First‐Principle Calculation and Assignment for Vibrational Spectra of Ba(Mg_1/2W_1/2)O₃ Microwave Dielectric Ceramic

Abstract

Ba(Mg1/2W1/2)O3 ceramic was synthesized using a conventional solid‐state reaction method at 1500°C for 4 h. The face‐centered cubic crystal structure of the material was confirmed by Rietveld refinement of X‐ray diffraction (XRD) data, and vibrational modes were obtained by Raman and Fourier transform far‐infrared (FTIR) reflection spectroscopies. First‐principle calculations based on density functional theory with local density approximation were used to calculate Gamma‐point modes and dielectric properties of Ba(Mg1/2W1/2)O3. The Raman spectrum with nine active modes can be fitted with Lorentzian function, and the modes were assigned as F2g(1) (126 cm−1), F2g(2) (441 cm−1), Eg(O) (538 cm−1), and A1g(O) (812 cm−1). Far‐infrared spectrum with 12 infrared active modes was fitted using both the Lorenz three‐parameter classical and four‐parameter semiquantum models. Consequently, the modes were assigned as F1u(1) (144 cm−1), F1u(2) (284 cm−1), F1u(3) (330–468 cm−1), and F1u(4) (593–678 cm−1). The active modes were represented by linear combinations of symmetry coordinates that were obtained by group theory analyses. The Raman mode A1g, which has the highest wave number (812 cm−1) is dominated by the breath vibration of the MgO6 octahedron. The infrared modes F1u(2), that can be described as the inverted vibrations of Mg atoms in the MgO6 octahedron along the xi, yi, and zi axes have the most contributions to the microwave permittivity and dielectric loss.

Calculation of the optical phonons in ordered Ba2MgWO6 perovskite using short‐range force field model

“…In Table , we exhibited the Raman and infrared modes calculated from the interatomic force constants of Table along the experimental bands at room temperature extracted from Diao and Liegeois‐Duyckaerts and Tarte . The PED coefficient for each calculated optical mode is also shown.…”

“…As one can verify, there is a satisfactory agreement between those values with a maximum perceptual deviation of ~11%. The optical modes calculated by density functional theory methods reported in Diao et al are also summarized. Such experimental results are concerned to highly ordered BMWO structure with its order parameter η = 1, being described by the site distribution listed in Table .…”

“…The green, blue, purple, and red spheres represent barium, magnesium, tungsten, and oxygen atoms, respectively. a In Diao et al [Colour figure can be viewed at wileyonlinelibrary.com]…”

“…Improvements in their performance are focusing on the increase of their dielectric constant for miniaturization (ε r ), on the obtention of low dielectric loss for high selectivity (tan δ = Q −1 , where Q is the microwave quality factor), and on a good thermal stability (τ f ~ 0 ppm.K −1 ), opening up new frontiers for the Information Communications Technology. In particular, Ba 2 MgWO 6 (here after: BMWO) has satisfactory values, including ε r = 15–20, Q × f = 57–82 THz, and τ f = −38 ppm.K −1 . Such a compound can be also used as an appropriated host for Eu 3+ ions in red emission phosphor .…”

“…By using group theory and Cartesian symmetry coordinates, the authors assigned both Raman and infrared modes to the internal modes of oxygen octahedra and translational displacements of A atoms. More recently, Diao et al determined the optical phonons of BMWO using density functional theory with local density approximation as an ab initio method, providing the eigenvector and vibrational pattern of each mode. However, to the best of our knowledge, there are no works reporting force‐field study on the optical modes at Γ‐point of ordered BMWO perovskites.…”