XII. The structure of diopside, CaMg(SiO3)2

Facing the phase problem

The marvel of X-ray crystallography is the beauty and precision of the atomic structures deduced from diffraction patterns. Since these patterns record only amplitudes, phases for the diffracted waves must also be evaluated for systematic structure determination. Thus, we have the phase problem as a central complication, both intellectually for the field and practically so for many analyses. Here, I discuss how we - myself, my laboratory and the diffraction community - have faced the phase problem, considering the evolution of methods for phase evaluation as structural biology developed to the present day. During the explosive growth of macromolecular crystallography, practice in diffraction analysis evolved from a universal reliance on isomorphous replacement to the eventual domination of anomalous diffraction for de novo structure determination. As the Protein Data Bank (PDB) grew and familial relationships among proteins became clear, molecular replacement overtook all other phasing methods; however, experimental phasing remained essential for molecules without obvious precedents, with multi- and single-wavelength anomalous diffraction (MAD and SAD) predominating. While the mathematics-based direct methods had proved to be inadequate for typical macromolecules, they returned to crack substantial selenium substructures in SAD analyses of selenomethionyl proteins. Native SAD, exploiting the intrinsic S and P atoms of biomolecules, has become routine. Selenomethionyl SAD and MAD were the mainstays of structural genomics efforts to populate the PDB with novel proteins. A recent dividend has been paid in the success of PDB-trained artificial intelligence approaches for protein structure prediction. Currently, molecular replacement with AlphaFold models often obviates the need for experimental phase evaluation. For multiple reasons, we are now unfazed by the phase problem. Cryo-EM analysis is an attractive alternative to crystallography for many applications faced by today's structural biologists. It simply finesses the phase problem; however, the principles and procedures of diffraction analysis remain pertinent and are adopted in single-particle cryo-EM studies of biomolecules.

The crystal structure and luminescence properties of the first lithium oxonitridolithosilicate Li3SiNO2:Eu2+

Obtained by a high temperature solid-state synthesis, the compound Li3SiNO2:Eu2+ was characterized via SCXRD, PXRD, and luminescence spectroscopy. This revealed a new structure type and interesting luminescence properties.

Pressure-Induced Coordination Changes in a Pyrolitic Silicate Melt From Ab Initio Molecular Dynamics Simulations

With ab initio molecular dynamics simulations on a Na-, Ca-, Fe-, Mg-, and Al-bearing silicate melt of pyrolite composition, we examine the detailed changes in elemental coordination as a function of pressure and temperature. We consider the average coordination as well as the proportion and distribution of coordination environments at pressures and temperatures encompassing the conditions at which molten silicates may exist in present-day Earth and those of the Early Earth's magma ocean. At ambient pressure and 2,000 K, we find that the average coordination of cations with respect to oxygen is 4.0 for Si-O, 4.0 for Al-O, 3.7 for Fe-O, 4.6 for Mg-O, 5.9 for Na-O, and 6.2 for Ca-O. Although the coordination for iron with respect to oxygen may be underestimated, the coordination number for all other cations are consistent with experiments. By 15 GPa (2,000 K), the average coordination for Si-O remains at 4.0 but increases to 4.1 for Al-O, 4.2 for Fe-O, 4.9 for Mg-O, 8.0 for Na-O, and 6.8 for Ca-O. The coordination environment for Na-O remains approximately constant up to core-mantle boundary conditions (135 GPa and 4000 K) but increases to about 6 for Si-O, 6.5 for Al-O, 6.5 for Fe-O, 8 for Mg-O, and 9.5 for Ca-O. We discuss our results in the context of the metal-silicate partitioning behavior of siderophile elements and the viscosity changes of silicate melts at upper mantle conditions. Our results have implications for melt properties, such as viscosity, transport coefficients, thermal conductivities, and electrical conductivities, and will help interpret experimental results on silicate glasses.

Facile emulsion mediated synthesis of phase-pure diopside nanoparticles

Diopside is a common natural pyroxene that is rarely found in a pure state, since magnesium is often partially substituted by iron, and other elements (sodium and aluminum) are often present. This pyroxene, along with feldspars and olivines, is common in concrete. As the prospective license renewal of light water reactors to 80 years of operation has raised concerns on the effects of radiation in the concrete biological shield surrounding the reactors, mineral nanoparticles can be valuable to perform amorphization studies to inform predictive models of mechanical properties of irradiated concrete. The synthesis of diopside nanoparticles was achieved in this study using a reverse-micelle sol-gel method employing TEOS, calcium chloride and Mg(MeO)2 in a methanol/toluene solution. Tert-butylamine and water were used as hydrolysis agents, and dodecylamine as a surfactant. The resulting amorphous precursor was centrifuged to remove organics and fired at 800 °C. Additional reaction with hydrogen peroxide was used to remove amine remnants. TEM and SEM examinations revealed a product comprised of 50-100 nm diameter nanoparticles. XRD indicated phase pure diopside and BET indicated a surface area of 63.5 m2/g before peroxide treatment, which at a bulk density of 3.4 g/cm3 is equivalent to particles with diameter of 28 nm.

The influence of cation properties on the shape of silicate chains

The shape of silicate single chains is described by their periodicity (number of tetrahedra in the repeat unit of the chain) and the degree of shrinkage compared with a maximum stretched chain.

From a regression analysis of 54 single chain silicates it is concluded that such silicates can be divided into two groups: (1) Silicates with odd-periodic chains (pyroxenoids and pyroxenes) and (2) silicates with even-periodic chains.

Although the results of the analysis are not accurate enough to make reliable quantitative predictions about the shape of a silicate chain merely from the chemical composition of the silicate, some general relations could be found. So it turned out that even-periodic chains become less stretched with higher mean electronegativity and higher mean valence of their cations. In contrast, for odd-periodic chain silicates the degree of chain shrinkage is strongly correlated with the mean electronegativity and less so with the mean radius of the cations. On the other hand, the periodicity of the silicate chains is directly correlated with their degree of shrinkage. These results of the regression analysis are explained in terms of simple crystal chemical considerations.

The thermal expansion of diopside

Die Wärmeausdehnung von Diopsid wurde im Bereich bis 825°C mit einer Guinier-Lenné-Kammer gemessen. Das Ergebnis:α1= 7,7,α2= 17,3,α3= 7,0 · 10−6°C−1stimmt mit den von Kôzuberichteten Werten gut überein. Das feste Strukturgerüst aus M(1)- und M(2)-Polyedern ließ nicht einen größeren Beitrag zur Ausdehnung von Schwingungen parallel zu den Ketten erwarten. Als Grund für die Höhe desα2-Werts sind daher senkrecht zu den Ketten schwingende Transversal- und Longitudinalwellen anzunehmen.

Bonded interactions and the crystal chemistry of minerals: a review

Connections established during last century between bond length, radii, bond strength, bond valence and crystal and molecular chemistry are briefly reviewed followed by a survey of the physical properties of the electron density distributions for a variety of minerals and representative molecules, recently generated with first-principles local energy density quantum mechanical methods. The structures for several minerals, geometry-optimized at zero pressure and at a variety of pressures were found to agree with the experimental structures within a few percent. The experimental Si–O bond lengths and the Si–O–Si angle, the Si–O bond energy and the bond critical point properties for crystal quartz are comparable with those calculated for the H6Si2O7disilicic acid molecule, an indication that the bonded interactions in silica are largely short ranged and local in nature. The topology of model experimental electron density distributions for first and second row metal M atoms bonded to O, determined with high resolution and high energy synchrotron single crystal X-ray diffraction data are compared with the topology of theoretical distributions calculated with first principles methods. As the electron density is progressively accumulated between pairs of bonded atoms, the distributions show that the nuclei are progressively shielded as the bond lengths and the bonded radii of the atoms decrease. Concomitant with the decrease in the M–O bond lengths, the local kinetic energy,G(rc), the local potential energy,V(rc), and the electronic energy density,H(rc) =G(rc) +V(rc), evaluated at the bond critical points,rc, each increases in magnitude with the local potential energy dominating the kinetic energy density in the internuclear region for intermediate and shared interactions. The shorter the bonds, the more negative the local electronic energy density, the greater the stabilization and the greater the shared character of the intermediate and shared bonded interactions. In contrast, the local kinetic energy density increases with decreasing bond length for closed shell interactions withG(rc) dominatingV(rc) in the internuclear region, typical of an ionic bond. ...