三阶泛函微分方程的周期解的存在性

本文利用重合度理论研究了一类三阶泛函微分方程方程的2π-周期解的问题,获得了该方程存在2π-周期解的若干新结论,改进推广了有关文献中的已有结果．     

Two scenarios for phase-transformation in disordered media

The reasons for the existence of various scenarios for structural transformations in disordered condensed media, such as liquids and amorphous substances, where both smeared transformations and sharp first-order transitions may occur, were analyzed. The ratio between the spatial scale of structural correlations and the size of the smallest possible region occupied by a new phase in the matrix of initial modification is the key parameter determining the scenario for equilibrium phase transformations in liquids. In amorphous substances, the experimentally observed transformations occur far from equilibrium, and the possible size of the region occupied by the new phase corresponds to the minimal nucleus size. For some amorphous solids, quantitative analysis of the transformation width was carried out and the main classes of covalent substances, in which the smeared or sharp transitions occur, were revealed. Specific features of the interparticle interactions determining various transformation scenarios are discussed.     

Toroid type high-pressure device: history and prospects

The Toroid type high-pressure device and its predecessor, the Chechevitsa (lentil) type high-pressure device, are known to be used efficiently for the synthesis of new materials in recent decades. It was through the Chechevitsa device the first ultradense modification of silica, ‘stishovite’, was obtained. Both devices were essential for the industrial production of superhard materials in the USSR and other socialist countries. In 1980s, almost half of the world synthetic diamond and c-BN products were manufactured by these devices. However, the application of the Toroid device for examining the structure and physical properties of highly compressed substances has been considerably less appreciated. Meanwhile, the device has some unique features that have made possible 35-years of an extensive investigation of physical properties of substances at pressures up to 150 kbar, including electron transport and thermodynamic properties, elastic characteristics, viscosity, thermo-conductivity and other physical properties. Also, the device has been widely employed for structural X-ray and neutron diffraction studies of many materials. But it is not until recently that the convenience of the Toroid device for physical studies has been fully recognized. Through this recognition, the Toroid type device is today becoming increasingly popular among the researchers in the field of high pressures around the world.     

Single-crystal growth of the high-pressure phase B2O3 II

The technique and results of the hydrothermal single-crystal growth of the high-pressure phase B₂O₃ II are described. Transparent colorless crystals 450 × 450 × 150 μm in size have been grown under hydrothermal conditions (pressure 5 GPa, temperature range 1425–1025 K, and cooling rate ∼100 K/h).     

<Emphasis Type="Italic">In situ</Emphasis> study of the mechanism of formation of pressure-densified Sio<Subscript>2</Subscript> glasses

The volume of glassy a-SiO₂ upon compression to 9 GPa was measured in situ at high temperatures up to 730 K and at both pressure buildup and release. It was established that the residual densification of a-SiO₂ glass after high-pressure treatment was due to the irreversible transformation accompanied by a small change in volume directly under pressure. The bulk modulus of the new amorphous modification was appreciably higher (80% more than its original value), giving rise to residual densification as high as 18% under normal conditions. It was shown that the transformation pressure shifted to a lower pressure of about 4 GPa with a rise in temperature. A conclusion was drawn about the existence of at least two pressure-induced phase transitions accompanied by structure rearrangement in a-SiO₂. A nonequilibrium phase diagram is suggested for glassy SiO₂. It accounts for all the presently available experimental data and is confirmed by the existing modeling data.     

The influence of dimerization on the orientational phase transition in the C<Subscript>60</Subscript> fullerite

The influence of dimerization of a C₆₀ fullerite subjected to thermobaric treatment on the change in linear dimensions upon the orientational phase transition is investigated. It is demonstrated that the effects associated with the dimerization of fullerites substantially affect the thermal expansion coefficient only for samples synthesized under the conditions P_syn≥8 GPa and T_syn≥70°C (where P_syn and T_syn are the pressure and temperature of the synthesis, respectively). These effects bring about a smearing of the phase transition, a shift of the transition toward low temperatures, and a decrease in the volume jump.     

Elastic properties of substances in the megabar pressure range: Inversion of shear rigidity

The behavior of elastic moduli of substances is analyzed in the megabar pressure range. A new effect—inversion of the shear moduli and mechanical properties upon compression—is predicted for various classes of substances. The melting-curve data for different materials confirm the predicted phenomenon. The materials traditionally considered the softest, such as rare gas solids and molecular substances, may become the hardest in the megabar range. This should be taken into account in developing the experimental high-pressure technique.     

High-pressure phases in the GaSb-Mn system

The effect of high pressure (6 GPa) on the formation of new phases in a polycrystalline mixture GaSb: Mn = 1: 1 upon heating was studied. Sphalerite-type solid solutions with a small amount of Mn form at temperatures below 520–600 K. At higher temperatures, new crystalline GaSbMn phases are synthesized: a phase with a simple cubic structure with a lattice parameter a = 2.946 ± 0.001 Å (at 620–670 K) and a phase with a tetragonal CuAl₂-type structure (space group I4/mcm) with lattice parameters a = 6.426 ± 0.004 Å and c = 5.349 ± 0.004 Å (at 690–870 K). These new phases are metastable under normal conditions and have magnetic properties. The structure, conductivity, and thermal stability of the synthesized phases are investigated, and the products of decomposition of these new phases upon annealing are analyzed.