Neutron powder diffraction in materials with incoherent scattering: an illustration of Rietveld refinement quality from nondeuterated gypsum

The power of the state-of-the-art neutron powder diffractometer suite at the Institut Laue-Langevin for investigating the structure of nondeuterated materials is presented using gypsum, CaSO₄·2H₂O, as a reference material. It is shown that flexible modern neutron powder diffraction instruments at reactor-based sources can yield data with sufficient counting statistics above the incoherent scattering contribution to perform unconstrained refinements in relatively short time periods (from minutes to a few hours, depending on the sample size and the instrument choice), without the requirement for significant changes to the standard operational modes of the instruments. The results are critically compared with previous literature from single-crystal and powder X-ray and neutron measurements on deuterated and nondeuterated gypsum.

Computing details

Data collection: SMART (Bruker, 2007); cell refinement: SAINT-Plus (Bruker, 2007); data reduction: SAINT-Plus (Bruker, 2007); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: X-SEED (Barbour, 2001); software used to prepare material for publication: X-SEED (Barbour, 2001).

1,2-Di-4-pyridylethane N,N'-dioxide–acetic acid (1/2)

Crystal data

C12H12N2O2·2C2H4O2	Z = 1
Mr = 336.34	F(000) = 178
Triclinic, P1	Dx = 1.370 Mg m^−3
Hall symbol: -P 1	Mo Kα radiation, λ = 0.71073 Å
a = 7.1109 (6) Å	Cell parameters from 3794 reflections
b = 7.1562 (6) Å	θ = 3.2–30.5°
c = 9.2888 (7) Å	µ = 0.11 mm^−1
α = 73.719 (1)°	T = 173 K
β = 87.508 (1)°	Block, colorless
γ = 64.424 (1)°	0.55 × 0.45 × 0.37 mm
V = 407.62 (6) Å^3

Data collection

Bruker SMART APEX CCD diffractometer	2446 independent reflections
Radiation source: fine-focus sealed tube	2228 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.011
ω scans	θmax = 30.5°, θmin = 2.3°
Absorption correction: multi-scan (SADABS; Bruker, 2001)	h = −10→10
Tmin = 0.944, Tmax = 0.962	k = −10→9
4857 measured reflections	l = −13→13

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)] = 0.044	Hydrogen site location: inferred from neighbouring sites
wR(F^2) = 0.133	H-atom parameters constrained
S = 1.09	w = 1/[σ^2(Fo^2) + (0.0796P)^2 + 0.0824P] where P = (Fo^2 + 2Fc^2)/3
2446 reflections	(Δ/σ)max = 0.001
114 parameters	Δρmax = 0.39 e Å^−3
0 restraints	Δρmin = −0.25 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
O1	0.13750 (10)	0.89616 (12)	0.18453 (8)	0.02574 (15)
O2	0.65037 (13)	1.15878 (12)	0.46617 (9)	0.03371 (18)
O3	0.86230 (12)	0.87364 (12)	0.65134 (8)	0.02891 (16)
H3	0.8470	0.9693	0.6925	0.043*
N1	0.32388 (11)	0.79711 (12)	0.13545 (9)	0.019
C1	0.48607 (14)	0.64120 (15)	0.23478 (10)	0.022
H1	0.4674	0.6045	0.3391	0.026*
C2	0.67866 (13)	0.53522 (15)	0.18518 (10)	0.02148 (17)
H2	0.7919	0.4267	0.2558	0.026*
C3	0.70835 (13)	0.58611 (14)	0.03222 (10)	0.01794 (15)
C4	0.53728 (13)	0.74729 (14)	−0.06672 (10)	0.01899 (16)
H4	0.5520	0.7860	−0.1717	0.023*
C5	0.34614 (13)	0.85159 (14)	−0.01355 (10)	0.01970 (16)
H5	0.2308	0.9614	−0.0819	0.024*
C6	0.91767 (13)	0.46745 (14)	−0.02202 (10)	0.01940 (16)
H6A	0.9022	0.5004	−0.1329	0.023*
H6B	0.9662	0.3095	0.0222	0.023*
C7	0.76154 (14)	0.96654 (16)	0.51521 (10)	0.02359 (18)
C8	0.80145 (17)	0.80587 (18)	0.42910 (12)	0.0301 (2)
H8A	0.6925	0.8686	0.3456	0.045*
H8B	0.7993	0.6741	0.4963	0.045*
H8C	0.9386	0.7700	0.3892	0.045*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O1	0.0129 (3)	0.0322 (4)	0.0298 (3)	−0.0051 (3)	0.0056 (2)	−0.0140 (3)
O2	0.0348 (4)	0.0244 (4)	0.0278 (4)	−0.0039 (3)	0.0014 (3)	−0.0014 (3)
O3	0.0253 (3)	0.0244 (3)	0.0276 (4)	−0.0027 (3)	−0.0033 (3)	−0.0063 (3)
N1	0.012	0.020	0.024	−0.005	0.003	−0.008
C1	0.017	0.024	0.021	−0.006	0.001	−0.006
C2	0.0149 (4)	0.0216 (4)	0.0235 (4)	−0.0041 (3)	0.0004 (3)	−0.0061 (3)
C3	0.0131 (3)	0.0171 (4)	0.0241 (4)	−0.0063 (3)	0.0025 (3)	−0.0073 (3)
C4	0.0157 (4)	0.0184 (4)	0.0214 (4)	−0.0069 (3)	0.0024 (3)	−0.0046 (3)
C5	0.0148 (3)	0.0184 (4)	0.0233 (4)	−0.0056 (3)	0.0010 (3)	−0.0047 (3)
C6	0.0136 (3)	0.0195 (4)	0.0260 (4)	−0.0064 (3)	0.0038 (3)	−0.0096 (3)
C7	0.0177 (4)	0.0260 (4)	0.0224 (4)	−0.0078 (3)	0.0058 (3)	−0.0036 (3)
C8	0.0292 (5)	0.0314 (5)	0.0272 (5)	−0.0109 (4)	0.0061 (4)	−0.0093 (4)

Geometric parameters (Å, º)

O1—N1	1.3358 (9)	C3—C6	1.5079 (11)
O2—C7	1.2107 (12)	C4—C5	1.3859 (11)
O3—C7	1.3231 (12)	C4—H4	0.9500
O3—H3	0.8400	C5—H5	0.9500
N1—C5	1.3506 (12)	C6—C6^i	1.5410 (17)
N1—C1	1.3530 (12)	C6—H6A	0.9900
C1—C2	1.3811 (12)	C6—H6B	0.9900
C1—H1	0.9500	C7—C8	1.5021 (14)
C2—C3	1.3950 (13)	C8—H8A	0.9800
C2—H2	0.9500	C8—H8B	0.9800
C3—C4	1.3951 (12)	C8—H8C	0.9800
O1—N1—C1	119.76 (8)	C1—C2—H2	119.7
C5—N1—C1	120.99 (8)	C2—C1—H1	119.8
O1—N1—C5	119.24 (7)	C3—C2—H2	119.7
N1—C1—C2	120.31 (8)	C3—C4—H4	119.6
N1—C5—C4	120.00 (8)	C3—C6—H6A	109.3
C1—C2—C3	120.58 (8)	C3—C6—H6B	109.3
C2—C3—C4	117.43 (8)	C4—C5—H5	120.0
C3—C4—C5	120.70 (8)	C5—C4—H4	119.6
C4—C3—C6	122.07 (8)	C6^i—C6—H6A	109.3
C2—C3—C6	120.50 (8)	C6^i—C6—H6B	109.3
C3—C6—C6^i	111.43 (8)	C7—C8—H8A	109.5
O2—C7—O3	123.73 (10)	C7—C8—H8B	109.5
O2—C7—C8	124.14 (9)	C7—C8—H8C	109.5
O3—C7—C8	112.13 (8)	H6A—C6—H6B	108.0
N1—C1—H1	119.8	H8A—C8—H8B	109.5
N1—C5—H5	120.0	H8A—C8—H8C	109.5
C7—O3—H3	109.5	H8B—C8—H8C	109.5

Symmetry code: (i) −x+2, −y+1, −z.

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O3—H3···O1^ii	0.84	1.72	2.5393 (11)	164
C1—H1···O2^ii	0.95	2.68	3.3915 (12)	132
C2—H2···O3^iii	0.95	2.45	3.3489 (11)	158
C5—H5···O1^iv	0.95	2.48	3.3341 (12)	149
C6—H6B···O1^v	0.99	2.66	3.6309 (12)	168
C8—H8C···O1^vi	0.98	2.52	3.3655 (13)	145

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