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The present paper reviews models of domain structure in ferroelectric crystals, thin films and bulk materials. Common crystal structures in ferroelectric materials are described and the theory of compatible domain patterns is introduced. Applications to multi-rank laminates are presented. Alternative models employing phase-field and related techniques are reviewed. The paper then presents methods of observing ferroelectric domain structure, including optical, polarized light, scanning electron microscopy, X-ray and neutron diffraction, atomic force microscopy and piezo-force microscopy. Use of more than one technique for unambiguous identification of the domain structure is also described.

Carbon nanotubes (CNTs) are regarded as small but strong due to their nanoscale microstructure and high mechanical strength (Young's modulus exceeds 1000 GPa). A longstanding question has been whether there exist other nanotube materials with mechanical properties as good as those of CNTs. In this study, we investigated the mechanical properties of single-walled aluminosilicate nanotubes (AlSiNTs) using a multiscale computational method and then conducted a comparison with single-walled carbon nanotubes (SWCNTs). By comparing the potential energy estimated from molecular and macroscopic material mechanics, we were able to model the chemical bonds as beam elements for the nanoscale continuum modeling. This method allowed for simulated mechanical tests (tensile, bending, and torsion) with minimum computational resources for deducing their Young's modulus and shear modulus. The proposed approach also enabled the creation of hypothetical nanotubes to elucidate the relative contributions of bond strength and nanotube structural topology to overall nanotube mechanical strength. Our results indicated that it is the structural topology rather than bond strength that dominates the mechanical properties of the nanotubes. Finally, we investigated the relationship between the structural topology and the mechanical properties by analyzing the von Mises stress distribution in the nanotubes. The proposed methodology proved effective in rationalizing differences in the mechanical properties of AlSiNTs and SWCNTs. Furthermore, this approach could be applied to the exploration of new high-strength nanotube materials.

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