Encyclopedia of Glass Science, Technology, History, and Culture. Группа авторов
systems to a widely used scheme for modeling variations of properties with composition in multicomponent glasses and glass‐forming liquids. The trends predicted by TCT are in good agreement with experimental results. This is largely because TCT takes as input the observed or modeled variation of topology with composition and a fundamentally sound temperature‐dependence of chemical bond strengths. In this sense, TCT represents a major leap in the development of science‐based engineering of new glass compositions.
In spite of its success, several limitations and fundamental issues remain unresolved. We list some of these here.
1 For systems with short‐range interactions where BCT is applicable, it is unclear when to treat the angular constraints as broken (even at low temperatures). For example, why is the angular constraint broken at oxygens in silica? Are they broken at Se in selenides? It appears that angular constraints are intact primarily in group III, IV, and V elements that exhibit sp(n) hybridization. Clearly, a more detailed understanding of the basis of the angular constraints will lead to more accurate predictions of BCT.
2 Extension of TCT to systems with long‐range potentials (especially ionic interactions) remains vague and questionable at present. Whereas BCT applies only to systems with short‐range covalent interactions, PCT works better for ionic systems. The effects of chemical order in BCT and of chemical disorder in PCT need further examination. There is a clear need for a more fundamental basis for applying TCT to chemically disordered systems having long‐range interactions.
3 It has been noted that the rigidity percolation threshold may not occur at a single composition, but over a range of compositions because of either localization of constraints or localization of degrees of freedom in an otherwise isostatic matrix. Whereas a discussion of iso‐Tg range is presented, there does not exist at present a theory to determine the rigidity percolation composition range.
4 The role of intermediate‐range topology (ring‐size distribution) in determining the deformation of a network remains unclear. For example, edge‐sharing between tetrahedra in the Ge–Se system appears to have no effect on the BCT results since both edge and corner sharing give rise to identical short‐range topology (i.e. the same value of r).
5 Whereas an approximate relation between configurational entropy and degrees of freedom has been discussed, a more rigorous understanding of constraints (or degrees of freedom) in general in terms of features of the PEL is needed to embed the TCT in the general statistical physics of the disordered condensed state.
6 The minimum free‐energy configuration in the supercooled liquid state corresponds to the most probable network configuration. Thus, a relationship between the free energy of the supercooled liquid and the nature of constraints is expected. Establishment of such a relationship will provide a sound thermodynamic foundation of TCT and will provide answers to the important questions as to why good glass‐forming compositions are also low‐temperature eutectics.
7 All systems have configurational fluctuations at a finite temperature. The present formulation of TCT applies only to the average network configuration so that the influence of fluctuations is not accounted for. Clearly, extension of TCT to include configurational fluctuations is desirable to model fluctuation‐based properties.
In spite of these limitations, it is important to emphasize that the success of TCT in some systems has been remarkable. But with increasing need to apply TCT to a large variety of systems, it is necessary to develop a theoretically sound basis to resolve these issues.
Acknowledgements
The author is extremely thankful to both reviewers for their thoughtful comments.
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