  We investigated the temperature dependence of the superlattice intensity and
thermal diffuse scattering intensity of BaAl2O4, which has a network structure
with corner-sharing AlO4 tetrahedra, via synchrotron X-ray diffraction
experiments. The temperature variation of the superlattice intensity revealed
that the structural phase transition occurs at TC = 451.4 K from the P6322
parent crystal structure to the low-temperature superstructure with a cell
volume of 2a x 2b x c. BaAl2O4 exhibits an unconventional structural phase
transition driven by two competing soft modes, q1/2 ~ (1/2, 1/2, 0) and q1/3 ~
(1/3, 1/3, 0). When approaching the TC from above, the soft mode with q1/3
appeared first and was followed by the q1/2 soft mode. The thermal diffuse
scattering intensities from both soft modes increased sharply at TC; therefore,
both modes condensed simultaneously. The first principles calculation revealed
that structural instabilities exist at the M- and K-points, at which the
calculated imaginary frequencies are similar. The small energy difference of
these structural instabilities generates the two competing soft modes and
determines the eventual low-temperature crystal structure.
