The present paper is part of a general investigation of the thermodynamic properties of metal-semiconductor systems involved in the nanowires growth. Here, we will show that many aspects of the growth mechanisms, such as the surface curvature of the solid phase (in the nano or micrometer range), in equilibrium with the liquid phase are extremely important. We calculate and construct all binary Au-Si phase diagrams corresponding to nanosystems. By choosing the S(V)LS process rather than the VLS process, we succeeded in answering not only the origin of the driving force needed to trigger off the precipitation of solid nanowire but also the thorny question of the size limit of nanowires in relation with our specific growth conditions.