Elastic and Anelastic Behavior of Materials in Small Dimensions
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Elastic and Anelastic Behavior of Materials in Small Dimensions
Shefford P. Baker, Richard P.Vinci, and Tomás Arias Abstract Under certain circumstances, decreasing the dimensions of a material may lead to elastic or anelastic properties that diverge from bulk behavior. A distinction is made between elastic deformation, for which bond rearrangements are not required, and anelastic behavior, which involves reversible deformation due to defect motion. Elastic deformation (due to bond stretching) remains structure-insensitive down to near-atomic length scales, and only small deviations are expected (of the order of 10%). More significant deviations can be observed in special cases, which are described in the article. However, elastic moduli that are much lower than expected are sometimes seen, even in careful experiments. It now appears that this behavior may be explainable by time-dependent anelastic relaxation mechanisms. In contrast to purely elastic behavior, anelastic behavior is very sensitive to microstructure and is found to be common and often significant when things become small. Keywords: elastic properties, internal friction, thin films.
Introduction This article addresses a fundamental question: When does decreasing the characteristic dimensions of a material lead elastic properties to diverge from bulk behavior? We are motivated to understand such deviations in order to produce reliable components and devices on the nanometer scale. In addition, tremendous benefits could be realized if a way were found to change elastic behavior by manipulating the microstructure on a very fine scale. One could imagine, for example, selecting a material for its conductivity, reflectivity, or chemical resistance and then making it stiffer in order for it to better resist deformation, or making it more compliant to reduce stress levels for a given strain. Elastic strain is deformation that is fully recovered upon removal of the applied load. This definition encompasses both elastic and anelastic behavior. Elastic deformation arises from bond stretching and twisting and is generally considered to be time-
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independent (elastic deformation is transmitted at phonon velocities). Anelastic deformation arises from atomic reconfigurations (e.g., defect motions) and is timedependent on a much longer scale. Since all elastic deformation is time-dependent on some scale, for this article we use the more crisp microstructural definition (stretching and twisting versus reconfiguration) as our operational distinction between elastic and anelastic behavior. In what follows, we briefly outline the state of knowledge regarding elastic and anelastic behavior in small dimensions, as well as the contributions of experiment, modeling, and simulation to this knowledge. We will argue that elastic deformation remains structure-insensitive down to near-atomic length scales (unfortunately so, from the standpoint of property engineering), and we will show that anelastic behavior is a surprisingly common, strong, and interesting source of devia
