A.B. Shubin. 

ABSTRACT

The definition of random packings of hard spheres, which does not imply any specific features of short-range order in an ensemble of particles, is considered. The results obtained allow us to determine the maximum possible density of random packing, in which there are no any types of explicit or hidden long-range order. New data from computer experiments are presented that describe the statistical-geometric properties of random packings of two-dimensional (2D) and three-dimensional (3D) hard spherical particles. The regularities of the behavior of a small group of randomly selected and fixed spheres at different packing densities, the differences between the properties of this group and the main “large” ensemble, which follow from the theoretical results obtained, are investigated. The regularities found experimentally are consistent with the proposed theoretical solution.

Let the ensemble consist of N particles occupying the volume V (with density η = Nu/V, where u –volume of one particle). The maximum possible density of random packing of spherical particles (η_max) is given by the following geometric condition: the average volume of the Voronoi polyhedron in a random packing cannot be less than the average value of the excluded volume <w> for all points of this packing.

For an arbitrary point of the ensemble lying at a distance x from the center of the sphere closest to it (of unit radius, R = 1), the excluded volume w is determined by the following relations. In two-dimensional space: w(x) = p(2 – x)² for 0 ≤ x ≤ 2; w(x) = 0 for x > 2. In three-dimensional space: w(x) = (4p/3) (2 – x)³ for 0 ≤ x ≤ 2; w(x) = 0 for x > 2. Averaging w(x) for all points of the volume of the ensemble of particles, we can find the average excluded volume <w> for given packing density (h).

We can also formulate the following statement, which follows from the condition described above: if the packing density η exceeds η_max, then such a packing cannot be statistically homogeneous.

The approach used in the work allows us to calculate the maximum possible value (upper bound) for the density of random close packing. This value is η_max = 0.6813 ± 0.001 (in the two-dimensional case, ensemble of hard disks) and η_max = 0.6329 ± 0.0005 (for a three-dimensional ensemble of hard spheres).

KEY WORDS:

 random close packing, average excluded volume, hard spheres, hard disks, maximum density, fixed particle, small group, random sublattice.

DOI: 10.31857/S0235010620050126

Mityushova Yu.A., Gibadullina A.F., Zhilina E.M., Russkih A.S., Krasikov S.A. 

ABSTRACT

High-entropy alloys (HEA) are the subject of interest for many scientific researchers, more than 200 thousand publications are currently known on the HEA topic, and their number is growing every day. Particular interest in HEA is caused by the features of their formation and structure, as well as the properties that such alloys possess. Predicting the formation of the structure of high entropy alloys is an important task that will allow obtaining information about new systems without resorting to a complex and expensive experiment.

At the moment, there are 2 basic approaches to forecasting the possible phase composition of HEA in the world. The first involves the use of phenomenological parameters based on the Hume-Rothery criteria and thermodynamic quantities, the second – thermodynamic modeling. In the present work, the probability for the existence of the AlNbTiVZrx system (x = 0.25, 0.5, 1, 1.25) as a high entropy alloy will be considered from a theoretical point of view.

HEA are singled out in a special group, since the processes of structure and phase formation in them, as well as the diffusion mobility of atoms, the mechanism of the formation of mechanical properties, and thermal stability differ significantly from similar processes in traditional alloys. The main feature of HEA is the formation of a single-phase thermodynamically stable and high-strength solid substitution solution mainly with an fcc or bcc lattice.

In this work, the prediction of a possible phase composition is considered on the example of alloys of the following compositions AlNbTiVZr_0.25, AlNbTiVZr_0.5, AlNbTiVZr, AlNbTiVZr_1.25. The calculations of the phenomenological parameters are performed, the boundary conditions that determine the stability and type of phases are identified. Binary phase diagrams were constructed using the CALPHAD method, which shows the formation of single-phase structures that can be formed in the AlNbTiVZr alloy under study.

According to the results of studies, it was found that most likely AlNbTiVZr-based alloys are disordered single-phase solid solutions with a bcc type structure.

KEY WORDS:

high-entropy alloys, thermodynamic parameters, phase formation.

DOI: 10.31857/S0235010620050084

V.V. Filippov, K. Yu. Shunyaev. 

ABSTRACT

The temperature dependences of the dynamic viscosity of InBi_100-хPb_х melts (where х = 19, 40, 60, 80, 100 at.%) in the range from the liquidus temperature to 1200 K are studied by the method of damped torsional oscillations. The temperature dependence of the viscosity of investigated melts is well described by the Arrhenius equation. The viscosity of InBi–Pb melts at a constant temperature has small negative deviations from the viscosity of an ideal mixture. The activation energy of a viscous flow has negative deviations from additive values with a minimum near 20 at. % lead. The concentration dependence of the viscosity of the melts of this system was calculated using well-known equations based on data on thermodynamic properties. The results obtained are compared with experimental data.

KEY WORDS:

temperature dependence, viscosity, viscous flow activation energy, InBi–Pb melts.

DOI: 10.31857/S0235010620050059

V.B. Malkov, I.V. Nikolaenko, G.P. Shveykin, V.G. Pushin, A.V. Malkov, B.V. Shulgin, O.V. Malkov. 

ABSTRACT

By analyzing the patterns of bending extinction contours present on the electron microscopic images of nanotubic (~ 80 nm) Spatial dissipative structures, the formation of dangling, low-angle, interblock boundaries in nanotin spatial dissipative structures of hexagonal selenium with elastically rotating rotational curvature around [001] is studied. The effect of a change in the sign of the misorientation vector along the torn-off, small-angle, interblock torsion boundaries was discovered. Taking into account the change along the interblock boundary and the modulus and the sign of the misorientation vector, a model for the formation of dangling, low-angle, interblock torsion boundaries in the nano-current spatial dissipative structures of hexagonal selenium, whose lattice undergoes elastic rotational curvature, is developed. A formula is derived for calculating the energy of dangling, small-angle, interblock torsion boundaries formed in nano-current spatial dissipative structures, along which both the modulus and the sign of the misorientation vector change.

KEY WORDS:

interfacial boundary, electron microscopy, bending extinction contours, dissipative structure, selenium.

DOI:10.31857/S0235010620050072

A.M. Makasheva, V.P. Malyshev. 

ABSTRACT

The aim of the research is to develop the temperature dependence of the dynamic viscosity for sodium fluoride. The relevance of the research is related to the insufficient knowledge of the nature of the viscous state and fluid flow, the scattered temperature dependences of the viscosity, the fragmentation and narrowness of the experimental determination of this characteristic and the impossibility of displaying it in the full temperature range of the liquid state, especially for melts.

The scientific novelty of the work consists in displaying the temperature dependence of the viscosity of a cluster and associate probabilistic mathematical model, the hierarchical structure of which is adequate to the physical nature of the aggregation of particles without taking into account their specific structure, but taking into account the change in the degree of their association with temperature.

The data were calculated on the basis of a new cluster and associate equation, which was derived in the framework of the concept of randomized particles. The calculated data are given in the temperature range from the melting point to the boiling point. It is shown that the degree of association of clusters with increasing temperature naturally decreases, equal on average to three to four-particle arrangement of clusters in an associate. The cluster and associate model is compared with the Frenkel’s equation in logarithmic coordinates. The approximation was carried out by two rectilinear dependences intersecting in the temperature range of 1500 K. The high correlation coefficient of the Frenkel and cluster and associate models indicates the functional nature of the relationship, mutual correspondence and complementarity of these models.

KEY WORDS:

Boltzmann’s distribution, dynamic viscosity, randomized particles, associate, cluster, sodium fluoride.

DOI: 10.31857/S0235010620050060

D.V. Alexandrov, I.G. Nizovtseva, I.V. Alexandrova, A.A. Ivanov, I.O. Starodumov, L.V. Toropova, O.V. Gusakova, V.G. Shepelevich. 

ABSTRACT

In this paper, a model of the directional solidification process of binary melts with a two-phase zone is developed in which the fraction of the liquid phase is described by the spatio-temporal scaling dependence. Self-similar variables with the growth laws of interphase boundaries, which are inversely proportional to the square root of time, are used. The mathematical model of the process is reformulated using the self-similar variables. Exact self-similar solutions to the heat and mass transfer equations are determined in the presence of two moving boundaries of the phase transition: solid phase – two-phase zone and two-phase zone – liquid phase. The distributions of temperature and impurity concentration in the solid phase, two-phase region, and melt are found in the form of integral expressions. A decrease in the dimensionless temperature of the cooled boundary leads to an increase in the crystallization rate and an increase in the liquid phase fraction. The crystallization rate, parabolic growth constants, and the liquid phase fraction at the solid-phase – two-phase zone are determined depending on the scaling parameter and the thermophysical constants of the solidified melt. The positions of the phase transition boundaries between the solid phase and the two-phase region, as well as the two-phase region and the binary melt, are found. The dependences for the solidification rate (inversely proportional to the square root of time) are analyzed. It was shown that the scaling parameter significantly affects the rate of the solidification process and the liquid phase fraction in the phase transformation region. The developed model and the method of its solution can be generalized to the case of directional solidification of multicomponent melts in the presence of several regions of phase transformation (for example, the main and cotectic two-phase zones during crystallization of three-component melts).

KEY WORDS:

phase transitions, crystallization, two-phase zone.

DOI: 10.31857/S0235010620050023

A.V. Rudenko, A.A. Redkin, S.V. Pershina, E.A. Ilina, A.A. Kataev, P.N. Chernenkiy, Yu.P. Zaykov. 

ABSTRACT

The phase equilibria in the system NaF–AlF₃–CaF₂ were studied at sodium and aluminum fluorides molar ratio equal to 1.17. This composition is eutectic with a melting point of 680°С. The thermal analysis, DSC and XRD methods were used. Samples were prepared from individual salts. Aluminum fluoride was purified from oxygen-containing impurities by ammonium fluoride in a glassy carbon crucible. For XRD and DSC, the melt was frozen on an alundum stick to obtain hardened samples. Liquidus temperatures were obtained by recording cooling curves in thermo-EMF – time coordinates using an APPA 502 multimeter. Solidus temperatures were studied using a STA 449C Jupiter synchronous heat analyzer (NETZSCH, Germany). A Rigaku MiniFlex 600 X-Ray diffractometer (Japan) with a copper anode was used for X-ray analysis. The XRD method allowed us to determine the phase composition of the samples. 7 samples were investigated. Calcium fluoride content ranged from 0 to 6.5 mol. %. The quasi-binary diagram of system (NaF–AlF₃) _eut – CaF₂ was obtained. The diagram has eutectic point with calcium fluoride content of 0.5 mol. % and temperature of 675°С. There are also two peritectic points on the diagram that correspond to the decomposition of complex compounds. The liquidus temperature after reaching the eutectic point increases sharply with calcium fluoride content, which results in the low solubility of CaF₂ in the low-melting eutectic NaF–AlF₃ at temperatures below 750°C. The data obtained are of interest for the development of technology for low-temperature electrolysis of aluminum.

KEY WORDS:

NaF–AlF₃–CaF₂, thermal analysis, DSC, X-ray phase analysis, phase equilibria.

DOI: 10.31857/S0235010620050114

А. V. Novoselova, V. V. Smolenski, А. L. Bovet. 

ABSTRACT

The cathodic reduction reaction of Dy(III) ions on inert molybdenum electrode in fused 3LiCl–2KCl eutectic in the temperature range 723–843 K in inert atmosphere was studied by electrochemical methods. On cyclic voltammogram in the investigated “electrochemical window”, one cathode current peak at potential of –3.19 ± 0.11 V and the corresponding anode current peak at potential of –2.95 ± 0.11 V vs. the reference chlorine electrode were fixed. Therefore, the recovery process proceeds by the reaction Dy³⁺ + 3ē → Dy. Analyzing of cyclic voltammograms showed that the potential of the current peak shifts to the negative region with increasing of scan rate, and the current of the cathode peak is directly proportional to the square root of the polarization rate. It was found that the increasing of scan rate led to a natural increase of the irreversibility of the cathode process. The number of electrons (n) of the electrode reaction for reduction Dy(III) ions was determined by the square-wave voltammetry method. The calculated value is equal to n = 2.93 ± 0.05. According to the theory of cyclic voltammetry, the cathode recovery process proceeds irreversibly, in one stage, and is controlled by the charge transfer rate. The dependence of the apparent standard potential of the Dy(III)/Dy couple vs. the temperature was determined by the chronopotentiometry method at zero current. Experimental values are described by the linear equation: . The apparent standard Gibbs energy change, enthalpy, and entropy of the dysprosium trichloride formation reaction from its elements in fused 3LiCl–2KCl eutectic and the activity coefficient of DyCl₃ were calculated.

KEY WORDS:

metallic dysprosium, dysprosium trichloride, molten salts, electrochemical characteristics of the cathode process, thermodynamics of dysprosium trichloride formation

DOI: 10.31857/S0235010620050102

O.V. Volkova, V.V. Zakharov, S.V. Plaksin, E.A. Il’ina, A.A. Pankratov. 

ABSTRACT

Discharge characteristics of the heat activated battery with CoCl₂–CoF₂ mixtures as a cathode material has been investigated. Composition and morphology of reduction products of the cathode materials have been determined. It was found that the use of mixtures instead of individual cobalt halides allows to stabilize the discharge characteristics and decrease of the discharge temperature of electrochemical cell. It was shown that the reduction process of Co²⁺ -ions to metal Co⁰ occurs under the conditions of diffusion control.

KEY WORDS:

thermally activated chemical current sources; cathode; cobalt chloride; cobalt fluoride

DOI: 10.31857/S0235010620030111

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