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Analysis of the Broadening of Powder Pattern Peaks from Cold-Worked Face-Centered and Body-Centered Cubic Metals

Published online by Cambridge University Press:  06 March 2019

C. N. J. Wagner  and
E. N. Aqua
C. N. J. Wagner
Affiliation:
Yale University New Haven, Connecticut
E. N. Aqua
Affiliation:
Yale University New Haven, Connecticut
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Abstract

The broadening of powder pattern peaks of metals is normally caused by small crystallite size and by distortions within the crystallites as a consequence of dislocation configurations. In addition, the experimental diffraction geometry contributes to the line broadening. Using Cu Kα radiation, we recorded the peak profiles of the cold-worked and annealed filings of tungsten, niobium, aluminum, and silver-indium alloys with a standard focusing diffractometer. The Rachinger method was applied to separate the Kα1 and Kα2 peaks, and the Kα1 peaks were subjected to a Fourier analysis. Elimination of the instrumental broadening was carried out by the Stokes method, which does not require any assumptions concerning the mathematical description of the diffraction peak profile.

The Fourier coefficients, AL, were separated into the fraction produced by particle size, ALFF, and by strains, ALe, by the Warren-Averbach method and plotted as a function of the distance L = ndhkl, normal to the reflecting planes (hkl) of spacing dhkl. The negative, reciprocal initial slope of the ALPF vs. L curve is equal to the effective particle size Deff, which contains the effects of the true crystallite size and faulting. The coefficients ALβ = AL/ALPF are used to calculate the root mean square strain <∊L2>1/2. The sum of the ALPF, which is proportional to a reciprocal integral breadth, leads to a different particle size, DWAPF, which is also dependent upon the crystallite size and faulting. The sum of the AL6 values is a measure of the strain ƐWA.

The integral breadths bst, corrected by the Stokes method, i.e.,

are separated into a particle size term bstPF and distortion term bSts using the relations . It is found that only the first relation leads to particle sizes DG,StPF and strains ∊G,st similar to those obtained by the summation of the ALPF and AL6, i.e., DWAPF and ∊wA, respectively. The integral breadths of the cold-worked peaks Bew and of the annealed standards bA. were also calculated, using the Lauc definition of B equal to area per peak maximum. A comparison of the values of bst/Bcw with bA/Bew for bA/Bew < 0.6 shows that all data follow the parabolic relation b/Bew = 1 − bA2/Bew2. The maximum deviation of bst/Bew from the parabola is less than 10%.

Type
Research Article
Information
Advances in X-Ray Analysis , Volume 7: Twelfth Annual Conference on Applications of X-ray Analysis, August 7-9, 1963 , 1963 , pp. 46 - 65
Copyright
Copyright © International Centre for Diffraction Data 1963

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