Crystallographic orientation inhomogeneity and crystal splitting in biogenic calcite

The calcitic prismatic units forming the outer shell of the bivalve Pinctada margaritifera have been analysed using scanning electron microscopy–electron back-scatter diffraction, transmission electron microscopy and atomic force microscopy. In the initial stages of growth, the individual prismatic units are single crystals. Their crystalline orientation is not consistent but rather changes gradually during growth. The gradients in crystallographic orientation occur mainly in a direction parallel to the long axis of the prism, i.e. perpendicular to the shell surface and do not show preferential tilting along any of the calcite lattice axes. At a certain growth stage, gradients begin to spread and diverge, implying that the prismatic units split into several crystalline domains. In this way, a branched crystal, in which the ends of the branches are independent crystalline domains, is formed. At the nanometre scale, the material is composed of slightly misoriented domains, which are separated by planes approximately perpendicular to the c-axis. Orientational gradients and splitting processes are described in biocrystals for the first time and are undoubtedly related to the high content of intracrystalline organic molecules, although the way in which these act to induce the observed crystalline patterns is a matter of future research

Power-law distributions in empirical data

Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution -- the part of the distribution representing large but rare events -- and by the difficulty of identifying the range over which power-law behavior holds. Commonly used methods for analyzing power-law data, such as least-squares fitting, can produce substantially inaccurate estimates of parameters for power-law distributions, and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all. Here we present a principled statistical framework for discerning and quantifying power-law behavior in empirical data. Our approach combines maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov-Smirnov statistic and likelihood ratios. We evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches. We also apply the proposed methods to twenty-four real-world data sets from a range of different disciplines, each of which has been conjectured to follow a power-law distribution. In some cases we find these conjectures to be consistent with the data while in others the power law is ruled out.Comment: 43 pages, 11 figures, 7 tables, 4 appendices; code available at http://www.santafe.edu/~aaronc/powerlaws

One-step synthesis of a highly homogeneous SBA-NHC hybrid material: En route to single-site NHC-metal heterogeneous catalysts with high loadings

The one-step synthesis of a mesoporous silica of SBA type, functionalized with a 1-(2,6-diisopropylphenyl)-3-propyl-imidazolium (iPr2Ar-NHC-propyl) cation located in the pore channels, is described. This material was obtained by the direct hydrolysis and co-condensation of tetraethylorthosilicate (TEOS) and 1-(2,6-diisopropylphenyl)-3-[3-(triethoxysilyl)propyl]-imidazolium iodide in the presence of Pluronic P123 as a non-ionic structure-directing agent and aqueous HCl (37%) as an acid catalyst. Small-angle X-ray diffraction measurements, scanning and transmission electron microscopies, as well as dinitrogen sorption analyses revealed that the synthesized material is highly mesoporous with a 2D hexagonal arrangement of the porous network. 13C and 29Si CP-MAS NMR spectroscopy confirmed that the material contains intact iPr2Ar-NHC-propyl cations, which are covalently anchored via silicon atoms fused into the silica matrix. Moreover, comparison of the latter data with those of an analogous post-synthetic grafted SBA–NHC material allowed us to establish that, as expected, (i) it is most probably more homogeneous and (ii) it shows a more robust anchoring of the organic units. Finally, elemental mapping by energy dispersive X-ray spectroscopy in the scanning electron microscope demonstrated a very homogeneous distribution of the imidazolium units within the one-pot material, moreover with a high content. This study thus demonstrates that a relatively bulky and hydrophilic imidazolium unit can be directly co-condensed with TEOS in the presence of a structure-directing agent to provide in a single step a highly ordered and homogeneous mesoporous hybrid SBA–NHC material, possessing a significant number of cationic NHC sites

Highly optimized tolerance and power laws in dense and sparse resource regimes

Power law cumulative frequency $(P)$ vs. event size $(l)$ distributions $P(\geq l)\sim l^{-\alpha}$ are frequently cited as evidence for complexity and serve as a starting point for linking theoretical models and mechanisms with observed data. Systems exhibiting this behavior present fundamental mathematical challenges in probability and statistics. The broad span of length and time scales associated with heavy tailed processes often require special sensitivity to distinctions between discrete and continuous phenomena. A discrete Highly Optimized Tolerance (HOT) model, referred to as the Probability, Loss, Resource (PLR) model, gives the exponent $\alpha=1/d$ as a function of the dimension $d$ of the underlying substrate in the sparse resource regime. This agrees well with data for wildfires, web file sizes, and electric power outages. However, another HOT model, based on a continuous (dense) distribution of resources, predicts $\alpha= 1+ 1/d$. In this paper we describe and analyze a third model, the cuts model, which exhibits both behaviors but in different regimes. We use the cuts model to show all three models agree in the dense resource limit. In the sparse resource regime, the continuum model breaks down, but in this case, the cuts and PLR models are described by the same exponent.Comment: 19 pages, 13 figure

Ordered structure of FeGe₂ formed during solid-phase epitaxy

Fe3Si/Ge(Fe,Si)/Fe3Si thin-film stacks were grown by a combination of molecular beam epitaxy and solid-phase epitaxy (Ge on Fe3Si). The stacks were analyzed using electron microscopy, electron diffraction, and synchrotron x-ray diffraction. The Ge(Fe,Si) films crystallize in the well-oriented, layered tetragonal structure FeGe2 with space group P4mm. This kind of structure does not exist as a bulk material and is stabilized by the solid-phase epitaxy of Ge on Fe3Si. We interpret this as an ordering phenomenon induced by minimization of the elastic energy of the epitaxial film

Tuning the surface structure of supported PtNi_x bimetallic electrocatalysts for the methanol electro-oxidation reaction

The structures of PtNix nanoalloy particles were modified through thermal annealing in different atmospheres. The evolution of surface structures was uncovered by advanced transmission electron microscopy, and the structure–function correlation in methanol electro-oxidation was probed. It provided new insights into the design and synthesis of highly efficient electrocatalysts

Fluctuation-driven capacity distribution in complex networks

Maximizing robustness and minimizing cost are common objectives in the design of infrastructure networks. However, most infrastructure networks evolve and operate in a highly decentralized fashion, which may significantly impact the allocation of resources across the system. Here, we investigate this question by focusing on the relation between capacity and load in different types of real-world communication and transportation networks. We find strong empirical evidence that the actual capacity of the network elements tends to be similar to the maximum available capacity, if the cost is not strongly constraining. As more weight is given to the cost, however, the capacity approaches the load nonlinearly. In particular, all systems analyzed show larger unoccupied portions of the capacities on network elements subjected to smaller loads, which is in sharp contrast with the assumptions involved in (linear) models proposed in previous theoretical studies. We describe the observed behavior of the capacity-load relation as a function of the relative importance of the cost by using a model that optimizes capacities to cope with network traffic fluctuations. These results suggest that infrastructure systems have evolved under pressure to minimize local failures, but not necessarily global failures that can be caused by the spread of local damage through cascading processes

A Poissonian explanation for heavy-tails in e-mail communication

Patterns of deliberate human activity and behavior are of utmost importance in areas as diverse as disease spread, resource allocation, and emergency response. Because of its widespread availability and use, e-mail correspondence provides an attractive proxy for studying human activity. Recently, it was reported that the probability density for the inter-event time $\tau$ between consecutively sent e-mails decays asymptotically as $\tau^{-\alpha}$, with $\alpha \approx 1$. The slower than exponential decay of the inter-event time distribution suggests that deliberate human activity is inherently non-Poissonian. Here, we demonstrate that the approximate power-law scaling of the inter-event time distribution is a consequence of circadian and weekly cycles of human activity. We propose a cascading non-homogeneous Poisson process which explicitly integrates these periodic patterns in activity with an individual's tendency to continue participating in an activity. Using standard statistical techniques, we show that our model is consistent with the empirical data. Our findings may also provide insight into the origins of heavy-tailed distributions in other complex systems.Comment: 9 pages, 5 figure

Methane Decomposition and Carbon Growth on Y₂O₃, Yttria-Stabilized Zirconia, and ZrO₂

Carbon deposition following thermal methane decomposition under dry and steam reforming conditions has been studied on yttria-stabilized zirconia (YSZ), Y2O3 and ZrO2 by a range of different chemical, structural and spectroscopic characterization techniques, including aberration-corrected electron microscopy, Raman spectroscopy, electric impedance spectroscopy and volumetric adsorption techniques. Concordantly, all experimental techniques reveal the formation of a conducting layer of disordered nanocrystalline graphite covering the individual grains of the respective pure oxides after treatment in dry methane at temperatures T ≥ 1000 K. In addition, treatment under moist methane conditions causes additional formation of carbon-nanotube-like architectures by partial detachment of the graphite layers. All experiments show that during carbon growth, no substantial reduction of any of the oxides takes place. Our results therefore indicate that these pure oxides can act as efficient nonmetallic substrates for methane-induced growth of different carbon species with potentially important implications regarding their use in solid oxide fuel cells. By comparison of the three oxides we could moreover elucidate differences in the methane reactivities of the respective SOFC-relevant purely oxidic surfaces under typical SOFC operation conditions without the presence of metallic constituents