This program examines the topological nature and mechanisms of 3D grain growth with the goal of describing how interconnected grains interact to perform the complex sequence of steps that must balance for self-similar grain growth to occur. The different types of topological events have long been known to be necessary for grain growth, and the rates of these different types of events must set the overall growth rate, but the inability to observe them in 3D has hindered the understanding of the mutual feedback that must exist between the grain volume distribution and the topological events to produce the observed steady state. Particular goals of the study are to determine to how the widths of the related grain volume and topological distributions evolve throughout growth, how and to what extent the initial distribution controls the final steady state distribution, and how the instantaneous distributions control the rate of topological events and overall grain growth. The study is founded on the triad of theoretical modeling and comparative computer simulation and experimental grain growth studies. Experimental studies will include direct imaging of the grain structure via three-dimensional x-ray diffraction (3DXRD) and tomography to monitor evolution of the grain volume distribution and topological events. Comparative grain growth experiments using serial section reconstruction and stereological analysis will also be performed for similar materials and conditions as the direct imaging. The 3D simulations will similarly examine the evolution of the grain volume distribution in relation to topological events and evolution. Data mining of the simulation results and reconstructed microstructures will help determine the grain volume and topological configurations leading to the different types of topological events. The results of this in-depth comparative study will provide a first-time view and understanding of the previously unknown means by which steady state grain growth occurs.
NON-TECHNICAL SUMMARY
The goal of this program is to understand the fundamental means by which the crystals, or ?grains?, in a metallic or ceramic material grow at high temperature, such as during industrial heat treatment or in high temperature use. The grain size of these materials is a primary factor controlling properties such as strength, ductility and ability to be formed to shapes, and controlling the amount of growth is a critical concern in materials science and engineering related industries. The overall ?grain growth? process involves a sequence of finite topological steps of growth and shrinkage among neighboring grains. These events cannot be directly observed in opaque materials, and the mechanism of the steady-state process has not previously been understood. This study will provide a first-time coordinated investigation of the grain growth process bringing together novel 3D x-ray diffraction techniques performed with scientists at Riso National Laboratory in Denmark, using the European Synchrotron Radiation Facility (ESRF) in Grenoble, computer simulation expertise at Sandia National Labs in Albuquerque, and experiments, computer simulations and theoretical development at the University of Alabama at Birmingham and the University of Florida. The results of these studies will provide a first-time understanding of this important process. In addition, the graduate students performing the Riso/ESRF experiments will gain experience in international collaboration, performing research and working in residence for several months per year at a major European research center. UAB also has a very strong history of outreach to minorities, including student recruitment.
The following are the project outcomes of our program on the topological nature of grain growth. This program determined the detailed mechanisms by which the crystals that metals are composed of, called "grains", grow and dissolve when they are heated. Topological refers to the number of neighbors or facets the "soap froth" shaped grains have on their surface. The numbers of these faces determine their curvature and are theorized to control their rates of growth and shrinkage. This process is called "grain growth" because although most of the smaller grains disappear by being consumed by the larger ones, the remaining grains grow larger. It is important to understand how this process occurs since the strength of metals is controlled by the sizes of the grains. Intellectual merit: This program determined for the first time that there is a simple linear relationship between the integral mean curvature of the grain faces and the growth and shrinkage rates of those grains. Although this result was by a long-held theory it had never been experimentally investigated and proven because it was not known how to measure this type of curvature on growing grains. This program determined how to measure this on grains in a 3D Monte Carlo grain growth simulation and proved that the theory was correct. This is an important finding in studies of materials and matching experiments with real metals are now being conducted. The program also determined the detailed shapes of grains in terms of the arrangements of these curved faces on the grains that are surrounded by different numbers of edges, as in froth cells. Maps of these face arrangements are called "Schlegel diagrams". There are numerous mathematically possible variations of these faces and knowing how the grains transition from one shape to another as they grow or shrink in size and change their numbers of faces is important in understanding the process. A computer simulation was performed to analyze hundreds of thousands of grain shapes and it was found that the simulation results matched experimental findings that only a very few of the dozens of possible shapes actually exist. This finding points the way to understanding how the grains change faces, curvatures and growth rates as they evolve. The program also used the 3D computer simulation of grain growth to determine the rates of "topological events" that occur, such as grains making and breaking contact with each other, changing the numbers of their faces, and thus their curvatures and growth rates. These rates were found to vary with the initial distribution of grain sizes in the overall grain structure and a computation was developed to explain the evolution of the distribution of faces on grains based on these event rates. The program has determined many pieces of the puzzle of how grain topology controls the process of grain growth and has found how these pieces fit together to produce a more unified explanation of the process in real metals. Broader impacts: The broader impacts of the program were the training of several graduate and undergraduate students in the field of computer simulation of materials at Sandia National Laboratory, Albuquerque. Three students were supported by Sandia to work intensively there for a summer using their supercomputing facilities. This training in one of the foremost centers for this work by a world expert who was a co-investigator on the program was tremendous preparation for their future careers in science and technology.
