Determination of the Anisotropic Rotational Diffusion Constant of Microcrystals Dispersed in Liquid Medium

Microcrystals of ErBa₂Cu₄O₈ suspended in a liquid medium were triaxially aligned by a frequency-modulated magnetic field and allowed a free rotational relaxation after the magnetic field was turned off. In situ X-ray diffraction measurements of the suspension were performed during relaxation, and the temporal change of the orientation fluctuation was monitored via broadening of the diffraction spots. The rotational diffusion constants were determined using the plot of the orientation fluctuation versus the elapsed time of rotational relaxation. The diffusion constants thus determined were in close agreement with those evaluated by the Stokes law but showed slight anisotropy, indicating that the microcrystals studied had shape anisotropy. The present method can provide a useful means for experimentally determining rotational diffusion constants of microcrystals suspended in viscous media. This paper shows that, due to the combination of the initial triaxial alignment and the subsequent monitoring of the relaxation process by means of X-ray diffraction, the diffusion constants along arbitrary crystallographic axes are determined separately.