General behavior of completely anisotropic ESR hyperfine centers under slow orientational diffusion motion.

Abstract

Based on the solution of an isotropic orientational diffusion equation, a restricted ensemble-averaging process has been formulated for completely anisotropic electron-spin-resonance (ESR) centers undergoing slow orientational diffusion motion in a restricted angular interval during their spin-spin relaxation time. By employing this averaging process, we have calculated the slow-tumbling motional linewidth and line shift of completely asymmetric ESR hyperfine centers (${g}_{x}$\ensuremath{\ne}${g}_{y}$\ensuremath{\ne}${g}_{z}$, ${A}_{x}$\ensuremath{\ne}${A}_{y}$\ensuremath{\ne}${A}_{z}$) for arbitrary orientations of their symmetric axes with respect to the ESR external magnetic field B\ensuremath{\rightarrow}. For B\ensuremath{\rightarrow} parallel to the ESR (x,y,z) principal axes, both the motional linewidth and line shift depend on the associated motional correlation time \ensuremath{\tau} as ${\ensuremath{\tau}}^{\mathrm{\ensuremath{-}}1/2}$. When B\ensuremath{\rightarrow} is oriented in the vicinity of 45\ifmmode^\circ\else\textdegree\fi{} with the principal z axis, the motional linewidth is proportional to ${\ensuremath{\tau}}^{\mathrm{\ensuremath{-}}1/3}$. There are ``magic'' orientations of B\ensuremath{\rightarrow} for which the motional line shift vanishes identically. It will be discussed that the analytical expressions obtained for the motional linewidth and line shift for B\ensuremath{\rightarrow} parallel to the principal axes enable one to determine reliable experimental motional correlation times from slow-tumbling ESR hyperfine spectra in polycrystalline-amorphous substances.