Raman spectroscopy of incommensurate ${\mathrm{Ba}}_2$${\mathrm{NaNb}}_5$${\mathrm{O}}_{15}$

We have performed Raman studies of the E-symmetry phonon modes in barium sodium niobate in the tetragonal ferroelectric phase above 582 K and measured carefully their splitting into pairs of ${\mathit{B}}_1$ and ${\mathit{B}}_2$ symmetry in the incommensurate (IC) phase between 543 and 582 K. For both heating and cooling cycles the data satisfy mean-field predictions with ${\mathit{B}}_1$-${\mathit{B}}_2$ frequency splitting proportional to the order parameter. The data show that the incommensurate-incommensurate transition at 565 K (heating) does not alter the orthorhombic symmetry; that is, it is not a true 1q-2q transition, and tetragonal symmetry does not set in until the incommensurate-normal transition at 582 K. This is compatible with very recent electron microscopy data (Verweft, Van Tendeloo, and Van Landuyt), which show that the incommmensurate-incommensurate transition near 565 K produces only short-range order in a direction perpendicular to the long-range 1q modulation, and with x-ray studies of this transition (Kiat, Toledano, and Schneck). An analogous situation is observed just below the incommensurate-commensurate transition at 105 K: Here the ${\mathit{C}}_{11}$ and ${\mathit{C}}_{22}$ elastic coefficients have minima at 105 K, signaling a phase transition, but they do not become equal (${\mathit{C}}_{11}$=${\mathit{C}}_{22}$) until approximately 90 K, indicating that there is an incommensurate-incommensurate transition from orthorhombic to tetragonal near 90 K. The 90-K IC-IC transition seems quite analogous to the 565-K IC-IC transition, but electron microscopy shows that these phases are not reentrant.