The Laboratory’s energy- and defense-related missions require the strongest possible metals, capable of performing as required under extreme conditions. In order to engineer metals that will not fail under stress, our scientists are combining computational and experimental techniques to improve our fundamental understanding of materials and how they deform.

Most metallic materials are polycrystals—large assemblages of single-crystal grains that meet at grain boundaries. These boundaries are essential to material strength, in that they block large-scale plastic deformation by containing material damage within localized regions. We are engineering materials that have stronger boundaries spread throughout the material, breaking up networks of weaker boundaries. This notion of grain-boundary engineering has produced materials with five-fold improvements in resistance to intergranular failure, with minimal added cost.

We discovered that the strong boundaries tend to cluster together far more than first expected, affecting material performance. Using a combination of mathematical theory, computation, and experiment, we are improving our material models by analyzing the mathematical correlations of grain-boundary networks and how they control the roughness scaling of fracture surfaces.

## Relevance to PLS Research Themes

A common type of materials failure in hot, high-pressure, corrosive liquid environments—such as in certain nuclear reactor designs—is caused by intergranular stress-corrosion cracking. Because grain-boundary-engineered materials are much more resistant to intergranular cracking than normal materials, our studies of microstructural correlations are providing the scientific underpinnings that will lead to substantially improved materials for such extreme applications.

We are also interested in the effects of shock loading on materials that are used in defense systems. To gain a better understanding of these fundamentals, we are generating more realistic computational microstructures for use in plasticity models that will help us understand the strength of materials under shock-wave conditions.

## Major Accomplishments in 2005

The key to the effectiveness of grain-boundary engineering lies in the microstructure of what we are calling twin-related domains, or TRDs. Twinning, known for its symmetrical crystal structure, occurs when crystals are subject to stress or other extreme conditions. Materials engineered with the grain-boundary process tend to have large, well-developed TRDs, which significantly improve the materials’ strength. A stress-corrosion crack encountering a TRD usually has to go around it; such a dense cluster of strong boundaries is too tough to crack. On the other hand, normal nonengineered materials have more weak boundaries and less well-developed TRDs, and a crack can easily find large, continuous paths of weak boundaries.

Figure 1. Perspective images of stress-corrosion crack surfaces from normal and grain-boundary-engineered materials. Not only do the engineered materials last up to five times longer, the difference in roughness shows that the material cracks in a completely different way that can be traced back to its grain-boundary structure. |

We discovered how strong boundaries tend to cluster into TRDs and how this clustering affects material performance in terms of failure resistance, uniformity, isotropy, and roughness of these fracture surfaces. Figure 1 shows how these surfaces roughened by corrosion look completely different in the two materials. While the normal material has prominent ridges and valleys aligned with the direction of the crack growth, the roughness in the engineered material is weaker, more uniform, and more random.

Our results have greatly clarified how these TRDs behave, how the boundaries connect together in networks, and how they control the fractal-like surfaces shown in the figure. The networks are highly correlated, so using a simple percolation theory of network connectivity was not sufficient to understand them.

Instead, we produced the first complete mathematical description of the relationships among the different types of strong boundaries, which enabled us to explore the constraints on grain-boundary networks in a simple, efficient, and mathematically rigorous manner.

The constraints impose a degree of order and structure on the TRDs, and we have found that the resulting computer-generated microstructures tend to naturally fall into quite realistic patterns that can be optimized to closely mimic an experimentally obtained microstructure (Figure 2). The computational microstructure shows clearly defined TRDs with complex networks of boundaries inside. If we count the grain-boundary populations in detail, we find that the match is quantitative as well as qualitative. We can match the statistics measured in real materials to within the limits of random sampling.

Figure 2. This comparison of (a) an experimentally measured microstructure from grain-boundary-engineered copper and (b) an optimized computational model designed to mimic it shows good agreement and similarity. Our model tends to produce grain-boundary networks that are quite similar to those in the real material. |

## Scientific Impact

Grain-boundary engineering techniques effectively improve fracture toughness,
stress-corrosion resistance, and superconducting properties by factors of five.
By understanding the laws governing grain-boundary network correlations and
how they translate into material properties, we will create better grain-boundary-engineered
materials designed for specific applications. There is a growing awareness
that crystallographic correlations on supra-grain length scales are essential
to the performance of many materials, and our techniques may be a key to understanding
these length scales.

## Related Publications

B. W. Reed et al., “The Structure of the Cubic Coincident Site Lattice
Rotation Group,” *Acta Cryst.* A60, 263 (2004).

V. Y. Gertsman and B. W. Reed, “On the Three-Dimensional Twin-Limited
Microstructure,” *Z. Metallkd.* 96, 1106 (2005).

B. W. Reed et al., “Mathematical Methods for Analyzing Highly-Twinned
Grain Boundary Networks,” *Scripta Materialia* 54, 1029 (2006).

**Contact:** Bryan Reed [bio],
925-423-3617, reed12@llnl.gov

### New Frontiers

We are scaling up the microstructure generation algorithms to higher resolutions and will include specific physics for a much larger class of materials. Using the material-modeling expertise and world-leading computational capabilities at LLNL (including BlueGene/L and Thunder) and working in collaboration with Michigan State University, we plan to address the issue of dimensionality.

Because percolation and network correlations behave extremely differently in two- and three-dimensional systems, we are currently studying this very challenging problem to understand exactly how the structure of a twin-related domain translates into improved performance. This may help guide the development of new grain-boundary-engineered materials for a broad range of extreme-stress applications.