X-ray diffraction experiment has been performed on powder Y₂O₃ at room temperature. The apparent diffuse scattering intensity of the vibration shape is observed. Based on the general equation of the background intensity of full diffraction, the thermal diffuse scattering intensity equation of Y₂O₃ is developed. According to the comparison between the experimental value and the theoretical value, the value of the inter-atomic thermal vibration correlation effects μ was obtained. It is observed that the thermal diffuse scattering intensity of Y₂O₃ mainly comes from the independent vibration of atoms; the shape of thermal diffuse scattering is mainly determined by the thermal vibration correlation effect between Sixth neighboring atoms. The force constants among neighboring atoms in Y₂O₃ are obtained from the values of inter-atomic thermal vibration correlation effects.