Lattice thermal expansion of complex oxides with intrinsic anharmonicity

The lattice thermal expansion of crystalline solids cannot be adequately modeled by Grüneisen approximation using either Einstein single harmonic frequency or Debye frequency spectrum because a true phonon spectrum does not follow either of the two kinds. The Debye model misfits to many observations due to the fact that real solids comprises of axial anisotropy, lattice waves with dispersion at the Brillouin zone boundaries, low/high frequency optical vibrations in excess of the Debye spectrum. The actual frequency distribution is a complicated function of frequency instead of a simple parabolic Debye spectrum. The frequency distribution can be simplified using power series [1] leading to singularities before and after the Debye cutoff frequency. Using multiple Debye or Einstein oscillators, or their mixtures, is also common practice to better describe the lattice expansion, however, these models extremely suffer from intrinsic anharmonicity in particular at high temperatures. It was demonstrated that even the noble monoatomic solids required inclusion of anharmonic terms in the harmonic model to better explain the observed values [2]. Worse even, when anharmonicity becomes dominant due to formation of vacancies and defects, anomalies of hard/soft modes or change of stereochemical activities of lone electron pairs (LEPs) as function of temperature. Herein we approach an extended Grüneisen approximation that includes harmonic, quasiharmonic and intrinsic anharmonic potentials to describe the internal energy of the crystal as function of temperature. The model has been applied to several complex oxides with LEPs (Bi₂Ga₄O₉ [3]) along with axial negative thermal expansion (PbFeBO₄) and rigid-unit-modes (KAsW₂O₉) reported here. The metric parameters were obtained from quality data collected from temperature-dependent neutron and X-ray powder diffractions.

Application of Charge & Band-flipping to Time-of-Flight Neutron Diffraction Data

Charge-flipping has become a popular approach to ab-initio structure solution from X-ray powder diffraction data in particular due to its speed and need for minimal input other than lattice parameters. Given the appetite of charge-flipping for low d-spacing reflections, time-of-flight (TOF) neutron data should be a good match from a resolution standpoint, with easy access to high Q and lack of form-factor drop-off. One obvious issue with neutron data is the presence of elements with negative scattering lengths, where the inherent assumption of atoms always having positive `density' in the algorithm breaks down. This means that portions of the structure can be effectively invisible. Given that some of these elements (e.g. H and Mn) are commonly found in samples of interest the issue is more than simple academic curiosity. Of course such atoms can be found by difference maps, but the issue has also been addressed within the charge-flipping algorithm with the `band-flipping' modification [1]. Although Oszlányi & Sütö demonstrated the approach was viable with simulated neutron single crystal data [1], to the authors' knowledge it hasn't been used previously with experimental single crystal or powder neutron diffraction data. Powder diffraction data from POWGEN and wavelength-resolved TOF Laue single crystal data from TOPAZ at the Spallation Neutron Source have been used to probe the relative ease of charge-flipping with different TOF data using the TOPAS software package [2]. In addition the effectiveness of different customized band-flipping approaches has been tested to extract positions for positive and negative scattering elements simultaneously.