Hafnium Allotrope First Principles Study

We present a study on the electronic, lattice dielectric, vibrational and elastic properties of HfO2structural phases using the first principles theory and norm conservering pseudopotential method in the different exchange correlation formalisms, which are Troullier-Martins type(TM), Hartwigzen Goedecker Hutter(HGH). All our results are carefully studied with both the local-density approximation(LDA) and the generalized gradient approximation(GGA). We obtain the electronic structure, electronic density of states(DOS), born effective charge tensors, dielectric permittivity tensors, phonon frequencies at the center of the Brillouin zone(BZ), dispersion curves of phonon, phonon-DOS and elastic constants. All our results are in fair agreement with the available published data both for computational and experimental. We focus on the relationship between the HfO2structures and the calculated paratermeters. The trends in these paratermeters during the transitions are also reported. Through the comprehensive study we find:(1) The LDA-TM is much more appropriate to study the elastic properties of HfO2than the GGA in their monoclinic,OI and OII phases. While for the two high temperature phases, our GGA calculations are in line with the previous reported results. All the calculated elastic constants satisfy the relevant mechanical stability criteria and are satisfactory with the available experimental and theoretical values.(2) The elastic constant B has increased significantly from the lower coordination01phases to the high coordination OII phases, indicating that the OII structure is less compressible than the01structure. This is also consistent with the smaller volume of OII-HfO2than that of OI-HfO2. And it also concludes that the tetragonal to cubic transformation of HfO2is accompanied by an increase in the elastic modulus C11, C44and B, but a decrease in C12.(3) We present a systematic analysis of phonon frequencies at the center of the BZ using the Linear-response approach within the framework of density-functional theory. A rigorous assignment of all the calculated modes is achieved by combining symmetry analysis with first-principles calculations, which helps to identify the main peak together with unresolved problems in experimental studies, such as issues concerning the number of modes and the mode assignments.(4) As for the monoclinic phase, LDA-HGH exchange and correlation functional is shown to reproduce quite accurate vibrational frequencies, gives the the rms of absolute deviation of7cm-1. And also these results are much better than the only previous theoretical estimations. The eigen-displacements, eigenvectors, Raman intensities and Raman spectrum are investigated for the first time, which are an important part of understanding of vibrations in this compound.(5) We study the featured vibrational frequencies along the the high-symmetry points of the BZ and list the non-equivalent atoms vibrations among the region of frequencies. The soft-mode instabilities of HfO2in cubic phase together with the phonon spectra evolution during the cubic to tetragonal transformation are also present, providing a theoretical basis for interpretation of the transition behaviors.To our knowledge, HfO2is similar to ZrO2in many physical and chemical properties, here we also investigate the elastic constants of ZrO2structural phases. We find the trends in the elastic constants for the HfO2structures are the same for the corresponding ZrO2structures. So the present study of all HfO2polymorphs could set a guide for the investigation of other lanthanide oxides.