Materials science is one of the major areas of expertise at NIST, and covers a broad range of both experimental and theoretical activities. Long-term mathematical modeling efforts with applications to problems in materials science have been under way by several division staff members for a number of years. The collaborations are necessarily interdisciplinary in nature, and the areas of knowledge required for effective modeling include theoretical physics, numerical techniques and software development, and analytical and computational methods in solving ordinary and partial differential equations. These activities therefore frequently benefit from the laboratory efforts in computational physics, high-performance computing, visualization, and mathematical software. Staff members cooperate closely with MSEL's Center for Theoretical and Computational Materials Science.
An outstanding problem in solidification theory is to predict the length scales and time scales that occur during crystal growth. These scales are crucial in determining the physical properties of the solidified material. Geoffrey McFadden, in collaboration with Sam Coriell of MSEL and Robert Sekerka of Carnegie Mellon University, have developed a model of solidification including diffusion and buoyancy-driven convection. With this model, they have achieved excellent agreement with experimental studies of dendritic growth of a single-component material from a supercooled melt, including fundamental properties such as velocities and radii of curvature of the dendrite tips.
Soldering is of great practical interest in a wide variety of industries. The understanding of solder joint formation can lead to more cost-effective and safe joining processes. Environmental legislation banning the use of lead in plumbing applications has aroused the interest of many groups in lead-free solder systems. Richard Braun, Geoffrey McFadden, and Bruce Murray, in collaboration with William Boettinger of MSEL, have undertaken fundamental studies of standardized solder tests in order to better understand the complex physical phenomena observed in soldering processes. The development and understanding of such standard tests is one of NIST's fundamental missions.
Composite materials with complicated microstructures, such as ceramics, are important in many industrial applications. Previous analyses and computer simulations of their properties have been based on idealized simplifications of the microstructure. Stephen Langer, in collaboration with Craig Carter, Edwin Fuller, and Andrew Roosen of MSEL, has begun a project to construct a finite-element computer model from a digitized image of a real microstructure. In this project, the structure will be numerically distorted, and the elastic and fracturing behavior will be studied. The simulation takes advantage of state-of-the-art sparse matrix methods, and is being designed with future parallel implementations in mind.