In the context of the investigation of particle formation, a potential model by means of the embedded atom method is developed for the hexagonal close packed metal zinc. This type of model includes many-body interactions caused by delocalised electrons in metals. The effective core charge as function of the distance is calculated here by an integral over the electron distribution function rather than fitting it to experimental data. In addition, the dimer potential is included in the parameterisation because we focus on the formation of nanoparticles from the vapour phase. With this potential model, the growth of zinc clusters consisting of 125 to 1000 atoms is investigated, which takes place at elevated temperatures in a liquid-like cluster state. The growing clusters are embedded in an argon carrier gas atmosphere which regulates the cluster temperature. The average thermal expansion of the clusters and the different lattice constants are analysed. For the determination of the cluster structure, the common-neighbour analysis method is extended to hexagonal close packed surface structures. During growth, small clusters with less than approximately 60 atoms develop transient icosahedral structure before transforming into hexagonal close-packed structure. The surface of the clusters exhibits a transformation from planes with high surface energy to the most stable ones. Besides ambiguous surface structures the final clusters are almost completely in an hexagonal close packed structure.