Commensuration and discommensuration in 2H-TaSe2

Changes of satellite dark-field images of the incommensurate phase in 2H-TaSe2 upon cooling are examined closely in order to investigate the behavior of the incommensurate-commensurate transition of this material. Moirélike fringes observed in the higher temperature range of the phase, which were confirmed to be due mostly to the interference of the first- and second-order diffraction beams from the incommensurate structure in our earlier, high-resolution study, are found to change, starting around 92 K, into the domain images of the commensurate structure which are due mostly to a dark-field diffraction contrast. The change from interference fringes to diffraction contrast is associated with the change of the modulation mode of the incommensurate phase from the incommensurate modulation of the normal structure in the upper temperature range to the incommensurate modulation of the commensurate structure. The upper temperature range above this transition corresponds to the hexagonal, triply incommensurate state while the lower temperature region is the transition region to the commensurate state. This is in variance with the double honeycomb discommensuration model (a model based on the incommensurate modulation of the commensurate structure) proposed for the explanation of the whole temperature range of the incommensurate phase. The shrinking motion of jellyfish patterns (which were called stripples, by Fung et al. [J. Phys. C. 14, 5417 (1981)], or charge-density-wave dislocations by Chen et al. [Phys. Rev. Lett. 47, 723 (1981); Phys. Rev. B 26, 184 (1982)] for those in 2H-TaSe2, but jellyfish patterns will be used to include these for more general cases and similar ones in other materials), consisting of three discommensuration lines that join at one point in the matrix of the commensurate structure in the transition region, leaves the commensurate structure in its wake and represents the kinetics of the commensuration process. This change in the modulation mode in the incommensurate phase also explains the change of the incommensurability, , with temperature in two steps as observed by x-ray diffraction experiments. A theoretical support of this behavior is given.