Unraveling the Ground-State Structure of BaZrO₃ by Neutron Scattering Experiments and First-Principles Calculations

Abstract

The all-inorganic perovskite barium zirconate, BaZrO 3 , is a widely used material in a range of different technological applications. However, fundamental questions surrounding the crystal structure of BaZrO 3 , especially in regard to its ground-state structure, remain. While diffraction techniques indicate a cubic structure all the way down to T = 0 K, several first-principles phonon calculation studies based on density functional theory indicate an imaginary (unstable) phonon mode due to the appearance of an antiferrodistortive transition associated with rigid rotations of ZrO 6 octahedra. The first-principles calculations are highly sensitive to the choice of exchange-correlation functional and, using six well-established functional approximations, we show that a correct description about the ground-state structure of BaZrO 3 requires the use of hybrid functionals. The ground-state structure of BaZrO 3 is found to be cubic, which is corroborated by experimental results obtained from neutron powder diffraction, inelastic neutron scattering, and neutron Compton scattering experiments.

BaZrO3 stability under pressure: The role of nonlocal exchange and correlation

“…We obtain the ZPE-corrected lattice constant a ZPE and the ZPEcorrected vibrational frequencies ω ZPE , as well as temperature effects, within the QHA. As we have reported before [11], and is shown in Fig. 2, the vibrational frequency for the R 25 mode is very sensitive to the lattice constant.…”

“…In that previous study [11], we also found that the PBE version of the GGA predicts the cubic phase down to T = 0, although the R 25 mode is significantly softer in PBE. By taking the effect of vibrational zero-point energy (ZPE) into account, the raw DFT lattice constant a 0 was seen to increase by a ZPE = a ZPE − a 0 = 0.007 Å in PBE and CX0p.…”

“…In our previous work [11], we concluded that BaZrO 3 is cubic down to zero kelvin by combining neutron measurements and DFT. The calculations ranged from LDA to hybrids based on both the generalized gradient approximation (GGA) and the truly nonlocal correlation formulations of the van der Waals density functional (vdW-DF) method [12][13][14].…”

“…BaZrO 3 exhibits imaginary phonon modes at the R point in some functional approximations [11]. The unstable mode has the irreducible representation R 25 .…”

“…Since no functional exhibits instabilities on the M point, we have not considered these [30]. There are also three ferroelectric modes, associated [11], showing zero-point-energy effects, moving the raw DFT lattice constants a 0 (squares) to the ZPE-corrected values a ZPE (circles) for CX0p, HSE, CX, and PBE.…”