Theoretical prediction of size and dimension dependent critical temperature for ferroelectric, ferromagnetic and superconductive nanomaterials

Abstract

In this study, interface energy and internal energy are used to characterize the contribution of the interface lattice and internal lattice to the phase transition of nanomaterials, respectively. And the equivalence principle of interface energy and internal energy is defined. According to the above assumptions, a novel theoretical model without any fitting parameters is established to quantitatively characterize the influence of size on the critical transition temperature of nanomaterials. A good agreement between the predicted results of our model and the available experimental results of ferroelectric, ferromagnetic and superconductive nanomaterials is obtained. The quantitative relationship between the size dependent critical temperature, melting enthalpy, melting point and atomic diameter is uncovered by the present model. Particularly, compared with the existing models, our model can more reasonably predict the change trend that the critical temperature decreases rapidly with the increase of the size when the size is less than a certain minimum value, and increases with the increase of the size when the size is larger than the value. Moreover, our model can reasonably predict the critical size at which ferroelectric properties of ferroelectric materials disappear. This study provides a convenient and practical method to further explore the change law of critical temperature with size.