The Determination of Crystallite Size and Size Distribution from Broadened X-Ray Diffraction Lines

Quinn, H. F.; Cherin, P.

doi:10.1154/s0376030800001464

Cited by 3 publications

(2 citation statements)

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“…Warren (1959) considered this possibility of little practical importance due to expansion of the experimental noise by the second derivative and problems with effective separation of the size and distortion coefficients. There are in the literature, however, examples of effective calculation of p(n) (Pielaszek et al, 1983;Quinn & Cherin, 1962;Sashital et al, 1977) and the concept is tempting. Typical errors of the Fourier coefficients are due to incorrect peak background estimation and are observed for small n as the so-called 'hook effect', causing the A n distribution to be concave downwards locally.…”

Section: Warren-averbach Methods and Background Estimationmentioning

confidence: 99%

“…The use of this method in its full original form is rather limited (e.g. Quinn & Cherin, 1962;Sashital et al, 1977;Pielaszek et al, 1983). The main difficulties in its application lay in the estimation of the diffraction pattern background intensity, especially for the overlapping peaks, determination of the correct instrumental function, and the need to measure several orders of the same reflection to separate strain and size effects.…”

Section: Introductionmentioning

confidence: 99%

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Ab initiotest of the Warren–Averbach analysis on model palladium nanocrystals

2005

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Model powder diffraction patterns were calculated via the Debye formula from atom positions of a range of energy‐relaxed closed‐shell cubooctahedral clusters. The energy relaxation employed the Sutton–Chen potential scheme with parameters for palladium. The assumed cluster size distribution followed lognormal distribution of a crystallite volume centred with the diameter of 5 nm, as well as two bimodal lognormal distributions centred around 4 nm and 7 nm. These models allowed an in‐depth analysis of the Warren–Averbach method of separating strain and size effects in a peak shape Fourier analysis. The atom‐displacement distribution in the relaxed clusters could be directly computed, as well as the strain Fourier coefficients. The results showed that in the case of the unimodal size distribution, the method can still be successfully used for obtaining the column length distribution. However, the strain Fourier coefficients obtained from three reflections (002, 004 and 008) cannot be reliably estimated with the Warren–Averbach method. The primary cause is a non‐Gaussian strain distribution and a shift of the diffraction maximum, inherent to the nanoparticles, differing for every constituent cluster in the size distribution. For the bimodal size distributions, the obtained column length distributions tend to be shifted towards the centres of the modes and are less sensitive to the larger size mode.

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Section: Warren-averbach Methods and Background Estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Ab initiotest of the Warren–Averbach analysis on model palladium nanocrystals

2005

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Effect of Cold Deformation and Multiphase Treatment Conditions on Low‐Carbon, Low‐Silicon Multiphase Steel

El-Din

2005

steel research international

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This paper presents multiphase (MP) treatments of a low‐C, low‐Si cold rolled steel. Despite the much lower content of Si compared to a typical TRIP steel, up to about 8 pct of retained austenite (γr) with 1.2 % carbon content can be obtained. Increasing prior cold deformation (i.e. decrease of parent austenite grain size) accelerates the transformation to bainite resulting in a decrease of the volume fraction of residual austenite (γr + martensite). Tensile strength of MP steel intercritically annealed at high temperature increases with higher cold reduction degree due to the smaller grain size of the present phases. On the contrary, the ductility and strength‐ductility balance deteriorate because the banded structure becomes more pronounced and the γr volume fraction diminishes. Decreasing intercritical annealing temperature results in an increasing γr fraction and a uniform distribution of second phases. Hence, the ductility and strength‐ductility balance are improved. Crystallographic preferred orientation is evident in the ferrite and martensite and its extent increases with higher cold deformation.

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