A procedure is shown to quantitatively analyze the morphology of the internal friction peak resulting from grain-boundary sliding. A Si3N4 polycrystal containing chlorine-doped SiO2 at grain boundaries is selected as a model system for discussing chemical (e.g., anion) gradients at glassy grain boundaries. In this model material, grain boundaries lodging Cl- anions show nonuniform thickness characteristics, which suggests a non-negligible dependence of the intergranular SiO2-network structure upon grain misorientation. Both chemical and microstructural inhomogeneities existing in a polycrystalline ceramic body can result in peak broadening. The key for separating broadening contributions of chemical gradients from grain-size/morphology distributions resides in analyzing the peak-width change upon damping frequency. Groups of grain boundaries with different chemical characteristics may produce broadening because different peak components are generated that obey a spectrum of activation energies. On the other hand, microstructural inhomogeneities obey a single activation energy, but they generate a distribution of relaxation times. As a result, when a chemical gradient is present at grain boundaries, the peak may shift upon changing damping frequency with obeying a true activation energy, but its width increases with decreasing damping frequency. When peak broadening results only from microstructural inhomogeneities, the peak width is independent of damping frequency.