Читать книгу Encyclopedia of Glass Science, Technology, History, and Culture - Группа авторов - Страница 294

For the binary Ge_xSe_(1−x) system, the average coordination number r(x) is (2 + 2x) since r(Ge) = 4 and r(Se) = 2, and the system is isostatic at x* = 0.2 (corresponding to the Ge_1/5 Se_4/5 composition). According to Tichy and Ticha [28], however, the best glass‐forming compositions lie on the Se‐rich side in the range 0.06 < x < 0.15. To rationalize this apparent discrepancy, Tichy and Ticha [28] suggested to view the Ge_xSe_(1−x) system as an extended chemically ordered network of short, linearly‐rigid (Se)_k chains containing k seleniums that are cross‐linked by Ge atoms. The ends of the Se chains are connected to Ge atoms so that four such chains share a Ge atom. Note that since x = 1/(1 + 2 k), k is 2 at x = 0.2. A network with k > 2 (corresponding to x < 0.2) should be floppy (f > 0). However, one can show that some of the degrees of freedom (let us denote these by f ^# ) in such a network for x < 0.2 are associated with the dihedral rotation of the inner seleniums (Se^#), those inside the selenium chains (–Se–Se^#–Se–). A Se^# atom can rotate dihedrally about the line joining its two neighboring Se without influencing the deformation pattern of the network (Figure 2). This is one example where certain internal degrees of freedom decouple from the rigidity of the overall network. In another example the extra degrees of freedom associated with a singly coordinated atom (i.e. a dangling vertex) decouple from the rigidity of the overall network. Clearly such decoupled degrees of freedom can be disregarded as far as network rigidity is concerned. The network, therefore, can satisfy the isostaticity condition in the range x < 0.2 by forming chemically ordered networks with an appropriate value of the k for the Se‐chains. A value of k = 3 corresponding to x = 1/7 (or about 0.14) is close to the composition where best glass formation is observed, explaining why good glass formation takes place for x < 0.15.

Figure 2 Schematic of a Se‐chain with five seleniums connecting two Ge atoms in an isostatic network (not shown). The inner Se^# can rotate dihedrally about the dashed line connecting its neighboring seleniums without influencing the rigidity of the network. This dihedral motion of inner seleniums is an internal degree of freedom decoupled from the rigidity of the overall network.

For x > 0.2, there is experimental evidence for edge‐shared GeSe₄ tetrahedra [29]. Because the presence of edge sharing does not change the value of r, the BCT results are not affected but edge sharing does cause differences in the intermediate‐range topology. When one considers a pair of edge‐shared tetrahedra as a single unit with four Se vertices (and two internal Ge atoms), such a bi‐tetrahedral unit has an internal degree of freedom, namely rotation about the shared edge. This additional flexibility allows isostaticity to hold beyond the GeSe₂ composition (x = 1/3) in the PCT formalism even though the BCT results do not change. It is also clear that the presence of Ge–Ge homopolar bonds [16] – that must exist for x > 0.33 – does not influence the short‐range topology of the network. Hence, the BCT consequences do not change.