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The history of the cooperation between the staff of the Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences and S.K. Godunov is described. Numerous novel and interesting results in the theory of kinetic equations and computational mathematics were obtained in the course of this cooperation.

The article describes the history of the development of cooperation between scientists from the Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences with S. K. Godunov. A lot of interesting results have been established in the theory of kinetic equations and computational mathematics in the process of this cooperation.

The coalescence and fragmentation of particles in a dispersion system are investigated by applying kinetic theory methods, namely, by generalizing the Boltzmann kinetic equation to coalescence and fragmentation processes. Dynamic equations for the particle concentrations in the system are derived using the kinetic equations of motion. For particle coalescence and fragmentation, equations for the particle momentum, coordinate, and mass distribution functions are obtained and the coalescence and fragmentation coefficients are calculated. The equilibrium mass and velocity distribution functions of the particles in the dispersion system are found in the approximation of an active terminal group (Becker–Doring-type equation). The transition to a continuum description is performed.

In this paper the generalizations of the physico-chemical kinetics equations, including classical and quantum physico-chemical kinetics, coagulation–fragmentation equations, discrete velocity models of classical and quantum kinetic equation and, generally speaking, all discrete physico-chemical kinetics is considered. We make time discrete in these equations and prove the H -theorem.

The question of constructing models for the evolution of clusters that differ in shape based on the Boltzmann&rsquo, s H-theorem is investigated. The first, simplest kinetic equations are proposed and their properties are studied: the conditions for fulfilling the H-theorem (the conditions for detailed and semidetailed balance). These equations are to generalize the classical coagulation&ndash, fragmentation type equations for cases when not only mass but also particle shape is taken into account. To construct correct (physically grounded) kinetic models, the fulfillment of the condition of detailed balance is shown to be necessary to monitor, since it is proved that for accepted frequency functions, the condition of detailed balance is fulfilled and the H-theorem is valid. It is shown that for particular and very important cases, the H-theorem holds: the fulfillment of the Arrhenius law and the additivity of the activation energy for interacting particles are found to be essential. In addition, based on the connection of the principle of detailed balance with the Boltzmann equation for the probability of state, the expressions for the reaction rate coefficients are obtained.

We have proposed synthesis of polydisperse particles of poorly soluble substances through precipitation in pores of a water-soluble matrix. As a matrix, we used sucrose pressed under mass production conditions. In its pores, we obtained highly dispersed BaSO4 particles precipitated by reacting Ba(NO3)2 and Na2SO4. The BaSO4 particles were separated from the aqueous phase using a track-etched membrane filter and characterized by electron microscopy.

The problem of the formation of a microrelief on the surfaces of polymeric bodies has been considered. The basis for a mesokinetic model of the formation of macromolecules, their aggregates, and polymeric bodies in a device filled with a monomeric solution has been reported. An equation for changes in the function of the distribution of structural elements of the body microrelief over states in the process of its formation is formulated. Experimental data have been reported on the microrelief of polymeric bodies that confirm the prevalence of morphological memory phenomena among polymers and can be used to create new materials.

A kinetic model for the precipitation of a dispersed compound from solutions is formulated, based on a description of the evolution in the function of its particle distribution according to its states during precipitation. A boundary problem about the precipitation of a compound during the evaporation of a solvent from a solution under conditions in which the rate of aggregate formation is high is considered. The solution to this boundary problem can be used to describe the formation of a film of polystyrene during the evaporation of its solution in toluene and o-xylene deposited onto a substrate.

In the present paper we make the transition from the Becker–Doring system of equations to the hybrid (discrete and continuum) description. This new type of system of equations consists of the equation of the Fokker–Planck–Einstein–Kolmogorov type added by the Becker–Doring equations. We consider the H -theorem for it. We also consider the H -theorem for the Becker–Doring system of equations with discrete time and showed that it is true for some partially implicit discretization in time. Due to generality of the kinetic approach the present work can be useful for specialists in different spheres engaged in modeling the evolution of structures differing by properties.

We formulate a mesokinetic model of feedstock transformation into a material based on a system of devices in which the material is mechanically, thermally, or chemically modified. The idea of a frequency function that describes the rate of change of the function of particle distribution for a substance over the states in each device has been introduced. The possible application of the model to the development of technology that provides the maximum contribution of every device to the feedstock transformation to material is considered. It has been shown that, in developing the technology of the materials, it should be taken into account that, in many systems, the function of the size distribution of the particle varies according to the Fokker–Planck equation.

The experience of the joint research by the Department of Chemistry, Lomonosov Moscow State University, and the Federal State Budgetary Scientific Institution “N.N. Blokhin Russian Cancer Research Center” (FSBSI “N.N. Blokhin RCRC”), on the application of medium-intensity ultrasound in combination with chemotherapy and sonosensitizers in the treatment of cancer diseases was summarized. A cycle of preclinical trials showed that the method allows enhancing the damaging effect of ultrasound on the tumor, while no metastasis-promoting and toxic effects are exerted. The combined method is being currently tested in clinical trials.

Using scanning electron microscopy and X-ray diffraction, we have examined processes that occur in tubular alumina during heating in air to temperatures in the range 1100–1200°C. The results demonstrate that, starting at temperatures between 600 and 700°C, α-Al2O3 (corundum) is formed in the solid material. Heating the tubular material to 1000°C converts some of the starting alumina into χ-Al2O3 and some into α-Al2O3. The samples calcined for 2–10 h at 1100°C contain α-Al2O3 and ae-Al2O3. Heating to 1000–1300°C has no effect on the shape of the tubular particles. The ceramics obtained in this way are stable in contact with water. When tubular alumina with a SiCl4 vapor hydrolysis product deposited on its surface is heat-treated at temperatures in the range 1100–1300°C, we observe the formation of mullite (Al2O3 · 2SiO2) on the surface of the tubular particles.

The removal of volatile 137Cs and 131I compounds from an air flow on various filtering elements was studied. 131I2 and 137CsOH are sorbed on basalt wool, but the degree of their recovery is low: ∼86 and 90–93%, respectively, at the basalt wool bed height of 15–18 cm. The use of a cascade of bubblers in combination with a column packed with basalt wool allows virtually complete (>99.9%) removal of 131I and 137Cs in the form of 131I2, 137Cs131I, and 137CsOH from an air flow.

As found experimentally, macromolecules in the near-surface sections of a film prepared by solvent evaporation from a solution of polyvinylformal in dichloroethane acquired mobility under an electron beam to increase the rate of macromolecular association with the formation of nanosized aggregates by three or more orders of magnitude.

We studied low-temperature plasma effects on Paramecium caudatum using the original electric arc plasmatron. The decrease in the number of experimental cells has been shown, which may indicate membrane destructive pathology due to oxidative stress induced by the plasma impact. It is concluded that reactions at the population level of Paramecium caudatum are effective indices of primary information about plasma radiation cytotoxicity.

A new method of obtaining magnetic porous composite materials is described, which is based on the self-propagating high-temperature synthesis (SHS) in the form of solid-phase combustion. The SHS process involves transformation of the nonmagnetic α-Fe2O3 particles (contained in the initial mixture) into magnetic Fe3O4 particles. The synthesized material comprises a porous carbonaceous matrix with immobilized Fe3O4 particles. The obtained composite has been characterized by electron microscopy, X-ray diffraction, Mossbauer spectroscopy, and magnetic measurements. The sorption capacity of the porous material has been studied.

This paper describes the features of zonal crystallization at high speeds of the process. Processes of heat release and change of the state of reagents in solution, associated with their high concentration, were taken into account. The kinetics of crystal growth in gel medium was investigated. The control algorithm for permeability of layer with precipitated solid phase was identified. The parameters defining the localization of the crystal growth were discussed. The possibility of forming an impermeable plug with specified location was shown. These results are of interest for the solution of certain medical problems associated with the controlled transport of drugs.

Variation of the charge of radioaerosols formed by condensation of supersaturated 137Cs131I vapor, observed when the gas flow passes through an aqueous solution, was studied. The supersaturated 137Cs131I vapor was formed by evaporation of salt crystals from the metal surface heated to high temperatures owing to ohmic resistance. The radioactive aerosols preserve their charge even after bubbling through aqueous solutions, which allows using electric filters for localizing the aerosols.

It is found that nano- and microcrystals of a number of compounds grown in ion-free vapor of high supersaturation acquire electric charge. The electrophoretic mobility of these crystals changes, as is demonstrated by the data concerning aerosols formed in cooling the vapor above boiling melts of a number of substances (boiling temperature, 500–1800 K) placed into a 300 K carrier gas. Nano- and microparticles assembled into aggregates are found in flows of the cooled vapor. It is found that the application of an electric field with an intensity of 150–1000 V/cm induces the movement of particles toward the negatively charged electrode at a rate of 5–15 cm/s, the speed of their movement being related linearly to the field intensity and corresponding to the presence of ∼103 charge carriers per every particle. It is established that the experimental data are in accordance with the assumption that the growth of each particle results in the decomposition of vapor molecules adsorbed by the particle into ions with the nonequivalent liberation of cations and anions into vapor; i.e., an adsorption-ionization-desorption route for the charging of growing particles is discovered.

The behavior of radioaerosols formed by condensation of supersaturated 137Cs131I and/or 137CsOH vapor in an electrostatic field was studied. Supersaturated 137Cs131I and/or 137CsOH vapor was generated by evaporation of salt crystals from a metal surface heated to high temperatures owing to ohmic resistance. By applying additional potential to the aerosol generator, it is possible to control the behavior of 137Cs131I, 137CsOH, or 137Cs131I + 137CsOH aerosols in an electrostatic field.

We discuss ways of overcoming the crisis in which an exponential accumulation of information about any specific material is not accompanied by the development of theories allowing the use of the accumulated information to create new materials. To systematize the existing information and identify process regularity leading to the transformation of a substance into material, the Fokker-Planck equation is proposed, with frequency functions subject to experimental determination. It is shown that the use of this equation will supplement currently adopted methods for the creation of functional materials so that materials are the most consistent with consumer requirements and that they contribute to development of the theory. This upgrade is an important tactical problem that will prepare the development of a material theory that ensures a priori selection its optimal technology.

A mesokinetic model of the formation of a solid substance and the change in its properties under the action of factors that transform a substance into a functional material is proposed. Equations are introduced that represent the conditions of preservation of the number of molecules and particles of the substance during their nucleation, growth, and aggregation in supersaturated environments as well as during the ordering of the particles after the imposition of a temperature field and the introduction of additives. The equations describe the rate of change in the state distribution function of particles and can be reduced to the Liouville equation and the Fokker-Planck equation. The model contains unknown frequency functions subject to experimental determination. After these functions are determined, the model makes it possible to construct a methodological scheme for seeking the optimum route for the preparation of a new nanomaterial with desired properties.

The behavior of aerosols formed over boiling melts of substances (boiling temperature 500–1800 K) in a stream of a carrier gas at 300 K was studied. Microparticles of size from 0.2 to 10 μm, partially aggregated, were detected in the aerosol. In an applied electric field with an intensity of 150–1000 V cm−1, the particles migrated toward the negatively charged electrode at a velocity of 5–15 cm s−1. The velocity of their motion was a linear function of the field intensity and depended on the melt boiling temperature in accordance with the Arrhenius equation. Experimental data were interpreted on the basis of a concept that, in the course of the growth of each microparticle, vapor molecules adsorbed by it decompose into ions with nonequivalent transfer of cations and anions into the particle volume, i.e., the microparticles undergo growth charging at the activation energy of the cation release from the particle surface into vapor of approximately 0.5 eV.

Peculiarities of impurity distributions in fine-dispersed specimens of high-purity substances are considered for the case when the number of particles is close to that of impurity atoms. The dependence that the portion of absolutely pure particles has on their size and impurity content in the entire specimen is found. Potential peculiarities of the purification processes of such objects are considered.

The effect of the ionizing radiation field on the behavior of CsI aerosols formed by condensation of supersaturated vapor was examined. Supersaturated CsI vapor was formed by evaporation from a metal surface ohmically heated to high temperatures. A study of the size distribution function of CsI particles showed that, both in the field of 60Co γ-radiation and in a stationary electron beam, three modes of particle size are observed with the mean sizes of 0.13, 0.57, and 0.76 μm. The amount of particles of size 0.13 μm is larger by a factor of ∼10–20 than the amount of particles of sizes 0.57 and 0.76 μm. Comparison of the distribution functions of CsI aerosol particles formed by supersaturated vapor condensation in an ionizing radiation field and without it showed that the ionizing radiation affected not only the size but also the amount of particles.

It was shown for the example of CsI aerosol that the aggregation of primary aerosol particles could be described in terms of either the discrete or continuum model. This conclusion was drawn on the basis of experiments performed by the method that allowed primary particles to be observed against the background of their aggregates and transfer of primary particles from aerosol volume to a collector to be provided. The size of primary particles on the collector was determined by transmission electron microscopy. It was found that, under the conditions used, the size distribution of primary particles corresponded to the Fokker-Planck equation.

The work analyzes the possibility of treating the production of a functional material as the realization of the stage of separation of the substance forming the material from a supersaturated medium and the stages of physical and chemical modification of the separated substance. The key kinetic equation of variation of the distribution function of states of the particles of the substance at each stage is formulated, considering the discrete nature of the nucleation, growth, and aggregation of particles. Solutions to continuous versions of the kinetic equation with regard to each stage are given. The conception of the path \( \vec Z(\vec g) \) of obtaining the material is introduced in the form of the coupling function of the target properties \( \vec Z \) of the compound with characteristics \( \vec g \)} of the reactors where the material is produced. The conditions are considered under which the path can be regarded as optimal at each stage, and the optimality criteria of the routes are introduced.

Taking CsI aerosol as an example, it was shown that growth of primary aerosol particles can be described in terms of both discrete and continuum models. This conclusion is based on the results of experiments carried out using a method that makes it possible to distinguish primary particles against the background of their aggregates, to provide a complete transfer of the primary particles from aerosol bulk to a collector, and to determine the particle sizes by transmission electron microscopy. Under the conditions studied, the size distribution of the primary particles is described by a Fokker—Planck type equation.

Using the example of studying the behavior of heated crystals of copper sulfate CuSO4 · 5H2O that are derived from an aqueous solution and contain three-dimensional inclusions of the mother environment, we show that the heating of these crystals in an inactive medium leads to the discharging of inclusions due to the emersion of their content on the surface. The routes for discharging mother-solution inclusions are determined using optical and electron microscopy and X-ray topography. According to the proposed model, the inclusions are discharged because they expand on being heated and press the crystal matrix. As a result, the solubility of copper sulfate in the mother environment increases, and, along the linear dislocation that passes close to the inclusions and emerges on the crystal surface, a cylindrical pore appears via which the mother solution goes from the bulk of the crystal to its surface. Finally, we obtain a porous material that can reversibly absorb appreciable amounts of an inert fluid (e.g., alcohol) from the ambient environment.

Discrete and continual versions of the rate equation for the size distribution function of primary aerosol particles were formulated. With the CsI aerosol as example, it was shown that coarsening of primary aerosol particles can be described in terms of both discrete and continual models. This conclusion is based on the results of experiments performed by the procedure that makes it possible to reveal primary particles against the background of their aggregates, ensures complete transfer of primary particles from the aerosol volume to the collector, and allows determination of their size on the collector by electron microscopy. Under the examined conditions, the size distribution of primary particles is described by an exponential function.

Proceeding from the idea of the isolation of a substance from a supersaturated medium as the nucleation, growth, and aggregation of substance particles, a kinetic equation for changes in the particle state distribution function corresponding to the experimental data was obtained. The equation satisfying the requirement of the conservation of the number of new phase particles was simplified to the Liouville, Fokker-Planck, Farkas, and Zel’dovich equations.

The mechanism of interaction of nanocrystals of hydroxyapatite with Staphylococcus aureus bacteria has been investigated. It was shown that the growth of bacteria and their colonies both in the presence and absence of hydroxyapatite nanocrystals can be described using the Fokker-Planck equation. It was found that hydroxyapatite nanocrystals adhere in a particular orientation on the surface of bacteria, decreasing substantially their colony-forming ability.

The knowledge accumulated by chemical engineering makes it possible to create a methodology of the rational development of new science intensive technologies. One of the versions of such a methodology implies the formulation of principles and the revelation of methods for study, which shortens the way from the technological idea formation to its industrial implementation. This version implies passing from an a priori physicochemical model of phenomena which led to a technological idea to an a posteriori model of processes in industrial apparatuses where these phenomena should occur. In doing this, it seems expedient to combine numerical and real experiments with an iterative extension of the range of implementation conditions of phenomena from laboratory to industrial ones. The efficiency of such a methodological approach is evidenced by the experience of the development of the technology of an Ostim medicinal preparation.

The mechanism of synchronization of molecular fluctuations operates on the surface of growing nanoparticles, increasing their scale up to macroscopic. The kinetic equation for the function of state distribution of nanoparticles therefore approaches the Fokker-Planck equation, which was established experimentally by the example of nanoparticles of different natures. In a number of suspensions and aerosols in which ordered aggregates of nanoparticles are formed, aggregation is a multistage process; at each stage, variation in the function of size distribution of the aggregates is also described by the Fokker-Planck equation. Multistage aggregation is completed when particles with multilevel hierarchical texture, which have a tendency to assume polyhedral form, appear in the system. The abovementioned features of nanosystems can be interpreted as indications of the variability and self-assembly ability of systems.

Authors’ concepts on the use of solid-phase sonosensitizer nanoinclusions in biological structures as ultrasonic energy concentrators in the therapy of oncological diseases are developed. The possibility of directed synthesis of nanoparticles and their aggregates in tumor tissue depending on its growth features is discussed. It was found that acoustic effects in polymer structures containing solid-phase inclusions depend on the nature of these inclusions and their bond with the polymer matrix. Using model gel systems, it was shown that solid-phase sonosensitizers enhance local thermal effects and amplitude-dependent scattering of ultrasound during its propagation in gel. Experimental studies on animals showed that the ultrasound exposure of malignant tumors containing nanoparticles of gold and some complex compounds results in a significant therapeutic effect.

Two states of surface valence electrons localized on faces with different molecular reliefs were observed for nanodisperse hydroxyapatite. Thermal treatment of nanocrystals caused a shift ΔEb = 0.5 eV of the spectrum of valence electrons on molecularly rough faces and a shift of 0.8 eV of the spectrum from smooth faces. Similar electron spectrum shifts were observed for sorption, in particular, of sodium succinate. These results are of importance for the diagnostics of various hydroxyapatite kinds, since hydroxyapatite is a constituent mineral component of living organisms, and for the synthesis of medicines with enhanced biological activity used in treatment of various bone diseases.

A kinetic model of the crystallization of substances in the volume of an agglomerate of many microparticles or in a polymeric gel in solution with a given composition and temperature was formulated. The model takes into account the diffusion of the crystallizing substance from outside into the space between microparticles in an agglomerate or between polymeric globules in a gel and then from this space into the volume of microparticles (globules) with the simultaneous nucleation and growth of microcrystals of the crystallizing substance. The possibility of simultaneous diffusion of several crystallizing substances, which chemically react with each other to produce product microcrystals, heating of the gel (solid) by the heat of crystallization, pushing the solution out from the space between microparticles, and changes in the volume of the gel (solid) as a result of crystallization is considered. The model was used to develop a classification of crystallization types in gels and porous solids and interpret several phenomena described in the literature. A hypothesis was advanced concerning some unknown phenomena related to crystallization.

The growth of gypsum CaSO4 · 2H2O crystals in aqueous solutions has been investigated, both on individual crystals and on crystals in a homogeneous suspension in the supersaturation range 1–20 and the temperature range 291–303 K. The dependence of the crystal growth rates on supersaturation is described by an S-shaped curve, which is due (i) to the specific features of CaSO4 self-adsorption on the surface of growing gypsum crystals and (ii) to the multistage character of dehydration of Ca2+ and SO 4 2− ions at the transition from the solution to the solid. At solution supersaturations of ∼20, at which the adsorption layer is close to saturation, the growth rate weakly depends on supersaturation, approaching the limit value G jp . A model of the crystal hydrate growth in the kinetic mode is constructed which reveals the conditions at which the growth rate reaches the limit value G jp and does not change with a further increase in supersaturation.

Aggregates of calcium carbonate microcrystals precipitated from a highly supersaturated aqueous solution were found to form in two stages. At the first stage, high-porosity disordered aggregates (floccules), and at the second, low-porosity ordered aggregates (agglomerates) formed. The application of an acoustic field with a frequency of 2.64 MHz and radiation power 3 W/cm2 did not influence the kinetics of formation of microcrystals but accelerated aggregation by four orders of magnitude. This effect was explained by the sonostimulated desolvation of microcrystals colliding with the surface of aggregates and the corresponding decrease in the probability of the detachment from aggregates after collisions. The formation of microcrystals and aggregates in an acoustic field can be described by a Fokker-Planck-type equation. Taking this into account, a model of sonostimulated agglomeration revealing the direction of further investigations was formulated.

A mathematical kinetic model is developed for sorption of radionuclides, occurring via transition of the sorbate atoms initially to the subsurface layer of the particles of a polydisperse sorbent with a known particle size distribution function ϕ(R), and then to the bulk of these particles. The variance of the function ϕ(R) was demonstrated to have a considerable effect on the sorption rate. The simulated results are compared with the experimental data on the sorption of 90Sr from an aqueous medium on polydisperse calcium carbonate in the forms of calcite and vaterite.

The behavior of 137Cs131I radioaerosols, yielded by CsI evaporation from a Pt healer into argon or air, during their localization with aqueous solutions and various filtration materials [filters based on Petryanov fabric (from here on, Petryanov filter), “while band” paper filter, and TRUMEM metallic membrane filter] was studied. The degree of localization of 137Cs131I radioaerosols was examined in relation to the amount of sublimed 137Cs131I, the number of bubblers in the system, the size of the nozzle in the bubbling system, and the gas stream flow rate. The efficiency of localization of 137Cs131I radioaerosols with a 10-layer stack of Petryanov filters from the gas stream with and without bubbling system was estimated. It was found that, at the stream velocity of 2–3 cm s−1, a 10-layer stack of Petryanov filters with the total thickness of 3 cm takes up ca. 97% of total 137Cs131I sublimed from the Pt heater. It was shown that the bubbling system does not affect the efficiency of localization of 137Cs131I radioaerosols by Petryanov filters but only favors decrease of the aerosol load on these filters. Electron-microscopic examination of the particle-size distribution of the CsI aerosols penetrating through aqueous solutions was carried out, and various filtration materials (Petryanov filter and “white band” paper filter) were tested.

The results of studies in the field of gas-phase chemistry of radioactive iodine, published in the past 15 years, are systematized and analyzed. The prospects for applying these data to various fields of nuclear power engineering are assessed. Particular attention is given to localization of nanodispersed aerosols of radioactive iodine and its poorly sorbable organic compounds. The topicality of further studies in the field of radioactive iodine chemistry, aimed to solve problems related to accidents at nuclear power plants and plants for reprocessing of spent nuclear fuel, is demonstrated.

Cocrystallization processes widely occur in the nature and are used in chemical technology. In radiochemistry, they came into use since the end of XIX-beginning of XX century owing to studies by M. Curie, O. Hahn, V.G. Khlopin, and his disciples. They formulated the laws of isomorphous cocrystallization involving microamounts of radioactive elements. However, the formation of anomalous mixed crystals remained poorly understood. Major contribution to the development of this problem was made by A.N. Kirgintsev. Thanks to his studies and the subsequent studies made by other researchers, it became possible to make substantiated conclusions on the charges of ions of the cocrystallizing microcomponents. The use of cocrystallization processes allowed determination of the main physicochemical properties of actinides that are inaccessible in weighable amounts.

R&D in nanotechnology can simultaneously belong to basic and applied science. In this field of research, not only results but also the direction of investigation may be a commercial secret. Financing R&D in nanotechnology is therefore an important issue. The author’s considerations in this respect deserve special attention.

The kinetic data on crystallization and a morphological analysis of a layer of CH4 · 6H2O hydrate crystals formed on the surface of water as a result of methane absorption showed that secondary nucleation occurred during hydrate crystallization. The mutual arrangement of crystals in the layer revealed photographically in situ was evidence that part of nuclei produced on the surface of previously formed crystals went away from the surface into solution and grew there independently of “mother” crystals, although the probability of such transfer into an immobile solution remained low. In view of this, a model of crystal growth generating secondary crystals was developed.

The extent to which actinides (An) are similar to other elements of the periodic table is discussed. Actinides show certain similarity with transition metals in trends in variation of the stability of the highest and lowest oxidation states with increasing atomic number. Similarity between elements of the first half of the lanthanide (Ln) family and those of the second half of the An family is demonstrated. In the lowest oxidation states, An and Ln are analogs of alkali and alkaline-earth elements, and in the tetravalent state they start to exhibit noticeable similarity with d elements. The formation of Pu(VIII) is suggested on the basis of essentially similar volatility of oxides ot Os and Ru with that of Pu. Of particular interest are bivalent An and Ln ions with one d electron. Being analogs of bivalent elements, they form various types of clusters.