In this investigation, we focus on the glass formation and crystallization process of Ag, Au pure metals as well as Ag-20%Au, Ag-50%Au, and Ag-80%Au (Atoms%) random alloys at the nanoscale. The thermodynamic properties such as solidification temperature and cohesive energy were calculated in the NVT ensemble by the molecular dynamics (MD) simulation technique. The Quantum Sutton-Chen (Q-SC) potential was used to study phase transition and thermal properties of nanoparticles. The temperature dependence of energy was calculated at various concentration of Au. Moreover, the solidification of pure nanoparticles, Ag, Au, and Ag-x%Au nanoalloys were studied at different cooling rates. Our molecular dynamics simulation results show glass structure at fast cooling rates while crystallization at a slow cooling rate. Moreover, the obtained results show that the solidification temperature decreases with decreasing nanoparticle size.