Determination of particle size and strain in cold-worked magnesium by the method of variance

Misra, N. K.; Mitra, G. B.

doi:10.1107/s0365110x6700386x

Cited by 11 publications

(14 citation statements)

References 1 publication

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“…The use of the variance-range function is a powerful method for investigating crystal imperfections (Misra & Mitra, 1967;Criado, GonzS.lez, Gonz;ilez & Real, 1982;Criado, Gonzfilez & Real, 1986), and the determination of quantities D and (e2) 1/2 is straightforward from the values of W0h, kh, W0g and kg. However, some errors can be introduced in the data-processing stage that influence the magnitude of the derived parameters.…”

Section: Introductionmentioning

confidence: 99%

The Use of the Pseudo-Voigt Function in the Variance Method of X-ray Line-Broadening Analysis

Sánchez-Bajo¹,

Cumbrera²

1997

J Appl Crystallogr

146

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A modified application of the variance method, using the pseudo‐Voigt function as a good approximation to the X‐ray diffraction profiles, is proposed in order to obtain microstructural quantities such as the mean crystallite size and root‐mean‐square (r.m.s.) strain. Whereas the variance method in its original form is applicable only to well separated reflections, this technique can be employed in the cases where there is line‐profile overlap. Determination of the mean crystallite size and r.m.s. strain for several crystallographic directions in a nanocrystalline cubic sample of 9‐YSZ (yttria‐stabilized zirconia) has been performed by means of this procedure.

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Section: Introductionmentioning

confidence: 99%

The Use of the Pseudo-Voigt Function in the Variance Method of X-ray Line-Broadening Analysis

Sánchez-Bajo¹,

Cumbrera²

1997

J Appl Crystallogr

146

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“…Similar study seems to be necessary for the Warren-Averbach method as well and the present work aims at achieving this. The present work also aims at examining the validity of some variants of the Warren-Averbach method, such as the single-line technique due to Mitra & Misra (1967), and also to evolve a technique relatively free from the limitations imposed by the Warren-Averbach approximations.…”

Section: Introductionmentioning

confidence: 99%

Remarks on separation of particle size and strain by line profile analysis using Fourier coefficients

Mitra¹,

Chaudhuri²

1974

J Appl Cryst

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The exact expression for A(t), the tth‐order Fourier coefficient of an X‐ray diffraction line profile in terms of column length distribution, mean thickness, the r.m.s. strain and various mean strain gradients, has been derived and the assumptions involved in the Warren–Averbach method of separating particle size and r.m.s. strain have been critically examined. It has been observed that the Warren–Averbach method gives a r.m.s. value of the pseudo strain 〈ē2〉1/2 which is equal to the true r.m.s. strain 〈e2〉1/2 only at t = 0. It has been further shown that ln J(t), where J(t) is the tth‐order Fourier coefficient of the strain profile, is not, as is taken in the Warren–Averbach method, linear in l20 when the given reflection hkl has been converted into a 00l0 reflection by suitable changes of axes. In the Warren–Averbach method, this essentially non‐linear curve is taken as linear and a straight line passing through two points on this curve is extended to meet the ln A(t) axis, the intercept on which is supposed to give ln N(t), where N(t) is the tth‐order Fourier transform of the particle‐size profile. Thus approximate values of the mean particle size 〈T〉 and the r.m.s. pseudo strain 〈ē2〉1/2 are obtained. Based on the exact expression for A(t) a new multiple‐order technique for determining not only the particle size and r.m.s. strain but also various strain derivatives has been developed and its limitations examined. It is found that an error introduced in the r.m.s. strain is of an order less than that of the experimental errors. Similarly, the single‐line technique of Mitra & Misra [Acta Cryst. (1967), 23, 867–868] has been shown to give correct values of 〈T〉 and 〈e2〉1/2 within experimental error. The single‐line technique has been proved to be quite a perfect and useful technique.

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“…It is seen that the formation of metakaolin and the collapse of the kaolinite structure is preceded and accompanied by a disordering of the basal planes so that the interlayer spacing is variable. Mitra (1958) and Brindiey & Nakahira (1959) have observed that basal reflexions from kaolinite become asymmetrical as a result of dehydration at the temperature at which metakaolin starts to form. The asymmetry of the intensity profiles has been attributed by Mitra (1958) to irregularities in the interlayer distances of the basal planes.…”

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confidence: 99%

“…Mitra (1958) and Brindiey & Nakahira (1959) have observed that basal reflexions from kaolinite become asymmetrical as a result of dehydration at the temperature at which metakaolin starts to form. The asymmetry of the intensity profiles has been attributed by Mitra (1958) to irregularities in the interlayer distances of the basal planes. Mitra (1963) observed that this disorder exists even in ordinary kaolinite not subject to any heat treatment and has developed a method for quantitative determination of g, the mean fractional change in interlayer spacing, and of y, the proportion of planes affected by such disorders.…”

mentioning

confidence: 99%

“…For samples treated at 500 and 600°C only 001 and 002 reflexions were present; the 001 reflexions in both samples were very broad and diffuse while the 002 reflexions were less so. Hence the y and g values in these samples were determined by adopting a single-line technique similar to that developed by Misra & Mitra (1967). For this purpose, the Fourier transform of the defect line-profile for the layer structure having a variable interlayer spacing in the [001] direction as derived, by Wilson (1962), has been calculated.…”

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confidence: 99%

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Layer disorders in kaolinite during dehydration

Mitra¹,

Bhattacherjee²

1969

Acta Crystallogr Sect B

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Determination of particle size and strain in cold-worked magnesium by the method of variance

Cited by 11 publications

References 1 publication

The Use of the Pseudo-Voigt Function in the Variance Method of X-ray Line-Broadening Analysis

The Use of the Pseudo-Voigt Function in the Variance Method of X-ray Line-Broadening Analysis

Remarks on separation of particle size and strain by line profile analysis using Fourier coefficients

Layer disorders in kaolinite during dehydration

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