CORRELATION BETWEEN THE ELASTIC AND THE VIBRONIC BEHAVIOR OF NANOSTRUCTURED TITANIA AND THEIR PRESSURE, SIZE, AND TEMPERATURE DEPENDENCE

Abstract

Correlation between the elastic and the vibronic behavior of TiO 2 and their responses to the variation of crystal size, applied pressure, and measuring temperature has been investigated based on the bond order–length-strength correlation mechanism. Theoretical reproduction of the measurements clarified that: (i) the elastic modulus (B) and the Raman shifts (Δω) are strongly correlated and we can know either one of the B or the Δω from the other; (ii) the under-coordination induced cohesive energy loss and the energy density gain in the surface up to skin depth determines the size effect; (iii) bond expansion and bond weakening due to thermal vibration originates the thermally softened elastic modulus and the Raman shifts; and (iv) bond compression and bond strengthening results in the mechanically stiffened elastic modulus and the Raman shifts. With the developed premise, one can predict the changing trends of the concerned properties with derivatives of quantitative information of the atomic cohesive energy, binding energy density, Debye temperature, and nonlinear compressibility of the specimen.