The main component of the toric Hilbert scheme

Let \X be an affine toric variety under a torus \T and let T be a subtorus. The general T-orbit closures in \X and their flat limits are parametrized by the main component H_0 of the toric Hilbert scheme. Further, the quotient torus \T/T acts on H_0 with a dense orbit. We describe the fan of this toric variety; this leads us to an integral analogue of the fiber polytope of Billera and Sturmfels. We also describe the relation of H_0 to the main component of the inverse limit of GIT quotients of \X by T.Comment: 18 page

Classification of affine homogeneous spaces of complexity one

The complexity of an action of a reductive algebraic group G on an algebraic variety X is the codimension of a generic B-orbit in X, where B is a Borel subgroup of G. We classify affine homogeneous spaces G/H of complexity one. These results are the natural continuation of the classification of spherical affine homogeneous spaces, i.e., spaces of complexity zero.Comment: 22 pages, 7 table

The moduli stack of affine stable toric varieties

Let X be an irreducible affine T-variety. We consider families of affine stable toric T-varieties over X and give a description of the corresponding moduli space as the quotient stack of an open subscheme in a certain toric Hilbert scheme under the action of a torus.Comment: 10 page

Preparation of Monodisperse Luminescent Particles of Y2-xGdxO3:Eu by Microwave-assisted Hydrolysis

Development of energy-saving methods of synthesis of monodisperse particles of rare-earth oxides with improved luminescent properties is very vital task. In present work we’ve developed new method of microwave-assisted synthesis of Y2-xGdxO3:Eu solid solutions, performed a study of influence of Y:Gd ratio on morphology and luminescent properties of monodisperse oxide particles. We’ve established monotonous dependence of mean size of particles on Y:Gd ratio. On the other hand dependence of intensity of luminescence on Y:Gd ratio has a clear maximum. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3490

High pressure synthesis and investigations of properties of boron allotropes and boron carbide

Boron, the 5th element of the Periodic Table, is nonmetallic, hard material with high melting point and boiling temperature. Despite decades of extensive investigations, boron and boron-rich solids remain in focus of modern research, because there are many long-standing fundamental questions related to boron chemistry, crystal-chemistry, bonding, polymorphism, and physical properties of boron allotropes and compounds, which have not been resolved yet. There are also a number of theoretical predictions, which require experimental verification. New knowledge is gained due to contemporary progress in materials synthesis and methods of their investigations. My work aimed at the development of the high-pressure high-temperature (HPHT) synthesis of single crystals of boron allotropes and boron-rich compounds, which could be used further for precise investigations of their structures, properties, and behavior at extreme conditions. The HPHT synthesis using the large-volume-press technique yields single crystals of especially high purity and quality. I performed the synthesis of single crystals of β-B using the large-volume press with toroidal anvils (toroidal press) recently installed in the Laboratory of Crystallography. I contributed to the development of the toroidal cell assembly and conducted pressure and temperature calibrations of this new press that I describe in the thesis in detail. Knowledge about the HPHT behavior of elemental materials and compounds is important for fundamental understanding of bonding evolution, phase transformations, and establishing of P,T-phase diagrams, which are of high significance for materials’ synthesis and applications. In my project I focused on high-pressure investigations of α-B, β-B and stoichiometric boron carbide, B13C2. Diamond anvil cell (DAC) technique was used for in situ studies of single crystals at high pressures and room temperature, as well as at extreme HPHT conditions with double-sided laser heating of samples in DACs. Various analytical techniques I used include synchrotron and in-house X-ray diffraction (XRD), Raman and infra-red (IR) spectroscopy, and scanning electron microscopy (SEM). The structure of α-B was studied at pressures up to 60 GPa by single-crystal XRD in a diamond anvil cell. The bulk modulus of α-B was found to be K300 = 224(7) GPa, while the bulk modulus of individual B12 icosahedra Kico appeared to be as high as 273(12) GPa. Thus, the compressibility of icosahedra is considerably lower than that of the bulk material. Measurements of interatomic distances as a function of pressure revealed that the intericosahedral two-electron-two-center (2e2c) bonds are almost as stiff as intraicosahedral ones, in accordance with the previous experimental data. The 2e3c intericosahedral bond shows much higher compliance compared to other bonds in α-B. The vibrational properties of α-B under pressure were investigated by Raman spectroscopy up to 160 GPa and synchrotron IR spectroscopy up to 53 GPa for the first time and gave evidence of the structural stability of this boron allotrope in the broad pressure interval, in agreement with X-ray diffraction data. Metallization of α-B was not observed up to 160 GPa. A comparison of theoretical calculations of the behavior of Raman modes of α-B under stress conditions with experimental data led to conclusion that stress in certain directions results in the splitting of some of the Raman modes. Structures of all hitherto known boron allotropes (α-B, β-B, γ-B, δ-B, and ε-B) are based on various arrangements of B12 icosahedra, since three valence electrons of boron are insufficient to form a simple covalent structure. However, theoretical calculations suggest a possibility of the existence of a non-icosahedral boron allotrope with the α-Ga type structure. Verifying this prediction was one of the tasks of my research. I conducted a series of high-pressure high-temperature experiments in diamond anvil cells (DACs) and demonstrated that the predicted boron allotrope (we denoted it as ζ-B) could be synthesized by laser-heating of single crystals of β-B to over 2100 K at pressures above 115 GPa. Synchrotron in situ single-crystal X-ray diffraction revealed the α-Ga-type orthorhombic structure (space group Cmce) with the unit cell parameters a = 2.7039(10) Å, b = 4.8703(32) Å, c = 2.9697(6) Å (Z=8). It may be described as a stacking along the (010) direction of distorted and corrugated hexagonal nets with the 36 topology. Measured precisely interatomic distances and linear compressibilities along the major crystallographic directions do not allow interpreting the structure as layered, as earlier proposed. The newly synthesized ζ-B studied in the pressure range from 115 to 132 GPa was found to be less compressible than any other of previously known boron allotropes. The single crystals of β-B used as precursors for synthesis of ζ-B were X-rayed upon compression up to 102 GPa that allowed me to get the equation of state of β-B in the Mbar pressure range: the bulk modulus was found to be K=183(3) GPa (K′=3.4(1)). No phase changes were observed. Additionally to boron allotropes, I investigated compressional behavior of stoichiometric boron carbide B13C2 up to 68 GPa using HP XRD. This study was motivated not only by availability of unique single crystals of the boron carbide synthesized in our group by the HPHT technique, but also by its practical importance. Boron carbide is used for manufacturing shielding powders and coatings applied as energy absorbers for dynamic protection and its mechanical properties and limits of stability under loading are of both scientific and practical interest for ballistic applications. Our single-crystal synchrotron X-ray diffraction investigations revealed structural stability of stoichiometric boron carbide B13C2 in the studied pressure range. A comparison of the unit cell volume reduction with the reduction of the volume of the B12 icosahedron upon compression of B13C2 from ambient pressure to 60 GPa revealed their similarity. This confirms that the stoichiometric boron carbide B13C2 is a true covalent compound and does show neither ‘molecular-like’ nor ‘inversed molecular-like’ solid behavior upon compression, as previously disputed. Our analysis has shown that, in agreement with the modern understanding of bonding in α–B, γ–B, and B13C2 based on the experimental electron-density studies, the compressional behavior of these boron allotropes and boron carbide depends on the types of bonding involved in the course of compression, so that the ‘effective compressibility’ of B12 icosahedra may vary in a broad range, from ca. 14% in α–B to ca. 18% in B13C2, as compared to ca. 18% of compression of the corresponding crystals. To summarize, the present work resulted in the HPHT synthesis of the first previously unknown non-icosahedral boron allotrope ζ-B. This finding confirmed earlier theoretical predictions, which stayed unproven for decades because of experimental challenges which couldn’t be overcome until recently. Structural stability of α-B and β-B in the Mbar pressure range and B13C2 up to 68 GPa was experimentally proven. Accurate measurements of the unit cell and B12 icosahedra volumes of the stoichiometric boron carbide B13C2 as a function of pressure led to conclusion that they undergo a similar reduction upon compression that is typical for covalently bonded solids. Neither ‘molecular-like’ nor ‘inversed molecular-like’ solid behavior upon compression was detected that has closed a long-standing scientific dispute. A comparison of the compressional behavior of B13C2 with that of α–B and γ–B allotropes and B4C showed that it is determined by the types of bonding involved in the course of compression

ORIGIN OF MELTING ANOMALIES IN THE JAPAN-BAIKAL CORRIDOR OF ASIA AT THE LATEST GEODYNAMIC STAGE: EVOLUTION FROM THE MANTLE TRANSITION LAYER AND GENERATION BY LITHOSPHERIC TRANSTENSION

At the latest geodynamic stage that is characterized by forces and processes of the last 90 Ma the lithosphere of Asia has been reactivated due to four main force factors: 1) mantle melting anomalies, 2) subduction-related interaction between the Pacific plates and the continental eastern margin, 3) convergent interaction between India and the continental southern margin, and 4) quasiperiodic orbital variations of the Earth. The starting point of the latest geodynamic stage [Rasskazov, Chuvashova, 2013] is consistent with the change of the Earth’s rotation due to the resonant interaction of its orbit with the orbit of the Mars in the time interval of 87–85 Ma [Ma et al., 2017].At the latest geodynamic stage that is characterized by forces and processes of the last 90 Ma the lithosphere of Asia has been reactivated due to four main force factors: 1) mantle melting anomalies, 2) subduction-related interaction between the Pacific plates and the continental eastern margin, 3) convergent interaction between India and the continental southern margin, and 4) quasiperiodic orbital variations of the Earth. The starting point of the latest geodynamic stage [Rasskazov, Chuvashova, 2013] is consistent with the change of the Earth’s rotation due to the resonant interaction of its orbit with the orbit of the Mars in the time interval of 87–85 Ma [Ma et al., 2017]

The synthesis of novel lanthanum hydroxyborate at extreme conditions

The novel structure of lanthanum hydroxyborate La2B2O5(OH)2 was synthesized by the reaction of partially hydrolyzed lanthanum and boron oxide in a diamond anvil cell under high-pressure/high-temperature (HPHT) conditions of 30 GPa and ∼2,400 K. The single-crystal X-ray structure determination of the lanthanum hydroxyborate revealed: P3¯c1, a = 6.555(2) Å, c = 17.485(8) Å, Z = 6, R1 = 0.056. The three-dimensional structure consists of discrete planar BO3 groups and three crystallographically different La ions: one is surrounded by 9, one by 10, and one by 12 oxygen anions. The band gap was estimated using ab initio calculations to be 4.64 eV at ambient pressure and 5.26 eV at 30 GPa. The current work describes the novel HPHT lanthanum hydroxyborate with potential application as a deep-ultraviolet birefringent material

GEOCHEMICAL AND CLAY-MINERAL STUDY OF HEALING MUD FROM WUDALIANCHI, NE CHINA

Over the centuries, people have used healing mud (peloids) to draw toxins out of the body, boost the immune system, cure psoriasis, acne, depression, and hair loss. The beauty industry has used mud-clay masks, body wraps, soaps, and baths. The useful properties of mud were established empirically. The most popular healing-mud spars are known in the Dead Sea in Israel, Baden-Baden in Germany, Calistoga in California, Budapest in Hungary, Akhtala and Kumisi in Georgia, Paratunka in Kamchatka, Wudalianchi in China.Over the centuries, people have used healing mud (peloids) to draw toxins out of the body, boost the immune system, cure psoriasis, acne, depression, and hair loss. The beauty industry has used mud-clay masks, body wraps, soaps, and baths. The useful properties of mud were established empirically. The most popular healing-mud spars are known in the Dead Sea in Israel, Baden-Baden in Germany, Calistoga in California, Budapest in Hungary, Akhtala and Kumisi in Georgia, Paratunka in Kamchatka, Wudalianchi in China