The wavelength dispersion delta lambda/lambda in a graphite (002) monochromated Mo K alpha beam was analyzed. A wavelength window was found with 0.68 < lambda < 0.79 A, i.e. delta lambda/lambda = 0.14. The very large dispersion leads to systematic errors in Iobserved(H) caused by scan-angle-induced spectral truncation. A limit on the scan angle during data collection is unavoidable, in order that an omega/2 theta measurement should not encompass neighboring reflections. The systematic intensity errors increase with the Bragg angle. Therefore they influence the refined X-ray structure by adding a truncational component to the temperature factor: B(X-ray) = B(true) + B(truncation). For an Mo tube at 50 kV, we find B(truncation) = 0.05 A2, whereas a value of 0.22 A2 applies to the same tube but operated at 25 kV. The values of B(truncation) are temperature independent. The model bias was verified via a series of experimental data collections on spherical crystals of nickel sulfate hexahydrate and ammonium hydrogen tartrate. Monochromatic reference structures were obtained via a synchrotron experiment and via a 'balanced' tube experiment.

The wavelength dispersion of graphite(002)-monochromated X-ray beams has been determined for a Cu, a Mo and an Rh tube. The observed values for Deltalambda/lambda were 0.03, 0.14 and 0.16, respectively. The severe reduction in monochromaticity as a function of wavelength is determined by the absorption coefficient mu of the monochromator. Mu(monochromator) varies with lambda3. For an Si monochromator with its much larger absorption coefficient, Deltalambda/lambda values of 0.03 were found, regardless of the X-ray tube. This value matches a beam divergence defined by the size of the focus and of the crystal. This holds as long as the monochromator acts as a mirror, i.e. mu(monochromator) is large. In addition to monochromaticity, homogeneity of the X-ray beam is also an important factor. For this aspect the mosaicity of the monochromator is vital. In cases like Si, in which mosaicity is practically absent, the reflected X-ray beam shows an intensity distribution equal to the mass projection of the filament on the anode. Smearing by mosaicity generates a homogeneous beam. This makes a graphite monochromator attractive in spite of its poor performance as a monochromator for lambda < 1 A. This choice means that scan-angle-induced spectral truncation errors are here to stay. These systematic intensity errors can be taken into account after measurement by a software correction based on the real beam spectrum and the applied measuring mode. A spectral modeling routine is proposed, which is applied on the graphite-monochromated Mo Kalpha beam. Both elements in that spectrum, i.e. characteristic alpha1 and alpha2 emission lines and the Bremsstrahlung, were analyzed using the 6,3,18 reflection of Al2O3 (s = 1.2 A(-1)). The spectral information obtained was used to calculate the truncation errors for intensities measured in an omega/2theta scan mode. The results underline the correctness of previous work on the structure of NiSO4*6H2O [Rousseau, Maes & Lenstra (2000). Acta Cryst. A56, 300-307].

2,3-Diketopiperazine (2,3-piperazinedione) crystallizes in the monoclinic space group P21/c with a = 5.941 (3), b = 10.080 (3), c = 8.282 (2) Å and β = 95.87 (3)°. The six-membered ring adopts a skew-boat conformation with Q = 0.467 (3) Å, θ = 64.6 (3)° and φ = 269.8 (4)°. Ab initio calculations show that the perfect skew-boat with its C 2 symmetry is broken by the formation of two intermolecular N—H...O bonds, involving only one of the C=O groups of the 2,3-diketopiperazine molecule. Vibrational spectra were recorded in solution and in the solid state. The assignment of the normal vibrations is proposed based on comparison with spectra of similar molecules and spectral changes due to deuteration. Ab initio calculations for the isolated molecule and the solid-state structure were used to calculate differences in the molecular geometry in the gas phase and crystalline state. Using these reference structures we calculated the stretching frequencies for the C=O groups. We predict an IR shift for C=O of 130 cm−1, when the molecule goes from the gas phase to the solid state. The observed shift is 110 cm−1. The differences between the C=O moieties in the solid state produce a calculated Δν of 55 cm−1, which matches satisfactorily the observed value of 49 cm−1.

The crystal structure of E-1,2-bis(3-methoxy-2-thienyl)ethene (C12H12O2S2) has been determined at five different temperatures, i.e. room temperature (293), 223, 173, 123 and 93 K. The solid-state work is complemented by the results of theoretical calculations of energies, geometries, difference electron densities and atomic charges of the free molecule. Analysis revealed static disorder caused by a higher energy conformer of the title compound, probably contaminating the crystal during its growth. The results support the contention that the electrical properties are mainly governed by the carbon backbone.

The background-peak-background procedure is applied to calculate I and o'2(1) from diffractometer data. A standard measurement produces a raw intensity R and a local background B. This standard operating procedure results in I = R -FB and o.2(/) = o-2(R ) + y2o'Z(B), in which y is the ratio of the times spent in measuring R and B. This approach has led to the conviction that the random error on I is determined by the signal and by the local background. Unfortunately, this concept is based on tradition. The strategic error in the background-peak-background routine is its complete neglect of the physical reality. Background intensities are produced by a single source, viz incoherent scattering. The relevant scattering processes are elastic (Rayleigh), inelastic (Compton) and pseudoelastic (TDS) scattering. Their intensities are proportional to f2, (Z-f2/Z) and f2[1 -exp(-2Bs2)], which results in a background intensity fully defined by 0 only. With observed backgrounds available, a background model has been constructed with its proper mix of the three scattering processes mentioned. This model is practically error free because it is based on a signal with size y~ B(H). The model-inferred background defines a zero level upon which the coherent Bragg intensities are superimposed. The distribution P(R) of the raw intensity is given by the joint probability P(I)P(B). P(R) is known via the observation R(H). The distribution P(B) is a counting statistical one, for which the mean and the variance are available through the background model. So P(/) = P(R)/P(B). This leads to I = R --b and 0.2(/) ~ I. If serious attention is paid to the observed background intensities, the latterironically enough -ceases to be an important element in the random error o-if).