Vibrational property of the slow N 2 + ions deposited SiNx films

We have investigated vibrational properties of silicon-nitride films, SiN_x (0.3×1.33), produced by a non-thermal method using high-resolution electron energy loss spectroscopy. The results, based on a continuous random network model assuming a planar XY₃ vibrational bond unit, show that the Si-N bonds in the films closely resemble those in typical thermal silicon nitride although nitrogens occupy some metastable binding sites. We estimate force constants of the restoring forces for a Si₃N bond unit, which tend to increase gradually with increasing nitrogen content x. In particular, the central force constant k₁ for the in-plane stretching mode of silicon atoms varies with x in the range 297k331 N/M, larger than the theoretical value for a nitrogen atom imbedded in a pure Si crystal.     

On Average Properties of Inhomogeneous Fluids in General Relativity: Dust Cosmologies

For general relativistic spacetimes filled with irrotational dust a generalized form of Friedmann's equations for an effective expansion factor a _D of inhomogeneous cosmologies is derived. Contrary to the standard Friedmann equations, which hold for homogeneous-isotropic cosmologies, the new equations include the backreaction effect of inhomogeneities on the average expansion of the model. A universal relation between backreaction and average scalar curvature is also given. For cosmologies whose averaged spatial scalar curvature is proportional to a _D ^-2, the expansion law governing a generic domain can be found. However, as the general equations show, backreaction acts as to produce average curvature in the course of structure formation, even when starting with space sections that are spatially flat on average.     

On X-ray measurements of residual stresses in materials with lattice strain gradient

The non-linear distribution of lattice strain ³¹⁰vs sin² observed on the surface of a polished steel specimen can be interpreted by tri-axial stress state with surface components of stress tensor ₁₁(0)= ₂₂(0) and gradientsg ₁₁= ₁₁/T, g ₃₃= ₃₃/T. The distribution of experimental values is duscussed from the viewpoint of various ways of calculating ₁₁.The authors would like to thank Dr. J. Musil, D. Sc. of the Institute of Physics of Czechoslovak Academy of Sciences for kindly providing the samples which made possible this study.     

Kinetic theory of granular shear flow: Constitutive relations for the hard-disk model

A kinetic theory for the constitutive Theological relations of rapid granular shear flow of hard circular disks, characterized by a coefficient of restitutione and a surface roughness coefficient, is formulated. From a set of general constitutive equations for single-particle dynamical variables, the approximate expressions for the limit of small and large dimensionless dissipative parameterR _t are obtained. HereR _t is defined as the ratio /, where is the fluctuation of translational velocity from the mean flow velocity, is the diameter of a disk, and is the shear rate. At smallR _t the theoretical predictions can be compared with exact computer simulation results of granular dynamics that are also reported. The agreement between theory and simulation is better than expected; the present theory is accurate up to high packing density in this region ofR _t .     

The Phase Transition in Statistical Models Defined on Farey Fractions

We consider several statistical models defined on the Farey fractions. Two of these models may be regarded as spin chains, with long-range interactions, while another arises in the study of multifractals associated with chaotic maps exhibiting intermittency. We prove that these models all have the same free energy. Their thermodynamic behavior is determined by the spectrum of the transfer operator (Ruelle–Perron–Frobenius operator), which is defined using the maps (presentation functions) generating the Farey tree. The spectrum of this operator was completely determined by Prellberg. It follows that these models have a second-order phase transition with a specific heat divergence of the form C [ ln² ]^–1. The spin chain models are also rigorously known to have a discontinuity in the magnetization at the phase transition.     

Conformal field theories,representations and lattice constructions

An account is given of the structure and representations of chiral bosonic meromorphic conformal field theories (CFT's), and, in particular, the conditions under which such a CFT may be extended by a representation to form a new theory. This general approach is illustrated by considering the untwisted andZ ₂-twisted theories, () and respectively, which may be constructed from a suitable even Euclidean lattice . Similarly, one may construct lattices and by analogous constructions from a doubly-even binary code . In the case when is self-dual, the corresponding lattices are also. Similarly, () and are self-dual if and only if is. We show that has a natural triality structure, which induces an isomorphism and also a triality structure on . For the Golay code, is the Leech lattice, and the triality on is the symmetry which extends the natural action of (an extension of) Conway's group on this theory to the Monster, so setting triality and Frenkel, Lepowsky and Meurman's construction of the natural Monster module in a more general context. The results also serve to shed some light on the classification of self-dual CFT's. We find that of the 48 theories () and with central charge 24 that there are 39 distinct ones, and further that all 9 coincidences are accounted for by the isomorphism detailed above, induced by the existence of a doubly-even self-dual binary code.     

Three-Mode Entangled State Representation of Continuum Variables and Optical Four-Wave Mixing

We establish a new three-mode entangled state representation , of continuum variables, which make up a complete set. Using optical four-wave mixing and a beam splitter transform we can prepare , . Based on , a new number-difference--operational-phase uncertainty relation is established and the corresponding squeezing dynamics is discussed.     

An investigation of finite-size scaling for systems with long-range interaction: The spherical model

A method is suggested for the derivation of finite-size corrections in the thermodynamic functions of systems with pair interaction potential decaying at large distancesr asr ^{–d –} , whered is the space dimensionality and>0. It allows for a unified treatment of short-range (=2) and long-range (<2) interaction. The asymptotic analysis is illustrated by the mean spherical model of general geometryL ^d–d× ^d subject to periodic boundary conditions. The Fisher-Privman equation of state is generalized to arbitrary real values ofd, 0d. It is shown that the-expansion may be used to study the breakdown of standard finite-size scaling at the borderline dimensionalities.     

Measurement of the refractive index and optical absorption spectra of epitaxial bismuth substituted yttrium iron garnet films at uv to near-ir wavelengths

Refractive-index and optical-absorption spectra of Bi-substituted yttrium iron garnet films, epitaxially grown by liquid-phase epitaxy, have been measured in the spectral regime 0.26 m1.9 m by thin-film interference for 0.52 m and by ellipsometry for0.52 m. The Y_3–x–y Bi _x Pb _y Fe_5–z Pt _z O₁₂ films contain bismuth in the range Ox 1.42, lead in the range 0.01 y0.08 and platinum in the range 0.005<=z0.03. There is satisfactory coincidence between the results from ellipsometry and thin-film interference in the overlapping wavelength region. The materials investigated are the same as reported earlier from this laboratory in ter mof their magnetic and magnetooptic properties.     

Static and Vibrational Properties of Transition Metals

A model pseudopotential depending on an effective core radius but otherwise parameter free is proposed to study the equation of state by incorporating the s-d hybridization effects. Very recently proposed screening function due to Sarkar et al has been used to obtain the screened form factor. The equations of state for Cu, Ta, Mo, W and Pt have been studied up to the pressure of 1000 GPa. The vibrational properties such as phonon dispersion curves (in q and r space), phonon density of states, mode Grüneisen parameters, maximum frequency _max, mean frequency , ^21/2 = (/ ^-1)^1/2 and fundamental frequency ² and static properties such as dynamical elastic constants of rhodium and iridium are also calculated. The theoretical results are compared with experimental findings wherever possible. A good agreement between theoretical investigations and experimental findings has confirmed our formulation.     

ЗАВИСИМОСТЬ ПОЧЕРНЕ НИЯ ФОТОГРАФИЧЕСКОЙ ЭМУЛЬСИИ ОТ ЭНЕРГИИβ-ИЗЛУЧЕНИЯ

, - - . , - , , :³²P,³⁵S ⁹⁰Sr+⁹⁰Y.     

Some problems of quantum mechanics possessing a non-negative phase-space distribution function

In order to clarify physical consequences due to the presence of a set of auxiliary functions _k (q,t) in quantum mechanics with a non-negative phase-space distribution function, the simplest quantum-mechanical problems are solved. It is shown that _k (q,t) influence upon the results of a problem. Therefore it is supposed that _k (q, t) reflect some physical reality (subquantum situation), interacting with a mechanical system. In particular the subquantum situation determines the minimum coordinate and momentum uncertainties ((q)² and (p)²) as well as the coordinate distribution of a fixed system and the momentum distribution of a free system. These results provide the opportunity to formulate the notion of a stationary homogeneous isotropic subquantum situation. Supposing thatq andp are small an attempt is made to develop an approximate method of solutions (quasi-orthodox approximation). Energy spectrum of an electron in a hydrogen atom is found in the second order of this approximation.On leave of absence from Peoples' Friendship University, Chair of Theoretical Physics, 3, Ordjonikidze Street, B-302, Moscow, U.S.S.R.     

К процессам в электро дных оБластях в силъноточных кратк овременных электрических разря дах

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On processes in electrode spaces of short-time high-intensity electric discharges

The conditions and causes of the interrupted emission of the vapours of the material of short-time high-intensity electric discharge electrodes are discussed on the basis of earlier and new observations.

     

Vibrational study of the initial stages of the oxidation of Si(111) and Si(100) surfaces

Using high-resolution electron energy loss spectroscopy (EELS) the vibrations of Si(111) and Si(100) surfaces in the early stages of oxidation have been investigated. Three different stages of oxidation, the last being the formation of a thin layer of vitreous SiO₂ are identified when the surfaces are held at a temperature of 700K during the exposure with molecular oxygen. We show that also the first two stages involve atomic oxygen in bridging positions between silicon atoms. Small exposures at low temperatures (100 K) produce vibrational features of a different, possibly molecular, species. For higher exposures at the same temperature the spectrum again develops the characteristics of atomic oxygen and the molecular species eventually disappears. Exposure at room temperature leads to a mixture of atomic and molecular oxygen for smaller exposures and to purely atomic oxygen for exposures greater than 10² L. At room temperature even exposures as high as 10¹¹ L do not produce the spectrum of vitreous SiO₂. The same is found for the natural, room temperature grown, oxide layer on silicon wafers which we have studied by introducing the sample into the spectrometer through an air-lock. Annealing of the wafer to 700 K produced the characteristic spectrum of vitreous SiO₂. The results are discussed in comparison with previous work.     

ЛОКАЛЬНЫЕ КОЛЕБАНлЯ ДВУХАТОМНОЙ ЛлНЕЙНО Й ЦЕПОЧКл С ДЕФЕКТАМл

. n : , . npou u , n . n n npocm .     

Anti-parallel ferroelectric domains in surface space-charge layers of BaTiO3

It is shown on simplified models of a surface space-charge layer of a single crystal of BaTiO ₃ that in the surface region, in which the direction of the electric field is opposite to the direction of spontaneous polarization inside the crystal, anti-parallel domains can exist. The dimensions of these domains are determined. The use of the results obtained is proposed for interpreting the microrelief of the etch figures and for explaining the different phases of the polarization reversal process of a single-domain single crystal of BaTiO ₃.

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BatiO₃

BaTiO₃ , , , . . BaTiO₃.

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The author would like to thank J. Kaczer, Z. Málek and V. Dvoák of the Institute of Physics, Czechoslovak Academy of Sciences, for valuable remarks on this paper and H. Havlíková for carefully carrying out the numerical calculations.     

On the critical exponent for random walk intersections

The exponent _d for the probability of nonintersection of two random walks starting at the same point is considered. It is proved that 1/2<₂3/4. Monte Carlo simulations are done to suggest ₂=0.61 and ₃0.29.     

A matrix method for estimating the Liapunov exponent of one-dimensional systems

Let : [0, 1][0, 1] be a piecewise monotonie expanding map. Then admits an absolutely continuous invariant measure. A result of Kosyakin and Sandler shows that can be approximated by a sequence of absolutely continuous measures _n invariant under piecewise linear Markov maps _itn. Each _itn is constructed on the inverse images of the turning points of . The easily computable measures _n are used to estimate the Liapunov exponent of . The idea of using Markov maps for estimating the Liapunov exponent is applied to both expanding and nonexpanding maps.     

ИССЛЕДОВАНИЕ ЭРОЗИЙ НОГО ДЕЙСТВИЯ ИМПУЛЬ СНЯХ ЭЛЕКТРИЧЕСКИХ РАЗРЯ ДОВ С СЛАБЫМ ТОКОМ

50–100 , 1–2 1–10 . - . - . , , - . -.     

Nelson's symmetry and the infinite volume behavior of the vacuum inP(φ)2

LetH _l be the Hamiltonian in aP()₂ theory with sharp space cutoff in the interval (–l/2,l/2). LetE _l =inf(H _l ), (l)=–E _l /l, and let _l be the vacuum forH _l . discuss properties of (l) and _l . In particular, asl, there are finite constants <0 and such that (l), ((l)–)l, and hence (l)=+/l+o(l ^–1). Moreover exp(–c ₁ l) _{l 1}exp(–c ₂ l) forc ₁,c ₂ positive constants, where _{l 1} is theL ¹(Q, d₀) norm of ₁ with respect to the Fock vacuum measure. We also present a new proof of recent estimates of Glimm and Jaffe on local perturbations ofH _l in the infinite volume limit.Research sponsored by AFOSR under Contract No. F44620-71-C-0108.On leave from Istituto di Fisica Teorica, Universitá di Napoli and Istituto Nazionale di Fisica Nucleare, Sezione di Napoli.A. Sloan Foundation Fellow.