M. S. Nikol’skii

Potential matrices for immobilization of the rare earth-actinide fraction of high-level waste in the REE2Zr2O7-REE2Ti2O7 system

Phase compositions, structural features, and element distributions were studied for samples of the compositions REE2(Zr2−xTix)O7, which are potential matrices for immobilization of the rare earth-actinide fraction of high-level waste from spent nuclear fuel reprocessing. Samples with x up to 0.8 consist of pyrochlore, and at higher titanium content, of pyrochlore and monoclinic REE titanate with perovskite-type structure. The monoclinic phase becomes prevalent at x > 1.2. With respect to the content of the incorporated waste, it surpasses pyrochlore matrices by 10 wt %. The radiation resistance of this phase is close to that of titanate pyrochlore, but its amorphization dose is lower than for zirconate and titanate-zirconate pyrochlore. To check the suitability of monoclinic titanate for immobilization of the REE-actinide waste fraction, it is necessary to study its behavior in solutions and the effect of amorphization on the actinide leaching. The matrix can be prepared by the cold pressing-sintering method suggested in the United States for the synthesis of pyrochlore matrices with plutonium. High rate of solid-phase reactions in titanate systems allows the equilibrium to be attained at a moderate temperature (1400°C) within short sintering time (the first hours). One more possible procedure for matrix fabrication is cold crucible induction melting followed by the melt crystallization.

Self-propagating high-temperature synthesis and characteristics of cermet matrices for isolation of wastes with long-lived radionuclides

The possibility of preparing by self-propagating high-temperature synthesis (SHS) metal-ceramic (cermet) matrices with simulated wastes of REE-actinide fraction and Tc was examined. The specimens consist of oxide crystalline phases, glass, and melts. In the aluminate composite, the component (Sm) simulating the REE-actinide fraction is in the garnet and glass phases, and in the titanate composite, in the pyrochlore, titanosilicate of perrierite structure, and glass phases. Rhenium (Tc simulator) is incorporated in alloy phases. To evaluate the prospects for radioactive waste immobilization by SHS, it is necessary to synthesize matrices containing actinide isotopes (Am) and Tc and to study their structure and isolation properties.

Brannerite, UTi2O6: Crystal chemistry, synthesis, properties, and use for actinide waste immobilization

The host materials suggested for immobilization of actinide waste of military or civil origin often contain the secondary (U,Pu)Ti2O6 phase of brannerite structure. For example, the materials for incorporation of excess plutonium, mainly consisting of pyrochlore, contain up to 30% brannerite. This is a usual phase in titanate host materials for isolating spent nuclear fuel (SNF) and products of its reprocessing, including waste from production of 99mТс for medical purposes and other kinds of waste with high U and Pu content. Despite simple ideal stoichiometry, brannerite can contain large amounts of rare earths. This feature is due to the presence of uranium not only in the 4+ oxidation state, but also in the 5+ and 6+ states, which favors the exchange of rare earth elements (REE), e.g., in accordance with the scheme 2U4+ ↔ U5+ + REE3+. The REE amount in brannerite reaches 0.5–0.7 atom per formula unit. Therefore, brannerite is of interest as a host material for the rare earth–actinide fraction of high-level waste (HLW). To evaluate the prospects for such use of brannerite, data on the radiation resistance of brannerite and its behavior in aqueous solutions are analyzed. In these properties, brannerite is inferior to pyrochlore and zirconolite. The rate of actinide leaching from brannerite is higher by an order of magnitude than from these phases, but lower by 3–4 orders of magnitude than from glass host materials. Natural brannerite is stable in media with weakly alkaline and reducing waters. Therefore, brannerite seems suitable for immobilization of rare earth–actinide waste. This host material can be synthesized by sintering or cold crucible induction melting followed by crystallization.

Matrices for immobilization of the rare earth–actinide waste fraction, synthesized by cold crucible induction melting

The structure of eight samples containing simulated rare earth–actinide fraction of high-level waste was studied. Samples of weight from 0.2 to 6 kg were prepared by cold crucible induction melting followed by crystallization of the melt. The target phases (britholite, pyrochlore, zirconolite, rhombic and monoclinic rare earth titanates) prevail in all the matrices; glass, zirconolite, and rutile were detected as impurities, sometimes in significant amounts. These phases do not contain waste components (rutile) or are stable in solutions (zirconolite); therefore, their presence should not impair the properties of the matrix. The possibility of controlling the phase composition of the matrix by introducing zirconium or aluminum oxide into the charge was demonstrated.

Phase distribution of uranium in matrices for immobilization of the rare earth–actinide fraction of high-level waste

The uranium distribution in candidate host materials for the rare earth–actinide fraction was studied. The compositions of the materials were set so as to obtain artificial phases with the structures of pyrochlore Ln2(Ti,Zr)2O7 (space group Fd3m, Z = 8) and of monoclinic (P21, Z = 4) and rhombic (Fddd, Z = 16) titanates with the formulas Ln2Ti2O7 and Ln4Ti9O24, respectively, where Ln is a mixture of lanthanides simulating the wastes. The uranium content was varied from 3.5 to 5.5 wt %. In some cases, an equiatomic amount of calcium was introduced into the charge to check the possibility of the replacement of two Ln3+ cations by the Ca2+ + U4+ pair. Samples were prepared by sintering of the oxide charge or by its melting and crystallization of the melt. Along with the prevalent target compounds, the products contained uranium and lanthanide oxides, titanate of Ln and U with brannerite structure, Ln titanosilicates, and other phases. The main uranium concentrators in the samples are pyrochlore, oxides, and brannerite; small amounts of uranium (1–2 wt %) are incorporated in titanosilicates and rhombic titanate. The addition of calcium does not influence the capacity of monoclinic and rhombic titanates for uranium. Based on these data and the results of previous studies, a conclusion is made that rhombic titanate Ln4Ti9O24 and brannerite (Ln,U)Ti2O6 deserve an additional study as candidate host materials for the rare earth–actinide fraction.

On the time optimization problem for two-dimensional control systems

We consider a time optimization problem for two-dimensional nonlinear control systems. For a constraint for the control vector u we take a convex polygon U. We obtain effective sufficient conditions under which the time-optimal control is equivalent in the Lebesgue sense to a piecewise constant control that has finitely many points of discontinuity and ranges in the set of vertices of U. We give examples illustrating the results.

On the time-optimal problem for three- and four-dimensional control systems

The paper is devoted to the time-optimal problem for three- and four-dimensional nonlinear control systems with one-dimensional control. We obtain sufficient conditions for a time-optimal control to be equivalent (in the Lebesgue sense) to a piecewise constant control that is also optimal, has a finite number of discontinuity points, and takes only extreme values. Such optimal controls are called bang-bang solutions and are of considerable interest in control theory and its applications.

On controllable variants of Richardson’s model in political science

The paper is devoted to studying the properties of optimal controls for two controlled variants of Richardson’s arms race model known in political science. The main investigation technique is Pontryagin’s maximum principle.

A Nonlinear Identification Problem

We consider a nonlinear dynamic system with an unknown vector parameter in its description. An observer can calculate the phase vector of this system on the interval [0, T] with an error not exceeding a small number h > 0 in absolute value. This information on the dynamics of the system should be used to find the unknown vector. We obtain constructive sufficient conditions under which it is possible to restore the unknown vector with decreasing error as the value of h tends to zero. It turns out that one can use only discrete measurements of the output of the system.

On the benefit of cooperation in three-person games

Three-person games in which each player maximizes his payoff function are considered. The question on the benefit of forming a coalition of three players, which is interesting for cooperative game theory, is studied. The aim of the cooperation is that each player increases his guaranteed payoff. Effective sufficient conditions are obtained under which the coalition of the players is beneficial for each of them. The linear case is considered separately. In this case, rather general results are obtained in a constructive form. In the second part of the paper, the question on the benefit of cooperation of three players in the presence of the fourth player—Nature—is studied. The behavior of Nature is assumed to be unpredictable; it may harm any individual player or the coalition of the players. Note that the situation considered in the second part is related to A.V. Kryazhimskii’s talk delivered in the summer of 2014. We obtain constructive conditions under which the union of the players is beneficial in this situation as well.