Volume 38, Issue 5

Upper and lower bounds on the eigenvalues of Schrödinger operators with simple one and a simple three dimensional potential (well of finite depth, spherical δ-potential) are given by means of a modification of Müller′s variational principle. The estimates, comparing them with the exact eigenvalues, show a localization of the eigenvalues even in a rough approximation for the trial operator.

It is shown that the physical mechanism of thermally activated subcritical crack growth is always a stochastic process and leads, therefore, to probabilistic crack propagation. This process is the result of the random breaking of atomic bonds and has to be clearly distinguished from the well known Weibull distribution. A Markov chain analysis leads to the normal distribution of crack sizes. The results demonstrate that conventional deterministic finite life-time designs are unsatisfactory and can lead to early failure of machine or structure elements as the consequence of the probabilistic process of crack propagation. The conclusions lead to the reliability analysis of Part II.

Debye-Waller factors at different temperatures of four alkali and three noble metals have been computed on the basis of a screened shell phenomenological model. The theoretical values are compared with existing experimental data. Particularly for lithium and potassium, most recent experimental information has been included. A critical examination of the results reveals a satis­factory agreement between the theoretical and experimental findings.

The low Q structure factors have been determined in the region down to Q = 0.08A -1 for liquid Na, K, Rb, Cs, Mg, Ca, Sr, Ba, Al and In at several temperatures by x-ray diffraction with the transmission mode. The low- Q structure factor is a slowly increasing function of Q, and its profile is quite similar among the liquid metals presently investigated. The long wavelength limit value of S(Q) derived from the present experimental structural data agrees well with that calculated from the isothermal compressibility for seven metals near the melting point. A differ­ence larger than 10% was found in the cases of liquid Cs, Ca and Al.

Diffusion and ionic conduction in pure 1:1 molten salts is described by an incomplete-disso­ciation model comprising neutral diatomic molecules and monoatomic ions. The internal mobility b +- and the self-diffusion coefficients D + and D - are given in terms of the six inter­particle friction coefficients and the degree of dissociation. By an approximation it is possible to derive from experimental D+ and D- values an apparent degree of dissociation which ranges from 0.93 for NaCl to 0.51 for TlCl and decreases with temperature.

Effective volumes, moments of inertia and Debye relaxation times in the excited state were determined for some oxido-substituted p-oligophenylenes by the method of fluorescence depolarization in nonpolar and polar solvents of different viscosities.

The kinetic energy released in the unimolecular decomposition of some metastable transitions has been investigated. It was found to have a significant temperature dependence in cases of H‘ loss from molecular ions. This is attributed to the tunelling of H • atom through the centrifugal barrier. The activation energies of the reverse reactions “ε r ≠ ” and the kinetic energy released “T B ” have been determined for the loss of H • from acetonitrile and elimination of HCN from benzonitrile. The partitioning energy quotients q=T B /ε r ≠ are found = 0.91 and 0.58 for acetonitrile and benzonitrile respectively.

The near infrared absorption of pure n-heptane between 5000 cm -1 and 6500 cm -1 was measured up to 250 °C and to pressures of 2000 bar. The procedure for measuring vibrational intensities at high pressures and temperatures with a precision of better than ± 1% is described. The integrated “molar absorptivity of the combination mode v a + v s of the methylene stretching fundamentals turns out to be independent of temperature and density. This offers important applications for high-pressure high-temperature thermodynamic and kinetic studies via quanti­tative near infrared spectroscopy.

The scattering of X-rays from a concentrated Ce(NO 3 ) 3 aqueous solution has been measured and analyzed. The experimental correlation function appears to be mainly characterized by the hydration of the cation: peaks at about 2.55 and 4.65 Å. Good agreement with experimental data is achieved through a model in which the Ce(III) ions have a first and a second hydration shell and also the nitrate group is considered hydrated. Complex formation between cation and anion is confirmed by using Raman spectroscopy.

The earlier suggested energy-level model based on an orbital singlet ground state for 3d 6 and 3d 4 ions at trigonal sites with large triclinic distortion is adopted to develop the single-ion theory of magnetic anisotropy. The Hamiltonian consisting of eight spin Hamiltonian terms and the molecular field is solved by perturbation theory. The resulting energies E Ms with M S = 0, ± 1, ± 2 are applied to calculate the free energy for Fe 2+ ions in Si- or Ge-substituted yttrium iron garnets where a uniform distribution of Fe 2+ ions over the 12 inequivalent sites is assumed. It turns out that the first two cubic anisotropy constants K 1 , and K 2 are insufficient to describe the anisotropy at high temperatures in the present model. By a least-squares method it is established that the anisotropy expansion series can be terminated at the fourth-order term for the present model. Thus K 1 , K 2, K 3 and K 4 are derived analytically in terms of the free energy for some choosen directions of magnetization. The analytical results agree very well with the correspond­ing ones obtained by the least-squares method. The temperature dependence of K i, i = 1. 2, 3, and 4, is calculated for a wide range of the spin Hamiltonian parameters (B q (k) ) and the molecular field (h). The theoretical K 1 , and K 2 are fitted to the experimental values of K 1 , and K 2 at low temperatures obtained by neglecting the higher-order anisotropy terms, to get the values of B q (h) and for YIG:Si and YIG:Ge. A comparison of the present results with The corresponding ones of the previous doublet model, is also discussed. The theoretical account of the experimentally observed temperature dependence of the ratio K 2 /K 1 for Fe 2+ in YIG:Ge speak in favour of the present model rather than the doublet model. The change in sign of K 1 observed for Fe 2+ in YIG:Si, which could not be explained by the doublet model with uniform distribu­tion of Fe 2+ ions, is well accounted for by the present model. The recently observed spin reorientation in YIG:Si can also be explained by the present model without resorting to a nonuniform distribution of Fe 2+ ions required by the previous model. This study indicates that the higher-order constants K 3 and K 4 are significant at high temperatures according to the present model, whereas at low temperatures according to the doublet model. Hence an experimental determination of K 3 and K 4 over a wide temperature range may provide a test of the applicability of the two models.

Far infrared, infrared and Raman spectra of tin hexathiohypodiphosphate Sn 2 P 2 S 6 (mono­clinic modification II) have been recorded. The observed frequencies are assigned on the basis of P 2 S 6 4- units with C 2h symmetry in the crystal. The assignment is supported by the correlation D 3d (dissolved P 2 S 6 4- ion) → C 2h . DTA-data have been determined and interpreted.

Four aqueous solutions of Ni(NO 3 ) 2 of concentrations ranging from 0.5 M to 4.0 M were examined by the EXAFS technique. The isolation and analysis of of the peak corresponding to the first coordination shell of the metal ion shows that the Ni 2+ ion is surrounded by about 6 water molecules at a distance of about 2.06 Å.

A complete assignment of previously reported vibrational spectra of the TcOX 4 - (X = Cl, Br, I) anions is proposed. Based on this assignment, force constants and mean amplitudes of vibration are evaluated and the most prominent aspects of the vibrational behaviour and structural charac­teristics of these species are discussed.

The absorption spectra of hydroxyindoles are calculated by means of the PPP and INDO/S-CI methods. The results of the PPP calculations are analyzed in terms of molecular subunits using the parsorbital method, similarity measure and configuration analysis. These methods show that the electronic states of the hydroxyindoles are best described by fragmentation in indole + hydroxyl groups. On the basis of this fragmentation the bathochromic shift of the first absorption band of 5- and 6-hydroxyindole as compared to 4- and 7-hydroxyindole and indole itself can be explained by the contribution of the charge transfer configuration from the hydroxyl group to the locally excited indole state.

The temperature dependence of the ESR spectra of 4-[(Mono-rsp. Di-organyl-amino)-methyl]- 2.6-di-tert.-butyl-phenoxyls is studied. The observed coalescence behaviour of the hfs-parameters of the methylene protons is interpreted by N-inversion in the amine group. Thus it is shown that the μsec time scale of ESR makes it possible to study these processes near ambient temperatures. Evaluation of rate constants and activation parameters was done by computer simulation of the DESR spectra. Comparing these values with those given by DNMR methods at low temperatures show that the radical state of the molecule has no significant effect on the inversion rate constants.

The dissociation constants and the equivalent conductances of 2,4-dinitrobenzoic acid and D-10-camphosulfonic acid have been determined in water-methanol mixtures at 25 °C. The experimental data have been analyzed with the “Fuoss 78” conductance equation. The Bjerrum critical distance was accepted instead of Gurney’s cosphere diameter. Values of K A and Λ 0 are reported.

A Wiener-Hermite set of statistically orthogonal random functions in phase space is introduced for investigation of electrostatic plasma turbulence. Expansions of the random distribution functions in terms of the random base are considered and the equations governing the dynamics of the deterministic Wiener-Hermite Kernels are derived.

We investigated the microwave spectrum of ethyliso-thiocyanate. CH 3 CH 2 NCS, for the nitrogen quadrupole coupling. The spectrum was first measured and assigned by Sakaizumi, Ohashi, and Yamaguchi [1]. By comparing the measured rotational constants with those resulting from an assumed structure they concluded that the synperiplanar (cis) form was measured.

The fluorescence spectra of Cr +3 in the presence of Nd +3 in glasses were studied. The “dips” observed in the spectra are interpreted as anti resonances due to Cr-Nd in­teraction.

The formation and decay of HȮ 2 and Ȯ 2 - transients was reinvestigated using oxygenated aqueous t-butanol solutions in the pH range from 1.5 to about 8. The ob­tained spectroscopic and kinetic characteristics of both superoxide radical forms are: for HȮ 2 λ max = 230 nm (ε 230 = 130 m 2 mol -1 ), 2k (HȮ 2 + HȮ 2 ) = (3.7 ± 0.2) x 10 6 dm 3 mol -1 and Ȯ 2 - λ max = 245 nm (ε 245 = 215 m 2 mol -1 ), 2k (Ȯ 2 - + Ȯ 2 - ) < 10 dm 3 mol -1 s -1 .

Photofragmentation of CH 2 J 2 and CHJ 3 by a pulsed laser beam (λ = 298 nm) was analysed with respect to the fragment energies (TOF distribution). From the angular distribution of the fragments shape factors b were deter­mined.

The diffusion of fluorine in KSn 2 F 5 has been studied by T 1 and T 2 relaxation time measurements of 19 F NMR (200-500 K) and pulsed magnetic Field gradient tech­niques (390-480 K). Near 423 K a sharp transition into the superionic state has been found, the fluorine diffusion increasing by a factor of 4 within a range of 3 K. Conduc­tivity measurements only show a change in the activation energy.

Direct PPP-type calculations of self-consistent (SC) density matrices for excited states are described and the corresponding “thawn” molecular orbitals (MO) are discussed. Special atten­tion is addressed to particular solutions arising in conjugated systems of a certain symmetry, and to their chemical implications. The U(2) and U(3) algebras are applied, respectively, to the 4- electron and 6-electron cases; a natural separation of excited states in different cases follows. A simple approach to the convergence problem for excited states is given. The complementarity relations, an alternative formulation of the pairing theorem valid for heteromolecules and non-alternant systems, allow some fruitful experimental applications. Together with the extended pairing relations shown here, they may help to rationalize general trends.