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Rare earth ternary borides, RRh3Bx (R = La, Gd, Lu and Sc) have been synthesized by arc melting method. Borides RRh 3Bx (R = La, Gd, Lu and Sc) have perovskite-type cubic structure: space group Pm3m; Z = 1. The lattice parameters a of the stoichiometric RRh3B for R = La, Gd, Lu and Sc are 0.4251(1), 0.4183(1), 0.4126(1) and 0.4080(1) nm, respectively. LaRh3B x does not have boron-nonstoichiometry as x = 0. In GdRh 3Bx and LuRh3Bx, boron- nonstoichiometry ranges between 0.55 ≦ x ≦ 1 and 0.30 ≦ x ≦ 1, respectively. The boron-nonstoichiometry range is the widest, 0 ≦ x ≦ 1, for R = Sc. Boron-nonstoichiometry increases with decreasing atomic radius of R. The microhardness of the stoichiometric RRh3B for R = La, Gd, Lu and Sc is 4.2 ± 0.1, 6.8 ± 0.1, 7.7 ± 0.5 and 9.9 ± 0.1 GPa, respectively. As a result, microhardness increases with decreasing atomic size of R in RRh3B; R is positioned at the eight corners of the cube in the perovskite-type structure. Thus, hardness is strongly dependent on R element. The hardness changes almost linearly with boron concentration x for R = Gd and Lu in RRh3Bx, while no linear dependency is found for R = Sc. Ab initio calculations have been performed to obtain the equilibrium lattice constants and the bulk moduli. The calculated lattice constants are in excellent agreement with experimental results. {\textcopyright} 2005 Elsevier B.V. All rights reserved.

World University root node

Journal of Alloys and Compounds

Synthesis, boron-nonstoichiometry and hardness of perovskite-type rare earth rhodium borides RRh3Bx (R = La, Gd, Lu and Sc)

Using ab initio calculations, we show that the encapsulation of Y, La and Ac metal (M) atom stabilizes the dodecahedral fullerene anion M@ Si20- in the icosahedral symmetry. Similar to C60, it is the ideal cage of silicon and the largest that can be stabilized by an M atom. Doping of other rare earths is further shown to stabilize magnetic dodecahedral fullerenes Pa@ Si20, Sm@ Si20, Pu@ Si20 and Tm@ Si20 with 1 $\mu$B, 4 $\mu$B, 4 $\mu$B and 3 $\mu$B spin magnetic moments, respectively, in contrast to most previous studies on M -encapsulated Si clusters in which the magnetic moment is completely quenched. The highest spin magnetic moment of 7 $\mu$B is achieved for Gd@ Si20- with half-filled 4f states. The orbital magnetic moment is also calculated and it is ∼1 $\mu$B in most cases. Neutral M@ Si20 (M=Y, La, Ac and Gd) behaves like superhalogen and interaction with a noble or alkali metal atom leads to salt like behavior. These findings could pave way for the realization of silicon fullerenes by doping of several elements. {\textcopyright} 2006 The American Physical Society.

Physical Review B - Condensed Matter and Materials Physics

Charged and magnetic fullerenes of silicon by metal encapsulation: Predictions from ab initio calculations

We report synthesis of perovskite-type boride CeRh3Bx using the arc melting method. The samples are characterized by powder X-ray diffraction which shows that the crystal structure of CeRh3Bx belongs to the cubic system (space group: Pm3m) in the range of 0 < x ≤ 1. Furthermore, CeRh3 (x = 0) has the ordered AuCu3-type structure (space group: Pm3m). As a result, CeRh3Bx exists in a wide range of nonstoichiometric boron concentration 0 ≤ x ≤ 1 with the space group Pm3m. The lattice parameter, a, changes almost linearly with x, varying from 0.4015(1) nm (x = 0) to 0.4180(1) nm (x = 1.0). The micro-Vickers hardness of the CeRh3Bx for x = 0 (0 at.%B), 0.210 (5 at.%B), 0.444 (10 at.%B), 0.706 (15 at.%B) and 1.0 (20 at.%B) are 2.0 ± 0.1, 4.3 ± 0.2, 1.8 ± 0.2, 5.5 ± 0.1 and 6.5 ± 0.2 GPa, respectively. Thermo-gravimetric analysis was done to study the oxidation resistance of the samples in air. It reveals that oxidation begins at 502 and 513 K for x = 0 and 1.0, respectively. A mixed phase of CeO2 + Rh is identified as an oxidized product for all samples. {\textcopyright} 2006 Elsevier B.V. All rights reserved.

Boron nonstoichiometry, hardness and oxidation resistance of perovskite-type CeRh3Bx (x = 0-1)

We report results of an ab initio study of the atomic structures of small zinc oxide clusters (ZnO)n n ≤ 6 using ultrasoft pseudopotential method and the generalized gradient approximation for the exchange-correlation energy. We optimize several isomers for each size in order to obtain the lowest energy structures and to understand the growth behavior. In all cases ring type structures are found to be most favorable. For n = 5 and 6, the ring structures are not planar suggesting that the bonding nature in these cluster has some covalent character. Small clusters are found to have small highest-occupied- lowest unoccupied molecular orbital (HOMO-LUMO) gap in contrast to the typical behavior of large gaps for small clusters that tend to decrease towards the bulk value with an increase in size. {\textcopyright} 2005 Elsevier B.V. All rights reserved.

Computational Materials Science

Ring structures of small ZnO clusters

We present a brief account of the recent progress in the theoretical understanding of the electronic and structural properties of clusters of metals and semiconductors from ab initio calculations. The origin of the recently observed permanent electric dipoles in Nb clusters, the occurrence of magnetism in clusters of non-magnetic elements such as Pd, Rh and Ru, as well as the findings of the metal encapsulated clusters of Si, Ge, Sn and Pb are discussed. Empty caged clusters of Si, Ge and Sn have also been shown to be stable with H capping. These can be functionalized by exohedral doping for different applications while endohedral doping of the cages can be used to tailor highest occupied-lowest unoccupied molecular orbital gaps as well as the magnetic properties. Assemblies of such clusters could lead to novel nanostructures and new phases of these materials. {\textcopyright} 2005 Elsevier B.V. All rights reserved.

Recent theoretical progress on electronic and structural properties of clusters: Permanent electric dipoles, magnetism, novel caged structures and their assemblies

First-principles calculations have been performed on perovskite-type Sc Rh3 Bx in order to understand the variation in the structural properties and bulk modulus as a function of the boron concentration. We use the projected augmented wave method with a supercell to treat different configurations of vacancies and boron atoms. The generalized gradient approximation is used for the exchange-correlation functional. The calculated lattice constants are found to be in excellent agreement with the experimental results. Maximum bulk modulus is realized surprisingly at x=0.5, contrary to the expectation that vacancies reduce the number of chemical bonds and hence the strength of the compounds. This is explained by examining the changes in the atomic and electronic structures upon B doping. We find that the doping enhances the cohesive energy monotonically due to the strong covalent bonding between B 2p and Rh 4d states. However, at x=0.5 a configuration is achieved in which each boron is surrounded by vacancies at the cube centers and vice versa. This reduces strain in the structure and the Rh-B bonds are short, leading to a maximum in the bulk modulus. The density of states at the Fermi energy is also minimum for x=0.5 which adds further stability to the structure. {\textcopyright} 2006 The American Physical Society.

Mechanism of the increase in bulk modulus of perovskite Sc Rh3 Bx by vacancies

We report results of ab initio calculations on NaN, N=55, 147 and 309 clusters that show icosahedral growth to be most favorable in agreement with the recent photoelectron spectroscopy data. The icosahedral structures are found to be significantly compressed in the central region. However, a vacancy at the center or the first shell is found to cost much higher energy compared to other sites in the clusters. The vacancy formation energy is the lowest at the vertex sites followed by the edge sites on the cluster surface. These results show that disordering is easier to happen at the surface region of the clusters. Recent experiments on sodium clusters also suggest surface premelting. Furthermore, we obtain a higher value of the vacancy formation energy for N=55 compared to the case of N=147 or 309. This is in agreement with the experimental finding of a higher melting temperature for Na55. The perturbation due to a central vacancy is found to be mainly confined to two atomic shells similar to the phenomena at surfaces of bulk metals. {\textcopyright} 2006 The American Physical Society.

Ab initio calculations of the stability of a vacancy in Na clusters and correlation with melting

Mixing of elements at the nanoscale can offer exciting possibilities of novel materials with compositions, structures and properties quite different from those known in bulk. Ab initio calculations are expected to play a major role in understanding their properties as well as in predicting and designing such materials. Here, we briefly review recent progress where encapsulation of an atom A or a group of atoms G or exohedral atom(s) have been used to stabilize cage-like nanoclusters/fullerenes of material B. The encapsulation enhances the stability of nanoclusters and can lead to striking preference for a specific size. This can facilitate the design and production of nanoclusters with specific properties in high abundances and the development of assemblies of such species. We discuss the electronic origin of the stability of such species as well as assemblies of size selected nanoparticles that have led to the formation of nanowires and nanotubes. Several examples of such clusters of semiconductors and metals are presented. {\textcopyright} 2005 Elsevier B.V. All rights reserved.

Alchemy at the nanoscale: Magic heteroatom clusters and assemblies

We report the results of first principles calculations on neutral magnesium oxide clusters (MgO)n n ≤ 13, using the parallelized all-electron Tohoku University Mixed-Basis Orbitals (TOMBO) program and local density approximation for the exchange-correlation energy. It uses both plane waves and atomic orbitals as the basis functions. Various isomers are studied for each size to find the lowest energy structures and to identify the magic clusters. Clusters with n = 4, 6, 9 and 12 are found to be magic in agreement with the available experimental data. The performance of the parallelized TOMBO is also studied by using different number of nodes on Hitachi SR8000 supercomputer. {\textcopyright} 2005 Elsevier B.V. All rights reserved.

First principles studies of magnesium oxide clusters by parallelized Tohoku University Mixed-Basis program TOMBO

Debates on ‘case studies and generalization' have been too strongly committed to dualisms (general/specific, explanation/understanding) that polarize social science into natural-science-inspired and humanities-inspired camps. One should be aware of a third option, a pragmatist (participationist) attitude. Rather than relying on parallels with external academic fields, this attitude thinks about research with reference to the conduct of social science only. This article discusses these three attitudes with reference to a single case study of the Israeli–Palestinian conflict (asking why that conflict became one of the deepest and most persistent conflicts in recent history). The three attitudes imply different strategies of generalization and specification. The single case study of the Middle East conflict relies on a pragmatist strategy of generalization and the rest of the methodological discussion shows how this strategy transcends the general/specific or explanation/ understanding dichotomies.