Calculation of diffraction line profiles from specimens with dislocations. A comparison of analytical models with computer simulations

A method is presented for the calculation of diffraction line profiles using Monte Carlo simulation. The method is used to calculate diffraction line profiles for specimens with some idealized distributions of dislocations. The results have been compared with analytical expressions available for these special dislocation distributions. This comparison has been used to validate some essential assumptions made in the derivation of the analytical expressions. In general, very good agreement has been found. Thus, the proposed method is shown to be a valuable tool for diffraction line profile analysis.

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Data-Driven Analysis of Neutron Diffraction Line Profiles: Application to Plastically Deformed Ta

10.21203/rs.3.rs-858939/v1 ◽

2021 ◽

Author(s):

Aaron Tallman ◽

Reeju Pokharel ◽

Darshan Bamney ◽

Douglas Spearot ◽

Bjorn Clausen ◽

...

Keyword(s):

Profile Analysis ◽

Constitutive Models ◽

Gaussian Process Regression ◽

Dislocation Dynamics ◽

Diffraction Line ◽

Data Driven ◽

Analytical Models ◽

Line Profile Analysis ◽

Line Profiles ◽

Dislocation Densities

Abstract Non-destructive evaluation of plastically deformed metals, particularly diffraction line profile analysis (DLPA), is valuable both to estimate dislocation densities and arrangements and to validate microstructure-aware constitutive models. To date, the interpretation of whole line diffraction profiles relies on the use of semi-analytical models such as the extended convolutional multiple whole profile (eCMWP) method. This study introduces and validates two data-driven DLPA models to extract dislocation densities from experimentally gathered whole line diffraction profiles. Using two distinct virtual diffraction models accounting for both strain and instrument induced broadening, a database of virtual diffraction whole line profiles of Ta single crystals is generated using discrete dislocation dynamics. The databases are mined to create Gaussian process regression-based surrogate models, allowing dislocation densities to be extracted from experimental profiles. The method is validated against 11 experimentally gathered whole line diffraction profiles from plastically deformed Ta polycrystals. The newly proposed model predicts dislocation densities consistent with estimates from eCMWP. Advantageously, this data driven LPA model can distinguish broadening originating from the instrument and from the dislocation content even at low dislocation densities. Finally, the data-driven model is used to explore the effect of heterogeneous dislocation densities in microstructures containing grains, which may lead to more accurate data-driven predictions of dislocation density in plastically deformed polycrystals.

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Effect of a crystallite size distribution on X-ray diffraction line profiles and whole-powder-pattern fitting

Journal of Applied Crystallography ◽

10.1107/s002188980000460x ◽

2000 ◽

Vol 33 (3) ◽

pp. 964-974 ◽

Cited By ~ 231

Author(s):

J. I. Langford ◽

D. Louër ◽

P. Scardi

Keyword(s):

Crystallite Size ◽

Line Profile ◽

Profile Analysis ◽

Diffraction Line ◽

Powder Pattern ◽

Line Profile Analysis ◽

Line Profiles ◽

Diffraction Line Profile ◽

Transmission Electron ◽

Using Data

A distribution of crystallite size reduces the width of a powder diffraction line profile, relative to that for a single crystallite, and lengthens its tails. It is shown that estimates of size from the integral breadth or Fourier methods differ from the arithmetic mean of the distribution by an amount which depends on its dispersion. It is also shown that the form of `size' line profiles for a unimodal distribution is generally not Lorentzian. A powder pattern can be simulated for a given distribution of sizes, if it is assumed that on average the crystallites have a regular shape, and this can then be compared with experimental data to give refined parameters defining the distribution. Unlike `traditional' methods of line-profile analysis, this entirely physical approach can be applied to powder patterns with severe overlap of reflections, as is demonstrated by using data for nanocrystalline ceria. The procedure is compared with alternative powder-pattern fitting methods, by using pseudo-Voigt and Pearson VII functions to model individual line profiles, and with transmission electron microscopy (TEM) data.

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