First‐Principle Calculation and Assignment for Vibrational Spectra of Ba ( Mg 1/2 W 1/2 ) O 3 Microwave Dielectric Ceramic

Ba ( Mg 1/2 W 1/2 ) O 3 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 ( Mg 1/2 W 1/2 ) O 3 . The Raman spectrum with nine active modes can be fitted with Lorentzian function, and the modes were assigned as F 2g (1) (126 cm −1 ), F 2g (2) (441 cm −1 ), E g (O) (538 cm −1 ), and A 1g (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 F 1u (1) (144 cm −1 ), F 1u (2) (284 cm −1 ), F 1u (3) (330–468 cm −1 ), and F 1u (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 A 1g , which has the highest wave number (812 cm −1 ) is dominated by the breath vibration of the MgO 6 octahedron. The infrared modes F 1u (2) , that can be described as the inverted vibrations of Mg atoms in the MgO 6 octahedron along the x i , y i , and z i axes have the most contributions to the microwave permittivity and dielectric loss.