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Predicting the properties and perform-ance of materials is central to the successof major industries producing a vast rangeof consumer goods and to research pro-grams at laboratories and universitiesaround the world. For many years, scien-tists have longed to have computer simula-tions that predict the behavior of materialsand track the evolution of their micro-

structures from the atomic to the engineer-ing scales. Until recently, such simulationshad been little more than an elusive goal.

In recent years, the advent of ever morepowerful, massively parallel computers,coupled with spectacular advances in thetheoretical framework that describes ma-terials, has enabled the development of newconcepts and algorithms for the computa-tional modeling of materials. As the fieldof computational materials science devel-ops and matures, the notion is taking holdin the community that modeling effortsshould be an integral part of interdiscipli-nary materials research and must includeexperimental validation.

In multiscale modeling, the goal is topredict the performance and behavior ofcomplex materials across all relevant lengthand time scales, starting from fundamen-tal physical principles and experimentaldata. The challenge is tremendous. At theatomic (nanometer) scale, electrons governthe interactions among atoms in a solid,and therefore quantum mechanical descrip-tions are required to characterize the col-lective behavior of atoms in a material.

However, at the engineering scale, forcesarising from macroscopic stresses and/ortemperature gradients may be the control-ling elements of materials performance.At scales in between, defects such as dis-locations control mechanical behavior onthe microscale (tens of micrometers), whilelarge collections of such defects, includinggrain boundaries and other microstructural

elements, govern mesoscopic properties(hundreds of micrometers). The net out-come of these interactions can be describedas a constitutive law that ultimately governscontinuum behavior on the macroscale(centimeters).

Conceptually, two different types ofmultiscale simulations have been consid-ered. One of them attempts to piece togethera hierarchy of computational approachesin which larger-scale models use coarse-grained representations of the material andits microstructure while using the dataobtained in more detailed, smaller-scalemodels as a material-defining input. Suchparameter-passing, sequential modelingapproaches have proven effective, espe-cially when material behavior can beparsed into several scales, each with itsown distinct characteristics. Another typeof multiscale simulation attempts to linkseveral computational approaches togetherin a combined model in which differentscales of material behavior are consideredconcurrently and communicate using somesort of handshaking procedure. Specificchoice and implementation of either se-

quential or concurrent multiscale ap-proaches depend on the task at hand.

In this issue ofMRS Bulletin, we havebrought together a collection of articlesthat illustrates the current status of thefield. Presented are representative examplesof materials modeling that both drive and

benefit from the application of variousmultiscale methodologies. Because of thetremendous increase in activity in recentyears, this is by no means a comprehen-sive review, but rather a representativevignette. Multiscale modeling is reachinga degree of maturity illustrated by thestrong implications for industrial applica-tions in these articles. The goal of this issueis to inform the community of materialsscientists of recent advances and to dis-cuss where the challenges lie in the future.

The article by Odette et al. tackles ra-diation damage in reactor steels, a well-established but very challenging and

inherently multiscale problem. The articleclearly illustrates the need for (and thepower of) coupling together experimentsand computations to solve real-worldproblems. The success in the last few yearsin addressing these complex damage is-sues from the atomistic to the continuumscales has been dramatic. A combinationof molecular-dynamics, kinetic Monte Carlo,and continuum mechanics approaches al-lows the authors to describe defect pro-duction in displacement cascades, defectdiffusion, and the effect of the modifiedmicrostructure on mechanical properties.Another article that demonstrates the power

of coupled experiments and computationsis the one by Baumann et al. As the semi-conductor industry moves to ever-smallerfeatures in transistors, manufacturing the

back-end lines that interconnect all of thesetransistors in an integrated circuit becomesa tremendous challenge. The simulationsdescribed in Baumanns article couple atom-istic studies of diffusion and film growthwith continuum mathematical descriptionsof advancing fronts to demonstrate that apredictive capability for modeling alu-minum metallization has been developed.This achievement would not have beenpossible without clever and definitive ex-periments that both challenge and guidethe model development.

Describing the complex behavior of re-alistic densities of interacting dislocationsduring plastic deformation has been a

beckoning yet elusive goal for the mate-rials community. In recent years, increasedcomputing power, combined with our en-hanced knowledge of the atomistic natureof dislocation core structure and motion,has enabled the development of three-dimensional dislocation-dynamics models

MRS BULLETIN/MARCH 2001 169

Materials Researchby Means ofMultiscaleComputerSimulation

Toms Daz de la Rubia and Vasily V. Bulatov,Guest Editors

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of single-crystal plasticity. The article byBulatov et al. describes recent progress inthis field and discusses the challenges forfuture work.

The article by Chen et al. charts a roadmap toward predictive modeling of micro-structure and its evolution in multicompo-

nent industrial alloys. The authors discussseveral promising approaches to model-ing alloy microstructure and outline pos-sible ways of connecting them into apredictive multiscale framework within theparameter-passing paradigm. Followingthe proposed route, simulations presentedin this article demonstrate a remarkableagreement with experimental data on themorphology of precipitate phases in Al-Cualloys. The authors argue that, similar tothe CALPHAD (calculated phase diagram)approach, it is possible to develop a prac-tical methodology for microstructural mod-eling of multicomponent alloys based on

phase-field computations. In this scheme,first-principles (nanoscale) calculations canplay an increasingly important role by fill-ing the gaps in the thermodynamics andkinetics databases, especially for metastablephases where experimental data are diffi-cult to obtain.

The article by Kremer and Mller-Plathestarts with a brief introduction on thescience of very long (macromolecular)polymers, which exhibit properties and

behaviors approaching those of biomo-lecular systems. Predictive simulations ofmacromolecules face several fascinatingand difficult challenges, including the in-

credible span of length and time scales in-herent in polymer behavior. The approachdescribed in this article involves sequen-tial coarse-graining from microscale (atoms)to mesoscale (molecular groups) to macro-scale (whole chains). The authors follow aparameter-passing strategy in which theeffective free-energy terms for the coarse-grained model are obtained by statisticalaveraging of fast degrees of freedomwithin the more detailed model. This ideais successfully used to map an atomisticmodel of polycarbonate polymers onto amesoscale description of polymer chains.The resulting prediction of the viscosityvariations with molecular weight is in

close agreement with experimental data.Further coarse-graining enables efficient

modeling of phase separation in polymermelts containing two types of polymermolecules. Here, chains are replaced withsemi-penetrable fuzzy particles, eachcharacterized by its mass tensor. Theauthors outline a strategy for further de-velopment to improve the links between

different levels of description and to retainthe chemical and structural specificity ofthe polymer chains.

Fracture simulations present anotherset of interesting challenges. Chief amongthem is a close interaction between differ-ent length scales involved in fracture. Fun-damentally, crack propagation proceedsthrough breaking interatomic bonds at thecrack tip. At the same time, the force driv-ing crack propagation is a complex func-tion of external stress, specimen geometry,and material microstructure. All of theseaspects are so tightly entangled that it isdifficult to parse the system into several

distinct scales. Needleman and Van derGiessen discuss a host of issues that arefundamental to the development of pre-dictive methodologies for fracture model-ing. One of the more pressing needs is anunderstanding of the role of dislocationsand plasticity in fracture. As an illustrativeexample, the authors discuss the effects ofirreversible buildup of dislocation micro-structure and its interaction with a crackgrowing in fatigue.

A promising new approach to con-current multiscale modeling is described

by Ortiz et al. It is based on the ideaof an atomisticcontinuum handshake

arranged in such a way that atomisticdetails of material microstructure are re-solved only where necessary, for example,in highly distorted regions in the coresof crystal defects. The rest of the materialis treated as a continuum within a finiteelement framework. Through the use ofadaptive mesh refinement, the interaction

between the atomistic and continuumdescriptions is organized in an entirelyseamless fashion. In this way, the numberof degrees of freedom to be considered isreduced by many orders of magnitude. Asan example, the authors discuss an appli-cation of the quasi-continuum (QC) ap-proach to nanoindentation simulations.

The continuum boundary value problemis solved on the micrometer scale, while si-

multaneously the atomistic details of dis-location nucleation under the indenter arefully resolved on the nanometer scale. Theauthors conclude that the QC approach isan exciting new venue for the develop-ment of computationally efficient contin-uum models with microstructural content.

As the field moves forward, it is essen-tial for the experimental community of re-searchers to be fully aware and cognizantof the possibilities and limitations of com-putational materials science. We hope thatthe combination of this issue with otherresources1 will enable students and pro-fessionals carrying out experiments tolearn more about the tools used in simula-tions and to develop a better appreciationfor and understanding of the power andlimitations of computational materials sci-ence. It is through close interactions andcollaborations among experimentalists,theorists, and computational scientists that

materials research will move forward inthe future.

References1. In conjunction with the appearance of thisissue, the Materials Research Society will behosting a symposium on computational mate-rials science focused on multiscale modeling atthe 2001 MRS Spring Meeting in San Francisco(Symposium AA: Advances in Materials The-ory and ModelingBridging Over MultipleLength and Time Scales). Also at this meeting,MRS is planning a tutorial consisting of lectureson the fundamentals of simulations at the fourlength scales described here, followed byhands-on tutorials. Over the last few years,MRS has sponsored symposia on this topic thathave resulted in several volumes with invitedand contributed papers. For example, see Com-

putational and Mathematical Models of Microstruc-tural Evolution, edited by J.W. Bullard, L.-Q.Chen, R.K. Kalia, and A.M. Stoneham (Mater.Res. Soc. Symp. Proc. 529, Warrendale, PA,1998);Multiscale Modeling of Materials, edited byV.V. Bulatov, T. Diaz de la Rubia, R. Phillips, E.Kaxiras, and N. Ghoniem (Mater. Res. Soc.Symp. Proc. 538, Warrendale, PA, 1999);Multi-scale Phenomena in MaterialsExperiments and

Modeling, edited by I.M. Robertson, D.H. Las-sila, B. Devincre, and R. Phillips (Mater. Res.Soc. Symp. Proc. 578, Warrendale, PA, 2000);andMultiscale Modeling of Materials2000, ed-ited by L.P. Kubin, J.L. Bassani, K. Cho, H. Gao,and R.L.B. Selinger (Mater. Res. Soc. Symp.Proc. 653, Warrendale, PA, 2001) to be pub-lished. s

170 MRS BULLETIN/MARCH 2001

Materials Research by Means of Multiscale Computer Simulation

APRIL 2001Theme topic: Microelectromechanical Systems

(MEMS) Technologies and Applications

Guest Editors: David J. Bishop (Lucent Techno-

logies, Bell Labs), Arthur H. Heuer (Case Western

Reserve University), and David Williams (Sandia

National Laboratories)

MAY 2001Theme: Hybrid Organic-Inorganic MaterialsGuest Editor: Doug Loy (Sandia National Laboratories)

JUNE 2001Theme: High-Thermal-Conductivity MaterialsGuest Editors: Koji Watari (National Industrial Research

Institute of Nagoya) and Subhash L. Shinde(IBM Microelectronics)

MRS BULLETIN UPCOMING THEMES

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