Ab initio and Model Calculations on Different Phases of Zirconia
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ABSTRACT In order to get a better understanding of the energetics of ZrO2 (zirconia) ab initio calculations with the full potential linear muffin tin orbital method ( fp LMTO) have been performed on the tetragonal structure over a range of c/a and sublattice displacement. A new semi-empirical shell model is developed which makes use of Hartree-Fock calculations and includes compressible anions and quadrupolar distortions. The empirical model predicts energies for tetragonal distortion in agreement with the fp LMTO calculations. Furthermore, it enables us to understand why the seven-fold coordinated monoclinic phase is the low temperature equilibrium structure. INTRODUCTION Zirconia is an important ceramic material with many applications particularly at high temperatures. Pure ZrO2 shows two temperature driven phase transitions which have been investigated experimentally [1-3 ]. The high temperature phase of zirconia has the cubic fluorite structure. With decreasing temperature there is a martensitic phase transition at 2300'C to a tetragonal phase (c-t) followed by a second martensitic transition to a monoclinic phase (t-m) at about 1000'C. Doping with MgO stabilizes the cubic phase down to 800'C and it shows a (c-t) transformation with decreasing Mg concentration. Yttria (Y203) also stabilizes the cubic and tetragonal phases to lower temperatures. One purpose of our study is to understand the stability of the phases by performing electronic structure calculations within density functional theory. These calculations extend the previous work of Jansen [4] which used the linear augmented plane wave (LAPW) method and use the fp LMTO method [8]. A second purpose of our study is to develop a potential model for accurately describing the high temperature behaviour. With the help of Hartree-Fock results a transferable model based on the ionic picture has been derived and successfully applied to the different phases of zirconia [5]. The biggest challenge for the potential model was to reproduce the seven coordinate monoclinic structure as groundstate. In terms of cation radii zirconia can be regarded as intermediate between the sixcoordinate rutile structure taken by intermediate sized cations, and the eightcoordinate fluorite structure taken by large cation systems (i.e actinides). Previous empirical models [6,71 have failed to predict the monoclinic phase as groundstate, instead favouring the orthorhombic ot-PbO2 structure [5] . In this paper the ab 321 Mat. Res. Soc. Symp. Proc. Vol. 408 01996 Materials Research Society
initio results for the tetragonal phase, the empirical model calculations and the experimental result are discussed. COMPUTATIONAL METHODS The ab initio total energy calculations have been performed with the fp LMTO method [8] within the local density approximation (LDA) with the exchange correlation potential of Hedin and Lundquist [9]. The fp LMTO method has been successfully applied to systems as diverse as transition metals, transition metal surfaces, phonon frequencies of Si, YBa2Cu3O7, MgO and me
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