Powder study of 3-aza­bicyclo­[3.3.1]nonane-2,4-dione form 2

Hulme, A.T.; Fernandes, P.; Florence, A.; Johnston, A.; Shankland, K.

doi:10.1107/S1600536806023312

organic compounds

CRYSTALLOGRAPHIC
COMMUNICATIONS

ISSN: 2056-9890

Volume 62| Part 7| July 2006| Pages o3046-o3048

https://doi.org/10.1107/S1600536806023312

Powder study of 3-azabicyclo[3.3.1]nonane-2,4-dione form 2

Ashley T Hulme,^a Philippe Fernandes,^b Alastair Florence,^b ^* Andrea Johnston ^b and Kenneth Shankland ^c

^aChristopher Ingold Laboratory, Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, England, ^bSolid-State Research Group, Department of Pharmaceutical Sciences, University of Strathclyde, 27 Taylor Street, Glasgow G4 0NR, Scotland, and ^cISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, England
^*Correspondence e-mail: alastair.florence@strath.ac.uk

(Received 12 May 2006; accepted 19 June 2006; online 28 June 2006)

A polycrystalline sample of a new polymorph of the title compound, C₈H₁₁NO₂, was produced during a variable-temperature X-ray powder diffraction study. The crystal structure was solved at 1.67 Å resolution by simulated annealing from laboratory powder data collected at 250 K. Subsequent Rietveld refinement yielded an R_wp of 0.070 to 1.54 Å resolution. The structure contains two molecules in the asymmetric unit, which form a C²₂(8) chain motif via N—H⋯O hydrogen bonds.

Comment

The crystal structure of the title compound, (I), was solved by simulated annealing using laboratory capillary X-ray powder diffraction data. The compound crystallizes in space group P2₁/c with two independent molecules of 3-azabicyclononane-2,4-dione in the asymmetric unit (Fig. 1).

The crystal structure of this polymorph (form 2) is approximately a cell-doubled modification of the stable room-temperature form of 3-azabicyclononane-2,4-dione (form 1) (Howie & Skakle, 2001 ), with the cell doubling in the c direction [18.8867 (4) versus 9.3384 (6) Å]. Form 2 is metastable with respect to form 1 at room temperature, with full conversion taking less than 1 h. However, with rapid cooling to 250 K (the data collection temperature), form 2 is kinetically trapped and stable for over 10 h.

The basic hydrogen-bond motif in (I) is a chain [graph set C₂²(8); Etter, 1990 ] running parallel to the a axis. Each chain contains alternating independent molecules linked by N—H⋯O hydrogen bonds (Table 1). Form 2 packs the chains in a manner similar to form 1, with the chains lying side by side to form layers (Fig. 2) parallel to the ab plane. The layers are related by the 2₁ screw axis and the stacking of the layers differs between the two forms, with form 1 showing an AB repeat packing and form 2 an ABCD repeat packing (Fig. 3). This stacking difference can be attributed to form 2 having two symmetry-independent molecules. The stacking in form 2 can be envisaged as related to that of form 1 by a translation of approximately half a unit cell parallel to the b axis of the C and D layers. With no strong interactions between the layers, the conversion from form 2 to form 1 would be facile and may account for the rapid conversion at room temperature.

Figure 1
The asymmetric unit of (I)

with the atom-numbering scheme. Displacement spheres are shown at the 50% probability level.

Figure 2
Four layers, each containing two ribbons, stacking in an ABCD repeat pattern. The view is parallel to the axis of propagation of the ribbons and the a axis.

Figure 3
Overlay of the layer stacking of form 1 (blue) and form 2 (red). The members of the uppermost layer and two bottom layers coincide, while the remaining two layers do not. Hydrogen bonds are shown as dashed lines.

Figure 4
Final observed (points), calculated (line) and difference [(y_obs − y_calc)/σ(y_obs)] profiles for the Rietveld refinement of the title compound.

Experimental

A polycrystalline sample of (I) was prepared by heating a sample of the raw material (form 1) to 420 K and subsequently quenching in situ to 250 K. The sample was held in a rotating 0.7 mm borosilicate glass capillary and the temperature controlled using an Oxford Cryosystems Cryostream Plus 700 series device. Data were collected over a period of 7.5 h using a variable-counting-time scheme (Shankland et al., 1997 ; Hill & Madsen, 2002 $[Hill, R. J. & Madsen, I. C. (2002). Structure Determination from Powder Diffraction Data, edited by W. I. F. David, K. Shankland, L. B. McCusker & Ch. Baerlocher, pp. 114-116. Oxford University Press.]$ ) in the range 7–60° 2θ. The final data set showed no evidence of diffraction associated with the form 1 structure.

Crystal data

C₈H₁₁NO₂
M_r = 153.18
Monoclinic, P 2₁ /c
a = 7.67102 (18) Å
b = 10.5483 (2) Å
c = 18.8867 (4) Å
β = 95.5800 (12)°
V = 1521.00 (6) Å³
Z = 8
D_x = 1.338 Mg m⁻³
Cu Kα₁ radiation
μ = 0.79 mm⁻¹
T = 250 K
Specimen shape: cylinder
12 × 0.7 × 0.7 mm
Specimen prepared at 420 K
Particle morphology: polycrystalline mass, white

Data collection

Bruker AXS D8 Advance diffractometer
Specimen mounting: 0.7 mm borosilicate capillary
Specimen mounted in transmission mode
Scan method: step
Absorption correction: none
2θ_min = 7.0, 2θ_max = 60.0°
Increment in 2θ = 0.017°

Refinement

R_p = 0.054
R_wp = 0.070
R_exp = 0.016
R_B = 3.058
S = 4.31
Profile function: Fundamental parameters with axial divergence correction.
142 parameters
H atoms treated by a mixture of independent and constrained refinement
w = 1/σ(Y_obs)²
(Δ/σ)_max = 0.111
Preferred orientation correction: a spherical harmonics-based preferred orientation correction (Järvinen, 1993 ) was applied with TOPAS (Coelho, 2003 ) during the Rietveld refinement.

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A	D—H	H⋯A	D⋯A	D—H⋯A
N1—H1⋯O1wⁱ	0.90 (1)	2.11 (1)	3.006 (4)	172 (1)
N1w—H1w⋯O1ⁱⁱ	0.91 (1)	2.03 (1)	2.931 (4)	172 (1)
Symmetry codes: (i) $[x+1, -y+{\script{1\over 2}}, z+{\script{1\over 2}}]$ ; (ii) $[x, -y+{\script{1\over 2}}, z-{\script{1\over 2}}]$ .

The diffraction pattern indexed to a monoclinic cell [M(18) = 28.0, F(18) = 65.9; DICVOL91; Boultif & Louër, 1991 ] and space group P2₁/c was assigned from volume considerations and a statistical consideration of the systematic absences (Markvardsen et al., 2001 ). P2₁/a and P2₁/n were discounted as they did not account for the peak attributable to form 2 at 15.63° 2θ.

The data were background subtracted and truncated to 54.8° 2θ for Pawley fitting (Pawley, 1981 ; χ²_Pawley = 18.50) and the structure solved using the simulated annealing (SA) global optimization procedure, described previously (David et al., 1998 ), that is now implemented in the DASH computer program (David et al., 2001 ). The internal coordinate description (including H atoms) of the molecules was constructed from standard bond lengths, bond angles and bond torsions where appropriate. The structure was solved using data to 54.8° 2θ, comprising 402 reflections. The structure was refined against data in the range 7.0–60.0° 2θ (448 reflections). The restraints were set such that bonds and angles did not deviate more than 0.01 Å and 1°, respectively, from their initial values during the refinement. Atoms C1, C5, C4, C2, O1, N1, O2 and H1 (first molecule) and atoms C1w, C5w, C4w, C1w, O1w, N1w, O2w and H1w (second molecule) of 3-azabicyclo[3.3.1]nonane-2,4-dione were restrained to be coplanar.

The SA structure solution involved the optimization of two independent molecules totaling 12 degrees of freedom (positional and orientational). All degrees of freedom were assigned random values at the start of the simulated annealing run. The best SA solution had a favourable χ²_SA/χ²_Pawley ratio of 4.5, had a chemically reasonable packing arrangement and exhibited no significant misfit to the data.

The solved structure was subsequently refined against data in the range 7.0–60.0° 2θ using a restrained Rietveld (1969 ) method as implemented in TOPAS (Coelho, 2003), with R_wp falling to 0.0698 during the refinement. All atomic positions (including H atoms) for the structure of (I) were refined, subject to a series of restraints on bond lengths, bond angles and planarity. A spherical harmonics (8th order) correction of intensities for preferred orientation was applied in the final refinement (Järvinen, 1993). An 8th order correction yielded a significant improvement in R_wp compared with lower orders. The need for such a high level of correction is most likely due to the effect of the in situ method of sample preparation on particle morphology. The observed and calculated diffraction patterns for the refined crystal structure are shown in Fig. 4.

Data collection: DIFFRAC plus XRD Commander (Kienle & Jacob, 2003 ); cell refinement: TOPAS (Coelho, 2003); data reduction: DASH (David et al., 2001); program(s) used to solve structure: DASH; program(s) used to refine structure: TOPAS; molecular graphics: MERCURY (Macrae et al., 2006 ) and PLATON (Spek, 2003 ); software used to prepare material for publication: enCIFer (Version 1.1; Allen et al., 2004 ).

Supporting information

Crystal structure: contains datablocks global, I. DOI: https://doi.org/10.1107/S1600536806023312/cv2057sup1.cif

Rietveld powder data: contains datablock I. DOI: https://doi.org/10.1107/S1600536806023312/cv2057Isup2.rtv

Computing details top

Data collection: DIFFRAC plus XRD Commander (Kienle & Jacob, 2003); data reduction: DASH (David et al., 2001); program(s) used to solve structure: DASH; program(s) used to refine structure: TOPAS (Coelho, 2003); software used to prepare material for publication: enCIFer (Version 1.1; Allen et al., 2004).

3-Azabicyclo[3.3.1]nonane-2,4-dione top

Crystal data top

C₈H₁₁NO₂	Z = 8
M_r = 153.18	F(000) = 656.0
Monoclinic, P2₁/c	D_x = 1.338 Mg m⁻³
Hall symbol: -P 2ybc	Cu Kα₁ radiation, λ = 1.54056 Å
a = 7.67102 (18) Å	µ = 0.79 mm⁻¹
b = 10.5483 (2) Å	T = 250 K
c = 18.8867 (4) Å	white
β = 95.5800 (12)°	cylinder, 12 × 0.7 mm
V = 1521.00 (6) Å³	Specimen preparation: Prepared at 420 K

Data collection top

Bruker AXS D8 Advance diffractometer	Data collection mode: transmission
Radiation source: sealed X-ray tube, Bruker-AXS D8	Scan method: step
Primary focussing, Ge 111 monochromator	2θ_min = 7.0°, 2θ_max = 60.0°, 2θ_step = 0.017°
Specimen mounting: 0.7 mm borosilicate capillary

Refinement top

Least-squares matrix: selected elements only	92 restraints
R_p = 0.054	2 constraints
R_wp = 0.070	H atoms treated by a mixture of independent and constrained refinement
R_exp = 0.016	Weighting scheme based on measured s.u.'s 1/σ(Y_obs)²
R_Bragg = 3.058	(Δ/σ)_max = 0.111
3070 data points	Background function: Chebyshev polynomial
Profile function: Fundamental parameters with axial divergence correction.	Preferred orientation correction: A spherical harmonics-based preferred orientation correction (Järvinen, 1993) was applied with Topas during the Rietveld refinement.
142 parameters

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

	x	y	z	U_iso*/U_eq
N1	0.7188 (2)	0.20485 (14)	0.59572 (18)	0.0380*
H1	0.8105 (12)	0.1517 (6)	0.5942 (4)	0.0760*
C1	0.5536 (2)	0.14964 (16)	0.5933 (2)	0.0380*
O1	0.5397 (5)	0.0342 (2)	0.5915 (3)	0.0380*
C2	0.3992 (2)	0.23660 (16)	0.59562 (9)	0.0380*
H2	0.3033 (12)	0.1955 (6)	0.5695 (4)	0.0760*
C3	0.4373 (2)	0.36391 (16)	0.56342 (9)	0.0380*
H3A	0.3414 (11)	0.4204 (6)	0.5661 (4)	0.0760*
H3B	0.4527 (10)	0.3553 (6)	0.5143 (5)	0.0760*
C4	0.6000 (2)	0.41980 (16)	0.60445 (9)	0.0380*
H4	0.6326 (12)	0.4984 (6)	0.5846 (4)	0.0760*
C5	0.7548 (2)	0.33355 (17)	0.5989 (2)	0.0380*
O2	0.9060 (3)	0.3689 (3)	0.6007 (3)	0.0380*
C6	0.5709 (2)	0.43895 (15)	0.68362 (8)	0.0380*
H6A	0.4815 (11)	0.5017 (6)	0.6831 (4)	0.0760*
H6B	0.6770 (13)	0.4725 (6)	0.7066 (4)	0.0760*
C7	0.5134 (2)	0.31638 (15)	0.71761 (9)	0.0380*
H7A	0.6069 (11)	0.2563 (6)	0.7206 (5)	0.0760*
H7B	0.4810 (10)	0.3317 (7)	0.7643 (4)	0.0760*
C8	0.3599 (2)	0.25471 (16)	0.67356 (9)	0.0380*
H8A	0.3286 (11)	0.1746 (7)	0.6922 (4)	0.0760*
H8B	0.2564 (12)	0.3047 (6)	0.6726 (4)	0.0760*
N1w	0.2227 (2)	0.62126 (15)	0.0902 (3)	0.0380*
H1w	0.3151 (11)	0.5676 (6)	0.0925 (6)	0.0760*
C1w	0.0572 (2)	0.56668 (17)	0.0834 (3)	0.0380*
O1w	0.0443 (5)	0.4507 (3)	0.0867 (4)	0.0380*
C2w	−0.0968 (2)	0.65429 (15)	0.08651 (9)	0.0380*
H2w	−0.1932 (11)	0.6143 (6)	0.0598 (4)	0.0760*
C3w	−0.0589 (2)	0.78378 (15)	0.05587 (9)	0.0380*
H3Aw	−0.1535 (11)	0.8405 (6)	0.0603 (4)	0.0760*
H3Bw	−0.0449 (10)	0.7782 (6)	0.0064 (4)	0.0760*
C4w	0.1043 (2)	0.83674 (16)	0.09717 (9)	0.0380*
H4w	0.1381 (12)	0.9151 (7)	0.0777 (4)	0.0760*
C5w	0.2583 (2)	0.75006 (17)	0.0912 (2)	0.0380*
O2w	0.4093 (3)	0.7853 (3)	0.0928 (4)	0.0380*
C6w	0.0742 (2)	0.85581 (15)	0.17599 (8)	0.0380*
H6Aw	−0.0119 (11)	0.9206 (7)	0.1752 (4)	0.0760*
H6Bw	0.1815 (12)	0.8864 (7)	0.1993 (4)	0.0760*
C7w	0.0097 (2)	0.73736 (16)	0.21080 (9)	0.0380*
H7Aw	0.1038 (12)	0.6790 (6)	0.2192 (5)	0.0760*
H7Bw	−0.0318 (10)	0.7583 (7)	0.2553 (4)	0.0760*
C8w	−0.1364 (2)	0.66815 (17)	0.16490 (9)	0.0380*
H8Aw	−0.1579 (11)	0.5853 (7)	0.1828 (4)	0.0760*
H8Bw	−0.2463 (12)	0.7112 (6)	0.1643 (4)	0.0760*

Geometric parameters (Å, º) top

O1—C1	1.223 (3)	C6—H6B	0.953 (9)
O2—C5	1.216 (3)	C7—H7B	0.953 (8)
O1W—C1W	1.230 (4)	C7—H7A	0.955 (8)
O2W—C5W	1.214 (3)	C8—H8B	0.952 (9)
N1—C5	1.386 (2)	C8—H8A	0.955 (8)
N1—C1	1.391 (2)	C1W—C2W	1.506 (2)
N1—H1	0.902 (8)	C2W—C8W	1.547 (2)
N1W—C5W	1.386 (2)	C2W—C3W	1.523 (2)
N1W—C1W	1.389 (2)	C3W—C4W	1.516 (2)
N1W—H1W	0.905 (8)	C4W—C5W	1.507 (2)
C1—C2	1.502 (2)	C4W—C6W	1.542 (2)
C2—C3	1.514 (2)	C6W—C7W	1.517 (2)
C2—C8	1.543 (2)	C7W—C8W	1.534 (2)
C3—C4	1.522 (2)	C2W—H2W	0.952 (8)
C4—C6	1.546 (2)	C3W—H3AW	0.951 (8)
C4—C5	1.508 (2)	C3W—H3BW	0.953 (8)
C6—C7	1.528 (2)	C4W—H4W	0.951 (8)
C7—C8	1.520 (2)	C6W—H6AW	0.950 (8)
C2—H2	0.950 (8)	C6W—H6BW	0.951 (9)
C3—H3B	0.951 (8)	C7W—H7AW	0.950 (8)
C3—H3A	0.952 (8)	C7W—H7BW	0.953 (8)
C4—H4	0.953 (7)	C8W—H8AW	0.957 (8)
C6—H6A	0.953 (8)	C8W—H8BW	0.957 (9)

C1—N1—C5	126.06 (15)	C7—C8—H8A	112.7 (5)
C1—N1—H1	116.7 (5)	C2—C8—H8A	108.8 (5)
C5—N1—H1	117.2 (5)	C2—C8—H8B	106.9 (5)
C1W—N1W—C5W	125.81 (16)	O1W—C1W—N1W	119.0 (2)
C5W—N1W—H1W	117.4 (5)	N1W—C1W—C2W	117.11 (16)
C1W—N1W—H1W	116.7 (5)	O1W—C1W—C2W	122.8 (2)
O1—C1—N1	119.6 (2)	C1W—C2W—C8W	108.9 (2)
N1—C1—C2	117.50 (14)	C3W—C2W—C8W	109.98 (14)
O1—C1—C2	122.8 (2)	C1W—C2W—C3W	110.87 (16)
C1—C2—C8	109.34 (19)	C2W—C3W—C4W	108.28 (14)
C3—C2—C8	109.67 (14)	C3W—C4W—C6W	110.56 (13)
C1—C2—C3	110.26 (14)	C3W—C4W—C5W	110.62 (16)
C2—C3—C4	108.64 (13)	C5W—C4W—C6W	110.10 (18)
C3—C4—C6	110.76 (13)	O2W—C5W—C4W	124.4 (2)
C3—C4—C5	110.07 (16)	N1W—C5W—C4W	116.18 (14)
C5—C4—C6	109.56 (18)	O2W—C5W—N1W	119.1 (2)
O2—C5—C4	124.7 (2)	C4W—C6W—C7W	113.38 (13)
N1—C5—C4	116.06 (14)	C6W—C7W—C8W	113.47 (14)
O2—C5—N1	119.2 (2)	C2W—C8W—C7W	112.66 (13)
C4—C6—C7	111.75 (13)	C1W—C2W—H2W	106.2 (5)
C6—C7—C8	111.85 (13)	C3W—C2W—H2W	111.3 (4)
C2—C8—C7	111.24 (13)	C8W—C2W—H2W	109.5 (5)
C1—C2—H2	106.2 (5)	C2W—C3W—H3AW	110.8 (5)
C3—C2—H2	111.5 (4)	C2W—C3W—H3BW	111.2 (4)
C8—C2—H2	109.8 (5)	C4W—C3W—H3AW	108.8 (5)
C2—C3—H3A	110.7 (5)	C4W—C3W—H3BW	111.2 (5)
H3A—C3—H3B	106.4 (6)	H3AW—C3W—H3BW	106.6 (6)
C2—C3—H3B	110.8 (4)	C3W—C4W—H4W	111.3 (5)
C4—C3—H3A	109.3 (5)	C5W—C4W—H4W	104.7 (6)
C4—C3—H3B	111.1 (5)	C6W—C4W—H4W	109.4 (5)
C3—C4—H4	111.7 (5)	C4W—C6W—H6AW	104.4 (5)
C5—C4—H4	105.0 (5)	C4W—C6W—H6BW	106.7 (5)
C6—C4—H4	109.6 (5)	C7W—C6W—H6AW	110.1 (5)
C7—C6—H6B	113.1 (4)	C7W—C6W—H6BW	112.5 (5)
H6A—C6—H6B	109.2 (6)	H6AW—C6W—H6BW	109.4 (7)
C4—C6—H6A	104.6 (5)	C6W—C7W—H7AW	109.4 (5)
C4—C6—H6B	107.0 (5)	C6W—C7W—H7BW	110.0 (5)
C7—C6—H6A	110.8 (5)	C8W—C7W—H7AW	106.7 (5)
C6—C7—H7B	110.9 (5)	C8W—C7W—H7BW	108.7 (5)
H7A—C7—H7B	108.7 (7)	H7AW—C7W—H7BW	108.4 (7)
C8—C7—H7A	106.6 (5)	C2W—C8W—H8AW	108.0 (5)
C6—C7—H7A	109.9 (5)	C2W—C8W—H8BW	106.8 (5)
C8—C7—H7B	108.7 (5)	C7W—C8W—H8AW	112.1 (5)
C7—C8—H8B	111.9 (5)	C7W—C8W—H8BW	112.1 (5)
H8A—C8—H8B	105.0 (7)	H8AW—C8W—H8BW	104.8 (7)

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
N1—H1···O1Wⁱ	0.90 (1)	2.11 (1)	3.006 (4)	172 (1)
N1W—H1W···O1ⁱⁱ	0.91 (1)	2.03 (1)	2.931 (4)	172 (1)
C2—H2···O1Wⁱⁱⁱ	0.95 (1)	2.56 (1)	3.355 (4)	141 (1)
C3W—H3BW···O2^iv	0.95 (1)	2.56 (1)	3.406 (5)	148 (1)
C3—H3B···O2W^v	0.95 (1)	2.49 (1)	3.384 (7)	158 (1)

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

Acknowledgements

We thank the Basic Technology programme of the UK Research Councils for funding under the project Control and Prediction of the Organic Solid State (https://www.cposs.org.uk). We also thank the EPSRC for grant GR/N07462/01.

References

Allen, F. H., Johnson, O., Shields, G. P., Smith, B. R. & Towler, M. (2004). J. Appl. Cryst. 37, 335–338. Web of Science CSD CrossRef CAS IUCr Journals Google Scholar
Boultif, A. & Louër, D. (1991). J. Appl. Cryst. 24, 987–993. CrossRef CAS Web of Science IUCr Journals Google Scholar
Coelho, A. A. (2003). TOPAS. Version 3.1 User Manual. Bruker AXS GmbH, Karlsruhe, Germany. Google Scholar
David, W. I. F., Shankland, K., Cole, J., Maginn, S., Motherwell, W. D. S. & Taylor, R. (2001). DASH. Version 3.0 User Manual. Cambridge Crystallographic Data Centre, Cambridge, England. Google Scholar
David, W. I. F., Shankland, K. & Shankland, N. (1998). Chem. Commun. pp. 931–932. Web of Science CSD CrossRef Google Scholar
Etter, M. C. (1990). Acc. Chem. Res. 23, 120–126. CrossRef CAS Web of Science Google Scholar
Hill, R. J. & Madsen, I. C. (2002). Structure Determination from Powder Diffraction Data, edited by W. I. F. David, K. Shankland, L. B. McCusker & Ch. Baerlocher, pp. 114–116. Oxford University Press. Google Scholar
Howie, R. A. & Skakle, J. M. S. (2001). Acta Cryst. E57, o822–o824. Web of Science CSD CrossRef IUCr Journals Google Scholar
Järvinen, M. (1993). J. Appl. Cryst. 26, 525–531. CrossRef Web of Science IUCr Journals Google Scholar
Kienle, M. & Jacob, M. (2003). DIFFRAC plus XRD Commander. Version 2.3. Bruker AXS GmbH, Karlsruhe, Germany. Google Scholar
Markvardsen, A. J., David, W. I. F., Johnson, J. C. & Shankland, K. (2001). Acta Cryst. A57, 47–54. Web of Science CrossRef CAS IUCr Journals Google Scholar
Macrae, C. F., Edgington, P. R., McCabe, P., Pidcock, E., Shields, G. P., Taylor, R., Towler, M. & van de Streek, J. (2006). J. Appl. Cryst. 39, 453–457. Web of Science CSD CrossRef CAS IUCr Journals Google Scholar
Pawley, G. S. (1981). J. Appl. Cryst. 14, 357–361. CrossRef CAS Web of Science IUCr Journals Google Scholar
Rietveld, H. M. (1969). J. Appl. Cryst. 2, 65–71. CrossRef CAS IUCr Journals Web of Science Google Scholar
Shankland, K., David, W. I. F. & Sivia, D. S. (1997). J. Mater. Chem. 7, 569–572. CSD CrossRef CAS Google Scholar
Spek, A. L. (2003). J. Appl. Cryst. 36, 7–13. Web of Science CrossRef CAS IUCr Journals Google Scholar

© International Union of Crystallography. Prior permission is not required to reproduce short quotations, tables and figures from this article, provided the original authors and source are cited. For more information, click here.