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

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

Geometric, electronic properties and the thermodynamics of pure and Al--doped Li clusters

The first--principles density functional molecular dynamics simulations have been carried out to investigate the geometric, the electronic, and the finite temperature properties of pure Li clusters (Li$_{10}$, Li$_{12}$) and Al--doped Li clusters (Li$_{10}$Al, Li$_{10}$Al$_2$). We find that addition of two Al impurities in Li$_{10}$ results in a substantial structural change, while the addition of one Al impurity causes a rearrangement of atoms. Introduction of Al--impurities in Li$_{10}$ establishes a polar bond between Li and nearby Al atom(s), leading to a multicentered bonding, which weakens the Li--Li metallic bonds in the system. These weakened Li--Li bonds lead to a premelting feature to occur at lower temperatures in Al--doped clusters. In Li$_{10}$Al$_2$, Al atoms also form a weak covalent bond, resulting into their dimer like behavior. This causes Al atoms not to `melt' till 800 K, in contrast to the Li atoms which show a complete diffusive behavior above 400 K. Thus, although one Al impurity in Li$_{10}$ cluster does not change its melting characteristics significantly, two impurities results in `surface melting' of Li atoms whose motions are confined around Al dimer.Comment: 9 pages, 7 figure

Solar Flare Intermittency and the Earth's Temperature Anomalies

We argue that earth's short-term temperature anomalies and the solar flare intermittency are linked. The analysis is based upon the study of the scaling of both the spreading and the entropy of the diffusion generated by the fluctuations of the temperature time series. The joint use of these two methods evidences the presence of a L\'{e}vy component in the temporal persistence of the temperature data sets that corresponds to the one that would be induced by the solar flare intermittency. The mean monthly temperature datasets cover the period from 1856 to 2002.Comment: 4 pages, 5 figure

A visual guide for lower limb prothetic alignment

A novel method to provide an objective visual guide during lower limb prosthetic alignment is proposed. A customized ambulatory device was built to collect kinematic and temporal gait data from 3 subjects walking in four different experiment setups. Multiple gait events within a gait cycle and stride time were derived as feature variables and were pre-processed using Principle Component Analysis (PCA). Distinctive clusters due to different walking setups were noticed in a PCA plot in two dimensions. Dispersion of each clusters and distances amongst each other explains the walking variability and differences under different setups