Line shape analysis of cold-worked magnesium

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

doi:10.1107/s0365110x67000969

Cited by 24 publications

(10 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Duration of run was 84 sec, including interference by spool operations. Renault & Brower (1971), from which crystallite size and r.m.s, strain in the BaSO4-SrSO4 solidsolution series were determined by the Fourier analysis method of Mitra & Misra (1967), have been reprocessed in order to test the use of standard deviation in the Scherrer equation. Crystallite size is the major component of broadening in these sulfate profiles, r.m.s.…”

Section: Notes On Application Of the Methodsmentioning

confidence: 99%

“…Results are summarized in Table 1. Columns one and two respectively give crystallite sizes in 5.ngstroms as determined by Fourier analysis (Mitra & Misra, 1967) and graphically in conjunction with equation (1) as outlined by Bartram (1967). In columns three, four and five, the crystallite sizes are given as determined by the Scherrer equation (2) using the standard deviation of the pure diffraction profile.…”

Section: Data Ofmentioning

confidence: 99%

See 1 more Smart Citation

The use of standard deviation of X-ray diffraction lines as a measure of broadening in the Scherrer equation: a curve fitting method

McGehee¹,

Renault²

1972

J Appl Cryst

View full text Add to dashboard Cite

The use of standard deviation as a measure of line broadening in the Scherrer equation is justified on the grounds that, for commonly used approximating curves which can be fitted to X-ray line profiles, the line breadth at half intensity is directly proportional to the standard deviation of the fitted curve.If the crystallite size is known a priori, a standard deviation-width scaling function can be calculated; also some insight can be gained into the nature of the curve describing the diffraction profile. A computer program in Fortran IV has been written which fits Gaussian curve forms to diffraction profiles and computes standard deviations and half widths. The program includes an estimation of background, achieves a fit with an error of 5 %, and runs rapidly. In 1956, Tournarie (1956a showed how variance could be used to determine crystallite size if account were taken of the range. Since that time there has been sporadic interest in this method of X-ray line profile analysis. Pitts & Willets (1961) used twice the standard deviation as a measure of line broadening in conjunction with the Scherrer equation: Introductionwhere J9 is the thickness of a coherently diffracting domain normal to an hkl plane, K is a constant depending on shape and is near unity, fl is a measure of the broadening of a diffraction line, 0 is the Bragg angle, and 2 is the wavelength of the incident X-radia- (1962, 1963a, b) in a series of important papers expanded and generalized Tournarie's theoretical groundwork, but questioned the theoretical justification of using the standard deviation of a line in the Scherrer equation.Wilson showed how strain and mistake information as well as particle size could be extracted from the variance of X-ray profiles, and Grimes (1968) and Grimes, Hilleard, Waters & Yerkess (1968) used Tournarie and Wilson's theory as a basis for a practical study of the Mg-Fe spinels. The variances of functions have the particularly attractive property of being additive in convolution, thus enabling instrumental contributions to an X-ray line profile to be simply subtracted out. Furthermore, it can be shown that this property is independent of the 366 STANDARD DEVIATION AS A MEASURE OF X-RAY LINE BROADENING function describing the line profile (Spencer, 1949). The use of variance in line-profile analysis also has an advantage over Fourier analysis in that it is less sensitive to background level and noise. However, the computation of variance as a function of range over a number of background decrements requires automatic computing facilities and the programs have long running times. Hilleard & Webster (1969)published such a program in Algol for the Atlas computer which has typical running times of something less than •20 sec.Estimates of the parameters for a chosen curve form, say Gaussian, by the usual moment equations are inherently dependent on the range of data, and approach true values as the range increases without limit.Estimates by the curve-fitting method we have used do not have this inherent range dep...

show abstract

Section: Notes On Application Of the Methodsmentioning

confidence: 99%

Section: Data Ofmentioning

confidence: 99%

The use of standard deviation of X-ray diffraction lines as a measure of broadening in the Scherrer equation: a curve fitting method

McGehee¹,

Renault²

1972

J Appl Cryst

View full text Add to dashboard Cite

show abstract

“…As for the single-line Fourier methods (Smith, 1960;Pines & Sirenko, 1962;Mitra & Misra, 1967;Gangulee, 1974;Mignot & Rondot, 1977) developed for separating the particle-size and distortion components of the Fourier coefficients in the difficult cases in which, for various reasons, it is not possible to measure for every set of reflecting planes more than one intensity profile, background and truncation errors may be quite substantial. Indeed, the same reasons, e.g.…”

Section: Introductionmentioning

confidence: 99%

An improved method for the determination of microstructural parameters by diffraction-profile Fourier analysis

Zocchi¹

1980

Acta Cryst Sect A

View full text Add to dashboard Cite

The analysis of the influence of the background and truncation errors on the Fourier transform of the diffraction profile is extended with respect to the work that has already been done by others and a critical evaluation of the established Fourier methods for the determination of the microstructural parametersaverage dimensions of crystallites and paracrystalline microdomains, lattice-distortion parameters and cumulants of the strain distribution -is presented. It is shown that, contrary to the case of the cosine transform and of its logarithm whose functional behaviour is drastically changed by the truncation error, the first derivative of that transform is modified by this error only by an oscillatory factor which multiplies the first term of its series expansion. The suggestion follows of using this derivative function in the least-squares or curve-fitting determination of the microstructural parameters. It seemed proper to check these theoretical results by comparing them with experimental data, determining by a simple curve-fitting procedure based on this derivative function the microstructural parameters of a high-density polyethylene fibre in directions perpendicular to the fibre axis. The parameters so obtained are in good agreement with the structural data found in the literature for the same material. It is concluded that the use of this derivative function makes possible the reliable determination of important features of the microstructure of materials by a single-line Fourier technique even in the presence of a large truncation error.

show abstract

“…Of all the substances having hexagonal-closepacked structure the only metals which have so far been considered are cobalt (Mitra and Halder 1964), zirconium (Mogard and Averbach 1958) and magnesium (Lele andAnantharaman 1964, Mitra andMisra 1967). Stratton andKitchingman (1965, 1966) have reported the effect of deformation on Ag-Sn, Ag-In, Au-Sn and Au-In alloys having hexagonal-close-packed structure, and x-ray studies of hexagonal-close-packed Cu-Ge alloys have been made by Sen Gupta and Goswami (1967).…”

Section: Introductionmentioning

confidence: 99%

Reading of optical information from a metal-insulator-semiconductor structure by an electron beam

Bel'skikh¹,

Vasil'ev²,

Plotnikov³

et al. 1975

Sov. J. Quantum Electron.

View full text Add to dashboard Cite

X-ray diffraction line profiles from the filings of cold-worked hexagonalclose-packed silver-antimony alloys have been recorded using a Geiger counter x-ray diffractometer and examined by Fourier analysis of line shapes. The composite broadening has been separated into that caused by particle size, lattice strain and the presence of stacking faults. The stacking-fault density has been found to be greatest for the alloy composition which is nearest to the primary face-centred-cubic phase boundary and to decrease almost linearly with increase in the solute content. The behaviour has been interpreted qualitatively in terms of the difference in free energies between the face-centred-cubic and hexagonal phases.

show abstract

Line shape analysis of cold-worked magnesium

Cited by 24 publications

References 7 publications

The use of standard deviation of X-ray diffraction lines as a measure of broadening in the Scherrer equation: a curve fitting method

The use of standard deviation of X-ray diffraction lines as a measure of broadening in the Scherrer equation: a curve fitting method

An improved method for the determination of microstructural parameters by diffraction-profile Fourier analysis

Reading of optical information from a metal-insulator-semiconductor structure by an electron beam

Contact Info

Product

Resources

About