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

Chong, S.; Perry, S.; Riley, B.J.; Nelson, Z.J.

doi:10.1107/S205698902001542X

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ISSN: 2056-9890

Volume 76| Part 12| December 2020| Pages 1871-1875

https://doi.org/10.1107/S205698902001542X

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

Saehwa Chong,^a ^* Samuel Perry,^b Brian J. Riley ^a and Zayne J. Nelson ^a

^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.

Keywords: rare-earth molybdate; lanthanide molybdate; single-crystal XRD.

CCDC references: 2045648; 2045647; 2045646; 2045645; 2045644; 2045643

1. Chemical context

Rare-earth (RE) molybdates have been studied extensively because of their luminescent, magnetoelectric, and ferroelectric properties (Borchardt & Bierstedt, 1967 ; Axe et al., 1971 ; Pratap et al., 1987 ; Ponomarev et al., 1994 ; Shi et al., 1996 ; Kut'ko, 2005 ; Wang et al., 2007 ; Ponomarev & Zhukov, 2012 ). 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 ; Hanuza & Fomitsev, 1980 ; Leask et al., 1981 ; Hanuza et al., 1994 ; Stedman et al., 1994 ; Shi et al., 1996; Voron'ko et al., 2004 ; Kut'ko, 2005; Wang et al., 2007; Mat'aš et al., 2010 ; Poperezhai et al., 2017 ). The ARE(MoO₄)₂ compounds having the I4₁/a space group have luminescent properties with high thermal and hydrolytic stability (Stedman et al., 1994; Shi et al., 1996; Voron'ko et al., 2004; Wang et al., 2007) whereas the compounds with the Pbcn space group are known for the structural phase transition by the Jahn–Teller effect (Kut'ko, 2005; Mat'aš et al., 2010; Kamenskyi et al., 2014 ; Poperezhai et al., 2017). 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 ; Jeitschko, 1973 ; Ponomarev & Zhukov, 2012; Pratap et al., 1987); these phases exhibit magnetoelectric and ferroelectric properties (Borchardt & Bierstedt, 1967; Axe et al., 1971; Ponomarev et al., 1994; Ponomarev & Zhukov, 2012). The RE molybdate compounds are synthesized using flux-assisted or solid-state synthesis methods. Wanklyn & Wondre (1978) synthesized KRE(MoO₄)₂ (RE = La, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Lu) compounds by the flux-assisted method using REO_x, 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). Shi et al. (1996) synthesized the AgRE(MoO₄)₂ (RE = Eu, Gd, Tb) compounds with a tetragonal scheelite-type structure by heating the stoichiometric mixtures of REO_x, Ag₂O, and MoO₃ at 800°C for 50 h. Wang et al. (2007) synthesized the tetragonal AEu(MoO₄)₂ (A = Li, Na, K) compounds by heating a mixture of REO_x, 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 REO_x and MoO₃ at 900–1000°C (Borchardt & Bierstedt, 1967; Guzmán-Afonso et al., 2013 ).

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. 1a). The [RE(MoO₄)₂]⁻ layer contains chains formed by edge-sharing REO₈ octahedra connected by MoO₄ tetrahedra along the c-axis direction (Fig. 1b). 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). 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). 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). 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).

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
(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
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

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 ). The stoichiometric mixture of REO_x 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) with different colors (Fig. 5).

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
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. 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 ) 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 ). 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 ). All structures were solved by the intrinsic phasing method using SHELXT and refined with SHELXL (Sheldrick, 2015a ,b ) within the OLEX2 software package (Dolomanov et al., 2009 ).

Table 2
Experimental details

	KTb(MoO₄)₂	KDy(MoO₄)₂	KHo(MoO₄)₂
Crystal data
M_r	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)
V (Å³)	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)
T_min, T_max	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
R_int	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
Δρ_max, Δρ_min (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
M_r	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)
V (Å³)	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)	Multi-scan (CrysAlis PRO; Rigaku OD, 2019 $[Rigaku OD (2019). CrysAlis PRO. Rigaku Oxford Diffraction, Yarnton, England.]$ )
T_min, T_max	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
R_int	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
Δρ_max, Δρ_min (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), SHELXT (Sheldrick, 2015a), SHELXL (Sheldrick, 2015b), OLEX2 (Dolomanov et al., 2009), and publCIF (Westrip, 2010 ).

Supporting information

CCDC references: 2045648; 2045647; 2045646; 2045645; 2045644; 2045643

Crystal structure: contains datablocks global, Tb_Molybdate, Dy_Molybdate, Ho_Molybdate, Er_Molybdate, Yb_Molybdate, Lu_Molybdate. DOI: https://doi.org/10.1107/S205698902001542X/ru2071sup1.cif

Structure factors: contains datablock Tb_Molybdate. DOI: https://doi.org/10.1107/S205698902001542X/ru2071Tb_Molybdatesup2.hkl

Structure factors: contains datablock Dy_Molybdate. DOI: https://doi.org/10.1107/S205698902001542X/ru2071Dy_Molybdatesup3.hkl

Structure factors: contains datablock Ho_Molybdate. DOI: https://doi.org/10.1107/S205698902001542X/ru2071Ho_Molybdatesup4.hkl

Structure factors: contains datablock Er_Molybdate. DOI: https://doi.org/10.1107/S205698902001542X/ru2071Er_Molybdatesup5.hkl

Structure factors: contains datablock Yb_Molybdate. DOI: https://doi.org/10.1107/S205698902001542X/ru2071Yb_Molybdatesup6.hkl

Structure factors: contains datablock Lu_Molybdate. DOI: https://doi.org/10.1107/S205698902001542X/ru2071Lu_Molybdatesup7.hkl

Bond-valence tables. DOI: https://doi.org/10.1107/S205698902001542X/ru2071sup8.pdf

checkCIF report

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)₂	F(000) = 928
M_r = 517.90	D_x = 4.674 Mg m⁻³
Orthorhombic, Pbcn	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2n 2ab	Cell parameters from 6923 reflections
a = 5.0826 (1) Å	θ = 2.3–33.5°
b = 18.1273 (7) Å	µ = 13.43 mm⁻¹
c = 7.9875 (2) Å	T = 100 K
V = 735.92 (4) Å³	Plate, white
Z = 4	0.36 × 0.20 × 0.04 mm

Data collection top

Rigaku XtaLAB Synergy-S, HyPix diffractometer	1350 independent reflections
Radiation source: micro-focus sealed X-ray tube	1238 reflections with I > 2σ(I)
Mirror monochromator	R_int = 0.069
Detector resolution: 10.0000 pixels mm^-1	θ_max = 33.7°, θ_min = 2.3°
ω scans	h = −7→6
Absorption correction: gaussian (CrysAlisPro; Rigaku OD, 2019)	k = −27→27
T_min = 0.035, T_max = 0.703	l = −12→12
13792 measured reflections

Refinement top

Refinement on F²	0 restraints
Least-squares matrix: full	0 constraints
R[F² > 2σ(F²)] = 0.033	Primary atom site location: dual
wR(F²) = 0.102	w = 1/[σ²(F_o²) + (0.0705P)² + 1.3389P] where P = (F_o² + 2F_c²)/3
S = 1.08	(Δ/σ)_max = 0.002
1350 reflections	Δρ_max = 2.63 e Å⁻³
56 parameters	Δρ_min = −2.78 e Å⁻³

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

	x	y	z	U_iso*/U_eq
Tb1	0.000000	0.49384 (2)	0.250000	0.00653 (12)
Mo1	0.48012 (7)	0.60289 (2)	0.48337 (5)	0.00701 (12)
K1	0.500000	0.77012 (8)	0.750000	0.0114 (2)
O2	0.7489 (5)	0.53496 (13)	0.5042 (2)	0.0089 (4)
O4	0.6111 (5)	0.69028 (13)	0.4759 (3)	0.0105 (5)
O1	0.2592 (5)	0.59503 (12)	0.3093 (3)	0.0099 (4)
O3	0.2716 (5)	0.60251 (12)	0.6603 (3)	0.0102 (4)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Tb1	0.00409 (18)	0.01076 (18)	0.00476 (17)	0.000	−0.00033 (5)	0.000
Mo1	0.00425 (19)	0.01069 (19)	0.00610 (19)	0.00024 (8)	−0.00066 (7)	−0.00020 (10)
K1	0.0118 (5)	0.0136 (5)	0.0089 (5)	0.000	−0.0008 (3)	0.000
O2	0.0056 (12)	0.0138 (9)	0.0073 (9)	0.0017 (9)	−0.0008 (6)	0.0002 (7)
O4	0.0096 (12)	0.0130 (10)	0.0089 (10)	−0.0036 (9)	0.0011 (7)	−0.0007 (8)
O1	0.0069 (10)	0.0143 (10)	0.0084 (10)	−0.0001 (8)	−0.0021 (8)	0.0002 (8)
O3	0.0089 (10)	0.0144 (10)	0.0073 (9)	−0.0003 (8)	0.0003 (8)	−0.0008 (7)

Geometric parameters (Å, º) top

Tb1—Tb1ⁱ	4.0000 (1)	Mo1—O3	1.767 (2)
Tb1—Tb1ⁱⁱ	4.0000 (1)	K1—Mo1^xi	3.8378 (9)
Tb1—K1ⁱⁱⁱ	4.2788 (14)	K1—Mo1^xii	3.7062 (11)
Tb1—O2^iv	2.399 (2)	K1—Mo1^xiii	3.8378 (9)
Tb1—O2^v	2.399 (2)	K1—O4	2.684 (2)
Tb1—O2^vi	2.511 (2)	K1—O4^xiv	2.771 (2)
Tb1—O2^vii	2.511 (2)	K1—O4^xii	2.684 (2)
Tb1—O1^viii	2.308 (2)	K1—O4^xv	2.771 (2)
Tb1—O1	2.308 (2)	K1—O1^xiii	2.817 (3)
Tb1—O3^ix	2.339 (2)	K1—O1^xi	2.817 (3)
Tb1—O3ⁱⁱ	2.339 (2)	K1—O3	3.330 (3)
Mo1—K1	3.7062 (11)	K1—O3^xii	3.330 (3)
Mo1—K1^x	3.9694 (9)	O2—Tb1^iv	2.399 (2)
Mo1—K1ⁱⁱⁱ	3.8378 (9)	O2—Tb1^xvi	2.511 (2)
Mo1—O2	1.847 (2)	O4—K1^x	2.771 (2)
Mo1—O4	1.719 (2)	O1—K1ⁱⁱⁱ	2.817 (3)
Mo1—O1	1.793 (2)	O3—Tb1ⁱⁱ	2.339 (2)

Tb1ⁱⁱ—Tb1—Tb1ⁱ	173.598 (18)	Mo1^xiii—K1—Mo1^xi	106.29 (4)
Tb1ⁱⁱ—Tb1—K1ⁱⁱⁱ	86.799 (9)	Mo1—K1—Mo1^xiii	103.230 (11)
Tb1ⁱ—Tb1—K1ⁱⁱⁱ	86.799 (9)	Mo1^xii—K1—Mo1^xiii	138.798 (13)
O2^iv—Tb1—Tb1ⁱ	146.02 (5)	Mo1—K1—Mo1^xii	70.24 (3)
O2^v—Tb1—Tb1ⁱ	36.40 (5)	Mo1^xii—K1—Mo1^xi	103.230 (11)
O2^vi—Tb1—Tb1ⁱ	34.54 (5)	O4^xii—K1—Mo1	91.25 (6)
O2^vii—Tb1—Tb1ⁱ	142.24 (5)	O4—K1—Mo1^xii	91.25 (6)
O2^iv—Tb1—Tb1ⁱⁱ	36.40 (5)	O4^xiv—K1—Mo1^xi	72.98 (5)
O2^v—Tb1—Tb1ⁱⁱ	146.02 (5)	O4^xiv—K1—Mo1^xii	127.27 (6)
O2^vi—Tb1—Tb1ⁱⁱ	142.24 (5)	O4^xii—K1—Mo1^xi	78.09 (5)
O2^vii—Tb1—Tb1ⁱⁱ	34.54 (5)	O4—K1—Mo1	25.32 (5)
O2^vi—Tb1—K1ⁱⁱⁱ	72.73 (5)	O4^xiv—K1—Mo1	79.53 (5)
O2^vii—Tb1—K1ⁱⁱⁱ	72.73 (5)	O4—K1—Mo1^xiii	78.09 (5)
O2^v—Tb1—K1ⁱⁱⁱ	102.57 (6)	O4—K1—Mo1^xi	148.56 (6)
O2^iv—Tb1—K1ⁱⁱⁱ	102.57 (6)	O4^xii—K1—Mo1^xiii	148.57 (6)
O2^vii—Tb1—O2^vi	145.47 (11)	O4^xv—K1—Mo1^xi	88.96 (6)
O2^iv—Tb1—O2^vi	117.12 (10)	O4^xv—K1—Mo1^xiii	72.98 (5)
O2^iv—Tb1—O2^vii	70.93 (9)	O4^xii—K1—Mo1^xii	25.32 (5)
O2^v—Tb1—O2^vi	70.93 (9)	O4^xiv—K1—Mo1^xiii	88.96 (6)
O2^v—Tb1—O2^vii	117.12 (10)	O4^xv—K1—Mo1	127.27 (6)
O2^v—Tb1—O2^iv	154.87 (11)	O4^xv—K1—Mo1^xii	79.53 (5)
O1—Tb1—Tb1ⁱ	99.23 (6)	O4^xii—K1—O4^xv	76.03 (6)
O1^viii—Tb1—Tb1ⁱ	75.57 (6)	O4—K1—O4^xv	121.38 (3)
O1—Tb1—Tb1ⁱⁱ	75.57 (6)	O4^xv—K1—O4^xiv	149.97 (11)
O1^viii—Tb1—Tb1ⁱⁱ	99.23 (6)	O4—K1—O4^xiv	76.03 (6)
O1^viii—Tb1—K1ⁱⁱⁱ	37.35 (6)	O4^xii—K1—O4^xiv	121.38 (3)
O1—Tb1—K1ⁱⁱⁱ	37.35 (6)	O4—K1—O4^xii	114.75 (11)
O1^viii—Tb1—O2^iv	130.14 (8)	O4^xii—K1—O1^xi	103.44 (7)
O1—Tb1—O2^vi	68.88 (7)	O4—K1—O1^xi	134.69 (7)
O1^viii—Tb1—O2^vii	68.88 (7)	O4—K1—O1^xiii	103.44 (7)
O1^viii—Tb1—O2^vi	83.59 (8)	O4^xiv—K1—O1^xiii	89.97 (8)
O1—Tb1—O2^iv	72.62 (8)	O4^xiv—K1—O1^xi	63.32 (7)
O1—Tb1—O2^vii	83.59 (8)	O4^xii—K1—O1^xiii	134.69 (7)
O1^viii—Tb1—O2^v	72.62 (8)	O4^xv—K1—O1^xiii	63.32 (7)
O1—Tb1—O2^v	130.14 (8)	O4^xv—K1—O1^xi	89.97 (8)
O1—Tb1—O1^viii	74.71 (11)	O4^xv—K1—O3	128.69 (7)
O1^viii—Tb1—O3^ix	150.21 (8)	O4^xv—K1—O3^xii	81.24 (7)
O1^viii—Tb1—O3ⁱⁱ	108.63 (9)	O4^xii—K1—O3	67.06 (7)
O1—Tb1—O3^ix	108.63 (9)	O4^xiv—K1—O3	81.24 (7)
O1—Tb1—O3ⁱⁱ	150.21 (8)	O4^xiv—K1—O3^xii	128.69 (7)
O3^ix—Tb1—Tb1ⁱ	74.69 (5)	O4—K1—O3^xii	67.06 (7)
O3^ix—Tb1—Tb1ⁱⁱ	110.34 (5)	O4—K1—O3	53.56 (7)
O3ⁱⁱ—Tb1—Tb1ⁱⁱ	74.69 (5)	O4^xii—K1—O3^xii	53.56 (7)
O3ⁱⁱ—Tb1—Tb1ⁱ	110.34 (5)	O1^xiii—K1—Mo1	128.75 (5)
O3ⁱⁱ—Tb1—K1ⁱⁱⁱ	138.32 (6)	O1^xiii—K1—Mo1^xi	81.87 (6)
O3^ix—Tb1—K1ⁱⁱⁱ	138.32 (6)	O1^xi—K1—Mo1^xii	128.75 (5)
O3^ix—Tb1—O2^vii	140.29 (7)	O1^xi—K1—Mo1	142.52 (5)
O3^ix—Tb1—O2^iv	76.95 (8)	O1^xiii—K1—Mo1^xii	142.52 (5)
O3ⁱⁱ—Tb1—O2^vii	70.98 (8)	O1^xiii—K1—Mo1^xiii	25.90 (5)
O3ⁱⁱ—Tb1—O2^v	76.95 (8)	O1^xi—K1—Mo1^xiii	81.87 (6)
O3^ix—Tb1—O2^vi	70.98 (8)	O1^xi—K1—Mo1^xi	25.90 (5)
O3ⁱⁱ—Tb1—O2^vi	140.29 (7)	O1^xiii—K1—O1^xi	59.61 (10)
O3ⁱⁱ—Tb1—O2^iv	84.31 (8)	O1^xiii—K1—O3^xii	131.66 (6)
O3^ix—Tb1—O2^v	84.31 (8)	O1^xi—K1—O3	131.66 (6)
O3ⁱⁱ—Tb1—O3^ix	83.37 (11)	O1^xi—K1—O3^xii	156.71 (6)
K1—Mo1—K1^x	77.135 (10)	O1^xiii—K1—O3	156.71 (6)
K1ⁱⁱⁱ—Mo1—K1^x	81.22 (2)	O3—K1—Mo1^xiii	131.63 (4)
K1—Mo1—K1ⁱⁱⁱ	78.802 (10)	O3—K1—Mo1	28.44 (4)
O2—Mo1—K1ⁱⁱⁱ	156.08 (6)	O3^xii—K1—Mo1^xi	131.63 (4)
O2—Mo1—K1^x	86.36 (7)	O3^xii—K1—Mo1^xiii	115.47 (4)
O2—Mo1—K1	118.26 (7)	O3^xii—K1—Mo1	52.19 (4)
O4—Mo1—K1ⁱⁱⁱ	71.14 (9)	O3—K1—Mo1^xi	115.47 (4)
O4—Mo1—K1^x	36.07 (8)	O3^xii—K1—Mo1^xii	28.44 (4)
O4—Mo1—K1	41.90 (7)	O3—K1—Mo1^xii	52.19 (4)
O4—Mo1—O2	109.34 (11)	O3—K1—O3^xii	48.36 (8)
O4—Mo1—O1	106.78 (11)	Tb1^iv—O2—Tb1^xvi	109.07 (9)
O4—Mo1—O3	105.28 (10)	Mo1—O2—Tb1^iv	127.76 (10)
O1—Mo1—K1	121.85 (7)	Mo1—O2—Tb1^xvi	120.07 (9)
O1—Mo1—K1ⁱⁱⁱ	43.35 (7)	Mo1—O4—K1	112.78 (11)
O1—Mo1—K1^x	95.66 (7)	Mo1—O4—K1^x	122.51 (11)
O1—Mo1—O2	118.69 (10)	K1—O4—K1^x	122.78 (9)
O3—Mo1—K1	63.88 (7)	Tb1—O1—K1ⁱⁱⁱ	112.84 (9)
O3—Mo1—K1ⁱⁱⁱ	90.54 (8)	Mo1—O1—Tb1	125.44 (11)
O3—Mo1—K1^x	141.01 (7)	Mo1—O1—K1ⁱⁱⁱ	110.75 (10)
O3—Mo1—O2	111.67 (10)	Tb1ⁱⁱ—O3—K1	145.20 (9)
O3—Mo1—O1	104.16 (12)	Mo1—O3—Tb1ⁱⁱ	127.02 (11)
Mo1—K1—Mo1^xi	138.799 (13)	Mo1—O3—K1	87.68 (8)

Symmetry codes: (i) −x, −y+1, −z; (ii) −x, −y+1, −z+1; (iii) −x+1/2, −y+3/2, z−1/2; (iv) −x+1, −y+1, −z+1; (v) x−1, −y+1, z−1/2; (vi) −x+1, y, −z+1/2; (vii) x−1, y, z; (viii) −x, y, −z+1/2; (ix) x, −y+1, z−1/2; (x) −x+3/2, −y+3/2, z−1/2; (xi) −x+1/2, −y+3/2, z+1/2; (xii) −x+1, y, −z+3/2; (xiii) x+1/2, −y+3/2, −z+1; (xiv) x−1/2, −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)₂	F(000) = 932
M_r = 521.48	D_x = 4.739 Mg m⁻³
Orthorhombic, Pbcn	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2n 2ab	Cell parameters from 5121 reflections
a = 5.0776 (2) Å	θ = 2.3–33.3°
b = 18.1214 (7) Å	µ = 14.07 mm⁻¹
c = 7.9428 (3) Å	T = 100 K
V = 730.84 (5) Å³	Plate, light yellow
Z = 4	0.11 × 0.11 × 0.03 mm

Data collection top

Rigaku XtaLAB Synergy-S, HyPix diffractometer	1388 independent reflections
Radiation source: micro-focus sealed X-ray tube	1196 reflections with I > 2σ(I)
Mirror monochromator	R_int = 0.075
Detector resolution: 10.0000 pixels mm^-1	θ_max = 34.0°, θ_min = 2.3°
ω scans	h = −7→7
Absorption correction: gaussian (CrysAlisPro; Rigaku OD, 2019)	k = −27→27
T_min = 0.247, T_max = 0.695	l = −11→11
17317 measured reflections

Refinement top

Refinement on F²	0 restraints
Least-squares matrix: full	0 constraints
R[F² > 2σ(F²)] = 0.033	Primary atom site location: dual
wR(F²) = 0.088	w = 1/[σ²(F_o²) + (0.0343P)² + 8.538P] where P = (F_o² + 2F_c²)/3
S = 1.10	(Δ/σ)_max = 0.001
1388 reflections	Δρ_max = 2.38 e Å⁻³
56 parameters	Δρ_min = −2.65 e Å⁻³

Special details top

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

	x	y	z	U_iso*/U_eq
Dy1	0.000000	0.49408 (2)	0.250000	0.00749 (11)
Mo1	0.48037 (7)	0.60238 (2)	0.48347 (5)	0.00769 (11)
K1	0.500000	0.77076 (9)	0.750000	0.0118 (3)
O4	0.6101 (7)	0.6900 (2)	0.4770 (4)	0.0121 (6)
O2	0.7489 (7)	0.53449 (19)	0.5049 (4)	0.0100 (6)
O1	0.2588 (6)	0.59449 (19)	0.3083 (4)	0.0111 (6)
O3	0.2709 (6)	0.60172 (19)	0.6610 (4)	0.0109 (6)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Dy1	0.00510 (15)	0.01210 (17)	0.00526 (16)	0.000	−0.00001 (8)	0.000
Mo1	0.00512 (18)	0.0115 (2)	0.00648 (18)	0.00032 (12)	−0.00022 (10)	−0.00023 (12)
K1	0.0125 (6)	0.0147 (6)	0.0083 (6)	0.000	−0.0006 (4)	0.000
O4	0.0098 (15)	0.0154 (16)	0.0109 (15)	−0.0020 (12)	0.0006 (11)	−0.0004 (12)
O2	0.0066 (13)	0.0161 (16)	0.0072 (14)	0.0018 (11)	−0.0009 (11)	−0.0015 (11)
O1	0.0081 (13)	0.0178 (16)	0.0074 (14)	−0.0013 (12)	−0.0010 (11)	0.0001 (12)
O3	0.0073 (13)	0.0171 (16)	0.0082 (14)	−0.0003 (12)	0.0008 (11)	0.0006 (11)

Geometric parameters (Å, º) top

Dy1—Dy1ⁱ	3.9772 (1)	Mo1—O3	1.766 (3)
Dy1—Dy1ⁱⁱ	3.9772 (2)	K1—Mo1^xi	3.8305 (10)
Dy1—K1ⁱⁱⁱ	4.2614 (16)	K1—Mo1^xii	3.7150 (13)
Dy1—O2^iv	2.384 (3)	K1—Mo1^xiii	3.8305 (10)
Dy1—O2^v	2.384 (3)	K1—O4	2.676 (4)
Dy1—O2^vi	2.502 (3)	K1—O4^xiv	2.770 (3)
Dy1—O2^vii	2.502 (3)	K1—O4^xii	2.676 (4)
Dy1—O1	2.292 (3)	K1—O4^xv	2.770 (3)
Dy1—O1^viii	2.292 (3)	K1—O1^xiii	2.812 (4)
Dy1—O3^ix	2.325 (3)	K1—O1^xi	2.812 (4)
Dy1—O3ⁱⁱ	2.325 (3)	K1—O3^xii	3.352 (4)
Mo1—K1	3.7150 (13)	K1—O3	3.352 (4)
Mo1—K1^x	3.9604 (10)	O4—K1^x	2.770 (3)
Mo1—K1ⁱⁱⁱ	3.8305 (10)	O2—Dy1^xvi	2.502 (3)
Mo1—O4	1.720 (4)	O2—Dy1^iv	2.384 (3)
Mo1—O2	1.845 (3)	O1—K1ⁱⁱⁱ	2.812 (4)
Mo1—O1	1.795 (3)	O3—Dy1ⁱⁱ	2.325 (3)

Dy1ⁱⁱ—Dy1—Dy1ⁱ	173.818 (18)	Mo1—K1—Mo1^xii	69.57 (3)
Dy1ⁱⁱ—Dy1—K1ⁱⁱⁱ	86.909 (9)	Mo1—K1—Mo1^xi	138.737 (15)
Dy1ⁱ—Dy1—K1ⁱⁱⁱ	86.909 (9)	Mo1^xii—K1—Mo1^xiii	138.737 (15)
O2^iv—Dy1—Dy1ⁱ	145.80 (8)	Mo1^xiii—K1—Mo1^xi	106.24 (4)
O2^v—Dy1—Dy1ⁱ	36.52 (8)	Mo1^xii—K1—Mo1^xi	103.540 (12)
O2^vi—Dy1—Dy1ⁱ	34.53 (8)	O4^xv—K1—Mo1^xii	79.68 (8)
O2^vii—Dy1—Dy1ⁱ	142.40 (8)	O4—K1—Mo1^xii	90.40 (9)
O2^iv—Dy1—Dy1ⁱⁱ	36.52 (8)	O4^xiv—K1—Mo1^xi	72.90 (7)
O2^v—Dy1—Dy1ⁱⁱ	145.80 (8)	O4^xii—K1—Mo1	90.40 (9)
O2^vi—Dy1—Dy1ⁱⁱ	142.40 (8)	O4^xii—K1—Mo1^xi	78.63 (8)
O2^vii—Dy1—Dy1ⁱⁱ	34.53 (8)	O4^xv—K1—Mo1	126.93 (8)
O2^vi—Dy1—K1ⁱⁱⁱ	72.98 (8)	O4^xiv—K1—Mo1	79.68 (8)
O2^vii—Dy1—K1ⁱⁱⁱ	72.98 (8)	O4—K1—Mo1^xiii	78.63 (8)
O2^v—Dy1—K1ⁱⁱⁱ	102.55 (8)	O4—K1—Mo1^xi	148.63 (8)
O2^iv—Dy1—K1ⁱⁱⁱ	102.55 (8)	O4^xii—K1—Mo1^xiii	148.63 (8)
O2^vii—Dy1—O2^vi	145.97 (16)	O4^xv—K1—Mo1^xi	89.19 (8)
O2^iv—Dy1—O2^vi	116.87 (14)	O4^xv—K1—Mo1^xiii	72.90 (7)
O2^iv—Dy1—O2^vii	71.05 (13)	O4—K1—Mo1	25.09 (8)
O2^v—Dy1—O2^vi	71.05 (13)	O4^xiv—K1—Mo1^xiii	89.19 (8)
O2^v—Dy1—O2^vii	116.87 (14)	O4^xii—K1—Mo1^xii	25.09 (8)
O2^v—Dy1—O2^iv	154.91 (17)	O4^xiv—K1—Mo1^xii	126.93 (8)
O1^viii—Dy1—Dy1ⁱ	75.84 (8)	O4^xii—K1—O4^xv	76.26 (9)
O1—Dy1—Dy1ⁱ	99.15 (8)	O4—K1—O4^xv	121.24 (5)
O1^viii—Dy1—Dy1ⁱⁱ	99.15 (8)	O4^xv—K1—O4^xiv	150.24 (16)
O1—Dy1—Dy1ⁱⁱ	75.84 (8)	O4—K1—O4^xiv	76.25 (8)
O1—Dy1—K1ⁱⁱⁱ	37.45 (8)	O4^xii—K1—O4^xiv	121.24 (5)
O1^viii—Dy1—K1ⁱⁱⁱ	37.45 (8)	O4—K1—O4^xii	113.67 (16)
O1—Dy1—O2^iv	72.59 (12)	O4^xii—K1—O1^xi	104.12 (10)
O1^viii—Dy1—O2^vi	84.04 (12)	O4—K1—O1^xi	134.94 (11)
O1—Dy1—O2^vii	84.04 (12)	O4—K1—O1^xiii	104.12 (10)
O1—Dy1—O2^vi	68.85 (11)	O4^xiv—K1—O1^xiii	90.21 (11)
O1^viii—Dy1—O2^iv	130.11 (12)	O4^xiv—K1—O1^xi	63.27 (10)
O1^viii—Dy1—O2^vii	68.85 (11)	O4^xii—K1—O1^xiii	134.94 (11)
O1—Dy1—O2^v	130.11 (12)	O4^xv—K1—O1^xiii	63.27 (10)
O1^viii—Dy1—O2^v	72.59 (12)	O4^xv—K1—O1^xi	90.21 (11)
O1^viii—Dy1—O1	74.89 (17)	O4^xv—K1—O3^xii	81.35 (10)
O1—Dy1—O3^ix	108.36 (12)	O4^xv—K1—O3	128.30 (10)
O1—Dy1—O3ⁱⁱ	150.54 (12)	O4^xii—K1—O3^xii	53.25 (10)
O1^viii—Dy1—O3^ix	150.54 (12)	O4^xiv—K1—O3^xii	128.30 (10)
O1^viii—Dy1—O3ⁱⁱ	108.36 (12)	O4^xiv—K1—O3	81.35 (10)
O3^ix—Dy1—Dy1ⁱ	74.74 (8)	O4—K1—O3	53.25 (10)
O3^ix—Dy1—Dy1ⁱⁱ	110.11 (8)	O4—K1—O3^xii	66.32 (10)
O3ⁱⁱ—Dy1—Dy1ⁱⁱ	74.74 (8)	O4^xii—K1—O3	66.32 (10)
O3ⁱⁱ—Dy1—Dy1ⁱ	110.11 (8)	O1^xiii—K1—Mo1	129.20 (7)
O3ⁱⁱ—Dy1—K1ⁱⁱⁱ	138.31 (8)	O1^xiii—K1—Mo1^xi	81.73 (8)
O3^ix—Dy1—K1ⁱⁱⁱ	138.31 (8)	O1^xi—K1—Mo1^xii	129.20 (7)
O3^ix—Dy1—O2^vii	139.98 (11)	O1^xi—K1—Mo1	142.63 (7)
O3^ix—Dy1—O2^iv	76.68 (11)	O1^xiii—K1—Mo1^xii	142.63 (7)
O3ⁱⁱ—Dy1—O2^vii	70.80 (12)	O1^xiii—K1—Mo1^xiii	26.02 (7)
O3ⁱⁱ—Dy1—O2^v	76.68 (11)	O1^xi—K1—Mo1^xiii	81.73 (8)
O3^ix—Dy1—O2^v	84.61 (12)	O1^xi—K1—Mo1^xi	26.02 (7)
O3^ix—Dy1—O2^vi	70.80 (12)	O1^xiii—K1—O1^xi	59.42 (14)
O3ⁱⁱ—Dy1—O2^iv	84.61 (12)	O1^xiii—K1—O3	157.10 (9)
O3ⁱⁱ—Dy1—O2^vi	139.98 (11)	O1^xi—K1—O3^xii	157.10 (9)
O3ⁱⁱ—Dy1—O3^ix	83.39 (16)	O1^xi—K1—O3	131.78 (9)
K1—Mo1—K1ⁱⁱⁱ	78.467 (11)	O1^xiii—K1—O3^xii	131.78 (9)
K1—Mo1—K1^x	76.833 (11)	O3^xii—K1—Mo1^xiii	115.44 (6)
K1ⁱⁱⁱ—Mo1—K1^x	81.33 (3)	O3^xii—K1—Mo1	51.60 (6)
O4—Mo1—K1^x	36.37 (12)	O3—K1—Mo1^xi	115.44 (6)
O4—Mo1—K1	41.29 (11)	O3—K1—Mo1^xiii	131.86 (6)
O4—Mo1—K1ⁱⁱⁱ	71.06 (12)	O3—K1—Mo1	28.36 (6)
O4—Mo1—O2	109.59 (16)	O3^xii—K1—Mo1^xi	131.86 (6)
O4—Mo1—O1	106.89 (16)	O3—K1—Mo1^xii	51.60 (6)
O4—Mo1—O3	105.13 (16)	O3^xii—K1—Mo1^xii	28.36 (6)
O2—Mo1—K1^x	86.44 (11)	O3^xii—K1—O3	47.91 (11)
O2—Mo1—K1ⁱⁱⁱ	156.32 (9)	Mo1—O4—K1^x	122.04 (17)
O2—Mo1—K1	118.38 (10)	Mo1—O4—K1	113.61 (16)
O1—Mo1—K1ⁱⁱⁱ	43.41 (11)	K1—O4—K1^x	122.44 (13)
O1—Mo1—K1	121.60 (11)	Dy1^iv—O2—Dy1^xvi	108.95 (13)
O1—Mo1—K1^x	95.79 (11)	Mo1—O2—Dy1^xvi	119.80 (14)
O1—Mo1—O2	118.81 (15)	Mo1—O2—Dy1^iv	128.01 (15)
O3—Mo1—K1ⁱⁱⁱ	90.42 (11)	Dy1—O1—K1ⁱⁱⁱ	112.84 (12)
O3—Mo1—K1^x	141.16 (11)	Mo1—O1—Dy1	125.41 (17)
O3—Mo1—K1	64.32 (11)	Mo1—O1—K1ⁱⁱⁱ	110.57 (15)
O3—Mo1—O2	111.51 (15)	Dy1ⁱⁱ—O3—K1	145.45 (13)
O3—Mo1—O1	103.94 (16)	Mo1—O3—Dy1ⁱⁱ	127.15 (18)
Mo1—K1—Mo1^xiii	103.540 (12)	Mo1—O3—K1	87.32 (12)

Potassium holmium bis(molybdate) (Ho_Molybdate) top

Crystal data top

KHo(MoO₄)₂	F(000) = 936
M_r = 523.91	D_x = 4.757 Mg m⁻³
Orthorhombic, Pbcn	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2n 2ab	Cell parameters from 2917 reflections
a = 5.0770 (15) Å	θ = 3.4–28.8°
b = 18.161 (5) Å	µ = 14.66 mm⁻¹
c = 7.934 (2) Å	T = 273 K
V = 731.5 (4) Å³	Plate, light red
Z = 4	0.06 × 0.06 × 0.04 mm

Data collection top

Bruker APEXII CCD diffractometer	818 reflections with I > 2σ(I)
Radiation source: X-ray tube	R_int = 0.032
φ and ω scans	θ_max = 28.9°, θ_min = 2.2°
Absorption correction: multi-scan (SADABS; Krause et al., 2015)	h = −6→6
T_min = 0.248, T_max = 0.343	k = −24→24
7665 measured reflections	l = −10→10
936 independent reflections

Refinement top

Refinement on F²	0 restraints
Least-squares matrix: full	0 constraints
R[F² > 2σ(F²)] = 0.027	Primary atom site location: dual
wR(F²) = 0.063	w = 1/[σ²(F_o²) + 11.609P] where P = (F_o² + 2F_c²)/3
S = 1.25	(Δ/σ)_max = 0.001
936 reflections	Δρ_max = 1.51 e Å⁻³
56 parameters	Δρ_min = −1.37 e Å⁻³

Special details top

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

	x	y	z	U_iso*/U_eq
Ho1	0.000000	0.49423 (2)	0.750000	0.00704 (12)
Mo1	0.47909 (9)	0.60179 (3)	0.51614 (6)	0.00726 (13)
K1	0.500000	0.77102 (11)	0.250000	0.0141 (4)
O4	0.6095 (9)	0.6894 (3)	0.5227 (6)	0.0122 (9)
O2	0.7503 (9)	0.5342 (2)	0.4941 (5)	0.0095 (8)
O1	0.2583 (8)	0.5939 (2)	0.6923 (5)	0.0096 (8)
O3	0.2700 (9)	0.6008 (2)	0.3389 (5)	0.0093 (8)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Ho1	0.00566 (18)	0.0094 (2)	0.00606 (18)	0.000	−0.00040 (14)	0.000
Mo1	0.0058 (2)	0.0084 (3)	0.0076 (2)	0.00040 (19)	−0.00009 (17)	0.00032 (17)
K1	0.0177 (9)	0.0132 (9)	0.0115 (8)	0.000	0.0013 (8)	0.000
O4	0.013 (2)	0.014 (2)	0.010 (2)	−0.0011 (18)	0.0002 (17)	0.0016 (17)
O2	0.0080 (19)	0.014 (2)	0.0061 (19)	0.0016 (17)	0.0037 (18)	−0.0005 (17)
O1	0.0072 (19)	0.013 (2)	0.0085 (19)	−0.0001 (17)	0.0015 (16)	0.0001 (17)
O3	0.013 (2)	0.012 (2)	0.0035 (19)	−0.0008 (19)	−0.0005 (15)	0.0000 (16)

Geometric parameters (Å, º) top

Ho1—Ho1ⁱ	3.9723 (11)	Mo1—O3	1.762 (4)
Ho1—Ho1ⁱⁱ	3.9723 (11)	K1—Mo1^xi	3.8332 (14)
Ho1—K1ⁱⁱⁱ	4.263 (2)	K1—Mo1^xii	3.7303 (18)
Ho1—O2^iv	2.372 (4)	K1—Mo1^xiii	3.8332 (14)
Ho1—O2^v	2.372 (4)	K1—O4	2.680 (5)
Ho1—O2^vi	2.501 (4)	K1—O4^xiv	2.775 (5)
Ho1—O2^vii	2.501 (4)	K1—O4^xii	2.681 (5)
Ho1—O1^viii	2.282 (4)	K1—O4^xv	2.775 (5)
Ho1—O1	2.282 (4)	K1—O1^xiii	2.819 (5)
Ho1—O3^ix	2.314 (4)	K1—O1^xi	2.819 (5)
Ho1—O3ⁱ	2.314 (4)	K1—O3	3.380 (5)
Mo1—K1	3.7303 (18)	K1—O3^xii	3.380 (5)
Mo1—K1^x	3.9713 (14)	O4—K1^x	2.775 (5)
Mo1—K1ⁱⁱⁱ	3.8332 (14)	O2—Ho1^xvi	2.501 (4)
Mo1—O4	1.724 (5)	O2—Ho1^v	2.372 (4)
Mo1—O2	1.853 (4)	O1—K1ⁱⁱⁱ	2.819 (5)
Mo1—O1	1.797 (4)	O3—Ho1ⁱ	2.314 (4)

Ho1ⁱⁱ—Ho1—Ho1ⁱ	173.96 (2)	Mo1^xii—K1—Mo1	69.05 (4)
Ho1ⁱⁱ—Ho1—K1ⁱⁱⁱ	86.979 (11)	Mo1^xii—K1—Mo1^xi	103.92 (2)
Ho1ⁱ—Ho1—K1ⁱⁱⁱ	86.979 (11)	Mo1—K1—Mo1^xiii	103.92 (2)
O2^iv—Ho1—Ho1ⁱ	145.79 (11)	Mo1^xiii—K1—Mo1^xi	105.89 (5)
O2^v—Ho1—Ho1ⁱ	36.49 (11)	Mo1—K1—Mo1^xi	138.79 (2)
O2^vi—Ho1—Ho1ⁱ	34.33 (10)	O4^xv—K1—Mo1	126.98 (10)
O2^vii—Ho1—Ho1ⁱ	142.68 (10)	O4—K1—Mo1	24.98 (10)
O2^iv—Ho1—Ho1ⁱⁱ	36.49 (11)	O4^xiv—K1—Mo1^xi	72.85 (10)
O2^v—Ho1—Ho1ⁱⁱ	145.79 (11)	O4^xii—K1—Mo1^xii	24.98 (10)
O2^vi—Ho1—Ho1ⁱⁱ	142.68 (10)	O4^xii—K1—Mo1^xi	79.11 (10)
O2^vii—Ho1—Ho1ⁱⁱ	34.33 (10)	O4^xv—K1—Mo1^xii	79.93 (10)
O2^vi—Ho1—K1ⁱⁱⁱ	73.13 (10)	O4^xiv—K1—Mo1^xii	126.98 (10)
O2^vii—Ho1—K1ⁱⁱⁱ	73.13 (10)	O4—K1—Mo1^xiii	79.11 (10)
O2^v—Ho1—K1ⁱⁱⁱ	102.57 (11)	O4—K1—Mo1^xi	148.80 (10)
O2^iv—Ho1—K1ⁱⁱⁱ	102.57 (11)	O4^xii—K1—Mo1^xiii	148.80 (10)
O2^vii—Ho1—O2^vi	146.3 (2)	O4^xv—K1—Mo1^xi	89.01 (10)
O2^iv—Ho1—O2^vi	117.06 (18)	O4^xv—K1—Mo1^xiii	72.85 (10)
O2^iv—Ho1—O2^vii	70.81 (17)	O4—K1—Mo1^xii	89.73 (11)
O2^v—Ho1—O2^vi	70.81 (17)	O4^xiv—K1—Mo1^xiii	89.01 (10)
O2^v—Ho1—O2^vii	117.06 (18)	O4^xii—K1—Mo1	89.73 (11)
O2^v—Ho1—O2^iv	154.9 (2)	O4^xiv—K1—Mo1	79.93 (10)
O1—Ho1—Ho1ⁱ	75.99 (11)	O4^xii—K1—O4^xv	76.52 (11)
O1^viii—Ho1—Ho1ⁱ	99.12 (11)	O4—K1—O4^xv	121.30 (6)
O1—Ho1—Ho1ⁱⁱ	99.12 (11)	O4^xv—K1—O4^xiv	150.0 (2)
O1^viii—Ho1—Ho1ⁱⁱ	75.99 (11)	O4—K1—O4^xiv	76.52 (11)
O1^viii—Ho1—K1ⁱⁱⁱ	37.49 (11)	O4^xii—K1—O4^xiv	121.30 (6)
O1—Ho1—K1ⁱⁱⁱ	37.50 (11)	O4—K1—O4^xii	112.9 (2)
O1^viii—Ho1—O2^iv	72.64 (15)	O4^xii—K1—O1^xi	104.69 (13)
O1—Ho1—O2^vi	84.17 (15)	O4—K1—O1^xi	135.12 (13)
O1^viii—Ho1—O2^vii	84.17 (15)	O4—K1—O1^xiii	104.69 (13)
O1^viii—Ho1—O2^vi	68.97 (15)	O4^xiv—K1—O1^xiii	90.09 (14)
O1—Ho1—O2^iv	130.07 (15)	O4^xiv—K1—O1^xi	63.11 (13)
O1—Ho1—O2^vii	68.97 (15)	O4^xii—K1—O1^xiii	135.13 (13)
O1^viii—Ho1—O2^v	130.06 (15)	O4^xv—K1—O1^xiii	63.11 (13)
O1—Ho1—O2^v	72.64 (15)	O4^xv—K1—O1^xi	90.09 (14)
O1—Ho1—O1^viii	75.0 (2)	O4^xv—K1—O3	128.28 (13)
O1^viii—Ho1—O3^ix	150.57 (15)	O4^xv—K1—O3^xii	81.63 (12)
O1^viii—Ho1—O3ⁱ	108.19 (16)	O4^xii—K1—O3	65.85 (13)
O1—Ho1—O3^ix	108.19 (16)	O4^xiv—K1—O3	81.63 (12)
O1—Ho1—O3ⁱ	150.57 (15)	O4^xiv—K1—O3^xii	128.28 (13)
O3^ix—Ho1—Ho1ⁱ	110.11 (10)	O4—K1—O3^xii	65.85 (13)
O3^ix—Ho1—Ho1ⁱⁱ	74.62 (10)	O4—K1—O3	52.94 (12)
O3ⁱ—Ho1—Ho1ⁱⁱ	110.11 (10)	O4^xii—K1—O3^xii	52.93 (12)
O3ⁱ—Ho1—Ho1ⁱ	74.62 (10)	O1^xiii—K1—Mo1^xii	142.71 (9)
O3ⁱ—Ho1—K1ⁱⁱⁱ	138.22 (11)	O1^xiii—K1—Mo1^xi	81.34 (10)
O3^ix—Ho1—K1ⁱⁱⁱ	138.21 (11)	O1^xi—K1—Mo1	142.71 (9)
O3^ix—Ho1—O2^vii	70.64 (15)	O1^xi—K1—Mo1^xii	129.66 (9)
O3^ix—Ho1—O2^iv	84.58 (15)	O1^xiii—K1—Mo1	129.66 (9)
O3ⁱ—Ho1—O2^vii	139.83 (14)	O1^xiii—K1—Mo1^xiii	26.09 (9)
O3ⁱ—Ho1—O2^v	84.58 (15)	O1^xi—K1—Mo1^xiii	81.34 (10)
O3^ix—Ho1—O2^v	76.70 (15)	O1^xi—K1—Mo1^xi	26.09 (9)
O3^ix—Ho1—O2^vi	139.83 (14)	O1^xiii—K1—O1^xi	59.05 (18)
O3ⁱ—Ho1—O2^iv	76.70 (15)	O1^xiii—K1—O3^xii	132.01 (12)
O3ⁱ—Ho1—O2^vi	70.64 (15)	O1^xi—K1—O3	132.01 (12)
O3ⁱ—Ho1—O3^ix	83.6 (2)	O1^xi—K1—O3^xii	157.36 (11)
K1—Mo1—K1ⁱⁱⁱ	78.20 (2)	O1^xiii—K1—O3	157.36 (11)
K1—Mo1—K1^x	76.49 (2)	O3—K1—Mo1^xiii	132.03 (7)
K1ⁱⁱⁱ—Mo1—K1^x	81.14 (4)	O3—K1—Mo1^xii	51.26 (8)
O4—Mo1—K1^x	36.25 (15)	O3^xii—K1—Mo1^xi	132.03 (7)
O4—Mo1—K1	41.04 (15)	O3^xii—K1—Mo1^xiii	115.66 (8)
O4—Mo1—K1ⁱⁱⁱ	70.92 (15)	O3^xii—K1—Mo1^xii	28.14 (7)
O4—Mo1—O2	109.2 (2)	O3—K1—Mo1^xi	115.66 (8)
O4—Mo1—O1	106.8 (2)	O3^xii—K1—Mo1	51.26 (8)
O4—Mo1—O3	105.4 (2)	O3—K1—Mo1	28.14 (7)
O2—Mo1—K1^x	86.25 (14)	O3—K1—O3^xii	47.61 (15)
O2—Mo1—K1ⁱⁱⁱ	156.40 (13)	Mo1—O4—K1^x	122.2 (2)
O2—Mo1—K1	118.13 (13)	Mo1—O4—K1	114.0 (2)
O1—Mo1—K1ⁱⁱⁱ	43.60 (14)	K1—O4—K1^x	121.97 (17)
O1—Mo1—K1	121.56 (14)	Ho1^v—O2—Ho1^xvi	109.19 (17)
O1—Mo1—K1^x	95.64 (14)	Mo1—O2—Ho1^xvi	119.50 (19)
O1—Mo1—O2	118.95 (19)	Mo1—O2—Ho1^v	128.2 (2)
O3—Mo1—K1ⁱⁱⁱ	90.59 (14)	Ho1—O1—K1ⁱⁱⁱ	112.98 (16)
O3—Mo1—K1^x	141.28 (15)	Mo1—O1—Ho1	125.3 (2)
O3—Mo1—K1	64.79 (14)	Mo1—O1—K1ⁱⁱⁱ	110.32 (19)
O3—Mo1—O2	111.44 (19)	Ho1ⁱ—O3—K1	145.41 (16)
O3—Mo1—O1	104.1 (2)	Mo1—O3—Ho1ⁱ	127.5 (2)
Mo1^xii—K1—Mo1^xiii	138.79 (2)	Mo1—O3—K1	87.06 (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) x−1, −y+1, z+1/2; (v) −x+1, −y+1, −z+1; (vi) x−1, 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, z−1/2; (xii) −x+1, y, −z+1/2; (xiii) x+1/2, −y+3/2, −z+1; (xiv) x−1/2, −y+3/2, −z+1; (xv) −x+3/2, −y+3/2, z−1/2; (xvi) x+1, y, z.

Potassium erbium bis(molybdate) (Er_Molybdate) top

Crystal data top

KEr(MoO₄)₂	F(000) = 940
M_r = 526.24	D_x = 4.810 Mg m⁻³
Orthorhombic, Pbcn	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2n 2ab	Cell parameters from 7328 reflections
a = 5.0602 (2) Å	θ = 3.4–34.0°
b = 18.1965 (8) Å	µ = 15.42 mm⁻¹
c = 7.8920 (3) Å	T = 100 K
V = 726.68 (5) Å³	Plate, light pink
Z = 4	0.28 × 0.15 × 0.02 mm

Data collection top

Rigaku XtaLAB Synergy-S, HyPix diffractometer	1386 independent reflections
Radiation source: micro-focus sealed X-ray tube	1255 reflections with I > 2σ(I)
Mirror monochromator	R_int = 0.072
Detector resolution: 10.0000 pixels mm^-1	θ_max = 34.0°, θ_min = 2.2°
ω scans	h = −7→7
Absorption correction: gaussian (CrysAlisPro; Rigaku OD, 2019)	k = −28→27
T_min = 0.091, T_max = 0.911	l = −12→10
21246 measured reflections

Refinement top

Refinement on F²	0 restraints
Least-squares matrix: full	0 constraints
R[F² > 2σ(F²)] = 0.027	Primary atom site location: dual
wR(F²) = 0.073	w = 1/[σ²(F_o²) + (0.0345P)² + 4.1539P] where P = (F_o² + 2F_c²)/3
S = 1.06	(Δ/σ)_max = 0.002
1386 reflections	Δρ_max = 2.04 e Å⁻³
56 parameters	Δρ_min = −1.62 e Å⁻³

Special details top

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
Er1	1.000000	0.50535 (2)	0.750000	0.00602 (9)
Mo1	0.52026 (6)	0.39859 (2)	0.51517 (4)	0.00637 (9)
K1	0.500000	0.22821 (7)	0.250000	0.0107 (2)
O4	0.3903 (5)	0.31111 (15)	0.5213 (3)	0.0102 (5)
O2	0.2497 (5)	0.46619 (15)	0.4954 (3)	0.0084 (5)
O1	0.7417 (5)	0.40581 (14)	0.6914 (3)	0.0100 (4)
O3	0.7315 (5)	0.39970 (14)	0.3369 (3)	0.0099 (5)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Er1	0.00367 (12)	0.00995 (13)	0.00443 (13)	0.000	−0.00030 (6)	0.000
Mo1	0.00374 (14)	0.00961 (16)	0.00575 (15)	0.00027 (9)	−0.00044 (8)	−0.00032 (9)
K1	0.0112 (5)	0.0124 (5)	0.0085 (5)	0.000	−0.0007 (3)	0.000
O4	0.0079 (11)	0.0127 (12)	0.0100 (11)	−0.0029 (9)	0.0009 (9)	−0.0003 (9)
O2	0.0052 (10)	0.0131 (12)	0.0067 (10)	0.0007 (9)	−0.0008 (8)	−0.0006 (8)
O1	0.0077 (10)	0.0142 (12)	0.0080 (10)	−0.0014 (9)	−0.0019 (9)	−0.0004 (9)
O3	0.0068 (10)	0.0153 (12)	0.0074 (10)	−0.0014 (9)	0.0006 (8)	−0.0003 (8)

Geometric parameters (Å, º) top

Er1—Er1ⁱ	3.9508 (2)	Mo1—O3	1.767 (2)
Er1—Er1ⁱⁱ	3.9508 (1)	K1—Mo1^xi	3.8277 (8)
Er1—K1ⁱⁱⁱ	4.2499 (13)	K1—Mo1^xii	3.7419 (10)
Er1—O2^iv	2.370 (2)	K1—Mo1^xiii	3.8277 (8)
Er1—O2^v	2.370 (2)	K1—O4	2.677 (3)
Er1—O2^vi	2.478 (2)	K1—O4^xiv	2.770 (3)
Er1—O2^vii	2.478 (2)	K1—O4^xii	2.677 (3)
Er1—O1^viii	2.281 (2)	K1—O4^xv	2.770 (3)
Er1—O1	2.281 (3)	K1—O1^xiii	2.805 (3)
Er1—O3^ix	2.303 (3)	K1—O1^xi	2.805 (3)
Er1—O3ⁱⁱ	2.303 (3)	K1—O3	3.403 (3)
Mo1—K1	3.7419 (10)	K1—O3^xii	3.403 (3)
Mo1—K1^x	3.9610 (8)	O4—K1^x	2.770 (3)
Mo1—K1ⁱⁱⁱ	3.8278 (8)	O2—Er1^xvi	2.478 (2)
Mo1—O4	1.723 (3)	O2—Er1^iv	2.370 (2)
Mo1—O2	1.847 (3)	O1—K1ⁱⁱⁱ	2.805 (3)
Mo1—O1	1.791 (2)	O3—Er1ⁱⁱ	2.303 (3)

Er1ⁱⁱ—Er1—Er1ⁱ	174.354 (13)	Mo1^xii—K1—Mo1	68.10 (2)
Er1ⁱⁱ—Er1—K1ⁱⁱⁱ	87.177 (7)	Mo1^xii—K1—Mo1^xi	104.243 (10)
Er1ⁱ—Er1—K1ⁱⁱⁱ	87.177 (7)	Mo1—K1—Mo1^xiii	104.243 (10)
O2^iv—Er1—Er1ⁱ	145.80 (6)	Mo1^xiii—K1—Mo1^xi	105.86 (3)
O2^v—Er1—Er1ⁱ	36.34 (6)	Mo1—K1—Mo1^xi	138.837 (12)
O2^vi—Er1—Er1ⁱ	34.52 (6)	O4^xv—K1—Mo1	126.73 (6)
O2^vii—Er1—Er1ⁱ	142.71 (6)	O4—K1—Mo1	24.71 (6)
O2^iv—Er1—Er1ⁱⁱ	36.34 (6)	O4^xiv—K1—Mo1^xi	73.00 (5)
O2^v—Er1—Er1ⁱⁱ	145.80 (6)	O4^xii—K1—Mo1^xii	24.71 (6)
O2^vi—Er1—Er1ⁱⁱ	142.71 (6)	O4^xii—K1—Mo1^xi	79.69 (6)
O2^vii—Er1—Er1ⁱⁱ	34.52 (6)	O4^xv—K1—Mo1^xii	80.21 (6)
O2^vi—Er1—K1ⁱⁱⁱ	73.29 (6)	O4^xiv—K1—Mo1^xii	126.73 (6)
O2^vii—Er1—K1ⁱⁱⁱ	73.29 (6)	O4—K1—Mo1^xiii	79.69 (6)
O2^v—Er1—K1ⁱⁱⁱ	102.63 (6)	O4—K1—Mo1^xi	149.13 (6)
O2^iv—Er1—K1ⁱⁱⁱ	102.63 (6)	O4^xii—K1—Mo1^xiii	149.13 (6)
O2^vii—Er1—O2^vi	146.57 (12)	O4^xv—K1—Mo1^xi	88.91 (6)
O2^iv—Er1—O2^vi	116.98 (11)	O4^xv—K1—Mo1^xiii	73.00 (5)
O2^iv—Er1—O2^vii	70.86 (10)	O4—K1—Mo1^xii	88.55 (6)
O2^v—Er1—O2^vi	70.86 (10)	O4^xiv—K1—Mo1^xiii	88.91 (6)
O2^v—Er1—O2^vii	116.98 (11)	O4^xii—K1—Mo1	88.55 (6)
O2^v—Er1—O2^iv	154.75 (13)	O4^xiv—K1—Mo1	80.21 (6)
O1—Er1—Er1ⁱ	99.40 (6)	O4^xii—K1—O4^xv	76.83 (6)
O1^viii—Er1—Er1ⁱ	76.03 (6)	O4—K1—O4^xv	121.26 (4)
O1—Er1—Er1ⁱⁱ	76.03 (6)	O4^xv—K1—O4^xiv	150.06 (12)
O1^viii—Er1—Er1ⁱⁱ	99.39 (6)	O4—K1—O4^xiv	76.83 (6)
O1^viii—Er1—K1ⁱⁱⁱ	37.43 (6)	O4^xii—K1—O4^xiv	121.26 (4)
O1—Er1—K1ⁱⁱⁱ	37.43 (6)	O4—K1—O4^xii	111.41 (12)
O1^viii—Er1—O2^iv	130.14 (9)	O4^xii—K1—O1^xi	105.16 (8)
O1—Er1—O2^vi	69.13 (8)	O4—K1—O1^xi	135.91 (8)
O1^viii—Er1—O2^vii	69.13 (8)	O4—K1—O1^xiii	105.16 (8)
O1^viii—Er1—O2^vi	84.23 (9)	O4^xiv—K1—O1^xiii	90.02 (8)
O1—Er1—O2^iv	72.69 (9)	O4^xiv—K1—O1^xi	63.29 (8)
O1—Er1—O2^vii	84.23 (9)	O4^xii—K1—O1^xiii	135.91 (8)
O1^viii—Er1—O2^v	72.70 (9)	O4^xv—K1—O1^xiii	63.29 (8)
O1—Er1—O2^v	130.14 (9)	O4^xv—K1—O1^xi	90.02 (8)
O1—Er1—O1^viii	74.85 (13)	O4^xv—K1—O3	127.86 (8)
O1^viii—Er1—O3^ix	150.89 (9)	O4^xv—K1—O3^xii	81.96 (7)
O1^viii—Er1—O3ⁱⁱ	108.55 (10)	O4^xii—K1—O3	64.73 (7)
O1—Er1—O3^ix	108.55 (10)	O4^xiv—K1—O3	81.96 (7)
O1—Er1—O3ⁱⁱ	150.89 (9)	O4^xiv—K1—O3^xii	127.86 (8)
O3^ix—Er1—Er1ⁱ	74.90 (6)	O4—K1—O3^xii	64.73 (7)
O3^ix—Er1—Er1ⁱⁱ	109.54 (6)	O4—K1—O3	52.66 (7)
O3ⁱⁱ—Er1—Er1ⁱⁱ	74.90 (6)	O4^xii—K1—O3^xii	52.66 (7)
O3ⁱⁱ—Er1—Er1ⁱ	109.54 (6)	O1^xiii—K1—Mo1^xii	143.10 (5)
O3ⁱⁱ—Er1—K1ⁱⁱⁱ	138.62 (6)	O1^xiii—K1—Mo1^xi	81.44 (6)
O3^ix—Er1—K1ⁱⁱⁱ	138.62 (6)	O1^xi—K1—Mo1	143.10 (5)
O3^ix—Er1—O2^vii	139.31 (8)	O1^xi—K1—Mo1^xii	129.86 (5)
O3^ix—Er1—O2^iv	76.40 (8)	O1^xiii—K1—Mo1	129.86 (5)
O3ⁱⁱ—Er1—O2^vii	70.94 (9)	O1^xiii—K1—Mo1^xiii	25.94 (5)
O3ⁱⁱ—Er1—O2^v	76.40 (8)	O1^xi—K1—Mo1^xiii	81.44 (6)
O3^ix—Er1—O2^v	84.67 (9)	O1^xi—K1—Mo1^xi	25.94 (5)
O3^ix—Er1—O2^vi	70.94 (9)	O1^xiii—K1—O1^xi	59.23 (10)
O3ⁱⁱ—Er1—O2^iv	84.67 (9)	O1^xiii—K1—O3^xii	132.07 (6)
O3ⁱⁱ—Er1—O2^vi	139.31 (8)	O1^xi—K1—O3	132.07 (6)
O3ⁱⁱ—Er1—O3^ix	82.76 (13)	O1^xi—K1—O3^xii	157.57 (7)
K1—Mo1—K1ⁱⁱⁱ	77.802 (9)	O1^xiii—K1—O3	157.57 (7)
K1—Mo1—K1^x	76.162 (9)	O3—K1—Mo1^xiii	132.33 (4)
K1ⁱⁱⁱ—Mo1—K1^x	81.02 (2)	O3—K1—Mo1^xii	50.39 (4)
O4—Mo1—K1^x	36.40 (9)	O3^xii—K1—Mo1^xi	132.33 (4)
O4—Mo1—K1	40.51 (8)	O3^xii—K1—Mo1^xiii	115.60 (4)
O4—Mo1—K1ⁱⁱⁱ	70.83 (9)	O3^xii—K1—Mo1^xii	28.12 (4)
O4—Mo1—O2	109.56 (12)	O3—K1—Mo1^xi	115.60 (4)
O4—Mo1—O1	106.55 (12)	O3^xii—K1—Mo1	50.39 (4)
O4—Mo1—O3	105.29 (12)	O3—K1—Mo1	28.12 (4)
O2—Mo1—K1^x	86.26 (8)	O3—K1—O3^xii	47.02 (9)
O2—Mo1—K1ⁱⁱⁱ	155.83 (7)	Mo1—O4—K1^x	121.94 (12)
O2—Mo1—K1	118.97 (8)	Mo1—O4—K1	114.78 (12)
O1—Mo1—K1ⁱⁱⁱ	43.23 (8)	K1—O4—K1^x	121.57 (10)
O1—Mo1—K1	120.81 (8)	Er1^iv—O2—Er1^xvi	109.14 (10)
O1—Mo1—K1^x	95.46 (8)	Mo1—O2—Er1^xvi	120.07 (10)
O1—Mo1—O2	118.71 (11)	Mo1—O2—Er1^iv	127.56 (11)
O3—Mo1—K1ⁱⁱⁱ	90.50 (8)	Er1—O1—K1ⁱⁱⁱ	112.96 (10)
O3—Mo1—K1^x	141.37 (9)	Mo1—O1—Er1	125.03 (13)
O3—Mo1—K1	65.21 (8)	Mo1—O1—K1ⁱⁱⁱ	110.84 (11)
O3—Mo1—O2	111.94 (11)	Er1ⁱⁱ—O3—K1	146.22 (10)
O3—Mo1—O1	103.83 (12)	Mo1—O3—Er1ⁱⁱ	127.06 (13)
Mo1^xii—K1—Mo1^xiii	138.837 (12)	Mo1—O3—K1	86.67 (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, z−1/2; (xii) −x+1, y, −z+1/2; (xiii) x−1/2, −y+1/2, −z+1; (xiv) x+1/2, −y+1/2, −z+1; (xv) −x+1/2, −y+1/2, z−1/2; (xvi) x−1, y, z.

Potassium ytterbium bis(molybdate) (Yb_Molybdate) top

Crystal data top

KYb(MoO₄)₂	F(000) = 948
M_r = 532.02	D_x = 4.866 Mg m⁻³
Orthorhombic, Pbcn	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2n 2ab	Cell parameters from 3007 reflections
a = 5.0417 (5) Å	θ = 2.2–29.2°
b = 18.3039 (19) Å	µ = 16.75 mm⁻¹
c = 7.8693 (8) Å	T = 273 K
V = 726.20 (13) Å³	Plate, white
Z = 4	0.06 × 0.06 × 0.04 mm

Data collection top

Bruker APEXII CCD diffractometer	845 reflections with I > 2σ(I)
Radiation source: X-ray tube	R_int = 0.038
φ and ω scans	θ_max = 29.5°, θ_min = 2.2°
Absorption correction: multi-scan (SADABS; Krause et al., 2015)	h = −6→6
T_min = 0.198, T_max = 0.301	k = −24→25
8164 measured reflections	l = −10→10
978 independent reflections

Refinement top

Refinement on F²	0 restraints
Least-squares matrix: full	0 constraints
R[F² > 2σ(F²)] = 0.022	Primary atom site location: dual
wR(F²) = 0.063	w = 1/[σ²(F_o²) + (0.0244P)² + 3.0168P] where P = (F_o² + 2F_c²)/3
S = 1.11	(Δ/σ)_max = 0.001
978 reflections	Δρ_max = 1.55 e Å⁻³
56 parameters	Δρ_min = −1.14 e Å⁻³

Special details top

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

	x	y	z	U_iso*/U_eq
Yb1	0.000000	0.49506 (2)	0.750000	0.01036 (11)
Mo1	0.47826 (7)	0.60027 (2)	0.51395 (5)	0.01066 (12)
K1	0.500000	0.77252 (9)	0.250000	0.0230 (3)
O4	0.6053 (7)	0.68778 (18)	0.5206 (4)	0.0188 (7)
O2	0.7521 (6)	0.53396 (17)	0.4939 (3)	0.0128 (6)
O1	0.2572 (6)	0.59262 (17)	0.6912 (4)	0.0149 (6)
O3	0.2661 (6)	0.59860 (17)	0.3360 (4)	0.0152 (6)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Yb1	0.00810 (17)	0.01404 (17)	0.00894 (16)	0.000	0.00084 (9)	0.000
Mo1	0.0085 (2)	0.0117 (2)	0.0118 (2)	0.00068 (12)	0.00134 (12)	0.00054 (13)
K1	0.0306 (9)	0.0195 (7)	0.0189 (7)	0.000	0.0019 (6)	0.000
O4	0.0212 (18)	0.0179 (17)	0.0173 (16)	−0.0025 (14)	−0.0044 (13)	0.0007 (13)
O2	0.0112 (15)	0.0184 (17)	0.0086 (14)	0.0033 (12)	0.0023 (12)	−0.0010 (11)
O1	0.0131 (14)	0.0175 (15)	0.0143 (15)	−0.0011 (12)	0.0039 (12)	−0.0038 (13)
O3	0.0142 (15)	0.0177 (16)	0.0137 (15)	−0.0024 (13)	0.0006 (12)	0.0003 (12)

Geometric parameters (Å, º) top

Yb1—Mo1ⁱ	3.6018 (5)	Mo1—O2	1.845 (3)
Yb1—Mo1ⁱⁱ	3.6294 (5)	Mo1—O1	1.791 (3)
Yb1—Mo1ⁱⁱⁱ	3.6294 (5)	Mo1—O3	1.762 (3)
Yb1—Mo1	3.6018 (5)	K1—Mo1^xi	3.9738 (11)
Yb1—O2^iv	2.351 (3)	K1—Mo1^xii	3.7772 (14)
Yb1—O2^v	2.476 (3)	K1—Mo1^xiii	3.8322 (11)
Yb1—O2^vi	2.351 (3)	K1—Mo1^xiv	3.8322 (11)
Yb1—O2^vii	2.476 (3)	K1—Mo1^xv	3.9738 (11)
Yb1—O1	2.255 (3)	K1—O4^xii	2.687 (3)
Yb1—O1ⁱ	2.255 (3)	K1—O4	2.687 (3)
Yb1—O3ⁱⁱ	2.280 (3)	K1—O4^xi	2.784 (3)
Yb1—O3ⁱⁱⁱ	2.280 (3)	K1—O4^xv	2.784 (3)
Mo1—Yb1ⁱⁱⁱ	3.6294 (5)	K1—O1^xiii	2.826 (3)
Mo1—Yb1^iv	3.7786 (5)	K1—O1^xiv	2.826 (3)
Mo1—Yb1^viii	3.7522 (5)	O4—K1^x	2.784 (3)
Mo1—K1^ix	3.8322 (11)	O2—Yb1^iv	2.351 (3)
Mo1—K1^x	3.9738 (11)	O2—Yb1^viii	2.476 (3)
Mo1—K1	3.7772 (14)	O1—K1^ix	2.826 (3)
Mo1—O4	1.726 (3)	O3—Yb1ⁱⁱⁱ	2.280 (3)

Mo1—Yb1—Mo1ⁱ	115.356 (17)	O2—Mo1—Yb1	101.15 (10)
Mo1ⁱ—Yb1—Mo1ⁱⁱⁱ	96.169 (13)	O2—Mo1—Yb1ⁱⁱⁱ	97.58 (10)
Mo1—Yb1—Mo1ⁱⁱⁱ	113.994 (10)	O2—Mo1—K1^ix	155.78 (8)
Mo1—Yb1—Mo1ⁱⁱ	96.168 (13)	O2—Mo1—K1^x	85.99 (10)
Mo1ⁱⁱⁱ—Yb1—Mo1ⁱⁱ	122.531 (16)	O2—Mo1—K1	118.71 (10)
Mo1ⁱ—Yb1—Mo1ⁱⁱ	113.994 (10)	O1—Mo1—Yb1ⁱⁱⁱ	89.70 (10)
O2^v—Yb1—Mo1ⁱ	85.88 (7)	O1—Mo1—Yb1^viii	90.61 (10)
O2^iv—Yb1—Mo1ⁱⁱ	90.31 (8)	O1—Mo1—Yb1^iv	145.62 (10)
O2^vii—Yb1—Mo1ⁱ	76.37 (8)	O1—Mo1—Yb1	30.68 (10)
O2^iv—Yb1—Mo1	49.00 (8)	O1—Mo1—K1	120.77 (10)
O2^vii—Yb1—Mo1ⁱⁱ	48.48 (8)	O1—Mo1—K1^x	95.37 (10)
O2^iv—Yb1—Mo1ⁱⁱⁱ	77.14 (8)	O1—Mo1—K1^ix	43.81 (10)
O2^vi—Yb1—Mo1ⁱ	49.00 (8)	O1—Mo1—O2	118.75 (14)
O2^vi—Yb1—Mo1	153.85 (8)	O3—Mo1—Yb1	89.67 (10)
O2^vi—Yb1—Mo1ⁱⁱ	77.14 (8)	O3—Mo1—Yb1^viii	144.09 (11)
O2^vii—Yb1—Mo1	85.88 (7)	O3—Mo1—Yb1ⁱⁱⁱ	29.97 (10)
O2^v—Yb1—Mo1ⁱⁱ	159.95 (7)	O3—Mo1—Yb1^iv	88.72 (10)
O2^v—Yb1—Mo1ⁱⁱⁱ	48.48 (8)	O3—Mo1—K1	66.11 (10)
O2^iv—Yb1—Mo1ⁱ	153.85 (8)	O3—Mo1—K1^x	141.56 (11)
O2^vi—Yb1—Mo1ⁱⁱⁱ	90.31 (8)	O3—Mo1—K1^ix	90.79 (10)
O2^vii—Yb1—Mo1ⁱⁱⁱ	159.95 (7)	O3—Mo1—O2	112.01 (14)
O2^v—Yb1—Mo1	76.37 (8)	O3—Mo1—O1	103.88 (15)
O2^iv—Yb1—O2^v	70.66 (12)	Mo1^xiv—K1—Mo1^xv	80.44 (3)
O2^iv—Yb1—O2^vii	117.45 (14)	Mo1^xii—K1—Mo1	66.83 (3)
O2^vi—Yb1—O2^vii	70.66 (12)	Mo1—K1—Mo1^xv	139.938 (17)
O2^vi—Yb1—O2^v	117.45 (14)	Mo1^xiii—K1—Mo1^xiv	105.17 (4)
O2^vii—Yb1—O2^v	146.58 (15)	Mo1—K1—Mo1^xi	102.288 (13)
O2^iv—Yb1—O2^vi	153.89 (16)	Mo1—K1—Mo1^xiii	105.003 (13)
O1—Yb1—Mo1	23.91 (8)	Mo1^xii—K1—Mo1^xv	102.287 (13)
O1ⁱ—Yb1—Mo1ⁱⁱⁱ	96.67 (8)	Mo1^xii—K1—Mo1^xiii	139.065 (16)
O1—Yb1—Mo1ⁱⁱ	96.67 (8)	Mo1^xiii—K1—Mo1^xv	56.91 (2)
O1ⁱ—Yb1—Mo1	93.86 (8)	Mo1^xiv—K1—Mo1^xi	56.91 (2)
O1ⁱ—Yb1—Mo1ⁱⁱ	130.19 (8)	Mo1^xii—K1—Mo1^xi	139.938 (17)
O1—Yb1—Mo1ⁱ	93.86 (8)	Mo1^xii—K1—Mo1^xiv	105.003 (13)
O1ⁱ—Yb1—Mo1ⁱ	23.91 (8)	Mo1^xiii—K1—Mo1^xi	80.44 (3)
O1—Yb1—Mo1ⁱⁱⁱ	130.19 (8)	Mo1—K1—Mo1^xiv	139.065 (16)
O1ⁱ—Yb1—O2^v	69.45 (10)	Mo1^xv—K1—Mo1^xi	108.26 (4)
O1—Yb1—O2^vii	69.45 (10)	O4—K1—Mo1^xiv	149.21 (8)
O1ⁱ—Yb1—O2^iv	130.70 (11)	O4^xi—K1—Mo1^xi	21.66 (7)
O1—Yb1—O2^iv	72.89 (11)	O4—K1—Mo1^xiii	80.93 (7)
O1ⁱ—Yb1—O2^vii	84.00 (11)	O4^xi—K1—Mo1^xiv	72.90 (7)
O1—Yb1—O2^v	84.00 (11)	O4^xi—K1—Mo1^xii	126.53 (8)
O1—Yb1—O2^vi	130.70 (11)	O4^xii—K1—Mo1	87.03 (8)
O1ⁱ—Yb1—O2^vi	72.89 (11)	O4^xii—K1—Mo1^xi	125.30 (8)
O1—Yb1—O1ⁱ	75.25 (16)	O4—K1—Mo1	24.24 (7)
O1ⁱ—Yb1—O3ⁱⁱⁱ	108.54 (12)	O4^xv—K1—Mo1^xiii	72.90 (7)
O1—Yb1—O3ⁱⁱⁱ	150.82 (12)	O4^xi—K1—Mo1	80.82 (7)
O1ⁱ—Yb1—O3ⁱⁱ	150.82 (12)	O4^xii—K1—Mo1^xiii	149.21 (8)
O1—Yb1—O3ⁱⁱ	108.54 (12)	O4^xv—K1—Mo1	126.53 (8)
O3ⁱⁱⁱ—Yb1—Mo1	130.01 (7)	O4^xi—K1—Mo1^xiii	88.68 (8)
O3ⁱⁱ—Yb1—Mo1ⁱⁱⁱ	101.50 (8)	O4^xii—K1—Mo1^xv	95.65 (7)
O3ⁱⁱ—Yb1—Mo1ⁱ	130.01 (7)	O4—K1—Mo1^xi	95.65 (7)
O3ⁱⁱ—Yb1—Mo1	99.27 (8)	O4—K1—Mo1^xv	125.30 (8)
O3ⁱⁱⁱ—Yb1—Mo1ⁱ	99.27 (8)	O4^xv—K1—Mo1^xi	128.58 (9)
O3ⁱⁱⁱ—Yb1—Mo1ⁱⁱⁱ	22.72 (8)	O4^xi—K1—Mo1^xv	128.58 (9)
O3ⁱⁱⁱ—Yb1—Mo1ⁱⁱ	101.50 (8)	O4—K1—Mo1^xii	87.03 (8)
O3ⁱⁱ—Yb1—Mo1ⁱⁱ	22.72 (8)	O4^xv—K1—Mo1^xv	21.66 (7)
O3ⁱⁱⁱ—Yb1—O2^iv	84.30 (11)	O4^xv—K1—Mo1^xii	80.82 (7)
O3ⁱⁱ—Yb1—O2^v	139.02 (10)	O4^xii—K1—Mo1^xii	24.25 (7)
O3ⁱⁱⁱ—Yb1—O2^v	71.18 (11)	O4^xv—K1—Mo1^xiv	88.68 (8)
O3ⁱⁱ—Yb1—O2^iv	76.09 (10)	O4^xii—K1—Mo1^xiv	80.93 (7)
O3ⁱⁱ—Yb1—O2^vi	84.30 (11)	O4^xii—K1—O4^xi	121.56 (5)
O3ⁱⁱⁱ—Yb1—O2^vi	76.09 (10)	O4^xii—K1—O4	109.49 (15)
O3ⁱⁱⁱ—Yb1—O2^vii	139.02 (10)	O4—K1—O4^xv	121.56 (5)
O3ⁱⁱ—Yb1—O2^vii	71.18 (11)	O4—K1—O4^xi	77.17 (8)
O3ⁱⁱⁱ—Yb1—O3ⁱⁱ	82.48 (16)	O4^xii—K1—O4^xv	77.17 (8)
Yb1^viii—Mo1—Yb1^iv	63.070 (9)	O4^xi—K1—O4^xv	149.74 (15)
Yb1ⁱⁱⁱ—Mo1—Yb1^viii	120.155 (13)	O4^xv—K1—O1^xiv	89.65 (10)
Yb1ⁱⁱⁱ—Mo1—Yb1^iv	85.752 (11)	O4^xv—K1—O1^xiii	63.27 (9)
Yb1—Mo1—Yb1ⁱⁱⁱ	66.007 (10)	O4^xii—K1—O1^xiv	106.49 (10)
Yb1—Mo1—Yb1^viii	86.536 (12)	O4^xi—K1—O1^xiii	89.65 (10)
Yb1—Mo1—Yb1^iv	120.176 (13)	O4^xi—K1—O1^xiv	63.27 (9)
Yb1—Mo1—K1	138.532 (12)	O4^xii—K1—O1^xiii	136.42 (10)
Yb1ⁱⁱⁱ—Mo1—K1^x	171.48 (2)	O4—K1—O1^xiii	106.49 (10)
Yb1^iv—Mo1—K1^ix	170.07 (2)	O4—K1—O1^xiv	136.42 (10)
Yb1ⁱⁱⁱ—Mo1—K1	96.075 (15)	O1^xiv—K1—Mo1^xiv	26.02 (6)
Yb1^viii—Mo1—K1^ix	120.864 (13)	O1^xiv—K1—Mo1^xiii	80.64 (7)
Yb1^viii—Mo1—K1	132.869 (12)	O1^xiii—K1—Mo1^xi	73.47 (7)
Yb1—Mo1—K1^x	121.021 (14)	O1^xiii—K1—Mo1^xiv	80.64 (7)
Yb1^iv—Mo1—K1^x	93.824 (14)	O1^xiii—K1—Mo1	130.72 (6)
Yb1^viii—Mo1—K1^x	66.75 (2)	O1^xiii—K1—Mo1^xii	143.68 (7)
Yb1—Mo1—K1^ix	69.74 (2)	O1^xiv—K1—Mo1^xi	42.36 (7)
Yb1ⁱⁱⁱ—Mo1—K1^ix	98.712 (15)	O1^xiv—K1—Mo1^xii	130.72 (6)
K1—Mo1—Yb1^iv	93.608 (16)	O1^xiv—K1—Mo1^xv	73.47 (7)
K1—Mo1—K1^ix	77.153 (12)	O1^xiii—K1—Mo1^xv	42.36 (7)
K1—Mo1—K1^x	75.448 (12)	O1^xiv—K1—Mo1	143.68 (7)
K1^ix—Mo1—K1^x	80.44 (3)	O1^xiii—K1—Mo1^xiii	26.02 (6)
O4—Mo1—Yb1	136.81 (11)	O1^xiii—K1—O1^xiv	58.30 (13)
O4—Mo1—Yb1^viii	101.62 (11)	Mo1—O4—K1	116.01 (15)
O4—Mo1—Yb1^iv	100.77 (12)	Mo1—O4—K1^x	121.81 (16)
O4—Mo1—Yb1ⁱⁱⁱ	135.23 (11)	K1—O4—K1^x	120.30 (12)
O4—Mo1—K1^x	36.53 (11)	Yb1^iv—O2—Yb1^viii	109.33 (12)
O4—Mo1—K1^ix	69.81 (12)	Mo1—O2—Yb1^iv	128.04 (14)
O4—Mo1—K1	39.74 (10)	Mo1—O2—Yb1^viii	119.82 (13)
O4—Mo1—O2	109.61 (16)	Yb1—O1—K1^ix	113.22 (12)
O4—Mo1—O1	106.25 (15)	Mo1—O1—Yb1	125.42 (16)
O4—Mo1—O3	105.38 (15)	Mo1—O1—K1^ix	110.17 (14)
O2—Mo1—Yb1^iv	29.34 (8)	Mo1—O3—Yb1ⁱⁱⁱ	127.31 (16)
O2—Mo1—Yb1^viii	34.93 (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) x−1, y, z; (vi) x−1, −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) x−1/2, −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, z−1/2; (xv) −x+3/2, −y+3/2, z−1/2.

Potassium lutetium bis(molybdate) (Lu_Molybdate) top

Crystal data top

KLu(MoO₄)₂	F(000) = 952
M_r = 533.95	D_x = 4.942 Mg m⁻³
Orthorhombic, Pbcn	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2n 2ab	Cell parameters from 6634 reflections
a = 5.0292 (2) Å	θ = 3.4–30.5°
b = 18.2519 (10) Å	µ = 17.68 mm⁻¹
c = 7.8174 (4) Å	T = 100 K
V = 717.58 (6) Å³	Plate, white
Z = 4	0.44 × 0.14 × 0.04 mm

Data collection top

Rigaku XtaLAB Synergy-S, HyPix diffractometer	1105 independent reflections
Radiation source: micro-focus sealed X-ray tube	1004 reflections with I > 2σ(I)
Mirror monochromator	R_int = 0.087
Detector resolution: 10.0000 pixels mm^-1	θ_max = 30.5°, θ_min = 2.2°
ω scans	h = −7→7
Absorption correction: multi-scan (CrysAlisPro; Rigaku OD, 2019)	k = −26→26
T_min = 0.240, T_max = 1.000	l = −11→11
19857 measured reflections

Refinement top

Refinement on F²	0 restraints
Least-squares matrix: full	0 constraints
R[F² > 2σ(F²)] = 0.027	Primary atom site location: dual
wR(F²) = 0.077	w = 1/[σ²(F_o²) + (0.0305P)² + 4.6788P] where P = (F_o² + 2F_c²)/3
S = 1.17	(Δ/σ)_max = 0.001
1105 reflections	Δρ_max = 2.05 e Å⁻³
57 parameters	Δρ_min = −3.03 e Å⁻³

Special details top

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

	x	y	z	U_iso*/U_eq
Lu1	1.000000	0.50463 (2)	0.750000	0.00674 (13)
Mo1	0.52103 (8)	0.39975 (3)	0.51329 (5)	0.00699 (13)
K1	0.500000	0.22690 (9)	0.250000	0.0116 (3)
O4	0.3935 (7)	0.31279 (19)	0.5200 (4)	0.0119 (7)
O2	0.2476 (7)	0.4667 (2)	0.4950 (4)	0.0098 (7)
O1	0.7429 (6)	0.40718 (19)	0.6920 (4)	0.0101 (6)
O3	0.7347 (6)	0.40152 (19)	0.3343 (4)	0.0098 (6)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Lu1	0.00628 (18)	0.0100 (2)	0.00389 (17)	0.000	0.00006 (8)	0.000
Mo1	0.0067 (2)	0.0091 (2)	0.0051 (2)	0.00028 (12)	−0.00024 (11)	−0.00031 (13)
K1	0.0142 (7)	0.0132 (8)	0.0073 (6)	0.000	−0.0006 (4)	0.000
O4	0.0128 (17)	0.0141 (17)	0.0087 (14)	−0.0011 (13)	0.0006 (12)	−0.0018 (12)
O2	0.0079 (15)	0.0168 (18)	0.0046 (14)	0.0006 (13)	−0.0051 (11)	0.0004 (11)
O1	0.0100 (14)	0.0130 (16)	0.0074 (14)	−0.0011 (13)	−0.0028 (12)	0.0009 (12)
O3	0.0118 (15)	0.0126 (16)	0.0051 (13)	0.0008 (13)	0.0002 (11)	−0.0001 (11)

Geometric parameters (Å, º) top

Lu1—Lu1ⁱ	3.9123 (2)	Mo1—O3	1.765 (3)
Lu1—Lu1ⁱⁱ	3.9123 (2)	K1—Mo1^xi	3.9540 (11)
Lu1—K1ⁱⁱⁱ	4.2257 (17)	K1—Mo1^xii	3.7684 (14)
Lu1—O2^iv	2.344 (3)	K1—Mo1^xiii	3.8171 (11)
Lu1—O2^v	2.344 (3)	K1—Mo1^xiv	3.8171 (11)
Lu1—O2^vi	2.450 (3)	K1—Mo1^xv	3.9540 (11)
Lu1—O2^vii	2.450 (3)	K1—O4	2.683 (3)
Lu1—O1	2.245 (3)	K1—O4^xii	2.683 (3)
Lu1—O1^viii	2.245 (3)	K1—O4^xv	2.770 (3)
Lu1—O3^ix	2.269 (3)	K1—O4^xi	2.770 (3)
Lu1—O3ⁱⁱ	2.269 (3)	K1—O1^xiii	2.805 (4)
Mo1—K1	3.7684 (14)	K1—O1^xiv	2.805 (4)
Mo1—K1^x	3.9540 (11)	O4—K1^x	2.770 (3)
Mo1—K1ⁱⁱⁱ	3.8171 (11)	O2—Lu1^iv	2.344 (3)
Mo1—O4	1.713 (4)	O2—Lu1^xvi	2.450 (3)
Mo1—O2	1.845 (4)	O1—K1ⁱⁱⁱ	2.805 (4)
Mo1—O1	1.793 (3)	O3—Lu1ⁱⁱ	2.269 (3)

Lu1ⁱⁱ—Lu1—Lu1ⁱ	175.051 (17)	Mo1^xiv—K1—Mo1^xv	80.64 (3)
Lu1ⁱⁱ—Lu1—K1ⁱⁱⁱ	87.526 (9)	Mo1—K1—Mo1^xv	139.788 (18)
Lu1ⁱ—Lu1—K1ⁱⁱⁱ	87.526 (9)	Mo1^xiii—K1—Mo1^xiv	105.46 (4)
O2^vii—Lu1—Lu1ⁱⁱ	34.41 (8)	Mo1^xii—K1—Mo1^xi	139.788 (18)
O2^vii—Lu1—Lu1ⁱ	143.18 (8)	Mo1^xii—K1—Mo1	66.31 (3)
O2^iv—Lu1—Lu1ⁱⁱ	36.22 (8)	Mo1^xiii—K1—Mo1^xi	80.64 (3)
O2^v—Lu1—Lu1ⁱⁱ	145.70 (8)	Mo1^xii—K1—Mo1^xv	102.429 (13)
O2^vi—Lu1—Lu1ⁱ	34.41 (8)	Mo1—K1—Mo1^xiii	105.066 (13)
O2^v—Lu1—Lu1ⁱ	36.22 (8)	Mo1^xiii—K1—Mo1^xv	56.95 (2)
O2^iv—Lu1—Lu1ⁱ	145.70 (8)	Mo1^xii—K1—Mo1^xiv	105.066 (14)
O2^vi—Lu1—Lu1ⁱⁱ	143.18 (8)	Mo1—K1—Mo1^xiv	138.944 (16)
O2^vii—Lu1—K1ⁱⁱⁱ	73.58 (8)	Mo1—K1—Mo1^xi	102.429 (13)
O2^iv—Lu1—K1ⁱⁱⁱ	102.92 (9)	Mo1^xiv—K1—Mo1^xi	56.95 (2)
O2^v—Lu1—K1ⁱⁱⁱ	102.92 (9)	Mo1^xii—K1—Mo1^xiii	138.944 (16)
O2^vi—Lu1—K1ⁱⁱⁱ	73.58 (8)	Mo1^xv—K1—Mo1^xi	108.45 (4)
O2^iv—Lu1—O2^vi	117.26 (15)	O4^xii—K1—Mo1^xiv	81.17 (8)
O2^v—Lu1—O2^vii	117.26 (15)	O4^xv—K1—Mo1^xi	128.63 (9)
O2^v—Lu1—O2^iv	154.16 (18)	O4^xv—K1—Mo1^xii	81.05 (7)
O2^v—Lu1—O2^vi	70.63 (14)	O4^xv—K1—Mo1^xiv	88.73 (8)
O2^vii—Lu1—O2^vi	147.15 (17)	O4—K1—Mo1	24.06 (8)
O2^iv—Lu1—O2^vii	70.63 (14)	O4^xi—K1—Mo1^xiv	72.87 (7)
O1—Lu1—Lu1ⁱ	99.65 (8)	O4—K1—Mo1^xi	96.06 (8)
O1—Lu1—Lu1ⁱⁱ	76.35 (8)	O4^xii—K1—Mo1	86.27 (8)
O1^viii—Lu1—Lu1ⁱ	76.35 (8)	O4^xi—K1—Mo1^xiii	88.73 (8)
O1^viii—Lu1—Lu1ⁱⁱ	99.65 (8)	O4^xv—K1—Mo1	126.40 (8)
O1^viii—Lu1—K1ⁱⁱⁱ	37.61 (8)	O4^xii—K1—Mo1^xii	24.06 (8)
O1—Lu1—K1ⁱⁱⁱ	37.61 (8)	O4^xi—K1—Mo1	81.05 (7)
O1^viii—Lu1—O2^iv	130.40 (12)	O4^xv—K1—Mo1^xiii	72.87 (7)
O1—Lu1—O2^vi	69.37 (11)	O4—K1—Mo1^xv	125.27 (8)
O1^viii—Lu1—O2^vii	69.37 (11)	O4^xii—K1—Mo1^xi	125.27 (8)
O1—Lu1—O2^iv	72.91 (12)	O4^xii—K1—Mo1^xv	96.06 (8)
O1^viii—Lu1—O2^v	72.91 (12)	O4^xi—K1—Mo1^xi	21.55 (7)
O1—Lu1—O2^vii	84.51 (12)	O4^xv—K1—Mo1^xv	21.55 (7)
O1—Lu1—O2^v	130.40 (12)	O4^xi—K1—Mo1^xii	126.40 (8)
O1^viii—Lu1—O2^vi	84.51 (12)	O4^xi—K1—Mo1^xv	128.63 (9)
O1^viii—Lu1—O1	75.22 (17)	O4—K1—Mo1^xiv	149.44 (8)
O1—Lu1—O3^ix	108.54 (13)	O4—K1—Mo1^xii	86.27 (8)
O1^viii—Lu1—O3^ix	151.41 (12)	O4^xii—K1—Mo1^xiii	149.44 (8)
O1^viii—Lu1—O3ⁱⁱ	108.54 (13)	O4—K1—Mo1^xiii	81.17 (8)
O1—Lu1—O3ⁱⁱ	151.41 (12)	O4—K1—O4^xv	121.38 (5)
O3ⁱⁱ—Lu1—Lu1ⁱⁱ	75.08 (8)	O4—K1—O4^xii	108.51 (16)
O3^ix—Lu1—Lu1ⁱⁱ	108.82 (8)	O4^xii—K1—O4^xi	121.38 (5)
O3ⁱⁱ—Lu1—Lu1ⁱ	108.82 (8)	O4^xii—K1—O4^xv	77.57 (9)
O3^ix—Lu1—Lu1ⁱ	75.08 (8)	O4—K1—O4^xi	77.57 (9)
O3ⁱⁱ—Lu1—K1ⁱⁱⁱ	139.02 (8)	O4^xv—K1—O4^xi	149.68 (16)
O3^ix—Lu1—K1ⁱⁱⁱ	139.02 (8)	O4^xi—K1—O1^xiv	63.09 (10)
O3ⁱⁱ—Lu1—O2^vii	71.24 (12)	O4^xi—K1—O1^xiii	89.78 (11)
O3ⁱⁱ—Lu1—O2^iv	84.63 (12)	O4—K1—O1^xiv	136.80 (10)
O3^ix—Lu1—O2^v	84.63 (12)	O4^xv—K1—O1^xiii	63.09 (10)
O3ⁱⁱ—Lu1—O2^v	75.88 (11)	O4^xv—K1—O1^xiv	89.78 (11)
O3^ix—Lu1—O2^vii	138.46 (11)	O4—K1—O1^xiii	106.89 (10)
O3ⁱⁱ—Lu1—O2^vi	138.46 (11)	O4^xii—K1—O1^xiii	136.80 (10)
O3^ix—Lu1—O2^vi	71.24 (12)	O4^xii—K1—O1^xiv	106.89 (10)
O3^ix—Lu1—O2^iv	75.88 (11)	O1^xiv—K1—Mo1^xiv	26.14 (7)
O3ⁱⁱ—Lu1—O3^ix	81.96 (17)	O1^xiv—K1—Mo1^xiii	80.84 (7)
K1—Mo1—K1^x	75.379 (13)	O1^xiii—K1—Mo1^xi	73.72 (7)
K1—Mo1—K1ⁱⁱⁱ	77.027 (12)	O1^xiii—K1—Mo1^xiv	80.84 (7)
K1ⁱⁱⁱ—Mo1—K1^x	80.64 (3)	O1^xiii—K1—Mo1	130.93 (6)
O4—Mo1—K1	39.69 (11)	O1^xiii—K1—Mo1^xii	143.70 (7)
O4—Mo1—K1^x	36.45 (11)	O1^xiv—K1—Mo1^xi	42.27 (7)
O4—Mo1—K1ⁱⁱⁱ	70.14 (12)	O1^xiv—K1—Mo1^xii	130.93 (6)
O4—Mo1—O2	109.68 (17)	O1^xiv—K1—Mo1^xv	73.72 (7)
O4—Mo1—O1	106.21 (16)	O1^xiii—K1—Mo1^xv	42.27 (7)
O4—Mo1—O3	105.63 (16)	O1^xiv—K1—Mo1	143.70 (7)
O2—Mo1—K1ⁱⁱⁱ	155.36 (9)	O1^xiii—K1—Mo1^xiii	26.14 (7)
O2—Mo1—K1	119.41 (10)	O1^xiii—K1—O1^xiv	58.48 (14)
O2—Mo1—K1^x	85.95 (11)	Mo1—O4—K1	116.25 (16)
O1—Mo1—K1ⁱⁱⁱ	43.56 (11)	Mo1—O4—K1^x	122.00 (16)
O1—Mo1—K1^x	95.28 (11)	K1—O4—K1^x	120.03 (13)
O1—Mo1—K1	120.42 (11)	Lu1^iv—O2—Lu1^xvi	109.37 (14)
O1—Mo1—O2	118.31 (14)	Mo1—O2—Lu1^iv	127.40 (15)
O3—Mo1—K1^x	141.76 (12)	Mo1—O2—Lu1^xvi	120.19 (14)
O3—Mo1—K1ⁱⁱⁱ	90.65 (11)	Lu1—O1—K1ⁱⁱⁱ	113.15 (12)
O3—Mo1—K1	66.38 (11)	Mo1—O1—Lu1	125.15 (17)
O3—Mo1—O2	112.35 (14)	Mo1—O1—K1ⁱⁱⁱ	110.29 (15)
O3—Mo1—O1	103.74 (16)	Mo1—O3—Lu1ⁱⁱ	127.02 (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) x−1/2, −y+1/2, −z+1; (xiv) −x+3/2, −y+1/2, z−1/2; (xv) −x+1/2, −y+1/2, z−1/2; (xvi) x−1, 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)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

Acknowledgements

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

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Volume 76| Part 12| December 2020| Pages 1871-1875

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