X-ray microtomography was used to follow the coarsening of the structure of a ternary silicate glass experiencing phase separation in the liquid state. The volumes, surfaces, mean, and Gaussian curvatures of the domains of minority phase were measured after reconstruction of the 3D images and segmentation. A linear growth law of the characteristic length scale ℓ∼t was observed. A detailed morphological study was performed. While dynamical scaling holds for most of the geometrical observables under study, a progressive departure from scaling invariance of the distributions of local curvatures was evidenced. The latter results from a gradual fragmentation of the structure in the less viscous phase that also leads to a power-law size distribution of isolated domains.