Annotation of the results obtained in 2021
During the third stage of the project, the problems related to experimental, simulation and theoretical studies were solved. The most significant results are summarized below. Experimental studies of the structural transformation in amorphous and amorphous-crystalline ribbons (Al87Ni8Y5 and Al90Y10) have been carried out at the external pressure 3 GPa and the torsional deformation at different rates. It was found that crystallization of the systems occurs with the formation of metastable phases Al4Y and Al2Y, as well as with the formation of crystalline α-Al inclusions. Nickel alloying increases both thermal and deformation stability of the amorphous phase. The results bring new insight into the established and important fact that aluminum-containing and nickel-containing alloys have a high glass-forming ability. Local structural features, microscopic dynamics, and transport characteristics of an equilibrium and supercooled pure nickel melt, nickel-containing binary and ternary metal melts were investigated using X-ray diffraction and viscometry experiments, the results of which were interpreted using large-scale molecular dynamics simulations. It was found that nickel melts are characterized by short-range order formed with inclusion of fragments of icosahedra and distorted icosahedral clusters. The liquid-crystal phase transition is accompanied by the transformation of these clusters into a cluster with fcc/hcp symmetry. It has been performed an accurate test of the currently popular hypothesis that the transport and thermodynamic characteristics can be interrelated by means of universal scale relations, such as the Dzugutov relation (for self-diffusion), the Li relation (for viscosity), and Rosenfeld's relations (for a set of transport parameters). Simulation studies of local structural features and microscopic collective dynamics of binary metal melt nickel-phosphorus NixP(100-x) (for concentrations x = 50, 60, 70, 80, 90, and 100 at.%) were carried out for various isobars and for a wide temperature range corresponding to the phases of equilibrium melt and supercooled melt. The found structural characteristics of the melts are in full agreement with the experimental results on X-ray diffraction which were obtained in the framework of the project. The experimental data on viscometry for concentration and temperature dependences of viscosity are found to agree with the results of molecular dynamics simulation, that provides evidence of the possibility of interpreting the experimental data in terms of microscopic characteristics. It was found that a significant increase in the viscosity of nickel-phosphorus melt is observed at nickel concentrations of ~ 70%. Original simulation protocols have been developed that reproduce the processes of foaming and quenching of metal melts and allow one the formation of porous amorphous alloys with different degrees of porosity and different pore morphology. The efficiency of the developed simulation protocols is demonstrated by the example of the formation of amorphous titanium nickelide alloy with a porosity of 15% to 35%. It has been established a correlation between the geometry of the porous structure and the degree of porosity in the amorphous alloy. It was found that quenching of the alloy with injection of argon, the proportion of which is from 10% to 30%, makes it possible to regulate the porosity of the system. It has been established the relationship between the porosity and the volume of the filler (argon), which obeys a power law. The maximum porosity of 55% is achieved with preliminary foaming of the melt through the injection of argon, the volume of which is related to the volume of the melt as 1: 4. The kinetics of crystallization of bulk amorphous Ni62Nb38 alloy under uniaxial compression (pressures from 200 GPa to 1000 GPa) and shear deformation has been investigated. It was found that with an increase in the applied pressure, the characteristic time scales of crystallization decrease, and at pressures exceeding 400 GPa, explosive crystallization is observed. The results obtained are fully reproduced by the scaling relations describing the crystallization kinetics. It was found that at pressures above 600 GPa, there is a significant difference in the rates of formation of crystalline clusters of nickel and niobium: nickel crystallites grow ~ 4 times faster than niobium crystallites. This is resulted in the formation of an inhomogeneous crystal structure of Ni62Nb38 alloy. An original method for characterizing the morphology of crystalline inclusions in an amorphous matrix has been developed. It was found that at pressures from 600 GPa to 1000 GPa the nonsphericity of the crystal grains forming in the amorphous Ni62Nb38 alloy increases. This leads to the formation of a percolating crystalline-structured network. At pressures of the order of 1000 GPa, phase separation occurs and crystalline domains formed either by nickel atoms or by niobium atoms appear. With increasing pressure, a crystalline phase characterized by a deformed hcp lattice is formed. A self-consistent relaxation theory of transverse collective dynamics in liquids is developed. The theory is a extension of the description of longitudinal collective dynamics in fluids, which was carried out earlier in the framework of this project. The theory satisfies the full set of so-called “sum rules”, known in spectroscopy, for the spectral density of the transverse current of particles. It generalizes the well-known viscoelastic model, the key parameters of which, as shown, can be calculated within the framework of the presented theory. Comparison with experimental data on inelastic X-ray scattering and with the obtained results of molecular dynamics simulations for nickel melt show complete agreement. Using lithium as an example, it is shown that, within the framework of the theory, such characteristics of the transverse vibrational dynamics of particles as the transverse sound velocity, the corresponding coefficient of sound attenuation, and kinematic shear viscosity can be calculated. The collective dynamics of ions in a Yukawa liquid is has been described in the framework of a developed self-consistent relaxation theory. It was found that such a description is realized on a wide range of spatial scales, and only information about the structure of the system (radial distribution of particles and static structure factor) is necessary. Analytical expressions are obtained for the key experimentally measured characteristics of the equilibrium collective dynamics of ions (spectra of the dynamic structure factor and characteristics of sound propagation). The theoretical results are found to be in complete agreement with the results of molecular dynamics simulations for various thermodynamic states corresponding to the equilibrium liquid phase of the Yukawa system. The quality of the results obtained turned out to be higher than the quality of the known theoretical models. On the basis on the results obtained in 2021, 9 papers were published in leading scientific journals, indexed in the Web of Science Core Collection and Scopus; 4 of these papers belong to the Q1 quartile. The certificate of state registration of computer programs was received. It is publishes the monograph [A.V. Mokshin et al., Physical-mechanical features of amorphous systems with inhomogeneous local viscoelastic properties (Kazan: RIC Shkola, 2021) - 196 pages; link: https://repository.kpfu.ru/?p_id=259566#], it is published the study guide [B.N. Galimzyanov et al., Collection of tasks for the course "Computer materials design (Kazan: Kazan University, 2021) - 36 pages; link: https://repository.kpfu.ru/?p_id=260181]. It is established international cooperation with a scientific group from Universitat Politecnica of Valencia (Spain). The results obtained within the framework of the project were covered in mass media (10 publications in mass media), including appearances in two TV stories: 1. The developed mathematical model will accelerate the creation of alloys with specified properties (05/14/2021), https://www.rscf.ru/news/physics/razrabotannaya-v-kfu-matematicheskaya-model-uskorit-sozdanie-splavov-s-zadannymi-svoystvami/ 2. Mechanical response of nitinol to deformations gives insight into materials with targeted properties (13/05/2021), https://sciencex.com/wire-news/382419852/mechanical-response-of-nitinol-to-deformations-gives-insight-int.html 3. Study of nitinol deformations to enrich understanding of materials with targeted properties (13/05/2021), https://www.eurekalert.org/news-releases/753650 4. Influence of pressure on amorphous metal alloys, portal "Scientific Russia" (09/15/2021), https://scientificrussia.ru/articles/vlianie-davlenia-na-amorfnye-metalliceskie-splavy 5. Interview to the TV channel UniverTV (23/05/2021), https://www.youtube.com/watch?v=I3HeflKMSXw 6. UniverTV interview: how does pressure affect amorphous alloys? (10/09/2021) https://www.youtube.com/watch?v=6wAJDXPH7N4 7. Effect of pressure on amorphous metal alloys (09/08/2021), https://media.kpfu.ru/news/uchenye-kfu-opredelili-granicy-primenimosti-obemnykh-metallicheskikh-stekol 8. A new way to classify materials (07/07/2021), https://media.kpfu.ru/news/uchenye-kfu-razrabotali-novyy-sposob-klassifikacii-materialov 9. Unique calculations of the mechanical properties of amorphous metal foam (04/28/2021), https://kpfu.ru/physics/struktura/kafedry/kafedra-vychislitelnoj-fiziki/sotrudnikami-kafedry-vypolneny-unikalnye-raschety.html 10. Interpretation of experimental data on the viscosity of substances of different types (07/10/2021), https://kpfu.ru/physics/struktura/kafedry/kafedra-vychislitelnoj-fiziki/sotrudnikami-kafedry-vychislitelnoj-fiziki-i.html

 

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Annotation of the results obtained in 2019
At the first stage of this project, it was organized a research work related with experimental measurements, classical molecular dynamics simulations and quantum mechanical calculations, as well as with development of the relevant theoretical models and concepts. Description of the work performed during this stage and the most important obtained results are given below. It is developed the original self-consistent relaxation theory that allows one to describe the collective dynamics of particles (atoms, molecules, ions) in high-density equilibrium liquids over the whole range of wave numbers: from the hydrodynamic limit to the wave numbers corresponding to the short wavelength limit. The key features of this theory, which distinguish it from the theories and theoretical models existing at present, are as follows: (1) the theory in a unified manner allows one to describe the relaxation processes in liquids that are related with the longitudinal and transverse dynamics of particles; (2) the theory predicts and reproduces the microscopic quasi-solid properties in the high-density liquids - namely, the properties that are manifested in appearance of a nonzero effective shear stiffness revealed from the analysis of the latest experiments on inelastic neutron and x-ray scattering; (3) the theory is applicable to describe the structure relaxation processes over the entire range of wave numbers, and the theory reproduces correctly the asymptotic solutions both for the hydrodynamic (long wavelength) limit and for the short wavelength limit corresponding to the free-moving particle dynamics; (4) only the interparticle interaction and the structural parameters are used as input parameters of the theory [Note: there are no restrictions by the specific interparticle interactions]; there are no abstract fitting parameters and no model functions are used to approximate the relaxation functions; (5) the theory satisfies the fundamental principle of spectroscopy: namely, it is capable to reproduce correctly all the so-called “sum rules" of the considered spectra; (6) the theory generalizes the ideas of the equilibrium hydrodynamic theory and the mode-coupling theory; (7) the theory allows one to calculate analytically the spectra of various experimentally measured quantities: the dynamic structure factor, the vibrational density of states for a many-particle system, the transport coefficients (self-diffusion, viscosity, thermal conductivity, thermal diffusivity), the sound propagation velocity, the sound attenuation coefficient, the shear modulus, etc.; allows one to interpret properly the experimental data on inelastic scattering of light, neutrons, and x-rays. It was performed the molecular dynamics simulations of an ultra-thin metal film with a thickness of five or more atomic layers, which is crystallizing under various supercooling levels. By the type of the interparticle interaction, the simulated system corresponds to the iron- and aluminum-based systems. It was developed an original method for analyzing the morphology of crystalline grains and the shape of crystallites that form under conditions of specific geometry. Special attention was paid to the study of the physical properties of the surface layer of emerging crystalline domains. The results of molecular dynamics simulations were compared with experimental data on x-ray diffraction for these systems. The correspondence of the simulation results to experimentally measured diffractograms made it possible to use the obtained configuration data to reveal the actual morphological features of the emerging and growing crystalline domains. It was performed a study to establish the characteristic universal regimes in the evolution of the crystalline domain size distribution during crystallization. A study has been done to detect the main mechanisms leading to coalescence of the growing crystalline domains and to estimate influence of the supercooling level on the physical mechanisms of the coalescence processes. In the framework of the adapted fractal analysis, it was developed the algorithm for accurate quantitative assessment of almost all the morphological characteristics of the emerging and growing crystalline domains: the full linear size, the linear size of the core (homogeneous) part, the thickness of the surface layer of the domains. The dependences of the morphological characteristics on the supercooling level of the system are estimated. It was studied the structural ordering in the quasi-two-dimensional systems under steady-state non-equilibrium conditions. In this case, not only an external field, but also the surfaces (or the substrate) bounding the system can act as a perturbation. Large-scale molecular dynamics simulations of the crystallization process in a thin film of supercooled water enclosed between parallel ideally even graphene layers have been performed. In this case, an external uniform electric field was imposed on the system. The crystallization of such the system is determined by three key motives: the usual relaxation of a metastable disordered phase into the crystalline phase, the effect of a confinement, and the influence of an external field. The stationary electric field was imposed by two various ways: in the directions perpendicular to and parallel to graphene layers. It was performed the detailed structural and cluster analysis based on evaluation of the local parameters of the orientational order, on the Delaunay triangulation procedure and on construction of the Voronoi polyhedra; statistical processing of the molecular dynamics simulation results was implemented. The most probable evolution trajectories of the disordered system into the ordered phase were determined, and the phase transition rates were estimated. Particular attention was paid to identifying conditions conducive to the formation of a crystalline phase with the square lattice that is exotic for this system under the chosen thermodynamic conditions. The obtained results are compared with the experimental data for water [A.K. Geim et al., Nature 519, 443 (2015)], as well as for iron [Science 343, 1228 (2014)] in graphene confinement. The concentration and temperature dependences of the viscosity coefficient of the binary and ternary Fe-, Zr- and Cu-based melts were experimentally measured for the temperatures corresponding to the states of equilibrium melt and supercooled melts. Large-scale molecular dynamics simulations of the viscosity properties of the metal melts CuAl, CuZr, CuMg, AlZr, AlCuZr and AgCuZr were performed. The experimental temperature dependences of the kinematic viscosity of liquid pure aluminum and AlNi melts with a low nickel content (up to 1 at.%) were obtained; as found, the temperature dependences are almost identical for heating and cooling protocols. In the case of liquid aluminum and melts with a nickel concentration up to 0.50 at.%, inclusively, a deviation of viscosity polytherms from the Arrhenius dependence was found for the temperatures 880 – 920 °С. It has been revealed that the increase of the nickel concentration in the melt leads to an increase of the viscosity values. Computations of the temperature dependences of the viscosity of these melts on the bases the molecular dynamics simulations were performed, and good agreement between the simulation results and experimental results was found. It was found that the experimentally observed features in the concentration and temperature dependences of shear viscosity are due to significant structural changes (the local structure of the melts changes significantly) and due to formation of relatively stable clusters of the type “nickel atom surrounded by aluminum atoms”. For the crystallizing molecular glasses of various types (ortho-terphenyl, griseofulvin, tris-naphthylbenzene, indomethacin, nifedipine), it was found that the universal scaling relations can be applied to describe the experimentally measured temperature dependences of the coefficient of surface self-diffusion, which is one of the key characteristics of the crystallization kinetics of molecular glasses. It is established that the coefficient of surface self-diffusion as a function of reduced temperature obeys a power law and is scaled universally for all the systems considered. Based on the analysis of experimental data, it is found relationship between the characteristics of the crystallization kinetics, the fragility index, and the glass-forming ability factor. It is shown that this relationship can be analytically obtained from the scaling law for the self-diffusion coefficient if one takes into account the generalized (fractional) Einstein-Stokes relation.

 

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Annotation of the results obtained in 2020
During the second stage of the project, the problems related to experimental and theoretical research were solved. The most important results are listed below. It was carried out a comprehensive study of the microscopic structure, collective dynamics of particles, and transport properties of high-density pure polyvalent metallic melts (using gallium as an example) , including experiments on inelastic neutron scattering, viscometric measurements, molecular dynamics calculations, and a theoretical description within the framework of the structural model and the original self-consistent relaxation theory. The original structural model, namely, the model of close-packed quasi-spheres, is proposed. This model explains the structural features in liquid polyvalent metals, which are detected in the recent neutron diffraction experiments, and the physical nature of which has not been generally understood until now. A critical analysis of the well-known hypothesis on the presence of Ga2 molecular dimers in an equilibrium gallium melt is performed. It was found that the "structural anomalies" in liquid polyvalent metals are a manifestation of the so-called extended short-range order. The experimental results on neutron spectroscopy, viscometry, and the results of molecular dynamics modeling obtained in the framework of this project are in agreement and are fully reproduced by the self-consistent relaxation theory. Convincing confirmation of the presence of solid-state properties on microscopic spatial scales in liquids, which are manifested in a shear quasi-rigidity and acoustic-like transverse wave processes has been obtained. These results are valid for an arbitrary fluid and can be classified as fundamental in the physics of fluids. It is developed the adapted cluster analysis, which makes it possible to detect with high accuracy the presence of stable local structures in high-density condensed matter. The key features of the cluster analysis are following: (1) there is an additional opportunity to treat the experimental data on neutron and X-ray diffraction, (2) the method makes it possible to reveal the presence of stable structural units (dimers, triplets, quasicrystalline structural complexes, etc.), (3 ) the method allows one to determine the characteristic lifetimes of these structural units, (4) the method is applicable to the configuration data obtained from molecular dynamics simulations, and to Monte-Carlo simulation data, (5) the method provides an convenient tool to explain the short-range and medium-range order features in simple liquids and molecular melts. It is developed the method for direct calculation of crystallization kinetics characteristics. The method is based on the main definitions and does not use any approximations, models; the applicability of the method is not limited to any specific crystallization scenarios. It was perfomed the estimations of the crystal growth rate as a function of crystal size for the case of a model crystallizing liquid. It was found that the transition to the stationary crystal growth scenario occurs when the growing crystals reach a size comparable to three times the critical size. The obtained results indicate the need to revise a number of postulats of the classical nucleation theory. High-precision viscometry measurements of nickel-containing equilibrium melts (aluminum-nickel, iron-nickel) were carried out for a wide range of temperatures and concentrations. It was found that the revealed features in the shear viscosity of these melts are explained, first, by the presence of clusters formed by atoms of different types and close in composition to the equiatomic system, and, second, by the presence of a weak effective interaction between atoms of different types. The experimental values of the viscosity of nickel-containing metal melts for the entire temperature and concentration range found are in a good agreement with the results of molecular dynamics simulations based on the EAM-type interparticle interaction potentials. It was found that changes in the concentration dependences of viscosity are accompanied by changes in the viscoelastic properties of melts, which are also manifested in the found values of the longitudinal and transverse sound velocities. An analysis of the obtained experimental data for the melts is carried out within the framework of the generalized kinetic model for the viscosity. The obtained values of the fragility index indicate the tendency of the melts to form stable amorphous phases. It is developed an original scheme for the classification of glassforming systems, whicha are alternative to the well-known Angell's classification. This scheme is based on the idea of a correct representation of the change in viscoelastic properties with temperature within the framework of simple scale relations. The key quantities for such the classification are the melting and glass transition temperatures, measured experimentally or calculated theoretically, and the scheme itself is built on the basis of the data for any of the quantities characterizing the kinetics of the system: viscosity, self-diffusion, and structural relaxation time. This scheme is implemented on the basis of our own obtained experimental results for the shear viscosity, as well as other experimental data available in the world scientific literature for polymer melts, metal melts, molecular liquids, germanium, silicate, borate melts. The main mechanical characteristics of such an exotic material as porous amorphous titanium nickelide, which has a number of unique physical and mechanical properties and belongs to the class of modern promising materials, have been calculated. Based on the data of nonequilibrium molecular dynamics, the "strain-stress" relation for the elastic and plastic deformation regimes was calculated, the elastic moduli in tension and compression, shear modulus, and yield strengths were determined, and the dependence of these characteristics on the degree of porosity of the system was defined. It was found that the calculated elastic moduli in tension and compression of porous amorphous titanium nickelide exceed the experimental values for crystalline analogs with the same porosity by more than two times. It was found that the amorphous phase of porous titanium nickelide is superior in elastic properties to its crystalline analogue. It was found that the elastic properties of the system decrease with increasing porosity according to a power law, that is fully consistent with the known experimental data for porous crystalline titanium nickelide and the cortical bone. A correlation has been established between the degree of porosity of the system and the geometry of the pores, namely, at porosity less than 15%, the system contains mainly the isolated spherically symmetric pores, while at high values of porosity, a porous percolating network is formed. A simple analytical approximation for the radial distribution function of particles is used to solve the problem of correct description of the short-range order in a one-component Yukawa liquid. Comparison of the obtained theoretical results for such physical characteristics as internal energy, internal pressure, excess entropy, dispersion of longitudinal acoustic-like collective excitations reveals good agreement with the molecular dynamics simulation results. Based on the results obtained in 2020, the monograph of 171 pages was published, 9 papers were published in leading scientific journals, indexed in the Web of Science Core Collection and Scopus; 4 of them belong to the first quartile (Q1). Received 2 certificates of state registration of computer programs. The obtained results were presented in 15 reports at Russian and international conferences, symposia and scientific seminars. As part of solving a number of project problems, international cooperation has been established with the leading scientific groups. There were 11 publications in Russian and foreign mass media about the results obtained in the framework of this project.

 

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