Crystal structure refinement of magnesium zinc divanadate, MgZnV2O7, from powder X-ray diffraction data

Hong, S.J.; Li, J.; Subramanian, M.A.

doi:10.1107/S2056989021004503

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Volume 77| Part 6| June 2021| Pages 588-591

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Crystal structure refinement of magnesium zinc divanadate, MgZnV₂O₇, from powder X-ray diffraction data

Stephanie J. Hong,^a Jun Li ^a ^* and Mas A. Subramanian ^a

^aDepartment of Chemistry, Oregon State University, Corvallis, Oregon 97331, USA
^*Correspondence e-mail: lijun@oregonstate.edu

Edited by M. Weil, Vienna University of Technology, Austria (Received 24 February 2021; accepted 28 April 2021; online 7 May 2021)

The crystal structure of magnesium zinc divanadate, MgZnV₂O₇, was determined and refined from laboratory X-ray powder diffraction data. The title compound was synthesized by a solid-state reaction at 1023 K in air. The crystal structure is isotypic with Mn_0.6Zn_1.4V₂O₇ (C2/m; Z = 6) and is related to the crystal structure of thortveitite. The asymmetric unit contains two metal sites with statistically distributed magnesium and zinc atoms with the atomic ratio close to 1:1. One (Mg/Zn) metal site (M1) is located on Wyckoff position 8j and the other (M2) on 4h. Three V sites (all on 4i), and eight O (three 8j, four 4i, and one 2b) sites complete the asymmetric unit. The structure is an alternate stacking of V₂O₇ layers and (Mg/Zn) atom layers along [20 $[\overline{1}]$ ]. It is distinct from other related structures in that each V₂O₇ layer consists of two groups: a V₂O₇ dimer and a V₄O₁₄ tetramer. Mixed-occupied M1 and M2 are coordinated by oxygen atoms in distorted trigonal bipyramidal and octahedral sites, respectively.

Keywords: crystal structure; powder X-ray diffraction; magnesium zinc divanadate; MgZnV₂O₇; thortveitite-related structures.

CCDC reference: 2080585

1. Chemical context

Mixed vanadium oxides with tetrahedrally coordinated pentavalent vanadium ions have been used as catalysts in the heterogeneous oxidation process (Chang & Wang, 1988 ). Since there is a strong correlation between the crystal structure and its properties, the phase relations of vanadates have been thoroughly investigated. During the course of studying the phase diagram in the MgO–ZnO–V₂O₅ system, a new phase was identified by its X-ray diffraction pattern in the solid-solution range between (Mg_0.80Zn_1.20)V₂O₇ and (Mg_1.16Zn_0.84)V₂O₇, which was completely different from Mg₂V₂O₇ or Zn₂V₂O₇ (Chang & Wang, 1988). The crystal structure of the new phase has not been reported to date. We present here the crystal structure of MgZnV₂O₇ (Fig. 1), as determined and refined from laboratory powder X-ray diffraction data (Table 1).

Table 1
Experimental details

Crystal data
Chemical formula	MgZnV₂O₇
M_r	303.56
Crystal system, space group	Monoclinic, C2/m
Temperature (K)	298
a, b, c (Å)	10.32882 (7), 8.50126 (5), 9.30814 (6)
β (°)	98.5748 (5)
V (Å³)	808.19 (1)
Z	6
Radiation type	Cu Kα₁, λ = 1.5405 Å
Specimen shape, size (mm)	Irregular, 24.9 × 24.9

Data collection
Diffractometer	PANalytical Empyrean
Specimen mounting	Dispersed powder
Data collection mode	Reflection
Scan method	Step
2θ values (°)	2θ_min = 5.012, 2θ_max = 119.991, 2θ_step = 0.013

Refinement
R factors and goodness of fit	R_p = 0.055, R_wp = 0.076, R_exp = 0.042, R(F²) = 0.20886, χ² = 3.276
No. of parameters	40
Computer programs: X'Pert Data Collector and X'Pert HighScore Plus (PANalytical, 2011), GSAS (Larson & Von Dreele, 2000), SHELXS97 (Sheldrick, 2008), CRYSTALS (Betteridge et al., 2003) and VESTA (Momma & Izumi, 2011 ).

Figure 1
The crystal structure of MgZnV₂O₇ with VO₄ tetrahedra, VO₅ trigonal bipyramids (light purple), and (Mg/Zn) atoms (green/yellow). (a) overview of the structure, (b) a selected slab of one V₂O₇ layer and the adjacent (Mg/Zn) layer, and (c) a top view of the slab of (b) and magnified local structure of V₄O₁₄ tetrameric and V₂O₇ dimeric units. [Symmetry codes: (xiii) −x + 1, −y + 1, −z; (xiv) x, y + 1, z − 1; (xv) −x + 1, −y + 1, −z + 1; (xvi) x + 1, y + 1, z + 1.]

2. Structural commentary

The crystal structure of magnesium zinc divanadate, MgZnV₂O₇, is isotypic with Mn_0.6Zn_1.4V₂O₇ (Knowles et al., 2009 ), where statistically distributed Mg and Zn atoms (Mn and Zn for Mn_0.6Zn_1.4V₂O₇) are located in disordered environments in the crystal structure. The unit-cell volume of MgZnV₂O₇ is smaller than that of Mn_0.6Zn_1.4V₂O₇ by 1.65%.

The crystal structure of MgZnV₂O₇ is shown in Fig. 1a. There are (Mg1/Zn1) (on Wyckoff position 8j, site symmetry 1), (Mg2/Zn2) (on 4h, 2), three V (all on 4i, m), and eight O (three 8j, four 4i, and one 2b, 2/m) sites in the asymmetric unit, where (Mg1/Zn1) and (Mg2/Zn2) represent statistically distributed magnesium and zinc atoms with the atomic ratio close to 1:1.

The crystal structure can be described as an alternate stacking of V₂O₇ layers and (Mg/Zn) atom layers along [20 $[\overline{1}]$ ] (Fig. 1b). Each V₂O₇ layer consists of two groups: a V₂O₇ dimer and a V₄O₁₄ tetramer. For illustration, a slab of one V₂O₇ layer and the adjacent (Mg/Zn) layer is shown in Fig. 1c, which is rotated by 90° from Fig. 1b. Two corner-sharing (V1)O₄ tetrahedra form the dimeric group. Two (V3)O₄ tetrahedra and two (V2)O₅ trigonal bipyramids form the tetrameric group, with a sequence of (V3)O₄–(V2)O₅–(V2)O₅–(V3)O₄. The two trigonal bipyramidal units in the middle are edge-sharing, each of which is corner-sharing with the adjacent terminal tetrahedron. (Mg1/Zn1) and (Mg2/Zn2) are coordinated by oxygen atoms in a distorted trigonal bipyramidal and a distorted octahedral environment, respectively (Table 2).

Table 2
Selected bond lengths (Å)

Mg1—O3ⁱ	1.975 (10)	V1—O3^vii	1.628 (10)
Mg1—O4ⁱ	1.929 (9)	V1—O3^viii	1.628 (10)
Mg1—O5ⁱⁱ	2.172 (10)	V1—O8	1.599 (15)
Mg1—O7ⁱⁱⁱ	2.081 (11)	V2—O1	1.959 (12)
Mg1—O8ⁱⁱⁱ	2.120 (11)	V2—O4	1.745 (9)
Mg2—O3^iv	2.354 (8)	V2—O4^ix	1.745 (9)
Mg2—O3ⁱⁱ	2.354 (8)	V2—O7^x	2.032 (11)
Mg2—O5^v	1.948 (10)	V2—O7^xi	1.898 (15)
Mg2—O5ⁱ	1.948 (10)	V3—O1^xi	1.824 (10)
Mg2—O6ⁱⁱⁱ	2.061 (10)	V3—O5^xi	1.703 (10)
Mg2—O6^vi	2.061 (10)	V3—O5^xii	1.703 (10)
V1—O2	1.757 (4)	V3—O6^xi	1.760 (15)
Symmetry codes: (i) $[-x+{\script{1\over 2}}, y+{\script{1\over 2}}, -z+1]$ ; (ii) ; (iii) x, y+1, z; (iv) ; (v) $[x-{\script{1\over 2}}, y+{\script{1\over 2}}, z]$ ; (vi) ; (vii) ; (viii) ; (ix) ; (x) x, y, z+1; (xi) ; (xii) .

The MgZnV₂O₇ structure (C2/m, Z = 6) is closely related to thortveitite-type α-Zn₂V₂O₇ (C2/c, Z = 4) (Gopal & Calvo, 1973 ), thortveite-type β'-Zn₂V₂O₇ (C2/m, Z = 2) (Krasnenko et al., 2003 ), and β-Mg₂V₂O₇ (P $[\overline{1}]$ , Z = 2) (Gopal & Calvo, 1974 ), as shown in Fig. 2, in which they have an alternate stacking of V₂O₇ layer and Zn or Mg layers. However, in contrast to MgZnV₂O₇, they only contain the V₂O₇ dimer groups. The relationships between other thortveitite-related phases are also well described in a previous work (Knowles et al., 2018 ).

Figure 2
Crystal structure of (a) α-Zn₂V₂O₇, (b) thortveite-type β'-Zn₂V₂O₇, and (c) β-Mg₂V₂O₇.

To check the refined structure model, empirical bond-valence sums (BVSs) were calculated (Brown & Altermatt, 1985 ; Brese & O'Keeffe, 1991 ), with the program Valence (Hormillosa et al., 1993 ). The expected charges of the ions match the obtained BVS values (given in valence units): (Mg1/Zn1) = 1.96, (Mg2/Zn2) = 2.11, V1 = 6.08, V2 = 4.31, V3 = 4.69, O1 = 1.60, O2 = 2.26, O3 = 2.25, O4 = 1.71, O5 = 2.10, O6 = 1.87, O7 = 2.02, and O8 = 2.38. The high value for V1 comes from the relatively short V—O distances (Table 2). The restrained distance was slightly longer than the final values, however, the refinement led to the shorter distances. Short bond lengths (1.56–1.60 Å) were also found in other materials, such as BiBa₂(VO₄)(V₂O₇) (Huang et al., 1994 ) Mg₂(V₂O₇) (Nielsen et al., 2001 ) or Th(V₂O₇) (Launay et al., 1992 ). The final atomic positions were confirmed in the Fourier maps (observed and difference map).

3. Synthesis and crystallization

MgZnV₂O₇ was synthesized by a solid-state reaction from a mixture of Mg(CH₃COO)₂·4H₂O (98.0–102.0%, Alfa-Aesar), ZnO (99.99%, Aldrich) and V₂O₅ (99.99%, Aldrich) with a nominal composition of Mg:Zn:V = 1:1:2. The mixture was thoroughly ground in an agate mortar with acetone, dried, pressed into a pellet, heated in air at 673 K for 3 h, at 943 K for 6 h, and again at 1023 K for 6 h with intermediate grinding and pressing. For the powder X-ray diffraction measurement, the pellet was ground again in an agate mortar and the resultant powder was dispersed on a zero-background Si sample holder.

4. Refinement details

Details of the crystal data collection and structure refinement are summarized in Table 1 and the supporting information. Powder X-ray diffraction (PXRD) data for MgZnV₂O₇ were collected from a Bragg-Brentano diffractometer (PANalytical, 2011 ) using Cu Kα₁ radiation, a focusing primary Ge(111) monochromator (λ = 1.5405 Å) and a position-sensitive PIXcel 3D 2×2 detector. The angular range was set to 8°≤ 2θ ≤ 120°, with a step of 0.0131° and a total measurement time of 8 h at room temperature. The PXRD pattern was indexed using the DICVOL algorithm (Boultif & Louër, 2004 ) run in WINPLOT (Roisnel & Rodríguez-Carvajal, 2000 $[Roisnel, T. & Rodríguez-Carvajal, J. (2000). WinPLOTR: a Windows tool for powder diffraction patterns analysis. Mater. Sci. Forum, Proc. 7th Europ. Powder Diff. Conf. (EPDIC 7), edited by R. Delhez & E. J. Mittenmeijer, pp. 118-123,]$ ) through the positions of 26 reflections, resulting in a monoclinic unit cell (step 1). The space groups from the systematic reflection conditions were suggested to be C2/m, C2, or Cm, which were indistinguishable from the reflection conditions. The highest symmetry, C2/m, was chosen first to determine the structure (step 2), and confirmed later. All the reflections were well indexed, except for a few minor unidentified impurity peaks. The structure determination was performed by a combination of the powder profile refinement program GSAS (Larson & Von Dreele, 2000 ) and the single-crystal structure-refinement program CRYSTALS (Betteridge et al., 2003 ). The software MCE was used to visualize the three-dimensional Fourier electron-density maps, (Rohlíček & Hušák, 2007 ). Initially, a structural model was used with only one dummy atom placed at the (0,0,0) position in the unit cell. A Le Bail fit was used to extract the structure factors from the powder data in GSAS (step 3), followed by applying direct methods to build the initial structural solution, using SHELXS97 (Sheldrick, 2008 ) run in CRYSTALS, which yielded three vanadium sites as the initial structural model (step 4). The initial dummy atom model was then replaced with the partial model containing only three vanadium atoms, and the Le Bail fit was applied in GSAS (step 5). Improved structure factors were then extracted, which were used for the refinement in CRYSTALS (step 6). This process (step 5 to 6) was repeated until a complete and satisfactory structural model was obtained. Finally, Rietveld refinement in GSAS was employed to complete the structure model, resulting in reasonable isotropic displacement parameters and agreement indices (step 7). The refinement parameters were scale factors, background, unit-cell parameters, peak profile coefficients, atomic coordinates, occupancies for the two (Mg/Zn) sites, common U_iso for the metal atoms, common U_iso for the oxygen atoms, and a March–Dollase preferential orientation coefficient (<111> direction). For the final Rietveld refinement cycles, the Mg—O, Zn—O, and V—O bond lengths were restrained with a tolerance value of 0.01 Å with respect to the distances determined from CRYSTALS, which matched reasonably well with the radii sums of Shannon (1976 ). Atomic coordinates and labeling were finally adapted from isotypic Mn_0.6Zn_1.4V₂O₇ (Knowles et al., 2009). The final Rietveld plot is displayed in Fig. 3.

Figure 3
Powder X-ray diffraction Rietveld refinement profiles for MgZnV₂O₇ from room-temperature data. Black dots mark experimental data, the solid red line represents the calculated profile, and the solid green line is the background. The bottom trace presents the difference curve (blue) and the ticks denote the expected Bragg reflection positions (magenta).

Supporting information

CCDC reference: 2080585

Crystal structure: contains datablock I. DOI: https://doi.org/10.1107/S2056989021004503/wm5602sup1.cif

checkCIF report

Computing details top

Data collection: X'Pert Data Collector (PANalytical, 2011); cell refinement: GSAS (Larson & Von Dreele, 2000); data reduction: X'Pert HighScore Plus (PANalytical, 2011); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008) and CRYSTALS (Betteridge et al., 2003); program(s) used to refine structure: GSAS (Larson & Von Dreele, 2000); molecular graphics: VESTA (Momma & Izumi, 2011); software used to prepare material for publication: GSAS (Larson & Von Dreele, 2000).

Magnesium zinc divanadate top

Crystal data top

MgZnV₂O₇	V = 808.19 (1) Å³
M_r = 303.56	Z = 6
Monoclinic, C2/m	F(000) = 864.0
Hall symbol: -C 2y	D_x = 3.743 Mg m⁻³
a = 10.32882 (7) Å	Cu Kα₁ radiation, λ = 1.5405 Å
b = 8.50126 (5) Å	T = 298 K
c = 9.30814 (6) Å	yellow
β = 98.5748 (5)°	irregular, 24.9 × 24.9 mm

Data collection top

PANalytical Empyrean diffractometer	Data collection mode: reflection
Radiation source: sealed X-ray tube, PANalytical Cu Ceramic X-ray tube	Scan method: step
Specimen mounting: dispersed powder	2θ_min = 5.012°, 2θ_max = 119.991°, 2θ_step = 0.013°

Refinement top

Least-squares matrix: full	Profile function: CW Profile function number 4 with 21 terms Pseudovoigt profile coefficients as parameterized in P. Thompson, D.E. Cox & J.B. Hastings (1987). J. Appl. Cryst.,20,79-83. Asymmetry correction of L.W. Finger, D.E. Cox & A. P. Jephcoat (1994). J. Appl. Cryst.,27,892-900. Microstrain broadening by P.W. Stephens, (1999). J. Appl. Cryst.,32,281-289. #1(GU) = 3.306 #2(GV) = 0.000 #3(GW) = 0.000 #4(GP) = 1.565 #5(LX) = 2.176 #6(ptec) = 0.00 #7(trns) = 0.00 #8(shft) = -0.5558 #9(sfec) = 0.00 #10(S/L) = 0.0005 #11(H/L) = 0.0005 #12(eta) = 0.7500 #13(S400 ) = 0.0E+00 #14(S040 ) = 0.0E+00 #15(S004 ) = 0.0E+00 #16(S220 ) = 0.0E+00 #17(S202 ) = 0.0E+00 #18(S022 ) = 0.0E+00 #19(S301 ) = 0.0E+00 #20(S103 ) = 0.0E+00 #21(S121 ) = 0.0E+00 Peak tails are ignored where the intensity is below 0.0020 times the peak Aniso. broadening axis 0.0 0.0 1.0
R_p = 0.055	40 parameters
R_wp = 0.076	0 restraints
R_exp = 0.042	(Δ/σ)_max = 0.03
R(F²) = 0.20886	Background function: GSAS Background function number 1 with 32 terms. Shifted Chebyshev function of 1st kind 1: 684.144 2: -705.826 3: 591.845 4: -383.442 5: 271.953 6: -144.446 7: 80.6035 8: -57.5987 9: 36.6287 10: -27.9916 11: 15.1285 12: -11.9775 13: 12.8819 14: -10.6721 15: 7.66251 16: -8.35018 17: 1.44025 18: -5.00721 19: 5.78817 20: -2.82870 21: 1.93935 22: -1.83947 23: 4.15929 24: 0.506732 25: -0.182215 26: 0.162584 27: 4.98669 28: 0.850932 29: -0.614188 30: -2.46723 31: 3.10631 32: 3.29784
8758 data points	Preferred orientation correction: March-Dollase AXIS 1 Ratio= 0.72861 h= 1.000 k= 1.000 l= 1.000 Prefered orientation correction range: Min= 0.62193, Max= 1.62737
Excluded region(s): The background is too high at low angles and there was no Bragg's peaks.

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

	x	y	z	U_iso*/U_eq	Occ. (<1)
Mg1	0.3477 (3)	0.8175 (3)	0.2035 (3)	0.0069 (3)*	0.508 (4)
Mg2	0.0	0.8191 (5)	0.5	0.0069 (3)*	0.484 (7)
Zn1	0.3477 (3)	0.8175 (3)	0.2035 (3)	0.0069 (3)*	0.492 (4)
Zn2	0.0	0.8191 (5)	0.5	0.0069 (3)*	0.516 (7)
V1	0.0517 (4)	0.0	0.1885 (4)	0.0069 (3)*
V2	0.3777 (4)	0.0	0.8892 (4)	0.0069 (3)*
V3	0.6962 (4)	0.0	0.4938 (4)	0.0069 (3)*
O1	0.4041 (12)	0.0	0.6850 (12)	0.0070 (8)*
O2	0.0	0.0	0.0	0.0070 (8)*
O3	0.0123 (9)	0.1586 (10)	0.7538 (9)	0.0070 (8)*
O4	0.2787 (9)	0.1666 (10)	0.8864 (9)	0.0070 (8)*
O5	0.3613 (10)	0.1678 (11)	0.4382 (10)	0.0070 (8)*
O6	0.1338 (13)	0.0	0.5091 (13)	0.0070 (8)*
O7	0.4380 (14)	0.0	0.1072 (12)	0.0070 (8)*
O8	0.2081 (15)	0.0	0.2045 (13)	0.0070 (8)*

Geometric parameters (Å, º) top

Mg1—Mg1ⁱ	3.104 (6)	V2—O1	1.959 (12)
Mg1—Mg2ⁱⁱ	3.185 (3)	V2—O4	1.745 (9)
Mg1—Zn1ⁱ	3.104 (6)	V2—O4^xv	1.745 (9)
Mg1—Zn2ⁱⁱ	3.185 (3)	V2—O7^xvi	2.032 (11)
Mg1—V3ⁱⁱⁱ	3.307 (5)	V2—O7^xvii	1.898 (15)
Mg1—O3^iv	1.975 (10)	V3—Mg1^xviii	3.307 (5)
Mg1—O4^iv	1.929 (9)	V3—Mg1^xix	3.307 (5)
Mg1—O5^v	2.172 (10)	V3—O1^xvii	1.824 (10)
Mg1—O7^vi	2.081 (11)	V3—O5^xvii	1.703 (10)
Mg1—O8^vi	2.120 (11)	V3—O5^xx	1.703 (10)
Mg2—Mg1ⁱⁱ	3.185 (3)	V3—O6^xvii	1.760 (15)
Mg2—Mg1^vii	3.185 (3)	O1—V2	1.959 (12)
Mg2—Mg2^viii	3.076 (9)	O1—V3^xvii	1.824 (10)
Mg2—Zn1ⁱⁱ	3.185 (3)	O2—V1	1.757 (4)
Mg2—Zn1^vii	3.185 (3)	O2—V1^xxi	1.757 (4)
Mg2—Zn2^viii	3.076 (9)	O3—Mg1^xxii	1.975 (10)
Mg2—O3^ix	2.354 (8)	O3—Mg2^ix	2.354 (8)
Mg2—O3^v	2.354 (8)	O3—Zn1^xxii	1.975 (10)
Mg2—O5^x	1.948 (10)	O3—Zn2^ix	2.354 (8)
Mg2—O5^iv	1.948 (10)	O3—V1^xii	1.628 (10)
Mg2—O6^vi	2.061 (10)	O4—Mg1^xxii	1.929 (9)
Mg2—O6^xi	2.061 (10)	O4—Zn1^xxii	1.929 (9)
Zn1—Mg1ⁱ	3.104 (6)	O4—V2	1.745 (9)
Zn1—Mg2ⁱⁱ	3.185 (3)	O5—Mg1^v	2.172 (10)
Zn1—Zn1ⁱ	3.104 (6)	O5—Mg2^xxiii	1.948 (10)
Zn1—O3^iv	1.975 (10)	O5—Zn1^v	2.172 (10)
Zn1—O4^iv	1.929 (9)	O5—Zn2^xxiii	1.948 (10)
Zn1—O5^v	2.172 (10)	O5—V3^xvii	1.703 (10)
Zn1—O7^vi	2.081 (11)	O6—Mg2^xxiv	2.061 (10)
Zn1—O8^vi	2.120 (11)	O6—Mg2^ix	2.061 (10)
Zn2—Mg1ⁱⁱ	3.185 (3)	O6—Zn2^xxiv	2.061 (10)
Zn2—Mg1^vii	3.185 (3)	O6—Zn2^ix	2.061 (10)
Zn2—Mg2^viii	3.076 (9)	O6—V3^xvii	1.760 (15)
Zn2—Zn2^viii	3.076 (9)	O7—Mg1^xxiv	2.081 (11)
Zn2—O3^ix	2.354 (8)	O7—Mg1^v	2.081 (11)
Zn2—O3^v	2.354 (8)	O7—Zn1^xxiv	2.081 (11)
Zn2—O5^x	1.948 (10)	O7—Zn1^v	2.081 (11)
Zn2—O5^iv	1.948 (10)	O7—V2^xxv	2.032 (11)
Zn2—O6^vi	2.061 (10)	O7—V2^xvii	1.898 (15)
Zn2—O6^xi	2.061 (10)	O8—Mg1^xxiv	2.120 (11)
V1—O2	1.757 (4)	O8—Mg1^v	2.120 (11)
V1—O3^xii	1.628 (10)	O8—Zn1^xxiv	2.120 (11)
V1—O3^xiii	1.628 (10)	O8—Zn1^v	2.120 (11)
V1—O8	1.599 (15)	O8—V1	1.599 (15)
V2—V2^xiv	3.014 (6)

Mg1ⁱ—Mg1—Mg2ⁱⁱ	111.37 (6)	O3^xii—V1—O3^xiii	111.9 (8)
Mg1ⁱ—Mg1—O3^iv	133.1 (3)	O3^xii—V1—O8	115.1 (4)
Mg1ⁱ—Mg1—O4^iv	131.7 (3)	O3^xiii—V1—O8	115.1 (4)
Mg1ⁱ—Mg1—O5^v	86.7 (2)	O1—V2—O4	98.7 (4)
Mg1ⁱ—Mg1—O7^vi	41.8 (3)	O1—V2—O4^xv	98.7 (4)
Mg1ⁱ—Mg1—O8^vi	42.9 (3)	O1—V2—O7^xvi	154.4 (6)
Mg2ⁱⁱ—Mg1—O3^iv	47.5 (3)	O1—V2—O7^xvii	74.5 (5)
Mg2ⁱⁱ—Mg1—O4^iv	110.4 (3)	O4—V2—O4^xv	108.5 (7)
Mg2ⁱⁱ—Mg1—O5^v	36.9 (3)	O4—V2—O7^xvi	96.1 (4)
Mg2ⁱⁱ—Mg1—O7^vi	116.7 (3)	O4—V2—O7^xvii	125.7 (3)
Mg2ⁱⁱ—Mg1—O8^vi	120.7 (4)	O4^xv—V2—O7^xvi	96.1 (4)
O3^iv—Mg1—O4^iv	93.5 (3)	O4^xv—V2—O7^xvii	125.7 (3)
O3^iv—Mg1—O5^v	84.3 (3)	O7^xvi—V2—O7^xvii	79.9 (7)
O3^iv—Mg1—O7^vi	103.6 (5)	O1^xvii—V3—O5^xvii	99.1 (4)
O3^iv—Mg1—O8^vi	167.9 (4)	O1^xvii—V3—O5^xx	99.1 (4)
O4^iv—Mg1—O5^v	114.4 (4)	O1^xvii—V3—O6^xvii	114.7 (7)
O4^iv—Mg1—O7^vi	128.8 (4)	O5^xvii—V3—O5^xx	113.8 (8)
O4^iv—Mg1—O8^vi	94.1 (4)	O5^xvii—V3—O6^xvii	114.2 (4)
O5^v—Mg1—O7^vi	115.1 (4)	O5^xx—V3—O6^xvii	114.2 (4)
O5^v—Mg1—O8^vi	84.0 (5)	V2—O1—V3^xvii	138.0 (7)
O7^vi—Mg1—O8^vi	78.8 (4)	V1—O2—V1^xxi	180.0
Mg1ⁱⁱ—Mg2—Mg1^vii	137.26 (13)	Mg1^xxii—O3—Mg2^ix	94.3 (4)
Mg1ⁱⁱ—Mg2—Mg2^viii	111.37 (6)	Mg1^xxii—O3—Zn1^xxii	0.0
Mg1ⁱⁱ—Mg2—O3^ix	147.6 (2)	Mg1^xxii—O3—V1^xii	145.2 (5)
Mg1ⁱⁱ—Mg2—O3^v	38.2 (2)	Mg2^ix—O3—Zn1^xxii	94.3 (4)
Mg1ⁱⁱ—Mg2—O5^x	105.2 (3)	Mg2^ix—O3—V1^xii	115.7 (4)
Mg1ⁱⁱ—Mg2—O5^iv	42.0 (3)	Zn1^xxii—O3—V1^xii	145.2 (5)
Mg1ⁱⁱ—Mg2—O6^vi	89.7 (3)	Mg1^xxii—O4—Zn1^xxii	0.0
Mg1ⁱⁱ—Mg2—O6^xi	123.3 (3)	Mg1^xxii—O4—V2	154.6 (5)
Mg1^vii—Mg2—Mg2^viii	111.37 (6)	Zn1^xxii—O4—V2	154.6 (5)
Mg1^vii—Mg2—O3^ix	38.2 (2)	Mg1^v—O5—Mg2^xxiii	101.1 (5)
Mg1^vii—Mg2—O3^v	147.6 (2)	Mg1^v—O5—Zn1^v	0.0
Mg1^vii—Mg2—O5^x	42.0 (3)	Mg1^v—O5—Zn2^xxiii	101.1 (5)
Mg1^vii—Mg2—O5^iv	105.2 (3)	Mg1^v—O5—V3^xvii	116.7 (5)
Mg1^vii—Mg2—O6^vi	123.3 (3)	Mg2^xxiii—O5—Zn1^v	101.1 (5)
Mg1^vii—Mg2—O6^xi	89.7 (3)	Mg2^xxiii—O5—Zn2^xxiii	0.0
Mg2^viii—Mg2—O3^ix	85.4 (2)	Mg2^xxiii—O5—V3^xvii	136.5 (5)
Mg2^viii—Mg2—O3^v	85.4 (2)	Zn1^v—O5—Zn2^xxiii	101.1 (5)
Mg2^viii—Mg2—O5^x	131.3 (3)	Zn1^v—O5—V3^xvii	116.7 (5)
Mg2^viii—Mg2—O5^iv	131.3 (3)	Zn2^xxiii—O5—V3^xvii	136.5 (5)
Mg2^viii—Mg2—O6^vi	41.7 (3)	Mg2^xxiv—O6—Mg2^ix	96.5 (6)
Mg2^viii—Mg2—O6^xi	41.7 (3)	Mg2^xxiv—O6—Zn2^xxiv	0.0
O3^ix—Mg2—O3^v	170.8 (4)	Mg2^xxiv—O6—Zn2^ix	96.5 (6)
O3^ix—Mg2—O5^x	80.2 (3)	Mg2^xxiv—O6—V3^xvii	131.6 (3)
O3^ix—Mg2—O5^iv	106.1 (4)	Mg2^ix—O6—Zn2^xxiv	96.5 (6)
O3^ix—Mg2—O6^vi	85.2 (4)	Mg2^ix—O6—Zn2^ix	0.0
O3^ix—Mg2—O6^xi	87.9 (4)	Mg2^ix—O6—V3^xvii	131.6 (3)
O3^v—Mg2—O5^x	106.1 (4)	Zn2^xxiv—O6—Zn2^ix	96.5 (6)
O3^v—Mg2—O5^iv	80.2 (3)	Zn2^xxiv—O6—V3^xvii	131.6 (3)
O3^v—Mg2—O6^vi	87.9 (4)	Zn2^ix—O6—V3^xvii	131.6 (3)
O3^v—Mg2—O6^xi	85.2 (4)	Mg1^xxiv—O7—Mg1^v	96.4 (6)
O5^x—Mg2—O5^iv	97.3 (5)	Mg1^xxiv—O7—Zn1^xxiv	0.0
O5^x—Mg2—O6^vi	164.7 (4)	Mg1^xxiv—O7—Zn1^v	96.4 (6)
O5^x—Mg2—O6^xi	91.2 (4)	Mg1^xxiv—O7—V2^xxv	109.8 (4)
O5^iv—Mg2—O6^vi	91.2 (4)	Mg1^xxiv—O7—V2^xvii	120.3 (4)
O5^iv—Mg2—O6^xi	164.7 (4)	Mg1^v—O7—Zn1^xxiv	96.4 (6)
O6^vi—Mg2—O6^xi	83.5 (6)	Mg1^v—O7—Zn1^v	0.0
O3^iv—Zn1—O4^iv	93.5 (3)	Mg1^v—O7—V2^xxv	109.8 (4)
O3^iv—Zn1—O5^v	84.3 (3)	Mg1^v—O7—V2^xvii	120.3 (4)
O3^iv—Zn1—O7^vi	103.6 (5)	Zn1^xxiv—O7—Zn1^v	96.4 (6)
O3^iv—Zn1—O8^vi	167.9 (4)	Zn1^xxiv—O7—V2^xxv	109.8 (4)
O4^iv—Zn1—O5^v	114.4 (4)	Zn1^xxiv—O7—V2^xvii	120.3 (4)
O4^iv—Zn1—O7^vi	128.8 (4)	Zn1^v—O7—V2^xxv	109.8 (4)
O4^iv—Zn1—O8^vi	94.1 (4)	Zn1^v—O7—V2^xvii	120.3 (4)
O5^v—Zn1—O7^vi	115.1 (4)	V2^xxv—O7—V2^xvii	100.1 (7)
O5^v—Zn1—O8^vi	84.0 (5)	Mg1^xxiv—O8—Mg1^v	94.1 (7)
O7^vi—Zn1—O8^vi	78.8 (4)	Mg1^xxiv—O8—Zn1^xxiv	0.0
O5^x—Zn2—O5^iv	97.3 (5)	Mg1^xxiv—O8—Zn1^v	94.1 (7)
O5^x—Zn2—O6^vi	164.7 (4)	Mg1^xxiv—O8—V1	132.7 (3)
O5^x—Zn2—O6^xi	91.2 (4)	Mg1^v—O8—Zn1^xxiv	94.1 (7)
O5^iv—Zn2—O6^vi	91.2 (4)	Mg1^v—O8—Zn1^v	0.0
O5^iv—Zn2—O6^xi	164.7 (4)	Mg1^v—O8—V1	132.7 (3)
O6^vi—Zn2—O6^xi	83.5 (6)	Zn1^xxiv—O8—Zn1^v	94.1 (7)
O2—V1—O3^xii	104.6 (3)	Zn1^xxiv—O8—V1	132.7 (3)
O2—V1—O3^xiii	104.6 (3)	Zn1^v—O8—V1	132.7 (3)
O2—V1—O8	104.2 (5)

Symmetry codes: (i) x, −y+2, z; (ii) −x+1/2, −y+3/2, −z+1; (iii) −x+1, y+1, −z+1; (iv) −x+1/2, y+1/2, −z+1; (v) x, −y+1, z; (vi) x, y+1, z; (vii) x−1/2, −y+3/2, z; (viii) −x, −y+2, −z+1; (ix) −x, −y+1, −z+1; (x) x−1/2, y+1/2, z; (xi) −x, y+1, −z+1; (xii) −x, y, −z+1; (xiii) −x, −y, −z+1; (xiv) −x+1, y, −z+2; (xv) x, −y, z; (xvi) x, y, z+1; (xvii) −x+1, y, −z+1; (xviii) −x+1, y−1, −z+1; (xix) −x+1, −y+1, −z+1; (xx) −x+1, −y, −z+1; (xxi) −x, y, −z; (xxii) −x+1/2, y−1/2, −z+1; (xxiii) x+1/2, y−1/2, z; (xxiv) x, y−1, z; (xxv) x, y, z−1.

Acknowledgements

This work was supported by the Oregon State University undergraduate internship program. We thank Dr S.-T. Hong at DGIST (Daegu Gyeongbuk Institute of Science and Technology) for assisting with the powder XRD data collection and for helpful discussions.

References

Betteridge, P. W., Carruthers, J. R., Cooper, R. I., Prout, K. & Watkin, D. J. (2003). J. Appl. Cryst. 36, 1487. Web of Science CrossRef IUCr Journals Google Scholar
Boultif, A. & Louër, D. (2004). J. Appl. Cryst. 37, 724–731. Web of Science CrossRef CAS IUCr Journals Google Scholar
Brese, N. E. & O'Keeffe, M. (1991). Acta Cryst. B47, 192–197. CrossRef CAS Web of Science IUCr Journals Google Scholar
Brown, I. D. & Altermatt, D. (1985). Acta Cryst. B41, 244–247. CrossRef CAS Web of Science IUCr Journals Google Scholar
Chang, L. L. Y. & Wang, F. Y. (1988). J. Am. Ceram. Soc. 71, 689–693. CrossRef CAS Web of Science Google Scholar
Gopal, R. & Calvo, C. (1973). Can. J. Chem. 51, 1004–1009. CrossRef ICSD CAS Web of Science Google Scholar
Gopal, R. & Calvo, C. (1974). Acta Cryst. B30, 2491–2493. CrossRef ICSD IUCr Journals Web of Science Google Scholar
Hormillosa, C., Healy, S., Stephen, T. & Brown, I. D. (1993). Bond Valence Calculator. Version 2.0. McMaster University, Canada. Google Scholar
Huang, J., Gu, Q. & Sleight, A. W. (1994). J. Solid State Chem. 110, 226–233. CrossRef ICSD CAS Web of Science Google Scholar
Knowles, K. M., Sil, A., Stöger, B. & Weil, M. (2018). Acta Cryst. C74, 1079–1087. Web of Science CrossRef ICSD IUCr Journals Google Scholar
Knowles, K. M., Vickers, M. E., Sil, A., Han, Y.-H. & Jaffrenou, P. (2009). Acta Cryst. B65, 160–166. Web of Science CrossRef ICSD IUCr Journals Google Scholar
Krasnenko, T. I., Zubkov, V. G. & Tjutinskaja, E. F. (2003). Kristallografiya, 48, 40–43. Google Scholar
Larson, A. C. & Von Dreele, R. B. (2000). General Structure Analysis System (GSAS). Report LAUR. 86–748 Los Alamos National Laboratory, New Mexico, USA. Google Scholar
Launay, S., Mahe, P., Quarton, M. & Robert, F. (1992). J. Solid State Chem. 97, 305–313. CrossRef ICSD CAS Web of Science Google Scholar
Momma, K. & Izumi, F. (2011). J. Appl. Cryst. 44, 1272–1276. Web of Science CrossRef CAS IUCr Journals Google Scholar
Nielsen, U. G., Jakobsen, H. J., Skibsted, J. & Norby, P. (2001). J. Chem. Soc. Dalton Trans. pp. 3214–3218. Web of Science CrossRef ICSD Google Scholar
PANalytical (2011). X'Pert Data Collector and X'Pert High Score Plus. PANalytical BV, Almelo, The Netherlands. Google Scholar
Rohlíček, J. & Hušák, M. (2007). J. Appl. Cryst. 40, 600–601. Web of Science CrossRef IUCr Journals Google Scholar
Roisnel, T. & Rodríguez-Carvajal, J. (2000). WinPLOTR: a Windows tool for powder diffraction patterns analysis. Mater. Sci. Forum, Proc. 7th Europ. Powder Diff. Conf. (EPDIC 7), edited by R. Delhez & E. J. Mittenmeijer, pp. 118–123, Google Scholar
Shannon, R. D. (1976). Acta Cryst. A32, 751–767. CrossRef CAS IUCr Journals Web of Science Google Scholar
Sheldrick, G. M. (2008). Acta Cryst. A64, 112–122. Web of Science CrossRef CAS IUCr Journals Google Scholar

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