Magic Melters' Have Geometrical Origin

Recent experimental reports bring out extreme size sensitivity in the heat capacities of Gallium and Aluminum clusters. In the present work we report results of our extensive {\it ab initio} molecular dynamical simulations on Ga$_{30}$ and Ga$_{31}$, the pair which has shown rather dramatic size sensitivity. We trace the origin of this size sensitive heat capacities to the relative order in their respective ground state geometries. Such an effect of nature of the ground state on the characteristics of heat capacities is also seen in case of small Gallium and Sodium clusters indicating that the observed size sensitivity is a generic feature of small clusters.Comment: 4 pages, 6 figure

Superconducting Gap Nodal Surface and Fermi Surface: their partial overlap in cuprates

Electron correlation in cuprates leads to a global constraint $\sum_{\bf k} \Delta_{\bf k} = 0$ on the gap function $\Delta_{\bf k}$ resulting in a gap nodal surface. We give physical arguments supported by numerical results and discuss some experimental results to argue that correlations also lead to a local constraint on charge fluctuations in ${\bf k}$-space close to the Fermi surface, which may result in a substantial overlap of the Fermi surface with the gap nodal surface.Comment: RevTeX 3.0, 4 Pages, 6 PostScript Figures

Effect of geometric and electronic structures on the finite temperature behavior of Na58_{58}, Na57_{57}, and Na55_{55} clusters

An analysis of the evolutionary trends in the ground state geometries of Na$_{55}$ to Na$_{62}$ reveals Na$_{58}$, an electronic closed--shell system, shows namely an electronically driven spherical shape leading to a disordered but compact structure. This structural change induces a strong {\it connectivity} of short bonds among the surface atoms as well as between core and surface atoms with inhomogeneous strength in the ground state geometry, which affects its finite--temperature behavior. By employing {\it ab initio} density--functional molecular dynamics, we show that this leads to two distinct features in specific heat curve compared to that of Na$_{55}$: (1) The peak is shifted by about 100 K higher in temperature. (2) The transition region becomes much broader than Na$_{55}$. The inhomogeneous distribution of bond strengths results in a broad melting transition and the strongly connected network of short bonds leads to the highest melting temperature of 375 K reported among the sodium clusters. Na$_{57}$, which has one electron less than Na$_{58}$, also possesses stronger short--bond network compared with Na$_{55}$, resulting in higher melting temperature (350 K) than observed in Na$_{55}$. Thus, we conclude that when a cluster has nearly closed shell structure not only geometrically but also electronically, it show a high melting temperature. Our calculations clearly bring out the size--sensitive nature of the specific heat curve in sodium clusters.Comment: 7 pages, 11 figure

First principles investigation of finite-temperature behavior in small sodium clusters

A systematic and detailed investigation of the finite-temperature behavior of small sodium clusters, Na_n, in the size range of n= 8 to 50 are carried out. The simulations are performed using density-functional molecular-dynamics with ultrasoft pseudopotentials. A number of thermodynamic indicators such as specific heat, caloric curve, root-mean-square bond length fluctuation, deviation energy, etc. are calculated for each of the clusters. Size dependence of these indicators reveals several interesting features. The smallest clusters with n= 8 and 10, do not show any signature of melting transition. With the increase in size, broad peak in the specific heat is developed, which alternately for larger clusters evolves into a sharper one, indicating a solidlike to liquidlike transition. The melting temperatures show irregular pattern similar to experimentally observed one for larger clusters [ M. Schmidt et al., Nature (London) 393, 238 (1998) ]. The present calculations also reveal a remarkable size-sensitive effect in the size range of n= 40 to 55. While Na_40 and Na_55 show well developed peaks in the specific heat curve, Na_50 cluster exhibits a rather broad peak, indicating a poorly-defined melting transition. Such a feature has been experimentally observed for gallium and aluminum clusters [ G. A. Breaux et al., J. Am. Chem. Soc. 126, 8628 (2004); G. A.Breaux et al., Phys. Rev. Lett. 94, 173401 (2005) ].Comment: 8 pages, 11 figure

Why do gallium clusters have a higher melting point than the bulk?

Density functional molecular dynamical simulations have been performed on Ga$_{17}$ and Ga$_{13}$ clusters to understand the recently observed higher-than-bulk melting temperatures in small gallium clusters [Breaux {\em et al.}, Phys. Rev. Lett. {\bf 91}, 215508 (2003)]. The specific-heat curve, calculated with the multiple-histogram technique, shows the melting temperature to be well above the bulk melting point of 303 K, viz. around 650 K and 1400 K for Ga$_{17}$ and Ga$_{13}$, respectively. The higher-than-bulk melting temperatures are attributed mainly to the covalent bonding in these clusters, in contrast with the covalent-metallic bonding in the bulk.Comment: 4 pages, including 6 figures. accepted for publication in Phys. Rev. Let