Pressure induced amorphization of AlPO4

AlPO₄ has been compressed to pressures of 16 GPa in a diamond anvil cell and its X-ray diffraction pattern studied by the energy-dispersive technique. The compound is observed to become amorphous at ∼ 12 GPa. This explains the loss of Raman spectrum of AlPO₄ reported by Jayaraman and coworkers (1987).     

A stochastic theory for clustering of quenched-in vacancies-V. Temperature dependence of cluster density

It is known that the density of vacancy loops in quenched aluminium and stacking fault tetrahedra in quenched gold show a saturation for low ageing temperatures. The physical mechanism leading to this effect is not well understood. In this paper we consider a simple model which allows us to obtain the temperature dependence of total density. The analysis shows that the plateau region arises due to the fact that the number of absorption sites of a cluster is larger than the number of emission sites. The temperature dependence of the average number of vacancies in a cluster and the single vacancy concentration in equilibrium with the clusters are discussed.     

Stochastic theory for clustering of quenched-in vacancies—1. General mathematical properties

The problem of clustering of quenched-in vacancies into various types of extended defects is considered. A master equation for the evolution of the concentration of clusters of various sizes is written down with general transition rates. It is shown that this model represents a continuous time non-stationary Markoff process. A particular choice of transition rates corresponding to the formation of vacancy loops and stacking fault tetrahedra is considered in some detail. It is shown that this choice of transition rates allows us to obtain the solution for the concentration of the single vacancy units, and hence yields some information on the nucleation time. Further, the transition matrix becomes stationary and doubly stochastic due to the short time constant of the concentration of single vacancy units. This in turn leads to an unphysical stationary state. Finally we show how the rate equations for the irradiated situation can be written down and derive the phenomenological rate equations that are conventionally used.