large magnetic entropy change and enhanced mechanical properties of ni–mn–sn–c alloys

4
Large magnetic entropy change and enhanced mechanical properties of Ni–Mn–Sn–C alloys Yu Zhang, a Jian Liu, a Qiang Zheng, b,c Jian Zhang, a Weixing Xia, a Juan Du a,and Aru Yan a a Key Laboratory of Magnetic Materials and Devices, Ningbo Institute of Material Technology and Engineering, Chinese Academy of Sciences, 519 Zhuangshi Road, Ningbo 315201, People’s Republic of China b School of Materials Science and Engineering, Ningbo University of Technology, Ningbo 315016, People’s Republic of China c Ningbo Branch of China Academy of Ordnance Science, Ningbo 315103, People’s Republic of China Received 19 August 2013; revised 7 November 2013; accepted 8 November 2013 Available online 21 November 2013 The microstructure, magnetocaloric effect and mechanical properties of carbon-doped Ni 43 Mn 46 Sn 11 C x (x = 0, 2, 4, 8) alloys have been investigated. The martensitic transformation temperatures increase remarkably, from 196 to 249 K, as the carbon doping content increases. A large magnetic entropy change, DS M , from 27.4 J kg 1 K 1 with x = 0 to 34.6 J kg 1 K 1 with x = 2, was obtained for a field change of 5 T. A significant enhancement of compressive strength from 556 MPa with x = 0 up to 1016 MPa with x = 8 is ascribed to the appearance of high amount of carbides. Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Ni–Mn–Sn–C; Martensitic transformation; Microstructure; Magnetic entropy change; Compressive strength Magnetic refrigeration based on the magnetocalo- ric effect (MCE) is potentially a high-efficiency, low-cost and greenhouse-gas-free refrigeration technology, which is drawing more attention as an alternative to the existing vapor compression refrigeration [1]. For a magnetic refrig- eration material, a high magnetic entropy change, DS M , is important for its application on the point of refrigeration capacity. In addition to magnetic properties, a magnetic refrigerant should have a certain degree of machinability in order to be fabricated into thin plates for the purpose of improving the heat-exchange performance [2]. Addi- tionally, excellent mechanical properties guarantee a long- er working life during magnetization–demagnetization cycles. Recently, magnetic refrigerants, such as Gd–Si– Ge [3], La–Fe–Si [4], Mn–Fe–P–As [5] and Ni–Mn-based Heusler alloys [6], have become the focus of research due to their giant MCE caused by first-order phase transition. Among them, the rare-earth-free Ni–Mn–X (X = Sn, In, Sb) Heusler alloy systems have provoked the greatest inter- est due to their large inverse MCEs [7–9]. To get a high DS M and a suitable magnetic transition temperature (T M ), interstitial atoms such as B [10],H [11] and C [12] have been investigated with regard to their enhancement of MCE. Xuan et al. [10] studied the effect of interstitial B atom on the MCE of Ni–Mn–Sn alloys. The T M could be changed markedly just by adjusting the amount of B, but the DS M was also reduced signifi- cantly when doped with excessive B. Mandal et al. [11] studied the effect of interstitial H atoms on the MCE of La–Fe–Si alloys. Though the T C could be changed mark- edly and the DS M could not be changed much, the thermal stability of the hydride deteriated. Chen et al. [12] investi- gated the effect of interstitial C atom on the MCE of La– Fe–Si alloys. They found that a certain amount of C can adjust the Curie temperature of the alloy; at the same time, it did not reduce the DS M substantially. So far, there have no reports on C doping in the Ni–Mn–Sn system, but it is expected that the DS M would not change a lot. There are many reports on adjusting the martensite transition temperature, enhancing the magnetic entropy change and reducing the hysteresis of the Ni–Mn–Sn alloy [13–16]. However, little research has been carried out on the machinability of the alloy, which is an addi- tional property for a magnetic cooling device. Feng et al. [17] found that the mechanical properties of Ni–Mn–In al- loys can be dramatically improved by adding Fe. It is thus possible to enhance the Ni–Mn-based alloys’ mechanical 1359-6462/$ - see front matter Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.scriptamat.2013.11.009 Corresponding author. Tel.: +86 0574 86685150; e-mail: [email protected] Available online at www.sciencedirect.com ScienceDirect Scripta Materialia 75 (2014) 26–29 www.elsevier.com/locate/scriptamat

Upload: aru

Post on 31-Dec-2016

212 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Large magnetic entropy change and enhanced mechanical properties of Ni–Mn–Sn–C alloys

Available online at www.sciencedirect.com

ScienceDirect

Scripta Materialia 75 (2014) 26–29

www.elsevier.com/locate/scriptamat

Large magnetic entropy change and enhanced mechanical propertiesof Ni–Mn–Sn–C alloys

Yu Zhang,a Jian Liu,a Qiang Zheng,b,c Jian Zhang,a Weixing Xia,a Juan Dua,⇑

and Aru Yana

aKey Laboratory of Magnetic Materials and Devices, Ningbo Institute of Material Technology and Engineering,

Chinese Academy of Sciences, 519 Zhuangshi Road, Ningbo 315201, People’s Republic of ChinabSchool of Materials Science and Engineering, Ningbo University of Technology, Ningbo 315016, People’s Republic of China

cNingbo Branch of China Academy of Ordnance Science, Ningbo 315103, People’s Republic of China

Received 19 August 2013; revised 7 November 2013; accepted 8 November 2013Available online 21 November 2013

The microstructure, magnetocaloric effect and mechanical properties of carbon-doped Ni43Mn46Sn11Cx (x = 0, 2, 4, 8) alloyshave been investigated. The martensitic transformation temperatures increase remarkably, from 196 to 249 K, as the carbon dopingcontent increases. A large magnetic entropy change, DSM, from 27.4 J kg�1 K�1 with x = 0 to 34.6 J kg�1 K�1 with x = 2, wasobtained for a field change of 5 T. A significant enhancement of compressive strength from 556 MPa with x = 0 up to 1016 MPawith x = 8 is ascribed to the appearance of high amount of carbides.� 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Ni–Mn–Sn–C; Martensitic transformation; Microstructure; Magnetic entropy change; Compressive strength

Magnetic refrigeration based on the magnetocalo-ric effect (MCE) is potentially a high-efficiency, low-costand greenhouse-gas-free refrigeration technology, whichis drawing more attention as an alternative to the existingvapor compression refrigeration [1]. For a magnetic refrig-eration material, a high magnetic entropy change, DSM, isimportant for its application on the point of refrigerationcapacity. In addition to magnetic properties, a magneticrefrigerant should have a certain degree of machinabilityin order to be fabricated into thin plates for the purposeof improving the heat-exchange performance [2]. Addi-tionally, excellent mechanical properties guarantee a long-er working life during magnetization–demagnetizationcycles. Recently, magnetic refrigerants, such as Gd–Si–Ge [3], La–Fe–Si [4], Mn–Fe–P–As [5] and Ni–Mn-basedHeusler alloys [6], have become the focus of research dueto their giant MCE caused by first-order phase transition.Among them, the rare-earth-free Ni–Mn–X (X = Sn, In,Sb) Heusler alloy systems have provoked the greatest inter-est due to their large inverse MCEs [7–9].

To get a high DSM and a suitable magnetic transitiontemperature (TM), interstitial atoms such as B [10], H

1359-6462/$ - see front matter � 2013 Acta Materialia Inc. Published by Elhttp://dx.doi.org/10.1016/j.scriptamat.2013.11.009

⇑Corresponding author. Tel.: +86 0574 86685150; e-mail:[email protected]

[11] and C [12] have been investigated with regard to theirenhancement of MCE. Xuan et al. [10] studied the effectof interstitial B atom on the MCE of Ni–Mn–Sn alloys.The TM could be changed markedly just by adjustingthe amount of B, but the DSM was also reduced signifi-cantly when doped with excessive B. Mandal et al. [11]studied the effect of interstitial H atoms on the MCE ofLa–Fe–Si alloys. Though the TC could be changed mark-edly and the DSM could not be changed much, the thermalstability of the hydride deteriated. Chen et al. [12] investi-gated the effect of interstitial C atom on the MCE of La–Fe–Si alloys. They found that a certain amount of C canadjust the Curie temperature of the alloy; at the sametime, it did not reduce the DSM substantially. So far, therehave no reports on C doping in the Ni–Mn–Sn system,but it is expected that the DSM would not change a lot.

There are many reports on adjusting the martensitetransition temperature, enhancing the magnetic entropychange and reducing the hysteresis of the Ni–Mn–Snalloy [13–16]. However, little research has been carriedout on the machinability of the alloy, which is an addi-tional property for a magnetic cooling device. Feng et al.[17] found that the mechanical properties of Ni–Mn–In al-loys can be dramatically improved by adding Fe. It is thuspossible to enhance the Ni–Mn-based alloys’ mechanical

sevier Ltd. All rights reserved.

Page 2: Large magnetic entropy change and enhanced mechanical properties of Ni–Mn–Sn–C alloys

Figure 2. SEM images of Ni43Mn46Sn11Cx (x = 0, 2, 4, 8) alloys.

Y. Zhang et al. / Scripta Materialia 75 (2014) 26–29 27

strength when an ingredient with a high mechanicalstrength, such as a carbide, is added. Moreover, it is wellknown that carbides with high hardness and high meltingpoint can enhance the mechanical properties of steel [18].

In this paper, C was introduced into Ni–Mn–Sn alloyswith the expectation of gaining not only a relative highDSM arising from the interstitial C atom, but also a relativehigh compressive strength due to the appearance of a sec-ond, carbide phase by appropriate adjustment of C content.

Ingots of Ni43Mn46Sn11Cx (x = 0, 2, 4, 8), denoted as C0,C2, C4 and C8, respectively, were prepared by arc-meltingunder a high-purity argon atmosphere. The purities of allof the raw elements are better than 99.9%. The ingots werehomogenized by annealing in an evacuated sealed quartztube at 1173 K for 24 h and then quenched in water. Thecrystal structure analyses were carried out by X-ray diffrac-tion (XRD) using a Cu Ka radiation source at room temper-ature. The microstructure and composition were determinedby scanning electron microscopy (SEM) using aJSM-6700F microscope equipped for energy-dispersivespectrometry (EDS). The magnetic measurements were car-ried out using a superconducting quantum interference de-vice. The mechanical properties were ascertained using anInstron testing machine.

XRD patterns of the Ni43Mn46Sn11Cx (x = 0, 2, 4, 8)alloys are shown in Figure 1. All of the peaks correspondto the Heusler L21 cubic structure, which indicates thatthey are all austenitic phase and that the martensite tran-sition temperature TM is below room temperature. Fromthe enlarged XRD pattern in the inset of Figure 1, all ofthe (220) peaks of samples C2–C8 are shifted towards low-er angles compared to that of the C0 sample, which indi-cates an increase in lattice volume due to C atoms enteringinto the lattices. In contrast, compared with C2, the (220)peaks of C4 and C8 samples are shifted towards higher an-gles, indicating that the lattice volumes of C4 and C8 aresmaller than that of C2. This may be caused by the changeof Mn/Ni ratio induced by the second phase formed fromC and manganese with increasing C content.

In fact, the second phase has already appeared fromsamples C2 to C8, as confirmed by the SEM images inFigure 2. The peaks of the second phase were not ob-served in the XRD pattern because of its low content ex-cept for C8, which has an extra peak corresponding tothe carbide phase. Due to manganese loss induced bythe second phase in the matrix phase, there is a shrink-

Figure 1. Top: XRD patterns of Ni43Mn46Sn11Cx (x = 0, 2, 4, 8) alloysat room temperature. The star symbol indicates manganese carbides.The enlarged (220) peak is presented in the inset. Bottom: the crystalstructure change from Hg2CuTi-type to Cu2MnAl-type.

age in cell volume caused by the smaller atomic radius ofnickel (1.25 A) than that of manganese (1.79 A). Subse-quently, the XRD peaks of the C4 and C8 samples areshifted towards higher angles compared with that ofC2. This is also confirmed by comparing the intensitiesof the (111) and (200) peaks. The higher intensity ofthe (111) peak compared to the (200) peak of samplesC0, C2 and C4 indicates a highly ordered Hg2CuTi-typestructure [19]. The opposite result observed in C8suggests that its crystal structure has changed toCu2MnAl-type. This change in crystal structure fromHg2CuTi-type to Cu2MnAl-type is shown in the lowerpart of Figure 1. The great loss of manganese from sam-ple C8 results in a distortion of the crystal structurefrom the Hg2CuTi-type to the Cu2MnAl-type.

In order to confirm the existence of the second phaseand the evolution of the composition with C doping,SEM was carried out on all of the samples, as shownin Figure 2. For Ni43Mn46Sn11 without any C doping,there was only one uniform phase, as presented inFigure 2a. After C doping, a dark stripe-like secondphase appears and its volume fraction increases withincreasing C doping, as revealed in Figure 2b–d. EDSanalysis showed that the second phase was manganesecarbides.

The exact composition of the L21 phase was analyzedby EDS for all samples. The results are shown in Table 1.The interstitial C in the L21 phase increases slightly withincreasing C doping. Except for the content enteringinterstitial positions, the excessive C would combine withthe manganese to form islands of second phase beyond

Table 1. Compositions of the L21 phase for all samples determined byEDS analysis and the valence electron concentrations per atom, e/a,determined as the concentration-weighted sum of s, d and p electrons.

Ni Mn Sn C e/a

C0 42.40 45.53 12.06 7.91C2 42.33 45.05 11.90 2.71 7.92C4 44.66 43.91 12.65 2.79 7.95C8 48.32 42.99 13.75 2.95 7.99

Page 3: Large magnetic entropy change and enhanced mechanical properties of Ni–Mn–Sn–C alloys

Figure 3. Temperature dependence of magnetization for Ni43Mn46Sn11Cx (x = 0, 2, 4, 8) alloys under a magnetic field of 100 Oe on heating andcooling (a); isothermal magnetization curves for the Ni43Mn46Sn11C0 from 181 to 208 K (b) and Ni43Mn46Sn11C2 from 181 to 214 K (c); andtemperature dependence of DSM in magnetic fields of 1, 2 and 5 T for Ni43Mn46Sn11Cx (x = 0, 2, 4, 8) (d).

28 Y. Zhang et al. / Scripta Materialia 75 (2014) 26–29

the saturation concentration, thus the manganesecontent reduced with higher C doping, as shown inTable 1. Additionally, as shown in Figure 2c, the manga-nese carbides tend to segregate along the grain boundary.

The temperature dependence of magnetization duringheating and cooling for Ni43Mn46Sn11Cx (x = 0, 2, 4, 8)alloys in a low magnetic field of 100 Oe is shown inFigure 3a. The values of martensitic transition tempera-ture TM are 196, 197, 222 and 249 K, respectively.According to previous reports [20–22], valance electronconcentration (e/a) and cell volume are two main factorsaffecting the TM of Ni–Mn-based Heusler alloys. In gen-eral, the TM increases with increasing e/a, while it de-creases with increasing cell volume. In our researchsystem, the cell volume of sample C2 is larger than thatof C0 but smaller than those of C4 and C8, as can be seenfrom the XRD results. Furthermore, due to the manga-nese loss in the matrix phase, the value of e/a calculatedfrom the composition increases with increasing C con-tent, as shown in Table 1. Accordingly, the TM of C2 issimilar to that of C0 and lower than those of C4 andC8. On the whole, TM increases as C doping increases.Moreover, because of the appearance of the secondphase, the force of friction between the grains would bestronger after the martensitic phase transformation hasoccurred, thus leading to the wide temperature range ofphase transformation from 13 K for C0 to 25 K forC8. A large thermal hysteresis was enhanced by the forceof friction at the interphase during phase transformation[23]. However, there is no obvious change in the thermalhysteresis, which remains about 8 K with different C con-tents. This may due to the slower phase transition frommartensitic to austensitic phase with increasing Ccontent.

Figure 3b and c shows the isothermal magnetization(M–H) curves up to 50 kOe near the TM. From theM–H curves, it is obvious that C0 and C2 show typicalferromagnetic behavior above 202 K. The metamagneticbehavior between 190 and 199 K was due to the field-induced martensitic transition. Apparently, the increas-ing manner of magnetization around 196 K is muchsharper for C2 than that for C0. The difference in

magnetization appearing during the process of martens-itic transition is induced by C doping, and ultimately re-sulted in the larger magnetic entropy change of DSM forC2 than that for C0. The DSMs for Ni43Mn46Sn11Cx alloyswere calculated under magnetic field changes of 1, 2 and 5T according to isothermal magnetization curves by usingMaxwell relations, as shown in Figure 3d. The maximumvalues of DSM under a magnetic field change of 5 T are27.4, 34.6, 21.3 and 17.1 J kg�1 K�1 for C0, C2, C4 andC8, respectively. The field-induced martensitic transitionin Ni–Mn-based Heusler alloys is highly relevant to theexchange interaction between Mn atoms, which is sensi-tive to the distance between adjacent Mn atoms [24–26].Carbon atoms, with small atomic size, could occupy theinterstitial sites of the lattice, thus leading to the expan-sion of the lattice and modification of the Mn–Mn dis-tance. Moreover, excess C atoms could combine withmanganese to form a second phase. These two factors af-fect DSM in competition. As only a few C atoms are added,a maximum DSM could be obtained for the C2 sample be-cause most C atoms are in the interstitial position, whichtunes the Mn–Mn distance and affects the martensitictransition. For the C4 and C8 samples, the excess C atomsform more second phase, thus the DSM decreases withincreasing C content.

Since machinability of a magnetic refrigerant is an-other important property for its practical application,compressive strength testing was carried out on all al-loys. The compressive stress vs. strain of the C0, C2,C4 and C8 alloys are illustrated in Figure 4. The com-pressive strengths of the four alloys are 556, 731, 995and 1016 MPa, respectively. In order to find out themechanism of the increasing compressive strength afterC doping, SEM and EDS were used to analyze the C4sample, as shown in the inset of Figure 4. Apparently,the change of compressive strength can be attributed tothe dispersion strengthening mechanism. As the hollowsshow in the fracture surface of C4 in Figure 4 (a), secondphase manganese carbides tend to disperse around thegrain boundary of the austenite phase. The scatteredparticles act as obstacles for the movement of disloca-tion. The main strengthening effect can be described by

Page 4: Large magnetic entropy change and enhanced mechanical properties of Ni–Mn–Sn–C alloys

Figure 4. Compressive stress–strain curves of Ni43Mn46Sn11Cx (x = 0,2, 4, 8) alloys at room temperature. Inset (a) shows the SEM image ofthe compressive fracture surface of C4 alloy. Inset (b) shows the SEMimage of the fracture surface of carbide in C4 alloy.

Y. Zhang et al. / Scripta Materialia 75 (2014) 26–29 29

the Orowan mechanism [27]. Moreover, the manganesecarbide particle sheared by dislocation was also foundin the alloy shown in the enlarged fracture surface in Fig-ure 4 (b). Both the appearance of new interfacial energybrought by the dislocation cutting through the secondphases and the strain energy caused by different latticeconstants between the main phase and the second phasecontribute to the improvement in compressive strength.In addition, since the solubility of C was actually de-tected, solution strengthening may be another way to im-prove the compressive strength [28]. Thus, thecompressive strength increases with higher C doping.

In summary, the microstructure, magnetocaloric effectand mechanical properties of C-doped Ni–Mn–Sn alloyswere studied systematically in this work. With a moderatenumber of C atoms occupying the interstitial sites of latticeand modifying the distance between Mn atoms, the DSM

increases remarkably and reaches a maximum of34.6 J kg�1 K�1 at a field change of 5 T for Ni43Mn46

Sn11C2 alloy. Moreover, because of the enhanced strength-ening by dispersion of the second carbide phase, the com-pressive strength of the alloy was improved to a high valueof 1016 MPa for the Ni43Mn46Sn11C8 alloy. It is worth not-ing that the maximum DSM of Ni43Mn46Sn11C4 with acompressive strength of 995 MPa still maintains a high va-lue of 21.3 J kg�1 K�1 for a field change of 5 T. In conclu-sion, a magnetocaloric material with high magneticentropy change and high compressive strength, which isof high significance for industrialization, was obtained byadjusting the C content appropriately.

This work was supported by the Natural Sci-ence Foundation of Zhejiang Province OutstandingYouth Fund (Grant No. LR12E01001), the Natural Sci-ence Foundation of China Youth Fund (Grant No.51101168), the Natural Science Foundation of China(Grant No. 51371184), the Natural Science Foundationof Ningbo City (Grant No. 2012A610102), the Key Re-search Program of the Chinese Academy of Sciences(Grant No. KGCX2-EW-215, the Ningbo City Scientificand Technological Project (Grant No. 2012B81001, No.2011B82004) and the Scientific Research Foundation forthe Returned Overseas Chinese Scholars, Ministry of

Human Resources and Social Security of the People’sRepublic of China.

[1] O. Gutfleisch, M.A. Willard, E. Bruck, C.H. Chen, S.G.Sankar, J.P. Liu, Adv. Mater. 23 (2011) 821–842.

[2] J. Liu, P. Zhang, F. Dai, A. Yan, Scr. Mater. 69 (2013)485–488.

[3] V.K. Pecharsky, K. Gschneidner Jr, Phys. Rev. Lett. 78(1997) 4494.

[4] B.G. Shen, J.R. Sun, F.X. Hu, H.W. Zhang, Z.H. Cheng,Adv. Mater. 21 (2009) 4545–4564.

[5] O. Tegus, E. Bruck, K. Buschow, F. De Boer, Nature 415(2002) 150–152.

[6] V.D. Buchelnikov, V.V. Sokolovskiy, Phys. Met. Metal-logr. 112 (2012) 633–665.

[7] T. Krenke, E. Duman, M. Acet, E.F. Wassermann, X.Moya, L. Manosa, A. Planes, Nat. Mater. 4 (2005) 450–454.

[8] J. Liu, T. Gottschall, K.P. Skokov, J.D. Moore, O.Gutfleisch, Nat. Mater. 11 (2012) 620–626.

[9] J. Du, Q. Zheng, W.J. Ren, W.J. Feng, X.G. Liu, Z.D.Zhang, J. Phy. D: Appl. Phys. 40 (2007) 5523–5526.

[10] H.C. Xuan, D.H. Wang, C.L. Zhang, Z.D. Han, B.X.Gu, Y.W. Du, Appl. Phys. Lett. 92 (2008) 102503.

[11] K. Mandal, D. Pal, O. Gutfleisch, P. Kerschl, K.H.Muller, J. Appl. Phys. 102 (2007) 053906.

[12] Y.F. Chen, F. Wang, B.G. Shen, G. Wang, J.R. Sun, J.Appl. Phys. 93 (2003) 1323.

[13] T. Krenke, M. Acet, E. Wassermann, X. Moya, L.Manosa, A. Planes, Phys. Rev. B 72 (2005) 014412.

[14] V.V. Khovaylo, K.P. Skokov, O. Gutfleisch, H. Miki, T.Takagi, T. Kanomata, V.V. Koledov, V.G. Shavrov, G.Wang, E. Palacios, J. Bartolome, R. Burriel, Phys. Rev. B81 (2010) 214406.

[15] V. Basso, C.P. Sasso, K.P. Skokov, O. Gutfleisch, V.V.Khovaylo, Phys. Rev. B 85 (2012) 014430.

[16] P. Shamberger, F. Ohuchi, Phys. Rev. B 79 (2009) 144407.[17] Y. Feng, J.H. Sui, Z.Y. Gao, J. Zhang, W. Cai, Mater.

Sci. Eng. A 507 (2009) 174–178.[18] V. Shabashov, L. Korshunov, A. Mukoseev, V. Saga-

radze, A. Makarov, V. Pilyugin, S. Novikov, N. Vildano-va, Mater. Sci. Eng. A 346 (2003) 196–207.

[19] S. Dwevedi, J. Alloys Compd. 574 (2013) 188–190.[20] Z.D. Han, D.H. Wang, C.L. Zhang, H.C. Xuan, B.X.

Gu, Y.W. Du, Appl. Phys. Lett. 90 (2007) 042507.[21] H. Zheng, W. Wang, S. Xue, Q. Zhai, J. Frenzel, Z. Luo,

Acta Mater. 61 (2013) 4648–4656.[22] Z.D. Han, D.H. Wang, C.L. Zhang, H.C. Xuan, J.R.

Zhang, B.X. Gu, Y.W. Du, Mater. Sci. Eng. B 157 (2009)40–43.

[23] W.H. Wang, J.L. Chen, Z.H. Liu, G.H. Wu, W.S. Zhan,Phys. Rev. B 65 (2001) 012416.

[24] S.Y. Yu, Z.X. Cao, L. Ma, G.D. Liu, J.L. Chen, G.H. Wu,B. Zhang, X.X. Zhang, Appl. Phys. Lett. 91 (2007) 102507.

[25] J. Kubler, A. William, C. Sommers, Phys. Rev. B 28(1983) 1745–1755.

[26] J. Enkovaara, O. Heczko, A. Ayuela, R. Nieminen, Phys.Rev. B 67 (2003) 212405.

[27] J.F. Nie, Scr. Mater. 48 (2003) 1009–1015.[28] I. Matsui, T. Uesugi, Y. Takigawa, K. Higashi, Acta

Mater. 61 (2013) 3360–3369.