The structures of α- and β-Bi2Ti4O11

The phase transition and the crystal structures of Bi 2 Ti 4 O 11 have been investigated by X-ray diffraction. The compounds possess the following parameters: α-Bi 2 Ti 4 O 11 : monoclinic, space group C2/c, a = 14.5999 (6), b = 3.8063 (2), c = 14.9418 (8) A, β = 93.129(4)°, V = 829.1(1)A 3 , Z = 4, D x = 6.29 g cm −3 , Mo Kα, μ = 44.31 mm −1 , wR = 0.029 for 2361 reflections; β-Bi 2 Ti 4 O 11 : monoclinic, space group C2/m, a' = 14.6412 (12), b'= 3.8032 (3), c'= 10.7824 (6) A, β = 136.135 (5)°, V = 416.06(10) A 3 , T = 573 K, Z = 2, wR = 0.043 for 1204 reflections. The transformation at 506 K leads from a paraelectric high-temperature modification (β-Bi 2 Ti 4 O 11 ), with the space group C2/m, to a C2/c antiferroelectric low-temperature phase (α-Bi 2 Ti 4 O 11 ) and is induced by a displacement of the Bi atoms at ca 0.29 A along [010] in the channels of the Ti−O network. For the description of the transition, it is convenient to transform the unit cell of α-Bi 2 Ti 4 O 11 according to a″ = a, b″ = b, c″ = -a + c. In this new setting, the position of superlattice reflections results in a cell doubling parallel [001], indicating a phonon condensation at the A-point [001/2] on the boundary of the Brillouin zone of C2/m. A symmetry analysis has been performed based on the Landau formalism and projection operator methods. The displacements parallel and antiparallel to b were taken as the primary-order parameter, which transforms according to the irreducible representation A 2 +