JOURNAL DE PHYSIQUE Research Articles

RECENT DEVELOPMENTS IN THE UNDERSTANDING OF SOLUTIONS OF SULFUR IN LIQUID AMMONIA

RECENT DEVELOPMENTS IN THE UNDERSTANDING OF SOLUTIONS OF SULFUR IN LIQUID AMMONIA

CYCLING EFFECTS, FATIGUE AND DEGRADATION OF SHAPE MEMORY ALLOYS

The stability and lifetime of a shape memory device is characterised by the changes of its transformation temperatures, its cold shape, its hot shape, its global two way shape memory effect, its recovery stress. This global behaviour is influenced by a complex combination of internal and external parameters. Internal parameters are : the alloy system, the alloy composition, the type of transformation and the lattice structure including defects. External parameters are : the thermomechanical treatments, the way of training, the applied stress, the imposed shape memory strain, the amplitude of temperature cycling, the absolute temperature of the environment. The possible physical mechanisms which are at the origin of the limited lifetime of any shape memory element and which are, to a greater or lesser extent, controlled by the above mentioned internal and external parameters, are : the stabilisation of specific martensite variants, the creation of lattice defects during transformation-cycling (transfornation plasticity or defects that could triger unwanted variants), changes in the order of the lattice. changes in defect density and/or defect configuration as a result of ageing. This paper will present an overview of reported and new observations related to those aspects of shape memory alloys. The specific functional properties of shape memory alloys, necessitate an extension of the usual definition of fatigue. Three different types of fatigue have to be considered in the case of shape memory alloys. 1. Failure by fracture due to stress or strain cycling at constant temperature. Three different situations are possible : the material is martensitic during cycling; the material remains beta during cycling: the martensite is stress induced during cycling above the Ar temperature. This type of fatigue has so far received the most attention in the literature / 1-20/. 2. Changes in physical, mechanical and functional properties such as the transformation temperatures, the transformation hysteresis, two way memory effect, ... due to pure thermal cycling through the transformation /21-28/. 3. The degradation of the shape memory effect due to stress, strain or temperature cycling in or through the transformation region /30-37/. The three main parameters to be considered in the study of the global lifetime of a shape memory alloy are thus temperature, stress and the macroscopic shape strain during deformation. It might be Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jp4:1991429 C4-190 JOURNAL DE PHYSIQUE IV important for the latter to distinguish between the transformation induced plasticity. this is the shape strain under load during the forward transformation and the spontaneous shape strain due to the one or two way memory effect. The origin of the global lifetime or fatigue behaviour of shape memory alloys is due to accumulation of defects and structural changes like the change in order of the beta phase or martensite or the formation of other types of martensite. All types of changes will have an influence on the transformation temperatures, the transformation hysteresis, the reproducibility of the one and two way memory effect, and the amount of cycles before fracture. Generally, the main concern in the lifetime of a shape memory alloy is the stability of the required shapes at different temperatures or the stability of recovery stress or work output. Therefore information on the temperature and stress profile including the amount of cycles during the required lifetime is a prerequisite to make the proper choices in alloy composition, thermomechanical treatment and design. This paper will present some important results related to classic fatigue, thermal cycling and degradation of the shape memory effect.

STRAIN RATE DEPENDENCE ON MECHANICAL PROPERTIES IN SOME COMMERCIAL ALUMINUM ALLOYS

The flow stress and ductility of some commercial aluminum alloys (1050, 3003, 3004, 5182 and 7N01) have been investigated as a function of strain rates over the range from 1x10 s to 4xl0s at room temperature. The maximum flow stress of both 1050 and 3003 alloys increases with increasing strain rate , but the maximum flow stress of 3004, 5182 and 7N01 alloy decreases with increasing strain rate in the low and intermediate ranges from lx l 0 3 to lxl0 s 1 .The above three alloys which showed the particular behavior of flow stress in this strain rate range contain magnesium atoms in solute. So, this behavior of flow stress in these alloys seemed to be concerned with the interaction between magnesium atoms in solute and dislocations. The elongation in failure increases with strain rate for most of the present alloys except for the 7N01 alloy. 1-INTRODUCTION Recently many kinds of commercial aluminum alloys have been used in press forming, and the forming rates in use are in the strain rate range from 1 to 100 s 1 . Therefore, the investigation of the mechanical properties of commercial aluminum alloys in these forming rates is important to use these alloys appropriately. It is well known that the change of flow stress of aluminum[l] and aluminum alloys[2) with strain rate at room temperature is negligible in a low strain rate range below 10 s; but the flow stress increases rapidly with strain rate in high strain rate ranges over 10s. A few reports about mechanical properties for aluminum alloys, however, were made for the strain rate ranges from 10' s 1 to 10sM31. Therefore, the flow stress and ductility of some commercial aluminum alloys(1050, 3003, 3004, 5182 and 7N01) have been investigated as a function of strain rates over the range from lx lO 3 to 4xl0 s' at room temperature. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jp4:1991349 C3-342 JOURNAL DE PHYSIQUE IV 2-EXPERIMENTAL PROCEDURE The chemical composition of the commercial aluminum alloys used in this study is given in Table 1. Tensile specimens, machined from hot rolled plates, had their tensile axes normal to the rolling direction. The gauge length of the specimen is 4.5 mm and the diameter is 3 rnm. All specimens were heated to 643 K with a heating rate of 47 K / hour and then annealed for 2 hours in air. The optical microstructures of these alloys after annealing are shown in Fig. 1 (a)-(e) respectively. The grains were elongated to the direction of rolling and fiber-structures are observed for all alloys. (a) 1050 alloy (b) 3003 alloy (c) 3004 alloy (dl 5182 alloy (e) 7N01 alloy Fig.1 The optical microstructures for all alloys after annealing Low strain rate tensile tests (lx103 l ~ l O ' s ~ ) were performed with an instron machine. and intermediate strain rate tensile tests (1x10-1-3x102s1) were performed with the hydraulic tensile testing machine, and the dynamic tensile tests (4x102 -4x103s-l) were performed using a split Hopkinson pressure bar system which incorporates a specific attachment. The incremental strain rate tests were performed by the hydraulic tensile testing machine. This machine has a valve corresponding proportionally to given voltage. Therefore, using a computer with a controlling voltage pattern, the constant strain rate tests or the incremental strain rate tests can be performed. Table 1 The chemical composition of the commercial aluminum alloys ELEMENT ( w t % ) ALLOY Z n Mg Cu Mn ~r Z r T i F e S i

BUMPER DEBRIS CLOUD STRUCTURE ESTIMATED BY SHOCK CALCULATIONS

BUMPER DEBRIS CLOUD STRUCTURE ESTIMATED BY SHOCK CALCULATIONS

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

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

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...

SECONDARY ELECTRON EMISSION BY LOW ENERGY ION IMPACT

SECONDARY ELECTRON EMISSION BY LOW ENERGY ION IMPACT

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

INCOMMENSURATE AND LOCK-IN MAGNETIC PHASE TRANSITIONS IN TbSi

INCOMMENSURATE AND LOCK-IN MAGNETIC PHASE TRANSITIONS IN TbSi

ANTIFERROMAGNETIC ORDER OF THE Cu IN RBa2Cu3O6+x

JOURNAL DE PHYSIQUE Colloque C8, Supplement au no 12, Tome 49, decembre 1988 ANTIFERROMAGNETIC ORDER OF THE Cu IN RBa2Cu3O6+, J. W. Lynn (I), W.-H. Li (I), H. A. Mook (2), B. C. Sales (2) and Z. Fisk (3) (I) Center for Superconductivity Research, Department of Physics, University of Maryland, College Park, MD 20742 ( U S A ) and National Bureau of Standards, Gaithersburg, M D 20899 U.S.A. (') Solid State Division, Oak Ridge National Laboratory, Oak Ridge, T N 37831 U.S.A. (3) MS-K764, Los Alamos National Laboratory, Los Alamos, N M 87545 U.S.A. Abstract. - Neutron diffraction measurements have been taken on single crystals of RBa2Cu3O6+, to explore the nature of the magnetic order a s a function of oxygen concentration x. The Cu-0 planes order antiferromagnetically at T N ~ with TN1 (a: % 0) N 450 K. At lower temperatures the oxygen-deficient Cu planes also order magnetically, with a substantial low temperature moment ( N 1/2 pB) and a simple antiferromagnetic sequencing along the c-axis. Both ordering temperatures much more sensitive to x than TN1. decrease with increasing x, with T N being The magnetic properties of the oxide superconduc- tors have been of particular interest due to the intrinsic interest in magnetism as well as because of the possi- bility that the magnetic fluctuations are responsible for the superconducting pairing [I]. The RBa2CusO6+, (R = rare earth) system orders antiferromagnetically [2-81 for small x (x (, 0.4), where the system is tetrag- onal and nonsuperconducting. The magnetic struc- ture consists [3, 41 of a simple antiparallel arrangement of Cu spins both within the Cu-0 planes as well as along the tetragonal c-axis, while the oxygen deficient Cu planes possess no ordered moment. The three- ~ M 0) dimensional ordering can be quite high ( T N (x 450 K) , indicating that the magnetic interaction en- ergies are large. The 3-d transition temperature is also very sensitive [2] to the oxygen concentration x, decreasing rapidly with increasing x and approaching zero for x 0.4. A second magnetic phase transition has recently been observed [5, 61, in which the oxygen-deficient Cu chain layers also order magnetically. We have been investigating the nature of this ordering and the ef- f6ct of oxygen concentration on T N and ~ have now ob- tained results on a number of single crystal specimens + ~ find : . that at small x and low T of N d B a 2 C ~ ~ 0 ~ We the basic magnetic structure consists of a simple an- tiferromagnetic arrangement of spins both within the planes as well as along the c-axis. In particular, we find an unexpectedly large magnetic moment on the Cu chain sites. At intermediate temperatures the spin arrangement is a superposition of the high T and low T configurations, and is noncollinear in nature. We also find that both transition temperatures decrease with increasing x, with the lower transition TN2 being much more sensitive to x than the higher transition T N ~ . The neutron measurements were carried out at the National Bureau of Standards Research Reactor using standard triple-axis instruments. Unpolarized diffrac- tion data were collected with an incident energy of either 14.8 or 13.7 meV using a pyrolytic graphite N N PG(002) monochromator. Polarized neutron measure- ments were then taken to establish that the new peaks are magnetic in origin, and this procedure has been described previously [4]. The Bragg peak correspond- reflection is shown in figure 1. ing to the Even though the Cu moments are quite small, the crys- tal is sufficiently large (N 50 mg) to obtain an excel- lent signal-to-noise ratio. Polarized neutron measure- ments were employed t o establish that the observed half-integral peaks are wholly magnetic in origin. The half-integral value for the third index demonstrates that the magnetic structure is doubled along all three crystallographic directions in comparison to the chem- ical unit cell. This contrasts with the spin configura- tion observed [3, 41 in the higher temperature magnetic phase, where the t index is integral and the magnetic and chemical unit cells are the same size along the tetragonal c-axis. Sample Rotation Fig. 1. - Observed magnetic Bragg peak for the peak at low temperatures. (f f t) peak The temperature dependence of the is shown in the bottom portion of figure 2. For this value of oxygen concentration (x M 0.1) the lower phase transition occurs at T N M ~ 80 K. The top por- tion of the figure compares the intensity of the whole- integral peaks such as 2) , which are associated Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19888964