South Valley, NM, United States
South Valley, NM, United States

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Kaatz F.H.,Mesalands Community College | Bultheel A.,Catholic University of Leuven | Ori O.,Actinium Chemical Research | Ori O.,West University of Timișoara
Journal of Mathematical Chemistry | Year: 2016

Abstract: The vacancy concentration dependence on temperature and diameter of noble metal (gold, silver, and copper) nanoclusters is investigated using a Kinetic Monte Carlo method. Icosahedral and decahedral nanoclusters are studied, with diameters up to 3.73 nm for icosahedral clusters and up to 6.65 nm for decahedral clusters. The cohesive energy is calculated using a coordination number approach, resulting in a linear relation with cluster size. Random Schottky defects are frozen into the clusters at low temperatures (100–600 K) and we find that the vacancy concentration increases with smaller diameters and higher temperatures. We develop a model for this behavior, which explains the temperature and size dependence. This model predicts silver icosahedra to have the highest concentration of vacancies in the clusters studied. Vacancy concentrations are related to the ratio of surface/interior sites based on nearest neighbor calculations. The modified enthalpy and entropy of constant diameter clusters are derived from a logarithmic model for the Gibbs energy. Melting entropy and enthalpy are calculated in this coordination type model and compare well with previously published molecular dynamics results. Graphical Abstract: [Figure not available: see fulltext.] © 2016 Springer International Publishing Switzerland


Ori O.,Actinium Chemical Research | Ori O.,West University of Timișoara | Cataldo F.,Actinium Chemical Research | Putz M.V.,West University of Timișoara | And 3 more authors.
Fullerenes Nanotubes and Carbon Nanostructures | Year: 2016

Present topological study focuses on the formation mechanism of clusters of vacancies in graphenic layers. An original effect that explains both accumulation and self-healing of vacancies represents the original outcome of our investigation whose results, based on the long-range topological properties of the honeycomb lattices, are applicable to defective graphene sheets and general honeycomb lattices when other elements other than carbon are present. Some speculations about the role of long-range bondonic states in such a kind of lattices contribute to the understanding of electronic and transport properties in graphenic nanomaterials. © 2016 Taylor & Francis Group, LLC.


Kaatz F.H.,Mesalands Community College | Bultheel A.,Catholic University of Leuven
Journal of Mathematical Chemistry | Year: 2014

Nanostructures may be fabricated from metal nanoclusters such as gold or platinum, which are of interest for catalytic and structural characteristics, or from nano forms of carbon allotropes. Here, informational thermodynamic properties such as free energy, enthalpy, and entropy are calculated using a graph network model at T = 298.15 K. We calculate the partition function using Euclidean adjacency matrices from the Hamiltonian and estimated bond energies. The summed atomic displacement from the Kirchhoff index has power law behavior, while the thermodynamic properties exhibit large N logarithmic behavior: however, the data shows structurally related anomalies. © 2014 Springer International Publishing Switzerland.


Hungerbuhler A.,Mesalands Community College | Mueller B.,Texas Tech University | Chatterjee S.,Texas Tech University | Cunningham D.P.,Texas Tech University
Earth and Environmental Science Transactions of the Royal Society of Edinburgh | Year: 2013

The skull anatomy of a new species of the phytosaur Machaeroprosopus is described for the first time on the basis of two specimens from the Upper Triassic Cooper Canyon Formation of Texas. Additional information is provided by a third specimen referred to Machaeroprosopus sp. A paranasal bone, an additional paired element of the narial region, is identified. Important new data are presented for the braincase, including the morphology of the epipterygoid and presphenoid, an anterior process of the prootic, an anteroventral process of the laterosphenoid, and a parasphenoid process. Machaeroprosopus lottorum n. sp. is characterised by four apomorphies: a supratemporal fenestra closed on the skull roof with bevelled anterior rim, a comparatively short squamosal, a flat and rugose narial rim, and medially extended palatines that come close to form an ossified secondary palate. With respect to the supratemporal fenestra, the supraoccipital-parietal complex and several features of the squamosal, Machaeroprosopus lottorum n. sp. bridges the morphological gap between species previously referred to the genera Pseudopalatus and Redondasaurus. A parsimony analysis of known species of Machaeroprosopus supports the hypothesis that the development of the rostral crest in Machaeroprosopus is a sexually dimorphic feature, and questions the validity of the genus Redondasaurus. Consequently, Redondasaurus is here considered a junior synonym of Machaeroprosopus. © 2013 The Royal Society of Edinburgh.


Parker W.G.,Petrified Forest National Park | Parker W.G.,University of Texas at Austin | Hungerbuhler A.,Mesalands Community College | Martz J.W.,Denver Museum of Nature and Science
Earth and Environmental Science Transactions of the Royal Society of Edinburgh | Year: 2013

The genus Machaeroprosopus has long been considered invalid because the type specimen of the Late Triassic phytosaur species, M. validus, has been lost. Re-examination of the primary literature regarding the establishment of the Late Triassic phytosaur genus Machaeroprosopus demonstrates that M. buceros is the correct type species, not M. validus. Thus, the genus level name Machaeroprosopus has priority over the genera Pseudopalatus and Arribasuchus and all nominal species should be reassigned. Reassignment of these species to Machaeroprosopus satisfies the requirements of the International Code of Zoological Nomenclature (ICZN) and preserves historical context. The name Pseudopalatinae is retained as the valid clade name for these phytosaurs because its usage falls outside of the ICZN. © 2013 The Royal Society of Edinburgh.


Kaatz F.H.,Mesalands Community College | Bultheel A.,Catholic University of Leuven
Journal of Mathematical Chemistry | Year: 2015

We investigate clusters of hypercubes in d-dimensional space as a function of the number of vertices, N, and number of cluster shells, L. The number of links, vertices, and exterior vertices exhibit ‘magic number’ characteristics versus L, as the dimension of the space changes. 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, Szeged, Balaban, and Kirchhoff indices. Some known topological formulas for hypercubes when L = 1 are experimentally verified. The asymptotic limits with N of the topological indices are shown to exhibit power law behavior whose exponent changes with d and type of topological index. The asymptotic graph energy is linear with N, whose slope changes with d, and in 2D agrees numerically with previous calculations. Also, the thermodynamic properties such as entropy, free energy, and enthalpy of these lattices show logarithmic behavior with increasing N. The hypercubic clusters are projected onto 3D space when the dimensionality (Formula presented.). © 2015 Springer International Publishing Switzerland


Kaatz F.H.,Mesalands Community College | Bultheel A.,Catholic University of Leuven
Computational Materials Science | Year: 2015

Nanoclusters create the possibility of designing novel properties and devices based on finite structures, with small dimensions. Clusters are of interest for catalytic, optical, biochemical, and structural characteristics. We examine clusters of icosahedral, cuboctahedral, and decahedral symmetry. Examples of these types of structures are shown from gold and platinum nanoclusters. Starting with only the atomic coordinates, we create an adjacency and distance matrix that facilitates the calculation of topological indices, including the Wiener, hyper-Wiener, reverse Wiener, Szeged, Balaban, and Kirchhoff indices. Some of these indices correlate to properties of the cluster. We find these indices exhibit polynomial and inverse behavior as a function of an increasing number of shells. Additionally, all the indices can be modeled with power law curves, as a function of N, the number of atoms. The magnitude of the exponent in the power law is associated with an index. The asymptotic limits of the topological indices are determined as a function of N. A conjecture previously published on the asymptotic behavior of the Wiener index is experimentally confirmed. © 2014 Elsevier B.V. All rights reserved.


Kaatz F.H.,Mesalands Community College | Estrada E.,University of Strathclyde | Bultheel A.,Catholic University of Leuven | Sharrock N.,Lochgardie Media
Physica A: Statistical Mechanics and its Applications | Year: 2012

Reduced dimensionality in two dimensions is a topic of current interest. We use model systems to investigate the statistical mechanics of ideal networks. The tilings have possible applications such as the 2D locations of pore sites in nanoporous arrays (quantum dots), in the 2D hexagonal structure of graphene, and as adsorbates on quasicrystalline crystal surfaces. We calculate the statistical mechanics of these networks, such as the partition function, free energy, entropy, and enthalpy. The plots of these functions versus the number of links in the finite networks result in power law regression. We also determine the degree distribution, which is a combination of power law and rational function behavior. In the large-scale limit, the degree of these 2D networks approaches 3, 4, and 6, in agreement with the degree of the regular tilings. In comparison, a Penrose tiling has a degree also equal to about 4. © 2012 Elsevier B.V. All rights reserved.


Kaatz F.H.,Mesalands Community College | Bultheel A.,Catholic University of Leuven
Journal of Mathematical Chemistry | Year: 2013

We look at modeling carbon nanostructures 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 structures, such as fullerenes and carbon nanotubes. 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. The number of bonds in a carbon nanotube is linear with the length of the nanotube, thus enabling us to calculate the heat of formation of capped (5,5) and (10,10) nanotubes. These properties are determined from atomic coordinates using MATLAB routines. © 2013 Springer Science+Business Media New York.


Kaatz F.H.,Mesalands Community College | Bultheel A.,Catholic University of Leuven
Journal of Mathematical Chemistry | Year: 2013

Graphene nanoflakes (GNFs) are predicted to possess novel magnetic, optical, and spintronic properties. They have recently been synthesized and a number of applications are being studied. Here we investigate the statistical properties of rippled GNFs (50-5,000 atoms) at T = 300 K. An adjacency matrix is calculated from the coordinates and we find that the free energy, enthalpy, entropy, and atomic displacement all show power law behavior. The vibrational energy versus the Wiener index also shows power law character. We distinguish between using Euclidean topographical indices and compare them to topological ones. These properties are determined from atomic coordinates using MATLAB routines. © 2013 Springer Science+Business Media New York.

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