Measurements have been made of integrated intensities of X-ray symmetrical reflections from single crystals of magnesium, cadmium and Mg_3Cd, kept at temperatures ranging from room temperature to about 90°K. It is observed that the thermal mean-square atomic displacements along two directions, the one parallel to the hexagonal c-axis u_z^2 and the other perpendicular to the c-axis u_x^2, are nearly the same in Mg_3Cd, showing little anisotropy. The result suggests that thermal vibrational amplitudes in the alloy can not be a simple average of those in magnesium and cadmium. No appreciable difference is observed between the mean-square displacements of an ordered and an imperfectly ordered Mg_3Cd. The mean-square atomic displacements is calculated for magnesium and cadmium applying Zener\u27s theory of thermal vibration in hexagonal crystals and is compared with the observed displacements. Discussions are given on the correlation between u_z^2 / u_x^2 and the axial ratio, c/a, of hexagonal close-packed metals and also on the thermal mean-square displacements in alloys
