Average and local strain fields in nanocrystals

2019 ◽  
Vol 52 (2) ◽  
pp. 262-273 ◽  
Author(s):  
Shangmin Xiong ◽  
Seung-Yub Lee ◽  
Ismail Cevdet Noyan
Keyword(s):  
Gold Nanoparticles ◽  
Strain Analysis ◽  
Local Strain ◽  
Real Space ◽  
Dynamics Modeling ◽  
Lattice Strains ◽  
Unit Cells ◽  
Local Lattice ◽  
Strain Components ◽  
Average Lattice

This article presents a rigorous and self-consistent comparison of lattice distortion and deformation fields existing in energy-optimized pseudo-spherical gold nanoparticles obtained from real-space and powder diffraction strain analysis techniques. The changes in atomic positions resulting from energy optimization (relaxation) of ideally perfect gold nanoparticles were obtained using molecular dynamics modeling. The relaxed atomic coordinates were then used to compute the displacement, rotation and strain components in all unit cells within the energy-optimized (relaxed) particles. It was seen that all of these terms were distributed heterogeneously along the radial and tangential directions within the nanospheroids. The heterogeneity was largest in the first few atomic shells adjacent to the nanoparticle surface, where the continuity of crystal lattice vectors originating from the interior layers was broken because of local lattice rotations. These layers also exhibited maximum shear and normal strains. These (real-space) strain values were then compared with the average lattice strains obtained by refining the computed diffraction patterns of such particles. The results show that (i) relying solely on full-pattern refinement techniques for lattice strain analysis might lead to erroneous conclusions about the dimensionality and symmetry of deformation within relaxed nanoparticles; (ii) the lattice strains within such relaxed particles should be considered `eigenstrains' (`inherent strains') as defined by Mura [Micromechanics of Defects in Solids, (1991), 2nd ed., Springer]; and (iii) the stress/strain state within relaxed nanoparticles cannot be analyzed rigorously using the constitutive equations of linear elasticity.

Strain Analysis of Si by FEM and Energy-Filtering CBED

2002 ◽  
Vol 8 (1) ◽  
pp. 11-15 ◽  
Author(s):  
Tetsuya Okuyama ◽  
Masaru Nakayama ◽  
Yoshitsugu Tomokiyo ◽  
Omer Van der Biest
Keyword(s):  
Maximum Shear Stress ◽  
Strain Analysis ◽  
Stress Fields ◽  
Shear Stresses ◽  
Direction Parallel ◽  
Energy Filtering ◽  
Lattice Strains ◽  
Probe Size ◽  
Local Lattice ◽  
Convergent Beam

Lattice strains around a platelet oxygen precipitate in Si wafer is studied by energy filtering convergent-beam electron diffraction (CBED) and calculations based on the finite element method (FEM). Local lattice strains are measured from CBED patterns obtained with a probe size less than 2 nm in a specimen thicker than 450 nm. Strains measured are compressive along a direction normal to a plate of the precipitate and tensile along a direction parallel to the plate. Two-dimensional stress fields near the precipitate are obtained with FEM computer analyses by fitting the measured strains. It appears that shear stresses are concentrated at the end of the precipitate edge and the maximum shear stress at an interface between the precipitate and the Si-matrix is 1.9 GPa. It is demonstrated that a combination of the energy filtering CBED and FEM is very useful for the study of local strains near interfaces in semiconductor devices, in particular for the study of stress fields that are too steep for application of the conventional CBED technique.

scholarly journals Local lattice strain around alloying element and martensitic transformation in titanium alloys

2020 ◽  
Vol 321 ◽  
pp. 11009
Author(s):  
M. Morinaga ◽  
H. Yukawa ◽  
M. Yoshino
Keyword(s):  
Martensitic Transformation ◽  
Titanium Alloys ◽  
Strain Energy ◽  
Lattice Strain ◽  
Extreme Case ◽  
Local Strain ◽  
Absolute Temperature ◽  
Lattice Strains ◽  
Local Lattice ◽  
First Time

Local strain is introduced into the lattice around solute atom due to the size mismatch between solute and solvent atoms in alloy. In this study, local lattice strains are calculated for the first time in titanium alloys, using the plane-wave pseudopotential method. As an extreme case, the local lattice strain around a vacancy is also calculated in various bcc, fcc and hcp metals. It is found that the local strain energy is very high in both bcc Ti and bcc Fe, where the martensitic transformation takes place. From a series of calculations, it is shown that the magnitude of the strain energy stored in the local lattice is comparable to the thermal energy, kBT, where kB is the Boltzmann constant and T is the absolute temperature. Therefore, the presence of local lattice strains in alloy could influence the phase stability that varies largely depending on temperatures. For example, the local lattice strain correlates with the martensitic transformation start temperature, Ms, in binary titanium alloys.

A study of the strain distribution by scanning X-ray diffraction on GaP/Si for III–V monolithic integration on silicon

2019 ◽  
Vol 52 (4) ◽  
pp. 809-815 ◽  
Author(s):  
Ang Zhou ◽  
Yan Ping Wang ◽  
Charles Cornet ◽  
Yoan Léger ◽  
Laurent Pédesseau ◽  
...  
Keyword(s):  
Plane Strain ◽  
Local Strain ◽  
Real Space ◽  
Monolithic Integration ◽  
Misfit Dislocations ◽  
X Ray Diffraction ◽  
X Ray ◽  
Microscopy Technique ◽  
Transmission Electron ◽  
Local Lattice

A synchrotron-based scanning X-ray diffraction study on a GaP/Si pseudo-substrate is reported, within the context of the monolithic integration of photonics on silicon. Two-dimensional real-space mappings of local lattice tilt and in-plane strain from the scattering spot distributions are measured on a 200 nm partially relaxed GaP layer grown epitaxially on an Si(001) substrate, using an advanced sub-micrometre X-ray diffraction microscopy technique (K-Map). Cross-hatch-like patterns are observed in both the local tilt mappings and the in-plane strain mappings. The origin of the in-plane local strain variation is proposed to be a result of misfit dislocations, according to a comparison between in-plane strain mappings and transmission electron microscopy observations. Finally, the relationship between the in-plane strain and the free surface roughness is also discussed using a statistical method.

The structure of gold nanoparticles: molecular dynamics modeling and its verification by X-ray diffraction

2020 ◽  
Vol 53 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Michał Kamiński ◽  
Karolina Jurkiewicz ◽  
Andrzej Burian ◽  
Aleksander Bródka
Keyword(s):  
Molecular Dynamics ◽  
Gold Nanoparticles ◽  
Real Space ◽  
Atomic Scale ◽  
Noble Metal Nanoparticles ◽  
Surface Relaxation ◽  
Detailed Knowledge ◽  
Dynamics Modeling ◽  
X Ray Diffraction ◽  
X Ray

Noble metal nanoparticles exhibit unique physical, chemical, biomedical, catalytic and optical properties. Understanding these properties and further development of production methods entail detailed knowledge of the structure at the atomic scale. Gold nanoparticles with multimodal size distribution were synthesized on porous silica and their atomic scale structure was studied by X-ray diffraction. The obtained experimental data are compared with molecular dynamics simulations. Spherical models of the Au nanoparticles, defined by ensembles of the Cartesian coordinates of constituent atoms, were generated and their geometry was optimized by applying the LAMMPS software. The comparison was performed in both reciprocal and real space. A good agreement is achieved for the models with disorder that can be related to surface relaxation effects and vacancy defects. The approach adopted here may have wider applications for further structural studies of other nanomaterials, offering direct verification of simulation results by experiment.

Correlation averaging of two-dimensional crystals: basic strategy and refinements

1986 ◽  
Vol 44 ◽  
pp. 136-139
Author(s):  
W. Baumeister ◽  
R. Rachel ◽  
R. Guckenberger ◽  
R. Hegerl
Keyword(s):  
Low Dose ◽  
Signal To Noise Ratio ◽  
Real Space ◽  
Fourier Domain ◽  
Two Dimensional ◽  
Signal To Noise ◽  
Unit Cells ◽  
Lateral Displacements ◽  
Established Technique ◽  
Crystalline Array

IntroductionCorrelation averaging (CAV) is meanwhile an established technique in image processing of two-dimensional crystals /1,2/. The basic idea is to detect the real positions of unit cells in a crystalline array by means of correlation functions and to average them by real space superposition of the aligned motifs. The signal-to-noise ratio improves in proportion to the number of motifs included in the average. Unlike filtering in the Fourier domain, CAV corrects for lateral displacements of the unit cells; thus it avoids the loss of resolution entailed by these distortions in the conventional approach. Here we report on some variants of the method, aimed at retrieving a maximum of information from images with very low signal-to-noise ratios (low dose microscopy of unstained or lightly stained specimens) while keeping the procedure economical.

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

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.

Delamination in the scoring and folding of paperboard

TAPPI Journal ◽  
2012 ◽  
Vol 11 (1) ◽  
pp. 61-66 ◽  
Author(s):  
DOEUNG D. CHOI ◽  
SERGIY A. LAVRYKOV ◽  
BANDARU V. RAMARAO
Keyword(s):  
Finite Element ◽  
Plane Deformation ◽  
Strain Analysis ◽  
Local Strain ◽  
Uniaxial Stress ◽  
Material Model ◽  
Element Model ◽  
Plastic Behavior ◽  
Stress Strain ◽  
Strain Fields

Delamination between layers occurs during the creasing and subsequent folding of paperboard. Delamination is necessary to provide some stiffness properties, but excessive or uncontrolled delamination can weaken the fold, and therefore needs to be controlled. An understanding of the mechanics of delamination is predicated upon the availability of reliable and properly calibrated simulation tools to predict experimental observations. This paper describes a finite element simulation of paper mechanics applied to the scoring and folding of multi-ply carton board. Our goal was to provide an understanding of the mechanics of these operations and the proper models of elastic and plastic behavior of the material that enable us to simulate the deformation and delamination behavior. Our material model accounted for plasticity and sheet anisotropy in the in-plane and z-direction (ZD) dimensions. We used different ZD stress-strain curves during loading and unloading. Material parameters for in-plane deformation were obtained by fitting uniaxial stress-strain data to Ramberg-Osgood plasticity models and the ZD deformation was modeled using a modified power law. Two-dimensional strain fields resulting from loading board typical of a scoring operation were calculated. The strain field was symmetric in the initial stages, but increasing deformation led to asymmetry and heterogeneity. These regions were precursors to delamination and failure. Delamination of the layers occurred in regions of significant shear strain and resulted primarily from the development of large plastic strains. The model predictions were confirmed by experimental observation of the local strain fields using visual microscopy and linear image strain analysis. The finite element model predicted sheet delamination matching the patterns and effects that were observed in experiments.

Stress Analysis of Tire Sections

1996 ◽  
Vol 24 (4) ◽  
pp. 349-366 ◽  
Author(s):  
T-M. Wang ◽  
I. M. Daniel ◽  
K. Huang
Keyword(s):  
Finite Element ◽  
Internal Pressure ◽  
Stress Analysis ◽  
Strain Analysis ◽  
Experimental Stress ◽  
Inflation Pressure ◽  
Substantial Agreement ◽  
Finite Element Stress Analysis ◽  
Strain Components ◽  
Fringe Patterns

Abstract An experimental stress-strain analysis by means of the Moiré method was conducted in the area of the tread and belt regions of tire sections. A special loading fixture was designed to support the tire section and load it in a manner simulating service loading and allowing for Moiré measurements. The specimen was loaded by imposing a uniform fixed deflection on the tread surface and increasing the internal pressure in steps. Moiré fringe patterns were recorded and analyzed to obtain strain components at various locations of interest. Maximum strains in the range of 1–7% were determined for an effective inflation pressure of 690 kPa (100 psi). These results were in substantial agreement with results obtained by a finite element stress analysis.

Waves and particles in the crystal

2020 ◽  
pp. 78-136
Author(s):  
Sandip Tiwari
Keyword(s):  
Real Space ◽  
Crystalline Solid ◽  
Space Filling ◽  
Periodic Oscillations ◽  
Crystalline Environment ◽  
Seitz Cell ◽  
Unit Cells ◽  
Bloch’S Theorem ◽  
Periodic Arrangement ◽  
Versus Crystal

This chapter provides the groundwork necessary to mathematically describe the crystalline solid that is to be the semiconductor used to explore the variety of interactions and cause and chance behaviors that physics builds insights into. The crystalline environment can be portrayed as a space-filling periodic arrangement consisting of a lattice with an atomic basis. The periodic arrangement leads to real space and reciprocal space descriptions with unit cells—the Wigner-Seitz cell and the Brillouin and Jones zones—where a variety of characteristics can be represented. Bloch’s theorem with its modulation function of the plane wave of a quantized wavevector, momentum versus crystal momentum, together with the consequences of symmetries and periodic perturbation in the appearance of bandgaps, is discussed for electron states. Phonons as particles for periodic oscillations of atoms, their modes and various branches, and consequences of ionicity leading to frequency-dependent permittivity are discussed.

Stress Analysis of Smart Beam Energy Harvesters

2016 ◽  
Author(s):  
Nathan S. Hosking ◽  
Zahra Sotoudeh
Keyword(s):  
Smart Materials ◽  
Mechanical Energy ◽  
Strain Analysis ◽  
Electrical Energy ◽  
Structural Dynamic ◽  
Energy Harvesters ◽  
Beam Equations ◽  
Variational Asymptotic ◽  
Strain Components ◽  
Smart Beam

In this paper, we study fully coupled electromagnetic-elastic behaviors present in the structures of smart beams using variational asymptotic beam sections and geometrically exact fully intrinsic beam equations combined in a consistent theory. We present results for smart beams under various oscillatory loads in both the axial and transverse directions and calculate the corresponding deformations. Recovery equations are employed to construct the full 3D stress and strain components in order to complete a full stress / strain analysis. Smart materials change mechanical energy to electrical energy; therefore, changing the structural dynamic behavior of the structure and its stiffness matrix.

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