scholarly journals The Convolutional Multiple Whole Profile (CMWP) Fitting Method, a Global Optimization Procedure for Microstructure Determination

Crystals ◽  
2020 ◽  
Vol 10 (7) ◽  
pp. 623
Author(s):  
Gábor Ribárik ◽  
Bertalan Jóni ◽  
Tamás Ungár
Keyword(s):  
Monte Carlo ◽  
Lattice Defect ◽  
Optimization Procedure ◽  
Monte Carlo Algorithm ◽  
Line Broadening ◽  
Strain Anisotropy ◽  
Crystalline Materials ◽  
Fitting Procedure ◽  
Fitting Method ◽  
Diffraction Patterns

The analysis of line broadening in X-ray and neutron diffraction patterns using profile functions constructed on the basis of well-established physical principles and TEM observations of lattice defects has proven to be a powerful tool for characterizing microstructures in crystalline materials. These principles are applied in the convolutional multiple-whole-profile (CMWP) procedure to determine dislocation densities, crystallite size, stacking fault and twin boundary densities, and intergranular strains. The different lattice defect contributions to line broadening are separated by considering the hkl dependence of strain anisotropy, planar defect broadening and peak shifts, and the defect dependent profile shapes. The Levenberg–Marquardt (LM) peak fitting procedure can be used successfully to determine crystal defect types and densities as long as the diffraction patterns are relatively simple. However, in more complicated cases like hexagonal materials or multiple-phase patterns, using the LM procedure alone may cause uncertainties. Here, we extended the CMWP procedure by including a Monte Carlo statistical method where the LM and a Monte Carlo algorithm were combined in an alternating manner. The updated CMWP procedure eliminated uncertainties and provided global optimized parameters of the microstructure in good correlation with electron microscopy methods.

Reverse Monte Carlo Analysis of Powder Patterns

1996 ◽  
Vol 29 (3) ◽  
pp. 285-290 ◽  
Author(s):  
W. Montfrooij ◽  
R. L. McGreevy ◽  
R. Hadfield ◽  
N. H. Andersen
Keyword(s):  
Monte Carlo ◽  
Bragg Peak ◽  
Monte Carlo Analysis ◽  
Monte Carlo Algorithm ◽  
Reverse Monte Carlo ◽  
Peak Intensity ◽  
Thermal Displacements ◽  
Diffraction Patterns ◽  
Best Fit

A Monte Carlo algorithm for the analysis of powder diffraction patterns is presented. One aim of this algorithm, which can be used as a supplement to the regular Rietveld refinement, is to provide a self-consistent determination of the thermal displacements of the atoms. This is achieved by modelling the total scattered intensity, comprising both the Bragg peak intensity and the diffuse contribution to the spectrum from the scattering density of an assembly of atoms. This assembly, which is constructed by the reverse Monte Carlo technique so as to yield a best fit with the data, is then used to calculate the average atomic thermal displacements. This allows for a refinement that, in principle, no longer requires angle-dependent background parameters, and that is well suited for dealing with highly anisotropic Debye–Waller factors and split atomic sites.

Automatic analysis of Kikuchi diffraction patterns

1994 ◽  
Vol 52 ◽  
pp. 900-901
Author(s):  
H. Weiland ◽  
D. P. Field
Keyword(s):  
Electron Beam ◽  
Electron Microscope ◽  
Spatial Resolution ◽  
Relevant Information ◽  
Crystalline Materials ◽  
Large Size ◽  
Transmission Electron ◽  
New Type ◽  
Diffraction Patterns ◽  
Orientation Determination

Recent advances in the automatic indexing of backscatter Kikuchi diffraction patterns on the scanning electron microscope (SEM) has resulted in the development of a new type of microscopy. The ability to obtain statistically relevant information on the spatial distribution of crystallite orientations is giving rise to new insight into polycrystalline microstructures and their relation to materials properties. A limitation of the technique in the SEM is that the spatial resolution of the measurement is restricted by the relatively large size of the electron beam in relation to various microstructural features. Typically the spatial resolution in the SEM is limited to about half a micron or greater. Heavily worked structures exhibit microstructural features much finer than this and require resolution on the order of nanometers for accurate characterization. Transmission electron microscope (TEM) techniques offer sufficient resolution to investigate heavily worked crystalline materials.Crystal lattice orientation determination from Kikuchi diffraction patterns in the TEM (Figure 1) requires knowledge of the relative positions of at least three non-parallel Kikuchi line pairs in relation to the crystallite and the electron beam.

A Structural Model for a Quasi-Crystalline Material Derived from TEM

1990 ◽  
Vol 48 (1) ◽  
pp. 48-49
Author(s):  
Jan-Olov Bovin ◽  
Osamu Terasaki ◽  
Jan-Olle Malm ◽  
Sven Lidin ◽  
Sten Andersson
Keyword(s):  
High Resolution ◽  
Electron Diffraction ◽  
Structural Model ◽  
Image Intensifier ◽  
Crystalline Materials ◽  
Icosahedral Phases ◽  
Transmission Electron ◽  
Electron Microscopes ◽  
Diffraction Patterns ◽  
Quasi Crystals

High resolution transmission electron microscopy (HRTEM) is playing an important role in identifying the new icosahedral phases. The selected area diffraction patterns of quasi crystals, recorded with an aperture of the radius of many thousands of Ångströms, consist of dense arrays of well defined sharp spots with five fold dilatation symmetry which makes the interpretation of the diffraction process and the resulting images different from those invoked for usual crystals. The atomic structure of the quasi crystals is not established even if several models are proposed. The correct structure model must of course explain the electron diffraction patterns with 5-, 3- and 2-fold symmetry for the phases but it is also important that the HRTEM images of the alloys match the computer simulated images from the model. We have studied quasi crystals of the alloy Al65Cu20Fe15. The electron microscopes used to obtain high resolution electro micrographs and electron diffraction patterns (EDP) were a (S)TEM JEM-2000FX equipped with EDS and PEELS showing a structural resolution of 2.7 Å and a IVEM JEM-4000EX with a UHP40 high resolution pole piece operated at 400 kV and with a structural resolution of 1.6 Å. This microscope is used with a Gatan 622 TV system with an image intensifier, coupled to a YAG screen. It was found that the crystals of the quasi crystalline materials here investigated were more sensitive to beam damage using 400 kV as electron accelerating voltage than when using 200 kV. Low dose techniques were therefore applied to avoid damage of the structure.

Examining sharp restart in a Monte Carlo method for the linearized Poisson–Boltzmann equation

2020 ◽  
Vol 26 (3) ◽  
pp. 223-244
Author(s):  
W. John Thrasher ◽  
Michael Mascagni
Keyword(s):  
Monte Carlo ◽  
Free Energy ◽  
Monte Carlo Algorithm ◽  
Significant Bias ◽  
Poisson Boltzmann ◽  
Electrostatic Free Energy ◽  
Poisson Boltzmann Equation ◽  
The Stability ◽  
Potential Methods ◽  
The Individual

AbstractIt has been shown that when using a Monte Carlo algorithm to estimate the electrostatic free energy of a biomolecule in a solution, individual random walks can become entrapped in the geometry. We examine a proposed solution, using a sharp restart during the Walk-on-Subdomains step, in more detail. We show that the point at which this solution introduces significant bias is related to properties intrinsic to the molecule being examined. We also examine two potential methods of generating a sharp restart point and show that they both cause no significant bias in the examined molecules and increase the stability of the run times of the individual walks.

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