Structural insights into M₂O-Al₂O₃-WO₃ (M = Na, K) system by electron diffraction tomography

The M₂O-Al₂O₃-WO₃ (M = alkaline metals) system has attracted the attention of the scientific community because some of its members showed potential applications as single crystalline media for tunable solid-state lasers. These materials behave as promising laser host materials due to their high and continuous transparency in the wide range of the near-IR region. A systematic investigation of these phases is nonetheless hampered because it is impossible to produce large crystals and only in a few cases a pure synthetic product can be achieved. Despite substantial advances in X-ray powder diffraction methods, structure investigation on nanoscale is still challenging, especially when the sample is polycrystalline and the structures are affected by pseudo-symmetry. Electron diffraction has the advantage of collecting data from single nanoscopic crystals, but it is frequently limited by incompleteness and dynamical effects. Automated diffraction tomography (ADT) recently emerged as an alternative approach able to collect more complete three-dimensional electron diffraction data and at the same time to significantly reduce dynamical scattering. ADT data have been shown to be suitable for ab initio structure solution of phases with large cell parameters, and for detecting pseudo-symmetry that was undetected in X-ray powder data. In this work we present the structure investigation of two hitherto undetermined compounds, K₅Al(W₃O₁₁)₂ and NaAl(WO₄)₂, by a combination of electron diffraction tomography and precession electron diffraction. We also stress how electron diffraction tomography can be used to obtain direct information about symmetry and pseudo-symmetry for nanocrystalline phases, even when available only in polyphasic mixtures.

Computing details

Data collection: ADT module for K5Al_W3O11_ADT, Na2W2O7_ADT, NaAl_WO4_2_ADT. Cell refinement: ADT3D for K5Al_W3O11_ADT, Na2W2O7_ADT, NaAl_WO4_2_ADT. Data reduction: own developed routines for K5Al_W3O11_ADT, Na2W2O7_ADT, NaAl_WO4_2_ADT. Program(s) used to solve structure: Delta recycling for K5Al_W3O11_ADT, Na2W2O7_ADT, NaAl_WO4_2_ADT. Program(s) used to refine structure: SHELXL97 (Sheldrick, 1997) for K5Al_W3O11_ADT, Na2W2O7_ADT, NaAl_WO4_2_ADT.

(K5Al_W3O11_ADT)

Crystal data

AlK5O22Ta6	Z = 4
Mr = 1660.17	F(000) = 678
Monoclinic, C2	Dx = 5.260 Mg m^−3
a = 13.6172 (4) Å	µ = 0.01 mm^−1
b = 7.8284 (2) Å	T = 293 K
c = 19.9190 (7) Å	Nanocrystal
β = 99.166 (2)°	0.00010 × 0.00007 × 0.00003 mm
V = 2096.28 (11) Å^3

Data collection

FEI Tecnai F30 ST diffractometer	Rint = 0.145
electron precession and ADT scans	θmax = 0.7°, θmin = 0.1°
6748 measured reflections	h = −17→17
3567 independent reflections	k = −9→9
2562 reflections with I > 2σ(I)	l = −22→22

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.210	w = 1/[σ^2(Fo^2) + (0.1P)^2] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.476	(Δ/σ)max = 0.019
S = 1.89	Δρmax = 0.68 e Å^−3
3567 reflections	Δρmin = −0.48 e Å^−3
137 parameters	Absolute structure: Flack H D (1983), Acta Cryst. A39, 876-881
442 restraints	Absolute structure parameter: −10 (10)

Special details

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

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > σ(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
W1	0.2240 (5)	0.0393 (9)	−0.0005 (4)	0.0411 (17)*
W2	0.1518 (5)	0.3480 (9)	0.1460 (4)	0.0463 (18)*
W3	0.3577 (5)	0.1525 (10)	0.1362 (4)	0.054 (2)*
W4	0.2931 (5)	−0.1895 (9)	0.3606 (4)	0.0429 (18)*
W5	0.0817 (5)	−0.0029 (8)	0.3575 (4)	0.0427 (17)*
W6	0.2185 (5)	−0.3478 (9)	0.4905 (4)	0.0434 (17)*
Al1	0.0000	0.261 (3)	0.0000	0.022 (6)*
Al2	0.5000	0.373 (4)	0.5000	0.033 (7)*
K1	0.3100 (15)	0.291 (3)	0.3371 (12)	0.062 (5)*
K2	0.0471 (15)	0.532 (3)	0.3049 (12)	0.069 (6)*
K3	0.5000	−0.170 (5)	0.5000	0.089 (10)*
K4	−0.097 (2)	0.123 (5)	0.192 (2)	0.123 (11)*
K5	0.5000	0.214 (4)	0.0000	0.067 (8)*
K6	0.1591 (16)	−0.139 (3)	0.1799 (12)	0.068 (6)*
O1	0.193 (2)	−0.035 (4)	0.3124 (19)	0.055 (9)*
O2	0.188 (8)	0.096 (16)	0.427 (5)	0.23 (5)*
O3	0.2165 (19)	0.172 (4)	0.0876 (14)	0.045 (7)*
O4	0.517 (4)	0.489 (8)	0.432 (2)	0.111 (19)*
O5	0.059 (3)	0.381 (5)	0.0675 (19)	0.068 (11)*
O6	0.0915 (18)	0.123 (4)	−0.0198 (19)	0.042 (7)*
O7	0.172 (2)	−0.226 (4)	0.4058 (16)	0.046 (8)*
O8	0.400 (2)	0.241 (5)	0.491 (3)	0.068 (11)*
O9	0.134 (2)	0.546 (4)	0.189 (2)	0.053 (8)*
O10	0.287 (2)	0.288 (4)	0.1918 (17)	0.047 (8)*
O11	0.301 (3)	−0.364 (5)	0.298 (2)	0.063 (10)*
O12	0.266 (3)	0.034 (6)	−0.0869 (19)	0.076 (12)*
O13	0.468 (2)	0.295 (5)	0.136 (2)	0.057 (9)*
O14	0.205 (5)	−0.187 (5)	0.021 (4)	0.109 (19)*
O15	−0.006 (3)	−0.139 (6)	0.302 (3)	0.082 (13)*
O16	0.329 (2)	−0.316 (4)	0.4403 (16)	0.053 (9)*
O17	0.088 (4)	0.173 (7)	0.188 (3)	0.101 (17)*
O18	0.175 (4)	−0.559 (5)	0.453 (3)	0.086 (14)*
O19	0.405 (2)	−0.064 (5)	0.376 (2)	0.060 (10)*
O20	0.384 (3)	−0.027 (5)	0.194 (2)	0.063 (10)*
O21	0.356 (2)	0.036 (5)	0.0542 (16)	0.056 (9)*
O22	0.553 (4)	0.727 (5)	0.337 (4)	0.103 (18)*

Geometric parameters (Å, º)

W1—O14	1.85 (4)	W5—O1	1.90 (3)
W1—O6	1.90 (2)	W5—O2	1.99 (3)
W1—O21	1.95 (3)	W5—O7	2.26 (3)
W1—O12	1.90 (3)	W6—O8^iii	1.85 (3)
W1—O3	2.05 (2)	W6—O18	1.87 (3)
W1—O14^i	2.41 (6)	W6—O2^iii	1.96 (3)
W1—W3	3.152 (11)	W6—O16	1.95 (3)
W2—O9	1.81 (3)	W6—O7	1.95 (3)
W2—O5	1.87 (3)	Al1—O5	1.73 (3)
W2—O17	1.89 (4)	Al1—O5^iv	1.73 (3)
W2—O10	1.98 (3)	Al1—O6	1.74 (3)
W2—O3	2.09 (2)	Al1—O6^iv	1.74 (3)
W2—O12^i	2.28 (4)	Al2—O4^v	1.68 (4)
W3—O20	1.81 (3)	Al2—O4	1.68 (4)
W3—O13	1.87 (3)	Al2—O8^v	1.70 (3)
W3—O21	1.87 (3)	Al2—O8	1.70 (3)
W3—O10	1.90 (3)	K2—O22^ii	2.47 (4)
W3—O3	2.02 (2)	K4—O17	2.56 (6)
W4—O19	1.80 (3)	K6—O9^vi	2.50 (4)
W4—O16	1.87 (3)	O2—W6^vii	1.96 (3)
W4—O11	1.86 (3)	O4—W5^viii	1.84 (3)
W4—O1	1.95 (3)	O8—W6^vii	1.85 (3)
W4—O7	2.03 (3)	O9—K6^ix	2.50 (4)
W4—W6	3.178 (11)	O12—W2^x	2.28 (4)
W5—O15	1.84 (3)	O14—W1^x	2.41 (6)
W5—O4^ii	1.84 (3)	O22—W5^viii	1.87 (4)
W5—O22^ii	1.87 (4)	O22—K2^viii	2.47 (4)
O14—W1—O6	102 (2)	O1—W4—W6	110.7 (10)
O14—W1—O21	90 (2)	O7—W4—W6	36.2 (8)
O6—W1—O21	151.7 (14)	O15—W5—O4^ii	96 (3)
O14—W1—O12	105 (3)	O15—W5—O22^ii	110 (3)
O6—W1—O12	103.7 (18)	O4^ii—W5—O22^ii	96 (3)
O21—W1—O12	97.1 (17)	O15—W5—O1	98 (2)
O14—W1—O3	105 (3)	O4^ii—W5—O1	154 (2)
O6—W1—O3	79.9 (13)	O22^ii—W5—O1	100 (2)
O21—W1—O3	72.4 (12)	O15—W5—O2	167 (4)
O12—W1—O3	148.1 (18)	O4^ii—W5—O2	81 (5)
O14—W1—O14^i	164.5 (10)	O22^ii—W5—O2	83 (4)
O6—W1—O14^i	93.0 (17)	O1—W5—O2	81 (4)
O21—W1—O14^i	75.5 (19)	O15—W5—O7	93.6 (19)
O12—W1—O14^i	71 (2)	O4^ii—W5—O7	86 (2)
O3—W1—O14^i	77.0 (19)	O22^ii—W5—O7	156 (2)
O14—W1—W3	99 (2)	O1—W5—O7	71.2 (12)
O6—W1—W3	118.5 (11)	O2—W5—O7	74 (4)
O21—W1—W3	33.5 (9)	O8^iii—W6—O18	100 (2)
O12—W1—W3	125.0 (14)	O8^iii—W6—O2^iii	113 (4)
O3—W1—W3	38.8 (7)	O18—W6—O2^iii	105 (4)
O14^i—W1—W3	73.0 (17)	O8^iii—W6—O16	145.6 (18)
O9—W2—O5	99.2 (17)	O18—W6—O16	98 (2)
O9—W2—O17	108 (3)	O2^iii—W6—O16	90 (4)
O5—W2—O17	100 (2)	O8^iii—W6—O7	79.4 (18)
O9—W2—O10	99.7 (14)	O18—W6—O7	93 (2)
O5—W2—O10	151.2 (18)	O2^iii—W6—O7	156 (4)
O17—W2—O10	95 (2)	O16—W6—O7	70.6 (12)
O9—W2—O3	158.8 (15)	O8^iii—W6—W4	114.9 (15)
O5—W2—O3	85.0 (16)	O18—W6—W4	98 (2)
O17—W2—O3	92 (2)	O2^iii—W6—W4	121 (4)
O10—W2—O3	69.8 (11)	O16—W6—W4	32.9 (9)
O9—W2—O12^i	79.2 (17)	O7—W6—W4	37.8 (8)
O5—W2—O12^i	78.7 (19)	O5—Al1—O5^iv	114 (3)
O17—W2—O12^i	173 (2)	O5—Al1—O6	104.7 (18)
O10—W2—O12^i	83.7 (16)	O5^iv—Al1—O6	115 (2)
O3—W2—O12^i	81.3 (15)	O5—Al1—O6^iv	115 (2)
O20—W3—O13	112.6 (18)	O5^iv—Al1—O6^iv	104.7 (18)
O20—W3—O21	99 (2)	O6—Al1—O6^iv	103 (2)
O13—W3—O21	100.7 (18)	O4^v—Al2—O4	115 (4)
O20—W3—O10	97.5 (19)	O4^v—Al2—O8^v	117 (3)
O13—W3—O10	98.6 (17)	O4—Al2—O8^v	102 (3)
O21—W3—O10	147.7 (13)	O4^v—Al2—O8	102 (3)
O20—W3—O3	116.2 (16)	O4—Al2—O8	117 (3)
O13—W3—O3	131.1 (16)	O8^v—Al2—O8	105 (3)
O21—W3—O3	74.8 (12)	W5—O1—W4	113.4 (18)
O10—W3—O3	73.0 (11)	W6^vii—O2—W5	167 (8)
O20—W3—W1	111.1 (14)	W3—O3—W1	101.5 (11)
O13—W3—W1	121.1 (14)	W3—O3—W2	103.7 (11)
O21—W3—W1	35.1 (9)	W1—O3—W2	153.1 (14)
O10—W3—W1	112.7 (9)	Al2—O4—W5^viii	145 (4)
O3—W3—W1	39.7 (7)	Al1—O5—W2	138 (2)
O19—W4—O16	92.9 (18)	Al1—O6—W1	149 (2)
O19—W4—O11	112 (2)	W6—O7—W4	106.0 (13)
O16—W4—O11	98.2 (18)	W6—O7—W5	145.6 (17)
O19—W4—O1	104.4 (17)	W4—O7—W5	97.2 (11)
O16—W4—O1	144.3 (14)	Al2—O8—W6^vii	157 (3)
O11—W4—O1	103.6 (17)	W2—O9—K6^ix	141 (2)
O19—W4—O7	137.2 (19)	W3—O10—W2	112.6 (16)
O16—W4—O7	70.6 (12)	W1—O12—W2^x	137 (2)
O11—W4—O7	109.4 (16)	W1—O14—W1^x	137 (4)
O1—W4—O7	75.7 (13)	W4—O16—W6	112.7 (15)
O19—W4—W6	116.8 (15)	W2—O17—K4	130 (3)
O16—W4—W6	34.4 (9)	W3—O21—W1	111.3 (16)
O11—W4—W6	108.6 (14)	W5^viii—O22—K2^viii	169 (4)

Symmetry codes: (i) −x+1/2, y+1/2, −z; (ii) x−1/2, y−1/2, z; (iii) −x+1/2, y−1/2, −z+1; (iv) −x, y, −z; (v) −x+1, y, −z+1; (vi) x, y−1, z; (vii) −x+1/2, y+1/2, −z+1; (viii) x+1/2, y+1/2, z; (ix) x, y+1, z; (x) −x+1/2, y−1/2, −z.

(Na2W2O7_ADT)

Crystal data

Na2O7Ta2	V = 1262.9 (2) Å^3
Mr = 519.87	Z = 8
Orthorombic, Cmce	F(000) = 388
a = 7.2220 (8) Å	Dx = 5.468 Mg m^−3
b = 11.8947 (9) Å	µ = 0.00 mm^−1
c = 14.7016 (13) Å	T = 293 K
α = 90°	Nanocrystal
β = 90°	0.00024 × 0.00014 × 0.00010 mm
γ = 90°

Data collection

FEI Tecnai F30 ST diffractometer	Rint = 0.298
electron precession and ADT scans	θmax = 0.6°, θmin = 0.1°
2867 measured reflections	h = −8→8
454 independent reflections	k = −11→12
440 reflections with I > 2σ(I)	l = −16→16

Refinement

Refinement on F^2	6 restraints
Least-squares matrix: full	Primary atom site location: structure-invariant direct methods
R[F^2 > 2σ(F^2)] = 0.250	Secondary atom site location: difference Fourier map
wR(F^2) = 0.537	w = 1/[σ^2(Fo^2) + (0.1P)^2] where P = (Fo^2 + 2Fc^2)/3
S = 3.33	(Δ/σ)max = 0.001
454 reflections	Δρmax = 0.83 e Å^−3
28 parameters	Δρmin = −0.84 e Å^−3

Special details

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

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > σ(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
W1	0.2500	0.4145 (6)	0.2500	0.027 (3)*
W2	0.0000	0.2534 (5)	0.0851 (4)	0.023 (3)*
Na1	0.259 (4)	0.0000	0.0000	0.047 (9)*
Na2	0.0000	0.178 (3)	0.340 (2)	0.042 (8)*
O1	0.202 (3)	0.264 (2)	0.1522 (17)	0.035 (6)*
O2	0.303 (3)	0.0131 (18)	0.1648 (13)	0.022 (5)*
O3	0.0000	0.390 (4)	0.281 (3)	0.046 (9)*
O4	0.0000	0.124 (2)	0.034 (2)	0.029 (7)*
O5	0.0000	0.358 (2)	0.0019 (19)	0.026 (7)*

Geometric parameters (Å, º)

W1—O2^i	1.76 (2)	Na1—O5^ix	2.42 (3)
W1—O2^ii	1.76 (2)	Na2—O5^x	2.41 (4)
W1—O3	1.884 (12)	Na2—O1^iv	2.39 (3)
W1—O3^iii	1.884 (12)	Na2—O1^xi	2.39 (3)
W1—O1	2.32 (2)	Na2—O2^xi	2.42 (3)
W1—O1^iv	2.32 (2)	Na2—O2^iv	2.42 (3)
W2—O4	1.72 (3)	Na2—O3	2.67 (5)
W2—O5	1.74 (3)	O1—Na2^iii	2.39 (3)
W2—O1	1.77 (2)	O2—W1^xii	1.76 (2)
W2—O1^v	1.77 (2)	O2—Na2^iii	2.42 (3)
Na1—O4^vi	2.43 (3)	O3—W1^xi	1.884 (12)
Na1—O4	2.43 (3)	O4—Na1^vi	2.43 (3)
Na1—O2^vii	2.45 (2)	O5—Na2^xiii	2.41 (4)
Na1—O2	2.45 (2)	O5—Na1^viii	2.42 (3)
Na1—O5^viii	2.42 (3)	O5—Na1^xiv	2.42 (3)
O2^i—W1—O2^ii	96.3 (13)	O5^viii—Na1—O5^ix	88.3 (13)
O2^i—W1—O3	98.4 (14)	O5^x—Na2—O1^iv	91.7 (11)
O2^ii—W1—O3	93.7 (13)	O5^x—Na2—O1^xi	91.7 (11)
O2^i—W1—O3^iii	93.7 (14)	O1^iv—Na2—O1^xi	128.7 (19)
O2^ii—W1—O3^iii	98.4 (14)	O5^x—Na2—O2^xi	83.6 (12)
O3—W1—O3^iii	162 (2)	O1^iv—Na2—O2^xi	151.5 (14)
O2^i—W1—O1	171.0 (9)	O1^xi—Na2—O2^xi	79.7 (8)
O2^ii—W1—O1	92.3 (9)	O5^x—Na2—O2^iv	83.6 (12)
O3—W1—O1	83.3 (15)	O1^iv—Na2—O2^iv	79.7 (8)
O3^iii—W1—O1	82.7 (14)	O1^xi—Na2—O2^iv	151.5 (14)
O2^i—W1—O1^iv	92.3 (9)	O2^xi—Na2—O2^iv	71.9 (13)
O2^ii—W1—O1^iv	171.0 (9)	O5^x—Na2—O3	119.4 (17)
O3—W1—O1^iv	82.7 (14)	O1^iv—Na2—O3	67.0 (10)
O3^iii—W1—O1^iv	83.3 (15)	O1^xi—Na2—O3	67.0 (10)
O1—W1—O1^iv	79.1 (12)	O2^xi—Na2—O3	138.9 (10)
O4—W2—O5	109.4 (14)	O2^iv—Na2—O3	138.9 (10)
O4—W2—O1	108.0 (10)	W2—O1—W1	121.5 (12)
O5—W2—O1	109.9 (10)	W2—O1—Na2^iii	137.8 (15)
O4—W2—O1^v	108.0 (10)	W1—O1—Na2^iii	99.7 (11)
O5—W2—O1^v	109.9 (10)	W1^xii—O2—Na1	129.3 (11)
O1—W2—O1^v	111.5 (17)	W1^xii—O2—Na2^iii	133.7 (13)
O4^vi—Na1—O4	79.3 (13)	Na1—O2—Na2^iii	95.6 (11)
O4^vi—Na1—O2^vii	82.0 (9)	W1^xi—O3—W1	147 (2)
O4—Na1—O2^vii	110.0 (11)	W1^xi—O3—Na2	103.1 (12)
O4^vi—Na1—O2	110.0 (11)	W1—O3—Na2	103.1 (12)
O4—Na1—O2	82.0 (9)	W2—O4—Na1^vi	129.3 (7)
O2^vii—Na1—O2	165.0 (16)	W2—O4—Na1	129.3 (7)
O4^vi—Na1—O5^viii	166.2 (10)	Na1^vi—O4—Na1	100.7 (13)
O4—Na1—O5^viii	97.7 (8)	W2—O5—Na2^xiii	124.4 (16)
O2^vii—Na1—O5^viii	86.5 (10)	W2—O5—Na1^viii	120.3 (10)
O2—Na1—O5^viii	82.7 (9)	Na2^xiii—O5—Na1^viii	96.4 (9)
O4^vi—Na1—O5^ix	97.7 (8)	W2—O5—Na1^xiv	120.3 (10)
O4—Na1—O5^ix	166.2 (10)	Na2^xiii—O5—Na1^xiv	96.4 (9)
O2^vii—Na1—O5^ix	82.7 (9)	Na1^viii—O5—Na1^xiv	91.7 (13)
O2—Na1—O5^ix	86.5 (10)

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

(NaAl_WO4_2_ADT)

Crystal data

Al0.50Na0.50O4Ta	Z = 8
Mr = 269.93	F(000) = 206
Monoclinic, C2/c	Dx = 5.323 Mg m^−3
a = 9.6264 (13) Å	µ = 0.00 mm^−1
b = 5.3844 (9) Å	T = 293 K
c = 12.9956 (2) Å	Nanocrystal
β = 90.176 (11)°	0.00010 × 0.00007 × 0.00003 mm
V = 673.59 (15) Å^3

Data collection

FEI Tecnai F30 ST diffractometer	Rint = 0.241
electron precession and ADT scans	θmax = 0.7°, θmin = 0.1°
1526 measured reflections	h = −11→11
563 independent reflections	k = −6→6
468 reflections with I > 2σ(I)	l = −16→16

Refinement

Refinement on F^2	9 restraints
Least-squares matrix: full	Primary atom site location: structure-invariant direct methods
R[F^2 > 2σ(F^2)] = 0.266	Secondary atom site location: difference Fourier map
wR(F^2) = 0.604	w = 1/[σ^2(Fo^2) + (0.1P)^2] where P = (Fo^2 + 2Fc^2)/3
S = 3.34	(Δ/σ)max < 0.001
563 reflections	Δρmax = 0.80 e Å^−3
24 parameters	Δρmin = −0.53 e Å^−3

Special details

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

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > σ(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
W1	0.8334 (4)	0.4715 (9)	0.6241 (3)	0.049 (2)*
Al1	1.0000	0.0000	0.5000	0.059 (6)*
O1	0.827 (3)	0.558 (5)	0.7593 (18)	0.066 (6)*
O2	0.655 (2)	0.428 (6)	0.579 (2)	0.071 (6)*
O3	0.920 (2)	0.171 (4)	0.6123 (19)	0.054 (5)*
O4	0.9176 (18)	0.714 (4)	0.5603 (16)	0.048 (4)*
Na1	1.0000	−0.096 (10)	0.7500	0.092 (10)*

Geometric parameters (Å, º)

W1—O2	1.83 (2)	Al1—O4^vi	1.900 (18)
W1—O4	1.750 (18)	O1—Na1^i	2.50 (5)
W1—O3	1.83 (2)	O2—Al1^vii	1.85 (2)
W1—O1	1.82 (2)	O3—Na1	2.42 (4)
W1—Na1^i	3.27 (4)	O4—Al1^i	1.900 (18)
Al1—O3	1.89 (2)	Na1—O1^vi	2.50 (5)
Al1—O3^ii	1.89 (2)	Na1—O1^viii	2.50 (5)
Al1—O2^iii	1.85 (2)	Na1—O3^ix	2.42 (4)
Al1—O2^iv	1.85 (2)	Na1—W1^vi	3.27 (4)
Al1—O4^v	1.900 (18)	Na1—W1^viii	3.27 (4)
O2—W1—O4	112.4 (12)	O2^iv—Al1—O4^vi	93.6 (11)
O2—W1—O3	106.8 (13)	O4^v—Al1—O4^vi	180.0000 (10)
O4—W1—O3	114.2 (9)	W1—O1—Na1^i	96.8 (11)
O2—W1—O1	107.7 (12)	W1—O2—Al1^vii	154.9 (19)
O4—W1—O1	106.5 (12)	W1—O3—Al1	133.1 (13)
O3—W1—O1	109.1 (11)	W1—O3—Na1	127.4 (15)
O2—W1—Na1^i	135.3 (11)	Al1—O3—Na1	98.7 (10)
O4—W1—Na1^i	58.4 (9)	W1—O4—Al1^i	174.3 (13)
O3—W1—Na1^i	116.8 (10)	O1^vi—Na1—O1^viii	84 (2)
O1—W1—Na1^i	49.6 (9)	O1^vi—Na1—O3^ix	128.1 (8)
O3—Al1—O3^ii	180.0 (9)	O1^viii—Na1—O3^ix	105.4 (8)
O3—Al1—O2^iii	90.1 (12)	O1^vi—Na1—O3	105.4 (8)
O3^ii—Al1—O2^iii	89.9 (12)	O1^viii—Na1—O3	128.1 (8)
O3—Al1—O2^iv	89.9 (12)	O3^ix—Na1—O3	107 (2)
O3^ii—Al1—O2^iv	90.1 (12)	O1^vi—Na1—W1^vi	33.6 (7)
O2^iii—Al1—O2^iv	180.000 (5)	O1^viii—Na1—W1^vi	76.8 (14)
O3—Al1—O4^v	95.5 (9)	O3^ix—Na1—W1^vi	161.7 (10)
O3^ii—Al1—O4^v	84.5 (9)	O3—Na1—W1^vi	84.2 (7)
O2^iii—Al1—O4^v	93.6 (11)	O1^vi—Na1—W1^viii	76.8 (14)
O2^iv—Al1—O4^v	86.4 (11)	O1^viii—Na1—W1^viii	33.6 (7)
O3—Al1—O4^vi	84.5 (9)	O3^ix—Na1—W1^viii	84.2 (7)
O3^ii—Al1—O4^vi	95.5 (9)	O3—Na1—W1^viii	161.7 (10)
O2^iii—Al1—O4^vi	86.4 (11)	W1^vi—Na1—W1^viii	88.9 (13)

Symmetry codes: (i) x, y+1, z; (ii) −x+2, −y, −z+1; (iii) x+1/2, y−1/2, z; (iv) −x+3/2, −y+1/2, −z+1; (v) −x+2, −y+1, −z+1; (vi) x, y−1, z; (vii) x−1/2, y+1/2, z; (viii) −x+2, y−1, −z+3/2; (ix) −x+2, y, −z+3/2.

(K5Al_W3O11_XRPD)

Crystal data

C2	α = 90°
a = 13.61724 Å	β = 99.166°
b = 7.82839 Å	γ = 90°
c = 19.91903 Å	V = 2096.28 Å^3

Data collection

h = →	l = →
k = →

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Biso*/Beq
W1	0.223	0.04974	−0.00113
W2	0.15137	0.34615	0.14572
W3	0.35933	0.15124	0.13765
W4	0.29572	−0.18732	0.36031
W5	0.08267	0.00174	0.35675
W6	0.21668	−0.3433	0.4895
Al1	0	0.25708	0
Al2	0.5	0.36173	0.5
K1	0.31055	0.3055	0.33464
K2	0.04905	0.55653	0.3103
K3	0.5	−0.15184	0.5
K4	−0.09344	0.13484	0.1818
K5	0.5	0.23589	0
K6	0.15169	−0.11518	0.16477
O1	0.21358	−0.00356	0.32072
O2	0.17954	0.08873	0.43574
O3	0.21497	0.18583	0.08467
O4	0.50863	0.48929	0.42844
O5	0.05995	0.3919	0.06363
O6	0.09024	0.1258	−0.02277
O7	0.17548	−0.19261	0.40948
O8	0.39438	0.23046	0.47999
O9	0.13671	0.54221	0.19444
O10	0.28679	0.29662	0.19389
O11	0.28693	−0.35922	0.29187
O12	0.26172	0.03886	−0.09106
O13	0.48345	0.27126	0.13927
O14	0.20324	−0.17838	0.02369
O15	−0.00609	−0.13196	0.29189
O16	0.32107	−0.34141	0.43477
O17	0.08815	0.15346	0.17837
O18	0.14877	−0.53412	0.44482
O19	0.42324	−0.08839	0.37634
O20	0.37766	−0.04058	0.19882
O21	0.35605	0.04526	0.05035
O22	0.04788	0.23558	0.33872