Phase separation, clustering, and fractal characteristics in glass: A magic-angle-spinning NMR spin-lattice relaxation study

A comparative study of the ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$ spin-lattice relaxation behavior (induced by trace amounts of paramagnetic dopants in the glass) in phase-separated ${\mathrm{Li}}_2$ ${\mathrm{Si}}_4$ ${\mathrm{O}}_9$ and monophasic ${\mathrm{Li}}_2$ ${\mathrm{Si}}_2$ ${\mathrm{O}}_5$ and ${\mathrm{Na}}_2$ ${\mathrm{Si}}_2$ ${\mathrm{O}}_5$ glasses has been made in order to understand the nature of clustering and the resulting intermediate-range ordering. Optically clear tetrasilicate and disilicate glasses were prepared with 500 to 2000 ppm of ${\mathrm{Gd}}_2$ ${\mathrm{O}}_3$, a paramagnetic dopant. The constituent structural units (${\mathit{Q}}^3$ and ${\mathit{Q}}^4$ species) in all tetrasilicate glasses show strong differential relaxation following a power-law behavior. This is due to preferential partitioning of ${\mathrm{Gd}}^{3+}$ into the lower silica (${\mathit{Q}}^3$-rich) regions of these glasses, indicating the presence of Q species clusters too small to produce optical opalescence (a few nm to perhaps tens of nm). Preliminary results on ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ spin-lattice relaxation in these glasses support this hypothesis. Differential relaxation becomes more pronounced on annealing due to growth of such clusters. No such differential relaxation was observed in the monophase disilicate glasses. For spin-lattice relaxation induced by direct dipolar coupling to paramagnetic ions, the recovery of magnetization is proportional to time as M(t)∼${\mathit{t}}^{\mathrm{\alpha }}$ where α is a function of the dimensionality D of mass distribution of the constituent Q species around the ${\mathrm{Gd}}^{3+}$ paramagnetic centers in the glass. For tetrasilicate glasses D≊2.62±0.22 and the system behaves as a mass fractal up to a length scale of 2 to 3 nm. D is thus equal to, within error, the theoretical value of 2.6 for an infinite percolation cluster of one type of Q species in another. For disilicate glasses, D≊3.06±0.18 which indicates a three-dimensional (and thus nonfractal) mass distribution of the constituent Q species over the same length scale.