Glass pair-correlation function

Chapter 4 deals with the local dynamics of polymer melts and the glass transition. NSE results on the self- and the pair correlation function relating to the primary and secondary relaxation will be discussed. We will show that the macroscopic flow manifests itself on the nearest neighbour scale and relate the secondary relaxations to intrachain dynamics. The question of the spatial heterogeneity of the a-process will be another important issue. NSE observations demonstrate a subhnear diffusion regime underlying the atomic motions during the structural a-relaxation. 

FIGURE 20.14 Pair correlation function for the case of a liquid, of glass, and/or amorphous solid. (From Gcpel, W. and Wiemhcfer, H.-D.,Statistische Thermodynamik, Spektrum Akademischer Verlag, Heidelberg, Berlin (2000).)... 

All the scattering expressions discussed above are relevant for single component materials. But most glasses are multicomponent materials and consist of several atoms with different scattering factors. In a material consisting of n different atoms, there are n n- )l2 pair correlation functions and each of them contribute to the observed scattering intensities. 

The MSDs are obtained by considering both ensemble and time averages. Particle coordinates having been known, the pair correlation functions are readily obtained. These pair correlation functions can be combined with the atomic scattering factors for the respective atoms and then convoluted to obtain a combined pair distribution function, which can be compared with experimental RDF. This is a vital step in the glass structure simulations. 

Viscous flow sets in only above about 0.6 of the glass transition temperature 7g which for many technical interesting alloys is between 400 and 600°C. Even though amorphous metals have an atomic structure (usually described by the pair correlation function) that is similar to the corresponding alloy in the liquid state, their viscous flow resembles rather the behavior of crystalline metals than those of liquids. 

The static structure factor can be Fourier transformed into real space to give the pair correlation function, g(r), which is proportional to the probability of finding an atom at a position r relative to a reference atom at the origin. Due to the isotropic nature of liquids and glasses it is only necessary to consider the distance from the reference atom hereafter the vector dependence becomes a magnitude dependence. Therefore the pair correlation function, g(r), is expressed in terms of S(q) ... 

The structure factors, S q), and pair correlation functions, g r) of Sb2Tc3 and Sb2Te in the liquid and amorphous phases are shown in Fig. 18.2. If the overall agreement between experiment and simulation is reasonable, it is not as good as in the case of other chalcogenide glasses, such as GeSc2 [22]. It was established [23] that the discrepancy is mostly due to an over coordination of Te atoms in DFT calculations. However, AIMD simulation reproduce all trends observed experimentally. 

FIGURE 21.7 Pair correlation and radial distribution function (RDF) for Figure A micro-structure. Results analogous to RDF for an atomic glass. ... 

---