Polycluster Structures

A structure model must be based on a noncontradictory, closed and complete definition. A definition is closed if it does not contain indefinite elements and notions, and it is complete if it includes the description of all structure elements. Thus, for instance, the model in which the amorphous structure is considered as a dislocationally disordered crystal [6.21, 22] becomes not closed if the dislocation structure (in particular, the one of dislocation core) is not defined. At high density of dislocations when their cores may overlap and their structure becomes very indefinite, the model is not closed. The free-volume model [6.23 25], in which the question about geometry and topology of atomic configurations is put aside, is not complete. 

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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). 

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. 

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... 

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]. 

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). 

Our main aim was to clarify the role of clusters in the process of liquid solidification and to show that formation of the polycluster glass structure is a typical result of this process. On the basis of the developed approach, such important problems as entropy crisis and relaxation phenomena in supercooled liquids can be considered in detail, but this is far from the topic of this paper and will be considered elsewhere. 

A.S. Bakai Polycluster amorphous structures and their properties. Preprint KFTI, 84-33 (TSNII Atominform, Moscow 1984) (In Russian)... 

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