Since the automation of the electron backscatter diffraction (EBSD) technique, EBSD systems have become commonplace in microscopy facilities within materials science and geology research laboratories around the world. The acceptance of the technique is primarily due to the capability of EBSD to aid the research scientist in understanding the crystallographic aspects of microstructure. There has been considerable interest in using EBSD to quantify strain at the submicron scale. To apply EBSD to the characterization of strain, it is important to understand what is practically possible and the underlying assumptions and limitations. This work reviews the current state of technology in terms of strain analysis using EBSD. First, the effects of both elastic and plastic strain on individual EBSD patterns will be considered. Second, the use of EBSD maps for characterizing plastic strain will be explored. Both the potential of the technique and its limitations will be discussed along with the sensitivity of various calculation and mapping parameters.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S1431927611000055

A review of strain analysis using electron backscatter diffraction.

Statistical Mechanics. — A Set of Lectures

In this series of talks, I will discuss the fluid-dynamic-type equations that is derived from the Boltzmann equation as its the asymptotic behavior for small mean free path. The study of the relation of the two systems describing the behavior of a gas, the fluid-dynamic system and the Boltzmann system, has a long history and many works have been done. The Hilbert expansion and the Chapman–Enskog expansion are well-known among them. The behavior of a gas in the continuum limit, however, is not so simple as is widely discussed by superficial understanding of these solutions. The correct behavior has to be investigated by classifying the physical situations. The results are largely different depending on the situations. There is an important class of problems for which neither the Euler equations nor the Navier–Stokes give the correct answer. In these two expansions themselves, an initialor boundaryvalue problem is not taken into account. We will discuss the fluid-dynamic-type equations together with the boundary conditions that describe the behavior of the gas in the continuum limit by appropriately classifying the physical situations and taking the boundary condition into account. Here the result for the time-independent case is summarized. The time-dependent case will also be mentioned in the talk. The velocity distribution function approaches a Maxwellian fe, whose parameters depend on the position in the gas, in the continuum limit. The fluid-dynamictype equations that determine the macroscopic variables in the limit differ considerably depending on the character of the Maxwellian. The systems are classified by the size of |fe− fe0|/fe0, where fe0 is the stationary Maxwellian with the representative density and temperature in the gas. (1) |fe − fe0|/fe0 = O(Kn) (Kn : Knudsen number, i.e., Kn = `/L; ` : the reference mean free path. L : the reference length of the system) : S system (the incompressible Navier–Stokes set with the energy equation modified). (1a) |fe − fe0|/fe0 = o(Kn) : Linear system (the Stokes set). (2) |fe − fe0|/fe0 = O(1) with | ∫ ξifedξ|/ ∫ |ξi|fedξ = O(Kn) (ξi : the molecular velocity) : SB system [the temperature T and density ρ in the continuum limit are determined together with the flow velocity vi of the first order of Kn amplified by 1/Kn (the ghost effect), and the thermal stress of the order of (Kn) must be retained in the equations (non-Navier–Stokes effect). The thermal creep[1] in the boundary condition must be taken into account. (3) |fe − fe0|/fe0 = O(1) with | ∫ ξifedξ|/ ∫ |ξi|fedξ = O(1) : E+VB system (the Euler and viscous boundary-layer sets). E system (Euler set) in the case where the boundary is an interface of the gas and its condensed phase. The fluid-dynamic systems are classified in terms of the macroscopic parameters that appear in the boundary condition. Let Tw and δTw be, respectively, the characteristic values of the temperature and its variation of the boundary. Then, the fluid-dynamic systems mentioned above are classified with the nondimensional temperature variation δTw/Tw and Reynolds number Re as shown in Fig. 1. In the region SB, the classical gas dynamics is inapplicable, that is, neither the Euler

Kinetic Theory and Fluid Dynamics

Electrons and Phonons

The accelerating rate at which new materials are appearing, and transforming the engineering world, only serves to emphasize the vast potential for novel material structure, and related performance. Microstructure-sensitive design (MSD) aims at providing inverse design methodologies that facilitate design of material internal structure for performance optimization. Spectral methods are applied across the structure, property and processing design spaces in order to compress the computational requirements for linkages between the spaces and enable inverse design. Research has focused mainly on anisotropic, polycrystalline materials, where control of local crystal orientation can result in a broad range of property combinations. This review presents the MSD framework in the context of both the engineering advances that have led to its creation, and those that complement or provide alternative methods for design of materials (meaning ‘optimization of material structure’ in this context). A variety of definitions for the structure of materials are presented, with an emphasis on correlation functions; and spectral methods are introduced for compact descriptions and efficient computations. The microstructure hull is defined as the design space for structure in the spectral framework. Reconstruction methods provide invertible links between statistical descriptions of structure, and deterministic instantiations. Subsequently, structure–property relations are reviewed, and again subjected to representation via spectral methods. The concept of a property closure is introduced as the design space for performance optimization, and methods for moving between the closures and hulls are presented as the basis for the subsequent discussion on microstructure design. Finally, the spectral framework is applied to deformation processes, and methodologies that facilitate process design are reviewed.

Microstructure Sensitive Design for Performance Optimization

http://li.mit.edu/Stuff/RHW/Upload/Kacher2009.pdf

Bragg's Law diffraction simulations for electron backscatter diffraction analysis.

We review Monte Carlo methods for solving the Boltzmann equation for applications to small-scale transport processes, with particular emphasis on nanoscale heat transport as mediated by phonons. Our discussion reviews the numerical foundations of Monte Carlo algorithms, basic simulation methodology, as well as recent developments in the field. Examples of the latter include formulations for calculating the effective thermal conductivity of periodically nanostructured materials and variance-reduction methodologies for reducing the computational cost associated with statistical sampling of field properties of interest, such as the temperature and heat flux. Recent developments are presented in the context of applications of current practical interest, including multiscale problems that have motivated some of the most recent developments.

Monte carlo methods for solving the boltzmann transport equation

We present a deviational Monte Carlo method for solving the Boltzmann-Peierls equation with ab initio 3-phonon scattering, for temporally and spatially dependent thermal transport problems in arbitrary geometries. Phonon dispersion relations and transition rates for graphene are obtained from density functional theory calculations. The ab initio scattering operator is simulated by an energy-conserving stochastic algorithm embedded within a deviational, low-variance Monte Carlo formulation. The deviational formulation ensures that simulations are computationally feasible for arbitrarily small temperature differences, while the stochastic treatment of the scattering operator is both efficient and exhibits no timestep error. The proposed method, in which geometry and phonon-boundary scattering are explicitly treated, is extensively validated by comparison to analytical results, previous numerical solutions and experiments. It is subsequently used to generate solutions for heat transport in graphene ribbons of various geometries and evaluate the validity of some common approximations found in the literature. Our results show that modeling transport in long ribbons of finite width using the homogeneous Boltzmann equation and approximating phonon-boundary scattering using an additional homogeneous scattering rate introduces an error on the order of 10% at room temperature, with the maximum deviation reaching 30% in the middle of the transition regime.

/pdf/deviational-simulation-of-phonon-transport-in-graphene-3ngz410l2s.pdf

Deviational simulation of phonon transport in graphene ribbons with ab initio scattering

The thermal conductivity of amorphous TaOx memristive films having variable oxygen content is measured using time domain thermoreflectance. Thermal transport is described by a two-part model where the electrical contribution is quantified via the Wiedemann-Franz relation and the vibrational contribution by the minimum thermal conductivity limit for amorphous solids. The vibrational contribution remains constant near 0.9 W/mK regardless of oxygen concentration, while the electrical contribution varies from 0 to 3.3 W/mK. Thus, the dominant thermal carrier in TaOx switches between vibrations and charge carriers and is controllable either by oxygen content during deposition, or dynamically by field-induced charge state migration.

Thermal transport in tantalum oxide films for memristive applications

It has become apparent through experimentation at the micro- and nanolevels that the crystalline defects known as dislocations have significant effects on a material's properties. Accordingly, a complete material state description must include the characterization of the dislocated state. However, this characterization presents a twofold problem: resolution and representation. In general, high-resolution microscopy techniques are only useful for considering a few dislocations at a time, but automated high-speed methods are only capable of resolving dislocation densities well above the average density in a typical annealed metal. The second challenge is developing a method of representation for the dislocated state. Unlike most state quantities, dislocation lengths are not conserved and complete representation would require tracking of position, momentum, and interactions, as well as the creation and annihilation of dislocations. Such a scheme becomes unwieldy when considering the large numbers of dislocations involved in common crystal plasticity. In 1970, Kroner ("Initial Studies of a Plasticity Theory Based Upon Statistical Mechanics," Inelastic Behaviors of Solids (Materials Sciences and Engineering), M. F. Kanninen et al., eds., McGraw-Hill, New York, pp. 137-147), a pioneer in the continuum representation of dislocations, proposed a statistical method using n-point correlations to classify the dislocated state in a compact form. In addition to providing a convenient form, the correlations naturally identify dipoles, multipoles, and other higher order structures, such as cells, networks, and braids. As formulated, Kroner's method would require high-resolution microscopy techniques, which limits its utility for experimental measurements. The current work presents a modification to Kroner's method that would allow it to be used within the currently available resolution limits of bulk microscopy. Furthermore, in this work, newly developed microscopy techniques are employed to refine those resolution limits to more significant levels. The high-resolution bulk dislocation characterization is applied to a well-annealed nickel specimen and the results including visualizations of mesoscale structures are presented.

Colin Landon

Papers

Bragg's Law diffraction simulations for electron backscatter diffraction analysis.

Monte carlo methods for solving the boltzmann transport equation

Deviational simulation of phonon transport in graphene ribbons with ab initio scattering

Thermal transport in tantalum oxide films for memristive applications

High-Resolution Methods for Characterizing Mesoscale Dislocation Structures