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Acta Metall Sin  2020, Vol. 56 Issue (4): 487-493    DOI: 10.11900/0412.1961.2020.00016
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A Method to Calculate the Dislocation Density of a TWIP Steel Based on Neutron Diffraction and Synchrotron X-Ray Diffraction
LI Yizhuang1,2,HUANG Mingxin1,2()
1.Department of Mechanical Engineering, The University of Hong Kong, Hong Kong 999077, China
2.Shenzhen Institute of Research and Innovation, The University of Hong Kong, Shenzhen 518057, China
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Abstract  

The modified Williamson-Hall method, which has been widely used to calculate dislocation densities of high-strength steels and other structural alloys, is re-examined in this work, and is further applied to calculate the dislocation density of a deformed twinning-induced plasticity (TWIP) steel by using its neutron diffraction patterns and synchrotron X-ray diffraction patterns. This paper aims not only to promote the proper use of the method but also to shed light on its underlying pre-requisites and assumptions, and is thus expected to help avoid any errors during its usage.

Key words:  modified Williamson-Hall method      dislocation density      TWIP steel      neutron diffraction      synchrotron X-ray diffraction     
Received:  13 January 2020     
ZTFLH:  TG115,TG142  
Fund: National Key Research and Development Program of China(2019YFA0209900);National Natural Science Foundation of China(U1764252);Research Grants Council of Hong Kong(17255016);Research Grants Council of Hong Kong(17210418);Research Grants Council of Hong Kong(R7066-18)
Corresponding Authors:  Mingxin HUANG     E-mail:  mxhuang@hku.hk

Cite this article: 

LI Yizhuang,HUANG Mingxin. A Method to Calculate the Dislocation Density of a TWIP Steel Based on Neutron Diffraction and Synchrotron X-Ray Diffraction. Acta Metall Sin, 2020, 56(4): 487-493.

URL: 

https://www.ams.org.cn/EN/10.11900/0412.1961.2020.00016     OR     https://www.ams.org.cn/EN/Y2020/V56/I4/487

Fig.1  Synchrotron XRD patterns (blue) and neutron diffraction patterns (red) of the undeformed and deformed twinning-induced plasticity (TWIP) steel (K is the reciprocal of the lattice spacing)Color online
Fig.2  The relationship between ΔK and K of the undeformed TWIP steel and the standard sample (ΔK is the full width at half maximum (FWHM) of the corresponding diffraction peak at K)Color online
Fig.3  The relationships between ΔK (corrected) and K of the deformed TWIP steel measured by neutron diffraction and synchrotron XRD
Fig.4  The modified Williamson-Hall plots obtained by neutron diffraction and synchrotron XRD (β=(1.5φs+φt)/a, where a is the lattice constant; φs and φt are the probability of finding a stacking fault and a twin boundary in {111} planes, respectively; Whkl is a factor to scale the faulting-induced peak broadening at different {hkl} reflections; Cˉ is the average dislocation contrast factor)
[1] Ungár T. Microstructural parameters from X-ray diffraction peak broadening [J]. Scr. Mater., 2004, 51: 777
[2] Serquis A, Zhu Y T, Peterson E J, et al. Effect of lattice strain and defects on the superconductivity of MgB2 [J]. Appl. Phys. Lett., 2001, 79: 4399
[3] Budrovic Z, Van Swygenhoven H, Derlet P M, et al. Plastic deformation with reversible peak broadening in nanocrystalline nickel [J]. Science, 2004, 304: 273
[4] Wang Y M, Sansoz F, LaGrange T, et al. Defective twin boundaries in nanotwinned metals [J]. Nat. Mater., 2013, 12: 697
[5] Berry J, Provatas N, Rottler J, et al. Defect stability in phase-field crystal models: Stacking faults and partial dislocations [J]. Phys. Rev., 2012, 86B: 224112
[6] Williamson G K, Hall W H. X-ray line broadening from filed aluminium and wolfram [J]. Acta Metall., 1953, 1: 22
[7] Brandstetter S, Derlet P M, Van Petegem S, et al. Williamson-Hall anisotropy in nanocrystalline metals: X-ray diffraction experiments and atomistic simulations [J]. Acta Mater., 2008, 56: 165
[8] Bakshi S D, Sinha D, Chowdhury S G. Anisotropic broadening of XRD peaks of α′-Fe: Williamson-Hall and Warren-Averbach analysis using full width at half maximum (FWHM) and integral breadth (IB) [J]. Mater. Charact., 2018, 142: 144
[9] Ungár T. Dislocation densities, arrangements and character from X-ray diffraction experiments [J]. Mater. Sci. Eng., 2001, A309-310: 14
[10] He B B, Hu B, Yen H W, et al. High dislocation density-induced large ductility in deformed and partitioned steels [J]. Science, 2017, 357: 1029
[11] Zhou P, Liang Z Y, Liu R D, et al. Evolution of dislocations and twins in a strong and ductile nanotwinned steel [J]. Acta Mater., 2016, 111: 96
[12] Liang Z Y, Li Y Z, Huang M X. The respective hardening contributions of dislocations and twins to the flow stress of a twinning-induced plasticity steel [J]. Scr. Mater., 2016, 112: 28
[13] Gutierrez-Urrutia I, Del Valle J, Zaefferer S, et al. Study of internal stresses in a TWIP steel analyzing transient and permanent softening during reverse shear tests [J]. J. Mater. Sci., 2010, 45: 6604
[14] Ungár T, Borbély A. The effect of dislocation contrast on X-ray line broadening: A new approach to line profile analysis [J]. Appl. Phys. Lett., 1996, 69: 3173
[15] Révész A, Ungár T, Borbély A, et al. Dislocations and grain size in ball-milled iron powder [J]. Nanostruct. Mater., 1996, 7: 779
[16] Gubicza J, Ribárik G, Goren-Muginstein G, et al. The density and the character of dislocations in cubic and hexagonal polycrystals determined by X-ray diffraction [J]. Mater. Sci. Eng., 2001, A309-310: 60
[17] Woo W, Balogh L, Ungár T, et al. Grain structure and dislocation density measurements in a friction-stir welded aluminum alloy using X-ray peak profile analysis [J]. Mater. Sci. Eng., 2008, A498: 308
[18] Holzwarth U, Gibson N. The Scherrer equation versus the 'Debye-Scherrer equation' [J]. Nat. Nanotechnol., 2011, 6: 534
[19] Stokes A R, Wilson A J C. The diffraction of X rays by distorted crystal aggregates-I [J]. Proceed. Phys. Soc., 1944, 56: 174
[20] Akama D, Tsuchiyama T, Takaki S. Change in dislocation characteristics with cold working in ultralow-carbon martensitic steel [J]. ISIJ Int., 2016, 56: 1675
[21] Venkateswarlu K, Bose A C, Rameshbabu N. X-ray peak broadening studies of nanocrystalline hydroxyapatite by Williamson-Hall analysis [J]. Physica, 2010, 405B: 4256
[22] Zak A K, Majid W H A, Abrishami M E, et al. X-ray analysis of ZnO nanoparticles by Williamson-Hall and size-strain plot methods [J]. Solid State Sci., 2011, 13: 251
[23] Prabhu Y T, Rao K V, Kumar V S S, et al. X-ray analysis by Williamson-Hall and size-strain plot methods of ZnO nanoparticles with fuel variation [J]. World J. Nano Sci. Eng., 2014, 4: 21
[24] Williamson G K, Smallman R E. III. Dislocation densities in some annealed and cold-worked metals from measurements on the X-ray debye-scherrer spectrum [J]. Philos. Mag., 1956, 1A: 34
[25] Ungár T, Ott S, Sanders P G, et al. Dislocations, grain size and planar faults in nanostructured copper determined by high resolution X-ray diffraction and a new procedure of peak profile analysis [J]. Acta Mater., 1998, 46: 3693
[26] Ungár T, Dragomir I, áRévész, et al. The contrast factors of dislocations in cubic crystals: The dislocation model of strain anisotropy in practice [J]. J. Appl. Cryst., 1999, 32: 992
[27] Ungár T, Groma I, Wilkens M. Asymmetric X-ray line broadening of plastically deformed crystals. II. Evaluation procedure and application to [001]-Cu crystals [J]. J. Appl. Cryst., 1989, 22: 26
[28] Bouaziz O, Allain S, Scott C. Effect of grain and twin boundaries on the hardening mechanisms of twinning-induced plasticity steels [J]. Scr. Mater., 2008, 58: 484
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