MgSO4·11H2O and MgCrO4·11H2O based on time-of-flight neutron single-crystal Laue data

Fortes, A.D.; Wood, I.G.; Gutmann, M.J.

doi:10.1107/S0108270113005751

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MgSO₄·11H₂O and MgCrO₄·11H₂O based on time-of-flight neutron single-crystal Laue data

A. D. Fortes, I. G. Wood and M. J. Gutmann

Hexaaquamagnesium(II) sulfate pentahydrate, [Mg(H₂O)₆]SO₄·5H₂O, and hexaaquamagnesium(II) chromate(II) pentahydrate, [Mg(H₂O)₆][CrO₄]·5H₂O, are isomorphous, being composed of hexaaquamagnesium(II) octahedra, [Mg(H₂O)₆]²⁺, and sulfate (chromate) tetrahedral oxyanions, SO₄²⁻ (CrO₄²⁻), linked by hydrogen bonds. There are two symmetry-inequivalent centrosymmetric octahedra: M1 at (0, 0, 0) donates hydrogen bonds directly to the tetrahedral oxyanion, T1, at (0.405, 0.320, 0.201), whereas the M2 octahedron at (0, 0, ${1 \over 2}$ ) is linked to the oxyanion via five interstitial water molecules. Substitution of Cr^VI for S^VI leads to a substantial expansion of T1, since the Cr—O bond is approximately 12% longer than the S—O bond. This expansion is propagated through the hydrogen-bonded framework to produce a 3.3% increase in unit-cell volume; the greatest part of this chemically induced strain is manifested along the b* direction. The hydrogen bonds in the chromate compound mitigate ∼20% of the expected strain due to the larger oxyanion, becoming shorter (i.e. stronger) and more linear than in the sulfate analogue. The bifurcated hydrogen bond donated by one of the interstitial water molecules is significantly more symmetrical in the chromate analogue.

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Supporting information

	Crystallographic Information File (CIF) https://doi.org/10.1107/S0108270113005751/ku3086sup1.cif Contains datablocks I, II, global
	Structure factor file (CIF format) https://doi.org/10.1107/S0108270113005751/ku3086Isup2.hkl Contains datablock I
	Structure factor file (CIF format) https://doi.org/10.1107/S0108270113005751/ku3086IIsup3.hkl Contains datablock II

Computing details top

For both compounds, data collection: SXD2001 (Gutmann, 2005); cell refinement: SXD2001 (Gutmann, 2005); data reduction: SXD2001 (Gutmann, 2005); program(s) used to solve structure: n/a; program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: DIAMOND (Brandenburg, 2006); software used to prepare material for publication: publCIF (Westrip, 2010).

(I) Hexaaquamagnesium(II) sulfate pentahydrate top

Crystal data top

[Mg(H₂O)₆](SO₄)·5H₂O	Z = 2
M_r = 318.53	F(000) = 26
Triclinic, P1	D_x = 1.508 Mg m⁻³
a = 6.7283 (13) Å	Melting point: 275 K
b = 6.7839 (14) Å	Neutron radiation, λ = 0.48-7.0 Å
c = 17.332 (4) Å	Cell parameters from 550 reflections
α = 88.181 (13)°	µ = 0.0 mm⁻¹
β = 89.349 (14)°	T = 5 K
γ = 62.515 (12)°	Cuboid, colourless
V = 701.5 (2) Å³	2.00 × 2.00 × 2.00 mm

Data collection top

SXD beamline diffractometer	R_int = 0.000
Radiation source: ISIS neutron spallation source	θ_max = 84.9°, θ_min = 9.0°
time–of–flight Laue diffraction scans	h = −17→16
14936 measured reflections	k = −18→16
14936 independent reflections	l = −37→25
14936 reflections with I > 2σ(I)

Refinement top

Refinement on F²	Secondary atom site location: difference Fourier map
Least-squares matrix: full	Hydrogen site location: inferred from neighbouring sites
R[F² > 2σ(F²)] = 0.067	All H-atom parameters refined
wR(F²) = 0.187	w = 1/[σ²(F_o²) + (0.1001P)² + 16.5668P] where P = (F_o² + 2F_c²)/3
S = 1.11	(Δ/σ)_max = 0.001
14936 reflections	Δρ_max = 1.97 e Å⁻³
367 parameters	Δρ_min = −2.09 e Å⁻³
0 restraints	Extinction correction: SHELXL97 (Sheldrick, 2008), Fc^*=kFc[1+0.001xFc²λ³/sin(2θ)]^-1/4
Primary atom site location: structure-invariant direct methods	Extinction coefficient: 0.0187 (4)

Special details top

Experimental. For peak integration a local UB matrix refined for each frame, using approximately 50 reflections from each of the 11 detectors. Hence _cell_measurement_reflns_used 550 For final cell dimensions a weighted average of all local cells was calculated. Because of the nature of the experiment, it is not possible to give values of theta_min and theta_max for the cell determination. The same applies for the wavelength used for the experiment. The range of wavelengths used was 0.48–7.0 Angstroms, BUT the bulk of the diffraction information is obtained from wavelengths in the range 0.7–2.5 Angstroms. The data-collection procedures on the SXD instrument used for the single-crystal neutron data collection are most recently summarized in the Appendix to the following paper: Wilson, C.C. (1997). J. Mol. Struct. 405, 207–217

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. The variable wavelength nature of the data collection procedure means that sensible values of _diffrn_reflns_theta_min & _diffrn_reflns_theta_max cannot be given. Instead, the following limits are given: _diffrn_reflns_sin(theta)/lambda_min 0.06 _diffrn_reflns_sin(theta)/lambda_max 1.38 _refine_diff_density_max/min is given in Fermi per per angstrom cubed not electrons per angstrom cubed. Another way to consider the _refine_diff_density_ is as a percentage of the scattering density of a given atom: _refine_diff_density_max = 4% of oxygen _refine_diff_density_min = -4% of oxygen 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 (Å²) top

	x	y	z	U_iso*/U_eq
Mg1	1.0000	0.0000	0.0000	0.00309 (17)
OW1	0.65691 (14)	0.17344 (16)	0.00821 (6)	0.00641 (14)
H1A	0.5556 (4)	0.2338 (5)	0.05090 (16)	0.0226 (5)
H1B	0.5648 (4)	0.1897 (4)	−0.03695 (15)	0.0195 (4)
OW2	0.99062 (15)	−0.26902 (14)	0.05542 (7)	0.00605 (14)
H2A	1.1165 (4)	−0.4050 (4)	0.07339 (18)	0.0214 (4)
H2B	0.8563 (3)	−0.2707 (4)	0.07618 (16)	0.0187 (4)
OW3	1.04714 (15)	0.11065 (15)	0.10544 (6)	0.00586 (14)
H3A	1.0430 (5)	0.0428 (4)	0.15481 (15)	0.0210 (4)
H3B	1.1320 (4)	0.1928 (4)	0.11117 (16)	0.0209 (4)
Mg2	1.0000	0.0000	0.5000	0.00292 (17)
OW4	1.15158 (14)	−0.11150 (15)	0.39413 (6)	0.00532 (13)
H4A	1.3000 (3)	−0.1225 (4)	0.38388 (15)	0.0181 (4)
H4B	1.0784 (4)	−0.0869 (4)	0.34364 (15)	0.0182 (4)
OW5	0.80442 (16)	−0.15462 (16)	0.48629 (7)	0.00664 (14)
H5A	0.7715 (4)	−0.2430 (4)	0.52506 (16)	0.0200 (4)
H5B	0.7129 (4)	−0.1394 (4)	0.44090 (16)	0.0195 (4)
OW6	0.75619 (14)	0.28506 (15)	0.44646 (6)	0.00600 (14)
H6A	0.7997 (4)	0.3342 (4)	0.39855 (16)	0.0192 (4)
H6B	0.6015 (3)	0.3155 (4)	0.43816 (17)	0.0197 (4)
S1	0.4053 (2)	0.3200 (3)	0.20064 (11)	0.0020 (2)
O1	0.31690 (14)	0.33018 (14)	0.12243 (6)	0.00443 (13)
O2	0.21813 (14)	0.43819 (14)	0.25486 (6)	0.00484 (13)
O3	0.53006 (14)	0.08315 (14)	0.22698 (6)	0.00493 (13)
O4	0.55692 (14)	0.42090 (15)	0.20021 (6)	0.00561 (14)
OW7	0.31115 (15)	0.40412 (15)	0.41252 (6)	0.00597 (14)
H7A	0.2872 (4)	0.4092 (4)	0.35678 (15)	0.0202 (4)
H7B	0.2379 (4)	0.5584 (4)	0.42643 (19)	0.0246 (5)
OW8	0.60549 (15)	−0.24763 (15)	0.11976 (6)	0.00598 (14)
H8A	0.5589 (4)	−0.1284 (4)	0.15631 (16)	0.0201 (4)
H8B	0.5906 (4)	−0.3698 (4)	0.14565 (17)	0.0205 (4)
OW9	0.56102 (15)	−0.14706 (15)	0.36038 (6)	0.00562 (13)
H9A	0.5357 (4)	−0.0430 (4)	0.31630 (16)	0.0192 (4)
H9B	0.6588 (4)	−0.2941 (3)	0.33980 (16)	0.0185 (4)
OW10	0.83217 (15)	0.43812 (16)	0.30797 (6)	0.00604 (14)
H10A	0.7453 (4)	0.4115 (4)	0.26813 (16)	0.0195 (4)
H10B	0.9726 (4)	0.4156 (4)	0.28472 (16)	0.0204 (4)
OW11	0.99540 (15)	−0.09053 (15)	0.24597 (7)	0.00620 (14)
H11A	1.0629 (4)	−0.2510 (3)	0.24017 (17)	0.0206 (4)
H11B	0.8344 (3)	−0.0324 (4)	0.23867 (16)	0.0194 (4)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Mg1	0.0020 (3)	0.0035 (3)	0.0033 (5)	−0.0009 (3)	0.0001 (3)	−0.0002 (3)
OW1	0.0027 (2)	0.0092 (3)	0.0057 (4)	−0.0014 (2)	0.0003 (2)	−0.0013 (3)
H1A	0.0161 (8)	0.0311 (11)	0.0151 (11)	−0.0058 (7)	0.0073 (7)	−0.0080 (9)
H1B	0.0150 (7)	0.0279 (10)	0.0139 (10)	−0.0082 (7)	−0.0035 (6)	−0.0019 (8)
OW2	0.0045 (2)	0.0048 (3)	0.0082 (4)	−0.0018 (2)	0.0005 (2)	0.0018 (3)
H2A	0.0144 (7)	0.0152 (7)	0.0271 (13)	−0.0008 (6)	−0.0029 (7)	0.0061 (8)
H2B	0.0129 (7)	0.0216 (8)	0.0232 (11)	−0.0095 (6)	0.0032 (7)	0.0017 (8)
OW3	0.0066 (3)	0.0083 (3)	0.0041 (4)	−0.0047 (2)	0.0004 (2)	−0.0009 (3)
H3A	0.0291 (10)	0.0277 (10)	0.0111 (10)	−0.0177 (9)	−0.0008 (8)	0.0050 (8)
H3B	0.0261 (10)	0.0261 (9)	0.0195 (12)	−0.0198 (8)	−0.0014 (8)	−0.0010 (9)
Mg2	0.0026 (3)	0.0031 (3)	0.0031 (5)	−0.0014 (3)	0.0000 (3)	−0.0003 (3)
OW4	0.0041 (2)	0.0078 (3)	0.0037 (4)	−0.0023 (2)	0.0006 (2)	−0.0010 (3)
H4A	0.0119 (6)	0.0245 (9)	0.0190 (11)	−0.0094 (6)	0.0026 (6)	−0.0019 (8)
H4B	0.0175 (7)	0.0245 (9)	0.0118 (10)	−0.0090 (7)	−0.0040 (6)	0.0003 (8)
OW5	0.0078 (3)	0.0094 (3)	0.0055 (4)	−0.0064 (2)	−0.0016 (3)	0.0015 (3)
H5A	0.0257 (9)	0.0248 (9)	0.0159 (11)	−0.0174 (8)	0.0001 (8)	0.0056 (8)
H5B	0.0201 (8)	0.0251 (9)	0.0159 (11)	−0.0127 (7)	−0.0071 (7)	0.0012 (8)
OW6	0.0038 (2)	0.0062 (3)	0.0063 (4)	−0.0010 (2)	−0.0003 (2)	0.0016 (3)
H6A	0.0178 (8)	0.0230 (9)	0.0160 (11)	−0.0094 (7)	0.0015 (7)	0.0062 (7)
H6B	0.0101 (6)	0.0251 (9)	0.0232 (12)	−0.0077 (6)	−0.0013 (6)	0.0018 (8)
S1	0.0013 (4)	0.0026 (4)	0.0020 (7)	−0.0009 (3)	0.0003 (4)	−0.0004 (4)
O1	0.0042 (2)	0.0060 (3)	0.0030 (4)	−0.0022 (2)	−0.0009 (2)	−0.0006 (2)
O2	0.0032 (2)	0.0056 (3)	0.0045 (4)	−0.0008 (2)	0.0019 (2)	−0.0017 (3)
O3	0.0047 (2)	0.0032 (2)	0.0056 (4)	−0.0007 (2)	−0.0003 (2)	0.0007 (2)
O4	0.0052 (3)	0.0076 (3)	0.0065 (4)	−0.0052 (2)	−0.0005 (2)	0.0004 (3)
OW7	0.0059 (3)	0.0057 (3)	0.0061 (4)	−0.0025 (2)	0.0002 (2)	−0.0001 (3)
H7A	0.0231 (9)	0.0258 (9)	0.0101 (10)	−0.0100 (8)	−0.0006 (7)	0.0000 (8)
H7B	0.0251 (10)	0.0139 (7)	0.0304 (15)	−0.0050 (7)	0.0027 (9)	−0.0081 (9)
OW8	0.0059 (3)	0.0068 (3)	0.0058 (4)	−0.0034 (2)	0.0001 (2)	−0.0002 (3)
H8A	0.0235 (9)	0.0174 (7)	0.0194 (11)	−0.0090 (7)	0.0047 (8)	−0.0077 (8)
H8B	0.0266 (10)	0.0175 (8)	0.0215 (12)	−0.0139 (7)	0.0011 (8)	0.0034 (8)
OW9	0.0052 (3)	0.0072 (3)	0.0044 (4)	−0.0028 (2)	0.0003 (2)	−0.0002 (3)
H9A	0.0214 (8)	0.0179 (8)	0.0168 (11)	−0.0080 (7)	−0.0004 (7)	0.0056 (7)
H9B	0.0181 (7)	0.0137 (7)	0.0200 (11)	−0.0040 (6)	0.0023 (7)	−0.0036 (7)
OW10	0.0055 (3)	0.0082 (3)	0.0052 (4)	−0.0038 (2)	0.0003 (2)	−0.0004 (3)
H10A	0.0199 (8)	0.0260 (9)	0.0164 (11)	−0.0136 (7)	−0.0035 (7)	−0.0022 (8)
H10B	0.0128 (7)	0.0266 (9)	0.0223 (12)	−0.0095 (7)	0.0057 (7)	−0.0034 (9)
OW11	0.0053 (3)	0.0065 (3)	0.0061 (4)	−0.0021 (2)	−0.0003 (2)	−0.0001 (3)
H11A	0.0206 (8)	0.0120 (6)	0.0256 (13)	−0.0043 (6)	0.0013 (8)	−0.0044 (8)
H11B	0.0106 (6)	0.0215 (8)	0.0228 (12)	−0.0047 (6)	−0.0010 (6)	0.0002 (8)

Geometric parameters (Å, º) top

Mg1—OW1	2.0566 (9)	OW4—H4B	0.980 (3)
Mg1—OW1ⁱ	2.0566 (9)	OW5—H5A	0.977 (3)
Mg1—OW2	2.0617 (11)	OW5—H5B	0.978 (3)
Mg1—OW2ⁱ	2.0618 (10)	OW6—H6A	0.976 (3)
Mg1—OW3	2.0794 (10)	OW6—H6B	0.975 (2)
Mg1—OW3ⁱ	2.0794 (10)	S1—O4	1.4673 (17)
OW1—H1A	0.964 (2)	S1—O1	1.473 (2)
OW1—H1B	0.975 (3)	S1—O2	1.4836 (17)
OW2—H2A	0.965 (2)	S1—O3	1.4875 (19)
OW2—H2B	0.974 (2)	OW7—H7A	0.978 (3)
OW3—H3A	0.965 (3)	OW7—H7B	0.966 (2)
OW3—H3B	0.972 (2)	OW8—H8A	0.973 (2)
Mg2—OW5	2.0458 (9)	OW8—H8B	0.975 (3)
Mg2—OW5ⁱⁱ	2.0458 (9)	OW9—H9A	0.984 (3)
Mg2—OW6	2.0699 (11)	OW9—H9B	0.983 (2)
Mg2—OW6ⁱⁱ	2.0699 (11)	OW10—H10A	0.983 (2)
Mg2—OW4ⁱⁱ	2.0767 (10)	OW10—H10B	0.970 (2)
Mg2—OW4	2.0767 (10)	OW11—H11A	0.975 (2)
OW4—H4A	0.981 (2)	OW11—H11B	0.975 (2)

OW1—Mg1—OW1ⁱ	180.0	OW5—Mg2—OW4ⁱⁱ	89.25 (4)
OW1—Mg1—OW2	89.36 (4)	OW5ⁱⁱ—Mg2—OW4ⁱⁱ	90.75 (4)
OW1ⁱ—Mg1—OW2	90.64 (4)	OW6—Mg2—OW4ⁱⁱ	89.77 (4)
OW1—Mg1—OW2ⁱ	90.64 (4)	OW6ⁱⁱ—Mg2—OW4ⁱⁱ	90.23 (4)
OW1ⁱ—Mg1—OW2ⁱ	89.36 (4)	OW5—Mg2—OW4	90.75 (4)
OW2—Mg1—OW2ⁱ	180.0	OW5ⁱⁱ—Mg2—OW4	89.25 (4)
OW1—Mg1—OW3	92.58 (4)	OW6—Mg2—OW4	90.23 (4)
OW1ⁱ—Mg1—OW3	87.42 (4)	OW6ⁱⁱ—Mg2—OW4	89.77 (4)
OW2—Mg1—OW3	90.06 (4)	OW4ⁱⁱ—Mg2—OW4	180.0
OW2ⁱ—Mg1—OW3	89.94 (4)	Mg2—OW4—H4A	119.50 (16)
OW1—Mg1—OW3ⁱ	87.42 (4)	Mg2—OW4—H4B	127.50 (15)
OW1ⁱ—Mg1—OW3ⁱ	92.58 (4)	H4A—OW4—H4B	105.8 (2)
OW2—Mg1—OW3ⁱ	89.94 (4)	Mg2—OW5—H5A	127.10 (17)
OW2ⁱ—Mg1—OW3ⁱ	90.06 (4)	Mg2—OW5—H5B	125.54 (18)
OW3—Mg1—OW3ⁱ	179.999 (2)	H5A—OW5—H5B	107.0 (2)
Mg1—OW1—H1A	133.41 (19)	Mg2—OW6—H6A	116.31 (15)
Mg1—OW1—H1B	119.44 (15)	Mg2—OW6—H6B	124.88 (18)
H1A—OW1—H1B	106.7 (2)	H6A—OW6—H6B	105.0 (2)
Mg1—OW2—H2A	127.25 (17)	O4—S1—O1	110.31 (13)
Mg1—OW2—H2B	125.06 (16)	O4—S1—O2	109.66 (10)
H2A—OW2—H2B	106.9 (2)	O1—S1—O2	110.04 (11)
Mg1—OW3—H3A	124.24 (15)	O4—S1—O3	109.34 (11)
Mg1—OW3—H3B	123.21 (19)	O1—S1—O3	108.82 (10)
H3A—OW3—H3B	108.4 (2)	O2—S1—O3	108.64 (13)
OW5—Mg2—OW5ⁱⁱ	179.998 (1)	H7A—OW7—H7B	104.1 (3)
OW5—Mg2—OW6	89.93 (4)	H8A—OW8—H8B	107.1 (2)
OW5ⁱⁱ—Mg2—OW6	90.07 (4)	H9A—OW9—H9B	104.3 (2)
OW5—Mg2—OW6ⁱⁱ	90.07 (4)	H10A—OW10—H10B	107.3 (2)
OW5ⁱⁱ—Mg2—OW6ⁱⁱ	89.93 (4)	H11A—OW11—H11B	107.0 (2)
OW6—Mg2—OW6ⁱⁱ	180.0

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

(II) Hexaaquamagnesium(II) chromate pentahydrate top

Crystal data top

[Mg(H₂O)₆](CrO₄)·H₂O	V = 724.8 (4) Å³
M_r = 338.46	Z = 2
Triclinic, P1	F(000) = 28
a = 6.7721 (18) Å	D_x = 1.551 Mg m⁻³
b = 6.917 (2) Å	Neutron radiation, λ = 0.48-7.0 Å
c = 17.410 (5) Å	Cell parameters from 330 reflections
α = 88.21 (2)°	T = 10 K
β = 89.43 (2)°	Cuboid, yellow
γ = 62.768 (18)°	2.00 × 2.00 × 2.00 mm

Data collection top

SXD beamline diffractometer	8624 independent reflections
Radiation source: ISIS neutron spallation source	8624 reflections with I > 2σ(I)
Detector resolution: 0 pixels mm^-1	R_int = 0.000
time–of–flight Laue diffraction scans	θ_max = 88.4°, θ_min = 8.0°
Absorption correction: numerical The linear absorption coefficient is wavelength-dependent and is calculated as: µ = 4.595 + 0.015 λ [cm^-1], as determined by Gaussian integration in SXD2001 (Gutmann, 2005)	h = −15→16
	k = −15→13
8624 measured reflections	l = −46→40

Refinement top

Refinement on F²	Secondary atom site location: difference Fourier map
Least-squares matrix: full	Hydrogen site location: inferred from neighbouring sites
R[F² > 2σ(F²)] = 0.083	All H-atom parameters refined
wR(F²) = 0.224	w = 1/[σ²(F_o²) + (0.1187P)² + 33.4697P] where P = (F_o² + 2F_c²)/3
S = 1.11	(Δ/σ)_max < 0.001
8624 reflections	Δρ_max = 1.88 e Å⁻³
369 parameters	Δρ_min = −1.66 e Å⁻³
0 restraints	Extinction correction: SHELXL97 (Sheldrick, 2008), Fc^*=kFc[1+0.001xFc²λ³/sin(2θ)]^-1/4
Primary atom site location: structure-invariant direct methods	Extinction coefficient: 0.0079 (3)

Special details top

Experimental. For peak integration a local UB matrix refined for each frame, using approximately 30 reflections from each of the 11 detectors. Hence _cell_measurement_reflns_used 330 For final cell dimensions a weighted average of all local cells was calculated. Because of the nature of the experiment, it is not possible to give values of theta_min and theta_max for the cell determination. The same applies for the wavelength used for the experiment. The range of wavelengths used was 0.48–7.0 Angstroms, BUT the bulk of the diffraction information is obtained from wavelengths in the range 0.7–2.5 Angstroms. The data-collection procedures on the SXD instrument used for the single-crystal neutron data collection are most recently summarized in the Appendix to the following paper: Wilson, C.C. (1997). J. Mol. Struct. 405, 207–217

Refinement. The variable wavelength nature of the data-collection procedure means that sensible values of _diffrn_reflns_theta_min and _diffrn_reflns_theta_max cannot be given. Instead, the following limits are given _diffrn_reflns_sin(theta)/lambda_min 0.08 _diffrn_reflns_sin(theta)/lambda_max 1.38 _refine_diff_density_max/min is given in Fermi per per angstrom cubed not electrons per angstrom cubed. Another way to consider the _refine_diff_density_ is as a percentage of the scattering density of a given atom: _refine_diff_density_max = 3% of oxygen _refine_diff_density_min = -3% of oxygen 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 (Å²) top

	x	y	z	U_iso*/U_eq
Mg1	1.0000	0.0000	0.0000	0.0031 (5)
OW1	0.6591 (3)	0.1751 (4)	0.00642 (11)	0.0070 (4)
H1A	0.5558 (7)	0.2382 (10)	0.0478 (3)	0.0242 (11)
H1B	0.5686 (7)	0.1860 (9)	−0.0386 (3)	0.0206 (9)
OW2	0.9837 (3)	−0.2640 (4)	0.05091 (11)	0.0062 (4)
H2A	1.1062 (7)	−0.4002 (9)	0.0673 (3)	0.0228 (10)
H2B	0.8512 (7)	−0.2622 (9)	0.0740 (3)	0.0202 (9)
OW3	1.0464 (3)	0.1017 (4)	0.10562 (11)	0.0067 (4)
H3A	1.0425 (8)	0.0365 (9)	0.1555 (2)	0.0216 (9)
H3B	1.1223 (8)	0.1903 (10)	0.1096 (3)	0.0232 (10)
Mg2	1.0000	0.0000	0.5000	0.0040 (5)
OW4	1.1484 (3)	−0.1033 (4)	0.39480 (11)	0.0062 (4)
H4A	1.2979 (6)	−0.1184 (9)	0.3850 (3)	0.0189 (9)
H4B	1.0780 (7)	−0.0798 (9)	0.3443 (2)	0.0197 (9)
OW5	0.8066 (3)	−0.1528 (4)	0.48574 (11)	0.0069 (4)
H5A	0.7719 (8)	−0.2393 (9)	0.5234 (3)	0.0209 (9)
H5B	0.7144 (7)	−0.1370 (9)	0.4409 (2)	0.0189 (9)
OW6	0.7564 (3)	0.2810 (4)	0.44853 (11)	0.0056 (4)
H6A	0.7983 (7)	0.3341 (9)	0.4012 (3)	0.0208 (9)
H6B	0.6015 (6)	0.3156 (9)	0.4411 (3)	0.0208 (10)
Cr1	0.4078 (4)	0.3200 (6)	0.20166 (15)	0.0022 (5)
O1	0.3001 (3)	0.3376 (4)	0.11601 (10)	0.0051 (3)
O2	0.2081 (3)	0.4569 (4)	0.26429 (11)	0.0060 (3)
O3	0.5424 (3)	0.0602 (4)	0.22978 (11)	0.0059 (4)
O4	0.5838 (3)	0.4215 (4)	0.19749 (11)	0.0062 (4)
OW7	0.3116 (3)	0.4086 (4)	0.41912 (11)	0.0062 (4)
H7A	0.2786 (7)	0.4262 (10)	0.3644 (2)	0.0221 (10)
H7B	0.2406 (9)	0.5530 (10)	0.4380 (4)	0.0276 (11)
OW8	0.6070 (3)	−0.2410 (4)	0.11869 (12)	0.0069 (4)
H8A	0.5670 (8)	−0.1290 (9)	0.1576 (3)	0.0207 (8)
H8B	0.6039 (8)	−0.3656 (9)	0.1452 (3)	0.0210 (9)
OW9	0.5608 (3)	−0.1510 (4)	0.36308 (11)	0.0064 (4)
H9A	0.5411 (7)	−0.0546 (9)	0.3179 (2)	0.0204 (9)
H9B	0.6573 (7)	−0.2973 (8)	0.3446 (3)	0.0196 (9)
OW10	0.8338 (3)	0.4416 (4)	0.31354 (11)	0.0070 (4)
H10A	0.7579 (7)	0.4168 (10)	0.2706 (3)	0.0213 (9)
H10B	0.9740 (6)	0.4303 (9)	0.2930 (3)	0.0210 (9)
OW11	0.9964 (3)	−0.0875 (4)	0.24672 (11)	0.0061 (4)
H11A	1.0639 (8)	−0.2447 (9)	0.2448 (3)	0.0225 (9)
H11B	0.8371 (6)	−0.0362 (9)	0.2411 (3)	0.0224 (10)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Mg1	0.0024 (8)	0.0037 (13)	0.0036 (9)	−0.0018 (8)	0.0000 (7)	0.0003 (9)
OW1	0.0038 (5)	0.0096 (10)	0.0058 (7)	−0.0016 (6)	0.0005 (5)	−0.0002 (7)
H1A	0.0193 (17)	0.030 (3)	0.0160 (17)	−0.0044 (18)	0.0077 (13)	−0.0074 (17)
H1B	0.0166 (15)	0.027 (3)	0.0164 (16)	−0.0083 (16)	−0.0042 (13)	−0.0008 (16)
OW2	0.0055 (6)	0.0056 (9)	0.0082 (7)	−0.0033 (6)	−0.0010 (5)	0.0026 (7)
H2A	0.0158 (15)	0.016 (2)	0.030 (2)	−0.0019 (16)	−0.0044 (15)	0.0075 (19)
H2B	0.0152 (14)	0.022 (2)	0.0236 (19)	−0.0084 (16)	0.0052 (13)	0.0009 (17)
OW3	0.0073 (6)	0.0089 (10)	0.0053 (7)	−0.0050 (7)	−0.0003 (5)	0.0002 (7)
H3A	0.030 (2)	0.026 (3)	0.0123 (15)	−0.016 (2)	0.0019 (14)	0.0045 (16)
H3B	0.029 (2)	0.025 (3)	0.026 (2)	−0.021 (2)	−0.0023 (17)	0.0004 (19)
Mg2	0.0034 (8)	0.0053 (13)	0.0029 (9)	−0.0016 (9)	−0.0001 (7)	−0.0002 (9)
OW4	0.0043 (6)	0.0087 (10)	0.0052 (6)	−0.0027 (6)	0.0009 (5)	−0.0010 (6)
H4A	0.0133 (13)	0.025 (2)	0.0208 (17)	−0.0109 (16)	0.0021 (12)	−0.0002 (17)
H4B	0.0197 (15)	0.027 (3)	0.0138 (15)	−0.0120 (17)	−0.0054 (13)	0.0008 (16)
OW5	0.0092 (7)	0.0098 (10)	0.0054 (6)	−0.0077 (7)	−0.0014 (5)	0.0008 (7)
H5A	0.0269 (18)	0.027 (3)	0.0179 (17)	−0.0203 (19)	−0.0013 (14)	0.0037 (17)
H5B	0.0204 (16)	0.024 (2)	0.0158 (16)	−0.0128 (17)	−0.0057 (13)	0.0018 (16)
OW6	0.0053 (6)	0.0045 (9)	0.0064 (7)	−0.0016 (6)	−0.0003 (5)	0.0018 (6)
H6A	0.0191 (15)	0.025 (2)	0.0179 (16)	−0.0105 (17)	0.0018 (13)	0.0084 (17)
H6B	0.0109 (13)	0.027 (3)	0.0235 (19)	−0.0081 (16)	−0.0021 (13)	0.0017 (18)
Cr1	0.0033 (8)	0.0025 (13)	0.0019 (9)	−0.0023 (9)	−0.0007 (7)	0.0006 (9)
O1	0.0045 (6)	0.0077 (10)	0.0025 (6)	−0.0023 (6)	−0.0009 (5)	0.0004 (6)
O2	0.0044 (6)	0.0060 (9)	0.0055 (6)	−0.0006 (6)	0.0017 (5)	−0.0015 (6)
O3	0.0050 (6)	0.0048 (9)	0.0057 (7)	−0.0004 (6)	−0.0003 (5)	0.0018 (6)
O4	0.0056 (6)	0.0082 (10)	0.0067 (7)	−0.0049 (7)	−0.0005 (5)	0.0007 (7)
OW7	0.0055 (6)	0.0070 (10)	0.0056 (6)	−0.0026 (6)	0.0004 (5)	0.0003 (6)
H7A	0.0236 (17)	0.029 (3)	0.0120 (15)	−0.0112 (19)	−0.0011 (13)	0.0031 (16)
H7B	0.026 (2)	0.014 (3)	0.039 (3)	−0.0056 (19)	0.0035 (19)	−0.010 (2)
OW8	0.0067 (6)	0.0082 (10)	0.0066 (7)	−0.0043 (7)	−0.0001 (5)	0.0012 (7)
H8A	0.028 (2)	0.018 (2)	0.0192 (18)	−0.0136 (18)	0.0047 (15)	−0.0074 (16)
H8B	0.030 (2)	0.018 (2)	0.0181 (17)	−0.0143 (18)	−0.0001 (15)	0.0036 (17)
OW9	0.0059 (6)	0.0078 (10)	0.0053 (6)	−0.0030 (6)	−0.0001 (5)	0.0001 (6)
H9A	0.0220 (16)	0.022 (2)	0.0148 (16)	−0.0085 (17)	−0.0011 (13)	0.0074 (16)
H9B	0.0191 (16)	0.012 (2)	0.025 (2)	−0.0048 (15)	0.0031 (14)	−0.0023 (17)
OW10	0.0067 (6)	0.0096 (10)	0.0055 (6)	−0.0045 (7)	0.0002 (5)	0.0002 (7)
H10A	0.0220 (17)	0.031 (3)	0.0155 (16)	−0.0161 (19)	−0.0007 (14)	−0.0065 (17)
H10B	0.0132 (13)	0.028 (3)	0.0219 (18)	−0.0099 (17)	0.0047 (13)	−0.0022 (18)
OW11	0.0048 (6)	0.0067 (10)	0.0059 (7)	−0.0017 (6)	0.0009 (5)	−0.0010 (6)
H11A	0.0214 (17)	0.012 (2)	0.030 (2)	−0.0036 (16)	0.0012 (16)	−0.0023 (18)
H11B	0.0110 (13)	0.024 (3)	0.029 (2)	−0.0053 (15)	−0.0031 (14)	0.003 (2)

Geometric parameters (Å, º) top

Mg1—OW2ⁱ	2.053 (2)	OW4—H4B	0.977 (4)
Mg1—OW2	2.053 (2)	OW5—H5A	0.972 (5)
Mg1—OW1ⁱ	2.0622 (19)	OW5—H5B	0.977 (4)
Mg1—OW1	2.0622 (19)	OW6—H6A	0.983 (4)
Mg1—OW3ⁱ	2.066 (2)	OW6—H6B	0.972 (4)
Mg1—OW3	2.066 (2)	Cr1—O4	1.637 (4)
OW1—H1A	0.964 (5)	Cr1—O1	1.643 (3)
OW1—H1B	0.980 (5)	Cr1—O3	1.660 (4)
OW2—H2A	0.965 (5)	Cr1—O2	1.667 (4)
OW2—H2B	0.974 (4)	OW7—H7A	0.971 (5)
OW3—H3A	0.972 (4)	OW7—H7B	0.957 (7)
OW3—H3B	0.967 (6)	OW8—H8A	0.985 (6)
Mg2—OW5	2.045 (2)	OW8—H8B	0.974 (5)
Mg2—OW5ⁱⁱ	2.045 (2)	OW9—H9A	0.984 (4)
Mg2—OW4	2.065 (2)	OW9—H9B	0.982 (6)
Mg2—OW4ⁱⁱ	2.065 (2)	OW10—H10A	0.973 (5)
Mg2—OW6ⁱⁱ	2.071 (2)	OW10—H10B	0.981 (4)
Mg2—OW6	2.071 (2)	OW11—H11A	0.969 (6)
OW4—H4A	0.983 (4)	OW11—H11B	0.975 (4)

OW2ⁱ—Mg1—OW2	179.999 (1)	OW5—Mg2—OW6ⁱⁱ	89.89 (9)
OW2ⁱ—Mg1—OW1ⁱ	89.78 (8)	OW5ⁱⁱ—Mg2—OW6ⁱⁱ	90.11 (9)
OW2—Mg1—OW1ⁱ	90.22 (8)	OW4—Mg2—OW6ⁱⁱ	89.43 (8)
OW2ⁱ—Mg1—OW1	90.22 (8)	OW4ⁱⁱ—Mg2—OW6ⁱⁱ	90.57 (8)
OW2—Mg1—OW1	89.78 (8)	OW5—Mg2—OW6	90.11 (9)
OW1ⁱ—Mg1—OW1	180.0	OW5ⁱⁱ—Mg2—OW6	89.89 (9)
OW2ⁱ—Mg1—OW3ⁱ	90.97 (9)	OW4—Mg2—OW6	90.57 (8)
OW2—Mg1—OW3ⁱ	89.03 (9)	OW4ⁱⁱ—Mg2—OW6	89.43 (8)
OW1ⁱ—Mg1—OW3ⁱ	92.78 (9)	OW6ⁱⁱ—Mg2—OW6	180.0
OW1—Mg1—OW3ⁱ	87.22 (9)	Mg2—OW4—H4A	120.0 (3)
OW2ⁱ—Mg1—OW3	89.03 (9)	Mg2—OW4—H4B	128.5 (3)
OW2—Mg1—OW3	90.97 (9)	H4A—OW4—H4B	105.5 (4)
OW1ⁱ—Mg1—OW3	87.22 (9)	Mg2—OW5—H5A	128.0 (3)
OW1—Mg1—OW3	92.78 (9)	Mg2—OW5—H5B	125.8 (3)
OW3ⁱ—Mg1—OW3	179.999 (1)	H5A—OW5—H5B	105.7 (4)
Mg1—OW1—H1A	134.3 (3)	Mg2—OW6—H6A	116.6 (3)
Mg1—OW1—H1B	119.2 (3)	Mg2—OW6—H6B	126.4 (4)
H1A—OW1—H1B	105.8 (4)	H6A—OW6—H6B	105.1 (4)
Mg1—OW2—H2A	127.3 (3)	O4—Cr1—O1	109.39 (17)
Mg1—OW2—H2B	125.1 (3)	O4—Cr1—O3	108.85 (17)
H2A—OW2—H2B	106.1 (4)	O1—Cr1—O3	109.2 (2)
Mg1—OW3—H3A	126.5 (4)	O4—Cr1—O2	109.5 (2)
Mg1—OW3—H3B	120.6 (3)	O1—Cr1—O2	110.17 (17)
H3A—OW3—H3B	110.1 (5)	O3—Cr1—O2	109.79 (18)
OW5—Mg2—OW5ⁱⁱ	180.0	H7A—OW7—H7B	104.8 (5)
OW5—Mg2—OW4	91.04 (9)	H8A—OW8—H8B	105.6 (5)
OW5ⁱⁱ—Mg2—OW4	88.96 (9)	H9A—OW9—H9B	104.0 (5)
OW5—Mg2—OW4ⁱⁱ	88.96 (9)	H10A—OW10—H10B	106.1 (4)
OW5ⁱⁱ—Mg2—OW4ⁱⁱ	91.03 (9)	H11A—OW11—H11B	106.1 (5)
OW4—Mg2—OW4ⁱⁱ	180.0

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

Comparison of interatomic distances (Å) and angles (°) in the coordination polyhedra (X = S1 or Cr1), including calculated polyhedral volumes (Å³), between MgSO₄.11H₂O and MgCrO₄.11H₂O top

	MgSO₄.11H₂O	MgCrO₄.11H₂O

Mg1—OW1	2.0566 (9)	2.062 (2)
Mg1—OW2	2.0617 (11)	2.053 (2)
Mg1—OW3	2.0794 (10)	2.066 (2)
Volume of M1 (Å³)	11.743 (5)	11.648 (12)

Mg2—OW4	2.0767 (10)	2.065 (2)
Mg2—OW5	2.0458 (9)	2.045 (2)
Mg2—OW6	2.0699 (11)	2.071 (2)
Volume of M2 (Å³)	11.722 (6)	11.657 (12)

X—O1	1.467 (2)	1.643 (3)
X—O2	1.473 (2)	1.667 (4)
X—O3	1.486 (2)	1.660 (4)
X—O4	1.488 (2)	1.637 (4)
Volume of T1 (Å³)	1.656 (1)	2.312 (4)

OW1—Mg1—OW2	89.36 (4)	89.78 (8)
OW1—Mg1—OW3	92.58 (4)	92.78 (9)
OW2—Mg1—OW3	90.06 (4)	90.97 (9)

OW4—Mg2—OW5	90.75 (4)	91.04 (9)
OW4—Mg2—OW6	90.23 (4)	90.57 (8)
OW5—Mg2—OW6	89.93 (4)	90.11 (9)

O1—X—O2	110.0 (1)	110.2 (2)
O1—X—O3	108.8 (1)	109.2 (2)
O1—X—O4	110.3 (1)	109.4 (2)
O2—X—O3	108.6 (1)	109.8 (2)
O2—X—O4	109.7 (1)	109.5 (2)
O3—X—O4	109.3 (1)	108.9 (2)

Polyhedral volumes computed using Cayley–Menger determinants (Wirth & Dreiding, 2009).

Comparison of distances (Å) and angles (°) pertaining to the hydrogen-bond geometry in MgSO₄.11H₂O (upper half) and MgCrO₄.11H₂O (lower half) top

MgSO₄.11H₂O
	D—H	H···A	D···A	D—H···A
OW1—H1A···O1	0.964 (2)	1.893 (2)	2.8406 (14)	167.1 (2)
OW1—H1B···OW8ⁱ	0.975 (3)	1.764 (3)	2.7363 (16)	174.0 (2)
OW2—H2A···O1ⁱⁱ	0.965 (2)	1.861 (3)	2.8124 (15)	168.2 (3)
OW2—H2B···OW8	0.974 (2)	1.783 (2)	2.7526 (14)	173.8 (2)
OW3—H3A···OW11	0.965 (3)	1.893 (3)	2.8505 (17)	171.3 (2)
OW3—H3B···O1ⁱⁱⁱ	0.972 (2)	1.882 (2)	2.8520 (12)	175.5 (3)
OW4—H4A···OW9ⁱⁱⁱ	0.981 (2)	1.731 (2)	2.7108 (13)	176.6 (2)
OW4—H4B···OW11	0.980 (3)	1.793 (3)	2.7603 (16)	168.4 (2)
OW5—H5A···OW7ⁱ	0.977 (3)	1.774 (3)	2.7461 (16)	173.2 (3)
OW5—H5B···OW9	0.978 (3)	1.755 (3)	2.7283 (15)	173.0 (2)
OW6—H6A···OW10	0.976 (3)	1.753 (3)	2.7212 (17)	170.6 (2)
OW6—H6B···OW7	0.975 (2)	1.815 (2)	2.7825 (14)	171.5 (3)
OW7—H7A···O2	0.978 (3)	1.813 (3)	2.7888 (16)	175.0 (2)
OW7—H7B···OW4^iv	0.966 (2)	2.096 (3)	2.9558 (15)	147.4 (3)
OW7—H7B···OW6^v	0.966 (2)	2.484 (3)	3.1694 (14)	127.7 (3)
OW8—H8A···O3	0.973 (2)	1.857 (2)	2.8176 (13)	168.7 (2)
OW8—H8B···O4^vi	0.975 (3)	1.780 (3)	2.7526 (15)	175.1 (2)
OW9—H9A···O3	0.984 (3)	1.737 (3)	2.7036 (16)	166.4 (2)
OW9—H9B···OW10^vi	0.983 (2)	1.749 (2)	2.7310 (13)	177.0 (3)
OW10—H10A···O4	0.983 (2)	1.718 (2)	2.6877 (15)	168.4 (2)
OW10—H10B···O2ⁱⁱⁱ	0.970 (2)	1.797 (2)	2.7455 (13)	165.1 (2)
OW11—H11A···O2ⁱⁱ	0.975 (2)	1.881 (2)	2.8359 (14)	165.3 (3)
OW11—H11B···O3	0.975 (2)	1.834 (2)	2.8095 (14)	178.3 (2)

MgCrO₄.11H₂O
OW1—H1A···O1	0.964 (5)	1.950 (5)	2.891 (3)	164.7 (5)
OW1—H1B···OW8ⁱ	0.980 (5)	1.757 (4)	2.732 (3)	172.8 (6)
OW2—H2A···O1ⁱⁱ	0.965 (5)	1.865 (5)	2.814 (3)	167.4 (5)
OW2—H2B···OW8	0.974 (4)	1.767 (4)	2.740 (3)	175.9 (6)
OW3—H3A···OW11	0.972 (4)	1.872 (4)	2.837 (3)	171.7 (4)
OW3—H3B···O1ⁱⁱⁱ	0.967 (6)	1.907 (5)	2.870 (3)	174.0 (5)
OW4—H4A···OW9ⁱⁱⁱ	0.983 (4)	1.730 (4)	2.712 (3)	176.9 (5)
OW4—H4B···OW11	0.977 (4)	1.801 (5)	2.766 (3)	168.4 (5)
OW5—H5A···OW7ⁱ	0.972 (5)	1.792 (5)	2.757 (3)	171.2 (5)
OW5—H5B···OW9	0.977 (4)	1.747 (5)	2.717 (3)	171.2 (5)
OW6—H6A···OW10	0.983 (4)	1.740 (4)	2.716 (3)	172.0 (4)
OW6—H6B···OW7	0.972 (4)	1.805 (4)	2.772 (3)	172.5 (5)
OW7—H7A···O2	0.971 (5)	1.793 (5)	2.763 (3)	177.7 (5)
OW7—H7B···OW4^iv	0.957 (7)	2.269 (6)	3.050 (4)	138.3 (5)
OW7—H7B···OW6^v	0.957 (7)	2.320 (7)	3.085 (4)	136.4 (5)
OW8—H8A···O3	0.985 (6)	1.794 (6)	2.770 (4)	170.6 (4)
OW8—H8B···O4^vi	0.974 (5)	1.764 (5)	2.737 (3)	176.0 (5)
OW9—H9A···O3	0.984 (4)	1.708 (4)	2.676 (3)	167.3 (5)
OW9—H9B···OW10^vi	0.982 (6)	1.748 (6)	2.731 (4)	178.6 (5)
OW10—H10A···O4	0.973 (5)	1.734 (5)	2.696 (3)	169.2 (5)
OW10—H10B···O2ⁱⁱⁱ	0.981 (4)	1.744 (5)	2.714 (3)	169.3 (6)
OW11—H11A···O2ⁱⁱ	0.969 (6)	1.857 (6)	2.810 (3)	167.1 (5)
OW11—H11B···O3	0.975 (4)	1.802 (4)	2.777 (3)	179.4 (5)

See Fig. 3 for a graphical representation of these data.

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

Principal axis magnitudes of the elastic strain tensor, and the corresponding direction cosines, computed from the change in unit-cell parameters on substitution of Cr^VI for S^VI in MgSO₄.11H₂O. See Fig. 5 for a graphical representation of this information. top

	This work,	5–10 K			Fortes & Wood (2012),	258 K
	Strain	Direction	cosines		Strain	Direction	cosines
ε₁	0.67 (7) %	0.9648	-0.0658	-0.3150	0.885 (6) %	0.9780	-0.1675	-0.1244
ε₂	2.20 (9) %	0.0748	0.9971	0.0166	2.182 (5) %	0.1837	0.9739	0.1331
ε₃	0.43 (7)%	0.3130	-0.0392	0.9489	0.458 (6) %	0.0989	-0.1530	0.9833
ε_V	3.30 (14) %				3.53 (1) %

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