Structural Properties of Fe2O3 at High Temperatures

Abstract

There has been recent interest in understanding the properties of transition-metal oxides, arising from their potential applications in novel electronic devices1) and as solar energy materials.2) As they are used at relatively high temperatures, sometimes over 1000K, it is essential to clarify the effects of intense atomic motion on these properties. Iron(III) oxide, Fe2O3, is one of the most common transitionmetal oxides. Not only is it an abundant mineral in the Earth’s crust, but it is also an important material for technological applications.3) In this study, the structural properties of Fe2O3 at high temperatures are investigated by using ab initio molecular-dynamics (MD) simulations. We demonstrate that the thermal decomposition behavior of Fe2O3 above the melting temperature4) is successfully reproduced on the basis of spin-polarized density functional theory (DFT). We calculated the electronic states using the projector augmented wave (PAW) method5) within the framework of DFT, in which the generalized gradient approximation6) was used for the exchange–correlation energy. To consider the onsite Coulomb repulsion among the localized 3d electrons of Fe, the DFT+U method was employed following Ref. 7, with an effective parameter U J 1⁄4 4 eV. The plane-wave cutoff energies were 30 and 300Ry for the electronic pseudowave functions and pseudo-charge density, respectively. The ¥ point was used for Brillouin zone sampling. Projector functions were generated for the 3d, 4s, and 4p states of Fe and for the 2s and 2p states of O. The number of atoms was 120 (48Fe+72O). Using the Nose–Hoover thermostat technique,8) the equations of motion were solved via an explicit reversible integrator.9) First, we performed MD simulations at room temperature (300K) to verify the stability of the crystal structure of hematite, i-Fe2O3, under ambient conditions. The total simulation time was 1.5 ps with a time step of 1.2 fs. An experimentally observed rhombohedral R3c structure10) was used for the initial configuration. To investigate the effects of spin polarization on the structural properties, antiferromagnetic (AFM) and ferromagnetic (FM) alignments of the spins, as well as a non-magnetic (NM) state, were considered. The local magnetic moments were jMsj 1⁄4 4:28 and 4.31 B/Fe for the AFM and FM states, respectively, which are consistent with previous theoretical and experimental observations.7) Figure 1 shows the partial pair distribution functions g ðrÞ. The thick solid, thin solid, and thin dashed lines indicate the correlations for the AFM, FM, and NM states, respectively. It can be seen that the AFM and FM states produce almost indistinguishable plots for g ðrÞ, and that their peak positions are in good agreement with the interatomic distances in the rhombohedral R3c structure. The coordination numbers obtained by the integration of the respective peaks of g ðrÞ also coincide with experimental values. On the other hand, the NM state produces a quite different profile of g ðrÞ, especially for the Fe–Fe pair, as shown by the dashed lines in Fig. 1. We conclude from these results that including the spin polarization is essential to reproduce the structural properties of hematite, i-Fe2O3, under ambient conditions. Next, we performed MD simulations with an isothermal– isobaric ensemble at a temperature of 3000K and ambient pressure in order to explore the disordered phase of Fe2O3. The total simulation time was 3.8 ps with a time step of 0.48 fs. Treatment with non-collinear magnetism may be needed to reproduce the paramagnetism above the Neel temperature of 955K. It is, however, known that the noncollinear magnetic state is not crucial for determining the local geometry around transition metals in a liquid state.11) The local interaction between atoms would be affected only slightly by the non-collinearity. Here, we consider the AFM and NM states in disordered Fe2O3. Since the temperature is sufficiently higher than the melting temperature of 1838K,4) the crystalline structure was lost and a disordered phase was successfully obtained. Figure 2 shows g ðrÞ at 3000K. The two profiles for the AFM (solid line) and NM (dashed line) states are somewhat different from each other, not only in gFeFeðrÞ but also in gOOðrÞ and gFeOðrÞ. Note that the AFM state has a peak at approximately 1.5A in gOOðrÞ, while there is no correspond0 2 4 6