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Abnormal kinetics of ordering transformation in Ni2(Cr0.5, Mo0.5) alloy
Journal of Alloys and Compounds 639 (2015) 341–345
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jalcom
Abnormal kinetics of ordering transformation in Ni2(Cr0.5, Mo0.5) alloy A. Verma ⇑, J.B. Singh, J.K. Chakravartty Mechanical Metallurgy Division, Bhabha Atomic Research Centre, Mumbai 400 085, India
a r t i c l e
i n f o
Article history: Received 3 January 2015 Received in revised form 18 March 2015 Accepted 19 March 2015 Available online 23 March 2015 Keywords: Continuous ordering Short-range order Transmission electron microscopy Nickel superalloys Splat-quenching
a b s t r a c t Ni–Cr–Mo alloys undergo a disorder to order transformation via a short-range order. Enhanced defect concentration is known to accelerate ordering kinetics. However, a sluggish ordering kinetics has been observed in splat-quenched Ni2(Cr0.5, Mo0.5) alloy that contained higher quenched-in defect. This curious observation of abnormal kinetics has been explained on the basis of smaller driving force for ordering due to the suppression of short-range order in splat-quenched samples. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction Many Ni-base alloys, such as Ni–Mo, Ni–Cr–Mo, Ni–Al–Mo and Ni–Cr–W, undergo a disorder (face centered cubic, fcc, structure) to order transformations via a {1 ½ 0} short-range order (SRO) to form long-range ordered (LRO) precipitates of NxM stoichiometry (where N = Ni; M = Mo, Cr, W, etc; and x = 2–4) [1–12]. The SRO forms via a 2nd order spinodal reaction while the LRO evolves by a 1st order reaction either via a continuous or a nucleation and growth mechanism decided by the ordering temperature [7,13]. The existence of the SRO is characterized by the appearance of diffuse intensity maxima at {1 ½ 0} positions in the selected area electron diffraction (SAED) which are different from those of the emerging LRO phases in the alloys [1–12]. In a recent study on Ni–16.7 at.%Cr–16.7 at.%Mo alloy, the {1 ½ 0} SRO has been shown to co-exists with 1/3{2 2 0} SRO and transforms to an ordered Ni2(Cr, Mo) phase having a Pt2Mo-prototype structure [12]. The ordered Ni2(Cr, Mo) phase is characterized by the appearance of superlattice (SL) reflections in electron diffraction patterns at 1/3{2 2 0} positions [10]. This phase is also known to form in many commercial Ni-base superalloys and its precipitation has been linked to their increased susceptibility to stress corrosion cracking (SCC) [14–16]. In addition, formation of the Ni2(Cr, Mo) phase produces substantial lattice contraction and causes significant stresses or dimensional changes (i.e., negative creep) which affects mechanical properties of the alloys [17]. Although, it may be
possible to eliminate this undesirable phase and rejuvenate alloy properties through proper heat treatments (see, for example [18]), this may sometimes be difficult due to design or operational limitations. Suppression of the formation of ordered Ni2(Cr, Mo) phase is thus expected to enhance the life expectancy of these materials in a cost-effective manner. As mentioned above, one of the common features of ordering in Ni–Cr–Mo alloys is that SRO always precedes the ordering process. It is therefore, imperative to understand the role of SRO on the evolving ordered phase by changing the initial microstructure. One of the ways to alter the initial microstructure is by rapidly quenching the alloy from the liquid state. In an earlier paper, splat-quenching has been shown to suppress the SRO in Ni– 16.7 at.%Cr–16.7 at.%Mo alloy [12]. Splat-quenched alloy was therefore studied to understand order evolution and its kinetics of transformation in the absence of SRO and compare them with those when SRO is present. During this study, anomalous kinetics of ordering has been observed in the splat-quench state. Rapid quenching of alloys from the liquid state are known to produce excess quenched-in vacancies and lattice defects, which otherwise enhances the rate of reaction due to increased mobility of diffusing species, see e.g., [4,19,20]. The ordering transformation in Ni– 16.7 at.%Cr–16.7 at.%Mo alloy has been analyzed in the light Landau theory [21] and a plausible explanation for the observed anomalous kinetics in the splat-quenched state has been extended. 2. Experiment
⇑ Corresponding author: Bhabha Atomic Research Centre, Trombay, Mumbai 400085, India. Tel.: +91 22 2559 0383. E-mail address: [email protected] (A. Verma). http://dx.doi.org/10.1016/j.jallcom.2015.03.157 0925-8388/Ó 2015 Elsevier B.V. All rights reserved.
An alloy of stoichiometric composition Ni–16.7 at.%Cr–16.7 at.%Mo was arc melted in argon atmosphere using a non-consumable tungsten electrode and a water cooled hearth. The alloy ingot was homogenized at 1573 K for 40 h under
342
A. Verma et al. / Journal of Alloys and Compounds 639 (2015) 341–345
flowing high purity argon followed by furnace cooling. From the homogenized ingot, samples with different initial microstructural states were created: (i) samples containing SRO induced by solution treating the alloy at 1423 K for 2 h followed by water quenching (henceforth, referred to as ST sample); (ii) samples containing no SRO (a fully disordered state) produced by splat-quenching of the alloy. Compositions of the homogenized and the splat-quenched alloys, each determined by averaging energy dispersive X-ray (EDX) microanalysis data from 10 different locations, was found to be Ni–12.9Cr–25.5Mo (wt.%) and Ni–13.0Cr–25.6Mo (wt.%) respectively, which was in agreement with the nominal composition of the alloy. The two sets of samples were aged at temperatures ranging from 798 K to 973 K for different periods of time varying from 2 min to 300 min to follow the order evolution path. Thin foils of samples for transmission electron microscopy (TEM) investigations were prepared by electrolytic jet polishing in a solution of 20% perchloric acid in 80% ethanol at 243 K. Standard TEM techniques such as bright-field (BF) and dark-field (DF) imaging and SAED were employed to analyze the microstructure. Owing to the streaking of {1 ½ 0} SRO along h4 2 0i, SAED patterns in h0 0 1i as well as h1 1 2i zone axes were recorded in order to unambiguously established the appearance of the ordered Ni2(Cr, Mo) phase in the investigated alloy.
3. Results Fig. 1 shows SAED patterns in h0 0 1i and h1 1 2i zone axes of ST as well as splat-quenched samples. The square shaped pattern of diffuse intensity observed in h0 0 1i zone axes of the ST sample (Fig. 1a), a characteristic of simultaneous presence of {1 ½ 0} and 1/3{2 2 0} SRO [10–12], was absent in the splat-quenched samples (Fig. 1b). The diffraction pattern with h1 1 2i zone axis clearly delineated diffuse intensities at 1/3{2 2 0} positions corresponding to the ordered Ni2(Cr, Mo) phase. The absence of any diffuse intensity confirmed the suppression of SRO in the splat-quenched sample. Observation of a mottled contrast in the BF image in the ST sample (Fig. 1c) and absence of it in splat-quenched samples (Fig. 1d) were consistent with the presence/absence of SRO in the two microstructures, respectively. It can be noticed that, during ageing, the ordered phase evolved continuously via the build-up of
intensities at 1/3{2 2 0} positions at the expense of intensities at {1 ½ 0} positions, and, finally transformed into sharp reflections with complete extinction of intensity at {1 ½ 0} positions (see Fig. 2). This nature of order evolution was observed in ST samples during ageing at 798 K and 898 K temperatures. The splatquenched samples also exhibited the same order evolution path as shown in Fig. 2b, however, it was preceded by the appearance of SRO from the disordered state at both the temperatures. The ageing time marked by total extinction of SRO intensity and the appearance of sharp SL reflections represented the time at which the nuclei of ordered Ni2(Cr, Mo) phase were first presumed to have formed. Further ageing continued to grow the intensity of SL reflections. It was clear from Fig. 2a that the reflections of Ni2(Cr, Mo) phase in ST samples started emerging out after 60 min of ageing at 798 K and became sharp at 120 min. Increase of ageing temperature to 898 K resulted in the appearance of sharp reflections of Ni2(Cr, Mo) phase within 3 min (Fig. 2a). In splatquenched samples, the ordered phase did not appear even after 300 min of ageing at 798 K, while it appeared only after 60 min at 898 K (Fig. 2b). Similar ordering sequence with enhanced kinetics was observed in splat-quenched samples aged at 973 K (Fig. 3). Fig. 3a also revealed that sharp reflections of ordered phase developed after 5 min of ageing at 973 K and were superimposed with traces of diffuse intensity of the SRO. This ageing treatment developed few nanometer-sized ordered domains distributed homogeneously within grains as well as heterogeneously at grain boundaries as marked by arrows in Fig. 3b. Surprisingly, in ST samples, sharp SL reflections of the ordered phase developed within 2 min of ageing at 973 K without any diffuse diffraction intensity of the SRO (Fig. 3c) suggesting of accelerated ordering kinetics in them. This was also confirmed by well developed ordered domains revealed in the DF image (Fig. 3d). This established a sluggish ordering kinetics in splat-quenched samples at all temperatures,
Fig. 1. TEM microstructures of the Ni2(Cr0.5Mo0.5) alloy: (a) and (b) h0 0 1i and h1 1 2i zone axes SAED patterns of ST and splat–quenched samples, respectively; (c) and (d) BF images of ST and splat–quenched samples, respectively. A mottled contrast can be observed only in (c) (see text for details).
A. Verma et al. / Journal of Alloys and Compounds 639 (2015) 341–345
343
Fig. 2. h0 0 1i and h1 1 2i zone axes SAED patterns of (a) ST and (b) splat-quenched samples, depicting order evolution during ageing at 698 K and 898 K temperatures (see text for details).
Fig. 3. h0 0 1i and h1 1 2i zone axes SAED patterns and DF images of ordered domains obtained after ageing at 973 K for different periods mentioned in respective figures: (a) SAED pattern, (b) DF image of splat-quenched samples; (c) SAED pattern and (d) DF image of ST samples.
though the formation of the ordered Ni2(Cr, Mo) phase would occur via a continuous mode at temperatures below 973 K and by a nucleation and growth mode at higher temperatures. 4. Discussion Present investigations have demonstrated a sluggish ordering kinetics in splat-quenched samples as revealed in Figs. 2 and 3. Since the splat-quenched samples are known to contain higher quenched-in vacancies as compared to those quenched from a solid solution state, they are expected to exhibit faster ordering kinetics [4,19,20]. The curious observation of anomalous ordering
kinetics during the present study has been rationalized in terms of weaker driving force for ordering as explained in the following. According to Landau [21], the free energy change, DF, in the close proximity of ordering temperature can be expressed in terms of a generalized order parameter, g, given by the following expression:
DF ¼ A g2 þ B g3 þ C g4
ð1Þ
where coefficients A, B and C depend up on wave vector, temperature, and alloy composition while g is proportional to the concentration wave amplitude. Symmetry considerations and 2nd order nature of the h1 ½ 0i spinodal ordering dictates A to be negative,
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B = zero and C = positive at temperatures lower than the instability temperature [1]. During initial stages of ordering, i.e., close to the disordered state (when g ffi 0) and for small wave amplitudes, the free energy change is governed by the first harmonic term in Eq. (1), as the contribution of higher order terms is negligible. For a given wave vector, k, the extent to which DF can be minimized thus determined primarily by A, which itself is governed by the pairinteraction function, V(k), as given by Mayer et al. [1]
AðkÞ ¼ Nv ½2 VðkÞ þ kB T=C N C M =2
ð2Þ
where Nv denotes the number of atoms per unit volume, kB, is Boltzmann’s constant, and CN and CM are atom fractions of the alloy constituents N and M. Since kBT/CNCM would always be positive, it is V(k) only that would be important in Eq. (2) for the coefficient A(k) to be negative. The occurrence of the diffuse intensity maxima at {1 ½ 0} positions in the early stages of ordering therefore could be correlated with V(k) which has absolute maxima at {1 ½ 0} positions [13]. The pair interaction function, thus, has an important role in stabilizing concentration waves during a second order reaction (i.e., SRO formation during spinodal ordering). The pair-interaction function in the initial ordering stages is also important in tailoring the order evolution sequences by changing individual pair interaction energies and such simulations have already been carried out in the past by Hata et al. [6] and Kulkarni [22]. Further, it has been established by Kulkarni that diffuse diffraction intensity map mimics the V(k) function in the initial ordering stages which depends upon wave vector and alloy composition [22]. The stabilization of only concentration waves with k = h1 ½ 0i and 1/3 h2 2 0i in the present case thus confirms the importance of their pair interaction functions during the evolution of order. The driving force for ordering transformation in the smaller amplitude limit is also dependent upon the amplitude of the concentration waves which evolve according to Eq. (1). Time evolution of the amplitude of concentration waves, Am, within small amplitude limits for a given wave vector during a diffusion reaction at smaller length scale [23], can be described by the following.
Am ðkÞ ¼ Am ðkÞ exp½aðkÞ t
ð3Þ
where Am° is the amplitude at t = 0 and can be found from Eq. (2) by knowing the value of V(k), and a(k) is the amplification factor which is also related to the second derivative of free energy [23]. This amplification factor, for a given Fourier component k, depends strongly on V(k) especially at temperatures relatively lower than the instability temperature as shown by Kulkarni [22]. The pair interaction energies, which have been shown to replicate an ordering behaviour in Ni2Mo alloy [22] similar to that observed in the present study, are used to understand the amplification of concentration waves having different k-vectors. An attempt is made to predict the temporal evolution of the amplification of concentration waves for wave vectors corresponding to disorder, LRO (1/3 h2 2 0i), and SRO (h1 ½ 0i) states on the basis of Eqs. (1)–(3) and is shown in Fig. 4. It is clear from Fig. 4 that h1 ½ 0i wave exhibited the largest amplification among all which is in agreement with our experimental evidences as well as with earlier studies [24]. Fig. 4 also demonstrated that, in the early stages of ordering, both h1 ½ 0i and 1/3 h2 2 0i waves grow simultaneously nearly at the same rate, which supports the simultaneous appearance of diffuse diffraction intensity maxima at 1/3{2 2 0} and {1 ½ 0} positions (see Fig. 2). On the other hand, wave amplification in the disordered state remains relatively a sluggish process as can be seen in Fig. 4 and is followed by the amplification of h1 ½ 0i and 1/3 h2 2 0i waves after attaining certain amplitude equivalent to either of the h1 ½ 0i or 1/3 h2 2 0i waves. The weaker pair interaction function in the disordered state, in fact, had suppressed the initial amplitude of the concentration waves as evident in Fig. 4 and resulted in a sluggish ordering kinetics. Continuation of
Fig. 4. Amplification of concentration waves with wave-vectors corresponding to disorder, long-range order and short-range order (see text for details).
ordering results in an increase in the amplitude of concentration waves. Once the amplitude of the concentration waves is high, the anharmonic terms in the free energy expansion become important and the harmonic waves are modulated by the emergence and preferred growth of higher order waves generally producing peaks at other SL positions [25]. This is consistent with present observations where SL reflections of the ordered phase appeared at positions different than those of the SRO as the transitory stages of ordering have to eventually make a way for the equilibrium/metastable ordered phase. The continuous nature of ordering transformation has a tendency to compete with a nucleation and growth mode at higher temperatures [7]. Observation of sharp superlattice reflections of the ordered phase appearing simultaneously with a diffuse diffraction intensity of the SRO state in splat-quenched samples at 973 K (Fig. 3a) is consistent with this competing nature. In the context of Landau model, this is possible since the ageing temperature (973 K) was close to the critical ordering temperature (1061 K [10]) where large amplitude of concentration fluctuations can easily initiate the nucleation process for the nucleation and growth mechanisms. 5. Conclusion Microscopic evidences supported by theoretical analysis have conclusively established a delayed ordering kinetics in the presence of excess quenched-in-vacancies in a splat-quenched Ni2(Cr0.5, Mo0.5) alloy. The time evolution of concentration waves responsible for the evolution of ordered phase, within the limits of Landau theory, has confirmed that the kinetics of the ordering transformations is strongly governed by pair interactions. A strong reduction of pair interactions by suppressing SRO retarded the evolution of concentration waves which resulted in a sluggish ordering kinetics. Thus, faster quenching methods or other means, which can suppress or reduce the initial SRO, offer means of retarding the evolution of the ordered Ni2(Cr, Mo) phase in Ni–Cr–Mo alloys. Acknowledgements Authors would like acknowledge Dr. Nelia Wanderka of HZB, Berlin and Dr. U.D. Kulkarni (Ex-BARC, Mumbai) for many fruitful discussions during the course of this study. This work was
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supported by a DAE-BRNS sponsored PRF project (Grant no. 2010/ 38/05-BRNS). References [1] J. Mayer, K. Urban, Spinodal ordering in Ni4Mo, Acta Metall. 33 (1985) 539– 543. [2] U.D. Kulkarni, S. Banerjee, Phase separation during the early stages of ordering in Ni3Mo, Acta Metall. 36 (1988) 413–424. [3] U.D. Kulkarni, G.K. Dey, S. Banerjee, Ordering in rapidly solidified Ni2Mo, Scr. Metall. 22 (1988) 437–440. [4] S. Banerjee, U.D. Kulkarni, K. Urban, Initial stages of ordering in Ni3Mo-thermal and irradiation ordering experiments, Acta Metall. 37 (1989) 35–48. [5] M. Kumar, V.K. Vasudevan, Ordering reactions in an Ni–25Mo–8Cr alloy, Acta Mater. 44 (1996) 1591–1600. [6] S. Hata, S. Matsumura, N. kuwano, K. Oki, Short range order and its transformation to long range order in Ni4Mo, Acta Mater. 46 (1998) 881–892. [7] A. Arya, S. Banerjee, G.P. Das, I. Dasgupta, T. Saha-Dasgupta, A. Mookerjee, A first-principles thermodynamic approach to ordering in Ni–Mo alloys, Acta Mater. 49 (2001) 3575–3587. [8] A. Arya, G.K. Dey, V.K. Vasudevan, S. Banerjee, Effect of chromium addition on the ordering behaviour of Ni–Mo alloy: experimental results vs. electronic structure calculations, Acta Mater. 50 (2002) 3301–3315. [9] U.D. Kulkarni, G.K. Dey, Ordering and topologically close packed-phase precipitation in a Ni–25 at.%Mo–5 at.%Al alloy, Acta Mater. 52 (2004) 2711– 2720. [10] A. Verma, J.B. Singh, M. Sundararaman, N. Wanderka, Resistivity and transmission electron microscopy investigations of ordering transformation in stoichiometric Ni2(Cr0.5Mo0.5) alloy, Metall. Mater. Trans. A 43 (2012) 3078– 3085. [11] A. Verma, N. Wanderka, J.B. Singh, B. Kumar, J. Banhart, Statistical analysis of composition fluctuations and short-range order in stoichiometric Ni–Cr–Mo alloys, Ultramicroscopy 132 (2013) 227–232.
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[12] A. Verma, N. Wanderka, J.B. Singh, M. Sundararaman, J. Banhart, On the evolution of long-range order from short-range order in a Ni2(Cr0.5Mo0.5) alloy, J. Alloys Comp. 586 (2014) 561–566. [13] D. de Fontaine, K-space symmetry rules for order–disorder reactions, Acta Metall. 23 (1975) 553–571. [14] B.J. Berkowitz, C. Miller, The effect of ordering on the hydrogen embrittlement susceptibility of Ni2Cr, Metall. Soc. AMIE 11A (1980) 1877–1881. [15] K. Miyata, M. Igarashi, Effect of ordering on susceptibility to hydrogen embrittlement of a Ni-base superalloy, Metall. Mater. Trans. A 23A (1992) 953–961. [16] P.E.A. Turchi, L. Kaufman, Z.-K. Liu, Modeling of Ni–Cr–Mo based alloys: Part I— Phase stability, Calphad 30 (2006) 70–87. [17] E. Metcalfe, B. Nath, Some effects of the ordering transformation in Nimonic 80A on stress relaxation behaviour, Mater. Sci. Eng. 67 (1984) 157–162. [18] J.K. Chakravartty, J.B. Singh, M. Sundararaman, Microstructural and mechanical properties of service exposed Alloy 625 ammonia cracker tube removed after 100 000 h, Mater. Sci. Technol. 28 (2012) 702–710. [19] H. Heidsiek, R. Scheffel, K. LÜCke, The influence of quenched-in and thermal vacancies upon short-range-order formation in a Ni11.4 at.% Cr alloy, Le J. de Phys. Colloq. 38 (1977) 174–177. [20] W. Kohl, R. Scheffel, H. Heidsiek, K. Lucke, Investigation of the kinetics of short range order formation and quenched-in vacancy annihilation in Au–l5 at.%Ag by resistivity measurements, Acta Metall. 31 (1983) 1895–1908. [21] L.D. Landau, E.M. Lifshitz, Statistical Physics, Addison-Wesley, Cambridge, 1958. [22] U.D. Kulkarni, Monte Carlo simulation of ordering transformations in Ni–Mobased alloys, Acta Mater. 52 (2004) 2721–2732. [23] H.E. Cook, D. Fontaine de, J.E. Hilliard, A model for diffusion on cubic lattices and its application to the early stages of ordering, Acta Metall. 17 (1969) 765– 773. [24] A.G. Khachaturyan, Theory of Structural Transformations in Solids, Wiley, New York, 1983. [25] W.A. Soffa, D.E. Laughlin, Solid ? Solid Phase Transformations, T.M.S.–A.I.M.E, Pa, U.S.A, 1982.
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jalcom
Abnormal kinetics of ordering transformation in Ni2(Cr0.5, Mo0.5) alloy A. Verma ⇑, J.B. Singh, J.K. Chakravartty Mechanical Metallurgy Division, Bhabha Atomic Research Centre, Mumbai 400 085, India
a r t i c l e
i n f o
Article history: Received 3 January 2015 Received in revised form 18 March 2015 Accepted 19 March 2015 Available online 23 March 2015 Keywords: Continuous ordering Short-range order Transmission electron microscopy Nickel superalloys Splat-quenching
a b s t r a c t Ni–Cr–Mo alloys undergo a disorder to order transformation via a short-range order. Enhanced defect concentration is known to accelerate ordering kinetics. However, a sluggish ordering kinetics has been observed in splat-quenched Ni2(Cr0.5, Mo0.5) alloy that contained higher quenched-in defect. This curious observation of abnormal kinetics has been explained on the basis of smaller driving force for ordering due to the suppression of short-range order in splat-quenched samples. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction Many Ni-base alloys, such as Ni–Mo, Ni–Cr–Mo, Ni–Al–Mo and Ni–Cr–W, undergo a disorder (face centered cubic, fcc, structure) to order transformations via a {1 ½ 0} short-range order (SRO) to form long-range ordered (LRO) precipitates of NxM stoichiometry (where N = Ni; M = Mo, Cr, W, etc; and x = 2–4) [1–12]. The SRO forms via a 2nd order spinodal reaction while the LRO evolves by a 1st order reaction either via a continuous or a nucleation and growth mechanism decided by the ordering temperature [7,13]. The existence of the SRO is characterized by the appearance of diffuse intensity maxima at {1 ½ 0} positions in the selected area electron diffraction (SAED) which are different from those of the emerging LRO phases in the alloys [1–12]. In a recent study on Ni–16.7 at.%Cr–16.7 at.%Mo alloy, the {1 ½ 0} SRO has been shown to co-exists with 1/3{2 2 0} SRO and transforms to an ordered Ni2(Cr, Mo) phase having a Pt2Mo-prototype structure [12]. The ordered Ni2(Cr, Mo) phase is characterized by the appearance of superlattice (SL) reflections in electron diffraction patterns at 1/3{2 2 0} positions [10]. This phase is also known to form in many commercial Ni-base superalloys and its precipitation has been linked to their increased susceptibility to stress corrosion cracking (SCC) [14–16]. In addition, formation of the Ni2(Cr, Mo) phase produces substantial lattice contraction and causes significant stresses or dimensional changes (i.e., negative creep) which affects mechanical properties of the alloys [17]. Although, it may be
possible to eliminate this undesirable phase and rejuvenate alloy properties through proper heat treatments (see, for example [18]), this may sometimes be difficult due to design or operational limitations. Suppression of the formation of ordered Ni2(Cr, Mo) phase is thus expected to enhance the life expectancy of these materials in a cost-effective manner. As mentioned above, one of the common features of ordering in Ni–Cr–Mo alloys is that SRO always precedes the ordering process. It is therefore, imperative to understand the role of SRO on the evolving ordered phase by changing the initial microstructure. One of the ways to alter the initial microstructure is by rapidly quenching the alloy from the liquid state. In an earlier paper, splat-quenching has been shown to suppress the SRO in Ni– 16.7 at.%Cr–16.7 at.%Mo alloy [12]. Splat-quenched alloy was therefore studied to understand order evolution and its kinetics of transformation in the absence of SRO and compare them with those when SRO is present. During this study, anomalous kinetics of ordering has been observed in the splat-quench state. Rapid quenching of alloys from the liquid state are known to produce excess quenched-in vacancies and lattice defects, which otherwise enhances the rate of reaction due to increased mobility of diffusing species, see e.g., [4,19,20]. The ordering transformation in Ni– 16.7 at.%Cr–16.7 at.%Mo alloy has been analyzed in the light Landau theory [21] and a plausible explanation for the observed anomalous kinetics in the splat-quenched state has been extended. 2. Experiment
⇑ Corresponding author: Bhabha Atomic Research Centre, Trombay, Mumbai 400085, India. Tel.: +91 22 2559 0383. E-mail address: [email protected] (A. Verma). http://dx.doi.org/10.1016/j.jallcom.2015.03.157 0925-8388/Ó 2015 Elsevier B.V. All rights reserved.
An alloy of stoichiometric composition Ni–16.7 at.%Cr–16.7 at.%Mo was arc melted in argon atmosphere using a non-consumable tungsten electrode and a water cooled hearth. The alloy ingot was homogenized at 1573 K for 40 h under
342
A. Verma et al. / Journal of Alloys and Compounds 639 (2015) 341–345
flowing high purity argon followed by furnace cooling. From the homogenized ingot, samples with different initial microstructural states were created: (i) samples containing SRO induced by solution treating the alloy at 1423 K for 2 h followed by water quenching (henceforth, referred to as ST sample); (ii) samples containing no SRO (a fully disordered state) produced by splat-quenching of the alloy. Compositions of the homogenized and the splat-quenched alloys, each determined by averaging energy dispersive X-ray (EDX) microanalysis data from 10 different locations, was found to be Ni–12.9Cr–25.5Mo (wt.%) and Ni–13.0Cr–25.6Mo (wt.%) respectively, which was in agreement with the nominal composition of the alloy. The two sets of samples were aged at temperatures ranging from 798 K to 973 K for different periods of time varying from 2 min to 300 min to follow the order evolution path. Thin foils of samples for transmission electron microscopy (TEM) investigations were prepared by electrolytic jet polishing in a solution of 20% perchloric acid in 80% ethanol at 243 K. Standard TEM techniques such as bright-field (BF) and dark-field (DF) imaging and SAED were employed to analyze the microstructure. Owing to the streaking of {1 ½ 0} SRO along h4 2 0i, SAED patterns in h0 0 1i as well as h1 1 2i zone axes were recorded in order to unambiguously established the appearance of the ordered Ni2(Cr, Mo) phase in the investigated alloy.
3. Results Fig. 1 shows SAED patterns in h0 0 1i and h1 1 2i zone axes of ST as well as splat-quenched samples. The square shaped pattern of diffuse intensity observed in h0 0 1i zone axes of the ST sample (Fig. 1a), a characteristic of simultaneous presence of {1 ½ 0} and 1/3{2 2 0} SRO [10–12], was absent in the splat-quenched samples (Fig. 1b). The diffraction pattern with h1 1 2i zone axis clearly delineated diffuse intensities at 1/3{2 2 0} positions corresponding to the ordered Ni2(Cr, Mo) phase. The absence of any diffuse intensity confirmed the suppression of SRO in the splat-quenched sample. Observation of a mottled contrast in the BF image in the ST sample (Fig. 1c) and absence of it in splat-quenched samples (Fig. 1d) were consistent with the presence/absence of SRO in the two microstructures, respectively. It can be noticed that, during ageing, the ordered phase evolved continuously via the build-up of
intensities at 1/3{2 2 0} positions at the expense of intensities at {1 ½ 0} positions, and, finally transformed into sharp reflections with complete extinction of intensity at {1 ½ 0} positions (see Fig. 2). This nature of order evolution was observed in ST samples during ageing at 798 K and 898 K temperatures. The splatquenched samples also exhibited the same order evolution path as shown in Fig. 2b, however, it was preceded by the appearance of SRO from the disordered state at both the temperatures. The ageing time marked by total extinction of SRO intensity and the appearance of sharp SL reflections represented the time at which the nuclei of ordered Ni2(Cr, Mo) phase were first presumed to have formed. Further ageing continued to grow the intensity of SL reflections. It was clear from Fig. 2a that the reflections of Ni2(Cr, Mo) phase in ST samples started emerging out after 60 min of ageing at 798 K and became sharp at 120 min. Increase of ageing temperature to 898 K resulted in the appearance of sharp reflections of Ni2(Cr, Mo) phase within 3 min (Fig. 2a). In splatquenched samples, the ordered phase did not appear even after 300 min of ageing at 798 K, while it appeared only after 60 min at 898 K (Fig. 2b). Similar ordering sequence with enhanced kinetics was observed in splat-quenched samples aged at 973 K (Fig. 3). Fig. 3a also revealed that sharp reflections of ordered phase developed after 5 min of ageing at 973 K and were superimposed with traces of diffuse intensity of the SRO. This ageing treatment developed few nanometer-sized ordered domains distributed homogeneously within grains as well as heterogeneously at grain boundaries as marked by arrows in Fig. 3b. Surprisingly, in ST samples, sharp SL reflections of the ordered phase developed within 2 min of ageing at 973 K without any diffuse diffraction intensity of the SRO (Fig. 3c) suggesting of accelerated ordering kinetics in them. This was also confirmed by well developed ordered domains revealed in the DF image (Fig. 3d). This established a sluggish ordering kinetics in splat-quenched samples at all temperatures,
Fig. 1. TEM microstructures of the Ni2(Cr0.5Mo0.5) alloy: (a) and (b) h0 0 1i and h1 1 2i zone axes SAED patterns of ST and splat–quenched samples, respectively; (c) and (d) BF images of ST and splat–quenched samples, respectively. A mottled contrast can be observed only in (c) (see text for details).
A. Verma et al. / Journal of Alloys and Compounds 639 (2015) 341–345
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Fig. 2. h0 0 1i and h1 1 2i zone axes SAED patterns of (a) ST and (b) splat-quenched samples, depicting order evolution during ageing at 698 K and 898 K temperatures (see text for details).
Fig. 3. h0 0 1i and h1 1 2i zone axes SAED patterns and DF images of ordered domains obtained after ageing at 973 K for different periods mentioned in respective figures: (a) SAED pattern, (b) DF image of splat-quenched samples; (c) SAED pattern and (d) DF image of ST samples.
though the formation of the ordered Ni2(Cr, Mo) phase would occur via a continuous mode at temperatures below 973 K and by a nucleation and growth mode at higher temperatures. 4. Discussion Present investigations have demonstrated a sluggish ordering kinetics in splat-quenched samples as revealed in Figs. 2 and 3. Since the splat-quenched samples are known to contain higher quenched-in vacancies as compared to those quenched from a solid solution state, they are expected to exhibit faster ordering kinetics [4,19,20]. The curious observation of anomalous ordering
kinetics during the present study has been rationalized in terms of weaker driving force for ordering as explained in the following. According to Landau [21], the free energy change, DF, in the close proximity of ordering temperature can be expressed in terms of a generalized order parameter, g, given by the following expression:
DF ¼ A g2 þ B g3 þ C g4
ð1Þ
where coefficients A, B and C depend up on wave vector, temperature, and alloy composition while g is proportional to the concentration wave amplitude. Symmetry considerations and 2nd order nature of the h1 ½ 0i spinodal ordering dictates A to be negative,
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B = zero and C = positive at temperatures lower than the instability temperature [1]. During initial stages of ordering, i.e., close to the disordered state (when g ffi 0) and for small wave amplitudes, the free energy change is governed by the first harmonic term in Eq. (1), as the contribution of higher order terms is negligible. For a given wave vector, k, the extent to which DF can be minimized thus determined primarily by A, which itself is governed by the pairinteraction function, V(k), as given by Mayer et al. [1]
AðkÞ ¼ Nv ½2 VðkÞ þ kB T=C N C M =2
ð2Þ
where Nv denotes the number of atoms per unit volume, kB, is Boltzmann’s constant, and CN and CM are atom fractions of the alloy constituents N and M. Since kBT/CNCM would always be positive, it is V(k) only that would be important in Eq. (2) for the coefficient A(k) to be negative. The occurrence of the diffuse intensity maxima at {1 ½ 0} positions in the early stages of ordering therefore could be correlated with V(k) which has absolute maxima at {1 ½ 0} positions [13]. The pair interaction function, thus, has an important role in stabilizing concentration waves during a second order reaction (i.e., SRO formation during spinodal ordering). The pair-interaction function in the initial ordering stages is also important in tailoring the order evolution sequences by changing individual pair interaction energies and such simulations have already been carried out in the past by Hata et al. [6] and Kulkarni [22]. Further, it has been established by Kulkarni that diffuse diffraction intensity map mimics the V(k) function in the initial ordering stages which depends upon wave vector and alloy composition [22]. The stabilization of only concentration waves with k = h1 ½ 0i and 1/3 h2 2 0i in the present case thus confirms the importance of their pair interaction functions during the evolution of order. The driving force for ordering transformation in the smaller amplitude limit is also dependent upon the amplitude of the concentration waves which evolve according to Eq. (1). Time evolution of the amplitude of concentration waves, Am, within small amplitude limits for a given wave vector during a diffusion reaction at smaller length scale [23], can be described by the following.
Am ðkÞ ¼ Am ðkÞ exp½aðkÞ t
ð3Þ
where Am° is the amplitude at t = 0 and can be found from Eq. (2) by knowing the value of V(k), and a(k) is the amplification factor which is also related to the second derivative of free energy [23]. This amplification factor, for a given Fourier component k, depends strongly on V(k) especially at temperatures relatively lower than the instability temperature as shown by Kulkarni [22]. The pair interaction energies, which have been shown to replicate an ordering behaviour in Ni2Mo alloy [22] similar to that observed in the present study, are used to understand the amplification of concentration waves having different k-vectors. An attempt is made to predict the temporal evolution of the amplification of concentration waves for wave vectors corresponding to disorder, LRO (1/3 h2 2 0i), and SRO (h1 ½ 0i) states on the basis of Eqs. (1)–(3) and is shown in Fig. 4. It is clear from Fig. 4 that h1 ½ 0i wave exhibited the largest amplification among all which is in agreement with our experimental evidences as well as with earlier studies [24]. Fig. 4 also demonstrated that, in the early stages of ordering, both h1 ½ 0i and 1/3 h2 2 0i waves grow simultaneously nearly at the same rate, which supports the simultaneous appearance of diffuse diffraction intensity maxima at 1/3{2 2 0} and {1 ½ 0} positions (see Fig. 2). On the other hand, wave amplification in the disordered state remains relatively a sluggish process as can be seen in Fig. 4 and is followed by the amplification of h1 ½ 0i and 1/3 h2 2 0i waves after attaining certain amplitude equivalent to either of the h1 ½ 0i or 1/3 h2 2 0i waves. The weaker pair interaction function in the disordered state, in fact, had suppressed the initial amplitude of the concentration waves as evident in Fig. 4 and resulted in a sluggish ordering kinetics. Continuation of
Fig. 4. Amplification of concentration waves with wave-vectors corresponding to disorder, long-range order and short-range order (see text for details).
ordering results in an increase in the amplitude of concentration waves. Once the amplitude of the concentration waves is high, the anharmonic terms in the free energy expansion become important and the harmonic waves are modulated by the emergence and preferred growth of higher order waves generally producing peaks at other SL positions [25]. This is consistent with present observations where SL reflections of the ordered phase appeared at positions different than those of the SRO as the transitory stages of ordering have to eventually make a way for the equilibrium/metastable ordered phase. The continuous nature of ordering transformation has a tendency to compete with a nucleation and growth mode at higher temperatures [7]. Observation of sharp superlattice reflections of the ordered phase appearing simultaneously with a diffuse diffraction intensity of the SRO state in splat-quenched samples at 973 K (Fig. 3a) is consistent with this competing nature. In the context of Landau model, this is possible since the ageing temperature (973 K) was close to the critical ordering temperature (1061 K [10]) where large amplitude of concentration fluctuations can easily initiate the nucleation process for the nucleation and growth mechanisms. 5. Conclusion Microscopic evidences supported by theoretical analysis have conclusively established a delayed ordering kinetics in the presence of excess quenched-in-vacancies in a splat-quenched Ni2(Cr0.5, Mo0.5) alloy. The time evolution of concentration waves responsible for the evolution of ordered phase, within the limits of Landau theory, has confirmed that the kinetics of the ordering transformations is strongly governed by pair interactions. A strong reduction of pair interactions by suppressing SRO retarded the evolution of concentration waves which resulted in a sluggish ordering kinetics. Thus, faster quenching methods or other means, which can suppress or reduce the initial SRO, offer means of retarding the evolution of the ordered Ni2(Cr, Mo) phase in Ni–Cr–Mo alloys. Acknowledgements Authors would like acknowledge Dr. Nelia Wanderka of HZB, Berlin and Dr. U.D. Kulkarni (Ex-BARC, Mumbai) for many fruitful discussions during the course of this study. This work was
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