Characterization of defects in ultrafine-grained interstitial-free steel prepared by severe plastic deformation

Transcription

1 Characterization of defects in ultrafine-grained interstitial-free steel prepared by severe plastic deformation J. Čížek, M. Janeček, T. Krajňák, J. Stráská, P. Hruška Faculty of Mathematics and Physics, Charles University Prague, Czech Republic J. Gubicza Department of Materials Physics, Eötvös Loránd University, Budapest, Hungary H.S. Kim Department of Materials Science and Engineering, POSTECH, Pohang, South Korea

2 Ultra fine grained (UFG) materials polycrystalline material grain interior grain boundary (GB) d d volume fraction of GB s f GB d d 1 d 3

3 Ultra fine grained (UFG) materials polycrystalline material grain interior grain boundary (GB) crystallographic width of GB s: d 1 nm d d volume fraction of GB s f GB d d 1 d 3

4 Ultra fine grained (UFG) materials polycrystalline material grain interior grain boundary (GB) crystallographic width of GB s: d 1 nm d d 0.6 f GB 0.4 volume fraction of GB s f GB d d 1 d d (nm)

5 polycrystalline material grain interior grain boundary (GB) d 1.0 d f GB UFG materials d nm Ultra fine grained (UFG) materials d < 100 nm nanocrystals d > 1 mm polycrystals 0.4 volume fraction of GB s f GB d d 1 d d (nm)

6 Severe plastic deformation plastic deformation grain refinement conventional plastic deformation

7 Severe plastic deformation plastic deformation grain refinement conventional plastic deformation formation of cracks

8 Severe plastic deformation plastic deformation grain refinement conventional plastic deformation formation of cracks material failure deformation under high pressure crack formation suppressed

9 High pressure torsion (HPT) the strongest grain refinement high pressure 1-10 GPa grain size 100 nm disk shaped samples diameter 10 0 mm, thickness mm UFG IF steel sample prepared by HPT dislocation density is an important parameter of UFG materials torsion deformation R.Z. Valiev, Nature Materials 3, (004)

10 Methods for determination of dislocation density in UFG materials TEM - direct observation of dislocations

11 Methods for determination of dislocation density in UFG materials TEM - direct observation of dislocations - hard to resolve individual dislocations due to high dislocation density HPT deformed IF steel

12 Methods for determination of dislocation density in UFG materials X-ray diffraction (XRD) - broadening of XRD profiles - crystallite size & microstrain broadening

13 Methods for determination of dislocation density in UFG materials X-ray diffraction (XRD) - broadening of XRD profiles coarse grained material - crystallite size & microstrain broadening - different dependence on scattering angle UFG material G. Ribárik et al. Mater. Sci. Eng. A , 343 (004)

14 XRD line profile analysis Williamson-Hall (W-H) method G.K. Williamson, W.H. Hall, Acta Metall. 1, (1953) - size broadening independent on q - strain broadening proportional to sin q

15 K XRD line profile analysis W-H plot Williamson-Hall (W-H) method G.K. Williamson, W.H. Hall, Acta Metall. 1, (1953) b - hkl peak width: K q cosq / hkl hkl - magnitude of diffraction vector: K sinq hkl / 0.9 D K K 0.9 b D crystallite size K Burgers vector dislocation density strain broadening size broadening

16 XRD line profile analysis W-H plot Williamson-Hall (W-H) method strain anisotropy 310 G.K. Williamson, W.H. Hall, Acta Metall. 1, (1953) hkl peak width: K q cosq / hkl hkl - magnitude of diffraction vector: K sinq hkl / K 0.9 b D crystallite size K Burgers vector dislocation density K (nm -1 ) HPT deformed IF steel strain broadening size broadening

17 Methods for determination of dislocation density in UFG materials modified Williamson-Hall (W-H) method T. Ungár, A. Borbély, Appl. Phys. Lett. 69, 3173, (1996) - hkl peak width: K q cosq / hkl hkl - magnitude of diffraction vector: K sinq hkl / Modified W-H plot K 0.9 D bm KC 1/ KC 1/ (nm -1 ) HPT deformed IF steel dislocation distribution parameter H h l h k l h k l k dislocation contrast factor C Ch 00 1 qh dislocation contrast factor for {h00} reflections for common slip systems in fcc and bcc structures calculated in T. Ungár et al. J. Appl. Cryst 3, 99 (1999) fraction of screw dislocations: f screw screw edge q edge edge / screw character of dislocations q q q

18 XRD line profile analysis modified Williamson-Hall (W-H) method linearization of relation K C 1 qh K gives parameters: 0.9 D h00 (crystallite size) H 1 q HPT deformed IF steel bm (dislocation density) q (screw / edge character of dislocations)

19 XRD line profile analysis dislocation distribution parameter M M 1 dislocations form dipoles smaller broadening G. Ribárik, PhD. Thesis (008)

20 XRD line profile analysis dislocation distribution parameter M M 1 M 1 dislocations form dipoles random orientation smaller broadening larger broadening G. Ribárik, PhD. Thesis (008)

21 XRD line profile analysis modified Warren-Averbach (MWA) method T. Ungár, A. Borbély, Appl. Phys. Lett. 69, 3173, (1996) Fourier transform of XRD profiles A L A LA L S D HPT deformed IF steel size coefficient distortion coefficient A D L b K C exp L f exp 7 4 L M strain (Wilkens) function describes dislocation-dislocation correlation strain function

22 XRD line profile analysis whole profile fitting G. Ribárik, T. Ungár, J. Gubicza, J. Appl. Cryst. 34, 669, (001) by self consistent MWH + MWA approach one gets: 1. mean crystallite size D HPT deformed IF steel. mean dislocation density 3. screw / edge character of dislocations q 4. dislocation distribution parameter M G. Ribárik, T. Ungár, J. Gubicza: Multiple Whole Profile fitting program MWP-fit,

23 Positron trapping at dislocations dislocation line is a shallow positron trap weak positron localization at dislocation diffusion along dislocation line final trapping at vacancy bound to dislocation or open volume at jog edge dislocation screw dislocation

24 Positron trapping at dislocations two-step positron trapping at dislocation K v << K dl d dl << K dv (vacancy is a point defect but dislocation is a line defect) (there is always enough vacancies attached to dislocation) positron binding energy E annihilation (values are for edge dislocation in Fe) E dl ~ 0.1 ev free positron dislocation line B = 1/t B dl = 1/t dl K dl d dl t B = 108 ps t dl = 108 ps E dv ~ 1 ev K v K dv vacancy bound to dislocation dv = 1/t dv t dv = 165 ps L.C. Smedskjaer et al., J. Phys. F 10, 37, (1980)

25 Positron trapping at dislocations two-state positron trapping at dislocation K v << K dl d dl << K dv (vacancy is a point defect but dislocation is a line defect) (there is always enough vacancies attached to dislocation) positron binding energy E annihilation (values are for edge dislocation in Fe) E dl ~ 0.1 ev free positron dislocation line B = 1/t B dl = 1/t dl K dl d dl t B = 108 ps t dl = 108 ps E dv ~ 1 ev K v K dv vacancy bound to dislocation dv = 1/t dv t dv = 165 ps specific positron trapping rate: = m s -1 dislocation density: = m -

26 Positron trapping at dislocations in Fe (or steels) open volumes attached to edge dislocations are larger Y.K. Park et al., PRB 34, 83 (1986) screw and edge dislocations can be distinguished edge dislocation t edge = 165 ps screw dislocation t screw = 14 ps

27 Positron trapping at dislocations in Fe (or steels) open volumes attached to edge dislocations are larger Y.K. Park et al., PRB 34, 83 (1986) screw and edge dislocations can be distinguished fraction of screw dislocations: edge dislocation t edge = 165 ps f screw t t t screw edge t edge screw dislocation t screw = 14 ps

28 Positron trapping at dislocations in Fe (or steels) open volumes attached to edge dislocations are larger Y.K. Park et al., PRB 34, 83 (1986) screw and edge dislocations can be distinguished typical lifetimes of trapped positrons in deformed steels: ps edge dislocation t edge = 165 ps screw dislocation t screw = 14 ps

29 Positron trapping at dislocations in Fe (or steels) open volumes attached to edge dislocations are larger Y.K. Park et al., PRB 34, 83 (1986) screw and edge dislocations can be distinguished unfortunately the lifetimes for edge and screw dislocations have been determined only for Fe so far edge dislocation t edge = 165 ps screw dislocation t screw = 14 ps

30 Positron trapping at dislocations distribution of dislocations uniform distribution of dislocations simple trapping model (hcp metals, metals with low SFE) 1 I I 1 1 t B 1 t D dislocation cell structure diffusion trapping model (cubic metals with medium and high SFE) specific positron trapping rate to dislocations HPT-deformed Mg-10wt.%Gd alloy HPT-deformed IF steel

31 Positron trapping at dislocations dislocation cell structure dislocation cell structure dislocation-free cell interiors HPT-deformed IF steel

32 Positron trapping at dislocations dislocation cell structure dislocation cell structure dislocation-free cell interiors distorted regions with high density of dislocations (dislocation walls) HPT-deformed IF steel

33 Diffusion trapping model (DTM) dislocation-free spherical cells with radius R surrounded by dislocation walls with thickness d thermalization d R 1. positrons stopped at distorted regions trapping at dislocations annihilation from free state n t. positrons stopped inside cells D D + - positron diffusion coefficient A. Dupasquier et al. PRB 48, 935 (1993) J. Čížek et al. PRB 65, (00) n r r n t n n r B rr n d n D R, t 1 4 / 3 R r,0 3 R 3 d R d 3 diffusion to distorted regions R 3 boundary condition initial condition volume fraction of distorted regions

34 Diffusion trapping model (DTM) spherical grains with radius R distorted regions along grain boundaries with thickness d R d d k t d d k t t k k e I e i t t S t t / 1 / 1 positron lifetime spectrum d k B k k k t t R i t t d 1 1 R D t k B k t infinite number of free positron components lifetime of positrons trapped at dislocations k d i k I 1 intensity of dislocation component t d 0 1 cot k k 1 k k D R d A. Dupasquier et al. PRB 48, 935 (1993) J. Čížek et al. PRB 65, (00)

35 Diffusion trapping model (DTM) direct fitting of positron lifetime spectra by DTM from fitting we obtain the following structural parameters: size of cells R mean dislocation density volume fraction of distorted regions residuals () / = 1.016(14) lifetime of positrons trapped at dislocations t d 10 4 HPT-deformed IF steel fraction of screw dislocations f screw counts channel (1 ch = 3.15 ps)

36 Diffusion trapping model (DTM) direct fitting of positron lifetime spectra by DTM fixed parameters width of distorted regions d = 10 nm HPT-deformed IF steel specific positron trapping rate to dislocations = m s -1 J. Čížek et al., Phys. Stat. Sol. A 178, 651 (000) bulk positron lifetime for Fe t B = 108 ps F. Bečvář et al., Appl. Surf. Sci. 55, 111 (008) positron diffusion coefficient for Fe D + = 1.87 cm s -1 F. Lukáč et al., J. Phys. Conf. Ser. 443, 0105 (013)

37 PAS and XRD PAS size of dislocation-free cells R mean dislocation density XRD line profile analysis size of crystallites D (coherently diffracting domains) mean dislocation density fraction of screw dislocations f screw open volume point defects (vacancies, vacancy clusters) fraction of screw dislocations f screw dislocation distribution parameter M lattice parameters

38 High pressure torsion (HPT) Interstitial-free steel Pohang Steel Company (POSCO), Korea composition (wt.%): C, Mn, Al, Ti high pressure.5 GPa number of HPT revolutions N = ¼, ½, 1, 3, 5 disk shaped samples diameter 14 mm, thickness 0.3 mm r t UFG IF steel sample prepared by HPT e 1 rn 3 l e - true strain N number of rotations r - distance from center l - sample thickness torsion deformation R.Z. Valiev, Nature Materials 3, (004)

39 High pressure torsion (HPT) Interstitial-free steel Pohang Steel Company (POSCO), Korea composition (wt.%): C, Mn, Al, Ti high pressure.5 GPa number of HPT revolutions N = ¼, ½, 1, 3, 5 disk shaped samples diameter 14 mm, thickness 0.3 mm center r = 0 half-radius r = 3.5 mm torsion deformation R.Z. Valiev, Nature Materials 3, (004)

40 LT spectroscopy Digital LT spectrometer: F. Bečvář et al., Nucl. Instr. Meth. A 539, 37 (005) Two photomultipliers Hamamatsu H3378 & BaF scintillators two 8-bit digitizers Acqiris DC11, sampling rate 4 GHz time resolution 145 ps (FWHM Na) at least 10 7 annihilation events collected in each LT spectrum 1 MBq Na source deposited on mm Mylar foil source contribution determined using well annealed Fe: t 1s 368 ps, I 1s 9 % t s 1.5 ns, I s 1 % detector AS BUS detector 1 data transfer to PC External trigger

41 X-ray diffraction XRD diffractometer: Double crystal diffractometer with negligible instrumental broadening Ge monochromator Co K 1 radiation ( = nm) size of X-ray beam spot: 0. mm linear position sensitive detector

42 lifetime (ps) intensity (%) Results of positron lifetime spectroscopy HPT deformed IF steels Decomposition of LT spectra into independent exponential components 500 t 1, free positrons, centre t, dislocations, centre t 3, vacancy clusters, centre t 1, free positrons, half-radius t, dislocations, half-radius t 3, vacancy clusters, half-radius 100 I 1, free positrons, centre I, dislocations, centre I 3, vacancy clusters, centre I 1, free positrons, half-radius I, dislocations, half-radius I 3, vacancy clusters, half-radius vacancy clusters,t 3 dislocations t 155 ps free positrons, t equivalent strain equivalent strain

43 Generation of vacacies during HPT jog jog jog Burgers vector moving direction movement of dislocation with a jog J. Čížek et al. J. Phys.: Conf. Series 443, (013)

44 Generation of vacacies during SPD jog jog jog Burgers vector moving direction vacancies agglomerate to small vacancy clusters J. Čížek et al. J. Phys.: Conf. Series 443, (013)

45 lifetime (ps) intensity (%) Results of positron lifetime spectroscopy HPT deformed IF steels Decomposition of LT spectra into independent exponential components 500 t 1, free positrons, centre t, dislocations, centre t 3, vacancy clusters, centre t 1, free positrons, half-radius t, dislocations, half-radius t 3, vacancy clusters, half-radius 100 I 1, free positrons, centre I, dislocations, centre I 3, vacancy clusters, centre I 1, free positrons, half-radius I, dislocations, half-radius I 3, vacancy clusters, half-radius vacancy clusters,t 3 dislocations t 155 ps free positrons, t equivalent strain equivalent strain

46 positron lifetime (ps) Results of positron lifetime spectroscopy Ab-initio theoretical calculations bcc Fe dependence of positron lifetime on the size of vacancy clusters 500 e 0 e 0.5 t ps t ps vacancies 9 vacancies 100 J. Čížek et al. J. Phys.: Conf. Series 443, (013) number of vacancies

47 Diffusion trapping model with vacancy clusters cells contain uniformly distributed vacancy clusters R R d d positron lifetime spectrum S t t k i e t I e t 1 t / tk 1 t / t d 1 t / t k k d d cl cl I e cl positrons trapped at vacancy clusters J. Čížek et al. PRB 65, (00)

48 (10 14 m - ) Dislocation density HPT deformed IF steel center, PAS half-radius, PAS equivalent strain

49 (10 14 m - ) fraction of screw dislocations Dislocation density HPT deformed IF steel good agreement between PAS and XRD dislocation density increases with strain and saturates at e 3 edge dislocations prevail 10 center, PAS half-radius, PAS center, XRD half-radius, XRD equivalent strain equivalent strain

50 d (nm) Dislocation cell size HPT deformed IF steel center, PAS half-radius, PAS equivalent strain

51 d (nm) Dislocation cell size HPT deformed IF steel cell size is close to 100 nm already at N = ¼ saturation at d 90 nm good agreement between PAS and XRD 140 center, PAS half-radius, PAS center, XRD half-radius, XRD equivalent strain

52 Electron backscatter diffraction (EBSD) HPT deformed IF steel early stage of HPT processing: bimodal structure center, N = 1 half-radius, N = 1

53 Electron backscatter diffraction (EBSD) HPT deformed IF steel early stage of HPT processing: bimodal structure N = 5: equiaxed fine grains center, N = 1 center, N = 5 grain refinement is faster at half-radius than in the centre half-radius, N = 1 half-radius, N = 5

54 area fraction (mm -1 ) Electron backscatter diffraction (EBSD) HPT deformed IF steel half radius, N = 5 ( e = 54 ) half-radius, N = 5 mean grain size 600 nm 6 TEM bright field image 5 4 EBSD grain size histogram d ( m m) grains consist of dislocation cells separated by dislocation walls grains dislocation cells 0 nm

55 mean grain size (mm) d (nm) (10 14 m - ) Development of mictrostructure during HPT processing HPT deformed IF steel dislocation density saturated at e cell size saturated at e equivalent strain equivalent strain grain size saturated at e 15 center half-radius equivalent strain

56 mean grain size (mm) d (nm) (10 14 m - ) Development of mictrostructure during HPT processing HPT deformed IF steel dislocation density saturated at e cell size saturated at e equivalent strain equivalent strain grain size saturated at e 15 center half-radius equivalent strain

57 Conclusions Positron lifetime spectroscopy enables to determine - size of dislocation cells - mean dislocation density - edge or screw character of dislocations PAS results are consistent with results of X-ray line profile analysis use of PAS combined with XRD is beneficial for characterization of UFG materials PAS is more sensitive to dislocations than XRD XRD enables to determine in materials containing very high number of dislocations PAS provides information not only about dislocations but also about open volume point defects (vacancies, vacancy clusters )