Direct determination of microstructural parameters from the X-ray diffraction profile of a crystal with stacking faults

Estévez-Rams, E.; Pentón-Madrigal, A.; Lora‐Serrano, R.; Martinez-Garcia, Jorge

doi:10.1107/s0021889801014091

Cited by 26 publications

(22 citation statements)

References 20 publications

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“…The reason for this is that the line profiles of faulted and twinned crystals consist of several subprofiles, where the number of subprofiles depends on hkl indices, and for special hkl index values, the subprofiles can be delta functions. [15,18,19,40] For the case of fcc crystals, when faulting or twinning occurs on the close-packed planes, Estevez-Rams and co-authors [19] developed a Fourier method in which the Fourier coefficients of the physical Fig. 6-Measured (open circles) and fitted (solid line) X-ray diffraction patterns of the specimen sintered at 1800°C and 2 GPa.…”

Section: B Profile Functions For Planar Defects Especially Stackingmentioning

confidence: 99%

Defect-Related Physical-Profile-Based X-Ray and Neutron Line Profile Analysis

Ungár

Balogh

Ribárik

2009

Metall Mater Trans A

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Diffraction line broadening is caused by different defects present in crystalline materials: (1) small coherent domains, (2) dislocations, (3) other types of microstrains, (4) twin boundaries, (5) stacking faults, (6) chemical inhomogeneities, and (7) grain-to-grain second-order internal stresses. Line profile analysis provides qualitative and quantitative information about defect types and densities, respectively. Line profiles can broaden, be asymmetric, and be shifted, and these features can be anisotropic in terms of hkl indices. A few thumb rules help qualitative selection of lattice defect types. If the breadths do not increase globally with hkl, the defects are of size type, i.e., either the domain size is small or twinning or faulting, or both, is present. Whenever the breadths increase globally, the defects produce microstrains. Physically based profile functions can be determined for the different defect types and hkl anisotropy. The qualitative input about defect types based on different experimental observations allows adequate quantitative evaluation of the densities of different defect types by using physically modeled profile functions.

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Section: B Profile Functions For Planar Defects Especially Stackingmentioning

confidence: 99%

Defect-Related Physical-Profile-Based X-Ray and Neutron Line Profile Analysis

Ungár

Balogh

Ribárik

2009

Metall Mater Trans A

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“…Planar faults can be separated into two main types: stacking faults and twin faults. The presence of planar faults on diffraction peaks has been investigated in several works [23,[32][33][34][35], with the work of Warren [23] being the most widely used for metal alloys.…”

Section: Planar Faultsmentioning

confidence: 99%

Peak Broadening Anisotropy and the Contrast Factor in Metal Alloys

Simm

2018

Crystals

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Diffraction peak profile analysis (DPPA) is a valuable method to understand the microstructure and defects present in a crystalline material. Peak broadening anisotropy, where broadening of a diffraction peak doesn't change smoothly with 2θ or d-spacing, is an important aspect of these methods. There are numerous approaches to take to deal with this anisotropy in metal alloys, which can be used to gain information about the dislocation types present in a sample and the amount of planar faults. However, there are problems in determining which method to use and the potential errors that can result. This is particularly the case for hexagonal close packed (HCP) alloys. There is though a distinct advantage of broadening anisotropy in that it provides a unique and potentially valuable way to develop crystal plasticity and work-hardening models. In this work we use several practical examples of the use of DPPA to highlight the issues of broadening anisotropy. of 31where, D is the crystal size, K Sch is the Scherrer constant (often taken as 0.9 for spherical crystals), g is the reciprocal of the d-spacing of a peak, f m is a function related to the arrangement of dislocations (and represents how the arrangement of groups of dislocations influence their total strain), ρ is the dislocation density and C hkl is the average contrast factor of dislocations in grains that contribute to the hkl diffraction peak. In Equation 1 and other DPPA approaches, C hkl is assumed to be the only term that accounts for broadening anisotropy and its value is required to be able to obtain the dislocation density.TEM to be able to identify details of dislocations [15,16], especially in cases when g.b=0 does not lead to vanishing contrast or due to practicalities of rotating a sample. In the same manner, the diffraction broadening caused by a dislocation varies depending on the diffraction vector, and can be calculated by modelling the dislocation's displacement field. The contribution of a dislocation's displacement field to the broadening of different diffraction profiles is through what is known as the contrast (or orientation) factor of dislocations. The contrast factor of an individual dislocation is dependent on the angles between the diffraction vector and the vectors that define the dislocation: it's Burgers vector (b), slip plane normal (n), and dislocation line (s). The contrast factor of an individual dislocation can be calculated using the computer program ANIZC [17]. For example, the edge dislocation in Figure 2 has a contrast factor of 0.46 when g is [110] and parallel to the dislocations Burgers vector. The value is 0.00 when g is parallel to the slip line ([11 2]) and 0.05 when g is parallel to the slip plane normal ([1 11]).

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“…[27,28,[33][34][35][36], and (vii) planar defect densities, cf. [1,2,29,[37][38][39][40][41][42][43][44][45][46][47][48][49][50][51] or (viii) different types of internal stresses of first and second order, (ix) especially longrange-internal stresses prevailing in heterogeneous microstructures, cf. [52][53][54][55][56][57][58], (x) fluctuation of chemical composition, cf.…”

Section: à2mentioning

confidence: 99%

Characterization of defect structures in nanocrystalline materials by X-ray line profile analysis

Gubicza

Ungár

2007

Zeitschrift Für Kristallographie - Crystalline Materials

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Abstract. X-ray line profile analysis is a powerful alternative tool for determining dislocation densities, dislocation type, crystallite and subgrain size and size-distributions, and planar defects, especially the frequency of twin boundaries and stacking faults. The method is especially useful in the case of submicron grain size or nanocrystalline materials, where X-ray line broadening is a well pronounced effect, and the observation of defects with very large density is often not easy by transmission electron microscopy. The fundamentals of X-ray line broadening are summarized in terms of the different qualitative breadth methods, and the more sophisticated and more quantitative whole pattern fitting procedures. The efficiency and practical use of X-ray line profile analysis is shown by discussing its applications to metallic, ceramic, diamond-like and polymer nanomaterials.

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Direct determination of microstructural parameters from the X-ray diffraction profile of a crystal with stacking faults

Cited by 26 publications

References 20 publications

Defect-Related Physical-Profile-Based X-Ray and Neutron Line Profile Analysis

Defect-Related Physical-Profile-Based X-Ray and Neutron Line Profile Analysis

Peak Broadening Anisotropy and the Contrast Factor in Metal Alloys

Characterization of defect structures in nanocrystalline materials by X-ray line profile analysis

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