xi81.73 (8)
O3ix—Dy1—K1iii138.31 (8)O1xi—K1—Mo1xii129.20 (7)
O3ix—Dy1—O2vii139.98 (11)O1xi—K1—Mo1142.63 (7)
O3ix—Dy1—O2iv76.68 (11)O1xiii—K1—Mo1xii142.63 (7)
O3ii—Dy1—O2vii70.80 (12)O1xiii—K1—Mo1xiii26.02 (7)
O3ii—Dy1—O2v76.68 (11)O1xi—K1—Mo1xiii81.73 (8)
O3ix—Dy1—O2v84.61 (12)O1xi—K1—Mo1xi26.02 (7)
O3ix—Dy1—O2vi70.80 (12)O1xiii—K1—O1xi59.42 (14)
O3ii—Dy1—O2iv84.61 (12)O1xiii—K1—O3157.10 (9)
O3ii—Dy1—O2vi139.98 (11)O1xi—K1—O3xii157.10 (9)
O3ii—Dy1—O3ix83.39 (16)O1xi—K1—O3131.78 (9)
K1—Mo1—K1iii78.467 (11)O1xiii—K1—O3xii131.78 (9)
K1—Mo1—K1x76.833 (11)O3xii—K1—Mo1xiii115.44 (6)
K1iii—Mo1—K1x81.33 (3)O3xii—K1—Mo151.60 (6)
O4—Mo1—K1x36.37 (12)O3—K1—Mo1xi115.44 (6)
O4—Mo1—K141.29 (11)O3—K1—Mo1xiii131.86 (6)
O4—Mo1—K1iii71.06 (12)O3—K1—Mo128.36 (6)
O4—Mo1—O2109.59 (16)O3xii—K1—Mo1xi131.86 (6)
O4—Mo1—O1106.89 (16)O3—K1—Mo1xii51.60 (6)
O4—Mo1—O3105.13 (16)O3xii—K1—Mo1xii28.36 (6)
O2—Mo1—K1x86.44 (11)O3xii—K1—O347.91 (11)
O2—Mo1—K1iii156.32 (9)Mo1—O4—K1x122.04 (17)
O2—Mo1—K1118.38 (10)Mo1—O4—K1113.61 (16)
O1—Mo1—K1iii43.41 (11)K1—O4—K1x122.44 (13)
O1—Mo1—K1121.60 (11)Dy1iv—O2—Dy1xvi108.95 (13)
O1—Mo1—K1x95.79 (11)Mo1—O2—Dy1xvi119.80 (14)
O1—Mo1—O2118.81 (15)Mo1—O2—Dy1iv128.01 (15)
O3—Mo1—K1iii90.42 (11)Dy1—O1—K1iii112.84 (12)
O3—Mo1—K1x141.16 (11)Mo1—O1—Dy1125.41 (17)
O3—Mo1—K164.32 (11)Mo1—O1—K1iii110.57 (15)
O3—Mo1—O2111.51 (15)Dy1ii—O3—K1145.45 (13)
O3—Mo1—O1103.94 (16)Mo1—O3—Dy1ii127.15 (18)
Mo1—K1—Mo1xiii103.540 (12)Mo1—O3—K187.32 (12)
Symmetry codes: (i) x, y+1, z; (ii) x, y+1, z+1; (iii) x+1/2, y+3/2, z1/2; (iv) x+1, y+1, z+1; (v) x1, y+1, z1/2; (vi) x+1, y, z+1/2; (vii) x1, y, z; (viii) x, y, z+1/2; (ix) x, y+1, z1/2; (x) x+3/2, y+3/2, z1/2; (xi) x+1/2, y+3/2, z+1/2; (xii) x+1, y, z+3/2; (xiii) x+1/2, y+3/2, z+1; (xiv) x1/2, y+3/2, z+1; (xv) x+3/2, y+3/2, z+1/2; (xvi) x+1, y, z.
Potassium holmium bis(molybdate) (Ho_Molybdate) top
Crystal data top
KHo(MoO4)2F(000) = 936
Mr = 523.91Dx = 4.757 Mg m3
Orthorhombic, PbcnMo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2n 2abCell parameters from 2917 reflections
a = 5.0770 (15) Åθ = 3.4–28.8°
b = 18.161 (5) ŵ = 14.66 mm1
c = 7.934 (2) ÅT = 273 K
V = 731.5 (4) Å3Plate, light red
Z = 40.06 × 0.06 × 0.04 mm
Data collection top
Bruker APEXII CCD
diffractometer
818 reflections with I > 2σ(I)
Radiation source: X-ray tubeRint = 0.032
φ and ω scansθmax = 28.9°, θmin = 2.2°
Absorption correction: multi-scan
(SADABS; Krause et al., 2015)
h = 66
Tmin = 0.248, Tmax = 0.343k = 2424
7665 measured reflectionsl = 1010
936 independent reflections
Refinement top
Refinement on F20 restraints
Least-squares matrix: full0 constraints
R[F2 > 2σ(F2)] = 0.027Primary atom site location: dual
wR(F2) = 0.063 w = 1/[σ2(Fo2) + 11.609P]
where P = (Fo2 + 2Fc2)/3
S = 1.25(Δ/σ)max = 0.001
936 reflectionsΔρmax = 1.51 e Å3
56 parametersΔρmin = 1.37 e Å3
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Refinement. Reflections were merged by SHELXL according to the crystal class for the calculation of statistics and refinement.

_reflns_Friedel_fraction is defined as the number of unique Friedel pairs measured divided by the number that would be possible theoretically, ignoring centric projections and systematic absences.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Ho10.0000000.49423 (2)0.7500000.00704 (12)
Mo10.47909 (9)0.60179 (3)0.51614 (6)0.00726 (13)
K10.5000000.77102 (11)0.2500000.0141 (4)
O40.6095 (9)0.6894 (3)0.5227 (6)0.0122 (9)
O20.7503 (9)0.5342 (2)0.4941 (5)0.0095 (8)
O10.2583 (8)0.5939 (2)0.6923 (5)0.0096 (8)
O30.2700 (9)0.6008 (2)0.3389 (5)0.0093 (8)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Ho10.00566 (18)0.0094 (2)0.00606 (18)0.0000.00040 (14)0.000
Mo10.0058 (2)0.0084 (3)0.0076 (2)0.00040 (19)0.00009 (17)0.00032 (17)
K10.0177 (9)0.0132 (9)0.0115 (8)0.0000.0013 (8)0.000
O40.013 (2)0.014 (2)0.010 (2)0.0011 (18)0.0002 (17)0.0016 (17)
O20.0080 (19)0.014 (2)0.0061 (19)0.0016 (17)0.0037 (18)0.0005 (17)
O10.0072 (19)0.013 (2)0.0085 (19)0.0001 (17)0.0015 (16)0.0001 (17)
O30.013 (2)0.012 (2)0.0035 (19)0.0008 (19)0.0005 (15)0.0000 (16)
Geometric parameters (Å, º) top
Ho1—Ho1i3.9723 (11)Mo1—O31.762 (4)
Ho1—Ho1ii3.9723 (11)K1—Mo1xi3.8332 (14)
Ho1—K1iii4.263 (2)K1—Mo1xii3.7303 (18)
Ho1—O2iv2.372 (4)K1—Mo1xiii3.8332 (14)
Ho1—O2v2.372 (4)K1—O42.680 (5)
Ho1—O2vi2.501 (4)K1—O4xiv2.775 (5)
Ho1—O2vii2.501 (4)K1—O4xii2.681 (5)
Ho1—O1viii2.282 (4)K1—O4xv2.775 (5)
Ho1—O12.282 (4)K1—O1xiii2.819 (5)
Ho1—O3ix2.314 (4)K1—O1xi2.819 (5)
Ho1—O3i2.314 (4)K1—O33.380 (5)
Mo1—K13.7303 (18)K1—O3xii3.380 (5)
Mo1—K1x3.9713 (14)O4—K1x2.775 (5)
Mo1—K1iii3.8332 (14)O2—Ho1xvi2.501 (4)
Mo1—O41.724 (5)O2—Ho1v2.372 (4)
Mo1—O21.853 (4)O1—K1iii2.819 (5)
Mo1—O11.797 (4)O3—Ho1i2.314 (4)
Ho1ii—Ho1—Ho1i173.96 (2)Mo1xii—K1—Mo169.05 (4)
Ho1ii—Ho1—K1iii86.979 (11)Mo1xii—K1—Mo1xi103.92 (2)
Ho1i—Ho1—K1iii86.979 (11)Mo1—K1—Mo1xiii103.92 (2)
O2iv—Ho1—Ho1i145.79 (11)Mo1xiii—K1—Mo1xi105.89 (5)
O2v—Ho1—Ho1i36.49 (11)Mo1—K1—Mo1xi138.79 (2)
O2vi—Ho1—Ho1i34.33 (10)O4xv—K1—Mo1126.98 (10)
O2vii—Ho1—Ho1i142.68 (10)O4—K1—Mo124.98 (10)
O2iv—Ho1—Ho1ii36.49 (11)O4xiv—K1—Mo1xi72.85 (10)
O2v—Ho1—Ho1ii145.79 (11)O4xii—K1—Mo1xii24.98 (10)
O2vi—Ho1—Ho1ii142.68 (10)O4xii—K1—Mo1xi79.11 (10)
O2vii—Ho1—Ho1ii34.33 (10)O4xv—K1—Mo1xii79.93 (10)
O2vi—Ho1—K1iii73.13 (10)O4xiv—K1—Mo1xii126.98 (10)
O2vii—Ho1—K1iii73.13 (10)O4—K1—Mo1xiii79.11 (10)
O2v—Ho1—K1iii102.57 (11)O4—K1—Mo1xi148.80 (10)
O2iv—Ho1—K1iii102.57 (11)O4xii—K1—Mo1xiii148.80 (10)
O2vii—Ho1—O2vi146.3 (2)O4xv—K1—Mo1xi89.01 (10)
O2iv—Ho1—O2vi117.06 (18)O4xv—K1—Mo1xiii72.85 (10)
O2iv—Ho1—O2vii70.81 (17)O4—K1—Mo1xii89.73 (11)
O2v—Ho1—O2vi70.81 (17)O4xiv—K1—Mo1xiii89.01 (10)
O2v—Ho1—O2vii117.06 (18)O4xii—K1—Mo189.73 (11)
O2v—Ho1—O2iv154.9 (2)O4xiv—K1—Mo179.93 (10)
O1—Ho1—Ho1i75.99 (11)O4xii—K1—O4xv76.52 (11)
O1viii—Ho1—Ho1i99.12 (11)O4—K1—O4xv121.30 (6)
O1—Ho1—Ho1ii99.12 (11)O4xv—K1—O4xiv150.0 (2)
O1viii—Ho1—Ho1ii75.99 (11)O4—K1—O4xiv76.52 (11)
O1viii—Ho1—K1iii37.49 (11)O4xii—K1—O4xiv121.30 (6)
O1—Ho1—K1iii37.50 (11)O4—K1—O4xii112.9 (2)
O1viii—Ho1—O2iv72.64 (15)O4xii—K1—O1xi104.69 (13)
O1—Ho1—O2vi84.17 (15)O4—K1—O1xi135.12 (13)
O1viii—Ho1—O2vii84.17 (15)O4—K1—O1xiii104.69 (13)
O1viii—Ho1—O2vi68.97 (15)O4xiv—K1—O1xiii90.09 (14)
O1—Ho1—O2iv130.07 (15)O4xiv—K1—O1xi63.11 (13)
O1—Ho1—O2vii68.97 (15)O4xii—K1—O1xiii135.13 (13)
O1viii—Ho1—O2v130.06 (15)O4xv—K1—O1xiii63.11 (13)
O1—Ho1—O2v72.64 (15)O4xv—K1—O1xi90.09 (14)
O1—Ho1—O1viii75.0 (2)O4xv—K1—O3128.28 (13)
O1viii—Ho1—O3ix150.57 (15)O4xv—K1—O3xii81.63 (12)
O1viii—Ho1—O3i108.19 (16)O4xii—K1—O365.85 (13)
O1—Ho1—O3ix108.19 (16)O4xiv—K1—O381.63 (12)
O1—Ho1—O3i150.57 (15)O4xiv—K1—O3xii128.28 (13)
O3ix—Ho1—Ho1i110.11 (10)O4—K1—O3xii65.85 (13)
O3ix—Ho1—Ho1ii74.62 (10)O4—K1—O352.94 (12)
O3i—Ho1—Ho1ii110.11 (10)O4xii—K1—O3xii52.93 (12)
O3i—Ho1—Ho1i74.62 (10)O1xiii—K1—Mo1xii142.71 (9)
O3i—Ho1—K1iii138.22 (11)O1xiii—K1—Mo1xi81.34 (10)
O3ix—Ho1—K1iii138.21 (11)O1xi—K1—Mo1142.71 (9)
O3ix—Ho1—O2vii70.64 (15)O1xi—K1—Mo1xii129.66 (9)
O3ix—Ho1—O2iv84.58 (15)O1xiii—K1—Mo1129.66 (9)
O3i—Ho1—O2vii139.83 (14)O1xiii—K1—Mo1xiii26.09 (9)
O3i—Ho1—O2v84.58 (15)O1xi—K1—Mo1xiii81.34 (10)
O3ix—Ho1—O2v76.70 (15)O1xi—K1—Mo1xi26.09 (9)
O3ix—Ho1—O2vi139.83 (14)O1xiii—K1—O1xi59.05 (18)
O3i—Ho1—O2iv76.70 (15)O1xiii—K1—O3xii132.01 (12)
O3i—Ho1—O2vi70.64 (15)O1xi—K1—O3132.01 (12)
O3i—Ho1—O3ix83.6 (2)O1xi—K1—O3xii157.36 (11)
K1—Mo1—K1iii78.20 (2)O1xiii—K1—O3157.36 (11)
K1—Mo1—K1x76.49 (2)O3—K1—Mo1xiii132.03 (7)
K1iii—Mo1—K1x81.14 (4)O3—K1—Mo1xii51.26 (8)
O4—Mo1—K1x36.25 (15)O3xii—K1—Mo1xi132.03 (7)
O4—Mo1—K141.04 (15)O3xii—K1—Mo1xiii115.66 (8)
O4—Mo1—K1iii70.92 (15)O3xii—K1—Mo1xii28.14 (7)
O4—Mo1—O2109.2 (2)O3—K1—Mo1xi115.66 (8)
O4—Mo1—O1106.8 (2)O3xii—K1—Mo151.26 (8)
O4—Mo1—O3105.4 (2)O3—K1—Mo128.14 (7)
O2—Mo1—K1x86.25 (14)O3—K1—O3xii47.61 (15)
O2—Mo1—K1iii156.40 (13)Mo1—O4—K1x122.2 (2)
O2—Mo1—K1118.13 (13)Mo1—O4—K1114.0 (2)
O1—Mo1—K1iii43.60 (14)K1—O4—K1x121.97 (17)
O1—Mo1—K1121.56 (14)Ho1v—O2—Ho1xvi109.19 (17)
O1—Mo1—K1x95.64 (14)Mo1—O2—Ho1xvi119.50 (19)
O1—Mo1—O2118.95 (19)Mo1—O2—Ho1v128.2 (2)
O3—Mo1—K1iii90.59 (14)Ho1—O1—K1iii112.98 (16)
O3—Mo1—K1x141.28 (15)Mo1—O1—Ho1125.3 (2)
O3—Mo1—K164.79 (14)Mo1—O1—K1iii110.32 (19)
O3—Mo1—O2111.44 (19)Ho1i—O3—K1145.41 (16)
O3—Mo1—O1104.1 (2)Mo1—O3—Ho1i127.5 (2)
Mo1xii—K1—Mo1xiii138.79 (2)Mo1—O3—K187.06 (16)
Symmetry codes: (i) x, y+1, z+1; (ii) x, y+1, z+2; (iii) x+1/2, y+3/2, z+1/2; (iv) x1, y+1, z+1/2; (v) x+1, y+1, z+1; (vi) x1, y, z; (vii) x+1, y, z+3/2; (viii) x, y, z+3/2; (ix) x, y+1, z+1/2; (x) x+3/2, y+3/2, z+1/2; (xi) x+1/2, y+3/2, z1/2; (xii) x+1, y, z+1/2; (xiii) x+1/2, y+3/2, z+1; (xiv) x1/2, y+3/2, z+1; (xv) x+3/2, y+3/2, z1/2; (xvi) x+1, y, z.
Potassium erbium bis(molybdate) (Er_Molybdate) top
Crystal data top
KEr(MoO4)2F(000) = 940
Mr = 526.24Dx = 4.810 Mg m3
Orthorhombic, PbcnMo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2n 2abCell parameters from 7328 reflections
a = 5.0602 (2) Åθ = 3.4–34.0°
b = 18.1965 (8) ŵ = 15.42 mm1
c = 7.8920 (3) ÅT = 100 K
V = 726.68 (5) Å3Plate, light pink
Z = 40.28 × 0.15 × 0.02 mm
Data collection top
Rigaku XtaLAB Synergy-S, HyPix
diffractometer
1386 independent reflections
Radiation source: micro-focus sealed X-ray tube1255 reflections with I > 2σ(I)
Mirror monochromatorRint = 0.072
Detector resolution: 10.0000 pixels mm-1θmax = 34.0°, θmin = 2.2°
ω scansh = 77
Absorption correction: gaussian
(CrysAlisPro; Rigaku OD, 2019)
k = 2827
Tmin = 0.091, Tmax = 0.911l = 1210
21246 measured reflections
Refinement top
Refinement on F20 restraints
Least-squares matrix: full0 constraints
R[F2 > 2σ(F2)] = 0.027Primary atom site location: dual
wR(F2) = 0.073 w = 1/[σ2(Fo2) + (0.0345P)2 + 4.1539P]
where P = (Fo2 + 2Fc2)/3
S = 1.06(Δ/σ)max = 0.002
1386 reflectionsΔρmax = 2.04 e Å3
56 parametersΔρmin = 1.62 e Å3
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Er11.0000000.50535 (2)0.7500000.00602 (9)
Mo10.52026 (6)0.39859 (2)0.51517 (4)0.00637 (9)
K10.5000000.22821 (7)0.2500000.0107 (2)
O40.3903 (5)0.31111 (15)0.5213 (3)0.0102 (5)
O20.2497 (5)0.46619 (15)0.4954 (3)0.0084 (5)
O10.7417 (5)0.40581 (14)0.6914 (3)0.0100 (4)
O30.7315 (5)0.39970 (14)0.3369 (3)0.0099 (5)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Er10.00367 (12)0.00995 (13)0.00443 (13)0.0000.00030 (6)0.000
Mo10.00374 (14)0.00961 (16)0.00575 (15)0.00027 (9)0.00044 (8)0.00032 (9)
K10.0112 (5)0.0124 (5)0.0085 (5)0.0000.0007 (3)0.000
O40.0079 (11)0.0127 (12)0.0100 (11)0.0029 (9)0.0009 (9)0.0003 (9)
O20.0052 (10)0.0131 (12)0.0067 (10)0.0007 (9)0.0008 (8)0.0006 (8)
O10.0077 (10)0.0142 (12)0.0080 (10)0.0014 (9)0.0019 (9)0.0004 (9)
O30.0068 (10)0.0153 (12)0.0074 (10)0.0014 (9)0.0006 (8)0.0003 (8)
Geometric parameters (Å, º) top
Er1—Er1i3.9508 (2)Mo1—O31.767 (2)
Er1—Er1ii3.9508 (1)K1—Mo1xi3.8277 (8)
Er1—K1iii4.2499 (13)K1—Mo1xii3.7419 (10)
Er1—O2iv2.370 (2)K1—Mo1xiii3.8277 (8)
Er1—O2v2.370 (2)K1—O42.677 (3)
Er1—O2vi2.478 (2)K1—O4xiv2.770 (3)
Er1—O2vii2.478 (2)K1—O4xii2.677 (3)
Er1—O1viii2.281 (2)K1—O4xv2.770 (3)
Er1—O12.281 (3)K1—O1xiii2.805 (3)
Er1—O3ix2.303 (3)K1—O1xi2.805 (3)
Er1—O3ii2.303 (3)K1—O33.403 (3)
Mo1—K13.7419 (10)K1—O3xii3.403 (3)
Mo1—K1x3.9610 (8)O4—K1x2.770 (3)
Mo1—K1iii3.8278 (8)O2—Er1xvi2.478 (2)
Mo1—O41.723 (3)O2—Er1iv2.370 (2)
Mo1—O21.847 (3)O1—K1iii2.805 (3)
Mo1—O11.791 (2)O3—Er1ii2.303 (3)
Er1ii—Er1—Er1i174.354 (13)Mo1xii—K1—Mo168.10 (2)
Er1ii—Er1—K1iii87.177 (7)Mo1xii—K1—Mo1xi104.243 (10)
Er1i—Er1—K1iii87.177 (7)Mo1—K1—Mo1xiii104.243 (10)
O2iv—Er1—Er1i145.80 (6)Mo1xiii—K1—Mo1xi105.86 (3)
O2v—Er1—Er1i36.34 (6)Mo1—K1—Mo1xi138.837 (12)
O2vi—Er1—Er1i34.52 (6)O4xv—K1—Mo1126.73 (6)
O2vii—Er1—Er1i142.71 (6)O4—K1—Mo124.71 (6)
O2iv—Er1—Er1ii36.34 (6)O4xiv—K1—Mo1xi73.00 (5)
O2v—Er1—Er1ii145.80 (6)O4xii—K1—Mo1xii24.71 (6)
O2vi—Er1—Er1ii142.71 (6)O4xii—K1—Mo1xi79.69 (6)
O2vii—Er1—Er1ii34.52 (6)O4xv—K1—Mo1xii80.21 (6)
O2vi—Er1—K1iii73.29 (6)O4xiv—K1—Mo1xii126.73 (6)
O2vii—Er1—K1iii73.29 (6)O4—K1—Mo1xiii79.69 (6)
O2v—Er1—K1iii102.63 (6)O4—K1—Mo1xi149.13 (6)
O2iv—Er1—K1iii102.63 (6)O4xii—K1—Mo1xiii149.13 (6)
O2vii—Er1—O2vi146.57 (12)O4xv—K1—Mo1xi88.91 (6)
O2iv—Er1—O2vi116.98 (11)O4xv—K1—Mo1xiii73.00 (5)
O2iv—Er1—O2vii70.86 (10)O4—K1—Mo1xii88.55 (6)
O2v—Er1—O2vi70.86 (10)O4xiv—K1—Mo1xiii88.91 (6)
O2v—Er1—O2vii116.98 (11)O4xii—K1—Mo188.55 (6)
O2v—Er1—O2iv154.75 (13)O4xiv—K1—Mo180.21 (6)
O1—Er1—Er1i99.40 (6)O4xii—K1—O4xv76.83 (6)
O1viii—Er1—Er1i76.03 (6)O4—K1—O4xv121.26 (4)
O1—Er1—Er1ii76.03 (6)O4xv—K1—O4xiv150.06 (12)
O1viii—Er1—Er1ii99.39 (6)O4—K1—O4xiv76.83 (6)
O1viii—Er1—K1iii37.43 (6)O4xii—K1—O4xiv121.26 (4)
O1—Er1—K1iii37.43 (6)O4—K1—O4xii111.41 (12)
O1viii—Er1—O2iv130.14 (9)O4xii—K1—O1xi105.16 (8)
O1—Er1—O2vi69.13 (8)O4—K1—O1xi135.91 (8)
O1viii—Er1—O2vii69.13 (8)O4—K1—O1xiii105.16 (8)
O1viii—Er1—O2vi84.23 (9)O4xiv—K1—O1xiii90.02 (8)
O1—Er1—O2iv72.69 (9)O4xiv—K1—O1xi63.29 (8)
O1—Er1—O2vii84.23 (9)O4xii—K1—O1xiii135.91 (8)
O1viii—Er1—O2v72.70 (9)O4xv—K1—O1xiii63.29 (8)
O1—Er1—O2v130.14 (9)O4xv—K1—O1xi90.02 (8)
O1—Er1—O1viii74.85 (13)O4xv—K1—O3127.86 (8)
O1viii—Er1—O3ix150.89 (9)O4xv—K1—O3xii81.96 (7)
O1viii—Er1—O3ii108.55 (10)O4xii—K1—O364.73 (7)
O1—Er1—O3ix108.55 (10)O4xiv—K1—O381.96 (7)
O1—Er1—O3ii150.89 (9)O4xiv—K1—O3xii127.86 (8)
O3ix—Er1—Er1i74.90 (6)O4—K1—O3xii64.73 (7)
O3ix—Er1—Er1ii109.54 (6)O4—K1—O352.66 (7)
O3ii—Er1—Er1ii74.90 (6)O4xii—K1—O3xii52.66 (7)
O3ii—Er1—Er1i109.54 (6)O1xiii—K1—Mo1xii143.10 (5)
O3ii—Er1—K1iii138.62 (6)O1xiii—K1—Mo1xi81.44 (6)
O3ix—Er1—K1iii138.62 (6)O1xi—K1—Mo1143.10 (5)
O3ix—Er1—O2vii139.31 (8)O1xi—K1—Mo1xii129.86 (5)
O3ix—Er1—O2iv76.40 (8)O1xiii—K1—Mo1129.86 (5)
O3ii—Er1—O2vii70.94 (9)O1xiii—K1—Mo1xiii25.94 (5)
O3ii—Er1—O2v76.40 (8)O1xi—K1—Mo1xiii81.44 (6)
O3ix—Er1—O2v84.67 (9)O1xi—K1—Mo1xi25.94 (5)
O3ix—Er1—O2vi70.94 (9)O1xiii—K1—O1xi59.23 (10)
O3ii—Er1—O2iv84.67 (9)O1xiii—K1—O3xii132.07 (6)
O3ii—Er1—O2vi139.31 (8)O1xi—K1—O3132.07 (6)
O3ii—Er1—O3ix82.76 (13)O1xi—K1—O3xii157.57 (7)
K1—Mo1—K1iii77.802 (9)O1xiii—K1—O3157.57 (7)
K1—Mo1—K1x76.162 (9)O3—K1—Mo1xiii132.33 (4)
K1iii—Mo1—K1x81.02 (2)O3—K1—Mo1xii50.39 (4)
O4—Mo1—K1x36.40 (9)O3xii—K1—Mo1xi132.33 (4)
O4—Mo1—K140.51 (8)O3xii—K1—Mo1xiii115.60 (4)
O4—Mo1—K1iii70.83 (9)O3xii—K1—Mo1xii28.12 (4)
O4—Mo1—O2109.56 (12)O3—K1—Mo1xi115.60 (4)
O4—Mo1—O1106.55 (12)O3xii—K1—Mo150.39 (4)
O4—Mo1—O3105.29 (12)O3—K1—Mo128.12 (4)
O2—Mo1—K1x86.26 (8)O3—K1—O3xii47.02 (9)
O2—Mo1—K1iii155.83 (7)Mo1—O4—K1x121.94 (12)
O2—Mo1—K1118.97 (8)Mo1—O4—K1114.78 (12)
O1—Mo1—K1iii43.23 (8)K1—O4—K1x121.57 (10)
O1—Mo1—K1120.81 (8)Er1iv—O2—Er1xvi109.14 (10)
O1—Mo1—K1x95.46 (8)Mo1—O2—Er1xvi120.07 (10)
O1—Mo1—O2118.71 (11)Mo1—O2—Er1iv127.56 (11)
O3—Mo1—K1iii90.50 (8)Er1—O1—K1iii112.96 (10)
O3—Mo1—K1x141.37 (9)Mo1—O1—Er1125.03 (13)
O3—Mo1—K165.21 (8)Mo1—O1—K1iii110.84 (11)
O3—Mo1—O2111.94 (11)Er1ii—O3—K1146.22 (10)
O3—Mo1—O1103.83 (12)Mo1—O3—Er1ii127.06 (13)
Mo1xii—K1—Mo1xiii138.837 (12)Mo1—O3—K186.67 (9)
Symmetry codes: (i) x+2, y+1, z+2; (ii) x+2, y+1, z+1; (iii) x+3/2, y+1/2, z+1/2; (iv) x+1, y+1, z+1; (v) x+1, y+1, z+1/2; (vi) x+1, y, z+3/2; (vii) x+1, y, z; (viii) x+2, y, z+3/2; (ix) x, y+1, z+1/2; (x) x+1/2, y+1/2, z+1/2; (xi) x+3/2, y+1/2, z1/2; (xii) x+1, y, z+1/2; (xiii) x1/2, y+1/2, z+1; (xiv) x+1/2, y+1/2, z+1; (xv) x+1/2, y+1/2, z1/2; (xvi) x1, y, z.
Potassium ytterbium bis(molybdate) (Yb_Molybdate) top
Crystal data top
KYb(MoO4)2F(000) = 948
Mr = 532.02Dx = 4.866 Mg m3
Orthorhombic, PbcnMo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2n 2abCell parameters from 3007 reflections
a = 5.0417 (5) Åθ = 2.2–29.2°
b = 18.3039 (19) ŵ = 16.75 mm1
c = 7.8693 (8) ÅT = 273 K
V = 726.20 (13) Å3Plate, white
Z = 40.06 × 0.06 × 0.04 mm
Data collection top
Bruker APEXII CCD
diffractometer
845 reflections with I > 2σ(I)
Radiation source: X-ray tubeRint = 0.038
φ and ω scansθmax = 29.5°, θmin = 2.2°
Absorption correction: multi-scan
(SADABS; Krause et al., 2015)
h = 66
Tmin = 0.198, Tmax = 0.301k = 2425
8164 measured reflectionsl = 1010
978 independent reflections
Refinement top
Refinement on F20 restraints
Least-squares matrix: full0 constraints
R[F2 > 2σ(F2)] = 0.022Primary atom site location: dual
wR(F2) = 0.063 w = 1/[σ2(Fo2) + (0.0244P)2 + 3.0168P]
where P = (Fo2 + 2Fc2)/3
S = 1.11(Δ/σ)max = 0.001
978 reflectionsΔρmax = 1.55 e Å3
56 parametersΔρmin = 1.14 e Å3
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Refinement. Reflections were merged by SHELXL according to the crystal class for the calculation of statistics and refinement.

_reflns_Friedel_fraction is defined as the number of unique Friedel pairs measured divided by the number that would be possible theoretically, ignoring centric projections and systematic absences.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Yb10.0000000.49506 (2)0.7500000.01036 (11)
Mo10.47826 (7)0.60027 (2)0.51395 (5)0.01066 (12)
K10.5000000.77252 (9)0.2500000.0230 (3)
O40.6053 (7)0.68778 (18)0.5206 (4)0.0188 (7)
O20.7521 (6)0.53396 (17)0.4939 (3)0.0128 (6)
O10.2572 (6)0.59262 (17)0.6912 (4)0.0149 (6)
O30.2661 (6)0.59860 (17)0.3360 (4)0.0152 (6)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Yb10.00810 (17)0.01404 (17)0.00894 (16)0.0000.00084 (9)0.000
Mo10.0085 (2)0.0117 (2)0.0118 (2)0.00068 (12)0.00134 (12)0.00054 (13)
K10.0306 (9)0.0195 (7)0.0189 (7)0.0000.0019 (6)0.000
O40.0212 (18)0.0179 (17)0.0173 (16)0.0025 (14)0.0044 (13)0.0007 (13)
O20.0112 (15)0.0184 (17)0.0086 (14)0.0033 (12)0.0023 (12)0.0010 (11)
O10.0131 (14)0.0175 (15)0.0143 (15)0.0011 (12)0.0039 (12)0.0038 (13)
O30.0142 (15)0.0177 (16)0.0137 (15)0.0024 (13)0.0006 (12)0.0003 (12)
Geometric parameters (Å, º) top
Yb1—Mo1i3.6018 (5)Mo1—O21.845 (3)
Yb1—Mo1ii3.6294 (5)Mo1—O11.791 (3)
Yb1—Mo1iii3.6294 (5)Mo1—O31.762 (3)
Yb1—Mo13.6018 (5)K1—Mo1xi3.9738 (11)
Yb1—O2iv2.351 (3)K1—Mo1xii3.7772 (14)
Yb1—O2v2.476 (3)K1—Mo1xiii3.8322 (11)
Yb1—O2vi2.351 (3)K1—Mo1xiv3.8322 (11)
Yb1—O2vii2.476 (3)K1—Mo1xv3.9738 (11)
Yb1—O12.255 (3)K1—O4xii2.687 (3)
Yb1—O1i2.255 (3)K1—O42.687 (3)
Yb1—O3ii2.280 (3)K1—O4xi2.784 (3)
Yb1—O3iii2.280 (3)K1—O4xv2.784 (3)
Mo1—Yb1iii3.6294 (5)K1—O1xiii2.826 (3)
Mo1—Yb1iv3.7786 (5)K1—O1xiv2.826 (3)
Mo1—Yb1viii3.7522 (5)O4—K1x2.784 (3)
Mo1—K1ix3.8322 (11)O2—Yb1iv2.351 (3)
Mo1—K1x3.9738 (11)O2—Yb1viii2.476 (3)
Mo1—K13.7772 (14)O1—K1ix2.826 (3)
Mo1—O41.726 (3)O3—Yb1iii2.280 (3)
Mo1—Yb1—Mo1i115.356 (17)O2—Mo1—Yb1101.15 (10)
Mo1i—Yb1—Mo1iii96.169 (13)O2—Mo1—Yb1iii97.58 (10)
Mo1—Yb1—Mo1iii113.994 (10)O2—Mo1—K1ix155.78 (8)
Mo1—Yb1—Mo1ii96.168 (13)O2—Mo1—K1x85.99 (10)
Mo1iii—Yb1—Mo1ii122.531 (16)O2—Mo1—K1118.71 (10)
Mo1i—Yb1—Mo1ii113.994 (10)O1—Mo1—Yb1iii89.70 (10)
O2v—Yb1—Mo1i85.88 (7)O1—Mo1—Yb1viii90.61 (10)
O2iv—Yb1—Mo1ii90.31 (8)O1—Mo1—Yb1iv145.62 (10)
O2vii—Yb1—Mo1i76.37 (8)O1—Mo1—Yb130.68 (10)
O2iv—Yb1—Mo149.00 (8)O1—Mo1—K1120.77 (10)
O2vii—Yb1—Mo1ii48.48 (8)O1—Mo1—K1x95.37 (10)
O2iv—Yb1—Mo1iii77.14 (8)O1—Mo1—K1ix43.81 (10)
O2vi—Yb1—Mo1i49.00 (8)O1—Mo1—O2118.75 (14)
O2vi—Yb1—Mo1153.85 (8)O3—Mo1—Yb189.67 (10)
O2vi—Yb1—Mo1ii77.14 (8)O3—Mo1—Yb1viii144.09 (11)
O2vii—Yb1—Mo185.88 (7)O3—Mo1—Yb1iii29.97 (10)
O2v—Yb1—Mo1ii159.95 (7)O3—Mo1—Yb1iv88.72 (10)
O2v—Yb1—Mo1iii48.48 (8)O3—Mo1—K166.11 (10)
O2iv—Yb1—Mo1i153.85 (8)O3—Mo1—K1x141.56 (11)
O2vi—Yb1—Mo1iii90.31 (8)O3—Mo1—K1ix90.79 (10)
O2vii—Yb1—Mo1iii159.95 (7)O3—Mo1—O2112.01 (14)
O2v—Yb1—Mo176.37 (8)O3—Mo1—O1103.88 (15)
O2iv—Yb1—O2v70.66 (12)Mo1xiv—K1—Mo1xv80.44 (3)
O2iv—Yb1—O2vii117.45 (14)Mo1xii—K1—Mo166.83 (3)
O2vi—Yb1—O2vii70.66 (12)Mo1—K1—Mo1xv139.938 (17)
O2vi—Yb1—O2v117.45 (14)Mo1xiii—K1—Mo1xiv105.17 (4)
O2vii—Yb1—O2v146.58 (15)Mo1—K1—Mo1xi102.288 (13)
O2iv—Yb1—O2vi153.89 (16)Mo1—K1—Mo1xiii105.003 (13)
O1—Yb1—Mo123.91 (8)Mo1xii—K1—Mo1xv102.287 (13)
O1i—Yb1—Mo1iii96.67 (8)Mo1xii—K1—Mo1xiii139.065 (16)
O1—Yb1—Mo1ii96.67 (8)Mo1xiii—K1—Mo1xv56.91 (2)
O1i—Yb1—Mo193.86 (8)Mo1xiv—K1—Mo1xi56.91 (2)
O1i—Yb1—Mo1ii130.19 (8)Mo1xii—K1—Mo1xi139.938 (17)
O1—Yb1—Mo1i93.86 (8)Mo1xii—K1—Mo1xiv105.003 (13)
O1i—Yb1—Mo1i23.91 (8)Mo1xiii—K1—Mo1xi80.44 (3)
O1—Yb1—Mo1iii130.19 (8)Mo1—K1—Mo1xiv139.065 (16)
O1i—Yb1—O2v69.45 (10)Mo1xv—K1—Mo1xi108.26 (4)
O1—Yb1—O2vii69.45 (10)O4—K1—Mo1xiv149.21 (8)
O1i—Yb1—O2iv130.70 (11)O4xi—K1—Mo1xi21.66 (7)
O1—Yb1—O2iv72.89 (11)O4—K1—Mo1xiii80.93 (7)
O1i—Yb1—O2vii84.00 (11)O4xi—K1—Mo1xiv72.90 (7)
O1—Yb1—O2v84.00 (11)O4xi—K1—Mo1xii126.53 (8)
O1—Yb1—O2vi130.70 (11)O4xii—K1—Mo187.03 (8)
O1i—Yb1—O2vi72.89 (11)O4xii—K1—Mo1xi125.30 (8)
O1—Yb1—O1i75.25 (16)O4—K1—Mo124.24 (7)
O1i—Yb1—O3iii108.54 (12)O4xv—K1—Mo1xiii72.90 (7)
O1—Yb1—O3iii150.82 (12)O4xi—K1—Mo180.82 (7)
O1i—Yb1—O3ii150.82 (12)O4xii—K1—Mo1xiii149.21 (8)
O1—Yb1—O3ii108.54 (12)O4xv—K1—Mo1126.53 (8)
O3iii—Yb1—Mo1130.01 (7)O4xi—K1—Mo1xiii88.68 (8)
O3ii—Yb1—Mo1iii101.50 (8)O4xii—K1—Mo1xv95.65 (7)
O3ii—Yb1—Mo1i130.01 (7)O4—K1—Mo1xi95.65 (7)
O3ii—Yb1—Mo199.27 (8)O4—K1—Mo1xv125.30 (8)
O3iii—Yb1—Mo1i99.27 (8)O4xv—K1—Mo1xi128.58 (9)
O3iii—Yb1—Mo1iii22.72 (8)O4xi—K1—Mo1xv128.58 (9)
O3iii—Yb1—Mo1ii101.50 (8)O4—K1—Mo1xii87.03 (8)
O3ii—Yb1—Mo1ii22.72 (8)O4xv—K1—Mo1xv21.66 (7)
O3iii—Yb1—O2iv84.30 (11)O4xv—K1—Mo1xii80.82 (7)
O3ii—Yb1—O2v139.02 (10)O4xii—K1—Mo1xii24.25 (7)
O3iii—Yb1—O2v71.18 (11)O4xv—K1—Mo1xiv88.68 (8)
O3ii—Yb1—O2iv76.09 (10)O4xii—K1—Mo1xiv80.93 (7)
O3ii—Yb1—O2vi84.30 (11)O4xii—K1—O4xi121.56 (5)
O3iii—Yb1—O2vi76.09 (10)O4xii—K1—O4109.49 (15)
O3iii—Yb1—O2vii139.02 (10)O4—K1—O4xv121.56 (5)
O3ii—Yb1—O2vii71.18 (11)O4—K1—O4xi77.17 (8)
O3iii—Yb1—O3ii82.48 (16)O4xii—K1—O4xv77.17 (8)
Yb1viii—Mo1—Yb1iv63.070 (9)O4xi—K1—O4xv149.74 (15)
Yb1iii—Mo1—Yb1viii120.155 (13)O4xv—K1—O1xiv89.65 (10)
Yb1iii—Mo1—Yb1iv85.752 (11)O4xv—K1—O1xiii63.27 (9)
Yb1—Mo1—Yb1iii66.007 (10)O4xii—K1—O1xiv106.49 (10)
Yb1—Mo1—Yb1viii86.536 (12)O4xi—K1—O1xiii89.65 (10)
Yb1—Mo1—Yb1iv120.176 (13)O4xi—K1—O1xiv63.27 (9)
Yb1—Mo1—K1138.532 (12)O4xii—K1—O1xiii136.42 (10)
Yb1iii—Mo1—K1x171.48 (2)O4—K1—O1xiii106.49 (10)
Yb1iv—Mo1—K1ix170.07 (2)O4—K1—O1xiv136.42 (10)
Yb1iii—Mo1—K196.075 (15)O1xiv—K1—Mo1xiv26.02 (6)
Yb1viii—Mo1—K1ix120.864 (13)O1xiv—K1—Mo1xiii80.64 (7)
Yb1viii—Mo1—K1132.869 (12)O1xiii—K1—Mo1xi73.47 (7)
Yb1—Mo1—K1x121.021 (14)O1xiii—K1—Mo1xiv80.64 (7)
Yb1iv—Mo1—K1x93.824 (14)O1xiii—K1—Mo1130.72 (6)
Yb1viii—Mo1—K1x66.75 (2)O1xiii—K1—Mo1xii143.68 (7)
Yb1—Mo1—K1ix69.74 (2)O1xiv—K1—Mo1xi42.36 (7)
Yb1iii—Mo1—K1ix98.712 (15)O1xiv—K1—Mo1xii130.72 (6)
K1—Mo1—Yb1iv93.608 (16)O1xiv—K1—Mo1xv73.47 (7)
K1—Mo1—K1ix77.153 (12)O1xiii—K1—Mo1xv42.36 (7)
K1—Mo1—K1x75.448 (12)O1xiv—K1—Mo1143.68 (7)
K1ix—Mo1—K1x80.44 (3)O1xiii—K1—Mo1xiii26.02 (6)
O4—Mo1—Yb1136.81 (11)O1xiii—K1—O1xiv58.30 (13)
O4—Mo1—Yb1viii101.62 (11)Mo1—O4—K1116.01 (15)
O4—Mo1—Yb1iv100.77 (12)Mo1—O4—K1x121.81 (16)
O4—Mo1—Yb1iii135.23 (11)K1—O4—K1x120.30 (12)
O4—Mo1—K1x36.53 (11)Yb1iv—O2—Yb1viii109.33 (12)
O4—Mo1—K1ix69.81 (12)Mo1—O2—Yb1iv128.04 (14)
O4—Mo1—K139.74 (10)Mo1—O2—Yb1viii119.82 (13)
O4—Mo1—O2109.61 (16)Yb1—O1—K1ix113.22 (12)
O4—Mo1—O1106.25 (15)Mo1—O1—Yb1125.42 (16)
O4—Mo1—O3105.38 (15)Mo1—O1—K1ix110.17 (14)
O2—Mo1—Yb1iv29.34 (8)Mo1—O3—Yb1iii127.31 (16)
O2—Mo1—Yb1viii34.93 (8)
Symmetry codes: (i) x, y, z+3/2; (ii) x, y+1, z+1/2; (iii) x, y+1, z+1; (iv) x+1, y+1, z+1; (v) x1, y, z; (vi) x1, y+1, z+1/2; (vii) x+1, y, z+3/2; (viii) x+1, y, z; (ix) x+1/2, y+3/2, z+1/2; (x) x+3/2, y+3/2, z+1/2; (xi) x1/2, y+3/2, z+1; (xii) x+1, y, z+1/2; (xiii) x+1/2, y+3/2, z+1; (xiv) x+1/2, y+3/2, z1/2; (xv) x+3/2, y+3/2, z1/2.
Potassium lutetium bis(molybdate) (Lu_Molybdate) top
Crystal data top
KLu(MoO4)2F(000) = 952
Mr = 533.95Dx = 4.942 Mg m3
Orthorhombic, PbcnMo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2n 2abCell parameters from 6634 reflections
a = 5.0292 (2) Åθ = 3.4–30.5°
b = 18.2519 (10) ŵ = 17.68 mm1
c = 7.8174 (4) ÅT = 100 K
V = 717.58 (6) Å3Plate, white
Z = 40.44 × 0.14 × 0.04 mm
Data collection top
Rigaku XtaLAB Synergy-S, HyPix
diffractometer
1105 independent reflections
Radiation source: micro-focus sealed X-ray tube1004 reflections with I > 2σ(I)
Mirror monochromatorRint = 0.087
Detector resolution: 10.0000 pixels mm-1θmax = 30.5°, θmin = 2.2°
ω scansh = 77
Absorption correction: multi-scan
(CrysAlisPro; Rigaku OD, 2019)
k = 2626
Tmin = 0.240, Tmax = 1.000l = 1111
19857 measured reflections
Refinement top
Refinement on F20 restraints
Least-squares matrix: full0 constraints
R[F2 > 2σ(F2)] = 0.027Primary atom site location: dual
wR(F2) = 0.077 w = 1/[σ2(Fo2) + (0.0305P)2 + 4.6788P]
where P = (Fo2 + 2Fc2)/3
S = 1.17(Δ/σ)max = 0.001
1105 reflectionsΔρmax = 2.05 e Å3
57 parametersΔρmin = 3.03 e Å3
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Refinement. Reflections were merged by SHELXL according to the crystal class for the calculation of statistics and refinement.

_reflns_Friedel_fraction is defined as the number of unique Friedel pairs measured divided by the number that would be possible theoretically, ignoring centric projections and systematic absences.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Lu11.0000000.50463 (2)0.7500000.00674 (13)
Mo10.52103 (8)0.39975 (3)0.51329 (5)0.00699 (13)
K10.5000000.22690 (9)0.2500000.0116 (3)
O40.3935 (7)0.31279 (19)0.5200 (4)0.0119 (7)
O20.2476 (7)0.4667 (2)0.4950 (4)0.0098 (7)
O10.7429 (6)0.40718 (19)0.6920 (4)0.0101 (6)
O30.7347 (6)0.40152 (19)0.3343 (4)0.0098 (6)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Lu10.00628 (18)0.0100 (2)0.00389 (17)0.0000.00006 (8)0.000
Mo10.0067 (2)0.0091 (2)0.0051 (2)0.00028 (12)0.00024 (11)0.00031 (13)
K10.0142 (7)0.0132 (8)0.0073 (6)0.0000.0006 (4)0.000
O40.0128 (17)0.0141 (17)0.0087 (14)0.0011 (13)0.0006 (12)0.0018 (12)
O20.0079 (15)0.0168 (18)0.0046 (14)0.0006 (13)0.0051 (11)0.0004 (11)
O10.0100 (14)0.0130 (16)0.0074 (14)0.0011 (13)0.0028 (12)0.0009 (12)
O30.0118 (15)0.0126 (16)0.0051 (13)0.0008 (13)0.0002 (11)0.0001 (11)
Geometric parameters (Å, º) top
Lu1—Lu1i3.9123 (2)Mo1—O31.765 (3)
Lu1—Lu1ii3.9123 (2)K1—Mo1xi3.9540 (11)
Lu1—K1iii4.2257 (17)K1—Mo1xii3.7684 (14)
Lu1—O2iv2.344 (3)K1—Mo1xiii3.8171 (11)
Lu1—O2v2.344 (3)K1—Mo1xiv3.8171 (11)
Lu1—O2vi2.450 (3)K1—Mo1xv3.9540 (11)
Lu1—O2vii2.450 (3)K1—O42.683 (3)
Lu1—O12.245 (3)K1—O4xii2.683 (3)
Lu1—O1viii2.245 (3)K1—O4xv2.770 (3)
Lu1—O3ix2.269 (3)K1—O4xi2.770 (3)
Lu1—O3ii2.269 (3)K1—O1xiii2.805 (4)
Mo1—K13.7684 (14)K1—O1xiv2.805 (4)
Mo1—K1x3.9540 (11)O4—K1x2.770 (3)
Mo1—K1iii3.8171 (11)O2—Lu1iv2.344 (3)
Mo1—O41.713 (4)O2—Lu1xvi2.450 (3)
Mo1—O21.845 (4)O1—K1iii2.805 (4)
Mo1—O11.793 (3)O3—Lu1ii2.269 (3)
Lu1ii—Lu1—Lu1i175.051 (17)Mo1xiv—K1—Mo1xv80.64 (3)
Lu1ii—Lu1—K1iii87.526 (9)Mo1—K1—Mo1xv139.788 (18)
Lu1i—Lu1—K1iii87.526 (9)Mo1xiii—K1—Mo1xiv105.46 (4)
O2vii—Lu1—Lu1ii34.41 (8)Mo1xii—K1—Mo1xi139.788 (18)
O2vii—Lu1—Lu1i143.18 (8)Mo1xii—K1—Mo166.31 (3)
O2iv—Lu1—Lu1ii36.22 (8)Mo1xiii—K1—Mo1xi80.64 (3)
O2v—Lu1—Lu1ii145.70 (8)Mo1xii—K1—Mo1xv102.429 (13)
O2vi—Lu1—Lu1i34.41 (8)Mo1—K1—Mo1xiii105.066 (13)
O2v—Lu1—Lu1i36.22 (8)Mo1xiii—K1—Mo1xv56.95 (2)
O2iv—Lu1—Lu1i145.70 (8)Mo1xii—K1—Mo1xiv105.066 (14)
O2vi—Lu1—Lu1ii143.18 (8)Mo1—K1—Mo1xiv138.944 (16)
O2vii—Lu1—K1iii73.58 (8)Mo1—K1—Mo1xi102.429 (13)
O2iv—Lu1—K1iii102.92 (9)Mo1xiv—K1—Mo1xi56.95 (2)
O2v—Lu1—K1iii102.92 (9)Mo1xii—K1—Mo1xiii138.944 (16)
O2vi—Lu1—K1iii73.58 (8)Mo1xv—K1—Mo1xi108.45 (4)
O2iv—Lu1—O2vi117.26 (15)O4xii—K1—Mo1xiv81.17 (8)
O2v—Lu1—O2vii117.26 (15)O4xv—K1—Mo1xi128.63 (9)
O2v—Lu1—O2iv154.16 (18)O4xv—K1—Mo1xii81.05 (7)
O2v—Lu1—O2vi70.63 (14)O4xv—K1—Mo1xiv88.73 (8)
O2vii—Lu1—O2vi147.15 (17)O4—K1—Mo124.06 (8)
O2iv—Lu1—O2vii70.63 (14)O4xi—K1—Mo1xiv72.87 (7)
O1—Lu1—Lu1i99.65 (8)O4—K1—Mo1xi96.06 (8)
O1—Lu1—Lu1ii76.35 (8)O4xii—K1—Mo186.27 (8)
O1viii—Lu1—Lu1i76.35 (8)O4xi—K1—Mo1xiii88.73 (8)
O1viii—Lu1—Lu1ii99.65 (8)O4xv—K1—Mo1126.40 (8)
O1viii—Lu1—K1iii37.61 (8)O4xii—K1—Mo1xii24.06 (8)
O1—Lu1—K1iii37.61 (8)O4xi—K1—Mo181.05 (7)
O1viii—Lu1—O2iv130.40 (12)O4xv—K1—Mo1xiii72.87 (7)
O1—Lu1—O2vi69.37 (11)O4—K1—Mo1xv125.27 (8)
O1viii—Lu1—O2vii69.37 (11)O4xii—K1—Mo1xi125.27 (8)
O1—Lu1—O2iv72.91 (12)O4xii—K1—Mo1xv96.06 (8)
O1viii—Lu1—O2v72.91 (12)O4xi—K1—Mo1xi21.55 (7)
O1—Lu1—O2vii84.51 (12)O4xv—K1—Mo1xv21.55 (7)
O1—Lu1—O2v130.40 (12)O4xi—K1—Mo1xii126.40 (8)
O1viii—Lu1—O2vi84.51 (12)O4xi—K1—Mo1xv128.63 (9)
O1viii—Lu1—O175.22 (17)O4—K1—Mo1xiv149.44 (8)
O1—Lu1—O3ix108.54 (13)O4—K1—Mo1xii86.27 (8)
O1viii—Lu1—O3ix151.41 (12)O4xii—K1—Mo1xiii149.44 (8)
O1viii—Lu1—O3ii108.54 (13)O4—K1—Mo1xiii81.17 (8)
O1—Lu1—O3ii151.41 (12)O4—K1—O4xv121.38 (5)
O3ii—Lu1—Lu1ii75.08 (8)O4—K1—O4xii108.51 (16)
O3ix—Lu1—Lu1ii108.82 (8)O4xii—K1—O4xi121.38 (5)
O3ii—Lu1—Lu1i108.82 (8)O4xii—K1—O4xv77.57 (9)
O3ix—Lu1—Lu1i75.08 (8)O4—K1—O4xi77.57 (9)
O3ii—Lu1—K1iii139.02 (8)O4xv—K1—O4xi149.68 (16)
O3ix—Lu1—K1iii139.02 (8)O4xi—K1—O1xiv63.09 (10)
O3ii—Lu1—O2vii71.24 (12)O4xi—K1—O1xiii89.78 (11)
O3ii—Lu1—O2iv84.63 (12)O4—K1—O1xiv136.80 (10)
O3ix—Lu1—O2v84.63 (12)O4xv—K1—O1xiii63.09 (10)
O3ii—Lu1—O2v75.88 (11)O4xv—K1—O1xiv89.78 (11)
O3ix—Lu1—O2vii138.46 (11)O4—K1—O1xiii106.89 (10)
O3ii—Lu1—O2vi138.46 (11)O4xii—K1—O1xiii136.80 (10)
O3ix—Lu1—O2vi71.24 (12)O4xii—K1—O1xiv106.89 (10)
O3ix—Lu1—O2iv75.88 (11)O1xiv—K1—Mo1xiv26.14 (7)
O3ii—Lu1—O3ix81.96 (17)O1xiv—K1—Mo1xiii80.84 (7)
K1—Mo1—K1x75.379 (13)O1xiii—K1—Mo1xi73.72 (7)
K1—Mo1—K1iii77.027 (12)O1xiii—K1—Mo1xiv80.84 (7)
K1iii—Mo1—K1x80.64 (3)O1xiii—K1—Mo1130.93 (6)
O4—Mo1—K139.69 (11)O1xiii—K1—Mo1xii143.70 (7)
O4—Mo1—K1x36.45 (11)O1xiv—K1—Mo1xi42.27 (7)
O4—Mo1—K1iii70.14 (12)O1xiv—K1—Mo1xii130.93 (6)
O4—Mo1—O2109.68 (17)O1xiv—K1—Mo1xv73.72 (7)
O4—Mo1—O1106.21 (16)O1xiii—K1—Mo1xv42.27 (7)
O4—Mo1—O3105.63 (16)O1xiv—K1—Mo1143.70 (7)
O2—Mo1—K1iii155.36 (9)O1xiii—K1—Mo1xiii26.14 (7)
O2—Mo1—K1119.41 (10)O1xiii—K1—O1xiv58.48 (14)
O2—Mo1—K1x85.95 (11)Mo1—O4—K1116.25 (16)
O1—Mo1—K1iii43.56 (11)Mo1—O4—K1x122.00 (16)
O1—Mo1—K1x95.28 (11)K1—O4—K1x120.03 (13)
O1—Mo1—K1120.42 (11)Lu1iv—O2—Lu1xvi109.37 (14)
O1—Mo1—O2118.31 (14)Mo1—O2—Lu1iv127.40 (15)
O3—Mo1—K1x141.76 (12)Mo1—O2—Lu1xvi120.19 (14)
O3—Mo1—K1iii90.65 (11)Lu1—O1—K1iii113.15 (12)
O3—Mo1—K166.38 (11)Mo1—O1—Lu1125.15 (17)
O3—Mo1—O2112.35 (14)Mo1—O1—K1iii110.29 (15)
O3—Mo1—O1103.74 (16)Mo1—O3—Lu1ii127.02 (17)
Symmetry codes: (i) x+2, y+1, z+2; (ii) x+2, y+1, z+1; (iii) x+3/2, y+1/2, z+1/2; (iv) x+1, y+1, z+1; (v) x+1, y+1, z+1/2; (vi) x+1, y, z+3/2; (vii) x+1, y, z; (viii) x+2, y, z+3/2; (ix) x, y+1, z+1/2; (x) x+1/2, y+1/2, z+1/2; (xi) x+1/2, y+1/2, z+1; (xii) x+1, y, z+1/2; (xiii) x1/2, y+1/2, z+1; (xiv) x+3/2, y+1/2, z1/2; (xv) x+1/2, y+1/2, z1/2; (xvi) x1, y, z.
Bond-valence (v.u.) calculations for the title KRE(MoO4)2 compounds top
Detailed tables are included in the supporting information.
KTb(MoO4)2KDy(MoO4)2KHo(MoO4)2KEr(MoO4)2KYb(MoO4)2KLu(MoO4)2
RE3.112.973.253.002.973.13
Mo5.665.665.625.655.665.70
K1.201.211.191.201.101.13
O11.991.972.001.981.982.00
O21.821.801.821.801.791.82
O31.901.921.971.921.911.91
O42.062.072.072.052.032.09
 

Acknowledgements

The Pacific Northwest National Laboratory is operated by Battelle under Contract Number DE-AC05–76RL01830.

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