effects of thermo-mechanical parameters on microstructure and mechanical properties of...

6
Materials Science and Engineering A 535 (2012) 164–169 Contents lists available at SciVerse ScienceDirect Materials Science and Engineering A journa l h o me pa ge: www.elsevier.com/locate/msea Effects of thermo-mechanical parameters on microstructure and mechanical properties of Ti–50 at.%Ni shape memory alloy produced by VAR method A. Foroozmehr, A. Kermanpur , F. Ashrafizadeh, Y. Kabiri Department of Materials Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran a r t i c l e i n f o Article history: Received 19 November 2011 Accepted 14 December 2011 Available online 22 December 2011 Keywords: Shape memory effect Ti–Ni alloy Thermo-mechanical treatment Cold rolling VAR a b s t r a c t In this work, effects of a thermo-mechanical treatment including cold rolling and annealing on microstructure, mechanical properties and shape memory characteristics of Ti–50 at.%Ni alloy were stud- ied. The vacuum arc remelted ingot was first homogenized followed by hot rolling and annealing to prepare the initial microstructure. The annealed specimens were then cold rolled to 10–40% thickness reduction at room temperature. Post deformation annealing was conducted at 400, 500 and 600 C for 1 h. Phase transformation and microstructural evolution was studied by X-ray diffraction and optical and scanning electron microscopes. Tensile, hardness and three-point bending tests were conducted to determine mechanical and shape memory properties. Experimental results showed that volume fraction of martensite, hardness and tensile strength were increased by increasing cold reduction. More recrystal- lization was occurred at 40% reduction followed by annealing at 600 C, leading to a significant decrease in hardness and the amount of remained martensite. Better shape memory characteristics were achieved by applying the thermo-mechanical treatment. Both a higher cold reduction and a lower annealing tem- perature caused more shape recovery. The specimen annealed at 400 C after 20% cold rolling showed full shape recovery. © 2011 Elsevier B.V. All rights reserved. 1. Introduction Shape memory alloys are an interesting class of materials exhibiting a transformation in crystal structure at low temper- atures, allowing for the metal to change shapes back and forth without any damage to the microstructure. Among shape memory alloys, Ti–Ni alloy system has attracted many researchers due to its proper shape memory effect and the ability of changing trans- formation temperature to the human body temperature [1]. The key issue behind achieving shape memory effect is that the stress required to induce martensite (B 19 ) should be lower than that required to cause dislocation slip; otherwise the material would show no unique behavior. As slip is so easily introduced in Ti–Ni alloys, the increase in the critical stress is especially important for these alloys [2]. A high critical stress for slip may be achieved by work hardening, precipitation hardening, alloy hardening or grain refinement. Work hardening alone increases strength of NiTi, but leads to a lower recoverable strain due to introduction of random dislocations. Annealing restores shape memory effect by rearrang- ing dislocations, but decreases strength [3–7]. Thermo-mechanical treatments provide a method to modify strength and shape mem- ory properties by introducing certain lattice defects in austenite Corresponding author. Tel.: +98 311 3915738; fax: +98 311 3912752. E-mail address: ahmad [email protected] (A. Kermanpur). (B 2 ) or martensite (B 19 ) and also grain refinement. From the engi- neering point of view, control of thermo-mechanical treatment is important from two aspects: (1) shaping of semi-finished prod- ucts, and (2) optimizing microstructures in order to obtain useful properties [8,9]. Previous works have mainly focused on investigating effects of precipitation in the deformed Ni-rich shape memory alloys and their mechanical properties and transformation temperatures. Chrobak et al. [10], studied the multi-step transformation occurring for 10% deformed Ti–50.6 at.%Ni followed by annealing at 400 C. They showed how transformation temperatures changed by pre- cipitation. In another research, the effect of thermo-mechanical process including hot rolling and/or hot rolling and cold draw- ing on fatigue properties of Ni-rich material was studied by Gall et al. [11]. They concluded that increasing of monotonic strength measured in both hot-rolled and cold-drawn NiTi materials led to an enhanced resistance to low-cycle fatigue. Mitwally and Farag [12] studied the effect of cold rolling and annealing on microstruc- ture, mechanical and shape memory properties of Ti–50.7 at.%Ni alloy. It was shown that fraction of martensite and tensile strength increased by cold rolling and decreased by annealing tempera- ture. They indicated that it is best to use the NiTi alloy in the as hot rolled condition if maximum shape memory effect is desired, but cold rolled NiTi would be preferable if high strength, hardness and acceptable recoverable strains are desirable. Wang et al. [13] investigated effect of such treatment on two-way shape memory 0921-5093/$ see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2011.12.059

Upload: a-foroozmehr

Post on 10-Sep-2016

222 views

Category:

Documents


1 download

TRANSCRIPT

Page 1: Effects of thermo-mechanical parameters on microstructure and mechanical properties of Ti–50 at.%Ni shape memory alloy produced by VAR method

Ep

AD

a

ARAA

KSTTCV

1

eawaifkrrsatwrldito

0d

Materials Science and Engineering A 535 (2012) 164– 169

Contents lists available at SciVerse ScienceDirect

Materials Science and Engineering A

journa l h o me pa ge: www.elsev ier .com/ locate /msea

ffects of thermo-mechanical parameters on microstructure and mechanicalroperties of Ti–50 at.%Ni shape memory alloy produced by VAR method

. Foroozmehr, A. Kermanpur ∗, F. Ashrafizadeh, Y. Kabiriepartment of Materials Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran

r t i c l e i n f o

rticle history:eceived 19 November 2011ccepted 14 December 2011vailable online 22 December 2011

eywords:hape memory effecti–Ni alloyhermo-mechanical treatment

a b s t r a c t

In this work, effects of a thermo-mechanical treatment including cold rolling and annealing onmicrostructure, mechanical properties and shape memory characteristics of Ti–50 at.%Ni alloy were stud-ied. The vacuum arc remelted ingot was first homogenized followed by hot rolling and annealing toprepare the initial microstructure. The annealed specimens were then cold rolled to 10–40% thicknessreduction at room temperature. Post deformation annealing was conducted at 400, 500 and 600 ◦C for1 h. Phase transformation and microstructural evolution was studied by X-ray diffraction and opticaland scanning electron microscopes. Tensile, hardness and three-point bending tests were conducted todetermine mechanical and shape memory properties. Experimental results showed that volume fraction

old rollingAR

of martensite, hardness and tensile strength were increased by increasing cold reduction. More recrystal-lization was occurred at 40% reduction followed by annealing at 600 ◦C, leading to a significant decreasein hardness and the amount of remained martensite. Better shape memory characteristics were achievedby applying the thermo-mechanical treatment. Both a higher cold reduction and a lower annealing tem-perature caused more shape recovery. The specimen annealed at 400 ◦C after 20% cold rolling showed

full shape recovery.

. Introduction

Shape memory alloys are an interesting class of materialsxhibiting a transformation in crystal structure at low temper-tures, allowing for the metal to change shapes back and forthithout any damage to the microstructure. Among shape memory

lloys, Ti–Ni alloy system has attracted many researchers due tots proper shape memory effect and the ability of changing trans-ormation temperature to the human body temperature [1]. Theey issue behind achieving shape memory effect is that the stressequired to induce martensite (B19′ ) should be lower than thatequired to cause dislocation slip; otherwise the material wouldhow no unique behavior. As slip is so easily introduced in Ti–Nilloys, the increase in the critical stress is especially important forhese alloys [2]. A high critical stress for slip may be achieved byork hardening, precipitation hardening, alloy hardening or grain

efinement. Work hardening alone increases strength of NiTi, buteads to a lower recoverable strain due to introduction of randomislocations. Annealing restores shape memory effect by rearrang-

ng dislocations, but decreases strength [3–7]. Thermo-mechanicalreatments provide a method to modify strength and shape mem-ry properties by introducing certain lattice defects in austenite

∗ Corresponding author. Tel.: +98 311 3915738; fax: +98 311 3912752.E-mail address: ahmad [email protected] (A. Kermanpur).

921-5093/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.msea.2011.12.059

© 2011 Elsevier B.V. All rights reserved.

(B2) or martensite (B19′ ) and also grain refinement. From the engi-neering point of view, control of thermo-mechanical treatment isimportant from two aspects: (1) shaping of semi-finished prod-ucts, and (2) optimizing microstructures in order to obtain usefulproperties [8,9].

Previous works have mainly focused on investigating effectsof precipitation in the deformed Ni-rich shape memory alloysand their mechanical properties and transformation temperatures.Chrobak et al. [10], studied the multi-step transformation occurringfor 10% deformed Ti–50.6 at.%Ni followed by annealing at 400 ◦C.They showed how transformation temperatures changed by pre-cipitation. In another research, the effect of thermo-mechanicalprocess including hot rolling and/or hot rolling and cold draw-ing on fatigue properties of Ni-rich material was studied by Gallet al. [11]. They concluded that increasing of monotonic strengthmeasured in both hot-rolled and cold-drawn NiTi materials led toan enhanced resistance to low-cycle fatigue. Mitwally and Farag[12] studied the effect of cold rolling and annealing on microstruc-ture, mechanical and shape memory properties of Ti–50.7 at.%Nialloy. It was shown that fraction of martensite and tensile strengthincreased by cold rolling and decreased by annealing tempera-ture. They indicated that it is best to use the NiTi alloy in the as

hot rolled condition if maximum shape memory effect is desired,but cold rolled NiTi would be preferable if high strength, hardnessand acceptable recoverable strains are desirable. Wang et al. [13]investigated effect of such treatment on two-way shape memory
Page 2: Effects of thermo-mechanical parameters on microstructure and mechanical properties of Ti–50 at.%Ni shape memory alloy produced by VAR method

ce and Engineering A 535 (2012) 164– 169 165

erTsabst

tie

2

rupaqmaa

irsfiPstTbvTl7e

%

wbm

3

3

qfimbmrdsbd

st

Fig. 1. Variation of martensite volume fraction by cold rolling.

A. Foroozmehr et al. / Materials Scien

ffect of Ti–50.6 at.%Ni spring. They found that the shape memoryecovery rate increased with increase of annealing temperature.hese results indicated that the effect of increasing critical stress forlip was most effective when high density small precipitates werevailable. According to the author’s knowledge, less attention haseen paid to the evolution of microstructures and mechanical andhape memory properties occurring during thermo-mechanicalreatments of NiTi alloys.

The aim of this study was to investigate the influences ofhermo-mechanical treatment of cold rolling followed by anneal-ng on microstructure, mechanical properties and shape memoryffect of the Ti–50.0 at.%Ni shape memory alloy.

. Materials and methods

The equiatomic Ti–50.0 at.%Ni alloy was prepared by vacuum arcemelting (VAR) method followed by homogenization at 1000 ◦Cp to 8 h. Details of the specimen preparation were previouslyublished [14]. The homogenized specimens were 50% hot rolledt 1000 ◦C and then annealed at 900 ◦C for 1 h followed by wateruenching. The hot rolled and annealed specimens with austeniticicrostructure were cold rolled to thickness reduction of 10–40%

t room temperature. Post deformation annealing was performedt 400, 500 and 600 ◦C for 1 h followed by water quenching.

The specimens were prepared by grinding, polishing and etch-ng with a solution of HF, HNO3 and H2O (volume ratio of 1:4:5,espectively). Microstructures were examined using optical andcanning electron microscopes (SEM Philips XL30). Phase identi-cation and calculation was conducted by X-ray diffraction (XRDhilips X’Pert with Cu K� radiation) employing direct compari-on method [15]. Hardness was measured by Vickers method, andensile test was carried out according to ASTM F2516 standard.o investigate shape memory behavior of the alloy, a three-pointending test was carried out at room temperature using a uni-ersal tensile testing machine at a cross head speed of 1 mm/min.he specimen with dimensions of 40 mm × 15 mm × 1 mm was firstoaded up to a bending of about 2 mm and then heated up to above0 ◦C. Total shape recovery (R) was measured by using the followingquation:

R =(

�F

180

)× 100

here �F is the final remain angle in respect of 180◦. Tensile andending specimens were cut parallel to the rolling direction by wireachining for characterizations.

. Results and discussion

.1. Microstructures

The results of direct comparison method presented in Fig. 1uantitatively shows the relationship between martensite volumeraction and amount of cold rolling. The zero value of cold rollings related to the hot rolled and annealed specimen (HRAN speci-

en). As it can be seen, the martensite volume fraction is increasedy cold rolling with a quadratic polynomial function; the speci-en cold rolled to 40% shows about 67% martensite. Over the cold

eduction of 40%, some micro-cracks were initiated in specimensue to low ductility of the alloy. Microscopic investigation washown that these cracks were mainly initiated from the interfaceetween matrix and some segregated Ti-rich precipitates formed

uring vacuum are remelting process [16].

The effect of temperature of post deformation annealing ishown in Fig. 2 for the specimen cold rolled to 40%. It is revealedhat increasing annealing temperature leads to a decrease in the

Fig. 2. Variation of martensite volume fraction by annealing temperature.

retained martensite content. However, all annealed specimens stillcontain martensite as a result of martensite stabilization. It has beenreported that martensite could remain even at high temperaturedue to the presence of dislocations impeding transformation frommartensite to austenite during post deformation annealing [17,18].

Fig. 3 shows microstructures of the HRAN specimen after coldrolling to 10% and 40% thickness reduction. As it can be seen, no sig-nificant change was occurred in grain size, but grains were alignedalong the rolling direction. The presence of twins as a result of for-mation of stress-induced martensite during cold rolling can also benoticed. The amount of twins was increased by rolling reduction;this effect is attributed to the formation of more martensite phase.

Microstructure of the specimen cold rolled to 40% followed byannealing at 400 ◦C is presented in Fig. 4. In comparison with Fig. 3c,it is obvious that no significant change in grain size of austenite hasoccurred under this condition. However, the amount of twins isdecreased due to the reverse transformation from martensite toaustenite.

Fig. 5 shows effect of cold reduction and temperature of postdeformation annealing on microstructure of the Ti–50.0 at.%Nialloy. As it can be seen in Fig. 5a–c, grain nucleation is occurredin the vicinity of particles at 500 ◦C (e.g. particle-stimulated nucle-ation). This phenomenon has already been observed in Ni and Alalloys [19–22]. The authors already showed that these particleswere mainly Ti2Ni precipitates [14]. Increasing annealing temper-ature to 600 ◦C has caused nucleation in the matrix (Fig. 5d–f)and increasing cold reduction resulted in an increase in nucleationdensity and, consequently, a decrease in grain size. Newly formed

grains (stimulated by particles and/or formed in the matrix) containno dislocation [23], hence, reverse transformation from marten-site to austenite can easily take place. As a result, the remained
Page 3: Effects of thermo-mechanical parameters on microstructure and mechanical properties of Ti–50 at.%Ni shape memory alloy produced by VAR method

166 A. Foroozmehr et al. / Materials Science and Engineering A 535 (2012) 164– 169

% and

mirp

Fa

Fig. 3. Microstructures of the (a) HRAN, (b) 10

artensite is decreased significantly by post deformation anneal-ng, as shown in Fig. 2. However, since dislocations are not

ecovered completely even by annealing at 600 C, the martensitehase is still remained in the alloy microstructure.

ig. 4. Microstructure of the 40% cold rolled specimen followed by post deformationnnealing at 400 ◦C.

(c) 40% cold rolled Ti–50.0 at.%Ni specimens.

3.2. Mechanical properties

Fig. 6 shows hardness increasing by cold rolling with a quadraticpolynomial function; this is attributed to the increase in dislocationdensity during cold rolling. The effect of post deformation anneal-ing on hardness after various reductions is shown in Fig. 7. As itis seen, annealing has caused a drop in hardness for each reduc-tion due to the recovery of dislocations [12]. Annealing at 500 and600 ◦C has led to a significant drop in hardness due to the particle-stimulated and matrix recrystallization. Although Mitwally andFarag [12] reported an increase in hardness for the Ti–50.7 at.%Nialloy after cold rolling to 40% and annealing at 600 ◦C due to theformation of fine Ti3Ni4 precipitates, this phenomenon was notobserved in the present equiatomic Ti–50.0 at.%Ni alloy.

Fig. 8 compares tensile stress–strain curve of the HRAN spec-imen with that of specimen cold rolled to 10%. As seen, thestress–strain curve of the HRAN specimen shows a phase pseudo-yield plateau region, occurred at the strain range of 2–7%. Thisplateau region is related to the stress-induced martensitic trans-formation [18]. After cold reduction to 10%, however, this regionhas disappeared. In addition, due to introducing defects during coldrolling, the fracture stress is increased, but elongation decreased.

Disappearance of the plateau region was also reported for the coldrolled Ti–50.0 at.%Ni alloy by Lin and Wu [18]. It is believed that dur-ing cold rolling, the accommodation process of martensite variantsis occurred, and at the same time, many deformed austenite and
Page 4: Effects of thermo-mechanical parameters on microstructure and mechanical properties of Ti–50 at.%Ni shape memory alloy produced by VAR method

A. Foroozmehr et al. / Materials Science and Engineering A 535 (2012) 164– 169 167

Fig. 5. Microstructures of the post deformation annealed specimens at (a–c) 500 ◦C and (20% and (c and f) 40%.

Fig. 6. Hardness values for cold rolled specimens as a function of cold rolling.

Fig. 7. Variation of hardness by post deformation annealing temperature for differ-ent cold reductions.

d–f) 600 ◦C which were cold rolled in various reductions of (a and d) 10%, (b and e)

defects are introduced. These deformed features inhibit the sub-sequent accommodation/reorientation process during tensile test,and consequently the martensitic transformation does not occur.

Tensile stress–strain curves of the specimens cold rolled to10% and 20% followed by post deformation annealing at differenttemperatures are presented in Fig. 9. For each cold rolling reduc-tion, softening mechanisms during annealing has caused a higherelongation and a lower fracture stress. The phase pseudo-yieldplateau region is found to be gradually recovered by increasingannealing temperature. In fact, through reverse transformation and

recovering of dislocations during annealing, part of the accom-modation/reorientation process can occur during tensile test,and consequently, the plateau region is appeared again. In both

Fig. 8. Tensile stress–strain curves for the (a) HRAN and (b) 10% cold rolled speci-mens.

Page 5: Effects of thermo-mechanical parameters on microstructure and mechanical properties of Ti–50 at.%Ni shape memory alloy produced by VAR method

168 A. Foroozmehr et al. / Materials Science and Engineering A 535 (2012) 164– 169

speci

cmttciia

3

srsictrb

gdpst

illustrated in Fig. 10 that at each annealing temperature (exceptfor 600 ◦C), the shape recovery is increased by cold rolling dueto introduction of more dislocations that prevent slip. At 600 ◦C,

Fig. 9. Tensile stress–strain curves for the (a) 10% and (b) 20% cold rolled

old reductions, accommodation/reorientation process is occurredore severely at 400 ◦C. The particle-stimulated and matrix recrys-

allization have taken place at 500 ◦C and 600 ◦C, respectively, andhus, the austenite recovery to its original un-deformed shape isonducted more than that of 400 ◦C. Fig. 9 also shows that increas-ng the cold rolling reduction from 10 to 20%, resulted in an increasen strength and a decrease in elongation for both cold rolled andnnealed specimens, as expected.

.3. Shape memory property

The results of bending test of thermo-mechanically treatedpecimens are shown in Fig. 10. The horizontal dashed line rep-esents the total shape recovery of the HRAN specimen. As it can beeen, by applying cold rolling followed by post deformation anneal-ng, the total shape recovery is increased compared to the initialondition (HRAN specimen). In addition, at each cold rolling reduc-ion, increasing annealing temperature has led to a lower shapeecovery. On the other hand, a higher shape recovery is achievedy increasing the cold reduction at each annealing temperature.

It is believed that the thermo-mechanical treatment leads to aood shape memory effect because of introducing a well developed

islocation substructure in the alloy [2]. In fact, there is a com-etition between deformation mechanisms (slip or twinning) andtress-induced martensitic transformation. If slip or twinning sys-ems are activated in austenite, some deformation remains, which

mens followed by post deformation annealing at different temperatures.

cannot be recovered during unloading and heating. By increas-ing temperature of post deformation annealing, more softening istaken place leading to the formation of newly defect-free grainsthat facilitates slip prior to martensitic transformation. It is also

Fig. 10. Variation of total shape recovery as a function of post deformation annealingtemperature for different cold reductions.

Page 6: Effects of thermo-mechanical parameters on microstructure and mechanical properties of Ti–50 at.%Ni shape memory alloy produced by VAR method

ce and

hrgtrtra

4

mtc

1

2

3

4

5

[[

[[[

[

[

[

[[[[21] L. Wang, G. Xie, J. Zhang, L.H. Lou, Scr. Mater. 55 (2006) 457–460.[22] T.A. Bennett, R.H. Petrov, L.A.I. Kestens, L.-Z. Zhuangd, P. de Smet, Scr. Mater.

A. Foroozmehr et al. / Materials Scien

owever, as recrystallization is taken place, the specimen coldolled to 20% may contain well developed recrystallized defect-freerains compared to that of cold rolled to 15%. This facilitated slip inhe specimen cold rolled to 20%, and consequently, the total shapeecovery of this specimen followed by annealing at 600 ◦C is lowerhan that of cold rolled to 15%. It can be seen that a complete shapeecovery is achieved for specimen cold rolled to 20% followed bynnealing at 400 ◦C.

. Conclusions

In this work, effects of cold rolling and annealing parameters onicrostructure, mechanical properties and shape memory effect of

he Ti–50 at.%Ni alloy were investigated. The main results obtainedan be summarized as follows:

- Increasing cold rolling reduction resulted in an increase in thevolume fraction of martensite, hardness and tensile strength.

- During post deformation annealing, softening was occurred bydifferent mechanisms: dislocation recovery followed by partialreverse transformation of martensite to austenite at lower tem-perature (e.g. 400 ◦C), particle-stimulated grain nucleation atmid-temperature (e.g. 500 ◦C), and matrix recrystallization athigher temperature (e.g. 600 ◦C).

- Thermo-mechanically treated specimens showed a phasepseudo-yield plateau region in the tensile stress–strain curve.

- The cold rolling-annealing thermo-mechanical treatment led toan increase in shape recovery of Ti–50.0 at%Ti alloy. A higher

cold reduction and a lower annealing temperature both resultedmore shape recovery.

- The maximum shape recovery was achieved for the specimencold rolled to 20% followed by annealing at 400 ◦C.

[

Engineering A 535 (2012) 164– 169 169

References

[1] K. Otsuka, X. Ren, Intermetallics 7 (1999) 511–528.[2] K. Otsuka, X. Ren, Prog. Mater. Sci. 50 (2005) 511–678.[3] P. Sittner, Y. Liu, V. Novak, J. Mech. Phys. Solid. 53 (2005) 1719–1746.[4] T.W. Deurig, K.N. Melton, D. StÖckel, C.M. Wayman, Engineering Aspects

of Shape Memory Alloys, Butterworth-Heinmann, England, 1990, pp.21–35.

[5] D. Favier, Y. Liu, L. Orgéas, A. Sandel, L. Debove, P. Comte-Gaz, Mater. Sci. Eng.A 429 (2008) 130–136.

[6] S.D. Prokoshkin, V. Brailovski, K.E. Inaekyan, V. Demers, I.Y. Khmelevskaya,S.V. Dobatkin, E.V. Tatyanin, Mater. Sci. Eng. A 481–482 (2008)114–118.

[7] I.Y. Khmelevskaya, S.D. Prokoshkin, I.B. Trubitsyna, M.N. Belousov, S.V.Dobatkin, E.V. Tatyanin, A.V. Korotitskiy, V. Brailovski, V.V. Stolyarov, E.A.Prokofiev, Mater. Sci. Eng. A 481–482 (2008) 119–122.

[8] D. Treppmann, E. Hornbogen, J. Phys. IV France 7 (1997) C5211–C5220.[9] E. Hornbogen, Mater. Sci. Eng. A 273–275 (1999) 630–633.10] D. Chrobak, D. StrÓz, H. Morawiec, Scr. Mater. 48 (2003) 571–576.11] K. Gall, J. Tyber, G. Wilkesanders, S.W. Robertson, R.O. Ritchie, H.J. Maier, Mater.

Sci. Eng. A 486 (2008) 389–403.12] M.E. Mitwally, M. Farag, Mater. Sci. Eng. A 519 (2009) 155–166.13] Z. Wang, X. Zu, X. Feng, J. Dai, Mater. Lett. 54 (2002) 55–61.14] A. Foroozmehr, A. Kermanpur, F. Ashrafizadeh, Y. Kabiri, Mater. Sci. Eng. A 528

(2011) 7952–7955.15] B.D. Cullity, Elements of X-ray Diffraction, 2nd edition, Addison-Wesley, Cali-

fornia, 1978.16] Y. Kabiri, A. Kermanpur, A. Foroozmehr, Vacuum (2011), doi:10.1016/j.

vacuum.2011.09.012.17] V. Brailovski, S.D. Prokoshkin, I.Y. Khmelevskaya, K.E. Inaekyan, V. Demers, S.V.

Dobatkin, E.V. Tatyanin, Mater. Trans. 47 (2006) 795–804.18] H.C. Lin, S.K. Wu, Acta Metall. Mater. 42 (1994) 1623–1630.19] F.J. Humphreys, Acta Metall. 25 (1977) 1323–1344.20] W. Xu, M. Ferry, J.M. Cairney, F.J. Humphreys, Acta Mater. 55 (2007) 5157–5167.

63 (2010) 461–464.23] F.J. Humphreys, M. Hatherly, Recrystallization and Related Annealing Phenom-

ena, 2nd edition, Pergamon, 2004.