J. Mater. Sci. Technol. ›› 2019, Vol. 35 ›› Issue (7): 1508-1514.DOI: 10.1016/j.jmst.2019.01.014
• Orginal Article • Previous Articles
Gábor Ribárika, Bertalan Jónia, Tamás Ungárab*()
Received:
2018-12-21
Revised:
2019-01-14
Accepted:
2019-01-14
Online:
2019-07-20
Published:
2019-06-20
Contact:
Tamás Ungár
About author:
1These authors contributed equally to this work.
Gábor Ribárik, Bertalan Jóni, Tamás Ungár. Global optimum of microstructure parameters in the CMWP line-profile-analysis method by combining Marquardt-Levenberg and Monte-Carlo procedures[J]. J. Mater. Sci. Technol., 2019, 35(7): 1508-1514.
Fig. 1. Krivoglaz-Wilkens function. The figure shows the Wilkens function f(η) as solid (blue) line, where η=L/Re. The logarithmic and hyperbolic components are shown as dash double-dot and dash lines, respectively.
Fig. 2. (a) Typical sub-profiles of the 311 reflection of copper containing 4% of intrinsic stacking faults. The number, positions and breadths of sub-profiles depend on the hkl indices of the fundamental Bragg peak. (b) Open circles are numerically calculated intensities using the DIFFaX [15] software, the solid black line is a Lorentzian profile function fitted to the open circles. (Figure (b) by courtesy of L. Balogh.).
Fig. 3. (a) Half-breadth of the parameter interval, Δ, as a function of the number of iterations, n. (b) A schematic relation between the random generated number, xni, and the consecutive parameter value on the biased cubic probability (BCP) function.
Fig. 4. Two typical diffraction pattern of strongly deformed metals. (a) Pure Nb HPT deformed at 4 GPa and 0.25 rotations. The pattern was taken at the center region of the disk. (b) A Cantor type high-entropy-alloy HPT deformed at 4 GPa and 5 rotations. The pattern was taken from the edge region of the disk. The open circles and the solid red line are the measured and CMWP calculated patterns. The black line in the bottom of the figure is the difference between the measured and calculated patterns. Enlarged parts of the low intensity peaks are shown as insets. SPP stands for second-phase-particle.
Fig. 5. The calculated dislocation density, ρfinal, as a function of the initial value, ρinitial. (a) Nb HPT deformed at 4 GPa 0.25 rotations at the center region of the disk. (b) Same as (a) only a section of ρfinal around the average value. (c) HEA alloy HPT deformed 5 rotations at the edge region of the disk. (d) Same as (c) only a section of ρfinal around the average value. CMWP-ML is the Marquardt-Levenberg algorithm used in the Linux platform. NRAD-ML is the Marquardt-Levenberg algorithm used in the Windows MATLAB platform. MC is the Monte-Carlo algorithm developed for CMWP. MC + CMWP-ML is the combined Marquardt-Levenberg and Monte-Carlo algorithm used in the present version of CMWP. (e) and (f) Statistics on the ρfinal values of the four different optimization procedures on the diffraction patterns of Nb (e) and HEA alloy (f), respectively.
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