Table of contents

The technique of x-ray standing waves as a means of structure determination is reviewed with special emphasis on its application to the investigation of adsorbed atoms and molecules at well-characterized single crystal surfaces in ultra-high vacuum. Topics covered include: the physical principles of the method and the underlying theory; methods of detection of the x-ray absorption and their relative merits; the specific advantages of photoelectron detection together with a description of the modified method of data analysis and its underlying physical basis (required to account for non-dipolar angular effects in the photoemission process); some practical issues of data analysis and interpretation including recent developments in the use of structural 'imaging' by direct inversion of the measured structural parameters. A broad survey of applications is included covering atomic and molecular adsorbates on semiconductors and metals as well as the use of the technique to obtain site-specific electronic structure information. Some comments on likely future developments and applications are given.

Density difference fluid flows and sedimentation of growing crystals are greatly reduced when crystallization takes place in a reduced gravity environment. In the case of macromolecular crystallography a crystal of a biological macromolecule is used for diffraction experiments (x-ray or neutron) so as to determine the three-dimensional structure of the macromolecule. The better the internal order of the crystal then the greater the molecular structure detail that can be extracted. It is this structural information that enables an understanding of how the molecule functions. This knowledge is changing the biological and chemical sciences, with major potential in understanding disease pathologies.

In this review, we examine the use of microgravity as an environment to grow macromolecular crystals. We describe the crystallization procedures used on the ground, how the resulting crystals are studied and the knowledge obtained from those crystals. We address the features desired in an ordered crystal and the techniques used to evaluate those features in detail. We then introduce the microgravity environment, the techniques to access that environment and the theory and evidence behind the use of microgravity for crystallization experiments. We describe how ground-based laboratory techniques have been adapted to microgravity flights and look at some of the methods used to analyse the resulting data. Several case studies illustrate the physical crystal quality improvements and the macromolecular structural advances. Finally, limitations and alternatives to microgravity and future directions for this research are covered.

Macromolecular structural crystallography in general is a remarkable field where physics, biology, chemistry and mathematics meet to enable insight to the fundamentals of life. As the reader will see, there is a great deal of physics involved when the microgravity environment is applied to crystallization, some of it known, and undoubtedly much yet to discover.

We examine the physical mechanisms governing the formation of snow crystals, treating this problem as a case study of the dynamics of crystal growth from the vapour phase. Particular attention is given to the basic theoretical underpinnings of the subject, especially the interplay of particle diffusion, heat diffusion and surface attachment kinetics during crystal growth, as well as growth instabilities that have important effects on snow crystal development.

The first part of this review focuses on understanding the dramatic variations seen in snow crystal morphology as a function of temperature, a mystery that has remained largely unsolved since its discovery 75 years ago. To this end we examine the growth of simple hexagonal ice prisms in considerable detail, comparing crystal growth theory with laboratory measurements of growth rates under a broad range of conditions. This turns out to be a surprisingly rich problem, which ultimately originates from the unusual molecular structure of the ice surface and its sensitive dependence on temperature. With new clues from precision measurements of attachment kinetics, we are now just beginning to understand these structural changes at the ice surface and how they affect the crystal growth process. We also touch upon the mostly unexplored topic of how dilute chemical impurities can greatly alter the growth of snow crystals.

The second part of this review examines pattern formation in snow crystals, with special emphasis on the growth of snow crystal dendrites. Again we treat this as a case study of the more general problem of dendritic growth during diffusion-limited solidification. Since snow crystals grow from the vapour, we can apply dendrite theory in the simplified slow-growth limit where attachment kinetics dominates over capillarity in selecting the tip velocity. Although faceting is quite pronounced in these structures, many aspects of the formation of snow crystal dendrites are fairly well described using a theoretical treatment that does not explicitly incorporate faceting. We also describe electrically modified ice dendrite growth, which produces some novel needle-like structures.

I investigate the relationship between physics and mathematics. I argue that physics can shed light on the proper foundations of mathematics, and that the nature of number can constrain the nature of physical reality. I show that requiring the joint mathematical consistency of the Standard Model of particle physics and the DeWitt–Feynman–Weinberg theory of quantum gravity can resolve the horizon, flatness and isotropy problems of cosmology. Joint mathematical consistency naturally yields a scale-free, Gaussian, adiabatic perturbation spectrum, and more matter than antimatter. I show that consistency requires the universe to begin at an initial singularity with a pure SU(2)_L gauge field. I show that quantum mechanics requires this field to have a Planckian spectrum whatever its temperature. If this field has managed to survive thermalization to the present day, then it would be the cosmic microwave background radiation (CMBR). If so, then we would have a natural explanation for the dark matter and the dark energy. I show that isotropic ultrahigh energy cosmic rays are explained if the CMBR is a pure SU(2)_L gauge field. The SU(2)_L nature of the CMBR may have been seen in the Sunyaev–Zel'dovich effect. I propose several simple experiments to test the hypothesis.