Professor Stewart Kurtz

Vitae

Electronic materials such as single-crystal silicon are constructred of highly regular arrays of atoms. By taking advantage of this geometric regularity, a complete description of crystalline solids in terms of 230 unique three-dimensional patterns of atoms is possible. Modern solid-state physics has scored significant successes in using this idealized geometric picture and its related symmetry operations (space groups) to simplify the calculation of such useful physical properties as elastic constants, electrical conductivity, and dielectric constants. However, for important classes of engineering materials such as electronic ceramics, metals, and composites, etc., this high degree of geometric regularity only exists within individual grains, of which there are literally billions per cubic centimeter, all of different shapes and orientations. In such cases, a variety of statistical averaging methods have been developed to obtain upper and lower bounds of important materials properties. Such averaging replaces the rich variety of grain shapes and sizes with spheres, ellipsoids, cubes, etc., usually of a uniform size. Since important failure and degradation mechanisms are closely related to the extremes in shape and size, rather than their averages, the conventional models of ceramics, metals, and composites thereof have had limited success in predicting their reliability in actual applications.

As a step toward overcoming this difficult, Dr. Kurtz and his group have developed a fully three-dimensional computer model of polycrystalline microstructures based on the principle of topological equivalence. Each polyhedra or grain is required to satisfy the Euler topological constants V-E+F = 2 (where V is the number of grain vertices [corners], E is the number of edges, and F is the number of faces) as well as the equation V = 2F-4. This model yields a geometrically correct array of space-filling polyhedra having the full range of shapes, sizes, edges, corners, dihedral angles, etc., observed in real engineering materials. Computer-generated arrays of space-filling polyhedra containing from hundreds to more than 100,000 grains can be used to calculate quite precise values for the physical properties of complex engineering materials rather than simply calculating the bounds. To do this, a complete 3D computer-generated micostructure is captured in a data file and used as a template along with newly developed 3D finite element techniques for random shapes to calculate the mechanical properties of important new engineering materials such as graphite fibers, diamond films, and ferroelectric or superconducting ceramics.

For the first time, Kurtz has analyzed the effects of elastic anisotropy on the three-dimensional distribution of stresses around individual grains of varying shape, size, and grain boundary orientations, as well as calculating the effects of nonspherical pores and inclusions at grain corners. These results are to be applied to developing improved models of materials reliability and failure prediction. In their application to developing improved models of stress corrosion, cracking, and effects of texture in thin-diamond and high-temperature superconductor films, Kurtz believes that such numerically intensive 3D micromechanical modeling of engineering materials will be instrumental in improving materials reliability and failure prediction. Acting together with new measurement methods, such simulations can become powerful new tools for the creation of complex, high-reliability "designer" materials envisaged for the next century.