Time-of-flight neutron powder diffraction with milligram samples: the crystal structures of NaCoF₃ and NaNiF₃ post-perovskites

Using the recently upgraded Polaris diffractometer at the ISIS Spallation Neutron Source (Rutherford Appleton Laboratory), the crystal structures of the post-perovskite polymorphs of NaCoF₃ and NaNiF₃ have been determined by time-of-flight neutron powder diffraction from samples, of mass 56 and 16 mg, respectively, recovered after synthesis at ∼20 GPa in a multi-anvil press. The structure of post-perovskite NaNiF₃ has also been determined by single-crystal synchrotron X-ray diffraction for comparison. All measurements were made at atmospheric pressure and room temperature. Despite the extremely small sample size in the neutron diffraction study, there is very good agreement between the positional parameters for NaNiF₃ obtained from the refinements of the X-ray and neutron data. Relative to the commonly used oxide post-perovskite analogue phases having calcium as the A cation, the axial ratios and derived structural parameters of these fluoride post-perovskites are more consistent with those of Mg_0.91Fe_0.09SiO₃ at high pressure and temperature. The structures of NaCoF₃ and NaNiF₃ are very similar, but the unit-cell and CoF₆ octahedral volumes of NaCoF₃ are larger than the corresponding quantities in NaNiF₃, which supports the hypothesis that the Co²⁺ ion has a high-spin state in this compound. The anisotropic atomic displacement parameters of the Na ions in NaNiF₃ post-perovskite are of similar magnitude to those of the F ions. The probability ellipsoid of the F1 ion is a prolate spheroid with its largest component parallel to the b axis of the unit cell, corresponding to rotational motion of the NiF₆ octahedra about the a axis of the crystal. Although they must be synthesized at pressures above about 18 GPa, these ABF₃ compounds are strongly metastable at atmospheric pressure and room temperature and so are highly suitable for use as analogues for (Mg,Fe)SiO₃ post-perovskite in the deep Earth, with significant advantages over oxides such as CaIrO₃ or CaPtO₃.

Computing details

Program(s) used to refine structure: SHELXL97 (Sheldrick, 1997).

(nanif3_anisotropic_synchrotron_Diamond)

Crystal data

F3NaNi	Z = 4
Mr = 138.70	F(000) = 264
Orthorhombic, Cmcm	Dx = 4.091 Mg m^−3
a = 3.0294 (4) Å	X-ray radiation, λ = 0.20675 Å
b = 10.0534 (12) Å	µ = 4.48 mm^−1
c = 7.3938 (7) Å	T = 293 K
V = 225.18 (5) Å^3	× × mm

Data collection

Radiation source: ID15 Diamond synchrotron	Rint = 0.111
Double-bounce silicon (1 1 1) plus mirrors monochromator	θmax = 14.0°, θmin = 1.6°
3527 measured reflections	h = −5→6
680 independent reflections	k = −21→21
438 reflections with I > 2σ(I)	l = −16→14

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)] = 0.098	w = 1/[σ^2(Fo^2) + (0.1879P)^2 + 0.8839P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.305	(Δ/σ)max = 1.166
S = 1.05	Δρmax = 6.69 e Å^−3
680 reflections	Δρmin = −8.85 e Å^−3
10 parameters	Extinction correction: SHELXL, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
0 restraints	Extinction coefficient: 0.00 (14)

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
Ni	0.0000	0.0000	0.0000	0.0108 (3)*
Na	0.0000	0.2538 (4)	0.2500	0.0188 (7)*
F1	0.0000	0.9275 (6)	0.2500	0.0164 (8)*
F2	0.0000	0.6275 (4)	0.0569 (5)	0.0141 (6)*

Geometric parameters (Å, º)

Ni—F1^i	1.987 (2)	Na—F2^ix	2.438 (4)
Ni—F1^ii	1.987 (2)	Na—F2^iii	2.438 (4)
Ni—F2^iii	2.029 (3)	Na—F2^x	2.564 (4)
Ni—F2^iv	2.029 (3)	Na—F2^ii	2.564 (4)
Ni—F2^v	2.029 (3)	Na—Na^xi	3.0294 (4)
Ni—F2^vi	2.029 (3)	Na—Na^xii	3.0294 (4)
Ni—Na	3.151 (4)	Na—Ni^xiii	3.151 (4)
Ni—Na^vii	3.151 (4)	F1—Ni^x	1.987 (2)
Ni—Na^v	3.441 (3)	F1—Ni^xiv	1.987 (2)
Ni—Na^iii	3.441 (3)	F1—Na^xv	2.311 (6)
Ni—Na^vi	3.441 (3)	F1—Na^xvi	2.311 (6)
Ni—Na^iv	3.441 (3)	F2—Ni^xv	2.029 (3)
Na—F1^iii	2.311 (6)	F2—Ni^xvi	2.029 (3)
Na—F1^v	2.311 (6)	F2—Na^xvi	2.438 (4)
Na—F2^v	2.438 (4)	F2—Na^xv	2.438 (4)
Na—F2^viii	2.438 (4)	F2—Na^ii	2.564 (4)
F1^i—Ni—F1^ii	180.0	F2^v—Na—F2^ix	71.69 (17)
F1^i—Ni—F2^iii	92.24 (15)	F2^viii—Na—F2^ix	76.82 (14)
F1^ii—Ni—F2^iii	87.76 (15)	F1^iii—Na—F2^iii	89.21 (11)
F1^i—Ni—F2^iv	87.76 (15)	F1^v—Na—F2^iii	143.17 (11)
F1^ii—Ni—F2^iv	92.24 (15)	F2^v—Na—F2^iii	76.82 (14)
F2^iii—Ni—F2^iv	180.0 (3)	F2^viii—Na—F2^iii	71.69 (17)
F1^i—Ni—F2^v	92.24 (15)	F2^ix—Na—F2^iii	117.2 (2)
F1^ii—Ni—F2^v	87.76 (15)	F1^iii—Na—F2^x	69.42 (11)
F2^iii—Ni—F2^v	96.61 (16)	F1^v—Na—F2^x	69.42 (11)
F2^iv—Ni—F2^v	83.39 (16)	F2^v—Na—F2^x	139.52 (8)
F1^i—Ni—F2^vi	87.76 (15)	F2^viii—Na—F2^x	73.98 (12)
F1^ii—Ni—F2^vi	92.24 (15)	F2^ix—Na—F2^x	73.98 (12)
F2^iii—Ni—F2^vi	83.39 (16)	F2^iii—Na—F2^x	139.52 (8)
F2^iv—Ni—F2^vi	96.61 (16)	F1^iii—Na—F2^ii	69.42 (11)
F2^v—Ni—F2^vi	180.00 (17)	F1^v—Na—F2^ii	69.42 (11)
F1^i—Ni—Na	75.61 (17)	F2^v—Na—F2^ii	73.98 (12)
F1^ii—Ni—Na	104.39 (17)	F2^viii—Na—F2^ii	139.52 (8)
F2^iii—Ni—Na	50.69 (8)	F2^ix—Na—F2^ii	139.52 (8)
F2^iv—Ni—Na	129.31 (8)	F2^iii—Na—F2^ii	73.98 (12)
F2^v—Ni—Na	50.69 (8)	F2^x—Na—F2^ii	124.5 (2)
F2^vi—Ni—Na	129.31 (8)	F1^iii—Na—Na^xi	130.95 (12)
F1^i—Ni—Na^vii	104.39 (17)	F1^v—Na—Na^xi	49.05 (12)
F1^ii—Ni—Na^vii	75.61 (17)	F2^v—Na—Na^xi	51.59 (7)
F2^iii—Ni—Na^vii	129.31 (8)	F2^viii—Na—Na^xi	128.41 (7)
F2^iv—Ni—Na^vii	50.69 (8)	F2^ix—Na—Na^xi	51.59 (7)
F2^v—Ni—Na^vii	129.31 (8)	F2^iii—Na—Na^xi	128.41 (7)
F2^vi—Ni—Na^vii	50.69 (8)	F2^x—Na—Na^xi	90.0
Na—Ni—Na^vii	180.00 (10)	F2^ii—Na—Na^xi	90.0
F1^i—Ni—Na^v	40.20 (12)	F1^iii—Na—Na^xii	49.05 (12)
F1^ii—Ni—Na^v	139.80 (12)	F1^v—Na—Na^xii	130.95 (12)
F2^iii—Ni—Na^v	132.22 (10)	F2^v—Na—Na^xii	128.41 (7)
F2^iv—Ni—Na^v	47.78 (10)	F2^viii—Na—Na^xii	51.59 (7)
F2^v—Ni—Na^v	90.83 (11)	F2^ix—Na—Na^xii	128.41 (7)
F2^vi—Ni—Na^v	89.17 (11)	F2^iii—Na—Na^xii	51.59 (7)
Na—Ni—Na^v	105.510 (9)	F2^x—Na—Na^xii	90.0
Na^vii—Ni—Na^v	74.490 (9)	F2^ii—Na—Na^xii	90.0
F1^i—Ni—Na^iii	40.20 (12)	Na^xi—Na—Na^xii	180.0 (3)
F1^ii—Ni—Na^iii	139.80 (12)	F1^iii—Na—Ni	127.71 (7)
F2^iii—Ni—Na^iii	90.83 (11)	F1^v—Na—Ni	127.71 (7)
F2^iv—Ni—Na^iii	89.17 (11)	F2^v—Na—Ni	40.07 (8)
F2^v—Ni—Na^iii	132.22 (10)	F2^viii—Na—Ni	85.52 (15)
F2^vi—Ni—Na^iii	47.78 (10)	F2^ix—Na—Ni	85.52 (15)
Na—Ni—Na^iii	105.510 (9)	F2^iii—Na—Ni	40.07 (8)
Na^vii—Ni—Na^iii	74.490 (9)	F2^x—Na—Ni	153.66 (16)
Na^v—Ni—Na^iii	52.24 (5)	F2^ii—Na—Ni	81.81 (9)
F1^i—Ni—Na^vi	139.80 (12)	Na^xi—Na—Ni	90.0
F1^ii—Ni—Na^vi	40.20 (12)	Na^xii—Na—Ni	90.0
F2^iii—Ni—Na^vi	47.78 (10)	F1^iii—Na—Ni^xiii	127.71 (7)
F2^iv—Ni—Na^vi	132.22 (10)	F1^v—Na—Ni^xiii	127.71 (7)
F2^v—Ni—Na^vi	89.17 (11)	F2^v—Na—Ni^xiii	85.52 (15)
F2^vi—Ni—Na^vi	90.83 (11)	F2^viii—Na—Ni^xiii	40.07 (8)
Na—Ni—Na^vi	74.490 (9)	F2^ix—Na—Ni^xiii	40.07 (8)
Na^vii—Ni—Na^vi	105.510 (9)	F2^iii—Na—Ni^xiii	85.52 (15)
Na^v—Ni—Na^vi	180.00 (10)	F2^x—Na—Ni^xiii	81.81 (9)
Na^iii—Ni—Na^vi	127.76 (5)	F2^ii—Na—Ni^xiii	153.66 (16)
F1^i—Ni—Na^iv	139.80 (12)	Na^xi—Na—Ni^xiii	90.0
F1^ii—Ni—Na^iv	40.20 (12)	Na^xii—Na—Ni^xiii	90.0
F2^iii—Ni—Na^iv	89.17 (11)	Ni—Na—Ni^xiii	71.84 (10)
F2^iv—Ni—Na^iv	90.83 (11)	Ni^x—F1—Ni^xiv	136.9 (3)
F2^v—Ni—Na^iv	47.78 (10)	Ni^x—F1—Na^xv	106.10 (10)
F2^vi—Ni—Na^iv	132.22 (10)	Ni^xiv—F1—Na^xv	106.10 (10)
Na—Ni—Na^iv	74.490 (9)	Ni^x—F1—Na^xvi	106.10 (10)
Na^vii—Ni—Na^iv	105.510 (9)	Ni^xiv—F1—Na^xvi	106.10 (10)
Na^v—Ni—Na^iv	127.76 (5)	Na^xv—F1—Na^xvi	81.9 (2)
Na^iii—Ni—Na^iv	180.00 (10)	Ni^xv—F2—Ni^xvi	96.61 (16)
Na^vi—Ni—Na^iv	52.24 (5)	Ni^xv—F2—Na^xvi	156.13 (18)
F1^iii—Na—F1^v	81.9 (2)	Ni^xvi—F2—Na^xvi	89.23 (8)
F1^iii—Na—F2^v	143.17 (11)	Ni^xv—F2—Na^xv	89.23 (8)
F1^v—Na—F2^v	89.21 (11)	Ni^xvi—F2—Na^xv	156.13 (18)
F1^iii—Na—F2^viii	89.21 (11)	Na^xvi—F2—Na^xv	76.82 (14)
F1^v—Na—F2^viii	143.17 (11)	Ni^xv—F2—Na^ii	96.35 (13)
F2^v—Na—F2^viii	117.2 (2)	Ni^xvi—F2—Na^ii	96.35 (13)
F1^iii—Na—F2^ix	143.17 (11)	Na^xvi—F2—Na^ii	106.02 (12)
F1^v—Na—F2^ix	89.21 (11)	Na^xv—F2—Na^ii	106.02 (12)

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