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Physical, microstructural and mechanical study of isochronal annealing of deformed commercial iron
Journal of Alloys and Compounds 656 (2016) 378e382
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
Physical, microstructural and mechanical study of isochronal annealing of deformed commercial iron K.M. Mostafa a, b, c, *, P.R. Calvillo d, J. De Baerdemaeker b, K. Verbeken a, C.A. Palacio b, D. Segers b, Y. Houbaert a a
Department of Materials Science and Engineering, Ghent University, Technologiepark 903, 9052 Ghent, Belgium Department of Physics and Astronomy, Ghent University, Proeftuinstraat 86, 9000 Ghent, Belgium Department of Math and Physics, Qatar University, Doha, Qatar d Metallurgy Department, ArcelorMittal Global R&D Gent, OCAS NV, Technologiepark 935, BE-9052 Zwijnaarde, Belgium b c
a r t i c l e i n f o
a b s t r a c t
Article history: Received 4 August 2015 Received in revised form 21 September 2015 Accepted 27 September 2015 Available online 30 September 2015
Isochronal annealing of deformed commercial iron samples (99.88 m.-% Fe) after cold deformation is studied by means of Vickers microhardness and physical techniques based on positron annihilation (positron annihilation lifetime spectroscopy (PALS) and Doppler broadening of the annihilation radiation (DBAR)). Undeformed Fe with a purity of 99.998 m.-% was used as a reference material to compare it with the used commercial Fe. Additionally, EBSD (electron backscatterded diffraction) was used to estimate the recrystallization fraction in the samples. In the temperature range 600e1000 C the recrystallization phenomenon can be followed with these techniques and similar results are obtained, while in the temperature range 20e600 C the recovery process has to be included and the results for positron annihilation lifetime presented a deviation due to its sensitiveness for changes in point defect configurations. © 2015 Elsevier B.V. All rights reserved.
Keywords: Commercial Fe Positron annihilation spectroscopy Annealing EBSD (electron backscatterded diffraction) Recrystallization Vickers microhardness
1. Introduction Different techniques can be used to study the evolution of plastically deformed iron during its isochronal annealing: mechanical testing (Vickers hardness), microstructural examination (metallography, electron backscattered diffraction (EBSD),…) and physical techniques involving positron annihilation (PA), such as PALS and Doppler broadening of the annihilation radiation (DBAR). Elements of the microstructure were determined by electron backscattered diffraction (EBSD) in a scanning electron microscope (SEM). This technique provides information on the crystallographic orientation of each grain [1]. Although PA techniques are well established in the area of experimental physics, in the industry and the more conventional research centers PA-techniques are not extensively used. There is a need to better correlate the conventional techniques based on mechanical testing and microstructural examination with the
* Corresponding author. Department of Physics and Astronomy, Ghent University, Proeftuinstraat 86, 9000 Ghent, Belgium. E-mail address: [email protected] (K.M. Mostafa). http://dx.doi.org/10.1016/j.jallcom.2015.09.233 0925-8388/© 2015 Elsevier B.V. All rights reserved.
fundamental physical technique of the PALS and the DBAR. PALS can quantify the size of open volume defects, as well as the defect concentration and is based on the precise measurement of the lifetime of a positron in a solid. The defect concentration is calculated from the different fractions of positrons that annihilate in the traps. The defect size and type is directly related to the value of the positron lifetime: the larger the defect, the lower the local electron density and consequently the longer the positron lifetime will be [2]. Values of the lifetime of positrons trapped in dislocations are close to or slightly below those for the vacancy lifetime [3e5]. For this reason, it is normally accepted that the positron lifetime can be related to vacancies trapped in the stress field around a dislocation line or in vacancies on a dislocation line, which would be equivalent to a pair of mono-atomic jogs [6]. Hidalgo et al. [7] measured the positron lifetime in deformed iron to be 150 ps. They suggested that positrons annihilate at associated defects (vacancies or dislocation jogs) rather than at the dislocation line. Park et al. [8] have studied the effectiveness of positron trapping by edge and screw dislocations and made an attempt to determine the fraction of dislocations of each type per unit area, although the difference in lifetimes is rather small. Calculation of positron lifetimes in jogs and vacancies
K.M. Mostafa et al. / Journal of Alloys and Compounds 656 (2016) 378e382
on an edge dislocation line in Fe was also reported by Yasushi Kamimura et al. [9]. The Doppler Broadening of the Annihilation Radiation (DBAR) is based on the measurement of the linear momentum of the annihilating electron-positron pair. The photons created during the electron-positron annihilation are detected by a germanium detector. The shape of the resulting photo-peak reflects the momentum distribution of the original electron-positron pair. This distribution is determined by the momentum distribution of the electrons seen by the positron, which is influenced by the size and the nature of the defects. Measurements of the Doppler broadening of the positron-electron annihilation radiation are generally characterized by the S (Shape) parameter, defined as the ratio between the surface of the central part of the annihilation spectrum and the total surface of the spectrum. This parameter reflects the positron annihilation with valence electrons (low momentum). In general, a high value of S indicates positron annihilation in open volume defects (vacancies and vacancy groups). A second useful parameter for the analysis of the DBAR is the W (Wing) parameter, which reflects the positron annihilation with high momentum electrons (core electrons). It is defined as the ratio of the counts in both side wings of the spectrum over the total number of counts in the annihilation line. The plastic deformation of metals and alloys provokes changes in the density and distribution of different kind of structural defects (mainly vacancies and dislocations), whereas the positrons are captured by dislocations and vacancies and their lifetimes increase. In polycrystalline samples, the deformation phenomena are relatively complex due to various interactions between dislocations and grain boundaries [4e6]. It is well known that cold deformation of metals such as a rolling process induces a high amount of defects (mono, di-vacancies, vacancy-interstitial agglomerates, dislocations,…) [10]. Plastic deformation of metals occurs by the generation and movement of dislocations, which stores a certain amount of deformation energy along each dislocation line in the form of an elastically distorted region. During deformation the dislocations gather together and produce tangled groups distributed over local bands and forming tangled networks defining ‘cells’ with a lower concentration of dislocations and a slight orientation difference [11e13]. The microstructural changes during the annealing of deformed metals are described in terms of recovery, recrystallization and grain growth (with increasing duration and temperature of the annealing process). Different rearrangements of the dislocation distribution occur during the annealing, depending on the amount of deformation. In the case of small deformation strains the annealing causes the dislocations to rearrange into local bands, similar to grain boundaries and may develop into a sub-grain structure. In metals deformed with large deformation strains a softening prior to the onset of recrystallization appears to be controlled by sub-grain growth [14]. Very pure iron will recrystallize easily (short time, lower temperature), whilst the presence of impurities (even in small concentrations) will clearly increase the resistance to recovery and recrystallization. Interstitial elements have an important effect on the recovery processes, even when present in very low concentrations: they are considered to be responsible for the retardation of recovery [15,16]. Ohkubo et al. stated that dislocations and vacancy clusters are introduced in bcc Fe regardless of the type or degree of deformation [17]. Hamdy F.M et al. studied cold-worked iron with different percentages of deformation up to 40% using the PALS [18]. Vacancy clusters, as well as dislocations are produced as a result of a cold-working. In our work only dislocation are detected as a result of the high degree of deformation (75% thickness reduction) and also the different kind of deformation.
379
2. Experimental procedure The effect of annealing of the commercial iron samples with a purity of 99.88 m.-% is studied using the PALS. The samples were cold rolled at room temperature with a thickness reduction of 75%. A totally annealed high purity Fe sample (with a purity of 99.998 m.-%) was used as a defect free sample for the reference. The chemical composition of the commercial iron samples used in the present work was determined with a LAVWA18A spectrometer of Spectro Analytical Instruments and is shown in Table 1. After cold deformation the samples were annealed at temperatures from 100 C (boiling distilled water) to 1000 C (vacuum furnace) during a constant time of one hour (isochronal annealing) in temperature intervals of 100 C. After annealing, each sample was cooled down in the furnace until room temperature. The evolution of the microstructure and corresponding properties during the process of isochronal annealing were investigated using different techniques: mechanical testing using the Vickers micro-hardness, the characteristics of the metallographic microstructure were observed by the EBSD and finally two physical techniques based on positron annihilation were used: PALS and DBAR. Vickers microhardness (HV) tests applying 300 g were performed on the surface of deformed and annealed commercial iron samples to quantify the softening fraction; at least six indentations were done in each material. The microstructure of the samples was evaluated after polishing with a colloidal silica solution by means of optical microscopy and EBSD scans. The EBSD-measurements were carried out on an FEG SEM Zeiss Ultra Plus microscope equipped with an hkl EBSD system and maps were generated with a step size of 1 mm, covering a total area of 400 400 mm2. Positron lifetime measurements were performed at room temperature using a fastefast lifetime spectrometer [19]. Each spectrum contained more than 106 counts and several spectra were accumulated for each sample in order to ensure the reproducibility of the data. The Doppler broadening (DB) of the 511 keV annihilation line was measured and the results were analyzed in terms of the so-called S and W parameters. The DBAR and the positron lifetime measurements were performed at room temperature after each annealing process. 3. Results 3.1. Softening behavior studied by microhardness measurements Vickers microhardness (HV) measurements for isochronally annealed samples are shown in Fig. 1. The error bar shows that there is a considerable scatter on the measurements. The microhardness of the cold rolled sample without any annealing (HVCR ) is 209, whilst the hardness of the fully recrystallized material (HVFR ) is 80, (the sample annealed at 700 C is considered to be completely recrystallized). In the annealing temperature range 100e500 C there is a slight reduction of hardness, which can be attributed to a recovery process. The hardness drops very clearly between 500 and 700 C because of the recrystallization of the material. Above 700 C the hardness values further decrease slightly due to grain growth as the annealing temperature increases. A softening fraction R for the isochronal annealed samples can be defined as follows: Table 1 Determined impurities in the used commercial iron sample [in ppm]. C
Si
Al
Nb
Cr
Mo
Ni
20
80
560
300
50
50
50
380
K.M. Mostafa et al. / Journal of Alloys and Compounds 656 (2016) 378e382
1,0
210 0,8
180
0,6
2
Hrec=A+BT+CT
150 120
0,4
90
0,2
60
0
200
400
and trapping rates were quantitatively calculated using the two state trapping model [20]. The as-such obtained values for the positron annihilation lifetimes (t1, t2) and their intensities (I1, I2) were used to calculate the mean positron annihilation lifetime using the following relation:
600
800
1000
Softening Fraction, R
Hardness value, HV0,3
1,2
Hardness Values Softening Fraction
240
tmean ¼ ðt1 I1 þ t2 I2 Þ
0,0
Temperature (ºC) Fig. 1. Vickers microhardness and corresponding softening fractions as a function of the isochronal annealing temperature (duration 1 h).
R¼
HVCR HV HVCR HVFR
(1)
where HV is the measured Vickers microhardness, CR and FR stand for cold-rolled and fully recrystallized, respectively. The softening fraction R is presented in Fig. 1 and includes the contributions by recovery, recrystallization and grain growth.
(2)
The effect of the annealing temperature on the positron annihilation mean lifetime tmean (calculated using Eq. (2)) of a highly deformed commercial iron samples is shown in Fig. 3. The lifetimes in the range of 150 ps for the cold deformed sample and for the samples annealed between 100 and 400 C are characteristic for the high concentration of defects due to the high degree of deformation (cold rolled with a thickness reduction of 75%). In the temperature range from 20 C to 400 C tmean shows the tendency to slightly decrease with increasing annealing temperature, which is probably due to static recovery. In the temperature range from 400 C to 700 C there is a clear drop in the mean lifetime, showing that the defects anneal out more rapidly. The mean lifetime decreases to a value of around 107 ps after annealing at 700 C, thus allowing the conclusion that the material is fully recrystallized at that stage. The positron trapping rate for defects k, and the expression for the bulk lifetime tb are given by:
k ¼ md Cd ¼
I2 ðl ld Þ I1 b
(3)
3.2. Microstructural evolution during isochronal annealing by EBSD The microstructure of the sample deformed at room temperature presents a typical pancake structure of elongated grains along the rolling direction. As the temperature of the isochronal annealing was increased a developed subgrain structure was observed within the grains as a result of static recovery, see Fig. 2a and b. At 600 C (Fig. 2b), the microstructure is partially recrystallized, showing an area fraction of recrystallized grains of 49% with an average grain size of 13 mm. For annealing at 700 up to 1000 C the material is fully recrystallized and only grain growth is taking place, resulting at 1000 C in the highest grain size with an average of 40 mm (see Fig. 2c). 3.3. Positron annihilation spectroscopy (PAS) 3.3.1. Positron annihilation lifetime spectroscopy (PALS) The positron annihilation lifetime for the undeformed pure Fe sample (reference material) is 107 ± 3 ps. The defect concentration
Fig. 3. Relation between annealing temperature and positron annihilation mean lifetime for the investigated commercial iron samples (cold rolled at room temperature to a thickness reduction of 75%).
Fig. 2. Band Contrast with superposition of the grain boundary maps, where the white and black lines correspond to misorientations below and above 15 , respectively, of samples annealed isochronally at (a) 200, (b) 600 and (c) 800 C.
K.M. Mostafa et al. / Journal of Alloys and Compounds 656 (2016) 378e382
tb ¼ ½ðI1 =t1 Þ þ ðI2 =t2 Þ1
0,066
4. Discussion This work on the high deformed commercial Fe is done to have a comparative date for all the iron based alloys or steels. In a previous work, the influence of annealing on the concentration of defects of different deformed FeSi alloys has been investigated by the PALS and the DBAR [5]. The values of the S parameter present a decrease for all studied FeSi alloys with the increase of the annealing temperature, being attributed to a decrease of the concentration of defects. A sudden increase of the S-parameter value at 600 C was observed for all samples, which is attributed to the change of the ordering of the FeSi alloys at that temperature. The PALS data showed that clustering in FeSi alloys are created at the annealing temperature 600 C, and 650 . The comparison of the data of the FeSi with the one of the commercial iron of the present work is supporting the idea that dislocations and vacancy clusters are introduced in Fe regardless of the type or degree of deformation [17]. We can add that added elements are affecting the type of defects formed with annealing. For the commercial Fe-sample, the recovery/recrystallization process occurs in the temperature range 400e700 C. The start of recovery at 400 C is a result of the rearrangement process of the dislocations. The SeW relation for all the isochronal annealing temperatures from 20 C up to 1000 C for the commercial iron samples, see Fig. 5, shows almost one straight line. This means that mainly one type of defect, i.e. dislocations as
0,063 0,060 0,057 0,054 0,051 0,048 0,460
S Parameter
0,455 0,450 0,445 0,440 0,435 0,430
0
200
400
600
800
1000
T(°C) Fig. 4. The annihilation line shape parameters (S, W) as a function of the isochronal annealing temperature of the deformed commercial iron samples (annealing time 1 h).
identified previously by the lifetime, exists in the deformed iron throughout the entire temperature range of the applied isochronal annealing. The density of dislocations, presented in Table 2, decreases with the increase of annealing temperature and its order of magnitude is as observed in literature [21]. At 700 C not enough trapping sites exist and no data can be obtained for the density of dislocations. It is known that iron undergoes an allotropic a/g phase transformation which is completed at 912 C. 5. Conclusions The isochronal annealing behavior of commercial iron samples with a purity of 99.88 m.-% and cold rolled to a thickness reduction
0,460 23°C 100°C 200°C 300°C 400°C 500°C 600°C 700°C 800°C 900°C 1000°C
0,455
S parameter
3.3.2. Doppler broadening of the annihilation radiation (DBAR): S parameter (bulk) and W-parameter The dependence of the S and W parameters on the isochronal annealing temperature for our deformed Fe is shown in Fig. 4. In the temperature range 20e400 C the S parameter slightly decreases while the W parameter slightly increases with increasing annealing temperature. Starting from 400 C, a significant decrease of the S parameter accompanied with a significant increase of the W parameter is observed and both become constant above 700 C. The behavior of the S parameter as presented in Fig. 4 is similar to the observed behavior for the tmean in Fig. 3.
W Parameter
(4)
In Eqs. (3) and (4), md is the trapping coefficient for defects (in this case: only dislocations), Cd is the dislocation density, tb and td are the positron annihilation lifetimes in the bulk material and when trapped in dislocations, respectively. lb and ld are the annihilation rates from the free (in the bulk, low defect concentration) and trapping state (in defect-rich zones). The concentration of dislocations (see Table 2) is calculated from Eq. (3) using the trapping model with a trapping efficiency of md ¼ 6 105 m2 s1 [8] for dislocations in iron. It was attempted to decompose all the lifetime data into two components. Only for the spectra measured at 500 C and 600 C the trapping model could be decomposed into two lifetime components. The bulk lifetime was calculated for both temperatures and it was found to be approximately 109 ps. Table 2 shows the values of the positron annihilation lifetime parameters and the concentration of defects in the cold rolled Fe samples annealed at 500 C and 600 C.
381
0,450 0,445 0,440 0,435
0,430 0,048 0,051 0,054 0,057 0,060 0,063 0,066
W parameter Fig. 5. Representation of the SeW relation for all the isochronal annealing temperatures.
Table 2 The positron annihilation lifetime parameters and the concentration of defects in the cold rolled Fe samples annealed at 500 C and 600 C. T ( C)
t1 (ps)
t2 (ps)
I2
tb (ps)
Dislocation concentration 1014 (m2)
500 600
62 63.9
155.3 146.9
0.713 0.724
109 109
1.15 1.0447
382
K.M. Mostafa et al. / Journal of Alloys and Compounds 656 (2016) 378e382
of 75% was studied. The EBSD microstructure observation showed that recovery is the only restoration mechanism up to 500 C, at 600 C the recrystallization fraction is around 60% and above this temperature only grain growth is observed. The evolution of the positron mean lifetime reveals that the traps for positrons in the deformed commercial iron are mainly dislocations and it was possible to calculate the dislocation density in the temperature range from 500 to 600 C. The Se W relation shows only one straight line, which means that only one type of defect exists in the deformed commercial iron through the whole isochronal annealing temperature range. With increasing the annealing temperature, the Doppler broadening parameter S, the positron annihilation mean lifetime tmean and the microhardeness values have a slight decrease before the recrystallization temperature region, while the W parameters slightly increases. References [1] Pablo R. Calvillo1, Petrov Roumen, Houbaert Yvan, Kestens Leo, Mater. Sci. Forum 550 (2007) 539e544. [2] P. Hautojarvi, J. Heinio, M. Mannien, R. Nieminen, Phil. Mag. 35 (1977) 973.
[3] C. Dauwe, M. Dorikens, L. Dorikens-Vanpraet, D. Segers, Appl. Phys. 5 (1974) 117. [4] B.T.A. McKee, S. Saimoto, A.T. Stewart, M.J. Stott, Can. J. Phys. 52 (1974) 759. [5] K.M. Mostafa, Fernando G. C amara, Roumen Petrov, Pablo Rodriguez Calvillo, Eddy De Grave, Danny Segers, Yvan Houbaert, J. Appl. Phys. 109 (07E303) (2011). [6] T. Wider, S. Hansen, U. Holzwarth, K. Maier, Phys. Rev. B 57 (1998) 5126. [7] C. Hidalgo, G. Gonz alez Doncel, S. Linderoth, J.S. Juan, Phys. Rev.B 45 (1992) 7017. [8] Y.K. Park, J.T. Waber, M. Meshii Jr., C.L. Snead, C.G. Park, Phys. Rev. B 34 (1986) p.823. [9] Y. Kamimura, T. Tsutsumi, E. Kuramoto, Phys. Rev. B (1995) 879, 52-2. [10] M. Militzer, W.P. Sun, J.J. Jonas, Acta Metall. Mater. 42 (1994) 97. €rvi, A. Tamminen, P. Janho, Phys. Rev. Lett. 24 (1970) 459. [11] P. Hautoja [12] C. Hidalgo, S. Linderoth, N. de Diego, Phys. Rev. B 36 (1987) 6740. [13] C. Hidalgo, S. Linderoth, N. de Diego, Phil. Mag. A 64 (1986) L61. [14] G. Gottstein, Physical Foundations of Materials Science, Springer, 2005. [15] M. Takahashi, A. Okamoto, Trans. ISIJ 19 (1979) 391. [16] W.B. Hutchinson, Int. Mater. Rev. 29 (1984) 25. [17] H. Ohkubo, Z. Tang, Y. Nagai, M. Hasegawa, T. Tawara, M. Kiritani, Mat. Sci. Eng. A 350 (2003) 95. [18] Hamdy F.M. Mohamed, Junhyun Kwon, Yong-Min Kim, Whungwhoe Kim, Nucl. Instr. Meth. Phys. Res. B 258 (2007) 429e434. [19] R. Krause-Rehberg, H.S. Leipner, Positron Annihilation in Semiconductors, Springer, Berlin, 1999. [20] R.N. West, 12, in: P. Hautojarvi (Ed.), “positrons in Solids, series” Topics in Current Physics, 89, Springer, Berlin, 1979. [21] J.R. Yang, H.K.D.H. Bhadeshia American, Weld. J. 69 (1990) 305.
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
Physical, microstructural and mechanical study of isochronal annealing of deformed commercial iron K.M. Mostafa a, b, c, *, P.R. Calvillo d, J. De Baerdemaeker b, K. Verbeken a, C.A. Palacio b, D. Segers b, Y. Houbaert a a
Department of Materials Science and Engineering, Ghent University, Technologiepark 903, 9052 Ghent, Belgium Department of Physics and Astronomy, Ghent University, Proeftuinstraat 86, 9000 Ghent, Belgium Department of Math and Physics, Qatar University, Doha, Qatar d Metallurgy Department, ArcelorMittal Global R&D Gent, OCAS NV, Technologiepark 935, BE-9052 Zwijnaarde, Belgium b c
a r t i c l e i n f o
a b s t r a c t
Article history: Received 4 August 2015 Received in revised form 21 September 2015 Accepted 27 September 2015 Available online 30 September 2015
Isochronal annealing of deformed commercial iron samples (99.88 m.-% Fe) after cold deformation is studied by means of Vickers microhardness and physical techniques based on positron annihilation (positron annihilation lifetime spectroscopy (PALS) and Doppler broadening of the annihilation radiation (DBAR)). Undeformed Fe with a purity of 99.998 m.-% was used as a reference material to compare it with the used commercial Fe. Additionally, EBSD (electron backscatterded diffraction) was used to estimate the recrystallization fraction in the samples. In the temperature range 600e1000 C the recrystallization phenomenon can be followed with these techniques and similar results are obtained, while in the temperature range 20e600 C the recovery process has to be included and the results for positron annihilation lifetime presented a deviation due to its sensitiveness for changes in point defect configurations. © 2015 Elsevier B.V. All rights reserved.
Keywords: Commercial Fe Positron annihilation spectroscopy Annealing EBSD (electron backscatterded diffraction) Recrystallization Vickers microhardness
1. Introduction Different techniques can be used to study the evolution of plastically deformed iron during its isochronal annealing: mechanical testing (Vickers hardness), microstructural examination (metallography, electron backscattered diffraction (EBSD),…) and physical techniques involving positron annihilation (PA), such as PALS and Doppler broadening of the annihilation radiation (DBAR). Elements of the microstructure were determined by electron backscattered diffraction (EBSD) in a scanning electron microscope (SEM). This technique provides information on the crystallographic orientation of each grain [1]. Although PA techniques are well established in the area of experimental physics, in the industry and the more conventional research centers PA-techniques are not extensively used. There is a need to better correlate the conventional techniques based on mechanical testing and microstructural examination with the
* Corresponding author. Department of Physics and Astronomy, Ghent University, Proeftuinstraat 86, 9000 Ghent, Belgium. E-mail address: [email protected] (K.M. Mostafa). http://dx.doi.org/10.1016/j.jallcom.2015.09.233 0925-8388/© 2015 Elsevier B.V. All rights reserved.
fundamental physical technique of the PALS and the DBAR. PALS can quantify the size of open volume defects, as well as the defect concentration and is based on the precise measurement of the lifetime of a positron in a solid. The defect concentration is calculated from the different fractions of positrons that annihilate in the traps. The defect size and type is directly related to the value of the positron lifetime: the larger the defect, the lower the local electron density and consequently the longer the positron lifetime will be [2]. Values of the lifetime of positrons trapped in dislocations are close to or slightly below those for the vacancy lifetime [3e5]. For this reason, it is normally accepted that the positron lifetime can be related to vacancies trapped in the stress field around a dislocation line or in vacancies on a dislocation line, which would be equivalent to a pair of mono-atomic jogs [6]. Hidalgo et al. [7] measured the positron lifetime in deformed iron to be 150 ps. They suggested that positrons annihilate at associated defects (vacancies or dislocation jogs) rather than at the dislocation line. Park et al. [8] have studied the effectiveness of positron trapping by edge and screw dislocations and made an attempt to determine the fraction of dislocations of each type per unit area, although the difference in lifetimes is rather small. Calculation of positron lifetimes in jogs and vacancies
K.M. Mostafa et al. / Journal of Alloys and Compounds 656 (2016) 378e382
on an edge dislocation line in Fe was also reported by Yasushi Kamimura et al. [9]. The Doppler Broadening of the Annihilation Radiation (DBAR) is based on the measurement of the linear momentum of the annihilating electron-positron pair. The photons created during the electron-positron annihilation are detected by a germanium detector. The shape of the resulting photo-peak reflects the momentum distribution of the original electron-positron pair. This distribution is determined by the momentum distribution of the electrons seen by the positron, which is influenced by the size and the nature of the defects. Measurements of the Doppler broadening of the positron-electron annihilation radiation are generally characterized by the S (Shape) parameter, defined as the ratio between the surface of the central part of the annihilation spectrum and the total surface of the spectrum. This parameter reflects the positron annihilation with valence electrons (low momentum). In general, a high value of S indicates positron annihilation in open volume defects (vacancies and vacancy groups). A second useful parameter for the analysis of the DBAR is the W (Wing) parameter, which reflects the positron annihilation with high momentum electrons (core electrons). It is defined as the ratio of the counts in both side wings of the spectrum over the total number of counts in the annihilation line. The plastic deformation of metals and alloys provokes changes in the density and distribution of different kind of structural defects (mainly vacancies and dislocations), whereas the positrons are captured by dislocations and vacancies and their lifetimes increase. In polycrystalline samples, the deformation phenomena are relatively complex due to various interactions between dislocations and grain boundaries [4e6]. It is well known that cold deformation of metals such as a rolling process induces a high amount of defects (mono, di-vacancies, vacancy-interstitial agglomerates, dislocations,…) [10]. Plastic deformation of metals occurs by the generation and movement of dislocations, which stores a certain amount of deformation energy along each dislocation line in the form of an elastically distorted region. During deformation the dislocations gather together and produce tangled groups distributed over local bands and forming tangled networks defining ‘cells’ with a lower concentration of dislocations and a slight orientation difference [11e13]. The microstructural changes during the annealing of deformed metals are described in terms of recovery, recrystallization and grain growth (with increasing duration and temperature of the annealing process). Different rearrangements of the dislocation distribution occur during the annealing, depending on the amount of deformation. In the case of small deformation strains the annealing causes the dislocations to rearrange into local bands, similar to grain boundaries and may develop into a sub-grain structure. In metals deformed with large deformation strains a softening prior to the onset of recrystallization appears to be controlled by sub-grain growth [14]. Very pure iron will recrystallize easily (short time, lower temperature), whilst the presence of impurities (even in small concentrations) will clearly increase the resistance to recovery and recrystallization. Interstitial elements have an important effect on the recovery processes, even when present in very low concentrations: they are considered to be responsible for the retardation of recovery [15,16]. Ohkubo et al. stated that dislocations and vacancy clusters are introduced in bcc Fe regardless of the type or degree of deformation [17]. Hamdy F.M et al. studied cold-worked iron with different percentages of deformation up to 40% using the PALS [18]. Vacancy clusters, as well as dislocations are produced as a result of a cold-working. In our work only dislocation are detected as a result of the high degree of deformation (75% thickness reduction) and also the different kind of deformation.
379
2. Experimental procedure The effect of annealing of the commercial iron samples with a purity of 99.88 m.-% is studied using the PALS. The samples were cold rolled at room temperature with a thickness reduction of 75%. A totally annealed high purity Fe sample (with a purity of 99.998 m.-%) was used as a defect free sample for the reference. The chemical composition of the commercial iron samples used in the present work was determined with a LAVWA18A spectrometer of Spectro Analytical Instruments and is shown in Table 1. After cold deformation the samples were annealed at temperatures from 100 C (boiling distilled water) to 1000 C (vacuum furnace) during a constant time of one hour (isochronal annealing) in temperature intervals of 100 C. After annealing, each sample was cooled down in the furnace until room temperature. The evolution of the microstructure and corresponding properties during the process of isochronal annealing were investigated using different techniques: mechanical testing using the Vickers micro-hardness, the characteristics of the metallographic microstructure were observed by the EBSD and finally two physical techniques based on positron annihilation were used: PALS and DBAR. Vickers microhardness (HV) tests applying 300 g were performed on the surface of deformed and annealed commercial iron samples to quantify the softening fraction; at least six indentations were done in each material. The microstructure of the samples was evaluated after polishing with a colloidal silica solution by means of optical microscopy and EBSD scans. The EBSD-measurements were carried out on an FEG SEM Zeiss Ultra Plus microscope equipped with an hkl EBSD system and maps were generated with a step size of 1 mm, covering a total area of 400 400 mm2. Positron lifetime measurements were performed at room temperature using a fastefast lifetime spectrometer [19]. Each spectrum contained more than 106 counts and several spectra were accumulated for each sample in order to ensure the reproducibility of the data. The Doppler broadening (DB) of the 511 keV annihilation line was measured and the results were analyzed in terms of the so-called S and W parameters. The DBAR and the positron lifetime measurements were performed at room temperature after each annealing process. 3. Results 3.1. Softening behavior studied by microhardness measurements Vickers microhardness (HV) measurements for isochronally annealed samples are shown in Fig. 1. The error bar shows that there is a considerable scatter on the measurements. The microhardness of the cold rolled sample without any annealing (HVCR ) is 209, whilst the hardness of the fully recrystallized material (HVFR ) is 80, (the sample annealed at 700 C is considered to be completely recrystallized). In the annealing temperature range 100e500 C there is a slight reduction of hardness, which can be attributed to a recovery process. The hardness drops very clearly between 500 and 700 C because of the recrystallization of the material. Above 700 C the hardness values further decrease slightly due to grain growth as the annealing temperature increases. A softening fraction R for the isochronal annealed samples can be defined as follows: Table 1 Determined impurities in the used commercial iron sample [in ppm]. C
Si
Al
Nb
Cr
Mo
Ni
20
80
560
300
50
50
50
380
K.M. Mostafa et al. / Journal of Alloys and Compounds 656 (2016) 378e382
1,0
210 0,8
180
0,6
2
Hrec=A+BT+CT
150 120
0,4
90
0,2
60
0
200
400
and trapping rates were quantitatively calculated using the two state trapping model [20]. The as-such obtained values for the positron annihilation lifetimes (t1, t2) and their intensities (I1, I2) were used to calculate the mean positron annihilation lifetime using the following relation:
600
800
1000
Softening Fraction, R
Hardness value, HV0,3
1,2
Hardness Values Softening Fraction
240
tmean ¼ ðt1 I1 þ t2 I2 Þ
0,0
Temperature (ºC) Fig. 1. Vickers microhardness and corresponding softening fractions as a function of the isochronal annealing temperature (duration 1 h).
R¼
HVCR HV HVCR HVFR
(1)
where HV is the measured Vickers microhardness, CR and FR stand for cold-rolled and fully recrystallized, respectively. The softening fraction R is presented in Fig. 1 and includes the contributions by recovery, recrystallization and grain growth.
(2)
The effect of the annealing temperature on the positron annihilation mean lifetime tmean (calculated using Eq. (2)) of a highly deformed commercial iron samples is shown in Fig. 3. The lifetimes in the range of 150 ps for the cold deformed sample and for the samples annealed between 100 and 400 C are characteristic for the high concentration of defects due to the high degree of deformation (cold rolled with a thickness reduction of 75%). In the temperature range from 20 C to 400 C tmean shows the tendency to slightly decrease with increasing annealing temperature, which is probably due to static recovery. In the temperature range from 400 C to 700 C there is a clear drop in the mean lifetime, showing that the defects anneal out more rapidly. The mean lifetime decreases to a value of around 107 ps after annealing at 700 C, thus allowing the conclusion that the material is fully recrystallized at that stage. The positron trapping rate for defects k, and the expression for the bulk lifetime tb are given by:
k ¼ md Cd ¼
I2 ðl ld Þ I1 b
(3)
3.2. Microstructural evolution during isochronal annealing by EBSD The microstructure of the sample deformed at room temperature presents a typical pancake structure of elongated grains along the rolling direction. As the temperature of the isochronal annealing was increased a developed subgrain structure was observed within the grains as a result of static recovery, see Fig. 2a and b. At 600 C (Fig. 2b), the microstructure is partially recrystallized, showing an area fraction of recrystallized grains of 49% with an average grain size of 13 mm. For annealing at 700 up to 1000 C the material is fully recrystallized and only grain growth is taking place, resulting at 1000 C in the highest grain size with an average of 40 mm (see Fig. 2c). 3.3. Positron annihilation spectroscopy (PAS) 3.3.1. Positron annihilation lifetime spectroscopy (PALS) The positron annihilation lifetime for the undeformed pure Fe sample (reference material) is 107 ± 3 ps. The defect concentration
Fig. 3. Relation between annealing temperature and positron annihilation mean lifetime for the investigated commercial iron samples (cold rolled at room temperature to a thickness reduction of 75%).
Fig. 2. Band Contrast with superposition of the grain boundary maps, where the white and black lines correspond to misorientations below and above 15 , respectively, of samples annealed isochronally at (a) 200, (b) 600 and (c) 800 C.
K.M. Mostafa et al. / Journal of Alloys and Compounds 656 (2016) 378e382
tb ¼ ½ðI1 =t1 Þ þ ðI2 =t2 Þ1
0,066
4. Discussion This work on the high deformed commercial Fe is done to have a comparative date for all the iron based alloys or steels. In a previous work, the influence of annealing on the concentration of defects of different deformed FeSi alloys has been investigated by the PALS and the DBAR [5]. The values of the S parameter present a decrease for all studied FeSi alloys with the increase of the annealing temperature, being attributed to a decrease of the concentration of defects. A sudden increase of the S-parameter value at 600 C was observed for all samples, which is attributed to the change of the ordering of the FeSi alloys at that temperature. The PALS data showed that clustering in FeSi alloys are created at the annealing temperature 600 C, and 650 . The comparison of the data of the FeSi with the one of the commercial iron of the present work is supporting the idea that dislocations and vacancy clusters are introduced in Fe regardless of the type or degree of deformation [17]. We can add that added elements are affecting the type of defects formed with annealing. For the commercial Fe-sample, the recovery/recrystallization process occurs in the temperature range 400e700 C. The start of recovery at 400 C is a result of the rearrangement process of the dislocations. The SeW relation for all the isochronal annealing temperatures from 20 C up to 1000 C for the commercial iron samples, see Fig. 5, shows almost one straight line. This means that mainly one type of defect, i.e. dislocations as
0,063 0,060 0,057 0,054 0,051 0,048 0,460
S Parameter
0,455 0,450 0,445 0,440 0,435 0,430
0
200
400
600
800
1000
T(°C) Fig. 4. The annihilation line shape parameters (S, W) as a function of the isochronal annealing temperature of the deformed commercial iron samples (annealing time 1 h).
identified previously by the lifetime, exists in the deformed iron throughout the entire temperature range of the applied isochronal annealing. The density of dislocations, presented in Table 2, decreases with the increase of annealing temperature and its order of magnitude is as observed in literature [21]. At 700 C not enough trapping sites exist and no data can be obtained for the density of dislocations. It is known that iron undergoes an allotropic a/g phase transformation which is completed at 912 C. 5. Conclusions The isochronal annealing behavior of commercial iron samples with a purity of 99.88 m.-% and cold rolled to a thickness reduction
0,460 23°C 100°C 200°C 300°C 400°C 500°C 600°C 700°C 800°C 900°C 1000°C
0,455
S parameter
3.3.2. Doppler broadening of the annihilation radiation (DBAR): S parameter (bulk) and W-parameter The dependence of the S and W parameters on the isochronal annealing temperature for our deformed Fe is shown in Fig. 4. In the temperature range 20e400 C the S parameter slightly decreases while the W parameter slightly increases with increasing annealing temperature. Starting from 400 C, a significant decrease of the S parameter accompanied with a significant increase of the W parameter is observed and both become constant above 700 C. The behavior of the S parameter as presented in Fig. 4 is similar to the observed behavior for the tmean in Fig. 3.
W Parameter
(4)
In Eqs. (3) and (4), md is the trapping coefficient for defects (in this case: only dislocations), Cd is the dislocation density, tb and td are the positron annihilation lifetimes in the bulk material and when trapped in dislocations, respectively. lb and ld are the annihilation rates from the free (in the bulk, low defect concentration) and trapping state (in defect-rich zones). The concentration of dislocations (see Table 2) is calculated from Eq. (3) using the trapping model with a trapping efficiency of md ¼ 6 105 m2 s1 [8] for dislocations in iron. It was attempted to decompose all the lifetime data into two components. Only for the spectra measured at 500 C and 600 C the trapping model could be decomposed into two lifetime components. The bulk lifetime was calculated for both temperatures and it was found to be approximately 109 ps. Table 2 shows the values of the positron annihilation lifetime parameters and the concentration of defects in the cold rolled Fe samples annealed at 500 C and 600 C.
381
0,450 0,445 0,440 0,435
0,430 0,048 0,051 0,054 0,057 0,060 0,063 0,066
W parameter Fig. 5. Representation of the SeW relation for all the isochronal annealing temperatures.
Table 2 The positron annihilation lifetime parameters and the concentration of defects in the cold rolled Fe samples annealed at 500 C and 600 C. T ( C)
t1 (ps)
t2 (ps)
I2
tb (ps)
Dislocation concentration 1014 (m2)
500 600
62 63.9
155.3 146.9
0.713 0.724
109 109
1.15 1.0447
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of 75% was studied. The EBSD microstructure observation showed that recovery is the only restoration mechanism up to 500 C, at 600 C the recrystallization fraction is around 60% and above this temperature only grain growth is observed. The evolution of the positron mean lifetime reveals that the traps for positrons in the deformed commercial iron are mainly dislocations and it was possible to calculate the dislocation density in the temperature range from 500 to 600 C. The Se W relation shows only one straight line, which means that only one type of defect exists in the deformed commercial iron through the whole isochronal annealing temperature range. With increasing the annealing temperature, the Doppler broadening parameter S, the positron annihilation mean lifetime tmean and the microhardeness values have a slight decrease before the recrystallization temperature region, while the W parameters slightly increases. References [1] Pablo R. Calvillo1, Petrov Roumen, Houbaert Yvan, Kestens Leo, Mater. Sci. Forum 550 (2007) 539e544. [2] P. Hautojarvi, J. Heinio, M. Mannien, R. Nieminen, Phil. Mag. 35 (1977) 973.
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