One of the fundamental goals of materials science is to understand and predict the formation of complex phases. In this study, FeSi2 is considered as an illustration of complex phase formation. Although Fe and Si both crystallize with a simple structure, namely, body-centered cubic (bcc A2) and diamond (A4) structures, respectively, it is rather intriguing to note the existence of two complex structures in the Si-rich part of the phase diagram around FeSi2: α-FeSi2 at high temperatures (HT) with a slight iron-deficient structure and β-FeSi2 (also referred to as Fe3Si7) at low temperatures (LT). We re-analyze the geometry of these two phases and rely on approximant phases that make the relationship between these two phases simple. To complete the analysis, we also introduce a surrogate of the C16 phase that is observed in FeGe2. We clearly identify the relationship that exists between these three approximant phases, corroborated by a ground-state analysis of the Ising model for describing ordering that takes place between the transition metal element and the “vacancies”. This work is further supported by ab initio electronic structure calculations based on density functional theory in order to investigate properties and transformation paths. Finally, extension to other alloys, including an entire class of alloys, is discussed.

—Over the whole area of the Eurasian lithospheric plate considered in the paper—from the Atlantic to the Pacific Ocean—the velocity vectors of the horizontal eastward displacements of GPS sites form a gentle, smooth, huge arc, convex towards the north. Three relatively narrow arc-shaped bands can be distinguished within the arc. The southernmost band, most provided with measurement data (referred to as a arc-shaped band A in this paper) is discussed in detail in (Shevchenko et al., 2021). The direct, real results of the published geodetic measurements have shown that the length of this band increases by 5 to 10 mm annually. The arc is lengthening. In the cited paper, we considered and rejected five interpretations of this lengthening, which involve the idea of external action on the rocks of the Earth’s crust/lithosphere of this arc-shaped band. It is most likely that the elongation is caused by the internal process of the increase in the volume of rocks within the band due to the supply of additional mineral material by deep fluids and its subsequent crystallization. In this paper, we present the results of similar geodetic measurements in other two arc-shaped bands, B and C . It turns out that the arc-shaped band C located to the north of the other bands is lengthening (and at a similar rate), as is band A located to the south of the other bands. At the same time, the arc-shaped band B , which is located between bands A and C , is moving eastward without lengthening. Geodetic measurements in the axial part of the Mid-Atlantic Ridge on the Iceland island suggest that the general expansion of the Atlantic Ocean and the corresponding eastward motion of the Eurasian lithospheric plate are associated with the injection of plastic magmatic wedges (of basic composition) in the axial, rift zone of the ridge. Against the background of this general eastward motion of the lithospheric plate, its constituent parts ( whose markers are the arc-shaped bands A and C ) are moving in the same eastward direction with a velocity increasing from west to east. We attribute this increase in the velocity and the corresponding lengthening of the two bands to the above inflow of the additional mineral material and its subsequent crystallization.

The review presents the results of theoretical and experimental studies of the structure, bonding between atoms, mechanical properties, thermal stability, and oxidation and corrosion resistance of films based on ternary tran-sition metal borides.

First-principles molecular dynamics simulations were used to investigate pressure- and temperature-induced phase transitions in different TaN polymorphs. The driving forces and intermediate structures were established for the CoSn-like TaN (& epsilon; phase) to WC-type TaN (& theta; phase) and & epsilon; to NaCl type-TaN (& delta; phase) structural transformations that were observed in experiments and for the & theta; to hP4-194, & theta; to cP2-221, & delta; to cP2-221 and & delta; to tP4-129 phase transitions that were predicted in this investigation. Other possible TaN polytypes were systematically investigated and five new prospective phases were found: oP8-25, oP12-25, hP8-194, tP8-105 and tI8109. All new structures are thermodynamically, dynamically and mechanically stable, and their formation energy is only slightly higher than that of the & theta; phase (by 0.014-0.032 eV/atom). The relative stability, electronic structure, chemical bonding, vibrational spectra, elastic moduli and their spatial anisotropy, Vickers hardness, fracture toughness, Debye temperature and optical properties (real and imaginary parts of the dielectric function, reflectivity spectrum) of the tantalum mononitrides mentioned above were systematically calculated and discussed. The oP12-25, tP8-105 and tI8-109 novel phases exhibit the Vickers hardness (33.1-34.2 GPa), fracture toughness (5.52-5.59 MPa m1/2) and Debye temperatures (609.7-616.1 K) that are higher compared to those of the known TaN structures. The TaN polytypes with the strong Ta-N bonds with minimal fraction of ionicity were found to possess the best mechanical properties. Further experimental investigations are highly desirable to confirm the results presented in this paper.

First-principles calculations and molecular dynamics (FPMD) simulations in the constant number of particles - pressure - temperature (NPT) ensemble were used to investigate the phase stability, phase diagram, electronic and phonon structures, chemical bonding, mechanical, thermodynamical and optical properties of various tungsten carbide polytypes as well as the hexagonal (alpha) and cubic (beta) Ti1-xWxCy solid solutions. The known alpha-WC (P-6m2) and beta-WCy (Fm-3m) polytypes and eight hypothetical ones were studied. Gibbs free energy calculations predicted the alpha-WC -> beta-WCy and alpha-WC -> tP4-129 (P4/nmm) phase transitions. The P-6m2 -> Fm-3m -> I41md, Fm-3m -> P4/nmm and P-6m2 -> Pm-3m phase transformations were revealed during FPMD simulations of: alpha-WC at T = 2500 K, beta-WC at T = 100 K, and alpha-WC at T = 2500 K and P = 500 GPa, respectively. It is found that the known alpha-polytype and new tI8-109 (I41md), oP12-25 (Pmm2), hP4-194 (P63/mmc), hP8-194 (P63/mmc), cP2-221 polytypes are ultraincompressible and ultrastiff materials, and exhibit the highest hardness (29-38 GPa), fracture toughness (4.7-7.2 MPa m1/2) and Debye temperature (615-663 GPa). Other characteristics of the WC polytypes, namely, the stress-shear strain curves, dielectric function, reflectivity spectra, heat capacity and spatial distribution of the elastic moduli, were calculated and discussed. The stability, mechanical properties and lattice parameter of beta-WCy and Ti1-xWxCy as functions of composition were studied. The binodal and spinodal for Ti1-xWxC were calculated. The calculated characteristics are compared with available experimental data and used for their interpretation.

First-principles calculations were carried out to study the hypothetical MoC, Mo2C, Mo3C2 and random MoCx, x = 1.0, 0.875, 0.75 and 0.5 phases, and those that were experimentally verified, as well as the random cubic and hexagonal TiC-MoC and cubic and orthorhombic Ti2C-Mo2C solid solutions (alloys). The electronic and phonon structures, formation energy, elastic constants and moduli, hardness, Debye temperature, fracture toughness and stress-strain relation for these structures were calculated in order to understand the differences in phase stability; to explain their properties; and to predict possible new stable phases. The phase diagrams of the Mo-C system for three compositions, 67 at.% Mo + 33 at.% C, 60 at.% Mo + 40 at.% C and 50 at.% Mo + 50 at.% C, were built in the temperature range of 0-4000 K. First-principles molecular dynamics simulations and the group-theoretical analysis are used to identify the plausible mechanisms of the temperature-induced structural transformations in the alpha-, gamma- and gamma'-phases of MoC. The composition dependence of the mechanical characteristics of the solid solutions was found to have an extremal character, and in particular a maximum hardness for the cubic Ti0.75Mo0.25C (27.2 GPa) and orthorhombic Ti0.5Mo1.5C (14.6 GPa) alloys. The theoretical phase stability diagrams for the Mo-C system and Ti-Mo-C alloys contain not only the structures experimentally observed but also hypothetical phases, and the available experimental properties were reproduced and explained.

Both first-principles study of the random TiC-NbC solid solutions and experimental investigation of the films in Ti-Nb-C system were carried out. The mixing energy, electronic and phonon structures, elastic constants and moduli, hardness, Debye temperature, fracture toughness, dielectric function, electron energy-loss spectra and heat capacity of the random Ti1-xNbxC solid solutions were calculated and analyzed depending on composition. The Ti-C, Nb-C and Ti-Nb-C films were deposited by magnetron sputtering. The deposited films were comprehensively studied with XRD, XPS, AFM, EDS, Raman spectroscopy, indentation and tribological tests. The Ti-Nb-C films with equi-atomic composition are found to exhibit the highest Knoop hardness and lowest friction coefficient as compared to those of the parent TiC and NbC carbides. The results obtained were used to establish the mechanism of the stabilization of the TiC-NbC solid solutions, and to predict their structural, mechanical, optical and thermodynamic properties.

The stability, electronic and phonon structures, optical, mechanical and thermodynamic properties of the random high entropy (TiZrHfNbTa)B2 solid solution (alloy) were studied in comparison with those of TiB2, ZrB2, HfB2, NbB2 and TaB2 using first-principles calculations. The mixing enthalpy of -0.842 kJ/mol of atoms for the high entropy diboride points to that it is stable against decomposition into the constituting binary diborides. All the diborides studied are thermodynamically, mechanically and dynamically stable. The dielectric function, reflectivity and extinction coefficient of the diboride compounds were comprehensively studied. Both (TiZrHfNbTa)B2 and binary diborides are found to be good reflective materials in infrared, visible and ultraviolet regions. The calculated elastic moduli, B/G ratio, Vickers hardness, fracture toughness and Debye temperature of (TiZrHfNbTa)B2 are medium between largest and lowest ones of the constituents, approximately obey the rule of mixture. Calculations of the stress-shear strain relations for (TiZrHfNbTa)B2 point to the possibility of the activation of both basal and prismatic slip systems. The elastic moduli and linear compressibility exhibit the spatial anisotropy inherent to hexagonal structures. The thermodynamic characteristics of the diborides studied are well reproduced in a temperature range up to 800-1000 K.

A sample of amorphous AlBN was generated using first-principles molecular dynamics simulations. Pair correlation functions, phonon spectra, stress-shear strain relation and elastic moduli of the sample were studied.

The stability, electronic and phonon structures, mechanical and thermodynamic properties as well optical spectra of the Ti1-xZrxB2 solid solutions were investigated in the framework of a first-principles approach. The miscibility gap was predicted with the consolute temperature T-C = 1973 K and composition x(C) = 0.4. The negative deviation of the calculated bulk, shear, Young moduli, Debye temperature, Vickers hardness and fracture toughness from the mixing rule is observed. The ideal shear stress of 41.1 GPa for Ti0.5Zr0.5B2 was found to be lower compared to that for TiB2 (43.5 GPa) and ZrB2 (43.1 GPa). The calculated elastic moduli and Poisson ratio exhibit the spatial anisotropy inherent to hexagonal structures. It was shown that the thermodynamic characteristics of the Zr-rich solid solutions could be well reproduced in a temperature range up to 1000-1400 K using the harmonic approximation. The calculated dielectric constants epsilon(R)(omega) and epsilon(I)(omega), and optical reflectivity spectra R(omega) for Ti1-xZrxB2 were analyzed in comparison with available optical spectra of parent diborides from other authors.

The neomobilist plate tectonic concept is currently at the forefront of geotectonics. This concept is based on the idea of the division of the Earth’s crust/lithosphere into plates, blocks, and massifs of different size that move laterally due to external forces. The greatest importance is attached to their movement due to the viscous coupling of plates with convective flows in the mantle. At the same time, the results available on geodetic (mainly GPS) measurements of real movements within the Eurasian lithospheric plate indicate that the size of its northern part is significantly increasing from west to east. Existing ideas about the geodynamics of the Earth’s crust/lithosphere do not take this phenomenon into account. Based on the materials of systematic repeated GPS measurements and focal mechanisms of earthquake foci, an interpretation of this elongation of the northern part of the Eurasian lithospheric plate to the east is provided in this paper. This elongation develops against the background of the predominance of subhorizontal compression stress in the Earth’s crust of the part of Eurasia under consideration. At the same time, there is a systematic reversal of the orientation of the main compression axis from 147° in the west within the European margin of the plate to 283° at the extreme eastern edge of the plate (Kolyma Highlands). The environs of the Upper Rhine Graben and the Baikal Rift with predominant subhorizontal stretching, corresponding to the known geological data by the orientation, fall out of this pattern. It is assumed that the observed elongation of the Earth’s crust/lithosphere of the considered part of the Eurasian lithospheric plate to the east, while being in a stressed state of subhorizontal near-meridional compression, may occur due to the development of strut stress in the crust/lithosphere. Such stress is most likely caused by an increase in the volume (and area) of layered rocks as a result of the introduction of additional mineral material by deep fluids from the lower crust/upper mantle and its subsequent crystallization.

Based on the available geological and geodetic data, it has been established that the structures of the Alpine–Himalayan–Indonesian mobile belt are oroclinally (horseshoe-shaped) closed at its western and eastern extremities. In the west, from the Atlantic Ocean, this closure is represented by the Bet–RIF arc and, in the east, from the Pacific Ocean, by the Band and Mindanao arcs. The presence of these closures means there is no structural connection between the mobile belt under discussion and the Atlantic and Pacific oceans, respectively. Thus, the existing plate-tectonic reconstructions, according to which the Tethys paleocean was a wide bay of the Pacific Ocean connected in the west with the Atlantic Ocean (wide Tethys), are in opposition to the facts. The Alpine–Himalayan–Indonesian mobile belt has to be considered an epigeosynclinal rather than an epioceanic structure.

Abstract—The leading role in geotectonics is currently played by the neomobilistic plate tectonic concept which is based on the division of the the Earth’s crust/lithosphere into plates, blocks, and massifs of different sizes. These crustal units move laterally, driven by the forces that are external to them. For example, it is assumed that under the action of gravity, a plate slips off the mid-ocean ridge and then moves horizontally following the heavy subducting slab sinking into the mantle. The motion due to viscous coupling between plates and convective flow in the mantle is considered as most important factor. Mechanical action from the neighboring lithospheric plates is not excluded. The data accumulated to date on the geodetic (mainly GPS) measurements of these real movements within the Eurasian continent indicate that the size of the northern part of the latter has significantly increased. This increase is not taken into account in the existing notions of geodynamics of the Earth’s crust/lithosphere. Several possible interpretations of this phenomenon are discussed.

—Based on the distribution of mantle seismicity and the sets of focal mechanisms of the earthquakes, the existence and deformation type of an allantoid mantle body within the eastern part of the Caucasus Isthmus is established. The body is inclined and plunges from the southeast to the northwest to a depth of 160 km. The shape of the mantle body and the type of its stress state which is fundamentally different from that for the Earth’s crust in the region precludes us from accepting plate-tectonic interpretation of this formation in the form of a concept implying the subsidence of the subducting part of the Arabian lithospheric plate underneath the Eurasian plate. We hypothesize that this phenomenon is associated with the tectogenesis process developing in the subcrustal mantle of the Caucasus irrespective of the collision processes.

The style of the seismotectonic deformation of the Earth’s crust in the Caucasus and its immediate surroundings corresponds to the thrust setting with a subhorizontal principal compression axis oriented north-northeast across the strike of the Caucasian structures and a subvertical principal extension axis, as established by the reconstruction of a representative set of focal mechanisms of earthquakes. Overall, this deformation style quite closely agrees with the notions developed in plate tectonics according to which the Caucasian segment of the Alpine–Indonesian mobile belt is experiencing strong transversal (across the strike) narrowing as a result of the convergence of the Arabian and Eurasian lithospheric plates. At the same time, the detailed geodetic measurements conducted in the territory of the Greater Caucasus established the GPS site displacements, testifying to the increase of its width. This widening cannot be attributed to the extension across the strike of this mountainous edifice because the focal mechanism solutions of earthquakes in this territory clearly indicate a setting of compressive stresses across the strike of the geological structures. We suggested interpreting this combination of the geodetic and seismological data by the active growth of the volume (and area) of layered rocks of the Greater Caucasus and the emergence of the setting of outward pressure probably as a result of the inflow of the additional mineral material carried by the ascending deep fluids.

— The formation of fold–thrust dislocations of stratified rocks in the Earth’s crust has been considered as a consequence of the lateral compression of such rocks by converging platforms or lithospheric plates over the last 150 years within the framework of a geosyncline concept and then according to the concept of plate tectonics. Such convergences are reliably confirmed by current geodetic measurements. At the same time there are less popular ideas that present the formation of these dislocations as a result of various local, autonomous processes. The essence of the problem is that the domination of directionally ordered horizontal compression over the value of lithostatic pressure in the Earth’s crust, which is unambiguously determined according to the data of focal mechanisms of earthquakes and in the measurements on stresses in situ in mine workings, makes it necessary to prefer the global mechanism of compression in the form of convergence of horizontally moving lithospheric plates. This convergence is reliably established on a global scale and by modern high-precision geodetic GPS measurements. However, similar GPS measurements, but on regional or local networks rather than on global ones, have shown an opposite result in a few cases. They revealed an increase in the width of representative segments of the mountain belts, rather than a decrease. A detailed study of the geological structure of such areas has indicated that the main role in their formation is played by scaly thrusts, sometimes transforming into small covers, and linear folds and groups of such folds associated with these dislocations and subordinate to them. The formation of such a cover-thrust tectonic structure continues now. For several years, the authors have developed a hypothesis according to which fold–thrust dislocations in the Earth’s crust are formed as a result of an increase in the volume of stratified rocks and as a consequence of an increase in the area of these rocks. They cause volume expansion stresses, similar to the stresses of external compression; crumple; and are dissected by thrusts and reverse faults, tending to cover adjacent territories. It is assumed that the increase in the volume (volume expansion) and the areas of stratified rocks is a result of the entry of additional mineral material with ascending flows of deep mineralized fluids. The increase in the volume and the width of the mountain structure during the formation of its tectonic structure is indirectly confirmed by the near-vertical formations detected in the Earth’s crust in several regions by geophysical methods, which have different velocity characteristics compared to the enclosing environment. These formations can be interpreted as channels of permeability for the penetration of deep fluids—the cause of an increase in rock volume. This suggests that the process of autonomous folding and thrusting in the Earth’s crust really exists in the regional plan, first and foremost, within the mobile mountain belts, along with a global plate-tectonic mechanism.

First-principles calculations were carried out to investigate electronic structure, phase stability, elastic properties, Debye temperature, and hardness of the TiC–HfC and TiC–TaC random solid solutions as functions of composition. For TiC–HfC, significant miscibility gaps with consolute temperatures about 1975 K are revealed in the binodal and spinodal curves. The negative deviation of the elastic moduli and hardness from linearity are obtained for TiC–HfC, whereas, for TiC–TaC, these characteristics are above their linear interpolation between the end members. Concentration dependences of the Debye temperature for both systems have a negative curvature. To clarify a possible mechanism of stabilization or destabilization of these solid solutions and other similar carbide systems, mixing energies of the M11−xM2xC alloys, where M1 and M2 are the transition metals of the IV, V, and partially VI groups, were calculated. It is found that the behavior of mixing energies for the M1C–M2C alloys with M1 and M2 of different groups depending on composition is determined by the difference between cell volumes of the end members, ΔVC, the degree of occupancy of the metal band, and the shape of the density of states in the metal band region. Values of ΔVC mainly are responsible for positive mixing energies of the alloys with valence electron concentrations (VECs) equal to 8 and 9 for which occupancy of the metal band weakly changes with composition. The maximum hardness of the solid solutions for which VECs of the end members are different is predicted to be reached for the compositions with VECs = 8.5–8.75.

The samples of amorphous silicon carbide and carbonitrides were generated by using first-principles molecular dynamics simulations. The atomic structure and stress-strain relations of the samples were investigated depending on sample composition.

First-principles calculations were carried out in order to investigate the stability and properties of the random Ti1-xSixC solid solutions (alloys) with both the B1 and B3 structures. Lattice parameter, total energy, formation energy, phonon spectra, and elastic properties were studied as functions of composition. The phase diagram, in particular, binodal and spinodal curves were calculated. It was established that at 0 K the B1 alloys are energetically favorable at 0 <= x < 0.5, while the B3 alloys are favorable at 0.5 <= x <= 1.0. It was found that the contribution to the Gibbs free energy coming from the lattice vibrations strongly reduces the critical temperature of stabilization of the solid solutions. Calculated elastic moduli, Debye temperature, and Vickers hardness do not point to any strength enhancement of the alloys compared to TiC and SiC. Analysis of the spatial distribution of the Young and shear moduli shows that the B3 alloys exhibit much more spatial anisotropy of the elastic moduli than the B1 alloys.