High Temperature Superconductors and Beyond: Open Issues in the Physics of Metals
Department of Physics and Astronomy
The Johns Hopkins University
One of the fundamental questions in solid state physics concerns the behavior of metals when the independent particle approximation breaks down and interactions, of electrons with each other and with the lattice, become qualitatively important. Advances in experimental technique and in materials science have exposed a host of sharply posed problems centering on this issue, while advances in theoretical concepts and methods have given us hope that we can make progress solving them. In this talk examples drawn from the behavior of high temperature superconductors and related compounds will be used to illustrate some recent successes and some fundamental open problems in the physics of metals. Issues discussed will include predictions of the symmetry of the superconducting state, the 'pseudogap' and the effect of intermediate length-scale fluctuations on physical properties, and the meaning of particles in a strongly interacting system.
Department of Physics
University of California at Irvine
The common structural feature of high temperature "cuprate" superconductors is the presence of two dimensional planes of copper and oxygen atoms. The 2D nature of the planes is clearly crucial to the unique properties of the cuprates. Cuprate ladder materials are cousins of the planar cuprates, in which, instead of CuO2 planes, the active units are long, narrow 2D strips. In the most common ladder materials, these strips are only two copper atoms wide, with interactions between nearest neighbor coppers giving rise to the term ``ladder''.
Striped phases, in contrast to ladders, do not involve any rearrangement of the atomic structure--stripes are arrangements of the electrons within an unmodified plane. In the absence of doping, the spins of the electrons within a CuO2 plane form an antiferromagnet. In a striped phase, the doped holes self-organize into hole-rich lines separating hole-poor antiferromagnetic domains. A number of experimental studies have now provided evidence for striped phases in the cuprate superconductors, although the evidence is not conclusive. A key question, which has not yet been answered, is: Do stripes suppress, enhance, or even induce high temperature superconductivity?
We have been investigating the properties of CuO2 planes and ladders using numerical simulations. We use the density matrix renormalization group[1] (DMRG), which allows more accurate and detailed studies at low temperature than previous numerical techniques. Our results have shown a number of similarities and connections between ladders, planes and stripes. First, our studies of the 2D t-J model indicate that striped ground states are present in planes over a broad range of dopings[2]. These stripes have spacings and linear hole densities which are in good agreement with neutron scattering experiments. The stripes often are two lattice spacings wide and appear to resemble doped two-leg ladders. In two leg ladders, holes are bound together in pairs, with a d-wave-like pairing symmetry similar to the high temperature superconductors. We believe the that the pairs found in the ladders are quite similar to those found in planes.
Our studies of wider ladders, with three to six legs, show stripes occur in these systems as well. For each width, the types of stripes which occur is different. For example, in the three leg ladder, short three-hole transverse stripe-like objects are observed for dopings above a critical doping. Similar four-hole transverse stripes are observed in four leg ladders. These stripes fluctuate strongly, although their predominant orientation appears to be diagonal. In these systems, enhanced d-wave superconducting pairing correlations acompany the occurence of stripes. However, in some other ladder systems pairing correlations seem to be suppressed by stripes. For example, in a six-leg system with cylindrical boundary conditions, the stripes have four holes and wrap around the cylinder. These stripes do not fluctuate so strongly and have minimal pairing.
Clearly more work is needed to unravel the mysteries of these subtle and complicated systems, but now at least some parts of the answer seem to be emerging. Some of our numerical results are displayed at http://hedrock.ps.uci.edu.
Fractional Charge in the Quantum Hall Effect
Institute for Theoretical Physics
University of California at Santa Barbara
At the foundation of the modern quantum theory of metals is Fermi liquid theory, in which the electrons effectively move through the material interacting only with the periodic potential of the ions, and not with one another. The strong Coulomb repulsion between electrons is subsumed into an effective electron mass, which accounts remarkably well for the behavior of simple metals and semiconductors. But in many exotic new material systems, ranging from carbon nanotubes to small semiconductor quantum wires and dots, the motion of electrons is severely restricted by spatial confinement. In such low dimensional systems Coulomb interactions are expected to have a profound effect potentially leading to exotic new states in which the electron is effectively ``splintered" into pieces. The new quasiparticles can carry fractional electric charge and in some cases are predicted to carry spin but no charge at all.
The quantum Hall effect provides a paradigm for such charge ``fractionalization". In his 1982 theory of the fractional quantum Hall effect Robert Laughlin proposed that objects with charge e/3 could exist in tiny semiconductor devices under appropriate conditions of strong magnetic fields and low temperatures. In this talk I will give an overview of charge fractionalization in the quantum Hall effect, focussing on a number of very recent experiments [1] which provide both indirect and direct evidence for fractional charge. Implications for other exotic material systems which might exhibit an analogous ``splintering'' of the electron (including carbon nanotubes and perhaps high temperature supercondutors) will be briefly discussed.
From the Electronic Structure of Solids to the Macroscopic Behavior of Materials
Department of Physics and Division of Engineering and Applied Sciences
Harvard University
Many aspects of the macroscopic behavior of materials are familiar to everyone from common experience, like brittle breaking (the shattering of a ceramic cup), the ductile response of metal wires and plates, corrosion and catalysis at different environments, plastic deformation under external pressure. While there is no doubt that such phenomena are ultimately related to the microscopic structure, that is the manner in which atoms are arranged and bonded together to form a solid, making the connection from the microscopic scale to the macroscopic behavior of real materials is very challenging. There is a wide gap between the length and time scales over which microscopic processes occur (of order nanometers and picoseconds), and the length and time scales over which macroscopic phenomena are observed (of order microns to meters, and seconds to hours). Recently, concerted efforts from experts in different subfields of materials science and condensed matter physics are attempting to bridge this gap, by developing both the conceptual tools as well as the computational methods for linking investigations of the microscopic features of a system to its macroscopic behavior.
In this talk, I will present examples of recent projects in which our group has been involved, in collaboration with other researchers, to investigate phenomena like brittle or ductile response, catalytic reactions at surfaces, plastic deformation under external loading, the fracture of a ceramic material, and the growth of a high quality semiconductor crystal. In all these cases, we attempt to provide a comprehensive picture, starting with the microscopic structure and exploring the atomic interactions at this level using quantum mechanical calculations where feasible. A well established methodology for performing such calculations exists, which allows accurate determination of the total energy, and gives insight to the electronic properties of systems containing up to a couple hundred atoms. This provides only the first glimpse into the behavior of the solid, which then has to be linked to macroscopic scales. To achieve this next step, we rely on phenomenological models based on continuum elasticity theory, stochastic simulations, or elaborate constitutive models which explicitly link the different scale regimes. Much of this latter methodology is still under development, and holds great promise for turning into a reality the dream of materials scientists to predict the macroscopic properties of materials directly from their microscopic structure.
References:
Large Scale Quantum-Mechanical Molecular Dynamics Simulations and Local Analysis of Systems with Low Symmetry: Initial Stage of Growth on Silicon
Department of Physics
University of Louisville
Research emphasis of our group is on the study of the structural, electronic, and dynamical properties of complex systems with low symmetry. Our treatment of these problems is based on a systematic approach to materials modeling which allows large scale simulations of systems as well as the analysis of these properties at the local microscopic level. For these purposes, we have developed an order-N (O(N)) non-orthogonal tight-binding (NOTB) molecular dynamics (MD) scheme [1] as well as a method of local analysis [2]. The O(N) scheme overcomes the bottleneck present in the conventional total energy and atomic force calculations by reducing the scaling of computational effort from N**3 to N. A NOTB Hamiltonian incorporates a quantum-mechanical description of electrons and it is best suited for situations with arbitrary coordination encountered in MD simulations. Hence, the O(N)/ NOTB-MD scheme provides an excellent means to study systems of realistic sizes which are currently outside the scope of first-principles MD simulations. Furthermore, using innovative local measures and the method of real space Green's function in conjunction with the O(N)/NOTB-MD scheme, we have now in place a powerful tool to analyze the vast amount of information obtained from a MD simulation. The twin theme of performing large scale simulations and predicting properties accurately at the microscopic level is one of the unique capabilities of our group.
In this talk, I will present some preliminary results of one of our on-going projects, namely, the study of initial stage of growth of Si/Si(100) using the combined approach of O(N)/NOTB-MD and the local analysis. Recent STM studies of Si/Si(100) and Ge/Si(100) exhibit chain structures consisting of two-atom units which were suggested to play a key role in the initial stage of epitaxial growth[3]. These paired adatom units were found to behave distinctly different from other ad-dimers. We have investigated the structure, energetics, and local electronic properties of Si/Si(100) using the O(N) molecular dynamics scheme based on a NOTB Hamiltonian which includes electron correlation via the Hubbard term. Our study reveals the nature of the metastable paired-adatom units and it also provides kinetic pathways for the formation of chain structures near the room temperature.
Modeling Mechanical Properties at the Mesoscale: Case Study of Ni3Al
Department of Materials Science and Mineral Engineering
University of California at Berkeley
The ability to connect directly atomic scale structural features and macroscopic mechanical properties holds great technological promise. This promise remains largely unfulfilled, due to the difficulties inherent in constructing theories which span many orders of magnitude in spatial and temporal scales. Current ab initio techniques are capable of predicting atomic scale structural features and dynamics for systems containing a few hundred atoms (i.e. lengths of approximately 30 Angstroms) , and time scales characterized reasonably in nanoseconds. In contrast, mechanical response most often persists for times best measured in seconds, and lengths best measured in cm. However, recent advances in computational power and algorithms, and the fundamental science of driven, dissipative systems presents an opportunity to establish a meaningful connection between the disparate scales.
This talk will describe one of the many possible approaches to spanning the length and time scales focusing on Ni3Al as a prototypical system. Ni3Al is the major component of a superalloy designed for high temperature structural applications. (The superalloy is commonly employed in the construction of turbine blades.) An unusual and important characteristic of this material is that its yield strength (i.e. the stress required to initiate plastic deformation) INCREASES with increasing temperature. This yield strength increase has been linked to the core structure of the dislocations mediating plastic deformation, and is well understood.
However, the yield strength is not the only relevant material characteristic. To model truly plastic deformation, one has to understand the origins and dynamics that result in hardening: A deformed material is more difficult to deform than an annealed material. Hardening most often has its roots in dislocation-dislocation interactions, either through their long-ranged elastic interaction, or through short-ranged "contact" forces. These interactions often lead to the formation of dislocation walls and boundaries. In Ni3Al, however, one does not observe such structures, and there is reason to believe that the hardening observed in this materials stems from the dynamic properties of a single dislocation.
Given this observation, it is reasonable to consider the dynamics of a single dislocation. Towards this end, simulations of dislocation dynamics have been developed and studied [1,2]. These simulations suggest that the dislocations display a pinning/depinning transition, and that the dynamics characterizing this transition are amenable to a scaling analysis [3,4]. The scaling analysis reveals directly the parameters governing the dislocation dynamics, and thus serve to focus further research efforts, for both experiment and theory.
[1] M. J. Mills and D. C. Chrzan, Acta metall. mater. 40, 3051 (1992).
[2] D. C. Chrzan and M. J. Mills in Dislocations in Solids, vol. 10, edited
by F. R. N. Nabarro and M. S. Duesbery (Elsevier, Amsterdam, 1996) p. 187.
[3] D. C. Chrzan and M. J. Mills, Physical Review B 50, 30 (1994).
[4] D. C. Chrzan and M. S. Daw, Physical Review B 55, 798 (1997).
Pearling and Pinching; Twisting and Writhing
Department of Physics
University of Arizona
One of the central topics in the study of nonequilibrium systems is the means by which coherent patterns develop from structureless continua. In this context, we have identified four broad issues that frame current research: The Laws of Motion of Fields and Surfaces, The Role of Geometric and Topological Constraints, The Structure of Variational Principles, and The Origins of Pattern Selection. Using these as unifying themes, I will describe experimental and theoretical progress in two areas that connect soft condensed matter physics and biology. These involve the interplay between elasticity and fluid mechanics - the study of "elastohydrodynamics."
In 1994, Bar-Ziv and Moses discovered the "pearling instability" in cylindrical fluid membranes [1]. This is a peristaltic shape deformation induced by illumination of the membrane with a tightly-focused laser, an optical trap. Theoretical explanations for this behavior invoke a tension created in the membrane by the laser tweezers. In this sense, the instability resembles the Rayleigh capillary instability of a cylindrical interface between two immiscible fluids, one of the most fundamental in fluid dynamics. As Plateau observed from energetic considerations and Rayleigh clarified through hydrodynamics, such an interface is linearly unstable to fission due to surface tension. In the pearling phenomenon however, breakup is prevented by the membrane bending elasticity. A more striking difference is that the pearling instability propagates---the modulated state is observed to invade the uniform cylindrical region at a constant velocity. This propagation is totally unlike traditional descriptions of the Rayleigh instability, in which perturbations grow uniformly along the length of the tube.
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Figure 1. Stages of the pearling instability of a cylindrical lipid bilayer vesicle, with time increasing downward. Arrows mark progression of front between pearled and unpearled states that moves out from optical trap (trap appears as bright spot of light reflected from microscope slide). Image courtesy of R. Bar-Ziv and E. Moses [1]. |
An understanding of such propagating instabilities requires a synthesis of elasticity theory, fluid mechanics, and the nonlinear dynamics of pattern selection [2]. In this half of my talk I will describe the essential features of this work and how it has led us to consider anew the familiar breakup of a column of fluid via the Rayleigh instability and how it too may proceed as a "propagating topological transition." Computational issues that arise in the study of model nonlinear partial differential equations for membrane dynamics will be discussed briefly, along with our experimental work on the relationship between fluid jets and elastic filaments.
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Figure 2. Numerical study of a propagating topological transition - the breakup of a fluid tether immersed in a second fluid. From Ref. [3]. |
In 1976 Mendelson discovered [4] that a mutant strain of the bacterium Bacillus subtilis possesses a remarkable property; the normal process of cell separation following cell division is lacking, so daughter cells remain attached to each other. Generation after generation of cell division continues to occur, producing a bacterial filament that can be thousands of cells long. By itself this is a fascinating phenomenon, but it is made even more compelling by the fact that these fibers buckle and twist up after reaching a critical length.
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Figure 3. Supercoiled filament of B. subtilis [4]. Scale bar is 10 microns. Image courtesy of N.H. Mendelson. |
Subsequent growth leads the plectoneme itself to supercoil forming a super-plectoneme, and the process continues generation after generation. The result is a macroscopic, highly-ordered supercoiled structure -- a beautiful example of self-organization driven completely by forces generated internal to the filaments. Mendelson and others have proposed that these shape instabilities are due to twisting stresses generated in the cell walls through the process of division without cell separation. The properties of the supercoiling (e.g. handedness) are sensitively dependent on certain solution properties (pH, divalent ion concentration, etc.), and can be varied through the action of enzymes, such as lysozyme, that cleave components of the peptidoglycans in the cell walls. Motivated by these experimental observations, and with the goal of understanding the microscopic origins of this phenomenon, I will describe in the second half of my talk our work on develop theoretical methods to understand the dynamics of elastic filaments in a viscous medium. A completely intrinsic formulation of the coupled evolution of filament curvature and twist density has been developed [5] using techniques from the differential geometry of curve motion first utilized in the study of integrable Hamiltonian systems. This formulation makes clear dynamical aspects of twist-bend coupling, and has important implications as well for computational studies of the strongly nonlinear regime. A novel, fundamentally nonlinear process known as "geometric untwisting" has been described that may relate to experimental observations in the bacterial system, and some intriguing aspects of self-propulsion in the inertialess world of low Reynolds number flows have also been elucidated [6]. I will also briefly mention our optical trapping studies of supercoiling forces and dynamics in this system.
Biophysics of Chromosome Disentanglement
Departments of Physics and Bioengineering
University of Illinois at Chicago
Cells must control the entanglement - the topology - of their long DNA molecules in order to manipulate them. This is particularly important during cell division when one copy of each chromosome must be segregated to the two new cells. The question of how small (< 10 nm diameter) topology-changing enzymes (topoisomerases) sense global topological properties of long (106 to 109 base pairs) flexible chromosomes is a challenging biophysics problem.
In bacteria, it is known that a specific enzyme (topo IV) effectively removes entanglements between small circular DNAs. Topo IV's effectiveness in the test tube and in the cell is stimulated by supercoiling [1] (interwinding driven by internal twisting, similar to the behavior of a twisted telephone cord). This can be understood as a consequence of the coupling between supercoiling and entanglement; supercoiling `crowds' entanglements together and greatly increases their free energy cost. Simple models for supercoiling and entanglement, including their coupling, will be described [2] along with experimental data indicating that supercoiling is required for efficient chromosome segregation in vivo.
In eukaryote cells, there is not supercoiling-driven crowding, but a conceptually similar scheme can be based on the `tethered loop' structure observed in electron micrographs of chromosomes from dividing cells. Given the experimental observation that the chromosome fiber in cytoplasm behaves roughly like a flexible polymer in good solvent, the packing together of chromosome `loops' will cost appreciable free energy, and should lead to an appreciable free energy cost for entanglements of different chromosomes [3]. Therefore, chromosome condensation during eukaryote cell division may be seen as a way to drive resolution of chromosomes [4], i.e. to progressively anneal away inter-chromosome entanglements. Two recent discoveries which are in accord with this picture will be described: chromosome-condensing `condensin' protein complexes [5], and hysteretic elasticity of condensed chromosomes.
[1] E. L. Zechiedrich, A. B. Khodursky and N. R. Cozzarelli, Topoisomerase
IV, not gyrase, decatenates products of site-specific recombination in
E. coli, Genes & Development 11, 2580-2592 (1997); C. Ullsperger and
N. R. Cozzarelli, Contrasting enzymatic activities of topoisomerase IV
and DNA gyrase from E. coil, J. Biol. Chem. 49, 31549-31555 (1997)
[2] J.F. Marko, Coupling of intra- and intermolecular linkage complexity
of two DNAs, preprint (1998)
[3] J. F. Marko and E. D. Siggia, Polymer models of meiotic and mitotic
chromosomes, Mol. Biol. Cell 8, 2217-2231 (1997)
[4] T. Hirano, Biochemical and genetic dissection of mitotic chromosome
condensation, Trends Biochem. Sci. 20, 357-361 (1995)
[5] T. Hirano SMC protein complexes and higher-order chromosome dynamics,
Curr. Opin. Cell. Biol. 10, 317-322 (1998)
Friction from Atomic to Tectonic Scales
Department of Physics
University of California at Santa Barbara
One of the most fundamental questions in seismology is what controls the dynamic rupture of earthquakes. If we knew the answer, we could explain why some earthquakes are small (millimeters of slip over an area of one square kilometer) and others are huge (meters of slip over an area of 20,000 square kilometers). This question is equivalent to asking, "Why do earthquakes-- the dynamic shear fracture that dislocates the earth-- start then stop?" A second issue of fundamental importance is that of estimating regional hazards. In addition to the question of when and where an earthquake is likely to occur, it is of interest to estimate the probable damage. Progress in this area is linked to developing a better understanding of patterns and correlations in complex, interconnected systems as well as the dynamical properties of disordered materials under shear. However, it is not possible to directly answer these questions using seismological observations alone. Even state of the art results rely on assumptions and uncertainties in order to deduce properties of the seismic source. To estimate the slip history at the fault during rupture, assumptions are made about the initial state of the fault, the frictional properties, the dynamics of slip, and the rheological properties of the rocks and soil through which seismic waves propagate. Numerical models play an important role in developing a firmer foundation for understanding the physical processes which underly seismic phenomena because they enable us to investigate the impact of different physical assumptions on seismic observables. In 1989 Jim Langer and I pointed out that the well-known Burridge--Knopoff model of a fault, without external noise or built in heterogeneity, is a deterministically chaotic system that generates a remarkably realistic statistical distribution of seismic events. Currently I am working with Olsen and Nielsen from the Institute for Crustal Studies at UCSB to develop a fully three-dimensional dynamic rupture model of earthquakes where the evolution of the rupture is determined from the initial stress conditions and a constitutive law for friction which is based in part on the laboratory experiments of Israelachvili and colleagues. It is our goal to integrate the innovative new ideas which are currently emerging in experimental and theoretical studies of friction, fracture, and deformation into state of the art seismological studies. Indeed, there is potential for widespread progress in understanding the processes which are central to the physics of earthquakes by studying analog processes in simpler, more controlled environments, and incorporating the results into simulations of seismic phenomena. Of course, the laboratory systems are much simpler than those which are of immediate relevance geologically. Nontheless, by studying seismic applications in parallel with theoretical, numerical, and experimental investigations of well characterized systems we can begin to determine how basic materials properties impact phenomena on larger scales. Indeed, many of the processes which are fundamental to the physics of earthquakes, have risen to the forefront in physics, engineering, and material science in recent years, due to the development of new experimental techniques, advances in computing, and the introduction of fundamentally new ideas. This has led to rapid growth in understanding driven, disordered systems far from equilibrium. Suggested References Include:
Atomic Effects in Brittle Fracture
Center for Nonlinear Dynamics and Department of Physics
University of Texas at Austin
One of the aims of condensed matter physics is to use knowledge of how matter is constructed at the atomic scale in order to make predictions for how it will behave at the macroscopic scale. This task becomes particularly difficult when one tries to predict mechanical properties of materials, since mechanical response is so often governed by rare and complex defects.
The fracture of brittle objects provides an example. Brittle objects shatter because of cracks, which are macroscopically long, but microscopically sharp. Knowing whether an object will be brittle or ductile depends upon knowing whether a sharp crack can propagate, something that is quite difficult to predict from first principles.
My research group has been focusing upon the brittle fracture of crystalline silicon, in the hopes of using it as a test case where brittle fracture can be understood in quantitative detail. We have been carrying out dynamic fracture experiments in crystalline silicon, have developed an analytical theory for the fracture of crystals, and have supplemented the theory with molecular dynamics calculations.
We have made a great deal of progress towards the goal of comparing theory and experiment, but still are confronted with several sources of uncertainty. Using scaling ideas that arise in analytical solutions, we have learned how to perform molecular dynamics simulations that can be compared directly with the laboratory experiments, although the experiments last for tens of microseconds in samples on the scale of centimeters. However, any molecular dynamics simulation is only as good as the force laws employed between atoms. We have recently found to our dismay that changing a single parameter in the heart of three-body force laws can completely change the character of dynamic fracture, while leaving most equilibrium properties of a crystal unchanged.
Therefore, we have powerful tools with which to address the relation between microscopic and macroscopic mechanical behavior, but the process of understanding these relations is only beginning. Brittle fracture is in many ways the simplest way that an object can respond to large mechanical stresses; much more difficult problems lie ahead, where many different sets of length scales are active simultaneously. More information concerning our work on fracture can be obtained at http://chaos.ph.utexas.edu/~marder/fracture/frac.html
Two relevant references are:
[1] D. Holland and M. Marder, "Ideal brittle fracture of silicon studied with molecular dynamics," Physical Review Letters, vol 80, pp. 746-9 (1988).
[2] M. Marder and S. Gross, "Origin of crack tip instabilities,
Journal of Mechanics and Physics of Solids," vol 43, pp. 1-48 (1995).
Where Does Friction Come From?
Department of Physics and Astronomy
The Johns Hopkins University
Hardly anything is more important in designing mechanical systems than friction. Not surprisingly, the study of friction and use of lubricants dates back as far as recorded history. The "laws" for static and dynamic friction we teach today date from empirical relationships observed by da Vinci and Amontons centuries ago. However, the origin of these laws has remained a mystery.
New experimental techniques and computer simulations allow us to measure and visualize the molecular interactions and motions that give rise to friction. They also reveal some counterintuitive behavior at the molecular scale. For example, solids may slide over each other with less friction than fluids[1], and fluid films may behave like solids[2]. These studies are beginning to answer the question of where friction comes from.
The talk will begin by reviewing macroscopic models of friction and then summarize results from our molecular dynamics simulations of both dry and lubricated friction. The most recent results suggest that the friction we observe between everyday objects is dominated by adsorbed surface films.
[1] M. Cieplak, E. D. Smith and Mark O. Robbins, ``Molecular origins
of friction: The force on adsorbed layers,'' Science 265, 1209 (1994)
[2] P. A. Thompson, M. O. Robbins and G. S. Grest, ``Structure and Shear
Response in Nanometer Thick Films,'' Israel Journal of Chemistry 35, 93
(1995). P. A. Thompson, Gary S. Grest and Mark O. Robbins, ``Phase Transitions
and Universal Dynamics in Confined Films,'' Phys. Rev. Lett. 68, 3448 (1992).
Peter A. Thompson and Mark O. Robbins, ``Origin of Stick-Slip Motion in
Boundary Lubrication,'' Science 250, 792 (1990).
Modeling Microstructural Evolution in Materials
Department of Materials Science and Engineering
Pennsylvania State University
Formation and temporal evolution of morphological patterns is a common phenomenon in many fields such as biology, materials science, and geology, governed by non-linear complex dynamics. In materials science, a morphological pattern is referred to as a microstructure which is characterized by the size, shape, and spatial arrangement of phases, grains, orientation variants, ferroelastic/ferroelectric/ferromagnetic domains and/or other structural defects. These structural features usually have an intermediate mesoscopic length scale in the range of nanometers to microns. Microstructure plays a critical role in determining the macroscopic physical properties and mechanical behavior of bulk and thin-film materials.
Microstructures are thermodynamically unstable features that evolve with time. The driving force for the temporal evolution of a microstructure usually consists of the following: the bulk chemical free energy, the total interfacial energy between different phases or between different orientation domains or grains of the same phase, the elastic strain energy generated by the lattice mismatch between different phases or different orientation domains, and the external fields such as applied stress, electrical, temperature and magnetic fields. The phase changes and related microstructural development driven by the decrease of the bulk chemical free energy are usually considered as phase transformations whereas the microstructural evolution driven by the reduction in the total interfacial free energy is called coarsening.
Computer modeling is playing an important role in our fundamental understanding of the mechanisms underlying microstructural evolution. There have been a number of techniques developed in recent years for modeling the formation and dynamic evolution of complex microstructures. The main focus of this presentation will be on one of the approaches, namely, the diffuse-interface phase-field approach [1]. Different from the conventional sharp interface approach, the phase-field approach describes a heterogeneous state consisting of phases and/or domains as a whole by using a set of field variables which are functions of spatial coordinates. The most familiar example of a field variable is the composition or concentration field that characterizes compositional heterogeneities. The temporal evolution of these field variables is then described by time-dependent kinetic field equations. One of the main advantages of the field approach is that any arbitrary microstructure can be easily treated without explicitly tracking the interfaces. In addition, different thermodynamic driving forces for microstructural evolution, and hence different processes such as nucleation, growth, coarsening and field-induced domain switching, can be described within the same physical and mathematical model. Finally, it is straightforward to include long-range diffusion, which takes place, for example, during precipitation of second phase particles and solute segregation at grain boundaries.
In this talk, various examples of application of the phase-field approach to modeling microstructural evolution will be presented, including structural transformations, precipitation reactions, ferroic domain growth, and grain growth, which underlying the processing of many advanced materials. Existing difficulties and new challenges, associated with the phase-field model in particular, and microstructural models in general, will be discussed. The need and potential benefits to employ parallel computing resources in large-scale microstructural modeling will also be briefly discussed.
[1] Chen, L. Q. and Wang, Y. Z., "Continuum Field Approach to Modeling Microstructural Evolution", Journal of Metals 48, 11-18 (1996).
Why Do Like-Charged Rods Attract?
Department of Chemistry and Biochemistry
University of California at Los Angeles
Research in my group focuses on the statistical mechanics of complex fluids, particularly polymers, liquid crystals and foams. In this talk, I will discuss our ongoing research on polyelectrolyte solutions. Polyelectrolytes are long-chain molecules with ionizable groups that can dissociate in solution, leaving ions of one sign bound to the chain and counterions free in solution.
Experiments on a variety of stiff polyelectrolyte chains, including DNA [1] and f-actin [2], show that they can self-assemble in solution into bundles of a well-defined size of densely-packed, approximately parallel chains when multivalent salts are present. In the case of DNA, this phenomenon is known as condensation and has attracted attention because of its implications for DNA packaging. DNA condensation leads to rodlike or toroidal bundles of comparable cross-sectional diameter, about 10-15 chains across. This diameter is roughly independent of the species of multivalent ion or the length or source of DNA. These observations pose many fundamental challenges to our understanding of electrostatic interactions in solutions.
We have focused on two questions: What is the origin of the attraction that draws the strongly-charged DNA chains together, and what controls the size of the bundles? Our theoretical results suggest that the attraction arises from fluctuations in the density of condensed counterions (i.e., oppositely-charged ions near the chains) along the chain axis that become correlated when chains are sufficiently close together. This interaction is reminiscent of the van der Waals attraction except that it originates from thermal fluctuations instead of quantum mechanical ones. While our results for this mechanism are in quantitative agreement with two-rod simulations with no adjustable parameters [3], a careful analysis of many-rod systems [4] shows that this attraction should lead to macroscopic phase separation of the DNA into a dilute phase and a concentrated phase of parallel chains. This appears to contradict the experimental finding of finite bundles. However, we find that kinetics can prevent the system from reaching equilibrium. When a DNA chain approaches a bundle, it encounters a free energy barrier whose height depends on the angle between the chain and the bundle, and increases with bundle thickness. This kinetic mechanism is consistent with known experimental trends and could explain why DNA condenses into bundles of a well-defined thickness.
First-Principles Materials Design: From Metal- Insulator Physics to Building a Better Battery
Department of Materials Science and Engineering
Massachusetts Institute of Technology
In principle, ab-initio computational methods, based solely on the basic laws of Physics, have the potential to predict materials properties without any experimental input. If successful, such methods would be invaluable for materials research and development as new materials could be evaluated "virtually" before they are synthesized. The large impact such an approach could have on materials research and development is often used to justify computational materials science.
A search through the literature and survey of some companies reveals only very few cases where ab-initio modeling has led to the design of a better material. This is because most engineering properties are difficult to relate to a single atomic-level variable. Other talks in this workshop illustrate this difficulty for mechanical properties such as ductility or brittleness.
For some properties, such as thermodynamic quantities, a well-defined coarse-graining algorithm has been developed to go from quantum mechanical energy results to macroscopic material properties. In these cases, where the link between microscpic and macroscopic properties can be established clearly, significant impact can be made on materials development. We illustrate this with an example from our research on Li batteries. The critical component of a rechargeable Li battery is a lithiated transition-metal oxide which can reversibly intercalate Li ions. The potential at which Li can be removed or inserted determines the battery voltage, whereas the amount of Li that can be cycled determines the battery capacity. I show how both properties can be predicted from Density Functional Theory and how this capability can be used to perform virtual experiments on new materials. This research, in collaboration with experimental groups, has led to the suggestion of novel battery materials.
Ab-initio research on complex materials often exposes the limits of current methods. The lithium-metal oxides in battery cathodes can undergo several electronically driven transitions, such as Jahn Teller distortions and metal- insulator transitions. While these physical phenomena have a substantial effect on the performance of the battery material, they pose significant problems for current approximations to Density Functional Theory. Better quantitative theories for correlated electron systems are therefore required.
Two relevant references:
Vulcanized Matter: Seeking Simplicity in Complex Media
Department of Physics
University of Illinois at Urbana-Champaign
As Goodyear discovered, when he first vulcanized rubber in 1839, a viscous liquid of macromolecules becomes solid when a sufficient density of permanent crosslinks is introduced. In common with the familiar simple atomic solids, the equilibrium rigidity of this crosslinked macromolecular solid is a consequence of the spontaneous breakdown of translational symmetry: the macromolecules no longer explore their container, instead becoming localized and fluctuating around preferred positions. In contrast with simple solids, however, the formation of a crystalline macromolecular solid is frustrated by the random locations of the permanent crosslinks and, as a result, rigidity is acquired through the formation of an equilibrium--and yet amorphous--solid state.
In this talk I shall describe certain recent approaches to the physics of vulcanized matter and other random network forming media, focusing on the transition to the amorphous solid state that occurs upon sufficient crosslinking. Despite the complexity of the media, these approaches, which involve the application of field-theoretic techniques to semi-microscopic models, yield surprisingly simple and universal descriptors of the amorphous solid state, at least in the vicinity of the vulcanization transition. Examples of such descriptors include the structure of the state [1-3] (as characterized by the fraction of localized monomers, as well as the statistical distribution of their r.m.s. displacements) and the response of the solid to shear deformations [4]. Extensive computer simulations [5] have recently confirmed aspects of the universality of these descriptors, and the origins of this universality [3,4] have been elucidated via the field-theoretic approach.
If time permits, I shall also mention analogies between vulcanized matter, spin-glass ordering in magnetic systems and folding in protein systems, and I shall explore related ideas concerning the physical properties of structural (i.e. real) glasses.
[1] P. M. Goldbart et al., Adv. Phys. 45 (1996) 393.
[2] M. Huthmann et al., Phys. Rev. E 54 (1996) 3943.
[3] W. Peng et al., Phys. Rev. B 57 (1998) 839.
[4] H. E. Castillo and P. M. Goldbart, Elasticity near the vulcanization
transition, Phys. Rev. E (1998, in press),cond-mat/9712050.
[5] S. J. Barsky and M. Plischke, Phys. Rev. E 53 (1996) 871; unpublished
(1997).
Quantum Computation: Theory, Practice, and Future Prospects
IBM Almaden Research Center
Information is physical, and computation obeys physical laws. Ones and zeros -- elementary classical bits of information -- must be represented in physical media to be stored and processed. Traditionally, these objects are well described by classical equations of motion. But increasingly, as we edge towards the limits of semiconductor technology, we reach a new regime where the laws of quantum physics become dominant. Strange new phenomena, like entanglement and quantum coherence, become available as new resources. How can such resources be utilized for computation? What physical systems allow construction and control of quantum phenomena? How is this relevant to future directions in information technology? These are the questions of quantum computation, which I will broadly overview in my talk.
The theoretical
promise of quantum computation is ultrafast solution of certain problems.
This capability was foreshadowed by Richard Feynman's realization that
a system with N degrees of freedom are fundamentally described differently
whether it is classical or quantum. Under classical mechanics, its dynamics
are described by about N differential equations, while a quantum system
is described by about 4^N differential equations! In 1994, Peter Shor showed
how this insight leads to the capability of solving a certain mathematical
problem -- factoring integers -- exponentially faster with quantum resources.
Other problems, like searching, can also be sped up,
albeit only by a square-root factor.
The experimental reality of quantum computation, however, is a collision
of requirements: quantum systems must be kept extremely well isolated from
their environments, but in order to perform computation, we must be able
to reach in and manipulate the system. Electromagnetically trapped ions
are one promising candidate, in which "quantum bits" are stored
in nuclear spin states, and pulsed laser light is used to control the dynamics.
Molecules controlled using nuclear magnetic resonance techniques, with
electronic bonds providing spin-spin interconnections, and nuclear spins
again representing information, provide another quantum computation system.
Simple quantum algorithms have been demonstrated using this approach.
The future of quantum computation is currently subject to intense scrutiny.
It may well be that these machines will not be practical. More quantum
algorithms must be discovered, and just as importantly, new material systems
must be realized. Observation and control of quantum coherence has been
a long sought goal, and quantum computation brings to this quest a new
motivation and framework for understanding.