# 1997 MRS Spring Meeting & Exhibit

**March 31 - April 4, 1997**

**| San Francisco**

Meeting Chairs: Linda G. Griffith-Cima, David J. Eaglesham, Alexander H. King

Meeting Chairs: Linda G. Griffith-Cima, David J. Eaglesham, Alexander H. King

## Symposium T—Computational Materials Science at the Mesoscale

### Chairs

Elizabeth Holm

Dept of Theoretical & Comp Matls

Sandia National Laboratories

MS 1400

Albuquerque, NM 87185-1411

505-844-7669

Richard LeSar

Modeling Ctr for Matls Science

Los Alamos National Laboratory

MS K765

Los Alamos, NM 87545

505-665-0420

Peter Voorhees

Dept of MS&E

Northwestern Univ

Evanston, IL 60208-3108

847-491-7815

In sessions below "*" indicates an invited paper.

SESSION T1: ATOMISTIC APPROACHES TO DISLOCATION MODELING

Chair: Richard A. LeSar

Tuesday Morning, April 1, 1997

Nob Hill D

**8:30 AM *T1.1
**ATOMISTIC SIMULATION OF GRAIN BOUNDARY DEFECTS: DISLOCATIONS AND STEPS, Richard G. Hoagland, Washington State Univ, Dept of M&ME, Pullman, WA; R. J. Kurtz, Pacific Northwest National Laboratory, Richland, WA; B. Ding, J. P. Hirth, Washington State Univ, Dept of M&ME, Pullman, WA.

Two symmetric tilt boundaries, Sigma11 and Sigma 19 , were modelled using EAM potentials for aluminum. Of particular interest is the resistance which the boundaries offer to sliding of one grain with respect to the other. Accordingly, we examined the dependence of the low temperature boundary energy on the relative intra-grain displacements and accompanying internal relaxations. Several low-energy, faulted structures are found that correspond to metastable intermediate states within the boundary unit cell. These metastable states point to the existence of stable partial dislocations. We introduced dislocations into the models using the exact displacement field for dislocations on the interface of two elastically dissimilar and anisotropic crystals. Some dislocations must be accompanied by steps (in which case the pair form a disconnection), to avoid the creation of high energy faults. The dichromatic complex is shown to be a simple tool to locate and identify candidate disconnections. We describe the relaxed properties of several disconnections and pure dislocations, some of which spontaneously decompose into partials. We also employ elastic band methods to examine the stresses required to move these defects and thereby promote grain boundary sliding.

**9:00 AM T1.2
**GREEN'S FUNCTION BOUNDARY CONDITIONS IN 2-D AND 3-D ATOMISTIC SIMULATIONS OF DISLOCATIONS, Satish I. Rao, Jeff Simmons, UES Inc, Dayton, OH.

Atomistic simulations of dislocation structures are necessary in order to account for nonlinear effects in the core region. For this reason, traditional approaches have involved fixing the atoms at some distance from the dislocation core, in order to provide the correct boundary conditions. However, since the fixed region does not respond to changes in the shape of the dislocation core, there is always an intrinsic incompatibility between the boundary conditions and the relaxed core region. This problem is usually circumvented by using large cells, so that the errors introduced in linking that continuum and atomistic length scales have only a negligible effect. In this work, a Green's function (GF) technique is developed, whereby the boundary region is allowed to relax, according to continuum elasticity theory, in response to core relaxation. This has the advantages of self-consistently linking the two length scales and reducing the total number of atoms required in the simulation. Since the boundary forces are self-consistently relaxed, this provides an accurate and efficient means of determining the energies and mobilities of point defect like perturbations on dislocation lines. In this work, both two-dimensional (2-D) and three-dimensional (3-D) methods are developed. The 2-D method Is useful for simulations of straight dislocations, while the 3-D method is useful for more complex geometries. Since the initial conditions for 3-D simulations are usually built up from 2-D segments, the 2-D technique is also valuable for insuring that the boundary conditions for the more complex simulations are self-consistent. Examples of recent dislocation simulations using GF boundary conditions are given.

**9:15 AM T1.3
**ACCURATE ATOMISTIC CALCULATIONS OF THE PEIERLS BARRIER AND KINK-PAIR FORMATION ENERGY FOR <111> SCREW DISLOCATIONS IN BCC Mo, Wei Xu, John A. Moriarty, Lawrence Livermore National Laboratory, Dept of Pysics & Space Tech, Livermore, CA; Satish Rao, Chris Woodward, UES Inc, Dayton, OH.

Multiscale modeling of plastic flow and other mechanical properties in bcc transition metals requires an accurate atomistic description of dislocation energetics as input to larger length scale theories and simulations. Using multi-ion MGPT interatomic potentials derived from first-principles generalized pseudopotential theory, we have recently calculated a wide variety of deformation and defect properties of bcc Mo with considerable success [1], including the equilibrium structure of the <111> screw dislocation core. In the present work, we are using the same MGPT potentials to investigate the energetic barriers to dislocation motion in Mo, including both the full orientation dependence of the Peierls stress required to move an ideal straight <111> screw dislocation and the activation barrier for kink-pair formation in nonstraight screw dislocations. Many-body angular forces, which are accounted for in the present theory through explicit three- and four-ion potentials, are generally important to such properties for the bcc transition metals. This is demonstrated explicitly through calculation of the closely related (110) and (112) gamma surfaces (generalized stacking fault energies). As expected, neither surface displays a stable stacking fault, but the magnitude of the unstable stacking fault energy for the (110) surface is enhanced by 50% over that obtained from a simple radial-force Finnis-Sinclair potential for Mo. By applying various external shear stresses on the relaxed equilibrium <111> screw dislocation core in Mo, we have found the (minimum) ideal Peierls stress for dislocation motion is on the order of 0.02G, where G is the shear modulus of the bulk metal. At the same time, we have found that the calculated Peierls barrier is sensitive to the orientation of the applied stress. A detailed comparison has also been made of two different treatments of the boundary conditions: (i) fixed boundary conditions obtained by anisotropic elasticity theory and (ii) boundary conditions determined from a Green's function approach.

**9:30 AM T1.4**

ATOMISTIC SIMULATIONS OF THE STRUCTURE, ENERGETICS, AND CROSS SLIP OF SCREW DISLOCATIONS IN COPPER, Torben Rasmussen, Karsten W. Jacobsen, Technical Univ of Denmark, Dept of Physics, Lyngby, DENMARK; Torben Leffers, Ole Boecker Pedersen, Riso National Laboratory, Dept of Materials, Roskilde, DENMARK.

The role of cross slip of screw dislocations in macroscopic phenomena such as fatigue and plastic deformation is well established. However, the intrinsic properties of cross slip of a dissociated screw dislocation is still not fully understood. We use a realistic many-body potential to perform atomistic simulations of the structure and energetics of different dislocation configurations relevant to cross slip. The minimum stress-free activation energy and activation length in the Friedel-Escaig cross slip mechanism are determined. The simulations show a new energetically favorable configuration of a dissociated screw dislocation not previously considered in elasticity theory. The importance of a free surface as a center of nucleation for this configuration is demonstrated, and simulations showing surface nucleated cross slip were performed. These simulations suggest that cross slip of a dissociated screw dislocation occurs preferentially at free surfaces.

**9:45 AM T1.5** **
**HYDROGEN DISTRIBUTION AROUND EDGE DISLOCATIONS IN FCC METALS, Bjorn von Sydow, Goran Wahnstrom, Jan Hartford, Chalmers Univ of Technology, Dept of Applied Physics, Goteborg, SWEDEN; Lars B. Hansen, Technical Univ of Denmark, Dept of Physics, Lyngby, DENMARK.

We have studied the hydrogen distribution around edge dislocations in Pd using the molecular-dynamics (MD) simulation technique. As the interaction potential, we have used the many-body alloy (MBA) potential by Tománek et al., modified to reproduce the intrinsic stacking-fault (ISF) energy. The ISF energy, , is calculated from first-principles, using a density-functional theory pseudo-potential approach. The influence of for the Peierls-barrier in dislocation slip, and the width of the dislocation core is discussed. Atomistic MD simulations reveals the mobility of the dislocations in the presence of variable hydrogen concentrations.

**10:30 AM T1.6**

THE IMAGE FORCE ON A DISLOCATION IN A BICRYSTAL: AN ATOMISTIC SIMULATION, Joel Lepinoux, Pierre Beauchamp, Univ of Poitiers, Dept of Physical Metallurgy, Futuroscope, FRANCE.

Dislocations in the vicinity of interfaces are submitted to forces of various magnitudes arising from the difference in nature between adjacent solids. A reasonable approach to understand the dislocation-interface interaction is to examine each effect separately. Image force is the longest range effect, induced by the elastic moduli mismatch. In linear elasticity the image force on a dislocation parallel to the interface diverges. Pacheco and Mura (1969) showed that this difficulty can be overcome by considering a Peierls-Nabarro dislocation instead of a singular dislocation. Modelling the behaviour of dislocations in multilayers is typical mesoscopic problem, requiring a reliable continuous approximation of the image force. The aim of the present work was to investigate this effect by computer simulation at the atomic scale to test the validity of existing solutions. The <001> and 1/2<111> screw dislocations in a BCC bicrystal have been compared. The former has an planar core extended along a <110> direction while the latter has a compact core. To construct the bicrystal, the same potential is used in medium (2) as in medium (1), but multiplied by a factor K, equal to the desired ratio of shear moduli. For values of K slightly larger than 1 an accurate calculation of the complete elastic energy E(x) can be performed, including the strain energy computed in the atomistic region and the elastic energy of the surrounding continuum. E(x) differs notably from elasticity only in a region of few atomic distances from the interface. For high values of K important nonlinear effects appear, e.g. new dislocation configurations, dissociation or twinning, depending on dislocation. Finally, a tentative law is proposed in reasonable agreement with present results.

**10:45 AM T1.7
**MOLECULAR DYNAMICS SIMULATIONS OF DISLOCATION-INTERFACE INTERACTIONS, Sriram Swaminarayan, Richard A. LeSar, Los Alamos National Laboratory, Ctr for Matls Science, Los Alamos, NM.

The mechanical, electrical and optical properties of metallic materials depend strongly on the microstructure in general and the dislocation substructure in particular. Understanding and predicting these properties requires an intimate knowledge of both the long range and short range interactions between dislocations and between dislocations and interfaces. Although the long range interactions can be determined using linear elasticity, the short range interactions are not as well understood. It is these short range forces that determine the dislocation substructures that are formed in highly worked materials both in the vicinity of other extended defects such as grain boundaries and within the grains themselves. The goal of the current work is to elucidate the behavior of dislocations when they approach grain boundaries (within twenty lattice parameters) where linear elastic concepts are no longer valid. We present results from simulations of dislocations in systems with over 10 atoms using Molecular Dynamics (MD) methods. Results from studies of dislocations crossing through each other and of dislocations cutting low angle grain boundaries will be presented. We will also present a comparison between the predictions of simulations and linear elasticity.

**11:00 AM T1.8
**ATOMIC-SCALE MECHANISM OF DISLOCATION NUCLEATION FROM A CRACK TIP, F. Cleri, Argonne National Laboratory, Matls Science Div, Argonne, IL; Simon R. Phillpot, D. Wolf, Argonne National Laboratory, Materials Science Div, Argonne, IL.

A recently developed fully atomistic technique for fracture simulations is applied to the study of the detailed atomic-scale mechanisms of dislocation nucleation and motion from a crack tip in an elastically anisotropic fcc crystal. In particular, atomic configurations around the crack tip provide information about the coupling of the dislocation to a surface step formed at the crack surface. Displacement and stress fields around the nucleating and moving dislocations are compared to the predictions of Rice's continuum-elastic model. Our results for the stress-displacement curves confirm that a nucleating (''incipient'') dislocation has a different character than a fully formed dislocation. However, we demonstrate that the unstabIe-stacking energy value estimated by means of the rigid-block sliding concept, a common feature to continuum-elastic models, greatly overestimates the activation energy for dislocation nucleation. These results show how atomistic simulations can be used to parametize continuum-elastic fracture mechanics through appropriate constitutive relations.

**11:15 AM T1.9**

ATOMIC-SCALE BLUNTING OF CRACK TIPS: POSSIBLY A SIGNIFICANT CONTRIBUTION TO THE FRACTURE TOUGHNESS, Jakob Schiotz, Technical Univ of Denmark, Dept of Physics, Lyngby, DENMARK; Anders E. Carlsson, Washington Univ, Dept of Physics, St. Louis, MO.

When a sharp crack propagates through a material it may collide with already existing dislocations, leading to blunting of the crack tip at the atomic scale. We present atomic scale simulations indicating that in some materials, where the sharp crack is stable (i.e. it will propagate rather than emit dislocations), a crack that has been blunted by just a single atomic layer may instead emit dislocations, leading to further blunting and to pinning of the crack front. This change of behavior has previously been reported in generic two-dimensional materials [Schiøtz et al.: Mat. Res. Soc. Symp. Proc. 409, 95 (1996)]. We have found that the effect is also present (and may be even stronger) in three-dimensional simulations of F.C.C. metals. The metals were studied using molecular dynamics and Effective Medium Theory (EMT) many-body potentials. Most pure F.C.C. metals where reliable EMT potentials exist are very ductile, a sharp crack will emit a dislocation instead of cleaving, but in some the sharp crack is stable. In these materials blunting the crack dramatically shifts the balance between cleavage and dislocation emission in favor of the latter. Since elastic interactions between a moving crack and preexisting dislocations make close encounters very likely [Mesarovic: Mat. Res. Soc. Symp. Proc. 409, 63 (1996)], this effect may have a significant effect on the fracture toughness of some materials.

**11:30 AM T1.10**

MECHANICAL DEFORMATION OF NANOCRYSTALLINE METALS, Jakob Schiotz, Francesco Di Tolla, Karsten W. Jacobsen, Jens K. Norskov, Technical Univ of Denmark, Dept of Physics, Lyngby, DENMARK.

Nanocrystalline metals are known to exhibit mechanical properties that are different from (and often superior to) conventional metals, e.g. increased hardness and fracture toughness. We present atomic-scale simulations of the deformation process in nanocrystalline copper using molecular dynamics and realistic many-body potentials. Since we can follow the positions and motion of dislocations and grain boundaries, we are able to observe the deformation process directly. In nanocrystalline metals a significant fraction of the atoms are at grain boundaries, and the grain boundaries have and important influence on the deformation process. In conventional materials the hardness and yield stress is known to increase with decreasing size (the Hall-Petch effect). The experimental results for nanocrystalline materials are not as clear, the Hall-Petch effect is seen in many (but not all) experiments, and in some cases a reverse Hall-Petch effect is seen for the smallest grain sizes. Since the grain sizes that can be realized in large-scale computer simulations are beginning to approach the smallest grain sizes that can be studied experimentally, it is possible to study the Hall-Petch effect by direct atomic-scale simulations.hima et al, J. Non-cryst. Solids 198-200 (1996) 1042. . Particularly this classical approach does not predict any saturation; actually it is invalid because for large biases the ground level in the subsurface well is essentially separated from the continuos spectrum.ion is formed in the sidewalls and near the surface. The contrast of the Al composition on different facets is quite sharp and reproducible. These growth features will facilitate the QD fabrication in the recesses on a substrate, when combined with heterostructure growths like GaAs/AlGaAs or InGaP/AlGaAs.

SESSION T2: DISLOCATION DYNAMICS

Chair: Richard G. Hoagland

Tuesday Afternoon, April 1, 1997

Nob Hill D

**1:30 PM *T2.1**

DISLOCATION DYNAMICS IN THE COMPOUNDS: EFFECTS OF THERMAL DEPINNING, D. C. Chrzan, Univ of California-Berkeley, Dept of MS&ME, Berkeley, CA; Murray S. Daw, Clemson Univ, Dept of Physics & Astronomy, Clemson, SC.

A new model for the dynamics of dislocation motion in the compounds displaying the yield strength anomaly is introduced and studied. The model includes thermally assisted formation and dissolution of Kear-Wilsdorf locks. In the absence of thermally assisted depinning, the model displays a pinning/depinning transition and associated critical behavior. Inclusion of thermally assisted depinning eliminates, strictly, the pinning/depinning transition. Hence hardening due to exhaustion of dislocation motion is possible only for a finite-sized dislocation. Scaling behavior, however, persists. In particular, the average velocity and time characterizing the velocity fluctuations are found to obey a dynamic scaling form. The implications of this scaling behavior for the mechanical properties of these compounds are discussed.

**2:15 PM T2.3**

KINETIC MONTE CARLO SIMULATION OF DISLOCATION DYNAMICS, Karin S. Lin, Univ of California-Berkeley, Dept of Physics & Matls Sci, Berkeley, CA; D. C. Chrzan, Univ of California-Berkeley, Dept of Matls Sci & Mineral Engr, Berkeley, CA.

A kinetic Monte Carlo based simulation of dislocation dynamics for materials with a medium to large stacking fault energy has been developed and preliminary results obtained. Dislocations within the simulations are assumed to consist of segments of either pure screw or pure edge character. Energies associated with configurations are calculated within isotropic elasticity theory. The stress dependence of the dislocation velocity is studied as a function of applied stress and sample temperature. Mesoscale structural features of the dislocations are presented and discussed with particular reference to their relevance to macroscopic mechanical properties. Results relevant to internal friction measurements are also presented. This work is supported by the United States Department of Energy, Office of Basic Energy Sciences, under contract DE-AC03-76SF00098.

**2:30 PM T2.4
**CONTINUUM ANALYSIS OF HALL-PETCH RELATION: INFLUENCE OF SOURCES, Lawrence H. Friedman, Univ of California-Berkeley, Dept of Physics, Berkeley, CA; Daryl C. Chrzan, Univ of California-Berkeley, Dept of MS&ME, Berkeley, CA.

The Hall-Petch relation, , has proven useful in relating grain sizes to yield stresses. In its original form, the Hall-Petch relation is derived from a continuum model of dislocations which lacks the degree of freedom necessary to account for variations in dislocation source characteristics, as well as the interfaces present in composite materials. Previous numerical work (Anderson and Li, 1995) has demonstrated that these factors may cause substantial deviation from the Hall-Petch predictions. Standard continuum models give the stress at the end points of a double pile-up as a function of of the applied stress, , and the length of the pileup, l, only. Allowing a finite-sized region in the center of the double pile-up to have non-zero stress but zero dislocation density produces configurations that are also in equilibrium and that reflect source characteristics. The results of this modified theory will be presented and analyzed. This work is supported through a grant from Sandia National Laboratories (the US Department of Energy, under contract DE-AC04-94AL85000).

**2:45 PM T2.5
**EVOLUTION OF DISLOCATION MICROSTRUCTURE SIMULATED WITH AN O(N) METHOD, Vijay Shastry, Anders E. Carlsson, Washington Univ, Dept of Physics, St Louis, MO.

We present results of an investigation of the evolution of microstructure in a large dislocation population. The calculations treat larger spatial and temporal scales than previous simulations. The elastic forces between the dislocations are calculated using an "Order N" scheme called PPPM method due to Barts and Carlsson [1]. The simulation uses upto 10,000 dislocations in a square simulation cell with periodic boundaries. The dislocations are moved using a dynamics algorithm which calculates the individual dislocation velocities as a linear function of the forces experienced by the dislocations. We observe the emergence of tilt walls comprised purely of positive or negative edge dislocations when a system with equal numbers of positive and negatively signed dislocations is allowed to relax. Annihilation of oppositely signed dislocations occurs when the dislocations wander within a specified distance of each other. The paper reports characteristics of the microstructure such as the average tilt wall length and final dislocation density as a function of annihilation distance. Further, the pair correlation function is calculated. These results are used to shed light on the spinodal decomposition theory of Holt [2]. The system can be subjected to cyclical external loading in the hope of understanding formation of Persistent Shear Bands (PSB).

**3:30 PM T2.6
**CALCULATION OF STRESS STRAIN CURVES BY USING 2D DISLOCATION DYNAMICS, F. Roters, Dierk R. Raabe, RWTH Aachen, Inst fur Metallkunde & Metalphysik, Aachen, GERMANY; G. Gottstein, RWTH Aachen, Inst fur Metalkunde & Metallphysik, Aachen, GERMANY.

A method is presented to derive stress-strain curves by using 2 dimensional dislocation dynamics. The simulation treats plastic deformation of single grains, in which one or more slip systems are active. The involved dislocations are regarded as infinite straight line defects which are embedded in an otherwise isotropic linear elastic medium. As the model is two-dimensional, only edge dislocations are incorporated. The calculation of the local stress field considers the long range elastic stress contribution of all dislocations within the grain and the externally imposed stress field. Due to the action of the local stress field, the dislocations may either glide or climb. dislocation multiplication and annihilation are taken into account, as well as the formation of dislocation locks. Thermal activation is considered. The simulations allow to compute the evolution of the dislocation distribution with high spatial resolution, the stress field and the plastic strain during a simulated deformation experiment. Therefore, the influence of a heterogeneous dislocation distribution on the mechanical behavior can be studied. The latter quantities were used for a calculation of stress-strain curves. These stress-strain curves reflect qualitatively correct the influence of changes in temperature and/or loading rate.

**3:45 PM T2.7**

DYNAMIC SIMULATION OF THE DISLOCATION STRUCTURE AHEAD OF A CRACK, Nikolas Zacharopoulos, David J. Srolovitz, Univ of Michigan, Dept of MS&E, Ann Arbor, MI; Richard A. LeSar, Los Alamos National Laboratory, Ctr for Matls Science, Los Alamos, NM.

We examine the dislocation microstructure that forms in front of a dynamically loaded crack. In particular, we consider the case of a Mode III crack and screw dislocations which are either pre-existing or generated at the crack tip. The dislocations move according to a simple equation of motion and the crack propagates when the stress intensity at the tip exceeds a critical value. Dislocations are nucleated either at the crack tip or within the material ahead of the crack. The dislocations emitted from the crack initially self-organize into a complex, highly ordered structure. As the load continues to increase, a well-defined plastic zone is produced. Based upon these detailed dislocation dynamics, we develop an analytical model for the evolution of the plastic zone size, the crack tip loading (including shielding) and crack propagation. Since the model is based upon dislocations with a finite mobility, the change in fracture toughness with loading rate is automatically accounted for. We will discuss the implication of this result for the brittle to ductile transition.

**4:00 PM *T2.8
**3D SIMULATION OF DISLOCATION DYNAMICS, Dierk R. Raabe, RWTH Aachen, Inst fur Metallkunde & Metalphysik, Aachen, GERMANY.

The dynamics of crystal dislocations are simulated in 3D. The simulations are discrete in space and time. The dislocations are described as line defects embedded in an otherwise isotropic or anisotropic linear elastic homogeneous solid medium. Each dislocation line is subdivided into interconnected segments. The segments may have have screw, kink, jog, or mixed character. The 3D stress field imposed by each segment is computed within the framework of piecewise straight dislocations using Volterra's formula and Hook's law. The dynamics of the dislocations are computed by solving Newton's law of motion for each segment assuming local stress equilibrium. The calculation considers the long range elastic interaction between different dislocations, the self forces (line tension) arising among segments belonging to the same dislocation, image forces, inertia, osmotic forces, thermal Langevin type forces with stochastic character, Peierls forces, external forces, and viscous damping forces (electron and phonon drag). This description leads to a coupled set of stochastic non-linear differential equations which must be solved numerically.

**4:30 PM T2.9**

3D DISLOCATION SIMULATIONS OF BCC SINGLE CRYSTAL PLASTICITY IN Ta, Meijie Tang, Lawrence Livermore National Laboratory, Dept of Physics & Space Technology, Livermore, CA; Gilles R. Canova, CNRS, GPM2/ENSPG, St. Martin D'heres, FRANCE; John A. Moriarty, Lawrence Livermore National Laboratory, Dept of Physics & Space Technology, Livermore, CA.

Constitutive models that aim at describing the plasticity of single crystals usually involve the collective motion of dislocations which is hard to model analytically. The present work is a first step in simulating BCC plasticity at the mesoscopic scale by introducing discretized dislocation segments (screw and edge). The segments are allowed to move in the crystal lattice according to the kinetic rules that relate the velocity to the local effective stress. The later one includes the applied stress, the long and short range stresses, as well as the line tension. Specific kinetic rules are introduced to describe the different behavior of screw and edge segments, particularly at low temperatures (or high strain-rates). The present work will show results concerning the temperature dependence of yield stress of Ta single crystal, in comparison with known experimental results.

SESSION T3: MICROSTRUCTURAL EVOLUTION

Chair: Harold J. Frost

Wednesday Morning, April 2, 1997

Nob Hill D

**8:15 AM *T3.1**

NUMERICAL SIMULATION OF OSTWALD RIPENING USING THE POTTS MODEL, Veena Tikare, Sandia National Laboratories, Theoretical & Computational Matls Modeling, Albuquerque, NM.

Modeling of Ostwald ripening presents unique challenges because of the large number of thermodynamic, mechanistic and spatial variables which must be considered simultaneously. Analytic methods have failed in predicting the details of the microstructure due to the many assumptions they make. The Potts model has been used to simulate Ostwald ripening while eliminating some of these assumptions: in particular, the assumptions about the concentration gradients in the matrix phase and about the grain shapes. In the Potts model, each individual grain is allowed to grow in response to its local environment which is controlled by several factors: these are solid/liquid interfacial energy, the spatial distribution and area fraction of other grains, wetting by and distribution of the liquid matrix and the concentration gradients in the liquid. The simulation technique will be presented and applied to two- and three dimensional, isotropic grain growth. It will also be used to study the two dimensional, anisotropic grain growth problem. Results of these simulations will be presented with emphasis on kinetics and grain size distributions. The discussion will compare these results to those obtained from previous analytical and numerical models as well as experimental studies.

**8:45 AM T3.2
**COMPUTER SIMULATIONS OF THE OSTWALD RIPENING IN TWO-PHASE SYSTEMS USING A DIFFUSE-INTERFACE FIELD MODEL, Danan Fan, Los Alamos National Laboratory, Los Alamos, NM; Long-Qing Chen, Pennsylvania State Univ, Dept of Ceramic Science, University Park, PA; Shao-Ping Chen, Los Alamos National Laboratory, Los Alamos, NM; Peter W. Voohees, Northwestern Univ, Dept of MS&E, Evanston, IL.

The characteristics of Ostwald ripening in a two-phase mixture have been systematically studied over the range of 25% to 95% of the coarsening phase by employing a new diffuse-interface field model. The microstructural developments and the shape accommodation of coarsening particles at high volume fractions have been realistically simulated. It was found that the growth exponent m=3, and is independent of volume fractions of the coarsening phase. The kinetic coefficient k increases as the volume fraction of coarsening phase increases. It was shown that the shape of size distribution changes dramatically with increasing the volume fraction of coarsening phase. The skewness continuously changes from negative to positive while the kurtosis decrease in the low fraction regime and increases in the high volume fraction regime as the volume fraction varies from 25% to 95%.

**9:00 AM T3.3
**COMPUTER SIMULATION OF OSWALD RIPENING OF MnS IN Fe-3Si STEEL, Narayanan Rajmohan, McGill Univ, Dept of Mining & Metallurgical Engr, Montreal, CANADA; Jerzy A. Szpunar, McGill Univ, Dept of Metallurgical Engr, Montreal, CANADA.

A computer model to simulate the ripening of MnS precipitates during anomalous grain growth in Fe-3Si steel is developed. The difference in grain boundary energy and diffusion coefficient which exists for different grain misorientations are incorporated into the simulation. The model utilizes the Monte-Carlo method for simulating the grain boundary movement and employs a calculated increase of average particle size with time as t and t for bulk and grain boundary diffusion, respectively. Each lattice site in the descritized 3-D computer specimen is assigned initially an average particle size value. The growing average particle size depends on the location of the lattice site under consideration. The changed average particle size distributions during the simulation are compared with existing experimental results.

**9:15 AM T3.4**

NUMERICAL SIMULATION OF COARSENING IN MULTIPHASE SYSTEMS, Will C. Holmes, Jeffrey J. Hoyt, Washington State Univ, Dept of Mech & Matls Engr, Pullman, WA.

Using the boundary integral technique of Akaiwa and Vorhees ( E, 49, 3860, 1994), we have performed simulations of the Ostwald ripening process in ternary, three-phase systems. The coarsening rate and the particle trajectories have been monitored as a function of time for various diffusivities, volume fractions, and shapes of the three-phase equilibrium triangle. Results are compared to the mean field prediction and to the single phase case. We have also examined the particle correlations which develop during the ripening process. In the three-phase system, correlations are a function not only of position and size but also depend on the type of precipitate as well.

**9:30 AM T3.5**

NUMERICAL SIMULATION OF GRAIN GROWTH AND PORE MIGRATION IN A THERMAL GRADIENT, Elizabeth Ann Holm, Sandia National Laboratories, Dept of Theoretical & Computational Matls Modeling, Albuquerque, NM; Veena Tikare, Sandia National Laboratories, Dept of Theoretical & Computational Matls Sci, Albuquerque, NM.

The Potts model has been used extensively to study microstructural evolution by processes such as normal and abnormal grain growth, recrystallization, phase transformation, grain growth in a thermal gradient and Ostwald ripening. In this paper, we will present a modified Potts model which can simulate simultaneous grain growth and pore migration in a thermal gradient. Nonconserved dynamics must be used to simulate grain growth. In contrast, conserved dynamics must be used to simulate pore migration which occurs by two long range diffusion mechanisms, surface diffusion and evaporation-condensation. Furthermore, in a thermal gradient, grain growth and pore migration will vary with temperature. Grains grow faster at higher temperature because grain boundary mobility is higher at higher temperatures. Pores migrate to the high temperature region because material diffuses/evaporates preferentially from the high temperature region to the low temperature region. The numerical techniques used to incorporate both conserved and non-conserved dynamics with the added complexity of a thermal gradient all in the same simulation will be presented. The simulated microstructures will be presented and compared to experimental systems.

**9:45 AM T3.6**

COMPUTATIONAL MODELING OF MICROSTRUCTURAL EVOLUTION IN CERAMICS: PHASE STABILITY AND GRAIN GROWTH, Satoshi Kitaoka, Hideaki Matsubara, Fine Ceramics Research Assoc, Synergy Ceramics Lab, Nagoya, JAPAN.

It is advantageous for development of new materials with complex microstructures to model and design microstructural evolution associated with changes of phase and grain size. Phase changes occur because of nucleation, formation of new compounds and solid solutions, etc., until equilibrium is attained. The grain growth proceeds in order to decrease grain boundary and/or interface energies. Computational modeling of microstructural evolution has been performed by determining phase stability based on thermodynamic calculations of phase diagrams and subsequent grain size change by the Monte Carlo method using two dimensional triangular lattices. Such simulations are useful for understanding microstructural development accompanying formation of stoichiometric compounds and solutions.

**10:30 AM *T3.7**

ABNORMAL GRAIN GROWTH - THE ORIGIN OF RECRYSTALLIZATION NUCLEI?, A. D. Rollett, W. W. Mullins, Carnegie Mellon Univ, Dept MS&E, Pittsburgh, PA; Elizabeth Ann Holm, Sandia National Laboratories, Dept of Theoretical & Computational Matls Modeling, Albuquerque, NM.

The origin of recrystallization nuclei is reviewed with particular emphasis on materials in which well developed cells are present in the deformed state. Nucleation is discussed in terms of coarsening of the subgrain network that develops on annealing and an analogy is made with abnormal grain growth. The results of a two-dimensional analysis show that a single grain can grow abnormally when its boundary has certain combinations of energies and mobilities. For reasonable variations in energy and mobility with size it can be shown that a subgrain network should be unstable over a certain range of misorientations. The Monte Carlo (Potts) model for grain growth has been adapted for variable grain boundary energy and mobility in order to investigate the behavior of individual grains with special properties. The results of simulations in two dimensions show that both energy and mobility affect abnormal growth as expected from the theoretical analysis. The results are discussed in terms of the stability or otherwise that subgrain networks may exhibit depending on their mean misorientation. Finally, the influence of particles is examined in the Potts model and compared to the example of abnormal grain growth (secondary recrystallization) in electrical steels.

**11:00 AM T3.8**

SIMULATION OF RECRYSTALLIZATION AT THE MESOSCALE USING 3D-CELLULAR AUTOMATA, Dierk R. Raabe, V. Marx, RWTH Aachen, Inst fur Metallkunde & Metalphysik, Aachen, GERMANY; G. Gottstein, RWTH Aachen, Inst fur Metalkunde & Metallphysik, Aachen, GERMANY.

A 3D cellular automaton algorithm has been developed to simulate both primary recrystallization and recovery of cold worked metals. Nucleation can take place site saturated or with a nucleation constant rate. The identification of potential nucleation sites is based on the local stored energy (thermodynamic instability criterion) and the local lattice curvature (kinetic instability criterion). Both, oriented nucleation and random nucleation, are investigated. Growth of nuclei terminates upon impingement. The local growth rate of nuclei is determined by the driving pressure and the character of the large angle grain boundary. The approach allows to introduce different conditions for recovery, nucleation and grain growth. The model simulates kinetics, microstructure and texture development during heat treatment discrete in time and space. The paper reviews the underlying physical concepts, the basic algorithms, applications, and combinations with preceding deformation simulations such as finite element, self consistent, and Taylor type models.

**11:15 AM T3.9
**GRAIN GROWTH SIMULATION: A NEW MODEL, Pascal Paillard, ISITEM, Lab de Genie des Materiaux, Nantes, FRANCE; Richard Penelle, Univ de Paris-Sud, Lab de Metallurgie Structurale, Orsay, FRANCE; Vassilis Pontikis, Ecole Polytechnique, Laboratorie des Solides Irradies, Palaiseau, FRANCE.

Recrystallization is one among phenomena of fundamental importance in materials engineering. However, due to the collective behavior of interfaces during grain growth and the difficulties inherent to its analytical description, computer simulation has revealed being a unique tool capable of a statistical treatment of the microstructural evolution during annealing. In this paper, a new simulation method of grain growth is presented which overcomes well known limitations of existing approaches and offers remarkable description capabilities of several experimental situations among which primary recrystallization, Zener drag effects and evolution features of an initially heterogeneous microstructure. The limitations of Monte Carlo and Vertex techniques are briefly discussed while compared to the solutions adopted by this new technique. The validation of the latter has been obtained by generic, two-dimensional simulations of grain growth. The results of which are briefly presented together with perspectives for future work.

**11:30 AM T3.10
**INFLUENCE OF EXPERIMENTAL INHOMOGENEITIES OF TEXTURE IN THE GRAIN GROWTH SIMULATION, Pascal Paillard, ISITEM, Lab de Genie des Materiaux, Nantes, FRANCE; Thierry Baudin, Richard Penelle, Univ de Paris-Sud, Lab de Metallurgie Structurale, Orsay, FRANCE.

The most common techniques (Monte Carlo, Vertex, Cellular Automata...) used for normal and abnormal grain growth simulation, give statistical results in agreement with the experimental measurements. One must note, however, that the initial microstructure is always an arbitrary one and the orientations of the individual grains are chosen according to a homogeneous distribution generally estimated from x-ray diffraction data and therefore at a macroscopic scale (about 25000 m x 15000 m). However, in a recent paper [1], it has been shown, using the Electron BackScattered Diffraction (EBSD) and precisely the Orientation Imaging Microscopy (OIM) at the mesoscopic scale (450 m x 450 m), that grain clusters can be observed in a real material and that therefore the volume fraction of each texture component so as their topology vary from one of analyzed area to another. In this paper, the clusters influence on the abnormal growth of Goss grains is studied using a Monte Carlo simulation starting from experimental data [2] and thus introducing a space scale that usually doesn't exist in a such approach. 6 areas (450 m x 450 m) selected on the same sample of Fe 3 Si sheet (grade HiB) were characterized by OIM after primary recrystallization. These 6 areas are used as starting data in simulations and the results are compared to those obtained from an initial arbitrary microstructure. The evolution of the mean diameter or of the surface of Goss grains as a function of the Monte Carlo steps shows large differences and thus points out the large influence of textural inhomogeneities on the Goss grain growth.

**11:45 AM T3.11**

EQUILIBRIUM HETEROPHASE MICROSTRUCTURE IN CONSTRAINED FILM, Alexander L. Roytburd, Univ of Maryland, Dept of Matls & Nuclear Engr, College Park, MD.

The effects of elastic energy in a system of coherent phases in a constrained film are considered. The equilibrium two- phase film has a transversely modulated microstructure with modulation period dependent on film thickness. The elastic interactions between the phases dramatically change phase diagrams which can be different qualitatively from the standard phase diagrams. The dependence of the equilibrium microstructures and the phase diagrams on film thickness and constraint conditions as well as effects of elastic interactions on the coarsening are discussed.

SESSION T4: PROCESS MODELING

Chair: Veena Tikare

Wednesday Afternoon, April 2, 1997

Nob Hill D

**1:30 PM *T4.1
**NUMERICAL SIMULATION OF DENDRITIC ALLOY SOLIDIFICATION USING A PHASE FIELD METHOD, James A Warren, NIST, Dept of MS&E, Gaithersburg, MD.

Phase field models have recently been shown to be a promising method of describing solidification phenomena. In a binary alloy, the diffusion of solute in the solid can be set much smaller than that in the liquid, resulting in the formation of realistic microsegregation patterns in the solid matrix. The phase field method enjoys much of its success because it removes the difficult numerical problem of tracking the liquid-solid interface, by giving up the notion of a mathematically sharp interface. One of the benefits of this diffuse interface is that it naturally allows for the coalescence of solidifying structures. We will examine the phenomena of coalescence and fragmentation of dendritic side branches and comment on the conditions required to form trapped liquid.

**2:00 PM T4.2
**MICROSTRUCTURAL MODELLING, John D. Hunt, George Antipas, Richard Thomas, Univ of Oxford, Dept of Materials, Oxford, UNITED KINGDOM.

A computer program predicting the solidification and heat treatment of alloys has been developed. Currently any binary phase diagram can be treated. The program is based on a finite-difference control-volume model solving the diffusion equations of any number of components in any number of phases. The diffusion length considered depends on the spacing of arrays of growing cells and/or dendrites. Analytical fits of previous numerical results for the spacing of such arrays have been used to predict the growth of an undercooled single solid phase from the liquid. In addition, eutectic, eutectoid, peritectic and peritectoid reactions have been treated. Three growth modes have been considered : 1) steady state directional growth, 2) constant cooling rate and 3) constant rate of heat extraction. The outputs are liquid/solid compositions and fractions solid as a function of temperature and time as well as on line graphical output of the predicted microstructure.

**2:15 PM T4.3**

INTERFACE DEMARCATION DURING Bi/MNBi EUTECTIC DIRECTIONAL SOLIDIFICATION (NUMERICAL AND EXPERIMENTAL), David J. Larson, Li-Li Zheng, SUNY-Stony Brook, Dept of Materials Science, Stony Brook, NY.

Interface demarcation during Bridgman-Stockbarger directional solidification of eutectic Bi/MnBi has been investigated numerically and experimentally. Numerical simulations were performed using an in-house two-dimensional code with a multizone adaptive grid scheme in a nonorthogonal coordinate system. The thermoelectric Joule, Peltier, Thomson, and Seebeck components were incorporated into the model. Thermoelectric properties of pure Bismuth were used in the simulations. Interface shape, interface location, interface velocity, and interface acceleration were modeled. Current densities of 20, 40 and 80 A/cm were investigated, since these bracketed our experimental test capabilities. Quasi-steady-state thermal response (v = 0) and a range of steady state solidification velocities, from 1.25 to 31.25 cm/h, were investigated since these conditions bracketed our experiment conditions. Numerical simulation showed that interface movement due to the current pulse occurs almost instantaneously and extending the pulse duration beyond this point introduces an interface velocity transient that approaches the steady state growth velocity as a function of time, establishing a new thermal equilibrium (with pulse). Termination of the pulse introduces a second transient that returns the pulsed region to the original steady state thermal equilibrium (sans pulse). Interface demarcation could be optimized by controlling the physical dimensions of these transients (pulse duration and experiment velocity), their sequence (pulse polarity), and their visibility (relative velocity within the transient regions which creates observable chemical and/or morphological differences). Experimental results support the development of two transients in sequence. Further, the very rapid refinement of the eutectic structure within the transient regions suggests that the new microstructure is achieved almost instantaneously, as predicted by the model. This suggests that the structure responds by a nucleation mechanism rather than by the branching mechanism usually attributed to these faceted/non-faceted eutectic structures. Lastly, the known relationship between the solidification velocity and inter-rod spacing was used to approximate the transient velocity within the pulse. The empirical results will be quantitatively compared to the numerical predictions.

**2 2:30 PM T4.4
**THERMOELECTRIC EFFECTS ON INTERFACE DEMARCATION AND DIRECTIONAL SOLIDIFICATION IN BISMUTH, Li-Li Zheng, David J. Larson, SUNY-Stony Brook, Dept of Materials Science, Stony Brook, NY.

This paper investigates thermoelectric effects on interface demarcation during the directional solidification of Bismuth. A complete description of thermoelectric effects is presented and calculations of related thermoelectric coefficients are elucidated. Numerical simulations of directional solidifications in Bismuth were carried out by using a computer code developed by Zhang et al., in which a nonorthogonal curvilinear coordinate system is adopted and a multi-zone adaptive grid generation scheme is used. Numerical results revealed that 1) for the directional solidification of Bismuth inside a silica ampoule the curvature of the interface is relatively small and it tends to be concave towards the liquid side. 2) thermoelectric effects include Peltier, Joule, Thomson, and Seebeck contributions. Peltier heat only occurs at the interface, while the Thomson and Joule effects occur throughout the bulk liquid and solid. The nondimensional Joule heating in the solid is of the same magnitude as that in the liquid, which is around 0.3-0.4. The Thomson effect in the liquid is close to zero and in the solid is around 2-3. The difference of Thomson effects on the solid and liquid sides represents the Peltier effect. 3) at the solid/liquid Interface, the Joule heat and Thomson effect appear sudden change. The former is attributed to the different electric conductivity for solid and liquid Bismuth, the latter is due to different thermoelectric power in solid and liquid Bismuth. The difference of Thomson effects on the solid and liquid sides represents the Peltier effect.

**2:45 PM T4.5
**DYNAMICAL DESCRIPTION OF THE MATERIALS STRUCTURE IN MACRO AND MESOSCALES, Nicolay Bodyagin, Moscow Inst of Electronic Engineering, Dept of Microtechnology, Ryazan, RUSSIA; Arcady Aivazov, Moscow Inst of Electronic Technology, Dept of Microtechnology, Zelenograd, RUSSIA; David T. Hoelzer, NYS College of Ceramics, School of Ceramic Engr & Sciences, Alfred, NY.

It is demonstrated that solidification can be described as self organization processes. Theoretic evidence of the existence maximum attractor in solidification processes of the different materials was carried out. It is demonstrated that solid state materials is spatially inhomogeneous, ''frozen,'' nonequilibrium system examined from the point of view of the nonlinear dynamics. Traditional approaches to the analysis of this system in terms of statistical characteristics such as spatial spectrum, correlation scale, and the like, don't give information about its deterministic origin. Possibility of using the well known in nonlinear dynamics approach is taken for investigation of dynamics of the materials growth processes and order parameters of the structure to be proved. Employing this approach, we can reconstruct these characteristics by space series of any material property. The calculation algorithms of the dynamics invariants (correlation dimension, order parameters, global and local Lyapunov exponents, topological invariants) from material surface profile and time series of some growth characteristics in situ are proposed. The principles of nonlinear modeling of the growth processes and structure of the materials on the basis of the dynamics invariants are considered. The analytical connection between the dynamics invariants, on the one hand, and stability, some post growth processes, limits of the properties reproductivity from one growth process to another accessible in the modern technologies, on the other hand, are proposed. Growth processes dynamics and structure order parameters in macro- and mesoscale are different. They are described accordingly by global and local Lyapunov exponents. Approaches to modeling of connection between them are proposed.

**3:15 PM *T4.6
**SIMULATION OF GRAIN GROWTH IN TEXTURED THIN FILMS, Harold J. Frost, Dartmouth College, Hanover, NH; Carl V. Thompson, MIT, Dept of MS&E, cambridge, MA; Johan Grape, Dartmouth College, Hanover, NH; Roland Carel, MIT, Dept of MS&E, Cambridge, MA.

We have developed a front-tracking simulation of the grain growth process in polycrystalline thin films in which we are able to handle a variety of different physical effects by making the local grain boundary migration velocity depend on the local boundary curvature and the crystallographic orientations of the neighboring grains. Grain growth in thin films will lead to development of preferred crystallographic orientations in those situations in which one or another factor favors grains of one orientation over those of other orientation. Important factors which we have modeled include: the anisotropy of surface energies for both the film-substrate and the film-covering interfaces; the anisotropy of elastic compliances and the related strain-energy densities when elastic strains are imposed; and the orientation dependence of the yield stresses of the individual grains, which limits the elastic strains and strain energy densities. When different factors favor different orientations, the evolution of texture depends on process variables in complicated ways. Our simulations also include several other effects, such as pinning by surface grooving, pinning by precipitate particles or holes in the film, solute drag, and variations in grain boundary energy and mobility, based on the relative misorientation of neighboring grains. We are able to simulate the complicated manner in which evolution of texture depends on process variables for those cases in which different driving forces favor different orientations.

**3:45 PM T4.7**

GROWTH AND SURFACE DIFFUSION-INDUCED PLANARIZATION OF CU AND AL FILMS IN INTERCONNECT TRENCHES AND VIAS, Nicholas I. Choly, Harry A. Atwater, California Inst of Technology, Dept of Applied Physics, Pasadena, CA; Imran Hashim, Applied Materials Inc, Physical Vapor Deposition Div, Santa Clara, CA.

Thin film evolution by concurrent film growth and surface diffusion-induced planarization ("reflow") has been simulated using a front-tracking model, and the results are related to fabrication of high aspect ratio submicron Cu and Al metallization structures in dielectric trenches and vias, for integrated circuit interconnect applications. The surfaces of thin films deposited on interconnect trenches were approximated as surfaces of constant cross-section and a shadow model of Bales and Zangwill was used to describe the local sputter deposition rate. Simultaneous growth and reflow for Al and Cu was found to result in two distinct phases of film evolution: 1) film roughening (growth-dominant), and 2) film planarization (reflow dominant). The boundary between phases was found to follow a simple physical scaling law on the temperature-flux plane where the critical parameter is the surface self-diffusion constant. We also report a first simple three-dimensional physical model for via filling, in which films deposited in vias were approximated as surfaces of revolution. An equation was developed that describes the evolution of such a surface due to reflow, and simulations were again performed with a finite-element simulation. Importantly, a critical film aspect ratio was identified that cause the film surface to be drawn into the axis of symmetry, leading to void formation in the via and preventing full planarization. This geometrically-based result for vias differs markedly from a trench of constant cross section, and may impose an important fundamental constraint for via filling by reflow.

**4:00 PM T4.8
**MODELLING AND SIMULATION OF EARLY FILM GROWTH MECHANISMS IN PVD-PROCESSES BY MOLECULAR DYNAMIC CALCULATIONS, Otto Knotek, Erich Lugscheider, RWTH Aachen, Materials Science Inst, Aachen, GERMANY; Cyrus Barimani, P. Eckert, G. v. Hayn, RWTH Aachen, Material Science Inst, Aachen, GERMANY.

The PVD-technology is a widely used and powerful method of thin-film coating technology due to the wide range of possible coating materials. However, the optimization of coatings has been depending mainly on empiricism and experiments. Therefore, it is our intention to investigate the influences of experimental conditions to the resulting film properties by computer simulation. Besides stress and texture, the microscopic characteristics film-substrate mixing and lattice defects are important influences for film adhesion and film density. In the Materials Science Institute, a molecular dynamic calculation model is developed to simulate the microscopic events of the early stages of film growth. In opposite to the often-used Monte-Carlo simulations, it is here possible to see the full dynamics of atomic motion of substrate and film. The present paper describes the influence of process temperature and the energy of the impinging atoms to the occurrence of point defects and local mixing.

**4:15 PM T4.9
**SIMULATIONS OF THE CHEMICAL VAPOR DEPOSITION OF DIAMOND FILMS NEAR THE MESOSCALE, Corbett C. Battaile, Univ of Michigan, Dept of MS&E, Ann Arbor, MI; David J. Srolovitz, Univ of Michigan, Dept of Matls Science, Ann Arbor, MI; James E. Butler, Naval Research Laboratory, Code 6174, Washington, DC.

The growth of thin diamond films by chemical vapor deposition has received considerable attention in the last two decades. Because of diamond's superlative properties, the ability to grow large high-quality diamond films could benefit a number of technologies. For example, diamond's high hardness, high thermal conductivity, optical and infrared transparency, and negative electron affinity make it useful for wear-resistant coatings, heat spreaders, windows, and cold cathodes. Since the microscopic processes that lead to diamond growth are difficult to observe in situ, much of our understanding in this regard is based upon modeling and simulation. Previous simulations of diamond growth have focused on one-dimensional chemical kinetic models, which do not explicitly account for the atomic structure of the film; and molecular dynamics methods that are viable only on very small time and length scales. We will present an atomistic simulation technique that is capable of simulating film growth near the mesoscale. The film is represented by a three-dimensional crystal lattice, and the various growth processes are included via surface chemical reactions parameterized by conventional reaction rate coefficients. The effects if both the surface chemical kinetics and the atomic structure and morphology of the film are thereby included. The evolution of the growing film in time is accomplished by a Monte Carlo approach similar to the N-Fold Way, and the method is efficient enough to handle films containing thousands of atomic surface sites and growth of hundreds of atomic planes in only a few hours on a desktop workstation. We will address the transition from a growth mode controlled by the kinetics of surface processes to one controlled by nucleation of diamond and step flow on smooth facets, and the incorporation of point defects during growth. Both of these phenomena require a three-dimensional atomistic treatment of the growth surface.

**4:30 PM T4.10
**ATOMIC-SCALE MODELING OF NANOCRYSTALLINE METALS, Francesco Di Tolla, Jakob Schiotz, Karsten W. Jacobsen, Jens K. Norskov, Technical Univ of Denmark, Dept of Physics, Lyngby, DENMARK.

In recent years new materials, composed by nano-grains, have been synthesized. In particular for metals, these materials show interesting mechanical properties, which differ from that of conventional metals. Here we try to address the modeling of nanocrystalline metals at the atomic-scale. We report results from simulations of nanocrystalline copper using molecular dynamics and realistic many-body potentials. Starting from a discussion on the preparation of realistic samples, we will focus our attention on the general properties of this model nanocrystals. We compare the behavior of ``cold''-simulated samples with that of annealed samples, we study the energetics and internal stresses of this samples, and analyze the grain boundary properties (extension, evolution, recrystallization kinetics, etc.).ks corresponding to different Al composion are observed. In order to know where each peak originated from, we took CL images at different wavelength. Ga-rich region is formed at the intersection regions between two sidewalls, while Al-rich region is formed in the sidewalls and near the surface. The contrast of the Al composition on different facets is quite sharp and reproducible. These growth features will facilitate the QD fabrication in the recesses on a substrate, when combined with heterostructure growths like GaAs/AlGaAs or InGaP/AlGaAs.

**4:45 PM T4.11**

MOLECULAR DYNAMICS SIMULATION OF VOID NUCLEATION IN 10NM POLYCRYSTALLINE COPPER AT HIGH STRAIN RATES, James F. Belak, Lawrence Livermore National Laboratory, Livermore, CA.

Isotropic tension is simulated in nanoscale polycrystalline copper with 10 nm grain sizes using large-scale molecular dynamics on an IBM SP2 parallel computer. Constant strain rates of 10-10 are considered for systems ranging from 10-10 atoms using an EAM interatomic potential for copper. The spacing between voids for room temperature simulations is found to scale approximately as /S, where C is the sound speed and S is the strain rate. Below strain rates of about 10, only one void is observed to nucleate and grow in the simulation cell. Results are presented for several grain boundary orientations (textures) and compared to macroscopic nucleation and growth remodels.

SESSION T5: POSTER SESSION

Chair: Elizabeth Ann Holm

Wednesday Evening, April 2, 1997

8:00 P.M.

Salon 7

**T5.1**

A MESOSCOPIC MODEL FOR THE EVOLUTION OF THE TARGET SURFACE ON LASER ABLATION, Ricardo Mendes Ribeiro, Marta M.D. Ramos, Univ do Minho, Dept of Physics, Braga, PORTUGAL; A. M. Stoneham, Univ College London, Dept of Physics, London, UNITED KINGDOM.

Pulsed Laser Ablation is a thin film deposition technique with a very simple experimental set-up. Nevertheless, the phenomena involved when a laser fluence of a few Joules per square centimeter hit the surface of a material during tens of nanoseconds are very complex. It involves both atomic processes in the absorption of the radiation, evaporation and ionization, as well as microscopic and macroscopic phenomena such as the desorption of large aggregates in the submicron range and the dynamic flow of a plasma in vacuum. Both atomistic and thermodynamical models have been developed for several years, but only a partial picture is possible in these frameworks. We developed a mesoscopic model which enables the understanding of several features that happen at the surface of the target and which play an important role in the evolution of the evaporation process. This model shows how and why the surface of a ceramic target acquires a cone structure, which has important consequences in the deposition process.

**T5.2
**A THREE-PARAMETER MODEL FOR THE PLASTIC DEFORMATION BEHAVIOR OF AA2024 BASED ON 2D DISLOCATION DYNAMICS SIMULATIONS, F. Roters, RWTH Aachen, Inst fur Metallkunde & Metalphysik, Aachen, GERMANY; G. Gottstein, RWTH Aachen, Inst fur Metalkunde & Metallphysik, Aachen, GERMANY.

A three parameter model for the plastic behavior of an aluminum alloy 2024 is presented. The composite model distinguishes two regions, namely the dislocation cell walls with high dislocation density, and the cell interiors with much lower dislocation density. The three parameters employed are the mobile dislocation density, the immobile dislocation density in the dislocation walls, and the immobile dislocation density inside the dislocation cells, respectively. The rate equations for these three dislocation populations are formulated in accordance with 2D dislocation dynamics simulations. The processes of dislocation multiplication, annihilation, and the formation of dislocation locks and dipoles are taken into account. This procedure allows the incorporation of future results attained by 2D simulations to account for the inhomogeneous dislocation distribution within both walls and cell interiors. The stress-strain behavior of a precipitation free AlCuMg model alloy is very well reproduced by the model. In addition, the influence of precipitation can be taken into account by modification of the mean free path of the dislocations. In this way the stress-strain curves of the commercial alloy AA2024 can be very well reproduced using the same fitting parameters as for the precipitate-free model alloy.

**T5.3
**A STATISTICAL MODEL FOR PRECIPITATION APPLICATION TO AlCu-ALLOYS, Lothar Lochte, J. Staudte, G. Gottstein, RWTH Aachen, Inst fur Metalkunde & Metallphysik, Aachen, GERMANY.

Within the framework of classical nucleation theory and deterministic rules for the growth and coarsening of precipitates, as originally proposed by Zener, the authors developed a statistical model for precipitation processes. The growth law for a single precipitate includes growth from the supersaturated matrix as well as coarsening due to the Gibbs-Thomson effect. Combining the nucleation rate and the growth law in the continuity equation, according to Langer and Schwartz, it is possible to describe the evolution of the whole precipitate size distribution. Since and analytical solution of this partial nonlinear inhomogeneous differential equation cannot be obtained, it was solve numerically in a similar manner as Kampmann and Wagner did. This approach guarantees that the information of the whole size distribution is considered. In contrast to simulations, taking into account local diffusion fluxes on a spatial grid net (e.g., Cahn-Hiliard simulations), the presented algorithms is fast and therefore of particular interest for industrial applications. The numerical results are compared and discussed with results of ageing experiments, especially measurements of the mean matrix composition, of several hardening AlCu-alloys at several temperatures.

**T5.4**

SIMULATION OF GP-ZONE FORMATION IN AlCu-ALLOYS BY USE OF THE CAHN-HILLIARD EQUATION, A. Gitt, Lothar Lochte, G. Gottstein, RWTH Aachen, Inst fur Metalkunde & Metallphysik, Aachen, GERMANY.

AlCu-alloys are of high practical interest because of their ability for precipitation hardening. The main effect of hardening is obtained by the stable -phase, but is due to the metastable coherent GPI- and GPII-zones, which are decomposition zones of Cu along -planes. Because of the high activation energy for nucleation of the -phase, owing to the high phase boundary energy, the precipitation of the metastable GP-zones prevails during the early stages of the phase transformation. In order to minimize the elastic energy, these GP-zones have platelike shapes. Based on ideas of A. Khatchaturyan, we developed an analytical term that takes into account the local elastic strain energy, which is caused by the concentration dependence of the lattice parameter. The elastic properties of the matrix were considered to be anisotropical. This term, representing the elastic distortions of the whole sample, was added to the classic non- linear Cahn-Hilliard-Equation (CHE), an extended form of the diffusion equation ( Fick's second law). Originally the CHE was used in a linear form to describe the early stages of spinodal decomposition analytically. In this work, we attempt to model the whole process of decomposition of coherent GP-zones, including coarsening, by means of a numerical solution of the CHE in two dimensions. Furthermore, the numerical solution of this time-dependent Ginzburg-Landau type field equation takes Into account the interaction of diffusion fields of all precipitates, as well as an interaction of their elastic stress fields.

**T5.5**

SELF-CONSISTENT CLUSTER INTERACTIONS APPROACH TO SOLIDS, Tome M. Schmidt, Manuel Berrondo, Brigham Young Univ, Dept of Physics & Astronomy, Provo, UT.

We have developed a self-consistent ab initio method based on cluster interactions to investigate crystal properties. It consists of an iterative procedure with a Hartree-Fock calculation for an "active cluster" in the field of the rest of the crystal represented by a set of frozen-orbital precalculated clusters. The active cluster and the frozen clusters are exchanged until the system has converged. Our first application to alkali halides runs very fast and yields excellent results. The present version is customized for ionic crystals, including complex ions such as ammonium halides. We will present both the methodology and results on ionic crystals.

**T5.6**

TOWARD THE UNDERSTANDING OF COMPLEX SYSTEMS WITH MULTIPLE PHASES BY NETWORKED BROWSING ENVIRONMENT, Naohiro Shichijo, Toshihiro Ashino, Shuichi Iwata, Univ of Tokyo, Dept of RACE, Tokyo, JAPAN.

In study of complex dynamic systems, the state space is divided into several subspaces each of which corresponds to a certain state. The difficulty arises from the geometrical complexity and the huge amount of data related to each point in the state space and relations among them. For the understanding of the nature of such complex system, a comprehensive presentation environment is required, which arranges various fact/knowledge on each state of the system in undestandable format and have the reorganization and refinement functionalities to establish up-to-date accumulation of all the knowledge resides in the system. In attacking to the real world problems, all the available data resources should be organized and users will make surgery in the presented object to find out a solution. For such a purpose, the system should be extensible and high capability of geometrical transformation and also has functionality of communication with available human/computer resources. Behaviour of multi-constituent alloy formation is one example of complex systems. Here we present a phase diagram browser with editing/annotating functionality. It allows the presentation and browsing of the knowlege stored in the diagram and also accerelates collaboration in the network keeping a common design guideline as well as a freedom to explore attarctive possibilities in the real diversity of materials. Our current stage is the preliminaly research on the practice especially with the binary alloy phase diagram.

**T5.7
**THERMODYNAMIC AND ELASTIC PROPERTIES OF CU, NI, AG, AU, PT, RH, AND NI-CU, AG-AU, PT-RH BINARY ALLOYS, Tahir Cagin, California Inst of Technology, Materials & Process Simulation Ctr, Pasadena, CA; Gulay Dereli, Mustafa Uludogan, Mehmet Tomak, Middle East Technical Univ, Dept of Physics, Ankara, TURKEY.

The temperature dependence of thermodynamic and mechanical properties of six fcc transition metals (Ni, Cu, Ag, Au, Pt, Rh) and the alloying behavior of Ag-Au, Ni-Cu and Pt-Rh are studied using molecular dynamics (MD) The structures are described at elevated temperatures by the force fields developed by Sutton and co-workers within the context of tight binding approach. The thermodynamic and mechanical properties are calculated in the temperature range between 300K to 1500K with 200K increments using the statistical fluctuation expressions over the MD trajectories.

**T5.8**

SIMULATIONS OF VISCOUS DEFORMATION FOR RATIONAL DESIGN AND PRODUCTION OF GLASS CAPILLARY X-RAY CONCENTRATORS, K. J. Hwang, Columbia Univ, Dept of Chemical Engr & Materials Science, New York, NY; G. Slade Cargill, J. F. Riordan, Columbia Univ, Dept of Chemical Engr, New York, NY.

We describe finite element computational studies of viscous deformation on millimeter to submicron length scales, applied to design and production of tapered glass capillary x-ray concentrators. Precisely controlled shapes are required to optimize x-ray throughput gain, and beam size. Finite element modeling is used to investigate effects of experimental parameters on capillary shape. Predictions from modeling are compared with results from experiments. The goal of these studies is rational design and production of glass capillary x-ray concentrators for micron and submicron beams. Uniform cross-section borosilicate glass cylinders with 3 mm outer diameter and 0.1 mm inner diameter are heated in a cylindrically symmetric furnace with a nonuniform temperature distribution along its axis. The maximum temperature is approximately 800C. A tensile force is applied to the capillary, which deforms nonuniformly because of its nonuniform temperature. The deformation is affected by the temperature profile, its movement during capillary deformation, and the time-dependent tensile force acting on the capillary. Complicating issues include triaxial stresses which develop for larger taper angles, and surface tension related forces which become increasingly important for smaller inner diameters. The surface tension effects may ultimately limit the stability of nanometer-size capillaries.

**T5.9**

MICRO VOID GROWTH IN A SINGLE CRYSTAL WITH STRAIN GRADIENT EFFECTS, John Yanjiang Shu, Lawrence Livermore National Laboratory, Dept of Chem & Matls Science, Livermore, CA; Norman A. Fleck, Cambridge Univ, Dept of Engr, Cambridge, UNITED KINGDOM; Wayne E King, Lawrence Livermore National Laboratory, Chem & Matls Sci Directorate, Livermore, CA.

Dislocation theory and accumulating experimental evidence suggest that the plastic flow strength of a solid depends on strain and strain gradients, which are associated with statistically stored dislocations and geometrically necessary dislocations, respectively. In general, strain gradients are inversely proportional to the length scale over which plastic flow occur. Thus, strain gradient effects become important when plastic deformation talking place at small scales, typically on the order of several microns as suggested by experimental evidence of materials exhibiting a size-dependence of plastic deformation. Fleck and Hutchinson have proposed continuum theories which include strain gradient effects through constitutive length scales. This work studies the problem of the growth of a void under remote tension in an infinitely large single crystal with strain gradient effects. The crystal is assumed to be planar with double slip systems and is rate dependent. The Fleck-Hutchinson strain gradient crystal plasticity theory is implemented in a new finite element code (GRACY2D) and used to simulate the void growth. Attention is focused on voids with a size on the order of 1-100 microns. It is found that smaller voids grow significantly slower than larger ones.

**T5.10**

SCALING OF DEFORMATION AND FRACTURE PARAMETERS OF SOLIDS AT ATOMIC, MESOSCOPIC AND MACROSCOPIC LENGTH SCALES, Valery P. Kisel, Inst of Solid State Physics, Dept of Crystal Growth, Chernogolovka, RUSSIA.

The remarkable finding of this work is the universal damping character of dislocation motion and multiplication in ionic and semiconductor crystals in the temperature range from liquid helium up to the melting point. Dislocation mean pathlengths under creep, impulse, impact and shock stress rates change synchronously with number of mobile dislocations and gradually reach the ultimate values, at which all dislocations begin to multiply. It is the dislocation double cross-slip, climb, and the bowing out between obstacles that play the crucial role in dislocation retardation, initiation of defects, formation of cells and grain boundaries at the mesoscale. Another remarkable finding is the same scaling between the parameters of dislocation motion and multiplication at atomic scale (ultrasound loadings), mesoscale (by etch pit method) and macroscopic scale (macrodeformation curves) which confirms the universality of the mechanisms of work-hardening in different crystals and solidified gases under various tests. It highlights the crucial role of these mechanisms in the strict chain of stages of micro- and macroplasticity, micro- and macrofracture: dislocation unpinning-motion-drag-initiation of defects full arrest, multiplication-retardation, grain boundary initiation microcrack nucleation-microcrack coalescence into macrocracks macrofracture and damage. High differences in the space density of defects and impurity precipitates, grain boundaries at various dislocation pathlength scales may infringe the universality of this scaling law.

**T5.11
**SIMULATION OF COARSENING KINETICS OF MISFITTING PARTICLES IN BINARY ALLOYS, Andrei V. Nazarov, Alexander A. Miheev, I.P. Bardin Central Research, Dept of Metal Physics, Moscow, RUSSIA; Maria Ganchenkova, Moscow Engineering Physics Inst, Dept of Matls Science, Moscow, RUSSIA.

We examine how elastic stress, arising from precipitate misfit strains, influences the diffusion fluxes and growth rate of precipitates. The elastic stress influence on diffusion flows in binary alloys is came into account by using new approach. This approach takes into consideration, that the stress fields can alter the surrounding atom configuration and consequently the local magnitude of the activation barrier. The change of activation barrier is obtained to depend on the displacement field, symmetry of crystal and pair potentials of atom interactions. Knowing this change it is possible to calculate the jump rate. The flux expressions are obtained with the help of the "hole gas" method, by using jump rate. The equation system for two components and vacancies in which the influence of elastic stress on flows was taken into account is resolved in the quasi-stationary approximation. The obtained kinetic equation for the growth rate of a precipitate differs from the corresponding equation of the LS theory. This equation contains the additional terms conditioned by the gradients in both vacancy concentration and misfit strains. The analysis shows that the kinetics of coarsening are altered by these terms, including the possibility of inverse coarsening. Simulation of this process is realized. The temporal dependency of misfitting particle sizes and forms is examined for different system.

**T5.12
**CLUSTERS FORMATION IN SOLID SOLUTIONS, Elena Rogacheva, Olga Nashchekina, State Technical Univ, Dept of Physics, Khavkov, UKRAINE.

The chemical interaction between the atoms of different dopants, especially the ones forming the stable chemical compound, can lead to appearance of molecular complexes (clusters) in solid solution. Increase in impurity content causes cluster size growth and gradual transition from the atomic scale to the mesoscale. As a result, the formation of certain substructure resulting in chemical inhomogeneity of solid solution occurs.

The experimental evidences of existence of subheterogeneous structure of solid solutions based on semiconductor compounds (PbTe, SbTe, GeTe) under introducing the chemical compounds (InTe, GaTe, CdTe, SbTe, BiTe) are presented. The dependences of properties (unit cell parameter, microhardness, charge carrier concentration, etc.) on composition along the isoconcentrates of doping elements are plotted. In the properties isotherms extremum points correspond to introduction of stoichiometric chemical compounds in the host material. The interpretation of results obtained is given in the framework of the phenomenological method of cluster components considering a real system as a gas of noninteracting subsystems. Conformity between experimental data and calculation results confirms the cluster structure of solid solutions.

**T5.13
**INFLUENCE OF IMPURITY CONCENTRATION ON DISLOCATION DYNAMICS IN SOLID SOLUTIONS, Elena Rogacheva, Olga Nashchekina, State Technical Univ, Dept of Physics, Khavkov, UKRAINE.

Theoretical models of solid-solution hardening based on dislocation impurity atom interactions are usually limited to dilute solutions. Interaction between impurity atoms in concentrated solid solutions is expected to lead to qualitative change of dislocation dynamics. The concentration dependences of microhardness H of polycrystalline samples in PbTe based semiconductor solid solutions were obtained. The anomalies H in the vicinity of 1 mol.% of impurity indicating partial loss of strength of crystal and qualitative change in dislocation motion character were detected. Influence on the observed effect of grain size, thermal treatment, and method of preparation of samples (cast or hot pressed) was studied. Interpretation of the experimental data was given in the framework of percolation theory. It is suggested that for every grain there exists a critical concentration of impurity at which the percolation channels penetrating the whole grain are formed. The formation of these channels is accompanied by increasing dislocation mobility and drop H. Thus, collective effects in a point defect system cause collective mesoscopic effects in the dislocation system.

**T5.14
**EQUILIBRIUM GROWTH MORPHOLOGIES OF SiC POLYTYPES, Stephan G. Muller, Robert Eckstein, Univ Erlangen-Nurnberg, Dept of Elektrotechnik, Erlangen, GERMANY; R. F.P. Grimbergen, Univ Nijmegen, Dept of Solid State Chemistry, Nijmegen, NETHERLANDS; Dieter Hofmann, Univ Erlangen-Nurnberg, Dept of Elektrotechnik, Erlangen, GERMANY.

The wide bandgap semiconductor SiC gains more and moreimportance for device applications involving high power, high temperatures or intense radiation, SiC AS a substrate material for epitaxial growth of nitride based III-V compounds is a promising perspective to improve the performance of devices for blue and UV optoelectronics, Still the present status of SiC bulk crystal growth does not meet the requirements for future device production. The density of defects e.g. micropipes and parasitic crystal modifications (polytypes) has to be reduced considerably. Although recently some possible stability criteria for SiC polytypes have been given [1], the origin of polytype formation is far from being resolved. There exists a deficiency in the understanding of basic mechanisms of defect generation in SiC. One way to approach aspects of this question is the study of the equilibrium grouch morphologies of SiC, from which important material data can be evaluated. We investigate the structural properties of SiC powder synthesized from purified graphite and silicon at different temperatures in a graphite furnace. Using a uniform temperature field the microcrystals formed within the powder undergo only a neligible sneak local supersaturation in comparison to typical conditions used for bulk crystal growth and therefore can evolve their equilibrium growth habits, SEM pictures of the micro-uystals show a clear correlation to the synthesis-temperature and to the polyt,ype, determined by X-ray powder diffraction. A Hartman-Perdok analysis [2] was performed to calculate the Bravais FriedelDonnay-Harker (BFDH) morphologies of SiC polytypes and compared to the experimental results. 3C- and 6H-SiC can be dearly distinguished and oven the more comipex habit of the polytype 15R could be identifled. The theoretical analysis also yields values for the specific surface energies, which play an essential role e.g. in the descripition of micropipe formation [3].

**T5.15
**THE ATOMIC DISPLACEMENTS STATIC WAVES ACCUMULATION AND REORGANIZATION EFFECT INSIDE A ZONE OF ELASTIC TO PLASTIC TRANSFORMATION, A. A. Ovcharov, S. V. Dmitriev, M. D. Starostenkov, Altai State Technical Univ, Dept of General Physics, Barnaul, RUSSIA.

The F.C.C. crystal relaxation under an impulsive pressure deformation was considered in this work. The empiric pair Lenard-Jones potential with the parameters for the solid argon was used as the interatomic interaction potential satisfiable the Koshi condition. The deformations range where the crystal behave elastic was investigated. As the result of research it was obtained an existence of three main phases of crystal relaxation:

1) The deformation level range O-5 stable phase. Homogeneous deformed crystal is stable.

2) Under the deformation level range 5-15, the perpendicular-to-load direction waves of atomic displacements are generated in crystal. Under the deformation at the beginning of the load interval, only one wave appeared, then with the deformation growth, the waves number and their amplitudes are increased.

3) Under the deformation level range 15-17.2, the perpendicular-to load direction waves of atomic displacements are transformed to the diagonal-to-load direction waves. Their directions are 120 degrees to the load. First there are many low-by-amplitude waves, but with the relaxation process their amount sufficiently decreased and their amplitudes are increased. These waves become nonstable with load growth up to 17.2.

With the deformation growth, the dislocation are generated inside these waves. It is obtained that there are three main relaxation phases inside the frame of Hooke law.

**T5.16
**KINETIC INSTABILITY IN THE STEP-FLOW GROWTH OF ALLOYS, Vitaliy A. Shchukin, IA P. Ipatova, A.F. Ioffe Phys-Technical Inst, St Petersburg, RUSSIA; Vadislav G. Malyshkin, West Michigan Univ, Dept of Physics, Kalamazoo, MI; Alexei A. Maradudin, Richard F. Wallis, Univ of California-Irvine, Dept of Physics & Astronomy, Irvine, CA.

A kinetic theory of the alloy growth instability with respect to fluctuations of alloy composition is developed. The step-flow growth of a binary alloy AB from the gas phase on a surface vicinal to the (001) surface of a cubic substrate is studied. The growth regime implies that the adsorbed atoms migrate on the surface during growth of each monolayer, and that their motion is ''frozen'' after the completion of the monolayer. If monolayers are completed, the migration of adatoms in the growing ( + l)st monolayer consists of diffusion and drift in some effective potential. This potential is a sum of a short range contribution caused by composition fluctuations in the top completed monolayer number and of a long-range elastic contribution caused by composition fluctuations in all completed monolayers , 1 . For temperatures lower than a certain critical temperature , drift dominates diffusion. It results in the amplification of alloy composition fluctuations from monolayer to monolayer in the process of the alloy growth. This amplification implies that the growth of a spatially homogeneous alloy is kinetically unstable. In contrast to the effect of long-range elastic forces on the thermodynamic instability of alloys, where they hinder the phase separation [1], the elastic forces [2] and lead to the increase of the critical temperature similar to the result of Ref. [3]. Proposed mechanism is applicable to pseudobinary alloys of III-V semiconductors and gives a possible explanation of composition modulation structures observed in as-grown samples of III-V alloys where bulk diffusion coefficients are too small to produce phase separation during the growth time.

**T5.17**

MONTE CARLO MODELLING OF MESOSCALE INTERACTIONS BETWEEN PARTICLES AND BOUNDARIES DURING GRAIN GROWTH, J. Miodownik, Oxford Univ, Matls Dept, Oxford, UNITED KINGDOM.

Despite much debate, there is still little consensus on the f-dependence of Zener Pinning (the effect of particles on grain growth). The controversy surrounds attempts to relate the volume fraction of particles (f) and the final pinned grain size (R). Analytical theories and 3D Monte Carlo (MC) simulations are in disagreement and experimental evidence is inconclusive. In this paper we contribute to the debate by describing mesoscale MC simulations of a single boundary moving through an array of particles of various sizes, d = 1 to 8 MC sites. By investigating the conditions under which the migrating boundary becomes pinned, the volume fraction dependence of the model is evaluated. The effect of temperature (T) on the shape of the boundary as it bypasses particles is also investigated. A characteristic dimple shape is expected from analytical considerations and has been observed in experimental systems. It is found that the simulated boundary possesses a mobility independent of driving force except for small boundary curvatures. In the presence of particles, the velocity of the boundary is linearly dependant on f; however, the pinned boundaries have an f-dependence with exponent n = -0.45. The effect of T is critical in determining geometry of the boundary during bypass. When T = 0, the dimple shape is not observed because the boundary is in a nonequilibrium state and this is the origin of the strong pinning observed in the simulations. When T = l/k, dimples are observed and the pinning force associated with these interactions is close to that expected from analytical considerations.

SESSION T6: MECHANICAL BEHAVIOR AND MATERIALS PROPERTIES

Chair: Dierk R. Raabe

Thursday Morning, April 3, 1997

Nob Hill D

**8:30 AM *T6.1
**MODELING OF DYNAMIC FRACTURE IN BRITTLE SOLIDS CONTAINING INHOMOGENEITIES, Xiaopeng Xu, Farid F. Abraham, IBM Almaden Research Center, San Jose, CA; Alan Needleman, Brown Univ, Div of Engr, Providence, RI.

A continuum mechanics framework for analyzing dynamic crack growth is described where the continuum is characterized by two constitutive relations; one that relates stress and strain in the bulk material, the other relates the traction and separation across a specified set of cohesive surface. The bulk elastic response is linear but the cohesive separation law is nonlinear. As the cohesive surfaces separate, the cohesive traction first increases, reaches a maximum and then decreases. Within this cohesive surface framework, the fracture process is incorporated into the problem formulation so that no separate fracture criterion needs to be specified. The parameters characterizing the cohesive surface separation law include a strength and the work of separation per unit area so that a characteristic length enters the formulation. The resistance to crack initiation, the crack speed history and crack branching are predicted without invoking any ad hoc criteria. In previous work, dynamic fracture was analyzed numerically for crack growth in a homogeneous solid. The qualitative features of the numerical results were in accord with a wide variety of experimental observations. In this study, the effects of inhomogeneities on brittle solids undergoing dynamic fracture are investigated. While the dynamic instability is found to be intrinsic to a fast growing crack, the evolution of the instability is affected by the density and size of the inhomogeneities.

**9:00 AM T6.2**

FRACTURE PROBABILITY OF INCLUSIONS AS A FUNCTION OF VARIOUS MICROSTRUCTURAL PARAMETERS, Thomas Antretter, Univ of Leoben, Christian Doppler Lab for Micromechanics of Matls, Leoben, AUSTRIA; Franz Dieter Fischer, Univ of Leoben, Inst of Mechanics, Leoben, AUSTRIA.

The internal stress distribution in a particulate two-phase composite shows a significant dependence on various parameters such as geometry, material, and arrangement of the inclusions, as well as external loading conditions. In the case of High-Speed Tool Steel (HSS), which can be regarded as composite consisting of hard and brittle carbides embedded in a martensitic matrix, it has been observed that material failure is initiated by cleavage fracture of the carbides rather than matrix rupture. The present study endeavors to develop a concept to predict inclusion failure based on statistical methods. Finite-element models of representative volume elements serve as the basis for the calculations. In order to reduce computing time, the case studies are carried out in two dimensions using plane-stress elements. Given a constant volume-fraction of inclusions in the composite material, a Weibull approach is employed to estimate the fracture probability of the particles. Various inclusion shapes such as ellipsoidal, rectangular, and dog-bone shaped geometries are examined for mechanical as well as thermal loading conditions. The interaction of one inclusion with its surrounding neighbors can be simulated by choosing appropriate boundary conditions for the unit cell. The correlations between the fracture probability of the particles and the parameters defining the geometry of the model as well as the influence of the inclusion size will be demonstrated. The significance of the Weibull modulus will be emphasized. As an example, the fracture probability of several carbides pertaining to a real microstructure of HSS will be evaluated.

**9:15 AM T6.3
**ESTIMATING VISCOELASTIC CONSTANTS OF TWO-PHASE COMPOSITES, James G. Berryman, Lawrence Livermore National Laboratory, Dept of Computational Physics, Livermore, CA; Graeme W. Milton, Univ of Utah, Dept of Mathematics, Salt Lake City, UT.

Hashin-Shtrikman-type variational pricniples have been formulated in order to obtain rigorous bounds on the shear modulus of two-phase viscoelastic composites. The simplest class of bounding regions is composed of circles in the complex plane containing four points related to the viscoelastic moduli of the constitutents, and depending on a scalar parameter. A method of generating the convex hull of all such bounding regions has been developed. Several examples of bounds computed using the method will be presented, including one for suspensions of solid particles in a viscous fluid. In the important limiting case when all the constituent moduli are real, the new shear bounds are shown to reduce precisely to the well-known Hashin-Shtrikman-Walpole bounds.

**9:30 AM T6.4**

CALCULATIONS OF PLASTIC DEFORMATION DURING SURFACE INDENTATION, Cynthia L. Kelchner, John C. Hamilton, Sandia National Laboratories, Dept of Computational Matls Sci, Livermore, CA.

Experimental techniques such as IFM, AFM, and nanoindentation allow measurements of force as a function of depth when a probe tip is pressed into a surface. Important thin film mechanical properties including elastic modulus, yield strength, and hardness can be derived from these force curves. The modeling of dislocation formation at the mesoscopic scale is important for the quantitative interpretation of these measurements, particularly as current applications involve smaller tip radii and film thicknesses. The strain produced by elastic compression of the surface under a load can be partially relieved by the formation of dislocations and defects in the near-surface region as the tip is pressed further into the surface. We have modeled this behavior using the Embedded Atom Method to calculate the forces on a spherical tip with radius of curvature between 20 and 80 Angstroms. In order to prevent avalanche bonding of the tip and the surface, the spherical tip has been replaced by a sphere with a nearly hard wall repulsive interaction with the surface atoms. Force vs. distance profiles for the (111) and (001) Au surfaces were calculated during indentation and retraction of the indenter, via minimum energy calculations. Images of atomic positions and dislocation structures were also obtained. Based on these results, we will discuss the plastic deformation of the two surfaces during indentation as well as after retraction of the tip from various stages of the indentation process. Comparison will be made with IFM and STM experiments by Hwang and Houston.

**10:00 AM T6.6**

SCALE EFFECT UNDER MICROINDENTATION, Elena Rogacheva, State Technical Univ, Dept of Physics, Khavkov, UKRAINE.

Scale effect (SE) under microindentation is well known and consists in growth of microhardness (H) when impression size (d) becomes lower than some critical value under conditions of geometric similarity. Transition from mesoscale to the microscopic level can be observed in the H (d) dependences. It corresponds to the value of d at which H becomes independent of d. The nature of SE has not been finally established. In the present paper, H of metals, semiconductors and ionic crystals was studied as a function of applied load and impression size. The influence of SE of different factors such as grain size, type and content of impurities, state of crystal surface, degree of preliminary deformation, type of chemical bond, was revealed. These factors determine the limits and character of the SE manifestation. It is suggested that the main reasons for SE are specificity of surface properties, elastic reconstruction of impressions, and existence of crystal substructure. The physical model of SE taking into account dynamics of dislocations generated under microindentation, their multiplication and motion, collective properties of dislocation assemblies and real structure of material is proposed.

**10:30 AM T6.7**

AN MD SIMULATION OF NANO-SCALE HETEROGENEITY IN FLUORINE-CONTAINING AMORPHOUS OXIDES AS A BASIS FOR MESO-SCALE STRUCTURES, Akiyoshi Osaka, Satoshi Hayakawa, Akira Nakao, Chikara Ohtsuki, Okayama Univ, Faculty of Engineering, Okayama, JAPAN.

Soft and hard tissues of body are composites of mesoscale arrangement: Bone consists of collagen layers and Ca-deficient apatite platelet sheets, where calcium and phosphate ions orderly are assembled together with carbonate anions through a biomineralization process. Fluorine can be one of the apatite components forming fluoroapatite though fluoride ions may not be distributed homogeneously in tooth enamel or bone. Such nanoscale micro-heterogeneity grows to meso- and macroscopic scale ones and causes segregation. One can take a microscopic phase-separated amorphous structure involving heterogeneous distribution of ions or clusters as a model structure that leads to mesoscale heterogeneous structure: a tens of cations and anions first gather in embryos to grow into nuclei with further attachment of ions and lead to macroscopic crystallization or phase separation via a mesoscopic intermediate state. We conducted an MD simulation of amorphous structures of the systems M Si-O-F (M: Ca, Sr, Ba) under fully ionic 2-body potentials of the Busing Ida-Gilbert type. The simulation indicated distinctive microscopic segregation of M and F in clusters, which was confirmed by F 1s X-ray photoelectron spectroscopy. Analysis of atomic correlation curves showed that M-F and M-O correlation peaks naturally appeared at a distance similar to that in the corresponding fluorides and oxides and that the Ca Ca curve had a sharper peak than the other indicating that smaller Ca-F clusters were distributed in the calcium system.

**10:45 AM T6.8
**PERCOLATION MODELING OF COMPLEX DIELECTRIC CONSTANT OF A HETEROGENEOUS MATERIAL, Christian Brosseau, Univ de Brest, Dept of Physics, Brest, FRANCE; A. Beroual, A. Boudida, Ecole Centrale Lyon, CEGELY, Ecully, FRANCE.

Computational electromagnetics for the characterization of dielectric heterostructures is a highly developed field. A number of phenomenological mixing laws have been proposed in the literature to interpret the conductivity- and permittivity-concentration characteristics. However, these methods are especially tied to the specific materials that they address, and are difficult to generalize. This problem, with ramifications in electronics and aerospace industries, is also important for fundamental reasons, e.g., photonic band structures and localization of electromagnetic waves. One fundamental issue that has driven many of the experiments on electromagnetic properties of disordered heterogeneous media is the nature of the conductivity- and permittivity-concentration characteristics. By way of contrast, the related problem for which both constituents of the composite have finite conductivities is in a somewhat primitive state. This owes partly to the fact that relatively little data existed until recently and partly to the somewhat greater complexity associated with the role of polarization mechanisms. Here we consider the dielectric properties of a two-component composite material consisting of inclusions of constituent 1 surrounded by a background material of constituent 2. The numerical results show that the complex effective permittivity is strongly affected by the contrast ratio between the dielectric constants of the background medium and the inclusions. This study is intended to examine in detail the relationship between the percolation transition and the permittivity ratio of the two constituents. The computer-simulation model is based upon a combination of finite elements and the resolution of boundary integral equations. By varying the geometric shape and the orientation of the inclusions, we obtain a diverse array of behaviors which may be useful in understanding the dielectric properties of real composite materials. Finally we compare the prediction of our numerical simulation with results of previous analytical works, e.g., MacLachlan equation, and numerical experiments.

**11:00 AM T6.9**

EFFECTS OF NANOSCALE STRUCTURAL INHOMOGENEITY ON DIELECTRIC RESPONSE IN COMPLEX PEROVSKITE RELAXORS, Hong Gui, Xiaowen Zhang, Tsinghua Univ, Dept of MS&E, Beijing, CHINA; Binglin Gu, Tsinghua Univ, Dept of Modern Applied Physics, Beijing, CHINA.

Relaxor ferroelectrics have special dielectric characteristics compared with normal ferroelectrics, such as the diffuse phase transition(DPT), strong frequency dispersion of the dielectric constant and the absence of macroscopic polarization and anisotropy at temperatures far below T. How these dielectric properties are formed remains to be an open question. It has been observed that the coexistence of nanoscale ordered microregions and the disordered matrix in complex perovskites makes this kind of material a highly inhomogeneous system. Based on this nanoscale-ordered structure, we proposed a dipole glass model to study its dielectric response. By using Monte Carlo simulation method, the relaxation time distributions at various temperatures and external fields are obtained. It is proved that the spectra move to the longer relaxation time direction with the decreasing temperature or the increasing external field. The relaxor is in a quasiequilibrium state when the relaxation times of some dipoles become comparable or longer than the observation time. It is showed that the frequency dispersion is caused by a gradual freezing process of dipoles as the temperature is lowered. The randomly distributed interactions between the nanoscale ordered microregions play an important role in causing the glassy freezing process, which is mainly responsible for the relaxor characteristics.

**11:15 AM T6.10
**COMPUTER SIMULATION OF DIFFUSION PROCESSES IN SOLIDS, Hualong Li, McGill Univ, Dept of Mining & Metallurgical Engr, Montreal, CANADA; Jerzy A. Szpunar, McGill Univ, Dept of Metallurgical Engr, Montreal, CANADA.

Diffiusion is a basic process that occurs in solids at high temperature. Understanding how atoms move during solid diffusion is very important in studying the kinetics of oxidation, precipitation, creep, annealing, etc. In this paper, a two-dimensional computer simulation model is proposed which is capable of simulating the diffusion process in solids, incorporating such defects as, point defects, dislocations, grain boundaries. In this model, the microstructure is discretized into 1 million sites which can be arranged so that the grain size and shape matches experimental data. Each site is assigned a bulk dislocation or grain boundary diffusion constant depending on its situation in the microstructure. The diffusion process is simulated using Random Walk method. The simulation produces normalized concentration profile and two-dimensional contour maps which display the distribution of diffusing species. With this simulation model, the effect that grain size, grain shape, and the various defects have on the diffusion process, can be studied. A comparison of the simulation results to experimental result or theoretical analysis such as Frick's Law, Fisher and Whipple's calculations, are also discussed

**11:30 AM T6.11**

OPTIMIZING SIZE DISTRIBUTIONS IN PARTICULATE SYSTEMS THROUGH SIMULATIONS OF DIE FILLING, Thomas P. Swiler, Sandia National Laboratories, Dept of Theoretical & Computaional Matls Modeling, Albuquerque, NM; Kevin G. Ewsuk, Sandia National Laboratories, Dept of Matls Processing, Albuquerque, NM; Joseph Cesarano, Sandia National Laboratories, Dept of Direct Fabrication Technologies, Albuquerque, NM.

To ensure the high quality of components formed by compaction, density variations and the size of internal voids in intermediate green parts must be minimized. Accordingly, packings produced during die filling must possess both uniformly high densities and narrow void size distributions. These requirements prompted a study of the complex dependence of particle size distribution and variations in container size and shape on the properties of simulated spherical particle packings. A simulated annealing technique was then used to find particle size distributions that would optimize various properties within the packings. Results include findings that higher fines contents than predicted by the Furnace model are needed to pack optimally in dies with fine detail and that packing of a narrow size distributed powder is most efficient when sizes are bimodally distributed towards the ends of the distribution.

**11:45 AM T6.12
**COMPUTER SIMULATION OF THREE DIMENSIONAL PARTICLE PACKING, Jong-Cheol Kim, David M. Martin, Iowa State Univ, Dept of MS&E, Ames, IA.

Three-dimensional packing of spherical particles is simulated. The packing process is multi-level: particles are packed to make clusters and clusters are packed to make aggregates. This packing concept is extended to more than two levels in order to represent multi-level powder agglomerates. Clusters are formed from particles condensed from space. Clusters are then moved towards the centers of agglomerates. Particle rearrangement is simulated by randomly rolling each particle across its neighbor's surface until it reaches a more stable position. The ratio of the condensation rate to the rearrangement rate controls the compactness of the cluster. Two types of the rearrangement are studied: rearrangement during packing and rearrangement after packing. This concept is also applied to cluster rearrangement using the simplifying assumption that the clusters are spheres with a radius equal to the mean interparticle distance. Particle clusters which are rearranged during packing have higher average coordination number and packing density than particle clusters rearranged after packing. The effect of cluster rearrangement during cluster agglomeration is comparable to the effect of particle rearrangement during packing.

We conclude that vibration during packing is more efficient than vibration after packing for achieving high packing density and uniformity.

SESSION T7: LINKING COMPUTATIONAL LENGTH AND TIME SCALES

Chair: Elizabeth Ann Holm

Thursday Afternoon, April 3, 1997

Nob Hill D

**1:30 PM *T7.1**

QUASI-CONTINUUM MODELS FOR MESOSCOPIC MECHANICS, Ellad Tadmor, Harvard Univ, Gordon McKay Lab, Cambridge, MA; R. Phillips, Brown Univ, Div of Engineering, Providence, RI; M. Ortiz, California Inst of Technology, Graduate Aeronautical Labs, Pasadena, CA; Richard A. LeSar, Los Alamos National Laboratory, Ctr for Matls Science, Los Alamos, NM.

Atomistic and continuum methods alike are often confounded when faced with mesoscopic problems in which multiple scales operate simultaneously. Atomistics suffers from an inability to treat either large enough lengths or long enough times, while continuum models lack the resolution to capture effects dictated by the discrete lattice. As an alternative, a mixed atomistic/continuum model which seamlessly bridges between lattice scales and those treated conventionally via continuum mechanics is considered. The key idea is the implementation of an atomistically based constitutive law within a finite-element formalism. It is shown how, in conjunction with adaptive meshing techniques, this method allows for the emergence of defects such as dislocations and interfaces. The method is illustrated concretely through several applications including the problem of nanoindentation, where it is shown how dislocations arise in response to the indentation process and how substrate crystallography dictates the resulting deformation mode.

**2:00 PM T7.2
**AN ATOMISTIC FINITE ELEMENT (ATFE) METHOD FOR MESOSCALE COMPUTATION, Patrick A. Klein, Stanford Univ, Dept of Applied Mechanics, Stanford, CA; Huajian Gao, Stanford Univ, Dept of Mech Engr, Stanford, CA.

We present a methodology for modelling material response for large deformations at the smallest length scales for which continuum theory is applicable. Our atomistically based finite element implementation addresses the kinematic nonlinearities arising from large strains, as well as nonlinearities in the material response. The constitutive relations are derived from an atomistic view of the material. The lattice structure and interatomic potentials appropriate for the given materials combine to produce behavior that is consistent with linear elastic approximations of the materials at small strains and transitions to generally anisotropic, nonlinear elastic behavior consistent with pure atomistic treatments with increased deformation. Through the incorporation of the interatomic potentials, this methodology inherits other advantageous characteristics from molecular dynamics. The materials cohesive strength is bounded therefore eliminating stress singularities generated by linear elastic theory. The brittle fracture of materials is produced entirely by the changes in the elastic moduli and appears without the introduction of additional fracture criteria. Constitutive models have been produced for the following systems: FCC lattices with the Lennard-Jones potential, diamond cubic lattices with the Stillinger-Weber potential, and FCC and BCC lattices with the embedded atom method. The method has been applied to a variety of problems ranging from the evolution of stresses and strains in the growth of germanium on silicon quantum dots to the effects of crystal orientation on brittle crack propagation.

**2:15 PM T7.3**

MICROSTRUCTURAL EVOLUTION IN THIN FILMS USING AN ATOMISTIC SIMULATOR, Vadali Mahadev, Dong Wang, Zongwu Tang, James B. Adams, Arizona State Univ, Dept of Chem Biochem & Matls Engr, Tempe, AZ; Timothy S. Cale, Arizona State Univ, Ctr for Solid State Electronics, Tempe, AZ.

Experimental investigations in recent years have identified several important processing variables and their influences on film microstructure, but many of the details of nucleation, growth, and texturing mechanisms are still poorly.understood. We have developed an atomistic Monte Carlo based simulator for cluster growth during thin film deposition. Our simulation package call be used to predict cluster size distributions, cluster impingement, continuous film formation and thermal grooving. The thrust of this research effort is to develop fundamental understanding of microscopic evolution of thin films starting from the model developed to study the very early stages of deposition of thin films, and to use that understanding to construct a numerical model required for nucleation, growth and coarsening. Experimental validation is being used to understand and to validate the model. Specifically, we will contrast the results from the model with experimental results from our work on low-pressure chemical vapor deposition of aluminum. To date, process models and associated simulation codes have been run in ''stand-alone'' mode; i.e., they have not been integrated. We are developing vertically integrated models and simulators, from the atomic scale to the reactor (equipment) scale for thermal and plasma processes. In addition to the increased savings in design resources which can result from these ''vertically'' integrating process simulators, they will also allow equipment/process control methodologies and models to be developed based upon the wafer state. We have recently integrated a feature scale (micron scale) simulator with a reactor scale simulator, through the use of a ''mesoscale'' (die scale) simulator. In this paper we discuss integration of an atomistic simulation package, to predict grain boundary formation, grain size distributions, thermal grooving, film morphology and composition (segregation), into these larger models.

**2:30 PM *T7.4**

THE CONNECTION BETWEEN IRRADIATION DEFECTS AND GROWTH OF REACTOR PRESSURE TUBES, Carlos N. Tome, Los Alamos National Laboratory, Ctr for Matls Sci, Los Alamos, NM; Nicholas Christodoulou, Atomic Energy of Canada Ltd, Ontario, CANADA.

Reactor pressure tubes made of zirconium alloys (Zr-2.5Nb) are heavily textured polycrystalline aggregates of hexagonal structure. Under normal operating conditions the neutron irradiation produces vacancies and self-interstitials which are driven towards defect sinks in the grain (such as dislocations, dislocation loops and grain boundaries) The fact that vacancies and interstitials have different diffusivities and Interact differently with the sinks induces a bias in the trapping and, as a consequence, dislocation climb and grain boundary migration. At the polycrystal level this process manifests itself as 'irradiation creep' (stress induced deformation) and ' irradiation growth' (deformation in the absence of an applied stress). In this work we model the irradiation growth of the pressure tube, which requires to correlate different material scales and various physical phenomena. First, the atomic configuration of vacancies and interstitials is calculated using interatomic potentials. These configurations are introduced in an atomistic elasto-diffusion model to calculate defect diffusivity (anisotropic) and the effect of strain fields on diffusivity. The latter is the main mechanism that drives irradiation creep. Next, a constitutive law for the single crystal is derived, which gives the strain rate as a function of the stress and the crystallographic mechanisms present in the grain. Finally, the single crystal constitutive law is introduced in a self-consistent polycrystal model of deformation which accounts for texture and grain interactions, and is used to calculate internal stresses and the overall growth of the pressure tube. From the comparison of the predicted macroscopic response with experimental data it is possible to infer information about the mechanisms acting at the microstructural level.

**3:30 PM T7.5**

DEFORMATION SIMULATIONS OF THREE-DIMENSIONAL POLYCRYSTALS, Thomas E. Buchheit, Sandia National Laboratories, Dept of Theoretical & Computational Materials Modeling, Albuquerque, NM; Roy J. Bourcier, Sandia National Laboratories, Mechanical and Corrosion Metal, Albuquerque, NM; Gerald W. Wellman, Michael K. Neilsen, Sandia National Laboratories, Engineering and Manufacturing, Albuquerque, NM.

A microstructural-based constitutive model has been implemented into a quasistatic, large deformation, nonlinear finite element code to examine the deformation of polycrystalline materials. The constitutive model describes the rate-dependent anisotropic mechanical response of a single FCC crystal. The deformation of polycrystalline microstructures (defined using a Potts approach) has been modeled, where each grain is composed of, on average, several hundred hexahedral finite elements. These simulations reveal inter- and intragranular stress and strain gradients due to differences in the morphology, orientation, and location of individual grains within the polycrystal. Results are presented for a variety of simulated polycrystalline microstructures, including single- and multiphase alloys. The polyphase microstructure results are compared to similar structures modeled using an isotropic continuum constitutive model. The original constitutive model (based on an empirical monotonic hardening law) is extended to simulate cyclic response by considering a work hardening theory based on statistical distributions of obstacles to dislocation slip. The simulated cyclic response results are compared with available experimental data. Experimental measurement of stress and strain gradients within polycrystalline microstructures for comparison with the model results are also discussed.

**3:45 PM T7.6**

COMPUTER SIMULATION OF CRACK PROPAGATION IN DESIGNED MICROSTRUCTURES, Satoshi Kitaoka, Hideaki Matsubara, Hiroshi Kawamoto, Fine Ceramics Research Assoc, Synergy Ceramics Lab, Nagoya, JAPAN.

Crack propagation in single-phase ceramics and composites containing dispersoids has been simulated for microstructures designed by Monte Carlo method using two-dimensional triangular lattices. The crack path is determined by selecting the neighboring lattice corresponding to the smallest fracture surface formation energy from five possible crack extension scenarios: cleavage plane in matrix grain, noncleavage plane in it, grain boundary, dispersoid, and interface between matrix and dispersoid. The simulated crack paths depended significantly on the constitution of the designed microstructure. For the single-phase ceramics, the surface ratio of the transgranular fracture and critical energy release rate increased with increasing grain size or fracture surface formation energy of the grain boundary. For the composites, crack deflection due to the dispersoids was more marked in the microstructures consisting of the matrix grains larger than the dispersoids.

**4:00 PM T7.7**

MULTISCALE MODELING OF THE CVD PROCESS, Seth T. Rodgers, Klavs F. Jensen, MIT, Dept of Chemical Engr, Cambridge, MA.

Linking strategies have been developed to facilitate multiscale modeling of chemical vapor deposition (CVD) processes. The macroscale problem (cm scale) of flow and transport in a single-wafer LPCVD reactor is solved using the finite element method. Interactions with the feature scale (microns) are treated with an effective area-flux concept, . represents the increased reaction area due to feature scale morphology and includes feature scale transport resistance. A time dependent function can be calculated from feature scale simulations using Monte Carlo methods. Iteration between macroscopic and and feature scale calculations ensures a consistent boundary condition at the macro-micro interface. In addition, both macroscale and feature scale processes are influenced by chemistry occurring on the atomic scale. A general method is presented for treating multiple reaction pathways, and is used to describe interactions between atomic scale chemistry and feature scale transport. The linking strategies described above result in unified models, enabling investigation of interactions between events occurring on widely separated length scales, such as microloading effects over patterned surfaces, as well as effects of macroscopic concentration and temperature profiles on film microstructure.

**4:15 PM T7.8**

A THREE-SCALE STUDY OF MICROLOADING FOR LPCVD IN SINGLE WAFER REACTORS, Matthias K. Gobbert, Univ of Minnesota, Inst for Mathematics & Applications, Minneapolis, MN; Tushar P. Merchant, Motorola Inc, Advanced Custom Technologies, Mesa, AZ; Timothy S. Cale, Arizona State Univ, Ctr for Solid State Electronics, Tempe, AZ; Leonard J. Borucki, Motorola Inc, Advanced Custom Technologies, Mesa, AZ.

For the purpose of the simulation of chemical vapor deposition in single wafer reactors, both reactor scale models (RSM) and feature scale models (FSM) are well-established. In order to obtain an overall simulation procedure that only uses macroscopic reactor parameters as input, but still yields microscopic information as output, these models have been directly coupled in the past. However, the quality of such a coupling suffers from the huge differences in length scale between the two models as well as typically from a lack of feedback from the small scale to the large scale. To alleviate these drawbacks of combined models, the authors have recently introduced a mesoscopic scale model (MSM) on the length scale of a die as well as an implementation of a three-scale integrated deposition model consisting of a reactor scale, a mesoscopic scale, and a feature scale model. This approach vastly improves the quality of the information exchanged between the scales, allows for the effective treatment of feedback, and provides information on the new intermediate length scale; it becomes possible to resolve variations between feature clusters within a die. This is demonstrated for the case of silicon dioxide deposition from tetraethoxysilane (TEOS). Results will be presented demonstrating the capability of the three-scale model to analyze microloading at several positions on the wafer and throughout the time of the deposition process.

**4:30 PM T7.9**

CORRELATING MICROTENSILE PROPERTIES OF STEEL WELDMENTS WITH MESO/MICROSTRUTURAL SCALE STUDIES, David A. LaVan, William N. Sharpe, Johns Hopkins Univ, Dept of Mech Engr, Baltimore, MD; Robert L. Tregonong, Naval Surface Warfare Center, Dept of Fatigue & Fracture, Bethesda, MD.

The performance of the hull of a large naval structure is determined by the properties of individual weld beads; the behavior of each weld bead is determined on the mesoscale by properties such as microstructure, grain size, and microhardness. Bridging these length scales will allow accurate modeling and optimization of the entire welded structure. This project investigates the directional and microstructural dependence of microtensile properties. Relations were developed to relate mesoscale variations in tensile properties to orientation, microstructural features, and microhardness data. Microtensile samples with gage cross section dimensions of less than 200 m were tested using a novel miniature tensile test machine. Dog bone-shaped samples were tested using two-sided laser interferometric strain measurement, a 10 Kg load cell, and an air-bearing to support the movable grip. Three samples in each of three orthogonal directions at locations representing five different microstructures were tested on samples removed from an undermatched multipass weld in HY-100 steel. Local modulus, yield strength, ultimate strength and elongation were found. The microstructure was investigated using SEM, TEM, and metallography.

**4:45 PM T7.10
**MECHANICS OF CARBON NANOTUBES: MOLECULE, STRUCTURE, MATERIALS, Boris I. Yakobson, North Carolina State Univ, Dept of Physics, Raleigh, NC.

We will discuss linking atomic-scale and continuum models, using carbon nanotube as an instructive test-bed example. Its monoelemental makeup allows to perform realistic MD simulations [1,2]. Their nonlinear elastic behavior, due to the hollow structure, is tractable within the macroscopic shell model. On the other hand, the mechanism of their fracture under tension [3] contrasts with the brittle fashion generally expected in macroscale [4]. The comparative analysis of a few intriguing results of the model and their experimental counterparts (monoatomic unraveling, extraordinary Young's modulus and breaking strain) will be presented. We will emphasize the synergism of the atavistic and continuum methods in application to mesoscale phenomena, as well as their limitations.

SESSION T8: ATOMISTIC SIMULATION METHODS AND RESULTS

Chair: Thomas P. Swiler

Friday Morning, April 4, 1997

Nob Hill D

**8:45 AM T8.1**

BEYOND THE BORN OPPENHEIMER APPROXIMATION, APPLICATION TO H2+, Amir Abbas Farajian, Keivan Esfarjani, Yoshiyuki Kawazoe, Tohoku Univ, Inst for Matls Research, Sendai, JAPAN.

The Born Oppenheimer (BO) approximation is widely used in classical or quantum Molecular dynamics simulations performed on materials. It has however limitations in its applications. For example in metals, where there is no gap, phonons can excite electrons to higher energy levels, and therefore, during the motion of the ions, the electrons do not stay at the ground state. The other case where BO is not valid, is in high-energy collisions, or some chemical reactions where again electrons can get excited to higher energy levels. For this purpose, we attempt to solve exactly a three-body problem beyond the BO approximation. We have considered the ionized hydrogen molecule, and solved this problem for all values of the reduced mass, thus identifying H2+, H- and charged exciton as the same quantum mechanical problem with different values for the reduced mass. We can therefore obtain an analytic from for the variational wavefunction of the two protons. We expect to apply our results to problems involving the motion of protons in materials.

**9:00 AM T8.2**

SELF-CONSISTENT, FIRST-PRINCIPLES DENSITY MATRIX METHOD FOR TOTAL ENERGIES AND ELECTRONIC STRUCTURE, James Edward Raynolds, Eric R. Roddick, Univ of Michigan, Dept of Matls Science, Ann Arbor, MI; John R. Smith, General Motors, Dept of Physics & Physical Chem, Warren, MI; David J. Srolovitz, Univ of Michigan, Dept of Matls Science, Ann Arbor, MI.

Most materials problems of practical interest involve more than one element and involve a combination of ionic, metallic and/or covalent bonding. Accurate trea tments of these materials require first-principles computations. However, tradit ional first-principles methods suffer from the important limitation that their c omputational time and storage requirements scale, at best, as the cube of the nu mber of electrons in the system, rendering it difficult to treat systems of more than one hundred atoms. By formulating a method in terms of the density matrix in a basis of localized orbitals (rather than wave functions) it is possible to obtain a sparse density matrix which enables a method which scales linearly with th e system size, thus allowing much larger systems to be treated. We hav e developed such a method and will present the details of its implementation. O ur new method allows the treatment of essentially all classes of materials. The novelty of this approach relative to other density matrix methods lies in our c hoice of the basis set and the manner in which the idempotency constraint is app lied. Results will be given for several different materials and defects. These results are in excellent agreement with results obtained using an all-electron wave-function-based method.

**9:15 AM T8.3
**GENERALIZED TIGHT-BINDING SCHEME FOR COMPUTATIONAL MATERIALS MODELING, Madhu Menon, K. R. Subbaswamy, Ernst Richter, Univ of Kentucky, Dept of Physics & Astronomy, Lexington, KY.

We describe a generalized tight-binding molecular dynamics scheme, useful in the simulations of real materials, and show its applications. The method, while quantum mechanical in nature, is orders of magnitude faster than schemes and provides a useful bridge between techniques and classical many-body potentials. We will discuss incorporation of state-of-the-art numerical techniques for the diagonalization of large scale matrices that enable as to perform simulations for systems consisting of several hundreds of atoms. For larger systems we use order-N methods that circumvent the direct diagonalization process. Application to large Si and C systems will be presented.

**9:30 AM T8.4**

TIGHT-BINDING PARAMETRIZATION FOR MOLECULAR DYNAMICS OF NI CLUSTERS, Keivan Esfarjani, Akito Taneda, Yoshiyuki Kawazoe, Tohoku Univ, Inst for Matls Research, Sendai, JAPAN.

We have performed ab-initio calculations of Ni clusters using the program Gaussian94. From the electronic eigenvalues and eigenvectors, we deduce the Hamiltonian matrix. That allows us to construct a tight-binding parameter set which reproduces the same Hamiltonian and eigenvalues. Furthermore, from the ab-initio total energies, we construct an additional short-range repulsive interaction, which added to the tight-binding eigenvalues, yields the total energy. The latter is in good agreement with the results of first-principle calculations. We have thus a tight-binding parametrization that allows us to perform molecular dynamics simulations of Ni clusters. We have used the latter to calculate the ground state configuration of Ni12 up to Ni20 by the simulated annealing method. We hope to use the same technique to get the tight-binding parameters of magnetic transition metal atoms.

**9:45 AM T8.5**

NEW INTERATOMIC POTENTIALS FOR SILICA, Tahir Cagin, Ersan Demiralp, William A. Goddard, California Inst of Technology, Materials & Process Simulation Ctr, Pasadena, CA.

In recent years, several new interatomic potentials were developed for the descriptions of the interatomic interactions of the silica, , forms. These force fields have exponential-6 type potentials for the short-range interactions and the electrostatic interactions with fix charges () for all silica forms. These potentials show unphysical behaviors for (``exponential-6 catastrophe") and may cause serious problems for high temperature simulations. We developed a new force field which has Morse potentials for the short-range interactions and the electrostatic interactions with variable charges for the different silica forms. The charges are calculated with Charge Equilibration Method (QEq). These new potentials should eliminate the disadvantages of the exponential-6 type potentials. The calculated charges are functions of the structures, thus the new force field should be suitable for glass simulations.

**10:30 AM T8.6**

AB INITIO ELASTIC PROPERTIES OF SINGLE-CRYSTAL DIAMOND AND SILICON, Daryl G. Clerc, NIST, Matls Reliability Div-853, Boulder, CO.

The elastic properties of single-crystal diamond and silicon were studied using ab initio periodic all-electron density-functional theory. The contribution of energy components to the bulk moduli and elastic stiffness coefficients were analyzed to explore the relationships between electronic structure and mechanical strength. Towards these ends, the second derivatives of the kinetic, coulomb, exchange-correlation, and total energies with respect to strain were calculated for diamond and silicon The corresponding results for uniform (hydrostatic) strain in units of k (diamond) are 5.1, -3.4, -0.7 for diamond and 6.3, -4.6, -0.8 for silicon, where k (diamond) is the said derivative of the diamond total energy. The kinetic and coulomb contributions are very different in the two materials, but collectively are nearly the same. Consequently, diamond and silicon have very similar electronic responses to hydrostatic pressure; k (diamond) = 1.05 k (silicon). It follows that the large bulk modulus of diamond (442 GPa) relative to silicon (98 GPa) results from diamond's smaller equilibrium volume (C: 11.28 A, Si; 40.04 A) rather than from differences in electronic pressure response.

**10:45 AM T8.7**

SHEAR VISCOSITIES OF SODIUM AND NICKEL FROM NONEQUILIBRIUM MOLECULAR DYNAMICS SIMULATIONS, Tahir Cagin, California Inst of Technology, Materials & Process Simulation Ctr, Pasadena, CA; Khalid A. Mansour, Cray Research Corp, Englewood, CO; William A. Goddard, California Inst of Technology, Materials & Process Simulation Ctr, Pasadena, CA.

Macroscopi and mesoscopic level modeling of materials utilize the response functions such as compressibility, shear modulus elastic constants for solids diffusion constants, viscosities for liquids as central quantities in the constitutive equations. Modeling transport and flow behavior in metal and metal alloy processing one need to know temperature and concentration dependence of alloy constituents. Atomistic level simulations are of considerable importance in the determination of such variables. As a part of our studies of transport and phase behaviour light weight high perfomance amorphous metal alloys we investigated the shear viscosities of liquid sodium and liquid nickel are determined using nonequilibrium molecular dynamics (NEMD) simulations. The interactions between sodium ions are represented using a density-dependent potential derived using second order perturbation theory with an empty core local pseudopotential. Using a 432 Na atom model system and the experimental density at each temperature we calculated the viscosity at a number of shear rates. The NEMD results for sodium are in better agreement with the experiment than earlier Green-Kubo calculations using the same potential. The interactions between atoms are represented by a many-body potential using form due to Sutton and Chen, parameters of the potentials are modified to accurately represent phonon spectra and vacancy and surface formation energies. Using a 500 Ni atom model system and the experimental density at each temperature we calculated the viscosity at a number of shear rates for nickel ( = 1726K) at temperature up to 3000K. The predicted visosity are in good agreement with experiment.

**11:00 AM T8.8**

MOLECULAR DYNAMIC STUDIES OF WETTING IN METALLIC SYSTEMS, Thomas P. Swiler, F. G. Yost, Sandia National Laboratories, Dept of Theoretical & Comp Matls Modeling, Albuquerque, NM.

Models of fluid dynamics generally use the Navier-Stokes equations and assume that the fluid is a continuum. The solution of these equations generally make use of a boundary condition that sets the fluid velocity to zero at solid-liquid interfaces. However, this leads to an inconsistency in wetting and spreading models that require fluid, or more precisely, liquid motion at the wetting line. In order to determine the true behavior of liquids at interfaces during wetting, we undertook an atomistic simulation study. Using molecular dynamics simulations with EAM and MEAM potential functions to model various systems, we observed atomic dynamics and structural correlations at the liquid-solid interface. We find that spreading is prompted by interactions between the liquid and the substrate surface that cause the liquid layer in contact with the substrate to take on some of the symmetry of the substrate surface and result in the formation of a liquid monolayer that extends beyond the major part of the liquid droplet. Although better potential functions are required to accurately model systems of technical interest, such as lead-tin solder on oxygen-contaminated copper-tin intermetallics, this study provides insight into the atomistic processes that control spreading kinetics.

**11:15 AM T8.9**

THEORETICAL PREDICTIONS ABOUT STABILITY OF MESOSCALE CARBON-WATER COMPLEXES: QUANTUM MECHANICS APPROACH COMBINED WITH CONTINUUM MODEL, Vyacheslav V. Rotkin, A.F. Ioffe Phys-Technical Inst, Dept of Solid State Electronics, St. Petersburg, RUSSIA.

On the base of simplest physical consideration we describe the Van-der-Waals crystal-solvate of the ultra-small diamonds (USD) in the water. Our experience in the field of the electromagnetic response of the fullerene clusters and result from the solid state theory of the plasma excitations in the superlattices were found to have a very close similarity to the calculation of the Van-der-Waals interaction between the water coated particles. A great deal of interest to the ultra-small diamond particles is connected with the advanced coating techniques achieved on the base of this material. However the technology of the process stays to be far from the optimum. Recently developed novel technique for the water colloids on the base of USDP allows to construct the 2D-crystal layers or the clustered surfaces. This paper is devoted to the calculation of the stability of the crystal-solvate of USD in the dissolved or solid state phase. In order to calculate quantum-mechanically the interaction energy one needs to know the response function of the system. It is suggested that the main contribution to the response is due to the self-consistent collective excitations in this medium. We suppose that the USD colloids can be described as the spherically coated particles with about of 40 double-charged layers. The basic idea is to make use of our model calculation for the solid state collective excitation in the system of the parallel conducting planes with the alternating sign of the surface charge density together with our model of the excitation in the Spherical Shell Quantum Well model for the fullerenes. We present the response function and it allowed us to calculate the energy of the attraction between the particles. On the base of these results we made the predictions about the stability of the crystal-solvate of the definite structure.

**11:30 AM T8.10
**ANISOTROPY OF ANTIPHASE BOUNDARY FORMATION ENERGY IN INTERMETALLICS NiAl, M. D. Starostenkov, A. V. Borissov, Altai State Technical Univ, Dept of General Physics, Barnaul, RUSSIA.

The anisotropy of antiphase boundary (APB) formation energies in plains , , , , , , , is calculated using an approximation taking into account atomic interactions for intermetallics NiAl by sets of Morse potentials. It was shown energy spectrum of different types APB and their complexes, from which may be suggested different reactions for transitions between defects. Possibility of an ''energetical'' superiority of TAPB (thermal APB) or DAPB (double complex APB) as compared with shift boundaries is noted. It means that thermoactivated transitions between different types of APBs are probable if the diffusion mobility of atoms in the alloy is quite high. Such transformations are real under strain in fine domain structures when takes place under high temperature plastic strain. If there are reactions in the alloy like APB DAPB or APB TAPB, blocking of movable dislocations should occur. To realize such reactions it is necessary that the component concentrations are sufficient to maintain the stoichiometry of the alloy and the diffusion mobility of atoms is high enough. It was shown that reaction APB DAPB is realized on and planes. When the composition deviates from stoichiometry, diffusion of the ''excessive'' component in shift APBs on planes , , , , is energetically advantageous. Energy of formation of tube of APB in NiAl was calculated for connection with their height. The dependence of energy spectrum of different types of APB and their complexes with the temperatures, pressibilites, and dopings by Nb, Fe was investigated in that paper. It was shown that all date factors may be changed energy spectrum of plane defects, and consequently may be changed dislocations reactions in materials.

**11:45 AM T8.11**

PROPERTIES OF TWIST BOUNDARIES IN ORDERED ALLOYS NiFe AND NiAl, M. D. Starostenkov, O. V. Brazovskaya, Altai State Technical Univ, Dept of General Physics, Barnaul, RUSSIA.

Structural and energetic characteristics of twist boundaries were investigated in ordered alloys CuAu, AuCu and NiFe with superstructure L1. The new investigate method of structural and energetic properties was obtained. This method based on the construction of local characteristics such as distribution density of potential energy and function of radial distribution. Equilibrium condition of twist boundaries were calculated in planes (001) and (111) with using pair potential Morse. The level of potential energy in alloys CuAu and AuCu increased under the segregation of alloys' components along boundaries, which generated unconservative antiphase boundaries. Fe boundary surface segregation decreased general level of potential energy in ordered alloy NiFe. The position of special angles with corresponded minimum significances of twist boundary potential energy, in particular under the = 16.26, 22.62, 28.07, 36.87, 43.6. Therefore, twist boundaries have to represent the educe zone pure Fe in ordered alloy NiFe. Unstable areas were extracted along the grain boundaries. Unstable areas were characterized as incipient zone of defects such as dislocations and disclinations.