Confusion over the description of the quartz structure yet again

Pathway for a martensitic quartz-coesite transition

An atomistic pathway for a strain-induced subsolidus martensitic transition between quartz and coesite was found by computing the set of the smallest atomic displacements required to transform a quartz structure into a coesite structure. A minimal transformation cell with 24 [Formula: see text] formula units is sufficient to describe the diffusionless martensitic transition from quartz to coesite. We identified two families of invariant shear planes during the martensitic transition, near the {10[Formula: see text]1} and {12[Formula: see text]2} set of planes, in agreement with the orientation of planar defect structures observed in quartz samples which experienced hypervelocity impacts. We calculated the reaction barrier using density functional theory and found that the barrier of 150 meV/atom is pressure invariant from ambient pressure up to 5 GPa, while the mean principal stress limiting the stability of strained quartz is [Formula: see text] 2 GPa. The model calculations quantitatively confirm that coesite can be formed in strained quartz at pressures significantly below the hydrostatic equilibrium transition pressure.

Thin Films of α-Quartz GeO2 on TiO2-Buffered Quartz Substrates

α-Quartz (SiO2) is one of the most widely used piezoelectric materials. However, the challenges associated with the control of the crystallization and the growth process limit its production to the hydrothermal growth of bulk crystals. GeO2 can also crystallize into the α-quartz phase, with a higher piezoelectric response and better thermal stability than SiO2. In a previous study, we have found that GeO2 crystallization on nonquartz substrates shows a tendency to form spherulites with a randomized orientation; while epitaxial growth of crystalline GeO2 thin films can take place on quartz (SiO2) substrates. However, in the latter case, the α-β phase transition that takes place in both substrates and thin films during heating deteriorates the long-range order and, thus, the piezoelectric properties. Here, we report the ousting of spherulitic growth by using a buffer layer. Using TiO2 as a buffer layer, the epitaxial strain of the substrates can be transferred to the growing films, leading to the oriented crystallization of GeO2 in the α-quartz phase. Moreover, since the TiO2 separates the substrates and the thin films, the thermal stability of the GeO2 is kept across the substrate's phase transitions. Our findings reveal the complexity of the crystallization process of quartz thin films and present a way to eliminate the tendency for spherulitic growth of quartz thin films by epitaxial strain.

Cobalt-Induced Phase Transformation of Ni3Ga4 Generates Chiral Intermetallic Co3Ni3Ga8

The scientific community has found immense difficulty to focus on the generation of chiral intermetallics compared to the chiral molecular structure, probably due to the technical difficulty in producing them as no general controlled protocol is available. Herein, using a conventional metal flux technique, we have discovered a new ternary intermetallic Co₃Ni₃Ga₈, substituting Co at the Ni sublattice in a highly symmetric Ni₃Ga₄ (Ia3̅d). Co₃Ni₃Ga₈ crystallizes in the I4₁32 space group, a Sohncke type, and can host the chiral structure. To the best of our knowledge, this is the first report of a ternary intermetallic crystallizing in this space group. The chiral structure of Co₃Ni₃Ga₈ is comprehensively mapped by various techniques such as single-crystal X-ray diffraction (XRD), synchrotron powder XRD, X-ray absorption spectroscopy (XAS), scanning transmission electron microscopy (STEM) and theoretically studied using density functional theory. The discovery of this chiral compound can inspire the researchers to design hidden ternary chiral intermetallics to study the exotic electrical and magnetic properties.

Calculating temperature-dependent X-ray structure factors of α-quartz with an extensible Python 3 package

A Python 3 software package for precise calculation of X-ray structure factors of α-quartz over a wide temperature range is presented. α-Quartz was chosen because of its practical application in high-resolution X-ray spectroscopy, but this software package can be easily extended to other crystals.

The design of X-ray optics based on diffraction from crystals depends on the accurate calculation of the structure factors of their Bragg reflections over a wide range of temperatures. In general, the temperature dependence of the lattice parameters, the atomic positions and the atomic thermal vibrations is both anisotropic and nonlinear. Implemented here is a software package for precise and flexible calculation of structure factors for dynamical diffraction. α-Quartz is used as an example because it presents the challenges mentioned above and because it is being considered for use in high-resolution X-ray spectroscopy. The package is designed to be extended easily to other crystals by adding new material files, which are kept separate from the package’s stable core. Python 3 was chosen as the language to allow the easy integration of this code into existing packages. The importance of a correct anisotropic treatment of the atomic thermal vibrations is demonstrated by comparison with an isotropic Debye model. Discrepancies between the two models can be as much as 5% for strong reflections and considerably larger (even to the level of 100%) for weak reflections. A script for finding Bragg reflections that backscatter X-rays of a given energy within a given temperature range is demonstrated. The package and example scripts are available on request. Also discussed, in detail, are the various conventions related to the proper description of chiral quartz.

Symmetry and chirality in crystals

A classification scheme relating the chirality of molecules to the type of crystal structures (chiral or achiral) they may form is presented. With respect to similar classifications proposed in the past, some corrections and extensions are introduced. In particular, (1) it is shown that chiral crystal structures from achiral molecules can occur in 28 types of space group having screw axes np , with p ≠ n/2, not in any Sohncke type of space group; (2) it is shown that the restriction on Z′ > 1 for kryptoracemates is contradicted by examples with Z′ = 1; and (3) the case of scalemic enantioenriched solutions, absent from most classifications, is included. Chiral crystal structures from purely inorganic (non-molecular) compounds are addressed too.

Rapid Discrimination of Crystal Handedness by X-ray Natural Circular Dichroism (XNCD) Mapping

An original method for determining the handedness of individual non-centrosymmetric crystals in a mixture using a tightly-focused, circularly polarized X-ray beam is presented. The X-ray natural circular dichroism (XNCD) spectra recorded at the metal K-edge on selected crystals of [Δ-M(en)₃ ](NO₃ )₂ and [Λ-M(en)₃ ](NO₃ )₂ (M=Co^II , Ni^II ) show extrema at the metal pre-edge (7712 eV for Co, 8335 eV for Ni). A mapping of a collection of some 220 crystals was performed at the respective energies by using left and right circular polarizations. The difference in absorption for the two polarizations, being either negative or positive, directly yielded the handedness of the crystal volume probed by the beam. By using this technique, it was found that the addition of l-ascorbic acid during the synthesis of [Co(en)₃ ](NO₃ )₂ resulted in an enantiomeric enrichment of the Λ-isomer of 67±13 %, whereas the Ni analogue was similarly, but conversely, enriched in the Δ-isomer (65±22 %).

Correct interpretation of diffraction properties of quartz crystals for X-ray optics applications. Corrigendum

Errors about left-handed (laevorotatory) quartz and right-handed (dextrorotatory) quartz in the paper by Huang, Gog, Kim, Kasman, Said, Casa, Wieczorek, Hönnicke & Assoufid [J. Appl. Cryst. (2016), 51, 140–147] are corrected.