Crystal growth model with stress development and relaxation

During crystallization of glass-forming melts an important amount of stress energy may develop. The reason for this development is the difference in volume of the new system and that in the ambient phase. Therefore, the growth rate decreases with time. Here we develop an algorithm for the process of crystallization using Monte Carlo simulation techniques that takes into account the stress energy. We find that there is a short period of initial fast growth stage followed by a second period of much slower growth, controlled by the relaxation rate. This picture has also been recently observed experimentally. Additionally, we find that during the growth process the shape of the crystal is changing. Although we start from a highly symmetric crystal with flat 〈10〉 interfaces, a shape with a large number of facets is soon created. Copyright c © EPLA, 2010 Introduction. – Crystal growth has been a very challenging topic over the years. Therefore, a large number of models and approaches were developed in the effort to better understand the microscopic mechanisms of growth, refs. [1–3]. Recently, a new model was suggested combining ideas from percolation theory and the glass-forming ability of silicates, refs. [4–7]. Most glass-forming systems consist of networks in which the network formers, NF, are connected via oxygen bridges. The network is “floppy” or “rigid”, depending on the number of broken oxygen bridges (NBO) per NF. According to the theoretical model developed in refs. [8–12], as well as from experimental estimations, refs. [4–7], the threshold number for the floppyto-rigid transition is NBOc = 1.6 for glasses composed by network formers with coordination number 4. If NBO is less than this critical value, the network is rigid. However, in such networks there are still some tiny floppy regions as this was experimentally proved in refs. [4,5]. Recently, ref. [13], it was shown that the exact threshold conditions for the rigid/floppy transition depend on the dimensionality of the space and on the coordination number. Moreover there is a NBO concentration interval, although relatively narrow, in which both rigid and floppy clusters percolate simultaneously in the system. In this concentration (a)E-mail: [email protected] interval the system behaves as floppy with respect to the diffusion of ions. At the same time, the existing rigid skeleton will make the system to behave as rigid with respect to the retaliation of deformations. Studying this behavior is one of the objectives of the present investigation. The present investigation aims to describe crystallization in multicomponent systems. Our basic starting assumption is that we expect some stress energy to develop, impeding the crystal growth. At a first stage, as the crystal grows, nuclei are formed inside the floppy regions of the glass. The size and concentration of these floppy regions in a rigid matrix is a type of percolation problem. We expect that the crystal can grow relatively fast until the entire floppy region is occupied. Further crystallization has to propagate inside the rigid region and it is to be accompanied by stress development. This is of particular importance if the chemical composition of the growing crystal is different from that of the ambient phase. Viscous relaxation could reduce, or even eliminate, the inhibiting effect of elastic stresses. This is why in most cases the effect of internal stress is neglected. The common argument is that stress energy is relaxing too fast to affect crystal nucleation or crystal growth. If the two scales (of growth rate and of relaxation rate) are comparable, the stress energy will not have enough time to dissipate completely during the crystallization. Although the relaxation time is long near the glass transition temperature,