High temperature phase transitions in barium sodium niobate: the wall roughening 1q-2q incommensurate transition and mean field tricritical behaviour in a disordered exclusion model.

Barium sodium niobate (BaNaNbO) is a tungsten bronze structure that exhibits a complicated sequence of six structural phase transitions, including three incommensurate (IC) phases. The phases are unusual in that all but the highest temperature P4/mbm structure are ferroelectric. Unlike the situation for most incommensurate insulators, in which ferroelectricity develops at low temperatures along the modulation direction, the polarization direction in barium sodium niobate is orthogonal to the modulation(s), permitting some unusual phenomena. In the present study we analyse the thermal and dielectric behaviour at the Curie temperature T near 830 K as well as that at the Ccm 2-IC(1q) transition near 543 K, the IC(1q)-IC(2q) transition near 565 K and the IC(2q)-P4bm transition at 582 K. The entropy change at 565 K is related to the wall roughening model of Rice et al (1981 Phys. Rev. B 24 2751). Data near T = 830 K indicate close proximity to a tricritical point, and discussions of critical exponents are presented, all of which are found to be mean field. Because of Na vacancies, transition temperature variation is found among specimens BaNaNbO  (830 K< T(x)< 865 K), and the system appears to be describable by the disordered exclusion model as a slightly first-order intrinsic system whose dynamics are suppressed by weak disorder. Near T the specific heat C(T) is compared with the random bond prediction of Harris (1974 J. Phys. C: Solid State Phys. 7 1671): C(T) = C(T)/[1+bxC(T)], where C(T) is the intrinsic specific heat of the vacancy-free crystal varying as (T-T) and x is the sodium vacancy concentration. In agreement with Harris's model, the shifts in T(x) are to lower T with increasing x and scale as x; the broadening scales as x; and the effective critical exponent remains unchanged at α = 1/2.