metal-organic compounds
catena-Poly[heptylenediammonium [[tetrachloridobismuthate(III)]-μ-chlorido]]
aDépartement de Physique-Chimie, Laboratoire de Chimie, Centre Régional des Métiers de l'Education et de la Formation, Souissi Rabat, Morocco, bEquipe de Physico-Chimie des Matériaux Inorganiques, Université Ibn Tofail, Faculté des Sciences, BP 133, 14000 Kénitra, Morocco, and cLaboratoire de Chimie du Solide Appliquée, Faculté des Sciences, Université Mohammed V-Agdal, Avenue Ibn Battouta, BP 1014, Rabat, Morocco
*Correspondence e-mail: a_ouasri@yahoo.fr
The title organic-inorganic hybrid compound, {(C7H20N2)[BiCl5]}n, consists of distorted corner-joined [BiCl6] octahedra forming zigzag polymeric anionic chains parallel to [001], separated by columns of heptylenediammonium cations. The contains two crystallographically independent bismuth metal atoms, one of which lies on an inversion centre and the other on a twofold axis. In the crystal, the polymeric chains and cations are linked by N—H⋯Cl hydrogen bonds, forming undulating layers parallel to (110).
Related literature
For potential applications of alkylammonium halogenidoantimonates and -bismuthates, see: Ciapala et al. (1997); Bednarska-Bolek et al. (2000); Bator et al. (1998). For the structures of related compounds see: Ouasri et al. (2001, 2012); Jeghnou et al. (2005); Rhandour et al. (2011).
Experimental
Crystal data
|
|
Data collection: APEX2 (Bruker, 2009); cell SAINT (Bruker, 2009); data reduction: SAINT; program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: ORTEP-3 for Windows (Farrugia, 2012); software used to prepare material for publication: PLATON (Spek, 2009) and publCIF (Westrip, 2010).
Supporting information
10.1107/S1600536813018102/rz5076sup1.cif
contains datablock I. DOI:Structure factors: contains datablock I. DOI: 10.1107/S1600536813018102/rz5076Isup2.hkl
Single crystals of the title compound were obtained by slow evaporation, at room temperature, of an aqueous solution containing stoichiometric amounts of 1,7-diaminoheptane NH2(CH2)7NH2 (acidified with HCl in a large excess) and bismuth(III) oxide Bi2O3.
All H atoms were located in a difference Fourier map and treated as riding, with C—H = 0.97 Å, N—H = 0.89 Å, and with Uiso(H) = 1.2 Ueq(C, N). One outlier (1 1 1) was omitted in the last cycles of refinement.
Data collection: APEX2 (Bruker, 2009); cell
SAINT (Bruker, 2009); data reduction: SAINT (Bruker, 2009); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: ORTEP-3 for Windows (Farrugia, 2012); software used to prepare material for publication: PLATON (Spek, 2009) and publCIF (Westrip, 2010).(C7H20N2)[BiCl5] | F(000) = 1952 |
Mr = 518.48 | Dx = 2.138 Mg m−3 |
Orthorhombic, Pbcn | Mo Kα radiation, λ = 0.71073 Å |
Hall symbol: -P 2n 2ab | Cell parameters from 3559 reflections |
a = 12.2451 (5) Å | θ = 2.5–27.1° |
b = 16.5509 (6) Å | µ = 11.75 mm−1 |
c = 15.8934 (6) Å | T = 296 K |
V = 3221.1 (2) Å3 | Block, colourless |
Z = 8 | 0.36 × 0.31 × 0.27 mm |
Bruker X8 APEX Diffractometer | 3559 independent reflections |
Radiation source: fine-focus sealed tube | 2700 reflections with I > 2σ(I) |
Graphite monochromator | Rint = 0.034 |
ϕ and ω scans | θmax = 27.1°, θmin = 2.5° |
Absorption correction: multi-scan (SADABS; Bruker, 2009) | h = −15→15 |
Tmin = 0.512, Tmax = 0.640 | k = −19→21 |
26890 measured reflections | l = −20→20 |
Refinement on F2 | Primary atom site location: structure-invariant direct methods |
Least-squares matrix: full | Secondary atom site location: difference Fourier map |
R[F2 > 2σ(F2)] = 0.021 | Hydrogen site location: inferred from neighbouring sites |
wR(F2) = 0.051 | H-atom parameters constrained |
S = 1.05 | w = 1/[σ2(Fo2) + (0.0185P)2 + 4.1437P] where P = (Fo2 + 2Fc2)/3 |
3559 reflections | (Δ/σ)max < 0.001 |
138 parameters | Δρmax = 0.70 e Å−3 |
0 restraints | Δρmin = −0.96 e Å−3 |
(C7H20N2)[BiCl5] | V = 3221.1 (2) Å3 |
Mr = 518.48 | Z = 8 |
Orthorhombic, Pbcn | Mo Kα radiation |
a = 12.2451 (5) Å | µ = 11.75 mm−1 |
b = 16.5509 (6) Å | T = 296 K |
c = 15.8934 (6) Å | 0.36 × 0.31 × 0.27 mm |
Bruker X8 APEX Diffractometer | 3559 independent reflections |
Absorption correction: multi-scan (SADABS; Bruker, 2009) | 2700 reflections with I > 2σ(I) |
Tmin = 0.512, Tmax = 0.640 | Rint = 0.034 |
26890 measured reflections |
R[F2 > 2σ(F2)] = 0.021 | 0 restraints |
wR(F2) = 0.051 | H-atom parameters constrained |
S = 1.05 | Δρmax = 0.70 e Å−3 |
3559 reflections | Δρmin = −0.96 e Å−3 |
138 parameters |
Geometry. All s.u.'s (except the s.u. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell s.u.'s are taken into account individually in the estimation of s.u.'s in distances, angles and torsion angles; correlations between s.u.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell s.u.'s is used for estimating s.u.'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. |
x | y | z | Uiso*/Ueq | ||
C1 | 0.6871 (4) | 0.7642 (3) | 0.0475 (3) | 0.0677 (14) | |
H1A | 0.7050 | 0.7509 | 0.1053 | 0.081* | |
H1B | 0.6323 | 0.7259 | 0.0286 | 0.081* | |
C2 | 0.6390 (3) | 0.8465 (2) | 0.0455 (2) | 0.0451 (9) | |
H2A | 0.6214 | 0.8611 | −0.0121 | 0.054* | |
H2B | 0.6916 | 0.8853 | 0.0668 | 0.054* | |
C3 | 0.5365 (3) | 0.8490 (2) | 0.0987 (3) | 0.0463 (9) | |
H3A | 0.4841 | 0.8114 | 0.0750 | 0.056* | |
H3B | 0.5547 | 0.8298 | 0.1547 | 0.056* | |
C4 | 0.4816 (3) | 0.9305 (2) | 0.1073 (3) | 0.0441 (9) | |
H4A | 0.4584 | 0.9489 | 0.0522 | 0.053* | |
H4B | 0.5339 | 0.9693 | 0.1290 | 0.053* | |
C5 | 0.3835 (3) | 0.9273 (2) | 0.1654 (2) | 0.0415 (9) | |
H5A | 0.3273 | 0.8947 | 0.1389 | 0.050* | |
H5B | 0.4048 | 0.9002 | 0.2169 | 0.050* | |
C6 | 0.3346 (3) | 1.0084 (2) | 0.1881 (2) | 0.0401 (9) | |
H6A | 0.3904 | 1.0421 | 0.2134 | 0.048* | |
H6B | 0.3094 | 1.0350 | 0.1373 | 0.048* | |
C7 | 0.2416 (4) | 0.9995 (2) | 0.2478 (2) | 0.0475 (11) | |
H7A | 0.1834 | 0.9698 | 0.2204 | 0.057* | |
H7B | 0.2655 | 0.9683 | 0.2960 | 0.057* | |
N1 | 0.7835 (4) | 0.7542 (3) | −0.0032 (2) | 0.0658 (11) | |
H11 | 0.8014 | 0.7021 | −0.0052 | 0.079* | |
H12 | 0.8382 | 0.7822 | 0.0192 | 0.079* | |
H13 | 0.7704 | 0.7720 | −0.0551 | 0.079* | |
N2 | 0.1985 (3) | 1.0779 (2) | 0.27729 (18) | 0.0453 (8) | |
H21 | 0.1546 | 1.0699 | 0.3211 | 0.054* | |
H22 | 0.1612 | 1.1015 | 0.2359 | 0.054* | |
H23 | 0.2537 | 1.1097 | 0.2926 | 0.054* | |
Cl1 | 0.55628 (8) | 0.15799 (5) | 0.13916 (5) | 0.0390 (2) | |
Cl2 | 0.29126 (8) | 0.25115 (6) | 0.19982 (6) | 0.0504 (2) | |
Cl3 | 0.54355 (11) | 0.38672 (7) | 0.12014 (7) | 0.0637 (3) | |
Cl4 | 0.54647 (9) | 0.38534 (6) | −0.11631 (6) | 0.0493 (2) | |
Cl5 | 0.29132 (8) | 0.45097 (6) | −0.01712 (6) | 0.0465 (2) | |
Bi1 | 0.5000 | 0.261494 (10) | 0.2500 | 0.02717 (6) | |
Bi2 | 0.5000 | 0.5000 | 0.0000 | 0.02820 (6) |
U11 | U22 | U33 | U12 | U13 | U23 | |
C1 | 0.073 (3) | 0.062 (3) | 0.068 (3) | 0.024 (3) | 0.022 (3) | 0.008 (2) |
C2 | 0.047 (2) | 0.043 (2) | 0.045 (2) | 0.0008 (18) | −0.0039 (18) | −0.0019 (17) |
C3 | 0.052 (2) | 0.040 (2) | 0.046 (2) | −0.0019 (19) | 0.0013 (19) | −0.0077 (18) |
C4 | 0.052 (2) | 0.035 (2) | 0.046 (2) | 0.0019 (17) | 0.0019 (18) | −0.0005 (17) |
C5 | 0.045 (2) | 0.038 (2) | 0.041 (2) | −0.0006 (17) | 0.0000 (17) | 0.0060 (16) |
C6 | 0.041 (2) | 0.041 (2) | 0.038 (2) | −0.0072 (16) | 0.0024 (18) | −0.0011 (16) |
C7 | 0.043 (2) | 0.046 (3) | 0.054 (3) | 0.0006 (17) | 0.007 (2) | 0.0091 (19) |
N1 | 0.065 (3) | 0.076 (3) | 0.057 (2) | 0.012 (2) | −0.002 (2) | 0.0057 (19) |
N2 | 0.0392 (17) | 0.061 (2) | 0.0356 (15) | −0.0007 (16) | 0.0033 (14) | 0.0017 (15) |
Cl1 | 0.0461 (5) | 0.0372 (5) | 0.0336 (4) | −0.0012 (4) | 0.0044 (4) | −0.0097 (4) |
Cl2 | 0.0391 (5) | 0.0545 (6) | 0.0575 (6) | 0.0042 (4) | −0.0104 (5) | 0.0104 (5) |
Cl3 | 0.0720 (7) | 0.0646 (8) | 0.0546 (6) | −0.0119 (6) | −0.0077 (6) | 0.0313 (6) |
Cl4 | 0.0520 (6) | 0.0497 (6) | 0.0463 (5) | −0.0004 (5) | 0.0114 (5) | −0.0126 (5) |
Cl5 | 0.0408 (5) | 0.0531 (6) | 0.0457 (5) | −0.0049 (4) | 0.0064 (4) | −0.0023 (4) |
Bi1 | 0.03136 (10) | 0.02362 (10) | 0.02653 (9) | 0.000 | 0.00112 (8) | 0.000 |
Bi2 | 0.03338 (10) | 0.02704 (11) | 0.02418 (9) | −0.00266 (8) | 0.00014 (8) | 0.00424 (6) |
C1—N1 | 1.439 (6) | C7—H7A | 0.9700 |
C1—C2 | 1.485 (6) | C7—H7B | 0.9700 |
C1—H1A | 0.9700 | N1—H11 | 0.8900 |
C1—H1B | 0.9700 | N1—H12 | 0.8900 |
C2—C3 | 1.515 (5) | N1—H13 | 0.8900 |
C2—H2A | 0.9700 | N2—H21 | 0.8900 |
C2—H2B | 0.9700 | N2—H22 | 0.8900 |
C3—C4 | 1.513 (6) | N2—H23 | 0.8900 |
C3—H3A | 0.9700 | Cl1—Bi1 | 2.5520 (8) |
C3—H3B | 0.9700 | Cl2—Bi1 | 2.6830 (10) |
C4—C5 | 1.517 (5) | Cl3—Bi2 | 2.7287 (10) |
C4—H4A | 0.9700 | Cl3—Bi1 | 2.9732 (10) |
C4—H4B | 0.9700 | Cl4—Bi2 | 2.7097 (9) |
C5—C6 | 1.512 (5) | Cl5—Bi2 | 2.6948 (9) |
C5—H5A | 0.9700 | Bi1—Cl1i | 2.5520 (8) |
C5—H5B | 0.9700 | Bi1—Cl2i | 2.6830 (10) |
C6—C7 | 1.490 (5) | Bi1—Cl3i | 2.9732 (10) |
C6—H6A | 0.9700 | Bi2—Cl5ii | 2.6948 (9) |
C6—H6B | 0.9700 | Bi2—Cl4ii | 2.7097 (9) |
C7—N2 | 1.477 (5) | Bi2—Cl3ii | 2.7287 (10) |
N1—C1—C2 | 114.8 (4) | C1—N1—H12 | 109.5 |
N1—C1—H1A | 108.6 | H11—N1—H12 | 109.5 |
C2—C1—H1A | 108.6 | C1—N1—H13 | 109.5 |
N1—C1—H1B | 108.6 | H11—N1—H13 | 109.5 |
C2—C1—H1B | 108.6 | H12—N1—H13 | 109.5 |
H1A—C1—H1B | 107.6 | C7—N2—H21 | 109.5 |
C1—C2—C3 | 109.9 (3) | C7—N2—H22 | 109.5 |
C1—C2—H2A | 109.7 | H21—N2—H22 | 109.5 |
C3—C2—H2A | 109.7 | C7—N2—H23 | 109.5 |
C1—C2—H2B | 109.7 | H21—N2—H23 | 109.5 |
C3—C2—H2B | 109.7 | H22—N2—H23 | 109.5 |
H2A—C2—H2B | 108.2 | Bi2—Cl3—Bi1 | 158.39 (5) |
C4—C3—C2 | 116.2 (3) | Cl1—Bi1—Cl1i | 95.67 (4) |
C4—C3—H3A | 108.2 | Cl1—Bi1—Cl2i | 84.55 (3) |
C2—C3—H3A | 108.2 | Cl1i—Bi1—Cl2i | 90.53 (3) |
C4—C3—H3B | 108.2 | Cl1—Bi1—Cl2 | 90.53 (3) |
C2—C3—H3B | 108.2 | Cl1i—Bi1—Cl2 | 84.55 (3) |
H3A—C3—H3B | 107.4 | Cl2i—Bi1—Cl2 | 172.69 (4) |
C3—C4—C5 | 112.0 (3) | Cl1—Bi1—Cl3i | 174.59 (3) |
C3—C4—H4A | 109.2 | Cl1i—Bi1—Cl3i | 86.58 (3) |
C5—C4—H4A | 109.2 | Cl2i—Bi1—Cl3i | 90.52 (3) |
C3—C4—H4B | 109.2 | Cl2—Bi1—Cl3i | 94.58 (4) |
C5—C4—H4B | 109.2 | Cl1—Bi1—Cl3 | 86.58 (3) |
H4A—C4—H4B | 107.9 | Cl1i—Bi1—Cl3 | 174.59 (3) |
C6—C5—C4 | 115.3 (3) | Cl2i—Bi1—Cl3 | 94.58 (4) |
C6—C5—H5A | 108.4 | Cl2—Bi1—Cl3 | 90.52 (3) |
C4—C5—H5A | 108.4 | Cl3i—Bi1—Cl3 | 91.61 (5) |
C6—C5—H5B | 108.4 | Cl5ii—Bi2—Cl5 | 180.0 |
C4—C5—H5B | 108.4 | Cl5ii—Bi2—Cl4ii | 85.37 (3) |
H5A—C5—H5B | 107.5 | Cl5—Bi2—Cl4ii | 94.63 (3) |
C7—C6—C5 | 111.6 (3) | Cl5ii—Bi2—Cl4 | 94.63 (3) |
C7—C6—H6A | 109.3 | Cl5—Bi2—Cl4 | 85.37 (3) |
C5—C6—H6A | 109.3 | Cl4ii—Bi2—Cl4 | 180.00 (4) |
C7—C6—H6B | 109.3 | Cl5ii—Bi2—Cl3ii | 92.81 (3) |
C5—C6—H6B | 109.3 | Cl5—Bi2—Cl3ii | 87.19 (3) |
H6A—C6—H6B | 108.0 | Cl4ii—Bi2—Cl3ii | 87.43 (3) |
N2—C7—C6 | 112.9 (3) | Cl4—Bi2—Cl3ii | 92.57 (3) |
N2—C7—H7A | 109.0 | Cl5ii—Bi2—Cl3 | 87.19 (3) |
C6—C7—H7A | 109.0 | Cl5—Bi2—Cl3 | 92.81 (3) |
N2—C7—H7B | 109.0 | Cl4ii—Bi2—Cl3 | 92.57 (3) |
C6—C7—H7B | 109.0 | Cl4—Bi2—Cl3 | 87.43 (3) |
H7A—C7—H7B | 107.8 | Cl3ii—Bi2—Cl3 | 180.00 (4) |
C1—N1—H11 | 109.5 |
Symmetry codes: (i) −x+1, y, −z+1/2; (ii) −x+1, −y+1, −z. |
D—H···A | D—H | H···A | D···A | D—H···A |
N1—H13···Cl2ii | 0.89 | 2.45 | 3.257 (4) | 151 |
N2—H22···Cl4iii | 0.89 | 2.37 | 3.222 (3) | 159 |
Symmetry codes: (ii) −x+1, −y+1, −z; (iii) x−1/2, −y+3/2, −z. |
Experimental details
Crystal data | |
Chemical formula | (C7H20N2)[BiCl5] |
Mr | 518.48 |
Crystal system, space group | Orthorhombic, Pbcn |
Temperature (K) | 296 |
a, b, c (Å) | 12.2451 (5), 16.5509 (6), 15.8934 (6) |
V (Å3) | 3221.1 (2) |
Z | 8 |
Radiation type | Mo Kα |
µ (mm−1) | 11.75 |
Crystal size (mm) | 0.36 × 0.31 × 0.27 |
Data collection | |
Diffractometer | Bruker X8 APEX Diffractometer |
Absorption correction | Multi-scan (SADABS; Bruker, 2009) |
Tmin, Tmax | 0.512, 0.640 |
No. of measured, independent and observed [I > 2σ(I)] reflections | 26890, 3559, 2700 |
Rint | 0.034 |
(sin θ/λ)max (Å−1) | 0.641 |
Refinement | |
R[F2 > 2σ(F2)], wR(F2), S | 0.021, 0.051, 1.05 |
No. of reflections | 3559 |
No. of parameters | 138 |
H-atom treatment | H-atom parameters constrained |
Δρmax, Δρmin (e Å−3) | 0.70, −0.96 |
Computer programs: APEX2 (Bruker, 2009), SAINT (Bruker, 2009), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), ORTEP-3 for Windows (Farrugia, 2012), PLATON (Spek, 2009) and publCIF (Westrip, 2010).
D—H···A | D—H | H···A | D···A | D—H···A |
N1—H13···Cl2i | 0.89 | 2.45 | 3.257 (4) | 150.8 |
N2—H22···Cl4ii | 0.89 | 2.37 | 3.222 (3) | 159.3 |
Symmetry codes: (i) −x+1, −y+1, −z; (ii) x−1/2, −y+3/2, −z. |
Acknowledgements
The authors thank the Unit of Support for Technical and Scientific Research (UATRS, CNRST) for the X-ray measurements.
References
Bator, G., Baran, J., Jakubas, R. & Sobczyk, L. (1998). J. Mol. Struct. 450, 89–100. Web of Science CrossRef CAS Google Scholar
Bednarska-Bolek, B., Zaleski, J., Bator, G. & Jakubas, R. (2000). J. Phys. Chem. Solids 61, 1249–1261. CAS Google Scholar
Bruker (2009). APEX2, SAINT and SADABS. Bruker AXS Inc., Madison, Wisconsin, USA. Google Scholar
Ciapala, P., Jakubas, R., Bator, G., Zaleski, J., Pietraszko, A., Drozd, M. & Baran, J. (1997). J. Phys. Condens. Matter 9, 627–645. CrossRef CAS Web of Science Google Scholar
Farrugia, L. J. (2012). J. Appl. Cryst. 45, 849–854. Web of Science CrossRef CAS IUCr Journals Google Scholar
Jeghnou, H., Ouasri, A., Rhandour, A., Dhamelincourt, M. C., Dhamelincourt, P., Mazzah, A. & Roussel, P. (2005). J. Raman Spectrosc. 36, 1023–1028. Web of Science CrossRef CAS Google Scholar
Ouasri, A., Elyoubi, M. S. D., Guedira, T., Rhandour, A., Mhiri, T. & Daoud, A. (2001). Spectrochim. Acta Part A 57, 2593–2598. CrossRef CAS Google Scholar
Ouasri, A., Jeghnou, H., Rhandour, A., Mazzah, A. & Rousseau, P. (2012). J. Mol. Struct. 1028, 79–87. Web of Science CrossRef CAS Google Scholar
Rhandour, A., Ouasri, A., Mazzah, A. & Rousseau, P. (2011). J. Mol. Struct. 990, 95–101. Web of Science CSD CrossRef CAS Google Scholar
Sheldrick, G. M. (2008). Acta Cryst. A64, 112–122. Web of Science CrossRef CAS IUCr Journals Google Scholar
Spek, A. L. (2009). Acta Cryst. D65, 148–155. Web of Science CrossRef CAS IUCr Journals Google Scholar
Westrip, S. P. (2010). J. Appl. Cryst. 43, 920–925. Web of Science CrossRef CAS IUCr Journals Google Scholar
This is an open-access article distributed under the terms of the Creative Commons Attribution (CC-BY) Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original authors and source are cited.
Alkylammonium halogenoantimonates and bismuthates of general formula R2MX5, R3M2X9 and R5M2X11 (R: organic cations, M: Sb or Bi, X: Cl, Br or I) have recently attracted considerable attention since some of these compounds have revealed interesting properties (ferroelectric and non-linear optical) which make them promising materials from the viewpoint of applications (Ciapala et al., 1997; Bednarska-Bolek et al., 2000; Bator et al., 1998). The crystal lattices of the halogenometallates compounds are built of distorted MX63- octahedra which are either isolated or linked to each other by corners, edges and faces. The anionic sublattices of the halogenoantimonates and bismuthates compounds of formula R3M2X9 (Ouasri et al., 2001; Jeghnou et al., 2005; Ouasri et al., 2012; Rhandour et al., 2011) are built of distorted MX63- octahedra connected with each other, by corners, edges and faces, in such a way that three halogen atoms of the coordination sphere of Sb or Bi atoms are bridging and three are terminal. The aim of the present work was to study the recently synthesized title compound by X-ray diffraction to obtain informations about its crystal structure at ambient temperature.
The structure of the organic-inorganic hybrid title compound is built up from inorganic polymeric anions and organic cations (Fig. 1). In this structure, each bismuth cation is surrounded by six chlorine anions building a distorted BiCl63- octahedron, with Bi—Cl distances varying from 2.5520 (8) to 2.9732 (10) Å. The octahedra are corner-joined to form one-dimensional zig-zag chains propagating along the c axis. The periodic length of this string is three octahedra. In the crystal structure, the chains and organic cations are linked together by N—H···Cl hydrogen bonds(Table 1) to build undulated sheets parallel to the (1 1 0) plane (Fig. 2).