Collaboration with Hans-Beat Bürgi: crystallography at Bern and Lausanne.

A personal recollection of scientific developments by Hans-Beat Bürgi and fellow crystallographers in Switzerland is given.

'Seeing' atoms: the crystallographic revolution.

Laue's experiment in 1912 of the diffraction of X-rays by crystals led to one of the most influential discoveries in the history of science: the first determinations of crystal structures, NaCl and diamond in particular, by W. L. Bragg in 1913. For the first time, the visualisation of the structure of matter at the atomic level became possible. X-ray diffraction provided a sort of microscope with atomic resolution, atoms became observable physical objects and their relative positions in space could be seen. All branches of science concerned with matter, solid-state physics, chemistry, materials science, mineralogy and biology, could now be firmly anchored on the spatial arrangement of atoms. During the ensuing 100 years, structure determination by diffraction methods has matured into an indispensable method of chemical analysis. We trace the history of the development of 'small-structure' crystallography (excepting macromolecular structures) in Switzerland. Among the pioneers figure Peter Debye and Paul Scherrer with powder diffraction, and Paul Niggli and his Zurich School with space group symmetry and geometrical crystallography. Diffraction methods were applied early on by chemists at the Universities of Bern and Geneva. By the 1970s, X-ray crystallography was firmly established at most Swiss Universities, directed by full professors. Today, chemical analysis by structure determination is the task of service laboratories. However, the demand of diffraction methods to solve problems in all disciplines of science is still increasing and powerful radiation sources and detectors are being developed in Switzerland and worldwide.

'Seeing' Atoms: The Crystallographic Revolution.

Laue's experiment in 1912 of the diffraction of X-rays by crystals led to one of the most influential discoveries in the history of science: the first determinations of crystal structures, NaCl and diamond in particular, by W. L. Bragg in 1913. For the first time, the visualisation of the structure of matter at the atomic level became possible. X-ray diffraction provided a sort of microscope with atomic resolution, atoms became observable physical objects and their relative positions in space could be seen. All branches of science concerned with matter, solid-state physics, chemistry, materials science, mineralogy and biology, could now be firmly anchored on the spatial arrangement of atoms. During the ensuing 100 years, structure determination by diffraction methods has matured into an indispensable method of chemical analysis. We trace the history of the development of 'small-structure' crystallography (excepting macromolecular structures) in Switzerland. Among the pioneers figure Peter Debye and Paul Scherrer with powder diffraction, and Paul Niggli and his Zurich School with space group symmetry and geometrical crystallography. Diffraction methods were applied early on by chemists at the Universities of Bern and Geneva. By the 1970s, X-ray crystallography was firmly established at most Swiss Universities, directed by full professors. Today, chemical analysis by structure determination is the task of service laboratories. However, the demand of diffraction methods to solve problems in all disciplines of science is still increasing and powerful radiation sources and detectors are being developed in Switzerland and worldwide.

The success story of crystallography.

Diffractionists usually place the birth of crystallography in 1912 with the first X-ray diffraction experiment of Friedrich, Knipping and Laue. This discovery propelled the mathematical branch of mineralogy to global importance and enabled crystal structure determination. Knowledge of the geometrical structure of matter at atomic resolution had revolutionary consequences for all branches of the natural sciences: physics, chemistry, biology, earth sciences and material science. It is scarcely possible for a single person in a single article to trace and appropriately value all of these developments. This article presents the limited, subjective view of its author and a limited selection of references. The bulk of the article covers the history of X-ray structure determination from the NaCl structure to aperiodic structures and macromolecular structures. The theoretical foundations were available by 1920. The subsequent success of crystallography was then due to the development of diffraction equipment, the theory of the solution of the phase problem, symmetry theory and computers. The many structures becoming known called for the development of crystal chemistry and of data banks. Diffuse scattering from disordered structures without and with partial long-range order allows determination of short-range order. Neutron and electron scattering and diffraction are also mentioned.

Neutron diffraction investigation of the temperature dependence of crystal structure and thermal motions of red HgI2.

The structure of, and anisotropic thermal motions in, the red semiconductor tetrahedral layer structure of HgI(2) have been studied with neutron powder diffraction as a function of temperature from 10 to 293 K. Average thermal displacement parameters U(eq) of the two atoms are comparable in size at 10 K, but U(eq)(Hg) increases considerably faster with temperature than U(eq)(I), the Hg-I bond being highly non-rigid. The anisotropic displacement tensor U(I) is strongly anisotropic with one term about twice as large as the others, while U(Hg) is nearly isotropic. All displacement tensor elements, except U(22)(I), increase faster with temperature than harmonic quantum oscillator curves indicating a softening of the isolated-atom potentials at large amplitudes. A lattice dynamical model provides arguments that the anisotropic thermal motions of I are dominated by a soft mode with a wavevector at the [(1/2) (1/2) 0] boundary of the Brillouin zone consisting essentially of coupled librations of the HgI(4) tetrahedra, and by translations of the entire layer. The large vibration amplitudes of Hg suggest weak Hg-I force constants compared with the I-I force constants, allowing Hg to move quite freely inside the tetrahedra. The libration mode induces dynamic deformations of the Hg-I bond with twice its frequency. This provides a mechanism for the anharmonicity and may explain the lightening of the color from red to orange upon cooling at ca 80 K.

Order-disorder twinning model and stacking faults in alpha-NTO.

Crystals of the recently published [Bolotina, Kirschbaum & Pinkerton (2005). Acta Cryst. B61, 577-584] triclinic (P\overline1) structure of 5-nitro-2,4-dihydro-1,2,4-triazol-3-one (alpha-NTO) occur as fourfold twins. There are Z' = 4 independent molecules per asymmetric unit. We show that the structure contains layers with 2-periodic layer-group symmetry p2(1)/b 1 (1). This symmetry is lost through the stacking of the layers, which is a possible explanation for Z' = 4. A layer can assume four different but equivalent positions with respect to its nearest neighbor. Twinning arises through stacking faults and is an instructive example of the application of order-disorder theory using local symmetry operations. The near-neighbor relations between molecules remain unchanged through all twin boundaries. The four structures with maximum degree of order, one of which is the observed one, and the family reflections common to all domains are identified. Rods of weak diffuse scattering confirm the stacking model.

The charge density of urea from synchrotron diffraction data.

The charge density of urea is studied using very high precision single-crystal synchrotron-radiation diffraction data collected at the Swiss-Norwegian Beam Lines at ESRF. An unprecedented resolution of 1.44 A(-1) in sin theta;/lambda is obtained at 123 K. The optimization of the experiment for charge-density studies is discussed. The high precision of the data allowed the refinement of a multipole model extending to hexadecapoles and quadrupoles on the heavy and H atoms, respectively, as well as a liberal treatment of radial functions. The topological properties of the resulting electron density are analysed and compared with earlier experimental results as well as with periodic Hartree-Fock calculations. The properties of the strongly polarized C-O bond agree with trends derived from previous experimental results while the ab initio calculations differ significantly. The results indicate that the description of the C-O bond requires more flexible basis sets in the theoretical calculations. The calculated integrated atomic charges are much larger than the observed ones. It is suggested that the present experimental results provide new target values for validation of future ab initio calculations. The molecular dipole moment derived from the integrated atomic properties is the same as the one obtained from the multipole model even though the individual atomic contributions differ. Comparison with literature data for urea in solution and the gas phase yields a dipole enhancement in the solid of about 1.5 D. The thermal expansion of urea is determined using synchrotron powder diffraction data. With decreasing temperature, an increasing anisotropic strain is observed.

A fully extended tetrapeptide consisting of natural amino acids.

FGFG is the first example of a non-protected peptide consisting of natural amino acids that adopt a fully extended conformation in the crystalline state.

The structure of orange HgI2. I. Polytypic layer structure.

The metastable orange crystals of HgI(2) comprise three different crystal structures, all of which are built from corner-linked Hg(4)I(10) supertetrahedra. Two of them are end members with the maximum degree of order (MDO) of a polytypic layer structure; the third shows a three-dimensional linkage. This paper presents the determination from X-ray diffraction data of the tetragonal polytypic structures and their stacking disorder. Diffraction patterns show sharp Bragg reflections and rods of diffuse intensity with pronounced maxima. In a first step, the diffuse intensity was neglected and all maxima were treated as Bragg reflections. The crystal was supposed to be a conglomerate of the two MDO structures diffracting independently, and their parameters and volume ratio were refined against the single data set. The geometries and anisotropic displacement parameters of the layers in the two structures are shown to be nearly identical. Layer contacts in the two stacking modes are identical. The structures are fractal complications of the stable red form of HgI(2). In a second step, the stacking disorder has been quantitatively analyzed with a Markov chain model. Two probabilities describing next-nearest-layer interactions were visually adjusted to observed intensity profiles extracted from image-plate detector data. Results consistently show that the crystal comprises nearly equal volumes of MDO structures with an average domain thickness of about 5 layers or 30 A

The structure of orange HgI2. II. Diamond-type structure and twinning.

The metastable orange crystals of HgI(2) comprise three different crystal structures all of which are built from corner-linked Hg(4)I(10) supertetrahedra. Two of the structures are end members with the maximum degree of order (MDO) of a polytypic layer structure. In this paper, the third structure (D) determined from X-ray diffraction, a crystal chemical discussion of the four known tetrahedral HgI(2) structures, and a twinning model are presented. All the various diffraction results published during the past 70 years are now explained. The Hg(4)I(10) supertetrahedra of the tetragonal structure D are corner-linked into two interpenetrating diamond-type networks. The stable red form and the three orange structures show the same cubic densest packing of I atoms and differ only in the distribution of Hg atoms in the tetrahedral voids. Transformations between the structures may involve only movements of Hg atoms, as implied by larger thermal displacement parameters of Hg than of I. A multiply twinned conglomerate of MDO1, MDO2 and D, each structure occurring in three orientations, results in metrically cubic crystals whose Bragg reflections are very close to reciprocal lattice points.