Crystallization of glasses in the system SiO2-Li2O-TiO2-Al2O3, investigated in situ at high temperature by XRD and DTA methods

The processes of crystallization of fibres (diameter 10–15m) and coarse powders (grain size 500–1000m) with four compositions in the system SiO₂-Li₂O-TiO₂-Al₂O₃ were studied by conventional and in situ high-temperature XRD, DTA, SEM and optical microscopy. Activation energies of crystallization and morphological indices were deduced from the kinetic curves obtained by recording the high-temperature XRD peak intensity as a function of time. The glass-ceramic fibres drawn from compositions which exhibit glass-inglass phase separation show prevailing not-oriented bulk crystallization, whereas prevailing surface crystallization was found for single-phase glass fibres. Homogeneously-dispersed crystallization was obtained on heating fibres of these compositions. The partially cocrystallized glass fibres of eutectic composition between Li-metasilicate and-spodumene gave rise to a very fine and homogeneously-dispersed sub-microstructure.

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Zusammenfassung Die Prozesse der Kristallisation von Fasern (Durchmesser 10–15m) und groben Pulvern (Korngröße 500–1000m) von SiO₂-LiO₂-TiO₂-Al₂O₃ in vier verschiedenen Zusammensetzungen wurden mittels herkömmlicher und in situ XRD, DTA, SEM und optischer Mikroskopie untersucht. Aktivierungsenergien der Kristallisation und morphologische Indices wurden aus den durch Registrierung der Intensität der Hochtemperatur-XRT-Peaks in Abhängigkeit von der Zeit erhaltenen kinetischen Kurven ermittelt. Die aus Gemischen einer die Glas-in-Glas-Phasentrennung bedingenden Zusammensetzung gezogenen Glas-Keramik-Fasern zeigen vorwiegend eine nicht-orientierte Bulk-Kristallisation, während vorherrschend Oberflächenkristallisation bei Einphasen-Glasfasern festgestellt wurde. Eine homogen verteilte Kristallisation wurde beim Erhitzen der Fasern dieser Zusammensetzungen erhalten. Bei partiell ko-kristallisierten Glasfasern einer eutektischen Mischung von Li-Metasilikat und (-Spodumen liegt eine sehr feine und homogen-disperse Submikrostruktur vor.

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( 10–15 ) ( 500–1000 ) SiO₂-Li₂O-iO₂AL₂O₃ , , . , - . , --, ë, - . - . — - - - .

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This work was supported by the Italian C. N. R., Progetto Finalizzato Chimica Fine e Secondaria — Sottoprogetto Metodologie.

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We are indebted to Dr. B. Locardi of Stazione Sperimentale del Vetro, Murano (Venice) for furnishing the initial glasses and fibres.

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We are also indebted to the G. Giacomello Institute (C. N. R., Rome) for furnishing the computer programme for the unit cell parameter refinement. Assistance by M. Pistolato and F. Venuda in the experimental work is gratefully acknowledged.     

The application of the ion-interaction model to multicomponent 1-1 type electrolytes in mixed solvents

The ion-interaction model has been applied to published measurements for the multicomponent electrolytes HCl+MCl (M means Na or K) in mixed solvents (urea + water or methanol + water). The Pitzer parameters _HCl ⁽⁰⁾ , _HCl ⁽¹⁾ , C _HCl , ( _NaCl ⁽⁰⁾ + _NaH), _NaCl ⁽¹⁾ , _NaHCl in the HCl+NaCl + urea + water system were obtained by the method of least squares. A temperature and molality dependent equation for _HCl in this system was obtained. In the HCl+MCl + methanol + water system, the mixing parameter _HCl was obtained in terms of the Harned Rule. The relationship between Pitzer parameters and the composition of the mixed solvent was discussed.on leave from Department of Chemistry, Liaoning University Shenyang, China.     

Kinetics of isotope exchange of dioxygen with a powdered high-temperature superconducting material Ba2YCu3O7?x

It has been found that the rate of isotope exchange in Ba₂YCu₃O_7–x–O₂ system is high. Its kinetics is exponential, first order with respect to dioxygen and the exchange is of the mixed first/third type.

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Ba₂YCu₃O_7–x–O₂ . -, -, - .

     

Thermal membrane potential across cation-exchange membranes for various halide solutions

Thermal membrane potential across cation-exchange membranes was measured for various halide solutions. Linear relationships between thermal membrane potential () and temperature difference (T) were observed, and the temperature coefficient of thermal membrane potential (/T) decreases with increase in the molality of the external solution as predicted by a theory reported. When counterions of membranes are hydrogen ions, the sign of the coefficients turns into minus near 0.01 mol/kg of the external solution for all membranes, although the coefficients are always positive for all the other forms. The dependence of the coefficients on the molality of the external solutions sometimes deviated slightly from the theory. This deviation is attributed to some change in water content of the membranes. A reproducible method of measuring water content of membranes was applied to discuss the change in the state of the membranes.     

Physico-chemical properties of catalysts: Thermal analysis,infrared spectroscopy,X-ray diffraction and magnetic susceptibility of the vanadates of zinc,manganese and silver

Thermal characteristics of the vanadates of zinc, manganese and silver have been studied by DTA and TG techniques and the different transition products thus obtained have been characterised by IR, X-ray diffraction and magnetic susceptibility data. Chemical analyses indicate the following compositions of these vanadates: (1) Zn₂V₂O₇.5H₂O, (2) Zn₃(VO₄)₂.3H₂O, (3) Mn(VO₃)₂.2H₂O and (4) Ag₃VO₄. The DTA curves indicate that zinc pyrovanadate undergoes endothermic changes at 110–195, 265, 365, 440, 660° and one exothermic change at 485°. This system is diamagnetic which becomes completely paramagnetic after 660°. Zinc orthovanadate exhibits a number of endothermic peaks at 300, 470, 700, 815 and 930° respectively. This system is feebly paramagnetic and retains this property up to 930°. Manganese metavanadate undergoes endothermic changes at 240, 280–590, 830 and 880° respectively. This vanadate is paramagnetic and paramagnetism increases appreciably at 590° and remains constant up 830°. Silver orthovanadate exhibits three endothermic changes at 180, 455 and 640°, respectively.

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Zusammenfassung Die thermischen Charakteristika der Vanadate von Zink, Mangan und Silber wurden durch DTA- und TG-Methoden untersucht und die auf diese Weise erhaltenen verschiedenen Übergangsprodukte durch Daten aus IR-, Röntgen- und magnetischer Susceptibilität charakterisiert. Die chemische Analyse deutet auf folgende Zusammensetzung dieser Vanadate: 1) Zn₂V₂O₇.5H₂O, 2) Zn₃(VO₄)₂.3H₂O, 3) Mn(VO₃)₂.2H₂O und 4) Ag₃VO₄. Die DTA-Kurven zeigen endotherme Veränderungen des Zink-pyrovanadats bei 110–195, 265, 365, 440 und 660° und eine exotherme Veränderung bei 485°. Dieses System ist diamagnetisch und wird nach 660° vollständig paramagnetisch. Zink-orthovanadat zeigt eine Anzahl exothermer Peaks bei 300, 470, 700, 815, bzw. 930°. Dieses System ist schwach paramagnetisch und behält diese Eigenschaft bis zu 930°. Im Manganmetavanadat vollziehen sich endotherme Veränderungen bei 240, 280–590, 830 und 880°. Dieses Vanadat is paramagnetisch, der Pararnagnetismus steigt zusehends bei 590° und bleibt bis zu 830° konstant. Silberorthovanadat zeigt drei endotherme Veränderungen bei 180, 455 bzw. 640°.

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Résumé On a étudié par ATD et TG les caractéristiques thermiques des vanadates de zinc, de manganèse et d'argent. La caractérisation des divers produits de transition ainsi obtenus a été effectuée à partir des données fournies par IR, rayons X et susceptibilité magnétique. Les analyses chimiques indiquent les compositions suivantes de ces vanadates: (1) Zn₂V₂O₇.5H₂O, (2) Zn₃(VO₄)₂.3H₂O, (3) Mn(VO₃)₂.2H₂O et (4) Ag₃VO₄. Les courbes ATD du pyrovanadate de zinc montrent des effets endothermiques à 110–195, 265, 365, 440 et 660° ainsi qu'un phénomène exothermique à 485°. Ce corps est diamagnétique; il devient complètement paramagnétique au-dessus de 660°. L'orthovanadate de zinc donne des pics endothermiques à 300, 470, 700, 815 et 930°. Il est faiblement paramagnétique jusqu'à 930°. Le métavanadate de manganèse est le siège de phénomènes endothermiques à 240, 280–590, 830 et 880°. Il est paramagnétique et son paramagnétisme augmente de manière appréciable à 590° pour rester constant jusqu'à 830°. L'orthovanadate d'argent montre trois effets endothermiques à 180, 455 et 640°.

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, . - , . : Zn₂V₂O₇·5H₂O, Zn₃(VO₄)₂ · 3H₂O, Mn(VO₃)₂· 2H₂O Ag₃VO₄. , 110–195°, 265, 365,440 660° 485°. , 660° . 300, 470, 700, 815 930°. 930°. 240, 280–590, 830 880°. , 590° 830°. 180, 455 640°.

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The authors are grateful to the Physical Research Wing and Catalyst Research and Development Section, F. C. I., Sindri and also the Analytical Physics Division and Catalyst Section, I.I.P., Dehradun (India) for their help in getting TG and X-ray patterns of the catalysts studied.     

Thermal properties of the clathrate compounds of binary cyanides

The stoichiometry of thermal decomposition of a particular group of clathrate compounds, of the type Cd(en)Pd(CN)₄·2G, with the same coordination component but different clathrate-enclosed components, was investigated. Irrespective of the experimental conditions, the liberation of the enclosed component G always proceeded in one step. Thermal investigation of the decomposition stoichiometry under identical experimental conditions showed that the temperature intervals in which the enclosed components are given off shift to lower temperatures in the order C₆H₅OH=> C₆H₆ > > C₄H₅N > C₄H₄S. Diffraction measurements indicated a considerable change in the structures of the original clathrate compounds after thermal release of the enclosed componentG.

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Zusammenfassung Die Stöchiometrie der thermischen Zersetzung einer bestimmten Gruppe von Klathratverbindungen vom Typ Cd(en)Pd(CN)₄·2G mit der gleichen Koordinationskomponente und verschiedenen Klathrat-Einschlußkomponenten wurde in dieser Studie untersucht. Ungeachtet der Versuchsbedingungen vollzieht sich die Freisetzung der eingeschlossenen KomponenteG stets in einer Stufe. Die unter gleichen Versuchsbedingungen durchgeführte thermische Untersuchung der Zersetzungsstöchiometrie zeigte, daß die Temperaturbereiche, in denen die eingeschlossenen Komponenten freigesetzt werden in der Reihenfolge C₆H₅OH > C₆H₆ > C₄H₅N > C₄H₄S in Richtung der niedrigeren Temperaturwerte verschoben werden. Die Diffraktionsmessungen weisen darauf hin, daß eine beträchtliche Änderung der Struktur der ursprünglichen Klathratverbindung nach thermischer Freisetzung der eingeschlossenen KomponenteG sichtbar wird.

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Résumé Dans cette étude on a établi la stoechiométrie de la décomposition thermique d'un groupe particulier de clathrates du type Cd(en)Pd(CN)₄·2G, avec le même composant de coordination et différents composants occlus. Indépendamment des conditions d'expériences, la libération du composant occlusG s'effectue toujours en une étape. L'étude thermique de la stoechiométrie de la décomposition effectuée dans les mêmes conditions d'expériences, a montré que les intervalles des températures dans lesquels les composants occlus sont libérés, se déplacent vers les températures plus faibles dans l'ordre suivant: C₆H₅OH > C₆H₆ > > C₄H₅N > C₄H₄S. Les mesures de diffraction indiquent qu'après la libération thermique du composant occlusG, une variation considérable de la structure initiale des clathrates originaux apparaît.

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Cd(en)Pd(CN)₄. 2G . , G . , , , ] ₆₅>₆₆>C₄H₆N>C₄H₄S. - , G.

     

Interdependence between the dispersion of a solid decomposition product and its formation rate

In an analysis of the possible mechanism and kinetics of a thermal decomposition reaction with the formation of a solid product, the following features were considered: the collective rearrangement character of the transformation; the formation of a product with a different non-equilibrium defectiveness and free energy; the free energy relationship in the series of processes leading to products with different dispersions; the formation of intermediate structures; and the spinodal character of their decomposition. Relationships are presented between the rate of solid product formation, the process temperature, and the surface area and size of the particles.

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Zusammenfassung In einer Analyse des möglichen Mechanismus und der Kinetik einer unter Bildung eines festen Produktes verlaufenden thermischen Zersetzungsreaktion werden folgende Besonderheiten erörtert: der kollektive Umordnungscharakter der Umwandlung, die Bildung eines Produktes mit unterschiedlicher Nichtgleichgewichts-Gitterstörung und unterschiedlicher freier Energie, die Beziehung der freien Energie in zu Produkten unterschiedlicher DispersitÄt führenden Prozessen, die Bildung intermediÄrer Strukturen und der spinodalen Charakter ihrer Zersetzung. Beziehungen zwischen der Bildungsgeschwindigkeit des festen Produktes, der Temperatur des Prozesses und der OberflÄchengrö\e und Grö\e der Partikel werden angegeben.

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: ; ; , ; . , , .

     

Kinetics and mechanism of the oxidation of benzyl alcohol by potassium chlorochromate

The kinetics of the oxidation of benzyl alcohol by potassium chlorochromate, KCrClO₃, has been studied in dimethyl sulfoxide-dichloromethane medium. The reaction is catalyzed by acid. The effects of temperature and solvent composition were studied and activation parameters evaluated. Probable mechanisms are discussed.

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, KCrClO₃, . . . .

     

Quantum chemical calculations on the catalytic dehydration of 2-propanol

The charge on atoms and the bond strengths in CH₃CHOHCH₃, CH₃ CH₃, CH₃CHOHCH ₂ ^– , CH₃ CH ₂ ^– and CH₃ CH₃...O(H)CH(CH₃)₂ have been calculated by the CNDO/2 method. The results are in agreement with published experimental observations on catalytic dehydration. A modified mechanism of anti-elimination on solid catalysts is proposed.

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CH₃CHOHCH₃, CH₃ CH₃, CH₃CHOHCH ₂ ^– , CH₃ CH ₂ ^– CH₃ CH₃...O(H)CH(CH₃)₂, CNDO/2. . .

     

IR and thermal studies on lithium oxomolybdenum(VI) oxalate

A new molybdenum(VI) complex, Li₂[Mo₂O₆(C₂O₄)] · 2 H₂O (LMO), was prepared and characterized by chemical analysis and IR spectral studies. Its thermal decomposition was studied by using TG and DTA techniques. LMO loses its two moles of water between 75 and 170° to give the anhydrous product, which decomposes in three stages between 240 and 380°. The first two stages occur in the temperature ranges 240–280° and 280–305°, to give intermediates with the tentative compositions Li₆[Mo₆O₁₉(C₂O₄)₂] and Li₆[Mo₆O₂₀(C₂O₄)], respectively. In the third stage, which extends up to 380°, Li₆[Mo₆O₂₀(C₂O₄)] decomposes to give the end-product, Li₂Mo₂O₇.

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Zusammenfassung Ein neuer Molybdän(VI)-Komplex der Formel Li₂[Mo₂O₆(C₂O₄)] · 2 H₂O (LMO) wurde dargestellt und durch chemische Analyse und IR-spektroskopisch charakterisiert. Die thermische Zersetzung dieses Komplexes wurde mittels TG und DTA untersucht. LMO verliert die zwei Wassermoleküle zwischen 75 und 170° unter Bildung des wasserfreien Produktes, das zwischen 240 und 380° in drei Stufen zersetzt wird. Die in den Temperaturbereich von 240–280° und 280–305° verlaufenden ersten zwei Reaktionsschritte ergeben Intermediäre der tentativen Zusammensetzung Li₆[Mo₆O₁₉(C₂O₄)₂] bzw. Li₆[Mo₆O₂₀(C₂O₄)]. In dem sich bis 380° erstreckenden dritten Reaktionsschritt wird Li₆[Mo₆O₂₀(C₂O₄)] unter Bildung des Endproduktes Li₂Mo₂O₇ zersetzt.

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Li₂[MO₂O₆(C₂O₄] · 2 ₂ . . - 70–170° , , 240–380°. 240–280° 280–305° - Li₆[Mo₆O₁₉(C₂O₄)₂] Li₆[Mo₆O₂₀(C₂O₄)]. - 380° Li₂Mo₂O₇.

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The authors are grateful to Prof. S. N. Tandon, Head of the Chemistry Department, for providing the research facilities.     

ESR studies of photoinduced centers on weakly reduced anatase

The paramagnetic centers of reduced anatase (g₁=1.999, g₂=1.984, g₃=1.979) and (g₁=2.046, g₂=2.008), assigned to the stabilization of photoinduced holes near anion vacancies, have been studied. For the reduced oxide a new type of O₂ photoadsorption at h >1 eV due to the generation of only electron surface centers has been discovered.

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, : (g₁=1,999, g₂=1,984, g₃=1,979) (g₁=2,046, g₂=2,008), . O₂ h>1 , .

     

On the Interaction of Two Finite-Dimensional Quantum Systems

Interaction of quantum system S ^a described by the generalised × eigenvalue equation A| _s =E _s S ^a | _s (s=1,...,) with quantum system S ^b described by the generalised n×n eigenvalue equation B| _i = _i S ^b | _i (i=1,...,n) is considered. With the system S ^a is associated -dimensional space X ^a and with the system S ^b is associated an n-dimensional space X _n ^b that is orthogonal to X ^a . Combined system S is described by the generalised (+n)×(+n) eigenvalue equation [A+B+V]| _k = _k [S ^a +S ^b +P]| _k (k=1,...,n+) where operators V and P represent interaction between those two systems. All operators are Hermitian, while operators S ^a ,S ^b and S=S ^a +S ^b +P are, in addition, positive definite. It is shown that each eigenvalue _{k i} of the combined system is the eigenvalue of the × eigenvalue equation . Operator in this equation is expressed in terms of the eigenvalues _i of the system S ^b and in terms of matrix elements _s |V| _i and _s |P| _i where vectors | _s form a base in X ^a . Eigenstate | _k ^a of this equation is the projection of the eigenstate | _k of the combined system on the space X ^a . Projection | _k ^b of | _k on the space X _n ^b is given by | _k ^b =( _k S ^b –B)^–1(V– _k P})| _k ^a where ( _k S ^b –B)^–1 is inverse of ( _k S ^b –B) in X _n ^b . Hence, if the solution to the system S ^b is known, one can obtain all eigenvalues _{k i} } and all the corresponding eigenstates | _k of the combined system as a solution of the above × eigenvalue equation that refers to the system S ^a alone. Slightly more complicated expressions are obtained for the eigenvalues _{k i} } and the corresponding eigenstates, provided such eigenvalues and eigenstates exist.     

The preparation, characterization, and thermal behaviour of some lithium aluminum oxides: Li3AlO3 and Li5AlO4

The purpose of this research was to study the best conditions for the synthesis of the double oxides Li₅AlO₄ and Li₃AlO₃ in the solid state starting from the simple oxides, and to determine their heats of formation.Li₅AlO₄ was obtained from Li₂O₂ or Li₂O and -Al₂O₃ in a Li/Al molar ratio of 51, and was characterized by X-ray methods. Lithium orthoaluminate, Li₃AlO₃, was obtained from Li₂O₂ and -Al₂O₃ in a molar ratio 31. The postulated formula, Li₃AlO₃, was confirmed by chemical analysis.The temperature ranges in which the compounds are stable were established by the DTA method, and were found to be very limited for Li₃AlO₃ (400–430°) but greater for Li₅AlO₄ (440 — more than 600°).The heats of formation of Li₅AlO₄ and Li₃A10₃, also determined by means of the DTA method, were found to be –552.3 ± 0.8 kcal/mole and –416.8 ± 2 kcal/mole, respectively.

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Zusammenfassung Es wurden die Bildungsverhältnisse der doppelten Oxide Li₅AlO₄ und Li₃AlO₃ in fester Phase ausgehend von den einfachen Oxyden geprüft und ihre Bildungswärmen bestimmt. Li₅AlO₄ wurde aus Li₂O₂ oder Li₂O und -Al₂O₃ beim Molverhältnis von Li/Al 5 1 erhalten und röntgenographisch identifiziert. Das Orthoaluminat Li₃AlO₃ erhielt man beim Molverhältnis 3 1 von Li₂O₂ und -Al₂O₃. Die Zusammensetzung von Li₃AlO₃ wurde durch chemische Analyse nachgewiesen. Die DTA-Prüfung zeigte, daß Li₃AlO₃ nur im sehr kleinen Temperaturgebiet (400–430°), Li₅AlO₄ hingegen im weiteren Bereich zwischen 440–600° stabil ist. Die Bildungswärmen betrugen für Li₅AlO₄ –552.3±0.8, für Li₃AlO₃ –416.8±2 kcal/Mol.

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Résumé On a recherché les meilleures conditions pour réaliser la synthèse à l'état solide des oxydes doubles Li₅AlO₃ et Li₃AlO₃ en partant des oxydes individuels et pour déterminer leur chaleur de formation. Li₅AlO₄ a été obtenu en partant de Li₂O₂ (ou Li₂O) et de -Al₂O₃ dans le rapport molaire Li/Al=5/1; il a été caractérisé par étude aux rayons X. L'orthoaluminate de lithium, Li₃AlO₃, a été obtenu en partant de Li₂O₂ et de -Al₂O₃ mélangés dans le rapport 3/1. L'analyse chimique a confirmé la formule présumée Li₃AlO₃. L'ATD a permis de déterminer le domaine de stabilité thermique de ces composés: très restreint pour Li₃AlO₃ (400–430°), plus grand pour Li₅AlO₄ (440-plus de 600°), ainsi que leurs chaleurs de formation: –416.8±2 kcal/mole et –552.3±0.8 kcal/mole, respectivement.

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— Li₅AlO₄ Li₃AlO₃ . Li₅AlO₄ Li₂O₂ Li₂O -l₂₃ Li/Al 51, . , Li₃AlO₃, Li₂O₂ -l₂₃ 31. . , , , Li₃AlO₃ (400—430 °?) Li₅AlO₄ (440- 600 °?). Li₅AlO₄ Li₃AlO₃ 552.3 ± 0.8 416.8 ± 2 /, .

     

Energetic and kinetic investigation of thermally induced molecular rearrangements of esters of (hydroxymethyl) hydridosilanes by DSC

Silanes of the type R¹R²Si(H)CH₂OEl(O)_xR _y ³ [R=organyl; El=C (x=y=1), S (x=2,y=1), P (x=1y=2)] undergo a thermally induced rearrangement to give silanes of the type R¹R²Si (CH₃)OEl(O)_xR _y ³ . The energetic (reaction enthalpy) and kinetic data (reaction order, enthalpy and entropy of activation) of this reaction were determined by means of differential scanning calorimetry. The results obtained are discussed in terms of mechanistic aspects.

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Zusammenfassung Silane des Typs R¹R²Si(H)CH₂OE10_xR _y ³ mit R=organyl; E1=C (x=y=1), S(x=2, y=1) oder P (x=1,y=2) zeigen eine thermisch induzierte Umlagerung zu Silanen des Typs R¹R²Si(CH₃)OE10_xR _y ³ . Energetische (Reaktionsenthalpie) und kinetische Daten (Reaktionsordnung, Aktivierungsenthalpie und -entropie) dieser Umlagerungsreaktion wurden mittels DSC ermittelt. Die mechanistischen Aspekte der Ergebnisse werden diskutiert.

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R¹R²Si(H)OE1(O)_xR _y ³ , R= , E1=C (x=y=1), S (x=2,y=1), P (x=1,y=2), R¹R²Si(CH₃)OE1(O)_xR _y ³ . ( ) ( , ) . .

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Investigation of catalytic purification of gases from aromatic hydrocarbons

1,1- (AH) ([AH]=6,9 /, 50°C). AH W_i/W_{O 3}=0,40±0,16.

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The kinetics and oxidation products of 1,1-diethoxyethane (AH) ozonolysis have been investigated at [AH]=6.9 mol/l and 50 °C. The initiation efficiency of radical oxidation by ozone is W_i/W_{O 3}=0.40±0.16.

     

Augmentation of the Generalised n×n Eigenvalue Equation to a Generalised (n+1)×(n+1) Eigenvalue Equation

Generalised n×n eigenvalue equation B| _i = _i S ^b | _i (i=1,...,n) where B and S ^b are n×n Hermitian matrices while S ^b is in addition positive definite is considered. This equation is augmented to a generalised (n+1)(n+1) eigenvalue equation H| _k = _k S| _k (k=1,...,n+1) where Hermitian matrices H and S represent matrices B and S ^b , respectively, augmented by one additional row and one additional column. It is shown how the eigenvalues _k and the eigenvectors | _k of the augmented eigenvalue equation can be expressed in terms of the eigenvalues _i and the eigenvectors | _i of the original eigenvalue equation. Operation count to obtain by this method all augmented eigenvalues and eigenvectors is of the order O(n ²). Unless matrices involved are of some special kind such as sparse matrices or alike, this operation count is one order of magnitude smaller than operation count required by other presently known methods. In many practical cases operation count to obtain a single selected eigenvalue and/or eigenvector by this method is of the order O(n). In the case of the generalised eigenvalue equation, all other methods usually require again O(n ³) operations, even if only a single eigenvalue and/or eigenvector is required. Thus in many cases of interest operation count to obtain a selected eigenvalue and/or eigenvector by this method is two orders of magnitude smaller than operation count required by other methods.     

Silane-silanol condensation catalyzed by organotin compounds

The rate of condensation of H–SiR₂–(OSiR₂)_n–H (n=2, 3 or 4 and R=CH₃) and HO-SiRR–(OSiRR)₃–OH (R=C₆H₅) in xylene at 100 °C, catalyzed by dibutyltin diacetate, dilaurate and di-(2-ethyl)hexanoate, has been studied by infrared spectroscopy. The kinetic law is first order in each reactant and the reaction is accompanied by autocondensation of the silanol. The mecha nism involves complexation of the silanol with the catalyst, followed by the attack of a silane or silanol molecule.

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H–SiR₂–(OSiR₂)_n–H ( n=2,3 4 R=CH₃) HO–SiRR–(OSiRR)₃–OH ( R=C₆H₅) 100° C, , -(2-) , . . .

     

Catalytic decomposition of N2O on La2CuO4 in the presence of LaNi5 alloy

Decomposition of N₂O has been studied on pure La₂CuO₄, La₂CuO₄ with 5 and 10 wt. % LaNi₅ and oxidized LaNi₅ in the temperature range of 240–490 °C at 50 and 200 Torr initial pressures of N₂O. The addition of LaNi₅ decreases the energy of activation compared to that of La₂CuO₄ which has been explained based on the dispersity of NiO over La₂CuO₄.

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N₂O La₂CuO₄ La₂CuO₄ LaNi₅ 5–10 .%, 240–490°C N₂O 50 200 . LaNi₅ , . NiO La₂CuO₄.

     

Hydrogen exchange in intramolecular cycloalkylation of phenylalkanols

Hydrogen exchange in intramolecular cycloalkylation of 2-methyl-4-phenyl-2-butanol (I) and 2-methyl-5-phenyl-2-pentanol (II) in the presence of 85% D₂SO₄ has been studied. The product 1,1-dimethylindane(III) is shown to contain deuterium in both aromatic ring and polymethylene fragment, whereas 1,1-dimethyltetralin (IV) contains deuterium only in the aromatic ring. A probable mechanism of the reaction is discussed.

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2--4--2- (I) 2--5--2- (II) 85% D₂SO₄. , 1,1- (III) , 1,1- (IV) . .