G. Bortel

Phase field theory of polycrystalline solidification in three dimensions

A phase field theory of polycrystalline solidification is presented that describes the nucleation and growth of anisotropic particles with different crystallographic orientation in three dimensions. As opposed to the two-dimensional case, where a single orientation field suffices, in three dimensions, a minimum number of three fields are needed. The free energy of grain boundaries is assumed to be proportional to the angular difference between the adjacent crystals expressed here in terms of the differences of the four symmetric Euler parameters. The equations of motion for these fields are obtained from variational principles. Illustrative calculations are performed for polycrystalline solidification with dendritic, needle and spherulitic growth morphologies.

Atomic structure of a single large biomolecule from diffraction patterns of random orientations

The short and intense pulses of the new X-ray free electron lasers, now operational or under construction, may make possible diffraction experiments on single molecule-sized objects with high resolution, before radiation damage destroys the sample. In a single molecule imaging (SMI) experiment thousands of diffraction patterns of single molecules with random orientations are recorded. One of the most challenging problems of SMI is how to assemble these noisy patterns of unknown orientations into a consistent single set of diffraction data. Here we present a new method which can solve the orientation problem of SMI efficiently even for large biological molecules and in the presence of noise. We show on simulated diffraction patterns of a large protein molecule, how the orientations of the patterns can be found and the structure to atomic resolution can be solved. The concept of our algorithm could be also applied to experiments where images of an object are recorded in unknown orientations and/or positions like in cryoEM or tomography.

Common arc method for diffraction pattern orientation

Very short pulses of X-ray free-electron lasers opened the way to obtaining diffraction signal from single particles beyond the radiation dose limit. For three-dimensional structure reconstruction many patterns are recorded in the objects unknown orientation. A method is described for the orientation of continuous diffraction patterns of non-periodic objects, utilizing intensity correlations in the curved intersections of the corresponding Ewald spheres, and hence named the common arc orientation method. The present implementation of the algorithm optionally takes into account Friedels law, handles missing data and is capable of determining the point group of symmetric objects. Its performance is demonstrated on simulated diffraction data sets and verification of the results indicates a high orientation accuracy even at low signal levels. The common arc method fills a gap in the wide palette of orientation methods.

Orientational ordering and low-temperature libration in the rotor-stator cocrystals of fullerenes and cubane.

Cocrystals of cubane and fullerenes, C60-cubane and C70-cubane, show distinct rotational ordering transitions. We studied the corresponding structural changes with temperature-dependent X-ray diffraction and the thermodynamics of the phase transitions with adiabatic microcalorimetry and differential scanning calorimetry. C60-cubane has one phase transition around 130 K from a high-temperature fcc phase with freely rotating C60 to a low-temperature orthorombic phase in which the fullerene rotation is frozen. The corresponding enthalpy change is approximately 1170 J/mol, and the entropy change is 9.6 J/(mol K). C70-cubane has two phase transitions. Around 380 K, the high-temperature fcc phase with freely rotating C70 transforms into a bct phase in which the C70 rotates uniaxially around an axis that precesses around the c direction with a full opening angle of 40 degree. Around 170 K, the uniaxial rotation also freezes out, with an accompanying structural transition to monoclinic and enthalpy and entropy changes of 620 J/mol and 8.7 J/(mol K), respectively. The low-temperature specific heat was analyzed in terms of the Debye-Einstein model to estimate the librational energies of the fullerenes and Debye temperatures. We found very similar values for the two cocrystals, approximately Elib = 2.2 meV and TDebye = 23 K. For reference, we also measured the specific heats of pure C60 and C70 and found Elib = 2.96 meV and TDebye = 32 K for C60 and Elib = 1.9 meV and TDebye = 20 K for C70.

Selection and orientation of different particles in single particle imaging.

The short pulses of X-ray free electron lasers can produce diffraction patterns with structural information before radiation damage destroys the particle. The particles are injected into the beam in random orientations and they should be identical. However, in real experimental conditions it is not always possible to have identical particles. In this paper we show that the correlation maximization method, developed earlier, is able to select identical particles from a mixture and find their orientations simultaneously.

Low-temperature phase transition in C60-n-pentane.

In this paper we report the results of x-ray powder diffraction experiments on C[sub 60]-[ital n]-pentane. This material is a typical C[sub 60] clathrate and shows orthorhombic symmetry at room temperature. At low temperature an orthorhombic to monoclinic phase transition can be observed which involves the distortion of the base plane from rectangular. A microscopic picture of the phase transition is given by molecular-dynamics calculations.

X-ray holography

In the last decade holographic methods using hard X-rays were developed. They are able to resolve atomic distances, and can give the 3D arrangement of atoms around a selected element. Therefore, hard X-ray holography has potential applications in chemistry, biology and physics. In this article we give a general description of these methods and discuss the developments in the experimental technique. The capabilities of hard X-ray holography are demonstrated by examples.

Coherent diffraction imaging: Consistency of the assembled three-dimensional distribution

The short pulses of X-ray free-electron lasers can produce diffraction patterns with structural information before radiation damage destroys the particle. From the recorded diffraction patterns the structure of particles or molecules can be determined on the nano- or even atomic scale. In a coherent diffraction imaging experiment thousands of diffraction patterns of identical particles are recorded and assembled into a three-dimensional distribution which is subsequently used to solve the structure of the particle. It is essential to know, but not always obvious, that the assembled three-dimensional reciprocal-space intensity distribution is really consistent with the measured diffraction patterns. This paper shows that, with the use of correlation maps and a single parameter calculated from them, the consistency of the three-dimensional distribution can be reliably validated.

Measurement of synchrotron-radiation-excited Kossel patterns

Kossel line patterns contain information on the crystalline structure, such as the magnitude and the phase of Bragg reflections. For technical reasons, most of these patterns are obtained using electron beam excitation, which leads to surface sensitivity that limits the spatial extent of the structural information. To obtain the atomic structure in bulk volumes, X-rays should be used as the excitation radiation. However, there are technical problems, such as the need for high resolution, low noise, large dynamic range, photon counting, two-dimensional pixel detectors and the small spot size of the exciting beam, which have prevented the widespread use of Kossel pattern analysis. Here, an experimental setup is described, which can be used for the measurement of Kossel patterns in a reasonable time and with high resolution to recover structural information.

Layer disorder in C60-ether clathrates

We report structural studies on new C60 clathrates formed with ether as a guest molecule. Single crystal x-ray diffraction shows that in C60- ether two different pseudo tetragonal unit cells exist, which correspond to different compositions. The unit cells are based on the same relative displacements of the square-planar layers as found in the C60-n-pentane clathrate [1, 2]. However, the stacking sequence of the layers is different and reciprocal space maps reveal a significant stacking disorder. Model calculations suggest that the disorder comes mainly from the random sequence of the relative displacements.