Scholarly article on topic 'Evolution and interaction of twins, dislocations and stacking faults in rolled α-brass during nanostructuring at sub-zero temperature'

Evolution and interaction of twins, dislocations and stacking faults in rolled α-brass during nanostructuring at sub-zero temperature Academic research paper on "Materials engineering"

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Academic research paper on topic "Evolution and interaction of twins, dislocations and stacking faults in rolled α-brass during nanostructuring at sub-zero temperature"


Evolution and interaction of twins, dislocations and stacking faults in rolled a-brass during nanostructuring at sub-zero temperature

Barna Roy, Nand Kishor Kumar, Padinharu Madathil Gopalakrishnan Nambissan, and Jayanta Das

Citation: AIP Advances 4, 067101 (2014); doi: 10.1063/1.4881376 View online:

View Table of Contents: Published by the AIP Publishing

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Evolution and interaction of twins, dislocations and stacking faults in rolled a-brass during nanostructuring at sub-zero temperature

Barna Roy,1 Nand Kishor Kumar,1 Padinharu Madathil Gopalakrishnan Nambissan,2 and Jayanta Das1,a

1 Department of Metallurgical and Materials Engineering, Indian Institute of Technology Kharagpur, West Bengal 721302, India

2Applied Nuclear Physics Division, Saha Institute ofNuclear Physics, 1/AF Bidhannagar, Kolkata 700064, India

(Received 5 March 2014; accepted 21 May 2014; published online 2 June 2014)

The effect of cryorolling (CR) strain at 153 K on the evolution of structural defects and their interaction in a-brass (Cu-30 wt.% Zn) during nanostructuring has been evaluated. Even though the lattice strain increases up to 2.1 x 10-3 at CR strain of 0.6 initially, but it remains constant upon further rolling. Whereas, the twin density (ft) increases to a maximum value of 5.9 x 10-3 at a CR strain of 0.7 and reduces to 1.1 x 10-5 at 0.95. Accumulation of stacking faults (SFs) and lattice disorder at the twin boundaries causes dynamic recrystallization, promotes grain refinement and decreases the twin density by forming subgrains. Detailed investigations on the formation and interaction of defects have been done through resistivity, positron lifetime and Doppler broadening measurements in order to understand the micro-mechanism of nanostructuring at sub-zero temperatures. © 2014 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License. (]

Severe plastic deformation (SPD) processes such as high pressure torsion, equal channel angular pressing, accumulative roll banding, reciprocating extrusion compression, cyclic closed die forging and repetitive corrugation and straightening are some of the most successful methods for processing bulk nanocrystalline metals and alloys for practical applications.1 Recently, many such SPD processes have been adopted for producing nanocrystalline Cu and its alloys.1-6 Dynamic recovery at room temperature reduces the defect density and restricts the formation of uniform nanocrystalline microstructure.2 However, the presence of solute atoms minimizes cross-slip during plastic deformation and helps in retaining large defect density at cryogenic temperatures.

The grain refinement in bulk solid requires the manipulation and rearrangement of dislocations, formation of primary and secondary twins with nano-scale twin/matrix (T/M) lamellae, and their fragmentation by shear banding.3,7 The microstructural refinement of a-brass is promoted by extensive nano-twinning (~50 nm) due to its low stacking fault energy (14 mJ/m2).4-8 Moreover, the twin lamellae thickness (X) and twin spacing (dtwin) reduce to a minimum value upon SPD and then saturate.7-9 Large plastic deformation induces shear bands in the microstructure, which intersect and break the twin lamellae.8,10 Therefore, it has been proposed that the grain refinement in a-brass is governed by the formation and subsequent fragmentation of twin lamellae causing microstructural refinement at nanoscale.

In this Letter, we report the evolution of various defects such as stacking fault, dislocation, twin and their interactions on the micromechanism of grain refinement in a-brass (Cu-30 wt.% Zn) during cryorolling.

Corresponding author: E-mail address:, Tel: +91-3222-283284, Fax: +91-3222-282280

2158-3226/2014/4(6)/067101/8 4,067101-1 © Author(s) 2014

FIG. 1. Typical TEM DF micrograph of CR02 showing the presence of twin in the microstructure (inset of (a): corresponding SAED pattern along [112] zone axis). (b) BF images of CR07 with curved TBs as marked by white rectangle, (c) CR095 shows the presence of secondary twin and (d) HR images of CR095 with SFs and plenty of dislocations.

Specimens having dimensions of 67 x 14 x 10 mm3 have been cut from an as-cast bar of a-brass (Cu70Zn30) (at.%), which have been solution treated (ST) at 560 °C for 3 h followed by furnace cooling. The samples were then dipped into liquid N2 container which has been maintained at 153 K for 10-15 minutes before and after each rolling pass. The thickness reduction during each rolling pass has been estimated to be ~5%. Samples were collected after achieving true strain of 0.2, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 and 0.95 along thickness direction and were identified as CR02, CR04, CR05, CR06, CR07, CR08, CR09 and CR095 respectively. Structural investigation of the rolled specimens along the cross-sectional (NW) direction has been performed by using X-ray diffraction (XRD) (X'pert PRO, PANalytical, HR3040/40, The Netherlands) with CuKa radiation. The XRD pattern has been analyzed using Rietveld whole X-ray profile fitting technique by using the recently developed Material Analysis Using Diffraction (MAUD) software. Thin slices from rolled samples were cut along the NW direction followed by mechanical polishing, dimpling and Ar-ion milling (PIPS-691, Gatan) with liquid N2 cooling facility for high resolution transmission electron microscopic (HRTEM, JEM-2100, JEOL, Japan) study. The electrical resistivity of rolled specimens was estimated by Hall measurement technique following van der Pauw four-probe method. Positron lifetime and Doppler broadening measurements were conducted on the unrolled and CR02, CR04, CR07, and CR09 specimens. A 22Na radioactive isotope which emits positrons was sandwiched between the two specimens of each sample and the out coming y -rays were recorded using radiation detectors-BaF2 scintillators coupled with XP2020Q photomultiplier tubes served as the detectors for positron lifetime measurements and a high pure germanium (HPGe) detector was used for Doppler broadening measurements.

The average grain size in ST specimen is found to be ~500 ^m. Fig. 1(a) shows the typical TEM dark field (DF) microstructure of CR02 observed along a direction close to[112]. It has been noticed that the large equiaxed grains are divided into twinned and untwinned (matrix) region of 66 ± 6 nm and 170 ± 9 nm thickness respectively. The selected area electron diffraction pattern (SAED) of the corresponding DF images are shown in the inset in Fig. 1(a). Double diffraction spot in the SAED pattern indicates the presence of twin in the microstructure. Fig. 1(b) shows the bright field (BF) images of CR07 specimens with reduced twin lamellae thickness (X = 44 ± 7 nm) and

FIG. 2. XRD patterns of rolled specimens showing peak broadening upon cryorolling.

twin spacing (dtwin = 57 ± 6 nm). Moreover, curved twin boundaries (TBs) have been frequently observed in the BF micrograph of CR07 specimens, as marked by the white rectangle, which occurs due to the accumulation of dislocations at TBs. Recent studies by Wang et al.11-16 have shown that serrated TBs are often observed in HCP metals due to the accumulation of lattice dislocations, which form steps to reduce the excess energy of a dissociated TB. However, accumulation of dislocations will either dissociate along TB or transmit across TBs or can activate other defects such as twin nucleation and twin shrinkage.14-16 The BF and high resolution (HR) images of CR095 are shown in Fig. 1(c) and 1(d) respectively. The BF micrograph shows the presence of some secondary twins along with primary twins, whereas, TBs with dislocations and SFs have been observed in the HR image.

The XRD patterns of rolled specimens are shown in Fig. 2. Analysis of all these patterns has revealed that the width of all the peaks became broader in deformed specimens than that of ST. The lattice parameter (a), crystallite size (d), lattice strain ((e2)2), twin fault probability (ft) and extrinsic fault (EF) of the rolled specimens have been estimated from the XRD peak broadening

using Rietveld method and the estimated values of d, (e2) 2, ft and EF are plotted as shown in Figs. 3 and 4. The lattice parameter of the ST specimen has been measured to be 3.69 A, which has been unchanged upon further CR indicating that no phase transformation had occurred during the entire range of cryorolling. Fig. 3 shows the change of d and EF with CR. The crystallite size has been found to decrease from 196 nm (ST) to 42 nm (CR095) indicating the formation of nanostructure during CR, whereas EF continuously increases from 8.05 x 10-13 (ST) to 3.19 x 10-3 (CR095) during CR.

2 1 2 1

Fig. 4(a) represents the effect of CR on ft and (e ) 2. It has been clearly observed that (e ) 2

of the CR specimens increases from 9.30 x 10-4 (ST) to 2.10 x 10-3 (CR07) and saturates to a similar value of 2.13 x 10-3 at CR095. Dislocation density (pd) has been calculated from (e2) 2 by the following equation:9

2V3 (e2

where, bis the absolute value of the Burgers vector, which has been estimated to be 0.26 nm for fcc brass.17 The dislocation densities of the CR specimens are higher than that of the ST specimen (6.3 x 1013 /m2). Moreover, pd increases considerably upon CR and reaches to pd = 8.7 x 1014 /m2 in CR07, which remain unchanged upon further rolling (8 x 1014 /m2 at CR09). On the other hand, a

FIG. 3. Plot showing the effect of cryorolling strain on the crystallite size and extrinsic faults.

certain increase in в has been observed at CR04. в increases from 1.7 x 10 12 (ST) to a maximum value of 5.9 x 10-3 at CR07 followed by a sudden decrease at CR08 (8.8 x 10-4) and reduces to a value of 1.1 x 10-5 atCR095.

Fig. 4(b) represents the change of electrical resistivity (at 298 K, 273 K, 223 K and 153 K) with CR. The room temperature (298 K) resistivity of ST has been measured to be 9.5 x 10-8 ^ ■ m, which decreases down to 3.9 x 10-8 ^ ■ m for CR07. The resistivity increases >0.7 and reaches to a maximum value of 15.1 x 10-8 ^ ■ m at CR095. It should be noted that the resistivity of the specimens at a particular CR decreases with temperature but the change of resistivity with CR follows the same trend as that of RT resistivity.

The variation of the S-parameter derived from the Doppler broadened positron annihilation Y-ray spectral line shape as a function of rolling strain is also shown in Fig. 4(b). The S-parameter increases form 0.394 (ST) to 0.399 (CR07) and decreases down to a value of 0.397 (CR09) during CR. The S-parameter is an integral line shape parameter, which is defined as the ratio of the area under the central channels (511 ± 0.8 keV) in the Doppler-broadened spectrum to the total area under the annihilation curve.18 Moreover, the positron annihilation events represented in terms of the S-parameter are significantly enhanced in solids with high defects concentration compared to those of defect-free solids.18 Therefore the variation of S-parameter with CR indicates that the defect concentration invariably changes during the cryorolling of the specimens.

Representative TEM images of CR02 and CR07 as shown in Fig. 1(a) and 1(b) show that twinning starts at the initial stage of CR and, as the CR strain increases, the fraction of twin in the microstructure increases resulting in the gradual increases of в up to CR07 as observed in Fig. 4. The decrease of twin density after a certain amount of deformation strain has been reported earlier.19-23 A number of factors can be considered as responsible for the decreases of twin density after a certain rolling strain, primary among them being the high dislocation density arrays, which form at very high strain and divide the twin lamellae into equiaxed nano-sized structures. This in turn

FIG. 4. Variation of (a) twin fault probability (fi) and lattice strain ((e2> 2), (b) resistivity (pr) and S-parameter with cryorolling strain.

has been converted to nanometer-sized sub-grains through dynamic recrystallization.19 Secondly, detwinning of very narrow twin lamellae (2-4 nm) at higher rolling strain is a subject of concern.20 Further, the inverse grain size effect on twinning21 and the activation of grain boundary sliding or rotation in the critically small grain can limit the formation of the twin.22,23 In the present study, a high-density dislocation flux encountered the TBs at higher CR and fragmented them into equiaxed structure as observed in Fig. 1(c). The fragmented TBs become high angle grain boundary (HAGB) by accumulating dislocations resulting sudden decreases in fi after CR07, as observed in Fig. 3.

Dislocations emitted from GBs or TBs and therefore, the dislocation density increases with the increase in rolling strain. Hence, high-density dislocation flux flows through the metals during CR. It has been well established that dislocation annihilation occurs when they interact either with GBs, TBs or when two dislocations of opposite sign come closer to each other. Li et al. have proposed that the dislocation density (p) measured from X-ray analysis should be written as:24

p = pd+pi - pa (2)

where p'd is the initial dislocation density, pfd is the flowing dislocation density and pa is the annihilated dislocation density. Dao et al. have reported that TBs act as preferential sites for dislocation accumulation by forming curved TBs.25 Therefore, the presence of curved TBs in the TEM BF

micrograph of CR07 confirms that dislocation accumulation must have occurred at TBs during CR. So, the constant dislocation density maintained at rolling strain >0.7 is due to the balance between dislocation multiplication and annihilation at TBs.

Fig. 3 shows that the refinement in crystallite size occurs down to nanometer range during CR. Microstructural refinement is effected by the formation of twins during initial stage of CR, which divide the microstructure into twin and untwinned (matrix) regions as observed in Fig. 1(a). Moreover, as the rolling strain increases, newer twins form and reduce both X and dtwin (Fig. 1(b)). XRD analysis shows that a high-density dislocation flux flows through the material during CR, which forms dislocation tangles inside twin and matrix lamellae. At higher CR strain, the dislocation flux transfer slips at the lamellae interface and increases the dislocation density inside both the twin and matrix lamellae. The dislocation tangles that form inside X and dtwin will convert into HAGBs by accumulating these dislocations. Therefore, the formation of nanograins inside T/M lamellae can be assumed to cause the microstructural refinement at higher CR strain as shown in Fig. 1(d).

In order to reveal the contribution of SFs during nanostructuring in a-brass, detailed structural characterization of SFs through XRD and TEM analysis has been carried out. Fig. 3 shows that probability of EFs increases with CR. Usually, EFs arise due to the change in stacking sequence by introduction of an extra solute layer, which does not belong to the continuing patterns of the regular lattice either above or below the fault.26 Therefore in the case of a-brass, agglomeration of Zn in Cu lattice forms the EFs and more number of such Zn layer has been incorporated resulting an increase of EFs upon CR. According to Vergnol et al., twinning is controlled by the nucleation and growth of EFs27 and therefore, an increase of EFs during CR facilitate twinning. Meyers etal.2 have reported that the critical thickness of a twin embryo that can form and subsequently grow should be proportional to the twin boundary energy, which is also proportional to SFE. HR images of CR095 as observed in Fig. 1(d) shows the presence of high-density dislocations and SFs. The width of the SFs has been found to vary in the range of 2.6 nm and 7.3 nm, with an average value of ~5 nm. Therefore, a low value of SFE in a-brass makes easier for the dissociation of a pure dislocation into two partial dislocations to form a wider stacking fault ribbon between them, which acts as a barrier for the full dislocation to either cross slip or climb when they encounters a barrier.17,29 This promotes the formation of narrower twins and thus restricts the growth rate of twin embryos during CR. Such a finding suggests that the increase in EFs restrict cross slip of dislocation and facilitates twinning during nanostructuring in a-brass.

The change in the electrical resistivity occurs due to the scattering of electrons by the disturbance in a crystal such as thermal vibration, impurities and defects.30 Chen et al. have reported that the reduction of grain size causes significant increase in the resistivity due to the presence of high-density GB dislocations, which increase the scattering of electrons at GBs.30 Whereas, the formation of twin in the microstructure reduces the total concentration of GB area as well as GB defects, and thus reduces the overall resistivity.22 TEM and XRD analyses revealed that twinning had occurred during the initial stage of CR and the twin density had increased with increasing CR strain, which were responsible for the decrease of resistivity during CR upto 0.7 as observed in Fig. 4(b). On the other hand, the formation of nano-grains from the fragmented twin lamellae increases the GB area and GB defects and causes an increase in the resistivity of the alloy beyond CR07. The variation of the S-parameter during deformation indicates the change of size and concentration of positron trapping sites within the lattice.18,31 It has been reported that interfacial defects, such as TBs act as an excellent traps for positrons.31 Therefore, the S-parameter in the experimental alloy increases during CR up to 0.7 strain due to an increase of twin density, whereas, detwinning at higher CR strain (>0.7) is responsible for the decrease of S-parameter due to the decrease of TBs.

The results of positron lifetime measurements are shown in Fig. 5. Two positron lifetimes t 1 and t2 with their relative intensities I1 and I2 have been observed (I1 +12 = 100%), which are consistent with the presence of defects in the form of dislocations and grain boundaries.18,32 Positron lifetimes have been well known to be 122 ps and 160 ps for bulk defect-free Cu and Zn, respectively, and a mean lifetime, denoted as tb, of 133 ps can be considered reasonable for the a-brass as used here. A shorter positron lifetime t 1 < tb along with a large intensity I2 indicate the presence of positron trapping defects in the CR specimens.33 Even in the case of ST sample, t2 has been measured to be as large as 185 ps, which results due to positron annihilation at the GBs and TBs. The large

FIG. 5. The positron lifetimes t 1 and t2 and their relative intensities I1 and I2 versus the cryorolling strain.

value of I2 (=64%) confirms that these defects are electron density deficient and are vacancy-type in nature. Moreover, the relative intensities I1 and I2 are directly proportional to defect density.32 The intensity I1 decreases and I2 steadily increases upon CR as shown in Fig. 5. Therefore, the defects in form of dislocations decreases as they got accumulated at TBs or GBs, whereas, boundary defects increases due to the formation of nano-twins at higher CR strain. Positron lifetime of Cu is about 180 ps for dislocations and its value may be slightly larger in a-brass about ~190 ps for ST specimens. Whereas, t 1 and t2 are found to be less in CR specimens than that of ST and they further reduces with the increase of CR strain. Annihilation of dislocation at TBs and GBs, and detwinning by fragmentation of T/M lamellae, are believed to be the reason for such observations. It should be noted that the decrease of crystallite size during CR may not influence the value of I2 since the sizes are well above the thermal diffusion length of positrons (~30-40 nm). However, the intensity I2 is as high as 84% in CR09, which indicates that the overall defect density within the samples is high enough to result in a near-saturation trapping of positrons. Therefore, the resistivity measurement, positron annihilation lifetime and Doppler broadening spectroscopy studies show that the twin density increases with CR and reaches to a maximum value at CR07 and then decreases.

In summary, the nanostructuring of a-brass during CR is controlled by the formation and interaction of vacancy, dislocations, stacking faults, and TBs. A high-density dislocation flux interacts with TBs athigher CR strain (>0.7) and fragments them into small domain structures, which appeared to nano-size grain at the later stage. The decrease of pR and increase of S-parameter during CR up to <0.7 suggests a decrease of dtwin whereas, the increase in resistivity and decrease of S-parameter at CR strain >0.7 are due to the formation of large HAGBs from the fragmented TBs causing nanocrystallization.


The authors thank P. Das, K. Sahoo, R. Basu, P. Guha and S. Bhattacharya for technical assistance. Financial support provided by DST, SERB, Govt. of India for the project entitled "Processing

and characterization of bulk nanostructured brass" (Grant number: D.O. SR/FTP/ETA-88/2010) is gratefully acknowledged.

1 R. Z. Valiev, R. K. Islamgaliev, and I. V. Alexandrov, Prog. Mater. Sci. 45, 103 (2000).

2 P. B. Prangnell, J. R. Bowen, and P. J. Apps, Mater. Sci. Eng. A. 375, 178 (2004).

3 Y. H. Zhao, Z. Horita, T. G. Langdon, and Y. T. Zhu, Mater. Sci. Eng. A. 474, 342 (2008).

4 J. Das, Mater. Sci. Eng. A. 530, 675 (2011).

5 Y. T. Zhu, X. Z. Liao, S. G. Srinivasan, and E. J. Lavernia, J. Appl. Phys. 98, 034319 (2005).

6 Y. T. Zhu, X. Z. Liao, and R. Z. Valiev, Appl. Phys. Lett. 86, 103112 (2005).

7 Y. S. Li, N. R. Tao, and K. Lu, Acta Mater. 56, 230 (2008).

8 A. M. Hodge, Y. M. Wang, and T. W. Barbee, Scr. Mater. 59, 163 (2008).

9 G. H. Xiao, N. R. Tao, and K. Lu, Scr. Mater. 59, 975 (2008).

10 Y. Li, Y. H. Zhao, W. Liu, C. Xu, Z. Horita, X. Z. Liao, Y. T. Zhu, T. G. Langdon, and E. J. Laverniaa, Mater. Sci. Eng. A 527, 3942 (2010).

11 J. Wang, Q. Yu, Y. Jiang, and I. J. Beyerlein, JOM 66, 95 (2014).

12 J. Tu, X. Zhang, J. Wang, Q. Sun, Q. Liu, and C. N. Tome, Appl. Phys. Lett. 103, 051903 (2013).

13 J. Wang, S. K. Yadav, J. P. Hirth, C. N. Tome, and I. J. Beyerlein, Mater. Res. Lett. 1, 126 (2013).

14 J. Wang, L. Liu, C. N. Tome, S. X. Mao, and S. K. Gong, Mater. Res. Lett. 1, 81 (2013).

15 J. Wang, I. J. Beyerlein, and C. N. Tome, Int. J. Plast. 56, 156 (2014).

16 J. Wang, I. J. Beyerlein, and J. P. Hirth, Modelling Simul. Mater. Sci. Eng. 20, 024001 (2012).

17 G. E. Dieter, Mechanical Metallurgy. (Elsevier, London, 1989).

18 R. Chidambaram, M. K. Sanyal, P. M. G. Nambissan, and P. Sen, J. Phys.: Condens. Matter. 2, 9941 (1990).

19 G. Csiszar, L. Balogh, A. Misra, X. Zhang, and T. Ungar, J. Appl. Phys. 110, 043502 (2011).

20 X. L. Wu and Y. T. Zhu, Phys. Rev. Lett. 101, 025503 (2008).

21X. Z. Liao, F. Zhou, E. J. Lavernia, S. G. Srinivasan, M. I. Baskes, D. W. He, and Y. T. Zhu, Appl. Phys. Lett. 83, 632 (2003).

22 H. V. Swygenhoven, and P. A. Derlet, Phys. Rev. B. 64, 224105 (2001).

23 S. Cheng, Y. H. Zhao, Y. Z. Guo, Y. Li, Q. M. Wei, X. L. Wang, Y. Ren, P. K. Liaw, H. Choo, and E. J. Lavernia, Adv. Mater. 21, 5001 (2009).

24 L. Li, T. Ungar, Y. D. Wang, G. J. Fan, Y. L. Yang, N. Jia, Y. Ren, G. Tichy, J. Lendvai, H. Choo, and P. K. Liaw, Scr. Mater. 60, 317 (2009).

25 M. Dao, L. Lu, Y. F. Shen, and S. Suresh, Acta Mater. 54, 5421 (2006).

26 D. Hull and D. J. Bacon, Introduction to Dislocations. (Pergamon Press, Oxford, 1984).

27 J. M. F. Vergnol and J. R. Grilhe, J. Physique. 45, 1479 (1984).

28 M. A. Meyers, O. Vohringer, and V. A. Lubarda, Acta Mater. 49, 4025 (2001).

29 H. Zhao, Y. T. Zhu, X. Z. Liao, Z. Horita, and T. G. Langdon, Appl. Phys. Lett. 89, 121906 (2006).

30 X. H. Chen, L. Lu, and K. Lu, J. Appl. Phys. 102, 083708 (2007).

31 J. Arunkumar, S. Abhaya, R. Rajaraman, G. Amarendra, K. G. M. Nair, C. S. Sundar, and B. Raj, J. Nucl. Mater. 384, 245 (2009).

32 T. Fengen, L. Baozhang, and L. Yanqin, Chinese Phys. Lett. 7, 312 (1990).

33 D. Sanyal, D. Banerjee, and U. De, Phys. Rev. B. 58, 226 (1998).