The nanoparticle phase diagram of an immiscible system is studied at the atomic level. Cu-Ag clusters with sizes 1000 and 2000 atoms, resulting from a global minimum search and belonging to icosahedral and crystalline structural motifs, are considered. We present the statistical analysis of the effect of temperature on the solubility of the two elements based on Metropolis Monte Carlo importance sampling. Our results suggest that the relevance of bulk phase diagrams to nanoparticles is limited to cases where the internal stress distribution does not deviate very much from uniform (e.g. sufficiently large crystalline clusters). In the general case, the principal interdependence between partial phase compositions and the overall cluster composition in nanoparticle phase diagrams need to be taken into account.