Congruent Melting Research Articles

Catastrophe theory and thermodynamic instability to predict congruent melting temperature of crystals

Melting temperature (Tm) is a crucial physical property of solids and plays an important role in the characterization of materials. Therefore, the capacity to predict Tm is a relevant issue for solid state sciences. This investigation aims i) to provide a theoretical basis for the link between catastrophe theory and thermodynamic instability; ii) to estimate Tm through the notion of “degenerate critical temperature” (Td), related to (Pd,Vd,Td), where KT → 0 and the Gibbs function shows a non-Morse behaviour; iii) to compare predictions of (Pm,Tm) with observations for three crystalline pure substances that undergo congruent melting and exhibit different bonding and stability ranges: NaCl (halite), SiO2,st (stishovite), and MgSiO3 (perovskite). The P-T locus of KT = 0 associated with melting is identified using the maximum values of Td and ΔH/ΔV at a given pressure. We observed an average absolute discrepancy ranging between 0.2 % (halite) and 5.8 % (stishovite), and an agreement between theoretical and experimental T(P)melting-points from better than 1 to approximately 14 %.

A Melt-Processable Metal Halide Perovskite Ferroelectric.

Molecular ferroelectrics have increasingly garnered significant attention in both fundamental scientific research and technological applications due to their ease of processing, lightweight nature, and mechanical flexibility. Among these, metal halide perovskite ferroelectrics (MHP FEs), a subset of molecule-based ferroelectrics, exhibit diverse functionalities owing to their distinctive structures, thus emerging as a focal point of molecular ferroelectrics research. However, thin films, the predominant application form for MHP FEs, primarily rely on spin-coating, which presents considerable limitations. The development of melt-processable MHP FEs has been sparse, largely due to the challenge of integrating ferroelectricity with meltability. In this context, we propose a rational strategy for the successful synthesis of a melt-processable MHP FE, (MBPA)2PbBr4 (MBPA = N-methyl bromopropylammonium), featuring a notably low congruent melting temperature and excellent molten stability. The reversibility of solid and liquid states was demonstrated by X-ray diffraction and Raman and IR spectrum. Scanning electron microscopy examinations show a better quality of the melt-processed thin films compared to spin-coated ones. This study marks the successful implementation of integrating ferroelectricity and melt-processability into melt-processable MHP FEs, paving the way for a novel approach in processing MHP FEs and facilitating their future applications.

K4Cd3Ge4O13: A Congruent-Melting Germanate Nonlinear Optical Crystal with a Moderate Second-Harmonic Generation Intensity and Broad Transparent Window.

Mid-infrared (IR) nonlinear optical (NLO) materials have generated extensive research interest because of their crucial role in laser technology applications. Here, we report the synthesis of a novel cadmium germanate NLO crystal, K4Cd3Ge4O13, using spontaneous crystallization. K4Cd3Ge4O13 demonstrates a distinct three-dimensional structural framework characterized by twisted [Ge4O13] and [Cd3O10] clusters, composed of [GeO4], [CdO4], [CdO5], and [CdO6] basic building units, respectively, which represents an unprecedented structural feature. The title compound undergoes a desirable congruent melting behavior at about 727 °C. Notably, K4Cd3Ge4O13 demonstrates a short UV cutoff edge at 261 nm, coupled with a wide energy gap of 4.4 eV, and maintains an extended IR transparency window at around 6.0 μm. More importantly, it demonstrates a strong second-harmonic generation activity comparable to that of KH2PO4 (KDP) at 1064 nm. Theoretical analyses further elucidate that the remarkable optical performances of K4Cd3Ge4O13 are predominantly attributed to the cooperative effects of Ge-O and Cd-O bond-based motifs. These desired characteristics underscore the potential of K4Cd3Ge4O13 as a good candidate material for mid-IR NLO applications.

Solid–Liquid Phase Equilibrium of the n-Nonane + n-Undecane System for Low-Temperature Thermal Energy Storage

The current article presents an exploration of the solid–liquid phase diagram for a binary system comprising n-alkanes with an odd number of carbon atoms, specifically n-nonane (n-C9) and n-undecane (n-C11). This binary system exhibits promising characteristics for application as a phase change material (PCM) in low-temperature thermal energy storage (TES), due to the fusion temperatures of the individual components, thereby motivating an in-depth investigation of the solid–liquid phase diagram of their mixtures. The n-nonane (n-C9) + n-undecane (n-C11) solid–liquid phase equilibrium study herein reported includes the construction of the phase diagram using Differential Scanning Calorimetry (DSC) data, complemented with Hot–Stage Microscopy (HSM) and low-temperature Raman Spectroscopy results. From the DSC analysis, both the temperature and the enthalpy of solid–solid and solid–liquid transitions were obtained. The binary system n-C9 + n-C11 has evidenced a congruent melting solid solution at low temperatures. In particular, the blend with a molar composition xundecane = 0.10 shows to be a congruent melting solid solution with a melting point at 215.84 K and an enthalpy of fusion of 13.6 kJ·mol–1. For this reason, this system has confirmed the initial signs to be a candidate with good potential to be applied as a PCM in low-temperature TES applications. This work aims not only to contribute to gather information on the solid–liquid phase equilibrium on the system n-C9 + n-C11, which presently are not available in the literature, but especially to obtain essential and practical information on the possibility to use this system as PCM at low temperatures. The solid–liquid phase diagram of the system n-C9 + n-C11 is being published for the first time, as far as the authors are aware.

Synergistic effect of stearic acid/bismuth oxychloride/cupric oxide for thermal storage applications: preparation, stability, rheological and thermophysical analysis

The present study reports the preparation of nanophase change materials (NPCMs) using a two-step method with an optimized ratio of 0.5 wt% of nanoparticles for thermal storage applications. Bismuth oxychloride (BiOCl), cupric oxide (CuO), and a mixture of BiOCl/CuO (composite) were used as nanoparticles, and stearic acid was used as the PCM. The crystallography, chemical/functional groups and morphologies of the prepared NPCMs have been analysed by XRD, FT-IR and SEM, respectively. Observations revealed that the presence of nanoparticles in NPCMs did not affect crystal formation or chemical disruption of molecular interactions. TGA was used to analyse the thermal stability and rate of deterioration of the NPCMs. The deterioration of the PCM occurs at 243 °C with a weight loss of 1.3% while 0.5 wt% concentrated BiOCl, CuO, and composite NPCMs exhibit weight losses of 1.8%, 2.3%, and 3.4%, respectively at 257 °C, 262 °C and 258 °C. In the DSC study, the phase-changing attributes of the NPCMs manifested in the onset temperature range between 53.4 °C and 59.8 °C. The potential enthalpy of the PCM is 209.1 kJ kg−1, whereas those of the 0.5 wt% concentrated BiOCl, CuO, and composite NPCMs are 204.6, 198.3, and 201.7 kJ kg−1, respectively. However, the enhanced thermal conductivities of 0.5 wt% concentrated BiOCl, CuO, and the composite NPCMs are 0.18, 0.22, and 0.20 W/(m.°C), respectively, which are 5.9%, 29.4% and 17.6% greater than that of PCM. Additionally, the congruent melting rate increased by 31% for 0.5 wt% CuO concentrated NPCM; therefore, it is a potential candidate than other NPCMs/PCM. Cyclic tests were conducted to assess the reliability of the NPCMs, and compatible results were obtained even after 500 cycles. The findings of this work indicate that all the prepared NPCMs could be a viable option for practical applications, including thermal comfort buildings, solar heating, and electronic cooling.

A congruent-melting rubidium zinc vanadium oxychloride exhibiting strong mid-infrared second-harmonic generation and high laser-induced damage threshold

A novel mid-infrared (MIR) nonlinear optical (NLO) crystal Rb4ZnV5O15Cl (RZVC) has been designed and sythesized by the aliovalent substitution strategy based on the parent structure Rb2(VO)(V2O7). Modification of square pyramidal VO5 units through introduction of chlorine ion and zinc metal caion significantly enhanced the dipole moments in a unit cell from 1.653 D for Rb2(VO)(V2O7) to 6.559 D for RZVC. Consequently, polycrystalline RZVC exhibits strong SHG responses of 12.5 × KDP @1064 nm and 1.2 × AGS @2 μm. Furthermore, RZVC features a congruent melting property, an ultra-high LIDT value (62 × AGS @1064 nm), and a deep IR transparency cutoff edge (10 μm). Most importantly, RZVC can achieve full-wavelength phase matching in a very wide MIR transparency range of 1.69–10 μm, completely covering the important atmospheric window (3–5 μm) through NLO processes. Because of its many outstanding properties, RZVC can be a highly desirable candidate for practical MIR NLO applications.

Fluorite Solid Solutions of Congruent Melting in the PbF2–CdF2–RF3 Systems

Fluorite Solid Solutions of Congruent Melting in the PbF2–CdF2–RF3 Systems

The Gd2O3 – GdSrFeO4 pseudo -binary phase diagram

The Gd2O3 – GdSrFeO4 pseudo-binary phase diagram is presented for the first time. The liquidus and eutectic temperatures, metatectic points of the Gd2O3 transformations in the Gd2O3 – GdSrFeO4 section were defined using the Schröder–Le Chatelier equation, neglecting the effect of the isobaric heat capacity. The calculations were based on experimental data on the melting points of the end-members and the eutectic composition. From the results of phase relationships studies (subsolidus and high temperature region including literature data as well) and the above approach the Gd2O3–GdSrFeO4 pseudo-binary phase diagram in the temperature range 1400–2410 °C in air was constructed.It was shown that GdSrFeO4 of the K2NiF4- type is stable from 1100°С to a congruent melting temperature of 1560°С in air. The Gd2O3 – GdSrFeO4 system is eutectic with no intermediate compounds.

Rational Design of 2D Metal Halide Perovskites with Low Congruent Melting Temperature and Large Melt-Processable Window.

Metal halide perovskites (MHPs) have garnered significant attention due to their distinctive optical and electronic properties, coupled with excellent processability. However, the thermal characteristics of these materials are often overlooked, which can be harnessed to cater to diverse application scenarios. We showcase the efficacy of lowering the congruent melting temperature (Tm) of layered 2D MHPs by employing a strategy that involves the modification of flexible alkylammonium through N-methylation and I-substitution. Structural-property analysis reveals that the N-methylation and I-substitution play pivotal roles in reducing hydrogen bond interactions between the organic components and inorganic parts, lowering the rotational symmetry number of the cation and restricting the residual motion of the cations. Additional I···I interactions enhance intermolecular interactions and lead to improved molten stability, as evidenced by a higher viscosity. The 2D MHPs discussed in this study exhibit low Tm and wide melt-processable windows, e.g., (DMIPA)2PbI4 showcasing a low Tm of 98 °C and large melt-processable window of 145 °C. The efficacy of the strategy was further validated when applied to bromine-substituted 2D MHPs. Lowering the Tm and enhancing the molten stability of the MHPs hold great promise for various applications, including glass formation, preparation of high-quality films for photodetection, and fabrication of flexible devices.

Pb3[O10Pb20](SiO4)4X10 (X = Cl, Br): The First Pb-Containing Halogen Silicates with Mirror-Symmetric Pseudo-Aurivillius Bilayers.

Two new congruently melting Pb-containing halogen silicates, Pb3[O10Pb20](SiO4)4X10 (X = Cl, Br), have been synthesized using a high-temperature solution method. Their crystal structures were determined by single-crystal X-ray diffraction, and both compounds crystallize in the orthorhombic space group Cmca. In both structures, the mirror-symmetric bilayer composed of Pb-O polyhedra is observed for the first time in Pb-containing silicates and belongs to α-PbO derivatives and is related to the Aurivillius phase. Thermal behavior analysis, UV-vis diffuse-reflectance spectroscopy, and IR spectroscopy were also performed. The Pb3[O10Pb20](SiO4)4Cl10 matrix was doped with Eu3+ ions as a dopant, and its potential application in fluorescence was confirmed from the resulting orange-red emission.

Single crystal growth of complex layered oxychalcogenide by melt-solidification method

We have successfully grown single crystals of layered mixed-anion compound Sr2ZnCu2Se2O2 by a simple melt-growth method. Single crystals of the layered oxychalcogenides Sr2ZnCu2Se2O2 were grown by melt-solidification of stoichiometric raw materials. Plate-like single crystals were obtained, and the maximum size of crystals was 2.5 × 1.4 mm2. Thermal analysis result indicates simple melting-solidification-like behavior, and the size of crystals increases significantly above the melting point revealed by this measurement. X-ray rocking curve (XRC) measurement results of the single crystal showed no peak splitting, with a narrow full width half maximum of 30 and 97 arcsec in (105) and (0012) peaks, respectively. The electrical conductivity of single crystals on the a(b) plane was 4.34 × 10−1 S/cm at room temperature. Obtained single crystals were transparent, and the absorption edge was observed around 560 nm in the transmittance measurement. Although layered oxychalcogenide Sr2ZnCu2Se2O2 has a complex composition and structure, this compound exhibits congruent melting behavior in a sealed environment. This feature enables us to grow single crystals of mixed-anion compounds easily by the melt-growth method.

Na12(NbO)3(PO4)7: A Congruent Melting Nonlinear Optical Crystal with Large NbO6 Distortion and High Laser-Induced Damage Threshold.

A new noncentrosymmetric crystal Na12(NbO)3(PO4)7 was successfully synthesized in the niobium phosphate system. Its structure characterizes isolated and highly distorted NbO6 octahedra joining with isolated PO4 groups to form a unit of a (Nb6P6O12) hexagonal star by sharing O atoms. In (Nb6P6O12) hexagonal stars, all Nb and P atoms are in a hexagonal star-like arrangement and all Na atoms are also in a hexagonal star-like arrangement, except for Na(3) and Na(10) atoms. Notably, it exhibits a strong phase-matched second harmonic response: 3 × KDP, which is rare in known niobium phosphate systems. Meanwhile, it also has a wide optically transparent window (0.29-4.44 μm) and a high laser-induced damage threshold (3.5 GW/cm2). More importantly, Na12(NbO)3(PO4)7 is a congruent melting compound that has the potential to be grown into large-sized single crystals by the Czochralski method. These excellent properties make it a promising candidate as a mid-infrared nonlinear optical crystal.

N-Alkylisoquinolinium bromides and α,ω-alkanediols: Eutectic systems with co-crystal formation

This research focuses on ionic liquids (ILs), specifically N-alkylisoquinolinium bromides with various chain lengths: octyl, decyl, dodecyl, and hexadecyl. The study covers the synthesis and thermophysical characterisation of these compounds, as well as crystal structure determination for all excluding N-decylisoquinolinium bromide ([i-QuinC10][Br]). The obtained thermophysical parameters were compared with the literature data and also within the extended homologous series.The solid–liquid phase equilibria (SLE) in mixtures of ILs with certain α,ω-alkanediols (1,6-hexanediol, 1,8-octanediol, 1,10-decanediol, 1,12-dodecanediol) were investigated. As a result of SLE studies, eutectic mixtures capable of acting as eutectic phase-change materials - ePCMs - were determined. Additionally, a self-organization phenomenon was observed between specific pairs, leading to the formation of co-crystals (solid-complex phase). All binary mixtures with [i-QuinC8][Br] formed a simple eutectic system, while in the case of [i-QuinC10][Br], the formation of a non-congruent melting compound was observed in the systems with 1,8-octanediol and 1,10-decanediol. Among the systems with [i-QuinC12][Br], congruent melting compounds were observed for mixtures with 1,8-octanediol, 1,10-decanediol and 1,12-dodecanediol, while a simple eutectic was recorded for 1,6-hexanediol. IL [i-QuinC16][Br] co-crystalised only with 1,12-dodecanediol, while with other diols formed simple eutectic systems. Calorimetric analysis (DSC) and crystal structure determination (X-ray diffraction) were used to characterize the obtained supramolecular compounds.As a result, a series of ePCMs with melting points ranging from 295 K to 343 K are presented, with the {[i-QuinC12][Br] + 1,10-decanediol} system showing the highest enthalpy of melting (173.5 J·g−1). The found features and correlations between structure and properties imply the necessity for additional investigation, indicating the potential for a new generation of compounds with customizable physicochemical properties.

KNa2Lu(BO3)2: A Rare-Earth Borate Crystal Characterized by an Enhanced Birefringence and Wide Ultraviolet Transparency Range.

Borate materials are of significant interest due to their versatile structural configuration and competitive ultraviolet (UV) transparency range. In this study, we present a novel rare-earth borate crystal, KNa2Lu(BO3)2, synthesized for the first time through a facile spontaneous crystallization method. It adopts the centrosymmetric space group Pnma (no. 62) and yields a unique three-dimensional (3D) structural network formed by isolated [BO3] plane triangles and distorted [LuO7] polyhedra. This compound displays excellent thermal stability up to ∼990 °C, demonstrating a favorable congruent melting nature. Moreover, KNa2Lu(BO3)2 achieves a notably short UV absorption cutoff at approximately 204 nm, yielding a large band gap of 5.58 eV. Remarkably, it showcases an enlarged birefringence of 0.044 at 1064 nm, implying its potential as a birefringent material. Moreover, density functional theory calculations demonstrate that the optical characteristics are predominantly influenced by fundamental building blocks [BO3] triangles and distorted [LuO7] polyhedra. Our findings demonstrate the potential of KNa2Lu(BO3)2 in the development of a birefringent candidate and enrich the structural chemistry of rare-earth-based borates.

Influence of Ultrahigh Dilution Treatment of the Charge on the Growth and Spectroscopic Properties of Nd:MgMoO4 Potential Laser Crystal

The influence of the charge treatment by ultrahigh dilution (UHD) technology on oxide single crystals grown by the Czochralski technique was studied for monoclinic MgMoO4 crystals doped by 1 at. % of Nd3+ ions. The series of 10 Nd:MgMoO4 crystals was grown from the charges that were subjected to UHD treatment, as well as from the charges treated with two types of control or with no special treatment at all. The grown crystals were studied by X-ray powder diffraction analysis, inductively coupled plasma atomic emission spectroscopy, mass-spectrometry, optical absorption, emission spectroscopy and luminescence kinetic analysis. We found that: (i) wetting of MgO + MoO3 mixture by a water-ethanol solution before calcining leads to some enrichment of the mixture with MoO3, whereas the wetting of the charge after the calcining leads to some enrichment of it with MgO; (ii) congruent melting composition of MgMoO4 crystal is in the field of some MoO3 excess; (iii) the solid-phase solubility of the excess MoO3 in MgMoO4 probably does not depend on temperature, whereas the solid-phase solubility of the excess MgO in MgMoO4 crystal depends on temperature. We suggest that the corresponding solidus line passes through the range of retrograde solubility; (iv) the crystals grown within this range are characterized by the enhanced Nd3+ segregation coefficient between the crystal and the melt (approximately 0.006 versus 0.004); (v) unit cell parameters of MgMoO4 crystal with the excess of MoO3 are larger than those of the crystal of the stoichiometric composition and of the crystal with the excess of MgO; (vi) the shapes of the optical absorption and luminescence spectra of Nd:MgMoO4 crystal do not depend on the charge treatment; (vii) luminescence decay kinetics are single-exponential for all the studied crystals, the luminescence decay time being different for the crystals grown from the charges that underwent different types of treatment; (viii) the luminescence intensity of Nd:MgMoO4 crystal grown from the charge that underwent UHD treatment before calcining (solid-phase synthesis) is reduced by an order of magnitude in comparison with the other studied crystals.

Rb8Nb10Ge6O41: a new niobium-germanate crystal featuring unique one-dimensional [Nb7O30]∞ chains and wide mid-IR transparency.

Germanate oxides have garnered considerable interest owing to their diverse structural configuration and intriguing properties. Herein, we present a novel niobium germanate crystal, Rb8Nb10Ge6O41, extracted through the process of spontaneous crystallization. It showcases a unique three-dimensional (3D) structural framework composed of one-dimensional (1D) twisted [Nb7O30]∞ chains and isolated [Ge3O9] rings, arising from the divergent polymerized manifestations of [NbO6] and [GeO4] basic building blocks, respectively, marking the first instance of such a topography in germanate materials. Notably, the title compound exhibits exceptional thermal stability up to 1250 °C with a good congruent melting nature. Moreover, it achieves a short ultraviolet edge at 306 nm and a favorable infrared edge cutoff exceeding 6.2 μm, thus indicating a wide transparency window. Additionally, this study elucidates the microscopic birefringence of Rb8Nb10Ge6O41 and clarifies the intricate relationship between its structure and properties. Our findings suggest that the polymerization of distinct structural motifs within a single compound is an effective strategy for exploring novel inorganic materials.

Bulk crystal growth and characterization of non-centrosymmetric single crystal CaTa4O11

For the first time, high-quality bulk single crystals of CaTa4O11 were grown by the floating-zone method, and thus the current phase-diagram was revised for the stoichiometry CaO·2Ta2O5, showing a congruent melting behavior.

Zinc Nitrate Hexahydrate Pseudobinary Eutectics for Near-Room-Temperature Thermal Energy Storage.

Stoichiometric salt hydrates can be inexpensive and provide higher volumetric energy density relative to other near-room-temperature phase change materials (PCMs), but few salt hydrates exhibit congruent melting behavior between 0 and 30 °C. Eutectic salt hydrates offer a strategy to design bespoke PCMs with tailored application-specific eutectic melting temperatures. However, the general solidification behavior and stability of eutectic salt hydrate systems remain unclear, as metastable solidification in eutectic salt hydrates may introduce opportunities for phase segregation. Here, we present a new family of low-cost zinc-nitrate-hexahydrate-based eutectics: Zn(NO3)2·6(H2O)-NaNO3 (Teu = 32.7 ± 0.3 °C; ΔHeu = 151 ± 6 J·g-1), Zn(NO3)2·6(H2O)-KNO3 (Teu = 22.1 ± 0.3 °C; ΔHeu = 140 ± 6 J·g-1), Zn(NO3)2·6(H2O)-NH4NO3 (Teu = 11.2 ± 0.3 °C; ΔHeu = 137 ± 5 J·g-1). While the tendency to undercool varies greatly between different eutectics in the family, the geologic mineral talc has been identified as an active and stable phase that dramatically reduces undercooling in Zn(NO3)2·6(H2O) and all related eutectics. Zn(NO3)2·6(H2O) and its related eutectics have shown stability for over a hundred thermal cycles in mL scale volumes, suggesting that they are capable of serving as robust and stable media for near-room-temperature thermal energy storage applications in buildings.

Enthalpies of mixing in ternary Ag–Eu–Sn liquid alloys

Abstract The enthalpies of mixing in liquid alloys of the ternary Ag–Eu–Sn system were determined over a wide range of concentrations by means of isoperibolic calorimetry in the temperature range from 1313 to 1373 K. The partial enthalpies of each component of the ternary system were measured along the following sections: Δ H ̄ Ag ${\Delta}{\bar{H}}_{\text{Ag}}$ along the section with x Eu /x Sn = 0.28/0.72 up to silver content of about x Ag = 0.2 at 1373 K; Δ H ̄ Sn ${\Delta}{\bar{H}}_{\text{Sn}}$ along three sections (x Ag/x Eu = 0.31/0.69, 0.50/0.50 and 0.70/0.30) up to x Sn = 0.35 at 1373 K; Δ H ̄ Eu ${\Delta}{\bar{H}}_{\text{Eu}}$ along the section x Ag/x Sn = 0.50/0.50 up to x Eu = 0.25 at 1313 K. The enthalpies of mixing in the liquid Ag–Eu–Sn alloys show exothermic effects, being more pronounced in the vicinity of the Eu–Sn binary constituent. The minimum value of the integral enthalpy of about −60 kJ mol−1 is observed in the composition region of the congruently melting Eu2Sn phase.

Thermodynamics of antimony—selenium alloys formation and evaporation

The thermodynamic functions of alloy formation and evaporation were considered for two particular systems — Sb – Sb2Se3 and Sb2Se3 – Se in connection with the presence of congruently melting compound Sb2Se3 in the antimony—selenium system. The calculations are based on the partial vapor pressure values of the components forming the particular systems. The thermodynamic activity of antimony selenide and selenium as the most volatile components in the systems was calculated based on the saturated vapor pressure values of antimony selenide over the Sb – Sb2Se3 and selenium melts over Sb2Se3 – Se liquid alloys determined by the boiling point method (isothermal variant). Similar functions of the low volatile components in the above systems: Sb in the first system and Sb2Se3 in the latter one was calculated by numerical integration of the Gibbs—Duhem equation using the substitution proposed by Darken. The partial pressures of antimony selenide and antimony over Sb – Sb2Se3 and Sb2Se3 – Se melts were approximated by temperature—concentration relationships. The system is distinguished with a positive deviation from ideality due to the presence of a delamination region in the first system. The partial and integral entropies and enthalpies of the formation of liquid alloys were calculated based on the values of component activities found as the ratio of the partial vapor pressure of an element or compound above the solution to the saturated vapor pressure of a pure element or compound. The partial and integral functions of alloy formation are presented in the form of graphical dependences on the selenium amount in the melt. The obtained thermodynamic constants will replenish the physical and chemical data base and will be used to calculate the boundaries of the vapor— liquid equilibrium fields on the diagram of state, allowing to determine the possibility and completeness of distillation separation of molten systems.