Phonon Dynamics in Anisotropic Dilute CuAl_1–xFe_xO₂ Delafossite Alloys by a Weighted Dynamical Matrix Approach

Abstract

Here we report a new versatile approach for the calculation of phonon modes which is applicable to anisotropic, dilute alloys with allowance for a large variety of alloying elements. This approach has significant advantages over previously reported methods, especially for the lattice dynamics of such complex alloys. We use this approach to model the effects of Fe-doping on the vibrational modes in dilute alloys of CuAl 1−x Fe x O 2 (x = 0, 0.01, 0.05, and 0.10) delafossite powders. These samples were structurally characterized with X-ray diffraction (XRD) combined with Rietveld refinement to measure their lattice parameters and Raman and FTIR spectroscopies to measure optical phonon frequencies. To compare experimental results from XRD with calculations for lattice parameters, we use a disordered supercell for x in the range 0−0.1. Both results agree well with Vegard's law. For the phonon calculations, an approach using a disordered supercell is not feasible because it is too computationally expensive. Instead, we developed our weighted dynamical matrix (WDM) approach that uses a straightforward ordered supercell for forceconstant calculations of the CuAlO 2 and CuFeO 2 parent end points, and combines them using a WDM approach leading to an effective medium for vibrational mode calculation in random alloys. Computationally, when Fe is substituted for Al (increasing x), an increase in the bond length is observed leading to a red-shift in the peak positions in all of the phonon modes vs x, in agreement with the experimentally observed trend.

Experimental and Computational Exploration of the Dilute Magnetic Delafossite CuAl1-xFexO2 Alloys

“…Steps involved in the formation of CuAlO 2 by the solid-state reaction of the single oxides. Four-step mechanism for the delafossites forming in air above 1273 K, Amrute et al [55] In our work, the samples are prepared by 30 minutes of ball milling of a stoichiometric mixture of Cu2O, Al2O3, and α-Fe2O3 before sintering the powders in the air at 1100 o C. However, only CuFeO2 powder is synthesized at 1000 o C in Ar [7,8,48,56].…”

“…Again, for the alloys, especially the dilute alloys, the very large supercells make the calculations too computationally demanding. For these reasons, we developed a new effective-medium approach using a weighted dynamical matrix (WDM), based on modifying the masses and interatomic force constants after calculation of Hellmann-Feynman forces [47] for parent compounds CuAlO2 and CuFeO2 [48][49][50][51] (details are in 2.2.2).…”

“…Understanding the vibrational properties of CuAl1-xFexO2 alloys is key to understanding the variation of optical (photon-photon interaction) and electronic (electron-phonon interaction) of properties with Fe concentration. To that end, we investigate the structural, electronic, magnetic, and optical properties of Fedoped CuAlO2 [48,54].…”

“…First, the samples of precursor oxides in stoichiometric ratios were ball milled for 30 minutes and then baked at 1100 °C in air. In this step, the necessary time for the purest delafossite phase is optimized [7,8,48]. The x-ray diffraction was done using a PANalytical X'Pert Pro x-ray Diffractometer (XRD) with a Cu-Kα source (λ = 1.542 Å).…”

“…Our computational strategy is the following: we use the supercell approach to determine the lattice associated with replacing Al with Fe, which shows up as the peaks shift to lower angles [7,48]. A more detailed explanation of the lattice parameter dynamics is in Chapter 2.…”