История появления в начале XX в. физико-химического анализа, как независимой научной дисциплины, необычна и поучительна. Академик Курнаков - создатель нового раздела химии доказал, опираясь на экспериментальный материал, что реальные кристаллы соединений, имеют переменный состав, представляют собой ограниченные твердые растворы, и, вопреки постулатам неорганической химии, применимость законов постоянства состава и кратных отношений ограничена. Учение Бертолле о подвижном равновесии, отвергнутое неорганической химией, оказалось действенным инструментом при описании фазовых превращений, а использование геометрических образов, предложенное Курнаковым для описания стабильных и метастабильных состояний многокомпонентных систем, облегчило работу материаловедов и обеспечило стремительное развитие физико-химического анализа. Устраняя противоречия между конфликтующими разделами химии, Курнаков ввел для ограниченных твердых растворов понятия «дальтонид» (стехиометрический состав соединения попадает в область гомогенности нестехиометрического кристалла) и «бертоллид» (стехиометрический состав находится за пределами области гомогенности). В статье приводятся результаты авторских физико-химических исследований ограниченных твердых растворов в рамках пространства давление - температура - химический состав конца XX в. - начала XXI в., с последовательным переходом от двухкомпонентных систем к трех- и четырехкомпонентным системам. The history of the emergence of physicochemical analysis as an independent scientific discipline at the beginning of the 20th century is unusual and instructive. Academician Kurnakov, the creator of a new section of chemistry, proved, based on experimental material, that real crystals of compounds have a variable composition, are limited solid solutions, and, contrary to the postulates of inorganic chemistry, the applicability of the laws of constancy of composition and multiple ratios is limited. Berthollet's doctrine of mobile equilibrium, rejected by inorganic chemistry, turned out to be an effective tool in describing phase transformations, and the use of geometric images proposed by Kurnakov to describe stable and metastable states of multicomponent systems facilitated the work of materials scientists and ensured the rapid development of physicochemical analysis. Eliminating contradictions between conflicting sections of chemistry, Kurnakov introduced the concepts of "daltonide" (the stoichiometric composition of the compound falls within the homogeneity region of a non-stoichiometric crystal) and "berthollide" (the stoichiometric composition is outside the homogeneity region) for limited solid solutions. The article presents the results of the author's physicochemical studies of limited solid solutions within the pressure-temperature-chemical composition space of the late 20th century - early 21st century, with a consistent transition from two-component systems to three- and four-component systems.

A phase equilibrium analysis was carried out for the Ni-Mn-Ga-Sb and Ni-Mn-In-Sb systems in the absence of melt. Using topological modeling based on concentration diagrams of the ternary systems Ni-Mn-Sb, Ni-Mn-Ga, Ni-Mn-In, Ni-Ga-Sb, Ni-In-Sb, Mn-Ga-Sb, Mn-In-Sb, and fragmentary experimental data on phase equilibria involving Heusler intermetallics Ni2Mn1+x(Ga,Sb)1-x and Ni2Mn1+x(In,Sb)1-x, isobaric-isothermal subsolidus concentration diagrams of the quaternary systems Ni-Mn-Ga-Sb and Ni-Mn-In-Sb were constructed. The key differences between them are demonstrated.

In the quasi-quaternary system BaO–Sc2O3–CuO–MoO3, the possibility of obtaining phases with perovskite structure was investigated by varying the chemical composition, temperature, and annealing atmosphere. A perovskite-like solid solution Ba4Sc2CuMoO11 with tetragonal structure was obtained by the gel combustion method followed by annealing in argon atmosphere at 900°C. Low-enthalpy solid-phase transformations of Ba4Sc2CuMoO11 at 810–820 and 960–975°C were found by DTA-TG.

A phase equilibrium analysis was carried out for the Ni–Mn–Ga–Sb and Ni–Mn–In–Sb systems in the absence of melt. Using topological modeling based on concentration diagrams of the ternary systems Ni–Mn–Sb, Ni–Mn–Ga, Ni–Mn–In, Ni–Ga–Sb, Ni–In–Sb, Mn–Ga–Sb, Mn–In–Sb, and fragmentary experimental data on phase equilibria involving Heusler intermetallics Ni2Mn1+x(Ga,Sb)1–x and Ni2Mn1+x(In,Sb)1–x, isobaric-isothermal subsolidus concentration diagrams of the quaternary systems Ni–Mn–Ga–Sb and Ni–Mn–In–Sb were constructed. The key differences between them are demonstrated.

To maintain the single-phase nature of the cubic solid solution Ba2(Y, Cu, Mo)2O6, which is prone to polymorphism, titanium oxide was used. As a result of the synthesis by gel burning, annealing at 1000°C, and subsequent cooling in an inertial thermal mode, the cubic modification F 4̅ 3m of Ba5Y2CuMoTiO14 was obtained for the first time without an admixture of perovskite Fm3m. A comparative study of samples Ba4Y2CuMoO11 and Ba5Y2CuMoTiO14 was carried out using X-ray powder diffraction, X-ray fluorescence spectrometry, IR spectroscopy, and diffuse reflectance spectroscopy.

We used topological modeling based on fragmentary experimental data on phase equilibria and phase transformations to construct for the first time P–T–x diagrams for Li–V, Li–O, and V–O binary systems and a complete isothermal concentration diagram of the Li–V–O system, the latter taking into account the formation of limited solid solutions and the presence of saturated vapor.

Using X-ray powder diffraction and thermal analysis (TG–DSC), samples of the quasi-ternary system Li 2 O–Mn 2 O 3 –Eu 2 O 3 , synthesized from precursors subjected to preliminary mechanochemical activation and annealed in air at 700–1100°C, have been studied. An assessment is given of the possibility of Mn for Eu substitution in the spinel LiMn 2 – x Eu x O 4 . A subsolidus isobaric diagram of the Li 2 O–Mn 2 O 3 –Eu 2 O 3 system was constructed. Using models of polythermal sections LiEuO 2 –LiMnO 2 and LiEuO 2 –LiMn 2 O 4 , a projection of the liquidus surface of the quasi-ternary system Li 2 O–Mn 2 O 3 –Eu 2 O 3 was obtained. The temperatures of eutectic and peritectic equilibria involving three crystalline phases and a melt have been determined.

Polycrystalline samples of the Li–Mn–Eu–O system were obtained by preliminarily ball-milled precursor mixtures annealing in air (700, 800, 900, 1000, and 1100°C). The obtained products were studied by X-ray powder diffraction and thermogravimetry (TG-DSC). The possibility of substituting Mn with Eu for spinel LiMn2–xEuxO4 was assessed. Within the framework of the Li–Mn–Eu concentration triangle, a subsolidus isobaric diagram and a projection of the liquidus surface of the Li–Mn–Eu–O system were constructed using models of polythermal phase diagrams of the LiEuO2–LiMnO2 and LiEuO2–LiMn2O4 sections. The temperatures of eutectic equilibria involving three crystalline phases and a melt were determined.

Phase equilibria in the Li–Mn–Eu–O system were studied for the first time in the temperature range 700–1000°С, and a concentration diagram was constructed within the Li–Mn–Eu triangle at an oxygen partial pressure of 21 kPa. It was shown that the LiEuO2–Li2MnO3 section can be represented as quasi-binary, unlike the sections LiEuO2–LiMnO2 and LiEuO2–LiMn2O4. It was determined that the isomorphic substitution of Eu for Mn in spinel LiMn2O4 (Fd 3̅ m) does not exceed 2 mol

A new phase Ba2(Y,Cu,Mo)2O6 with the cubic perovskite structure Fm-3m has been obtained in the BaO–CuO–Y2O3–MoO3 quasiquaternary system, and the possibility of coexistence of two limited solid solutions with cubic structures Fm-3m and F-43m has been established. The samples were synthesized by gel combustion followed by calcination at 1000°C and cooling in the inertial thermal regime. The studies were carried out by X-ray phase analysis, X-ray fluorescence spectrometry, infrared spectroscopy, and diffuse reflectance spectroscopy.

Using X-ray powder diffraction and thermal analysis (TG–DSC), samples of the quasi-ternary system Li2O–Mn2O3–Eu2O3, synthesized from precursors subjected to preliminary mechanochemical activation and annealed in air at 700–1100°C, have been studied. An assessment is given of the possibility of Mn for Eu substitution in the spinel LiMn2 – xEuxO4. A subsolidus isobaric diagram of the Li2O–Mn2O3–Eu2O3 system was constructed. Using models of polythermal sections LiEuO2–LiMnO2 and LiEuO2–LiMn2O4, a projection of the liquidus surface of the quasi-ternary system Li2O–Mn2O3–Eu2O3 was obtained. The temperatures of eutectic and peritectic equilibria involving three crystalline phases and a melt have been determined.

Polycrystalline samples of the pseudobinary system Ba2YMoO6–[Ba2YCuO5] were synthesized using the gel combustion method. The obtained samples were investigated using X-ray diffraction and photoluminescence spectroscopy. The substitution of Mo with Cu led to the stabilization of cubic phases Fm3̅m and F4̅3m of the solid solution Ba2YMo1 – xCuxO6 – δ (0 ≤ x ≤ 0.5) in air.

Samples of Mg3 – nNinBPO7 (n = 0–3), synthesized by gel combustion followed by annealing at 980°C and cooled in the inertial-thermal mode, were studied by X‑ray powder diffraction, infrared spectroscopy, and X-ray fluorescence spectrometry. For the first time, the crystalline phase of Ni3BPO7 with the β-Zn3BPO7 structure has been experimentally obtained. When the composition of the samples changed from Mg3BPO7 to Ni3BPO7, a region of coexistence of α‑Mg3BPO7 and β-Ni3BPO7 phases was found. An analysis of the diffuse reflectance spectra of the Mg1.5Ni1.5BPO7 sample showed the presence of Ni2+ cations in an arrangement not symmetric octahedral or tetrahedral.

Mg 3 – n Ni n BPO 7 samples ( n = 0–3) were synthesized by gel combustion followed by annealing at 980°C, cooled under inertial-thermal conditions, and then studied by X-ray powder diffraction analysis, IR spectroscopy, and X-ray fluorescence spectrometry. A crystalline phase of Ni 3 BPO 7 with the β-Zn 3 BPO 7 structure was experimentally obtained for the first time. When varying the composition of the samples from Mg 3 BPO 7 to Ni 3 BPO 7 , in borophosphate, a region of coexistence of α‑Mg 3 BPO 7 and β-Ni 3 BPO 7 was discovered. Analysis of diffuse reflectance spectra of Mg 1.5 Ni 1.5 BPO 7 showed the presence of Ni 2+ cations in an environment different from the symmetrical octahedral or tetrahedral environment.

Samples of the composition Ce 0.9 (Mg 1 – x Ni x ) 0.1 O 2 (0 ≤ x ≤ 1, step x = 0.1) have been obtained by gel combustion followed by hydrothermal treatment. X-ray powder diffraction data have showed that after gel combustion and annealing at 1100°C, composite CeO 2 (fluorite structure)/solid solution Mg 1 – x Ni x O (halite structure) is formed, and additional hydrothermal treatment followed by annealing promotes the formation of limited solid solution Ce 0.9 (Mg 1 – x Ni x ) 0.1 O 2 . According to the results of IR spectroscopy, the CeO 2 /Mg 1 – x Ni x O composite does not adsorb CO 2 even in the presence of water vapor, which is also confirmed by diffuse reflectance spectra in the UV-visible region. On the contrary, the Ce 0.9 (Mg 1 – x Ni x ) 0.1 O 2 solid solution absorbs CO 2 , as evidenced by the results of IR spectroscopy and thermogravimetric analysis.

The Mg3 – nNinBPO7 (n = 0.0, 0.5, 1.0, 1.5, 2.0, 2.5, and 3.0) samples were prepared by solid-phase reactions at 980°C followed by inertial cooling, and then were characterized by X-ray powder diffraction, IR spectroscopy, diffusive reflectance and X-ray fluorescence spectrometry. It was for the first time that experiments yielded Ni3BPO7 crystals having the β-Zn3BPO7 non-centrosymmetrical hexagonal structure. The α-Mg3BPO7 and Ni3BPO7 coexistence range was determined. The diffuse reflectance spectra of an Mg1.5Ni1.5BPO7 sample featured a strong Ni2+ absorption band in the blue spectral range.

The Mg3 – nNinBPO7 (n = 0.0, 0.5, 1.0, 1.5, 2.0, 2.5, and 3.0) samples were prepared by solid-phase reactions at 980°C followed by inertial cooling, and then were characterized by X-ray powder diffraction, IR spectroscopy, diffusive reflectance and X-ray fluorescence spectrometry. It was for the first time that experiments yielded Ni3BPO7 crystals having the β-Zn3BPO7 non-centrosymmetrical hexagonal structure. The α-Mg3BPO7 and Ni3BPO7 coexistence range was determined. The diffuse reflectance spectra of an Mg1.5Ni1.5BPO7 sample featured a strong Ni2+ absorption band in the blue spectral range.

The Mg3 – nNinBPO7 (n = 0.0, 0.5, 1.0, 1.5, 2.0, 2.5, and 3.0) samples were prepared by solid-phase reactions at 980°C followed by inertial cooling, and then were characterized by X-ray powder diffraction, IR spectroscopy, diffusive reflectance and X-ray fluorescence spectrometry. It was for the first time that experiments yielded Ni3BPO7 crystals having the β-Zn3BPO7 non-centrosymmetrical hexagonal structure. The α-Mg3BPO7 and Ni3BPO7 coexistence range was determined. The diffuse reflectance spectra of an Mg1.5Ni1.5BPO7 sample featured a strong Ni2+ absorption band in the blue spectral range.

Samples of the composition Ce0.9(Mg1 – xNix)0.1O2 (0 ≤ x ≤ 1, step x = 0.1) have been obtained by gel combustion followed by hydrothermal treatment. X-ray powder diffraction data have showed that after gel combustion and annealing at 1100°C, composite CeO2 (fluorite structure)/solid solution Mg1 – xNixO (halite structure) is formed, and additional hydrothermal treatment followed by annealing promotes the formation of limited solid solution Ce0.9(Mg1 – xNix)0.1O2. According to the results of IR spectroscopy, the CeO2/Mg1 – xNixO composite does not adsorb CO2 even in the presence of water vapor, which is also confirmed by diffuse reflectance spectra in the UV-visible region. On the contrary, the Ce0.9(Mg1 – xNix)0.1O2 solid solution absorbs CO2, as evidenced by the results of IR spectroscopy and thermogravimetric analysis.