Phase coexistence in clusters: An “experimental” isobar and an elementary model

Behind the Quantum and Size Effects: Broken-Bond-Induced Local Strain and Skin-Depth Densified Quantum Trapping of Charge and Energy

Shrinking the size of a solid down to nanometer scale is indeed fascinating, which makes all the otherwise constant physical quantities to be tunable such as the Young’s modulus, dielectric constant, melting point, etc. The variation of size also generates novel properties that can hardly be seen in the bulk such as the conductor-insulator and nonmagnetic-magnetic transition of noble metals at the nanoscale. Although the physics of materials at the nanoscale has been extensively investigated, the laws governing the energetic and dynamic behavior of electrons at such a scale and their consequences on the tunable physical properties of nanostructures have not been well understood [C. Q. Sun, Prog Solid State Chem 35, 1-159 (2007); Prog Mater Sci 54, 179-307 (2009)]. The objective of the contribution is to update the recent progress in dealing with the coordination-resolved energetic and dynamic behavior of bonds in the low-dimensional systems with consideration of the joint effect of temperature and pressure. It is shown that the broken-bond-induced local strain and the associated charge and energy quantum trapping at the defect sites perturbs the atomic cohesive energy, electroaffinity, the Hamiltonian and the associated properties of entities ranging from point defects, surfaces, nanocavities and nanostructures. Application of the theories to observations has led to consistent understanding of the behavior of nanometer-sized materials and the interdependence of these entities as well as the means of determining the bond energy through the temperature-dependent measurements.

Metal clusters with hidden ground states: Melting and structural transitions in Al115(+), Al116(+), and Al117(+)

Heat capacities measured as a function of temperature for Al(115)(+), Al(116)(+), and Al(117)(+) show two well-resolved peaks, at around 450 and 600 K. After being annealed to 523 K (a temperature between the two peaks) or to 773 K (well above both peaks), the high temperature peak remains unchanged but the low temperature peak disappears. After considering the possible explanations, the low temperature peak is attributed to a structural transition and the high temperature peak to the melting of the higher enthalpy structure generated by the structural transition. The annealing results show that the liquid clusters freeze exclusively into the higher enthalpy structure and that the lower enthalpy structure is not accessible from the higher enthalpy one on the timescale of the experiments. We suggest that the low enthalpy structure observed before annealing results from epitaxy, where the smaller clusters act as a nucleus and follow a growth pattern that provides access to the low enthalpy structure. The solid-to-solid transition that leads to the low temperature peak in the heat capacity does not occur under equilibrium but requires a superheated solid.

Metal clusters that freeze into high energy geometries

Heat capacities measured for isolated aluminum clusters show peaks due to melting. For some clusters with around 60 and 80 atoms there is a dip in the heat capacities at a slightly lower temperature than the peak. The dips have been attributed to structural transitions. Here we report studies where the clusters are annealed before the heat capacity is measured. The dips disappear for some clusters, but in many cases they persist, even when the clusters are annealed to well above their melting temperature. This indicates that the dips do not result from badly formed clusters generated during cluster growth, as originally suggested. We develop a simple kinetic model of melting and freezing in a system consisting of one liquidlike and two solidlike states with different melting temperatures and latent heats. Using this model we are able to reproduce the experimental results including the dependence on the annealing conditions. The dips result from freezing into a high energy geometry and then annealing into the thermodynamically preferred solid. The thermodynamically preferred solid has the higher freezing temperature. However, the liquid can bypass freezing into the thermodynamically preferred solid (at high cooling rates) if the higher energy geometry has a larger freezing rate.

Melting, freezing, sublimation, and phase coexistence in sodium chloride nanocrystals

Calorimetry measurements, performed by multicollision induced dissociation, have been used to probe the melting of a number of (NaCl)nNa+ clusters with n=22-37. The clusters anneal at 225-325 K and melt at 750-850 K. (NaCl)22Na+ and (NaCl)37Na+, which can adopt geometries that are perfect fragments of the bulk lattice melt at around 850 K. The other clusters, which (except for n=31) must have defects, melt at temperatures which are up to 100 K lower than the perfect nanocrystals. The internal energy distributions become bimodal near the melting temperature. This is the signature of slow dynamic phase coexistence where clusters spontaneously jump back and forth between the solid and liquid states with an average period that is longer than required for thermal equilibration. The jump frequency must be between 10(4) and 10(7) s(-1) for the bimodal distribution to be observable in our experiments. The (NaCl)nNa+ clusters can dissociate by an unusual thermally activated process where melting and freezing raise the internal energy to generate hot solid clusters that can sublime before they cool to the ambient temperature.

Structural relaxation in atomic clusters: master equation dynamics

The role of the potential energy landscape in determining the relaxation dynamics of model clusters is studied using a master equation. Two types of energy landscape are examined: a single funnel, as exemplified by 13-atom Morse clusters, and the double funnel landscape of the 38-atom Lennard-Jones cluster. Interwell rate constants are calculated using Rice-Ramsperger-Kassel-Marcus theory within the harmonic approximation, but anharmonic model partition functions are also considered. Decreasing the range of the potential in the Morse clusters is shown to hinder relaxation toward the global minimum, and this effect is related to the concomitant changes in the energy landscape. The relaxation modes that emerge from the master equation are interpreted and analyzed to extract interfunnel rate constants for the Lennard-Jones cluster. Since this system is too large for a complete characterization of the energy landscape, the conditions under which the master equation can be applied to a limited database are explored. Connections are made to relaxation processes in proteins and structural glasses.