In principle, all materials science problems are easy to solve. One describes the system using quantum mechanical wave functions, solves the Schrödinger equation using the appropriate boundary conditions, and converts the result into the microscopic and/or macroscopic observables of interest. Unfortunately, carrying out this program is usually many orders of magnitude too difficult. As a result, various approximations and simplifications are introduced to obtain descriptions having the minimum complexity to describe a given class of phenomena. (A simple example is the treatment of lattice vibrations in solids using a ball-and-spring description.) Such a simplified description is called a model.

Due to the complexity of virtually all problems concerning materials, it is fair to say that the use of models is ubiquitous in materials science. In many situations, however, models sufficiently complex to describe the phenomena of interest are too difficult to be solved analytically. The computer has played an essential role in obtaining descriptions of material behavior based on such complex models. Traditionally, the amount of computer power available has restricted such models to idealized problems, which are then used as prototypes for the actual problems. Recently, however, the role of modeling has expanded to include treatment of specific and realistic materials problems. Development of these new classes of applications has been driven by the tremendous increase in computer power which has become available to the average researcher. The increase in computer capacity has catalyzed implementation of more realistic descriptions of material response.

Common experience with the thermomechanical properties and behavior of matter is usually at the continuum level, i.e., observations concern such phenomena as elastic and inelastic deformation of solids, flow of fluids, and conduction of heat. Continuum descriptions of these phenomena are expressed in terms of partial differential equations representing the principles of balance of mass, momentum, and energy. Since the basic principles apply to all materials, it is apparent that they alone will not suffice for solving specific problems. The peculiarities of individual materials are expressed in terms of constitutive equations, of which Hooke's law of elasticity and Newton's law of viscosity are examples. For the most part, “continuum modeling” refers to the process of devising constitutive equations. This work requires exercise of physical insight at both the macroscopic and microscopic levels, consideration of experimental observations, and application of formal mathematical principles.

Much of materials science is devoted to development and application of materials that have been selected for, or designed to have, useful properties different from those of existing materials. Many materials are of interest precisely because they have unusual properties. For example, paints and other coatings are often designed to flow easily when spread, but resist running afterward. Much work is devoted to analyzing manufacturing processes, whether they be processing of foodstuffs, forging metals, drawing films and fibers, or curing polymers. Properties and physical states of materials that are important during manufacture are often very different from those desired under service conditions.

Science often advances through the introdction of new ideas which simplify the understanding of complex problems. Materials science is no exception to this rule. Concepts such as nucleation in crystal growth and spinodal decomposition, for example, have played essential roles in the modern understanding of the structure of materials. More recently, fractal geometry has emerged as an essential idea for understanding the kinetic growth of disordered materials. This review will introduce the concept of fractal geometry and demonstrate its application to the understanding of the structure of materials.

Fractal geometry is a natural concept used to describe random or disordered objects ranging from branched polymers to the earth's surface. Disordered materials seldom display translational or rotational symmetry so conventional crystallographic classification is of no value. These materials, however, often display “dilation symmetry,” which means they look geometrically self-similar under transformation of scale such as changing the magnification of a microscope. Surprisingly, most kinetic growth processes produce objects with self-similar fractal properties. It is now becoming clear that the origin of dilation symmetry is found in disorderly kinetic growth processes present in the formation of these materials.

Realistic simulation of the atomic-scale properties of complex systems has long been a goal of scientists interested in the behavior of condensed matter. Until recently, the role of atomistic simulation techniques has been to address rather idealized problems in statistical mechanics. Treatment of more realistic materials has been uncommon not because suitable approaches toward simulating such materials were unknown, but rather because the computer power available was inadequate. Recently, major advances have occurred in the complexity of systems subject to atomistic simulation, primarily due to a dramatic increase in availability of computer power. These new capabilities have driven the development of atomic-scale descriptions of real materials accurate enough for atomistic simulation of a wide range of specific materials science problems.

In this section, we will outline several of the techniques used to simulate the microscopic behavior of an atomistic system. The first method introduced for atomistic simulation was the molecular dynamics technique, in which Newton's equations of motion for the individual atoms are integrated numerically for given interatomic and external forces. One of the first uses of this technique was the study, by Fermi, Pasta, and Ulam, of randomization of vibrational energy in a one-dimensional chain of atoms. Although the results of this initial application were to some extent unsatisfactory, the molecular dynamics technique has since been applied to a wide range of problems in the statistical mechanics of condensed media.

Extended X-Ray Absorption Fine Structure (EXAFS) is a technique capable of probing local structure in condensed- matter systems, determining distances, coordination numbers, and species of atoms near an x-ray excited atom. Further, this information is obtained separately for each constituent atomic species. EXAFS can be applied equally well to crystals, alloys, or even systems having no long-range order such as liquids, gases, and amorphous materials.

Here we review EXAFS spectroscopy and its use in studying semiconductors. First, we show EXAFS in the study of impurities to determine the local environment of Fe implanted in Si. Second, we show how EXAFS can be used to determine local structural distortion in diluted magnetic semiconductors. We next demonstrate that EXAFS can determine the nature of the phase transition in ferroelectric Pb1-x Gex Te, where the transition is revealed to have an order-disorder character in contrast to GeTe where the transition is purely displacive. The theme of these examples is that EXAFS can determine the relative positions of atoms in condensed matter and that the short-range order as determinedn by EXAFS often differs from the long-range order or theoretical expectations.

In the EXAFS technique, one measures the x-ray absorption coefficient as a function of x-ray energy. The absorption spectrum shows a number of x-ray edges corresponding to the threshold of excitation of core electrons from the sample's various atomic species. At energies above each of these edges, oscillations in the absorption coefficient are due to backscattering of the photoelectron from the neighboring atoms.

The 1988 Spring Meeting of the Materials Research Society will be held at Bally's in Reno, Nevada, with events spanning April 4-10. Program Chairs David Clark, Clif Draper, and Chain T. Liu have planned the most diversified topical symposia coverage to date. In addition to a thorough examination of the popular and “hot news” areas, the meeting will also offer a selection of intriguing specialty topics never before offered at an MRS meeting. This year's Spring meeting will feature 16 topical symposia, a program of 23 short courses, and an equipment show. Highlights of the symposia are described below. The names of the short courses and equipment exhibitors are listed elsewhere in this issue. For details see the 1988 MRS Spring Meeting Preliminary Program mailed to all MRS members.

During the Plenary and Student Awards session, Raymond D. Tuminaro of AT&T Bell Laboratories will present the Plenary Address on “Materials Aspects of the SL Undersea Optical Cable Design.” Tuminaro will focus on the fiber and cable materials, review their vulnerabilities to degradation mechanisms, and explore methods currently being used to assure acceptable performance levels for the projected 25-year service life of these systems.

A special feature is being planned for the 1988 MRS Spring Meeting. A major photomicrography exhibition—Microscapes: The Hidden Art of High Technology—will focus on the seldom-seen world of advanced developments in microelectronics and lightwave communications.