X-ray diffraction study of oxygen-conducting compounds Ln₂Mo₂O₉ (Ln = La, Pr)

The La₂Mo₂O₉ (LM) and Pr₂Mo₂O₉ (PM) single crystals are studied using precision X-ray diffraction and high-resolution transmission microscopy at room temperature. The crystal structures are determined in the space group P2₁3. La and Pr atoms, as well as Mo1 and O1 atoms, are located in the vicinity of the threefold axes rather than on the axes as in the high-temperature cubic phase. In both structures studied, the O2 and O3 positions are partially occupied. The coexistence of different configurations of the Mo coordination environment facilitates the oxygen-ion migration in the structure. Based on the X-ray data, the activation energies of O atoms are calculated and the migration paths of oxygen ions in the structures are analysed. The conductivity of PM crystals is close to that of LM crystals. The O2 and O3 atoms are the main contributors to the ion conductivity of LM and PM.

S1. Experimental

S1.1. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 1.

S2. Results and discussion

Computing details

Figures

(I)

Crystal data

La2Mo2O9	F(000) = 531
Mr = 613.7	Dx = 5.477 Mg m^−3
Cubic, P213	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 2ac;2ab;3	µ = 14.78 mm^−1
a = 7.1552 (9) Å	T = 293 K
V = 366.32 (8) Å^3	Sphere, colorless
Z = 2	0.30 × 0.30 × 0.30 × 0.15 (radius) mm

Data collection

Oxford Diffraction CCD diffractometer	710 reflections with I > 3σ(I)
Radiation source: X-ray tube	Rint = 0.022
Graphite monochromator	θmax = 48.9°, θmin = 4.9°
Absorption correction: for a sphere ?	h = −15→15
Tmin = 0.776, Tmax = 1.000	k = −15→15
14670 measured reflections	l = −15→15
767 independent reflections

Refinement

Refinement on F	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.000225F^2)
R[F^2 > 2σ(F^2)] = 0.019	(Δ/σ)max = 0.045
wR(F^2) = 0.024	Δρmax = 0.48 e Å^−3
S = 1.15	Δρmin = −0.76 e Å^−3
767 reflections	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
63 parameters	Extinction coefficient: 1690 (80)
0 restraints	Absolute structure: 312 of Friedel pairs used in the refinement
2 constraints	Absolute structure parameter: −0.016 (19)

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
La1	0.151 (4)	0.135 (4)	0.1235 (17)	0.0226 (12)	0.170 (14)
Mo1	0.8147 (8)	0.8235 (5)	0.8696 (16)	0.0252 (9)	0.191 (10)
O1	0.686 (2)	0.6743 (14)	0.6830 (8)	0.072 (4)	0.3333
O2	0.8129 (11)	0.6583 (8)	1.0123 (5)	0.079 (2)	0.745 (17)
O3	0.923 (2)	0.849 (3)	1.0430 (16)	0.113 (8)	0.323 (16)
Mo2	0.8303 (5)	0.8303 (5)	0.8303 (5)	0.0279 (9)*	0.43 (3)
La2	0.1784 (19)	0.1482 (10)	0.1353 (12)	0.0395 (10)	0.163 (14)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
La1	0.021 (3)	0.026 (2)	0.0200 (13)	−0.009 (3)	0.0042 (11)	0.0013 (8)
Mo1	0.0224 (9)	0.0160 (6)	0.037 (2)	−0.0065 (5)	−0.0060 (11)	0.0008 (7)
O1	0.127 (9)	0.067 (6)	0.023 (3)	−0.057 (5)	−0.005 (4)	0.019 (3)
O2	0.135 (6)	0.065 (3)	0.0363 (16)	0.027 (3)	−0.014 (2)	0.0010 (15)
O3	0.099 (10)	0.20 (2)	0.036 (4)	0.027 (12)	−0.004 (5)	0.014 (9)
La2	0.0208 (14)	0.069 (3)	0.0292 (11)	−0.0052 (10)	−0.0001 (9)	−0.0221 (16)

Bond lengths (Å)

La1—La1^i	0.25 (3)	O1—O2^xxiv	2.725 (15)
La1—La1^ii	0.25 (3)	O1—O3	3.324 (18)
La1—Mo1^iii	3.48 (3)	O1—O3^xix	2.725 (18)
La1—Mo1^iv	3.451 (16)	O1—O3^i	3.328 (19)
La1—O1^v	2.81 (3)	O1—O3^xxi	2.654 (19)
La1—O1^vi	2.498 (19)	O1—O3^ii	3.354 (18)
La1—O1^iii	2.62 (3)	O1—O3^xxv	2.761 (17)
La1—O1^vii	2.73 (3)	O1—Mo2	1.849 (11)
La1—O1^viii	2.74 (3)	O1—La2^xxvi	2.922 (19)
La1—O1^iv	2.47 (2)	O1—La2^xxvii	2.482 (12)
La1—O1^ix	2.57 (2)	O1—La2^xxviii	2.649 (12)
La1—O1^x	2.66 (3)	O1—La2^xxix	2.821 (16)
La1—O1^xi	2.71 (3)	O1—La2^xxx	2.543 (17)
La1—O2^xii	2.624 (13)	O1—La2^xxxi	2.692 (11)
La1—O2^iii	2.58 (3)	O1—La2^xxxii	2.858 (15)
La1—O2^xiii	2.45 (3)	O1—La2^xxxiii	2.442 (13)
La1—O2^iv	2.66 (2)	O1—La2^xxxiv	2.754 (15)
La1—O2^xiv	2.57 (3)	O2—O2^i	3.110 (8)
La1—O2^xi	2.80 (3)	O2—O2^xx	3.198 (8)
La1—O3^xv	2.68 (3)	O2—O2^xxi	3.027 (9)
La1—O3^xii	2.88 (2)	O2—O2^ii	3.110 (8)
La1—O3^xvi	2.60 (3)	O2—O2^xxxv	3.027 (9)
La1—O3^xiii	2.75 (3)	O2—O2^xviii	3.198 (8)
La1—O3^xvii	2.68 (3)	O2—O3	1.59 (2)
La1—O3^xiv	2.72 (3)	O2—O3^xix	2.820 (18)
La1—La2	0.23 (3)	O2—O3^i	2.768 (17)
La1—La2^i	0.38 (3)	O2—O3^xx	2.249 (16)
La1—La2^ii	0.393 (18)	O2—O3^xxi	3.25 (2)
Mo1—Mo1^i	0.517 (12)	O2—O3^ii	2.837 (13)
Mo1—Mo1^ii	0.517 (12)	O2—Mo2	1.796 (6)
Mo1—O1	1.941 (13)	O2—La2^xxxvi	2.523 (9)
Mo1—O1^i	1.951 (14)	O2—La2^xxviii	2.618 (10)
Mo1—O1^ii	1.934 (14)	O2—La2^xxix	2.956 (13)
Mo1—O2	1.562 (9)	O2—La2^xxxvii	2.461 (8)
Mo1—O2^i	2.071 (10)	O2—La2^xxxviii	2.237 (14)
Mo1—O2^ii	1.801 (7)	O2—La2^xxxiii	2.768 (11)
Mo1—O2^xviii	3.388 (13)	O3—O3^i	1.72 (2)
Mo1—O3	1.472 (17)	O3—O3^xx	3.43 (2)
Mo1—O3^xix	3.126 (18)	O3—O3^ii	1.72 (2)
Mo1—O3^i	1.787 (14)	O3—O3^xviii	3.43 (2)
Mo1—O3^xx	3.310 (19)	O3—Mo2	1.664 (13)
Mo1—O3^xxi	3.420 (19)	O3—Mo2^xxxix	3.311 (18)
Mo1—O3^ii	1.634 (13)	O3—La2^xl	2.89 (2)
Mo1—Mo2	0.307 (11)	O3—La2^xxxvi	2.807 (17)
O1—O1^i	0.109 (16)	O3—La2^xli	2.91 (2)
O1—O1^ii	0.109 (16)	O3—La2^xxxvii	2.557 (17)
O1—O2	2.527 (9)	O3—La2^xlii	2.78 (2)
O1—O2^xxii	2.675 (11)	O3—La2^xxxviii	2.56 (2)
O1—O2^i	2.541 (15)	La2—La2^i	0.387 (15)
O1—O2^xxiii	2.743 (10)	La2—La2^ii	0.387 (15)
O1—O2^ii	2.599 (11)

Symmetry codes: (i) z, x, y; (ii) y, z, x; (iii) x−1/2, −y+1/2, −z+1; (iv) −z+1, x−1/2, −y+1/2; (v) −x+1/2, −y+1, z−1/2; (vi) −x+1, y−1/2, −z+1/2; (vii) z−1/2, −x+1/2, −y+1; (viii) −z+1/2, −x+1, y−1/2; (ix) −y+1, z−1/2, −x+1/2; (x) y−1/2, −z+1/2, −x+1; (xi) −y+1/2, −z+1, x−1/2; (xii) −x+1, y−1/2, −z+3/2; (xiii) −z+3/2, −x+1, y−1/2; (xiv) y−1/2, −z+3/2, −x+1; (xv) x−1, y−1, z−1; (xvi) z−1, x−1, y−1; (xvii) y−1, z−1, x−1; (xviii) −y+3/2, −z+2, x+1/2; (xix) x−1/2, −y+3/2, −z+2; (xx) z−1/2, −x+3/2, −y+2; (xxi) −z+2, x−1/2, −y+3/2; (xxii) −x+3/2, −y+1, z−1/2; (xxiii) z−1/2, −x+3/2, −y+1; (xxiv) −y+1, z−1/2, −x+3/2; (xxv) −y+3/2, −z+2, x−1/2; (xxvi) −x+1/2, −y+1, z+1/2; (xxvii) −x+1, y+1/2, −z+1/2; (xxviii) x+1/2, −y+1/2, −z+1; (xxix) z+1/2, −x+1/2, −y+1; (xxx) −z+1/2, −x+1, y+1/2; (xxxi) −z+1, x+1/2, −y+1/2; (xxxii) −y+1, z+1/2, −x+1/2; (xxxiii) y+1/2, −z+1/2, −x+1; (xxxiv) −y+1/2, −z+1, x+1/2; (xxxv) y+1/2, −z+3/2, −x+2; (xxxvi) −x+1, y+1/2, −z+3/2; (xxxvii) −z+1, x+1/2, −y+3/2; (xxxviii) −y+1, z+1/2, −x+3/2; (xxxix) x+1/2, −y+3/2, −z+2; (xl) x+1, y+1, z+1; (xli) z+1, x+1, y+1; (xlii) y+1, z+1, x+1.

(II)

Crystal data

La2Mo2O9	F(000) = 527
Mr = 613.7	Dx = 5.444 Mg m^−3
Cubic, P213	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 2ac;2ab;3	µ = 14.78 mm^−1
a = 7.155 (1) Å	T = 293 K
V = 366.29 (9) Å^3	Sphere, colorless
Z = 2	0.30 × 0.30 × 0.30 × 0.15 (radius) mm

Data collection

Oxford Diffraction CCD diffractometer	1281 independent reflections
Radiation source: X-ray tube	820 reflections with I > 3σ(I)
Graphite monochromator	Rint = 0.059
ω scans	θmax = 49.7°, θmin = 4.9°
Absorption correction: for a sphere (Jana2000; Petricek, Dusek & Palatinus, 2000)	h = −15→15
Tmin = 0.614, Tmax = 1.000	k = −15→15
33307 measured reflections	l = −15→15

Refinement

Refinement on F	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.000225F^2)
R[F^2 > 2σ(F^2)] = 0.021	(Δ/σ)max = 0.047
wR(F^2) = 0.030	Δρmax = 0.57 e Å^−3
S = 1.08	Δρmin = −0.46 e Å^−3
1281 reflections	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
63 parameters	Extinction coefficient: 950 (60)
0 restraints	Absolute structure: 551 of Friedel pairs used in the refinement
2 constraints	Absolute structure parameter: 0.017 (19)

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
La1	0.8489 (12)	0.8639 (10)	0.8726 (9)	0.0276 (8)	0.188 (8)
Mo1	0.1855 (6)	0.1764 (4)	0.1315 (13)	0.0280 (7)	0.203 (8)
O1	0.3132 (16)	0.3243 (14)	0.3175 (7)	0.075 (3)	0.3333
O2	0.1869 (11)	0.3408 (7)	−0.0120 (5)	0.079 (2)	0.709 (16)
O3	0.078 (2)	0.150 (3)	−0.0414 (14)	0.108 (7)	0.321 (15)
Mo2	0.1695 (4)	0.1695 (4)	0.1695 (4)	0.0286 (7)*	0.39 (2)
La2	0.8184 (11)	0.8529 (9)	0.8669 (11)	0.0404 (8)	0.146 (8)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
La1	0.0277 (17)	0.0266 (12)	0.0287 (12)	−0.0117 (10)	0.0082 (9)	0.0002 (7)
Mo1	0.0245 (7)	0.0189 (5)	0.041 (2)	−0.0059 (4)	−0.0061 (9)	−0.0004 (6)
O1	0.111 (7)	0.090 (6)	0.023 (2)	−0.062 (5)	0.013 (3)	0.010 (3)
O2	0.142 (5)	0.061 (2)	0.0356 (14)	0.025 (3)	−0.0119 (19)	0.0018 (12)
O3	0.103 (9)	0.187 (18)	0.035 (3)	0.008 (11)	0.000 (5)	0.012 (7)
La2	0.0209 (10)	0.0679 (18)	0.0323 (10)	−0.0034 (8)	0.0024 (9)	−0.0217 (11)

Bond lengths (Å)

La1—La1^i	0.210 (11)	O1—O2^ii	2.589 (10)
La1—La1^ii	0.210 (11)	O1—O2^xxvi	2.740 (12)
La1—Mo1^iii	3.491 (8)	O1—O3	3.315 (16)
La1—Mo1^iv	3.473 (7)	O1—O3^xix	2.742 (16)
La1—O1^v	2.796 (14)	O1—O3^i	3.315 (17)
La1—O1^vi	2.518 (10)	O1—O3^xxi	2.668 (17)
La1—O1^iii	2.625 (11)	O1—O3^ii	3.340 (16)
La1—O1^vii	2.716 (13)	O1—O3^xxvii	2.762 (15)
La1—O1^viii	2.724 (11)	O1—Mo2	1.845 (10)
La1—O1^iv	2.501 (11)	O1—La2^xxviii	2.947 (14)
La1—O1^ix	2.589 (13)	O1—La2^xxix	2.455 (10)
La1—O1^x	2.644 (10)	O1—La2^xxii	2.660 (11)
La1—O1^xi	2.708 (12)	O1—La2^xxx	2.859 (12)
La1—O2^xii	2.598 (7)	O1—La2^xxxi	2.520 (14)
La1—O2^iii	2.609 (9)	O1—La2^xxxii	2.687 (10)
La1—O2^xiii	2.448 (9)	O1—La2^xxxiii	2.879 (10)
La1—O2^iv	2.679 (9)	O1—La2^xxiii	2.431 (12)
La1—O2^xiv	2.554 (8)	O1—La2^xxxiv	2.754 (13)
La1—O2^xi	2.796 (10)	O2—O2^i	3.100 (7)
La1—O3^xv	2.692 (19)	O2—O2^xx	3.195 (7)
La1—O3^xii	2.869 (15)	O2—O2^xxi	3.033 (9)
La1—O3^xvi	2.626 (19)	O2—O2^ii	3.100 (7)
La1—O3^xiii	2.748 (16)	O2—O2^xxxv	3.033 (9)
La1—O3^xvii	2.69 (2)	O2—O2^xviii	3.195 (7)
La1—O3^xiv	2.734 (15)	O2—O3	1.587 (19)
La1—La2	0.236 (11)	O2—O3^xix	2.823 (17)
La1—La2^i	0.378 (11)	O2—O3^i	2.749 (16)
La1—La2^ii	0.390 (10)	O2—O3^xx	2.256 (15)
Mo1—Mo1^i	0.506 (10)	O2—O3^xxi	3.266 (18)
Mo1—Mo1^ii	0.506 (10)	O2—O3^ii	2.822 (12)
Mo1—O1	1.930 (11)	O2—Mo2	1.790 (5)
Mo1—O1^i	1.937 (12)	O2—La2^xxxvi	2.540 (9)
Mo1—O1^ii	1.922 (12)	O2—La2^xxii	2.602 (9)
Mo1—O2	1.561 (8)	O2—La2^xxx	2.984 (10)
Mo1—O2^i	2.060 (9)	O2—La2^xxxvii	2.474 (7)
Mo1—O2^ii	1.791 (6)	O2—La2^xxxviii	2.218 (9)
Mo1—O2^xviii	3.397 (11)	O2—La2^xxiii	2.776 (9)
Mo1—O3	1.471 (15)	O3—O3^i	1.69 (2)
Mo1—O3^xix	3.136 (17)	O3—O3^xx	3.44 (2)
Mo1—O3^i	1.776 (12)	O3—O3^ii	1.69 (2)
Mo1—O3^xx	3.312 (17)	O3—O3^xviii	3.44 (2)
Mo1—O3^xxi	3.428 (17)	O3—Mo2	1.652 (12)
Mo1—O3^ii	1.626 (11)	O3—Mo2^xxxix	3.322 (16)
Mo1—Mo2	0.299 (9)	O3—La2^xl	2.897 (19)
Mo1—La2^xxii	3.499 (7)	O3—La2^xxxvi	2.843 (16)
Mo1—La2^xxiii	3.499 (8)	O3—La2^xli	2.91 (2)
O1—O1^i	0.099 (14)	O3—La2^xxxvii	2.564 (15)
O1—O1^ii	0.099 (14)	O3—La2^xlii	2.774 (19)
O1—O2	2.528 (8)	O3—La2^xxxviii	2.565 (17)
O1—O2^xxiv	2.689 (10)	La2—La2^i	0.438 (11)
O1—O2^i	2.531 (12)	La2—La2^ii	0.438 (11)
O1—O2^xxv	2.748 (8)

Symmetry codes: (i) z, x, y; (ii) y, z, x; (iii) x+1/2, −y+3/2, −z+1; (iv) −z+1, x+1/2, −y+3/2; (v) −x+3/2, −y+1, z+1/2; (vi) −x+1, y+1/2, −z+3/2; (vii) z+1/2, −x+3/2, −y+1; (viii) −z+3/2, −x+1, y+1/2; (ix) −y+1, z+1/2, −x+3/2; (x) y+1/2, −z+3/2, −x+1; (xi) −y+3/2, −z+1, x+1/2; (xii) −x+1, y+1/2, −z+1/2; (xiii) −z+1/2, −x+1, y+1/2; (xiv) y+1/2, −z+1/2, −x+1; (xv) x+1, y+1, z+1; (xvi) z+1, x+1, y+1; (xvii) y+1, z+1, x+1; (xviii) −y+1/2, −z, x−1/2; (xix) x+1/2, −y+1/2, −z; (xx) z+1/2, −x+1/2, −y; (xxi) −z, x+1/2, −y+1/2; (xxii) x−1/2, −y+3/2, −z+1; (xxiii) y−1/2, −z+3/2, −x+1; (xxiv) −x+1/2, −y+1, z+1/2; (xxv) z+1/2, −x+1/2, −y+1; (xxvi) −y+1, z+1/2, −x+1/2; (xxvii) −y+1/2, −z, x+1/2; (xxviii) −x+3/2, −y+1, z−1/2; (xxix) −x+1, y−1/2, −z+3/2; (xxx) z−1/2, −x+3/2, −y+1; (xxxi) −z+3/2, −x+1, y−1/2; (xxxii) −z+1, x−1/2, −y+3/2; (xxxiii) −y+1, z−1/2, −x+3/2; (xxxiv) −y+3/2, −z+1, x−1/2; (xxxv) y−1/2, −z+1/2, −x; (xxxvi) −x+1, y−1/2, −z+1/2; (xxxvii) −z+1, x−1/2, −y+1/2; (xxxviii) −y+1, z−1/2, −x+1/2; (xxxix) x−1/2, −y+1/2, −z; (xl) x−1, y−1, z−1; (xli) z−1, x−1, y−1; (xlii) y−1, z−1, x−1.

(III)

Crystal data

Pr2Mo2O9	F(000) = 546
Mr = 617.7	Dx = 5.729 Mg m^−3
Cubic, P213	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 2ac;2ab;3	µ = 16.92 mm^−1
a = 7.0849 (11) Å	T = 293 K
V = 355.63 (10) Å^3	Sphere, colorless
Z = 2	0.30 × 0.30 × 0.30 × 0.15 (radius) mm

Data collection

Oxford Diffraction CCD diffractometer	512 reflections with I > 3σ(I)
Radiation source: X-ray tube	Rint = 0.025
Graphite monochromator	θmax = 48.2°, θmin = 5.0°
Absorption correction: for a sphere ?	h = −13→14
Tmin = 0.716, Tmax = 1.000	k = −13→14
10229 measured reflections	l = −14→14
551 independent reflections

Refinement

Refinement on F	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.000225F^2)
R[F^2 > 2σ(F^2)] = 0.017	(Δ/σ)max = 0.047
wR(F^2) = 0.022	Δρmax = 0.33 e Å^−3
S = 1.06	Δρmin = −0.22 e Å^−3
551 reflections	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
62 parameters	Extinction coefficient: 570 (40)
0 restraints	Absolute structure: 220 of Friedel pairs used in the refinement
2 constraints	Absolute structure parameter: 0.01 (2)

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Pr1	0.1352 (9)	0.1615 (13)	0.1327 (17)	0.0437 (11)	0.285 (19)
Mo1	0.8154 (9)	0.8262 (7)	0.8837 (16)	0.0294 (10)	0.132 (8)
O1	0.693 (3)	0.6724 (17)	0.6853 (11)	0.089 (5)	0.3333
O2	0.8117 (12)	0.6565 (9)	1.0136 (6)	0.083 (3)	0.722 (19)
O3	0.920 (3)	0.849 (4)	1.0458 (19)	0.178 (15)	0.40 (2)
Mo2	0.8294 (5)	0.8294 (5)	0.8294 (5)	0.0379 (6)*	0.60 (2)
Pr2	0.115 (7)	0.188 (4)	0.172 (10)	0.045 (4)	0.049 (19)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Pr1	0.0420 (16)	0.053 (2)	0.0358 (18)	0.0206 (9)	−0.0115 (12)	−0.0199 (18)
Mo1	0.0273 (14)	0.0219 (11)	0.039 (3)	−0.0081 (9)	−0.0063 (13)	−0.0054 (13)
O1	0.163 (13)	0.072 (8)	0.030 (4)	−0.065 (8)	0.005 (6)	0.017 (5)
O2	0.130 (6)	0.070 (3)	0.048 (2)	0.024 (4)	−0.015 (2)	0.005 (2)
O3	0.143 (15)	0.34 (4)	0.049 (5)	0.022 (18)	−0.012 (7)	0.050 (13)
Pr2	0.065 (8)	0.035 (3)	0.036 (9)	0.023 (4)	−0.022 (7)	−0.014 (4)

Bond lengths (Å)

Pr1—Pr1^i	0.277 (14)	O1—O2^ii	2.590 (13)
Pr1—Pr1^ii	0.277 (14)	O1—O2^xxviii	2.717 (19)
Pr1—Mo1^iii	3.432 (13)	O1—O3	3.27 (2)
Pr1—O1^iv	2.63 (2)	O1—O3^xix	2.72 (2)
Pr1—O1^v	2.563 (16)	O1—O3^i	3.27 (2)
Pr1—O1^vi	2.725 (15)	O1—O3^xxi	2.59 (2)
Pr1—O1^vii	2.88 (2)	O1—O3^ii	3.32 (2)
Pr1—O1^viii	2.511 (13)	O1—O3^xxix	3.45 (3)
Pr1—O1^iii	2.518 (16)	O1—O3^xxx	2.76 (2)
Pr1—O1^ix	2.68 (2)	O1—Mo2	1.794 (14)
Pr1—O1^x	2.764 (15)	O1—Pr2^xxii	2.40 (5)
Pr1—O1^xi	2.471 (14)	O1—Pr2^xxxi	2.87 (7)
Pr1—O2^xii	2.535 (13)	O1—Pr2^xxxii	2.80 (4)
Pr1—O2^vi	2.777 (12)	O1—Pr2^xxiv	2.23 (5)
Pr1—O2^xiii	2.502 (8)	O1—Pr2^xxxiii	2.99 (7)
Pr1—O2^iii	2.538 (13)	O1—Pr2^xxxiv	2.84 (4)
Pr1—O2^xiv	2.341 (10)	O1—Pr2^xxxv	2.29 (5)
Pr1—O2^xi	2.724 (11)	O1—Pr2^xxxvi	2.82 (7)
Pr1—O3^xv	2.76 (3)	O1—Pr2^xxxvii	2.96 (4)
Pr1—O3^xii	2.67 (2)	O2—O2^i	3.107 (9)
Pr1—O3^xvi	2.71 (3)	O2—O2^xx	3.159 (9)
Pr1—O3^xiii	2.79 (2)	O2—O2^xxi	2.992 (10)
Pr1—O3^xvii	2.66 (3)	O2—O2^ii	3.107 (9)
Pr1—O3^xiv	2.60 (2)	O2—O2^xxxviii	2.992 (10)
Pr1—Mo2^v	3.493 (12)	O2—O2^xviii	3.159 (9)
Pr1—Pr2	0.36 (6)	O2—O3	1.58 (3)
Pr1—Pr2^i	0.57 (5)	O2—O3^xix	2.81 (2)
Pr1—Pr2^ii	0.40 (3)	O2—O3^i	2.76 (2)
Mo1—Mo1^i	0.637 (13)	O2—O3^xx	2.19 (2)
Mo1—Mo1^ii	0.637 (13)	O2—O3^xxi	3.23 (3)
Mo1—O1	1.980 (15)	O2—O3^ii	2.849 (16)
Mo1—O1^i	1.997 (17)	O2—Mo2	1.794 (7)
Mo1—O1^ii	1.964 (18)	O2—Pr2^xxiii	2.30 (7)
Mo1—O2	1.514 (10)	O2—Pr2^xxxii	3.10 (4)
Mo1—O2^i	2.138 (11)	O2—Pr2^xxiv	2.59 (5)
Mo1—O2^ii	1.814 (9)	O2—Pr2^xxv	2.14 (3)
Mo1—O2^xviii	3.244 (14)	O2—Pr2^xxxix	2.63 (5)
Mo1—O3	1.376 (19)	O2—Pr2^xxxvi	2.65 (6)
Mo1—O3^xix	3.11 (2)	O3—O3^i	1.73 (3)
Mo1—O3^i	1.779 (16)	O3—O3^xx	3.35 (3)
Mo1—O3^xx	3.21 (2)	O3—O3^ii	1.73 (3)
Mo1—O3^xxi	3.46 (2)	O3—O3^xviii	3.35 (3)
Mo1—O3^ii	1.595 (15)	O3—Mo2	1.668 (15)
Mo1—Mo2	0.398 (12)	O3—Mo2^xl	3.29 (2)
Mo1—Pr2^xxii	3.40 (6)	O3—Pr2^xli	2.91 (5)
Mo1—Pr2^xxiii	3.33 (7)	O3—Pr2^xxiii	2.32 (6)
Mo1—Pr2^xxiv	3.33 (5)	O3—Pr2^xlii	2.79 (6)
Mo1—Pr2^xxv	3.38 (4)	O3—Pr2^xxv	2.59 (5)
O1—O1^i	0.18 (2)	O3—Pr2^xliii	3.01 (6)
O1—O1^ii	0.18 (2)	O3—Pr2^xxxix	2.82 (6)
O1—O2	2.477 (11)	Mo2—Pr2^xxii	3.34 (5)
O1—O2^xxvi	2.629 (13)	Mo2—Pr2^xxiv	3.34 (5)
O1—O2^i	2.488 (19)	Mo2—Pr2^xxxv	3.34 (5)
O1—O2^xxvii	2.736 (13)	Pr2—Pr2^i	0.66 (7)
O1—O2^xxi	3.482 (16)	Pr2—Pr2^ii	0.66 (7)

Symmetry codes: (i) z, x, y; (ii) y, z, x; (iii) −z+1, x−1/2, −y+1/2; (iv) −x+1/2, −y+1, z−1/2; (v) −x+1, y−1/2, −z+1/2; (vi) x−1/2, −y+1/2, −z+1; (vii) z−1/2, −x+1/2, −y+1; (viii) −z+1/2, −x+1, y−1/2; (ix) −y+1, z−1/2, −x+1/2; (x) y−1/2, −z+1/2, −x+1; (xi) −y+1/2, −z+1, x−1/2; (xii) −x+1, y−1/2, −z+3/2; (xiii) −z+3/2, −x+1, y−1/2; (xiv) y−1/2, −z+3/2, −x+1; (xv) x−1, y−1, z−1; (xvi) z−1, x−1, y−1; (xvii) y−1, z−1, x−1; (xviii) −y+3/2, −z+2, x+1/2; (xix) x−1/2, −y+3/2, −z+2; (xx) z−1/2, −x+3/2, −y+2; (xxi) −z+2, x−1/2, −y+3/2; (xxii) −x+1/2, −y+1, z+1/2; (xxiii) −x+1, y+1/2, −z+3/2; (xxiv) z+1/2, −x+1/2, −y+1; (xxv) −z+1, x+1/2, −y+3/2; (xxvi) −x+3/2, −y+1, z−1/2; (xxvii) z−1/2, −x+3/2, −y+1; (xxviii) −y+1, z−1/2, −x+3/2; (xxix) −y+2, z−1/2, −x+3/2; (xxx) −y+3/2, −z+2, x−1/2; (xxxi) −x+1, y+1/2, −z+1/2; (xxxii) x+1/2, −y+1/2, −z+1; (xxxiii) −z+1/2, −x+1, y+1/2; (xxxiv) −z+1, x+1/2, −y+1/2; (xxxv) −y+1, z+1/2, −x+1/2; (xxxvi) y+1/2, −z+1/2, −x+1; (xxxvii) −y+1/2, −z+1, x+1/2; (xxxviii) y+1/2, −z+3/2, −x+2; (xxxix) −y+1, z+1/2, −x+3/2; (xl) x+1/2, −y+3/2, −z+2; (xli) x+1, y+1, z+1; (xlii) z+1, x+1, y+1; (xliii) y+1, z+1, x+1.

(IV)

Crystal data

Pr2Mo2O9	F(000) = 543
Mr = 617.7	Dx = 5.686 Mg m^−3
Cubic, P213	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 2ac;2ab;3	µ = 16.82 mm^−1
a = 7.0992 (18) Å	T = 293 K
V = 357.79 (16) Å^3	Sphere, colorless
Z = 2	0.30 × 0.30 × 0.30 × 0.15 (radius) mm

Data collection

Oxford Diffraction CCD diffractometer	592 reflections with I > 3σ(I)
Radiation source: X-ray tube	Rint = 0.025
Graphite monochromator	θmax = 48.8°, θmin = 5.0°
Absorption correction: for a sphere ?	h = −14→14
Tmin = 0.662, Tmax = 1.000	k = −13→14
11700 measured reflections	l = −14→13
634 independent reflections

Refinement

Refinement on F	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.000225F^2)
R[F^2 > 2σ(F^2)] = 0.019	(Δ/σ)max = 0.046
wR(F^2) = 0.025	Δρmax = 0.48 e Å^−3
S = 1.22	Δρmin = −0.43 e Å^−3
634 reflections	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
63 parameters	Extinction coefficient: 860 (70)
0 restraints	Absolute structure: 255 of Friedel pairs used in the refinement
2 constraints	Absolute structure parameter: −0.02 (2)

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Pr1	0.1353 (10)	0.1600 (13)	0.1317 (10)	0.0414 (11)	0.274 (13)
Mo1	0.8147 (7)	0.8254 (6)	0.8852 (12)	0.0238 (9)	0.123 (6)
O1	0.694 (3)	0.6716 (17)	0.6845 (10)	0.084 (5)	0.3333
O2	0.8122 (12)	0.6571 (10)	1.0131 (7)	0.077 (3)	0.72 (2)
O3	0.913 (3)	0.851 (4)	1.047 (2)	0.171 (17)	0.39 (2)
Mo2	0.8301 (3)	0.8301 (3)	0.8301 (3)	0.0336 (5)*	0.630 (18)
Pr2	0.129 (4)	0.186 (3)	0.162 (4)	0.046 (4)	0.059 (13)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Pr1	0.0363 (15)	0.053 (2)	0.035 (2)	0.0193 (9)	−0.0132 (12)	−0.0222 (13)
Mo1	0.0221 (12)	0.0169 (10)	0.032 (2)	−0.0091 (8)	−0.0049 (11)	−0.0043 (10)
O1	0.159 (13)	0.070 (7)	0.023 (4)	−0.064 (8)	0.001 (6)	0.018 (4)
O2	0.120 (7)	0.066 (3)	0.046 (2)	0.026 (4)	−0.015 (2)	0.004 (2)
O3	0.110 (13)	0.35 (5)	0.050 (6)	0.002 (17)	−0.012 (7)	0.049 (15)
Pr2	0.073 (7)	0.030 (4)	0.034 (7)	0.020 (3)	−0.037 (4)	−0.013 (4)

Bond lengths (Å)

Pr1—Pr1^i	0.267 (12)	O1—O3	3.27 (2)
Pr1—Pr1^ii	0.267 (12)	O1—O3^xix	2.76 (2)
Pr1—Mo1^iii	3.429 (9)	O1—O3^i	3.26 (3)
Pr1—O1^iv	2.65 (2)	O1—O3^xxvi	2.61 (2)
Pr1—O1^v	2.552 (13)	O1—O3^ii	3.32 (2)
Pr1—O1^vi	2.723 (15)	O1—O3^xxviii	3.42 (4)
Pr1—O1^vii	2.90 (2)	O1—O3^xxix	2.79 (2)
Pr1—O1^viii	2.512 (13)	O1—Mo2	1.808 (14)
Pr1—O1^iii	2.516 (13)	O1—Pr2^xxx	2.51 (3)
Pr1—O1^ix	2.694 (19)	O1—Pr2^xxxi	2.77 (3)
Pr1—O1^x	2.753 (14)	O1—Pr2^xxxii	2.80 (3)
Pr1—O1^xi	2.482 (14)	O1—Pr2^xxii	2.33 (3)
Pr1—O2^xii	2.549 (9)	O1—Pr2^xxxiii	2.90 (3)
Pr1—O2^vi	2.775 (11)	O1—Pr2^xxxiv	2.84 (3)
Pr1—O2^xiii	2.510 (9)	O1—Pr2^xxxv	2.38 (3)
Pr1—O2^iii	2.546 (10)	O1—Pr2^xxxvi	2.71 (3)
Pr1—O2^xiv	2.360 (11)	O1—Pr2^xxxvii	2.97 (3)
Pr1—O2^xi	2.731 (10)	O2—O2^i	3.104 (9)
Pr1—O3^xv	2.76 (3)	O2—O2^xx	3.168 (9)
Pr1—O3^xii	2.68 (2)	O2—O2^xxvi	2.999 (10)
Pr1—O3^xvi	2.72 (3)	O2—O2^ii	3.104 (9)
Pr1—O3^xiii	2.79 (2)	O2—O2^xxxviii	2.999 (10)
Pr1—O3^xvii	2.66 (3)	O2—O2^xviii	3.168 (9)
Pr1—O3^xiv	2.60 (2)	O2—O3	1.58 (3)
Pr1—Pr2	0.29 (3)	O2—O3^xix	2.86 (2)
Pr1—Pr2^i	0.48 (3)	O2—O3^i	2.72 (2)
Pr1—Pr2^ii	0.36 (2)	O2—O3^xx	2.17 (2)
Mo1—Mo1^i	0.661 (10)	O2—O3^xxvi	3.27 (3)
Mo1—Mo1^ii	0.661 (10)	O2—O3^ii	2.873 (17)
Mo1—O1	1.989 (14)	O2—Mo2	1.792 (6)
Mo1—O1^i	2.006 (15)	O2—Pr2^xxi	2.35 (3)
Mo1—O1^ii	1.968 (17)	O2—Pr2^xxxii	3.03 (3)
Mo1—O2	1.501 (9)	O2—Pr2^xxii	2.69 (3)
Mo1—O2^i	2.149 (9)	O2—Pr2^xxiii	2.15 (2)
Mo1—O2^ii	1.816 (8)	O2—Pr2^xxxix	2.54 (3)
Mo1—O2^xviii	3.247 (12)	O2—Pr2^xxxvi	2.64 (3)
Mo1—O3	1.360 (19)	O3—O3^i	1.74 (3)
Mo1—O3^xix	3.15 (2)	O3—O3^xx	3.29 (3)
Mo1—O3^i	1.782 (17)	O3—O3^ii	1.74 (3)
Mo1—O3^xx	3.16 (2)	O3—O3^xviii	3.29 (3)
Mo1—O3^ii	1.610 (17)	O3—Mo2	1.659 (16)
Mo1—Mo2	0.408 (9)	O3—Mo2^xl	3.48 (2)
Mo1—Pr2^xxi	3.39 (3)	O3—Mo2^xli	3.34 (2)
Mo1—Pr2^xxii	3.44 (3)	O3—Pr2^xlii	2.94 (4)
Mo1—Pr2^xxiii	3.35 (3)	O3—Pr2^xxi	2.39 (3)
O1—O1^i	0.20 (2)	O3—Pr2^xliii	2.82 (4)
O1—O1^ii	0.20 (2)	O3—Pr2^xxiii	2.52 (3)
O1—O2	2.481 (11)	O3—Pr2^xliv	2.99 (4)
O1—O2^xxiv	2.632 (13)	O3—Pr2^xxxix	2.75 (3)
O1—O2^i	2.483 (19)	Mo2—Pr2^xxx	3.47 (3)
O1—O2^xxv	2.747 (13)	Mo2—Pr2^xxii	3.47 (3)
O1—O2^xxvi	3.478 (17)	Mo2—Pr2^xxxv	3.47 (3)
O1—O2^ii	2.602 (13)	Pr2—Pr2^i	0.50 (4)
O1—O2^xxvii	2.735 (19)	Pr2—Pr2^ii	0.50 (4)

Symmetry codes: (i) z, x, y; (ii) y, z, x; (iii) −z+1, x−1/2, −y+1/2; (iv) −x+1/2, −y+1, z−1/2; (v) −x+1, y−1/2, −z+1/2; (vi) x−1/2, −y+1/2, −z+1; (vii) z−1/2, −x+1/2, −y+1; (viii) −z+1/2, −x+1, y−1/2; (ix) −y+1, z−1/2, −x+1/2; (x) y−1/2, −z+1/2, −x+1; (xi) −y+1/2, −z+1, x−1/2; (xii) −x+1, y−1/2, −z+3/2; (xiii) −z+3/2, −x+1, y−1/2; (xiv) y−1/2, −z+3/2, −x+1; (xv) x−1, y−1, z−1; (xvi) z−1, x−1, y−1; (xvii) y−1, z−1, x−1; (xviii) −y+3/2, −z+2, x+1/2; (xix) x−1/2, −y+3/2, −z+2; (xx) z−1/2, −x+3/2, −y+2; (xxi) −x+1, y+1/2, −z+3/2; (xxii) z+1/2, −x+1/2, −y+1; (xxiii) −z+1, x+1/2, −y+3/2; (xxiv) −x+3/2, −y+1, z−1/2; (xxv) z−1/2, −x+3/2, −y+1; (xxvi) −z+2, x−1/2, −y+3/2; (xxvii) −y+1, z−1/2, −x+3/2; (xxviii) −y+2, z−1/2, −x+3/2; (xxix) −y+3/2, −z+2, x−1/2; (xxx) −x+1/2, −y+1, z+1/2; (xxxi) −x+1, y+1/2, −z+1/2; (xxxii) x+1/2, −y+1/2, −z+1; (xxxiii) −z+1/2, −x+1, y+1/2; (xxxiv) −z+1, x+1/2, −y+1/2; (xxxv) −y+1, z+1/2, −x+1/2; (xxxvi) y+1/2, −z+1/2, −x+1; (xxxvii) −y+1/2, −z+1, x+1/2; (xxxviii) y+1/2, −z+3/2, −x+2; (xxxix) −y+1, z+1/2, −x+3/2; (xl) −x+3/2, −y+2, z+1/2; (xli) x+1/2, −y+3/2, −z+2; (xlii) x+1, y+1, z+1; (xliii) z+1, x+1, y+1; (xliv) y+1, z+1, x+1.