Structure and transport of epitaxial rare earth silicides

A multi-technique investigation of the growth, structure, and transport behavior in two epitaxial rare earth silicides: erbium silicide, ErSi\sb{\rm 2-x}, and terbium silicide, TbSi\sb{\rm 2-x}, has been conducted. The rare earth silicides form in a planar hexagonal AlB\sb2 structure with a good lattice match to the Si(111) surface. This is the first time these materials have been formed under ultra high vacuum conditions, allowing the characterization of the structure and transport behavior of the heteroepitaxial systems. The growth was studied under ultrahigh vacuum conditions with both metal and silicon evaporators used to form epitaxial material. Modification of the growth procedures resulted in Rutherford Backscattering channeling minimum yields of 9% and 2.2% for TbSi\sb{\rm 2-x} and ErSi\sb{\rm 2-x}, respectively. These results are an order of magnitude lower than among previous measurements and, in the case of erbium silicide, among the best reported for any crystalline material. The microscopic structure and morphology was investigated with transmission electron microscopy. Defects of pinholes, ordered vacancy networks, and fault structures were found to be modified by changing the growth conditions, with the best results occurring from using template layers of metal and silicon followed by codeposition of the metal and silicon constituents. More specifically, a room temperature deposition of about 4 A of metal followed by 6 A of silicon and annealed to 200\sp\circC was found to result in a 1 x 1 low energy electron diffraction pattern. This removed the surface reconstruction of the Si(111) surface, changed the surface free energy, and provided an appropriate template onto which codeposited thicker layers were continuous even after being annealed to 800\sp\circC to obtain good crystallinity. Transport measurements were conducted to investigate the magnetic character of terbium silicide. Resistivity measurements showed an anomalous drop at 38K, where terbium silicide is known to have a magnetic phase transition. Magnetoresistance experiments revealed an anomalous cusp in the resistivity at high fields (8 Tesla) which is thought to be related to spin scattering from the antiferromagnetic to paramagnetic transition in the magnetic structure of terbium silicide

Polyhedral effects on the mass activity of platinum nanoclusters

We use a coordination-based kinetics model to look at the kinetics of the turnover frequency (TOF) for the oxygen reduction reaction (ORR) for platinum nanoclusters. Clusters of octahedral, cuboctahedral, cubic, and icosahedral shape and size demonstrate the validity of the coordination-based approach. The Gibbs adsorption energy is computed using an empirical energy model based on density functional theory (DFT), statistical mechanics, and thermodynamics. We calculate the coordination and size dependence of the Gibbs adsorption energy and apply it to the analysis of the TOF. The platinum ORR follows a Langmuir–Hinshelwood mechanism, and we model the kinetics using a thermodynamic approach. Our modeling indicates that the coordination, shape, and the Gibbs energy of adsorption all are important factors in replicating an experimental TOF. We investigate the effects of size and shape of some platinum polyhedra on the oxygen reduction reaction (ORR) and the effect on the mass activity. The data are modeled quantitatively using lognormal distributions. We provide guidance on how to account for the effects of different distributions due to shape when determining the TOF.status: publishe

Modeling finite nanostructures

© 2014 by Nova Science Publishers, Inc. All rights reserved. Modeling the nanoscale can occur by limiting the large-scale nature of arrays and nanostructures to a finite size, or by modeling a single nano object. We look at modeling nano systems from a theoretical graph network view, where a graph has atoms at a vertex and links represent bonds. In this way, we can calculate standard statistical mechanics functions (entropy, enthalpy, and free energy) and matrix indices (Wiener index) of finite nanostructures such as fullerenes, carbon nanotubes, and graphenenanoflakes. The Euclidean Wiener index (topographical index) is compared with its topological (standard) counterpart. For many of these parameters, the data have power law behavior, especially when plotted versus the number of bonds or the number of atoms. Ideally, the placement of nanosized structures could be fabricated in such a way that the order and location of the objects is as desired. We consider measuring the order in finite nanoporous arrays via the pair distribution function and by reciprocal space parameters. Porous arrays have been made in triangular, hexagonal, and square geometries, and we compare the experimental versions with ideal models. An order parameter derived from the pair distribution function takes values from near zero to one; whereas, a reciprocal space parameter has nominal values from one to forty. We conclude with a summary and indications for future work.status: publishe

Size, shape, and compositional effects on the order–disorder phase transitions in Au–Cu and Pt–M (M = Fe, Co, and Ni) nanocluster alloys

Au–Cu and Pt–M (M = Fe, Co, and Ni) nanocluster alloys are currently being investigated world-wide by many researchers for their interesting catalytic and nanophase properties. The low temperature behavior of the phase diagrams is not well understood for alloys with nanometer sizes and shapes. We consider two models for low temperature ordering in the phase diagrams of Au–Cu and Pt–M nanocluster alloys. These models are valid for sizes ~5 nm and approach bulk values for sizes ~20 nm. We study the phase transitions in nanoclusters with cubic, octahedral, and cuboctahedral shapes, covering the compositions of interest. These models are based on studying the melting temperatures in nanoclusters using the regular solution, mixing model for alloys. From our data, experiments on nanocubes about 5 nm in size, of stoichiometric AuCu and PtM composition, could help differentiate between the models. Dispersion data shows that for the three shapes considered, octahedra have the highest percentage of surface atoms for the same relative diameter. We summarize the effects of structural ordering on the catalytic activity and suggest a method to avoid sintering during annealing of Pt–M alloysstatus: publishe

Size, shape, and compositional effects on the order-disorder phase transitions in {Au-Cu and Pt-M (M = Fe,Cu, and Ni)} nanocluster alloys

edition: General Program XXVII IMRCstatus: publishe

Catalytic thermodynamic model for nanocluster adsorbates

We present an approach to study nanocatalysis using density functional theory (DFT), statistical mechanics, andthermodynamics. The analysis starts by using a coordination style approach, which is key to producing a me-soscale model free of arbitrary parameters for sizes of∼3nm <D< 100 nm. We apply DFT in a coordinationtype calculation of the nanocrystal binding energy and the adatom adsorption energy to give us a Hamiltonian ofthe nanocluster-adatom system. This is followed by informational statistical mechanical principles and ther-modynamics to complete the model. Carbon monoxide adsorbates are studied on gold clusters, hydrogen mo-lecules on palladium clusters, and oxygen radicals on platinum clusters. The data exhibits size effects for themeasured thermodynamic properties with cluster diameters between 3 and 9 nm. In spite of modeling threedifferent systems, wefind only small differences in the large-scale entropy (∼−70 J/K-mol) and enthalpy(∼−20 kJ/mol) of the nanoclusters. Shape effects are predicted to be greatest for nanoclusters of size∼10 nm.For the Pd-H2system, we use a cubic model which has close agreement with experimental data for Pd cubes. Thecomputationally efficient procedure we derive provides a theoretical scheme to determine the size and shapedependence of the entropy and enthalpy of nanocluster-adsorbate systems from sequential single molecule adsorption.status: Published onlin

Magic Mathematical Relationships for Nanoclusters - Errata and Addendum

We correct magic formulas for body centered cubic (bcc) structures. The logical rational for this is further corroborated by calculations of the radial distribution function (RDF) for several crystal structures. We add results for truncated cubes which may be found in nature.status: publishe

Catalytic Thermodynamics of Nanocluster Adsorbates from Informational Statistical Mechanics

© 2018, Springer Science+Business Media, LLC, part of Springer Nature. Abstract: This letter presents a new approach for studying the catalytic thermodynamics of cuboctahedral nanoclusters, using informational statistical mechanics. The Morse potential determines bond energies between cluster atoms in a coordination type calculation. Applied density functional theory calculations demonstrate adatom effects on the thermodynamic quantities, which are derived from a Hamiltonian. Calculations of the entropy, free energy, and total energy show linear behavior, as the coverage of oxygen on platinum, and hydrogen on palladium, increases from bridge sites on the surface. The data exhibits size effects for the measured thermodynamic properties with cluster diameters between 2 and 5 nm. Entropy and enthalpy calculations of Pt–O2 compare well with previous theoretical data for Pt(111)–O2, and trends for Pd–H are similar to experimental measurements on Pd–H2 nanoclusters. These techniques are applicable to a wide variety of cluster–adsorbate interactions, encouraging further research. Graphical Abstract: [Figure not available: see fulltext.]status: publishe

Magic Mathematical Relationships for Nanoclusters

Size and surface properties such as catalysis, optical quantum dot photoluminescense, and surface plasmon resonances depend on the coordination and chemistry of metal and semiconducting nanoclusters. Such coordination-dependent properties are quantified herein via "magic formulas" for the number of shells, n, in the cluster. We investigate face-centered cubic, body-centered cubic, simple cubic clusters, hexagonal close-packed clusters, and the diamond cubic structure as a function of the number of cluster shells, n. In addition, we examine the Platonic solids in the form of multi-shell clusters, for a total of 19 cluster types. The number of bonds and atoms and coordination numbers exhibit magic number characteristics versus n, as the size of the clusters increases. Starting with only the spatial coordinates, we create an adjacency and distance matrix that facilitates the calculation of topological indices, including the Wiener, hyper-Wiener, reverse Wiener, and Szeged indices. Some known topological formulas for some Platonic solids when n=1 are computationally verified. These indices have magic formulas for many of the clusters. The simple cubic structure is the least complex of our clusters as measured by the topological complexity derived from the information content of the vertex-degree distribution. The dispersion, or relative percentage of surface atoms, is measured quantitatively with respect to size and shape dependence for some types of clusters with catalytic applications.status: publishe