The vanadate garnet Ca₂NaCd₂V₃O₁₂: a single-crystal X-ray diffraction study

Single crystals of the vanadate garnet Ca₂NaCd₂V₃O₁₂ (dicalcium sodium dicadmium trivanadate) were synthesized using the floating-zone method and the crystal structure was investigated using single-crystal X-ray diffraction. We considered the effectiveness of substitution of the Y-site cation with reference to previous structural studies of vanadate garnets. The structures of vanadate garnets are subject to geometric constraints similar to those of silicate garnets. These constraints force the tetra­hedral–dodeca­hedral shared edge length in vanadate garnets to become shorter than the unshared dodeca­hedral edge length, as in ugrandite (uvarovite, grossular and andradite) garnets. However, the vanadate garnet Ca₂NaCd₂V₃O₁₂ exhibits the normal structural feature, similar to pyralspite (pyrope, almandine and spessartine) garnets, namely that the dodeca­hedral–dodeca­hedral shared edge length is shorter than the unshared dodeca­hedral edge length. With increasing ionic radius of the Y-site cation, the atomic coordinates x, y and z of oxygen adopt values which satisfy Pauling's third rule.

Computing details

Data collection: Software for data collection?; cell refinement: Software for cell refinement?; data reduction: Software for data reduction?; program(s) used to solve structure: OLEX2 (Dolomanov et al., 2009) and SHELXT2014 (Sheldrick, 2015a); program(s) used to refine structure: SHELXL2016 (Sheldrick, 2015b); molecular graphics: Software for molecular graphics?.

Dicalcium sodium dicadmium trivanadate

Crystal data

Ca2NaCd2V3O12	Mo Kα radiation, λ = 0.71073 Å
Mr = 672.77	Cell parameters from 6959 reflections
Cubic, Ia3d	θ = 2.2–55.3°
a = 12.7576 (1) Å	µ = 7.72 mm^−1
V = 2076.38 (5) Å^3	T = 293 K
Z = 8	Sphere, orange
F(000) = 2496	0.12 × 0.12 × 0.12 × 0.06 (radius) mm
Dx = 4.304 Mg m^−3

Data collection

Rigaku SuperNova Single source diffractometer with an HyPix3000 area detector	675 reflections with I > 2σ(I)
ω scans	Rint = 0.016
Absorption correction: for a sphere	θmax = 45.0°, θmin = 3.9°
Tmin = 0.506, Tmax = 0.533	h = −22→19
8486 measured reflections	k = −25→18
719 independent reflections	l = −24→25

Refinement

Refinement on F^2	2 restraints
Least-squares matrix: full	w = 1/[σ^2(Fo^2) + (0.024P)^2 + 1.850P] where P = (Fo^2 + 2Fc^2)/3
R[F^2 > 2σ(F^2)] = 0.016	(Δ/σ)max < 0.001
wR(F^2) = 0.055	Δρmax = 0.61 e Å^−3
S = 1.17	Δρmin = −1.60 e Å^−3
719 reflections	Extinction correction: SHELXL2016 (Sheldrick, 2015b), Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
22 parameters	Extinction coefficient: 0.00177 (9)

Special details

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 (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
Cd01	0.500000	0.500000	0.500000	0.01059 (6)
V002	0.625000	0.500000	0.250000	0.00741 (6)
Ca1	0.375000	0.500000	0.250000	0.01115 (15)	0.660 (14)
O004	0.54015 (4)	0.44169 (4)	0.33734 (4)	0.01230 (10)
Na1	0.375000	0.500000	0.250000	0.01115 (15)	0.34 (2)
Cd1	0.375000	0.500000	0.250000	0.01115 (15)	0.021 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Cd01	0.01059 (6)	0.01059 (6)	0.01059 (6)	−0.00065 (1)	−0.00065 (1)	−0.00065 (1)
V002	0.00688 (9)	0.00767 (7)	0.00767 (7)	0.000	0.000	0.000
Ca1	0.00856 (18)	0.01245 (16)	0.01245 (16)	0.000	0.000	0.00144 (7)
O004	0.01415 (19)	0.01295 (19)	0.00979 (17)	−0.00146 (14)	0.00159 (14)	0.00008 (14)
Na1	0.00856 (18)	0.01245 (16)	0.01245 (16)	0.000	0.000	0.00144 (7)
Cd1	0.00856 (18)	0.01245 (16)	0.01245 (16)	0.000	0.000	0.00144 (7)

Geometric parameters (Å, º)

Cd01—O004	2.2632 (5)	V002—O004^vii	1.7224 (5)
Cd01—O004^i	2.2632 (5)	V002—O004^viii	1.7224 (5)
Cd01—O004^ii	2.2632 (5)	V002—O004	1.7224 (5)
Cd01—O004^iii	2.2632 (5)	V002—Ca1	3.1894 (1)
Cd01—O004^iv	2.2632 (5)	V002—Ca1^ix	3.1894 (1)
Cd01—O004^v	2.2632 (5)	Ca1—O004^x	2.4968 (6)
Cd01—Ca1	3.5659 (1)	Ca1—O004^xi	2.4968 (6)
Cd01—Ca1^ii	3.5659 (1)	Ca1—O004^vii	2.4968 (6)
Cd01—Ca1^i	3.5659 (1)	Ca1—O004	2.4968 (6)
Cd01—Ca1^iii	3.5659 (1)	Ca1—O004^xii	2.5443 (5)
Cd01—Ca1^iv	3.5659 (1)	Ca1—O004^xiii	2.5443 (5)
Cd01—Ca1^v	3.5659 (1)	Ca1—O004^xiv	2.5443 (5)
V002—O004^vi	1.7224 (5)	Ca1—O004^iv	2.5443 (5)
O004—Cd01—O004^i	91.12 (2)	O004^vii—V002—Ca1^ix	128.938 (19)
O004—Cd01—O004^ii	88.88 (2)	O004^viii—V002—Ca1^ix	51.062 (19)
O004^i—Cd01—O004^ii	180.0	O004—V002—Ca1^ix	128.937 (19)
O004—Cd01—O004^iii	91.12 (2)	Ca1—V002—Ca1^ix	180.0
O004^i—Cd01—O004^iii	88.88 (2)	O004^x—Ca1—O004^xi	64.90 (2)
O004^ii—Cd01—O004^iii	91.12 (2)	O004^x—Ca1—O004^vii	167.96 (2)
O004—Cd01—O004^iv	88.88 (2)	O004^xi—Ca1—O004^vii	116.50 (2)
O004^i—Cd01—O004^iv	91.12 (2)	O004^x—Ca1—O004	116.50 (2)
O004^ii—Cd01—O004^iv	88.88 (2)	O004^xi—Ca1—O004	167.96 (2)
O004^iii—Cd01—O004^iv	180.0	O004^vii—Ca1—O004	64.90 (2)
O004—Cd01—O004^v	180.0	O004^x—Ca1—O004^xii	121.891 (11)
O004^i—Cd01—O004^v	88.884 (19)	O004^xi—Ca1—O004^xii	77.90 (2)
O004^ii—Cd01—O004^v	91.12 (2)	O004^vii—Ca1—O004^xii	69.15 (2)
O004^iii—Cd01—O004^v	88.884 (19)	O004—Ca1—O004^xii	92.131 (14)
O004^iv—Cd01—O004^v	91.116 (19)	O004^x—Ca1—O004^xiii	92.130 (14)
O004—Cd01—Ca1	44.037 (14)	O004^xi—Ca1—O004^xiii	69.15 (2)
O004^i—Cd01—Ca1	86.822 (14)	O004^vii—Ca1—O004^xiii	77.90 (2)
O004^ii—Cd01—Ca1	93.178 (14)	O004—Ca1—O004^xiii	121.891 (11)
O004^iii—Cd01—Ca1	134.753 (13)	O004^xii—Ca1—O004^xiii	115.00 (2)
O004^iv—Cd01—Ca1	45.247 (13)	O004^x—Ca1—O004^xiv	77.90 (2)
O004^v—Cd01—Ca1	135.964 (14)	O004^xi—Ca1—O004^xiv	121.891 (11)
O004—Cd01—Ca1^ii	45.246 (13)	O004^vii—Ca1—O004^xiv	92.130 (14)
O004^i—Cd01—Ca1^ii	135.964 (14)	O004—Ca1—O004^xiv	69.15 (2)
O004^ii—Cd01—Ca1^ii	44.036 (14)	O004^xii—Ca1—O004^xiv	158.23 (2)
O004^iii—Cd01—Ca1^ii	86.822 (14)	O004^xiii—Ca1—O004^xiv	69.43 (3)
O004^iv—Cd01—Ca1^ii	93.178 (14)	O004^x—Ca1—O004^iv	69.15 (2)
O004^v—Cd01—Ca1^ii	134.753 (13)	O004^xi—Ca1—O004^iv	92.130 (14)
Ca1—Cd01—Ca1^ii	66.4	O004^vii—Ca1—O004^iv	121.891 (11)
O004—Cd01—Ca1^i	134.754 (13)	O004—Ca1—O004^iv	77.90 (2)
O004^i—Cd01—Ca1^i	44.036 (14)	O004^xii—Ca1—O004^iv	69.43 (3)
O004^ii—Cd01—Ca1^i	135.964 (14)	O004^xiii—Ca1—O004^iv	158.23 (2)
O004^iii—Cd01—Ca1^i	93.178 (14)	O004^xiv—Ca1—O004^iv	115.00 (2)
O004^iv—Cd01—Ca1^i	86.822 (14)	O004^x—Ca1—V002^xv	32.451 (12)
O004^v—Cd01—Ca1^i	45.247 (13)	O004^xi—Ca1—V002^xv	32.451 (12)
Ca1—Cd01—Ca1^i	113.6	O004^vii—Ca1—V002^xv	147.549 (12)
Ca1^ii—Cd01—Ca1^i	180.0	O004—Ca1—V002^xv	147.548 (12)
O004—Cd01—Ca1^iii	86.823 (14)	O004^xii—Ca1—V002^xv	100.886 (12)
O004^i—Cd01—Ca1^iii	45.247 (13)	O004^xiii—Ca1—V002^xv	79.114 (12)
O004^ii—Cd01—Ca1^iii	134.753 (13)	O004^xiv—Ca1—V002^xv	100.886 (12)
O004^iii—Cd01—Ca1^iii	44.036 (14)	O004^iv—Ca1—V002^xv	79.114 (12)
O004^iv—Cd01—Ca1^iii	135.964 (14)	O004^x—Ca1—V002	147.549 (12)
O004^v—Cd01—Ca1^iii	93.178 (14)	O004^xi—Ca1—V002	147.549 (12)
Ca1—Cd01—Ca1^iii	113.6	O004^vii—Ca1—V002	32.451 (12)
Ca1^ii—Cd01—Ca1^iii	113.6	O004—Ca1—V002	32.452 (12)
Ca1^i—Cd01—Ca1^iii	66.4	O004^xii—Ca1—V002	79.114 (12)
O004—Cd01—Ca1^iv	93.177 (14)	O004^xiii—Ca1—V002	100.886 (12)
O004^i—Cd01—Ca1^iv	134.753 (13)	O004^xiv—Ca1—V002	79.114 (12)
O004^ii—Cd01—Ca1^iv	45.247 (13)	O004^iv—Ca1—V002	100.886 (12)
O004^iii—Cd01—Ca1^iv	135.964 (14)	V002^xv—Ca1—V002	180.0
O004^iv—Cd01—Ca1^iv	44.036 (14)	O004^x—Ca1—Cd01^xvi	39.056 (12)
O004^v—Cd01—Ca1^iv	86.822 (14)	O004^xi—Ca1—Cd01^xvi	91.247 (12)
Ca1—Cd01—Ca1^iv	66.4	O004^vii—Ca1—Cd01^xvi	130.081 (12)
Ca1^ii—Cd01—Ca1^iv	66.4	O004—Ca1—Cd01^xvi	96.366 (12)
Ca1^i—Cd01—Ca1^iv	113.6	O004^xii—Ca1—Cd01^xvi	160.758 (12)
Ca1^iii—Cd01—Ca1^iv	180.0	O004^xiii—Ca1—Cd01^xvi	74.662 (12)
O004—Cd01—Ca1^v	135.963 (14)	O004^xiv—Ca1—Cd01^xvi	39.175 (11)
O004^i—Cd01—Ca1^v	93.178 (14)	O004^iv—Ca1—Cd01^xvi	95.486 (13)
O004^ii—Cd01—Ca1^v	86.822 (14)	V002^xv—Ca1—Cd01^xvi	63.4
O004^iii—Cd01—Ca1^v	45.247 (13)	V002—Ca1—Cd01^xvi	116.6
O004^iv—Cd01—Ca1^v	134.753 (13)	O004^x—Ca1—Cd01	96.367 (12)
O004^v—Cd01—Ca1^v	44.036 (14)	O004^xi—Ca1—Cd01	130.081 (12)
Ca1—Cd01—Ca1^v	180.0	O004^vii—Ca1—Cd01	91.247 (12)
Ca1^ii—Cd01—Ca1^v	113.6	O004—Ca1—Cd01	39.056 (12)
Ca1^i—Cd01—Ca1^v	66.4	O004^xii—Ca1—Cd01	74.662 (12)
Ca1^iii—Cd01—Ca1^v	66.4	O004^xiii—Ca1—Cd01	160.758 (12)
Ca1^iv—Cd01—Ca1^v	113.6	O004^xiv—Ca1—Cd01	95.486 (13)
O004^vi—V002—O004^vii	113.27 (2)	O004^iv—Ca1—Cd01	39.175 (11)
O004^vi—V002—O004^viii	102.12 (4)	V002^xv—Ca1—Cd01	116.6
O004^vii—V002—O004^viii	113.27 (2)	V002—Ca1—Cd01	63.4
O004^vi—V002—O004	113.26 (2)	Cd01^xvi—Ca1—Cd01	101.5
O004^vii—V002—O004	102.13 (4)	V002—O004—Cd01	126.40 (3)
O004^viii—V002—O004	113.26 (2)	V002—O004—Ca1	96.48 (2)
O004^vi—V002—Ca1	128.938 (19)	Cd01—O004—Ca1	96.91 (2)
O004^vii—V002—Ca1	51.062 (19)	V002—O004—Ca1^ii	131.59 (3)
O004^viii—V002—Ca1	128.938 (19)	Cd01—O004—Ca1^ii	95.580 (18)
O004—V002—Ca1	51.063 (19)	Ca1—O004—Ca1^ii	101.582 (19)
O004^vi—V002—Ca1^ix	51.062 (19)

Symmetry codes: (i) −y+1, −z+1, −x+1; (ii) y, z, x; (iii) −z+1, −x+1, −y+1; (iv) z, x, y; (v) −x+1, −y+1, −z+1; (vi) −x+5/4, z+1/4, −y+3/4; (vii) x, −y+1, −z+1/2; (viii) −x+5/4, −z+3/4, y−1/4; (ix) x+1/2, y, −z+1/2; (x) −x+3/4, −z+3/4, −y+3/4; (xi) −x+3/4, z+1/4, y−1/4; (xii) −z+3/4, y+1/4, x−1/4; (xiii) z, −x+1, −y+1/2; (xiv) −z+3/4, −y+3/4, −x+3/4; (xv) x−1/2, y, −z+1/2; (xvi) −y+3/4, −x+3/4, −z+3/4.