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.

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.

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.

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.

The energies of mixing (interaction parameters) in the Sc1–xLn x PO4 (Ln = Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Y) systems have been calculated using Urusov’s crystal energy theory of isomorphous substitutions. The decomposition (stability) temperatures of the solid solutions have been plotted against the atomic number of the rare-earth elements at x = 0.01, 0.03, 0.05, 0.10, 0.20, and 0.50. The present results can be helpful in a search for host and activator compositions for new luminescence, laser, and other materials based on the zircon-structured rare-earth orthophosphates.

AbstractPb8‐xLnxNa2(PO4)6 (x = 0—2.0; Ln: Y, La, Pr—Ho, Tm—Yb) with void structural channels are prepared by solid state reaction of PbO, Na2CO3, (NH4)2HPO4, and Ln oxides (Al2O3 crucible, 800 °C, 2—10 d).

The substitution of rare-earth elements (REEs) for Pb in the lacunary apatite Pb8Na2(PO4)6 with void structural channels was studied by means of powder X-ray diffraction (including the Rietveld refinement), scanning electron microscopy, energy-dispersive X-ray microanalysis, and IR spectroscopy and also measurements of the electrical conductivity. The substitution limits (xmax in Pb8-xLnxNa2(PO4)6Ox/2) at 800 °C were found to decrease with the atomic number of the REE from 1.40 for La to 0.12 for Yb with a rapid drop from light to heavy lanthanides (between Gd and Tb). The REE atoms substitute for Pb predominantly at Pb2 sites of the apatite structure according to the scheme 2Pb(2+) + □ → 2Ln(3+) + O(2-), where □ is a vacancy in the structural channel. The substitution in lacunary apatite produces quite different changes in the structural parameters compared with broadly studied alkaline-earth hydroxyapatites. In spite of the much lower ionic radii of REE than that of Pb(2+), the mean distances ⟨Pb1-O⟩ somewhat increase, whereas the distances ⟨Pb2-Pb2⟩ and ⟨Pb2-O4⟩ do not change considerably with the degree of substitution. This implies control of the substitution by not only spatial and charge accommodation of REE ions but also the availability of a stereochemically active 6s(2) electron pair on Pb(2+). The high-temperature electrical conductivity shows dependence on the degree of substitution with a minimum at x = 0.2 indicative of a possible change of the type of conductivity.

Neodymium substitution in rare earth elements (REE) was studied in the systems Nd(5-x)Ln(x)Mo(3)O(16+y), where Ln = La, Ce, Pr with y similar to 0.5 by means of X-ray powder diffraction (including the Rietveld algorithm), scanning electron microscopy (SEM) and by measurements of the electrical conductivity. At x values of 0.5, 0.3, and 5.0 the mixtures of REE oxides with MoO3 transform to single-phase solid solutions with fluorite-related structure and doubled fluorite unit cell parameters as a result of solid state reactions occurring at 1050 degrees C. In the systems with La and Pr the unit cell parameter of solid solutions increases with x. While in the system with Ce this parameters decrease. Conductivity of ceramic solid electrolytes increases up to 17 times compared with the unmodified Nd5Mo3O16+y. (C) 2016 Elsevier B.V. All rights reserved.

Substitution rare-earth elements for cadmium in the monoclinic compounds Ln2MoO6 (Ln – Gd, Ho) leads to the formation of fluorite-related cubic structure. Series Ln2xCdxMoO6x/2 was investigated by XRD (with structure refinement), scanning electron microscopy, FTIR-spectroscopy and conductivity measurements.

Samarium substitution for neodymium in the Nd 5 Mo 3 O 16 compound has been studied by X-ray diffraction, scanning electron microscopy, and IR spectroscopy. The results demonstrate that fluorite-like Nd 5– x Sm x Mo 3 O 16 solid solutions exist in the range x ≤ 2. The electrical conductivity of the solid solutions increases with increasing samarium content in the range x = 0–1. Structure refinement by the Rietveld method for Nd 4 SmMo 3 O 16 has shown that the Nd(2) coordination polyhedron in this solid solution is distorted more severely than that in the structure of Nd 5 Mo 3 O 16 .

Substitution rare-earth elements for cadmium in the monoclinic compounds Ln 2 MoO 6 (Ln – Gd, Ho) leads to the formation of fluorite-related cubic structure. Series Ln 2 x Cd x MoO 6 x/2 was investigated by XRD (with structure refinement), scanning electron microscopy, FTIR-spectroscopy and conductivity measurements.