Crystallographic Classes Research Articles

Effekt of adsorbed Ge atoms on the photoemission properties of GaAs

A3B5 semiconductor compounds in the future are the most promising for further detailed consideration. In this regard, gallium arsenide is a semiconductor compound formed by elements of groups III and V of the periodic system – gallium Ga and arsenic As. Gallium arsenide and its surface properties attract much attention of researchers due to the possibility of its wide application in micro- and nanoelectronics technology. Despite numerous studies of the surface of semiconductors, many issues related to its properties and processes at the interface between two phases remain insufficiently clarified, especially in terms of the effect of the surface state on the energy spectrum of electrons in crystals. Interest in these issues is constantly growing not only from a scientific point of view, but also from a practical one, in connection with the development of semiconductor micro- and nanotechnologies. The development of its sections such as thin-layer nanoelectronics and optoelectronics, devices with MIS structures and charge coupling, cold cathodes and efficient photocathodes require an understanding of the processes in the near-surface layer of a semiconductor both with a free surface and with this free surface during the adsorption of other substances on it. This is also important for elucidating the possibility of changing the surface and near-surface properties of solids in a quite definite way. Gallium arsenide is the closest binary analog of germanium. By introducing appropriate impurities, gallium arsenide can be obtained with both n-type and p-type conductivity with different current carrier concentrations. This structure belongs to the crystallographic class of the cubic system, like germanium. Gallium arsenide and germanium crystallize in the structure of zinc blende. In view of the foregoing, it is interesting to study the influence of adsorbed germanium layers on the surface properties of gallium arsenide single crystals of various types of conductivity by photoemission method in ultrahigh vacuum. The questions of the influence of these coatings not only on the emission properties of gallium arsenide single crystals, but also the influence of these adsorbed germanium atoms on the energy structure in the near-surface region of single crystals are considered.

Nonequilibrium statistical mechanics of crystals

The local equilibrium approach previously developed by the authors (J Mabillard and P Gaspard 2020 J. Stat. Mech. 103203) for matter with broken symmetries is applied to crystalline solids. The macroscopic hydrodynamics of crystals and their local thermodynamic and transport properties are deduced from the microscopic Hamiltonian dynamics. In particular, the Green–Kubo formulas are obtained for all the transport coefficients. The eight hydrodynamic modes and their dispersion relation are studied for general and cubic crystals. In the same twenty crystallographic classes as those compatible with piezoelectricity, cross effects coupling transport between linear momentum and heat or crystalline order are shown to split the degeneracy of damping rates for modes propagating in opposite generic directions.

Information significance of the volume/surface ratio of the simple forms of the hexoctahedral crystallographic class

Information significance of the volume/surface ratio of the simple forms of the hexoctahedral crystallographic class

The Crystallography of SARS-CoV-2 Suggests Its Deactivation

Background: The materials science may come to assist pharmacists to fabricate new drugs for coronavirus disease 2019 (COVID-19). Objectives: The geometrical structure of elements on the surface of severe acute respiratory syndrome-coronavirus 2 (SARS-CoV-2) is analyzed to illustrate some hints about the possible choosing the factors captivating the surface of SARS-CoV-2. Methods: The crystallographic classes and their sub-structures can be indicative of practical selection of macromolecules in drug pharmacy. Results: The macromolecular structures with hexagonal and its sub-structures are suggested for pharmacists to probe a novel drug for COVID-19. Conclusions: Any progress in the field of fabricating macromolecular drugs for COVID-19 is strongly dependent on finding the hexagonal and its sub-structures such as triangular and rhombus geometries.

Surface Pyroelectricity in Cubic SrTiO3.

Symmetry-imposed restrictions on the number of available pyroelectric and piezoelectric materials remain a major limitation as 22 out of 32 crystallographic material classes exhibit neither pyroelectricity nor piezoelectricity. Yet, by breaking the lattice symmetry it is possible to circumvent this limitation. Here, using a unique technique for measuring transient currents upon rapid heating, direct experimental evidence is provided that despite the fact that bulk SrTiO3 is not pyroelectric, the (100) surface of TiO2 -terminated SrTiO3 is intrinsically pyroelectric at room temperature. The pyroelectric layer is found to be ≈1 nm thick and, surprisingly, its polarization is comparable with that of strongly polar materials such as BaTiO3 . The pyroelectric effect can be tuned ON/OFF by the formation or removal of a nanometric SiO2 layer. Using density functional theory, the pyroelectricity is found to be a result of polar surface relaxation, which can be suppressed by varying the lattice symmetry breaking using a SiO2 capping layer. The observation of pyroelectricity emerging at the SrTiO3 surface also implies that it is intrinsically piezoelectric. These findings may pave the way for observing and tailoring piezo- and pyroelectricity in any material through appropriate breaking of symmetry at surfaces and artificial nanostructures such as heterointerfaces and superlattices.

Variation of second-order piezoelectric coefficients with respect to a finite strain measure.

In this article the consequence of a change of finite strain measure is theoretically considered for nonlinear piezoelectric crystals. Analytical predictions show that second-order piezoelectric coefficients are finite strain measure dependent. Therefore, the use of any finite strain measure in constitutive modelling of piezoelectric materials requires an adequate choice of higher-order piezoelectric coefficients. This allows one to avoid unwanted corrections to the elastic and electric fields in the case of nonlinear modelling of piezoelectric materials, e.g. for piezoelectric heterostructures such as quantum wells or dots. A general transformation formula for second-order piezoelectric coefficients (elastostriction) is derived. As an example, specific transformation formulae for two common crystallographic classes, namely {\bar 4}3m and 6mm, are presented. The piezoelectric coefficients for GaN and GaAs crystals, as representative cases of these crystal classes, are recalculated and their dependence on the strain measure is demonstrated. A further implication of that effect is that a complete set of second-order piezoelectric coefficients should contain additional information about the strain measure applied during calculations or measurements.

Towards Generalized Noise-Level Dependent Crystallographic Symmetry Classifications of More or Less Periodic Crystal Patterns

Geometric Akaike Information Criteria (G-AICs) for generalized noise-level dependent crystallographic symmetry classifications of two-dimensional (2D) images that are more or less periodic in either two or one dimensions as well as Akaike weights for multi-model inferences and predictions are reviewed. Such novel classifications do not refer to a single crystallographic symmetry class exclusively in a qualitative and definitive way. Instead, they are quantitative, spread over a range of crystallographic symmetry classes, and provide opportunities for inferences from all classes (within the range) simultaneously. The novel classifications are based on information theory and depend only on information that has been extracted from the images themselves by means of maximal likelihood approaches so that these classifications are objective. This is in stark contrast to the common practice whereby arbitrarily set thresholds or null hypothesis tests are employed to force crystallographic symmetry classifications into apparently definitive/exclusive states, while the geometric feature extraction results on which they depend are never definitive in the presence of generalized noise, i.e., in all real-world applications. Thus, there is unnecessary subjectivity in the currently practiced ways of making crystallographic symmetry classifications, which can be overcome by the approach outlined in this review.

Dislocation strengthening in FCC metals and in BCC metals at high temperatures

Till now, it was widely believed that the dislocation strengthening coefficients used in the Taylor-like relation were universal for a given crystallographic class of materials. In the present study, it is shown that this is actually untrue because of two effects that influence the strength of interactions between slip systems, namely the value of the Poisson ratio and the occurrence of doubly degenerated, asymmetric, junction configurations. New strengthening coefficient values for reactions between slip systems were determined using dislocation dynamics simulations on five representative FCC metals, plus germanium, and on five BCC transition metals for {110} and {112} slip systems at high homologous temperatures. The value of the Poisson ratio affects all the strengthening coefficients to various extents ranging from small to substantial. The effects of configuration asymmetry and Poisson's ratio are more marked in BCC metals than in FCC metals. These two major effects arise from a number of concurring dislocation mechanisms, which are discussed in some detail. It is expected that the use of accurate material-dependent coefficients will notably improve the predictive ability of current models for strain hardening.

On the Bertin surfaces of photoelastic crystals.

Conoscopic analysis of interference fringes is one of the most useful tools for investigating the mechanical properties of a crystal. These fringes are generated by a surface of constant phase difference, called the Bertin surface, whose shape depends on the piezo-optic properties of the material and on the applied stress. Here we investigate systematically for the first time, to the best of our knowledge, these surfaces as algebraic surfaces. We also describe their dependence on the stress when these are "small" and give a detailed analysis for all crystallographic classes.

Emergence of a few distinct structures from a single formal structure type during high-throughput screening for stable compounds: The case of RbCuS and RbCuSe

Theoretical sorting of stable and synthesizable ``missing compounds'' from those that are unstable is a crucial step in the discovery of previously unknown functional materials. This active research area often involves high-throughput (HT) examination of the total energy of a given compound in a list of candidate formal structure types (FSTs), searching for those with the lowest energy within that list. While it is well appreciated that local relaxation methods based on a fixed list of structure types can lead to inaccurate geometries, this approach is widely used in HT studies because it produces answers faster than global optimization methods (that vary lattice vectors and atomic positions without local restrictions). We find, however, a different failure mode of the HT protocol: specific crystallographic classes of formal structure types each correspond to a series of chemically distinct ``daughter structure types'' (DSTs) that have the same space group but possess totally different local bonding configurations, including coordination types. Failure to include such DSTs in the fixed list of examined candidate structures used in contemporary high-throughput approaches can lead to qualitative misidentification of the stable bonding pattern, not just quantitative inaccuracies. In this work, we (i) clarify the understanding of the general DST-FST relationship, thus improving current discovery HT approaches, (ii) illustrate this failure mode for RbCuS and RbCuSe (the latter being a yet unreported compound and is predicted here) by developing a synthesis method and accelerated crystal-structure determination, and (iii) apply the genetic-algorithm-based global space-group optimization (GSGO) approach which is not vulnerable to the failure mode of HT searches of fixed lists, demonstrating a correct identification of the stable DST. The broad impact of items (i)--(iii) lies in the demonstrated predictive ability of a more comprehensive search strategy than what is currently used---use HT calculations as the preliminary broad screening followed by unbiased GSGO of the final candidates.

Anisotropic spin–orbit stark effect in cubic semiconductors without an inversion center

The effect of external electric and magnetic fields on shallow donor levels in a semiconductor of the Td crystallographic class is analyzed. Application of an electric field eliminates the symmetry of the donor potential with respect to space inversion; as a result, corrections from the momentum-odd spin–orbit Dresselhaus term appear in the donor levels. In a strong electric field, such corrections determine the anisotropy of spin splitting of the donor levels relative to the directions of the external fields in the crystallographic coordinate system. Analytic expressions are derived for the spin splitting anisotropy for various relations between the magnitudes of the magnetic and electric fields. The results of this study can be used to determine the Dresselhaus spin–orbit interaction constant by a new method (in experiments on spin splitting of donor levels).

Influence of the Dzyaloshinskii–Moriya interaction on the spin-wave spectra of thin films

We have developed a theory that describes the spin-wave spectra of ferromagnetic films with Dzyaloshinskii–Moriya interactions. In agreement with recent experiments (Zakeri et al 2010 Phys. Rev. Lett. 104 137203), we demonstrate that the spin-wave dispersion relation is asymmetric with respect to wave vector inversion for a variety of ferromagnetic films with Dzyaloshinskii–Moriya interactions and different crystallographic classes. It is also predicted that, for non-zero wave vectors, the resonance frequency and resonance field can increase or decrease depending on the spin-wave vector orientation. We provide explicit formulas for the spin-wave dispersion relation and its asymmetry, as well as for the dynamic susceptibility for a film under microwave excitation, that can be used to understand ferromagnetic resonance as well as Brillouin light scattering experiments in these classes of magnetic thin films.

Symmetry trends of monoelement minerals

The number of the symmetry of each crystallographic class (NSCC) includes the sum of the orders of symmetry axes plus the number of symmetry planes plus one for a center of symmetry, if present. In 94.44% of cases, with increasing of NSCC values, the number of monoelement minerals crystallizing in the respective symmetry classes also increases. The density values Dc (gm/Å3) and Dcalc (g/cm3) of the monoelement minerals decrease with the increase of the atomic weight of chemical elements with consecutive or close atomic numbers in the periodic table. The NSCC values show a tendency to decrease with decreasing temperature and pressure of formation of monoelement minerals. At certain NSCC values, the highest the Dc (gm/Å3) and Dcalc (g/cm3) of monoelement minerals, the less probable becomes the possibility their polymorphic forms to be established. Polymorphic modifications denser than α-Fe (having Dc = 4.7049 gm/Å3 and Dcalc = 7.81 g/cm3) have not yet been established. The monoelement polymorphic modifications of As and S, crystallizing in the low symmetry crystal systems, are exceptions to Groth’s law. Most (91.67%) of the monoelement minerals crystallize in the holohedral classes. 2932 of all known 4106 mineral species (71.41%) also crystallize in the holohedral classes of different systems. The data presented suggest that the mineral species in general prefer holohedral classes, having also the highest NSCC values for the respective system. Therefore, the quantitative integral characteristic NSCC is informative in studies of all kinds of mineral assemblages grouped on the basis of different characteristics.

Dispersion of optical activity of magnesium sulfite hexahydrate single crystals

The magnesium sulfite hexahydrate (MgSO3.6H2O) crystals are unique because they are the only representative (with sodium periodate) of the crystallographic class C3 (without a center of symmetry). The crystal symmetry suggests presence of nonlinearity, piezo- and pyro-electric properties and gyrotropy as well. Single crystals of MgSO3.6H2O (pure and doped with Ni, Co and Zn) for the time being are grown only by the original method developed in the Laboratory for Crystal growth at the Faculty of Physics in Sofia University. The first results of optical activity of pure MgSO3.6H2O and Zn doped MgSO3.6H2O crystals are described and analyzed in a wide spectral range. The optical activity manifests itself in the direction (0001) as a rotation of the polarization plane.

Improper Ferroelectric Antiferromagnetics

Experiments reveal that magnetoelectric crystals usually experience incommensurate magnetic ordering. In this work we present symmetry arguments for the intimate coupling between ferroelectric magnetically ordered phases and modulated magnetic order. The obtained results are applied to crystals belonging to the D2h (mmm) crystallographic class and illustrated by two examples of rare-earth manganites RMn2O5 and MnWO4.

Magnetic symmetry of the plain domain walls in ferro- and ferrimagnets

Magnetic symmetry of all possible plane domain walls in ferro- and ferrimagnets is considered. Magnetic symmetry classes of non 180 degree (including 0 degree) domain walls are obtained. The domain walls degeneracy is investigated. The symmetry classification is applied for research of all possible plane domain walls in crystals of the hexoctahedral crystallographic class.

Crystallographic classes on the Minkowski space R 1,2. II. Tables of groups

For the Minkowski spaces, the traditional definition of a crystallographic group yields only trivial groups that are isomorphic to the Euclidean groups. In this article, we use a weaker definition (the topological discreteness). We classify the isomorphism types of the groups in the six crystallographic classes in the 3-dimensional Minkowski space: three classes are determined by the unimodular subgroups of the general Lorentz group, and the other three classes, by the subgroups unimodular in isotropic coordinates.

Crystallographic classes on the minkowski space R 1,2. I. Theorems

Some preliminary statements are proved necessary for calculating the crystallographic groups in six crystallographic classes in the 3-dimensional Minkowski space. Three classes are determined by the unimodular subgroups of the general Lorentz group and three more classes, by subgroups unimodular in a certain isotropic coordinate system.

Crystallographic classes in a 4-dimensional Minkowski space

On a crystallographic group, a condition of being topologically discrete is imposed which is weaker than is the conventional requirement for an action on space to be discontinuous. Isomorphism classification is given for crystallographic groups in three crystallographic classes in a 4-dimensional Minkowski space, which are defined by unimodular subgroups of the general Lorentz group. In these classes are, respectively, 24, 36, and 68 crystallographic groups.

Classification of perovskites with supervised self-organizing maps

In this work supervised self-organizing maps were used for structural classification of perovskites. For this purpose, structural data for total number of 286 perovskites, belonging to ABO 3 and/or A 2BB′O 6 types, were collected from literature: 130 of these are cubic, 85 orthorhombic and 71 monoclinic. For classification purposes, the effective ionic radii of the cations, electronegativities of the cations in B-position, as well as, the oxidation states of these cations, were used as input variables. The parameters of the developed models, as well as, the most suitable variables for classification purposes were selected using genetic algorithms. Two-third of all the compounds were used in the training phase. During the optimization process the performances of the models were checked using cross-validation leave-1/10-out. The performances of obtained solutions were checked using the test set composed of the remaining one-third of the compounds. The obtained models for classification of these three classes of perovskite compounds show very good results. Namely, the classification of the compounds in the test set resulted in small number of discrepancies (4.2–6.4%) between the actual crystallographic class and the one predicted by the models. All these results are strong arguments for the validity of supervised self-organizing maps for performing such types of classification. Therefore, the proposed procedure could be successfully used for crystallographic classification of perovskites in one of these three classes.