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4.1 Non‐ergodicity and Elastic Moduli
ОглавлениеBeyond the length scales of LRO and MRO are the DFs characteristic of the liquid state. They originate from the dynamics of the liquid state in thermodynamic response to temperature and pressure. Whereas liquids are in equilibrium and ergodic above the melting point, supercooled liquids are non‐ergodic at Tg, which is reflected in the size of the non‐ergodicity factor f(Q,T) (Section 2). In particular f(Q → 0,T) is related to the magnitude of DFs, and as T → Tg, a dynamic crossover occurs to non‐ergodicity – typically ~1.2Tg. On vitrification DFs increase in amplitude and eventually become frozen in.
In glasses the spatial extent and amplitude of DFs can be determined from IXS and S(0) [1]. In glass formers DFs are typically ≥20 Å in scale, their amplitude being proportional to the melt compressibility κ, which is greater for network glasses than metallic glasses, for example, reflecting the considerable differences in atomic packing (Figure 7). In network glasses like silica, light scattering from DFs limits losses in fiber‐optic applications [7]. Interestingly the amplitude of DFs is inversely related to Poisson's ratio, which is smaller for oxide glasses, which are usually brittle, than for many metallic glasses, which are tough [17].