Journal De Research Articles

FABRICATION AND EVALUATION OF SiC/C FUNCTIONALLY GRADIENT MATERIAL

A plate-like deposit having a compositional gradient from carbon (C) to silicon carbide (Sic) (SiCJC FGM) was obtained on a graphite substrate with chemical vapour deposition (CVD) by changing the SiJC molar ratio in input gas during deposition. Cracking due to heat flux was investigated using a C02 laser setup. Heat flux which resulted in cracking in Sic-coated graphite (Sic NFGM) was 5.8 M W ~ I ~ at a surface temperature (Ts) of 1300 K and a reverse surface temperature (Tb) of 1220 K. In the case of SiCJC FGM, heat flux occurred cracking was 7.4 ~ r n ~ at a Ts of 1650 K and a Tb of 1080 K. The temperature difference between Ts and Tb was 570 K in FGM and 80 K in NFGM. Thermal stress calculation showed that in cracking caused by hoop stress, the stress was close to the fracture strength of Sic. It was clear that SiCIC FGM has effective thermal shock resistance and thermal barrier characteristics. In recent years, much attention has been focused on the development of high-temperature functional materials, especially in the field of aerospace applications 111. Functionally gradient materials (FGMs) have been developed which have a compositional or structural distribution from one side to the other side. It is necessary to have both high oxidation resistance and high fracture strength at high temperatures. We have attempted to fabricate an FGM consisting of S ic and C, taking into consideration the high oxidation resistance and high fracture strength of Sic, as well as the low Young's modulus and easy-processing of C /2,3/. An SiCJC FGM which has a compositional gradient from C to S ic has been fabricated with the CVD method by changing the SiJC molar ratio in input gas. The fabrication and thermal properties of Sic-C composites were also investigated. The authors previously clarified the effect of the addition of C on the lower thermal conductivity of Sic-C composites 141 and on the superior thermal barrier characteristics of Sic-C composites. Furthermore, they clarified the thermal barrier characteristics and thermal shock resistance of SiCJC FGM using a Xenon arc lamp heating method. As a result, it was shown experimentally and by calculation of thermal stress that SiCIC FGM has thermal barrier characteristics because of lower thermal conductivity, as well as thermal stress relaxation due to a lower Young's modulus 15-7J. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jp4:1991278 C2-650 JOURNAL DE PHYSIQUE IV The authors have already investigated the thermal shock resistance of SiC/C FGM using the C02 laser (50 W) method /8,9/. However, the difference between Sic-single-layer-coated graphite (Sic NFGM) and SiC/C FGM was not clarified of the lower laser power (50 W) of this method. In the present study, we report the thermal shock resistance of SiC/C FGM having a graphite substrate (30 mm in diameter, 5 mm in thickness) using the 5 kW-C02-laser-heating method, and the effect of laser spot diameter.

EPITAXIAL SILICON GROWTH BY RAPID THERMAL CVD

A rapid thermal chemical vapour deposition system has been used for the growth of epitaxial silicon layers on silicon substrates in the temperature range 590°C 1000°C. Low pressure deposition schedules have been found essential in order to minimise the concentrations of oxygen and carbon in the layers. In-situ pre-cleaning schedules have been established to remove oxide layers from the substrates prior to layer deposition. The application of these deposited epitaxial layers to the production of a buried gate static induction thyristor is described. The deposition of polycrystalline silicon and the growth of epitaxial silicon are vital steps in advanced integrated circuit processes. The technique in almost universal use for the production of these films is chemical vapour deposition (CVD), wherein gaseous species (eg SiH4, SiH2C12) react on a substrate and a solid phase material (silicon) is produced. Both polysilicon and epitaxial silicon have traditionally been produced in atmospheric pressure reactors. However, in the case of polysilicon, low pressure reactors have largely taken over because of improved uniformity and reduced gas consumption. Reduced pressures are also beneficial for the growth of epitaxial silicon, as autodoping and pattern shift effects are alleviated [l] and homogeneous gas phase nucleation of silane is retarded [ Z ] . Low pressure (LP) CVD is thus, becoming the most technologically important means of producing silicon films. Recently, much attention has been given to a refinement of LPCVD which incorporates the concept of rapid thermal processing (RTP). In RTP, the single process wafer is heated by a high-intensity light source, and very fast ramp rates can be achieved. The combination of LPCVD and RTP is known as rapid thermal chemical vapour deposition (RTCVD). In particular, when reactions are triggered by a temperature pulse (rather than by gas switching), the technique has been termed limited reaction processing (LRP) 1 3 1 . Rapid thermal processes have the advantage of a reduced thermal budget, as the fast ramp rates minimize the time for which the wafer is at elevated temperatures. This is an important consideration for high-speed VLSI circuitry, where lateral and vertical device dimensions must be tightly controlled. Because RTP minimises unwanted dopant diffusion, shallow junctions of high quality are more readily obtained by this technique than by traditional furnace methods. The ability to switch temperatures rapidly also means that several different process steps can be carried out sequentially in-situ. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jp4:1991291 C2-780 JOURNAL DE PHYSIQUE IV LRP shares the advantages of RTP, and may be used to deposit a sequence of thin, highly abrupt semiconducting layers. Applications include shallow emitter-base structures for heterojunction bipolar transistors [4, 53 and superlattices [ 6 ] , and buried p ' grid structures for advanced static induction thyristors. This paper will describe a twin reactor system used for the production of epitaxial silicon layers for device manufacture. One of the reactors has been dedicated to high temperature epitaxy from SiH2C12 and the other to low temperature epitaxy from SiH,,. The requirements and properties of the two processes will be contrasted.

COPPER AND COPPER OXIDE THIN FILMS OBTAINED BY METALORGANIC MICROWAVE PLASMA CVD

Microwave Plasma Enhanced Chemical Vapor Deposition (MPECVD) is an innovative technique allowing the direct preparation, at low temperature, of different valence states of copper (Cu°, Cu, Cu). The precursor used is a volatile metalorganic one (copper acetylacetonate) with helium as a carrier gas. The precursor is then transported in a remote plasma of Ar, A1/O2 or A r / ^ O gas at low pressure. A judicious choice of the process parameters microwave power, substrate temperature and nature of the oxidant gas (N2O or O2)allows to favour the formation of metallic copper, Q12O or CuO. Copper and its oxides have been deposited as thin films on silicon and magnesium oxide single crystals. The techniques used for the characterization of the as deposited polycrystalline films are X-ray diffraction, Auger Electron Spectroscopy and Scanning Electron Microscopy. IINTRODUCTION The discovery of high temperature superconductors in the systems La-Cu-O, Y-Ba-Cu-O, Bi-Sr-Cu-O and Tl-Ba-Ca-Cu-O has initiated some important research on single oxide phases. As copper oxide is found in all high Tc superconductors, copper (II) oxide thin layers can be considered as good models for studies directed towards the improved formation of thin films of the copper oxide based high Tc superconductors [1]. Among the techniques used for copper and copper oxide deposition, one can distinguish : spray pyrolysis of a salt solution [2], RF sputtering of copper and copper oxides [3], metal organic Chemical Vapor Deposition [4], plasma enhanced CVD [5] and laser CVD [6]. The purpose of this work was to use a method able to lead to copper and copper oxides thin layers at low temperature. A new technique has been investigated : metalorganic microwaves plasma enhanced chemical vapor deposition (MOMPECVD). Microwave plasmas was initially employed for semi-conductor etching [7], but the technique has also been developed for thin film deposition. Among the various materials prepared, one can mention diamond [8] and even Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jp4:1991247 C2-390 JOURNAL DE PHYSIQUE IV YBaCuO superconductors [9]. In this study, this innovative technique has been used for the synthesis of copper and copper oxides thin films from volatile organometallic precursors.

Orientational glasses. I. A random compressible model for KCN-KBr

The full phase diagram of K(CN)~Bri _~ mixtures is obtained using a mean-field treatment of a dilute random anharmonic compressible ferroelastic model. Integration of elastic degrees of freedom leads to a non-linear percolating problem. No random competing interactions are found. In parallel a simple linear hypothesis for an effective density of cyanides is assumed to account for the asymmetric shape of the cyanide versus the spherical bromide shape. Site percolation of cyanides is thus discriminated from the corresponding orientational percolation. Three characteristic values of cyanide concentration x = 0.2, 0.5 and 0.6 are obtained. For x < 0.6 the ferroelastic transition is lost. In the range 0.5 < x < 0.6, at low temperatures, cyanides form ferroelastic domains with random orientations. When 0.2 < x < 0.5 a collective dynamical glass is obtained. It tums to a single ion state for x < 0.2. It is then shown that the corresponding phase diagram of K~(Naj ~)CN mixtures is of a different physical nature. It involves in particular random competing interactions. A critical review of the orientational random field model is presented. The results are found to provide a unified and consistent framework to various experimental data. 1196 JOURNAL DE PHYSIQUE I M 8

Deformation twinning in metals and ordered intermetallics-Ti and Ti-aluminides

The role of deformation twinning in the strength and ductility of metals and ordered interrnetallic alloys is examined on the basis of crystallography, energetics and kinetics of deformation twinning. A systematic analysis is made by taking Ti, T13Al, TiAl, and A13Ti as four model systems. In comparison with profuse twinning in Ti, the intrinsic difficulty of twinning in T13Al is rationalized in terms of the interchange shuffling mechanism. A fault (SISF) dragging mechanism based on the interaction torque explains the physical source for the low mobility of screw superdislocations in TiAI, which may lead to (1Ii) [1Ii] twin nucleation. In TiAI and A13Ti alloys, the twin-slip (ordinary) conjugate relationship makes an important contribution to the strain compatibility for high,temperature plasticity. Potentially beneficial alloying additions to promote twinning are discussed. (I) Research sponsored by the Division of Materials Sciences, Office of Basic Energy Sciences, U-SDepartment of Energy, under contract DE-ACo5-840R21400 with Martin Marietta Energy Systems, Inc. (2) Permanent address.Department of Metallurgical and Materials Engineering, Michigan Technological University, Houghton, MI 49931, U-S-Aloss JOURNAL DE PHYSIQUE III M 6

The Impact of Increased LDC Food Production on LDC Food Imports: Comment

If a less developed country (LDC) increases its food production, will its food imports decrease or increase? This question is of obvious importance not only to those concerned with development of LDCs but also to agricultural exporters in the United States and elsewhere.' In a series of papers (beginning with one in this Journal) de Janvry and Sadoulet (hereafter JS) have used simulation models to examine the impact of increased LDC food production on LDC food imports (1986, 1988; De Janvry, Sadoulet, and White). I offer a critique of their model after presenting a brief background to the debate.

Time resolved transient absorption probing of a laser plasma

The described experimental setup allows the kinetic analysis of a pulsed-laser generated gas-plasma by transient visible absorption spectroscopy at a time resolution of 10 ns and a spectral resolution of 0.3 cm-I. Absorption from the first-4s level manifold towards the 5p level manifold of the argon atom is reported in the spectral range around 420 nm. An example of time dependence is given for the 4s[3/2]~ level population. Since the advent of lasers their ability to generate plasmas has been recognized and widely used and the physical properties of such plasmas extensively studied [I]. Quite a number of those works dealt with rare gas laser plasmas but very few have been devoted to spectroscopical properties of these plasmas. However during the last two decades dense rare gases have attracted considerable attention due to their potentiality as laser media [2]. In this respect a detailed knowledge of plasma kinetics is of great importance. The present report describes a method allowing the kinetic study of a gas plasma by transient visible absorption spectroscopy at high spectral and temporal resolution. The experimental setup is sketched in figure I. The pulsed-laser generated plasma, recently used as a vacuum ultraviolet source [3], is created by focusing the 1064 nm radiation of a pulsed 585-20 Quantel Nd : YAG laser (YAG 1, 350 mJ) at the center of a 6-way gas cell by means of the spherical lens Ll of focal length 20 mm. The stainless steel gas cell, mounted with metallic Helicoflex gaskets from Cefilac, is evacuated with a turbopurnp and refilled before each run with a gas at a pressure typically in the atmospheric range (10~ Pa). This is a very clean technique as the medium is excited far from the cell walls. The probe beam is obtained by irradiating a laser dye cell by part of the frequency tripled radiation at 355 nm of a 2062 JOURNAL DE PHYSIQUE III M 12

POLITICS AND JOURNALISM IN THE FRENCH REVOLUTION: THE READERSHIP OF THE JOURNAL DE LA MONTAGNE AND THE JACOBIN CLUBS

POLITICS AND JOURNALISM IN THE FRENCH REVOLUTION: THE READERSHIP OF THE JOURNAL DE LA MONTAGNE AND THE JACOBIN CLUBS Get access HARVEY CHISICK HARVEY CHISICK Search for other works by this author on: Oxford Academic Google Scholar French History, Volume 5, Issue 3, September 1991, Pages 345–372, https://doi.org/10.1093/fh/5.3.345 Published: 01 September 1991

Oral effects of chronic alcoholism

British Journal of AddictionVolume 85, Issue 12 p. 1664-1665 Free Access Oral effects of chronic alcoholism J. SCOTT, J. SCOTT Department of Clinical Dental Sciences, School of Dentistry, The University of Liverpool, PO Box 147, Liverpool 169 3BX, UK.Search for more papers by this author J. SCOTT, J. SCOTT Department of Clinical Dental Sciences, School of Dentistry, The University of Liverpool, PO Box 147, Liverpool 169 3BX, UK.Search for more papers by this author First published: December 1990 https://doi.org/10.1111/j.1360-0443.1990.tb01659.xAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. References Abelson, D. C., Mandel, I. D. & Karmiol, M. (1975) Salivary studies in alcoholic cirrhosis, Oral Surgery, 41, pp 188– 192. Dutta, S. K., Dukenhart, M., Narang, A. & Latham, P. S. (1989) Functional and structural changes in parotid glands of alcoholic cirrhotic patients, Gastro-enterology, 96, pp 510– 518. Gupta, P.C. (1984) Epidemiologic study of the association between alcohol habits and oral leukoplakia, Community Dentistry and Oral Epidemiology, 12, pp 47– 50. Robb, N. (1990) Alcohol and the dentist, British Journal of Addiction, 85, p 437. Rothmann, K. J. & Keller, A. Z. (1972) The effect of joint exposure to alcohol and tobacco on risk of cancer of the mouth and pharynx, Journal of Chronic Disease, 25, pp 711– 716. Scott, J., Burns, J. & Flower, E. A. (1988) Histological analysis of parotid and submandibular glands in chronic alcohol abuse: a necropsy study, Journal of Clinical Pathology, 41, pp 837– 840. Scott, J., Berry, M. & Woods, K. (1989a) Effects of acute ethanol administration on stimulated parotid secretion in the rat, Alcoholism: Clinical and Experimental Research, 13, pp 560– 563. Scott, J., Woods, K. & Baxter, P. (1989b) Salivary flow rate, protein and electrolyte concentrations in chronic alcoholic patients, Journal de Biologic Buccale, 16, pp 215– 218. Valentine, J. A., Scott, J., West, C. R. & St. Hill, C. A. (1985) A histological analysis of the early effects of alcohol and tobacco usage on human lingual epithelium, Journal of Oral Pathology, 14, pp 654– 665. Wynder, E. L., Bross, I. J. & Fieldman, R. M. (1957) A study of the etiological factors in cancer of the mouth, Cancer, 10, pp 1300– 1323. Volume85, Issue12December 1990Pages 1664-1665 ReferencesRelatedInformation

Chemistry and Cannon: J.-L. Proust and Gunpowder Analysis

Chemistry and Cannon: J.-L. Proust and Gunpowder Analysis SEYMOUR H. MAUSKOPF D’un instrument de guerre à un instrument de labo­ ratoire, les affinités ne changent certainement pas. [J.-L. Proust, “Cinquième mémoire sur la poudre à canon,” Journal de physique, de chimie et d’histoire na­ turelle 73 (novembre 1811): 390] This is the story of an attempt by a major chemist of the late 18th century to develop “useful knowledge” for industry under govern­ ment patronage. The chemist was Joseph-Louis Proust (1754—1826; known as Luis José Proust in Spain); the industry was munitions; the government was Spanish. It is not a success story in any simple sense; Proust’s research did not bring about any change in the manufacture of gunpowder (although Proust rather passionately argued for some reforms based on his experiments) and his work on gunpowder has been all but forgotten. Yet, on closer scrutiny of Proust’s career, I came to realize the significance of the gunpowder research for it. Although Proust is best known for his work in analytical chemistry (the enunciation of the law of definite proportions, a basic principle of chemical stoichiometry), he carried out research and taught on a wide range of chemical topics, many of them practical. Indeed, it was primarily through his practical chemistry that Proust was enabled to spend his mature and most creative years in Spain in the employ of the Spanish government. Of central importance were his activities as researcher, consultant, and teacher concerning munitions, carried on when he was professor of chemistry at the Royal Artillery School in Segovia (1785—98). Proust Dr. Mauskopf is professor of history at Duke University and, in 1988—89, was Edelstein International Fellow in the History of Chemical Sciences and Technologies at the Beckman Center for the History of Chemistry and the Edelstein Center, Hebrew University of Jerusalem. He is currently researching scientific involvement in explo­ sives and munitions from the late 18th century through World War I. He thanks the secretarial staffs of the Duke Department of History and of the Beckman Center for their expert services; and Alex Roland, Joe Burchfield, and the Beckman Center “brown bag seminar” for their helpful, frank readings of various drafts of the article.© 1990 by the Society for the History of Technology. All rights reserved. 0040-165X/90/3103-0003$01.00 398 Chemistry and Cannon: J -L. Proust and Gunpowder Analysis 399 certainly did not regard his practical chemistry as any less important than his “pure” chemical analysis; as we shall see, he placed high value on his gunpowder research. In fact, this research was probably the most comprehensive and systematic study of gunpowder chemistry of its day. Moreover, it was part of a scientific research tradition devoted to the elucidation of the physics and chemistry of gunpowder that spanned the 18th century.1 Therefore, one of the objectives of this study is to present and analyze Proust’s scientific research on gunpowder for its intrinsic scientific interest and significance. That this work has been neglected is only partly due to its limited application to the munitions industry in its own day; it is also a part of the general neglect that the history of modern scientific investigations of munitions has suffered. The classical study by J. R. Partington has for its focus the medieval and early modern eras and is very sketchy about the history of gunpowder after 1700.2 To discover information about the later period, one is forced to turn to state-of-the-art treatises of the 19th century, with their inevitable “textbook” orientation to the history of science.3 This study and its companion in Osiris are intended to provide partial redress for the shortcomings in the history of the scientific study of munitions. There is also a second objective related to the state patronage of Proust as practical chemist: the examination of Proust’s gunpowder research as a species of the “useful knowledge” so prized by 18thcentury reformers, bureaucrats, and entrepreneurs. There has devel­ oped a vast literature on the issue of the relationship between science and industry encapsulated by this phrase. Much of it has focused on 'Seymour H...

The Geneva Conference of August 1864 as seen by the Geneva press

The Geneva Conference of August 1864 was held behind closed doors. A drawing published in the satirical paper the Carillon de Saint-Gervais is indicative of the reaction of journalists to this decision. It depicts three characters, symbolizing three Geneva newspapers, the Journal de Genève, La Démocratic suisse and the Carillon de Saint-Gervais, locked out of the International Congress whose door bears a sign saying “no entry”. The caption translates as follows: Tribune open to the press, courtesy of the International Congress”. This was probably the first manifestation of a certain reserve which has been apparent on occasion in relations between the humanitarian agencies and the media. Happily, times have changed. Nowadays, information and dissemination have become essential components of the policy of the International Committee of the Red Cross, and it may safely be assumed that a cartoonist illustrating an International Conference would now show the doors wide open.

SECONDARY ELECTRON EMISSION BY LOW ENERGY ION IMPACT

SECONDARY ELECTRON EMISSION BY LOW ENERGY ION IMPACT

La Révolution et le premier journal illustré paru en France (1785-1793)

Annemarie Kleinert : The revolution and the first French illustrated magazine. The first illustrated magazine published in France was one of the periodicals that survived the fall of the monarchy in 1792 even though it was pro-monarchist. It changed its title twice between 1785 and 1793, being called Cabinet des Modes in its first year, Magasin des Modes nouvelles from its second to fourth years, and Journal de la Mode et du Goût in its last three years. It was illustrated with coloured engravings. Its articles and engravings allow us to study the importance of the Revolution for its authors. It moved from reticence towards acceptance, then enthousiasm and finally a refusal of the policies of the years 1789 to 1793.

Journal de mon voyage à Jocja Karta en 1825: the outbreak of the Java war (1825–1830) as seen by a painter. By A. A. J. Payen, edited by Peter Carey. (Cahierd'Archipel, No. 17.)pp. xiv, 180, front., 18 illus., 2 maps. Paris, Association Archipel, 1988. FF 95.

Journal de mon voyage à Jocja Karta en 1825: the outbreak of the Java war (1825–1830) as seen by a painter. By A. A. J. Payen, edited by Peter Carey. (Cahierd'Archipel, No. 17.)pp. xiv, 180, front., 18 illus., 2 maps. Paris, Association Archipel, 1988. FF 95. - Volume 121 Issue 1

THEORY OF MAGNETOSTRICTION IN AMORPHOUS FERROMAGNETS

THEORY OF MAGNETOSTRICTION IN AMORPHOUS FERROMAGNETS

NQR STUDY OF COPPER IN REBa2Cu3O7-y

NQR STUDY OF COPPER IN REBa₂Cu₃O_7-y

MODE-COUPLING APPROACH TO THE SPIN DYNAMICS OF EUROPIUM COMPOUNDS

The results of a numerical solution of the mode-coupling equations for EuO and EuS taking into account the microscopical properties of the compounds are presented. Good agreement with the available neutron scattering data is found and predictions for further experiments on EuS are given. The results of high resolution neutron scattering experiments on insulating ferromagnetic Europium compounds EuO and EuS appeared in literature in recent years [I-41. The particular attention devoted to such compounds, is due to the fact that already in the earlier neutron scattering comprehensive investigation on E n 0 and EuS [I] it was shown that the magnetic behaviour of these systems is very well described by a simple isotropic Heisenberg exchange interaction. The availability of experimental data at and above the ordering temperature Tc has encouraged a renewal of theoretical studies on critical and paramagnetic spin fluctuations in Heisenberg ferromagnets. The most successful theories appear to be those ones based on Renormalization Group (RG) or on the mode-coupling approximation. RG techniques constitute a well established method to study the static and dynamic critical properties of a system; they allow to evaluate critical exponents as well as universal functions which characterize the critical behaviour. Very recently an attempt has been made to extend RG calculations to temperatures above Tc [5], but some problems persist to make possible a quantitative comparison with experimental data. The mode coupling approximation, in spite of its heuristic character, has revealed very useful in many problems of condensed matter physics [6]. For pure Heisenberg magnets, for example, it gives for the critical dynamical scaling ex,ponent z the value z = 171, in a agreement with 2 the experiments. Moreover it has been shown very recently [8] that by taking into account the dipolar macroscopic interaction, the mode-coupling theory can be able to interpret the unexpected simple exponential decay obtained in neutron spin-echo experiment on EuO at T = Tc and very small wave vector [4], which remained until now inexplicable. However the mode-coupling theory appears also suitable to investigate the dynamical behaviour of ferromagnetic systems in all the paramagnetic region and throughout the Brillouin Zone. In this paper we present the results of a numerical solution of the modecoupling equations for EuO and EuS taking into account the microscopical features of these compounds. This allows to show some distinctive characters which distinguish EuS from EuO that cannot be accounted by previous approximate solutions, which were limited to simple cubic nearest neighbours interaction [7] or confined to the continuum limit [6]. Europium compounds can be described by a Heisenberg exchange hamiltonian: I for an FCC lattice of magnetic ions with S = -. The 2 experiments [I] have shown that the interaction is restricted to nearest neighbours (J1) and next nearest neighbours (Jz ) . For EuO: J1 = 1.22' K , J2 = 0.25' K and a = 5.12 A; for EuS: J1 = 0.48' K , J2 = -0.24' K and a = 5.95 A, a being the lattice constant. The final result given by the mode-coupling theory is the following integr~differential equation: for the relaxation function Fq ( t ) , whose Fourier Transform is related to the measured scattering function S (q, w ) by the relation: W (q' W, = 1 exp (-v/KBT) .x (4) F, ( w ) . (3) Not with standing formal differences in the various derivations, behind equation (2) is the following fundamental approximation: correlation and relaxation functions among more than two spin operators have been decoupled. Equation (2) is only one of the forms in which this equation is obtained, however all such forms are equivalent if we use for the static susceptibility that one given by the spherical model: Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19888720 C8 1572 JOURNAL DE PHYSIQUE This susceptibility turns out to be compatible with the dynamical equation (2). The temperature dependent parameter X appearing in equation (4) can be evaluated by using the sum rule: (I/N) C T X ~ = s(S + 1) /3.

A CLASS OF TRANSPORT PROBLEMS IN STATISTICAL MIXTURES WITH SCATTERING

For time independent transport in one dimensional systems, a formalism is discussed to treat radiative transfer in statistical mixtures, including the scattering interaction, for a certain class of problems. As a special case, binary homogeneous Markov statistics are treated in detail, for both the model of transport and planar geometry. Results are given for several classical transport problems. In the case of the Milne problem, an ambiguity in its definition is pointed out, and the solution is discussed for two different interpretations. 1 INTRODUCTION In recent years there has been considerable interest in developing a formalism to describe radiative transfer (or any linear transport) in a statistical medium consisting of two or more immiscible fluids /1-9/. A complete and rigorous description has been given for time independent problems in the absence of the scattering interaction in the underlying physics of the transport process, both for Markov statistics /1,2/ and non-Markov statistics /3-5/. With scattering and/or time dependence present, a general phenomenological model has been suggested /4,5/ for Markov statistics, using the master equation approach /10/. This model gives the correct result for time independent problems with no scattering, and is always a robust one, but it has recently been shown /6,7/ to give an inexact result for a certain time independent purely scattering problem. This led to the development of a formalism to treat a certain restricted class of statistical time independent transport problems including the scattering interaction /7,8/. In this paper we review some explicit results for certain classic transport problems obtained with this formalism /7-9/. Specifically, we give the results for a transmission problem, the halfspace albedo and emissivity problems, and the Milne problem. In all cases, the statistics of the two fluid random mixture are assumed homogeneous and Markovian. Results are given for both the rod model /ll/ of transport, in which particles are constrained to move along a line, and in the more physical planar geometry. A particularly interesting point is that, in this statistical setting, there is a nonuniqueness in the definition of the Milne problem, which leads to two different approaches giving two different results /9/. 2 GENERAL FORMALISM The starting point of our analysis is the monoenergetic, time independent linear transport equation in planar geometry, given by U) Partially supported by the U.S. National Science Foundation Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988739 C7-322 JOURNAL DE PHYSIQUE Here I(x,/i) is the radiative, or particle, intensity defined as the product of the particle speed and the particle number distribution function, with x and n representing the spatial and angular variables respectively. Specifically, ft is the cosine of the angle between the particle velocity and the positive x axis. The quantity <r(x) is the total (collision) cross section, and os(x,/i'-*/*) denotes the scattering kernel describing the scattering of particles from angle cosine p' to angle cosine /». Q(x,/i) represents any external source of particles. As indicated, Eq. (1) holds for a planar system occupying 0 < x < t. The quantities a, as, and Q in Eq. (1) are treated as stochastic variables, each obeying known statistics. Nonstochastic boundary conditions are assigned to Eq. (1) of the form (2) (3) where r+(/i) are the known boundary data. We seek a solution for I(x,p), the ensemble averaged solution of Eqs. (l)-(3). The key to the analysis is the introduction of an optical depth variable r defined as

THEORY OF STATIC AND DYNAMIC PROPERTIES OF SUPERLATTICES WITH FERROMAGNETIC AND ANTIFERROMAGNETIC COUPLING

THEORY OF STATIC AND DYNAMIC PROPERTIES OF SUPERLATTICES WITH FERROMAGNETIC AND ANTIFERROMAGNETIC COUPLING

OBSERVATION OF A STRONGLY ENHANCED MAGNETO-OPTICAL KERR EFFECT IN COMPOSITIONALLY MODULATED FeTb/SiO FILMS

OBSERVATION OF A STRONGLY ENHANCED MAGNETO-OPTICAL KERR EFFECT IN COMPOSITIONALLY MODULATED FeTb/SiO FILMS