Modelling and Theory of Interfaces

Major Program Thrusts
* Multiscale simulation of polycrystalline materials
* Multiscale simulation of thermal transport in nanostructures
* Atomic-level simulation of ferroelectrics
* Nanocrystalline materials

Other Capabilities
* Dynamical phenomena in grain boundaries
* Electronic-structure and atomic-level simulations of interfaces in silicon and diamond
* Free surfaces
* Theory and modelling of ionic systems
* Melting and solid-state amorphization: theory and simulation
* Mechanical properties of multilayers, thin films and grain boundaries


Multiscale simulation of polycrystalline materials

This work, initiated in 1998, aims at the development of the conceptual framework and a systematic computational approach for the simulation of polycrystalline materials that incorporates all the relevant length and time scales controlling microstructural evolution, ranging from the atomic-level, via the microstructural length and time scales, to the continuum level. The scope of this approach is presently being broadened to include self assembly of nanostructures and alloy oxidation, two new mostly experimental program directions at Argonne.

Our work in this area is closely coordinated with, and complemented by, a recently formed, DOE/BES funded multi-laboratory computational thrust within the Computational Materials Science Network (CMSN). This virtual-team thrust, titled Microstructural Effects on the Mechanics of Materials, is co-directed by D. Wolf and R. LeSar (LANL); for details, see http://www.msd.anl.gov/groups/im/research/cmsn/. The modest "glue funding" received through this thrust (of about $300k/year) is used to connect our multiscale approach for polycrystals with the dislocation-dynamics approach which is being used extensively to simulate dislocation processes in single-crystal plasticity.

Key references
* Combined Atomistic and Mesoscale Simulation of Grain Growth in Nanocrystalline Thin Films, A. J. Haslam, D. Moldovan, S. R. Phillpot, D. Wolf and H. Gleiter,  Computational Materials Science 23, 15-32 (2001).

* Theory of Diffusion-Accommodated Grain Rotation in Columnar Polycrystalline Microstructures, D. Moldovan, D. Wolf and S. R. Phillpot, Acta Mat. 49, 3521-3532 (2001).

* Mesoscopic simulation of two-dimensional grain growth with anisotropic grain-boundary properties, D. Moldovan, D. Wolf, S. R. Phillpot,  and A. J. Haslam, Phil. Mag. A 82, 1271-97 (2002).

* Role of grain rotation in grain growth by mesoscale simulation, D. Moldovan, D. Wolf, S. R. Phillpot and A. J. Haslam,  Acta Mater. 50, 3397-3414 (2002).

* Scaling behavior of grain-rotation induced grain growth, D. Moldovan, V. Yamakov, D. Wolf and  S. R. Phillpot, Phys. Rev. Lett. 89 (Nov. 11, 2002).

* Grain-boundary diffusion controlled stress concentration in polycrystals, D. Moldovan, D. Wolf, S. R. Phillpot, H. Gleiter and A. K.  Mukherjee, Phil. Mag. Lett. (accepted Sep. 2002).

* Grain growth as case study for multiscale simulation of polycrystalline materials, invited manuscript to be published in Phil. Mag. A (Jan. 2003).

Highlights

* MULTISCALE SIMULATION OF POLYCRYSTALLINE MICROSTRUCTURES @ ANL

* MULTISCALE SIMULATION OF GRAIN GROWTH
 
 
 

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Multiscale simulation of thermal transport in nanostructures

This work, initiated in 1999, is aimed at developing a detailed microscopic understanding of phonon-mediated thermal transport in materials microstructures. In addition to using standard techniques for simulating the thermal conductivity, we have developed a unique capability for studying the dynamics of individual phonon wavepackets.  This has allowed us to explore the elementary processes involved in  phonon/interface interactions.  We are also trying to elucidate the origin of the anomalously high  thermal-transport coefficients of heat-transfer liquids containing suspensions of small amounts of nanosized particles (so-called nanofluids).

Key references

* Mechanism of Thermal Transport in Zirconia and Yttria-Stabilized Zirconia By Molecular-Dynamics Simulation. P. K. Schelling and S. R. Phillpot, Journal of the American Ceramic Society 84, 2997 (2001).

* Towards a Theory of Heat Flow in Suspensions containing Nano-sized Particles (Nanofluids), P. Keblinski, S. R. Phillpot, S. U.-S. Choi and J. A. Eastman, International Journal of Heat and Mass Transfer 45, 855 (2002).

* Phonon Scattering at a Semiconductor Interface by Molecular-Dynamics Simulation, P. K. Schelling, S. R. Phillpot and P. Keblinski, Applied Physics Letters 80 2484-2486 (2002).

* Comparison of Atomic-Level Simulation Methods for Computing Thermal Conductivity, P. K. Schelling, S. R. Phillpot and P. Keblinski, Physical Review B 65, 144306 (2002).

* Thermal Resistance of a Liquid-Solid Interface, L. Xue, P. Keblinski, S. R. Phillpot. S. U.-S. Choi and J. A. Eastman, Journal of Chemical Physics (in press, July 2002).

* Multiscale Simulation of Phonon Transport in Superlattices, P. K. Schelling and S. R. Phillpot, submitted to Journal of Applied Physics (May 2002)

* Optimum Pyrochlore Compositions for Low Thermal Conductivity by Simulation, P. K. Schelling, S. R. Phillpot and R. Grimes, submitted to Philosophical Magazine Letters (November 2002).

Highlights
 

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Atomic-level simulation of ferroelectrics

After years of investment, we have succeeded in developing the first atomic-level interaction potentials for ferroelectric perovskite oxides which capture the complete phase diagram. This breakthrough has enabled entirely new, large-scale simulations of ferroelectric materials which, to date, had been amenable only via full electronic-structure approaches and were hence limited essentially to zero temperature. We have exploited this capability by fully elucidating the complex long-ranged electrical interactions between the ferroelectric and dielectric components of perovskite solid solution and heterostructures.  We have also begun to explore the physics of ferroelectric domain switching. This effort is a key component of the project on Nanoscale Phenomena in Perovskite Thin Films within the DOE Center for Excellence on Synthesis and Processing. Two proposals submitted with colleagues at Lehigh and Penn State would extend our program on ferroelectrics to LiNbO3, an important optoelectronic material.

Key references

* Ferroelectric-Monolayer Reconstruction of the SrTiO3 (100) Surface, V. Ravikumar, D. Wolf and V. P. Dravid, Phys. Rev. Letters 74, 960-963 (1995).

* Atomic-level Simulation of Ferroelectricity in Perovskite Solid Solutions, M. Sepliarsky, S. R. Phillpot, D. Wolf, M. G. Stachiotti and R. L. Migoni, Appl. Phys. Lett. 76, 3986-3988 (2000).

* Atomic Structure and Properties of the (310) Symmetric Tilt Grain Boundary in SrTiO3. Part I: Atomistic Simulations, V. Ravikumar, V. P. Dravid and D. Wolf, Interface Science 8, 157-175 (2000).

* Ferroelectric Properties of KNbO3/KTaO3 Superlattices by Atomic-Level Simulation, M. Sepliarsky, S. R. Phillpot, D. Wolf, M. G. Stachiotti and R. L. Migoni, Journal of Applied Physics 90, 4509-4519 (2001).

* Long-ranged ferroelectric interactions in perovskite superlattices, M. Sepliarsky, S. R. Phillpot, D. Wolf, M. G. Stachiotti and R. L. Migoni, Phys. Rev. B 64, 60101-4 (2001).

* Dynamics of Polarization Reversal in a Perovskite Ferroelectric by Molecular-Dynamics Simulation, M. Sepliarsky, S. R. Phillpot, S. K. Streiffer, M. G. Stachiotti and R. L. Migoni, Applied Physics Letters 79 4417 (2001).

* Phase Transitions and Dynamical Behavior in KNbO3/KTaO3 Superlattices by Molecular-Dynamics Simulation, M. Sepliarsky, S. R. Phillpot, M. G. Stachiotti and R. L. Migoni, Journal of Applied Physics 91, 3165 (2002).

Highlights

* ATOMIC-LEVEL SIMULATION OF PEROVSKITE FERROELECTRICS
 

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Nanocrystalline materials

As a natural outcome of our extensive earlier work on grain boundaries, in 1994 we performed the first atomistic simulations of nanocrystalline materials. Since then we have developed extensive capabilities for molecular-dynamics simulations of the synthesis, characterization and determination of thermo-mechanical properties of nanocrystalline materials (in collaboration with H. Gleiter, Karlsruhe and A. Argon and S. Suresh, MIT).

Key references

* Molecular-Dynamics Study of the Synthesis and Characterization of a Fully Dense  Three- Dimensional Nanocrystalline Material, S. R. Phillpot, D. Wolf and H. Gleiter, Journal of Applied Physics 78, 847-861 (1995).

* A Structural Model for Grain Boundaries in Nanocrystalline Materials, S. R. Phillpot, D. Wolf and H. Gleiter, Scripta Met. et Mat.  33, 1245-1251 (1995).

* On The Thermodynamic Relationship Between Nanocrystalline Materials and Glasses, D. Wolf, J. Wang, S. R. Phillpot and H. Gleiter, Phys. Lett. A 205, 274-280 (1995).

* Phonon-induced Anomalous Specific Heat of a Nanocrystalline Model Material by Computer Simulation, D. Wolf, J. Wang, S. R. Phillpot and H. Gleiter, Phys. Rev. Letters 74, 4686-4689 (1995).

* Molecular-Dynamics Simulation of Grain-Boundary Diffusion Creep, P. Keblinski, D. Wolf and H. Gleiter, Interface Science 6, 205-212 (1998).

* Mechanisms of Grain Growth in Nanocrystalline fcc Metals by Molecular-Dynamics Simulation, A. J. Haslam, S. R. Phillpot, D. Wolf, D. Moldovan and H. Gleiter , Mat. Sci. & Eng. A 318,  293-312 (2001).

* Length-scale Effects in the Nucleation of Extended Dislocations in Nanocrystalline Al by Molecular-Dynamics Simulation, V. Yamakov, D. Wolf,. M. Salazar, S. R. Phillpot and H. Gleiter, Acta Mater. 49, 2713-22 (2001).

* Dislocation processes in the deformation of nanocrystalline aluminum by molecular-dynamics simulation, V. Yamakov, D. Wolf, S. R. Phillpot, A. K. Mukherjee and H. Gleiter, Nature Materials 1, 1-4 (2002).

* Grain-boundary diffusion creep in nanocrystalline palladium by molecular-dynamics simulation, V. Yamakov, D. Wolf, S. R. Phillpot and H. Gleiter, Acta Mater. 50, 61-73 (2002).

* Deformation twinning in nanocrystalline Al by molecular-dynamics simulation, V. Yamakov, D. Wolf, S. R. Phillpot and H. Gleiter, Acta Mater. 50, 5005-20 (2002).

* Stress-Enhanced Grain Growth in a Nanocrystalline Material by Molecular-Dynamics Simulation, A.J. Haslam, D. Moldovan, V. Yamakov, D. Wolf, S.R. Phillpot and H. Gleiter, Acta Mater. (submitted Sep. 2002).

* Deformation-Mechanism Crossover and Mechanical Behavior in Nanocrystalline Materials, V. Yamakov, D. Wolf and  S. R. Phillpot, H. Gleiter and A. K.  Mukherjee, Nature (submitted Nov. 2002).

Highlights

* MOLECULAR-DYNAMICS SIMULATION OF GRAIN-BOUNDARY DIFFUSION CREEP
 

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Dynamical phenomena in grain boundaries

Grain boundaries have represented the "backbone" for the development of our interface simulation program. Our work on grain boundaries has challenged, and continues to challenge, many traditional views on how their geometry and structure is coupled to their physical properties. This unconventional, physics-based description of internal interfaces has enabled us to establish the conceptual links among all types of solid interfaces, including thin films, multilayers and free surfaces. This approach has also enabled us to expose the intricate connection between the properties of nanocrystalline materials and the underlying grain-boundary atomic structure, and the relationship with the structure and physics of grain boundaries in coarse-grained materials. The recognition of the intricate interrelation among free surfaces, internal interfaces and finite-size effects provides a promising tool towards understanding the physical consequences of nanostructuring.

Key references

* Structure and Energy of Grain Boundaries in Metals, K. L. Merkle and D. Wolf, MRS Bulletin XV No. 9, 42-50 (1990).

* Correlation Between the Structure and Energy of Grain Boundaries in Metals, D. Wolf and K. L. Merkle, a chapter in Materials Interfaces: Atomic-Level Structure and Properties, D. Wolf and S. Yip, eds., Chapman and Hall, London, 1992, pp. 87-150.

* Thermodynamic Criterion for the Stability of Amorphous Intergranular Films in Covalent Materials, P. Keblinski, S. R. Phillpot, D. Wolf and H. Gleiter, Phys. Rev. Lett. 77, 2965-2968 (1996).

* Amorphous Structure of Grain Boundaries and Grain Junctions in Nanocrystalline Silicon by Molecular-Dynamics Simulation, P. Keblinski, S. R. Phillpot, D. Wolf and H. Gleiter, Acta mater. 45, 987-998 (1997).

* Molecular-Dynamics Method for the Simulation of Grain-Boundary Migration, B. Schoenfelder, D. Wolf, S. R. Phillpot and M. Furtkamp, Interface Science 5, 245-262 (1997).

* Self-diffusion in High-angle fcc Metal Grain Boundaries by Molecular Dynamics Simulation, P. Keblinski, D. Wolf, S. R. Phillpot and H. Gleiter, Phil. Mag. A 79, 2735-2762 (1999).

* Grain Boundaries: Structure, D. Wolf, invited article in The Encyclopedia of Materials: Science and Technology, Robert Cahn, principal editor, Pergamon Press, 2001, pp. 3597-3609.

* High-Temperature Structure and Properties of Grain Boundaries: Long-range vs. Short-Range Structural Effects, D. Wolf, invited article in Current Opinion in Solid State and Materials Science 5, 435 (2001).

Highlights
 

* THERMODYNAMIC-EQUILIBRIUM NATURE OF INTERGRANULAR AMORPHOUS FILMS IN CERAMICS

* MOLECULAR-DYNAMICS METHOD FOR THE SIMULATION OF GRAIN-BOUNDARY MIGRATION

* RELATIONSHIP BETWEEN GRAIN-BOUNDARY DIFFUSION AND MIGRATION BY MOLECULAR-DYNAMICS SIMULATION
 

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Electronic-structure and atomic-level simulations of interfaces in silicon and diamond

We have performed extensive molecular dynamics simulations of interfaces in nanocrystalline diamond and silicon using both a tight-binding approach and three-body interatomic potentials. This has enabled us to expose the intricate coupling between structural disorder and electronic behavior of these important electronic materials.

Key references

* On the Nature of Grain Boundaries in Nanocrystalline Diamond,  P. Keblinski, D. Wolf, F. Cleri, S. R. Phillpot and H. Gleiter, MRS Bulletin Vol. 23, No. 9 (Sep. 1998), pp. 36-41.

* Thermodynamically Stable Amorphous Intergranular Films in Nanocrystalline Silicon, P. Keblinski, S. R. Phillpot, D. Wolf and H. Gleiter, Phys. Lett. A 226, 205-211 (1997).

* Role of Bonding and Coordination in the Atomic Structure of Grain Boundaries of Diamond and Silicon, P. Keblinski, D. Wolf, S. R. Phillpot and H. Gleiter, J. Mat. Res. 13, 2077-99 (1998).

* Correlation between Atomic Structure and Localized Gap States in Silicon Grain Boundaries, F. Cleri, P. Keblinski, L. Colombo, S. R. Phillpot and D. Wolf, Phys. Rev. B 57, 6247-50 (1998).

* Atomic and Electronic Structure of a High-energy Grain Boundary in Diamond, F. Cleri, P. Keblinski, L. Colombo, D. Wolf and S. R. Phillpot, Europhysics Letters 46, 671-5 (1999).

* Relationship Between Nanocrystalline and Amorphous Silicon by Molecular-Dynamics Simulation, P. Keblinski, S. R. Phillpot, D. Wolf and H. Gleiter, Nanostructured Materials 9, 651-660 (1997).

Highlights

* COMPUTER SIMULATION OF THE STRUCTURE, ELECTRICAL AND MECHANICAL PROPERTIES OF NANOCRYSTALLINE DIAMOND FILMS
 

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Free surfaces

The recognition that a common conceptual, and hence physical framework exists for internal interfaces and free surfaces represents a unique feature of our program. For example, interfacial fracture may be viewed as a conversion of (strongly interacting) interfacial dislocations into (weakly interacting) surface steps. This has enabled comparisons, both conceptual and computational, between the physics of these distinct ? but closely related - types of planar defects. This common conceptual framework now enables the distinction between strongly coupled bulk nanostructures (e.g., nanocrystalline materials) and the weakly coupled nanostructures consisting of free, interacting nanoparticles.

Key references

* Atomic-Level Geometry of Solid Interfaces, D. Wolf, Introductory Chapter in Materials Interfaces: Atomic-Level Structure and Properties, D. Wolf and S. Yip, eds., Chapman and Hall, London, 1992, pp. 1-57.

* Role of Interface Dislocations and Surface Steps in the Work of Adhesion, D. Wolf and J. A. Jaszczak, a chapter in Materials Interfaces: Atomic-Level Structure and Properties, D. Wolf and S. Yip, eds., Chapman and Hall, London, 1992, pp. 662-690.

* Correlation Between the Energy, Surface Tension and Structure of Free Surfaces in fcc Metals, D. Wolf, Surf. Science 226, 389-406 (1990).

* On the Interaction Between Steps in Vicinal FCC Surfaces, D. Wolf and J. A. Jaszczak, Surf. Sci. 277, 301-322 (1992).

* Should all Surfaces be Reconstructed?  D. Wolf, Phys. Rev. Letters 70, 627-630 (1993).

Highlights
 

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Theory and simulation of ionic systems

Based on fundamental insights into the nature of the conditional convergence in the classic Madelung problem we have developed a novel, highly efficient simulation approach for the evaluation of the Coulomb energy, forces and stresses in molecular-dynamics simulation. The approach involves direct 1/r summation over the Coulomb pair potential with spherical cutoff. These novel insights into the nature of long-ranged interactions have enabled us to predict entirely unanticipated surface reconstructions in ionic materials, such as the ground-state structure of polar surfaces; several of these predicted reconstructions have since been observed experimentally. Our novel simulation approach has also enabled us to elucidate the nature of screening in ionic fluids all the way from the dilute, Debye-Hueckel limit to the high-concentration regime and even the ionic melt. Our approach is presently being extended to include the conditionally convergent interactions between monopoles and dipoles, and between point dipoles. Combined these developments provide a comprehensive, highly efficient and physically transparent computational approached, for example, for the simulation of ionic solutions, chemical self assembly and biological systems.

Key references

* Reconstruction of NaCl Surfaces from a Dipolar Solution to the Madelung Problem, D. Wolf, Phys. Rev. Letters 68, 3315-3318 (1992).

* Structure of Ionic Interfaces from an Absolutely Convergent Solution of the Madelung Problem, D. Wolf, Solid. St. Ionics 75, 3-11 (1995).

* Method for Growth of Polycrystalline Ionic Thin Films by Large-Scale Molecular Dynamics Simulations, S. R. Phillpot, D. Wolf, P. Keblinski and F. Cleri, Interface Science 7, 15 (1999).

* Exact Method for the Simulation of Coulombic Systems by Spherically Truncated, Pairwise 1/r Summation, D. Wolf, P. Keblinski, S. R. Phillpot and J. Eggebrecht, J. Chem. Phys. 110, 8254-82 (1999).

* Molecular Dynamics Study of Screening in Ionic Fluids, P. Keblinski, J. Eggebrecht, D. Wolf and S. R. Phillpot, J. Chem. Phys. 113, 282-291 (2000).

* Mechanism of the Cubic-to-Tetragonal Phase Transition in Zirconia and Yttria-Stabilized Zirconia by Molecular-Dynamics Simulation, P. Schelling, S. R. Phillpot and D. Wolf, Journal of American Ceramic Society, 84, 1609 (2001).

Highlights
 

* EXACT METHOD FOR THE SIMULATION OF COULOMBIC SYSTEMS BY SPHERICALLY TRUNCATED, PAIRWISE 1/r SUMMATION
 

* ON THE NATURE OF SCREENING IN IONIC SYSTEMS

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Melting and solid-state amorphization: theory and simulation

For over a decade now, we have pursued the fundamental question as to why and how crystals melt (in collaboration with S. Yip). Most importantly, we were able to demonstrate that every crystal can, in principle, melt by two distinct causes and, hence, mechanisms (based on the free energy and Bornís instability criterion, respectively). These novel insights obtained by molecular dynamics simulation have lead us to formulate a theoretical framework for solid-state amorphization and to an understanding of phase stability in systems experiencing internal or external strains. Application of these concepts now promises to shed light on issues of size effects and phase stability in nanoscale materials and phenomena.

Key references

* Molecular Dynamics Study of Lattice-Defect Nucleated Melting in Metals Using an Embedded Atom Potential, J. F. Lutsko, D. Wolf, S. R. Phillpot and S. Yip, Phys. Rev. B40, 2841-2855 (1989).

* How do Crystal Melt? , S. R. Phillpot, S. Yip and D. Wolf, invited contribution to Computers in Physics, Vol. 3, pp. 20-31 (1989).

* Thermodynamic Parallels Between Solid-State Amorphization and Melting, D. Wolf, P. R. Okamoto, S. Yip, J. F. Lutsko and M. Kluge, J. Mat. Res. 5, 286-301 (1990).

* Effects of Atomic-Level Disorder at Solid Interfaces, S. R. Phillpot, D. Wolf and S. Yip, MRS Bulletin XV No. 10, 38-45 (1990).

* Role of Interfaces in Melting and Solid-State Amorphization, S. R. Phillpot, S. Yip, P. R. Okamoto and D. Wolf, a chapter in Materials Interfaces: Atomic-Level Structure and Properties, D. Wolf and S. Yip, eds., Chapman and Hall, London, 1992, pp. 228-254.

* Crystal Instabilities at Finite Strain, J. Wang, S. Yip, S. R. Phillpot and D. Wolf, Phys. Rev. Letters 71, 4182-4185 (1993).

* Unifying two criteria of Born, Elastic instability and melting of homogeneous crystals, J. Wang, S. Yip, S. R. Phillpot and D. Wolf, Physica A 240, 396-403 (1997).

* Continuous Thermodynamic-Equilibrium Glass Transition in High-Energy Grain Boundaries? P. Keblinski, D. Wolf, S. R. Phillpot and H. Gleiter, Phil. Mag. Lett. 76, 143-151 (1997).

Highlights
 
 

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Mechanical properties of multilayers, thin films and grain boundaries

For well over a decade now we have performed extensive simulations on the thermo-elastic behavior of thin films, multilayers and grain boundaries and on grain-boundary fracture. This has enabled us to elucidate the interrelation between structural disorder (in grain boundaries, free surfaces or induced by elastic strain) and the thermoelastic behavior of interfacial materials. This work represents the foundation for a promising approach to understanding the thermo-elastic and fracture behavior of nanostructures.

Key references

* Structurally-Induced Supermodulus Effect in Superlattices, D. Wolf and J. F. Lutsko, Phys. Rev. Letters 60, 1170-1173 (1988).

* Computer Simulation of Elastic and Structural Properties of Thin Films. 1. (001) Orientation in fcc Metals , D. Wolf, Surf. Science 225, 117-129 (1990).

* Supermodulus Effect in Metallic Superlattices of Grain Boundaries , D. Wolf, Mat. Sci. Eng. A 126, 1-12 (1990).

* On the Role of Atomic-Level Disorder in the Supermodulus Effect, S. R. Phillpot and D. Wolf, Scripta Metall. Mater. 24, 1109-1115 (1990).

* Role of Coherency in the Elastic Behavior of Composition-Modulated Superlattices, J. A. Jaszczak, S. R. Phillpot and D. Wolf, J. Appl. Phys. 68, 4573-4580 (1990).

* Surface-Stress-Induced Structure and Elastic Behavior of Thin Films, Appl. Phys. Lett. 58, 2081-2083 (1991).

* Thermoelastic Behavior of Structurally Disordered Interface Materials: Homogeneous versus Inhomogeneous Effects, J. A. Jaszczak and D. Wolf, Phys. Rev. B 46, 2473-2480 (1992).

* Tailored Elastic Behavior of Multilayers by Controlled Interface Structure, D. Wolf and  J. A. Jaszczak, invited review in J. of Computer-Aided Materials Design 1, 111-148 (1993).

* Atomistic Simulation of Dislocation Nucleation and Motion from a Crack Tip, F. Cleri, D. Wolf, S. Yip and S. R. Phillpot, Acta Materialia 45, 4993-5003 (1997).

* Atomistic Simulations of Materials Fracture and the Link Between Atomic and Continuum Length Scales, F. Cleri, S. R. Phillpot, D. Wolf and S. Yip, J. Am. Cer. Soc. 81, 501-516 (1997).

Highlights
 
 

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