Metal Ti, Zr And Hf Nanoparticles Structural Transformation Theory Research

Based on the Debye model of Helmholtz free energy for bulk metals and Bond Energy model developed by our group, by considering the different vibrational energy and vibrational entropy between surface atoms and inner atoms, size and shape effects on cohesive energy and Debye temperature, and the effects of surface stress, a Gibbs free energy model for nanomaterials is established. This model can be regarded as the extending of Debye model in bulk state. Based on this model, we calculated the Gibbs free energy of Ti, Zr and Hf nanoparticles, and studied the structure transformations among HCP, FCC and BCC structures. The main results are obtained as follows.1, Gibbs free energy for HCP, FCC and BCC structures of Ti, Zr and Hf nanoparticles decreases with the increase of temperature or particle size, and increases with the increase of shape factor. The size effects on Gibbs free energy are more and more distinct with the decrease of particle size.2, The HCP, FCC and BCC structures of Ti, Zr and Hf can transformation with each other under certain conditions. At fixed sizes, the structures will change from HCP at low temperatures to BCC at high temperatures with the rise of temperature for the three elements. At specified temperature, the structures will change from HCP to FCC (or have this tendency).3, The temperature induced HCP to BCC transformation originates from the different lattice vibration state (characterized by Debye temperature) of the three structures while the size induced HCP to FCC transformation originates from the different molar volumes of the three structures. There exist competitions between these two transformations, and it causes the structure transformations between BCC and FCC structures. In other words, the structure transformation between BCC and FCC is induced by the co-effects of temperature and particle size.4, The size-temperature phase diagrams for Ti, Zr and Hf nanoparticles are obtained based on the minimal of Gibbs free energy principles. In the phase diagrams, the HCP, BCC and FCC structures are low-temperature stable structure, high-temperature stable structure and small-size stable structure, respectively. There exists an unreported phase transformation from FCC to BCC structures in small size and high temperature ranges.The thermodynamic theories for bulk materials had been introduced to nanoscale in this paper, which extended the meaning of thermodynamics. The obtained size-temperature phase diagrams of Ti, Zr and Hf elements can deepen our knowledge of the three elements and it will promote the designing of relative new materials.