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The effect of M23C6 carbides on the formation of grain boundary serrations in a wrought Ni-based superalloy
Materials Science and Engineering A 536 (2012) 37–44
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The effect of M23 C6 carbides on the formation of grain boundary serrations in a wrought Ni-based superalloy Li Jiang, Rui Hu ∗ , Hongchao Kou, Jinshan Li, Guanghai Bai, Hengzhi Fu State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an 710072, China
a r t i c l e
i n f o
Article history: Received 4 June 2011 Received in revised form 31 October 2011 Accepted 21 November 2011 Available online 1 December 2011 Keywords: Grain boundary serrations M23 C6 Haynes 230 alloy Diffusion
a b s t r a c t The effect of M23 C6 carbides on the formation of grain boundary serrations (GBSs) has been systematically investigated in a solid solution strengthened Haynes 230 alloy. It is found that GBS occur in this alloy during the slow cooling process and are accompanied by the precipitation of intergranular planar M23 C6 carbides. The amplitude and proportion of GBS increase with the rise of the solution temperature and time. If the specimens are cooled directly without any solution treatments, the grain boundaries remain planar and granular M23 C6 carbides precipitate at them. The sequential evolutions of GBS and M23 C6 carbides are investigated by scanning electron microscopy (SEM) examination. High-resolution transmission electron microscope (HRTEM) investigations reveal the coherent interfacial plane of M23 C6 carbides formed at ¯ These facts indicate that the nucleation and oriented growth of M23 C6 grain boundaries to be (1 1 1). carbides at grain boundaries play an important role in the formation of GBS. Based on the interfacial energy calculations and the tensions balance relation, a semi-quantitative model about the GBS formation is proposed. © 2011 Elsevier B.V. All rights reserved.
1. Introduction It has been reported that GBS occur widely in cast, powder processed and wrought Ni-based superalloys [1]. The GBS can lead to a lower rate of creep strain and crack propagation to improve creep property [2–4]. The mechanism of GBS strengthening has been investigated by means of experimental research and theory analysis, and the strengthening by GBS is attributed to the retardation of grain boundary sliding [5,6]. The GBS formation mechanism in Ni-based superalloys has been studied widely. Early investigations [2,7–9] mainly focused on the interaction between ␥ particles and grain boundary segments. Some researchers [2,7,8] proposed that the thermal migration of grain boundary segments between the primary ␥ particles is responsible for the formation of GBS during the cooling process. Subsequently, migrating segments are pinned by the fine second ␥ particles at a lower temperature. Koul and Gessinger [9] proposed that the movement of the boundary primary ␥ particles causes the displacement of the local grain boundary segments to form serrations. In this model, the strain energy difference provides a driving force for the movement of the primary ␥ in the vertical direction of the boundary segments until this force is balanced by the line tension of the boundary segments. Furthermore, Koul and Thamburaj
∗ Corresponding author. Tel.: +86 29 88491764; fax: +86 29 88460294. E-mail address: [email protected] (R. Hu). 0921-5093/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2011.11.060
[1] found that ␥ solvus temperature which is higher than the solvus temperature of M23 C6 and M6 C carbides is a prerequisite condition for the formation of GBS in almost all Ni-based superalloys. Recently, it is found that [10] GBS form prior to M23 C6 carbides in Nimonic 263 wrought Ni-based superalloy, and then the M23 C6 carbides grow along the serrated grain boundaries. The similar results were also found in AISI 304 and AISI 316 austenitic stainless steels [11,12]. Ye et al. [13] argued that carbides and coexisting ␥ phases account for the formation of GBS at the same time. It can be concluded that the relation between M23 C6 carbides and GBS is still unclear in Ni-based superalloys until now. Therefore, the purpose of this study is to investigate the effect of intergranular M23 C6 carbides on GBS to understand the mechanism of GBS formation in Ni-based superalloys. In addition, this study tries to introduce GBS to Ni–Cr–W superalloy whose creep property has been focused on recently due to its potential application in GEN IV program [13–16]. 2. Experimental procedure In order to investigate the effect of M23 C6 carbides on GBS, the commercially available Haynes 230 alloy was used in this study. The chemical composition is given in Table 1. The initial morphology in the annealed condition is shown in Fig. 1. Granular M6 C carbides are observed to be randomly dispersed throughout the grain structure. To investigate the behaviours of GBS under different heat treatment conditions, the heat treatment processes shown in Table 2
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L. Jiang et al. / Materials Science and Engineering A 536 (2012) 37–44
Table 1 Nominal chemical composition of Haynes230 alloy. Nominal chemical composition, weight percent Ni
Cr
W
Mo
Fe
Co
Mn
Si
Al
C
La
B
57
22
14
2
3
5
0.5
0.4
0.3
0.10
0.02
0.015
were conducted. The specimens were solution-treated at various temperatures from 1220 ◦ C to 1280 ◦ C for times from 0 min to 15 min, and then slow-cooled at a rate of 6.7 ◦ C/min. The end temperature of the slow cooling was in a range of 1080–1160 ◦ C. The specimens were water-quenched after the slow cooling process. Metallographic samples were prepared using standard metallographic mechanical grinding and polishing techniques. The polished samples were etched with aqua regia (HCl:HNO3 = 3:1) to reveal the microstructures. SEM examinations were carried out using a JSM-6700 scanning electron microscope, operating at 15 kV. The geometric features of serrated grain boundaries such as the amplitude and the proportion can be easily recorded from SEM micrographs. Transmission electron microscopy (TEM, Tecnai G2 F30) was applied to investigate the orientation relationship between M23 C6 carbides and two neighbouring grains. HRTEM investigations were conducted to obtain the interfacial planes between M23 C6 carbides and the matrix. TEM foils were prepared by the twin-jet method using 8% perchloric acid carbinol solution at −30 ◦ C. 3. Results 3.1. The behaviour of GBS and M23 C6 carbide with different heat treatment conditions Although GBS occur in the slow cooling process, the effect of the solution treatment cannot be neglected. The solution treatment can promote grain growth, GBS formation and intragranular carbides decomposition. As shown in Table 2, the initial grain size of 70 m keeps invariant at 1220 ◦ C, but at a solution temperature higher than 1240 ◦ C, the grains grow to a size of 200 m. Meanwhile, the amplitude of serrations and the proportion of serrated boundaries increase with the rise of solution temperature (Table 2 No. 1–4). Fig. 2 shows the changes of grain boundary morphologies with the solution temperature. On the other hand, GBS develop more sufficiently during the cooling process with the increase of solution time. When the solution time is 5 min, the amplitude of serrations and the proportion of serrated boundaries reach 5.1 m and 90%, respectively and are close to the maximum (Table 2 No. 4,6,7). So, it can be concluded that a higher solution temperature and a longer solution time are beneficial to GBS formation in this alloy. In Fig. 2, it can also be observed that the size of intragranular M6 C carbides decreases from 20 m to 8 m with the solution temperature
Fig. 1. The initial microstructure of the as-received material.
increasing. As shown in Fig. 3, the serrations are accompanied by intergranular M23 C6 carbides, while the grain boundary segments without intergranular M23 C6 carbides always remain planar. When specimens cooled directly from 1280 ◦ C without the solution treatment as described in Table 2 (No. 5), the morphology of grain boundaries and M23 C6 carbides are totally different. As shown in Fig. 4b, intergranular granular M23 C6 carbides precipitate densely at almost all grain boundaries when specimens cooled to 1190 ◦ C. And the density of M23 C6 carbides is unchanged during the whole cooling process as shown in Fig. 4c and d. The grain boundaries remain planar during the whole cooling process as shown in Fig. 4. Fig. 5 shows the sequential evolutions of GBS and the M23 C6 carbides at grain boundaries during the cooling process. As shown in Fig. 5a, in the initial stage (cooled to 1160 ◦ C), only a few planar or granular M23 C6 carbides can be observed, and the local grain boundary segments still remain planar. When specimens cooled further to 1220 ◦ C, the serrations occur at 20% of grain boundaries. At this time, planar M23 C6 carbides just appear at one side of serrations as shown in Fig. 5b. In the final stage (cooled to 1080 ◦ C), almost all grain boundaries become serrated. Some M23 C6 carbides grow into another side of serrations and evolve into a hoop-like structure as shown in Fig. 5c.
Table 2 Effect of solution temperature(T1 ), solution time(t) and the end temperature of slow cooling(T2 ) on the characteristics (amplitude of serration: A, proportion of serrated boundaries: P) of grain boundaries. No.
T1 (◦ C)
t (min)
T2 (◦ C)
A (m)
Pa
Grain size (m)
1 2 3 4 5 6 7 8 9
1220 1240 1260 1280 1280 1280 1280 1280 1280
15 15 15 15 0 5 10 15 15
1080 1080 1080 1080 1080 1080 1080 1120 1160
0 2.2 5.8 7.8 0 5.1 5.8 5.5 0
0% 30–40% >90% 100% 0% >90% >90% 20% 0%
70 200 200 200 70 130 150 200 200
a
The twin boundaries are not taken into consideration.
L. Jiang et al. / Materials Science and Engineering A 536 (2012) 37–44
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Fig. 2. Optical micrograph of different solution temperature treated samples at: (a) 1220 ◦ C, (b) 1240 ◦ C, (c) 1260 ◦ C and (d) 1280 ◦ C.
Fig. 3. SEM micrographs of GBS. (a) Homogenizing at 1280 ◦ C/15 min and slowly cooling to 1080 ◦ C, the two arrows mark two kinds of grain boundaries and (b) EDS spectra of M23 C6 .
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L. Jiang et al. / Materials Science and Engineering A 536 (2012) 37–44
Fig. 4. SEM micrographs of granular M23 C6 carbides (without solution treatment) in grain boundaries within the temperature range of controlled cooling, (a) 1280 ◦ C → 1240 ◦ C; (b) 1280 ◦ C → 1190 ◦ C; (c) 1280 ◦ C → 1150 ◦ C and (d) 1280 ◦ C → 1070 ◦ C.
3.2. Crystallographic features of grain boundary carbides Crystallographic analysis has been carried out on the planar M23 C6 carbides formed at the serrated grain boundaries and the granular M23 C6 carbides formed at the planar grain boundaries. The coincidence of selected area diffraction pattern (SADP) between
M23 C6 carbides and the matrix (Fig. 6) shows that they have a lattice parameter ratio of about 3:1. A series of SADP taken from different tilt angles confirmed that each carbide is crystallographically in exactly parallel orientation with one of its neighbouring matrix grains, i.e., 1 0 0 // 1 0 0 ; (1 0 0)M23 C6 //(1 0 0) . Fig. 7 M23 C6
shows the HR image for an intergranular carbide when the beam
Fig. 5. SEM micrographs of GBS as well as the carbides in grain boundaries within the temperature range of controlled cooling, (a)1280 ◦ C → 1160 ◦ C; (b) 1280 ◦ C → 1120 ◦ C and (c) 1280 ◦ C → 1080 ◦ C.
L. Jiang et al. / Materials Science and Engineering A 536 (2012) 37–44
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Fig. 6. TEM morphology and corresponding electron diffraction pattern of a intergranular M23 C6 and carbide the matrix in the 1 1 2 direction.
Fig. 7. HRTEM image of M23 C6 formed at the serrated grain boundary.
direction is [0 1 1]. It shows that the carbide shares a coherency with the matrix, and the orientation relationship was revealed to ¯ M C //(1 1 1) ¯ Grain 1 . be (1 1 1) 23 6 4. Discussion From the experimental results, it can be summarized that the formation of GBS is related to the nucleation and growth of M23 C6 carbides in this alloy system. Morphology evolution of M23 C6 carbides from planar to granular is accompanied by the increase of carbide density at grain boundaries. Because all heat treatments are carried out at one cooling rate, the increase of carbide density cannot be explained by the effect of cooling rate to nucleation rate. During the cooling process, the planar M23 C6 carbides and serrations seemingly form preferentially at some specific boundaries and then expand to almost all boundaries (0–20–100%). Some researchers [4,12,17,18] have confirmed that GBS indeed occur at certain boundaries preferentially. In contrast, the granular M23 C6 carbides precipitate at almost all boundaries at the same time, and have a higher critical precipitation temperature (1190 ◦ C) than that of planar M23 C6
carbides(1120–1160 ◦ C). The stronger nucleation ability of granular M23 C6 carbides probably results from the inducing of nuclei or impurities which densely distributed at all boundaries in the specimens without high temperature solution treatment. The density of granular M23 C6 carbides depends on the density of nucleuses or impurities. The small spacing between granular M23 C6 carbides is not enough for their further growth along grain boundaries, and the local segments remain planar. While high temperature solution treatment is introduced to destroy these nucleation sites, M23 C6 carbides precipitate sparsely and grow into planar shape along the grain boundaries. Then, the planar M23 C6 carbides grow from one grain into the adjacent grain and push the local boundary segment to form serrations. It can be concluded that nucleation mode and the morphology of M23 C6 carbides have direct influences on the formation of GBS. It was observed that the size of M6 C particles decreases obviously from 20 m to 8 m in comparison to that in as-received materials as indicated in Fig. 2. This fact indicates that M6 C particles dissolve at a high solution temperature (1280 ◦ C), which agrees well with one previous investigation in Ni–Cr–W superalloy [18]. Subsequently, W atoms and C atoms from dissolved M6 C particles are released into the matrix and increase the supersaturation degree of these atoms in the matrix. C atoms in the matrix diffuse to grain boundaries to participate in the nucleation and growth of M23 C6 carbides. At the higher solution temperature, the rapid dissolving of M6 C carbides causes a higher C content in the matrix and product more M23 C6 carbides and GBS during the cooling process as shown in Fig. 2. The effect of C on the occurrence of GBS is also reported in one previous research in AISI 316 stainless steel [19]. The crystallographic features of the interface between M23 C6 carbides and the matrix imply that the related interface energy may work in the formation of GBS. The characteristics of M23 C6 crystal structure and related interfacial structures as well as the interface energy calculations are discussed next. The crystal structure of Cr-rich M23 C6 carbides belongs to space ¯ as described in Bowman’s work [20]. The unit cell group Fm3m of M23 C6 carbides consists of 92 metal atoms at 4a, 8c, 32f and 48h symmetry sites and 24 C atoms. In multicomponent Ni-based superalloy, Cr atoms at the 8c sites are occupied by Mo, W atoms [21,22]. The EDS spectra of M23 C6 in Fig. 3b also agrees with this fact. So, it can be deduced that {1 1 1} planes which are made up of metal atoms at 4a and 32f sites mainly contain Cr atoms. On the other hand, Beckitt [23] proposed that {1 1 1} planes in the austenite matrix and M23 C6 provide a good atomic correspondence. There are only 4 atoms out of 28 not fully in the M23 C6 plane and the four
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L. Jiang et al. / Materials Science and Engineering A 536 (2012) 37–44
Fig. 8. (a) The initial growth stage of M23 C6 carbides along the grain boundary and (b) the balance of three kinds of interfaces tension at the triple point.
atoms occur slightly above or below the plane. The overall misfit of {1 1 1} planes between the austenite and M23 C6 carbides is 0.99%. So, the coherent interface made up of {1 1 1} planes in M23 C6 carbides and the matrix is regular in both component and structure. This kind of coherent interface possesses a low interfacial energy. The energy of the coherent interface between M23 C6 carbides and the matrix can be split into two components: structural interfacial energy and chemical interfacial energy. By calculating structural interfacial energy [24] and chemical interfacial energy [25], some researchers [25,26] obtained the value of coherent interfacial energy which coincides with the experimental results. In the present paper, this model is used to calculate the energy. The details about the calculation processes and related parameters selection are given in Appendices A and B. The energy of the coherent interface between M23 C6 carbides and the matrix is: co = 0.209 J/m2 It is considerably lower than measured grain boundary energies in pure nickel (0.866 J/m2 [27]). Due to the segregation of microelements at grain boundaries, the grain boundary energy of Haynes 230 alloy is lower than that of pure nickel. Considering the different segregation degrees at certain grain boundaries, the grain boundary energy is described as below:
Fig. 9. The distribution map of ␣ in GBS.
tensions balance formula is illustrated by Fig. 8b. The formula is given as below: co gb in = = ˛ ˇ
gb ≤ 0.866 J/m2
where ˛, ˇ, are tension angles as marked in Fig. 8b. This procedure gives the angle of serrations:
The incoherent interface is considered to have many features in common with high-angle grain boundaries and also possesses a high energy (0.5 − 1 J/m2 ) [28]. For simplifying subsequent analysis, the energy value of the incoherent interface between M23 C6 and matrix in is assumed to be equal to gb . The minimization of interfacial energy leads to planar semicoherent (or coherent) interfaces and smoothly curved incoherent interfaces [28]. The initial stage of growth of M23 C6 carbides along the grain boundaries is illustrated by Fig. 8a. co and gb are in a parallel and opposite direction. Due to tensions balance relation, this state cannot be maintained. The final state according to the
˛ ≥ 83◦ which matches well with enough metallographic observations as illustrated in Fig. 9. It must be noted that the angle between the grain boundary traces recorded from metallographic pictures may be smaller than the angle between the grain boundary plane. It is reasonable that the small proportion of GBS possesses a ␣ angle smaller than 83◦ as shown in Fig. 9. Furthermore, one special case can be predicted on the coherent twin boundaries which divide the two sets of crystal lattice with
L. Jiang et al. / Materials Science and Engineering A 536 (2012) 37–44 Table 3 Related parameters of Haynes230 Alloy. E is modulus of elasticity, and v is Poisson’s ratio, and a is atomic spacing at {1 1 1} planes. Parameter
Value
Reference
EI EM VI VM a1 a2
218.936 MPa 210 MPa 0.367 0.303 0.2510 nm 0.2531 nm
[22] This work [22] This work This work This work
Table 4 Related parameters of Haynes230 Alloy. Hsm is the heat of sublimation, and Tc is the critical ordering temperature of Ni–Cr system, and D0 is the pair potential of Cr–C bond. Parameter
Value
Reference
Hsm
430.1 (KJ/mol) for Ni 397.48 (Kj/mol) for Cr 6.0221415 × 1023 (mol−1 ) 12 for Ni 8 for Cr 1.3806503 × 10−23 (m2 kg s−2 K) 863.15 (K) 0.779 (eV)
[31]
NA (Avogadro’ constant) NB (coordination number) B (Boltzmann’ constant) Tc D0
– – – [32] [22]
mirror symmetry relation. Because M23 C6 carbides have coherent interfaces with both twins, the planar M23 C6 carbides probably grow along the coherent twin boundary and remain planar. The morphology of planar M23 C6 carbides at the coherent twin boundary can be found to confirm the above inference in one previous work [29]. Based on aforementioned phenomenological analyses, it can be deduced the orientated growth of M23 C6 is related to a diffusional flux difference between various interfaces. It has been widely accepted that the diffusivity of grain boundaries is far greater than that of lattice. At a low nucleation rate, the intergranular precipitations tend to grow along grain boundaries. So, it is reasonable to assume the existence of a chemical force from growth tip of M23 C6 along the grain boundary marked as F1 in Fig. 8a. On the other hand, it is shown that completely-coherent {1 1 1} planar twin boundary possesses a very low diffusivity [30]. Similarly, the regular coherent interface between M23 C6 and matrix also has a lower diffusivity than the corresponding incoherent interface. A chemical force can also be assumed to exist at the side of the incoherent interface in the vertical direction marked as F2 in Fig. 8a. Under the joint action of the two chemical forces, the tip of planar M23 C6 grows from one grain into adjacent grain in a certain angle up to the equilibrium state. When M23 C6 carbides grow along one side of serrations, another side of serrations plays a role of the diffusion path. Cr atoms diffuse along the grain boundary segments at a higher rate than W atoms. In front of the grain boundary segments, there is a high vacancy concentration zone to drive their farther migration due to Kirkendall effect occurring in the grain boundary diffusion.
5. Conclusions The higher solution temperature and the longer solution time raise the content of C atoms in the matrix and increase the amplitude of serrations and the proportion of serrated boundaries. The planar M23 C6 carbides result in the formation of GBS at some certain boundaries preferentially, then GBS expand to almost all boundaries during the cooling process. When specimens cooled directly without the solution treatment, all grain boundaries remain planar with granular M23 C6 carbides precipitating at them.
43
M23 C6 carbides are crystallographically in exactly parallel orientation and share a coherency with one of their neighbouring matrix grains. The final equilibrium state of GBS obeys the tension balance relation. The orientated growth of planar M23 C6 carbides results from the relatively larger diffusivity of Cr and C atoms at grain boundaries and incoherent interfaces than that at coherent interfaces. Acknowledgements The authors are grateful to the financial support from the project supported by Research Fund of the State Key Laboratory of Solidification Processing, China (62-TP-2011), National basic Research Program of China (No. 2011CB610404) and National Natural Science Foundation of China (51171150). Appendix A. Calculation of the structural interfacial energy by the van der Merwe model [24] is as follows: struct =
Gb 1/2 1/2 [1 + ˇ − (1 + ˇ2 ) − ˇ ln{2ˇ(1 + ˇ2 ) − 2ˇ2 }] 42
ˇ=
2GI b c p[(1 − I ) + (1 − M )GI /GM ]G
p=
a1 a2 a2 − a1
G=
GI + GM 2
GX =
EX 2(1 + X )
(X = I, M)
where I is intergranular M23 C6 and M is the matrix. On the basis of the parameters listed in Table 3, this procedure gives struct = 0.0714 J/m2
Appendix B. Calculation of chemical interfacial energy based on a brokenbond model [25] is as follows: H S = HM−I −
1 (HM−M + HI−I ) 2
HM−I = 48VNi−Cr HM−M = 54VNi−Ni HI−I = 34VCr−Cr + 12VCr−C
where the numbers of related bonds between {1 1 1} planes in M23 C6 and matrix (48, 54, 34, 12) are from the unit cell structure and the interface structure with 28 atoms. The value of bond energy VCr–Cr and VNi–Ni are estimated from the heat of sublimation Hsm of the pure metals as below: V=
2Hsm NA NB
VNi–Cr is obtained from the Bragg–Williams approximation: 1 B Tc = VNi−Cr − (VNi−Ni + VCr−Cr ) 4 2
44
L. Jiang et al. / Materials Science and Engineering A 536 (2012) 37–44
The value of VCr–C are assumed to be equal to pair potential D0 . On the basis of the parameters listed in Table 4, this procedure gives
chem =
H S = 0.1374 J/m2 area ({1 1 1})
References [1] A. Koul, R. Thamburaj, Metall. Mater. Trans. A 16 (1985) 17–26. [2] J. Larson, S. Floreen, Metall. Mater. Trans. A 8 (1977) 51–55. [3] P.A.A.K. Koul, N. Bellinger, R. Thamburaj, W. Wallace, J.-P. Immarigeon, in: D.N.D.S. Reichman, G. Maurer, S. Antolovich, C. Lund (Eds.), The Metallurgical Society Superalloys, Warrendale, PA, 1988, pp. 3–12. [4] M.M.H. Loyer Danflou, A. Walder, in: R.W.S.S.D. Antolovich, R.A. MacKay, D.L. Anton, T. Khan, R.D. Kissinger, D.L. Klarstrom (Eds.), The Minerals, Metals & Materials Society Superalloys, Warrendale, PA, 1992, pp. 63–72. [5] M. Tanaka, O. Miyagawa, T. Sakaki, H. Iizuka, F. Ashihara, D. Fujishiro, J. Mater. Sci. 23 (1988) 621–628. [6] M. Tanaka, H. Iizuka, F. Ashihara, J. Mater. Sci. 27 (1992) 2636–2640. [7] J. Larson, Metall. Mater. Trans. A 7 (1976) 1497–1502. [8] J.C. Beddoes, W. Wallace, Mater. Charact. 13 (1980) 185–194. [9] A.K. Koul, G.H. Gessinger, Acta Metall. 31 (1983) 1061–1069. [10] H.U. Hong, H.W. Jeong, I.S. Kim, B.G. Choi, Y.S. Yoo, C.Y. Jo, Thermec 2009 638–642 (Pts 1–4) (2010) 2245–2250. [11] H.U. Hong, S.W. Nam, J. Mater. Sci. 38 (2003) 1535–1542.
[12] K.J. Kim, H.U. Hong, S.W. Nam, J. Nucl. Mater. 393 (2009) 249–253. [13] R. Ye, Z. Xu, Z. Ge, L. Gao, T. Yu, R. Zhang, L. Li, P. Zhang, Acta Metall. Sinica 21 (1985) A131–A138. [14] R.W. Swindeman, M.J. Swindeman, Int. J. Pres. Ves. Pip. 85 (2008) 72–79. [15] M. Maldini, G. Angella, V. Lupinc, Thermec 2009 638–642 (Pts 1–4) (2010) 2285–2290. [16] A.K. Roy, S. Chatterjee, M.H. Hasan, J. Pal, L. Ma, Mater. Sci. Eng. A 527 (2010) 4830–4836. [17] E.A. Trillo, L.E. Murr, J. Mater. Sci. 33 (1998) 1263–1271. [18] Y.S. Lim, J.S. Kim, H.P. Kim, H.D. Cho, J. Nucl. Mater. 335 (2004) 108–114. [19] K.J. Kim, J. Ginsztler, S.W. Nam, Mater. Lett. 59 (2005) 1439–1443. [20] A.L. Bowman, G.P. Arnold, E.K. Storms, N.G. Nereson, Acta Crystallogr. B 28 (1972) 3102–3103. [21] M. Vardavoulias, G. Papadimitriou, Phys. Status Solidi A 134 (1992) 183–191. [22] J. Xie, J. Shen, N. Chen, S. Seetharaman, Acta Mater. 54 (2006) 4653–4658. [23] F.R. Beckitt, B.R. Clark, Acta Metall. 15 (1967) 113–129. [24] G.J. Shiflet, Mater. Sci. Eng. 81 (1986) 61–100. [25] D.E. Stephens, G.R. Purdy, Acta Metall. 23 (1975) 1343–1352. [26] Q. Li, F. Wawner, J. Mater. Sci. 32 (1997) 5363–5370. [27] L.E. Murr, Interfacial Phenomena in Metals and Alloys, Addison-Wesley Educational Publishers Inc., Reading, MA, 1975. [28] D.A. Porter, K.E. Easterling, Phase Transformations in Metals and Alloys, Second Edition, CRC Press, Boca Raton, 1992. [29] H. Hong, B. Rho, S. Nam, Mater. Sci. Eng. A 318 (2001) 285–292. [30] R.S. Barnes, Philos. Mag. 5 (1960) 635–646. [31] D.R. Lide, CRC Handbook of Chemistry and Physics, 86 edition, CRC Press, Boca Raton, 2005, pp. 9–63. [32] P. Nash, J. Phase Equilib. 7 (1986) 466–476.
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The effect of M23 C6 carbides on the formation of grain boundary serrations in a wrought Ni-based superalloy Li Jiang, Rui Hu ∗ , Hongchao Kou, Jinshan Li, Guanghai Bai, Hengzhi Fu State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an 710072, China
a r t i c l e
i n f o
Article history: Received 4 June 2011 Received in revised form 31 October 2011 Accepted 21 November 2011 Available online 1 December 2011 Keywords: Grain boundary serrations M23 C6 Haynes 230 alloy Diffusion
a b s t r a c t The effect of M23 C6 carbides on the formation of grain boundary serrations (GBSs) has been systematically investigated in a solid solution strengthened Haynes 230 alloy. It is found that GBS occur in this alloy during the slow cooling process and are accompanied by the precipitation of intergranular planar M23 C6 carbides. The amplitude and proportion of GBS increase with the rise of the solution temperature and time. If the specimens are cooled directly without any solution treatments, the grain boundaries remain planar and granular M23 C6 carbides precipitate at them. The sequential evolutions of GBS and M23 C6 carbides are investigated by scanning electron microscopy (SEM) examination. High-resolution transmission electron microscope (HRTEM) investigations reveal the coherent interfacial plane of M23 C6 carbides formed at ¯ These facts indicate that the nucleation and oriented growth of M23 C6 grain boundaries to be (1 1 1). carbides at grain boundaries play an important role in the formation of GBS. Based on the interfacial energy calculations and the tensions balance relation, a semi-quantitative model about the GBS formation is proposed. © 2011 Elsevier B.V. All rights reserved.
1. Introduction It has been reported that GBS occur widely in cast, powder processed and wrought Ni-based superalloys [1]. The GBS can lead to a lower rate of creep strain and crack propagation to improve creep property [2–4]. The mechanism of GBS strengthening has been investigated by means of experimental research and theory analysis, and the strengthening by GBS is attributed to the retardation of grain boundary sliding [5,6]. The GBS formation mechanism in Ni-based superalloys has been studied widely. Early investigations [2,7–9] mainly focused on the interaction between ␥ particles and grain boundary segments. Some researchers [2,7,8] proposed that the thermal migration of grain boundary segments between the primary ␥ particles is responsible for the formation of GBS during the cooling process. Subsequently, migrating segments are pinned by the fine second ␥ particles at a lower temperature. Koul and Gessinger [9] proposed that the movement of the boundary primary ␥ particles causes the displacement of the local grain boundary segments to form serrations. In this model, the strain energy difference provides a driving force for the movement of the primary ␥ in the vertical direction of the boundary segments until this force is balanced by the line tension of the boundary segments. Furthermore, Koul and Thamburaj
∗ Corresponding author. Tel.: +86 29 88491764; fax: +86 29 88460294. E-mail address: [email protected] (R. Hu). 0921-5093/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2011.11.060
[1] found that ␥ solvus temperature which is higher than the solvus temperature of M23 C6 and M6 C carbides is a prerequisite condition for the formation of GBS in almost all Ni-based superalloys. Recently, it is found that [10] GBS form prior to M23 C6 carbides in Nimonic 263 wrought Ni-based superalloy, and then the M23 C6 carbides grow along the serrated grain boundaries. The similar results were also found in AISI 304 and AISI 316 austenitic stainless steels [11,12]. Ye et al. [13] argued that carbides and coexisting ␥ phases account for the formation of GBS at the same time. It can be concluded that the relation between M23 C6 carbides and GBS is still unclear in Ni-based superalloys until now. Therefore, the purpose of this study is to investigate the effect of intergranular M23 C6 carbides on GBS to understand the mechanism of GBS formation in Ni-based superalloys. In addition, this study tries to introduce GBS to Ni–Cr–W superalloy whose creep property has been focused on recently due to its potential application in GEN IV program [13–16]. 2. Experimental procedure In order to investigate the effect of M23 C6 carbides on GBS, the commercially available Haynes 230 alloy was used in this study. The chemical composition is given in Table 1. The initial morphology in the annealed condition is shown in Fig. 1. Granular M6 C carbides are observed to be randomly dispersed throughout the grain structure. To investigate the behaviours of GBS under different heat treatment conditions, the heat treatment processes shown in Table 2
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Table 1 Nominal chemical composition of Haynes230 alloy. Nominal chemical composition, weight percent Ni
Cr
W
Mo
Fe
Co
Mn
Si
Al
C
La
B
57
22
14
2
3
5
0.5
0.4
0.3
0.10
0.02
0.015
were conducted. The specimens were solution-treated at various temperatures from 1220 ◦ C to 1280 ◦ C for times from 0 min to 15 min, and then slow-cooled at a rate of 6.7 ◦ C/min. The end temperature of the slow cooling was in a range of 1080–1160 ◦ C. The specimens were water-quenched after the slow cooling process. Metallographic samples were prepared using standard metallographic mechanical grinding and polishing techniques. The polished samples were etched with aqua regia (HCl:HNO3 = 3:1) to reveal the microstructures. SEM examinations were carried out using a JSM-6700 scanning electron microscope, operating at 15 kV. The geometric features of serrated grain boundaries such as the amplitude and the proportion can be easily recorded from SEM micrographs. Transmission electron microscopy (TEM, Tecnai G2 F30) was applied to investigate the orientation relationship between M23 C6 carbides and two neighbouring grains. HRTEM investigations were conducted to obtain the interfacial planes between M23 C6 carbides and the matrix. TEM foils were prepared by the twin-jet method using 8% perchloric acid carbinol solution at −30 ◦ C. 3. Results 3.1. The behaviour of GBS and M23 C6 carbide with different heat treatment conditions Although GBS occur in the slow cooling process, the effect of the solution treatment cannot be neglected. The solution treatment can promote grain growth, GBS formation and intragranular carbides decomposition. As shown in Table 2, the initial grain size of 70 m keeps invariant at 1220 ◦ C, but at a solution temperature higher than 1240 ◦ C, the grains grow to a size of 200 m. Meanwhile, the amplitude of serrations and the proportion of serrated boundaries increase with the rise of solution temperature (Table 2 No. 1–4). Fig. 2 shows the changes of grain boundary morphologies with the solution temperature. On the other hand, GBS develop more sufficiently during the cooling process with the increase of solution time. When the solution time is 5 min, the amplitude of serrations and the proportion of serrated boundaries reach 5.1 m and 90%, respectively and are close to the maximum (Table 2 No. 4,6,7). So, it can be concluded that a higher solution temperature and a longer solution time are beneficial to GBS formation in this alloy. In Fig. 2, it can also be observed that the size of intragranular M6 C carbides decreases from 20 m to 8 m with the solution temperature
Fig. 1. The initial microstructure of the as-received material.
increasing. As shown in Fig. 3, the serrations are accompanied by intergranular M23 C6 carbides, while the grain boundary segments without intergranular M23 C6 carbides always remain planar. When specimens cooled directly from 1280 ◦ C without the solution treatment as described in Table 2 (No. 5), the morphology of grain boundaries and M23 C6 carbides are totally different. As shown in Fig. 4b, intergranular granular M23 C6 carbides precipitate densely at almost all grain boundaries when specimens cooled to 1190 ◦ C. And the density of M23 C6 carbides is unchanged during the whole cooling process as shown in Fig. 4c and d. The grain boundaries remain planar during the whole cooling process as shown in Fig. 4. Fig. 5 shows the sequential evolutions of GBS and the M23 C6 carbides at grain boundaries during the cooling process. As shown in Fig. 5a, in the initial stage (cooled to 1160 ◦ C), only a few planar or granular M23 C6 carbides can be observed, and the local grain boundary segments still remain planar. When specimens cooled further to 1220 ◦ C, the serrations occur at 20% of grain boundaries. At this time, planar M23 C6 carbides just appear at one side of serrations as shown in Fig. 5b. In the final stage (cooled to 1080 ◦ C), almost all grain boundaries become serrated. Some M23 C6 carbides grow into another side of serrations and evolve into a hoop-like structure as shown in Fig. 5c.
Table 2 Effect of solution temperature(T1 ), solution time(t) and the end temperature of slow cooling(T2 ) on the characteristics (amplitude of serration: A, proportion of serrated boundaries: P) of grain boundaries. No.
T1 (◦ C)
t (min)
T2 (◦ C)
A (m)
Pa
Grain size (m)
1 2 3 4 5 6 7 8 9
1220 1240 1260 1280 1280 1280 1280 1280 1280
15 15 15 15 0 5 10 15 15
1080 1080 1080 1080 1080 1080 1080 1120 1160
0 2.2 5.8 7.8 0 5.1 5.8 5.5 0
0% 30–40% >90% 100% 0% >90% >90% 20% 0%
70 200 200 200 70 130 150 200 200
a
The twin boundaries are not taken into consideration.
L. Jiang et al. / Materials Science and Engineering A 536 (2012) 37–44
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Fig. 2. Optical micrograph of different solution temperature treated samples at: (a) 1220 ◦ C, (b) 1240 ◦ C, (c) 1260 ◦ C and (d) 1280 ◦ C.
Fig. 3. SEM micrographs of GBS. (a) Homogenizing at 1280 ◦ C/15 min and slowly cooling to 1080 ◦ C, the two arrows mark two kinds of grain boundaries and (b) EDS spectra of M23 C6 .
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L. Jiang et al. / Materials Science and Engineering A 536 (2012) 37–44
Fig. 4. SEM micrographs of granular M23 C6 carbides (without solution treatment) in grain boundaries within the temperature range of controlled cooling, (a) 1280 ◦ C → 1240 ◦ C; (b) 1280 ◦ C → 1190 ◦ C; (c) 1280 ◦ C → 1150 ◦ C and (d) 1280 ◦ C → 1070 ◦ C.
3.2. Crystallographic features of grain boundary carbides Crystallographic analysis has been carried out on the planar M23 C6 carbides formed at the serrated grain boundaries and the granular M23 C6 carbides formed at the planar grain boundaries. The coincidence of selected area diffraction pattern (SADP) between
M23 C6 carbides and the matrix (Fig. 6) shows that they have a lattice parameter ratio of about 3:1. A series of SADP taken from different tilt angles confirmed that each carbide is crystallographically in exactly parallel orientation with one of its neighbouring matrix grains, i.e., 1 0 0 // 1 0 0 ; (1 0 0)M23 C6 //(1 0 0) . Fig. 7 M23 C6
shows the HR image for an intergranular carbide when the beam
Fig. 5. SEM micrographs of GBS as well as the carbides in grain boundaries within the temperature range of controlled cooling, (a)1280 ◦ C → 1160 ◦ C; (b) 1280 ◦ C → 1120 ◦ C and (c) 1280 ◦ C → 1080 ◦ C.
L. Jiang et al. / Materials Science and Engineering A 536 (2012) 37–44
41
Fig. 6. TEM morphology and corresponding electron diffraction pattern of a intergranular M23 C6 and carbide the matrix in the 1 1 2 direction.
Fig. 7. HRTEM image of M23 C6 formed at the serrated grain boundary.
direction is [0 1 1]. It shows that the carbide shares a coherency with the matrix, and the orientation relationship was revealed to ¯ M C //(1 1 1) ¯ Grain 1 . be (1 1 1) 23 6 4. Discussion From the experimental results, it can be summarized that the formation of GBS is related to the nucleation and growth of M23 C6 carbides in this alloy system. Morphology evolution of M23 C6 carbides from planar to granular is accompanied by the increase of carbide density at grain boundaries. Because all heat treatments are carried out at one cooling rate, the increase of carbide density cannot be explained by the effect of cooling rate to nucleation rate. During the cooling process, the planar M23 C6 carbides and serrations seemingly form preferentially at some specific boundaries and then expand to almost all boundaries (0–20–100%). Some researchers [4,12,17,18] have confirmed that GBS indeed occur at certain boundaries preferentially. In contrast, the granular M23 C6 carbides precipitate at almost all boundaries at the same time, and have a higher critical precipitation temperature (1190 ◦ C) than that of planar M23 C6
carbides(1120–1160 ◦ C). The stronger nucleation ability of granular M23 C6 carbides probably results from the inducing of nuclei or impurities which densely distributed at all boundaries in the specimens without high temperature solution treatment. The density of granular M23 C6 carbides depends on the density of nucleuses or impurities. The small spacing between granular M23 C6 carbides is not enough for their further growth along grain boundaries, and the local segments remain planar. While high temperature solution treatment is introduced to destroy these nucleation sites, M23 C6 carbides precipitate sparsely and grow into planar shape along the grain boundaries. Then, the planar M23 C6 carbides grow from one grain into the adjacent grain and push the local boundary segment to form serrations. It can be concluded that nucleation mode and the morphology of M23 C6 carbides have direct influences on the formation of GBS. It was observed that the size of M6 C particles decreases obviously from 20 m to 8 m in comparison to that in as-received materials as indicated in Fig. 2. This fact indicates that M6 C particles dissolve at a high solution temperature (1280 ◦ C), which agrees well with one previous investigation in Ni–Cr–W superalloy [18]. Subsequently, W atoms and C atoms from dissolved M6 C particles are released into the matrix and increase the supersaturation degree of these atoms in the matrix. C atoms in the matrix diffuse to grain boundaries to participate in the nucleation and growth of M23 C6 carbides. At the higher solution temperature, the rapid dissolving of M6 C carbides causes a higher C content in the matrix and product more M23 C6 carbides and GBS during the cooling process as shown in Fig. 2. The effect of C on the occurrence of GBS is also reported in one previous research in AISI 316 stainless steel [19]. The crystallographic features of the interface between M23 C6 carbides and the matrix imply that the related interface energy may work in the formation of GBS. The characteristics of M23 C6 crystal structure and related interfacial structures as well as the interface energy calculations are discussed next. The crystal structure of Cr-rich M23 C6 carbides belongs to space ¯ as described in Bowman’s work [20]. The unit cell group Fm3m of M23 C6 carbides consists of 92 metal atoms at 4a, 8c, 32f and 48h symmetry sites and 24 C atoms. In multicomponent Ni-based superalloy, Cr atoms at the 8c sites are occupied by Mo, W atoms [21,22]. The EDS spectra of M23 C6 in Fig. 3b also agrees with this fact. So, it can be deduced that {1 1 1} planes which are made up of metal atoms at 4a and 32f sites mainly contain Cr atoms. On the other hand, Beckitt [23] proposed that {1 1 1} planes in the austenite matrix and M23 C6 provide a good atomic correspondence. There are only 4 atoms out of 28 not fully in the M23 C6 plane and the four
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L. Jiang et al. / Materials Science and Engineering A 536 (2012) 37–44
Fig. 8. (a) The initial growth stage of M23 C6 carbides along the grain boundary and (b) the balance of three kinds of interfaces tension at the triple point.
atoms occur slightly above or below the plane. The overall misfit of {1 1 1} planes between the austenite and M23 C6 carbides is 0.99%. So, the coherent interface made up of {1 1 1} planes in M23 C6 carbides and the matrix is regular in both component and structure. This kind of coherent interface possesses a low interfacial energy. The energy of the coherent interface between M23 C6 carbides and the matrix can be split into two components: structural interfacial energy and chemical interfacial energy. By calculating structural interfacial energy [24] and chemical interfacial energy [25], some researchers [25,26] obtained the value of coherent interfacial energy which coincides with the experimental results. In the present paper, this model is used to calculate the energy. The details about the calculation processes and related parameters selection are given in Appendices A and B. The energy of the coherent interface between M23 C6 carbides and the matrix is: co = 0.209 J/m2 It is considerably lower than measured grain boundary energies in pure nickel (0.866 J/m2 [27]). Due to the segregation of microelements at grain boundaries, the grain boundary energy of Haynes 230 alloy is lower than that of pure nickel. Considering the different segregation degrees at certain grain boundaries, the grain boundary energy is described as below:
Fig. 9. The distribution map of ␣ in GBS.
tensions balance formula is illustrated by Fig. 8b. The formula is given as below: co gb in = = ˛ ˇ
gb ≤ 0.866 J/m2
where ˛, ˇ, are tension angles as marked in Fig. 8b. This procedure gives the angle of serrations:
The incoherent interface is considered to have many features in common with high-angle grain boundaries and also possesses a high energy (0.5 − 1 J/m2 ) [28]. For simplifying subsequent analysis, the energy value of the incoherent interface between M23 C6 and matrix in is assumed to be equal to gb . The minimization of interfacial energy leads to planar semicoherent (or coherent) interfaces and smoothly curved incoherent interfaces [28]. The initial stage of growth of M23 C6 carbides along the grain boundaries is illustrated by Fig. 8a. co and gb are in a parallel and opposite direction. Due to tensions balance relation, this state cannot be maintained. The final state according to the
˛ ≥ 83◦ which matches well with enough metallographic observations as illustrated in Fig. 9. It must be noted that the angle between the grain boundary traces recorded from metallographic pictures may be smaller than the angle between the grain boundary plane. It is reasonable that the small proportion of GBS possesses a ␣ angle smaller than 83◦ as shown in Fig. 9. Furthermore, one special case can be predicted on the coherent twin boundaries which divide the two sets of crystal lattice with
L. Jiang et al. / Materials Science and Engineering A 536 (2012) 37–44 Table 3 Related parameters of Haynes230 Alloy. E is modulus of elasticity, and v is Poisson’s ratio, and a is atomic spacing at {1 1 1} planes. Parameter
Value
Reference
EI EM VI VM a1 a2
218.936 MPa 210 MPa 0.367 0.303 0.2510 nm 0.2531 nm
[22] This work [22] This work This work This work
Table 4 Related parameters of Haynes230 Alloy. Hsm is the heat of sublimation, and Tc is the critical ordering temperature of Ni–Cr system, and D0 is the pair potential of Cr–C bond. Parameter
Value
Reference
Hsm
430.1 (KJ/mol) for Ni 397.48 (Kj/mol) for Cr 6.0221415 × 1023 (mol−1 ) 12 for Ni 8 for Cr 1.3806503 × 10−23 (m2 kg s−2 K) 863.15 (K) 0.779 (eV)
[31]
NA (Avogadro’ constant) NB (coordination number) B (Boltzmann’ constant) Tc D0
– – – [32] [22]
mirror symmetry relation. Because M23 C6 carbides have coherent interfaces with both twins, the planar M23 C6 carbides probably grow along the coherent twin boundary and remain planar. The morphology of planar M23 C6 carbides at the coherent twin boundary can be found to confirm the above inference in one previous work [29]. Based on aforementioned phenomenological analyses, it can be deduced the orientated growth of M23 C6 is related to a diffusional flux difference between various interfaces. It has been widely accepted that the diffusivity of grain boundaries is far greater than that of lattice. At a low nucleation rate, the intergranular precipitations tend to grow along grain boundaries. So, it is reasonable to assume the existence of a chemical force from growth tip of M23 C6 along the grain boundary marked as F1 in Fig. 8a. On the other hand, it is shown that completely-coherent {1 1 1} planar twin boundary possesses a very low diffusivity [30]. Similarly, the regular coherent interface between M23 C6 and matrix also has a lower diffusivity than the corresponding incoherent interface. A chemical force can also be assumed to exist at the side of the incoherent interface in the vertical direction marked as F2 in Fig. 8a. Under the joint action of the two chemical forces, the tip of planar M23 C6 grows from one grain into adjacent grain in a certain angle up to the equilibrium state. When M23 C6 carbides grow along one side of serrations, another side of serrations plays a role of the diffusion path. Cr atoms diffuse along the grain boundary segments at a higher rate than W atoms. In front of the grain boundary segments, there is a high vacancy concentration zone to drive their farther migration due to Kirkendall effect occurring in the grain boundary diffusion.
5. Conclusions The higher solution temperature and the longer solution time raise the content of C atoms in the matrix and increase the amplitude of serrations and the proportion of serrated boundaries. The planar M23 C6 carbides result in the formation of GBS at some certain boundaries preferentially, then GBS expand to almost all boundaries during the cooling process. When specimens cooled directly without the solution treatment, all grain boundaries remain planar with granular M23 C6 carbides precipitating at them.
43
M23 C6 carbides are crystallographically in exactly parallel orientation and share a coherency with one of their neighbouring matrix grains. The final equilibrium state of GBS obeys the tension balance relation. The orientated growth of planar M23 C6 carbides results from the relatively larger diffusivity of Cr and C atoms at grain boundaries and incoherent interfaces than that at coherent interfaces. Acknowledgements The authors are grateful to the financial support from the project supported by Research Fund of the State Key Laboratory of Solidification Processing, China (62-TP-2011), National basic Research Program of China (No. 2011CB610404) and National Natural Science Foundation of China (51171150). Appendix A. Calculation of the structural interfacial energy by the van der Merwe model [24] is as follows: struct =
Gb 1/2 1/2 [1 + ˇ − (1 + ˇ2 ) − ˇ ln{2ˇ(1 + ˇ2 ) − 2ˇ2 }] 42
ˇ=
2GI b c p[(1 − I ) + (1 − M )GI /GM ]G
p=
a1 a2 a2 − a1
G=
GI + GM 2
GX =
EX 2(1 + X )
(X = I, M)
where I is intergranular M23 C6 and M is the matrix. On the basis of the parameters listed in Table 3, this procedure gives struct = 0.0714 J/m2
Appendix B. Calculation of chemical interfacial energy based on a brokenbond model [25] is as follows: H S = HM−I −
1 (HM−M + HI−I ) 2
HM−I = 48VNi−Cr HM−M = 54VNi−Ni HI−I = 34VCr−Cr + 12VCr−C
where the numbers of related bonds between {1 1 1} planes in M23 C6 and matrix (48, 54, 34, 12) are from the unit cell structure and the interface structure with 28 atoms. The value of bond energy VCr–Cr and VNi–Ni are estimated from the heat of sublimation Hsm of the pure metals as below: V=
2Hsm NA NB
VNi–Cr is obtained from the Bragg–Williams approximation: 1 B Tc = VNi−Cr − (VNi−Ni + VCr−Cr ) 4 2
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The value of VCr–C are assumed to be equal to pair potential D0 . On the basis of the parameters listed in Table 4, this procedure gives
chem =
H S = 0.1374 J/m2 area ({1 1 1})
References [1] A. Koul, R. Thamburaj, Metall. Mater. Trans. A 16 (1985) 17–26. [2] J. Larson, S. Floreen, Metall. Mater. Trans. A 8 (1977) 51–55. [3] P.A.A.K. Koul, N. Bellinger, R. Thamburaj, W. Wallace, J.-P. Immarigeon, in: D.N.D.S. Reichman, G. Maurer, S. Antolovich, C. Lund (Eds.), The Metallurgical Society Superalloys, Warrendale, PA, 1988, pp. 3–12. [4] M.M.H. Loyer Danflou, A. Walder, in: R.W.S.S.D. Antolovich, R.A. MacKay, D.L. Anton, T. Khan, R.D. Kissinger, D.L. Klarstrom (Eds.), The Minerals, Metals & Materials Society Superalloys, Warrendale, PA, 1992, pp. 63–72. [5] M. Tanaka, O. Miyagawa, T. Sakaki, H. Iizuka, F. Ashihara, D. Fujishiro, J. Mater. Sci. 23 (1988) 621–628. [6] M. Tanaka, H. Iizuka, F. Ashihara, J. Mater. Sci. 27 (1992) 2636–2640. [7] J. Larson, Metall. Mater. Trans. A 7 (1976) 1497–1502. [8] J.C. Beddoes, W. Wallace, Mater. Charact. 13 (1980) 185–194. [9] A.K. Koul, G.H. Gessinger, Acta Metall. 31 (1983) 1061–1069. [10] H.U. Hong, H.W. Jeong, I.S. Kim, B.G. Choi, Y.S. Yoo, C.Y. Jo, Thermec 2009 638–642 (Pts 1–4) (2010) 2245–2250. [11] H.U. Hong, S.W. Nam, J. Mater. Sci. 38 (2003) 1535–1542.
[12] K.J. Kim, H.U. Hong, S.W. Nam, J. Nucl. Mater. 393 (2009) 249–253. [13] R. Ye, Z. Xu, Z. Ge, L. Gao, T. Yu, R. Zhang, L. Li, P. Zhang, Acta Metall. Sinica 21 (1985) A131–A138. [14] R.W. Swindeman, M.J. Swindeman, Int. J. Pres. Ves. Pip. 85 (2008) 72–79. [15] M. Maldini, G. Angella, V. Lupinc, Thermec 2009 638–642 (Pts 1–4) (2010) 2285–2290. [16] A.K. Roy, S. Chatterjee, M.H. Hasan, J. Pal, L. Ma, Mater. Sci. Eng. A 527 (2010) 4830–4836. [17] E.A. Trillo, L.E. Murr, J. Mater. Sci. 33 (1998) 1263–1271. [18] Y.S. Lim, J.S. Kim, H.P. Kim, H.D. Cho, J. Nucl. Mater. 335 (2004) 108–114. [19] K.J. Kim, J. Ginsztler, S.W. Nam, Mater. Lett. 59 (2005) 1439–1443. [20] A.L. Bowman, G.P. Arnold, E.K. Storms, N.G. Nereson, Acta Crystallogr. B 28 (1972) 3102–3103. [21] M. Vardavoulias, G. Papadimitriou, Phys. Status Solidi A 134 (1992) 183–191. [22] J. Xie, J. Shen, N. Chen, S. Seetharaman, Acta Mater. 54 (2006) 4653–4658. [23] F.R. Beckitt, B.R. Clark, Acta Metall. 15 (1967) 113–129. [24] G.J. Shiflet, Mater. Sci. Eng. 81 (1986) 61–100. [25] D.E. Stephens, G.R. Purdy, Acta Metall. 23 (1975) 1343–1352. [26] Q. Li, F. Wawner, J. Mater. Sci. 32 (1997) 5363–5370. [27] L.E. Murr, Interfacial Phenomena in Metals and Alloys, Addison-Wesley Educational Publishers Inc., Reading, MA, 1975. [28] D.A. Porter, K.E. Easterling, Phase Transformations in Metals and Alloys, Second Edition, CRC Press, Boca Raton, 1992. [29] H. Hong, B. Rho, S. Nam, Mater. Sci. Eng. A 318 (2001) 285–292. [30] R.S. Barnes, Philos. Mag. 5 (1960) 635–646. [31] D.R. Lide, CRC Handbook of Chemistry and Physics, 86 edition, CRC Press, Boca Raton, 2005, pp. 9–63. [32] P. Nash, J. Phase Equilib. 7 (1986) 466–476.