Multicomponent atomic clusters (i.e. nanoalloys) are currently a subject of intense interest because their properties can be tuned by adjusting the cluster size and composition. Previous work has demonstrated the sensitivity of cluster structure and melting temperature to the presence of a single dopant atom. This thesis theoretically examines the effect of a single dopant on the solid-solid transitions of LJ clusters characterised by a double-funnel energy landscape. The incorporation of a dopant atom into LJ38 or LJ31 offers a tunable change in the transition temperature between two competing solid states by influencing the potential energy and vibrational entropy of low-lying minima. A two-state approximation is utilised to calculate the solid-solid transition temperatures and is shown to agree with trends in heat capacity features even when only one minimum is used to describe each solid state. The observed sensitivity of preferred cluster geometry to a single dopant and resulting trends in solid-solid transition temperature provide a theoretical precursor for the structural control of solid-state nanoalloys.