Small particles have a lower melting point than bulk material 1 . The physical cause lies in the fact that small particles have a higher proportion of surface atoms than larger particles-surface atoms have fewer nearest neighbours and are thus more weakly bound and less constrained in their thermal motion 2,3 than atoms in the body of a material. The reduction in the melting point has been studied extensively for small particles or clusters on supporting surfaces. One typically observes a linear reduction of the melting point as a function of the inverse cluster radius 2,4,5 . Recently, the melting point of a very small cluster, containing exactly 139 atoms, has been measured in a vacuum using a technique in which the cluster acts as its own nanometre-scale calorimeter 6,7 . Here we use the same technique to study ionized sodium clusters containing 70 to 200 atoms. The melting points of these clusters are on average 33% (120 K) lower than the bulk material; furthermore, we observe surprisingly large variations in the melting point (of Ϯ30 K) with changing cluster size, rather than any gradual trend. These variations cannot yet be fully explained theoretically.The melting point (T melt ) of small particles is not only of scientific interest, but also has some technological implications. In sintering processes, fine powders are compressed and heated until they coalesce. If extremely fine powders are employed, a lower sintering temperature could be used. Also, the present drive towards nanoscale technology leads to smaller and smaller geometric dimensions with a concomitant reduction of T melt and consequently reduced electrical and mechanical stability at elevated temperatures.The standard way to measure T melt of a material is to heat it and record the temperature at which it becomes liquid. In order to do this, one needs some physical property which changes measurably at T melt . For example, the electron-diffraction pattern of a crystalline solid, which vanishes on melting, has been used to study the melting of small particles supported on surfaces 4,5 or in cluster beams 8 . In both cases one has to work with broad size distributions. Moreover, in the case of the surface experiments the physical properties of the clusters could be affected by the surface contact. There exist two earlier experiments on the melting of free, size-selected clusters: one studied the temperature dependence of the ionization energy of sodium clusters 9 , the other looked for a transition of methanol hexamers 10 .A deeper insight into the solid-to-liquid phase transition may be gained by measuring the relation between temperature and internal energy across the melting point. For a macroscopic material this is achieved by placing the sample in a thermally insulated box, containing an electric heater and a thermometer. Some known amount of energy U is supplied to the material by heating, and its temperature T is measured. The relation between temperature and energy, U ¼ UðTÞ, is called the caloric curve, its derivative is the heat capaci...

There exists a surprising theoretical prediction for a small system: its microcanonical heat capacity can become negative. An increase of energy can-under certain conditions-lead to a lower temperature. Here we present experimental evidence that a cluster containing exactly 147 sodium atoms does indeed have a negative microcanonical heat capacity near its solid to liquid transition.

The heat capacity of a free cluster has been determined from the temperature dependence of its photofragmentation mass spectrum. The data for the spherical sodium cluster Na 1 N , with N 139, show a maximum at 267 K, which is interpreted as the solid-to-liquid phase transition in this finite system. The melting point lies 104 K, or 28% lower than that of bulk sodium. The latent heat of fusion is reduced by 46%.

The large collective resonance of the spherical cluster Na 1 93 has been studied using a femtosecond laser, which directly excites the resonance. Photofragment size and charge distributions have been measured. A large intensity of doubly and triply charged fragments has been observed, which is absent when applying nanosecond laser pulses of the same wavelength and pulse energy. The efficient ionization processes can be understood as autoionization of the multiply excited collective resonance. A simple rate model gives an estimate of about 10 fs for the lifetime of the resonance.[ S0031-9007(97)

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