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A comparison is made between theoretical and experimental studies of the position of eutectics in two-component systems consisting of tetrachlorethylene and n-alkanes with 10 to 20 carbon atoms. Data on the composition of the eutectics, their temperatures of melting, and the coefficients of activity of each component are calculated in three ways: using experimental data, the UNIFAC procedure, and a modified UNIFAC Dortmund procedure. The equilibria of liquid–solid phases are studied theoretically using Schroder’s equation and the UNIFAC and modified UNIFAC Dortmund procedure. Experimental data were obtained via DTA. Relative deviations of the calculated melting temperatures and compositions of the eutectics from the corresponding experimental data are reported.

The Na+,Ba2+||Br–, $${\text{WO}}_{4}^{{2 - }}$$ three-component reciprocal system was partitioned into simplexes by the conversion method; basic thermodynamic characteristics (enthalpy and Gibbs free energy changes) were calculated at the conversion point for the standard temperature and pressure. The direction of the exchange reaction and its stable products in the title three-component reciprocal system were determined. Chemical reactions were described, and the phase tree of the system was built. The numbers and compositions of crystallizing phases were predicted for the stable and secant elements. The partition of the Na+,Ba2+||Br–, $${\text{WO}}_{4}^{{2 - }}$$ system into simplexes was verified by DTA and X-ray powder diffraction: the stable diagonal of the composition square was determined, the crystallizing phases were identified, and the melting point and composition of the quasi-binary eutectic were determined. The system was studied experimentally by DTA. The melting points and compositions of the alloys that correspond to invariant equilibrium points were determined. Phase equilibria were described for each stable element of the ternary reciprocal system. The crystallization tree was built. The projection of the phase complex of the system onto the composition square is represented by four crystallization fields of the initial components; the barium tungstate crystallization field is dominant.

The ternary reciprocal system Na+,Ba2+||Br–, $${\text{SO}}_{{\text{4}}}^{{{\text{2}} - }}$$ has been divided into simplexes by a thermodynamic method, chemical interaction in the system has been described, and its phase tree has been constructed. The melting points and compositions of the eutectic alloys in the binary system BaBr2–BaSO4 and pseudobinary system NaBr–BaSO4 have been calculated by the Schroeder method, and those of the eutectic alloys in the stable triangles NaBr–BaBr2–BaSO4 and NaBr–Na2SO4–BaSO4 of the ternary reciprocal system have been calculated by a Martynova–Susareva method. Differential thermal analysis has been used to confirm the division of the Na+,Ba2+||Br–, $${\text{SO}}_{{\text{4}}}^{{{\text{2}} - }}$$ system and experimentally study the phase compatibility triangles. We have determined the melting points and compositions of the alloys corresponding to points of invariant equilibria, described equilibrium states for each element of the ternary reciprocal system, constructed a crystallization tree, and calculated the principal thermodynamic parameters of the ternary eutectic alloys.

We have studied phase equilibria in the quaternary system NaF–NaCl–NaBr–Na2CrO4. The results demonstrate that the continuous series of NaClxBr1 – x solid solutions persists in the system. The chemical composition and melting point (507°C) of a mixture with the composition corresponding to the quaternary minimum have been determined by differential thermal analysis, and its enthalpy of fusion (232 J/g) has been determined by differential scanning calorimetry. Its phase composition has been confirmed by X-ray diffraction. Theoretical and experimental techniques have been used to identify phase equilibria and the phase crystallization sequence and construct a 3D computer model of phase relations, which makes it possible to predict phase transformations for arbitrary representative points in the system studied.

One of the key explanations for the peculiarities of the change in the first ionization energies (IE Ei1) of the elements of the periodic table is based on the postulation of an unambiguous relationship between Ei1 and atomic radii (rat). Due to the certain conventionality of the rat parameters, they do not belong to the category of attributive atomic characteristics. Usually they are found either by implementing various kinds of theoretical or semi-empirical calculation schemes, or by using experimental data on Ei1 for the corresponding approximations. As follows from the literature data, the known values of rat, even in the case of "quasi-hydrogen-like" alkali metals (AM), –relatively simple manyelectron systems – are characterized, as a rule, by a significant scatter. In addition, the canonical analytical formulas describing rаt within the framework of a hydrogen-like model with two effective interaction parameters (according to Slater) do not ultimately lead to adequate results in this set of elements. In this work, to correct the relationship rat = f (Еi1) related to the properties of the aggregate of alkaline elements, the publication of the effective Slater radii (reff) and Weber-Cromer orbital radii (rorb), and some results of later data are used. The effective principal quantum numbers n* for each of the AM (except for Li, for which it is assumed that n*=n=2) are estimated on the basis of the values of Ei1. A further step, by introducing n*, made it possible to use the criterion for optimizing the value of the effective radius r* and to correct the formula that determines its relationship with Ei1 in the form of a simple power function. At the same time, the radii Li, Na, and Fr have been refined towards some underestimation, compared with rorb. Arguments are presented in favor of the reliability of the proposed approach. It is shown that the obtained estimates of r* correlate better with the amplitudes of the solution of the wave equation covering all AMs than the known corresponding values of rorb and reff.

Theoretical calculations are compared to data from an experimental study of the position of eutectics in two-component systems consisting of benzene, diphenyl, and n-alkanes with 12 to 17 carbon atoms. Data on diphenyl–n-alkane (n = 12–17) and benzene–n-alkane (n = 12–17) systems are given for the composition of eutectics, their melting points, and activity coefficients of each component. The theoretical study is based on the Schroder–Le Chatelier approach and the original UNIFAC system; the experimental study is performed via DTA. Deviations of the experimental data from ones calculated for the studied systems are presented. The change in the activity coefficients of benzene and n-hexadecane is illustrated graphically according to UNIFAC and the experimental data.

A theoretical and experimental study is performed for liquid–solid phase equilibria in the two-component diphenyl oxide–n-hexadecane system. The results show that this system is eutectic. Two means are chosen for the theoretical study of the system: the Schroder–Le Chatelier equations and the original UNIFAC system. Experimental studies are made via differential thermal analysis on a DSC unit. Results from the theoretical and experimental studies are presented in the form T–x diagrams of the system. The theoretical and experimental data are compared to one another. Each way of calculating is assessed, and recommendations are made for their application. The eutectic coordinates (melting point and composition) are determined experimentally. The following values are determined experimentally for a eutectic melt: the enthalpy of melting; density at 25°C; kinematic viscosity in the temperature range of 25 to 50°C; flash point in an open cup; boiling point, and refractive index in the temperature range of 25 to 40°C. The composition of the eutectic melt can be used in industry as a heat transfer fluid.

The phase complex of the quinary reciprocal system Li+,Na+,K+||F–,Cl–,Br– was studied for the first time. Partition according to graph theory determined that the tree of phases of the system has linear structure and comprises stable polytopes: the pentatope LiF–NaF–KF–KBr–KCl, the hexatope LiF–NaBr–NaCl–KCl–KBr–NaF, and the heptatope NaCl–KCl–KBr–LiBr–LiCl–LiF–NaBr, connected by the stable tetrahedron LiF–NaF–KCl–KBr and the stable pentatope LiF–KBr–NaBr–NaCl–KCl. Phase equilibria in the stable tetrahedron LiF–NaF–KCl–KBr were studied by differential thermal analysis and confirmed by X-ray powder diffraction analysis. In the tetrahedron, there is monovariant phase equilibrium L ⇄ LiF + α + KClxBr1 – x, where α is a limited solid solution based on NaF (LiF–NaF system), and KClxBr1 – x is a continuous series of solid solutions based on KCl and KBr. A 3D computer model of the projection of the phase complex on the concentration tetrahedron was constructed using the KOMPAS 3D software. The crystallization volumes of equilibrium phases are determined.

The ternary systems with a common cation, NaCl–NaI–Na2WO4 and KCl–KI–K2WO4, were studied by differential thermal analysis. The composition point of the congruently melting compound NaCl ⋅ Na2WO4 formed in the NaCl–Na2WO4 system divides the NaI–NaCl–Na2WO4 system into two triangles, in each of which there is a ternary eutectic. The characteristics of invariant points were determined, and phase equilibria in the studied systems were described.

A theoretical analysis is performed of the topology of the liquidus in the NaBr–Na2CO3–Na2SO4, KBr–K2CO3–K2SO4 systems. The coordinates of minimum point on the monovariant curve in the NaBr–Na2CO3–Na2SO4 system are calculated using the Martynova–Susarev approach. An experimental design is devised for studying systems via differential thermal analysis. The melting point and composition of the salt mixture corresponding to the minimum on the monovariant curve of the NaBr–Na2CO3–Na2SO4 system are determined. The absence of nonvariant equilibrium points in the KBr–K2CO3–K2SO4 system is proved. The NaBr–Na2CO3–Na2SO4, KBr–K2CO3–K2SO4 systems have yet to be studied. They are of interest, since their components have a number of valuable properties, e.g., thermal stability and the possibility of using them as solvents for some other salts over a wide range of temperatures.

By differential thermal analysis, the ternary systems MCl–MI–M2CrO4 (M = Rb, Cs) were studied, and the characteristics (melting points, concentrations of components) of alloys at invariant equilibrium points of the systems were determined. The studied systems are systems of the same type that form by varying the alkali metal cation with increasing atomic number of the cation. In all the binary systems constituting the ternary systems, eutectics form. Based on analyzing the faceting elements, it was assumed that eutectics form in the ternary systems. Low-melting eutectic mixtures of alkali-metal halides and chromates are chemically stable even in the molten state and have low viscosity and low volatility, which makes them suitable for using as heat-storage materials or electrolytes for chemical current sources. Consideration of the systems MCl–MI–M2CrO4 (M = Li, Na, K, Rb, Cs) showed that the varying alkali metal cation in them does not affect the morphology of the liquidus.

An experimental study is performed of phase equilibria in the three-component NaCl–NaBr–Na2CrO4 system. Differential thermal analysis curves for cooling the compositions with a constant sodium chromate content of 82 eq % display thermal effects characteristic of the primary crystallization of sodium chromate and its joint crystallization with solid solutions of NaClxBr1 – x. No extrema are found on the monovariant curve corresponding to joint crystallization.

Produced review scientific and technical reference books on individual substances and the two-component systems forming part of the water-salt system K2HPO4 – (NH2)2CO – H2O. To predict phase equilibria in a real system, a mathematical model is proposed that allows one to determine the dependence of the activity coefficient of a substance or ion on the concentration and temperature of the solution. The solution of the system of equations was carried out in the environment of the table processor Microsoft Excel as a result, in terms of potassium hydrogen phosphate, the following characteristics of the eutectic alloy with the calculated content of components in the eutectic were obtained: 36.5 % wt. K2HPO4, 11.5 % wt. (NH2)2CO, 52.0 % wt. H2O, melting point 250.6 K (-22.6 C). In order to search for a composition with a minimum crystallization temperature in the ternary urea – potassium hydrogen phosphate – water system, the simplex K2 HPO46H2O – (NH2)2 was studied CO – H2O by visual polythermal method. The eutectic in the studied system crystallizes at a temperature of minus 28 С and contains 8 % wt. carbamide, 35 % wt. potassium hydrogen phosphate, 57 % wt. water. An analysis of the data obtained by experimental and computational methods showed satisfactory convergence. The average deviation of the calculated data from the experimental ones was 18.9% in composition and 2.3% in terms of the eutectic melting point. The proposed calculation algorithm can be used to predict the characteristics of eutectics in ternary water - salt systems for planning the experiment.

Three-component systems containing cyclododecane and two n-alkanes are studied via differential thermal analysis (DTA) using a differential scanning microcalorimeter (DSC). It is concluded that thirteen experimentally studied three-component systems, n-CnH2n + 2–C12Н24–n-CmH2m + 2 (n, m = 2k, k = 5, …, 12), are characterized by the formation of triple eutectics. Most of the results obtained for these systems are in satisfactory agreement with the data predicted by the methods proposed and developed earlier.

The liquidus lines of binary systems of dibasic carboxylic acids HOOC–(CH2)n–COOH (n = 3, 4, 7, 8) and eutectic coordinates were calculated by the Schrӧder–Le Chatelier equation. The experimental studies were performed by differential thermal analysis on a DSC heat flux microcalorimeter. Five or six mixtures with different contents of components were studied in each system. The phase diagrams were constructed based on the set of DSC data. The experimental melting temperatures and the composition of binary eutectics were compared with the calculated values. All the systems were of the eutectic type. A theoretical analysis of the solubility of the acids was performed, and the equations of solubility of acids in water were obtained. The eutectic composition of the pentanedioic–hexanedioic acids system was chosen based on the analysis of the solubility data; it can be used to obtain anodic coatings on aluminum. For the eutectics of the system, the solubility in water was experimentally studied at temperatures from 20 to 60°C. The composition of electrolyte for aluminum anodization was developed: eutectic mixture of pentadioic and hexanedioic acids, ethanedioic acid, and water. The temperature and time of aluminum anodization were recommended.

Phase equilibria in the ternary salt system LiBr–Li2CO3–Li2SO4 were studied by differential thermal analysis. The coordinates of a eutectic were found to be 65.0 mol % LiBr, 20.0 mol % Li2CO3, 15.0 mol % Li2SO4, and a melting point of 429°C. Data on the binary systems LiBr–Li2CO3 and Li2CO3–Li2SO4 were refined. The specific enthalpy of melting of the eutectic (97.0 ± 2.3 kJ/kg) was found by differential scanning calorimetry on a DSK-500 setup. The series of the systems LiHal–Li2CO3–Li2SO4 (Hal = F, Cl, Br, I) was analyzed, and models of the liquidi of the systems LiBr–Li2CO3–Li2SO4 and LiI–Li2CO3–Li2SO4 were constructed. Before experimental investigation, the expected melting points of the eutectics in these systems were calculated from the dependences on the atomic number of the halogen and on the melting point of the eutectics in the faceting binary systems in the above series. The eutectic alloy in the salt system LiBr–Li2CO3–Li2SO4 can be recommended for the possible use as a fusible electrolyte for chemical power sources.

The paper presents the results of a theoretical study of the phase complex of a three-component system consisting of tungstates, molybdates and sodium chlorides for equilibrium "liquid - solid". Previously, a literature review was conducted on data on phase equilibria in the condensed state of individual salts, binary faceting systems. In two NaCl-Na2MoO4 and NaCl-Na2WO4 binary systems, a eutetic equilibrium is observed with the formation of solid phases corresponding to the system components and Na3ClMoO4 and Na3ClWO4, and in binary faceting system Na2MoO4 – Na2WO4, one phase of a continuous series of solid solutions crystallizes. Based on the mathematical model of the molar balance, one can uniquely determine the quantities of reaction products, the molecular formulas of solid solutions, and the equations of chemical reactions for an arbitrary mixture of system components. This model represents a set of algebraic equations by which the balance is calculated. To build a 3D computer model, the paper presents the equations for the conversion of coordinates from barycentric to Cartesian. The model is implemented in concentration-temperature coordinates using the KOMPAS-3D program using experimental data on the system. With 3D model it is possible to conduct a preliminary a priori forecast of phase equilibria in order to identify the structure of phase diagrams at the qualitative and quantitative levels. The projection of the crystallization polytherm onto the square of the compositions is represented by three fields of solid solutions – NaCl, Na3ClMoxW1-xO4 and Na2MoxW1-xO4. Isothermal and polythermal sections were constructed. The system implements di- and monovariant equilibria. A diagram of the material balance of crystallizing phases is constructed. The paper presents the calculation of the ratio of equilibrium phases, as well as their qualitative and quantitative composition for the two-phase and three-phase regions according to the coordinates of the points - the vertices of the conode segments and conode triangles, which are extracted from the 3D model. The calculation is implemented for a given composition and temperature.

Theoretical partition of the ternary reciprocal system Na,Ba||Br,MoO4 into simplexes was performed, the stable diagonal of the system was determined, and the heat of the reaction at the conversion point was calculated. The chemical interaction in the system and the phase equilibria were described, and the crystallization fields of phases were delimited. The validity of the theoretical partition was confirmed by experimental investigation of the stable diagonal and two stable elements of the ternary reciprocal system Na,Ba||Br,MoO4 by differential thermal analysis. It was found that the system Na,Ba||Br,MoO4 is a singular irreversible reciprocal system with eutectic melting. The system is divided by the stable cutting diagonal NaBr–BaMoO4 into two stable phase triangles, NaBr–BaBr2–Na2MoO4 and NaBr–BaMoO4–Na2MoO4. The results of the partition were corroborated by the X-ray powder diffraction analysis data. In the stable cutting diagonal, a saddle quasi-binary eutectic point, e 721°C, was revealed. The coordinates (melting point and composition) of two ternary eutectics, E1 586°C and E2 525°C, were found. The maximum crystallization field in the composition square corresponds to high-melting barium molybdate.

The quaternary reciprocal system Na,Rb||F,I,CrO4 was studied, low-melting mixtures based on which are promising as fusible electrolytes for chemical current sources, heat-storage materials, and media for growing single crystals. The system was partitioned into simplexes using graph theory, and the tree of phases of the system was constructed. The tree of phases is linear and contains four stable tetrahedra sharing stable cutting triangles. The combined stable tetrahedron NaF–RbI–RbF–Rb2CrO4 was investigated by differential thermal analysis. The crystallization surface of this stable tetrahedron is represented by the volumes of sodium fluoride, rubidium iodide, rubidium fluoride, rubidium chromate, and the compound Rb3CrO4F. Monovariant equilibrium lines meet at two quaternary invariant points: eutectic E◻491 and peritectic P◻508.

Nonvariant equilibrium points in diphenyl oxide–n-heptadecane and biphenyl–diphenyl oxide–n-heptadecane systems are calculated according to Schroeder–Le Chatelier’s method. The experimental studies of the binary and ternary eutectic systems by DSC method are planned using the calculated data. The melting points and compositions of binary and ternary eutectics are determined. Calculated and experimental data are compared. Densities and flash points in open cup are measured.

Phase equilibria in the binary system NaCl-RaCl2 were predicted based on the binary systems NaCl–MCl2 (M = Ca, Sr, Ba). All the considered systems are of the eutectic type. Experimental data were processed, and functional dependences Te/Z = f(Z) and Te/r = f(r) were obtained, where Te is the melting point of the eutectic in the binary systems NaCl–CaCl2, NaCl–SrCl2, and NaCl–BaCl2; Z is the atomic number of Ca, Sr, or Ba; and r is its ionic radius. By further calculations using these functions, the melting point of the eutectic in the NaCl–RaCl2 system was found. Using the Schroder–Le Châtelier equation, the composition of the binary eutectic in the predicted system and the molar enthalpy of melting of RaCl2 were calculated, and branches of the liquidus of the system were constructed.

The phase complex is found and the chemical interaction is studied in the composition polyhedra of a quinary reciprocal system based on halides, metavanadates, and molybdates of lithium and potassium. The compositions of low-melting mixtures were determined for the possible use as electrolytes for chemical power sources and heat-storage materials.

Investigation of multicomponent salt systems is important in the context of the wide use of invariant mixtures as electrolytic media for separation of metals and heat-storage materials. In this work, the quaternary reciprocal system Na,K∥Cl,I,CrO4 was partitioned into simplexes using graph theory. The tree of phases of the system was constructed, and stable elements were determined. The stable tetrahedron NaCl–KCl–KI–K2CrO4 of the system Na,K∥Cl,I,CrO4 was studied by differential thermal analysis. In the stable tetrahedron, the melting point and composition (equiv. %) of a quaternary eutectic were found: (0.25% KCl, 42.40% NaCl, 30.92% KI, 26.43% K2CrO4; 451°C).

The secant tetrahedron LiF–KBr–KVO3–LiKMoO4 of the five-component reciprocal system Li,K‖F,Br,VO3,MoO4 was studied by differential thermal analysis (DTA). The composition corresponding to the quaternary eutectic (mol %) was determined to be the following: LiF, 6.0; KBr, 11.4; KVO3, 57.0; Li2MoO4 + K2MoO4, 25.6; the melting temperature: 358°С.

The quaternary reciprocal system Li, Na, Cs∥F, I was partitioned into simplexes, and the tree of phases was constructed. By differential thermal analysis, the stable triangle LiF–NaF–CsI was studied, and the characteristics of a ternary eutectic were determined.

The phase equilibrium of the three-component n-decane-n-octadecane-cyclododecane system in the temperature range from −50 to 70°С is studied via differential thermal analysis. It is established that the investigated system is of the eutectic type. The eutectic composition is 84.5 wt % n-С10Н22, 5.5 wt % n‑С16Н34, and 10.0 wt % С12Н24. It has a melting point of −35.0°C. The obtained data could be of interest to researchers in the field of the thermodynamics of phase equilibria.

The three-component reciprocal system Na,K║I,MoO4 has been studied by differential thermal analysis (DTA). The compositions and melting temperatures have been determined, and the enthalpies of melting of eutectic mixtures measured. Phase equilibria in the system are described, and phase fields are demarcated.

The three-component system RbF–RbBr–Rb2SO4 has been studied by differential thermal analysis (DTA). The melting temperatures and compositions corresponding to a eutectic point and a peritectic point have been determined. Invariant, monovariant, and divariant equilibrium states are described.

Phase equilibria in a four-component system of pentanedioic, hexanedioic, nonanedioic, and decanedioic acids are studied via differential thermal analysis. The determined eutectic composition is pentanedioic acid, 48.1 wt %; hexanedioic acid, 10.0 wt %; nonanedioic acid, 25.7 wt %; and decanedioic acid, 16.2 wt %. The melting point of the eutectic mixture is 63.1°C.

The binary system KVO3–K2CrO4 and two ternary systems, LiBr–LiVO3–Li2CrO4 and KBr–KVO3–K2CrO4, were studied. In the ternary systems, the compositions and melting points of eutectic alloys were determined by differential thermal analysis: (49.0 mol % LiBr, 5.0 mol % LiVO3, 46.0 mol % Li2CrO4, 400°C) and (17.0 mol % KBr, 78.0 mol % KVO3, 5.0 mol % K2CrO4, 458°C), respectively.

The cutting element LiF–LiVO3–LiKMoO4–KBr of the quinary reciprocal system Li, K||F, Br, VO3, MoO4 was studied by differential thermal analysis. The composition and melting point of the alloy corresponding to a quaternary eutectic were determined (7.0 mol % LiF, 32.0 mol % LiVO3, 47.7 mol % Li2MoO4 + K2MoO4, 12.3 mol % KBr, 410°С).

A three-component system comprising cyclododecane and n-alkanes is studied by means of differential thermal analysis on a differential scanning microcalorimeter. It is concluded that the investigated system is of the eutectic type and the n-dodecane–n-hexadecane–cyclododecane eutectic mixture system is 73.0 wt % n-С12Н26, 9.0 wt % n-С16Н34, and 18.0 wt % С12Н24. Its melting point is found to be −17.7°C.

The cutting tetrahedron LiVO3–KBr–KVO3–LiKMoO4 of the quinary reciprocal system Li, K||F, Br, VO3, MoO4 was studied by differential thermal analysis. The composition and melting point of the alloy corresponding to a quaternary eutectic were determined (11.3 mol % LiVO3, 18.0 mol % KBr, 57.0 mol % KVO3, 13.7 mol % Li2MoO4 + K2MoO4, 318°С).

The n-decane–n-hexadecane–cyclododecane, n-decane–cyclododecane, and n-hexadecane–cyclododecane systems are studied by means of low-temperature differential thermal analysis using a differential scanning heat flow calorimeter. It is noted that all studied systems belong to the eutectic type. It is concluded that in the n-decane–n-hexadecane–cyclododecane system, the eutectic composition contains 85.0 wt % n-С10Н22, 4.0 wt % n-С16Н34, and 11.0 wt % С12Н24. It has a melting point of −35.0°C.

Phase equilibria in the ternary systems NaHal–NaVO3–Na2CrO4 (Hal = Cl, Br) were studied. By differential thermal analysis, eutectic alloys were found at points with coordinates (14.0 mol % NaCl, 66.5 mol % NaVO3, 19.5 mol % Na2CrO4, 530°C) and (27.0 mol % NaBr, 47.5 mol % NaVO3, 25.5 mol % Na2CrO4, 499°C). By differential scanning calorimetry, the specific enthalpies of melting of the eutectics were determined. X-ray powder diffraction analysis of the eutectic alloy in the system NaBr–NaVO3–Na2CrO4 was made.