Some remarks on the solubility of gases in liquid long-chainn-alkanes andn-alkan-1-ols

The Ostwald coefficients L_2,1 of He, Ne, Ar, Kr, Xe, N₂, O₂, CH₄ CF₄ and SF₆ dissolved in several homologous_n-alkanes,_n-C₁H₂₁₊₂, 6l16, andn-alkan-1-ols,n-C₁H₂₁₊₁OH, 1l11, were recently measured at 298.15 K and atmospheric pressure with a modified Ben-Naim/Baer apparatus. Altogether, 201 gas/liquid systems were investigated. For about half of these systems, both pressure control and measurement of the volume of gas dissolved in a given volume of solvent were achieved with a microprocessor. This improved medium-precision instrument (0.5% in most cases) combines easy handling with fully automated data retrieval, and is totallymercury-free. In this communication, the salient points of data reduction are presented, with the focus on the estimation of several important auxiliary quantities such as second virial coefficients and partial molar volumes at infinite dilution. The effect of the chain lengthl of then-alkane or then-alkan-1-ol upon solubility is demonstrated, and some correlations betweenL _2,1, or the derived Henry fugacitiesH _2,1, and appropriate molecular and/or bulk properties of the gases and the solvents are discussed.     

Correlation of the Prigogine-Flory theory with isothermal compressibility and excess enthalpy data for cyclohexane + alkane mixtures

The Prigogine-Flory theory is applied to isothermal compressibilities, at 25, 35, 45 and 60°C and to heats of mixing at 25°C for cyclohexane + n-alkane systems. To this purpose, the van der Waals and the Lennard-Jones potentials have been adopted. The energy parameter ₁₂ has been calculated from the experimental data, and its dependence on the n-alkane number of carbons has been studied. Taking the ₁₂ value obtained for the equimolecular mixture, the excess functi¹/ns (V^E/P)_T, H^E and V^E have been calculated and the results compared with experimental values.     

Schrödinger Equation Solutions for the Central Field Power Potential Energy II. V(r) = −V 0(r/a 0)2ν−2, 0 ≤ ν ≤ 1, the Bound States

The bound states of the generalized Schrödinger equation system with radial potential energy V(r) = –V ₀(r/a ₀)^2–2, 0 1, are described. The solutions of the differential equation are related to the functions for the bound state problem with 1. The Green's function is constructed as well as its first iteration, the traces of both functions are calculated, and an upper and lower bound for the ground state is established. A WKB-like approximate solution for the eigenvalues and eigenfunctions is derived.     

Diatomic interactions in momentum space. The 2pπ u and 3dπ g states of H 2 + system

The recently proposed method of momentum electron density for interatomic interactions is applied to the two states of the H ₂ ⁺ system. The processes of the attractive 2P _u and repulsive 3d _g interactions are analysed based on the behaviour of the momentum density and Compton profile. The results are compared with the previous ones for the 1 _{S g} and 2p _u states. The guiding principle of contraction and expansion for the energy-density relation in momentum space is shown to be common to both the and states.     

Fossil age determination by thermal analysis

Subsequent to a comparative examination of recent bone material the author has recently completed the paleobiogeochemical evaluation of classical Quaternary and Pliocene terrestrial fossils of vertebrata from Hungary. A derivatograph (MOM) has been used to determine two thermoanalytical parameters which are closely associated with the passage of geological time: the total bound organic-matter content of the fossil and the fossilization cofficient.Derivatographic measurement of the organic matter in the bones is supplemented by fine-structure analysis of bone-tissue slides.Sample material of unknown age from several provenances was evaluated with the new dating method. The importance of the procedure is even greater in cases when only indefinite sporadic finds can be obtained from the sediments.

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Zusammenfassung Nach einer vergleichenden Untersuchung an neuzeitlichem Knochenmaterial hat der Autor kürzlich die paleobiogeochemische Auswertung der klassischen Quaternären und Pliocenen terrestren Fossilien von Vertebraten aus Ungarn ergänzt.Ein Derivatograph (MOM) wurde zur Bestimmung zweier thermoanalytischer Parameter eingesetzt, die eng mit dem Fortschreiten der geologischen Zeit verbunden waren: dem Gesamtgehalt an gebundenem organischem Material und dem Fossilisationskoeffizienten.Die derivatographische Messung der organischen Substanz in den Knochen wurde durch die Feinstrukturanalyse von Knochengewebeschnitten ergänzt.Probenmaterial unbekannten Alters verschiedener Herkunft wurde mit der neuen Methode ausgewertet. Die Bedeutung des Verfahrens ist in den Fällen noch grösser, wenn aus den Sedimenten nur unbestimmte sporadische Funde erhalten werden können.

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, . (MOM) , : . - . . , .

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The author wishes to thank the staff of the Department of Experimental Physics of L. Kossuth University for the neutron activation measurements and the Computer Center of the University for the calculation work.     

Kinetics of the thermal decomposition of alkaline earth metal hydrofluorides

The thermal stability of alkaline earth metal hydrofluorides was studied by means of a Derivatograph. The values of the activation energy, reaction order and rate constant were determined. The comparison of the kinetic parameters of the decomposition process for the complete series of hydrofluorides studied led to a certain regularity in the differences in their thermal stabilities and its correlation with the strength of the hydrogen bond in their structure.

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Zusammenfassung Die thermische Stabilität von Erdalkalihydrofluoriden wurde mit Hilfe eines Derivatographen untersucht, die Werte der Aktivierungsenergien, der Reaktionsordnung und der Geschwindigkeitskonstanten bestimmt. Der Vergleich der kinetischen Parameter des Zersetzungsvorganges wies auf eine gewisse Regelmäßigkeit in ihrer verschiedenen thermischen Stabilität, die in Zusammenhang mit der Stärke ihrer strukturalen Wasserstoffbindung steht.

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Résumé On a étudié la stabilité thermique des hydrogénofluorures des métáux alcalinoterreux et déterminé les valeurs des énergies d'activation, des ordres de réaction et des constantes de vitesse de réaction à l'aide d'un Dérivatographe. Après comparaison des paramètres cinétiques on a pu établir une certaine régularité dans le changement de la stabilité thermique en corrélation avec la force de liaison de l'hydrogène dans la structure.

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. , . .

     

Kinetics and mechanism of redox reactions of U(III) ions with 2-chloro and 2-bromopropanoic acids

The kinetics and mechanism of redox reactions of U³⁺ ions with 2-chloro and 2-bromopropanoic acids were studied. The influence of pH led to the determination of the rate constants corresponding to two parallel steps. The influence of binary mixtures on the reaction rate was followed. The kinetic results for halogen-substituted carboxylic acids forming an isokinetic series have been compared.

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U⁺³ 2-- 2- . pH . . , .

     

Dinuclear Complexes Contributing to Softness of Metal Acceptors

Since emf measurements with amalgam electrodes have been used, in most studies of the stabilities of complexes between soft metal acceptors and halide ions a series of investigations of the kinetics of electrode reactions were accomplished with halide systems of metal ions in the Groups 11 and 12 in aqueous and/or DMSO solutions. The aim was to establish which complexes contribute to the exchange current density, i _o. Such measurements are found to be a very sensitive method for identifying dinuclear complexes that can display much higher charge transfer rate constants than mononuclear complexes can. From these results it can be stated that hard acceptors do not show any tendency to form dinuclear halide complexes, whereas soft acceptors are apt to do so. This fact leads to the conclusion that dinuclear complexes have a strong internuclear bond. In determinations of the overall stability constant _j of a complex ML _j there is an influence from a complex M₂L _j with a constant _j , resulting in the substitution of _j for ( _j + 2a _{j j} ), where a _j = [M] when the ligand number n = (C _L – [L])/C _M has the value j. An approximate value of the association constant, K _ass, of the internuclear bond can be calculated from _j if _j is known. On the basis of these measurements the most probable types of the internuclear bonds are discussed.     

Thermal decompositions of kaolinite intercalation compounds

Through a combination of X-ray diffraction and thermal analysis (simultaneous TG-DTG-DTA and quasi-isothermal TG), it was shown that the molar ratio intercalation agent/kaolinite in all intercalation compounds is approximately 1. In a saturated atmosphere of the corresponding intercalation agent, the intercalation compounds are stable up to more than 150 °C.Decomposition of the potassium acetate intercalation compound proceeds simultaneously with the dehydroxylation of kaolinite at an extrapolated onset temperature of 360 °C. The high-temperature reactions (dehydroxylation and transformation) of kaolinite obtained through the decomposition of intercalation compounds with volatile intercalation agents depend on the conditions applied during decomposition.

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Zusammenfassung Mittels Röntgenbeugung und thermischer Analyse (simultane TG-DTG-DTA und quasi-isotherme-quasi-isobare TG) konnte gezeigt werden, daß das molare Verhältnis Einlagerungsmedium/Kaolinit in allen Einlagerungsverbindungen etwa 1 ist. In gesättigter Atmosphäre des jeweiligen Einlagerungsmediums ist die Einlagerungsverbindung stabil bis über 150 °C. Die Zersetzung der Kaliumacetat-Einlagerungsverbindung läuft zusammen mit der Dehydroxylation des Kaolinits bei einer extrapolierten onset-Temperatur von 360 °C ab. Die Hochtemperaturreaktionen (Dehydroxylation, Phasenneubildung) von Kaolinit, der aus der Zersetzung von Einlagerungsverbindungen mit flüchtigen Einlagerungsmedien erhalten würde, werden von den Zersetzungsbedingungen beeinflußt.

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- ( , , ) , - 1. , , 150°. — ** 360°, ** . , , .

     

Molecular Recognition Based on Roof-shaped Diol Hosts. X-Ray Crystal Structures of Inclusion Compounds with Methanol, Pyridine and Toluene

Three crystalline inclusion compounds of roof-shapedtrans-11,12-bis(diaryl-hydroxymethyl)-9,10-dihydro-9,10-ethanoanthracene host molecules [where aryl is 4-methyl-phenyl (3) or4-t-butylphenyl (4)] have been studied by X-ray diffraction.The crystals of both the 3methanol (2 : 1) [a = 10.755(1),b = 11.571(1), c = 14.697(2) Å, = 75.12(1), = 89.67(1), = 87.13(1) °] and the 4-pyridine (2 : 3) compounds[a = 14.045(3), b = 14.366(3), c = 15.607(3) Å, = 91.62(1), = 103.65(1) and =116.05(1)°] are triclinic (P–1),while the 3toluene (1 : 1) complex has orthorhombic (Fddd) symmetry [a = 16.041(1), b = 25.008(1), c = 40.440(4) Å]. The host–guest interactions in both triclinic crystals are characterised by hydrogen bonds, with different patterns however. The determined crystal structures indicate a compromise between the requirement of hydrogen bonding on the one hand and close packing on the other. The highly symmetrical host framework in the toluene (1 : 1) complex of 3 seems to be the result of shape recognition, although atendency towards weak (C_methyl)H _arylinteractions [C_methyl = 3.533(7) and 3.674(6) Å] between the hosts was observed. The present roof-shaped diol hosts give excellent examples of molecular recognition by exhibiting two significantly different conformations, mostly depending on the proton donor/acceptor ability of the guest component. (O)H O intramolecular bonding between the two alcoholic groups characterises the so-called active form, whereas weaker (O)H and interactions stabilise the `inactive'conformation.     

Thermal and some other properties of the complexes crystallizing from the system Ni(II)-en-[Ni(CN)4]2−-H2O

Seven complex compounds exhibiting the compositions Ni(en)₃Ni(CN)₄·H₂O (I), Ni(en)₃Ni(CN)₄ (II),-Ni(en)₂Ni(CN)₄ (III), Ni(en)Ni(CN)₄·2H₂O (IV), Ni(en)Ni(CN)₄ (V), Ni(en)₂Ni(CN)₄ · 2.5H₂O (VI) and-Ni(en)₂Ni(CN)₄ (VII) were prepared from the system Ni-en-[Ni(CN)₄]^2–-H₂O. These compounds were examined by the methods of infrared spectroscopy, X-ray powder diffractometry, UV-VIS reflectance spectroscopy, and also by the measurement of magnetic moments. The thermal stability, the stoichiometry of thermal decomposition and the mutual transformations were investigated with a derivatograph. The reactions proceeding according to the following schemes were observed if the system was heated to appropriate temperature: (I)(II)(III)(V)(IV) and (VI)(VII)(III)(V)(IV) Process (VII)(III) represents isomerization. The reversibility of the process (V)(IV) is due to the high hygroscopicity of the anhydrous complex. The changes in structure in the course of the individual processes are discussed.

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Zusammenfassung Aus einem System Ni-en-[Ni(CN)₄]^2–-H₂O wurden sieben Komplexe der Formeln Ni(en)₃Ni(CN)₄·H₂O (I), Ni(en)₃Ni(CN)₄ (II),-Ni(en)₂Ni(CN)₄ (III), Ni(en)Ni(CN)₄·2H₂O (IV), Ni(en)Ni(CN)₄ (V), Ni(en)₂Ni(CN)₄ · 2.5H₂O (VI) und-Ni(en)₂Ni(CN)₄ (VII) hergestellt. Diese Verbindungen wurden mittels IR-Spektroskopie, Röntgenpulverdiffraktometrie, UV-Reflexionsspektroskopie und durch Messungen des magnetischen Momentes untersucht. Die Wärmestabilität, die Stöchiometrie des thermischen Zerfalles und die gegenseitigen Umwandlungen wurden mittels eines Derivatographen untersucht. Wird das System auf geeignete Temperaturen erhitzt, kann der Reaktionsverlauf durch folgendes Schema dargestellt werden: (I)(II)(III)(V)(IV) und (VI)(VII)(III)(V)(IV).Der Prozeß (VII)(III) verkörpert eine Isomerisierung. Die Umkehrbarkeit von Prozeß (V)(IV) ist auf die ausgeprägten Hygroskopieeigenschaften des wasserfreien Komplexes zurückzuführen. Es werden die im Ablaufe der einzelnen Prozesse vorgehenden Strukturveränderungen besprochen.

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Ni- -[No(N)]² -₂ Ni(en)₃Ni(CN)₄ · ₂ (I), Ni(en)₃Ni(CN)₄ (II),-Ni(en)₂Ni(CN)₄ (III), Ni(en)Ni(CN)₄-2H₂O (IV), Ni(en)Ni(CN)₄ (V), Ni(en)₂Ni(CN)₄ · 2,5H₂O (VI) -Ni(en)₂Ni(CN)₄ (VII). , , - , . , . (I)(II)(III)(V)(IV) (VI)(VII)(III)(V)(IV). (VII)(III) . (V)(IV) . .

     

A novel synthesis of N-acetyl-α-d-fucosamine 1-phosphate and uridine 5"-diphospho-N-acetyl-α-d-fucosamine

In connection with studies on the biosynthesis of capsular polysaccharides from Staphylococcus aureus, a new synthesis of uridine 5"-(2-acetamido-2,6-dideoxy--d-galactopyranosyl diphosphate) (uridine 5"-diphospho-N-acetyl--d-fucosamine) using 2-azido-3,4-di-O-acetyl-2,6-dideoxy--d-galactopyranosyl nitrate as the key intermediate was carried out. The reaction of this product with cesium dibenzyl phosphate smoothly affords the corresponding -glycosyl dibenzyl phosphate, which undergoes anomerization on treatment with BF₃·Et₂O and 2-bromopyridine to give -glycosyl dibenzyl phosphate in high yield. This product was then transformed into 2-amino-3,4-di-O-acetyl-2,6-dideoxy--d-galactopyranosyl phosphate, subsequently converted into 2-acetamido-2,6-dideoxy--d-galactopyranosyl phosphate and the target nucleoside diphosphate sugar.     

Lewis-Base Adducts of Group 11 Metal(I) Compounds. LXXVI Structural Studies in the Copper(I) Halide : Norbornadiene System

The structural characterizations of some copper(I) halide (CuX) adducts with norbornadiene (nbd) are recorded. CuCl : nbd (1:1)₄ (a redetermination), (2:1)_2(|), are systems both based around Cu₄Cl₄ cubane-type cluster arrays. CuBr : nbd (7:3)_(|)( 0.5 MeOH), a complex polymer with 3-symmetry, is believed to be the complex previously described as an adduct of 2:1 stoichiometry. Attempts to obtain an iodide counterpart have resulted in the definition of an ephemeral adduct CuI : MeCN (3:2)_(|). 0.5 C₇H₈ in which, remarkably, the nbd is uncoordinated; the complex is a polymer, related to the [AgX(quinoline)]_(|) (X = Cl, Br) saddle polymer.     

XPS studies of Cu-Cr catalyst deactivation in catalytic heat generators

Changes in the valence state of transition metal cations on the CuCr₂O₄/–Al₂O₃ catalyst under its deactivation in catalytic heat generators have been studied by the XPS method. Partial reduction of the catalyst active component has been revealed. It has been established that a freshly prepared catalyst contains Cr(VI) that is most likely responsible for its high initial activity.

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CuCr₂O₄/–Al₂O₃ (). , . , Cr(VI), .

     

Catalytic activity of perovskite-type oxides LaMeO3

Catalytic activities for CO oxidation of a series of LaMeO₃(Me³⁺=V³⁺, Cr³⁺, Mn³⁺, Fe³⁺, Co³⁺, Ni³⁺) perovskite-type oxides were measured. Maxima for Mn³⁺ and Co³⁺ were found. The relation between local symmetry of solid surfaces and chemisorption and catalysis is discussed.

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, LaMeO₃ (Me⁺³=V⁺³, Cr⁺³, Mn⁺³, Fe⁺³, Co⁺³, Ni⁺³) CO. Mn⁺³ Co⁺³. , .

     

Décomposition thermique du sulfite de fer(II) anhydre

Résumé Sous azote ou sous vide, le sulfite ferreux anhydre se décompose vers 210° en magnétite, pyrite et dioxyde de soufre. Concurremment une réaction de dismutation intervient avec formation de FeSO₄, Fe₃O₄ et FeS₂. Lorsque la température atteint 320°, la pyrite et le sulfate réagissent ensemble pour donner Fe_1–xS, Fe₃O₄ et SO₂. Au-delà de 370° le sulfure ferreux non-stchiométrique commence à réagir à son tour avec le sulfate restant pour former de la magnetite et du dioxyde de soufre.

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In nitrogen or under vacuum, anhydrous iron(II) sulfite decomposes near 210° to magnetite, pyrite and sulfur dioxide. A parallel disproportionation reaction occurs with formation of FeSO₄, Fe₃O₄ and FeS₂. When the temperature reaches 320°, pyrite and sulfate react together to give Fe_1–xS, Fe₃O₄ and SO₂. Above 370° the non-stoichiometric ferrous sulfide begins to react with the remaining sulfate to give magnetite and sulfur dioxide.

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Zusammenfassung Unter Stickstoff oder im Vakuum zersetzt sich das wasserfreie Eisen(II)-sulfit in der Nähe von 210 °C zu Magnetit, Pyrit und Schwefeldioxid. Parallel hierzu findet eine Disproportionierung unter Bildung von FeSO₄, Fe₃O₄ und FeS₂ statt. Wenn die Temperatur 320 °C erreicht, reagieren Pyrit und Sulfat unter Bildung von Fe_1–xS, Fe₃O₄ und SO₂ Oberhalb von 370 °C beginnt das nichtstöchiometrische Eisensulfit seinerseits mit dem restlichen Sulfat zu reagieren um Magnetit und Schwefeldioxid zu ergeben.

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(II) 210° , . FeSO₄, Fe₃O₄ FeS₂. 320°, , Fe_1–xS, Fe₃O₄ SO₂. 370° .

     

Dynamic shear modulus in the splitting region of poly(alkyl methacrylates)

A systematic study of the dynamic shear modulusG ^*=G+G in three poly(alkyl methacrylates) (PEMA, PnPMA, PnBMA) at frequencies between 0.001 and 500 rad/s is presented. As the splitting frequencies _s are low, aging effects can be observed in the splitting region. There is a systematic shift of the splitting frequency _s to lower values with increasing length of the alkyl side group. In PnBMA a separate shear appearance is observed about two frequency decades below the local mode . This is discussed in terms of the concept of minimal cooperativity. Aging effects are: Shift of the maximum loss frequency to lower values, peak sharpening of the relaxation, and intensity changes of and . These effects are discussed in terms of the sequential aging concept. Aging leads to a pronounced bending of the traces upwards from the equilibrium line in the Arrhenius diagram. These non-equilibrium phenomena are promoted by the small slope m=d(log )/dT of the trace in the splitting region.Dedicated to Prof. E. W. Fischer at the occasion of his 65th Birthday Lieber Herr Fischer, die Hallenser Polymerphysiker danken Ihnen aufrichtig für die warmherzige und effektive Förderung der Polymerwissenschaften im Raum Halle-Merseburg.     

Temperature dependence of the volumetric properties of binary mixtures containing oxaalkane +n-heptane

Excess molar volumes of mixtures of n-heptane + 2,5-dioxahexane and n-heptane + 2,5,8-trioxanonane were determined from density measurentents at 5, 15, 25 and 35°C. These results allowed the following mixing quantities to be reported in all range of concentrations: , (v ^E /T) _P and (h ^E /P) _T , at 25°C. The obtained values were then compared with the calculated values by using the Flory theory and the Nitta-Chao theory of liquid mixtures. The results are discussed in terms of order or disorder creation.     

Reduction of CuO-containing catalysts, CuO: I: TPR and TGA

For CuO/ZnO reduction has been shown [M. S. W. Vong et al., Catal. Lett.,4, 15 (1990)] to be faster and more extensive with CO than by H₂ and here this is shown to be the case for CuO itself, this being so then it may be preferable to characterize CuO-containing catalysts by temperature-programmed reduction with CO than with H₂. The activation energies of reduction (57–82 kJ/mol) are those expected for chemical reduction, but it is an important finding that the order with respect to hydrogen partial pressure (0.04) is extremely low and far removed from the value of unity often assumed. Different samples of CuO exhibit different reduction characteristics.

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CuO/ZnO, (Vong, M. S. W. et al., Catal. Lett. (in press)), CO, H₂. , CuO. CO , CuO, . Cu₂O , . . . (57–82 /) , . ,

     

Thermal decomposition of zirconyl oxalates

Conditions for the preparation of stoichiometric barium zirconyl oxalate heptahydrate (BZO) have been standardized. The thermal decomposition of BZO has been investigated employing TG, DTG and DTA techniques and chemical and gas analysis. The decomposition proceeds through four steps and is not affected much by the surrounding gas atmosphere. Both dehydration and oxalate decomposition take place in two steps. The formation of a transient intermediate containing both oxalate and carbonate groups is inferred. The decomposition of oxalate groups results in a carbonate of composition Ba₂Zr₂O₅CO₃, which decomposes between 600 and 800° and yields barium zirconate. Chemical analysis, IR spectra and X-ray powder diffraction data support the identity of the intermediate as a separate entity.

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Zusammenfassung Die Bedingungen für die Herstellung von stöchiometrischem Barium-zirconyl-oxalat Heptahydrat (BZO) wurden standardisiert. Die thermische Zersetzung von BZO wurde unter Einsatz der TG-, DTG- und DTA, sowie der chemischen und Gasanalyse untersucht. Die Zersetzung verläuft über vier Stufen und wird von der umgebenden Gasathmosphäre nicht besonders beeinflusst. Sowohl die Dehydratisierung als auch die Oxalatzersetzung erfolgt in zwei Stufen. Die Bildung einer intermediären Übergangsverbindung mit sowohl Oxalat- als auch Carbonatgruppen wirken hierbei mit. Die Zersetzung der Oxalatgruppen ergibt ein Carbonat der Zusammensetzung Ba₂Zr₂O₅CO₃, das zwischen 600 und 800° zersetzt wird und Bariumzirconat ergibt. Die Angaben der chemischen Analyse, der IR-Spekren und der Röntgen-Pulver-Diffraktion unterstützen die Identität der Intermediärverbindung als eine separate Einheit.

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Résumé On a standardisé les conditions de préparation de l'oxalate heptahydraté de zirconyle et de baryum (BZO) stoechiométrique. On a étudié la décomposition thermique de BZO par TG, TGD et ATD ainsi que par analyses chimiques et analyses des gaz. La décomposition a lieu en quatre étapes et n'est pas trop influencée par l'atmosphère ambiante. La déshydratation et la décomposition de l'oxalate ont lieu en deux étapes. Il se forme un composé intermédiaire de transition contenant à la fois les groupes oxalate et carbonate. La décomposition des groupes oxalate fournit un carbonate de composition Ba₂Zr₂O₅CO₃ qui se décompose entre 600 et 800° pour fournir du zirconate de baryum. L'analyse chimique, les spectres IR et la diffraction des rayons X sur poudre, apportent les preuves de l'existence d'un composé intermédiaire comme entité séparée.

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() . , , . . . , . Ba₂Zr₂O₅CO₃, 600–800 c . , .

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The authors express their sincere thanks to Professor A. R. Vasudevamurthy for his keen interest and constant encouragement. One of us (TG) is grateful to the Council of Scientific and Industrial Research, India, for the award of a research fellowship.