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Discussion of tools and computational methods So far, this article has presented the views and programs of attendees at the ICCCRD meeting. Some other related ongoing efforts to model properties and behavior of ceramic materials are summarized hereafer. A report of a NIST-supported study conducted by The Minerals, Metals, and Materials Society (TMS), “Modeling across scales,”12 discusses many procedures that apply to modeling materials across length and time scales. Figure 2 illustrates some of the connections among modeling methods. For example, TMS report authors at the ICCCRD workshop suggest DFT as the primary technique available for calculating many properties of inorganic solids. The TMS report suggests that DFT is limited to strongly correlated materials with volumes of localized electrons, e.g., molecular materials and some insulating solids. A 2008 publication13 details some of the limitations of DFT. The authors note that DFT succeeds in predicting structure and thermodynamic properties of molecules and solids. Nevertheless, they point out some of the major failures of this technique, namely, underestimation of barriers to chemical reactions, band gaps of materials, energies of dissociation, and charge transfer excitation energies. DFT also overestimates binding energies of charge transfer complexes and response to an electric field in molecules and materials. The authors also note that DFT can describe accurately a chemical bond, e.g., H2, but fails as the molecule is stretched. This failure perhaps explains the difficulty in calculating fracture behavior. The TMS report mentions another modeling tool: quantum Monte Carlo (QMC). This is a relatively new technique that is undergoing development. However, the computational expense to use QMC is quite high. The TMS report suggests other possible modeling methods, including use of classical potentials to represent the complex bonding interaction between atoms. The report notes that “when deriving a potential for a specific system, Figure 2. Modeling methods across length scales.12 it is important to recognize in advance that properties are ultimately to be predicted by the simulation.” Fracture of brittle materials Fracture of brittle materials is an area of computation and modeling particularly relevant to the ceramics field. Researchers can calculate elastic properties of a single crystal fairly accurately. However, fundamental resistance to fracture of this crystal, fracture toughness (KIC) or fracture energy (ϒ)—although known to be directly proportional to the elastic modulus14—cannot be determined a-priori. Most factors that influence fracture behavior of even simple single crystals are available only through direct measurements, many of which are difficult to conduct, and are not necessarily fundamental in nature. This measurement problem becomes more severe as the size of materials reaches nanoscale regimes. In addition, there are anomalies to fracture behavior that researchers cannot explain. A recent review article15 gives an up-to-date perspective on the atomistics of fracture. Environmentally enhanced crack growth under stress that can lead to time-dependent failure occurs in most ceramics. Researchers have attempted to predict stress-dependent reactions of environments, e.g., in water, with silica and silicon. Wong-Ng et al.16 used molecular orbital calculations to determine effects of bond strain on charge distribution in silica. They noted that although absolute value of the electron distribution depends on the exact configuration of strain, the general trends remain the same. In another part of the study, Lindsay et al.17 used the same molecular orbital approach to examine effects of applying stress to the Si—O bond in the presence of environments, including water and other crack-growthenhancing environments. Credit: TMS Bartlett and co-workers18 conducted a quantum mechanics calculation on the reaction of water with silica using secondorder perturbation theory. Their calculations showed that it should be a water molecule dimer rather than a monomer that reacts with the Si—O—Si bond. West and Hench19 used a semiempirical method to model fracture of silica rings. Although a drawback of semiempirical techniques is their reliance on experimental data, they can model much larger groups of atoms. West and Hench concluded that in the presence of water, threefold rings will be the primary site at which bond rupture will occur, i.e., cracks will seek out threefold ring structures to follow as they grow. Silicon in bulk form shows no evidence of water-enhanced crack growth. Molecular orbital calculations on strained silicon20 suggest that silicon shows no tendency to charge polarization as a result of strain and that straining a Si—Si bond does not lead to an attractive force between the bond and a water molecule. Molecular dynamics (MD) is an approach to model the fracture process, in which researchers can follow simu- American Ceramic Society Bulletin, Vol. 95, No. 3 | www.ceramics.org 39


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