Haberland's team used a laser technique known as photofragmentation to measure the internal energy of the clusters at different temperatures. Photons deliver energy to the clusters - each containing 147 sodium atoms - prompting atoms to evaporate. The researchers determined how much energy the clusters absorbed from the number of atoms ejected. This yields the energy-temperature profile of the clusters from which the researchers calculated their heat capacity. They found that, around the melting point of the clusters, the temperature fell as the energy increased - in other words, the heat capacity was negative. This phenomenon is expected to exist in many small clusters of atoms. Haberland's team chose sodium atoms because their electronic structure is simple and well understood.

We are familiar with how large quantities of solids melt. When we warm an ice cube, for example, the kinetic energy or heat is converted continuously into the potential energy needed to break down the crystalline structure. This is the latent heat that increases the entropy of the system without raising the temperature. The amount of solid in the ice cube decreases evenly as it melts. In bulk quantities of ice, only a minuscule fraction - around 10-7 - of the atoms are at the interface between solid and liquid. This ratio makes the increase in entropy energetically favourable.

In contrast, a large fraction - around 20% - of the atoms in tiny clusters are at the interface between the liquid and solid phases. This makes a partially melted state energetically unfavourable. Consequently, the atoms convert some of their kinetic energy into potential energy to help the melting process. The temperature therefore falls - even though the total energy has increased.

Haberland told PhysicsWeb that although an application for the discovery may be some way off, it is nevertheless a significant contribution to our understanding of atomic systems, which is crucial in the rapidly expanding field of nanotechnology.

Physicists have observed similar phenomena in fragmenting nuclei and astronomical objects, suggesting that they share a certain characteristic. Haberland notes that none of these systems can be treated as simple aggregates of their parts. Local effects - for example, gravity between different parts of a binary star system - must be taken into account. A star system sounds enormous compared atom clusters, but is actually very small in terms of the long-range action of gravity. "When Donald Lynden-Bell first applied the concept of negative heat capacity to astrophysical systems, the physics community thought it was nonsense", said Haberland, "but we have proved that the phenomenon is real".