Powdery metal borides have high hardness, so they can be used as abrasives. Thus, the goal of this study was investigation of oxidation of chrome, titanium, zirconium and hafnium borides on air in the range of temperatures 25–1000°C in non-isothermal conditions using the derivatograph Q-1500 with the heating rates 5 and 10 K/min with simultaneous differential thermal analysis. Powdery CrB2, TiB2 ZrB2, HfB2 of “pure 99% were used. The sizes of the studied powders were determined by granulometric analysis. It turned out that particles with a diameter of 5-10 microns predominate in all powders. The studied powders of compounds interact with atmospheric oxygen in different ways. It is shown that powders TiB2 and ZrB2 begin oxidized at 540, 560°C, and CrB2, HfB2 –at 508, 780°C respectively. From TG curves calculated oxidation degree ().The composition of oxidation products was determined by the X-ray method using the DRON-3 device. According to X-ray data, the following oxides are formed: MO2(M=Ti,Zr,Hf), Cr2O3 i B2O3. Using the DTA-curves, calculated the heat effects of oxidation processes. At 1000°C, the oxidation degrees of the studied borides are as follows: CrB2(0,13), TiB2(0,15), HfB2 (0,41), ZrB2(0,81). From the obtained DTA curves, the thermal effects of the studied oxidation processes MB2 were calculated. Proportionality coefficient k between the thermal effect and the peak area under the DTA curve were assessed using similar data obtained from derivatographic studies of KCl and Na2WO4, the melting enthalpies of which are known. Taking into account the degree of transformation of the studied substances, we calculated the heat that was released in the studied processes during the complete oxidation of 1 mole of MB2. These data are qualitatively with those calculated according to Hess’s law.

The isoperibolic calorimetry method was employed to determine, for the first time, the partial and integral mixing enthalpies for melts in the Eu–Ge system over the entire composition range at 1200 K and 1370–1440 K. The minimum mixing enthalpy for these melts was –49.1 ± 4.4 kJ/mol and was shown by the alloy with xGe = 0.45, while ΔH_Eu^∞ = –145.7 ± 22.3 kJ/mol and ΔH_Ge^∞ = –166.8 ± ± 19.8 kJ/mol at 1400 ± 3 K, correlating with the solid-state behavior of these melts. This allows categorizing these melts within the series of the Ge–Ln (lanthanide) systems and justifying the thermodynamic properties of melts in the Eu–Ge system, in particular, and in the Ge–Ln system, in general. Using the thermochemical properties for melts in the Eu–Ge system, the ideal associated solution model was employed to optimize and calculate the Gibbs energies, enthalpies, and entropies of formation for the melts, associates in melts, and intermetallics. A large number of associates, especially EuGe, formed in the studied melts because of the highest probability of collision between two dissimilar atoms in liquid alloys. The maximum mole fraction of the EuGe associate reached 0.48 and those of Eu3Ge, Eu2Ge, EuGe2, and EuGe3 were 0.2, 0.26, 0.24, and 0.26, respectively. The activities of components in melts of the Eu–Ge system showed substantial negative deviations from the ideal solution, correlating with our thermochemical properties. This all indicated strong interactions between dissimilar atoms in melts of the Eu–Ge system, likely involving the transfer of valence electrons of europium to the 4p orbital of germanium. The ΔG values over the entire composition range were greater than ΔH, with ΔGmin = –28.8 kJ/mol at xGe = 0.45. Moreover, the ΔG function was also almost symmetrical because of the entropy contribution (mixing entropy of the studied melts was negative, and ΔSmin = –15.0 J/mol K at xGe = 0.45). The calculations based on the ideal associated solution model also established that the ΔH_Eu^∞ values for melts in the Eu–Ge system increased insignificantly with temperature, while ΔH_Ge^∞ increased more substantially. This might be due to the break of covalent bonds between germanium atoms. Complete information on the thermodynamic properties of all phases was obtained, enabling a thermodynamic description of the Eu–Ge system for the first time.

The thermochemical properties of melts of the Al—Ce system at temperatures of (1380—1490)  3 K in range of compositions 0 < xAl < 0,38 were determined by the method of isoperibolic calorimetry. It was established that the minimum value of the enthalpy of mixing of these melts is −40,9  4.1 kJ/mol and corresponds to the melt with xAl = 0,67, and =−83,3 ± 4,8; = −200 ± 26,0 kJ/mol. Using our own and literature thermochemical data for melts and intermediate phases of the Al—Ce system, as well as its diagram state according to the ideal associated solution (IAS) model, all thermodynamic properties of melts and associates in melts and intermetallics were calculated and optimized. It was established that the calculated activities of the components in the melts of this system show large negative deviations from ideal solutions. which correlates with their thermochemical properties. The maximum mole fraction of associates CeAl2, CeAl reaches values of 0,4 and 0,24, and the other three (Ce2Al, CeAl3, CeAl5) — 0,16; 0,08, and 0,11, respectively. The minimum values of Gibbs energies and entropies of melt formation are equal to -28,2 kJ/mol and -7,6 J/mol∙K. The temperature-concentration dependences of Gibbs energies, enthalpies and entropies of melt formation and temperature for intermetallics were also calculated using the IAS model, and from them, the liquidus curve of the phase diagram of this system. As a result, complete information on the thermodynamic properties of all phases and the liquidus curve of the phase diagram of the Al—Ce system was obtained. In order to confirm the reliability of the obtained data and search for general regularities of the thermodynamic characteristics of alloying of the Al—Ce system, it was considered as a member of the series of Al—Ln(Ln-lanthanide) systems. For this, the enthalpies of formation were analyzed. intermetallics LnAl2, as well as the minimum values of thermochemical properties of melts, relative differences in molar radii and differences in electronegativities of the components of the Al—Ln systems and their dependence on the lanthanide serial number. It is shown that all dependences, except for the electronegativity differences of the components, are compatible with each other. This indicates that the thermodynamic properties of compounds and melts of Al—Ln systems are determined by the size factor. Keywords:: method calorimetry, mixing enthalpy, activity, aluminum, cerium, melts, intermetallics, thermodynamic properties, ideal associated solution model.

Enthalpies of alloy formation in the Sb-Sc system have not been previously studied because scandium is refractory metal whereas stibium is extremely volatile. In this study, for the first time, the mixing enthalpies of melts in the Sb-Sc system were determined by the calorimetric method in wide concentration regions at 1413-1423 K. The minimum of the integral enthalpy of mixing is –44.8 ±2.3 kJ/mol is observed near the equiatomic composition. Such significant exothermic effects are explained by the large difference in electronegativities of the components. The limiting partial enthalpies of the components are –125±4 kJ/mol for scandium and –129±9 kJ/mol for stibium. In order to monitor how ΔН min of liquid alloys and Δ f H of monostibides in the Sb–3d-metal systems change, as well as predict similar data for unstudied systems, we presented them depending on the serial number of the transition metal. For this purpose, we used the most reliable literature data as well as our data obtained in the present study. It was established that ΔН of melts of the Sс–Sb system obtained in the work correlate with similar data for the Sb–3d-metal systems. In addition, they are the most exothermic. This can be explained by the electronic structure of 3d metals. It is known that there are 9 electrons on the 3d-orbitals of Ni, therefore, when forming alloys with Sb, nickel accepts the outer electrons of the latter, forming a donor-acceptor bond. On the contrary, at the formation of liquid alloys of the Sc–Sb system, most likely, occurs the transition of one electron from the 3d-orbitals of Sc to the outer orbital of Sb. Based on the values of ΔНmin of melts of Sb–3d-metal systems, it can be concluded that the formation of bonds in liquid alloys of the Sc–Sb system is energetically more advantageous than even in melts of the Ni–Sb system.

The isoperibolic calorimetry method was used to determine the mixing enthalpy of liquid alloys in the Ni–Tb system in the composition range 0 < xNi < 0.6 at 1660 ± 1 K. The minimum mixing enthalpy of melts in this system was –41.8 ± 0.9 kJ/mol at xNi = 0.6. The activities of components and the mole fractions of associates in these melts were calculated according to the ideal associated solution (IAS) model with our and literature values of formation enthalpies for compounds in the Ni–Tb system and with phase diagram data. Two associates were selected for the calculations: TbNi and TbNi5. The activities of the components showed large negative deviations from the ideal solution, with the simplest associate, TbNi, being predominant (xmax = 0.65). The second associate was present in a much smaller proportion (xmax = 0.22). These data correlate with the mixing enthalpies of the melts, formed with significant exothermic effects. To assess the reliability of the formation enthalpies of compounds and melts in the Ni–Tb system, they were compared with those of LnNi5 compounds and liquid alloys in the Ni–Ln system. All were determined with different options of the calorimetry method. Hence, to be compared, they were plotted as a function of the Ln atomic number. Most of the data points aligned with two trend lines, except for the data for compounds in binary Ni–Gd(Dy, Er) systems and melts in binary Ni–Ce (Eu, Yb) systems. Regarding these ΔHmin values, which are more exothermic (Ni–Ce system) and less exothermic (Ni–Eu(Yb) systems) than all others, they may be attributed to the electronic structures of atoms in the components of the melts. The Eu and Yb atoms are known to have half-filled and completely filled 4f orbitals, while the Ce atom contains one electron in the 4f orbital. Therefore, Eu and Yb are divalent and Ce is tetravalent in the nickel alloys. Since nickel is a strong electron acceptor, the energy of its interaction with Ce is greater and that with Eu and Yb is lower compared to other neighboring lanthanides.

Alloys and compounds of bismuth with lanthanides (Ln) exhibit thermoelectric, magnetic and other properties. For their scientifically based production, it is necessary to know both their state diagrams and the thermodynamic properties of various phases, including the liquid one, because one of the important stages of the technological processes is the melting of the initial mixtures. Thermodynamic properties of liquid solutions based on Bi of the Bi–La system were studied by the EMF method in a number of works. In this work, for the first time, the partial and integral enthalpies of the formation of melts of the Bi–La system in the entire range of compositions were determined by the method of calorimetry at 1220-1274 K. It was established that ΔHmin= −118±4 kJ/mol falls on the melt with xBi = 0.4, and =−401±23; = −212±8 kJ/mol. It has been established that ours and all known ones, except data [1], agree with each other To confirm the reliability of the obtained data and search for regularities in the thermodynamic characteristics of melts of the Bi–La system, it was considered as a member of the Bi–Ln system series. For this, the enthalpies of formation and Tmelt were analyzed of intermetallics LnBi, as well as ΔHmin of melts, relative differences of molar radii and electronegativities of components of Bi–Ln systems, based on which their dependence on the ordinal number of the lanthanide is constructed. It is shown that all dependences, except for the electronegativity differences of the components, are compatible with each other. This indicates that the thermodynamic properties of all phases of the Bi–Ln systems are determined by the size factor.

Partial for the components and integral enthalpies of mixing of the ternary melts of the Cu—In—La system were determined for the first time by the method of calorimetry on five radial sections with a constant ratio of two components:, and (up to xIn = 0,02, 0,14, and 0,42, respectively) and and (up to xCu = 0,15 and 0,2, respectively) at 1220—1450 K. It is shown that when indium 1 is added to the CuxLa1-x melt, the thermal effect of its dissolution increases, which is caused by the formation of strong bonds between In and La. In the other two sections (and), the enthalpies of mixing of ternary melts decrease during dissolution. Using the reliable mixing enthalpies of the melts of the dual systems Cu—In(La) and In—La, similar parameters for liquid alloys of the Cu—In—La system were calculated according to various “geometric” and “analytical” models. It was found that the values calculated by the Redlich—Kister—Mujianu model with the triple contribution –200 agree with the determined enthalpies of mixing of melts of the Cu—In—La system within the limits of experimental errors. It was established that the minimum enthalpy of mixing of melts of the Cu—In—La system falls on the alloy of the In—La subsystem (−43,4 ± 2,1) at xLa = 0,4 at T = 1450 K, i. e., the largest contribution to the enthalpy of mixing of melts of the Cu—In—La system is made by boundary subsystem In—La. The activity of the components in the melts of this system was calculated according to the same model. It is shown that they exhibit small negative deviations from ideal solutions at 1450 K. From these data, G, S of melts of the Cu—In—La system were estimated. It was established that Gmin = –26 kJ/mol, Smin = –12 J/mol∙K, which are attributed to the In0.6La0.4 alloy. Keywords: calorimetry, copper, lanthanum, indium, thermodynamic properties, modeling, mixing enthalpies, activity of components.

Для розроблення найбільш раціональних методів отримання та застосування сплавів і лігатур визначеного складу необхідна точна інформація про їхні термодинамічні характеристики та фазові рівноваги в них. Методом ізопериболічної калориметрії встановлено парціальні й інтегральні ентальпії змішування розплавів системи Pb – Yb у всьому діапазоні в інтервалі температур 1 100–1 200 К. Установлено, що утворення супроводжується виділенням великої кількості теплоти: мінімальна ентальпія змішування розплавів дорівнює −45,4 ± 0,8 кДж/моль і припадає на розплав із xPb = 0,4 за Т = 1 200 ± 3, згідно з даними діаграми стану досліджуваної системи. За допомогою моделі ідеального асоційованого розчину (ІАР) оптимізовано та проведено розрахунки всіх термодинамічних властивостей (енергія Гіббса, ентальпія й ентропія утворення) розплавів, асоціатів у розплавах та інтерметалідів системи Pb –Yb. Показано, що максимальна мольна частка асоціату YbPb досягає значення 0,75, а Yb2Pb, YbPb2 – 0,59 і 0,28 відповідно. Активності компонентів у розплавах системи Pb – Yb мають дуже значні від’ємні відхилення від ідеальних розчинів, що корелює з установленими нами термохімічними властивостями. Розрахунки на основі моделі IAP також дозволили встановити, що значення у розплавах системи Pb – Yb з підвищенням температури зростають незначно, а – більш суттєво. Згідно з моделлю IAP було проведено розрахунки температурно-концентраційної залежності енергій Гіббса, а також ентальпій і ентропій утворення розплавів та інтерметалідів, що дали змогу встановити координати кривої ліквідусу діаграми стану досліджуваної системи. Розраховані й експериментальні дані добре узгоджуються одне з одним. У результаті отримано детальну інформацію щодо термодинамічних властивостей усіх фаз і фазових рівноваг у сплавах, а саме: було виконано термодинамічний опис системи Pb – Yb.

The magneto-optical Kerr effect in Gd20Co80 alloy and cobalt thin films has been studied in a broad spectral range applying spectral ellipsometry experimental technique. The results of the experiments showed the complex nature of the complex Kerr angle dispersion curves. A quantum mechanical formalism for degenerate and non-degenerate Landau levels for quasi-free electrons in ferromagnetic material has been developed in order to analyze the experimental data. The equivalence of relations for off-diagonal dielectric tensor elements for non-degenerate Landau levels to the classical case of the motion of quasi-free electrons along circular trajectories in a magnetic field has been theoretically shown. The degenerate Landau levels in this approach are the result of motion of electrons in small confined volumes near rare-earth alloy atoms. Rotation of light polarization occurs in this case due to transitions between subbands having different magnetic quantum numbers. This theoretical approach allowed us to interpret in detail shapes and sign of the complex Kerr angle dispersion curves, which actually include the contributions of optical transitions between degenerate and non-degenerate energy levels. The complex Kerr angle sign is determined by the magnetization magnetic field direction for non-degenerate Landau levels and the Hund rule for degenerate Landau levels.

Firstthe partial and integral enthalpies of mixing of the melts of the Eu—Pb system were determined at a temperature of 1100—1350 K in everything range the composition by method isoperibolical calorimetry. It was established that of the melts of the Eu—Pb system are formed with the release of a big amount of heat: the minimum H = –51,7  ± 0,8 (at xPb = 0,4). Using the model of ideal associated solutions, all the thermodynamic properties (Gibbs energies, enthalpy and entropy of formation of melts, intermetallic compounds and associates) of the Eu—Pb system were calculated. It turned out that the activity of the components in the melts of this system exhibit moderate negative deviations from ideal solutions. According to the IAR model, the temperature-concentration dependences of the Gibbs energies, enthalpies and entropies formation of melts and intermetallics were calculated, and from them were obtained the coordinates of the liquidus curve of the diagram state of the studied system. As a result, the temperature-concentration dependences of the thermodynamic properties of all phases and the liquidus of the Eu—Pb system are obtained, those a thermodynamic description of this system is made. Keywords: calorimetry, melts, intermetallics, thermodynamic properties, Eu, Pb, model of ideal associated solutions, phase equilibria.

The partial and integral enthalpies of mixing of the melts the Cu-Yb system in the composition range 0 < xCu <0,7 and for 5 sections of Cu – In – Yb system with a constant ratio of the other two components (xCu/xIn=0,36/0,64; xCu/xIn= 0,62/0,38; xIn/xYb= 0,62/0,38; xCu/xYb =0,64/0,36; xCu/xYb =0,21/0,79) to x3 = 0.3 by method isoperibolical calorimetry in the temperature range 1453-1473K first were determined. Using the model of ideal associated solutions (IAR), all the thermodynamic properties (Gibbs energies of mixing melts, enthalpy and entropy of formation of intermetallic compounds and associates) of the Cu–Yb system were calculated. It turned out that the activity of the components in the melts of this system exhibit small negative deviations from ideal solutions. Calculations using the IAR model also made it possible to establish that with increasing temperature it increases slightly, but more significantly. Also were obtained the coordinates of the liquidus curve of the diagram state of the studied system. The principal contribution to the enthalpies of mixing in the liquid alloysof the Cu–In–Yb system gives the border subsystem In–Yb. Because the minimum of the mixing enthalpies in the ternary sysytem Cu–In–Yb shifts towards the equiatomic alloy concentration of subsystem In–Yb (-36,5±1,0) at Т= 1453 К. Using the experimental partial and integral enthalpies of mixing, the activities of the components in the melts of binary limiteyted system of melts of the Cu–In–Yb ternary system, calculated according to «geometric» and the Redlich-Kister-Mujian models in a wide range of concentrations. It is established that the experimental ∆H, and calculated analogical datas according to the Redlich-Kister-Mujianu model agree between. It is shown that the activities of the components in the melts of this system, calculated according to the Redlich-Kister model, show small negative deviations from ideal solutions at 1453 K. From these of data calculated G, S. It was found that Gmin = –19 kJ/mol, Smin = –15 J/mol*K for the alloy In0,5Yb0,5. This correlates with the determined thermochemical properties of the melts Cu –In– Yb system. Keywords: calorimetry, the melts, intermetallic, thermodynamic properties, Cu, Yb, In, the model of ideal associated solutions, the Redlich—Kister—Mujianu model, phase equilibria.

The thermochemical properties of the melts of the Bi—Tm system at a temperature of 1100 K in the range of compositions 0 ≤ xTm ≤ 0,2 were determined for the first time by the calorimetry method. It is established that the minimum value of the enthalpy of mixing of these liquid alloys is equal to –75,7 ± 0,5 kJ / mol at xTm = 0,65. = = –150,7 ± 16,7 kJ / mol, = –230,9 ± 21,8 kJ / mol. The activities of the components and molar particles of associates were calculated according to the model of an ideal associated solution (IAR), using data on the thermochemical properties of melts of the Bi—Tm system. It was found that the activities of the components in these metallic solutions show very large negative deviations from ideal solutions with a high content of TmBi and Tm2Bi associates. The obtained dependences of the first i i melts of the Bi—Tm system on temperature showed a large steepness of the Bi Bi curve in contrast to the gradual decrease of exothermic values Tm of Tm. This indicates large changes in the structure of the Bi atom with increasing temperature. Excess integral and partial Gibbs energies of Bi-Tm system melt mixing calculated from component activities The absolute values of G in the whole concentration range are smaller than H (G min = –41,8 kJ / mol at xTm = 0,58), and the function G of is more asymmetric, which is caused by the entropy contribution (entropy of mixing of the studied melts is negative, and Smin min = −30,5 J / mol ∙ K at xTm = 0,65). Keywords: thermochemical properties, compounds, melts, Bi, Tm.

Enthalpies of mixing of liquid alloys are determined via isoperibol calorimetry for the Gd–Sn system throughout the range of concentrations at 1873, 1640, and 1510 K, and for the Gd–Sn–Ni system along the radial section with a constant ratio of atomic fractions of tin and nickel: xSn/xNi = 0.68/0.32 at 1873 ± 5 K up to xGd ∼ 0.25. It is found that the melts of the Gd–Sn system form with the release of a large amount of heat ( $$\Delta {{{H}}_{{\min }}}$$ = −68.4 ± 0.4 kJ/mol at xSn = 0.45). The calculations are performed using the geometric and analytical Redlich–Kister–Muggianu models of ΔH for melts of the ternary Gd–Sn–Ni system from similar data for binary boundary subsystems at 1873 K. The results show the minimum enthalpy of mixing of these ternary melts was established for the Gd0.55Sn0.45 alloy. It is shown that the experimentally investigated enthalpies of mixing of the Gd–Sn–Ni melts and calculated data using the Redlich–Kister–Muggianu model with ternary interaction parameter L = 500 kJ/mol agree satisfactorily with one another.

Gd20Co80 alloy was studied applying experimental methods of spectral ellipsometry, atomic force and scanning tunneling microscopy. The experimental results exhibit the eutectic two-phase structure of this alloy. Clusters of a phase with a lower content had a lesser concentration of free carriers, which resulted in smaller tunnel currents during the measurements. To analyze the experimental data, a theoretical approach was developed, which was based both on the quantum-mechanical methods of configurational interaction and on three-diagonal Toeplitz matrices formalism. This approach allowed us to describe in detail the energy bands formation process in solid clusters with a relatively small quantity of atoms, which as a consequence enabled to describe the Shockley surface states as well as the existence of a surface layer with partially formed energy bands. Spectral-ellipsometric measurements of Gd20Co80 alloy thin films confirmed a significant difference between the measured optical constants for 20-nm thick films and larger films. Quantum-mechanical molecular calculus allowed to obtain optical constants for several supercells of Gd-Co chemical compounds and confirmed the acquired experimental and theoretical results.

The method of isoportic calorimetry investigated the thermochemical properties of the melt In—Tb system in the range of compositions 0 < xIn < 0,4 at 1625 ± 1 K. The obtained data were extrapolated on a non-investigated concentration interval, given that when xTb = 1 integral and partial to Tb enthalpia mixing is zero. It was established that the first partial for Terbium and the minimum enthalpy of mixing is –145 ± 7 and –40,1 ± 0,2 kJ/mol respectively. Comparison of ΔHmin, the melt of five previously investigated In—Ln systems from the serial number Ln (zLn), together with the data obtained in this papper, showed that they are described by one trend line. For ΔHmin In—Eu (Yb) melts (Yb) are very slight deviations from the trend line. But for dimensional factor, these deviations from the trend line are more significant. Enthalpia of the formation of some In—Ln intermetallides are known, with most of them relate to the LnIn3 compound. But there is no full reconciliation between these data. The results of the most modern work exhibit less dependence on the serial number of lanthanides and are more exothermic for heavy lanthanides, compared with other data. Comparing thermochemical properties of double Sn (Sb) —REM melt systems. It has been established that the energy of the interaction between the data p-elements and REM increases in such a sequence: In-REM → Sn—REM → Sb—REM. This is due to the fact that the stibium is the best acceptor of electrons. Keywords: thermochemical properties, melts, compounds, In, Tb.

The calorimetry method was employed to determine the mixing enthalpies of Gd–Sn melts and the ideal associated solution (IAS) model to calculate and optimize the thermodynamic properties of Gd–Sn alloys at 1510, 1640, and 1873 K in the composition range 0 ≤ xSn ≤ 1.0. The minimum mixing enthalpies were –69.7 ± 0.6 kJ/mole (1873 K) and –77.9 ± 0.7 (1510 K) kJ/mole at xSn = = 0.45. Using our own and published data on the thermochemical properties of melts and compounds and assuming the formation of two associates in the melt, Gd2Sn and GdSn, we calculated the activities of components, enthalpies, Gibbs energies, and entropies of formation for the liquid alloys and intermediate phases within the IAS model. The thermodynamic activities of components in the studied melts showed very large negative deviations from the ideal solutions. The mixing enthalpies of Sn–Gd melts optimized within the IAS model agreed well with the experimental values. The $$ \Delta {\overline{H}}_{\mathrm{Gd}}^{\infty } $$ temperature dependence agrees only qualitatively with other experimental data because of great errors in the published data. The excess Gibbs energy and mixing enthalpy of Gd–Sn melts calculated with the IAS model at 1873 K greatly differed in magnitude, being indicative of a significant contribution of the entropy component to the excess molar Gibbs energy. According to the calculations, the minimum excess mixing entropy for Gd–Sn melts at 1873 K was –20.3 J/(mole · K) at xSn = 0.45. The calculated and optimized enthalpies and entropies of formation for intermetallic phases in the Gd–Sn system, along with the IAS model parameters for melts, were used to calculate the liquidus and solidus curves of the phase diagram. Good agreement with most experimental data on the phase equilibria involving liquid and crystalline phases was shown.

Isoperibolic calorimetry is used to determine the enthalpies of mixing of liquid alloys of the Ag‒Al–Yb system along two radial sections with a constant ratio of atomic fractions of aluminum and silver: (1) xAg/xAl = 0.46/0.54 at 1271 ± 1 K and (2) xAg/xAl = 0.19/0.81 for 1454 ± 5 K up to xYb ∼ 0.2. It is found that melts of the studied system form with the release of a small amount of heat (ΔHmin = −29 kJ/mol), and the minimum ΔH accounts for the middle of the concentration triangle. Using the geometric and analytical Redlich–Kister models, calculations are made for ΔH triple system melts Ag–Al–Yb using similar data for double boundary subsystems.