On increased variance of coherent solids

In order to explain the experimentally observed and previously discussed in the literature increased variance of coherent solids (J.W. Cahn, F. Larché, Acta Metal. Mater., 32 (1984) 1915; W.C. Johnson, Metall. Trans. Ser. A 18A (1987) 1093; R.O. Williams, Metall. Trans. 11A (1980) 247; M.E. Gurtin, Thermomechanics of Evolving Phase Boundaries in the Plane. Clarendon Press, Oxford, 1993; Z.-K. Liu, J. Ågren, Acta Metal. Mater., 38 (1990) 561–572) we propose a simple qualitative model featuring the concept of a coherent interface which is characterized by residual stress (in the form of surface tension) and is capable of supporting force. The mechanical implications of this idea introduced earlier (see, e.g. M.E. Gurtin, Thermomechanics of Evolving Phase Boundaries in the Plane. Clarendon Press, Oxford, 1993) have been analyzed elsewhere; here an emphasis was made on its metallurgical aspects as related to the problem of coherent phase equilibria, and also on the corresponding changes in the thermodynamic variance of such systems. The existence of such interfaces may result in the violation of the traction continuity requirement between coherent coexisting phases and automatically results in a situation when the number of degrees of freedom of a system, f, depends only on the number of components, k, and is independent of the number of phases, f=k+1. An interesting similarity of the phase rule for coherent solids in the form f=k+1 to the one derived earlier for capillary systems, is also discussed.