Structures of Na0.74WO3

Darlington, C.N.W.; Hriljac, J.A.; Knight, K.S.

doi:10.1107/S0108768103015738

Structures of Na_0.74WO₃

C. N. W. Darlington, J. A. Hriljac and K. S. Knight

The structures of the four phases exhibited by Na_0.74WO₃, sodium tungstate, with a change in temperature have been refined from powder diffraction patterns obtained on the high-resolution powder diffractometer (HRPD), ISIS, Rutherford Appleton Laboratory, England. At temperatures above 430 K, the stable phase has the ideal perovskite structure, with space group Pm $\bar 3$ m (No. 221). Below that temperature, the octahedra are tilted about pseudocubic <100> directions; the tilts are produced by the condensation of the normal modes of vibration of the octahedra in the high-temperature cubic phase. Using Glazer's notation, the tilt system undergoes the following sequence:

$a^+a^+a^+ \buildrel {\rm 293\, K} \over \longrightarrow a^+a^+a^0 \buildrel {\rm 343\, K} \over \longrightarrow a^0a^0a^+ \buildrel {\rm 430\, K} \over \longrightarrow a^0a^0a^0 .$

The structural refinements presented here confirm the sequence of the transitions first proposed by Clarke [(1977). Phys. Rev. Lett. 39, 1550-1553]. This is the first time that a structure determination of a perovskite with the tilt system a⁺a⁺a⁰ has been reported in the literature. In addition, we evaluate the weights, or importance, of the condensed modes in each low-temperature phase.

Keywords: tunsgten bronze; tilted octahedra; Glazer's notation; transitions; perovskite.

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Supporting information

	Crystallographic Information File (CIF) https://doi.org/10.1107/S0108768103015738/ws0005sup1.cif Contains datablocks I, II, III, IV, global, G24741_phase_1, G24746_phase_1, G24749_phase_1, G24752_phase_1, G24741_p_01, G24741_p_02, G24746_p_01, G24746_p_02, G24749_p_01, G24749_p_02, G24752_p_01, G24752_p_02, G24741_overall, G24746_overall, G24749_overall, G24752_overall
	Rietveld powder data file (CIF format) https://doi.org/10.1107/S0108768103015738/ws0005Isup2.rtv Contains datablock I
	Rietveld powder data file (CIF format) https://doi.org/10.1107/S0108768103015738/ws0005IIsup3.rtv Contains datablock II
	Rietveld powder data file (CIF format) https://doi.org/10.1107/S0108768103015738/ws0005IIIsup4.rtv Contains datablocks III, G24749_overall, G24749_phase_1, G24749_p_01
	Rietveld powder data file (CIF format) https://doi.org/10.1107/S0108768103015738/ws0005IVsup5.rtv Contains datablock IV

Computing details top

(G24741_phase_1) top

Crystal data top

Na_0.74O₃W	V = 57.41 Å³
M_r = 248.86	Z = 1
Cubic, Pm3m	? radiation, λ = ? Å
a = 3.857719 (7) Å	?; ?, ?; ? × ?; ? mm

Data collection top

Refinement top

Least-squares matrix: full	Profile function: TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.1087 #2 (bet-0) = 0.024227 #3 (bet-1) = 0.010405 #4 (sig-0) = 0.0 #5 (sig-1) = 466.8 #6 (sig-2) = 0.0 #7 (gam-0) = 0.00 #8 (gam-1) = 6.45 #9 (gam-2) = 0.00 #10(gsf ) = 0.00 #11(g1ec ) = 0.00 #12(g2ec ) = 0.00 #13(rstr ) = 0.000 #14(rsta ) = 0.000 #15(rsca ) = 0.000 #16(L11) = 0.000 #17(L22) = 0.000 #18(L33) = 0.000 #19(L12) = 0.000 #20(L13) = 0.000 #21(L23) = 0.000 Peak tails are ignored where the intensity is below 0.0010 times the peak Aniso. broadening axis 0.0 0.0 1.0
R_p = 0.046	32 parameters
R_wp = 0.051	0 restraints
R_exp = 0.044	(Δ/σ)_max = 0.07
χ² = 2.372	Background function: GSAS Background function number 1 with 10 terms. Shifted Chebyshev function of 1st kind 1: 0.790740 2: 0.291302 3: 5.900010E-02 4: 3.989270E-02 5: 3.126530E-02 6: 3.091920E-02 7: 2.270200E-02 8: 2.076490E-02 9: 1.844210E-0210: 1.743170E-02
4404 data points

Crystal data top

Na_0.74O₃W	V = 57.41 Å³
M_r = 248.86	Z = 1
Cubic, Pm3m	? radiation, λ = ? Å
a = 3.857719 (7) Å	?; ?, ?; ? × ?; ? mm

Data collection top

Refinement top

R_p = 0.046	4404 data points
R_wp = 0.051	32 parameters
R_exp = 0.044	0 restraints
χ² = 2.372

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

	x	y	z	U_iso*/U_eq	Occ. (<1)
Na	0.5	0.5	0.5	0.0277 (6)*	0.74
W	0.0	0.0	0.0	0.0084 (3)*
O	0.5	0.0	0.0	0.01589

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
O	0.0089 (5)	0.0194 (3)	0.0194 (3)	0.0	0.0	0.0

Geometric parameters (Å, º) top

Na—Naⁱ	3.8577 (1)	Na—O^xvi	2.7278
Na—Naⁱⁱ	3.8577 (1)	Na—O^xvii	2.7278
Na—Naⁱⁱⁱ	3.8577 (1)	Na—O^xviii	2.7278
Na—Na^iv	3.8577 (1)	W—Na^xix	3.3409
Na—Na^v	3.8577 (1)	W—Na^xx	3.3409
Na—Na^vi	3.8577 (1)	W—Na^xxi	3.3409
Na—W	3.3409	W—Naⁱ	3.3409
Na—W^iv	3.3409	W—Na^xxii	3.3409
Na—W^v	3.3409	W—Naⁱⁱ	3.3409
Na—W^vii	3.3409	W—Naⁱⁱⁱ	3.3409
Na—W^vi	3.3409	W—Na	3.3409
Na—W^viii	3.3409	W—Oⁱ	1.9289
Na—W^ix	3.3409	W—O	1.9289
Na—W^x	3.3409	W—O^xxiii	1.9289
Na—O	2.7278	W—O^xi	1.9289
Na—O^iv	2.7278	W—O^xxiv	1.9289
Na—O^v	2.7278	W—O^xv	1.9289
Na—O^vii	2.7278	O—Na^xxii	2.7278
Na—O^xi	2.7278	O—Naⁱⁱ	2.7278
Na—O^xii	2.7278	O—Naⁱⁱⁱ	2.7278
Na—O^xiii	2.7278	O—Na	2.7278
Na—O^xiv	2.7278	O—W	1.9289
Na—O^xv	2.7278	O—W^vi	1.9289

O—Na—O^iv	90.0000 (1)	O^xii—Na—O^xvi	60.0
O—Na—O^v	90.0000 (1)	O^xii—Na—O^xvii	120.0
O—Na—O^vii	180.0	O^xii—Na—O^xviii	120.0
O—Na—O^xi	60.0000 (1)	O^xiii—Na—O^xiv	90.0000 (1)
O—Na—O^xii	120.0000 (1)	O^xiii—Na—O^xv	120.0
O—Na—O^xiii	60.0000 (1)	O^xiii—Na—O^xvi	120.0
O—Na—O^xiv	120.0000 (1)	O^xiii—Na—O^xvii	60.0
O—Na—O^xv	60.0	O^xiii—Na—O^xviii	60.0
O—Na—O^xvi	120.0	O^xiv—Na—O^xv	120.0
O—Na—O^xvii	60.0	O^xiv—Na—O^xvi	120.0
O—Na—O^xviii	120.0	O^xiv—Na—O^xvii	60.0
O^iv—Na—O^v	180.0	O^xiv—Na—O^xviii	60.0
O^iv—Na—O^vii	90.0000 (1)	O^xv—Na—O^xvi	90.0
O^iv—Na—O^xi	120.0000 (1)	O^xv—Na—O^xvii	90.0
O^iv—Na—O^xii	60.0000 (1)	O^xv—Na—O^xviii	180.0
O^iv—Na—O^xiii	120.0000 (1)	O^xvi—Na—O^xvii	180.0
O^iv—Na—O^xiv	60.0000 (1)	O^xvi—Na—O^xviii	90.0
O^iv—Na—O^xv	60.0	O^xvii—Na—O^xviii	90.0
O^iv—Na—O^xvi	120.0	Oⁱ—W—O	180.0
O^iv—Na—O^xvii	60.0	Oⁱ—W—O^xxiii	90.0
O^iv—Na—O^xviii	120.0	Oⁱ—W—O^xi	90.0
O^v—Na—O^vii	90.0000 (1)	Oⁱ—W—O^xxiv	90.0
O^v—Na—O^xi	60.0000 (1)	Oⁱ—W—O^xv	90.0
O^v—Na—O^xii	120.0000 (1)	O—W—O^xxiii	90.0
O^v—Na—O^xiii	60.0000 (1)	O—W—O^xi	90.0
O^v—Na—O^xiv	120.0000 (1)	O—W—O^xxiv	90.0
O^v—Na—O^xv	120.0	O—W—O^xv	90.0
O^v—Na—O^xvi	60.0	O^xxiii—W—O^xi	180.0
O^v—Na—O^xvii	120.0	O^xxiii—W—O^xxiv	90.0
O^v—Na—O^xviii	60.0	O^xxiii—W—O^xv	90.0
O^vii—Na—O^xi	120.0000 (1)	O^xi—W—O^xxiv	90.0
O^vii—Na—O^xii	60.0000 (1)	O^xi—W—O^xv	90.0
O^vii—Na—O^xiii	120.0000 (1)	O^xxiv—W—O^xv	180.0
O^vii—Na—O^xiv	60.0000 (1)	Na^xxii—O—Naⁱⁱ	90.0000 (1)
O^vii—Na—O^xv	120.0	Na^xxii—O—Naⁱⁱⁱ	90.0000 (1)
O^vii—Na—O^xvi	60.0	Na^xxii—O—Na	180.0
O^vii—Na—O^xvii	120.0	Na^xxii—O—W	90.0
O^vii—Na—O^xviii	60.0	Na^xxii—O—W^vi	90.0
O^xi—Na—O^xii	90.0000 (1)	Naⁱⁱ—O—Naⁱⁱⁱ	180.0
O^xi—Na—O^xiii	90.0000 (1)	Naⁱⁱ—O—Na	90.0000 (1)
O^xi—Na—O^xiv	180.0	Naⁱⁱ—O—W	90.0
O^xi—Na—O^xv	60.0	Naⁱⁱ—O—W^vi	90.0
O^xi—Na—O^xvi	60.0	Naⁱⁱⁱ—O—Na	90.0000 (1)
O^xi—Na—O^xvii	120.0	Naⁱⁱⁱ—O—W	90.0
O^xi—Na—O^xviii	120.0	Naⁱⁱⁱ—O—W^vi	90.0
O^xii—Na—O^xiii	180.0	Na—O—W	90.0
O^xii—Na—O^xiv	90.0000 (1)	Na—O—W^vi	90.0
O^xii—Na—O^xv	60.0	W—O—W^vi	180.0

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

(G24746_phase_1) top

Crystal data top

Na_0.74O₃W	V = 114.35 Å³
M_r = 248.86	Z = 2
Tetragonal, P4/mbm	? radiation, λ = ? Å
a = 5.44556 (2) Å	?; ?, ?; ? × ?; ? mm
c = 3.85598 (3) Å

Data collection top

Refinement top

Least-squares matrix: full	Profile function: TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.1087 #2 (bet-0) = 0.024227 #3 (bet-1) = 0.010405 #4 (sig-0) = 0.0 #5 (sig-1) = 469.4 #6 (sig-2) = 0.0 #7 (gam-0) = 0.00 #8 (gam-1) = 7.11 #9 (gam-2) = 0.00 #10(gsf ) = 0.00 #11(g1ec ) = 0.00 #12(g2ec ) = 0.00 #13(rstr ) = 0.000 #14(rsta ) = 0.000 #15(rsca ) = 0.000 #16(L11) = 0.000 #17(L22) = 0.000 #18(L33) = 0.000 #19(L12) = 0.000 #20(L13) = 0.000 #21(L23) = 0.000 Peak tails are ignored where the intensity is below 0.0010 times the peak Aniso. broadening axis 0.0 0.0 1.0
R_p = 0.048	37 parameters
R_wp = 0.054	0 restraints
R_exp = 0.048	(Δ/σ)_max = 0.05
χ² = 2.250	Background function: GSAS Background function number 1 with 10 terms. Shifted Chebyshev function of 1st kind 1: 0.713459 2: 0.254215 3: 5.217530E-02 4: 3.596190E-02 5: 3.009830E-02 6: 2.752810E-02 7: 2.302580E-02 8: 1.725840E-02 9: 1.697440E-0210: 1.641710E-02
4404 data points

Crystal data top

Na_0.74O₃W	V = 114.35 Å³
M_r = 248.86	Z = 2
Tetragonal, P4/mbm	? radiation, λ = ? Å
a = 5.44556 (2) Å	?; ?, ?; ? × ?; ? mm
c = 3.85598 (3) Å

Data collection top

Refinement top

R_p = 0.048	4404 data points
R_wp = 0.054	37 parameters
R_exp = 0.048	0 restraints
χ² = 2.250

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

	x	y	z	U_iso*/U_eq	Occ. (<1)
Na	0.0	0.5	0.5	0.0227 (6)*	0.74
W	0.0	0.0	0.0	0.0085 (3)*
O1	0.0	0.0	0.5	0.0122
O2	0.23390 (14)	0.73390 (14)	0.0	0.01401

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
O1	0.0150 (10)	0.0150 (10)	0.0065 (13)	0.0	0.0	0.0
O2	0.0126 (6)	0.0126 (6)	0.0168 (9)	0.0039 (7)	0.0	0.0

Geometric parameters (Å, º) top

Na—Naⁱ	3.8560 (1)	W—Na^xviii	3.3363 (1)
Na—Naⁱⁱ	3.8560 (1)	W—Na^xix	3.3363 (1)
Na—Naⁱⁱⁱ	3.8506 (1)	W—Naⁱ	3.3363 (1)
Na—Na^iv	3.8506 (1)	W—Na	3.3363 (1)
Na—Na^v	3.8506 (1)	W—Na^xx	3.3363 (1)
Na—Na^vi	3.8506 (1)	W—Naⁱⁱⁱ	3.3363 (1)
Na—W	3.3363 (1)	W—Na^xxi	3.3363 (1)
Na—Wⁱⁱ	3.3363 (1)	W—Na^v	3.3363 (1)
Na—W^vii	3.3363 (1)	W—O1ⁱ	1.9280 (1)
Na—W^viii	3.3363 (1)	W—O1	1.9280 (1)
Na—W^ix	3.3363 (1)	W—O2^xix	1.9293 (1)
Na—W^x	3.3363 (1)	W—O2^v	1.9293 (1)
Na—W^xi	3.3363 (1)	W—O2^xiv	1.9293 (1)
Na—W^xii	3.3363 (1)	W—O2^xxii	1.9293 (1)
Na—O1	2.7228 (1)	O1—Na^xix	2.7228 (1)
Na—O1^vii	2.7228 (1)	O1—Na	2.7228 (1)
Na—O1^ix	2.7228 (1)	O1—Naⁱⁱⁱ	2.7228 (1)
Na—O1^xi	2.7228 (1)	O1—Na^v	2.7228 (1)
Na—O2	2.6386 (7)	O1—W	1.9280 (1)
Na—O2ⁱⁱ	2.6386 (7)	O1—Wⁱⁱ	1.9280 (1)
Na—O2^v	2.8136 (8)	O2—Naⁱ	2.6386 (7)
Na—O2^xiii	2.8136 (8)	O2—Na	2.6386 (7)
Na—O2^xiv	2.6386 (7)	O2—Na^xxiii	2.8136 (8)
Na—O2^xv	2.6386 (7)	O2—Na^vi	2.8136 (8)
Na—O2^xvi	2.8136 (8)	O2—W^vii	1.9293 (1)
Na—O2^xvii	2.8136 (8)	O2—W^xi	1.9293 (1)

O1—Na—O1^vii	180.0	O1ⁱ—W—O2^xxii	90.0
O1—Na—O1^ix	90.0	O1—W—O2^xix	90.0
O1—Na—O1^xi	90.0	O1—W—O2^v	90.0
O1—Na—O2	118.865 (10)	O1—W—O2^xiv	90.0
O1—Na—O2ⁱⁱ	118.865 (10)	O1—W—O2^xxii	90.0
O1—Na—O2^xiv	61.136 (10)	O2^xix—W—O2^v	90.0
O1—Na—O2^xv	61.136 (10)	O2^xix—W—O2^xiv	180.0
O1^vii—Na—O1^ix	90.0	O2^xix—W—O2^xxii	90.0
O1^vii—Na—O1^xi	90.0	O2^v—W—O2^xiv	90.0
O1^vii—Na—O2	61.136 (10)	O2^v—W—O2^xxii	180.0
O1^vii—Na—O2ⁱⁱ	61.136 (10)	O2^xiv—W—O2^xxii	90.0
O1^vii—Na—O2^xiv	118.865 (10)	Na^xix—O1—Na	180.0
O1^vii—Na—O2^xv	118.865 (10)	Na^xix—O1—Naⁱⁱⁱ	90.0
O1^ix—Na—O1^xi	180.0	Na^xix—O1—Na^v	90.0
O1^ix—Na—O2	118.865 (10)	Na^xix—O1—W	90.0
O1^ix—Na—O2ⁱⁱ	118.865 (10)	Na^xix—O1—Wⁱⁱ	90.0
O1^ix—Na—O2^xiv	61.136 (10)	Na—O1—Naⁱⁱⁱ	90.0
O1^ix—Na—O2^xv	61.136 (10)	Na—O1—Na^v	90.0
O1^xi—Na—O2	61.136 (10)	Na—O1—W	90.0
O1^xi—Na—O2ⁱⁱ	61.136 (10)	Na—O1—Wⁱⁱ	90.0
O1^xi—Na—O2^xiv	118.865 (10)	Naⁱⁱⁱ—O1—Na^v	180.0
O1^xi—Na—O2^xv	118.865 (10)	Naⁱⁱⁱ—O1—W	90.0
O2—Na—O2ⁱⁱ	93.89 (3)	Naⁱⁱⁱ—O1—Wⁱⁱ	90.0
O2—Na—O2^xiv	86.11 (3)	Na^v—O1—W	90.0
O2—Na—O2^xv	180.0	Na^v—O1—Wⁱⁱ	90.0
O2ⁱⁱ—Na—O2^xiv	179.9657	W—O1—Wⁱⁱ	180.0
O2ⁱⁱ—Na—O2^xv	86.11 (3)	Naⁱ—O2—Na	93.89 (3)
O2^xiv—Na—O2^xv	93.89 (3)	Naⁱ—O2—W^vii	92.51 (2)
O1ⁱ—W—O1	180.0	Naⁱ—O2—W^xi	92.51 (2)
O1ⁱ—W—O2^xix	90.0	Na—O2—W^vii	92.51 (2)
O1ⁱ—W—O2^v	90.0	Na—O2—W^xi	92.51 (2)
O1ⁱ—W—O2^xiv	90.0	W^vii—O2—W^xi	172.63 (6)

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

(G24749_phase_1) top

Crystal data top

Na_0.74O₃W	V = 456.32 Å³
M_r = 248.86	Z = 8
Tetragonal, I4/mmm	? radiation, λ = ? Å
a = 7.70190 (3) Å	?; ?, ?; ? × ?; ? mm
c = 7.69267 (6) Å

Data collection top

Refinement top

Least-squares matrix: full	Profile function: TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.1087 #2 (bet-0) = 0.024227 #3 (bet-1) = 0.010405 #4 (sig-0) = 0.0 #5 (sig-1) = 481.3 #6 (sig-2) = 0.0 #7 (gam-0) = 0.00 #8 (gam-1) = 7.01 #9 (gam-2) = 0.00 #10(gsf ) = 0.00 #11(g1ec ) = 0.00 #12(g2ec ) = 0.00 #13(rstr ) = 0.000 #14(rsta ) = 0.000 #15(rsca ) = 0.000 #16(L11) = 0.000 #17(L22) = 0.000 #18(L33) = 0.000 #19(L12) = 0.000 #20(L13) = 0.000 #21(L23) = 0.000 Peak tails are ignored where the intensity is below 0.0010 times the peak Aniso. broadening axis 0.0 0.0 1.0
R_p = 0.049	43 parameters
R_wp = 0.056	0 restraints
R_exp = 0.048	(Δ/σ)_max = 0.04
χ² = 2.434	Background function: GSAS Background function number 1 with 10 terms. Shifted Chebyshev function of 1st kind 1: 0.700080 2: 0.250900 3: 5.047870E-02 4: 3.875940E-02 5: 3.333130E-02 6: 3.318560E-02 7: 2.564440E-02 8: 2.055490E-02 9: 1.710380E-0210: 1.936660E-02
4404 data points

Crystal data top

Na_0.74O₃W	V = 456.32 Å³
M_r = 248.86	Z = 8
Tetragonal, I4/mmm	? radiation, λ = ? Å
a = 7.70190 (3) Å	?; ?, ?; ? × ?; ? mm
c = 7.69267 (6) Å

Data collection top

Refinement top

R_p = 0.049	4404 data points
R_wp = 0.056	43 parameters
R_exp = 0.048	0 restraints
χ² = 2.434

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

	x	y	z	U_iso*/U_eq	Occ. (<1)
Na1	0.0	0.0	0.0	0.017 (7)*	0.78743
Na2	0.0	0.0	0.5	0.016 (10)*	0.67771
Na3	0.5	0.0	0.0	0.021 (7)*	0.74743
W	0.25	0.25	0.25	0.0077 (3)*
O1	0.2348 (3)	0.2348 (3)	0.0	0.01152
O2	0.0	0.2502 (10)	0.2645 (3)	0.01221

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
O1	0.0140 (11)	0.0140 (11)	0.0067 (14)	0.000 (2)	0.0	0.0
O2	0.0088 (8)	0.0132 (12)	0.0146 (11)	0.0	0.0	0.0025 (19)

Geometric parameters (Å, º) top

Na1—Na2ⁱ	3.8463 (1)	Na3—Na1	3.8510 (1)
Na1—Na2	3.8463 (1)	Na3—Na1^xxii	3.8510 (1)
Na1—Na3ⁱⁱ	3.8510 (1)	Na3—Na2^xxiii	3.8510 (1)
Na1—Na3	3.8510 (1)	Na3—Na2^xxiv	3.8510 (1)
Na1—Na3ⁱⁱⁱ	3.8510 (1)	Na3—Na3^xxv	3.8463 (1)
Na1—Na3^iv	3.8510 (1)	Na3—Na3^xv	3.8463 (1)
Na1—W	3.3337 (1)	Na3—W	3.3337 (1)
Na1—W^iv	3.3337 (1)	Na3—W^xxvi	3.3337 (1)
Na1—W^v	3.3337 (1)	Na3—W^xxvii	3.3337 (1)
Na1—W^vi	3.3337 (1)	Na3—W^vi	3.3337 (1)
Na1—W^vii	3.3337 (1)	Na3—W^xxviii	3.3337 (1)
Na1—W^viii	3.3337 (1)	Na3—W^viii	3.3337 (1)
Na1—W^ix	3.3337 (1)	Na3—W^ix	3.3337 (1)
Na1—W^x	3.3337 (1)	Na3—W^xxix	3.3337 (1)
Na1—O1	2.557 (4)	Na3—O1	2.7281 (2)
Na1—O1^iv	2.557 (4)	Na3—O1^xxvi	2.7281 (2)
Na1—O1^v	2.557 (4)	Na3—O1^xxvii	2.7281 (2)
Na1—O1^vi	2.557 (4)	Na3—O1^vi	2.7281 (2)
Na1—O2	2.802 (5)	Na3—O2^xxvi	2.800 (6)
Na1—O2^iv	2.802 (5)	Na3—O2^vi	2.800 (6)
Na1—O2^v	2.802 (5)	Na3—O2^viii	2.800 (6)
Na1—O2^vi	2.802 (5)	Na3—O2^xxix	2.800 (6)
Na1—O2^vii	2.802 (5)	Na3—O2^xxiii	2.643 (6)
Na1—O2^viii	2.802 (5)	Na3—O2^xxx	2.643 (6)
Na1—O2^ix	2.802 (5)	Na3—O2^xxxi	2.643 (6)
Na1—O2^x	2.802 (5)	Na3—O2^xxxii	2.643 (6)
Na2—Na1	3.8463 (1)	W—Na1	3.3337 (1)
Na2—Na1^xi	3.8463 (1)	W—Na1^xxxiii	3.3337 (1)
Na2—Na3^xii	3.8510 (1)	W—Na2	3.3337 (1)
Na2—Na3^xiii	3.8510 (1)	W—Na2^xxiv	3.3337 (1)
Na2—Na3^xiv	3.8510 (1)	W—Na3	3.3337 (1)
Na2—Na3^xv	3.8510 (1)	W—Na3^iv	3.3337 (1)
Na2—W	3.3337 (1)	W—Na3^xiii	3.3337 (1)
Na2—W^iv	3.3337 (1)	W—Na3^xv	3.3337 (1)
Na2—W^v	3.3337 (1)	W—O1	1.9303 (3)
Na2—W^vi	3.3337 (1)	W—O1^xx	1.9303 (3)
Na2—W^xvi	3.3337 (1)	W—O2	1.9287 (1)
Na2—W^xvii	3.3337 (1)	W—O2^vi	1.9287 (1)
Na2—W^xviii	3.3337 (1)	W—O2^xxxi	1.9287 (1)
Na2—W^xix	3.3337 (1)	W—O2^xxxiv	1.9287 (1)
Na2—O1^xii	2.889 (4)	O1—Na1	2.557 (4)
Na2—O1^xv	2.889 (4)	O1—Na2^xxiv	2.889 (4)
Na2—O1^xx	2.889 (4)	O1—Na3	2.7281 (2)
Na2—O1^xxi	2.889 (4)	O1—Na3^iv	2.7281 (2)
Na2—O2	2.645 (6)	O1—W	1.9303 (3)
Na2—O2^iv	2.645 (6)	O1—W^ix	1.9303 (3)
Na2—O2^v	2.645 (6)	O2—Na1	2.802 (5)
Na2—O2^vi	2.645 (6)	O2—Na2	2.645 (6)
Na2—O2^xvi	2.645 (6)	O2—Na3^iv	2.800 (6)
Na2—O2^xvii	2.645 (6)	O2—Na3^xiii	2.643 (6)
Na2—O2^xviii	2.645 (6)	O2—W	1.9287 (1)
Na2—O2^xix	2.645 (6)	O2—W^iv	1.9287 (1)

O1—Na1—O1^iv	90.0	O1^vi—Na3—O2^xxiii	61.15 (9)
O1—Na1—O1^v	179.972	O1^vi—Na3—O2^xxx	118.85 (9)
O1—Na1—O1^vi	90.0	O1^vi—Na3—O2^xxxi	118.85 (9)
O1^iv—Na1—O1^v	90.0	O1^vi—Na3—O2^xxxii	61.15 (9)
O1^iv—Na1—O1^vi	179.9657	O2^xxvi—Na3—O2^vi	86.8 (2)
O1^v—Na1—O1^vi	90.0	O2^xxvi—Na3—O2^viii	180.0
O2—Na2—O2^iv	62.02 (13)	O2^xxvi—Na3—O2^xxix	93.2 (2)
O2—Na2—O2^v	93.5 (2)	O2^xxvi—Na3—O2^xxiii	119.88 (13)
O2—Na2—O2^vi	62.02 (13)	O2^xxvi—Na3—O2^xxx	119.88 (13)
O2—Na2—O2^xvi	180.0	O2^xxvi—Na3—O2^xxxi	60.12 (13)
O2—Na2—O2^xvii	117.98 (13)	O2^xxvi—Na3—O2^xxxii	60.12 (13)
O2—Na2—O2^xviii	86.5 (2)	O2^vi—Na3—O2^viii	93.2 (2)
O2—Na2—O2^xix	117.98 (13)	O2^vi—Na3—O2^xxix	180.0
O2^iv—Na2—O2^v	62.02 (13)	O2^vi—Na3—O2^xxiii	119.88 (13)
O2^iv—Na2—O2^vi	93.5 (2)	O2^vi—Na3—O2^xxx	119.88 (13)
O2^iv—Na2—O2^xvi	117.98 (13)	O2^vi—Na3—O2^xxxi	60.12 (13)
O2^iv—Na2—O2^xvii	180.0	O2^vi—Na3—O2^xxxii	60.12 (13)
O2^iv—Na2—O2^xviii	117.98 (13)	O2^viii—Na3—O2^xxix	86.8 (2)
O2^iv—Na2—O2^xix	86.5 (2)	O2^viii—Na3—O2^xxiii	60.12 (13)
O2^v—Na2—O2^vi	62.02 (13)	O2^viii—Na3—O2^xxx	60.12 (13)
O2^v—Na2—O2^xvi	86.5 (2)	O2^viii—Na3—O2^xxxi	119.88 (13)
O2^v—Na2—O2^xvii	117.98 (13)	O2^viii—Na3—O2^xxxii	119.88 (13)
O2^v—Na2—O2^xviii	180.0	O2^xxix—Na3—O2^xxiii	60.12 (13)
O2^v—Na2—O2^xix	117.98 (13)	O2^xxix—Na3—O2^xxx	60.12 (13)
O2^vi—Na2—O2^xvi	117.98 (13)	O2^xxix—Na3—O2^xxxi	119.88 (13)
O2^vi—Na2—O2^xvii	86.5 (2)	O2^xxix—Na3—O2^xxxii	119.88 (13)
O2^vi—Na2—O2^xviii	117.98 (13)	O2^xxiii—Na3—O2^xxx	93.4 (3)
O2^vi—Na2—O2^xix	180.0	O2^xxiii—Na3—O2^xxxi	179.972
O2^xvi—Na2—O2^xvii	62.02 (13)	O2^xxiii—Na3—O2^xxxii	86.6 (3)
O2^xvi—Na2—O2^xviii	93.5 (2)	O2^xxx—Na3—O2^xxxi	86.6 (3)
O2^xvi—Na2—O2^xix	62.02 (13)	O2^xxx—Na3—O2^xxxii	180.0
O2^xvii—Na2—O2^xviii	62.02 (13)	O2^xxxi—Na3—O2^xxxii	93.4 (3)
O2^xvii—Na2—O2^xix	93.5 (2)	O1—W—O1^xx	180.0
O2^xviii—Na2—O2^xix	62.02 (13)	O1—W—O2	89.82 (14)
O1—Na3—O1^xxvi	96.98 (15)	O1—W—O2^vi	89.82 (14)
O1—Na3—O1^xxvii	180.0	O1—W—O2^xxxi	90.18 (14)
O1—Na3—O1^vi	83.02 (15)	O1—W—O2^xxxiv	90.18 (14)
O1—Na3—O2^xxvi	120.96 (9)	O1^xx—W—O2	90.18 (14)
O1—Na3—O2^vi	59.04 (9)	O1^xx—W—O2^vi	90.18 (14)
O1—Na3—O2^viii	59.04 (9)	O1^xx—W—O2^xxxi	89.82 (14)
O1—Na3—O2^xxix	120.96 (9)	O1^xx—W—O2^xxxiv	89.82 (14)
O1—Na3—O2^xxiii	118.85 (9)	O2—W—O2^vi	89.9 (5)
O1—Na3—O2^xxx	61.15 (9)	O2—W—O2^xxxi	179.9802
O1—Na3—O2^xxxi	61.15 (9)	O2—W—O2^xxxiv	90.1 (5)
O1—Na3—O2^xxxii	118.85 (9)	O2^vi—W—O2^xxxi	90.1 (5)
O1^xxvi—Na3—O1^xxvii	83.02 (15)	O2^vi—W—O2^xxxiv	179.9802
O1^xxvi—Na3—O1^vi	180.0	O2^xxxi—W—O2^xxxiv	89.9 (5)
O1^xxvi—Na3—O2^xxvi	59.04 (9)	Na1—O1—Na3	93.49 (8)
O1^xxvi—Na3—O2^vi	120.96 (9)	Na1—O1—Na3^iv	93.49 (8)
O1^xxvi—Na3—O2^viii	120.96 (9)	Na1—O1—W	94.93 (11)
O1^xxvi—Na3—O2^xxix	59.04 (9)	Na1—O1—W^ix	94.93 (11)
O1^xxvi—Na3—O2^xxiii	118.85 (9)	Na3—O1—Na3^iv	173.02 (15)
O1^xxvi—Na3—O2^xxx	61.15 (9)	Na3—O1—W	89.700 (13)
O1^xxvi—Na3—O2^xxxi	61.15 (9)	Na3—O1—W^ix	89.700 (13)
O1^xxvi—Na3—O2^xxxii	118.85 (9)	Na3^iv—O1—W	89.700 (13)
O1^xxvii—Na3—O1^vi	96.98 (15)	Na3^iv—O1—W^ix	89.700 (13)
O1^xxvii—Na3—O2^xxvi	59.04 (9)	W—O1—W^ix	170.1 (2)
O1^xxvii—Na3—O2^vi	120.96 (9)	Na2—O2—Na3^iv	176.6 (2)
O1^xxvii—Na3—O2^viii	120.96 (9)	Na2—O2—Na3^xiii	93.48 (8)
O1^xxvii—Na3—O2^xxix	59.04 (9)	Na2—O2—W	92.23 (18)
O1^xxvii—Na3—O2^xxiii	61.15 (9)	Na2—O2—W^iv	92.23 (18)
O1^xxvii—Na3—O2^xxx	118.85 (9)	Na3^iv—O2—Na3^xiii	89.9 (2)
O1^xxvii—Na3—O2^xxxi	118.85 (9)	Na3^iv—O2—W	87.63 (17)
O1^xxvii—Na3—O2^xxxii	61.15 (9)	Na3^iv—O2—W^iv	87.63 (17)
O1^vi—Na3—O2^xxvi	120.96 (9)	Na3^xiii—O2—W	92.31 (17)
O1^vi—Na3—O2^vi	59.04 (9)	Na3^xiii—O2—W^iv	92.31 (17)
O1^vi—Na3—O2^viii	59.04 (9)	W—O2—W^iv	173.38 (14)
O1^vi—Na3—O2^xxix	120.96 (9)

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

(G24752_phase_1) top

Crystal data top

Na_0.74O₃W	V = 455.34 Å³
M_r = 248.86	Z = 8
Cubic, Im3	? radiation, λ = ? Å
a = 7.693272 (17) Å	?; ?, ?; ? × ?; ? mm

Data collection top

Refinement top

Least-squares matrix: full	Profile function: TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.1087 #2 (bet-0) = 0.024227 #3 (bet-1) = 0.010405 #4 (sig-0) = 0.0 #5 (sig-1) = 525.5 #6 (sig-2) = 0.0 #7 (gam-0) = 0.00 #8 (gam-1) = 9.12 #9 (gam-2) = 0.00 #10(gsf ) = 0.00 #11(g1ec ) = 0.00 #12(g2ec ) = 0.00 #13(rstr ) = 0.000 #14(rsta ) = 0.000 #15(rsca ) = 0.000 #16(L11) = 0.000 #17(L22) = 0.000 #18(L33) = 0.000 #19(L12) = 0.000 #20(L13) = 0.000 #21(L23) = 0.000 Peak tails are ignored where the intensity is below 0.0010 times the peak Aniso. broadening axis 0.0 0.0 1.0
R_p = 0.053	37 parameters
R_wp = 0.059	0 restraints
R_exp = 0.047	(Δ/σ)_max = 0.05
χ² = 2.789	Background function: GSAS Background function number 1 with 10 terms. Shifted Chebyshev function of 1st kind 1: 0.705347 2: 0.243401 3: 5.377270E-02 4: 3.556460E-02 5: 3.400190E-02 6: 2.800950E-02 7: 2.381710E-02 8: 1.530960E-02 9: 1.581240E-0210: 1.597880E-02
4404 data points

Crystal data top

Na_0.74O₃W	V = 455.34 Å³
M_r = 248.86	Z = 8
Cubic, Im3	? radiation, λ = ? Å
a = 7.693272 (17) Å	?; ?, ?; ? × ?; ? mm

Data collection top

Refinement top

R_p = 0.053	4404 data points
R_wp = 0.059	37 parameters
R_exp = 0.047	0 restraints
χ² = 2.789

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

	x	y	z	U_iso*/U_eq	Occ. (<1)
Na1	0.0	0.0	0.0	0.011 (7)*	0.95606
Na2	0.0	0.5	0.5	0.018 (4)*	0.66798
W	0.25	0.25	0.25	0.0065 (3)*
O	0.0	0.2346 (4)	0.2629 (4)	0.00999

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
O	0.0073 (5)	0.013 (3)	0.010 (3)	0.0	0.0	−0.0010 (9)

Geometric parameters (Å, º) top

Na1—Na2ⁱ	3.8466 (1)	Na2—W^xxvi	3.3313 (1)
Na1—Na2ⁱⁱ	3.8466 (1)	Na2—W^xxvii	3.3313 (1)
Na1—Na2ⁱⁱⁱ	3.8466 (1)	Na2—W^xxviii	3.3313 (1)
Na1—Na2^iv	3.8466 (1)	Na2—W^xxix	3.3313 (1)
Na1—Na2^v	3.8466 (1)	Na2—O	2.738 (4)
Na1—Na2^vi	3.8466 (1)	Na2—O^xxiv	2.738 (4)
Na1—W	3.3313 (1)	Na2—O^xxx	2.738 (4)
Na1—W^vii	3.3313 (1)	Na2—O^xxxi	2.738 (4)
Na1—W^viii	3.3313 (1)	Na2—O^xxii	2.5661 (9)
Na1—W^ix	3.3313 (1)	Na2—O^xxiii	2.8739 (9)
Na1—W^x	3.3313 (1)	Na2—O^xxxii	2.5661 (9)
Na1—W^xi	3.3313 (1)	Na2—O^xxxiii	2.8739 (9)
Na1—W^xii	3.3313 (1)	Na2—O^xxxiv	2.5661 (9)
Na1—W^xiii	3.3313 (1)	Na2—O^xxxv	2.8739 (9)
Na1—O	2.711 (4)	Na2—O^xxxvi	2.5661 (9)
Na1—O^xiv	2.711 (4)	Na2—O^xxxvii	2.8739 (9)
Na1—O^xv	2.711 (4)	W—Na1	3.3313 (1)
Na1—O^vii	2.711 (4)	W—Na1^xxi	3.3313 (1)
Na1—O^viii	2.711 (4)	W—Na2	3.3313 (1)
Na1—O^ix	2.711 (4)	W—Na2^xiv	3.3313 (1)
Na1—O^x	2.711 (4)	W—Na2^xv	3.3313 (1)
Na1—O^xi	2.711 (4)	W—Na2ⁱⁱ	3.3313 (1)
Na1—O^xvi	2.711 (4)	W—Na2^iv	3.3313 (1)
Na1—O^xvii	2.711 (4)	W—Na2^vi	3.3313 (1)
Na1—O^xviii	2.711 (4)	W—O	1.9295 (1)
Na1—O^xix	2.711 (4)	W—O^xiv	1.9295 (1)
Na2—Na1^xx	3.8466 (1)	W—O^xv	1.9295 (1)
Na2—Na1^xxi	3.8466 (1)	W—O^xxxiv	1.9295 (1)
Na2—Na2^iv	3.8466 (1)	W—O^xxxv	1.9295 (1)
Na2—Na2^xxii	3.8466 (1)	W—O^xxxviii	1.9295 (1)
Na2—Na2^vi	3.8466 (1)	O—Na1	2.711 (4)
Na2—Na2^xxiii	3.8466 (1)	O—Na2	2.738 (4)
Na2—W	3.3313 (1)	O—Na2^iv	2.8739 (9)
Na2—W^xxiv	3.3313 (1)	O—Na2^vi	2.5661 (9)
Na2—W^viii	3.3313 (1)	O—W	1.9295 (1)
Na2—W^xxv	3.3313 (1)	O—W^viii	1.9295 (1)

O—Na1—O^xiv	60.213 (3)	O^xvi—Na1—O^xvii	96.51 (4)
O—Na1—O^xv	60.213 (3)	O^xvi—Na1—O^xviii	60.213 (3)
O—Na1—O^vii	96.51 (4)	O^xvi—Na1—O^xix	119.787 (3)
O—Na1—O^viii	60.213 (3)	O^xvii—Na1—O^xviii	119.787 (3)
O—Na1—O^ix	119.787 (3)	O^xvii—Na1—O^xix	119.787 (3)
O—Na1—O^x	119.787 (3)	O^xviii—Na1—O^xix	119.787 (3)
O—Na1—O^xi	119.787 (3)	O—Na2—O^xxiv	83.56 (4)
O—Na1—O^xvi	179.972	O—Na2—O^xxx	180.0
O—Na1—O^xvii	83.49 (4)	O—Na2—O^xxxi	96.44 (4)
O—Na1—O^xviii	119.787 (3)	O—Na2—O^xxii	117.94 (5)
O—Na1—O^xix	60.213 (3)	O—Na2—O^xxxii	117.94 (5)
O^xiv—Na1—O^xv	60.213 (3)	O—Na2—O^xxxiv	62.06 (5)
O^xiv—Na1—O^vii	119.787 (3)	O—Na2—O^xxxvi	62.06 (5)
O^xiv—Na1—O^viii	96.51 (4)	O^xxiv—Na2—O^xxx	96.44 (4)
O^xiv—Na1—O^ix	60.213 (3)	O^xxiv—Na2—O^xxxi	179.9802
O^xiv—Na1—O^x	180.0	O^xxiv—Na2—O^xxii	62.06 (5)
O^xiv—Na1—O^xi	119.787 (3)	O^xxiv—Na2—O^xxxii	62.06 (5)
O^xiv—Na1—O^xvi	119.787 (3)	O^xxiv—Na2—O^xxxiv	117.94 (5)
O^xiv—Na1—O^xvii	60.213 (3)	O^xxiv—Na2—O^xxxvi	117.94 (5)
O^xiv—Na1—O^xviii	83.49 (4)	O^xxx—Na2—O^xxxi	83.56 (4)
O^xiv—Na1—O^xix	119.787 (3)	O^xxx—Na2—O^xxii	62.06 (5)
O^xv—Na1—O^vii	60.213 (3)	O^xxx—Na2—O^xxxii	62.06 (5)
O^xv—Na1—O^viii	119.787 (3)	O^xxx—Na2—O^xxxiv	117.94 (5)
O^xv—Na1—O^ix	96.51 (4)	O^xxx—Na2—O^xxxvi	117.94 (5)
O^xv—Na1—O^x	119.787 (3)	O^xxxi—Na2—O^xxii	117.94 (5)
O^xv—Na1—O^xi	179.972	O^xxxi—Na2—O^xxxii	117.94 (5)
O^xv—Na1—O^xvi	119.787 (3)	O^xxxi—Na2—O^xxxiv	62.06 (5)
O^xv—Na1—O^xvii	119.787 (3)	O^xxxi—Na2—O^xxxvi	62.06 (5)
O^xv—Na1—O^xviii	60.213 (3)	O^xxii—Na2—O^xxxii	90.62 (19)
O^xv—Na1—O^xix	83.49 (4)	O^xxii—Na2—O^xxxiv	179.972
O^vii—Na1—O^viii	119.787 (3)	O^xxii—Na2—O^xxxvi	89.38 (19)
O^vii—Na1—O^ix	119.787 (3)	O^xxxii—Na2—O^xxxiv	89.38 (19)
O^vii—Na1—O^x	60.213 (3)	O^xxxii—Na2—O^xxxvi	179.9802
O^vii—Na1—O^xi	119.787 (3)	O^xxxiv—Na2—O^xxxvi	90.62 (19)
O^vii—Na1—O^xvi	83.49 (4)	O—W—O^xiv	89.60 (18)
O^vii—Na1—O^xvii	179.972	O—W—O^xv	89.60 (18)
O^vii—Na1—O^xviii	60.213 (3)	O—W—O^xxxiv	90.40 (18)
O^vii—Na1—O^xix	60.213 (3)	O—W—O^xxxv	90.40 (18)
O^viii—Na1—O^ix	119.787 (3)	O—W—O^xxxviii	179.972
O^viii—Na1—O^x	83.49 (4)	O^xiv—W—O^xv	89.60 (18)
O^viii—Na1—O^xi	60.213 (3)	O^xiv—W—O^xxxiv	179.972
O^viii—Na1—O^xvi	119.787 (3)	O^xiv—W—O^xxxv	90.40 (18)
O^viii—Na1—O^xvii	60.213 (3)	O^xiv—W—O^xxxviii	90.40 (18)
O^viii—Na1—O^xviii	180.0	O^xv—W—O^xxxiv	90.40 (18)
O^viii—Na1—O^xix	60.213 (3)	O^xv—W—O^xxxv	179.972
O^ix—Na1—O^x	119.787 (3)	O^xv—W—O^xxxviii	90.40 (18)
O^ix—Na1—O^xi	83.49 (4)	O^xxxiv—W—O^xxxv	89.60 (18)
O^ix—Na1—O^xvi	60.213 (3)	O^xxxiv—W—O^xxxviii	89.60 (18)
O^ix—Na1—O^xvii	60.213 (3)	O^xxxv—W—O^xxxviii	89.60 (18)
O^ix—Na1—O^xviii	60.213 (3)	Na1—O—Na2	173.52 (4)
O^ix—Na1—O^xix	179.972	Na1—O—Na2^vi	93.56 (10)
O^x—Na1—O^xi	60.213 (3)	Na1—O—W	90.15 (13)
O^x—Na1—O^xvi	60.213 (3)	Na1—O—W^viii	90.15 (13)
O^x—Na1—O^xvii	119.787 (3)	Na2—O—Na2^vi	92.91 (11)
O^x—Na1—O^xviii	96.51 (4)	Na2—O—W	89.33 (12)
O^x—Na1—O^xix	60.213 (3)	Na2—O—W^viii	89.33 (12)
O^xi—Na1—O^xvi	60.213 (3)	Na2^vi—O—W	94.57 (3)
O^xi—Na1—O^xvii	60.213 (3)	Na2^vi—O—W^viii	94.57 (3)
O^xi—Na1—O^xviii	119.787 (3)	W—O—W^viii	170.81 (6)
O^xi—Na1—O^xix	96.51 (4)

Symmetry codes: (i) x−1/2, y−1/2, z−1/2; (ii) x+1/2, y−1/2, z−1/2; (iii) z−1/2, x−1/2, y−1/2; (iv) z−1/2, x+1/2, y−1/2; (v) y−1/2, z−1/2, x−1/2; (vi) y−1/2, z−1/2, x+1/2; (vii) x, y, −z; (viii) −z, x, y; (ix) y, −z, x; (x) −z, x, −y; (xi) −y, −z, x; (xii) y, −z, −x; (xiii) −x, −y, −z; (xiv) z, x, y; (xv) y, z, x; (xvi) x, −y, −z; (xvii) −x, −y, z; (xviii) z, −x, −y; (xix) −y, z, −x; (xx) x−1/2, y+1/2, z+1/2; (xxi) x+1/2, y+1/2, z+1/2; (xxii) z−1/2, x+1/2, y+1/2; (xxiii) y−1/2, z+1/2, x+1/2; (xxiv) x, y, −z+1; (xxv) y, −z+1, x; (xxvi) −z, x, −y+1; (xxvii) −y, −z+1, x; (xxviii) y, −z+1, −x+1; (xxix) −x, −y+1, −z+1; (xxx) x, −y+1, −z+1; (xxxi) −x, −y+1, z; (xxxii) −z+1/2, x+1/2, y+1/2; (xxxiii) y−1/2, −z+1/2, x+1/2; (xxxiv) −z+1/2, x+1/2, −y+1/2; (xxxv) −y+1/2, −z+1/2, x+1/2; (xxxvi) z−1/2, −x+1/2, −y+1/2; (xxxvii) −y+1/2, z+1/2, −x+1/2; (xxxviii) x+1/2, −y+1/2, −z+1/2.

Experimental details

	(G24741_phase_1)	(G24746_phase_1)	(G24749_phase_1)	(G24752_phase_1)
Crystal data
Chemical formula	Na_0.74O₃W	Na_0.74O₃W	Na_0.74O₃W	Na_0.74O₃W
M_r	248.86	248.86	248.86	248.86
Crystal system, space group	Cubic, Pm3m	Tetragonal, P4/mbm	Tetragonal, I4/mmm	Cubic, Im3
Temperature (K)	?	?	?	?
a, b, c (Å)	3.857719 (7), 3.857719, 3.857719	5.44556 (2), 5.445564, 3.85598 (3)	7.70190 (3), 7.701902, 7.69267 (6)	7.693272 (17), 7.693272, 7.693272
α, β, γ (°)	90, 90, 90	90, 90, 90	90, 90, 90	90, 90, 90
V (Å³)	57.41	114.35	456.32	455.34
Z	1	2	8	8
Radiation type	?, λ = ? Å	?, λ = ? Å	?, λ = ? Å	?, λ = ? Å
Specimen shape, size (mm)	?; ?, ?; ? × ?; ?	?; ?, ?; ? × ?; ?	?; ?, ?; ? × ?; ?	?; ?, ?; ? × ?; ?

Data collection
Diffractometer	?; ?	?; ?	?; ?	?; ?
Specimen mounting	?; ?	?; ?	?; ?	?; ?
Data collection mode	?; ?	?; ?	?; ?	?; ?
Scan method	?; ?	?; ?	?; ?	?; ?
2θ values (°)	2θ_min = ? 2θ_max = ? 2θ_step = ?	2θ_min = ? 2θ_max = ? 2θ_step = ?	2θ_min = ? 2θ_max = ? 2θ_step = ?	2θ_min = ? 2θ_max = ? 2θ_step = ?

Refinement
R factors and goodness of fit	R_p = 0.046, R_wp = 0.051, R_exp = 0.044, χ² = 2.372	R_p = 0.048, R_wp = 0.054, R_exp = 0.048, χ² = 2.250	R_p = 0.049, R_wp = 0.056, R_exp = 0.048, χ² = 2.434	R_p = 0.053, R_wp = 0.059, R_exp = 0.047, χ² = 2.789
No. of data points	4404	4404	4404	4404
No. of parameters	32	37	43	37

Computer programs: GSAS.

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