E6 Nanoscale Crystal Structure

Topic

The fact that the grain size of this material is nanometric—rather than micrometric, as in a conventional polycrystal—increases the material's grain-boundary volume fraction. Each grain boundary occupies a virtually fixed thickness of just a few atomic layers, regardless of the size of the grain it delimits; consequently, the smaller the grain, the greater the proportion of the total volume occupied by that fixed-thickness grain boundary. Reducing the grain size to the nanometric scale causes this grain-boundary volume fraction to grow until it is comparable to the volume fraction occupied by the crystalline interior of each grain—a proportion that would be entirely negligible in a conventional polycrystal.

It is this comparability between the grain-boundary fraction and the crystalline interior of each grain that gives the nanocrystal properties intermediate between those of a fully crystalline material and those of a fully amorphous material: the crystalline interior of each grain, with its periodic atomic order, continues to provide the properties characteristic of the crystalline phase, whereas the grain-boundary fraction—with its much more disordered atomic structure—contributes properties resembling those of an amorphous material. A larger grain-boundary fraction within the nanocrystal causes its overall properties to lean closer to those of an amorphous material, while a smaller fraction causes them to lean closer to those of a fully crystalline material. Therefore, this model—given the nanometric grain size and the specific grain-boundary fraction involved—calculates the nanocrystal's effective modulus by combining, via a rule of mixtures, the modulus of the crystalline interior of each grain and the modulus of the grain-boundary fraction itself (which is much softer than the crystalline interior). This rule of mixtures weights each of the two moduli according to its respective volume fraction within the nanocrystal. As the grain-boundary volume fraction increases—driven by an even smaller nanometric grain size—the nanocrystal's effective modulus becomes increasingly dominated by the much softer modulus of the grain boundaries, and consequently, the effective modulus decreases.

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