Using the crystal energy theory of isomorphous miscibility, the mixing energies, critical decomposition temperatures, and substitution limits were calculated, and the thermodynamic stability ranges of solid solutions Sr1-x(Na0.5Ln0.5)xMoO4 (where Ln represents rare-earth elements, REEs) were determined. It was shown that both the mixing energies and the critical decomposition temperatures increase systematically with the REE atomic number. A thermodynamic stability diagram and dependencies of solubility limits of the solid solutions were built for concentrations ranging from x = 0 to x = 1.0 with a step of Delta x = 0.05. These diagrams allow one to determine the limits of equilibrium substitution at a given decomposition temperature, decomposition temperatures for a specified substitution limit, or the thermodynamically stable composition regions. The results may be helpful for immobilizing radioactive isotopes of REEs, actinides, and strontium-90 in nuclear waste disposal and developing new inorganic materials for phosphors and lasers.

Using Urusov’s crystal energy theory of isomorphous miscibility, the mixing energy and critical (maximum) decomposition temperature of solid solutions in the Pb10–xCux(PO4)6O system were calculated. Decomposition domes were constructed for the Pb10–xCux(PO4)6O system under the approximation of regular and asymmetric regular solid solutions, allowing for graphical determination of decomposition temperature at a given substitution limit or equilibrium substitution limit at a specified temperature, as well as thermodynamically stable regions of the solid solutions. It was shown that isomorphous substitution in the approximation of asymmetric regular solid solutions follows the Goldschmidt polarity rule: a smaller component dissolves in a larger one to a higher limit than in the reverse case. Additionally, our findings align with our established rule, which states that “the decomposition temperature is higher for the component with a smaller substituent structural unit and lower for the larger one”. It is hypothesized that the synthesis of Pb9Cu[(PO4)6O] (LK-99) at temperatures below the calculated values is influenced by sodium cations or other single-charged cations from uncontrolled impurities, which may stabilize the apatite structure at temperatures of 1100–1200 K.

Within the framework of Urusov’s crystal energy theory of isomorphous substitutions, the mixing energies (interaction parameters) in (Y1–xLnx)2SiO5 systems, where Ln represents rare-earth elements (REEs), have been calculated. It has been demonstrated that the mixing energy during the substitution of yttrium by REEs from the cerium subgroup is determined mainly by the size differences of the substituting structural units. At the same time, the yttrium subgroup is primarily influenced by the differences in the degree of ionicity of the chemical bonds of the system's components. The solid solutions’ decomposition (stability) temperatures were calculated, and based on these, thermodynamic stability diagrams for all systems and decomposition domes for each system were constructed. These diagrams allow for predicting the equilibrium substitution limits (x) as a function of temperature or the decomposition temperature based on specified substitution limits and the areas of thermodynamic stability. The results of this work can help choose the component ratios in matrices and the amount of activator (dopant) in new luminescent, scintillation, and other materials based on REEs oxyorthosilicate solid solutions of the composition (Y1–xLnx)2SiO5 with the space group P21/c.

Using Urusov’s crystal-energetic theory of isomorphous miscibility, the mixing energies (interaction parameters), critical decomposition (stability) temperatures and limits of isomorphous substitutions were calculated, and the areas of thermodynamic stability, instability and presumed metastability of solid solutions Y1–xLnxVO4, with zircon structure where Ln—rare earth elements (REE) and scandium were estimated. It was shown that the mixing energies and critical decomposition temperatures decrease significantly within the cerium subgroup and slightly increase within the yttrium subgroup with increasing REEs’ atomic numbers. Diagram of the thermodynamic stability of the solid solutions and domes of their decomposition for all systems Y1–xLnxVO4, Ln = Ce–Lu, Sc was presented. The results of this study can be useful in choosing the compositions of matrices and activators for new luminescent, laser and other materials based on solid solutions, including nanomaterials.

Using Urusov's crystal-energetic theory of isomorphous miscibility, the mixing energies (interaction parameters), critical decomposition (stability) temperatures and limits of isomorphous substitutions were calculated, and the areas of thermodynamic stability, instability and presumed metastability of solid solutions Y(1-x)Ln(x)VO(4), with zircon structure where Ln-rare earth elements (REE) and scandium were estimated. It was shown that the mixing energies and critical decomposition temperatures decrease significantly within the cerium subgroup and slightly increase within the yttrium subgroup with increasing REEs' atomic numbers. Diagram of the thermodynamic stability of the solid solutions and domes of their decomposition for all systems Y(1-x)Ln(x)VO(4), Ln = Ce-Lu, Sc was presented. The results of this study can be useful in choosing the compositions of matrices and activators for new luminescent, laser and other materials based on solid solutions, including nanomaterials.

Solid solutions of trifluorides of rare-earth elements (REEs) are being intensively studied since they can find practical application as materials for phosphors, lasers, scintillators, displays, light sources, catalysts, ionic conductors, fiber-optic amplifiers.

The mixing energies (interaction parameters) and the critical decomposition (stability) temperatures of Y1–xLnxFeAsO0.6 solid solutions, where Ln = La–Er, 0 < x < 1.0, were determined within the framework of the V. S. Urusov crystal-energetic approach in the approximation of regular solid solutions. Diagram of thermodynamic stability and domes of the solid solution decomposition have been plotted, which make it possible to calculate the equilibrium isomorphous substitution limits of yttrium for rare earth elements x depending on the decomposition temperature Td, or the decomposition temperature depending on the substitution limit. The results of calculation do not contradict to the experimental data found earlier in the literature for La1–xYxFeAsO0.6 and related systems La1–yYvFeAsO, La0.8Y0.2FeAsO0.7, and Y0.95La0.05FeAsO1–vH0.15. The results of this work can be useful in choosing the components’ ratio in “mixed” matrices and the dopant content in high-temperature superconductors, effective magnetic and other materials.

Urusov’s crystal energy theory of isomorphous substitutions was used to calculate mixing energies (interaction parameters) and critical decomposition temperatures (stability temperatures) of solid solutions in the systems Lu1–xLnxAsO4, Ln = Sm–Yb, Sc, Y with zircon structure, and La1–xLnxAsO4, Ln = Ce, Pr, Nd with monazite structure. For the Lu1–xLnxAsO4 system, a diagram of the thermodynamic stability of solid solutions is built that makes it possible to predict the thermodynamic stability of solid solutions. It is characterized by the presence of regions of thermodynamic stability and metastability of solid solutions. Above the critical temperatures, solid solutions are thermodynamically stable, and below the critical temperatures, they are metastable. The present results can be useful in choosing the ratio of components in “mixed” matrices, the amount of activator in luminescent, laser, and other practically important materials, as well as in matrices for immobilization of toxic and radioactive waste.

This work is devoted to the design and development of an intelligent information system for predicting the phase stability of solid solutions. Such solutions are used as a base for new luminescent materials. The main trends in the development of intelligent information systems were analyzed that led to a modification of a model for predicting the phase stability of solid solutions. The paper presents a variant review and selection of software design and development methods. Oracle Application Express (programming languages javascript, HTML, pl/SQL) and pl/SQL developer (programming language pl/SQL) were chosen as the software design environment. The paper also contains the analysis of database design methods with the software developed, including a definition of the main functions of the system.

Within the framework of the crystal–energy theory of isomorphous substitutions, the mixing energies and critical temperatures of decomposition (stability) of solid solutions with the tizonite structure in the La 1-x Ln x F 3 , Ln = Ce–Ho systems are calculated. A diagram of the thermodynamic stability of solid solutions is presented, which makes it possible to predict the limits of substitutions depending on the temperature or the temperature of decomposition according to the given limits of substitutions. The regions of thermodynamic stability, instability and metastability of solid solutions are determined. The calculation results in a number of systems that do not contradict the experimental data described earlier in the literature. They can be useful in choosing the ratio of components in “mixed” matrices, the amount of activator in luminescent, laser and other practically important materials, as well as for the immobilization of toxic and radioactive waste.

This paper presents the investigation of the heterovalent substitution of cadmium for lanthanum in the La2-xCdxMoO6-x/2 system. The samples were synthesized by the solid state reaction method at 1000°C. The samples were characterized by X-ray powder diffraction with Rietveld refinements, scanning electron microscopy with energy-dispersive X-ray spectroscopy, and Fourier transform infrared spectroscopy methods. The study results revealed that cadmium incorporation in the lanthanum molybdate leads to the transformation of the tetragonal structure of La2MoO6 to a cubic fluorite-like one. The content of the cubic phase reaches 94% in the Lа1.4Cd0.6MoO5.7 sample. The unit cell parameter of fluorite-like-phase decreases with cadmium content rising. The preferred location of cadmium ions in the cubic structure was established by the Rietveld refinement method. The heterovalent substitution cadmium for lanthanide in tetragonal La2MoO6 molybdate leads to the cubic fluorite phase stabilization in a similar way as it occurs in the process of reduction.

The energies of mixing (interaction parameters) and critical decomposition temperatures of Sc 1-x Ln x VO 4 solid solutions (where Ln is a rare-earth element (REE), Ln = Ce - Lu) with the zircon structure were calculated using the crystal-energy theory of isomorphous miscibility. Decomposition temperatures for Sc 1-x Ln x VO 4 solid solutions with x = 0.01, 0.02, 0.05, 0.10, and 0.20 were calculated with crystal chemical method of regular solution approximation. A diagram which allows to determine decomposition temperature with given equilibrium substitution limit (x), or substitution limit with given temperature and assess areas of stability, instability, and metastability for Sc 1-x Ln x VO 4 solid solutions is presented. Results of calculations were compared with literature data on thermodynamic stability of solid solutions and on substitution limits. The results of the study can be used during development of new luminescent materials based on ScVO 4 , which are modified with rare-earth elements, at defining rare-earth elements in matrix and activator, at defining optimal proportions of REE in Sc 1-x Ln x VO 4 matrixes. Using the XRD method, including the Rietveld structure refinement was found that the substitutional limit of Gd for Sc (x) in a series of solid solutions Sc 1-x Ln x VO 4 is about 0.13, which is in satisfactory agreement with the result of the calculation (x = 0.18). The effect of substitutions on the luminescent properties of Sc 1-x Ln x VO 4 is shown: with the introduction of 9% Gd in ScVO 4 , the intensity of intrinsic luminescent radiation increases to a greater degree.

The purpose of the work is influence investigation of modifying Nd5Mo3O16+δ oxygen-conducting fluorite-related compound by lead at the crystal structure and conductivity. The substitution of lead for neodymium was studied by XRD (with structure refinement), scanning electron microscopy, FTIR-spectroscopy and conductivity measurements. The compositions Nd5-xPbxMo3O16+δ (x = 0 – 1.6) were obtained by a solid state reaction from the oxides. It was determined that single-phase solid solution Nd5-xPbxMo3O16+δ is formed up to x ≈ 0.82. The Rietveld structure refinement shows that lead is statistically located in the Ln1 and Ln2 positions. The introduction of lead does not significantly affect the nature and values of conductivity.

The aim of the paper is to define the limits of substitution and phase stability for solidsolutions of orthovanadates with zircon structure Sc1–xLnxVO4, where Ln is a rare-earth element(REE), Ln = Ce – Lu. The mixing energies (interaction parameters) and critical decompositiontemperatures of Sc1–xLnxVO4 solid solutions with the zircon structure were calculated using thecrystal-energy theory of isomorphous miscibility. Diagram of thermodynamic stability visualizingthe substitution limits (x) by the decomposition temperature or the decomposition temperature bythe substitution limits, the dependencies of the decomposition temperatures on the REE atomicnumbers is presented. This diagram also allows assessing areas of stability, instability, andmetastability for Sc1–xLnxVO4 solid solutions. Results of calculations were compared with literaturedata on thermodynamic stability of solid solutions and on substitution limits. The results of thisstudy can be used in the development of new luminescent materials based on ScVO4 modified withREE, in the selection of REE for matrix and activator, in defining optimal proportions of REE inSc1–xLnxVO4 matrices.

Objectives. This study aimed to predict the limits of substitution and stability of luminescent materials based on low-temperature modifications of solid solutions (spatial group P21/c) with lutetium oxyorthosilicates (Lu1−xLnx)[(SiO4)0.5O0.5], where Ln represents the rare-earth elements (REEs) of the La–Yb series.Methods. The V.S. Urusov’s crystal energy theory of isomorphous substitutions and a crystallochemical approach in the regular solid solution approximation were used to calculate the energies of the mixing (interaction parameters) of the solid solutions.Results. Using the V.S. Urusov’s theory, we calculated the energies of mixing (interaction parameters) in the systems under study. The dependences of the decomposition temperatures of solid solutions on the REE number and composition (x) were obtained and used to create a diagram of the thermodynamic stability of the solid solutions, allowing us to predict the substitution limits depending on the temperature or determine the decomposition temperature using the given substitution limits.Conclusions. The results of the study can be useful when choosing the ratio of components in matrices (host materials) and the amount of the activator (dopant) in the new luminescent, laser, and other materials based on low-temperature modifications of solid solutions of “mixed” REE oxyorthosilicates (Lu1−xLnx)[(SiO4)0.5O0.5].

The energies of mixing (interaction parameters) and temperature ranges of stability of solid solutions Lu 1 − x Ln x VO 4 (where Ln is a rare-earth element (REE), scandium, or yttrium) with the zircon structure were calculated using the crystal-energy theory of isomorphous miscibility. It was shown that, with increasing atomic number of REE in the Ce—Lu series, the calculated energies of mixing and critical decomposition temperatures of the solid solutions regularly decrease. The substitution limits at various temperatures, the thermodynamic phase stability, and the temperature of transition to a metastable state were determined. The thermodynamic stability diagram of the REE vanadate solid solutions Lu 1 − x Ln x VO 4 was presented. The results of the work can be used for searching the compositions of matrices and activators of new laser and other materials.

Mixing energies (17.2–44.9 kJ/mole), critical temperatures of decomposition (1029–2700 K), and decomposition temperatures for systems of nanoscale REE oxyorthosilicates Ln 1  х [(SiO 4 ) 0.5 O 0.5 ]:Ce х (Ln  Tb–Lu, Y) for compositions with x  0.01, 0.02, 0.05, 0.10, and 0.20, which have luminescent properties, are calculated by means of the crystal-chemical method within the regular-solution approximation. A diagram is presented, which allows to determine decomposition temperature with a given equilibrium substitutional limit ( x ) or substitutional limit with a given temperature as well as to assess areas of stability, instability, and metastability

The substitution of gadolinium by lead in the compound Pb8-xNa2Gdx(PO4)(6)O-x/2, in accordance with the scheme 2Pb(2+) + center dot -> 2Gd(3+) + O2- was studied by means of powder X-ray diffraction (including the Rietveld refinement). It was established that solid solutions apatite samples are synthesized at 900 degrees C between the range from x = 0.0 up to x = 1.0. Rietveld method shows that Gd3+ is located in positions Pb(2), resulting in the distance in a polyhedron Pb(2) where the structure of apatite decreased.