Simple functional-differential equations for the bound-state wave-function components

We present a new method of a direct derivation of differential equations for the wave-function components of identical-pariticles systems. The method generates in a simple manner all the possible variants of these equations. In some cases they are the differential equations of Faddeev of Yakubovskii. It is shown that the case of the bound states allows to formulate very simple equations for the components which are equivalent to the Schrödinger equation for the complete wave function. The components with a minimal antisymmetry are defined and the corresponding equations are derived.     

Thermodynamic properties of ternary semiconducting alloys

Using the new information supplied by extended-x-ray-absorption-fine-structure measurements and the results of our structural model, we compute the bond probability of a few ternary semiconducting III–V and II–VI alloys as a function of temperature and composition in the framework of a modified quasi-chemical approximation. We derive the thermodynamic functions of mixing, considering both elastic and chemical contributions to the bond energies. We examine how the deviation from the full randomness affects the ordering of such alloys and we construct the phase diagrams in the region of phase separation. Possible formation of ordered compounds at low temperatures is predicted.     

Structure and Thermal Stability of La0.10WO3+y; A Hexagonal Tungsten Bronze Related Phase Formed at High Pressure

The structure and thermal stability of a hexagonal tungsten bronze (HTB) related compound, La_xWO_3+y with x≈0.10 and y≈0.15, has been studied by X-ray diffraction, thermal analysis, and electron microscopy. The structure was refined by the Rietveld method from X-ray powder diffractometer data of a La_0.10WO₃ sample prepared at T=1250°C and P=25 kbar, which consisted of two tungsten bronze related phases in 1:1 proportion. The unit cell dimensions are as follows: La_0.108WO_3+y (y≈0.16), a=7.40890(5), and c=3.79329(4) Å (HTB-related structure); La_0.091WO₃, a=3.82458(6) Å (cubic perovskite tungsten bronze (PTB) structure). The lanthanum atoms in La_0.108WO_3+y are located on the hexagonal axis and statistically distributed on two sites close to the tungsten atom plane. Thermal stability studies of the La_0.10WO₃ sample in an argon atmosphere under ambient pressure conditions revealed that the HTB-related compound is metastable, decomposing to the stable PTB-type structure and WO₃. It was also found from the TG experiments in argon and oxygen that additional oxygen atoms (y) are present in the structure, thus forming a lanthanum tungsten oxide of the above composition. The electron diffraction and microanalysis studies confirmed that crystals of the HTB- and PTB-type structures were formed, with a lanthanum content of x≈0.1.     

Embedded cluster calculation of the Ce3+ impurity in Lu2SiO5 crystals including crystal lattice relaxation and polarization

Results of electronic structure studies of the Ce³⁺ impurity in Lu₂SiO₅ crystals allowing for lattice polarization and relaxation are given. The calculations were performed by the embedded cluster method combining the scattered wave and molecular static methods. The effect of lattice deformation induced by the defect on the results of calculations is discussed. Translated fromZhurnal Strukturnoi Khimii, Vol. 38, No. 6, pp. 1046–1052, November–December, 1997.     

An investigation of the structure of butadiene by high resolution infra-red and raman spectroscopy

The rotational Raman spectra of butadiene and butadiene-d₆ are found to consist of discrete lines having small ≈0·4 cm⁻¹) yet almost constant spacings, as would be expected for symmetric or nearly symmetric top molecules. An infra-red absorption band (Type C) of butadiene at 908 cm⁻¹ is observed to have a spacing of about 2·5 cm⁻¹. Both the Raman and infra-red spectra provide evidence for the trans structure of the butadiene molecule. From the rotational constants A″ and ″ the following structural parameters were obtained: C=C---C) = 122·9 ± 0·5° rC---C) = 1·47₆ ± 0·010 Å dy]somewhat shorter than recently determined from electron-diffraction experiments).     

Preparation-Proprietes physico-chimiques enthalpie de formation de l'hydrure d'aluminium AlH3α′

Résumé L'hydrure d'aluminium AlH₃- a été obtenu par action de LiAlH₄ sur AlCl₃ ou ZnCl₂ dans l'éther éthylique. La décomposition thermique a été étudiée par thermogravimé trie sous pression réduite (10^–2 torr). La capacité calorifique molaire à 298 K, l'enthalpie de décomposition, ainsi que l'enthalpie de formation ont été déterminées avec un microcalorimètre Calvet.

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Aluminium hydride,-AlH₃, was prepared by reaction of LiAlH₄ on A1C1₃ or ZnCl₂ in diethyl ether. Thermogravimetry was used to investigate its thermal decomposition under low pressure (10^–2 torr). The molar heat capacity at 298 K, the heat of decomposition, and the heat of formation, were measured with a Calvet microcalorimeter.

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Zusammenfassung Aluminiumhydrid AlH₃- wurde durch Einwirkung von LiAlH₄ auf AlCl₃ oder ZnCl₂ in DiÄthylether hergestellt. Die Thermo gravimetrie wurde zur Untersuchung der thermischen Zersetzung bei niedrigem Druck (10^–2 torr) herangezogen. Die molare WÄrmekapazitÄt bei 298 K, die Zersetzungsenthalpie sowie die Bildungsenthalpie wurden mit einem Calvet-Mikrokalorimeter bestimmt.

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— - l₃ LiAlH₄ ll₃ ZnCl₂ . (10^–2 ) . 298 , .

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Ce travail a été effectué dans le cadre d'un contrat de recherches passé par le laboratoire de Thermochimie Minérale avec la Direction des Recherches et Moyen d'Essai. Nous remercions bien vivement cet organisme de l'aide qu'il nous a apportée.     

Investigation of N-nitrohydrazines by the NMR method

Functionally substituted N-nitrohydrazines were studied by heteronuclear NMR. It was shown that all the investigated products from nitration of the trimethylsilyl derivatives of functionally substituted hydrazines contain the N-NO₂ fragment. The chemical shift of the nitrogen atoms of the hydrazine fragment in the¹⁵N NMR spectra and the spin-spin coupling constants were used as the main tests for structural identification. It was established that the number of recordable conformers decreases in the transition from the trimethylsilyl phenylhydrazine derivatives to the nitrohydrazines as a result of the conformational flexibility of the N(NO₂)CO fragment.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 9, pp. 2024–2031, September, 1991.     

Electronic structures and MCD spectra of trigonal Cr(III)S6 systems

MCD, electronic absorption, external heavy atom, and crystal field data are presented for the low energy region (² E _g, ² T _1g, ⁴ T _2g) and high energy region (² T _2g, ⁴ T _1g) of Cr(dtp)₃, Cr(dtc)₃, and Cr(exan)₃. At low energy, MCD intensities of ² E(² E _g) and ² E(² T _g) are as large or larger than ⁴ T _2g, and the MCD technique is advantageous over electronic absorption in this respect. The MCD positions of ² E _g and ² T _1g are nearly the same for these molecules ( 13 kK and 13.6 kK) · ⁴ T _2g of this region appears trigonally split ( 500 cm^–1) in the MCD of dtp but to a smaller extent than in the electronic crystal spectrum of Lebedda and Palmer ( 600 cm^–1). MCD did not resolve such components for exan and dtc. The higher energy region includes ² T _2g and ⁴ T _1g, and the combined MCD and electronic absorption data of the three compounds taken together lead us to conclude the ordering ² A ₁(² T _2g)<² E(² T _2g)<⁴ E(⁴ T _1g). The potentially useful external heavy atom affect on the solution-observed electronic ² E and ⁴ E bands of Cr(dtp)₃ did not shed additional light on this order of E states. Finally, it is concluded that the order of ⁴ T _1g and ² T _2g cannot be decided from O _h crystal field calculations because of experimental uncertainties about choosing centers of gravity. In addition, ⁴ T _1g and ² T _2g are close together so that ordering ² E<⁴ E does not guarantee ² T _2g<⁴ T _1g. However, it can be concluded that the ratio C/B4 is not correct, whereas the larger 7<(C/B)<8 is consistent with the data of all three molecules because of small B parameters ( 0.4). Locating OO transitions may somewhat decrease C/B and Dq.

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Zusammenfassung In der vorliegenden Arbeit werden folgende Meßergebnisse mitgeteilt; MCD, elektronische Absorption, Einfluß eines äußeren schweren Atoms sowie Kristallfelddaten für den Bereich niedriger Energie (² E _g, ² T _1g, ⁴ T _2g) und den Bereich hoher Energie (² T _2g, ⁴ T _1g) von Cr(dtp)₃, Cr(dtc)₃ und Cr(exan). Bei niedriger Energie sind die MCD-Intensitäten von ² E(² E _g) und ² E(² T _1g) genau so groß, oder größer als ⁴ T _2g, und die MCD-Technik bietet Vorteile gegenüber der elektronischen Absorptionsmethode. Die MCD-Werte von ² E _g und ² T _1g sind für die genannten Moleküle etwa gleich ( 13 kK und 13,6 kK). ⁴ T _2g dieses Gebietes erscheint trigonal aufgespalten ( 500 cm^–1) bei MCD von dtp, aber in einem geringeren Maß als im elektronischen Kristallspektrum von Lebedda und Palmer ( 600 cm^–1) MCD löste solche Komponenten bei exan und dtc nicht auf. Der Bereich höherer Energie enthält ² T _2g und ⁴ T _1g, und aus der Kombination von Daten der MCD-Methode sowie der elektronischen Absorption schlossen wir auf die Anordnung ² A _1g(² T _2g)<² E(² T _2g)<⁴ E(⁴ T _1g). Der möglicherweise nützliche Effekt eines äußeren schweren Atoms auf die in Lösung beobachteten elektronischen ² E- und ⁴E-Banden von Cr(dtp)₃ brachte bezüglich dieser Anordnung der E-Zustände nichts Neues. Weiterhin wird gefolgert, daß die Ordnung von ⁴ T _1g und ² T _2g nicht aus O _h-Kristallfeldberechnungen entschieden werden kann, da experimentelle Unsicherheiten bezüglich der Wahl von Schwerpunkten bestehen. Außerdem liegen ⁴ T _1g und ² T _2g nahe zusammen, sodaß aus der Anordnung ² E<⁴ E nicht notwendig ² T _2g<⁴ T _1g folgt. Es kann jedoch gefolgert werden, daß das Verhältnis C/B4 nicht korrekt ist, während 7<(C/B)<8 konsistent mit den Daten aller drei Moleküle ist, da die B-parameter klein sind (0,4). Die Vokalisierung der OO-Übergänge könnten C/B und Dq etwas erniedrigen.

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Presented in part at the 161st American Chemical Society National Meeting, Los Angeles, California, March–April, 1971.

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NDEA Pre-Doctoral Fellow.