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At least 37 records · Page 2

Gaps labeling theorem for the bubble-diamond self-similar graphs

Abstract Motivated by the appearance of fractals in several areas of physics, especially in solid state physics and the physics of aperiodic order, and in other sciences, including the quantum information theory, we present a detailed spectral analysis for a new class of fractal-type diamond graphs, referred to as bubble-diamond graphs, and provide a gap-labeling theorem in the sense of Bellissard for the corresponding probabilistic graph Laplacians using the technique of spectral decimation. Labeling the gaps in the Cantor set by the normalized eigenvalue counting function, also known as the integrated density of states, we describe the gap labels as orbits of a second dynamical system that reflects the branching parameter of the bubble construction and the decimation structure. The spectrum of the natural Laplacian on limit graphs is shown generically to be pure point supported on a Cantor set, though one particular graph has a mixture of pure point and singularly continuous components.

Physics↗

Solid state crystal physics at very low temperatures

The properties of nearly perfect crystals was studied at cryogenic temperatures. A large Helium 3 and Helium 4 dilution refrigerator has been assembled, and is described. A cryostat suitable for cooling a 35 liter volume to .020 Kelvin was designed and constructed, together with instrumentation to observe the properties of nearly perfect crystals.

Davis, W.↗

Solid state crystal physics at very low temperatures

The mechanical dissipation (Q) and resonant frequency of a 15 kg silicon crystal were measured at cryogenic temperatures. In the experiment described, temperature control was incorporated to reduce the time derivative of the temperature. The results of the Q measurements with and without this temperature control are quite different. Measurements of the resonant frequency of the fundamental longitudinal mode of the silicon crystal from 6 to 300 Kelvin are presented and discussed with respect to temperature, df/dT. It is observed that frequency increases as temperature decreases down to about 16 Kelvin, i.e. dt/dT is negative. However, below this temperature the frequency decreases as temperature decreases, i.e. dt/dT is positive. It is suggested that this behavior is related to the coefficient of thermal contraction of silicon, which changes sign at 18 Kelvin. Continuation of these experiments to 20 mK is discussed.

Davis, W.↗

Highly ordered graphite (HOPG) to hexagonal diamond (lonsdaleite) phase transition observed on picosecond time scales using ultrafast x-ray diffraction

Here, the response of rapidly compressed highly oriented pyrolytic graphite (HOPG) normal to its basal plane was investigated at a pressure of ~80 GPa. Ultrafast x-ray diffraction using ~100 fs pulses at the Materials Under Extreme Conditions sector of the Linac Coherent Light Source was used to probe the changes in crystal structure resulting from picosecond timescale compression at laser drive energies ranging from 2.5 to 250 mJ. A phase transformation from HOPG to a highly textured hexagonal diamond structure is observed at the highest energy, followed by relaxation to a still highly oriented, but distorted graphite structure following release. We observe the formation of a highly oriented lonsdaleite within 20 ps, subsequent to compression. This suggests that a diffusionless martensitic mechanism may play a fundamental role in phase transition, as speculated in an early work on this system, and more recent static studies of diamonds formed in impact events.

58 GEOSCIENCES↗

Development of neural network force fields for corrosion studies

To fully understand the chemistry and physics of corrosion, novel methods of simulation must be developed. One approach is designing machine learning (ML) algorithms integrated with density functional theory to develop adaptive force fields to gain insight into corrosion behavior namely at the surface of metal oxides. Current methods of modeling corrosion are slow due to the computational cost of resolving both reaction mechanics and mass transport processes. Machine learning methods can be implemented to obtain structure-activity relationships at both the molecular and bulk scale while still retaining the accuracy of density functional theory (DFT) and significantly decreasing the time needed for simulations of complex chemical processes in the various environments of corrosion. Multiscale models are needed for corrosion studies to fully understand its processes not only at the atomic length scale (chemical bonding, energies, and forces), but also at the nano and meso length scales (solid-state physics and material science processes). Current methods of study include DFT, molecular dynamics, and Monte Carlo. The limitation of DFT is that only a small number of atoms or molecules can be simulated at that level of theory. Density functional theory is used to study the electronic structure of atoms and molecules, and calculate the force component of each atom. However, these calculations are limited to about 1000 atoms. Custom periodic boundary conditions (PBC) can be used to describe the various environments and defects that affect the atomic forces to produce a large data set from which a training set can be derived. Machine learning can be utilized to overcome the barrier of modeling macroscopic and multi-scale processes from ab initio calculations through the development of adaptive force fields. Local environments determine the atomic forces of a given system, therefore adaptive force fields must be created to produce reliable quantum mechanical calculations. This can be achieved by developing a learning algorithm that uses the mapped atomic forces or fingerprint as an input to produce energies and magnetic moments as output. A systematic approach was used to begin to build a data set in order to accurately describe the atomic forces in various environments. In Figure 4 below, a simple PBC cell of Fe{sub 2}O{sub 3} was first optimized. A surface optimization was performed next, followed by a hydroxylated surface optimization. Once this calculation has converged, the adsorption of halide species to the hydroxylated surface will be investigated. TensorFlow is an open source platform for machine learning developed by Google. Using a high level application program interface (API) such as Keras allows for building and training ML models easily in a number of different environments and languages. For this project, a neural network was developed within Anaconda in Python. Future Work: Further development of reference data set; Refining neural network and learning algorithm; Fingerprinting atomic environment to enable mapping of atomic force components; Choosing appropriate training set from reference data; Learning from training set and enabling non-linear mapping of training set fingerprints and the atomic forces; Estimation of uncertainty to identify ranges of outside applicability; Testing and analysis of molecular dynamic simulations.

36 MATERIALS SCIENCE↗

Point defects and impurities in fluorite PuO 2

The native surface oxide of plutonium plays a critical role in ensuring the stability and safe storage of the underlying metal; consequently, understanding the role of defects and impurities in determining the properties of the oxide layer is critical. Here, in this study, we use hybrid density-functional theory calculations to evaluate the electronic structure and defect chemistry of PuO 2 , the most stable of the native oxide phases, including both native and extrinsic defects. We find that oxygen vacancies (𝑉 O ) form readily in PuO 2 , as do polarons. Electron polarons (𝜂 − ) are the lowest-energy acceptor species in PuO 2 , while the charge compensating donor species will shift from 𝑉 O under O-poor conditions to hole polarons (𝜂 + ) under O-rich conditions. Nitrogen and fluorine can substitute readily for oxygen atoms under O-poor conditions, while fluorine can also incorporate in an interstitial configuration (F$^−_i$) under more O-rich conditions. Carbon and chlorine incorporation in PuO 2 will be very limited. We also evaluate the kinetic barriers for oxygen-related defects, which we find to diffuse readily when present. Our results provide valuable insights into the critical role and variable chemistry of point defects and impurities in PuO 2 , which in turn have important implications for the safe storage of the underlying metal layer. In short, exposure of freshly prepared plutonium to reactive nitrogen- and fluorine-containing contaminants should be avoided, while carbon- or chlorine-containing contaminants are less likely to incorporate readily into the oxide.

Materials science↗

Crystallographic map: A general lattice and basis formalism enabling efficient and discretized exploration of crystallographic phase space

Three-dimensional lattices are fundamental to solid-state physics. The description of a lattice with an atomic basis constitutes the necessary information to predict solid phase properties and evolution. Here, we present an algorithm for systematically exploring crystallographic phase space. Further, coupled with ab initio techniques, such as density functional theory, this algorithm offers an approach for exploring and tuning materials behavior, with a broad range of potential applications: particularly martensitic phase transformations and materials stability.

36 MATERIALS SCIENCE↗

Applications of surface analysis and surface theory in tribology

Tribology, the study of adhesion, friction and wear of materials is a complex field which requires a knowledge of solid state physics, surface physics, chemistry, material science and mechanical engineering. It has been dominated, however, by the more practical need to make equipment work. With the advent of surface analysis and advances in surface and solid state theory, a new dimension has been added to the analysis of interactions at tribological interfaces. In this paper the applications of tribological studies and their limitations are presented. Examples from research at the NASA Lewis Research Center are given. Emphasis is on fundamental studies involving the effects of monolayer coverage and thick films on friction and wear. A summary of the current status of theoretical calculations of defect energetics is presented. In addition, some new theoretical techniques which enable simplified quantitative calculations of adhesion, fracture and friction are discussed.

Ferrante, John↗

Applications of surface analysis and surface theory in tribology

Tribology, the study of adhesion, friction and wear of materials, is a complex field which requires a knowledge of solid state physics, surface physics, chemistry, material science, and mechanical engineering. It has been dominated, however, by the more practical need to make equipment work. With the advent of surface analysis and advances in surface and solid-state theory, a new dimension has been added to the analysis of interactions at tribological interfaces. In this paper the applications of tribological studies and their limitations are presented. Examples from research at the NASA Lewis Research Center are given. Emphasis is on fundamental studies involving the effects of monolayer coverage and thick films on friction and wear. A summary of the current status of theoretical calculations of defect energetics is presented. In addition, some new theoretical techniques which enable simplified quantitative calculations of adhesion, fracture, and friction are discussed.

Ferrante, John↗

Pressure-Induced Phase Transformations

The study of phase transitions in solids under high pressure conditions is a very active and vigorous research field. In recent decades, thanks to the development of experimental techniques and computer simulations, a plethora of important discoveries has been made under high-pressure conditions. Many of the achievements accomplished in recent years a affect various research fields, from solid-state physics to chemistry, materials science, and geophysics. They not only contribute to a deeper understanding of solid-sold phase transitions but also to a better understanding of melting under compression.

36 MATERIALS SCIENCE↗