Study of Glass Transition Based on the Fragmentation Model
- PDF / 306,517 Bytes
- 6 Pages / 414.72 x 648 pts Page_size
- 81 Downloads / 216 Views
Further,
thermodynamic aspects were discussed using the model and it was concluded that the glass transition is a sort of the first order transition. INTRODUCTION To explain complex phenomena observed for glass transition, we have developed a new model based on the fragmentation of a glass system [1,2]. The outline of the fragmentation model is as follows: Non-crystalline solids are assumed to be an assembly of pseudo-molecules or structural
units.
When the non-crystalline solid is heated, a bond breaking process becomes dominant
compared with a rebinding process of broken bonds. At high temperatures, successive bond breaking causes the fragmentation of the solid. As the temperature is further increased, the fragment size becomes smaller and the hole density due to an increasing free volume increases. As a result, the viscosity of the system rapidly decreases with increasing temperature. From the view points of fragmentation model, stoichiometric V2 -VI 3 compounds are interesting materials because they are semiconductive even above their melting points T,, [3]. This implies that some structural unit with semiconductive characters exists in the liquid state, probably due to the structural stability. In noncrystalline solids, it could be thought that the system decomposes gradually toward the structural units containing a certain number of atoms because of its structural randomness with a large number of defects, i.e., the fragmentation process occurs. In this paper, we first briefly describe the fragmentation model and then illustrate the application of the model to a fictive stoichiometric V2 -VI 3 compound. Finally, thermodynamic 369 Mat. Res. Soc. Symp. Proc. Vol. 398 01996 Materials Research Society
aspects based on this model is given. BRIEF REVIEW OF FRAGMENTATION MODEL Amorphous materials are known to involve a number of dangling bonds, weak bonds and wrong bonds. At high temperature, bond breaking takes place briskly, but some pairs of broken bonds rebind again. The number of bonds per unit volume N(t) at time I is determined by solving the rate equation: dN(t)/dt = kfN(t) - (1/2) kr nD(), where nD is a dangling bond density, kf(=Fexp[-Ef /kBT]) and kr (=Rexp[-E /kBT]) the rate constants for the forward and backward reactions, T the 2
temperature in Kelvin and kB the Boltzmann constant. Supposing N(t)-NO-(1/ )nD(t) and the system
be heated up at a constant heating rate a (T(t)=T 0+ai), the solution of the rate equation above is given by [1]:
T1 0
flD(T) (C (T) +NDYOCXP
CfTa'T
k W(X)
T
(1)
-4fT0kf(x) +kr(x) I
-fT ax
Lkf (z)+
k,
z)
d
(2
where ND0 is a dangling bond density at T=T 0 (T0 : an initial temperature) and No the bond density. As temperature increases, microcracks are expected to arise here and there in the solid, and to spread out due to successive bond breaking, so that the network would at last breaks into fragments. According to the original paper of the fragmentation model [1], the fragment density is estimated as a function of nD, i.e., functions of T and a, assuming the f
Data Loading...
