Phase segregation dynamics in particle systems with long range interactions. I. Macroscopic limits

We present and discuss the derivation of a nonlinear nonlocal integrodifferential equation for the macroscopic time evolution of the conserved order parameter (r, t) of a binary alloy undergoing phase segregation. Our model is ad-dimensional lattice gas evolving via Kawasaki exchange with respect to the Gibbs measure for a Hamiltonian which includes both short-range (local) and long-range (nonlocal) interactions. The nonlocal part is given by a pair potential ^dJ(|x–y|), >0 x and y in ^d, in the limit 0. The macroscopic evolution is observed on the spatial scale ^–1 and time scale ^–2, i.e., the density (r, t) is the empirical average of the occupation numbers over a small macroscopic volume element centered atr=x. A rigorous derivation is presented in the case in which there is no local interaction. In a subsequent paper (Part II) we discuss the phase segregation phenomena in the model. In particular we argue that the phase boundary evolutions, arising as sharp interface limits of the family of equations derived in this paper, are the same as the ones obtained from the corresponding limits for the Cahn-Hilliard equation.     

Analytical electron microscopy study of diffusion-bonded multiphase system

This study presents diffusion experiments of NiAl coupled with pure Ni (Ni/NiAl). The couple produces the Ni₃Al-based intermetallic phase ( phase) as an intermediate layer at the interface during diffusion annealing. Analytical electron microscopy is used to examine microstructural features, crystallographic orientation and compositional variations across the interface. Interdiffusivities are measured from the compositional variations. It is shown that the growing behavior of the phase changes between higher and lower annealing temperatures. The growth kinetics of the phase is also discussed.     

The exact phase diagram of the quantumXY spin glass model in a transverse field

The infinite rangeXY spin glass model in a transverse field is investigated by means of the Trotter-Suzuki approach. The exact phase diagram is obtained showing that a spin glass transition takes place for non-zero values of the transverse field up to a critical value _c =1.440.01. The present numerically exact calculations are in good agreement with our previous approximate results and they clear remaining discrepancies from previous work.     

The van der Waals limit for classical systems

For a -dimensional system of particles with the two-body potentialq(r)+ ^v K(r) and density , it is proved under fairly weak conditions onq andK that the canonical pressure (, ) and chemical potential (, ) tend to definite limits when 0. The limiting functions are absolutely continuous and are given in terms of the derivative of the limiting free energy density which was found in Part I.     

Influence of γ radiation on the structure-sensitive properties of CuTi amorphous alloy

The influence of small doses of radiation on the structure-sensitive properties of CuTi amorphous metallic alloy (AMA) is investigated. The AMA exhibit brittle behavior. It is found that, in samples exposed to radiation, the nonlinear behavior of the load-elongation curve is more pronounced and begins sooner. A small change in the fracture morphology in these samples is observed by raster electron microscopy. The additional broadening of the first amorphous maximum and its shift on the x-ray diffraction patterns correlates with increase in the dose. The modification of the structural-relaxation processes on heating the initial and irradiated samples is traced by the acoustic-emission method. The activation energy of these processes is determined.Tomsk State Architectural and Building Academy. Translated from Izestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 55–59, August, 1994.     

Ordered nickel-iron-nitrogen phase produced by elevated temperature nitrogen ion implantation

Implantation of 1×10¹⁸N ₂ ⁺ /cm² at 60 keV ion energy into pure bcc-Fe held at 400°C during implantation yields the well-known ferromagnetic '-Fe₄N ordered fcc compound with two inequivalent crystallographic sites, one of which consists of two different magnetic sites. These sites are readily identified via their hyperfine interaction parameters as detected by conversion electron Mössbauer spectroscopy of the near-surface layer. X-ray diffraction confirms the N sublattice ordering. Here, nitrogen implantation under identical conditions into a disordered fcc Ni_0.8Fe_0.2 alloy (permalloy) yields a paramagnetic phase with only one site defined by a rather large quadrupole interaction (1.15 mm/s). The X-ray pattern is clearly that of the ordered '-(Ni_0.8Fe_0.2)₄N structure so we conclude that the Fe atoms occupy only the face-centered lattice sites where each can bond with two nearest-neighbour N atoms on opposite sides. Thus, additional ordering within the Ni-Fe sublattice has been induced by the elevated temperature implantation process. Post-implantation annealing at 400°C decomposes the ' phase.     

Stochastic Schrödinger operators and Jacobi matrices on the strip

We discuss stochastic Schrödinger operators and Jacobi matrices with wave functions, taking values in ^l so there are 2l Lyaponov exponents ₁..._l0 _l+1..._2l =–₁. Our results include the fact that if ₁=0 on a set positive measure, thenV is deterministic and one that says that {E|exactly 2j 's are zero} is the essential support of the a.c. spectrum of multiplicity 2j.Research partially supported by USNSF under grant DMS-8416049     

Mössbauer Spectroscopy Study of Iron Nickel Alloys

Three samples of Fe_100–x Ni _x (with x=30, 35 and 40) were prepared by arc melting technique. The Mössbauer spectra of the three samples were collected and analyzed. The spectrum of the sample with x=30 consists of a singlet and a sextet. The singlet component which has isomer shift (IS=–0.08 mm/s) is attributed to a superparamagnetic phase. The value of the magnetic hyperfine field associated with the sextet component, 34.0 T, is consistent with that of -Fe–Ni alloy. In the spectra of the other samples the central line disappears. The magnetic component, used in fitting the spectrum of the sample with x=40 has a hyperfine magnetic field B _hf=30.0 T. This component is assigned to the high-spin -FCC Fe–Ni phase. Two magnetic components of 16.3 T and 27.3 T are used to fit the spectrum of the sample with x=35. The 27.3 T component is associated with the typical high-spin -FCC Fe–Ni phase while the 16.3 T component is associated with a -FCC Fe–Ni phase with magnetic relaxation.     

Structural and phase transformations in a carbide-strengthened alloy based on Ni3Al at high temperatures

A comprehensive study was made of structural and phase transformations in an alloy based on Ni₃Al. It is shown that the aggregate structure formed in the alloy —in which particles of Cr₇C₃ carbides are located preferentially along grain boundaries — block the migration of the carbides. The intensive dissolution of the strengthening carbide phase seen at T 1573 K is accompanied by the formation of two-phase ( + ) boundary regions. These regions are the result of an increase in the concentration of chromium. The method of differential thermal analysis was used to detect the occurrence of an endothermic reaction in the alloy at T>1573 K. This reaction is associated with saturation of the -phase with carbon up to the eutectic concentration and the fusion of the eutectic.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 55–58, March, 1987.     

On the 3+ level in Os186 populated in Re186 Β-decay

The coincidences of the 400–1100 keV gammas with the conversion electrons of the 137 keV transition were measured with the intermediate image spectrometer modified for - coincidences. The e_L 137- 770 keV coincidences were observed. Consequently, in addition to the known 768 keV transition, there is another one with closed energy. For this transition the relative intensity ratioI ⁶³² /I ⁷⁷³ =8±2 was determined. The corrected decay scheme of Re¹⁸⁶ is presented.     

Asymptotic Expansion of the Pressure in the Inverse Interaction Range

We consider an Ising system in d2 dimensions with a ferromagnetic Kac potential whose scaling parameter is denoted by . We derive an asymptotic series for the thermodynamic pressure P _, in powers of . The 0th-order term of the expansion is the mean-field pressure of the Lebowitz and Penrose theory.     

On birth and death processes in symmetric random environment

We prove a limit theorem for a process in a random one-dimensional medium, which has been considered before as a model for hopping conduction in a disordered medium. To the edge between the two integersj and (j+ 1) a rate _j > 0 is attached. These _j :j integral are taken as independent, identically distributed random variables, and represent the medium. For given values _j, X(t) is a Markov chain in continuous time which jumps fromj to (j + 1) and from (j + 1) toj at the same rate _j. We show that in many cases there exists normalizing constants y(t) (which tend to oo witht) such that the distribution of X(t)/(t), or more generally of the whole processX(st)/(t) _S0, converges to a limit as t . The limit process is continuous and self-similar.     

High-spin isomer in 93Mo

The high-spin states of ⁹³Mo have been studied by a ⁸²Se( ¹⁶O, 5n) ⁹³Mo reaction at a beam energy of 100 MeV using techniques of in-beam -ray spectroscopy. Measurements of -t, --t coincidences, -ray angular distributions and -ray linear polarizations were performed. The high-spin isomer was found as a (39/2^-) state at about 9.7 MeV. The near-yrast states in ⁹³Mo were interpreted using the weak-coupling picture of a d_5/2 neutron to a neutron magic core nucleus ⁹²Mo.     

Some critical exponent inequalities for percolation

For a large class of independent (site or bond, short- or long-range) percolation models, we show the following: (1) If the percolation densityP (p) is discontinuous atp _c , then the critical exponent (defined by the divergence of expected cluster size, nP _n (p) (P _c –P)^– asp p _c ) must satisfy 2. (2) or (defined analogously to, but asp p _c ) and [P _n (p _c ) (n ^–1–1/) asn ] must satisfy, 2(1 – 1/). These inequalities for improve the previously known bound 1(Aizenman and Newman), since 2 (Aizenman and Barsky). Additionally, result 1may be useful, in standardd-dimensional percolation, for proving rigorously (ind>2) that, as expected,P _x has no discontinuity atp _c .     

A dynamical system with integer information dimension and fractal correlation exponent

In this paper we construct a family {T }, 0<<1/2, of exact endomorphisms of [0, 1] such that the invariant measurem ofT is equivalent to Lebesgue measure but has fractal correlation exponent =2. This shows that an almost complete dichotomy can exist between the information dimension and the correlation exponent in observable dynamical systems.Research supported by the Natural Sciences and Engineering Research Council of Canada     

Effects of short-range order on the widths of split dislocations in Cu-Ga solid solutions

Transmission electron microscopy has been used to examine the packing-defect energy of a Cu-Ga alloy as a function of composition. The effective is increased after recrystallization annealing. Destruction of short-range order by cold deformation reduces .Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, Vol. 12, No. 1, pp. 112–117, January, 1969I am indebted to V. E. Panin and A. D. Korotaev for valuable advice and discussions.     

Interface Microstructures of Si3N4/Fe and Fe-Cr Alloys Joints

Interfaces of solid state bonded Si₃N₄ceramics with Fe and Fe-(5, 10, 15 wt%)Cr alloy interlayers inArgon for 1 h at 1100°, 1200° and 1300°C have beencharacterized by electron probe microanalysis (EPMA) and transmissionelectron microscopy (TEM). Smooth interfaces with no evidence ofreactions products resulted when bonding at 1100°C. However, theinteraction between the ceramic and the metal increased at higherbonding temperatures and Cr-contents. In all samples Si and N fromthe ceramic dissolve and diffuse in the metal interlayer, whereas thesintering additives of the ceramic remain inactive.Low Cr-content (5%) interlayers resulted in the formationof an interfacial zone composed of two sublayer structures; adjacentto the ceramic was a thin one containing the sintering aids ofSi₃N₄ and fine precipitates of Fe₃Si and -Fe₄N in a bcc-Fe matrix. The second was thicker and includedfine Fe₃Si,-Fe₄N and-Fe₂N precipitates in abcc-Fe matrix. The bond region with high Cr-content interlayersincluded three sublayer structures. The first one next to the ceramicwas a bcc-Fe matrix containing sintering aids, fine dispersedFe₃Si and-Fe₄N, and CrN. The secondsublayer was similar but without any segregants from the ceramic. Thethird one, finally had a lamellae structure of Cr₂N/bcc-Fe and the Fe matrix contained also-Fe₄N.The interactionbetween the ceramic and the metal interlayer is believed to becontrolled by the solution rate of N in the alloy foils.     

Transient and steady state creep of Al-4.5 wt.% Mg during phase transformation

Transient and steady state creep of Al-4.5 wt. % Mg alloy was studied under various constant stresses ranging from 91 MPa to 117 MPa in the temperature range from 473 K to 553 K. The results of creep characteristics have shown two main deformation temperature regions (below 493 K and above 513 K as well as a transient region between these temperatures). Peak values of transient creep parametersB andn were obtained at 493 K. The transient creep parameterB was related to the steady state creep rate _st through the exponent which was found to range from 0.85 to 0.5. The stress exponentm of the steady state creep has been found to be minimum at the steady state strain peaks, which is characteristic of dislocation climb along the grain boundaries. Microstructural analysis confirmed that the above mentioned mechanism took place in the dissolution region of-phase.     

Analysis of Similarity of Dislocation Interactions in Single Crystal Ni3Ge

Using the methods of diffraction electron microscopy and mechanical testing, the evolution of dislocation structure accompanied by deformation of single-crystal Ni₃Ge with different orientation of the axis of straining is studied at a range of temperatures. A linear relationship between shear stress and dislocation density ^0.5 is established. An analysis of the similarity of dislocation interactions is conducted in Ni₃Ge over a range of temperatures with developed octahedral and cubic slips, i.e. up to the anomaly peak temperature and higher, respectively. It is found out that under the octahedral slip, the dislocation interactions up to fracture deformations are similar at different temperatures in question. The similarity is also observed within the temperature range with developed cubic slip.     

A “hydrodynamic” theory of surface reaction rates

The Brownian motion of adsorbed particles is described in terms of the first four velocity moments of the distribution function (number density, momentum density, energy density and energy current density). The resulting hydrodynamic equations turn out to be sufficient for a simple derivation and extension of Kramers' results for chemical reaction rates in terms of the friction constant of an underlying Fokker-Planck equation. An interpolation formula is obtained for() containing Kramers' results for small and large as limiting cases. For temperaturesT small compared to the well depthV ₀ one finds a large regionT/V ₀/v ₀V ₀/T in which Eyring's absolute rate theory is approximately valid.On leave of absence from Physikdepartment der TUM, München-Garching