Size and shape-dependent formation enthalpy of binary alloy nanoparticles

The size- and shape-dependent formation enthalpy has been studied based on size and shape-dependent cohesive energy, where the shape effect is described by the shape factor. For Cu–Au alloy particles, the formation enthalpy is more negative than that of the bulk alloy. For Cu–Ni alloy particles, the formation enthalpy is negative despite of the positive value of bulk. To study the shape effect on formation enthalpy, the cubic and the spherical nanoparticle are discussed in details. There are eight shape configurations for the initial pure metallic particles and the alloy particles. By calculation of the formation enthalpy of Cu–Au and Cu–Ni alloy nanoparticles, it is found that the most negative formation enthalpy is for cubic+cubic→spherical case, and the highest energy is for spherical+spherical→cubic case. The curve of formation enthalpy may be approximately symmetric if the initial shapes of the two pure metallic particles are the same and asymmetric if the two initial shapes are different. The shape effect on formation enthalpy decreases with increasing the particle size. The present results also suggest that one may prepare some non-spherical alloy particles experimentally in some concentration ranges although the bulk elements are immiscible.