Topological Origin of the Network Dilation Anomaly in Ion-Exchanged Glasses

Ion exchange is commonly used to strengthen oxide glasses. However, the resulting stuffed glasses usually do not reach the molar volume of as-melted glasses of similar composition—a phenomenon known as the network dilation anomaly. This behavior seriously limits the potential for the chemical strengthening of glasses and its origin remains one of the mysteries of glass science. Here, based on molecular dynamics simulations of sodium silicate glasses coupled with topological constraint theory, we show that the topology of the atomic network controls the extent of ion-exchange-induced dilation. We demonstrate that isostatic glasses do not show any network dilation anomaly. This is found to arise from the combined absence of floppy modes of deformation and internal eigenstress in isostatic atomic networks.

Figure 1

Number of constraints per atom $n_c$ for permanently densified sodium silicate glasses, with respect to the pressure applied during the cooling path. The solid line is a linear fit. The gray area indicates the domain of maximum expansion due to ion exchange, as shown in Fig. 3.

Figure 2

Molar volume of a sodium silicate glass, cooled under zero pressure, after replacement of a given fraction of Na by K atoms. The solid line is a linear fit. The red (blue) dashed line indicates the molar volume of as-melted sodium (potassium) silicate.

Figure 3

Linear network dilation coefficient (LNDC, $B$) after substitution of all Na by K atoms, with respect to the number of constraints per atom. The black dashed line serves as a guide for the eye. The blue dashed line indicates the maximum theoretical LNDC $B_{\max }$, as obtained from the molar volumes of as-melted sodium and potassium silicate glasses. The gray area indicates the domain of maximum expansion due to ion exchange.

Figure 4

Cooper coefficient $B$ as a function of the number of atoms for selected pressures. The lines serve as guides for the eye.

Figure 5

Cooper coefficient $B$ as a function of the cooling rate for selected pressures. The lines serve as guides for the eye.

Figure 6

(left axis) Increase in the average coordination number (CN) of the replaced atoms upon ion exchange, normalized by the difference of CN between the as-melted sodium and potassium silicate glasses. (right axis) Average tensile stress experienced by Si atoms in the ion-exchanged glasses, using as-melted potassium silicate glasses as a reference. The dashed lines serve as guides for the eye. The gray area indicates the domain of maximum expansion due to ion exchange, as shown in Fig. 3.