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The temperature dependence of the elastic properties of polycrystalline manganites La
0.5Ca
0.5MnO
3 has been studied by means of ultrasonic measurements and low-frequency internal friction apparatus. It was found that both the longitudinal modulus and the low-frequency shear modulus starts to soften obviously with a decrease in temperature from higher temperature to the charge-ordering transition temperature
T
CO, and stiffens dramatically just below
T
CO. The abnormal temperature dependence of the elastic modulus around
T
CO is fitted with the mean-field theory, which describes the coupling of Jahn–Teller ions to distortions of lattice of the cooperative Jahn–Teller system. The good fit of the theory to the data indicates that the Jahn–Teller effect is the dominant mechanism responsible for the charge-ordering state of the system.