Polycluster

Similarly, the reaction of several I with each other may form a polymeric chain of clusters ( polycluster ) as in reaction 5... 

Fig. 6. Infinite chain of the polycluster in 13. The pj-oxygen atoms and propionate ligands were omitted for the sake of clarity, The O—H—O bonds in the H3O7 ligands are represented by dotted lines. Ref. 3...

Fig. 7. The infinite chain of polycluster in 14. The H3O2 ligands are represented by dashed lines. Ref. 25...

Contrary to a periodic lattice, the symmetry of which is entirely characterized by its space group, the description of an amorphous structure faces the problem of no long-range order and of a local coordination that varies from site to site. The polycluster description of amorphous solids is a classification based on a set of Coordination Polyhedra (CP) for each atom determined by its nearest neighbors. Topologically equivalent polyhedra form classes and are referred to as... 

This chapter is the introduction to the physics of polycluster amorphous solids. At first the polycluster model was developed as a constructive foundation to describe some properties of metallic glasses. The assumption about the presence of a comparatively perfect local order (LO) (not necessarily of one type) leads naturally to the definition of the locally regular cluster (LRC), after which one must make only one step (not quite ambiguous) to introduce the definition of the polycluster structure. From this definition, there evolves the description of structure defects (Sect. 6.4). 

Studying the kinetics of the liquid-solid transformation shows that the polycluster-structure formation competes with crystallization and, under certain conditions, it becomes dominant and leads the liquid to transfer to the glassy state (Sect. 6.2). 

In the phenomena of reversible and irreversible relaxation in metallic glasses, the low-energy excitations connected with the rearrangement of atomic configurations including the tunneling states play an essential role. The description of low-energy excitations and diffusion mechanisms in polyclusters is contained in Sects. 6.6 and 6.7. 

In the physics of glasses, the clarification of the nature and the description of the glass-liquid transition are of particular interest. In polyclusters, the restoration of ergodicity begins with the melting of boundaries. The thermodynamics of this transition is considered in Sect. 6.8. 

The mechanisms of plastic deformation and mechanical states of polyclusters are described in Sect. 6.9. The comparatively high density of cluster boundaries (experimental data point to the fact that cluster sizes are about 102a, a being the average interatomic distance), peculiarities of structure and displacement of dislocations under the action of stress determine the dominant deformation mechanisms in some region of temperature T and stress a. 

It needs to be established whether the concept and model developed are adequate to real objects. This question is answered to some extent by the experimental data given in Sects. 6.3 and 6.5. We also discuss briefly some other structure models of metallic glasses to establish the connection between them and the polycluster model (6.4.5). 

One may say that the polycluster model has deep historical roots despite the fact that its formulation was not directly connected with the development and formalization of the ideas existing earlier about the structure of nonmetallic and metallic glasses. The common features of different approaches in the description of any object are usually prompted by the nature of the object itself and by the requirement that the assumptions suggested do not contradict the firmly established experimental facts. 

The main purpose of this section is to give an account of general peculiarities of the microscopic scenarios of the supercooled liquid solidification and to show that formation of the polycluster glasses is a commonplace case. A more detailed consideration of the supercooled liquid structure, its thermodynamics and solidification kinetics is given in Sect. 6.10. 

Al the basis of the polyclustcr model, there lies the assumption of the presence of one or several types of atom LO in a solid. At this point, the polycluster model is close to the so-called stereochemical models [6.8]. Besides, it includes the definition of a cluster as a set of locally ordered atoms and the definition of the boundaries as the closing of this set. Finally, the assumption that clusters conjoin along common boundaries completes the definition of a polyclustcr structure. The polycluster model includes a rather wide set of structures. This model was suggested in [6.26, 27] and developed and applied while describing various properties of metallic glasses [6.28 33]. 

Fig. 6.6. A fragment of the 2-D polycluster Intercluster and inner boundaries are shown, -regular sites, O-coincident sites, -noncoincident sites...

It can be demonstrated [6.27] that Elnl(N, m) has its maximum at m N/2, when the elastic compression fields generated by partial interstitials essentially compensate for the elastic extension fields surrounding partial vacancies. At m as N/2, the configurational entropy of the complex is also maximum. Therefore, m w N/2 is the most probable number of atoms disposed in the complex of N noncoincident sites, so that nearly one half of the noncoincident sites is occupied by atoms, and another half is vacant. The existence of two-level systems, high diffusion mobility of atoms along non-coincidence sections, low-energy structural fluctuations in polyclusters is connected with this circumstance (Sect. 6.6). 

Note that the 3-D model is considerably more complicated than its 2-D analog. It seems desirable to add this model with a consideration of cluster energetics (free energy) and to perform the natural generalization including the extended defects, i.e., dislocations and boundaries, as a result of which an example of polycluster structure would be obtained. 

The presence of one or several types of LO for the dominating number of atoms is, essentially, a sufficient condition for the existence of a polycluster structure. Therefore, the experimental data on LO in real metallic glasses becomes important. 

The low-energy excitations described above contribute essentially to the reversible relaxation processes [6.32], to the internal friction [6.33], and to the specific heat. The expressions for the excitation contributions ii)—iii) to the specific heat are given in [6.29, 30], where it is also shown that cooperative rearrangements iii) contribute greatly to the melting of cluster boundaries which is treated as the glass-liquid transition in polyclusters (Sect. 6.8). 

In polyclusters, atoms can diffuse on vacant cavities, viz., regular vacancies, interstitial holes in the LRC bulk, and partial vacancies or vacant coincident sites at the boundaries. Since the formation and migration energies of regular... 

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