This document discusses the state of the art in analyzing crystallite size and lattice strain using x-ray powder diffraction line profile analysis. It describes how classical single-line methods provide some characterization of material imperfections but are difficult to interpret quantitatively. More advanced methods now focus on anisotropic broadening effects from dislocations and compositional variations. The most promising new approach is line profile synthesis, where a microstructure model is used to calculate profiles and fit measured data without assumptions about line shapes. This allows direct evaluation of microstructure parameters used in materials science.
Wavelet based histogram method for classification of textuIAEME Publication
This document summarizes a research paper that proposes a new method called Wavelet based Histogram on Texton Patterns (WHTP) for classifying textures. The method applies a discrete wavelet transform to texture images and extracts texton frequencies from the approximation and detail subbands at different scales. It calculates texton frequencies for original images and wavelet-transformed images. Combining these texton frequencies improves classification success rates when distinguishing between various types of stone textures. The paper aims to improve on other texture classification methods by incorporating spatial information using textons in the wavelet domain. An experimental evaluation finds the proposed WHTP method achieves more accurate classification of stone textures compared to other approaches.
This document summarizes a research paper on using bilateral symmetry analysis to detect brain tumors from MRI images. It begins by introducing the problem of brain tumor detection and importance of asymmetry analysis. It then describes the proposed algorithm which involves defining a bilateral symmetry axis between the two brain hemispheres and detecting any regions of asymmetry that could indicate a tumor. The algorithm uses edge detection techniques to find the symmetry axis. Performance is evaluated on sample patient data and results show the method can successfully identify tumor locations and sizes. In conclusion, analyzing bilateral symmetry is an effective approach for automated brain tumor detection from MRI images.
This document summarizes a research article that proposes using a Bayesian classifier to aid in level set segmentation for early detection of diabetic retinopathy. Level set segmentation is used to segment retinal images and detect small blood clots. A Bayesian classifier is applied to help propagate the level set contour and classify pixels as normal blood vessels or abnormal blood clots. The method was tested on retinal images and showed it could detect small clots of 0.02mm, indicating it may help detect early proliferation stages. Results demonstrated it outperformed other methods in detecting minute clots for early stage proliferation detection.
Hybrid Approach for Brain Tumour Detection in Image Segmentationijtsrd
In this paper we have considered illustrating a few techniques. But the numbers of techniques are so large they cannot be all addressed. Image segmentation forms the basics of pattern recognition and scene analysis problems. The segmentation techniques are numerous in number but the choice of one technique over the other depends only on the application or requirements of the problem that is being considered. Analysis of cluster is a descriptive assignment that perceive homogenous group of objects and it is also one of the fundamental analytical method in facts mining. The main idea of this is to present facts about brain tumour detection system and various data mining methods used in this system. This is focuses on scalable data systems, which include a set of tools and mechanisms to load, extract, and improve disparate data power to perform complex transformations and analysis will be measured between the way of measuring the Furrier and Wavelet Transform distance. Sandeep | Jyoti Kataria "Hybrid Approach for Brain Tumour Detection in Image Segmentation" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-6 , October 2020, URL: https://www.ijtsrd.com/papers/ijtsrd33409.pdf Paper Url: https://www.ijtsrd.com/medicine/other/33409/hybrid-approach-for-brain-tumour-detection-in-image-segmentation/sandeep
ADAPTIVE SEGMENTATION OF CELLS AND PARTICLES IN FLUORESCENT MICROSCOPE IMAGEJournal For Research
The document presents an adaptive segmentation method for segmenting cells and particles in fluorescent microscope images. It involves applying a coherence-enhancing diffusion filter to reduce noise and enhance structures, followed by using the Chan-Vese model to detect cell boundaries. The method allows simultaneous tracking of multiple cells over time by integrating both fast level set and graph cut frameworks with a topological prior. It is demonstrated on 2D and 3D time-lapse images of stem cells and carcinoma cells.
A comparative study on classification of image segmentation methods with a fo...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
This document describes Marco Antonio Escobar Acevedo's Master's thesis which compares calculations of nonlinear optical response in semiconductors using two different gauges: the length gauge and transversal gauge. The thesis derives the expressions for calculating second-order optical susceptibilities in both gauges from quantum mechanics perturbation theory. It then presents ab initio calculations of second-order optical susceptibilities for GaAs using the local density approximation with scissors corrections. The results from both gauges are compared and the issue of gauge invariance in the calculations is discussed.
In this paper we will review some of the technology being used in the development of new
stents and how, in particular, computational modelling and material characterisation are
helping to improve clinical outcomes. Finally we will look at the future perspectives for next
generation stent technology.
Wavelet based histogram method for classification of textuIAEME Publication
This document summarizes a research paper that proposes a new method called Wavelet based Histogram on Texton Patterns (WHTP) for classifying textures. The method applies a discrete wavelet transform to texture images and extracts texton frequencies from the approximation and detail subbands at different scales. It calculates texton frequencies for original images and wavelet-transformed images. Combining these texton frequencies improves classification success rates when distinguishing between various types of stone textures. The paper aims to improve on other texture classification methods by incorporating spatial information using textons in the wavelet domain. An experimental evaluation finds the proposed WHTP method achieves more accurate classification of stone textures compared to other approaches.
This document summarizes a research paper on using bilateral symmetry analysis to detect brain tumors from MRI images. It begins by introducing the problem of brain tumor detection and importance of asymmetry analysis. It then describes the proposed algorithm which involves defining a bilateral symmetry axis between the two brain hemispheres and detecting any regions of asymmetry that could indicate a tumor. The algorithm uses edge detection techniques to find the symmetry axis. Performance is evaluated on sample patient data and results show the method can successfully identify tumor locations and sizes. In conclusion, analyzing bilateral symmetry is an effective approach for automated brain tumor detection from MRI images.
This document summarizes a research article that proposes using a Bayesian classifier to aid in level set segmentation for early detection of diabetic retinopathy. Level set segmentation is used to segment retinal images and detect small blood clots. A Bayesian classifier is applied to help propagate the level set contour and classify pixels as normal blood vessels or abnormal blood clots. The method was tested on retinal images and showed it could detect small clots of 0.02mm, indicating it may help detect early proliferation stages. Results demonstrated it outperformed other methods in detecting minute clots for early stage proliferation detection.
Hybrid Approach for Brain Tumour Detection in Image Segmentationijtsrd
In this paper we have considered illustrating a few techniques. But the numbers of techniques are so large they cannot be all addressed. Image segmentation forms the basics of pattern recognition and scene analysis problems. The segmentation techniques are numerous in number but the choice of one technique over the other depends only on the application or requirements of the problem that is being considered. Analysis of cluster is a descriptive assignment that perceive homogenous group of objects and it is also one of the fundamental analytical method in facts mining. The main idea of this is to present facts about brain tumour detection system and various data mining methods used in this system. This is focuses on scalable data systems, which include a set of tools and mechanisms to load, extract, and improve disparate data power to perform complex transformations and analysis will be measured between the way of measuring the Furrier and Wavelet Transform distance. Sandeep | Jyoti Kataria "Hybrid Approach for Brain Tumour Detection in Image Segmentation" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-6 , October 2020, URL: https://www.ijtsrd.com/papers/ijtsrd33409.pdf Paper Url: https://www.ijtsrd.com/medicine/other/33409/hybrid-approach-for-brain-tumour-detection-in-image-segmentation/sandeep
ADAPTIVE SEGMENTATION OF CELLS AND PARTICLES IN FLUORESCENT MICROSCOPE IMAGEJournal For Research
The document presents an adaptive segmentation method for segmenting cells and particles in fluorescent microscope images. It involves applying a coherence-enhancing diffusion filter to reduce noise and enhance structures, followed by using the Chan-Vese model to detect cell boundaries. The method allows simultaneous tracking of multiple cells over time by integrating both fast level set and graph cut frameworks with a topological prior. It is demonstrated on 2D and 3D time-lapse images of stem cells and carcinoma cells.
A comparative study on classification of image segmentation methods with a fo...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
This document describes Marco Antonio Escobar Acevedo's Master's thesis which compares calculations of nonlinear optical response in semiconductors using two different gauges: the length gauge and transversal gauge. The thesis derives the expressions for calculating second-order optical susceptibilities in both gauges from quantum mechanics perturbation theory. It then presents ab initio calculations of second-order optical susceptibilities for GaAs using the local density approximation with scissors corrections. The results from both gauges are compared and the issue of gauge invariance in the calculations is discussed.
In this paper we will review some of the technology being used in the development of new
stents and how, in particular, computational modelling and material characterisation are
helping to improve clinical outcomes. Finally we will look at the future perspectives for next
generation stent technology.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
This document describes a study using rheo-optical near-infrared (NIR) spectroscopy to analyze the molecular-level deformation of low-density polyethylene (LDPE) during mechanical tensile testing. NIR spectra were collected from an LDPE sample under increasing strain. Two-dimensional correlation analysis with projection was used to filter out spectral changes from baseline fluctuations caused by sample thickness changes, in order to reveal deformation-related spectral features. The analysis identified predominant extension of amorphous tie chains followed by rotation of crystalline lamellae, corresponding to elastic and plastic deformation of the LDPE.
This document presents a new approach for segmenting skin lesions in dermoscopic images using a fixed-grid wavelet network (FGWN). The FGWN takes R, G, and B color values as inputs and determines the network structure without training. The image is then segmented and the exact lesion boundary is extracted. Experimental results on 30 images showed the FGWN approach achieved better segmentation accuracy than other methods according to 11 evaluation metrics, extracting lesion boundaries more precisely. In conclusion, the FGWN provides an effective tool for automated skin lesion segmentation in dermoscopy images.
Color Image Segmentation Technique Using “Natural Grouping” of PixelsCSCJournals
This paper focuses on the problem Image Segmentation which aims at sub dividing a given image into its constituent objects. Here an unsupervised method for color image segmentation is proposed where we first perform a Minimum Spanning Tree (MST) based “natural grouping” of the image pixels to find out the clusters of the pixels having RGB values within a certain range present in the image. Then the pixels nearest to the centers of those clusters are found out and marked as the seeds. They are then used for region growing based image segmentation purpose. After that a region merging based segmentation method having a suitable threshold is performed to eliminate the effect of over segmentation that may still persist after the region growing method. This proposed method is unsupervised as it does not require any prior information about the number of regions present in a given image. The experimental results show that the proposed method can find homogeneous regions present in a given image efficiently.
Analysis of microscope images_FINAL PRESENTATIONGeorge Livanos
This document outlines the presentation scheme for a thesis on the analysis of microscope images. The thesis will analyze tissue samples using both polarimetric imaging at a macroscopic level and microscope imaging at a cellular level. For polarimetric imaging, the thesis will develop statistical models to characterize tissue properties based on how polarized light interacts with tissue elements. For microscope imaging, it will automatically segment cells from immunohistochemistry images and evaluate biomarkers like Her2 to characterize cancer impacts. Key techniques will include membrane boundary estimation, image clustering, and watershed transforms. The goal is both material characterization from polarimetric signatures and cancer analysis from cellular-level microscope images.
Medical Image Segmentation Based on Level Set MethodIOSR Journals
This document presents a new medical image segmentation technique based on the level set method. The technique uses a combination of thresholding, morphological erosion, and a variational level set method. Thresholding is applied to determine object pixels, followed by optional erosion to remove small fragments. Then a variational level set method is applied on the original image to evaluate the contour and segment objects. The technique is tested on various medical images and provides good segmentation results, though it struggles with complex images containing multiple distinct objects.
3D EBSD Overview - Metallurgical Mater Trans A Vol 39 A (2008) 374Dierk Raabe
This document describes a new technique for 3D characterization of crystalline microstructures using serial sectioning with a focused ion beam and electron backscatter diffraction (EBSD) in a scanning electron microscope. Key points:
- Serial sectioning is used to cut thin sections from the sample, which are then characterized using EBSD orientation microscopy to determine crystal orientations in 3D.
- This allows full crystallographic characterization of microstructural features like interfaces that is not possible with conventional 2D analysis.
- The technique achieves resolutions as fine as 50x50x50 nm3 and can characterize sample volumes up to 50x50x50 μm3.
- Examples demonstrate applications to characterize microstructures like
Flower Classification Using Neural Network Based Image ProcessingIOSR Journals
Abstract: In this paper, it is proposed to have a method for classification of flowers using Artificial Neural Network (ANN) classifier. The proposed method is based on textural features such as Gray level co-occurrence matrix (GLCM) and discrete wavelet transform (DWT). A flower image is segmented using a threshold based method. The data set has different flower images with similar appearance .The database of flower images is a mixture of images taken from World Wide Web and the images taken by us. The ANN has been trained by 50 samples to classify 5 classes of flowers and achieved classification accuracy more than 85% using GLCM features only. Keywords: Artificial Neural Network, DWT, GLCM, Segmentation.
Alzheimer’s disease(AD) is a neurological disease. It affects memory. The livelihood of the people that are
diagnosed with AD. In this paper, we have discussed various imaging modalities, feature selection and
extraction, segmentation and classification techniques.
An efficient fuzzy classifier with feature selection basedssairayousaf
This document presents an efficient fuzzy classifier with feature selection capabilities. A fuzzy entropy measure is used to partition the input feature space into non-overlapping decision regions and to select relevant features. Fuzzy entropy evaluates the information of pattern distribution in the pattern space. The decision regions do not overlap, reducing computational complexity and load. Classification speed is extremely fast while still achieving good performance by correctly determining decision region boundaries. Feature selection via fuzzy entropy reduces dimensionality by discarding noisy, redundant, and unimportant features. The proposed classifier is applied to two databases with good classification results, demonstrating its effectiveness.
High volume computational histopathology 3Scan3Scan
Light microscopy is the gold standard for investigating microscopic structures and
pathological alterations in both human and animal models of disease. However, due
to tedious manual interventions, quantification of histopathologic markers is
classically performed on only a few 2D tissue sections, thus restricting
measurements and observations to limited portions of the sample volume.
Understanding vascular networks within tissues is a critical component to identifying pathophysiology. The work presented here introduces a methodology for multi-parametric quantification of vascular networks for whole-mount tissues. Our approach streamlines the histopathology workflow, enables observations within large 3D sample volumes, and provides opportunities for automated image analysis.
Fully Automatic Method for 3D T1-Weighted Brain Magnetic Resonance Images Seg...CSCJournals
In the domain of medical imaging, accurate segmentation of brain MR images is of interest for many brain disorders. However, due to several factors such noise, imaging artefacts, intrinsic tissue variation and partial volume effects, tissue segmentation remains a challenging task. So, in this paper, a full automatic method for segmentation of brain MR images is presented. The method consists of four steps segmentation procedure. First, noise removing by median filtering is done; second segmentation of brain/non-brain tissue is performed by using a Threshold Morphologic Brain Extraction method (TMBE). Then initial centroids estimation by gray level histogram analysis based is executed. Finally, Fuzzy C-means Algorithm is used for MRI tissue segmentation. The efficiency of the proposed method is demonstrated by extensive segmentation experiments using simulated and real MR images.
Fractal characterization of dynamic systems sectional imagesAlexander Decker
This document discusses using fractal analysis to characterize sectional images of dynamic systems. It simulates three systems - a hollow sphere, transmissibility ratio, and Lorenz weather model. For each system, it generates the governing equations, simulates the surface, takes 200 sectional images by passing a plane through the surface, and uses fractal disk dimension to characterize the roughness of each image. It finds the hollow sphere surface is smoothest, transmissibility ratio is rougher, and Lorenz weather model is roughest, indicating fractal analysis can distinguish linear from nonlinear system surfaces. The study demonstrates fractals' potential for image characterization in engineering applications.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
A brief review of segmentation methods for medical imageseSAT Journals
Abstract For medical diagnosis and laboratory study applications we cannot directly use image that are acquired and detect the disorder because it is not efficient and unrealistic. These images need processing and extracting portions from them that can be used for further study or diagnosis. The main goal of this paper is to give overview about segmentation methods that are used for medical images for detecting the edges and based on this detection the disease prediction and diagnosis is done. There are a lot of tools available for this purpose such as STAPLE and FreeSurfer whole brain segmentation tool etc. Some of these methods are semi-automatic i.e. they require human intervention for their completion and some of them are automatic. The methods are totally divided into four types namely, edge based segmentation, region based segmentation, data clustering and matching. The aim of segmenting medical images is that to detect the ROI and diagnose for a disease based on the detected part. Segmentation is partitioning a image into meaningful regions based upon a specific application. Generally segmentation can be based on the measurements like gray level, color, texture, motion, depth or intensity. Segmentation is necessary in two situations, namely, set-off segmentation i.e. when the object to be segmented is interesting in itself and can be used separately for further studies, and secondly concealing segmentation i.e. suppose there are some noise or vision blockers in the image, so this segmentation aims at deleting the disturbing elements in an image. This paper focuses only on the working of different methods that are used for segmentation whether they segment well or poor. Index Terms: Image Registration, Image Segmentation, Reinforcement Learning,
This document discusses using smoothing filters based on rough set theory for medical image enhancement. It introduces common smoothing filters like mean, median, mode, and triangular filters. These filters can reduce noise and enhance edges in medical images. The document proposes a parallel rough set based model that implements multiple smoothing filters at once to obtain independent results and generate an enhanced mean image for improved medical image quality and complex image processing.
Moodle generalised formulation of laminate theory using beam fe for delaminat...Shree Bineet Kumar Kavi
This document presents a generalized formulation of laminate theory using beam finite elements to model delaminated composite beams with piezoelectric actuators and sensors. A coupled linear layerwise laminate theory and beam finite element model are developed that include delaminations as additional degrees of freedom. Numerical results illustrate the effects of delamination on sensor voltage, displacements, stresses, and modal frequencies/shapes. The model can predict the response of laminated composite beams with piezoelectric layers and various delamination sizes.
Brain Tumor Segmentation Based on SFCM using Neural NetworkIRJET Journal
This document describes a proposed system for brain tumor segmentation using neural networks. The system involves 4 phases: 1) Preprocessing MRI images using dual-tree complex wavelet transforms for feature extraction. 2) Spatial fuzzy C-means clustering to classify tissues into normal, tumor core and edema classes. 3) Extracting features using the dual-tree complex wavelet transforms. 4) Classifying the features using a backpropagation neural network to identify normal and abnormal brain tissues. The goal is to automatically and accurately segment brain tumors from MRI images to aid diagnosis and reduce analysis time for radiologists. The system was tested on real patient MRI data and achieved accurate segmentation results.
Literature Survey on Image Deblurring TechniquesEditor IJCATR
Image restoration and recognition has been of great importance nowadays. Face recognition becomes difficult when it comes
to blurred and poorly illuminated images and it is here face recognition and restoration come to picture. There have been many
methods that were proposed in this regard and in this paper we will examine different methods and technologies discussed so far. The
merits and demerits of different methods are discussed in this concern
A Review on Detection of Cracks Present in Composite Cantilever Beam by using...ijtsrd
The aim of this paper is to discuss various techniques used by various researchers for vibration based crack detection in cracked composite structures. In aeronautical, mechanical and civil engineering fields various structural systems are likely to damage and deterioration during their working period. So it is very important to find damage and deterioration in structural member by an effective and reliable methodology. Interest in various damage detection methods has considerably increased in last few decades. A local flexibility is introduced in structural member due to the presence of crack that would affect the vibration response of structure. Due to the presence of crack there is reduction in stiffness of structure and increase in damping of the structure. Since there are changes in physical properties there are reductions in natural frequencies and deviation in mode shapes. Therefore by measuring the vibration parameters it is possible to predict crack depth and crack location in structural member. In this paper effect of various parameters like crack depth, crack location on natural frequency of beam is studied.Presence of crack in a beam decreases the natural frequency which is more pronounced when the crack is near the fixed support and the crack depth is more. Mr. Kadam Satish P | Dr. Kachare P.S."A Review on Detection of Cracks Present in Composite Cantilever Beam by using Vibration Analysis Technique" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-1 | Issue-6 , October 2017, URL: http://www.ijtsrd.com/papers/ijtsrd4617.pdf http://www.ijtsrd.com/engineering/mechanical-engineering/4617/a-review-on-detection-of-cracks-present-in-composite-cantilever-beam-by-using-vibration-analysis-technique/mr-kadam-satish-p
Study of Crystallite Size and Microstrain Using X-Ray Diffractometer (XRD)IRJET Journal
This document summarizes a study on using X-ray diffraction (XRD) to analyze crystallite size and microstrain in materials. XRD works by passing X-rays through a material and analyzing the diffraction patterns. This can provide information about the material's crystal structure, orientation, density, and residual stress and strain. The study examines how factors like temperature and pressure affect mineral crystal structure and properties. It also discusses how the Scherrer equation can be used to calculate crystallite size from XRD peak broadening measurements and how microstrain within crystals can be analyzed. The conclusions summarize that XRD allows characterization of properties like crystallite size, residual stress, and identification of crystal structures and phases present.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
This document describes a study using rheo-optical near-infrared (NIR) spectroscopy to analyze the molecular-level deformation of low-density polyethylene (LDPE) during mechanical tensile testing. NIR spectra were collected from an LDPE sample under increasing strain. Two-dimensional correlation analysis with projection was used to filter out spectral changes from baseline fluctuations caused by sample thickness changes, in order to reveal deformation-related spectral features. The analysis identified predominant extension of amorphous tie chains followed by rotation of crystalline lamellae, corresponding to elastic and plastic deformation of the LDPE.
This document presents a new approach for segmenting skin lesions in dermoscopic images using a fixed-grid wavelet network (FGWN). The FGWN takes R, G, and B color values as inputs and determines the network structure without training. The image is then segmented and the exact lesion boundary is extracted. Experimental results on 30 images showed the FGWN approach achieved better segmentation accuracy than other methods according to 11 evaluation metrics, extracting lesion boundaries more precisely. In conclusion, the FGWN provides an effective tool for automated skin lesion segmentation in dermoscopy images.
Color Image Segmentation Technique Using “Natural Grouping” of PixelsCSCJournals
This paper focuses on the problem Image Segmentation which aims at sub dividing a given image into its constituent objects. Here an unsupervised method for color image segmentation is proposed where we first perform a Minimum Spanning Tree (MST) based “natural grouping” of the image pixels to find out the clusters of the pixels having RGB values within a certain range present in the image. Then the pixels nearest to the centers of those clusters are found out and marked as the seeds. They are then used for region growing based image segmentation purpose. After that a region merging based segmentation method having a suitable threshold is performed to eliminate the effect of over segmentation that may still persist after the region growing method. This proposed method is unsupervised as it does not require any prior information about the number of regions present in a given image. The experimental results show that the proposed method can find homogeneous regions present in a given image efficiently.
Analysis of microscope images_FINAL PRESENTATIONGeorge Livanos
This document outlines the presentation scheme for a thesis on the analysis of microscope images. The thesis will analyze tissue samples using both polarimetric imaging at a macroscopic level and microscope imaging at a cellular level. For polarimetric imaging, the thesis will develop statistical models to characterize tissue properties based on how polarized light interacts with tissue elements. For microscope imaging, it will automatically segment cells from immunohistochemistry images and evaluate biomarkers like Her2 to characterize cancer impacts. Key techniques will include membrane boundary estimation, image clustering, and watershed transforms. The goal is both material characterization from polarimetric signatures and cancer analysis from cellular-level microscope images.
Medical Image Segmentation Based on Level Set MethodIOSR Journals
This document presents a new medical image segmentation technique based on the level set method. The technique uses a combination of thresholding, morphological erosion, and a variational level set method. Thresholding is applied to determine object pixels, followed by optional erosion to remove small fragments. Then a variational level set method is applied on the original image to evaluate the contour and segment objects. The technique is tested on various medical images and provides good segmentation results, though it struggles with complex images containing multiple distinct objects.
3D EBSD Overview - Metallurgical Mater Trans A Vol 39 A (2008) 374Dierk Raabe
This document describes a new technique for 3D characterization of crystalline microstructures using serial sectioning with a focused ion beam and electron backscatter diffraction (EBSD) in a scanning electron microscope. Key points:
- Serial sectioning is used to cut thin sections from the sample, which are then characterized using EBSD orientation microscopy to determine crystal orientations in 3D.
- This allows full crystallographic characterization of microstructural features like interfaces that is not possible with conventional 2D analysis.
- The technique achieves resolutions as fine as 50x50x50 nm3 and can characterize sample volumes up to 50x50x50 μm3.
- Examples demonstrate applications to characterize microstructures like
Flower Classification Using Neural Network Based Image ProcessingIOSR Journals
Abstract: In this paper, it is proposed to have a method for classification of flowers using Artificial Neural Network (ANN) classifier. The proposed method is based on textural features such as Gray level co-occurrence matrix (GLCM) and discrete wavelet transform (DWT). A flower image is segmented using a threshold based method. The data set has different flower images with similar appearance .The database of flower images is a mixture of images taken from World Wide Web and the images taken by us. The ANN has been trained by 50 samples to classify 5 classes of flowers and achieved classification accuracy more than 85% using GLCM features only. Keywords: Artificial Neural Network, DWT, GLCM, Segmentation.
Alzheimer’s disease(AD) is a neurological disease. It affects memory. The livelihood of the people that are
diagnosed with AD. In this paper, we have discussed various imaging modalities, feature selection and
extraction, segmentation and classification techniques.
An efficient fuzzy classifier with feature selection basedssairayousaf
This document presents an efficient fuzzy classifier with feature selection capabilities. A fuzzy entropy measure is used to partition the input feature space into non-overlapping decision regions and to select relevant features. Fuzzy entropy evaluates the information of pattern distribution in the pattern space. The decision regions do not overlap, reducing computational complexity and load. Classification speed is extremely fast while still achieving good performance by correctly determining decision region boundaries. Feature selection via fuzzy entropy reduces dimensionality by discarding noisy, redundant, and unimportant features. The proposed classifier is applied to two databases with good classification results, demonstrating its effectiveness.
High volume computational histopathology 3Scan3Scan
Light microscopy is the gold standard for investigating microscopic structures and
pathological alterations in both human and animal models of disease. However, due
to tedious manual interventions, quantification of histopathologic markers is
classically performed on only a few 2D tissue sections, thus restricting
measurements and observations to limited portions of the sample volume.
Understanding vascular networks within tissues is a critical component to identifying pathophysiology. The work presented here introduces a methodology for multi-parametric quantification of vascular networks for whole-mount tissues. Our approach streamlines the histopathology workflow, enables observations within large 3D sample volumes, and provides opportunities for automated image analysis.
Fully Automatic Method for 3D T1-Weighted Brain Magnetic Resonance Images Seg...CSCJournals
In the domain of medical imaging, accurate segmentation of brain MR images is of interest for many brain disorders. However, due to several factors such noise, imaging artefacts, intrinsic tissue variation and partial volume effects, tissue segmentation remains a challenging task. So, in this paper, a full automatic method for segmentation of brain MR images is presented. The method consists of four steps segmentation procedure. First, noise removing by median filtering is done; second segmentation of brain/non-brain tissue is performed by using a Threshold Morphologic Brain Extraction method (TMBE). Then initial centroids estimation by gray level histogram analysis based is executed. Finally, Fuzzy C-means Algorithm is used for MRI tissue segmentation. The efficiency of the proposed method is demonstrated by extensive segmentation experiments using simulated and real MR images.
Fractal characterization of dynamic systems sectional imagesAlexander Decker
This document discusses using fractal analysis to characterize sectional images of dynamic systems. It simulates three systems - a hollow sphere, transmissibility ratio, and Lorenz weather model. For each system, it generates the governing equations, simulates the surface, takes 200 sectional images by passing a plane through the surface, and uses fractal disk dimension to characterize the roughness of each image. It finds the hollow sphere surface is smoothest, transmissibility ratio is rougher, and Lorenz weather model is roughest, indicating fractal analysis can distinguish linear from nonlinear system surfaces. The study demonstrates fractals' potential for image characterization in engineering applications.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
A brief review of segmentation methods for medical imageseSAT Journals
Abstract For medical diagnosis and laboratory study applications we cannot directly use image that are acquired and detect the disorder because it is not efficient and unrealistic. These images need processing and extracting portions from them that can be used for further study or diagnosis. The main goal of this paper is to give overview about segmentation methods that are used for medical images for detecting the edges and based on this detection the disease prediction and diagnosis is done. There are a lot of tools available for this purpose such as STAPLE and FreeSurfer whole brain segmentation tool etc. Some of these methods are semi-automatic i.e. they require human intervention for their completion and some of them are automatic. The methods are totally divided into four types namely, edge based segmentation, region based segmentation, data clustering and matching. The aim of segmenting medical images is that to detect the ROI and diagnose for a disease based on the detected part. Segmentation is partitioning a image into meaningful regions based upon a specific application. Generally segmentation can be based on the measurements like gray level, color, texture, motion, depth or intensity. Segmentation is necessary in two situations, namely, set-off segmentation i.e. when the object to be segmented is interesting in itself and can be used separately for further studies, and secondly concealing segmentation i.e. suppose there are some noise or vision blockers in the image, so this segmentation aims at deleting the disturbing elements in an image. This paper focuses only on the working of different methods that are used for segmentation whether they segment well or poor. Index Terms: Image Registration, Image Segmentation, Reinforcement Learning,
This document discusses using smoothing filters based on rough set theory for medical image enhancement. It introduces common smoothing filters like mean, median, mode, and triangular filters. These filters can reduce noise and enhance edges in medical images. The document proposes a parallel rough set based model that implements multiple smoothing filters at once to obtain independent results and generate an enhanced mean image for improved medical image quality and complex image processing.
Moodle generalised formulation of laminate theory using beam fe for delaminat...Shree Bineet Kumar Kavi
This document presents a generalized formulation of laminate theory using beam finite elements to model delaminated composite beams with piezoelectric actuators and sensors. A coupled linear layerwise laminate theory and beam finite element model are developed that include delaminations as additional degrees of freedom. Numerical results illustrate the effects of delamination on sensor voltage, displacements, stresses, and modal frequencies/shapes. The model can predict the response of laminated composite beams with piezoelectric layers and various delamination sizes.
Brain Tumor Segmentation Based on SFCM using Neural NetworkIRJET Journal
This document describes a proposed system for brain tumor segmentation using neural networks. The system involves 4 phases: 1) Preprocessing MRI images using dual-tree complex wavelet transforms for feature extraction. 2) Spatial fuzzy C-means clustering to classify tissues into normal, tumor core and edema classes. 3) Extracting features using the dual-tree complex wavelet transforms. 4) Classifying the features using a backpropagation neural network to identify normal and abnormal brain tissues. The goal is to automatically and accurately segment brain tumors from MRI images to aid diagnosis and reduce analysis time for radiologists. The system was tested on real patient MRI data and achieved accurate segmentation results.
Literature Survey on Image Deblurring TechniquesEditor IJCATR
Image restoration and recognition has been of great importance nowadays. Face recognition becomes difficult when it comes
to blurred and poorly illuminated images and it is here face recognition and restoration come to picture. There have been many
methods that were proposed in this regard and in this paper we will examine different methods and technologies discussed so far. The
merits and demerits of different methods are discussed in this concern
A Review on Detection of Cracks Present in Composite Cantilever Beam by using...ijtsrd
The aim of this paper is to discuss various techniques used by various researchers for vibration based crack detection in cracked composite structures. In aeronautical, mechanical and civil engineering fields various structural systems are likely to damage and deterioration during their working period. So it is very important to find damage and deterioration in structural member by an effective and reliable methodology. Interest in various damage detection methods has considerably increased in last few decades. A local flexibility is introduced in structural member due to the presence of crack that would affect the vibration response of structure. Due to the presence of crack there is reduction in stiffness of structure and increase in damping of the structure. Since there are changes in physical properties there are reductions in natural frequencies and deviation in mode shapes. Therefore by measuring the vibration parameters it is possible to predict crack depth and crack location in structural member. In this paper effect of various parameters like crack depth, crack location on natural frequency of beam is studied.Presence of crack in a beam decreases the natural frequency which is more pronounced when the crack is near the fixed support and the crack depth is more. Mr. Kadam Satish P | Dr. Kachare P.S."A Review on Detection of Cracks Present in Composite Cantilever Beam by using Vibration Analysis Technique" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-1 | Issue-6 , October 2017, URL: http://www.ijtsrd.com/papers/ijtsrd4617.pdf http://www.ijtsrd.com/engineering/mechanical-engineering/4617/a-review-on-detection-of-cracks-present-in-composite-cantilever-beam-by-using-vibration-analysis-technique/mr-kadam-satish-p
Study of Crystallite Size and Microstrain Using X-Ray Diffractometer (XRD)IRJET Journal
This document summarizes a study on using X-ray diffraction (XRD) to analyze crystallite size and microstrain in materials. XRD works by passing X-rays through a material and analyzing the diffraction patterns. This can provide information about the material's crystal structure, orientation, density, and residual stress and strain. The study examines how factors like temperature and pressure affect mineral crystal structure and properties. It also discusses how the Scherrer equation can be used to calculate crystallite size from XRD peak broadening measurements and how microstrain within crystals can be analyzed. The conclusions summarize that XRD allows characterization of properties like crystallite size, residual stress, and identification of crystal structures and phases present.
1. The document discusses various methods used to investigate the structure of fibers, including nuclear magnetic resonance, infrared spectroscopy, optical and x-ray diffraction, thermal analysis, optical microscopy, electron microscopy, and density measurement.
2. It provides details on specific techniques like nuclear magnetic resonance spectroscopy, optical diffraction, x-ray diffraction, and electron microscopy and electron diffraction. These techniques help determine properties of fibers like composition, molecular structure, crystallinity, and orientation.
3. The structure investigation of fibers is important to understand fiber properties in order to improve their use in textiles. Different methods are used to study characteristics like chemical bonding, molecular spacing, and cross-sectional structure.
Study on Effect of Crack Inclination and Location on Natural Frequency for In...IRJET Journal
This document presents a study on the effect of crack inclination and location on the natural frequency of an inclined edge cracked cantilever beam using finite element analysis. 16 models of a cantilever beam with various crack inclinations were created in ANSYS with the crack located at L/2 and L/4 from the fixed end. Modal analysis was performed to determine the natural frequencies and mode shapes. The results show that the natural frequency decreases with increasing crack inclination and depth due to reduced beam stiffness. Natural frequency is also affected by crack location, with frequencies lower for cracks closer to the fixed end. In conclusion, crack parameters such as inclination, depth and location significantly influence a beam's natural frequency.
This document discusses advances in laser holographic lithography techniques for fabricating 3D nanostructures. It describes how holographic lithography can be achieved using a single optical element such as a diffractive phase mask or deflective prism. Specifically, it provides examples of using a 2D phase mask and a 4-sided prism to generate interference patterns that can produce diamond-like 3D photonic crystal structures in a single laser exposure, overcoming limitations of previous multi-element approaches. Controlling the phase of laser beams is shown to be crucial for enabling the fabrication of complex 3D structures using these single-element holographic lithography methods.
X-ray diffraction is a technique that uses X-rays to determine the structure of crystalline materials. When X-rays interact with a crystalline material, they are scattered at specific angles that are dependent on the spacing of atoms in the material. This scattering pattern is unique to each material and can be used to identify unknown compounds. Polycapillary optics can focus X-rays into a small beam and overcome limitations of traditional XRD systems, allowing the analysis of small samples and thin films with lower power X-ray sources. X-ray crystallography is a related technique that uses X-ray diffraction data to determine the three-dimensional atomic structure of crystals.
X-ray diffraction is a technique that uses X-rays to determine the structure of crystalline materials. When X-rays interact with a crystalline material, they are scattered at specific angles that are dependent on the spacing of atoms in the material. This scattering pattern is unique to each material and can be used to identify unknown compounds. Polycapillary optics can focus X-rays into a small beam and overcome limitations of traditional XRD systems, allowing the technique to be applied to small samples and thin films. X-ray crystallography uses diffraction patterns to determine the three-dimensional electron density within a crystal and precisely define the positions of atoms within it.
Vibration analysis of a cantilever beam with crack depth and crack location e...editorijrei
This document summarizes a study that analyzed the natural frequency of a cracked cantilever beam made of different metal alloys using finite element analysis. The researchers varied the crack depth and location in the beam and measured the resulting changes in natural frequency. They found that increasing crack depth or moving the crack location closer to the fixed end resulted in decreasing natural frequency. Aluminum alloy beams exhibited the highest natural frequencies while magnesium alloy beams had the lowest.
Regression model for analyzing the dgs structures propagation characterisitcseSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
A review on study of composite materials in presence of crackseSAT Journals
This document reviews composite materials in the presence of cracks. It discusses four main fatigue failure mechanisms: debonding at the fiber-matrix interface, matrix cracking, delamination between plies, and fiber breakage. The review covers analytical models used to predict fatigue life and analyze stiffness degradation due to these failure mechanisms. While models have varying accuracy, micromechanics-based approaches have yielded good results. The review concludes that systematically modeling and analyzing defects is needed to better estimate composite stiffness degradation by considering the effects of failure mechanisms like matrix cracks, debonding, delamination, and fiber breaks.
X-Ray Diffraction (XRD) is a technique used in the pharmaceutical industry to analyze crystal structures. It involves using x-rays to diffract off the planes of atoms in a crystal. By analyzing the angles and intensities of the diffracted x-rays, properties of the crystal such as its unit cell, polymorphism, purity, and compatibility with excipients can be determined. These properties have important implications for drug development, manufacturing, and quality control in the pharmaceutical industry.
Synchrotron X-ray topography (SXRT) is a non-destructive method for studying crystalline materials like defects and strain fields within crystals. Using a white beam for SXRT provides benefits such as not requiring sample orientation, recording multiple reflections simultaneously, visualizing all crystal parts at once with good resolution. X-ray diffraction is also non-destructive and provides information on chemical composition and crystal structure of materials through Bragg's law relating wavelength and diffraction angle. Section mode SXRT imaging is essential to avoid sample heating from large beams and allow separation of cap and substrate images for future reconstruction of MEMS structures. CdTe samples showed high quality with some scratches and inclusions observed.
2011-IPP-CT Data Evaluation of Fibre Reinforced Polymers to Determine Fibre L...Kana Arunachalam Kannappan
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Pearling stroke segmentation with crusted pearl stringsSalman Rashid
The document describes a novel segmentation technique called Pearling for extracting idealized models of networks of strokes from images. Pearling computes the centerlines, bifurcations, and thickness of strokes in real-time by optimizing the positions and radii of a discrete series of overlapping disks (pearls) traced along each stroke. A continuous stroke model is defined by interpolating between the discrete pearl positions and radii. Pearling is designed to produce a model slightly wider than the stroke to ensure it fully contains the stroke boundary. It simultaneously computes a narrower core model inside the stroke boundary. The difference between the outer pearl string and inner core captures the stroke boundary and surrounding image data.
MODELING STUDY OF LASER BEAM SCATTERING BY DEFECTS ON SEMICONDUCTOR WAFERSjmicro
Accurate modeling of light scattering from nanometer scale defects on Silicon wafersiscritical for enabling
increasingly shrinking semiconductor technology nodes of the future. Yet, such modeling of defect
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wafer geometries. Here, we present results of laser beam scattering from spherical and ellipsoidal
particles located on the surface of a silicon wafer. A commercially available electromagnetic field solver
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A Novel Method for Detection of Architectural Distortion in MammogramIDES Editor
Among various breast abnormalities architectural
distortion is the most difficult type of tumor to detect. When
area of interest is medical image data, the major concern is to
develop methodologies which are faster in computation and
relatively noise free in processing. This paper is an extension
of our own work where we propose a hybrid methodology that
combines a Gabor filtration with directional filters over the
directional spectrum for digitized mammogram processing.
The most commendable thing in comparison to other
approaches is that complexity has been lowered as well as the
computation time has also been reduced to a large extent. On
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This document summarizes research on predicting the shear strength of reinforced concrete beams without web reinforcement. It begins by introducing the topic and noting that shear strength decreases as beam depth increases. It then reviews existing literature on shear strength mechanisms and factors that influence strength. The document discusses the challenges of theoretical models given complexities and uncertainties. It proposes using genetic programming and fuzzy set theory to develop empirical models from an existing database of over 2000 test results. The models would express shear strength as a function of concrete strength, reinforcement ratio, depth and other variables.
This document describes a finite element method for modeling complex 3D crack propagation in quasi-brittle materials under static and dynamic loading conditions. The method embeds cohesive elements, which model potential cracks, between solid elements in regions of interest in the initial mesh. Neither remeshing nor predefined crack paths are required. The method was implemented in Abaqus and used to model crack propagation in four concrete structure examples, showing good agreement with experiments or other simulations. The method offers engineers an efficient tool for modeling 3D fracture problems using Abaqus' preprocessing, solving, and postprocessing capabilities.
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This document provides instructions for using the JEOL 2000FX transmission electron microscope at North Carolina State University. It outlines safety procedures and describes how to prepare the microscope, align the illumination system, perform imaging alignments, and shut down the microscope. Appendices provide additional details on specific tasks like adjusting the condenser aperture, acquiring images with the CCD camera, and handling liquid nitrogen.
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The document provides information about various electron microscopy techniques, including transmission electron microscopy (TEM), scanning transmission electron microscopy (STEM), and analytical electron microscopy (AEM). It discusses the development of TEM since its invention in the 1930s. It describes various imaging modes in TEM and STEM such as bright field, dark field, high-resolution, and techniques that provide elemental composition like energy-dispersive X-ray spectroscopy (EDXS) and electron energy loss spectroscopy (EELS). The document is an introduction to electron microscopy methods.
Este capítulo descreve as técnicas experimentais utilizadas, incluindo a técnica de deposição por pulverização catódica e as técnicas de caracterização dos revestimentos, como a microscopia eletrónica e espectroscopia. A pulverização catódica envolve a remoção de átomos de uma superfície por impacto iónico em um plasma, resultando na deposição de um filme fino no substrato. Os parâmetros do processo afetam as propriedades dos revestimentos.
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Atomic force microscopy (AFM) is a type of scanning probe microscopy that uses a sharp probe to scan over a sample surface. It operates by measuring the forces between the probe and sample using a laser beam and photodetector to measure the probe's deflection. There are three main imaging modes: contact mode, non-contact mode, and tapping mode. AFM provides topographic, mechanical, and other property information with nanoscale resolution and is widely used in materials science and biology.
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2. O STM, inventado em 1981, foi o primeiro instrumento capaz de gerar imagens de superfícies com resolução atômica usando o princípio do efeito túnel quântico.
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Rietveld refinement is a technique for determining crystal structures from powder diffraction data. It involves minimizing the difference between observed and calculated powder diffraction patterns through least squares refinement of structural and instrumental parameters. GSAS is a software package that performs Rietveld refinement across multiple diffraction data types. It allows refinement of parameters related to lattice constants, atomic positions, thermal motion, and instrumental profile shapes. EXPGUI provides a graphical user interface for GSAS, while EXPEDT is the text-based interface that allows access to all GSAS capabilities.
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This presentation discusses techniques for analyzing crystallite size in nanomaterials using powder X-ray diffraction data. It introduces the Scherrer formula for relating crystallite size to peak broadening. However, the formula assumes uniform crystallite size and shape when in reality there is usually a size distribution. The presentation demonstrates how the particle size algorithm in DDView+ can model crystallite size distributions, like the more realistic lognormal distribution, and extract mean size and variance. It shows examples of fitting simulated and experimental data to validate the approach for studying nanocrystalline materials.
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1. X-ray diffraction relies on constructive interference of x-rays scattered from the regular arrangement of atoms in a crystal structure.
2. When x-rays interact with a crystal, the x-rays will be scattered in all directions but will experience constructive interference only in certain directions defined by Bragg's law, leading to diffraction.
3. By analyzing the diffraction pattern including the intensities and angles of the diffracted beams, information can be obtained about the crystal structure such as the unit cell dimensions and atomic positions.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help alleviate symptoms of mental illness and boost overall mental well-being.
The document introduces several free and inexpensive software alternatives for analyzing X-ray diffraction data, as commercial software packages can be very expensive. It recommends the Collaborative Computational Project #14 (CCP14) website as the best source for free software information. It then describes several free data conversion tools, including the PowDLL Converter and ConvX, which can convert between different file formats. Finally, it summarizes the capabilities of the free PowderX software for general data processing tasks like smoothing, background subtraction, and pattern indexing.
The "state of the art" of diffraction analysis of crystallite size and lattice strain.
1. 552 Z. Kristallogr. 223 (2008) 552–560 / DOI 10.1524/zkri.2008.1213
# by Oldenbourg Wissenschaftsverlag, Munchen
¨
The “state of the art” of the diffraction analysis of crystallite size
1
and lattice strain
Eric J. Mittemeijer* and Udo Welzel
Max Planck Institute for Metals Research, Heisenbergstraße 3, 70569 Stuttgart, Germany
Received June 1, 2008; accepted July 4, 2008
X-ray powder diffraction / Line-profile analysis / many cases such information is not easily and statistically
Crystallite size / Microstrain / Coherency of diffraction assured accessible by methods other than diffraction.
The analysis of diffraction-line broadening, the topic of
Abstract. This paper addresses both old, but “renovated” this paper, evolved already shortly after the discovery of
methods and new methods for diffraction line-profile diffraction of X-rays by crystals by Friedrich, Knipping
analysis. Classical and even extremely simple single-line and von Laue (1912): Scherrer (1918) found that the
methods for separating “size” and “strain” broadening breadth of a diffraction line is related to the finite size of
effects have merit for characterization of the material im- the diffracting crystals. Considering that, as follows from
perfectness, but it is generally very difficult to interpret differentiating Bragg’s law, lattice-parameter fluctuations
the data obtained in terms of microstructure parameters as are also exhibited by diffraction-line broadening, Dehlin-
used in materials science. Developments of recent years, ger and Kochendorfer, already as early as 1939, realized
¨
focusing on distinct anisotropic line-broadening effects, as that a separation of the diffraction-line broadening in size-
due to the type, orientation and distribution of dislocations and strain-related contributions can, in principle, be
and minute compositional variation, will be touched upon. achieved provided that the diffraction angle dependence of
The most promising development may be the synthesis of the line breadth is known [2].
line profiles on the basis of a microstructure model and Unfortunately, straightforward extraction of quantitative
application of the (kinematical) diffraction theory without information on size and strain from the shape (“width”) data
any further assumption, which contrasts with the other is normally impossible. The least of the problems met is
methods. This approach can in principle be applied in sin- probably the elimination of instrumental broadening effects,
gle-line and multiple-line variants and also in analyses of for which more or less reliable approaches exist which
the whole diffraction pattern. The advantage is the direct depart either from recordings of broadening by standard
evaluation of microstructure parameters as used in materi- specimens, or, more recently, from calculation of the instru-
als science. The challenge is to develop microstructure mental broadening on the basis of the known instrumental/
models which are flexible enough to be applicable in geometrical details of the diffraction experiment.
more than one case . . . Fundamental problems are the unravelling of the var-
ious contributions to the observed, broadened diffraction
lines due to the various types of microstructural details, as
crystallite size, lattice (micro)strain, planar faults (not con-
1. Introduction
sidered in this paper; cf. e.g. Refs. [3, 4]), etc., and their
interpretation in terms of parameters that are used in mate-
Diffraction lines of crystalline materials contain a wealth rials science, as dislocation densities, faulting probabilities
of microstructural information: The amount and distribu- and crystallite size.
tion of the phases in the material, compositional inhomo- On the one hand, more and more advanced methods to
geneity, the crystallite size and shape distributions, the extract microstructural parameters from the profile para-
crystallographic orientation distribution function, the con- meters of a single or multiple diffraction lines using more
centrations and distributions of crystal defects such as va- or less realistic, general assumptions on the material im-
cancies, dislocations, stacking and twin faults, and, not perfection/line shape are developed: line-profile decompo-
least, lattice distortions due to mechanical stresses, etc. sition. On the other hand, a recent, powerful, yet virginal
(see, for example, Ref. [1] and references therein). In approach appears to be line-profile synthesis, where the
microstructural parameters are determined by fitting line
1
Presented as keynote lecture at the International Conference on profiles, calculated on the basis of a model for the micro-
the Diffraction Analysis of the Microstructure of Materials (“Size- structure specific for the material investigated, to measured
Strain V”; Garmisch-Partenkirchen, Germany, October 7–9, 2007).
Full Proceedings available at www.zkristallogr.de (Z. Kristallogr. profiles (i.e. no line-shape assumptions are employed).
Suppl. 27 (2008); open access). The length of the diffraction vector (and the correlation
* Correspondence author (e-mail: e.j.mittemeijer@mf.mpg.de) of the positions of the scattering atoms) is crucial for the
2. The “state of the art” of the diffraction analysis of crystallite size and lattice strain 553
occurrence of incoherency of diffraction, and as a conse- beam diffractometer is insensitive to defocusing errors.
quence, apart from extreme cases, the so-called crystallite- This implies that the specimen can be tilted and rotated in
size values depend on the reflection considered. Thereby, a parallel-beam diffractometer, as is required for stress and
and this is not often realized, classical methods for line- texture measurements and investigations of the inhomo-
profile analysis, but also recent developments, where all geneity and anisotropy of the microstructure [18], without
reflections in the entire diffraction pattern are simulta- changing the (extent of) instrumental broadening. This
neously analysed, under simple assumptions as a size (invariance of) instrumental broadening has been investi-
broadening independent of the length of the diffraction gated both for diffractometers based on X-ray (polycapil-
vector, can become invalidated. lary) lenses [12, 17] and X-ray mirrors [18, 19].
2.2 Subtraction/incorporation
2. Correction for instrumental broadening of the instrumental broadening
The measurement apparatus, usually a diffractometer or Depending on the strategy of analysis of diffraction-line
some type of camera, generally brings about a significant broadening, line-profile decomposition versus line-profile
intrinsic, instrumental broadening of the diffraction lines. synthesis (cf. Section 1), instrumental diffraction-line
Two approaches can be considered to determine instru- broadening has to be taken into account differently.
mental line broadening: On the one hand, a specimen with Whereas the former approach requires a subtraction of the
negligible structural line broadening can be investigated; instrumental from the measured broadening, the latter ap-
the observed broadening is then (taken as) the instrumen- proach requires an ‘addition’ of the instrumental to the
tal broadening. On the other hand, the broadening can be (calculated/modelled) specimen broadening. This is usual-
calculated provided that sufficiently accurate models/meth- ly achieved by a deconvolution method and a convolution
ods exist. The determination of the instrumental broaden- method, respectively.
ing is dealt with in Section 2.1. Various approximate strategies for a correction of
For analysing the line broadening measured for a parti- breadth parameters (as full widths at half maximum and
cular specimen under investigation, a correction for instru- integral breadths) by “simple subtraction” of the corre-
mental broadening has to be performed. This is dealt with sponding breadth parameters for the instrumental broaden-
in Section 2.2. ing have been developed (cf. Refs. [20, 21] and references
therein). Since the pioneering work of Stokes [22] invol-
2.1 Determination of the instrumental profile ving a rigorous deconvolution of the measured broadening
The selection of an appropriate reference specimen for with the instrumental broadening in Fourier space, no ma-
characterising instrumental diffraction-line broadening re- jor progress in deconvolutive methods has been made until
quires careful consideration. In passing it is noted here recently: a novel method for deconvolution has been pro-
that the standard reference material SRM 660 distributed posed both for laboratory [23] and synchrotron [24] pow-
by the National Institute of Standard and Technology exhi- der diffractometers. This method combines scale transfor-
bits a small, but in some cases, even for a laboratory pow- mation, data interpolation and fast Fourier transformation
der diffractometer, non-negligible structural diffraction-line and permits a rigorous subtraction, in steps, of broadening
broadening obscuring the genuine instrumental line broad- contributions due to axial divergence, flat specimen aberra-
ening [5, 6]. A newer batch SRM 660a should lift this tion, specimen transparency and the wavelength distribu-
problem (cf. also Ref. [7]). tion of the X-ray source, provided that the individual in-
For a calculation of the instrumental diffraction-line strumental aberrations can be parameterized each by only
broadening, the fundamental parameter [8, 9] and ray-tra- one diffraction-angle dependent width parameter.
cing [10–12] approaches are usually adopted. Whereas the
former presupposes that the aberrations due to different in- 3. Size-strain broadening
strumental aberrations can each be quantified by analytical
functions and can be treated independently, the latter is time 3.1 Simple approaches
consuming. An approach overcoming both drawbacks, by
considering different aberrations simultaneously and provid- If data of high quality are unavailable (e.g. in the analysis of
ing calculation efficiency, has been proposed recently for in-situ, non-ambient measurements) or an application does
laboratory Bragg-Brentano powder diffractometers [13]. A not merit the expenditure of time and effort required for
comparison of methods for modelling the effect of axial di- advanced line-profile analysis/synthesis methods (as whole
vergence in laboratory powder diffraction arrived at the con- powder pattern modelling), a simple analysis of integral
clusion that a computationally simplified approximation breadths may be appropriate for obtaining semi-quantitative
based on Edgeworth series can be employed [14]. Special estimates of crystallite size and microstrain. Two basic ap-
attention has also been paid to instrumental diffraction-line proaches for the separation of size and strain broadening on
broadening of synchtrotron-based diffractometers based on the basis of integral breadths can be adopted:
collimating [6] and focusing [15] optics. (i) Single-line method [25]. A diffraction line is con-
In recent years diffractometers operating in parallel- ceived as a convolution of a Gaussian and a Lorentzian
beam geometry mode have become available also for la- (also called Cauchy) profile (i.e. as a Voigt function),
boratory measurements [12, 16–19]. As the parallel beam where the Gaussian component is due to microstrain and
geometry does not rely on a focusing condition, a parallel- the Lorentzian component is due to finite crystallite size.
3. 554 E. J. Mittemeijer and U. Welzel
Determination of the crystallite size (volume-weighed do- crystallite-size distribution and vice versa if a crystallite
main size in the direction parallel to the diffraction vector) shape is adopted; see e.g. Ref. [33]). In principle the col-
D and of a measure for the width of the microstrain distri- umn-length distribution is given by the second derivative
bution e is possible making use of the equations of the Fourier transform of the only size-broadened profile
l [34, 35]. However, reliable determination of the column-
bL ¼ ; ð1Þ length distribution on this basis suffers from problems due
D cos q to background subtraction and truncation [20]. In particu-
bG ¼ 4e tan q ð2Þ lar, the obtained size distributions can be highly unreliable
where l is the wavelength, 2q is the Bragg angle of reflec- in the presence of general strain broadening, which, in the
tion, bL is the integral breadth of the Lorentzian compo- line-profile decomposition approach, has to be separated
nent and bG is the integral breadth of the Gaussian com- from the size broadening on the basis of usually unvali-
ponent (for details, see Ref. [20] and references therein). dated assumptions (corresponding results, for example ob-
For the case of a Gaussian microstrain distribution it is tained in Ref. [36], should be mistrusted) [37].
possible to calculate the local root-mean-square strain An alternative approach departs from the presupposi-
h"2 i1=2 from e: h"2 i1=2 ¼ ð2=pÞ1=2 e [20, 26]. tion of a certain type of column-length or crystallite size
0 0
(ii) Williamson-Hall (WH) method [27]. Assuming that distribution. For the description of monomodal distribu-
the size and strain profile components are Lorentzian pro- tions, the Gamma- and lognormal distributions have been
files, the corresponding integral breadths are linearly addi- proposed:
tive to obtain the total integral breadth in reciprocal space Gamma distribution [20]:
b* ¼ ðb cosqÞ=l (cf. Eqs. (1) and (2): 1 r
pðnÞ ¼ n exp ðÀunt Þ ð4Þ
1 C
b* ¼ þ 2ed * ; ð3Þ
D where n denotes column length or crystallite size, C is a
where d * ¼ ð2 sin qÞ=l. A plot of b* versus d * should re- normalisation constant and r, u and t are adjustable para-
sult in a straight line and the values for size and strain can meters (note that usually, t is (unnecessarily) taken as
then be obtained directly from the intercept and the slope one).
of the straight line, respectively. Equation (3) presents one Log-normal distribution:
specific expression for a ubiquitously adopted (but non-tri-
pðnÞ ¼ ðð2pÞ1=2 sÞÀ1 exp ðÀðln n=no Þ2 =ð2s 2 ÞÞ=n ð5Þ
vial, see what follows in Section 3.5) assumption that size
broadening does not depend on the length of the diffraction where no , the median, and s, the variance, are the adjusta-
vector whereas strain broadening does. Other variants of ble parameters (cf., for example, Refs. [38, 39]). It has
the WH method exist [e.g. adopting Gaussian shaped func- been found that in particular highly deformed metals often
tions, taking into account anisotropic line broadening (see exhibit log-normal column length/size distributions (e.g.
Section 3.3.3), as due to dislocations etc.], but all are based Refs. [38–40]).
on the assumption of specific profile shapes. Recently, the determination of column-length/crystal-
Integral-breadth methods have been used in various also lite-size distributions without a prior assumption about the
recent studies with the supposition that the results have a type of distribution has been attempted on the basis of
quantitative meaning (e.g. Refs. [5, 28–30]; for a critical whole powder pattern modelling. An approach involving
overview of such methods, see also Ref. [21]). Results quan- histograms with “tuned” bin width and adjustable bin
titatively consistent with results obtained by more advanced height, but assuming a spherical crystallite shape, has been
methods can be obtained, in particular and obviously for proposed in Ref. [41] (see Fig. 1).
cases where one source of line broadening prevails [31, 32]. An approximate solution for obtaining the crystallite-
size distribution together with information on crystallite
3.2 Column length/crystallite size distribution shape has been proposed in Refs. [42, 43]. In the latter ap-
proach a microstrain distribution with a homogeneous strain
The column length will generally exhibit a distribution in each crystallite has been presupposed (this can be a se-
(the column-length distribution can be calculated from the vere limitation; cf. Section 3.5 and see next paragraph).
Fig. 1. Whole powder pattern modelling: Crystallite size, D (diameter of the sphere (¼ crystallite)), distributions, pðDÞ, of nanocrystalline ceria
powders calcinated for 1 hour at different temperatures (increasing from the left to the right). The full histogram is the result of the analysis
without prior assumption on the crystallite size distributions, whereas the line is the result of the analysis restricted to a log-normal size distribu-
tion. Taken from Ref. [41].
4. The “state of the art” of the diffraction analysis of crystallite size and lattice strain 555
The two categories of approaches (i.e. whether or not the distance between the defects (projected onto the dif-
assuming a distribution function) for determining the col- fraction vector), the probability function for the amplitude
umn-length distribution (and, possibly, the crystallite-size of the component strain fields and a function describing
distribution on the basis of an additional assumption on the average shape (width) of the component strain fields.
crystallite shape) both require that broadening from In the simplest case for application of the strain-field mod-
sources other than finite size (as microstrains) is marginal el, the Fourier coefficient for the only strain broadened
or absent: the required assumptions to separate the size profile Ad ðLÞ is described by only three parameters (cf.
broadening from the other broadening components renders Eq. (7) of van Berkum et al. [47]): (i) the mean projected
a subsequent determination of column-length or crystallite- (onto the diffraction vector) defect distance hsi, (ii) the
size distributions unreliable (corresponding results, e.g. as root-mean-square strain he2 i, and (iii) the width of the
o
published in Ref. [36] (see first paragraph of this section) (Lorentz shaped) component strain fields, w. A component
or Ref. [42] (see above paragraph) should be mistrusted). representing a possible size broadening can simply be in-
cluded [39]. For applications of this strain-field model to
3.3 Microstrain broadening ball-milled metal powders, see Refs. [39, 47, 48].
Methods departing from specific microstructural models
Whereas the fundamentals of size broadening are well es- have been developed for analysing line broadening due to
tablished and in a mature state already since the 1950s, inclusions in a crystalline matrix [49] and due to disloca-
[34, 35] analysis of strain broadening is a field of currently tions. In the following the focus is on dislocation line
strong activity, where both methods imposing assumptions broadening.
on the kinematical diffraction theory and methods depart- The pioneering work in this field is due to Krivoglaz
ing from a microstructural model are developed. and Ryaboshapka [50] and Wilkens [51]. Krivoglaz and
Ryaboshapka considered sets of statistically random distri-
3.3.1 Methods imposing assumptions butions of non-interacting (edge or) screw dislocations.
on the kinematical diffraction theory Wilkens demonstrated that a random distribution of dislo-
cations (in a set) is unrealistic and introduced the concept
An overview of the methods based on specific assump- of the restrictedly random dislocation arrangement. To this
tions about the strain distributions in materials without re- end, the degree of correlation in the dislocation distribu-
ferring to a specific microstructural model is provided by tion of a set was described by the so-called cut-off radius
Table 1 [27, 35, 44–46]. Re , which can be considered as the radius of a cylinder
A quantitative evaluation of size and strain parameters within which the dislocation arrangement is random: No
derived from broadened line profiles requires thorough con- elastic interaction of the various dislocations sets in the
sideration of the underlying assumptions in the methods crystal is considered to occur.
used. A comparative application of the different methods to The strain Fourier coefficients Ad ðLÞ can be approxi-
an imperfect material is not straightforward because the as- mated by [52]:
sumptions are incompatible (e.g. Gaussian strain distribu-
tions in the Warren-Averbach method versus small strain gra- Ad ðLÞ ¼ exp ½ÀðcLÞp Š ; ð6Þ
dients in the alternative method) and the resulting parameters d
where c characterizes the width of A ðLÞ and the exponent
are not defined in the same way (e.g. volume-versus area-
p takes values between 1 (Lorentzian line profile) and 2
weighted crystallite size) [39]; see also Fig. 1 in Ref. [46].
(Gaussian line profile). The shape parameter M,
3.3.2 Methods departing from a microstructural model M ¼ Re ðrÞ1=2 ; ð7Þ
A flexible general method based on a microstructural can be calculated from p (cf. Eq. (2.19) of Vermeulen et al.
model without referring to a particular type of defect is [52]). c is related to the square-root of the dislocation density
the strain-field model proposed by Van Berkum et al. [47]. r. Note that dislocation line broadening is usually anisotro-
In this approach, the strain field is composed of a super- pic, i.e. it depends on the hkl reflection (i.e. it depends on the
position of the (component) strain fields of individual de- orientation and length of the diffraction vector; cf. Section
fects. The strain fields of the lattice defects are described 3.3.3). This can be rationalized by the so-called dislocation-
statistically by three functions: the probability function for contrast factor, which is contained in c in Eq. (6).
Table 1. Summary of basic assumptions made in line profile decomposition methods and the type of size and strain data obtained [39]. Ad ðLÞ is
the strain (‘distortion’) Fourier coefficient of a line profile, L is the correlation distance perpendicular to the diffracting planes.
Method Assumptions Size Strain
Williamson-Hall conventional Lorentz shaped peak Volume-weighted Maximum strain, e related to local
plot [27, 44] 1949, 1953 profiles for size- and strain- column length mean squared strain he02i
broadened profile for Gaussian strain distributions
Warren-Averbach [35, 45] Gaussian strain distribution Area-weighted column length Mean squared strain, he2(L)i,
1950, 1952 or small strains related to Ad(L)
Alternative method [46] 1994 Small strain gradients Area-weighted column length No analytical relation between
and broad size distribution he2(L)i and the strain Fourier
coefficients
5. 556 E. J. Mittemeijer and U. Welzel
Dislocation densities and configurations have been in- tropic diffraction-line broadening may be categorized as
vestigated in thin films and plastically deformed materials follows:
(see, for example, Refs. [39, 54, 55]). In addition to the (i) Only small (negligible) microstrain gradients within
dislocation density and the cut-off radius, the fractions of crystallites. In this case, the increase of line broadening
screw and edge dislocations can be determined. For a re- with increasing length of the diffraction vector, for a given
cent review on dislocation line broadening, see Ref. [56]. set of diffracting lattice planes, is proportional to tan q (cf.
also Section 3.5) [47, 57]. Phenomenological models for
3.3.3 Anisotropic microstrain-like diffraction-line this type of anisotropic microstrain diffraction-line broaden-
broadening ing have been developed and implemented in Rietveld-re-
finement programs (see, for example, Ref. [58]). A model
The occurrence of anisotropic diffraction-line broadening
case for this type of line broadening is a (hypothetical) iso-
(i.e. the diffraction-line broadening depends non-monoto-
tropic microstress distribution which, in combination with
nously on the hkl reflection when plotted versus 2q) is a
single-crystal elastic anisotropy, results in an anisotropic
quite general phenomenon which has attracted consider-
microstrain distribution [57].
able attention both in phenomenological and microstruc-
This approach is likely to overestimate the anisotropy of
ture-based modelling of diffraction-line broadening. Aniso-
diffraction-line broadening, as an isotropic microstress distri-
bution gives rise to geometrically incompatible strains in dif-
ferently oriented crystallites. The real grain interaction in a
polycrystalline material is more likely to be between isotro-
pic stress and isotropic strain distributions. Another recently
considered source of anisotropic (microstrain-like) line
broadening are composition fluctuations in a non-cubic ma-
a
a
b
Fig. 2. (a) Full width at half-maximum (FWHM) of the reflections of
a e-FeN0.433 powder and LaB6 (used for the determination of the in-
strumental line broadening) measured using a Bragg-Brentano dif-
b
fractometer with Co Ka radiation. The apparent ‘scatter’ of the line
widths of the powder is due to compositional inhomogeneities. Fig. Fig. 3. (a) The FWHM (w*) and the integral breaths (B*) as a func-
f
2a and b have been taken from Ref. [59]. (b). The anisotropy of the tion of the reciprocal space coordinate d* in the classical Williamson-
microstrain-like broadening observed from a e-FeN0.433 powder. The Hall plot in the case of Nb ball milled for one day. The indices of the
direction dependence of the FWHM, BfD2 q;hkl , as a function of the reflections have also been indicated in the figure. Note the pronounc-
angle of the diffraction vector relative to the c axis for the hexagonal edly anisotropic nature of line broadening. (b) The modified William-
crystals system. The separate points indicate the experimental data; son-Hall plot of the same data as in Fig. 3a. As a function of d *C 1/2
the solid line represents the curve obtained by fitting a model for line (where C is the dislocation contrast factor). The indices of the reflec-
broadening due to compositional fluctuations to the experimental tions have also been indicated in the figure. Fig. 3a and b have been
data. A compositional fluctuation of e-FeN0.433Æ0.008 is obtained. taken from Ref. [62].
6. The “state of the art” of the diffraction analysis of crystallite size and lattice strain 557
terial (see Fig. 2 for an example) [59]. For a recent general a so-called columnar microstructure occurs, where the film
treatment on anisotropic microstrain broadening due to a consists of e.g. columnar-shaped grains separated by grain
field-tensor (rank 0, pertaining to composition variation; rank boundaries oriented more or less perpendicularly to the
2, pertaining to stress/strain distributions), cf. Ref. [60]. layer surface. For such a thin film, the crystallite size is an
(ii) No assumption about microstrain gradients: Adop- anisotropic quantity: the crystallite size along the surface
tion of a microstructural model. In this case, the depen- normal is much larger than the crystallite size in the plane
dence of strain broadening on the length of the diffraction of the film. Thus, macroscopically anisotropic size broad-
vector follows from the microstructural model. The re- ening occurs (see Fig. 4a for an example) [18]. Anisotro-
cently most frequently studied case is dislocation line pic size broadening can be accompanied by anisotropic
broadening, for which anisotropic line broadening is due strain broadening (see Fig. 4b) [18], which can also occur
to the orientation of the diffraction vector with respect to due to unequal densities of defects (as dislocations on dis-
slip systems and the anisotropy of elastic constants (cf. tinct slip systems) along different directions in the speci-
Section 3.3.2 and Fig. 3; e.g. Refs. [56, 61–63]). men [52].
The analysis of macroscopically anisotropic diffraction-
3.4 Macroscopic anisotropy line broadening is considerably simplified experimentally
by the use of parallel-beam diffractometers, because instru-
Massive and polycrystalline specimens generally exhibit mental aberrations occurring for focusing diffractometers
an anisotropic microstructure. Consider, as an example, (i.e. ‘defocusing’) upon changing the orientation of the
thin films deposited by physical vapour deposition: Often diffraction vector (from e.g. the specimen surface normal
direction, for the case of Bragg-Brentano diffractometers)
can be avoided [18].
3.5 Crystallite size and coherency of diffraction
For most polycrystalline specimens, the phase difference
(reduced modulo 2p) of a wave scattered by one crystal-
lite and the wave scattered by a second crystallite takes
values between 0 and 2p with equal probability. In this
case, the total diffracted intensity can be taken as the sum
of intensities scattered by the individual crystallites sepa-
rately. This naturally leads to the usually adopted concept
of size broadening due to the finite size of individual crys-
tallites and strain broadening related to the relative displa-
a cement of atoms within one grain. A more general ap-
proach is to consider the whole irradiated volume of a
polycrystal as a coherently scattering domain. Such an ap-
proach has been followed by van Berkum et al. for analys-
ing strain broadening on the basis of a flexible model for
strain fields associated with lattice defects (cf. also Section
3.3.2) [47]. As the phase difference of scattered waves
originating from different scatterers (atoms) is the scalar
product of the diffraction vector and the position (differ-
ence) vector of the scatterers, both the character of the
strain fields in a specimen and the length of the diffraction
vector are decisive for diffraction-line broadening. It has
been demonstrated that for general strain broadening, the
order-dependence of the diffraction-line width is complex,
b i.e. neither order-independent broadening (traditionally
termed ‘size broadening’) nor broadening proportional to
Fig. 4. (a) The crystallite, grain sizes of a 250 nm thick Ti3Al layer the length of the diffraction vector (traditionally termed
as viewed along different hhkli* directions, i.e. as function of the ‘strain broadening’) occurs (see Fig. 5a). Two limiting
tilting angle w. The schematic figure represents the rectangular Ti3Al
grains (with a height of 50 nm and a width of 6 nm) in the Ti3Al
cases have been identified:
layer, the crystallite size of the rectangular grain Dhhklià measured (i) For infinitely broad component strain fields of lat-
along the hhkli* direction is 50 nm/cos w for 0 w 6.89 ; 6 nm/ tice defects (w=hsi ! 1; cf. Section 3.3.2), the broaden-
sin w for 6.89 w 90 , as shown by the solid and dashed lines. ing is proportional to the length of the diffraction vector
(b) The microstrains and the grain boundary fraction FGB of the d * (cf. Eq. (3)):
Ti3Al layer as viewed along different hhkli* directions, i.e. as func-
tion of the tilting angle w. FGB ¼ gD=D, where D is a constant rela-
tive to the grain boundary thickness, and equals 1.0 nm here; g is a b ¼ ð2pÞ1=2 d *he2 i1=2 ; ð8Þ
geometrical constant and equals 1. The results suggest that FGB and
the microstrain behave similarly as function of w. Fig. 4a and b have where he2 i is the mean squared strain. This is the well-
been taken from Ref. [18]. known strain broadening for a specimen with a constant
7. 558 E. J. Mittemeijer and U. Welzel
and constant at large lengths; see Fig. 5b) has recently
been experimentally confirmed on the basis of measured
line broadening of nanocrystalline thin films by Rafaja
et al. (see Fig. 5b) [64]: i.e. a loss of coherency with in-
creasing length of the diffraction vector at small lengths of
d * leading to incoherent diffraction of the individual crys-
tallites at larger length d*. For another study of the effect
´
of partial coherence on size broadening, see Ribarik et al.
[65] For an application of the strain-field model incorpor-
ating coherency effects, see Lucks et al. [39].
a 4. Concluding remarks and perspectives
(1) Whereas unprejudiced individual peak-profile analysis
(still) allows the most severe microstructural model
testing, a simultaneous analysis of all reflections, sub-
ject to more severe (e.g. profile-shape) constraints, is
required if overlap of diffraction lines occurs. Distinc-
tion of both evaluation approaches can be expected to
diminish as more sound microstructure-based diffrac-
tion models are developed.
(2) For sensitive crystal-imperfection analysis, an evalua-
tion of anisotropic diffraction-line broadening, with re-
spect to the (orientation and) length of the diffraction
b
vector in either the reciprocal lattice or the specimen
frame of reference, is a prerequisite.
Fig. 5. (a) Application of the strain-field model: Relative integral (3) Preference for microstructure model-based line-profile
breadths of line profiles in reciprocal space for different relative synthesis methods over line-profile decomposition
widths w, of the component strain fields. The subscript ‘r’ indicates methods is due to the application of flawed micro-
that the respective quantity has been normalized by the mean pro-
jected (on the diffraction vector) defect distance. Taken from Ref. structure/diffraction models in line-profile decomposi-
[47]. (b) Diffraction line broadening measured for a nanocrystalline tion methods.
Ti0.38Al0.62N thin film (points) and the numerical simulation (solid (4) Is a general, practically applicable microstructure/dif-
line) taking into account the partial coherence of neighbouring nano- fraction model possible?
sized crystallites. Taken from Ref. [64]. Note the similarity with re-
sults shown in Fig. 5a for, e.g., wr ¼ 0:03.
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Zeitschrift für Kristallographie
New Supplements to be Published
International journal for structural, physical,
Z. Kristallogr. Suppl. 27 (2008)
and chemical aspects of crystalline materials
Proceedings of the ”5th Size Strain“ Conference
ZEITSCHRIFT FÜR
KRISTALLOGRAPHIE
(Diffraction Analysis of the Microstructure of Materials)
held in October 2007 in Garmisch-Partenkirchen, Germany
16. Jahrestagung
Editors: Eric J. Mittemeijer, Paolo Scardi, Andreas
der Deutschen Gesellschaft für Kristallographie
f
Erlangen, 3.– 6. März 2008
Leineweber and Udo Welzel
Referate
Oldenbourg
Z. Kristallogr. Suppl. 28 (2008)
Supplement Issue No. 28 2008
Abstract of the 16th Annual Meeting
of the German Crystallographic Society
Oldenbourg
held in March 2008 in Erlangen, Germany
www.zkristallogr.de