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Grain growth kinetics in CoCrFeNi and CoCrFeMnNi high entropy alloys processed by spark plasma sintering
Journal of Alloys and Compounds 791 (2019) 1114e1121
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Grain growth kinetics in CoCrFeNi and CoCrFeMnNi high entropy alloys processed by spark plasma sintering M. Vaidya a, *, Ameey Anupam a, J. Vijay Bharadwaj a, Chandan Srivastava b, B.S. Murty a a b
Department of Metallurgical & Materials Engineering, Indian Institute of Technology Madras, Chennai, 600036, India Department of Materials Engineering, Indian Institute of Science, Bangalore, 560012, India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 December 2018 Received in revised form 20 March 2019 Accepted 25 March 2019 Available online 26 March 2019
Nanocrystalline CoCrFeNi and CoCrFeMnNi high entropy alloys have been processed by mechanical alloying followed by spark plasma sintering. Grain growth kinetics has been estimated for both the alloys by subjecting them to heat treatment in the temperature range 1073e1373 K. These alloys possess a thermally stable single phase FCC structure along with Cr7C3 contamination. Electron back scattered diffraction (EBSD) has been used to determine grain size of all the heat treated samples. Both CoCrFeNi and CoCrFeMnNi alloys exhibit a grain growth exponent, n ¼ 3, suggesting long-range diffusioncontrolled grain growth in these alloys. Activation energies for grain growth are 134 and 197 kJ/mol for CoCrFeNi and CoCrFeMnNi, respectively, which are significantly lower than the activation energy of lattice diffusion in these alloys. Hardness is measured for CoCrFeMnNi alloy as function of grain size and is found to follow the Hall-Petch type relation. The strength coefficient (slope of Hall-Petch relation) is calculated as 1.92 GPa, which is nearly three times that of the value reported in literature for coarse grained CoCrFeMnNi. Presence of carbides enhances the hardness of these HEAs. The maximum contribution to strengthening comes from the FCC-carbide phase boundaries. © 2019 Elsevier B.V. All rights reserved.
Keywords: High entropy alloys Grain growth Activation energy Hall-Petch hardness
1. Introduction The recently developed high entropy alloys (HEAs) combine constituents in equimolar or near equimolar proportions. Their unique multi-element matrix and high configurational entropy is believed to be responsible for enhanced phase stability and superior properties [1]. Nanostructured HEAs combine the synergistic effects of increased configurational entropy and nano-size regime, and have shown exciting properties [2]. Nanocrystalline CoCrFeMnNi produced by severe plastic deformation showed very high strength of 1.9 GPa [3]. Zou et al. [4] showed that nanocrystalline refractory HEAs exhibit remarkably low strain rate sensitivity and high strength to weight ratios. Nanocrystalline AlCoCrFeNi2.1 eutectic HEA has been shown to display simultaneous enhancement of strength and ductility [5]. Mechanical alloying (MA) is a well-known solid-state, nonequilibrium, top-down approach to produce nanocrystalline materials with excellent homogeneity [6] and has been widely used for processing HEAs [7]. Spark plasma sintering (SPS) has become an
* Corresponding author. E-mail address: [email protected] (M. Vaidya). https://doi.org/10.1016/j.jallcom.2019.03.341 0925-8388/© 2019 Elsevier B.V. All rights reserved.
increasingly attractive option for the consolidation of MAed powders [8], owing to shorter times required relative to conventional sintering and thus ensuring better retention of nanocrystallinity. However, HEAs containing strong carbide forming elements like Cr, V, and Mo have frequently exhibited carbide contamination during MA and subsequent consolidation and thermal exposure, as summarized in Table 1. The exact mechanism of carbide formation has not been deciphered yet, but the source of carbon is suggested to be process controlling agent used during MA [9] and the extent of it is determined by the constituent elements present in the HEA [10]. Nonetheless, the carbide formation is not always detrimental. And has been shown to contribute to the strength of nanocrystalline HEAs [11]. One of the important aspects of nanocrystalline HEAs is their thermal stability, which decides their potential for any high temperature application. Diffusion controlled processes like phase transformation, grain growth etc. have increased proclivity in nanocrystalline alloys on thermal exposure. Retention of nanostructure and phase stability form the two attributes of thermal stability investigations. AlCoCrFeMnNi HEA produced by mechanochemical synthesis has shown thermal stability up to 500 C after which it undergoes diffusional transformation to complex
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Table 1 Formation of Cr-carbides reported in literature for MAed HEAs after consolidation and heat treatment. Alloy
Phases
Consolidation/Heat treatment
Phases
Ref.
CoCrFeMnNiNx AlCoCrFe Al0.3CoCrFeMnNi CoCrFeMnNi Al0.3CoCrFeMnNi CoCrFeMnNiC0.3Ti0.3 CoCrFeNi Al0.5C0.2Co0.3CrFeNi CoCr0.25CuFeNi1.5V0.25 CoCrFeNi AlCoCrFe Co20Cr20Fe20Mn5Ni20Zn15 CoCrFe(Mn)Ni
FCC BCC FCC FCC FCC FCC þ BCC FCC þ BCC BCC þ FCC FCC þ BCC FCC þ BCC B2 þ Cr23C6 FCC FCC þ WC
VHPS SPS SPS VHPS SPS VHPS SPS SPS SPS 900 C, 600 h 900 C, 600 h 500 C, 1 h 800e1100 C
FCC þ Cr23C6 þ Cr2N B2 þ Cr23C6 FCC þ B2 þ Cr carbide FCC þ M7C3 þ M23C6 FCC þ B2 þ Cr carbide FCC þ þ TiC þ M7C3 þ M23C6 FCC þ Cr7C3 þ Cr2O3 FCC þ BCC þ Cr23C6 þ B2 FCC1 þ FCC2 þ (V, Cr)7C3 FCC þ Cr7C3 þ Cr2O3 B2 þ Cr23C6 FCC þ a-FeCo þ b-NiZn þ Cr23C6 FCC þ Cr7C3
[34] [11,35] [36] [33] [36] [33] [14] [37] [38] [14] [11] [39] [9]
phases [12]. Nanocrystalline AlCoCrFeNi has shown transformation from BCC to B2 structure and formation of intermetallics on thermal exposure [13]. High resistance to grain growth has been observed in CoCrFeNi during long term heat treatment (600 h) at 900 C [14]. Grain growth in nanocrystalline materials, at elevated temperatures, leads to reduction in strength and abates the other benefits of nano-sized microstructure. Liu et al. [15] studied the grain growth behaviour in fine grained CoCrFeMnNi and showed that it is controlled by bulk diffusion of Ni. Wu et al. [16] derived grain growth parameters and Hall Petch relation for lower component constituents of CoCrFeMnNi HEA having fine grain microstructure. The only reports, to the best of our knowledge, on coarsening of nanocrystalline HEAs have been by Praveen et al. [14,17]. They demonstrated excellent resistance to grain growth in nanostructured CoCrFeNi, and calculated grain growth exponent (n ¼ 4) by assuming activation energy equivalent to that of bulk diffusion of Ni [17]. However, increased grain boundary fraction in SPSed HEAs (owing to their nano-size) indicates the possibility of high diffusivity path being dominant for grain growth and calls for careful analysis of this assumption. Tracer diffusion measurements in CoCrFeNi and CoCrFeMnNi HEAs have shown that the grain boundary contribution to diffusion profiles exist even at relatively higher homologous temperatures [18]. Laplanche et al. [19] have demonstrated that the activation energy for the precipitation of phase in Cr26Mn20Fe20Co20Ni14 HEA is close to that of Ni GB diffusion CoCrFeMnNi. Lee et al. [20] have also indicated the contribution of grain boundary diffusion to the plastic flow mechanism in nanocrystalline HEAs. The present work examines the grain growth behaviour of nanocrystalline CoCrFeNi and CoCrFeMnNi HEAs produced by MA and SPS. The activation energy for the grain growth has been determined and correlated with the measured diffusivities in the literature. Hardness of these HEAs is also measured as a function of grain size and contributions from reduced grain size and second phase particles are delineated.
2. Experimental details Nanocrystalline CoCrFeNi and CoCrFeMnNi alloy powders were prepared high energy ball milling as described in Ref. [9]. The milled powders were consolidated by SPS in Dr. Sinter unit (Model SPS- 625, SPS Syntex Inc., Japan) at a temperature of 1173 K, with holding time of 5 min and a pressure of 60 MPa. 2 mm thick slices were cut from SPS pellets and sealed in quartz tube under Ar atmosphere and subjected to heat treatment at 1073, 1173 and 1373 K in a muffle furnace with SiC heating coils and subsequently quenched in water. Phase formation in as processed and heat
treated samples was studied by X-ray diffraction (XRD) analysis, using Panalytical X-ray diffractometer with Cu-Ka radiation. Transmission electron microscopy investigations were carried out, to confirm phase structure, in FEI TITAN microscope. The electron back-scattered diffraction (EBSD) was used to determine the grain sizes of heat treated SPS samples. EBSD scans were performed on finely polished samples using a TSL-OIM software attached to field emission scanning electron microscope (SEM) at 30 kV and maps were collected using a step size of 75 nm using a hexagonal grid. All the points with a confidence index (CI) of less than 0.15 were removed from the scan before further analysis. To determine grain size, intercept length method in-built in EBSD software has been used for alloys. It was ensured that the area of EBSD scan was sufficient to cover at least 2500 grains. Hardness was measured on the polished samples under a load of 500 gf with a dwell time of 10s on a Wilpert Wilson Vickers Hardness instrument. Reported values are an average of 10 readings across the pellet.
3. Results and discussion 3.1. Phase and microstructure evolution in heat treated SPS alloys Fig. 1a presents the XRD patterns of as-SPSed CoCrFeNi and CoCrFeMnNi HEAs and after heat treatment at 1373 K for 96 h. SPSed alloys show a single phase FCC structure along with Cr7C3 contamination and this mixture is retained even after heat treatment at 1373 K for 96 h. The two most intense peaks of Cr7C3 lie very close (on the either side) to the (111) peak of FCC, as illustrated in XRD patterns of SPSed alloys (Fig. 1a). Since the diffractograms taken at different temperatures are stacked together, therefore an existence of Cr7C3 peak is often not evident. Therefore slow scan in the 2q range 40e55 is shown for CoCrFeMnNi heat treated at 1373 K for 96 h in Fig. 1b, which clearly shows the peaks of FCC and Cr7C3. The high angle annular dark field (HAADF) image of SPSed CoCrFeNi is presented in Fig. 1c. In addition to FCC phase and Cr7C3, small particles belonging to a possible third phase are observed. Elemental mapping using scanning transmission electron microscopy (STEM) mode shows the regions rich in CreCeO in addition to enriched regions of CreO and Cr-depleted FCC HEA matrix. In our recent work [9], the selected area diffraction (SAD) patterns confirming the orthorhombic structure of Cr7C3 and FCC matrix in SPSed CoCrFeMnNi HEA have been presented. Among the constituent elements of HEAs studied, Cr has the highest tendency to form carbide [21] and oxide [22], as reflected in their respective Ellingham diagrams. Phase fraction of Cr7C3 phase is estimated for CoCrFeNi and CoCrFeMnNi as a function of temperature (Fig. 2a) and time (Fig. 2b) using the method described in Vaidya et al. [10] (Fig. 2). No significant change is observed in amount of Cr7C3. Thus,
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Fig. 1. (a) XRD patterns of SPS and heat treated (1373 K, 96 h) CoCrFeNi and CoCrFeMnNi HEAs. Mixture of FCC and Cr7C3 is retained on thermal exposure. (b) Slow scan of heat treated CoCrFeMnNi to clearly show the peaks of FCC and Cr7C3. (c) High angular annular dark field (HAADF) image of CoCrFeNi after SPS. Elemental mapping shows Cr-depleted FCC matrix, Cr7C3 and Cr-rich oxide particles.
it is suggested that the dissolution of Cr7C3 is insignificant during the thermal exposure up to 1373 K. This can be attributed to the stability of Cr7C3 at these temperatures, as depicted in its Ellingham diagram [21]. Fig. 3a and b illustrate microstructure of CoCrFeMnNi samples heat treated at 1073 and 1373 K, respectively. At 1073 K, matrix region consists of fine particles of Cr7C3 and Cr-rich oxide. On thermal exposure at 1373 K, the microstructure consists of matrix with Cr7C3 and Cr-rich oxide particles grown in size relative to lower temperatures. Fig. 4 presents the composition plot for CoCrFeNi and CoCrFeMnNi HEAs heat treated at 1373 K for 96 h, giving the compositions of Cr-depleted FCC matrix, Cr7C3 and CreO regions. The extended FCC phase field of CoeCreFeeMneNi system has been well documented [23] and thus FCC structure is retained even with the Cr depletion.
3.2. Grain growth kinetics in CoCrFeNi and CoCrFeMnNi HEAs EBSD measurements have been performed on heat treated CoCrFeNi and CoCrFeMnNi HEAs to determine grain size as a function of temperature (1073, 1173 and 1373 K for 96 h) and time (24, 48, 72 and 96 h at 1373 K). In this work, our objective is to study the grain growth of FCC phase. Therefore, in EBSD analysis, only FCC phase has been indexed using Ni standard due to their close proximity in lattice parameter (aNi ¼ 0.352 nm, aCoCrFeMnNi ¼ 0.357 nm). Fig. 5a exemplifies the phase map determined using EBSD for CoCrFeMnNi HEA heat treated at 1073 K for 96 h. The grey region corresponds to the FCC phase while black area conforms to Cr carbide and oxide phases. Grain growth at elevated temperature (1373 K) is clearly demonstrated in Fig. 5b. Fig. 5c reveals the grain size distribution in CoCrFeMnNi heat treated at 1073
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Fig. 2. Phase fraction of Cr7C3 as a function of a) temperature and b) time at 1373 K. No significant dissolution of carbides is seen on thermal exposure.
Fig. 3. Microstructure of heat treated CoCrFeMnNi at (a) 1073 and (b) 1173 K for 96 h. Growth of carbide particles can be clearly seen with increasing annealing temperature.
Fig. 4. Composition (at.%) plot of various phases in SPSed CoCrFeNi and CoCrFeMnNi heat treated at 1373 K for 96 h. FCC is depleted in Cr for both quaternary and quinary HEA.
and 1373 K, from which corresponding average grain sizes are determined as 416 and 1766 nm, respectively. Occurrence of abnormal grain growth is hinted as the grain size distribution becomes wider at elevated temperature. The initial grain sizes of as-
SPS alloys have been determined using TEM analysis (not presented here) and the corresponding values are 114 and 185 nm for CoCrFeNi and CoCrFeMnNi, respectively. It may be noted that although standard deviations in grain size
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Fig. 5. EBSD phase maps of SPSed CoCrFeMnNi heat treated for 96 h at a) 1073 K and b) 1373 K and c) corresponding grain size distribution. Grey regions correspond to FCC phase and black areas are un-indexed Cr-rich carbide and oxides. Grain growth and wider distribution of grain size at 1373 K are revealed.
determined from EBSD are high, an average value of grain size can give a reasonable idea of the trend and corresponding kinetic parameters. For more meaningful statistics, grain-sizes which occupy less than 5% area fraction are excluded from grain size determination. Grain growth factor, Gf (df e d0/d0) is defined as the ratio of final and initial grain sizes after the heat treatment at a specified temperature (T) and time (t). Table 2 compares the Gf of CoCrFeNi and CoCrFeMnNi HEAs at different temperatures used in the present study. A normalized grain growth factor, Gf* ¼ Gf/(Th.t) is also calculated, where Th ¼ T/Tm is the homologous temperature of the alloy. Tm is melting point; 1717 and 1607 K for CoCrFeNi and CoCrFeMnNi, respectively. It can be inferred that Gf is slightly higher for CoCrFeMnNi alloy than CoCrFeNi at 1373 K, which indicates enhanced grain growth in quinary alloy. When normalized with homologous temperature, Gf* for CoCrFeNi and CoCrFeMnNi turns out to be similar. This is in agreement with the conclusions of
Vaidya et al. [24] that the role of configurational entropy in slowing down atomic transport rates diminishes at elevated temperatures. Grain growth kinetics in a polycrystalline material is often described by the power law expression as [25]:
dn dn0 ¼ kt
(1)
where n is the grain growth exponent, k is the temperature coefficient, t is the holding time, d0 and d are the grain sizes at t ¼ 0 and after time t, respectively. The temperature dependence of k follows Arrhenius behaviour as k ¼ k0exp(-Q/RT). Here k0 is the preexponential factor, Q is the activation energy of grain growth, and RT has usual meaning. Partial differentiation of eq. (1) w.r.t time followed by taking natural logarithm on both sides gives:
Table 2 Grain growth factor, Gf and normalized grain growth factor, Gf* for CoCrFeNi and CoCrFeMnNi (SPS) HEAs studied in the present work. Alloy
T (K)
t (h)
Th ¼ T/Tm
d0 (nm)
df (nm)
Gf¼ (df - d0)/d0
Gf* ¼ Gf/(Th*t)
CoCrFeNi
1073 1173 1373 1073 1173 1373
96 96 96 96 96 96
0.62 0.68 0.80 0.67 0.73 0.85
114 114 114 185 185 185
340 360 930 416 518 1766
1.98 2.16 7.16 1.25 1.80 8.55
0.03 0.03 0.09 0.02 0.03 0.10
CoCrFeMnNi
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ln ðvd=vtÞ ¼ lnðk=nÞ ðn 1Þ:ln d
(2)
Thus, the slope of ln (vd/vt) vs. ln d curve can be used to determine the grain growth exponent, n. Fig. 6a represents the variation of ln (vd/vt) vs. ln d at 1373 K for CoCrFeNi and CoCrFeMnNi HEAs. It may be noted here, again, that the grain size, d corresponds to the FCC phase. The n ¼ 2.98 and 3.08, is estimated for CoCrFeNi and CoCrFeMnNi, respectively, with R2 value of 0.91 and 0.93, respectively. The n value obtained for both the alloys (n ~ 3) is higher than that observed for normal parabolic grain growth (n ¼ 2) in pure metals. The value of exponent, n ¼ 3, lies in agreement with the long-range diffusion controlled grain growth in two phase materials [26,27]. Using the value of n ¼ 3 for both the HEAs, k is determined from eq. (1) at different temperatures. Subsequently, ln k is plotted against inverse of absolute temperature and activation energy is derived from the slope of the ln k vs 1/T curve (Fig. 6b). Q is calculated as 134 ± 51 kJ/mol and 197 ± 45 kJ/ mol for CoCrFeNi and CoCrFeMnNi, respectively, with R2 value greater than 0.80. Table 3 summarizes the parameters of grain growth kinetics and GB diffusion of Ni determined in the present work for SPSed CoCrFeNi and CoCrFeMnNi. Activation energy of Ni GB diffusion for CoCrFeNi and CoCrFeMnNi HEAs is 158 and 221 kJ/ mol [28], respectively, which is close to activation barrier for grain growth as calculated above. In comparison, the bulk diffusivity of Ni in these alloys was found to be 253 and 304 kJ/mol, respectively [24]. There are two aspects of obtained activation parameters that need to be carefully understood: 3.2.1. Reduced activation barrier for grain growth in SPSed HEAs Liu et al. [15] and Wu et al. [16] reported activation energy of grain growth in bulk CoCrFeMnNi alloy to be close to activation energy of Ni lattice diffusion. The HEAs studied by Liu et al. [15] and Wu et al. [16] were prepared by melting route and had coarse grain size with no second phase particles. In the present work, SPS alloys have much finer initial grain size (d0 < 200 nm for both the HEAs), consequently a greater driving force for grain growth, along with the Cr7C3 precipitates at the grain boundaries. These second phase particles coarsen on thermal exposure, without significant dissolution as depicted in phase fraction plots in Fig. 2. Fig. 4a shows finer dispersion of carbide particles in CoCrFeMnNi matrix at 1073 K, which grow substantially after heat treatment at 1173 K as depicted in Fig. 4b. The average size of carbide particle in SPSed CoCrFeMnNi is
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150 nm (not presented here), whereas it is 1.6 mm after heat treatment at 1373 K. This is also in agreement with observation of Praveen et al. [14] who showed that carbides and FCC grains grow at a similar rate. Assuming normal grain growth behaviour, the maximum grain size in presence of precipitate is given by Dmax ¼ 4r/3f [25], where r is size of precipitate and f is the volume fraction. Since there is no dissolution, f remains same and therefore grain growth is enhanced with increasing size of carbide precipitate. In single phase alloys, grain growth proceeds via grain boundary migration, which involves atomic transport across the grain boundaries. The presence of second phase particles exerts a pinning force, which acts opposite to the driving force for grain boundary migration. As the particle coarsens with increasing temperature, the pinning force is reduced and enhancement in grain growth rate is observed. Although there can be additional factors like nature of grain boundary, presence of impurity affecting the grain boundary migration, the rate controlling step can be assumed to be the coarsening of these second phase particles. 3.2.2. Resemblance of activation energy of grain growth and GB diffusion Although the obtained activation energy of grain growth is in close agreement with energy barrier for GB diffusion, it is improbable that it is the rate-controlling mechanism. As explained above, the coarsening of carbide particles controls the grain growth in the SPSed HEAs studied in the present work. However, the mechanism of coarsening of carbide particles can be complex. As explained by Aaron, Aaronson and Brailsford [29,30], the coarsening of grain boundary precipitates is a combination of lengthening and thickening processes, which occurs via different diffusion paths. Lengthening happens in two steps (a) volume diffusion of solutes (Cr in the present case) to the grain boundaries which serve as collector plates for solutes (b) diffusion of solutes along the grain boundaries extending to the precipitate rims. The thickening of the precipitates (normal to the grain boundary) is regulated by diffusion along the matrix/precipitate interfaces allowing enhanced thickening. This suggests that all three diffusion paths, volume, grain boundary and interface contribute to the particle coarsening. It has been shown by Vaidya et al. [24] that a distinct grain boundary diffusion contribution is observed in CoCrFeNi and CoCrFeMnNi HEAs at higher temperatures. Thus, higher diffusivity paths are active in these HEAs even at elevated temperatures. Therefore, the resemblance of activation energy of grain growth to the activation
Fig. 6. Parameters of grain growth kinetics for FCC phase in CoCrFeNi and CoCrFeMnNi HEAs a) grain growth exponent, n and, b) activation energy, Q.
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Table 3 Comparison of parameters of grain growth and Ni diffusion in CoCrFeNi and CoCrFeMnNi. Alloy
CoCrFeNi CoCrFeMnNi CoCrFeMnNi [15]
Initial grain size, d (nm)
114 185 1000
Volume fraction of GBs, f ¼ 3d/d d ¼ 0.5 nm
0.13 0.08 0.001
energy of GB diffusion only highlights accelerated growth kinetics in SPSed alloys when compared to bulk HEAs. However, it does not convey that the rate controlling step for carbide coarsening is Cr diffusion along grain boundary, particularly when the obtained value of n ¼ 3 suggests a volume diffusion regulated growth. It is, therefore, difficult to assign a single diffusion mechanism dominant in grain growth of SPSed HEAs, containing carbide particles at the grain boundaries. 3.3. Grain size effect on hardness of CoCrFeNi and CoCrFeMnNi HEAs An increase in grain size at elevated temperatures causes loss in strength of nanocrystalline materials and directly impacts their performance. This has been investigated for CoCrFeMnNi HEA in the present work. Fig. 7 demonstrates the variation of hardness with inverse of grain size (d1/2) for CoCrFeMnNi. A Hall-Petch relationship is observed for nanocrystalline CoCrFeMnNi with strength coefficient, kn ¼ 1.92 GPa mm1/2. For comparison, HallPetch plot reported for bulk CoCrFeMnNi [15] is also presented, which shows a strength coefficient, kb ¼ 0.68 GPa mm1/2. Clearly, kn/ kb ~3, which can be attributed to the effect of second phase particles present along with the FCC matrix. Fig. 7 also reveals that the contribution to hardness due to the second phase (i.e. difference between hardness of bulk and SPSed HEAs) become less with increasing grain size (or lower d1/2) of FCC matrix. This is in accordance with the fact that size of carbide particles increase at a similar rate as that of FCC matrix, which causes reduction in their hardness. The Hall-Petch equation obtained for SPSed CoCrFeMnNi
Grain growth kinetics
Activation energy (kJ/mol) of Ni diffusion
n
Q (kJ/mol)
QGB [28]
Qbulk [25]
3.9 3.8 3.0
175 241 321
158 221 e
253 304 e
needs to be assessed using a two phase model as described by Lee et al. [27,31] and recently used by Praveen et al. [17] to describe strengthening in nanocrystalline CoCrFeNi. Three types of boundaries contribute to the strengthening of the alloys viz. a) matrixmatrix (a) b) carbide-carbide (ε) and (c) matrix-carbide boundaries. Their respective contribution to the hardness of the alloy can be delineated as mentioned below: Hall-Petch relation for the nanocrystalline two phase alloy:
Hn ¼ H0;n þ kn d1=2 Here Hn and H0,n are the hardness and hardness intercept of nanocrystalline HEA in GPa, respectively. Kn is the strength coefficient in GPa.mm1/2 and d is the grain size in mm.
H0;n ¼ H0;a :f ac þ H0;ε :f εc þ H0;aε :Fs kn ¼ ka :f ac þ kε :f εc þ kaε :Fs
(3)
Here, the subscripts a, ε and aε represent the contributions from matrix-matrix, carbide-carbide and matrix-carbide boundaries, respectively. fac and fεc are the continuous volume fractions of FCC and carbide phases, respectively and Fs is the degree of separation of FCC and carbides as detailed by Brook [31]. For SPSed CoCrFeMnNi studied in the present work, fac ¼ 0.85, fεc ¼ 0.15. The strength coefficient ka can be taken as equal to that reported for bulk CoCrFeMnNi by Fang et al. [15], ka ¼ 0.68 GPa mm1/2. Since strength coefficient for carbide is not available in literature, HallPetch slope for pure Cr can be used [32] and thus kε ¼ 1.38 GPa mm1/2. Substituting these values in equation (3), we get kaε.Fs ¼ 1.13 GPa mm1/2. Also, the values of ka.fac ¼ 0.58 GPa mm1/ 2 and kε.fεc ¼ 0.20 GPa mm1/2. Clearly, the maximum contribution to strengthening comes from the second phase particle-matrix boundaries. It may be noted that the small strengthening coming from a minor fraction of oxide particles has been neglected in the present analysis. It is thus evident that Cr7C3 can provide an effective way of strengthening the HEA matrix, even though it is deemed an undesired contamination in the literature. The two-phase microstructure of SPSed CoCrFeMnNi HEA consisting of FCC and Cr7C3 provides an insight into designing HEAs for high temperature applications. Deliberate additions of carbon can be made to control the phase fraction of carbide particles and achieve the desired two phase microstructure with enhanced strength. Such intentional alloying of carbon has already been investigated for cast CoCrFeMnNi and showed improvement in alloy properties [33].
4. Conclusions
Fig. 7. a) Hall-Petch relationship observed for nanocrystalline CoCrFeMnNi HEA and compared with the Hall-Petch equation reported in literature [15] for corresponding bulk alloy.
Grain growth kinetics has been investigated for SPS CoCrFeNi and CoCrFeMnNi HEAs, which show major FCC phase along with Cr7C3 particles. EBSD measurements have been employed to determine the grain sizes for the heat-treated samples. The value of n ¼ 3 is obtained for CoCrFeNi and CoCrFeMnNi HEAs indicating the
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long range diffusion-controlled grain growth. Activation energy for grain growth in both the HEAs (Q(CoCrFeNi) ¼ 134 kJ/mol and Q(CoCrFeMnNi) ¼ 194 kJ/mol), which is lower than the energy barrier for lattice diffusion in these HEAs. The rate controlling step for grain growth is the coarsening of carbide particles residing at GBs that involves Cr diffusion along grains, grain boundaries and matrix/particles interfaces. Increase in grain size leads to the reduction in hardness following a Hall-Petch relationship. Strength coefficient for SPSed CoCrFeMnNi (kn ¼ 2.1 GPa) is observed to be three times higher than reported for bulk CoCrFeMnNi. The FCCcarbide phase boundaries provide maximum contribution to strengthening in the SPSed HEA. Acknowledgements The authors would like to thank Prof. V.S. Sarma, Department of Metallurgical & Materials Engineering, Indian Institute of Technology Madras for his valuable inputs to optimize EBSD parameters needed for the present study. We are also grateful to PD Dr. Sergiy Divinski, Institute of Materials Physics, University of Münster, for providing important insights that helped improve the quality of the manuscript. References [1] B.S. Murty, J.W. Yeh, S. Ranganathan, High-entropy Alloys, Butterworth-Heinemann, 2014. [2] C.C. Koch, Nanocrystalline high-entropy alloys, J. Mater. Res. 32 (2017) 3435e3444, https://doi.org/10.1557/jmr.2017.341. €lker, E.P. George, H. Clemens, R. Pippan, [3] B. Schuh, F. Mendez-Martin, B. Vo A. Hohenwarter, Mechanical properties, microstructure and thermal stability of a nanocrystalline CoCrFeMnNi high-entropy alloy after severe plastic deformation, Acta Mater. 96 (2015) 258e268, https://doi.org/10.1016/ j.actamat.2015.06.025. [4] Y. Zou, J.M. Wheeler, H. Ma, P. Okle, R. Spolenak, Nanocrystalline high-entropy alloys: a new paradigm in high-temperature strength and stability, Nano Lett. 17 (2017) 1569e1574, https://doi.org/10.1021/acs.nanolett.6b04716. [5] T. Bhattacharjee, I.S. Wani, S. Sheikh, I.T. Clark, T. Okawa, S. Guo, P.P. Bhattacharjee, N. Tsuji, Simultaneous strength-ductility enhancement of a nano-lamellar AlCoCrFeNi2.1 Eutectic high entropy alloy by Cryo-rolling and annealing, Sci. Rep. 8 (2018) 1e8, https://doi.org/10.1038/s41598-018-21385y. [6] B.S. Murty, S. Ranganathan, Novel materials synthesis by mechanical alloying/ milling, Int. Mater. Rev. 43 (1998) 101e141, https://doi.org/10.1179/ imr.1998.43.3.101. [7] A.S. Sharma, S. Yadav, K. Biswas, B. Basu, High-entropy alloys and metallic nanocomposites: processing challenges, microstructure development and property enhancement, Mater. Sci. Eng. R Rep. 131 (2018) 1e42, https:// doi.org/10.1016/j.mser.2018.04.003. [8] M. Omori, Sintering, consolidation, reaction and crystal growth by the spark plasma system (SPS), Mater. Sci. Eng. A 287 (2000) 183e188, https://doi.org/ 10.1016/S0921-5093(00)00773-5. [9] M. Vaidya, A. Karati, A. Marshal, K.G. Pradeep, B.S. Murty, Phase evolution and stability of nanocrystalline CoCrFeNi and CoCrFeMnNi high entropy alloys, J. Alloys Compd. 770 (2019) 1004e1015, https://doi.org/10.1016/ J.JALLCOM.2018.08.200. [10] M. Vaidya, A. Prasad, A. Parakh, B.S. Murty, Influence of sequence of elemental addition on phase evolution in nanocrystalline AlCoCrFeNi: novel approach to alloy synthesis using mechanical alloying, Mater. Des. 126 (2017) 37e46, https://doi.org/10.1016/j.matdes.2017.04.027. [11] S. Praveen, A. Anupam, R. Tilak, R.S. Kottada, Phase evolution and thermal stability of AlCoCrFe high entropy alloy with carbon as unsolicited addition from milling media, Mater. Chem. Phys. 210 (2018) 57e61, https://doi.org/ 10.1016/j.matchemphys.2017.10.040. [12] V. Shivam, J. Basu, Y. Shadangi, M.K. Singh, N.K.K. Mukhopadhyay, Mechanochemical synthesis, thermal stability and phase evolution in AlCoCrFeNiMn high entropy alloy, J. Alloys Compd. 757 (2018) 87e97, https://doi.org/ 10.1016/j.jallcom.2018.05.057. [13] V. Shivam, J. Basu, V.K. Pandey, Y. Shadangi, N.K. Mukhopadhyay, Alloying behaviour, thermal stability and phase evolution in quinary AlCoCrFeNi high entropy alloy, Adv. Powder Technol. 29 (2018) 2221e2230, https://doi.org/ 10.1016/J.APT.2018.06.006. [14] S. Praveen, J. Basu, S. Kashyap, R.S. Kottada, Exceptional resistance to grain growth in nanocrystalline CoCrFeNi high entropy alloy at high homologous temperatures, J. Alloys Compd. 662 (2016) 361e367, https://doi.org/10.1016/ j.jallcom.2015.12.020.
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Berglund, C. Reinhart, A. Kostka, F. Fox, E.P. George, Phase stability and kinetics of s-phase precipitation in CrMnFeCoNi high-entropy alloys, Acta Mater. 161 (2018) 338e351, https://doi.org/10.1016/ j.actamat.2018.09.040. [20] D.-H. Lee, I.-C. Choi, G. Yang, Z. Lu, M. Kawasaki, U. Ramamurty, R. Schwaiger, J. Jang, Activation energy for plastic flow in nanocrystalline CoCrFeMnNi highentropy alloy: a high temperature nanoindentation study, Scr. Mater. 156 (2018) 129e133, https://doi.org/10.1016/J.SCRIPTAMAT.2018.07.014. [21] S.R. Shatynski, The thermochemistry of transition metal carbides, Oxid. Metals 13 (1979) 105e118, https://doi.org/10.1007/BF00611975. [22] G. Brook, Smithells Light Metals Handbook, 1998. [23] D.B. Miracle, O.N. Senkov, A critical review of high entropy alloys and related concepts, Acta Mater. 122 (2017) 448e511, https://doi.org/10.1016/ j.actamat.2016.08.081. [24] M. Vaidya, S. Trubel, B.S.S. Murty, G. Wilde, S.V.V. Divinski, Ni tracer diffusion in CoCrFeNi and CoCrFeMnNi high entropy alloys, J. Alloys Compd. 688 (2016) 994e1001, https://doi.org/10.1016/j.jallcom.2016.07.239. [25] D. Porter, K. Easterling, M. Sherif, Phase Transformations in Metals and Alloys, (Revised Reprint), CRC Press, 2009. [26] D. Fan, Diffusion-controlled grain growth 45 (1997) 3297e3310. [27] D. Fan, L.-Q. Chen, Computer simulation of grain growth and ostwald ripening in alumina-zirconia two-phase composites, J. Am. Ceram. Soc. 80 (2005) 1773e1780, https://doi.org/10.1111/j.1151-2916.1997.tb03051.x. [28] M. Vaidya, K.G. Pradeep, B.S. Murty, G. Wilde, S.V. Divinski, Radioactive isotopes reveal a non sluggish kinetics of grain boundary diffusion in high entropy alloys, Sci. Rep. 7 (2017) 1e11, https://doi.org/10.1038/s41598-01712551-9. [29] H.B. Aaron, H.I. Aaronson, Growth of grain boundary precipitates in Al-4% Cu by interfacial diffusion, Acta Metall. 16 (1968) 789e798, https://doi.org/ 10.1016/0001-6160(68)90097-7. 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Grain growth kinetics in CoCrFeNi and CoCrFeMnNi high entropy alloys processed by spark plasma sintering M. Vaidya a, *, Ameey Anupam a, J. Vijay Bharadwaj a, Chandan Srivastava b, B.S. Murty a a b
Department of Metallurgical & Materials Engineering, Indian Institute of Technology Madras, Chennai, 600036, India Department of Materials Engineering, Indian Institute of Science, Bangalore, 560012, India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 December 2018 Received in revised form 20 March 2019 Accepted 25 March 2019 Available online 26 March 2019
Nanocrystalline CoCrFeNi and CoCrFeMnNi high entropy alloys have been processed by mechanical alloying followed by spark plasma sintering. Grain growth kinetics has been estimated for both the alloys by subjecting them to heat treatment in the temperature range 1073e1373 K. These alloys possess a thermally stable single phase FCC structure along with Cr7C3 contamination. Electron back scattered diffraction (EBSD) has been used to determine grain size of all the heat treated samples. Both CoCrFeNi and CoCrFeMnNi alloys exhibit a grain growth exponent, n ¼ 3, suggesting long-range diffusioncontrolled grain growth in these alloys. Activation energies for grain growth are 134 and 197 kJ/mol for CoCrFeNi and CoCrFeMnNi, respectively, which are significantly lower than the activation energy of lattice diffusion in these alloys. Hardness is measured for CoCrFeMnNi alloy as function of grain size and is found to follow the Hall-Petch type relation. The strength coefficient (slope of Hall-Petch relation) is calculated as 1.92 GPa, which is nearly three times that of the value reported in literature for coarse grained CoCrFeMnNi. Presence of carbides enhances the hardness of these HEAs. The maximum contribution to strengthening comes from the FCC-carbide phase boundaries. © 2019 Elsevier B.V. All rights reserved.
Keywords: High entropy alloys Grain growth Activation energy Hall-Petch hardness
1. Introduction The recently developed high entropy alloys (HEAs) combine constituents in equimolar or near equimolar proportions. Their unique multi-element matrix and high configurational entropy is believed to be responsible for enhanced phase stability and superior properties [1]. Nanostructured HEAs combine the synergistic effects of increased configurational entropy and nano-size regime, and have shown exciting properties [2]. Nanocrystalline CoCrFeMnNi produced by severe plastic deformation showed very high strength of 1.9 GPa [3]. Zou et al. [4] showed that nanocrystalline refractory HEAs exhibit remarkably low strain rate sensitivity and high strength to weight ratios. Nanocrystalline AlCoCrFeNi2.1 eutectic HEA has been shown to display simultaneous enhancement of strength and ductility [5]. Mechanical alloying (MA) is a well-known solid-state, nonequilibrium, top-down approach to produce nanocrystalline materials with excellent homogeneity [6] and has been widely used for processing HEAs [7]. Spark plasma sintering (SPS) has become an
* Corresponding author. E-mail address: [email protected] (M. Vaidya). https://doi.org/10.1016/j.jallcom.2019.03.341 0925-8388/© 2019 Elsevier B.V. All rights reserved.
increasingly attractive option for the consolidation of MAed powders [8], owing to shorter times required relative to conventional sintering and thus ensuring better retention of nanocrystallinity. However, HEAs containing strong carbide forming elements like Cr, V, and Mo have frequently exhibited carbide contamination during MA and subsequent consolidation and thermal exposure, as summarized in Table 1. The exact mechanism of carbide formation has not been deciphered yet, but the source of carbon is suggested to be process controlling agent used during MA [9] and the extent of it is determined by the constituent elements present in the HEA [10]. Nonetheless, the carbide formation is not always detrimental. And has been shown to contribute to the strength of nanocrystalline HEAs [11]. One of the important aspects of nanocrystalline HEAs is their thermal stability, which decides their potential for any high temperature application. Diffusion controlled processes like phase transformation, grain growth etc. have increased proclivity in nanocrystalline alloys on thermal exposure. Retention of nanostructure and phase stability form the two attributes of thermal stability investigations. AlCoCrFeMnNi HEA produced by mechanochemical synthesis has shown thermal stability up to 500 C after which it undergoes diffusional transformation to complex
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Table 1 Formation of Cr-carbides reported in literature for MAed HEAs after consolidation and heat treatment. Alloy
Phases
Consolidation/Heat treatment
Phases
Ref.
CoCrFeMnNiNx AlCoCrFe Al0.3CoCrFeMnNi CoCrFeMnNi Al0.3CoCrFeMnNi CoCrFeMnNiC0.3Ti0.3 CoCrFeNi Al0.5C0.2Co0.3CrFeNi CoCr0.25CuFeNi1.5V0.25 CoCrFeNi AlCoCrFe Co20Cr20Fe20Mn5Ni20Zn15 CoCrFe(Mn)Ni
FCC BCC FCC FCC FCC FCC þ BCC FCC þ BCC BCC þ FCC FCC þ BCC FCC þ BCC B2 þ Cr23C6 FCC FCC þ WC
VHPS SPS SPS VHPS SPS VHPS SPS SPS SPS 900 C, 600 h 900 C, 600 h 500 C, 1 h 800e1100 C
FCC þ Cr23C6 þ Cr2N B2 þ Cr23C6 FCC þ B2 þ Cr carbide FCC þ M7C3 þ M23C6 FCC þ B2 þ Cr carbide FCC þ þ TiC þ M7C3 þ M23C6 FCC þ Cr7C3 þ Cr2O3 FCC þ BCC þ Cr23C6 þ B2 FCC1 þ FCC2 þ (V, Cr)7C3 FCC þ Cr7C3 þ Cr2O3 B2 þ Cr23C6 FCC þ a-FeCo þ b-NiZn þ Cr23C6 FCC þ Cr7C3
[34] [11,35] [36] [33] [36] [33] [14] [37] [38] [14] [11] [39] [9]
phases [12]. Nanocrystalline AlCoCrFeNi has shown transformation from BCC to B2 structure and formation of intermetallics on thermal exposure [13]. High resistance to grain growth has been observed in CoCrFeNi during long term heat treatment (600 h) at 900 C [14]. Grain growth in nanocrystalline materials, at elevated temperatures, leads to reduction in strength and abates the other benefits of nano-sized microstructure. Liu et al. [15] studied the grain growth behaviour in fine grained CoCrFeMnNi and showed that it is controlled by bulk diffusion of Ni. Wu et al. [16] derived grain growth parameters and Hall Petch relation for lower component constituents of CoCrFeMnNi HEA having fine grain microstructure. The only reports, to the best of our knowledge, on coarsening of nanocrystalline HEAs have been by Praveen et al. [14,17]. They demonstrated excellent resistance to grain growth in nanostructured CoCrFeNi, and calculated grain growth exponent (n ¼ 4) by assuming activation energy equivalent to that of bulk diffusion of Ni [17]. However, increased grain boundary fraction in SPSed HEAs (owing to their nano-size) indicates the possibility of high diffusivity path being dominant for grain growth and calls for careful analysis of this assumption. Tracer diffusion measurements in CoCrFeNi and CoCrFeMnNi HEAs have shown that the grain boundary contribution to diffusion profiles exist even at relatively higher homologous temperatures [18]. Laplanche et al. [19] have demonstrated that the activation energy for the precipitation of phase in Cr26Mn20Fe20Co20Ni14 HEA is close to that of Ni GB diffusion CoCrFeMnNi. Lee et al. [20] have also indicated the contribution of grain boundary diffusion to the plastic flow mechanism in nanocrystalline HEAs. The present work examines the grain growth behaviour of nanocrystalline CoCrFeNi and CoCrFeMnNi HEAs produced by MA and SPS. The activation energy for the grain growth has been determined and correlated with the measured diffusivities in the literature. Hardness of these HEAs is also measured as a function of grain size and contributions from reduced grain size and second phase particles are delineated.
2. Experimental details Nanocrystalline CoCrFeNi and CoCrFeMnNi alloy powders were prepared high energy ball milling as described in Ref. [9]. The milled powders were consolidated by SPS in Dr. Sinter unit (Model SPS- 625, SPS Syntex Inc., Japan) at a temperature of 1173 K, with holding time of 5 min and a pressure of 60 MPa. 2 mm thick slices were cut from SPS pellets and sealed in quartz tube under Ar atmosphere and subjected to heat treatment at 1073, 1173 and 1373 K in a muffle furnace with SiC heating coils and subsequently quenched in water. Phase formation in as processed and heat
treated samples was studied by X-ray diffraction (XRD) analysis, using Panalytical X-ray diffractometer with Cu-Ka radiation. Transmission electron microscopy investigations were carried out, to confirm phase structure, in FEI TITAN microscope. The electron back-scattered diffraction (EBSD) was used to determine the grain sizes of heat treated SPS samples. EBSD scans were performed on finely polished samples using a TSL-OIM software attached to field emission scanning electron microscope (SEM) at 30 kV and maps were collected using a step size of 75 nm using a hexagonal grid. All the points with a confidence index (CI) of less than 0.15 were removed from the scan before further analysis. To determine grain size, intercept length method in-built in EBSD software has been used for alloys. It was ensured that the area of EBSD scan was sufficient to cover at least 2500 grains. Hardness was measured on the polished samples under a load of 500 gf with a dwell time of 10s on a Wilpert Wilson Vickers Hardness instrument. Reported values are an average of 10 readings across the pellet.
3. Results and discussion 3.1. Phase and microstructure evolution in heat treated SPS alloys Fig. 1a presents the XRD patterns of as-SPSed CoCrFeNi and CoCrFeMnNi HEAs and after heat treatment at 1373 K for 96 h. SPSed alloys show a single phase FCC structure along with Cr7C3 contamination and this mixture is retained even after heat treatment at 1373 K for 96 h. The two most intense peaks of Cr7C3 lie very close (on the either side) to the (111) peak of FCC, as illustrated in XRD patterns of SPSed alloys (Fig. 1a). Since the diffractograms taken at different temperatures are stacked together, therefore an existence of Cr7C3 peak is often not evident. Therefore slow scan in the 2q range 40e55 is shown for CoCrFeMnNi heat treated at 1373 K for 96 h in Fig. 1b, which clearly shows the peaks of FCC and Cr7C3. The high angle annular dark field (HAADF) image of SPSed CoCrFeNi is presented in Fig. 1c. In addition to FCC phase and Cr7C3, small particles belonging to a possible third phase are observed. Elemental mapping using scanning transmission electron microscopy (STEM) mode shows the regions rich in CreCeO in addition to enriched regions of CreO and Cr-depleted FCC HEA matrix. In our recent work [9], the selected area diffraction (SAD) patterns confirming the orthorhombic structure of Cr7C3 and FCC matrix in SPSed CoCrFeMnNi HEA have been presented. Among the constituent elements of HEAs studied, Cr has the highest tendency to form carbide [21] and oxide [22], as reflected in their respective Ellingham diagrams. Phase fraction of Cr7C3 phase is estimated for CoCrFeNi and CoCrFeMnNi as a function of temperature (Fig. 2a) and time (Fig. 2b) using the method described in Vaidya et al. [10] (Fig. 2). No significant change is observed in amount of Cr7C3. Thus,
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Fig. 1. (a) XRD patterns of SPS and heat treated (1373 K, 96 h) CoCrFeNi and CoCrFeMnNi HEAs. Mixture of FCC and Cr7C3 is retained on thermal exposure. (b) Slow scan of heat treated CoCrFeMnNi to clearly show the peaks of FCC and Cr7C3. (c) High angular annular dark field (HAADF) image of CoCrFeNi after SPS. Elemental mapping shows Cr-depleted FCC matrix, Cr7C3 and Cr-rich oxide particles.
it is suggested that the dissolution of Cr7C3 is insignificant during the thermal exposure up to 1373 K. This can be attributed to the stability of Cr7C3 at these temperatures, as depicted in its Ellingham diagram [21]. Fig. 3a and b illustrate microstructure of CoCrFeMnNi samples heat treated at 1073 and 1373 K, respectively. At 1073 K, matrix region consists of fine particles of Cr7C3 and Cr-rich oxide. On thermal exposure at 1373 K, the microstructure consists of matrix with Cr7C3 and Cr-rich oxide particles grown in size relative to lower temperatures. Fig. 4 presents the composition plot for CoCrFeNi and CoCrFeMnNi HEAs heat treated at 1373 K for 96 h, giving the compositions of Cr-depleted FCC matrix, Cr7C3 and CreO regions. The extended FCC phase field of CoeCreFeeMneNi system has been well documented [23] and thus FCC structure is retained even with the Cr depletion.
3.2. Grain growth kinetics in CoCrFeNi and CoCrFeMnNi HEAs EBSD measurements have been performed on heat treated CoCrFeNi and CoCrFeMnNi HEAs to determine grain size as a function of temperature (1073, 1173 and 1373 K for 96 h) and time (24, 48, 72 and 96 h at 1373 K). In this work, our objective is to study the grain growth of FCC phase. Therefore, in EBSD analysis, only FCC phase has been indexed using Ni standard due to their close proximity in lattice parameter (aNi ¼ 0.352 nm, aCoCrFeMnNi ¼ 0.357 nm). Fig. 5a exemplifies the phase map determined using EBSD for CoCrFeMnNi HEA heat treated at 1073 K for 96 h. The grey region corresponds to the FCC phase while black area conforms to Cr carbide and oxide phases. Grain growth at elevated temperature (1373 K) is clearly demonstrated in Fig. 5b. Fig. 5c reveals the grain size distribution in CoCrFeMnNi heat treated at 1073
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Fig. 2. Phase fraction of Cr7C3 as a function of a) temperature and b) time at 1373 K. No significant dissolution of carbides is seen on thermal exposure.
Fig. 3. Microstructure of heat treated CoCrFeMnNi at (a) 1073 and (b) 1173 K for 96 h. Growth of carbide particles can be clearly seen with increasing annealing temperature.
Fig. 4. Composition (at.%) plot of various phases in SPSed CoCrFeNi and CoCrFeMnNi heat treated at 1373 K for 96 h. FCC is depleted in Cr for both quaternary and quinary HEA.
and 1373 K, from which corresponding average grain sizes are determined as 416 and 1766 nm, respectively. Occurrence of abnormal grain growth is hinted as the grain size distribution becomes wider at elevated temperature. The initial grain sizes of as-
SPS alloys have been determined using TEM analysis (not presented here) and the corresponding values are 114 and 185 nm for CoCrFeNi and CoCrFeMnNi, respectively. It may be noted that although standard deviations in grain size
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Fig. 5. EBSD phase maps of SPSed CoCrFeMnNi heat treated for 96 h at a) 1073 K and b) 1373 K and c) corresponding grain size distribution. Grey regions correspond to FCC phase and black areas are un-indexed Cr-rich carbide and oxides. Grain growth and wider distribution of grain size at 1373 K are revealed.
determined from EBSD are high, an average value of grain size can give a reasonable idea of the trend and corresponding kinetic parameters. For more meaningful statistics, grain-sizes which occupy less than 5% area fraction are excluded from grain size determination. Grain growth factor, Gf (df e d0/d0) is defined as the ratio of final and initial grain sizes after the heat treatment at a specified temperature (T) and time (t). Table 2 compares the Gf of CoCrFeNi and CoCrFeMnNi HEAs at different temperatures used in the present study. A normalized grain growth factor, Gf* ¼ Gf/(Th.t) is also calculated, where Th ¼ T/Tm is the homologous temperature of the alloy. Tm is melting point; 1717 and 1607 K for CoCrFeNi and CoCrFeMnNi, respectively. It can be inferred that Gf is slightly higher for CoCrFeMnNi alloy than CoCrFeNi at 1373 K, which indicates enhanced grain growth in quinary alloy. When normalized with homologous temperature, Gf* for CoCrFeNi and CoCrFeMnNi turns out to be similar. This is in agreement with the conclusions of
Vaidya et al. [24] that the role of configurational entropy in slowing down atomic transport rates diminishes at elevated temperatures. Grain growth kinetics in a polycrystalline material is often described by the power law expression as [25]:
dn dn0 ¼ kt
(1)
where n is the grain growth exponent, k is the temperature coefficient, t is the holding time, d0 and d are the grain sizes at t ¼ 0 and after time t, respectively. The temperature dependence of k follows Arrhenius behaviour as k ¼ k0exp(-Q/RT). Here k0 is the preexponential factor, Q is the activation energy of grain growth, and RT has usual meaning. Partial differentiation of eq. (1) w.r.t time followed by taking natural logarithm on both sides gives:
Table 2 Grain growth factor, Gf and normalized grain growth factor, Gf* for CoCrFeNi and CoCrFeMnNi (SPS) HEAs studied in the present work. Alloy
T (K)
t (h)
Th ¼ T/Tm
d0 (nm)
df (nm)
Gf¼ (df - d0)/d0
Gf* ¼ Gf/(Th*t)
CoCrFeNi
1073 1173 1373 1073 1173 1373
96 96 96 96 96 96
0.62 0.68 0.80 0.67 0.73 0.85
114 114 114 185 185 185
340 360 930 416 518 1766
1.98 2.16 7.16 1.25 1.80 8.55
0.03 0.03 0.09 0.02 0.03 0.10
CoCrFeMnNi
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ln ðvd=vtÞ ¼ lnðk=nÞ ðn 1Þ:ln d
(2)
Thus, the slope of ln (vd/vt) vs. ln d curve can be used to determine the grain growth exponent, n. Fig. 6a represents the variation of ln (vd/vt) vs. ln d at 1373 K for CoCrFeNi and CoCrFeMnNi HEAs. It may be noted here, again, that the grain size, d corresponds to the FCC phase. The n ¼ 2.98 and 3.08, is estimated for CoCrFeNi and CoCrFeMnNi, respectively, with R2 value of 0.91 and 0.93, respectively. The n value obtained for both the alloys (n ~ 3) is higher than that observed for normal parabolic grain growth (n ¼ 2) in pure metals. The value of exponent, n ¼ 3, lies in agreement with the long-range diffusion controlled grain growth in two phase materials [26,27]. Using the value of n ¼ 3 for both the HEAs, k is determined from eq. (1) at different temperatures. Subsequently, ln k is plotted against inverse of absolute temperature and activation energy is derived from the slope of the ln k vs 1/T curve (Fig. 6b). Q is calculated as 134 ± 51 kJ/mol and 197 ± 45 kJ/ mol for CoCrFeNi and CoCrFeMnNi, respectively, with R2 value greater than 0.80. Table 3 summarizes the parameters of grain growth kinetics and GB diffusion of Ni determined in the present work for SPSed CoCrFeNi and CoCrFeMnNi. Activation energy of Ni GB diffusion for CoCrFeNi and CoCrFeMnNi HEAs is 158 and 221 kJ/ mol [28], respectively, which is close to activation barrier for grain growth as calculated above. In comparison, the bulk diffusivity of Ni in these alloys was found to be 253 and 304 kJ/mol, respectively [24]. There are two aspects of obtained activation parameters that need to be carefully understood: 3.2.1. Reduced activation barrier for grain growth in SPSed HEAs Liu et al. [15] and Wu et al. [16] reported activation energy of grain growth in bulk CoCrFeMnNi alloy to be close to activation energy of Ni lattice diffusion. The HEAs studied by Liu et al. [15] and Wu et al. [16] were prepared by melting route and had coarse grain size with no second phase particles. In the present work, SPS alloys have much finer initial grain size (d0 < 200 nm for both the HEAs), consequently a greater driving force for grain growth, along with the Cr7C3 precipitates at the grain boundaries. These second phase particles coarsen on thermal exposure, without significant dissolution as depicted in phase fraction plots in Fig. 2. Fig. 4a shows finer dispersion of carbide particles in CoCrFeMnNi matrix at 1073 K, which grow substantially after heat treatment at 1173 K as depicted in Fig. 4b. The average size of carbide particle in SPSed CoCrFeMnNi is
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150 nm (not presented here), whereas it is 1.6 mm after heat treatment at 1373 K. This is also in agreement with observation of Praveen et al. [14] who showed that carbides and FCC grains grow at a similar rate. Assuming normal grain growth behaviour, the maximum grain size in presence of precipitate is given by Dmax ¼ 4r/3f [25], where r is size of precipitate and f is the volume fraction. Since there is no dissolution, f remains same and therefore grain growth is enhanced with increasing size of carbide precipitate. In single phase alloys, grain growth proceeds via grain boundary migration, which involves atomic transport across the grain boundaries. The presence of second phase particles exerts a pinning force, which acts opposite to the driving force for grain boundary migration. As the particle coarsens with increasing temperature, the pinning force is reduced and enhancement in grain growth rate is observed. Although there can be additional factors like nature of grain boundary, presence of impurity affecting the grain boundary migration, the rate controlling step can be assumed to be the coarsening of these second phase particles. 3.2.2. Resemblance of activation energy of grain growth and GB diffusion Although the obtained activation energy of grain growth is in close agreement with energy barrier for GB diffusion, it is improbable that it is the rate-controlling mechanism. As explained above, the coarsening of carbide particles controls the grain growth in the SPSed HEAs studied in the present work. However, the mechanism of coarsening of carbide particles can be complex. As explained by Aaron, Aaronson and Brailsford [29,30], the coarsening of grain boundary precipitates is a combination of lengthening and thickening processes, which occurs via different diffusion paths. Lengthening happens in two steps (a) volume diffusion of solutes (Cr in the present case) to the grain boundaries which serve as collector plates for solutes (b) diffusion of solutes along the grain boundaries extending to the precipitate rims. The thickening of the precipitates (normal to the grain boundary) is regulated by diffusion along the matrix/precipitate interfaces allowing enhanced thickening. This suggests that all three diffusion paths, volume, grain boundary and interface contribute to the particle coarsening. It has been shown by Vaidya et al. [24] that a distinct grain boundary diffusion contribution is observed in CoCrFeNi and CoCrFeMnNi HEAs at higher temperatures. Thus, higher diffusivity paths are active in these HEAs even at elevated temperatures. Therefore, the resemblance of activation energy of grain growth to the activation
Fig. 6. Parameters of grain growth kinetics for FCC phase in CoCrFeNi and CoCrFeMnNi HEAs a) grain growth exponent, n and, b) activation energy, Q.
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Table 3 Comparison of parameters of grain growth and Ni diffusion in CoCrFeNi and CoCrFeMnNi. Alloy
CoCrFeNi CoCrFeMnNi CoCrFeMnNi [15]
Initial grain size, d (nm)
114 185 1000
Volume fraction of GBs, f ¼ 3d/d d ¼ 0.5 nm
0.13 0.08 0.001
energy of GB diffusion only highlights accelerated growth kinetics in SPSed alloys when compared to bulk HEAs. However, it does not convey that the rate controlling step for carbide coarsening is Cr diffusion along grain boundary, particularly when the obtained value of n ¼ 3 suggests a volume diffusion regulated growth. It is, therefore, difficult to assign a single diffusion mechanism dominant in grain growth of SPSed HEAs, containing carbide particles at the grain boundaries. 3.3. Grain size effect on hardness of CoCrFeNi and CoCrFeMnNi HEAs An increase in grain size at elevated temperatures causes loss in strength of nanocrystalline materials and directly impacts their performance. This has been investigated for CoCrFeMnNi HEA in the present work. Fig. 7 demonstrates the variation of hardness with inverse of grain size (d1/2) for CoCrFeMnNi. A Hall-Petch relationship is observed for nanocrystalline CoCrFeMnNi with strength coefficient, kn ¼ 1.92 GPa mm1/2. For comparison, HallPetch plot reported for bulk CoCrFeMnNi [15] is also presented, which shows a strength coefficient, kb ¼ 0.68 GPa mm1/2. Clearly, kn/ kb ~3, which can be attributed to the effect of second phase particles present along with the FCC matrix. Fig. 7 also reveals that the contribution to hardness due to the second phase (i.e. difference between hardness of bulk and SPSed HEAs) become less with increasing grain size (or lower d1/2) of FCC matrix. This is in accordance with the fact that size of carbide particles increase at a similar rate as that of FCC matrix, which causes reduction in their hardness. The Hall-Petch equation obtained for SPSed CoCrFeMnNi
Grain growth kinetics
Activation energy (kJ/mol) of Ni diffusion
n
Q (kJ/mol)
QGB [28]
Qbulk [25]
3.9 3.8 3.0
175 241 321
158 221 e
253 304 e
needs to be assessed using a two phase model as described by Lee et al. [27,31] and recently used by Praveen et al. [17] to describe strengthening in nanocrystalline CoCrFeNi. Three types of boundaries contribute to the strengthening of the alloys viz. a) matrixmatrix (a) b) carbide-carbide (ε) and (c) matrix-carbide boundaries. Their respective contribution to the hardness of the alloy can be delineated as mentioned below: Hall-Petch relation for the nanocrystalline two phase alloy:
Hn ¼ H0;n þ kn d1=2 Here Hn and H0,n are the hardness and hardness intercept of nanocrystalline HEA in GPa, respectively. Kn is the strength coefficient in GPa.mm1/2 and d is the grain size in mm.
H0;n ¼ H0;a :f ac þ H0;ε :f εc þ H0;aε :Fs kn ¼ ka :f ac þ kε :f εc þ kaε :Fs
(3)
Here, the subscripts a, ε and aε represent the contributions from matrix-matrix, carbide-carbide and matrix-carbide boundaries, respectively. fac and fεc are the continuous volume fractions of FCC and carbide phases, respectively and Fs is the degree of separation of FCC and carbides as detailed by Brook [31]. For SPSed CoCrFeMnNi studied in the present work, fac ¼ 0.85, fεc ¼ 0.15. The strength coefficient ka can be taken as equal to that reported for bulk CoCrFeMnNi by Fang et al. [15], ka ¼ 0.68 GPa mm1/2. Since strength coefficient for carbide is not available in literature, HallPetch slope for pure Cr can be used [32] and thus kε ¼ 1.38 GPa mm1/2. Substituting these values in equation (3), we get kaε.Fs ¼ 1.13 GPa mm1/2. Also, the values of ka.fac ¼ 0.58 GPa mm1/ 2 and kε.fεc ¼ 0.20 GPa mm1/2. Clearly, the maximum contribution to strengthening comes from the second phase particle-matrix boundaries. It may be noted that the small strengthening coming from a minor fraction of oxide particles has been neglected in the present analysis. It is thus evident that Cr7C3 can provide an effective way of strengthening the HEA matrix, even though it is deemed an undesired contamination in the literature. The two-phase microstructure of SPSed CoCrFeMnNi HEA consisting of FCC and Cr7C3 provides an insight into designing HEAs for high temperature applications. Deliberate additions of carbon can be made to control the phase fraction of carbide particles and achieve the desired two phase microstructure with enhanced strength. Such intentional alloying of carbon has already been investigated for cast CoCrFeMnNi and showed improvement in alloy properties [33].
4. Conclusions
Fig. 7. a) Hall-Petch relationship observed for nanocrystalline CoCrFeMnNi HEA and compared with the Hall-Petch equation reported in literature [15] for corresponding bulk alloy.
Grain growth kinetics has been investigated for SPS CoCrFeNi and CoCrFeMnNi HEAs, which show major FCC phase along with Cr7C3 particles. EBSD measurements have been employed to determine the grain sizes for the heat-treated samples. The value of n ¼ 3 is obtained for CoCrFeNi and CoCrFeMnNi HEAs indicating the
M. Vaidya et al. / Journal of Alloys and Compounds 791 (2019) 1114e1121
long range diffusion-controlled grain growth. Activation energy for grain growth in both the HEAs (Q(CoCrFeNi) ¼ 134 kJ/mol and Q(CoCrFeMnNi) ¼ 194 kJ/mol), which is lower than the energy barrier for lattice diffusion in these HEAs. The rate controlling step for grain growth is the coarsening of carbide particles residing at GBs that involves Cr diffusion along grains, grain boundaries and matrix/particles interfaces. Increase in grain size leads to the reduction in hardness following a Hall-Petch relationship. Strength coefficient for SPSed CoCrFeMnNi (kn ¼ 2.1 GPa) is observed to be three times higher than reported for bulk CoCrFeMnNi. The FCCcarbide phase boundaries provide maximum contribution to strengthening in the SPSed HEA. Acknowledgements The authors would like to thank Prof. V.S. Sarma, Department of Metallurgical & Materials Engineering, Indian Institute of Technology Madras for his valuable inputs to optimize EBSD parameters needed for the present study. We are also grateful to PD Dr. Sergiy Divinski, Institute of Materials Physics, University of Münster, for providing important insights that helped improve the quality of the manuscript. References [1] B.S. Murty, J.W. Yeh, S. Ranganathan, High-entropy Alloys, Butterworth-Heinemann, 2014. [2] C.C. Koch, Nanocrystalline high-entropy alloys, J. Mater. Res. 32 (2017) 3435e3444, https://doi.org/10.1557/jmr.2017.341. €lker, E.P. George, H. Clemens, R. Pippan, [3] B. Schuh, F. Mendez-Martin, B. Vo A. Hohenwarter, Mechanical properties, microstructure and thermal stability of a nanocrystalline CoCrFeMnNi high-entropy alloy after severe plastic deformation, Acta Mater. 96 (2015) 258e268, https://doi.org/10.1016/ j.actamat.2015.06.025. [4] Y. Zou, J.M. Wheeler, H. Ma, P. Okle, R. Spolenak, Nanocrystalline high-entropy alloys: a new paradigm in high-temperature strength and stability, Nano Lett. 17 (2017) 1569e1574, https://doi.org/10.1021/acs.nanolett.6b04716. [5] T. Bhattacharjee, I.S. Wani, S. Sheikh, I.T. Clark, T. Okawa, S. Guo, P.P. Bhattacharjee, N. Tsuji, Simultaneous strength-ductility enhancement of a nano-lamellar AlCoCrFeNi2.1 Eutectic high entropy alloy by Cryo-rolling and annealing, Sci. Rep. 8 (2018) 1e8, https://doi.org/10.1038/s41598-018-21385y. [6] B.S. Murty, S. Ranganathan, Novel materials synthesis by mechanical alloying/ milling, Int. Mater. Rev. 43 (1998) 101e141, https://doi.org/10.1179/ imr.1998.43.3.101. [7] A.S. Sharma, S. Yadav, K. Biswas, B. Basu, High-entropy alloys and metallic nanocomposites: processing challenges, microstructure development and property enhancement, Mater. Sci. Eng. R Rep. 131 (2018) 1e42, https:// doi.org/10.1016/j.mser.2018.04.003. [8] M. Omori, Sintering, consolidation, reaction and crystal growth by the spark plasma system (SPS), Mater. Sci. Eng. A 287 (2000) 183e188, https://doi.org/ 10.1016/S0921-5093(00)00773-5. [9] M. Vaidya, A. Karati, A. Marshal, K.G. Pradeep, B.S. Murty, Phase evolution and stability of nanocrystalline CoCrFeNi and CoCrFeMnNi high entropy alloys, J. Alloys Compd. 770 (2019) 1004e1015, https://doi.org/10.1016/ J.JALLCOM.2018.08.200. [10] M. Vaidya, A. Prasad, A. Parakh, B.S. Murty, Influence of sequence of elemental addition on phase evolution in nanocrystalline AlCoCrFeNi: novel approach to alloy synthesis using mechanical alloying, Mater. Des. 126 (2017) 37e46, https://doi.org/10.1016/j.matdes.2017.04.027. [11] S. Praveen, A. Anupam, R. Tilak, R.S. Kottada, Phase evolution and thermal stability of AlCoCrFe high entropy alloy with carbon as unsolicited addition from milling media, Mater. Chem. Phys. 210 (2018) 57e61, https://doi.org/ 10.1016/j.matchemphys.2017.10.040. [12] V. Shivam, J. Basu, Y. Shadangi, M.K. Singh, N.K.K. Mukhopadhyay, Mechanochemical synthesis, thermal stability and phase evolution in AlCoCrFeNiMn high entropy alloy, J. Alloys Compd. 757 (2018) 87e97, https://doi.org/ 10.1016/j.jallcom.2018.05.057. [13] V. Shivam, J. Basu, V.K. Pandey, Y. Shadangi, N.K. Mukhopadhyay, Alloying behaviour, thermal stability and phase evolution in quinary AlCoCrFeNi high entropy alloy, Adv. Powder Technol. 29 (2018) 2221e2230, https://doi.org/ 10.1016/J.APT.2018.06.006. [14] S. Praveen, J. Basu, S. Kashyap, R.S. Kottada, Exceptional resistance to grain growth in nanocrystalline CoCrFeNi high entropy alloy at high homologous temperatures, J. Alloys Compd. 662 (2016) 361e367, https://doi.org/10.1016/ j.jallcom.2015.12.020.
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