In this paper, we provide a theoretical basis using thermodynamic stability analysis for explaining the spontaneous nucleation and growth of a high density of 1-D structures of a variety of materials from low-melting metals such as Ga, In, or Sn. The thermodynamic stability analysis provides a theoretical estimate of the extent of supersaturation of solute species in molten metal solvent. Using the extent of maximum supersaturation, the size and density of critical nucleus were estimated and compared with experimental results using nucleation and growth of Ge nanowires using Ga droplets. The consistency of the proposed model is validated with the size and density of the resulting nanowires as a function of the synthesis temperature and droplet size. Both the experimental evidence and the theoretical model predictions point that the diameters of the resulting nanowires decrease with the lowering of synthesis temperatures and that the nucleation density decreases with the size of metal droplet diameter and increasing synthesis temperature.