Abstract: The electrical resistivity, magnetization, and ultrasonic velocity were investigated systematically in polycrystalline (Nd_0.75Na_0.25)_1-x(Nd_0.5Ca_0.5)_xMnO₃ (x=0, 0.25, 0.5, 0.75, 1). A charge ordering transition was observed in
all samples through resistivity and magnetization measurements. With increasing Na content, the charge ordering transition temperature (T_co)
shifts to lower temperature, the magnetization of the system is strengthened
and charge ordering becomes more unstable and short-ranged. It is found that
the longitudinal sound velocity shows a dramatic softening and stiffening around T_co. The ultrasonic anomaly near T_co indicates the existence of strong electron-phonon interaction, which originates from Jahn-Teller effect of Mn^3+. By fitting the experimental longitudinal modulus above T_co with the cooperative
Jahn-Teller theory, one can establish that the Jahn-Teller coupling energy E_JT decreases with increasing Na content. The analysis of experimental results suggests that the charge mismatch should be the main reason for the suppression of the charge ordering and the weakening of cooperative Jahn-Teller effect.

Key words: ultrasonic velocity, charge ordering, charge mismatch effect, Jahn-Teller effect