Meetings & Events

Spring 1999 logo1999 MRS Spring Meeting & Exhibit

April 5-9, 1999 | San Francisco
Meeting Chairs: Katayun Barmak, James S. Speck, Raymond T. Tung, Paul D. Calvert



Symposium G—Linking Materials Computation and Experiment

Chairs

Long-Qing Chen 
Dept of MS&E 
Penn State Univ 
118 Steidle Building 
University Park, PA 16802-5006 
814-863-8101

Richard LeSar
Structure/Property Relations
Los Alamos National Lab
MST-8 MS G755
Los Alamos, NM 87545
505-665-0420

Jeffrey Rickman 
Dept of MS&E 
Lehigh Univ 
Bethlehem, PA 18015 
610-758-4236

* Invited paper

SESSION G1: METHODS/TRANSPORT PROPERTIES 
Chair: Long-Qing Chen 
Monday Morning, April 5, 1999 
City (A)
8:30 AM *G1.1 
TOWARD A FIRST PRINCIPLES THEORY OF SPECTRAL DATA. Daryl W. Hess , Naval Research Laboratory, Complex Systems Theory Branch, Washington, DC; Joseph W. Serene, Georgetown University, Department of Physics, Washington, DC.

The past decade has brought amazing advances in angle resolved photoemission spectroscopies and scanning microscopies that probe electronic excitation and response spectra. These have enabled spectroscopic measurements on novel materials such as organometallic compounds and the high temperature superconductors. The result has been to find cases where our concepts of the nature of electronic excitations in metals and insulators are inadequate. While density functional theory can provide accurate calculations of total energies, the calculation of true excitation spectra lies outside this theoretical framework. On the other hand, thermodynamic properties and spectral functions are precisely defined within the propagator-functional formalism developed in the 60's. Advances in computer technology are bringing `first principles' calculations using these formal techniques within range. I will discuss the potential of self-consistent approximations within this theoretical framework to calculate excitation and response spectra in materials that have modest to strong electronic correlations with particular focus on quasi-one and -two dimensional organometallics. Provocative experimental data and numerical calculations performed as part of a DoD computational Grand Challenge project will provide illustrations.

9:00 AM G1.2 
AN ANALYTIC BOND-ORDER POTENTIAL FOR BORON NITRIDE. Detlef Conrad , Ivan I. Oleinik, David G. Pettifor, University of Oxford, Department of Materials, Oxford, UNITED KINGDOM.

An analytic bond-order potential is developed for boron nitride that is based on the real-space bond-order expansion within the tight-binding method. It includes not only the  bond contribution that is correct up to the fourth moment in the electronic density of states, but also a novel  bond contribution that handles correctly the formation of  states at the surface. We present molecular dynamics simulations for crystalline and amorphous boron nitride.

9:15 AM G1.3 
SENSITIVITY ANALYSIS, MODEL VERIFICATION AND EXPERIMENTAL DESIGN USING GENETIC ALGORITHMS. Brian J. Reardon , Los Alamos National Laboratory, Los Alamos, NM.

A fuzzy logic based multi-objective genetic algorithm (GA) is introduced and ultimately used as a Bayesian inference engine in model parameter optimization and experimental design. It will be shown that the uncertainties of the experimental observables to which one is optimizing can be propagated through to give uncertainties in the optimized model parameters. Given a distribution of optimized input parameters, a distribution of outcomes can be determined when using the model in a predictive fashion. This distribution of parameters and predicted outcomes is then used as a basis of discussion in terms of the model's ultimate predictive capabilities and guidance in experimental design. The models and corresponding experimental data that will be discussed include powder consolidation & sintering models for beryllium and tantalum.

9:30 AM G1.4 
INTERMOLECULAR POTENTIALS AND NANOSTRUCTURES OF CRYONIC ATOMIC-DISPERSED SOLUTIONS OF TRANSITION METALS IN CARBON. Tatyana M. Zhukovsky, Altai State Technical University, Department of General Physics, Barnaul, RUSSIA; Mark S. Zhukovsky, Serge A. Beznosyuk , Altai State University, Department of Physical Chemistry, Barnaul, RUSSIA.

Computer simulation of sandwich structure of graphitic carbon encapsulation of transition metal atoms in cryonic atomic-dispersed (AD) solutions of transition metals has been studied by using of the approximating quasi-particle density functional (AQDF) method. We have calculated intermolecular potentials for bonds of single transition metal atoms (Cr, Fe, Co, Ni, Mo, Ru, Rh) with single graphite sixty-atomic ring. All of this transition metals have a weak but very different interaction with C-ring originating from contact gluing exchange-correlation forces. Calculating bond lengths and cohesive energies dramatically modified by the metals. New ``sandwich-flip'' mechanism of the nanostructure atomic ordering in cryonic atomic dispersed solutions of transition metal atom (A) in aromatic carbon ring (R) systems is proposed and investigated by means of computer experiment. Calculations of activating energy potential barriers for sandwich-flips are based on interparticle potentials obtained by functional density methods. Presented results of computer simulating of A-R AD-solution are in a agreement with experiments.

9:45 AM G1.5 
THE BOND PASSIVATION MODEL: DIAGRAM OF CARBON NANOPARTICLE STABILITY. Slava V. Rotkin , Robert A. Suris, Ioffe Institute, St. Petersburg, Polytehnicheskaya, RUSSIA.

We present the modified phenomenological model of the energetics of carbon clusters. This approach being complementary to standard quantum-chemical calculations allows to evaluate the formation energies of carbon clusters with curved surface and to propose a growth mechanism. The modified model is applied to the pure carbon nanocluster formation process as well as to the formation of clusters with the passivated bonds (and to the formation from hydrocarbons). Taking into account the possible variation of the dangling bond energy leads to the significant changes in the diagram of cluster stability. Namely, at some critical bond softening (2-3 times comparing with the pure graphite bond) the region of the stability of planar graphene structure (piece of graphite monolayer) appears. For comparison, in frame of the original model (when the dangling bond energy is taken as a constant) a planar fragment of graphene is always unstable. The similar region was found corresponding to the optimal nanotube which becomes energetically favourable than the sphere. These results are in contrast with the conclusions made within the original model. Support of RFBR-96-02-17926, FAC-98062.

10:30 AM *G1.6 
EXTENDING ATOMISTIC SIMULATION TIME SCALES. Arthur F. Voter , Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM.

A significant problem in the atomistic simulation of materials is the time scale limitation of the molecular dynamics method. While molecular dynamics can easily access nanoseconds with empirical potentials, many of the most interesting diffusive events occur on time scales of microseconds and longer. If the transition state (i.e., the saddle point) for a given reaction pathway is known, transition state theory can be applied to compute a rate constant directly. If all possible events are known for a given system, these rate constants can be employed in a kinetic Monte Carlo algorithm to evolve the system from state to state over long time scales. Unfortunately, for realistic systems, the transition states are often hard to find. Moreover, it is often the case that our intuition about how the system will behave breaks down, so that key events are missing from the kinetic Monte Carlo treatment. This situation is typical in metallic surface growth, where complicated exchange events prevail, and in many other physically important processes, such as annealing after radiation damage, or diffusion at a grain boundary. I will discuss some new methods for treating this problem of complex, infrequent-event processes. The idea is to directly accelerate the molecular dynamics simulation to achieve longer times, rather than trying to specify in advance what the available mechanisms are. These new methods, hyperdynamics, parallel replica dynamics, and temperature extrapolated dynamics, can be used individually, or in combination, to extend the molecular dynamics simulation time by orders of magnitude, thus making much closer contact with experimental conditions. I will discuss the relative merits of the different methods and present results demonstrating the power of this general type of approach. Examples will include growth of a copper surface from vapor deposition and from ionized physical vapor deposition.

11:00 AM G1.7 
THE CONTRIBUTION OF THE SIX-JUMP-CYCLE MECHANISM TO TRACER DIFFUSION IN INTERMETALLIC COMPOUNDS. Graeme E. Murch and Irina V. Belova, University of Newcastle, Dept of Mechanical Engineering, Callaghan, AUSTRALIA.

It is well known that the six jump cycle mechanism provides the lowest energy penalty path for atomic diffusion in certain fully ordered structures of intermetallic compounds, notably in the B1/B2 and L12 structures. Although this mechanism has been discussed and analysed on numerous occasions certain basic inconsistencies have arisen about its occurrence and importance. These center on the contribution to tracer diffusion of the mechanism at levels of order above perfectly ordered ones. 
We have undertaken an extensive Monte Carlo computer simulation study of tracer diffusion in a four atom-vacancy exchange frequency model. Although it is clear that the vacancy frequently follows six-jump-cycle-like paths most of these paths are not actually pure cycles i.e. perfectly ordered starting configurations but are corrupted by existing antistructural atoms. Importantly, these corrupted cycles lead to extremely inefficient diffusion compared with the pure cycles. This is reflected in very small values of the tracer correlation factor near perfect order even after the filtering of simple jump reversals (disordering/reordering jumps). The ratio of experimental tracer diffusion coefficients in, say, B2 structures is frequently within the limits 0.5 and 2 for the six-jump-cycle mechanism. But because of effective concellation of many inefficient aspects of the diffusion process this does not imply that the six-jump-cycle actually dominates diffusion even in highly ordered situations.

11:15 AM G1.8 
ON THE PRESSURE DEPENDENCE OF SELF-DIFFUSION IN BODY-CENTERED CUBIC METALS. Peter Knorr , Christian Herzig, Institut fuer Metallforschung, Universitaet Muenster, GERMANY.

Research on the atomic mobility in solids has largely passed from measurements in pure metals to the study of more complicated structures like intermetallic compounds, amorphous metallic alloys, quasi- and nanocrystalline materials and even polymers during the past decade. Bearing this in mind, one might conclude that diffusion in pure metals is essentially understood and may be dealt with in the textbooks. However, while self-diffusion in face-centered cubic metals is indeed largely compatible with the underlying theory, there is a considerable lack in understanding self-diffusion in body-centered cubic (bcc) metals. Self-diffusion in bcc metals does not follow a simple Arrhenius law, and the violation of this law is still subject to a vigorous controversy. To contribute to this problem, the pressure effect of self-diffusion in the bcc modifications of iron, zirconium and thallium has been measured with the radiotracer technique. The experimentally accessible quantity, the activation volume, provides important supplementary information on the diffusion mechanism. However, comparison with theoretical results is indispensable for a meaningful interpretation of the experimental results. Since the increase of computational power in recent years has made it possible to calculate defect enthalpies and defect volumes with unprecedented accuracy, the new experimental data should prove particularly stimulating for theoretical calculations.

11:30 AM G1.9 
DYNAMIC PAIR MECHANISM OF DIFFUSION IN ORDERED STRUCTURES. Maria G. Ganchenkova and Andrei V. Nazarov, Dept of Material Science, Moscow Engineering Physics Institute, Moscow, RUSSIA.

The analysis of results of diffusion migration modeling in the ordered structures of B2-type allows us to make the conclusion about new diffusion mechanism - DP or Dynamic Pair mechanism as the leading mechanism in these structures. The simulation was made using Monte Carlo method. The activation barriers of atom jumps to vacancy are calculated by the static relaxation technique for both vacancy exchanges: with nearest-neighbour atoms and next-nearest-neighbour atoms. This is done for all possible positions of the second vacancy. Knowing these barriers it is possible to calculate the jump rates and to model the vacancy migration. From our simulation we have seen the following features of diffusion in ordered structures of B2-type: 1) In the case of ordered B2-type structure the vacancies, which are arrangement on the different sublatticies, are tending to form a dynamic pair, which is stable within certain intervals of parameters change. 2) The dynamic pair has a high diffusivity and gives an essential contribution to the diffusion in these structures. The simulation results are used for analysis of experimental data obtained by the different methods 
 

SESSION G2: PROCESS MODELING/POINT AND LINE DEFECTS 
Chair: Brent Fultz 
Monday Afternoon, April 5, 1999 
City (A)
1:30 PM *G2.1 
KINETIC MONTE CARLO MODELS FOR THE CHEMICAL VAPOR DEPOSITION OF THIN FILMS. David J. Srolovitz , Chaitanya Deo, Dept. of Materials Science & Eng., University of Michigan, Ann Arbor, MI; Corbett Battaile, Sandia National Laboratory, Albuquerque, NM.

Kinetic Monte Carlo simulations provide an ideal approach to modeling film growth process in situations in which crystal structure information is necessary and disparate kinetic time scales are important. This approach may be used to model hundreds of millions of reactions and can, in some circumstances, account for hours of chemical vapor deposition of thin films. Two specific examples will be emphasized. The first is the chemical vapor deposition of diamond. This area is now well developed and examples will be shown of morphology development, growth rate prediction and point defect incorporation. An example will also be presented on the use of this approach for optimizing reactor conditions. The second example will be the growth of ordered crystal structures. We will examine the issues associated with multi-component film growth and present some preliminary results.

2:00 PM G2.2 
MODELING THE PHOTOCHEMICAL REACTIONS OF DIAMOND. John B. Miller , Western Michigan University, Kalamazoo, MI.

Photochemistry is a successful method for modifying diamond surfaces under mild, area-specific, and controllable conditions. Observed reaction mechanisms include radical substitution and photoinduced electron-transfer. These reactions can introduce a broad range of chemical functionality to the diamond surface including hydride, halide, amines, alcohol, ethers, thiols, and sulfides. Molecular dynamics have been used to: (1) verify surface structure through comparison with observed infrared spectra, (2) examine molecular-level effects leading to observed tribological and surface-energy measurements. In addition, ab initio calculations were employed to examine the reactive systems, calculating energies along the observed reaction pathway, and predicting optical spectra, comparable to the observed wavelength dependence of the surface photoreactions.

2:15 PM G2.3 
POLYCRYSTALLINE ALUMINUM DEPOSITION: A KINETIC MONTE CARLO ATOMISTIC SIMULATION. J. Emiliano Rubio , Luis A. Marques, Martin Jaraiz, Luis A. Bailon, Juan Barbolla, Univ. of Valladolid, Dept de Electricidad y Electronica, Valladolid, SPAIN; Maria J. Lopez, Univ. of Valladolid, Dept de Fisica Teorica, Atomica y Nuclear, Valladolid, SPAIN; George H. Gilmer, Lucent Technology Bell Labs, Murray Hill, NJ.

The microstructure of the polycrystalline metal films used for interconnects in integrated circuits plays a crucial role in determining their properties and reliability. Accurate models for polycrystalline materials are required in the design of new interconnect technologies, especially as the dimensions of device components become comparable to grain sizes. In the sub-quarter-micron regime, atomistic simulations can provide a unique insight into the nucleation and growth mechanisms which eventually determine the morphology and microstructure of the deposited films. We have developed a Monte Carlo atomistic deposition simulator that includes a detailed model for the polycrystalline structure of thin films. In this work, we have simulated sputter-deposition of polycrystalline aluminum films onto amorphous substrates at different temperatures and various deposition rates, as well as post-deposition annealing. The initial nucleation of microcrystals with different orientations and the subsequent growth and interaction between them give rise to samples with different textures. At high temperatures and low deposition rates, we have observed a strong (111) texture, as well as a large average grain size. After deposition, the average grain size increases as a function of annealing time in agreement with experiments. The grain size distribution and the development of preferred crystallographic orientations will be discussed and compared with experimental results.

2:30 PM G2.4 
DYNAMIC MODELING OF UNDERFILL FLOW FOR MICROELECTRONICS PACKAGING. N. Iwamoto , Johnson Matthey Electronics, San Diego, CA; M. Nakagawa, G. Mustoe, Colorado School of Mines, Particulate Science and Technology Group, Golden, CO.

Underfill materials within the microelectronics packaging industry consist of filled polymer matrices which protect the interconnect and the silicon chip from stress induced failure. The uncured materials are often deposited using capillary action underneath the chip. However, underfill flow simulation using contiuum technique overlooks the importance of the micromechanics which exists. Although capillary action generally drives the filling phenomenon, it is the underlying principles that govern the underfill performance properties that are in need of understanding. For instance flow speed, filler settling, filler striation and voiding are all performance properties that require a mechanistic understanding in order to improve the materials. Although binder and filler effects are expected from a combination of surface energy and particle dynamics drivers, the simple identification of the problem does not instruct how to control these effects. In order to address these issues in connection with formulation constituent effect, two types of dynamic modeling have been initiated: molecular modeling and discrete element modeling. Molecular modeling was engaged in order to understand the specific molecular compositional effects and the interfacial energetics that drive capillary action with the intent to use this understanding in the particle dynamics simulations. Discrete element modeling was engaged in order to scale the simulations to a macroscopic scale and to understand how energy and particle distribution effects the particle dynamics of the fill phenomenon. We have found that three fundamental forces, lubrication, drag and adhesion are required in order to begin to define the model parameters involved in the flow simulation.

3:15 PM *G2.5 
SLIDING AND SLIP RESISTANCE OF DISLOCATIONS ON AND NEAR GRAIN BOUNDARIES AND INTERFACES. R.G. Hoagland , School of Mechanical and Materials Engineering, Washington State University, Pullman, WA.

Grain boundaries and interfaces generally separate two elastically dissimilar materials. Consequently, lattice dislocations experience image forces which either attract or repel them away from boundaries. Such interactions are described by linear elasticity, either in the isotropic approximation or the fully anisotropic formalisms. However, slip through an interface involves energetics that are highly nonlinear as it passes through the elastically nonlinear regime of the boundary itself and creates and leaves behind a grain boundary dislocation in the process. In addition, dislocations that reside on grain boundaries and interfaces enable sliding at stress levels that are significantly below that required to slide dislocation-free interfaces. This paper describes the results of atomistic simulations to determine the energetics of both classes of problems, i.e., slip transection of boundaries and sliding. Some of the nomenclature relevant to boundaries and defects that in boundaries is briefly described. We also describe the use of elastic band methods for characterizing the shape of energy barriers separating adjacent equilibrium states of the system and the stresses required to move the system from one state to the other. We show that dislocations on boundaries in Al often, but not always, reduce their sliding resistance. We also discuss the energetics associated with the transection of an interface in the Cu-Ag system. This work was supported by the U. S. Dept. of Energy, Office of Basic Energy Sciences, Department of Materials Science.

3:45 PM G2.6 
MODELING AND EXPERIMENTAL OBSERVATION OF GRAIN BOUNDARY DISLOCATION STRUCTURE AND DYNAMICS. D.L. Medlin and S.M. Foiles, Sandia National Laboratories, Materials and Engineering Sciences Center, Livermore, CA.

Interfacial dislocations play important roles in determining the structure and behavior of grain boundaries. In this presentation we discuss atomistic and continuum models for the interfacial dislocations present at the =3 {112} and {111} interfaces in FCC metals and relate these results to experimental electron microscopic observations of dynamic grain boundary processes. Two classes of interfacial dislocations play a role in this system: Dislocations with Burgers vector a/6<112> and with Burgers vector a/3<111>. Such dislocations originate as a means of accommodating deviations from ideal lattice coincidence or through lattice dislocation decomposition reactions. Even this relatively simple system yields a rich variety of phenomena that can be directly understood and predicted from the interfacial dislocation structure. In particular, we will focus on two examples: (1) glide and climb processes of a/3<111> dislocations leading to interfacial sliding and twin growth and (2) shear processes of a/6<112> dislocations and their impact on interfacial dissociation. Throughout, we emphasize the necessarily close coupling between computation and experiment, with experimental observation of defect configurations motivating the atomistic and continuum calculations and the resulting calculations providing insight critical to interpreting the observations. This work is supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Science, under contract DE-AC04-94AL85000.

4:00 PM G2.7 
GREEN'S FUNCTION METHOD FOR MODELING DISLOCATIONS IN CRYSTALS AND INTERPRETATION OF OBSERVED X-RAY DIFFRACTION SPECTRA. Vinod K. Tewary , Materials Reliability Div, National Institute of Standards and Technology, Boulder, CO.

The effect of dislocations and other extended defects in crystals is to broaden the X-ray diffraction lines. The broadening occurs because of the long-range displacement field of the dislocations and provides useful information about the mechanical properties of crystals. We calculate the displacement field for a dislocation in fcc copper by using the lattice Green's function method. We then use the displacement field to calculate the broadening of the X-ray diffraction lines due to a single dislocation and average over a distribution of dislocations. Lattice Green's functions are calculated by using a recently developed method of the defect space Fourier transform that exploits the local periodicity of large defects for solving the Dyson equation in reciprocal space. The main advantages of the lattice Green's function method used along with the defect space Fourier transform method are that (i) it gives semi-analytical expressions for interpreting the measured X-ray diffraction spectrum, (ii) it is a multi-length scale approach that spans the length scales from atomistic to continuum, and (iii) it can model large crystallites containing million or more atoms with relatively small CPU effort. The ability to model large crystallites is especially useful for interpreting X-ray diffraction spectra because the finite size of the model may introduce spurious broadening in the calculated spectra. The calculated displacement field automatically reduces to the continuum result in the asymptotic limit without any need to prescribe special boundary conditions.

4:15 PM G2.8 
SOLUTE DISTRIBUTIONS AROUND MOVING DISLOCATIONS. Yi Wang , David J. Srolovitz, University of Michigan, Dept. of Materials Science & Engineering, Ann Arbor, MI; Jeffrey M. Rickman, Lehigh University, Dept. of Materials Science & Engineering, Bethlehem, PA; Richard A. LeSar, Los Alamos National Laboratory, Los Alamos, NM.

The distribution of solute atoms around dislocations is key to determining the magnitude of the solute strengthening effect in metals. The steady state solute atom distribution around both static and dynamic (constant velocity) dislocations has received considerable theoretical attention. In the present study, we address the issue of determining the general, non-steady-state distribution of solutes around a dislocation. We perform Monte Carlo simulations of a single edge dislocation in a field of discrete, diffusing impurity atoms. We explicitly consider such effects as solute concentration, solute strength, solute mobility, dislocation mobility, temperature and external stress. In this study we examine, the spatial distribution of solute in both the transient and steady-state regime and the retarding force exerted on the dislocation by the impurities. The latter may be directly compared with analytical, steady-state predictions. Preliminary results for a finite dislocation density will also be presented.

4:30 PM G2.9 
MAGNETIC FIELD INDUCED GENERATION OF A-LIKE CENTERS IN Cz-Si CRYSTALS. Mark N. Levin , Boris A. Zon, Voronezh State University, Dept of Physics, Voronezh, RUSSIA.

The effect of constant magnetic field (CMF) induced generation of oxygen-vacancy defects in Czochralski-grown silicon crystals (Cz-Si) was detected for the first time. It occurs in the narrow interval of magnetic fields near the threshold of the earlier observed effect of the pulsed magnetic field (PMF) generation of A-like centers (JETP 84, 1997, 760). We suggested an excitation of Si-O bond of interstitial oxygen as a possible start-up mechanism of the A-like centers generation in Cz-Si crystal. The necessary stages of the excitation are the magnetic field controlled population of the low vibrational level of the Si-O bond metastable term and the phonon assisted population of its upper levels. The two processes go on consecutively in the PMF and concurrently in the CMF. The Si-O bond excitation in the CMF is limited from below by severe decrease of the tunnel population of its metastable state and it is limited from above by increase of the reverse tunneling from the metastable state into the ground one when the process prevails over the phonon assisted population of the upper vibrational levels of the metastable term. Unlike the case of CMF, the Si-O bond excitation in the PMF is not limited from above as the phonon assisted population of the upper vibrational levels of the metastable term occurs in pauses between the magnetic pulses when the terms are restored to their original forms. The experiment on the combined PMF-CMF treatment definitely confirms the predicted suppression of the PMF-induced defect generation by the unidirectional CMF in the region above the threshold and thereby gives a strong additional support to the model. 
 

SESSION G3: INTERFACIAL STRUCTURE AND THERMODYNAMICS 
Chair: Jeffrey M. Rickman 
Tuesday Morning, April 6, 1999 
City (A)
8:30 AM *G3.1 
ROLE OF COHERENCY STRAIN IN MICROSTRUCTURAL EVOLUTION. Jong K. Lee , Department of Metallurgical and Materials Engineering, Michigan Technological University, Houghton, MI.

Recent explosion of advanced computational methods-boundary element, boundary variational, phase field, and discrete atom method-has shed much light to our understanding both coherent phase equilibria and coherent precipitate morphology. This presentation will focus on the discrete atom method and its recent findings. Wetting of one phase by another phase is commonly accepted as a surface energy-related phenomenon. Instead of surface energy minimization, however, strain energy minimization can induce wetting. In a multi-phase system, a misfit-free, soft particle can migrate toward a misfitting hard particle and reduce its strain energy, resulting in a complete wetting. Depending on the misfit nature, a partial wetting is also possible. Most ordering phenomena are understood in terms of an attractive interaction between unlike neighbors, but rarely in terms of a strain relaxation theory. Thus, according to quasi-chemical theory, a repulsive interaction between unlike neighbors leads to a phase separation in a binary system. It is demonstrated that the presence of coherency strain can lead such a system to an ordered, superlattice structure.