Layers Of Equal Thickness Research Articles

Temperature dependence of interface anisotropy in Ni/Mo multilayers

Equal layer thickness Ni/Mo multilayer samples ranging in Ni layer thickness d from 14 to 340 Å have been investigated by x-band ferromagnetic resonance at temperatures between 4 and 293 K. The dependence of anisotropy (less demagnetization) Ha upon d clearly indicates the interface anisotropy plays a significant role in these samples. Interface (Ks) and volume (Kv) contributions to the anisotropy are extracted at each temperature using an approximate form of Ha=2(Kv+2Ks/d)/M. The Ks temperature dependence is shown to be inconsistent with a simple mean field model and indicates that interface strain due to the Ni-Mo lattice mismatch is largely responsible for the origin of Ks.

Planar channeling in superlattices: Theory.

The well-known continuum model theory for planar channeled energetic particles in perfect crystals is extended to layered crystalline structures and applied to superlattices. In a strained-layer structure, the planar channels with normals which are not perpendicular to the growth direction change their direction at each interface, and this dramatically influences the channeling behavior. The governing equation of motion for a planar channeled ion in a strained-layer superlattice with equal layer thicknesses is a one degree of freedom nonlinear oscillator which is periodically forced with a sequence of \ensuremath{\delta} functions. These \ensuremath{\delta} functions, which are of equal spacing and amplitude with alternating sign, represent the tilts at each of the interfaces. Thus upon matching an effective channeled particle wavelength, corresponding to a natural period of the nonlinear oscillator, to the period of the strained-layer superlattice, corresponding to the periodic forcing, strong resonance effects are expected. The condition of one effective wavelength per period corresponds to a rapid dechanneling at a well-defined depth (catastrophic dechanneling), whereas two wavelengths per period corresponds to no enhanced dechanneling after the first one or two layers (resonance channeling). A phase plane analysis is used to characterize the channeled particle motion. Detailed calculations using the Moliere continuum potential are compared with our previously described modified harmonic model, and new results are presented for the phase plane evolution, as well as the dechanneling as a function of depth, incident angle, energy, and layer thickness. General scaling laws are developed and nearly universal curves are obtained for the dechanneling versus depth under catastrophic dechanneling.

Enhanced spin-density waves in Co-Cr superlattices

The electrical resistivity of a series of Co-Cr multilayered thin films (MLS) of equal layer thickness of ∼30–30 Å made at various substate temperatures and deposition rates of 0.5 and 2 Å/s was measured over the temperature range of 4.2–350 K. The most striking feature seen in several of these MLS was that the bump near the Néel temperature TN of the spin-density wave (SDW) of Cr was 2–4 times greater than that seen in CrCo alloys. The bump in the MLS is also much sharper than that of the alloys. The resistivity bump and an increase in TN in the alloys has been attributed to an enhancement of the SDW due to the exchange interaction between the Co moments and the SDW. It is proposed that the even larger enhancement of the SDW in the MLS is due to the superlattice structure of the MLS. This changes the Cr Fermi surface by introducing new Brillouin zones and thus increases the nesting which gives rise to the SDW. The variation of the TN values of the MLS varies systematically with the substrate temperature. Other similarities and differences between the MLS and the alloys resistivity behavior are discussed.

Hyperfine field measurements of Co-Cr multilayered films (abstract)

The hyperfine field distributions of equal layer thickness multilayered films (MLS) having nominal Co layer thicknesses of 21, 28, and 54 Å and total thickness of about 3000 Å have been measured by NMR spin-echo experiments. We have determined the actual thicknesses of the Co layers using saturation magnetization measurements and modelling the interface shape. Defining the Co layer thickness as where the magnetization drops to one-half of that of pure Co, we find that these thicknesses are 14±2, 17±3, and 38±4 Å, respectively, for the 21-, 28-, and 54-Å MLS. These thicknesses are quite insensitive to whether the interfacial shape of the composition profile is assumed to be trapezoidal, sinusoidal (Hanning function) or Gaussian. Co atoms in the magnetic portion of the film having one or more nearest-neighbor Cr atoms would be expected to have hyperfine fields that were so different and spread out from that of Co atoms with all near-neighbor Co atoms that they could contribute negligible intensity to the spectra. Thus it was anticipated that the hyperfine field spectra would mainly arise from Co atoms having all Co nearest neighbors and therefore the spectra of all the MLS would be similar. Indeed the spectra obtained for all these MLS, as well as for a pure Co film, are very similar. They have two broad peaks of slightly lower values than those of pure powdered Co (224±1 vs 228 MHz for the wall center resonance and 218±1 MHz vs 220 MHz for the wall edge resonance). The slight decrease of the resonance frequency is reasonable in these thin film MLS.

An exactly solvable model for calculating critical misfit and thickness in epitaxial superlattices. II. Layers of unequal elastic constants and thicknesses

In this paper we have extended the exact predictions of critical misfit fc and critical thickness hc —based on equilibrium suppositions and a parabolic interfacial potential of shear strength μ—in superlattices of layer pairs A and B introducing the thicknesses ha=ηac and hb=ηbc, and moduli μa, μb, and μ as variables. The extension involved an explicit relation between the homogeneous misfit strains ēa and ēb on the one hand and the thicknesses and moduli on the other in order to ensure lateral force balance. Analytical expressions for the energies ED and Eē per unit area per interface for misfit dislocations and mistfit strains, respectively, have been derived and minimized to obtain the equilibrium value ēm needed to predict fc and hc. The expression for ED is rather complicated. However, a variety of simplifying approximations were feasible, which not only facilitated numerical evaluation but also made it possible to draw various conclusions. The case of equal elastic constants but variable layer thicknesses shows that a maximum value of fc occurred when the superlattice layers have equal thickness and that the layers of equal thickness produced the minimum value of ED. Scaling relations were found that could be used to calculate ED values simply by selecting the appropriate combinations of thicknesses and elastic constants. The effect of changing elastic constants or the values of critical thickness or critical misft could also be represented through scaling relations.

An exactly solvable model for calculating critical misfit and thickness in epitaxial superlattices: Layers of equal elastic constants and thicknesses

A parabolic interaction potential has been used to develop a model for calculating the misfit dislocation (MD) energy in the case of a superlattice of alternating layers of materials with equal elastic constants and thicknesses. The model, which is believed to be a good one for small misfits and to have some merit for covalent bonded materials, is exactly solvable for the critical thickness above which it is energetically favorable to lose coherency by the introduction of MDs into the interfaces. It was found, for a given misfit f, that the critical thickness for epitaxial superlattices free from their substrate is somewhat more than 4 times that for a single epilayer on a thick substrate. Furthermore, the critical thickness varies almost inversely with misfit to the power 1.22 when Poisson’s ratio is 1/3. It was also shown that the critical misfit fc obtained by equating maximal misfit strain and MD energies is a significant overestimate of fc. The results for a superlattice are compared with those of a thin layer on a thick substrate.

The nature of upstream blocking in uniformly stratified flow over long obstacles

The general method described in Baines 1988 has been applied to stratified flows of finite depth over long obstacles where the flow initially has uniform horizontal velocity. The fluid consists of a finite number of homogeneous layers of equal thickness and with equal density increments. This represents the state of continuous stratification with constant density gradient as closely as possible, for a given number of layers. Two-, three-, four- and sixty-four-layered models are studied in detail. The results are expressed in terms of the initial Froude number F0 (F0 = U/ĉ1 where U is the fluid speed and ĉ1 is the speed of the fastest long internal wave mode in the fluid at rest) and the obstacle height. In general, introduction of an obstacle into the flow causes disturbances to propagate upstream (columnar disturbance modes) which alter the velocity and density profiles there. These may accumulate to cause upstream blocking of some of the fluid layers if F0 is sufficiently small. As the number of fluid layers increases, so does the range of F0 for which this upstream blocked flow occurs. There are no upstream disturbances for F0 > 1, and for F0 < 1 the upstream disturbances are of the rarefaction type if upstream blocking does not occur. The results for three and four layers show how several coexisting modes may interact to affect the upstream profiles. The results for sixty-four-layers provide theoretical support for the observational criterion (Baines 1979b) that blocking in initially uniformly stratified flow occurs when Nhm/U > 2 (N is the Brunt—Väisälä frequency and hm the obstacle height), provided that more than two modes are present. In some situations, layered models are found to be inadequate as a representation of continuous stratification when one or more layers thicken to the extent that their discreteness is significant.

An Experimental Study of Waterflooding From a Two-Dimensional Layered Sand Model

Summary The effect of flow rate on oil recovery by waterflooding is studied with a two-dimensional (2D), layered sand model that allows visual observation. The model consists of three communicating layers of equal thickness of water-wet sand with the permeability ratio of 2 :4 : 1 from top to bottom. Three white mineral oils of viscosity 15, 30, and 150 cp [15, 30, and 150 mPa · s] have been used for immiscible liquid/liquid displacement under constant pressure drops covering a range of flow rates. The changes in flow regimes in the various layers are observed with respect to the variations in pressure drop across the model. The effects of capillary imbibition, gravity segregation, and viscous pressure gradient are observed and an attempt is made to calculate the instantaneous crossflow. Crossflow of oil from the tight layers to the most-permeable layer increases the intermediate oil recovery for a given volume of water injected. Oil recovery increases somewhat with a decrease in flow rate and considerably with a decrease in oil viscosity. Slow flow rates produce higher recovery but may not be feasible in the field for economic reasons. For M > 1, viscous crossflow contributes very slightly to oil recovery until the time of breakthrough of water from the most-permeable layer. After that, the viscous crossflow increases and creates a secondary oil stream close to the interfaces of the most-permeable layer. The additional oil is produced until the least-permeable layer also breaks through. A sequence of slow flow rate followed by a fast flow rate is shown to improve oil recovery for a given volume of water injected, and this occurs within a reasonable experimental time frame. The slow flow rate is set from a criterion of stable displacement in the most-permeable layer based on stability analysis, and the fast flow rate is based on the maximum pressure the model can take. The effect of variation in interfacial tension (IFT) on the displacement behavior was also studied. IFT is reduced from 35 to 4 and 0.5 dynes/cm [35 to 4 and 0.5 mN/m], respectively, by addition of two surfactants to the injected flood water. These IFT ranges are not sufficiently low to increase oil recovery from interfacial effects. The two surfactants influenced the recovery behavior differently.

Effect of contact-dehydrating sheet treatment on the color of bigeye tuna muscle.

A dehydrating device called contact-dehydrating sheet, is known to have an excellent capacity in dehydrating foodstuffs when it comes in contact with them. The effect of the sheet treatment on the color of bigeye tuna muscle was studied. Samples of 1.5cm thick were dehydrated by covering the sample slab with the sheet on the top side. After dehydrating for 5, 12h, 1, 2, 3 and 5 days at 3°C, each of the sample slabs wassliced horizontally along the treated side into 3 layers of equal thickness. It was found that the distribution of water removal in tuna muscle was more uniform than what occurred in beef and this uniformity might be due to less adipose and connective tissues. The ratio of metmyoglobin formation inupperlayerof dehydrated sample was the same with that of control and gradually increased with the prolonged treatment time. The iron content of samples rose from about 0.8 to 1.1mg% during the 5-day period dehydration. However, there was not much difference in redness of bigeye tuna muscle with the controls at varied iron content in this range. This phenomenon was thought to be due to the particular pattern of color (Mb) change in bigeye tuna muscle. This pattern was not significantly influenced by the formation of metmyoglobin.

What is responsible for thermal coupling in layered convection ?

Laboratory experiments have been conducted on convection in a layered system. The system consists in two liquid layers of equal thickness. The liquids are immiscible: the upper one is silicon oil, and the lower one is glycerol. The structure of convection has been analysed, and data obtained both on the temperature field and the velocity field. It is shown that the coupling between the two convecting systems in thermal, i.e. convection cells are superposed with uprising currents above uprisings. This result is surprising because it contradicts numerical experiments recently obtained for layered convection. These find mechanical coupling (cells are superposed but turn in opposite senses) to be the stable mode for the conditions we tried to reproduce in the laboratory. Several tests have been conducted in order to isolate the phenomenon which is responsible for the discrepancy between the two types of analyses. A tentative mechanism is proposed: it involves an equivalent interfacial longitudinal viscosity, whose origin is not yet clearly understood Etude experimentale de la convection dans un systeme forme de deux couches de liquides non miscibles superposees de meme epaisseur: huile au silicone en haut, glycerol en bas. Mesure des champs de temperature et de vitesse. Le couplage entre les deux systemes convectifs est «thermique» ce qui est en desaccord avec les experiences numeriques montrant que le couplage est «mecanique»

Interfacial Cracks in Ceramic‐to‐Metal Bonds under Transient Thermal Loads

The effect of a transient thermal load on an interfacial edge crack and center crack between a ceramic‐to‐metal bond was analyzed with the use of fracture mechanics. The deformations of the crack and the strain energy release rate were calculated for the case of a ceramic layer of equal thickness to the metal, one with one‐tenth the thickness of the metal, and one with 10 times the thickness of the metal. It was determined that for an edge crack, under slow cooling conditions, the steady‐state value of G is the largest, and G is largest for equal thicknesses of ceramic and metal. For a center crack, a maximum transient G occurs which is larger than the steady‐state value and the strain energy release rate is smallest for equal thicknesses of ceramic and metal.

Formation of PtSi in the presence of Al

The formation of Pt silicides in the presence of Al is studied using Al/Pt/Si structures with different layer thicknesses of Al. Both the Pt-Si and Pt-Al reactions take place simultaneously, starting around 200 °C, with the formation of PtSi and PtAl2 completed at 400 °C. With an equal layer thickness for all three layers, the two alloys formed stay in contact with each other in a stable form up to about 500 °C. With a layer thickness of Al twice or more that of Pt and Si, the PtSi layer is completely converted to PtAl2 at 450 °C. The released Si from such a reaction is mostly located under the PtAl2 formed. The relation between these results and the unstable PtSi/Al contact in devices is discussed.

On the relation between initial conditions and late stages of Rayleigh-Taylor instabilities

It is well known that the geometry and spacing of structures (diapirs) due to Rayleigh-Taylor instabilities developing in initially horizontal layers depend on the viscosities, the initial layer thicknesses and the boundary conditions of the layers. As all these factors have been investigated previously by other workers, this study examines systematically how the final wavelength and geometry of Rayleigh-Taylor instabilities are influenced by the shape of the initial deformable interface. Emphasis is placed on the distinction between the characteristic wavelength λ c (which is potentially the fastest growing) and the dominant wavelength λ d (which dominates the final stage): they may differ significantly. Assuming two layers of equal viscosities, equal or different thicknesses, and a rigid top and bottom, a series of two-dimensional finite element models is calculated varying the wavelength λ o and the amplitude h o of the initial perturbations. For harmonic initial perturbations, Fourier analysis of the early stages reveals the development and nonlinear “feeding” of higher orders which cannot be predicted by linear stability analysis. If these higher orders grow significantly faster than the initial wavelength they may overtake and dominate the final stage. As a result, h o , λ o -space is separated into regimes in which the characteristic wavelength dominates and in which the initial wavelength has sufficiently large amplitudes to control the final stage. In some cases the final wavelength differs from the characteristic wavelength by a factor as large as 4. Generalisation of the results for arbitrary structures is attempted using only growth rate curves known from linear stability analysis. Faulting, folding, differential erosion and deposition, and episodic sedimentation are proposed as potential candidates for initiating wavelengths different from that characteristic in the case of salt structures. In the case of a thin source layer the existence of diapiric overhangs and pendant peripheral lobes are found to depend on the initial wavelength. Fourier analysis is proposed as a powerful tool for determining the growth rates of geological structures which depart from sinusoidal geometries.

Color changes of beef using contact-dehydrating sheet.

A sheet containing highly osmotic agents was used for foodstuff dehydration. This sheet can remove the water in the foodstuffs when it comes in direct contact with them. Color changes of sheet-dehydrated beef were studied. Beef round cuts of 1.5cm thick were dehydrated by covering the samples with the sheet on the top side. After dehydration for 5, 12 hours as well as 1, 2, 3 and 5 days at 3°C, samples were sliced horizontally along the treated side into 3 layers of equal thickness. The uppermost layer (U) was found to be dehydrated the most, wherein the moisture content decreased from 71.7 to 59.1%. A dark red color has gradually developed in the U when dehydration time was prolonged. There was a parallel increase in both the TBA value and ratio of metmyoglobin in both the control and dehydrated U. A preventive effect on oxidations of lipid and myoglobin could be observed when beef was dehydrated for more than 2 days. However, oxidations of myoglobin and lipid were not the main factors in the formation of the dark color of U, but rather the concentration of red myoglobin pigment, in which the iron level was considered over 4mg of Fe/100g meat was considered to be the main cause of this darkening. There was a gradual change in the color at the surface of control and lower layer forming into a yellowish-brown color of metmyoglobin due to exposure to air. The inner layers were dehydrated less (from 71.7 to 68.0%) which might suggest that owing to indirect exposure to air, maintained a desirable redness.

Instability of Poiseuille flow of two immiscible liquids with different viscosities in a channel

We study the stability of plane Poiseuille flow of two immiscible liquids of different viscosities and equal densities. The problem is like one considered by C. S. Yih who found that flow in two layers of equal thickness was always unstable. We find regions of stability when there are three layers with one of the fluids centrally located. We view our contribution as a study of selection of stable steady flow from a nonunique continuum of Poiseuille flows all of which satisfy the steady Navier-Stokes and which differ from another in the number and thickness of layers of different viscosity. Experiments have shown that there is a tendency for the less viscous fluid to encapsulate the more viscous one. This arrangement of components, with the more viscous fluid in the center of the channel maximizes the mass flux for a fixed pressure gradient. A linear stability analysis of centrally located configuration to long waves is carried out by the analytic methods introduced by Yih [1]. The stability results depend on the viscosity and volume ratio in a fairly complicated way. The flow with the high viscosity fluid centrally located is always stable. Centrally located layers of less viscous fluid, called fingering flows, are always unstable.

Band structure of III–V and II–VI superlattices

The subband structure of semiconductor quantum wells and superlattices are calculated using the envelope function approximation. The dispersion relations in the plane of the layers of III–V ( GaAs Ga(Al)As ) and II–VI ( HgTe OdTe ) super lattices are analysed as a function of the superlattice wave vector. Pseudo-alloy ( GaAs AlAs ) structures with equal layer thicknesses have also been considered.

Energy spectra of donors in GaAs-Ga1-xAlxAs superlattice

The binding energies of the ground state of a donor atom in realistic GaAs-Ga1-xAlxAs superlattices which consist of a large number of equal thickness layers which alternate are calculated using a variational approach. The energy spectra are calculated as a function of layer thickness for the position of an impurity located both at the centre and at the edge of a GaAs layer. The effects due to different effective masses and dielectric constants in GaAs-Ga1-xAlxAs layers and the non-parabolicity of the GaAs conduction band are taken into account. The results show that the binding energy, as a function of layer thickness, exhibits only one peak in agreement with the conjecture of Chaudhuri (1983). Moreover, as the layer thickness reduces it approaches a stable limiting value. In addition, the authors result shows that the influence of non-parabolicity of the GaAs conduction band is considerably smaller than that predicted by other authors. In order to check the validity of their method, the authors have also calculated the corresponding quantity in the case of three quantum wells and compared it with the results of Chaudhuri and found that the correction to the main peak value of the binding energy is remarkable.

Correspondence between coherently strained multilayers and a single coherently strained layer on lattice mismatched substrate

The equilibrium in-plane lattice parameter for lattice mismatched multilayers, as first derived by Matthews and Blakeslee [J. Cryst. Growth 32, 265 (1976)], has been used to obtain an expression for the misfit between the multilayers as a whole and a lattice mismatched substrate. The resulting expression immediately suggests a correspondence between the multilayers as a whole and a single coherently strained layer of equal thickness but having a misfit equal to the misfit between the constituent layers spatially averaged over a single repeat distance. The present results are obtained without reference to the energy density of a misfit dislocation. In particular, the present correspondence allows one to predict the critical thickness of coherently strained multilayers if single-layer critical thicknesses are known.

Voidage profiles in packed beds of spheres

Voidage profiles in randomly packed beds of uniformly sized spheres are analysed by dividing the bed into a number of concentric layers of equal thickness, and by expressing the void fraction in a layer in terms of the contributions to the solid volume by spheres with centres lying in appropriate neighbouring layers. The number of spheres in a layer is expressed as a fraction of the total number in the bed. Sets of number fractions in layers up to a distance of about 4–5 particle diameters from the wall are estimated for different aspect ratios using several sets of reported void fraction data obtained by a variety of experimental methods. The number of fractions in the layer next to the one at 0.5 particle diameter from the wall and at 1.5 particle diameters completely characterize the voidage variations up to a distance of about 2 particle diameters from the wall. In this region the confining effect of the wall gives rise to these two non-random layers of the spheres. The two number fractions are correlated exponentially with the aspect ratio. Beyond this region, the structure of the packing becomes more and more random. A procedure is suggested for predicting the void fractions at distances between 2 and 4 particle diameters.

Both Surface Inequi-thickness Removal-both Surface X-ray Diffraction Method for Residual Stress Measurement in a Plate

The authors have proposed a method to measure the residual stress by X-ray on both surface after removing thin layers of equal thicknesses from both surfaces of a plate. In this paper is derived a new method of X-ray after removing inequithickness from both surfaces of a plate. The theories of the formar Single Surface Removal Method and Both Surface Removal Method are derived from the present theory as special cases. The authors applied this method to a quenched and tempered alloy steel plate of SKS 51 and discussed the influence of neglecting the inequality of removal thickness on both surface.