Abstract
A temperature-size (T-N) phase diagram is derived for Na clusters of up to N\ensuremath{\sim}1000 atoms. It is based on first-order pseudopotential calculations and the Lindemann criterion for melting. It contains three regions of stability: (1) a liquid (jellium) phase at temperatures above the melting line ${\mathit{T}}_{\mathit{M}}$(N); (2) a phase related to the body-centered-cubic structure at temperatures below the melting line; and (3) a close-packed structure at very low temperatures and sufficiently large N. The melting line drops to ${\mathit{T}}_{\mathit{M}}$(N)=0 for N65. The phase diagram reduces asymptotically to the known phases of Na as N\ensuremath{\rightarrow}\ensuremath{\infty}, including the known martensitic transformation at T\ensuremath{\approxeq}5 K.
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