  This review is on the phase field modelling studies in elastic stress effects
on microstructural instabilities. We will focus primarily on four elastic
stress driven instabilities: (i) Spinodal phase separation; (ii) Particle
splitting; (iii) Rafting; and, (iv) Asaro-Tiller-Grinfeld (ATG) instabilities.
This review is organised as follows: in Section 1, we briefly describe some of
the important and interesting experimental observations on elastic stress
effects on microstructural instabilities; in Section 2, we describe, in
reasonable detail, the theoretical developments in understanding the effects of
elastic stress on microstructural instabilities in solids. Both Section 1 and 2
are neither comprehensive nor complete; however, they are helpful in setting
the stage for discussion of (and, in giving a perspective on) phase field
modelling studies that will be discussed in Section 3. In Section 4, we
conclude with a summary and indication of future directions.
