Exploring the tetragonal crystal structure of perovskites BaLa ₂ Cu _{1− <i>x</i>} Ba <i> _x </i> Ti ₂ O ₉ ( <i>x</i>  = 0.00, 0.15, 0.30) via X-ray diffraction and the Rietveld method

Abstract BaLa 2 Cu 1− x Ba x Ti 2 O 9 ( x = 0.00, 0.15, and 0.30) ceramics were synthesized in polycrystalline form via the conventional solid-state reaction techniques in air. The crystal structure of the title compositions was characterized by room-temperature X-ray powder diffraction and analyzed using the Rietveld refinement method. All the compositions crystallize in the tetragonal symmetry of space group I 4/ mcm (No. 140) with cell volumes: 249.43(1) Å 3 for x = 0.00, 249.42(1) Å 3 for x = 0.15, and 250.05(1) Å 3 for x = 0.30. The tilt system of the M O 6 octahedra ( M = Cu(Ba2)/Ti) corresponds to the notation a 0 a 0 c − . The M O 6 octahedra share the corners via oxygen atoms in 3 D. Along the c -axis, the octahedra are connected by O(1) atoms of (0, 0, 1/4) positions; while in the ab -plane, they are linked by O(2) atoms of ( x , x + 1/2, 0) positions. The bond angle of M –O2– M is 168.6(7)° for x = 0.00, 168.6(6)° for x = 0.15, and 166.8(6)° for x = 0.30, whereas the bond angle of M –O1– M is constrained to be 180° by space group I 4/ mcm.