Microcosmic mechanism of carbon influencing on NiTiNb9 alloy

Journal of Alloys and Compounds 542 (2012) 170–176

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Microcosmic mechanism of carbon influencing on NiTiNb9 alloy G.F. Li a,b,⇑, S.Q. Lu a, X.J. Dong a, P. Peng b a b

School of Material Science and Engineering, Nanchang Hangkong University, Jiangxi 330063, China School of Materials Science and Engineering, Hunan University, Hunan 410082, China

a r t i c l e

i n f o

Article history: Received 11 January 2012 Accepted 8 July 2012 Available online 20 July 2012 Keywords: NiTiNb9 alloy Carbon solution First principles calculation Electron density Atom diffusivity

a b s t r a c t The microcosmic mechanism, by which the C impurity decreases the Ms and fracture toughness, remains mysterious at present. Using first-principles pseudo-potential plane wave method, the formation enthalpy DH, binding energy DE, electronic structure and diffusivity of the C element in NiTiNb9 shape memory alloy have been systematically calculated and analyzed in the thermodynamic and kinetic processes. The results show that the addition of C trends to compose carbonization ‘‘cluster’’ in NiTi matrix phase, which not only can decrease the Ms of alloy by enhancing the ratio Ni/Ti, but also it can slack down the ductility by its special ‘‘jujube nut ’’ system. Otherwise, because of the unfilled s orbits, the Nb element can enhance the formation ability and diffusivity of carbonization ‘‘cluster’’ structure, and promote the impact of the C element to the shape memory effect and mechanics performance in NiTiNb alloy. Thus, our findings open an avenue for detailed and comprehensive studies of alloying shape memory alloy. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction Because of the special shape memory effect and super-elasticity, shape memory alloys have attracted much attention [1,2]. However, during their casting process, some impurities, i.e., oxygen, carbon, can not be filtrated because of the vacuum limits of furnace and the use of the graphite crucible, obviously affecting the performance of such functional materials [3–8]. Previous researches reported that the C has two impacts on NiTi shape memory alloy. Firstly, the C could form a petrous TiC precipitate in the NiTi matrix, which increases the embrittlement of NiTi alloy and decreases its ductility [3]. Secondly, in virtue of the precipitated phase TiC to take some Ti atoms, the ratio Ni/Ti is rising by which the martensite phase transformation temperature (Ms) is reducing immediately [4]. Considering the obvious impact from C element, researchers have studied deeply and widely on the influence by C and its derivatives [5–9]. For example, in Fe–Mn–Si–Cr–Nb–C shape memory alloy, there will only separate out NbC precipitate [10] without any other, but the microcosmic mechanism still remains intangibly. In recent years, NiTiNb9 shape memory alloy has attracted a lot of attention for their remarkable transformation hysteresis, and has thus been used in pipe joints and similar applications [11,12]. Thereby researches are mainly focused on its recovery stress, transformation hysteresis, recovery strain under different prestrain conditions [13], such as temperature, prestrain, ⇑ Corresponding author at: School of Material Science and Engineering, Nanchang Hangkong University, Jiangxi 330063, China. Tel./fax: +86 791 86453203. E-mail address: [email protected] (G.F. Li). 0925-8388/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2012.07.043

and heating temperature [14]. The results show that there is a characteristic deformation temperature (MS + 30 °C) and critical deformation strain (16%) for NiTiNb9. In such prestrain conditions, the transformation hysteresis and recovery stress of NiTiNb9 alloy can be kept in an upper level, which is a good substituting material to NiTiFe shape memory alloy [15]. However, the effect of impurity to NiTiNb9 alloy is only focused on oxidation resistance at present [16], few reports about the impact from C solution, indeed, which is the most vital component affecting the mechanical performance of shape memory alloy [3–10]. Hence, based on first principles calculation [17], this paper systematically scrutinizes the formation and diffusion mechanism of C element to reveal the alloying methods in NiTiNb9 alloy. 2. Calculation models and method NiTi unit cell is B2 crystal structure [18], and space group is Pm3m. NiTi B2 crystal structure can be treated as two simple cubes a and b interleaving each other, as Fig. 1(a), therein to Nb is dissolved in NiTi matrix phase by substituting the Ti elements [19]. In order to eliminate the mutual effect between Nb–Nb and C–C element, we construct a 3  3  3 supercell model in structural relaxation simulation. Followed by the C radius, 0.7 Å, the C element can only resolve in the octahedral interstices of NiTiNb alloy, e.g., NiTi matrix phase (shown in Fig. 1(b)), in addition the C atom can be the nearest neighbor (as in Fig. 1(c)) or the next-nearest-neighbor (as in Fig. 1(d)) to Nb in NiTi(Nb) phase [19]. All of these point defect models are relaxed as the following process: A first-principles pseudopotential plane-wave method, based on density functional theory, is used in this work [17,20]. Ultrasoft pseudopotentials in reciprocal space with the exchange–correlation energy represented by a local density approximation (LDA) [21] and improved by Cepeley–Alder [22] are adopted for all elements in our models. In our calculation, the cut-off energy of atomic wave functions (PWs), Ecut, is set at 300 eV. A finite basis set correction [23] and the Pulay scheme of density mixing [24] are

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Ni Site-1 Ti

Nb

Site-2

C

(b)

(a) Site-3

Site-5

Site-4

Site-6

(c)

(d)

Fig. 1. Carbon impurity’s models of NiTi and NiTi(Nb) (a) NiTi matrix phase (b) C occupying tetrahedron interstice of NiTi (c) C being the nearest neighbor to Nb in the octahedron interstice of NiTi(Nb) (d) C being the next nearest neighbor to Nb in the octahedron interstice of NiTi(Nb). applied for evaluation of energy and stress. All atomic positions in the supercell with and without C-doping have been relaxed according to the total energy and force using the BFGS scheme [25], based on the cell optimization criterion (RMS force of 0.05 eV/Å, stress of 0.1 GPa, and displacement of 0.002 Å). The calculation of total energy and electronic structure is followed by cell optimization with SCF tolerance of 1  105 eV under LDA Cepeley–Alder potential [22].

Table 2 The lattice constant (a), formation enthalpy (DH), bulk modulus (B) of Ni.

3. Testing potential function In such tests, the crystal lattice (a), formation enthalpy (DH), and bulk module (B) of NiTi crystal and Ni crystal have been calculated and listed in Tables 1 and 2. Compared with previous experiments [26,27] and calculations [28–31], the calculated crystal lattice constant in this paper is very close to previous results, although there are some differences in formation enthalpy and bulk module. This indicates present calculation sets and method are appropriate for investigating the electronic structures of NiTiNb alloy. 4. Results and discussion 4.1. Binding energy and formation enthalpy In order to scrutinize the solution ability of C into NiTiNb alloy, the formation enthalpy (DH) and binding energy (DE) of six NiTi(Nb) point defect models have been systematically calculated. As well known, the formation enthalpy DH refers to the energy of a compound composed from several simple substances. Therefore, the smaller the negative DH is, the more easily the compound composed. The binding energy DE is representative to the work of a crystal decomposed into atoms, which denotes the stability of an alloy respectively. Herein, the DH and DE of several C solution models (Fig. 1(b–d)) have been calculated as following equation [32]: Nil Timn ðNbn Þ l Timn ðNbn ;CÞ DHC ¼ ENi  Esolid solid   1 Ni Nil Timn ðNbn ;CÞ Nb C Esolid DE ¼  lEgas  mETi gas  nEgas  Egas lþmþ1

ð1Þ ð2Þ

Structural Parameters

This work

Exp. [27]

LDA Ref. [30]

LSDA Ref. [31]

a (Å) DH (eV/atom) B (MPa)

3.591 4.506 2.652

3.528 4.44 1.86

3.553 3.900 2.130

– 4.180 2.500

where l, m and n represent the number of Ni, Ti, Nb atoms in NilTimn(Nbn,C) crystal respectively. In this paper, we consider only one Nb atom substituting a Ti atom in super cell models for the first Ni Ti

l mn step as in Fig. 1. Esolid

ðNbn ;CÞ

, ENi27 Ti27 ; ENi27 Ti26 Nb denote the total en-

ergy of NilTim–n(Nbn,C) phase, NiTi matrix phase and NiTi(Nb) phase respectively, thereinto ENi27 Ti27 equals to 79675.847 eV and Ti Nb C ENi27 Ti26 Nb equals to 79623.232 eV. ENi gas ; Egas ; Egas and Egas are the energy of the gaseous atom Ni, Ti, Nb and C respectively. Before optimizing gaseous atom, we construct a 10  10  10 (Å3) vacuum box and put a single atom, such as Ni, Ti, Nb, C, in the center of the box to relax to get its global energy minimum. The results exhibit as Ti Nb ENi gas = 1341.487 eV, Egas = 1594.300 eV, Egas = 1538.946 eV and ECgas = 144.966 eV, respectively in Table 3. Table 3 indicates that the smallest formation enthalpy reaction (DH = 2.540 eV) is the C in the octahedral structure of Ti4Ni1Nb1 components in NiTi(Nb) phase (being Site-4 model in Fig. 1(c)), which means such a kind of C solution is the most easily reacting. The next is as the Site-6 model (DH = 2.359 eV) and Site-2 model (DH = 2.018 eV), which is constituted by Ti4Ni2 format obviously. On the contrary, the maximal formation enthalpy is being Site-1 model (DH = 0.605 eV) and Site-3 model (DH = 0.418 eV), which is composed by Ni4Ti2 in form. From the difference of formation enthalpy for six octahedral models, the C tends to solubilize in the octahedral interstices which have more Ti atoms, i.e., Site-2, Site-4, Site-6, than which have more Ni atoms, i.e., Site-1, Site-3, Site-5. That is to say, the impurity induced by C element mainly interacts with Ti atoms instead of Ni atoms. Furthermore, the substitutional solution of Nb element can

Table 1 The lattice constant (a), formation enthalpy (DH), bulk modulus (B) of NiTi. Structure parameters

This work

Exp. [26]

Tan et al. [28]

Borgia et al. [29]

a (Å) DH (eV/atom) B (MPa)

3.033 0.632 0.812

3.018 – –

3.015 0.601 –

2.998 – –

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Table 3 The total energy E, formation enthalpy DH, binding energy DE of C impurity in NiTi(Nb). Model

Site

Etotal (eV)

DH (eV)

DE (eV/atom)

NiTi

Site-1 Site-2 Site-3 Site-4 Site-5 Site-6

79829.811 79832.434 79778.219 79780.340 79778.981 79780.159

0.605 2.018 0.418 2.540 1.180 2.359

7.611 7.658 7.686 7.724 7.700 7.721

NiTi(Nb) (nearest neighbor) NiTi (next nearest neighbor)

improve the C solubilizing in NiTi matrix phase in some ways, e.g. |DHSite-6| > |DHSite-2|, |DHSite-5| > |DHSite-1| in Table 3 and Fig. 1. From the perspective of binding energy DE, it also shows that the most stable structure is the solution models of Site-4 (DE = 7.724 eV) and Site-6 (DE = 7.721 eV), which are mainly occupied by Ti element too. Hence, it can be postulated that the covalent bonding between C and Ti can decrease the total energy of the alloy system and enhance their stability. The precipitate in NiTi alloy is somewhere TiC particles unsuspiciously in experiment [3,4]. 4.2. Mulliken charge and population analysis In order to qualitatively evaluate the interaction between C element and Ni, Ti, Nb elements, this paper further investigates the covalent bonding between C and its nearest-neighbor Ni, Ti, Nb atoms by using Mulliken’s population analysis method. Mulliken’s charge Q(A) of A atom and a bond overlap population QA–B between A and B atoms are defined as follows [33]:

Q ðAÞ ¼

A X A X X wk Plv ðkÞSlv ðkÞ

Q AB ¼

ð3Þ

v

l

k

A X A X X wk 2Plv ðkÞSlv ðkÞ k

l

ð4Þ

v

where Plv ðkÞ and Slv ðkÞ are the density matrix and the overlap matrix, respectively. wk is the weight associated with the calculated Kpoints in Brillouin zone. Usually, the magnitude and sign of Q(A) characterize the ionicity of A atom in the supercell, and QA–B can be used to approximately measure the average covalent bonding strength between A and B atoms. The results are shown in Table 4. Table 4 shows that C and Ni element exhibit electronegativity, and Ti element is electropositivity from Mulliken charge calculation. By carefully analyzing, it can be found that C element gains more charges in the octahedral solution models which have more Ti components (such as Site-2, Site-4, Site-6) than the others which have more Ni components (such as Site-1, Site-3, Site-5)), i.e., the Q(C) in the Site-2 model (0.75e) is larger than that in Site-1 (0.68e), and the Q(C) in the Site-4 model (0.73e) is also larger than that in Site-3 (0.68e) too. From the periodic table of chemical elements, it is known that the C is the metalloid elements, which can attract more free electrons to form the covalent bond from neighbor metal elements. That is to say, the C solubilizing

in the octahedral interstices of NiTiNb alloy can localize more electrons from its nearest neighbor Ti or Nb atoms. Ulteriorly deducing, such localized strengthening effect for C element should act as a ‘‘cluster’’ in matrix phase, which may weaken the deformation ability of such material, especially the plastic deformation ability. Next, we will reveal the electronic character of carbonization ‘‘cluster’’ and the micromechanism of its influence on the mechanical property of NiTiNb alloy. Moreover, the Mulliken population for C impurity in NiTi(Nb) alloy has been calculated deeply. From above Mulliken charge analysis, it can be concluded that the carbonization ‘‘cluster’’ will localize the free electrons to form C–Ni and C–Ti covalent bond, and then slack down the next nearest-neighbor Ni–Ti metal bond. Table 4 shows that the Ni–Ti bonds QNi–Ti is reducing from QNi– Ti = 0.22 in NiTi crystal to 0.04 or 0.10 in Site-1 or Site-2 models respectively, the same as the other four C impurity models (Site3–Site-6 models in Fig. 1), which means the C can impact the next nearest-neighbor bonds or further. However, compared to the effect of C in NiTi(Nb) phase (as shown in Site-3–Site-6) with NiTi matrix phase (as shown in Site-1 or Site-2), because of the difference from substituting Ti by Nb atom, the Ni–Ti bonds QNi–Ti in Site-4 or Site-6 model in NiTi(Nb) phase is smaller than that in the Site-2 model in NiTi matrix phase, as well as the QNi–Ti in Site-3 or Site-5 model is smaller than that in the Site-1 model. In a word, the QNi–Ti is degrading to 0.1 in C solution phase from 0.22 in NiTi matrix phase, and new chemical bond QC–M (M = Ti, Ni, Nb) is appearing. Examining the effect from the electron’s distribution profile, the chemical bond QC–M (M = Ti, Ni, Nb) is pulling electrons to center from QNi–Ti on the surface of octahedral interstice. Thus, it can infer that: on one side, the Nb solution can strengthen the localizing electron effect of carbonization ‘‘cluster’’ and promote them emerging; on the other hand, because of strong covalent bond QC–M (M = Ti, Ni, Nb) in the center and the weak metal bond QNi–Ti on the surface of carbonization ‘‘cluster’’, such special structure looks like a ‘‘sweet jujube ’’ with a hard ‘‘nut’’, which could intrinsically depress the ductility and plastic deformation performance of NiTiNb or NiTi alloy [3,4,34]. 4.3. Density of state and electron density difference In order to further reveal the bonding character of C impurity in NiTiNb alloy, especially to the Ni–Ti bonds on the surface of carbonization ‘‘cluster’’ structure, the average partial electron density of states (PDOS) of Ni–Ti bonds and electron density difference (EDD) are analyzed and compared in Fig. 2 and Fig. 3. It is well known the valence electrons of Ti is in 3d24s2, Ni is in 3d84s2, Nb is in 4d45s1, and C is in 2s22p2 respectively. In the NiTi matrix phase, the Ni-Ti metallic bonds are primarily formed by d electrons, as in Fig. 2(a). Along with the solution of C impurity, the Ni–Ti bonds are changed as following: First, a new bonding peak appears near 11 eV level (as showed in Fig. 2(b–g)) compared with Ni–Ti PDOS in Fig. 2(a), even though the position of such new bonding peaks have some difference, i.e., the energy of the new bonding peak in Site-1, Site-3 and Site-5, which have more

Table 4 The bond strength QA-B and Mulliken charge QA of C impurity in NiTi(Nb). Model

Site

QC–Ni

QC–Ti

QC–Nb

QNi–Ti

Q(C)

Q(Ti)

Q(Ni)

Q(Nb)

NiTi NiTi

Matrix phase Site-1 Site-2 Site-3 Site-4 Site-5 Site-6

– 0.42 0.37 0.42 0.33 0.44 0.39

– 0.33 0.34 0.31 0.32 0.29 0.34

– – – 0.35 0.35 – –

0.22 0.04 0.10 0.01 0.08 0.02 0.07

– 0.68 0.75 0.68 0.73 0.69 0.74

0.29 0.37 0.44 0.40 0.46 0.40 0.44

0.29 0.10 0.23 0.14 0.23 0.13 0.24

– – – 0.20 0.17 0.09 0.08

NiTi(Nb) (nearest neighbor) NiTi (next-nearst-neighbor)

G.F. Li et al. / Journal of Alloys and Compounds 542 (2012) 170–176

6

(a)

Site3

Site1

(b)

Site4

(e)

Site2

(c)

Site5

(f)

Site6

(g)

EF

NiTi matrix Phase

EF

(d)

DOS(electrons/eV)

3

0 6

3

0 6

3

0 6

s p d sum

3

0 -12

-8

-4

0

-12

-8

-4

0

Energy(eV) Fig. 2. The PDOS of Ni–Ti bonds in NiTi crystal and that in C impurity in NiTiNb alloy. (a) NiTi matrix phase (b and c) C occupying the tetrahedron interstice of NiTi (d and e) C being the nearest neighbor to Nb in the octahedron interstice of NiTi(Nb) (f and g) C being the next nearest neighbor to Nb in the octahedron interstice of NiTi(Nb).

Ni components obviously, is lower than that in Site-2, Site-4 and Site-6, which have more Ti components. And the new bonding peak is mainly erecting from the interaction between p-orbital electrons of C and d-orbital electrons of Ni; Secondly, the energy gap, which emerges at 1 eV in NiTi matrix phase (as pointed by an arrow in Fig. 2(a)), is narrowing down slowly, and so much as some pseudo energy gaps appear in Site-1, Site-2, Site-3 and Site-5 (as shown in Fig. 2(b–f)) respectively; Thirdly, the main bonding peak below Fermi level (standing at 3 eV energy level) in NiTi matrix phase, is concentrative, higher, and narrow breadth. However, as C solubilizing, it is forced to be declining and broadening, which is proven that the C solution indeed weakens the bonds of next nearest-neighbor Ni–Ti obviously. Furthermore, the electronic density differences of NiTi matrix phase and NiTiNb alloy have been calculated meticulously in Fig. 3. Fig. 3(a) reveals a cross key type bond between Ni and Ti, indicating their major bonding electron is in d orbital electrons. When the C is intermingled, a butterfly p bond appears obviously around Ti (as showed arrows r s in Fig. 3(b–g)), which means a strong covalent bond between C and Ti atoms in NiTi matrix phase. Making further investigation, because of the C–Ti and C–Ni approaches/interactions, the electrons surrounding C are localized to form ‘‘cluster’’ structure (as showed arrows t in Fig. 3(b)), which is testified by experiments in NiTi alloy [8]. Analyzing the EDD around carbonization ‘‘cluster’’, it reveals a strong bonding between C–Ti and C–Ni in the center zone, although there is a faint bonding in the next nearest-neighbor Ni–Ti bonds outside, which looks like a ‘‘jujube’’ nut structure. These results are consisting with previous Mulliken analysis in Part 4.2. Further analysis on C solution in NiTiNb alloy (shown in Fig. 3(d–g)), it can be divided into two situations, i.e., the C is in the nearest-neighbor (as shown in Fig. 3(d and e)) or the nextnearest-neighbor site to Nb element (as shown in Fig. 3(f and g)). When C atom is in the nearest neighbor site to Nb (as in Fig3(d and e)), there exists a strong covalent bond (QC–Nb = 0.35 in

173

Table 3) for Nb–C, whose Mulliken population is even larger than that of Ti–C covalent bond (QC–Ti = 0.31 in Table 3). Furthermore, the electron densities between Nb and C in Ni4TiNb octahedron exhibit some nodes clearly, which illuminates some p bonds appearing between C and Nb atom (as showed arrows r, s in Fig. 3(d)). However for Ti3Ni2Nb octahedron, no bond node between C-Nb atoms, which means there is an r bond between C and Nb atoms (as showed arrows r, s in Fig. 3(e)). Such phenomena indicates Nb element has partial nonmetal character in NiTiNb alloy (as showed arrows s in Fig. 3(d–g)), which may be related to the unfilled s orbital electrons. Moreover, an obvious strong bonding area ‘‘cluster’’ was also formed around C (showed by arrow t in Fig. 3(d)) just as TiC in NiTi matrix phase in Fig. 3(b), meaning the C can form ‘‘jujube’’ nut structure in NiTiNb alloy too. So in experiments [35] there appear (Ti,Nb)2Ni second phase particles to depress the plastic performance of NiTiNb alloy. Similarly, the effect of Nb is homologous when the C in the next nearest-neighbor Nb site (as showed in Fig. 3(f and g)). So now deriving from the difference of electron density in the center and the surface of carbonization ‘‘cluster’’, when the NiTiNb alloy is deformed by pressure or pull, it will promote small crack around the TiC second phase particle because of such as ‘‘jujube’’ nut structure, whose surface bonds are so weak and the center’s are soy strong by C–X (X = Ni, Ti, Nb) bonds oppositely, without doubt the mechanical performance of NiTi alloy is declining in engineering application [3,35]. Otherwise, the influence of TiC ‘‘cluster’’ in NiTi alloy has not been cleared up in NiTiNb alloy, by contraries the ‘‘jujube’’ nut trends to spread widely by Nb furtherance, where its valence electrons become more itinerant and participate in bonding as the atomic overlap increasing. 4.4. Carbon transference Owing to the unfilled s orbital electrons, the Nb element has the ability to promote the C influence on the mechanical performance and martensite phase transformation temperature of NiTiNb alloy by the static electronic structure analyzing. Furthermore, in this paper, the diffusivity of C in NiTiNb alloy has been carried out by a linear synchronous transit (LST) method [36]. From the solution models in Fig. 1, the shortest, most efficient diffusing way for C from Ni4Ti2 octahedron (shown in Fig. 4(a) by full curve model) to Ti4Ni2 octahedron (shown in Fig. 4(a) by dotted line model) is indicated by arrow r ? s in Fig. 4(a), the same as the other diffusing process of C solution, i.e., Site1 ? Site2 in Fig. 4(b), Site3? Site4 in Fig. 4(c), and Site5 ? Site6 in Fig. 4(d). The results are shown in Fig. 4. Fig. 4(b–d) shows that some energy barriers need to be overcome for C diffusing, meaning the diffusivity of C impurity is the endothermic reaction. Thereinto, the energy barrier for the diffusion of C atoms in NiTi matrix phase (DE1?2 = 0.620 eV) is larger than the others (DE3?4 = 0.406 eV and DE5?6 = 0.446 eV). Ulterior analyzing the transition state structure (TSs in Fig. 4(b–d)), it is found that the energy barrier is originated from the Ni-Ni bond broken, such as the Ni–Ni bond is extending from 2.741 Å in the Site-1 model to 3.004 Å in the Site-2 model as in Fig. 4(b), similarly to the others as Site3 ? Site4 and Site5 ? Site6 diffusion process. Comparing carefully Fig. 4(b) with Fig. 4(d), although there have similar TS structures, the energy barriers are different obviously, where the DE1?2 = 0.620 eV in Fig. 4(b) is larger than the DE5?6 = 0.446 eV. Probing into what making the difference between them in components? We can see the only hetero-configuration is there existing Nb solution in the Fig. 4(d). Forwardly contrasting with them, it can be seen that the energy barrier in the octahedron models with Nb solution (DE3?4 = 0.406 eV, DE5?6 = 0.446 eV) is smaller than that without Nb solution in Fig. 4(a) (DE1?2 = 0.620 eV). All indications point to that the Nb element not only extend the carbonization ‘‘cluster’’ region by its

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Fig. 3. The electron density difference of NiTi matrix phase and that of C impurity in NiTiNb alloy. (a) NiTi matrix phase (b and c) C occupying the tetrahedron interstice of NiTi (d and e) C being the nearest neighbor to Nb in the octahedron interstice of NiTi(Nb) (f and g) C being the next nearest neighbor to Nb in the octahedron interstice of NiTi(Nb).

metalloid characters, but also reduce the energy barriers of C diffusion, enhancing the diffusivity of the C in NiTiNb alloy. That is to say, the more the Nb contents in NiTiNbx alloy, the more influence for C elements on the mechanical performance and Martensite phase temperature [37]. When the content of Nb and C is increasing together, the second phase clustering will precipitate more, then the mechanical performance, especially the ductility of alloy,

will be declined, and the Martensite phase temperature (Ms) will be reduced absolutely [37]. So the researchers want to improve the performance of NiTiNb shape memory alloy by alloying Mo [38], Cr [39,40], whose electronic character is similar to Nb element. Combining foregoing observations, we now may present the microcosmic mechanism for C solution in NiTiNb alloy. The

G.F. Li et al. / Journal of Alloys and Compounds 542 (2012) 170–176

175

Fig. 4. The diffusion pathway of a single C solution atom in NiTiNb alloy. (a) C diffusion in Ni4Ti2 ? Ti4Ni2 (b) C diffusion in NiTi matrix phase (c) C diffusion in NiTi(Nb) (d) the diffusion for C being the next nearest neighbor site.

Carbon’s favorable solution site is in the octahedral interstice structures which have more Ti components, such as Ti4Ni2 group, resulting in an obviously strong bond region as ‘‘cluster’’ structure. Therein to for such as carbonization ‘‘cluster’’ structure in NiTiNb alloy, there exists strong interacting between C–Ti, C–Ni, or C–Nb bonds in the center. However, the Ni–Ti bonds outside are faint oppositely. Then we can presume that when such alloy is deformed by pressure or pull, it is easy to crack around the electronic ‘‘cluster’’ from the weak bonding area, which is the microcosmic mechanism to explain why C compound declines the mechanical performance of shape memory alloy obviously. On the other hand, because of the C element being apt to bonding with Ti, more Ti atoms will be then localized and losing activation energy than the Ni atoms, obviously resulting in the ratio of Ni/Ti adding silently. It is well known the larger the ratios of Ni/Ti are, the lower the temperature of martensite phase transformation (Ms) is. So the intrinsic electron mechanism for C influencing the shape memory effect has been unveiled detailedly. So such simulation method has great significance to design alloy components by revealing the thermodynamic and kinetics process of compound. 5. Conclusions (1) The C element prefers to solubilize in the octahedral interstice which with more Ti atoms instead of Ni atoms. Therefore, the lowest binding energy and formation enthalpy structure is the Ti3Ni2NbC octahedron; meanly such solution of C is the most stable reaction.

(2) Due to the unfilled s orbital electron, the Nb element in NiTiNb has some metalloid chemical character. In the process of C solubilizing in the octahedral interstice which have more Ti atoms, there appears carbonization ‘‘cluster’’ strong bonding region. Such ‘‘jujube’’ nut structure has violent electron interaction in the center. However, the Ni–Ti bonds outside is faint oppositely. Then, it is easy to crack around the carbonization ‘‘cluster’’ in the deformation of NiTi or NiTiNb alloy, resulting in the decline on mechanical performance of shape memory alloy. On the other hand, because of C loving bonding with Ti, more Ti atoms will be localized than the Ni atoms, obviously resulting in the ratio of Ti/Ni adding silently and reducing the temperature of martensite phase transformation (Ms) of NiTi or NiTiNb alloys. (3) The dynamics simulation shows that the Nb element can depress the strength of Ni–Ti bonds in the nearest-neighbor or the next nearest-neighbor sites. So it then decreases the energy barrier of C diffusing in NiTi(Nb) supercell structures than that in NiTi matrix phase, and enhances the diffusivity of C in NiTiNb alloy, meanly the Nb element can improve the influence of C element on the mechanical performance and shape memory effect.

Acknowledgements We would like to thank our anonymous reviewers for extremely helpful comments. We acknowledge the support from the National

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Natural Science Foundation of China (Grant No. 50771044), the Doctor Startup Foundation of Nanchang Hangkong University (EA201001034) and Youth Science Foundation of Jiangxi Educational Committee (GJJ11157). References [1] A. Mehmet, Nat. Mater. 8 (2009) 854–855. [2] M. Lluís, G.A. David, P. Antoni, B. Erell, B. Maria, J.L. Tamarit, A. Seda, A. Mehmet, Nat. Mater. 9 (2010) 478–481. [3] J. Otubo, O.D. Rigo, A.A. Coelho, C.M. Neto, P.R. Mei, Mater. Sci. Eng. A 481–482 (2008) 639–642. [4] J. Otubo, O.D. Rigo, C.M. Neto, P.R. Mei, Mater. Sci. Eng. A 438–440 (2006) 679–682. [5] B.C. Bayer, S. Sanjabi, C. Baehtz, C.T. Wirth, S. Esconjauregui, R.S. Weatherup, Z.H. Barber, S. Hofmann, J. Thin Solid Films 519 (2011) 6126–6129. [6] K.N. Nigussa, J.A. Støvneng, Comput. Phys. Commun. 182 (2011) 1979–1983. [7] Y.H. Wen, M. Yan, N. Li, Scr. Mater. 50 (2004) 441–444. [8] V.V. Bliznuk, V.G. Gavriljuk, B.D. Shanina, A.A. Konchits, S.P. Kolesnik, Acta Mater. 51 (2003) 6095–6103. [9] E.D. Moor, C. Föjer, J. Penning, A.J. Clarke, J.G. Sper, Phys. Rev. B 82 (2010) 104210(1)–104210(5). [10] W.B. Liu, Y.H. Wen, N. Li, S.Z. Yang, J. Alloys Compd. 472 (2009) 591–594. [11] K. Uchida, N. Shigenaka, T. Sakuma, Y. Sutou, K. Yamauchi, Mater. Trans. 49 (2008) 1650–1655. [12] X. M He, L.J. Rong, D.S. Yan, Y.Y. Li, Acta Metall. Sinica 40 (2004) 721–725. [13] C.S. Zhang, W. Cai, L.C. Zhao, Acta Metal. Sinica 4 (1991) 436–440. [14] W. Cai, C.S. Zhang, L.C. Zhao, J. Mater. Sci. Technol. 10 (1994) 27–30. [15] V.B. Krishnan, R.M. Manjeri, B. Clausen, Mater. Sci. Eng. A 481-482 (2008) 3–10. [16] X.Q. Zhao, J. Xu, L. Tang, S.K. Gong, Intermetallics 15 (2007) 1105–1115. [17] C.L. Tan, X.H. Tian, W. Cai, Physica B 404 (2009) 3662–3665. [18] L.C. Zhao, T.W. Duerig, C.M. Wayman, in: Proc. Int. Mtg. On Adv. Mates., Tokyo, 9 (1989) 171–76.

[19] X.M. He, L.J. Rong, D.S. Yan, Y.Y. Li, Mater. Sci. Eng. A 371 (2004) 193–197. [20] M.D. Segall, J.D. Lindan, M.J. Probert, J. Phys. Condens. Matter 14 (2002) 2717– 2744. [21] S.H. Vosko, L. Wilk, M. Nusair, Can. J. Phys. 58 (1980) 1200–1210. [22] D. Vanderbilt, Phys. Rev. B 41 (1990) 7892–7895. [23] G.P. Francis, M.C. Payne, J. Phys. Condens. Matter 2 (1990) 4395–4404. [24] P. Pulay, Theory Mol. Phys. 17 (1969) 197–208. [25] T.H. Fischer, J. Phys. Chem. 96 (1992) 9768–9774. [26] Q. Mercier, K.N. Melton, G. Gremaud, J. Appl. Phys. 51 (1980) 1833–1837. [27] C. Kittel, Introduction to Solid State Physics, sixth ed., Wiley, New York, 1986. 55–67. [28] C.L. Tan, X.H. Tian, W. Cai, Phys. B: Condens. Matter 404 (2009) 3662–3668. [29] C. Borgia, S. Olliges, M. Dietiker, G. Pigozzi, R. Splenak, Thin Solid Films 518 (2009) 1879–1885. [30] P. Peng, D.W. Zhou, J.S. Liu, R. Yang, Z.Q. Hu, Mater. Sci. Eng. A 416 (2006) 169– 175. [31] T.C. Leung, C.T. Chan, B.N. Harmon, Phys. Rev. B 144 (1991) 2923–2927. [32] N.I. Medvedeva, Yu.N. Gornostyrev, D.L. Novikov, O.N. Mryasov, A.J. Freeman, Acta Mater. 46 (1998) 3433–3442. [33] M.D. Segall, R. Shah, C.J. Pickard, M.C. Payne, Phys. Rev. B 54 (1996) 16317– 16320. [34] C.S. Zhang, Y.Q. Wang, W. Cai, Mater. Chem. Phys. 28 (1991) 43–47. [35] L.S. Castleman, S.M. Mofzkin, F.P. Alicandri, V.L. Bonawit, J. Biomed. Mater. Res. 10 (1976) 695–731. [36] T.A. Halgren, W.N. Lipscomb, Chem. Phys. Lett. 49 (1977) 225–232. [37] C.S. Zhang, W. Cai, Y.Q. Wang, L.C. Zhao, Chin. J. Nonferrous Met. 4 (1994) 82– 85. [38] Y. Chen, H.C. Jiang, S.W. Liu, L.J. Rong, X.Q. Zhao, Mater. Sci. Eng. A 512 (2009) 26–31. [39] N.N. Sia, Y.C. Jeom, Acta Mater. 53 (2005) 449–454. [40] S.F. Hsieh, S.L. Chen, H.C. Lin, M.H. Lin, J.H. Huang, M.C. Lin, J. Alloys Compd. 494 (2010) 155–160.