The FCC to BCC phase transformation kinetics in an

Journal of Alloys and Compounds 710 (2017) 144e150

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The FCC to BCC phase transformation kinetics in an Al0.5CoCrFeNi high entropy alloy Jun Wang*, Sizhe Niu, Tong Guo, Hongchao Kou, Jinshan Li** State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi'an, 710072, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 16 January 2017 Received in revised form 9 March 2017 Accepted 21 March 2017 Available online 22 March 2017

In this paper, thermal expansion method is used to characterize the phase transformation process of Al0.5CoCrFeNi high entropy alloy (HEA), and the FCC-BCC phase transformation kinetics, microstructure and mechanical properties are investigated. Results show that during continuous heating process, three stages of phase transformation process for Al0.5CoCrFeNi HEA are characterized by thermal expansion curves, and the third stage is corresponding to FCC-BCC phase transformation. The FCC-BCC phase transformation kinetics is analyzed using the thermal expansion experiments carried out at different heating rates. The FCC-BCC phase transformed fraction, f, as a function of temperature is determined from thermal expansion curve. The activation energies, Q, determined by KAS model show an increasing trend which is from 144.4 kJ/mol at initial stage (f ¼ 0.2) to 209.2 kJ/mol when f ¼ 0.8, indicating the barrier for transformation is increasing. The Avrami exponent, n, determined by modified JMA model, varies with transformed fraction, indicating the FCC-BCC phase transition firstly is interface controlled with decreasing nucleation rate (f < 0.05), and changed to diffusion controlled with an increasing nucleation rate (f < 0.15), then diffusion controlled with decreasing nucleation rate. The microstructure and mechanical properties of the corresponding FCC-BCC phase transformation process are also studied. © 2017 Elsevier B.V. All rights reserved.

Keywords: High entropy alloys Phase transformation Kinetics Microstructure

1. Introduction High entropy alloys (HEAs) have attracted the interest of researchers as a new concept of alloys designing due to its excellent properties, such as high strength, good plasticity and high fracture toughness [1e6]. With the further study of HEAs, phase transformation has been crucial for controlling the microstructure thereby obtaining the superior properties [7e10]. Many HEAs systems have multiple phases, depending on the compositions or some external parameters, such as, temperature and pressure. Actually only a small amount of HEAs consist of single phase, e.g. CoCrFeNi [11], Al0.1CoCrFeNi [12], and CoCrFeNiMn discovered firstly [13,14] and even quickly manifested not to be single phase in subsequent studies [15e17]. Generally, FCCstructured alloys possess high ductility and low strength [18,19], whereas BCC-structured alloys are hard and brittle [19,20]. As a result, combining the advantages of FCC and BCC phases will obtain the balanced mechanical properties of strength-toughness

* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (J. Wang), [email protected] (J. Li). http://dx.doi.org/10.1016/j.jallcom.2017.03.249 0925-8388/© 2017 Elsevier B.V. All rights reserved.

matching. Therefore, multi-phase configurations should be important future research goals in the field of HEAs. Li et al. [9] designed the nanostructured, bulk HEAs with multiple compositionally equivalent high-entropy phases overcoming the strengtheductility trade-off by means of interfacing hardening due to a dual-phase microstructure and transformation-induced hardening. Though lots of papers have covered the phase transformation in HEAs [21e25], the mechanism of phase evolution is still less understood. Kinetics way of tailoring phases in HEAs is significant for obtaining comprehensive performance. He et al. [10] investigated the kinetic effect in CoCrFeNiTi0.4 HEA to reveal the possibility of controlling phase selection via kinetic ways for HEAs and the CCT, TTT curves were calculated. However, we still have less knowledge about the dynamical processes that occur as the temperature changes in HEAs and the activation energy of phase transformation is unknown. The correct understanding of these features is of great scientific and technological importance. AlxCoCrFeNi is a well-studied alloy system with good mechanical properties in the field of HEAs [26e28]. The phase transforms from FCC to BCC gradually with the increasing Al content, at the same time, the lattice distortion increases accompanied by an increase in strength. The alloy can remain good ductility and

J. Wang et al. / Journal of Alloys and Compounds 710 (2017) 144e150

improving strength near the critical Al content. If we have a good command of the dynamical processes of FCC to BCC, the size and distribution of precipitated phase can be adjusted to improve the mechanical properties. In this paper, we focus on the mechanism of FCC to BCC phase transformation kinetics in an Al0.5CoCrFeNi high entropy alloy. The relation between temperature and volume fraction of phase transformation will be established. 2. Experimental HEA ingots with a nominal composition of Al0.5CoCrFeNi were prepared by arc-melting under an inert (argon) atmosphere. The purity of each element is at least 99.95 wt%. To achieve a homogeneous distribution of elements in the alloys, each ingot was remelted at least four times. After that, alloy ingots were polished and cleaned with ethanol. Then the ingots were casted into plates (50 20 3 mm) and rods (Ф 6 70 mm) by vacuum suction casting. The rods were machined to Ф 6 25 for thermal dilation test and heat-treatment of the high entropy alloy plate samples was performed at 1123 K under air atmosphere followed by waterquenching. Finally, tensile specimens were cut from the plates. Dog bone-shaped tensile specimens with a gauge length of 14 mm, a width of 2 mm and an approximate thickness around 1.5 mm were prepared. The thermal dilation curves were tested using Netzsch®DIL-402C under the protection of argon. The crystalline structure was characterized by DX 2700 X-ray diffractometer (XRD). Microstructure of heat-treated alloys was studied by a SUPRA 55 scanning electron microscope (SEM) equipped with energydispersive spectroscopy (EDS), and standard bright-field images and diffraction patterns were obtained using a transmission electron microscope from Tecnai FG2. Uniaxial tensile tests of the heattreatment samples were carried out by a MTS SANS CMT5105 testing machine at room temperature with the strain rate of 103 s1. 3. Results and discussion 3.1. Thermal dilation curves of continuous heating Fig. 1 (a) shows the thermal dilation curves of Al0.5CoCrFeNi HEA at different heating rates (3 K/min, 5 K/min, 8 K/min, 10 K/min). All the curves show the same trend in Fig. 1 (a) demonstrating good repeatability of experiment. There appears to be several

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characteristic temperature intervals with the increase of temperature, indicating that Al0.5CoCrFeNi HEA has undergone the process of phase transformation. Fig. 1 (b) is the differential curves of Fig. 1 (a). The phase transformation can be divided into three stages, taking 5 K/min as an example, the starting temperatures are 677 K, 805 K and 1044 K, respectively. The first is very weak, and the last one is the strongest. For the first two peaks, denoted as T1 and T2 in Fig. 1 (b), our previous study [29] proved that it involved nanophase precipitation in the matrix for T2 while the transformation for T1 is still unclear, which needs further investigations. It should be noted that the T1, T2 and T3 increase with the increase of heating rates expressing the kinetics effect of the phase transformation process. Similar phenomenon can be found in Refs. [30e33]. In this paper, we will focus on phase transformation kinetics of the largest peak (the third peak) during continuous heating which is characterized as FCC-BCC transition later. Some published results can also give evidence for the FCC-BCC phase transformation [34]. Fig. 2 (a) displays the heating and cooling curves at 5 K/min of Al0.5CoCrFeNi alloy. Apparently, the cooling curve without any detectable transition does not coincide with the heating curve manifesting that the phase transformation is irreversible. 3.2. Phase transition kinetics Fig. 3 shows how to calculate the phase transition kinetics curves. The lines AA0 and BB0 can be obtained by extending the linear expansion section of the thermal expansion curve. Then the point C is the intersection of A0 B0 and thermal expansion curve. Finally, the theoretical volume fraction of phase transition will be calculated using Eq. (1) [35].

f ¼

y0A yC y0A y0B

(1)

Where f is the volume fraction, and yA0 , yB0 , yC are the values of expansion corresponding to the value of Y-axis in Fig. 3 (a) and (b) shows the transformed fractions as a function of temperature at different heating rates. As shown in Fig. 3 (b), all the f T curves show the similar “S” type trend. During the whole process of phase transition, the phase transformation rate firstly increases, then decreases gradually and the transition curve is roughly “S” indicating that the FCC-BCC transformation is controlled by the nucleation-growth mechanism [36]. Activation energy is an important thermodynamic parameter to

Fig. 1. (a) The thermal dilation curves of Al0.5CoCrFeNi alloy measured at different heating rates, (b) the differential curves of (a).

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Fig. 2. The heating and cooling curves at 5 K/min of Al0.5CoCrFeNi alloy, (a) 987 K, (b) 1273 K.

Fig. 3. (a) An example of calculating the phase transition kinetics curve measured at 3 K/min, (b) phase transition kinetics curves with different heating rates.

assess phase transition, and a single phase transition usually has stable activation energy [37]. However, due to the variation of the chemical composition in the region where Al0.5CoCrFeNi phase transition occurs, the activation energy will change with the mechanism of BCC transformation during the whole process of phase transformation. By taking into account the change of activation energy at each stage of phase transition, the apparent activation energy can be obtained. The activation energy can reflect not only the difficulty of BCC phase transition, but also the thermal stability of the FCC matrix. For Al0.5CoCrFeNi alloy, the larger the activation energy, the harder the phase transformation is. The activation energy of the FCC-BCC phase transition can be calculated using the Kissinger-Akahira-Sunose (KAS) method [38]. The equation is as follows.

2 T E ¼ C þ ln RT 4

expediently. The results of regression are shown in Fig. 4 and the value of activation energy E can be obtained by calculating the slope. The activation energies are 144.4 kJ/mol, 178.7 kJ/mol, 224.7 kJ/mol and 284.3 kJ/mol, respectively, when the transformed

(2)

Where T is temperature, ∅ is the heating rate, E is the activation energy, C is constant and R is the molar gas constant. Linear regression between ln(T2/Ф) and 1/T is performed by bringing the temperature corresponding to the heating rates (3 K/min, 5 K/min, 8 K/min, 10 K/min) and BCC transformed fraction into the Eq. (2). Since 1/T is small, 10000/T is used instead in order to calculate

Fig. 4. Plot of 10000/T~ln(T2/Ф) with different phase transition volume fraction.


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fraction is 0.2, 0.4, 0.6 and 0.8. Obviously, the activation energy increases with the increase of transformed fraction. The average activation is calculated to be 209.2 kJ/mol. Solid state phase transformations usually involve the process of nucleation and growth. Non-isothermal experiments are commonly used to explore the transformation processes, and the kinetic parameters are generally analyzed based on the well-known JohnsonMehl-Avrami (JMA) model [39]. The equation is as follows.

f ¼ 1 expð Kt n Þ

(3)

Where n is the Avrami index. However, the JMA equation is not applicable to the process of non-isothermal phase transformation. For this reason, S. Blazquez, C. F. Conde and A. Cond expand Eq. (3) simply and directly using the following assumptions [40].

t t0 ¼

T T0 4

(4)

Where T0 is the starting temperature of phase transition. We can rewrite equation (3) in the following form.

0 K ðT T0 Þ n f ¼ 1 exp 4

(5)

Where K0 is a new frequency factor. Eventually, the Avrami index n can be calculated. Avrami exponent“n”is a useful parameter that can express the nucleation and growth mechanisms during solid state phase transformations. Acturally, the classic JMA equation is valid only in isothermal phase transformations and the nucleation rate and growth rate are assumed to be constant. For the application of continuous heating process, the classic JMA equation is modified. For a real phase transformation process, the Avrami exponent n will change with the transformed volume fraction in most cases, thus many modifications of the classic model are made. In this paper, we use a simple deviative equation that can determine the Avrami exponent as variables as in many previous published papers such as references [35,40,41].

vln½lnð1 f Þ n¼ E vRT

(6)

The activation energy E calculated by Eq. (2) is taken into Eq. (6) to obtain the curve of E=RT ln½lnð1 f Þ, the differential of which is Avrami exponent n. The variation in n with the increasing volume fraction under the heating rate 3 K/min is shown in Fig. 5. When f < 0.015, n value is greater than 4. According to the theory of phase transition, in the early stage the phenomenon that n anomalies has no physical significance. In addition, at the end of the phase transition (f > 0.99), an anomalous increase in the value of n appears again. This anomaly is also of no physical significance [40,42]. Therefore we do not take these two stages into account. There are three main stages to be discussed, namely 0.015 < f < 0.05, 0.05 < f < 0.15 and 0.15 < f < 0.99. J. W. Christian used the JMA equation to simulate the progress of various phase transitions, and the n-index of the phase transition-time relation in the different cases was obtained [36]. In stage I (0.015 < f < 0.05), the value of n decreases indicating that the decreasing nucleation rate and the phase transition is interface controlled in the early stage. The nucleation rate decreases due to the consumption of elements at the location of nucleation. In stage II (0.05 < f < 0.15), n increases with the increasing transformed fraction indicating the increase of nucleation rate and the phase transition is diffusion controlled. The elements required by phase transformation near the nucleation site are relatively high giving rise to the increasing

Fig. 5. Variation in n with the increasing volume fraction (3 K/min).

nucleation rate. In stage III (0.15 < f < 0.99), generally, the value of n continues to decrease as the transformed fraction f increases. However, it should be noted that the nucleation rate is 0, when n is about 1.5, which can divide the stage into stage III1 and stage III2. In stage III1, Avrami exponent n decreases indicating the decreasing nucleation rate. In stage II of the phase transformation, the composition of the FCC matrix changes and formation of BCC structure lead to the depletion or enrichment of different regions by diffusion. The result is that the BCC phase forming elements at the nucleation interface are consumed and the element concentration gradient decrease leading to a decrease in nucleation rate.

3.3. The evolution of microstructure The first two stages of phase transformation in Fig. 1 are proved to be nanoscale precipitates without difference on macrostructure [29]. The evolution of microstructure of the third phase transformation is as follow. The XRD patterns of the as-cast and heattreated are presented in Fig. 6. As can be seen, the as-cast alloy consists of FCC and BCC structure consistent with previous research [29]. After heat treatment, the diffraction peak corresponding to (110) is more obvious than that of as-cast alloy, while the peak corresponding to (100) can be found indicating the formation of B2

Fig. 6. XRD patterns of as-cast and heat-treated (at 1123 K) Al0.5CoCrFeNi alloys.

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Fig. 7. SEM images showing the evolution of microstructure of (a) as-cast and (b) heat treated at 1123 K for 8 h.

phase. The peak between BCC and B2 phases is coincident showing that the lattice parameter is the same, thus the thermal dilation only involves the process of FCC to BCC. The evolution of microstructure after heat treatment is shown in Fig. 7, suggesting that the

microstructures are all dendrites. In addition, the precipitates in the FCC matrix can be observed evidently. In order to further analyze the type of phase transformation, TEM bright images are shown in Fig. 8 and corresponding electron

Fig. 8. TEM bright images, (a) as-cast alloy, (b) (c) corresponding selected electron diffraction image, (d) (g) heat-treated alloy at 1123 K/8 h, (e) (f) (h) corresponding selected electron diffraction image.


149

(4) The obvious relationship between FCC and BCC phases can be found and they meet K-S relationship that [111]bcc//[101]fcc, (011)bcc//(111)fcc. (5) After heat treatment, the ultimate tensile strength increases to 1143 MPa and the elongation decreases to 21.5% manifesting that we get the good combination of strength and plasticity. Acknowledgement

Fig. 9. (a) Engineering stress-strain curves of Al0.5CoCrFeNi alloys, (b) the size of tensile samples.

diffraction patterns are calibrated according to reference [43]. From Fig. 8 (a), (b) and (c), the conclusion that the as-cast alloy contains FCC and BCC phases can be obtained, which is consistent with the results of XRD pattern. Fig. 8 (d) is the bight field image of heattreated alloy at 1123 K for 8 h and the corresponding electron diffraction patterns are shown in Fig. 8 (e) and (f), respectively. As shown in Fig. 8 (d), the structure of thick slat is B2 phase and the thin slat is BCC phase. This also manifests that the phase transformation of the last stage is FCC to BCC. Further analysis is shown in Fig. 8 (g) and (h), the obvious relationship between FCC and BCC phase can be found and they meet K-S relationship that [111]bcc// [101]fcc, (011)bcc//(111)fcc. The engineering stress-strain curve of as-cast and heat-treated Al0.5CoCrFeNi alloys are shown in Fig. 9 (a) and the size of tensile specimen is shown in Fig. 9 (b). The yield strength, ultimate tensile strength and elongation of as-cast alloy are 334 MPa, 709 MPa and 43.0%, respectively. After heat treatment, the ultimate tensile strength increases to 1143 MPa and the elongation decreases to 21.5% getting the good combination of strength and plasticity. The variation in strength and elongation is well understood. FCCstructured alloys possess high ductility and low strength [18,19], whereas BCC-structured alloys are hard and brittle [19,20]. The precipitation of BCC structure in FCC matrix gives rise to the improving strength and decreasing elongation. 4. Conclusions In this paper, the phase transformation kinetics and the evolution of microstructure in Al0.5CoCrFeNi high entropy alloy were studied. The main conclusions are: (1) The phase transformation can be divided into three stages, taking 5 K/min as an example, the starting temperatures are 677 K, 805 K and 1044 K, respectively. (2) The corresponding activation energies determined by KAS method are 144.4 kJ/mol, 178.7 kJ/mol, 224.7 kJ/mol and 284.3 kJ/mol, when the transformed fraction is 0.2, 0.4, 0.6 and 0.8, respectively. (3) There are three main stages to be discussed, namely 0.015 < f < 0.05, 0.05 < f < 0.15 and 0.15 < f < 0.99. In stage I (0.015 < f < 0.05), the value of n decreases indicating that the phase transition is interface controlled in the early stage. In stage II (0.05 < f < 0.15), n increases with the increasing transformed fraction indicating the phase transition is diffusion controlled with increasing nucleation rate. In stage III (0.15 < f < 0.99), generally, the value of n continues to decrease indicating the nucleate rate is decreasing as the transformed fraction f increases.

This study was financially supported by the National Natural Science Foundation of China (Grant No. 51571161 and 51271151), the Natural Science Basic Research Plan in Shaanxi Province of China (2016JQ5003), and the Program of Introducing Talents of Discipline to Universities (Grant No. B08040). References [1] M.C. Gao, J.W. Yeh, P.K. Liaw, Y. Zhang, High-entropy Alloys, Springer International Publishing, 2016. [2] B.S. Murty, J.W. Yeh, S. Ranganathan, High Entropy Alloy (2014). [3] Y. Zhang, T.T. Zuo, Z. Tang, M.C. Gao, K.A. Dahmen, P.K. Liaw, Z.P. Lu, Microstructures and properties of high-entropy alloys, Prog. Mater. Sci. 61 (2014) 1e93. [4] B. Gludovatz, A. Hohenwarter, D. Catoor, E.H. Chang, E.P. George, R.O. Ritchie, A fracture-resistant high-entropy alloy for cryogenic applications, Science 345 (2014) 1153e1158. [5] D.B. Miracle, O.N. Senkov, A critical review of high entropy alloys and related concepts, Acta Mater. 122 (2017) 448e511. [6] D. Miracle, J. Miller, O. Senkov, C. Woodward, M. Uchic, J. Tiley, Exploration and development of high entropy alloys for structural applications, Entropy 16 (2014) 494e525. [7] J.Y. He, H. Wang, H.L. Huang, X.D. Xu, M.W. Chen, Y. Wu, X.J. Liu, T.G. Nieh, K. An, Z.P. Lu, A precipitation-hardened high-entropy alloy with outstanding tensile properties, Acta Mater. 102 (2016) 187e196. [8] T.T. Shun, Y.C. Du, Microstructure and tensile behaviors of FCC Al0.3CoCrFeNi high entropy alloy, J. Alloys Compd. 479 (2009) 157e160. [9] Z. Li, K.G. Pradeep, Y. Deng, D. Raabe, C.C. Tasan, Metastable high-entropy dual-phase alloys overcome the strengtheductility trade-off, Nature 534 (2016) 227e230. [10] H. Feng, Z. Wang, Y. Li, Q. Wu, J. Li, J. Wang, C.T. Liu, Kinetic ways of tailoring phases in high entropy alloys, Sci. Rep. 6 (2016). [11] M.S. Lucas, G.B. Wilks, L. Mauger, J.A. Munoz, O.N. Senkov, E. Michel, J. Horwath, S.L. Semiatin, M.B. Stone, D.L. Abernathy, Absence of long-range chemical ordering in equimolar FeCoCrNi, Appl. Phys. Lett. 100 (2012) 251907. [12] N. Kumar, M. Komarasamy, P. Nelaturu, Z. Tang, P.K. Liaw, R.S. Mishra, Friction stir processing of a high entropy alloy Al0.1CoCrFeNi, Jom 67 (2015) 1007e1013. [13] F. Otto, Y. Yang, H. Bei, E.P. George, Relative effects of enthalpy and entropy on the phase stability of equiatomic high-entropy alloys, Acta Mater. 61 (2013) 2628e2638. [14] B. Cantor, I.T.H. Chang, P. Knight, A.J.B. Vincent, Microstructural development in equiatomic multicomponent alloys, Mater. Sci. Eng. A 1 (2004) 213e218. ~ oz-Moreno, H.J. Stone, N.G. Jones, Precipitation in the [15] E.J. Pickering, R. Mun equiatomic high-entropy alloy CrMnFeCoNi, Scr. Mater. 113 (2016) 106e109. [16] J. Li, W. Jia, J. Wang, H. Kou, D. Zhang, E. Beaugnon, Enhanced mechanical properties of a CoCrFeNi high entropy alloy by supercooling method, Mater. Des. 95 (2016) 183e187. [17] F. He, Z. Wang, Q. Wu, J. Li, J. Wang, C.T. Liu, Phase separation of metastable CoCrFeNi high entropy alloy at intermediate temperatures, Scr. Mater. 126 (2016) 15e19. [18] F. Wang, Y. Zhang, G. Chen, H.A. Davies, Tensile and compressive mechanical behavior of a CoCrCuFeNiAl0.5 high entropy alloy, Int. J. Mod. Phys. B 23 (2012) 1254e1259. [19] Y. Lu, Y. Dong, S. Guo, L. Jiang, H. Kang, T. Wang, B. Wen, Z. Wang, J. Jie, Z. Cao, H. Ruan, T. Li, A promising new class of high-temperature alloys: eutectic high-entropy alloys, Sci. Rep. 4 (2014) 6200. [20] C.W. Tsai, M.H. Tsai, J.W. Yeh, C.C. Yang, Effect of temperature on mechanical properties of Al0.5CoCrCuFeNi wrought alloy, J. Alloys Compd. 490 (2010) 160e165. [21] L. Jiang, H. Jiang, Y.P. Lu, T.M. Wang, Z.Q. Cao, T.J. Li, Mechanical properties improvement of AlCrFeNi2Ti0.5 high entropy alloy through annealing design and its relationship with its particle-reinforced microstructures, J. Mater. Sci. Technol. 31 (2015) 397e402. [22] F. He, Z. Wang, S. Niu, Q. Wu, J. Li, J. Wang, C.T. Liu, Y. Dang, Strengthening the CoCrFeNiNb 0.25 high entropy alloy by FCC precipitate, J. Alloys Compd. 667 (2016) 53e57. [23] X.D. Xu, P. Liu, S. Guo, A. Hirata, T. Fujita, T.G. Nieh, C.T. Liu, M.W. Chen,

150

[24] [25]

[26] [27]

[28]

[29]

[30]

[31]

[32]

J. Wang et al. / Journal of Alloys and Compounds 710 (2017) 144e150 Nanoscale phase separation in a fcc-based CoCrCuFeNiAl0.5 high-entropy alloy, Acta Mater. 84 (2015) 145e152. S.S. Ghazi, K.R. Ravi, Phase-evolution in high entropy alloys: role of synthesis route, Intermetallics 73 (2016) 40e42. N.G. Jones, R. Izzo, P.M. Mignanelli, K.A. Christofidou, H.J. Stone, Phase evolution in an Al0.5 CrFeCoNiCu high entropy alloy, Intermetallics 71 (2016) 43e50. Y. Zhang, X. Yang, P.K. Liaw, Alloy design and properties optimization of highentropy alloys, Jom 64 (2012) 830e838. Y.F. Kao, T.J. Chen, S.K. Chen, J.W. Yeh, Microstructure and mechanical property of as-cast, -homogenized, and -deformed AlxCoCrFeNi (0x2) highentropy alloys, J. Alloys Compd. 488 (2009) 57e64. W.R. Wang, W.L. Wang, J.W. Yeh, Phases, microstructure and mechanical properties of AlxCoCrFeNi high-entropy alloys at elevated temperatures, J. Alloys Compd. 589 (2014) 143e152. S. Niu, H. Kou, T. Guo, Y. Zhang, J. Wang, J. Li, Strengthening of nanoprecipitations in an annealed Al0.5CoCrFeNi high entropy alloy, Mater. Sci. Eng. A 671 (2016) 82e86. R.P. Santana, N.A.D. Oliveira, P.J.V. Ranke, Magnetocaloric properties of compounds with first order phase transition: hysteresis effect, J. Alloys Compd. 509 (2011) 6346e6349. n, N. Maso , E. Cordoncillo, A.R. West, Phase transition M. Prades, H. Beltra hysteresis and anomalous CurieeWeiss behavior of ferroelectric tetragonal tungsten bronzes Ba2ReTi2Nb3O15:RE¼Nd,Sm, J. Appl. Phys. 104 (2008) 104118. X.L. Zhu, X.M. Chen, Phase transition hysteresis of ferroelectric Sr5EuTi3Nb7O30 ceramics with tetragonal tungsten bronze structure, J. Appl. Phys. 111 (2012) 044104.

[33] J. Du, Y. Gao, H. Luo, L. Kang, Z. Zhang, C. Zhang, C. Cao, Significant changes in phase-transition hysteresis for Ti-doped VO2 films prepared by polymerassisted deposition, Sol. Energy Mater. Sol. Cells 95 (2011) 469e475. [34] C.M. Lin, H.L. Tsai, Evolution of microstructure, hardness, and corrosion properties of high-entropy Al0.5CoCrFeNi alloy, Intermetallics 19 (2011) 288e294. [35] Z. Zhou, M. Lai, B. Tang, H. Kou, H. Chang, Z. Zhu, J. Li, L. Zhou, Non-isothermal phase transformation kinetics of u phase in TB13 titanium alloys, Mater. Sci. Eng. A 527 (2010) 5100e5104. [36] J.W. Christian, Formal theory of transformation kinetics, Theory Trans. Met. Alloys (2002) 529e552. [37] Y.H. Wang, H. Kou, H. Chang, Z.S. Zhu, X.F. Su, J. Li, L. Zhou, Phase transformation in TC21 alloy during continuous heating, J.Alloys Compd. 472 (2009) 252e256. [38] H.E. Kissinger, Reaction kinetics in differential thermal analysis, Anal. Chem. 29 (2002) 1702e1706. [39] M. Avrami, Kinetics of Phase Change I,II,III, 1939. [40] K. Majhi, K.B.R. Varma, Crystallization kinetic studies of CaBi2B2O7 glasses by non-isothermal methods, J. Mater. Sci. 44 (2009) 385e391. [41] W. Lu, J. Niu, T. Wang, K. Xia, Z. Xiang, Y. Song, Z. Mi, W. Zhang, W. Tian, Y. Yan, Phase transformation kinetics and microstructural evolution of MnAl permanent magnet alloys, J. Alloys Compd. 685 (2016) 992e996. ski, Decoupled bulk and surface crystallization in Pd85Si15 [42] A. Calka, A.P. Radlin glassy metallic alloys: description of isothermal crystallization by a local value of the Avrami exponent, J. Mater. Res. 3 (1988) 59e66. [43] D.H. Xiao, P.F. Zhou, W.Q. Wu, H.Y. Diao, M.C. Gao, M. Song, P.K. Liaw, Microstructure, mechanical and corrosion behaviors of AlCoCuFeNi-(Cr,Ti) high entropy alloys, Mater. Des. 116 (2017) 438e447.