Object Kinetic Monte Carlo calculations of irradiated Fe-Cr dilute alloys: The effect of the interaction radius between substitutional Cr and self-interstitial Fe

ObjectKineticMonteCarlo models allow for the study of the evolution of the damage created by irradiation to time scales that are comparable to those achieved experimentally. Therefore, the essential ObjectKineticMonteCarlo parameters can be validated through comparison with experiments. However, this validation is not trivial since a large number of parameters is necessary, including migration energies of point defects and their clusters, binding energies of point defects in clusters, as well as the interactionradii. This is particularly cumbersome when describing an alloy, such as the Fe–Cr system, which is of interest for fusion energy applications. In this work we describe an ObjectKineticMonteCarlo model for Fe–Cr alloys in the dilute limit. The parameters used in the model come either from density functional theory calculations or from empirical interatomic potentials. This model is used to reproduce isochronal resistivity recovery experiments of electron irradiateddiluteFe–Cr alloys performed by Abe and Kuramoto. The comparison between the calculated results and the experiments reveal that an important parameter is the capture radius between substitutionalCr and self-interstitialFe atoms. A parametric study is presented on the effect of the capture radius on the simulated recovery curves.

A new set of relativistic screening constants for the screened hydrogenic model

AnewRelativisticScreenedHydrogenicModel has been developed to calculate atomic data needed to compute the optical and thermodynamic properties of high energy density plasmas. The model is based on anewset of universal screeningconstants, including nlj-splitting that has been obtained by fitting to a large database of ionization potentials and excitation energies. This database was built with energies compiled from the National Institute of Standards and Technology (NIST) database of experimental atomic energy levels, and energies calculated with the Flexible Atomic Code (FAC). The screeningconstants have been computed up to the 5p3/2 subshell using a Genetic Algorithm technique with an objective function designed to minimize both the relative error and the maximum error. To select the best set of screeningconstants some additional physical criteria has been applied, which are based on the reproduction of the filling order of the shells and on obtaining the best ground state configuration. A statistical error analysis has been performed to test the model, which indicated that approximately 88% of the data lie within a ±10% error interval. We validate the model by comparing the results with ionization energies, transition energies, and wave functions computed using sophisticated self-consistent codes and experimental data.

Optimal fits of diffusion constants from single-time data points of Brownian trajectories

Experimental methods based on single particle tracking (SPT) are being increasingly employed in the physical and biological sciences, where nanoscale objects are visualized with high temporal and spatial resolution. SPT can probe interactions between a particle and its environment but the price to be paid is the absence of ensemble averaging and a consequent lack of statistics. Here we address the benchmark question of how to accurately extract the diffusion constant of one single Brownian trajectory. We analyze a class of estimators based on weighted functionals of the square displacement. For a certain choice of the weight function these functionals provide the true ensemble averaged diffusion coefficient, with a precision that increases with the trajectory resolution.

MMonCa: A flexible and powerful new Kinetic Monte Carlo simulator

Kinetic Monte Carlo (KMC) is a widely used technique to simulate the evolution of radiation damage inside solids. Despite de fact that this technique was developed several decades ago, there is not an established and easy to access simulating tool for researchers interested in this field, unlike in the case of molecular dynamics or density functional theory calculations. In fact, scientists must develop their own tools or use unmaintained ones in order to perform these types of simulations. To fulfil this need, we have developed MMonCa, the Modular Monte Carlo simulator. MMonCa has been developed using professional C++ programming techniques and has been built on top of an interpreted language to allow having a powerful yet flexible, robust but customizable and easy to access modern simulator. Both non lattice and Lattice KMC modules have been developed. We will present in this conference, for the first time, the MMonCa simulator. Along with other (more detailed) contributions in this meeting, the versatility of MMonCa to study a number of problems in different materials (particularly, Fe and W) subject to a wide range of conditions will be shown. Regarding KMC simulations, we have studied neutron-generated cascade evolution in Fe (as a model material). Starting with a Frenkel pair distribution we have followed the defect evolution up to 450 K. Comparison with previous simulations and experiments shows excellent agreement. Furthermore, we have studied a more complex system (He-irradiated W:C) using a previous parametrization [1]. He-irradiation at 4 K followed by isochronal annealing steps up to 500 K has been simulated with MMonCa. The He energy was 400 eV or 3 keV. In the first case, no damage is associated to the He implantation, whereas in the second one, a significant Frenkel pair concentration (evolving into complex clusters) is associated to the He ions. We have been able to explain He desorption both in the absence and in the presence of Frenkel pairs and we have also applied MMonCa to high He doses and fluxes at elevated temperatures. He migration and trapping dominate the kinetics of He desorption. These processes will be discussed and compared to experimental results. [1] C.S. Becquart et al. J. Nucl. Mater. 403 (2010) 75

Bare-tether sheath and current: comparison of asymptotic theory and kinetic simulations in stationary plasma

Analytical expressions for current to a cylindrical Langmuir probe at rest in unmagnetized plasma are compared with results from both steady-state Vlasov and particle-in-cell simulations. Probe bias potentials that are much greater than plasma temperature (assumed equal for ions and electrons), as of interest for bare conductive tethers, are considered. At a very high bias, both the electric potential and the attracted-species density exhibit complex radial profiles; in particular, the density exhibits a minimum well within the plasma sheath and a maximum closer to the probe. Excellent agreement is found between analytical and numerical results for values of the probe radiusR close to the maximum radius Rmax for orbital-motion-limited (OML) collection at a particular bias in the following number of profile features: the values and positions of density minimum and maximum, position of sheath boundary, and value of a radius characterizing the no-space-charge behavior of a potential near the high-bias probe. Good agreement between the theory and simulations is also found for parametric laws jointly covering the following three characteristic R ranges: sheath radius versus probe radius and bias for Rmax; density minimum versus probe bias for Rmax; and (weakly bias-dependent) current drop below the OML value versus the probe radius for R > Rmax.

MMonCa: An Object Kinetic Monte Carlo simulator for damage irradiation evolution and defect diffusion

In this work, we introduce the Object Kinetic Monte Carlo (OKMC) simulator MMonCa and simulate the defect evolution in three different materials. We start by explaining the theory of OKMC and showing some details of how such theory is implemented by creating generic structures and algorithms in the objects that we want to simulate. Then we successfully reproduce simulated results for defect evolution in iron, silicon and tungsten using our simulator and compare with available experimental data and similar simulations. The comparisons validate MMonCa showing that it is powerful and flexible enough to be customized and used to study the damage evolution of defects in a wide range of solid materials.

Determination of the JWL constants for ANFO and emulsion explosives from cylinder test data

The Jones-Wilkins-Lee (JWL) equation of state parameters for ANFO and emulsion-type explosives have been obtained from cylinder test expansion measurements. The calculation method comprises a new radial expansion function, with a non-zero initial velocity at the onset of the expansion in order to comply with a positive Gurney energy at unit relative volume, as the isentropic expansion from the CJ state predicts. The equations reflecting the CJ state conditions and the measured expansion energy were solved for the JWL parameters by a non-linear least squares scheme. The JWL parameters of thirteen ANFO and emulsion type explosives have been determined in this way from their cylinder test expansion data. The results were evaluated through numerical modelling of the tests with the LS-DYNA hydrocode; the expansion histories from the modelling were compared with the measured ones, and excellent agreement was found.

Low Work-Function Thermionic Emission and Orbital-Motion-Limited Ion Collection at Bare-Tether Cathodic Contact

Una amarra electrodinámica (electrodynamic tether) opera sobre principios electromagnéticos intercambiando momento con la magnetosfera planetaria e interactuando con su ionosfera. Es un subsistema pasivo fiable para desorbitar etapas de cohetes agotadas y satélites al final de su misión, mitigando el crecimiento de la basura espacial. Una amarra sin aislamiento captura electrones del plasma ambiente a lo largo de su segmento polarizado positivamente, el cual puede alcanzar varios kilómetros de longitud, mientras que emite electrones de vuelta al plasma mediante un contactor de plasma activo de baja impedancia en su extremo catódico, tal como un cátodo hueco (hollow cathode). En ausencia de un contactor catódico activo, la corriente que circula por una amarra desnuda en órbita es nula en ambos extremos de la amarra y se dice que ésta está flotando eléctricamente. Para emisión termoiónica despreciable y captura de corriente en condiciones limitadas por movimiento orbital (orbital-motion-limited, OML), el cociente entre las longitudes de los segmentos anódico y catódico es muy pequeño debido a la disparidad de masas entre iones y electrones. Tal modo de operación resulta en una corriente media y fuerza de Lorentz bajas en la amarra, la cual es poco eficiente como dispositivo para desorbitar. El electride C12A7 : e−, que podría presentar una función de trabajo (work function) tan baja como W = 0.6 eV y un comportamiento estable a temperaturas relativamente altas, ha sido propuesto como recubrimiento para amarras desnudas. La emisión termoiónica a lo largo de un segmento así recubierto y bajo el calentamiento de la operación espacial, puede ser más eficiente que la captura iónica. En el modo más simple de fuerza de frenado, podría eliminar la necesidad de un contactor catódico activo y su correspondientes requisitos de alimentación de gas y subsistema de potencia, lo que resultaría en un sistema real de amarra “sin combustible”. Con este recubrimiento de bajo W, cada segmento elemental del segmento catódico de una amarra desnuda de kilómetros de longitud emitiría corriente como si fuese parte de una sonda cilíndrica, caliente y uniformemente polarizada al potencial local de la amarra. La operación es similar a la de una sonda de Langmuir 2D tanto en los segmentos catódico como anódico. Sin embargo, en presencia de emisión, los electrones emitidos resultan en carga espacial (space charge) negativa, la cual reduce el campo eléctrico que los acelera hacia fuera, o incluso puede desacelerarlos y hacerlos volver a la sonda. Se forma una doble vainas (double sheath) estable con electrones emitidos desde la sonda e iones provenientes del plasma ambiente. La densidad de corriente termoiónica, variando a lo largo del segmento catódico, podría seguir dos leyes distintas bajo diferentes condiciones: (i) la ley de corriente limitada por la carga espacial (space-charge-limited, SCL) o (ii) la ley de Richardson-Dushman (RDS). Se presenta un estudio preliminar sobre la corriente SCL frente a una sonda emisora usando la teoría de vainas (sheath) formada por la captura iónica en condiciones OML, y la corriente electrónica SCL entre los electrodos cilíndricos según Langmuir. El modelo, que incluye efectos óhmicos y el efecto de transición de emisión SCL a emisión RDS, proporciona los perfiles de corriente y potencial a lo largo de la longitud completa de la amarra. El análisis muestra que en el modo más simple de fuerza de frenado, bajo condiciones orbitales y de amarras típicas, la emisión termoiónica proporciona un contacto catódico eficiente y resulta en una sección catódica pequeña. En el análisis anterior, tanto la transición de emisión SCL a RD como la propia ley de emisión SCL consiste en un modelo muy simplificado. Por ello, a continuación se ha estudiado con detalle la solución de vaina estacionaria de una sonda con emisión termoiónica polarizada negativamente respecto a un plasma isotrópico, no colisional y sin campo magnético. La existencia de posibles partículas atrapadas ha sido ignorada y el estudio incluye tanto un estudio semi-analítico mediante técnica asintóticas como soluciones numéricas completas del problema. Bajo las tres condiciones (i) alto potencial, (ii) R = Rmax para la validez de la captura iónica OML, y (iii) potencial monotónico, se desarrolla un análisis asintótico auto-consistente para la estructura de plasma compleja que contiene las tres especies de cargas (electrones e iones del plasma, electrones emitidos), y cuatro regiones espaciales distintas, utilizando teorías de movimiento orbital y modelos cinéticos de las especies. Aunque los electrones emitidos presentan carga espacial despreciable muy lejos de la sonda, su efecto no se puede despreciar en el análisis global de la estructura de la vaina y de dos capas finas entre la vaina y la región cuasi-neutra. El análisis proporciona las condiciones paramétricas para que la corriente sea SCL. También muestra que la emisión termoiónica aumenta el radio máximo de la sonda para operar dentro del régimen OML y que la emisión de electrones es mucho más eficiente que la captura iónica para el segmento catódico de la amarra. En el código numérico, los movimientos orbitales de las tres especies son modelados para potenciales tanto monotónico como no-monotónico, y sonda de radio R arbitrario (dentro o más allá del régimen de OML para la captura iónica). Aprovechando la existencia de dos invariante, el sistema de ecuaciones Poisson-Vlasov se escribe como una ecuación integro-diferencial, la cual se discretiza mediante un método de diferencias finitas. El sistema de ecuaciones algebraicas no lineal resultante se ha resuelto de con un método Newton-Raphson paralelizado. Los resultados, comparados satisfactoriamente con el análisis analítico, proporcionan la emisión de corriente y la estructura del plasma y del potencial electrostático. ABSTRACT An electrodynamic tether operates on electromagnetic principles and exchanges momentum through the planetary magnetosphere, by continuously interacting with the ionosphere. It is a reliable passive subsystem to deorbit spent rocket stages and satellites at its end of mission, mitigating the growth of orbital debris. A tether left bare of insulation collects electrons by its own uninsulated and positively biased segment with kilometer range, while electrons are emitted by a low-impedance active device at the cathodic end, such as a hollow cathode, to emit the full electron current. In the absence of an active cathodic device, the current flowing along an orbiting bare tether vanishes at both ends and the tether is said to be electrically floating. For negligible thermionic emission and orbital-motion-limited (OML) collection throughout the entire tether (electron/ion collection at anodic/cathodic segment, respectively), the anodic-to-cathodic length ratio is very small due to ions being much heavier, which results in low average current and Lorentz drag. The electride C12A7 : e−, which might present a possible work function as low as W = 0.6 eV and moderately high temperature stability, has been proposed as coating for floating bare tethers. Thermionic emission along a thus coated cathodic segment, under heating in space operation, can be more efficient than ion collection and, in the simplest drag mode, may eliminate the need for an active cathodic device and its corresponding gas-feed requirements and power subsystem, which would result in a truly “propellant-less” tether system. With this low-W coating, each elemental segment on the cathodic segment of a kilometers-long floating bare-tether would emit current as if it were part of a hot cylindrical probe uniformly polarized at the local tether bias, under 2D probe conditions that are also applied to the anodic-segment analysis. In the presence of emission, emitted electrons result in negative space charge, which decreases the electric field that accelerates them outwards, or even reverses it, decelerating electrons near the emitting probe. A double sheath would be established with electrons being emitted from the probe and ions coming from the ambient plasma. The thermionic current density, varying along the cathodic segment, might follow two distinct laws under different con ditions: i) space-charge-limited (SCL) emission or ii) full Richardson-Dushman (RDS) emission. A preliminary study on the SCL current in front of an emissive probe is presented using the orbital-motion-limited (OML) ion-collection sheath and Langmuir’s SCL electron current between cylindrical electrodes. A detailed calculation of current and bias profiles along the entire tether length is carried out with ohmic effects considered and the transition from SCL to full RDS emission is included. Analysis shows that in the simplest drag mode, under typical orbital and tether conditions, thermionic emission provides efficient cathodic contact and leads to a short cathodic section. In the previous analysis, both the transition between SCL and RDS emission and the current law for SCL condition have used a very simple model. To continue, considering an isotropic, unmagnetized, colissionless plasma and a stationary sheath, the probe-plasma contact is studied in detail for a negatively biased probe with thermionic emission. The possible trapped particles are ignored and this study includes both semianalytical solutions using asymptotic analysis and complete numerical solutions. Under conditions of i) high bias, ii) R = Rmax for ion OML collection validity, and iii) monotonic potential, a self-consistent asymptotic analysis is carried out for the complex plasma structure involving all three charge species (plasma electrons and ions, and emitted electrons) and four distinct spatial regions using orbital motion theories and kinetic modeling of the species. Although emitted electrons present negligible space charge far away from the probe, their effect cannot be neglected in the global analysis for the sheath structure and two thin layers in between the sheath and the quasineutral region. The parametric conditions for the current to be space-chargelimited are obtained. It is found that thermionic emission increases the range of probe radius for OML validity and is greatly more effective than ion collection for cathodic contact of tethers. In the numerical code, the orbital motions of all three species are modeled for both monotonic and non-monotonic potential, and for any probe radius R (within or beyond OML regime for ion collection). Taking advantage of two constants of motion (energy and angular momentum), the Poisson-Vlasov equation is described by an integro differential equation, which is discretized using finite difference method. The non-linear algebraic equations are solved using a parallel implementation of the Newton-Raphson method. The results, which show good agreement with the analytical results, provide the results for thermionic current, the sheath structure, and the electrostatic potential.

Application of the homogenization techniques to the determination of the effective flexure constants of plate structural systems

A Mindlin plate with periodically distributed ribs patterns is analyzed by using homogenization techniques based on asymptotic expansion methods. The stiffness matrix of the homogenized plate is found to be dependent on the geometrical characteristics of the periodical cell, i.e. its skewness, plan shape, thickness variation etc. and on the plate material elastic constants. The computation of this plate stiffness matrix is carried out by averaging over the cell domain some solutions of different periodical boundary value problems. These boundary value problems are defined in variational form by linear first order differential operators on the cell domain and the boundary conditions of the variational equation correspond to a periodic structural problem. The elements of the stiffness matrix of homogenized plate are obtained by linear combinations of the averaged solution functions of the above mentioned boundary value problems. Finally, an illustrative example of application of this homogenization technique to hollowed plates and plate structures with ribs patterns regularly arranged over its area is shown. The possibility of using in the profesional practice the present procedure to the actual analysis of floors of typical buildings is also emphasized.