Strain distribution due to surface domains: a self-consistent approach with respect to surface elasticity

Elastically mediated interactions between surface domains are classically described in terms of point forces. Such point forces lead to local strain divergences that are usually avoided by introducing a poorly defined cut-off length. In this work, we develop a self-consistent approach in which the strain field induced by the surface domains is expressed as the solution of an integral equation that contains surface elastic constants, S ij . For surfaces with positive S ij the new approach avoids the introduction of a cut-off length. The classical and the new approaches are compared in case of 1-D periodic ribbons.

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Strain distribution due to surface domains: a self-consistent approach with respect to surface elasticity

nano Online ◽

10.1515/nano.bjneah.6.30 ◽

2016 ◽

Author(s):

Fuhr ◽

Müller

Keyword(s):

Strain Distribution ◽

Surface Elasticity ◽

Self Consistent ◽

Surface Domains ◽

Consistent Approach

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A New Approach to Model Heterogonous Recrystallization Kinetics Based on the Natural Inhomogeneity of Deformation

Materials Science Forum ◽

10.4028/www.scientific.net/msf.558-559.1139 ◽

2007 ◽

Vol 558-559 ◽

pp. 1139-1144 ◽

Cited By ~ 1

Author(s):

Hai Wen Luo ◽

Lian Zi An ◽

Hong Wei Ni

Keyword(s):

Standard Deviation ◽

Normal Distribution ◽

Strain Distribution ◽

Distribution Density ◽

Local Strain ◽

Avrami Exponent ◽

Recrystallization Process ◽

Rate Parameter ◽

New Approach ◽

Modified Equation

The classical JMAK equation was modified by combination with distribution density of the rate parameter k, which was deduced from a normal distribution of local strain. The modified equation is able to calculate the JMAK plots and the average Avrami exponent to characterize the entire heterogeneous recrystallization process. This new extension can successfully describe the relevant experimental observations, such as a smaller exponent than the basic JMAK theory predicts, and a decreasing slope of JMAK plots with the proceeding recrystallization. Moreover, it reveals that the Avrami exponent observed experimentally should significantly decrease with the increasing standard deviation of local strain distribution. In addition, it has a great potential to explain why most of experimentally observed values of Avrami exponents are less than 2 and why the Avrami exponent is insensitive to temperature and deformation conditions when the real standard deviation of local strain distribution in deformed metals is known.

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Strain analysis with nanometer resolution using a conventional transmission electron microsopy technique: electron diffraction contrast imaging revisited

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100137215 ◽

1995 ◽

Vol 53 ◽

pp. 168-169

Author(s):

Koenraad G F Janssens ◽

Omer Van der Biest ◽

Jan Vanhellemont ◽

Herman E Maes ◽

Robert Hull

Keyword(s):

Electron Diffraction ◽

Strain Field ◽

Elastic Strain ◽

Strain Analysis ◽

Local Strain ◽

Contrast Imaging ◽

Strain Characterization ◽

Physical Mechanisms ◽

Diffraction Contrast ◽

Transmission Electron

There is a growing need for elastic strain characterization techniques with submicrometer resolution in several engineering technologies. In advanced material science and engineering the quantitative knowledge of elastic strain, e.g. at small particles or fibers in reinforced composite materials, can lead to a better understanding of the underlying physical mechanisms and thus to an optimization of material production processes. In advanced semiconductor processing and technology, the current size of micro-electronic devices requires an increasing effort in the analysis and characterization of localized strain. More than 30 years have passed since electron diffraction contrast imaging (EDCI) was used for the first time to analyse the local strain field in and around small coherent precipitates1. In later stages the same technique was used to identify straight dislocations by simulating the EDCI contrast resulting from the strain field of a dislocation and comparing it with experimental observations. Since then the technique was developed further by a small number of researchers, most of whom programmed their own dedicated algorithms to solve the problem of EDCI image simulation for the particular problem they were studying at the time.

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On the Modular Operator of Mutli-component Regions in Chiral CFT

Communications in Mathematical Physics ◽

10.1007/s00220-021-04054-6 ◽

2021 ◽

Author(s):

Stefan Hollands

Keyword(s):

Field Theory ◽

Integral Equation ◽

Hilbert Problem ◽

Matrix Elements ◽

New Approach ◽

Conformal Field ◽

The Matrix ◽

Kms Condition ◽

Modular Operator ◽

Riemann Hilbert Problem

AbstractWe introduce a new approach to find the Tomita–Takesaki modular flow for multi-component regions in general chiral conformal field theory. Our method is based on locality and analyticity of primary fields as well as the so-called Kubo–Martin–Schwinger (KMS) condition. These features can be used to transform the problem to a Riemann–Hilbert problem on a covering of the complex plane cut along the regions, which is equivalent to an integral equation for the matrix elements of the modular Hamiltonian. Examples are considered.

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