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A generalized T‐dependent activation energy, H(T), is defined as the slope of the Arrhenius plot of viscosity:

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The ratio, H(T_g, x)/(k_B T_g), is proportional to the fragility m. In some systems, the activation energy (or fragility) shows rounded discontinuities as a function of T or as a function of composition, X. These jumps are referred to as fragility transitions. An example of such transition in the alkali‐borate systems is shown in Figure 5. Fragility transition as a function of temperature for a fixed composition is illustrated in Figure 6. In a temperature‐induced fragility transition, a system always becomes more fragile at higher temperatures simply because more constraints are broken as the temperature is increased.

Mauro et al. [8] made an interesting observation in the binary alkali‐borate melt xM₂O·(1 − x)B₂O₃ systems where T_g appears to be a constant function of composition for a small composition range. They called this composition range the “iso‐T_g regime” (Figure 4). The iso‐T_g step results when a bond constraint breaks exactly at T_g. It can be shown that, within the iso‐T_g regime, the fragility remains constant and equal to the low value of about 16 that is observed for strong glasses. Interestingly, the composition range of the iso‐T_g regime (at least in the alkali‐borate system) is nearly the same as that of the reversibility window observed by Boolchand and colleagues [22]. This coincidence raises the possibility of some connection between the two phenomena, an area that requires further investigation.

Figure 6 Contrast between strong (SiO₂) and highly fragile (O‐Terphenyl, OTP) in plots of viscosity against reciprocal temperature, and intermediate cases of liquids fragile at high temperatures and becoming strong at low temperatures (water, glass‐forming metals) through a diffuse transition (cf. Chapter 3.8;

Source: From [35]).