Strain engineering of the elasticity and the Raman shift of nanostructured TiO₂

Correlation between the elastic modulus (B) and the Raman shift (δω) of TiO₂ and their responses to the variation of crystal size, applied pressure, and measuring temperature have been established as a function depending on the order, length, and energy of a representative bond for the entire specimen. In addition to the derived fundamental information of the atomic cohesive energy, binding energy density, Debye temperature and nonlinear compressibility, theoretical reproduction of the observations clarified that (i) the size effect arises from the under-coordination induced cohesive energy loss and the energy density gain in the surface up to skin depth; (ii) the thermally softened B and δω results from bond expansion and bond weakening due to vibration; and, (iii) the mechanically stiffened B and δω results from bond compression and bond strengthening due to mechanical work hardening. With the developed premise, one can predict the changing trends of the concerned properties with derivatives of quantitative information as such from any single measurement alone.