- Email: [email protected]
Experimental and theoretical study of microstructural characteristics and phase stability in equiatomic CrFeMoV alloy
Materials Characterization 154 (2019) 449–457
Contents lists available at ScienceDirect
Materials Characterization journal homepage: www.elsevier.com/locate/matchar
Experimental and theoretical study of microstructural characteristics and phase stability in equiatomic CrFeMoV alloy
T
⁎
A. Saikumarana, Jaiganeshb, Chanchal Ghoshc, R. Mythilic,e, , D. Sornaduraib, N. Subramanianb,e, S. Mathi Jayab,e, Saroja Saibabad a
Homi Bhabha National Institute, Indira Gandhi Centre for Atomic Research, Kalpakkam, India Materials Science Group, IGCAR, Kalpakkam, India c Metallurgy and Materials Group, IGCAR, Kalpakkam, India d Formerly with IGCAR, HBNI, Kalpakkam 603102, India e HBNI, IGCAR, Kalpakkam, India b
A R T I C LE I N FO
A B S T R A C T
Keywords: High entropy alloys Microstructure Density functional theory Micro-segregation Scheil cooling XRD
Multi-principal elemental or high entropy alloys are viewed as promising class of materials with enhanced performance in a variety of environments. Study of microstructure of these alloys is essential to understand its influence on various properties. This study is aimed at the synthesis of an equiatomic Cr-Fe-Mo-V alloy by conventional casting method and its microstructural characterization. For the first time, crystal structure of this alloy has been predicted by ab-initio density functional approach and found to be in close agreement with the experimental results. Micro-segregation observed during solidification is also predicted by Scheil cooling model and is attributed to the higher melting point and partition coefficient of Molybdenum. This alloy may be a potential radiation resistant alloy, in view of the possibility of formation of a single BCC solid solution, shown experimentally and theoretically.
1. Introduction Alloy design recipe has been gradually changing from single principal element based alloys to multi-principal elemental alloys (MPEAs) also called as High Entropy Alloys (HEAs), since they offer promising engineering properties [1–9] and myriad of microstructures by fine tuning the composition. Initially, it was proposed that [10–12], HEAs formed single-phase solid solutions with simple crystal structures, of predominantly bodycentered cubic (BCC) and face-centered cubic (FCC), and quite less frequently hexagonal closed-packed (HCP) [13,14], mainly due the high configurational entropy, achieved by increasing the number of alloying elements. However, it has been realized by recent experiments that the high configurational entropy is neither a sufficient nor an essential condition to form single-phase solid solution in all MPEAs [15,16]. Most of the MPEAs constituting four or more elements form multiphase structures. Experimentally, to explore immense compositional space spanned by these HEAs will be a nightmare. Hence, it will be promisingly practical to predict the phase stability of HEAs through some reliable theoretical criteria. In the early days of the HEA development, several
⁎
proposals for stability of high entropy alloys are reported in literature, which are an extension of Hume-Rothery rules like empirical relations about difference in atomic size, electro-negativity, entropy of mixing, e/a ratio, enthalpy of mixing using Midemma approach, Valence electron concentration, etc. [9,17–24]. Later Yiping Lu et al. [25] proposed a quantity called average value of d-orbital energy level (Md ) which quite successfully predicted the formation of topological close packed phases in Ni based Superalloys and further validated in HEAs [26]. Calphad based techniques were also employed by several researchers to determine the phases in HEAs of particular composition [27–30]. However, none of these methods can successfully predict the phases experimentally observed in many alloys. Recently, ab initio calculations have emerged as a powerful approach that complements experiment and serves as a predictive tool for the identification and characterization of promising alloys. Such calculations are based only on quantum mechanical laws and natural constants and hence offers an advantage of the prediction and investigation of materials structure and properties without empirical input [31]. In this work, an equiatomic CrFeMoV alloy has been characterized through extensive X-Ray diffraction and electron microscopy techniques. Employment of various theoretical tools mentioned above also
Corresponding author at: Metallurgy and Materials Group, IGCAR, Kalpakkam, India. E-mail address: [email protected] (R. Mythili).
https://doi.org/10.1016/j.matchar.2019.06.027 Received 4 May 2019; Received in revised form 13 June 2019; Accepted 14 June 2019 Available online 15 June 2019 1044-5803/ © 2019 Elsevier Inc. All rights reserved.
Materials Characterization 154 (2019) 449–457
A. Saikumaran, et al.
Fig. 1. (a, b, c) Optical, SE, BSE micrographs of as cast CrFeMoV alloy showing dendritic morphology (d) EDX spectra of dendrites and interdendrites showing Mo and Fe enrichment respectively.
diffractometer (STOE, Darmstadt, GmbH) operated in Bragg - Brentano geometry and in θ–θ mode. Room temperature Powder - XRD measurements were carried out on a 10 mm diameter pellet of CrFeMoV alloy mounted on the Si(911) single crystal sample holder. The Si (911) single crystal was employed as it does not give any Bragg peak in the 2θ range 10 – 100° with Cu Kα radiation (1.54060 Å). XRD data was collected at a step size of 0.05° 2θ, with a counting time of 7 s per step with spinning of the sample holder. The diffracted X-rays were detected with a NaI:Tl point detector attached with a secondary monochromator. The as cast alloy sample surfaces were sequentially polished down to the 1 μm grit diamond paste, and then chemically etched using a solution containing 95% nitric acid and 5% hydrofluoric acid for microstructural analysis. Preliminary microstructural and microchemical analysis of the as cast alloy was carried out using Zeiss Optical microscope and Helios Nanolab 600i Dual beam FESEM equipped with EDX spectrometer. Specimens for Transmission Electron Microscopy (TEM) were prepared by mechanical grinding and thinning up to ~40 μm,
showed a close correspondence with the experimental results. The composition of this alloy has been chosen from the major alloying elements in ferritic steels, which exhibit good irradiation resistance due to their more open BCC structure, less dislocation bias and higher defect sink strength than FCC structured alloys [32]. 2. Materials and methods Equiatomic CrFeMoV alloy was synthesized by vacuum arc melting technique from high purity raw materials of Cr, Fe, Mo and V (each 25 at.%) using a tungsten electrode tri-arc furnace with water cooled copper hearth. The alloys were re-melted 5 to 8 times due to the large difference in melting points and densities of the pure elements and also flipped between two melting processes to obtain chemical homogeneity. Further some of these pellets of the melted alloy were subjected to suction casting as a rod of 3 mm diameter. X-ray diffraction (XRD) patterns were recorded using a STOE X-ray 450
Materials Characterization 154 (2019) 449–457
A. Saikumaran, et al.
followed by ion milling using a Technoorg Linda IV4/H ion miller. Detailed investigations on microstructure, chemistry and phase analyses were carried out using Philips CM200 Analytical Transmission Electron Microscope (ATEM) equipped with Oxford X-Max SDD detector for EDX analysis 3. Computational methods In the present work, phase stability calculations have been made through empirical equations reported in literature [17,25] and also Calphad based thermodynamic calculations using JMatpro software [33] under the Stainless steel module with an alloy of Cr-Fe-Mo-V of equiatomic composition and also to predict the phases formed during non-equilibrium cooling from the liquid. Also, detailed theoretical calculations have been made to predict the possible structure of the CrFeMoV alloy based on global minimization of free energy surfaces by using the particle-swarm optimization method, which is implemented in the CALYPSO (Crystal structure AnaLYsis by Particle Swarm Optimization) package [34] and using the evolutionary algorithm based tool USPEX (Universal Structure Predictor: Evolutionary Xtallography) [35]. USPEX and CALYPSO techniques need no prior information on the system and these methods utilize ab-initio free energies for predicting the crystal structure. For structural search, calculations are carried out from one formula unit to four formula units per simulation cell. All the structural relaxations and the electronic property calculations are achieved in the framework of density functional theory [36] within the projector augmented wave (PAW) method [37], by using the Vienna Ab-initio Simulation Package (VASP) [38]. Herein, the Fe 3d74s1 electrons, Cr 3d54s1, Mo 4d55s1 and the V 3d44s1 electrons are treated as valence electrons. The exchange and correlation interactions are considered within the GGA approach by adopting the Perdew-Burke-Ernzerhof functional [39]. To ensure that the total energy calculations are well converged, a kinetic energy cutoff of 750 eV and the (8 × 8 × 8) Monkhorst-Pack (MP) [40] k-point mesh has been chosen with uniform spacing of 2π × 0.03 Å−1. The convergence for the energy and force is chosen as 10−6 eV and 0.01 eV/Å, respectively.
Fig. 2. EDX maps of as cast CrFeMoV alloy showing distribution of (a) Mo (b) Fe (c) Cr (d) V from region marked in Fig. 1(c). Table 1 Variation of concentrations of constituent elements of the as cast alloy during solidification. Concentrations and partition coefficients
Mo
V
Cr
Fe
Nominal alloy composition Co (at.%) Average dendritic composition, CSexp (at.%) Average inter-dendritic composition, CLexp (at. %) Partition coefficient, kexp = CSexp/CLexp Solid composition, CScal (at.%) Liquid composition, CLcal (at.%) Partition coefficient, kcal = CScal/CLcal ΔC = CSexp − C0 (at.%)
25 33.31 17.91
25 25.83 24.43
25 22.6 23.06
25 18.25 34.6
1.85 25.49 8.17 3.12 8.31
1.05 25.01 25.57 0.98 0.83
0.98 25.36 16.88 1.50 −2.40
0.52 24.14 49.38 0.49 −6.75
consisting of columnar grains along the edges with central equiaxed grains. Further, it is observed that the average dendritic arm spacing in this case is ~1–2 μm, which is much lower than in the as cast pellets (~10 μm), suggesting that the cooling rate is higher during suction casting. However, the EDX maps clearly reveal the enrichment of Mo to the dendrites, indicating that micro-segregation cannot be suppressed even at a high cooling rate. In order to understand this segregation effect, solidification under non- equilibrium conditions was simulated by Scheil cooling model, using JMatpro software. The liquidus and solidus of the alloy is predicted to be 1900 and 1605 °C respectively using the Scheil cooling model, though the equilibrium solidus temperature would be higher, since this model assumes no diffusion in the solid in contrast to a fast diffusion in the liquid. The variation of concentration of different alloying elements in the liquid and solid on cooling is shown in Fig. 4. It is observed that during the initial stages of solidification, there is a depletion of Mo and an enrichment of Fe in the liquid, while in the solid depletion of Fe and an enrichment of Mo is predicted. It is also clearly observed that the liquid to finally solidify is enriched with Fe and depleted in Mo. However, the concentration of V in the liquid and solid does not show a significant change with cooling, though there is a slight depletion of Cr in the liquid at the end of solidification. Micro-segregation of solute elements between the liquid and the solid during solidification can be explained by the partition coefficient [41] of the solute defined by the following equation:
4. Results and discussion 4.1. Microstructural characterization Fig. 1(a) shows the optical micrograph of the as cast alloy, where the presence of a dendritic microstructure is observed. Such microstructures are commonly observed in castings [41]. Fig. 1(b) shows the Secondary Electron (SE) image of as cast alloy which shows the presence of columnar grain structure with dendrites along the solidification direction. The average inter-dendritic arm spacing in the as cast alloy was determined to be ~10 μm. The contrast in BSE image of the alloy in Fig. 1(c) suggests a difference in composition between the dendrites and inter-dendrites as revealed in EDX spectra in Fig. 1(d). Further EDX maps from several regions of the specimen were acquired and a typical one from region marked in Fig. 1(c) is shown in Fig. 2. It is clearly observed that Mo and Fe are enriched in the dendrites and interdendrites respectively, while Cr and V are distributed more or less uniformly in both dendrites and interdendrites, which is also evident from quantitative analysis of the composition in Table 1. It is well known that instabilities at the solid liquid interface due to constitutional supercooling leads to a dendritic solidification, which is strongly influenced by the cooling rate from the melting temperature of the alloy. The dendrites are the first to solidify, while the inter-dendritic region represents the liquid at the instant of solidification. In order to check if a high cooling rate can suppress the microsegregation, few molten pellets were also subjected to suction casting into rods of 3 mm diameter. The SEM images of the alloy after suction casting are shown in Fig. 3 (a and b) along with the EDX maps (Fig. 3(e–f)). The SE micrograph shows a typical cast microstructure
k = CS /CL
(1)
where, CS and CL are the concentration of the solute in solid and liquid respectively. k < 1 implies the segregation of solute to the liquid, 451
Materials Characterization 154 (2019) 449–457
A. Saikumaran, et al.
Fig. 3. (a, b) SE micrograph of suction cast CrFeMoV alloy; EDX maps of (c) Mo; (d) Fe; (e) Cr; (f) V showing micro-segregation of Mo and Fe along dendrites and interdendrites respectively.
accounts for the segregation of Mo in the dendrites that solidify first, leaving the surrounding liquid to be enriched with Fe. Additionally, the excess concentration of an alloying element i inside the dendritic arm is calculated as ΔC = Cda − Cavg, where Cda is the concentration of an alloying element i inside the dendritic arm and Cavg is the average concentration of an alloying element i. The difference in melting point is calculated as ΔTi = Tmi − Tmalloy. The melting point of CrFeMoV alloy is calculated using the rule of mixtures.
while k > 1 implies the segregation of solute to the solid. With a large difference in the melting point of the alloying elements, the solidus temperature is further depressed during non-equilibrium cooling. The partition coefficient determined experimentally and reported in Table 1 is from the measured composition of the dendritic and interdendritic regions of the as cast pellet, which has comparatively a larger dendritic arm spacing by both SEM and TEM – EDX analysis. These compositions are compared with the theoretically calculated compositions of liquid and solid (using Scheill cooling model) at the end of solidification, as per Eq. (1) in Table 1. These observations suggest that the partition coefficients (k) of the alloying elements are as follows: Mo ≫ 1; Fe < 1; V and Cr ≈ 1, which
n
Tmalloy =
∑ Ci Tmi i=1
(2)
where, Ci and Tmi is the concentration and melting temperature of 452
Materials Characterization 154 (2019) 449–457
A. Saikumaran, et al.
4.2. Structural characterization From the XRD spectrum of the as cast CrFeMoV alloy, it was observed that it consists of 2 BCC phases with close by lattice parameters, which could be due to the Mo rich and Fe rich regions observed in the microstructure. In order to confirm this point, Rietveld analysis has been carried out (Fig. 6) and the refined lattice parameters of the two phases are determined to be 3.0094 ± 0.0003 and 2.9696 ± 0.0005 Å. Further TEM analysis of the as cast alloy, whose results are shown in Fig. 7(a,b,d,e) confirmed the BCC structure of dendritic and inter-dendritic regions with lattice parameters of 2.99 ± 0.2 and 2.97 ± 0.2 Å. The enrichment of Mo (Fig. 7(c)) and Fe (Fig. 7(f)) in the dendrites and inter-dendrites respectively was also observed similar to the SEM observations. Typical HRTEM image from a dendritic region is shown in Fig. 8(a), with the inset showing the Fast Fourier Transform (FFT) from the region marked, the analysis of which confirmed a BCC structure with a lattice parameter of 3 ± 0.2 Å, which is in line with above analysis. Fig. 8(b) shows the inverse FFT of the region marked in Fig. 8(a). Fig. 8(c) shows the lattice imaging of (211) planes with an interplanar distance of 0.129 nm. From the above analysis, it is clear that equiatomic CrFeMoV alloy forms two BCC phases with very close lattice parameters. This very small difference in lattice parameters can be due to the micro-segregation effect of Mo and Fe in the dendrites and interdendrites respectively. A comparison of atomic size shows that the Mo has much larger atomic size (190 pm) than that of Fe (126 pm). Hence, it can be understood that the lattice parameter of dendrites enriched with Mo is slightly higher than that of the interdendrites enriched with Fe.
Fig. 4. Simulated concentration profile in the solid and liquid during cooling from the liquidus. Table 2 Calculation of Tm of alloy and ΔTi. Element
Melting temperature (°C)
ΔTi (°C) = Tmi − Tmalloy
Fe Cr Mo V Tm of alloy
1538 1907 2617 1890 1988
−450 −81 629 −98
4.3. Thermodynamic phase stability Many theoretical means of prediction of possible phases in high entropy alloys have been reported including the empirical relations, Calphad based approaches, ab-initio density functional theoretical calculations though none of them satisfactorily predict or match with the experimental observations. This could be due to the metastability of some of the phases formed in these alloys stemming from the prevailing non-equilibrium conditions during processing of the alloy. In this study, an attempt has been made to compare the experimental observations to theoretical predictions from empirical relations, thermodynamic calculations using JMatpro software and also an ab-initio DFT based calculations, which are explained in the following sections. a. Empirical analysis Various empirical equations have been reported in literature to predict the phase stability like difference in atomic size, VEC, electronegativity, enthalpy and entropy of mixing through Midemma relations, Ω parameter based on average melting point of the alloy, etc. These values obtained for this alloy are listed in Table 3, which are calculated using standard well established empirical equations which are given in references [9, 17, 25]. From these values the formation of single BCC solid solution is predicted for this composition. However, a high value of the average d-orbital energy (Md ) suggests the possibility of formation of an intermetallic compound.
Fig. 5. Dependence of excess concentration of a particular element i (Fe, Cr, V, Mo) inside the dendritic arm on the temperature difference (between Tm of element i and that of the alloy).
b. Calphad approach
element i respectively. The computed values are shown in Table 2. The dependence of ΔC on ΔTi plotted in Fig. 5 clearly shows that, the segregation of an element in the dendritic arm increases with an increase in ΔT, which explains the enrichment of Mo inside the dendrites.
Thermodynamic equilibrium phase stability calculations have been carried out using JMatpro software and the results are shown in Fig. 9. It is observed that a stable BCC solid solution exists in the temperature range of 1180 to 1778 °C, while Sigma and Laves phase are predicted at lower temperatures up to 1180 and 266 °C respectively. Though the formation of Sigma and Laves phases is predicted in this alloy, 453
Materials Characterization 154 (2019) 449–457
A. Saikumaran, et al.
Fig. 6. Rietveld refined XRD spectrum (wRp = 0.19; Rp = 0.13; χ2 = 1.829) of as cast CrFeMoV alloy showing the presence of two BCC phases with near-by lattice parameters.
Fig. 7. (a) BF image of dendrite with SAD pattern confirming BCC structure along [−111] zone axis in inset (b) DF image of dendrite with (0−11) reflection (c) EDX spectrum of dendrites showing enrichment of Mo (d) BF image of inter-dendrite with SAD pattern confirming BCC structure along [−113] zone axis in inset (e) DF image of interdendrite with (110) reflection (f) EDX spectrum of dendrites showing enrichment of Fe.
may be noted that the equilibrium solidus temperature is higher than that estimated during cooling from the liquidus, which is 1605 °C. In the light of the above empirical and thermodynamic predictions, it is inferred that a single BCC solid solution is possible in this alloy. However, the experimental observations show the presence of two BCC
experimental observations did not show any signature for the existence of these phases. This is attributed to the fact that these calculations are carried out at equilibrium conditions, while during arc melting nonequilibrium cooling conditions prevail. The equilibrium liquidus and solidus of the alloy are estimated to be 1900 and 1778 °C respectively. It 454
Materials Characterization 154 (2019) 449–457
A. Saikumaran, et al.
Fig. 8. (a) HRTEM image from the dendritic region with FFT in the inset from the region marked; (b) Inverse FFT from the region marked in (a); (c) Fourier filtered inverse FFT showing lattice imaging of (211) planes with an interplanar distance of 0.129 nm.
c. Ab-initio structure prediction
Table 3 Empirically calculated parameters for phase prediction in CrFeMoV alloy. Parameter
Value in CrFeMoV alloy
Phase predicted
δ
3.88
BCC + Intermetallics
ΔSmix
11.52
ΔHmix
-3
Ω
7.637
VEC
1.25
Md
1.27
There are few literature reports available on first principle calculations of phase stability in high entropy alloys [31]. Since such calculations are based on quantum mechanical laws, the predictions require only the atomic number of the constituent elements and no other empirical input. To explore the stable structure for this alloy, an extensive structural search has been performed by both particle swarm optimization [34] and evolutionary algorithm techniques [35]. Using the above-said techniques, the enthalpy of formation per atom of this CrFeMoV alloy was calculated through the following relation:
ΔH (CrFeMoV ) =
1 ⎡H (CrFeMoV ) − a. H (Fe ) − a. H (Cr ) − a a + b + c + d⎢ ⎣ . H (Mo) − a. H (V )
(3)
where, ΔH is the enthalpy of formation per atom and H is the calculated enthalpy per chemical unit for each system at their respective groundstate structure and a, b, c, d are number of atoms per unit cell of respective elements. Although, it is true that Gibb's free energy dictates the stability of different phases at equilibrium, enthalpy of formation has been used to predict the crystal structure of this alloy. The DFT calculations for structure prediction reported in the current study have been carried out using USPEX and CALYPSO packages, where the enthalpy of formation only are computed at absolute zero Kelvin [34, 35]. Hence the enthalpy of formation represents the Gibb's free energy. Also, since the configurational entropy of the alloy is high, even at high temperatures, it is expected to aid the stability of the phase with low enthalpy of formation. This is evident from the Calphad calculations, which predict a BCC solid solution at high temperatures. The computed results using both the techniques predicted that the enthalpy of formation for this alloy is −10.543 eV/atom for two structures, namely tetragonal P4mm (Space Group: 99) and cubic F43 m (Space Group: 216) with lattice parameter of 5.7594 Å. This suggests that if sufficient energy is supplied to overcome the reaction barrier, CrFeMoV alloy can be formed at ambient conditions with a face centred cubic or a primitive tetragonal structure. The BCC structure of the alloy from experimental observation and other computations, may be seemingly contradict the DFT prediction of an FCC structure. However, the underlying topology of F-43 m FCC can be understood to be made up as a supercell of 2 × 2 × 2 BCC crystals, which has been shown in Fig. 10(a,b), demonstrated using the crystal visualization program VESTA [42]. These structural features can further be explained as follows: Close-packed Fe layers in c stacking; Cr in octahedral voids, Mo and V in tetrahedral voids. Fe4(Mo,V) tetrahedra
Fig. 9. JMatPro simulation of variation of phases in CrFeMoV alloy with temperature.
structures with close lattice parameters. This could be attributed to the micro-segregation effects formed in the casting during non-equilibrium cooling and proper homogenization is expected to yield a homogeneous BCC alloy. The presence of sigma and Laves predicted at low temperatures has not been experimentally observed when cooled from the liquid state. This suggests the sluggish kinetics of these transformations, which may be observed if the alloy is subjected to long term aging in these temperature ranges. 455
Materials Characterization 154 (2019) 449–457
A. Saikumaran, et al.
Fig. 10. Crystal structure of CrFeMoV alloy along [100] with 2 × 2 × 2 supercells of BCC lattice (a) 3D view (b) in plane view (c) Structural features of CrFeMoV showing Fe4(Mo,V) tetrahedra sharing vertices to form a 3D-framework (d) Predicted variation of energy with volume of the BCC unit cell.
5. Conclusions
share vertices to form a 3D-framework as shown in Fig. 10(c). Substitution derivative of W, which is the prototype for a BCC atomic arrangement, with a sequence along 〈111〉 forms the Fe-Cr-Mo-V alloy. Hence the BCC structure is considered for further computations for analyzing the stability of the optimized structure. To obtain optimized volume or lattice constants of this alloy in ground state, first, the total energy of the system was computed at different volume or lattice constants around the relaxed value. Then energy-volume data was fitted to the second order Birch-Murnaghan equation of state (EOS) [43] to give the theoretical equilibrium volume and minimum energy. The obtained energy versus volume results are plotted in Fig. 10(d). The optimized computed lattice constant is 2.87 Å, which is in good agreement with the experimental results. To summarise, the empirical parameters, Calphad and DFT calculations suggest a single BCC solid solution except for the high Md values, which only indicates a possibility for formation of an intermetallic phase. However, the experimental observation of 2 BCC phases is due to the micro-segregation effects and the very close lattice parameters also reflect this. Hence an appropriate homogenization treatment can remove such segregations.
The present study is on evaluation of phase stability in an equiatomic Cr-Fe-V-Mo alloy by experimental observations and theoretical calculations. The important conclusions drawn from this work are as follows: 1. As cast alloy showed a dendritic structure with enrichment of Mo, which is understood to be due to the higher partition coefficient and melting point of Mo. 2. Microstructure of the as cast alloy is found to consist of two BCC phases with close lattice parameters, though thermodynamic phase stability calculations show the possibility of getting a single BCC solid solution for the alloy at high temperatures. Hence the presence of two BCC phases is attributed to the segregation Mo to dendrites and Fe to interdendrites. 3. For the first time, energetically stable crystal structure of the alloy has been predicted using DFT calculations, as a 2 × 2 × 2 super cell of BCC unit cell of lattice parameter of 2.87 Å, which is in close agreement with the experimentally determined value. The above analysis and predictions suggest that, it is possible to 456
Materials Characterization 154 (2019) 449–457
A. Saikumaran, et al.
obtain a stable BCC solid solution in this equiatomic Cr-Fe-Mo-V alloy. Since the current alloy composition is based on alloying elements in ferritic steels and possesses similar crystal structure, it is expected to exhibit good irradiation resistance, which is an important criterion for a good candidate core structural material for nuclear applications [32].The evaluation of mechanical and irradiation properties of this alloy are currently in progress.
[17] G. Sheng, C.T. Liu, Phase stability in high entropy alloys: formation of solid-solution phase or amorphous phase, Pro Nat Sci-Mater 21 (2011) 433–446, https://doi.org/ 10.1016/S1002-0071(12)60080-X. [18] Y. Zhang, Y.J. Zhou, J.P. Lin, G.L. Chen, P.K. Liaw, Solid-solution phase formation rules for multi-component alloys, Adv. Eng. Mater. 10 (2008) 534–538, https://doi. org/10.1002/adem.200700240. [19] D. King, S. Middleburgh, A. McGregor, M. Cortie, Predicting the formation and stability of single phase high-entropy alloys, Acta Mater. 104 (2016) 172–179, https://doi.org/10.1016/j.actamat.2015.11.040. [20] S. Guo, Q. Hu, C. Ng, C. Liu, More than entropy in high-entropy alloys: forming solid solutions or amorphous phase, Intermetallics 41 (2013) 96–103, https://doi. org/10.1016/j.intermet.2013.05.002. [21] Y. Ye, Q. Wang, J. Lu, C. Liu, Y. Yang, Design of high entropy alloys: a singleparameter thermodynamic rule, Scr. Mater. 104 (2015) 53–55, https://doi.org/10. 1016/j.scriptamat.2015.03.023. [22] M.C. Troparevsky, J.R. Morris, P.R. Kent, A.R. Lupini, G.M. Stocks, Criteria for predicting the formation of single-phase high-entropy alloys, Phys. Rev. X 5 (2015) 011041, , https://doi.org/10.1103/PhysRevX.5.011041. [23] S. Guo, C. Ng, J. Lu, C. Liu, Effect of valence electron concentration on stability of fcc or bcc phase in high entropy alloys, J. Appl. Phys. 109 (2011) 103505, , https:// doi.org/10.1063/1.3587228. [24] K. Guruvidyathri, B. Murty, J. Yeh, K.H. Kumar, Gibbs energy-composition plots as a tool for high-entropy alloy design, J. Alloys Compd. 768 (2018) 358–367, https:// doi.org/10.1016/j.jallcom.2018.07.264. [25] Y. Lu, Y. Dong, L. Jiang, T. Wang, T. Li, Y. Zhang, A criterion for topological closepacked phase formation in high entropy alloys, Entropy 17 (2015) 2355–2366, https://doi.org/10.3390/e17042355. [26] A. Saikumaran, R. Mythili, S. Saroja, V. Srihari, Microstructural characterization of Equiatomic CrFeNbNiV alloy, T Indian I Metals 72 (2019) 111–121, https://doi. org/10.1007/s12666-018-1466-x. [27] F. Zhang, C. Zhang, S.-L. Chen, J. Zhu, W.-S. Cao, U.R. Kattner, An understanding of high entropy alloys from phase diagram calculations, CALPHAD 45 (2014) 1–10, https://doi.org/10.1016/j.calphad.2013.10.006. [28] M. Gao, D. Alman, Searching for next single-phase high-entropy alloy compositions, Entropy 15 (2013) 4504–4519, https://doi.org/10.3390/e15104504. [29] M. Vaidya, K. Guruvidyathri, B. Murty, Phase formation and thermal stability of CoCrFeNi and CoCrFeMnNi equiatomic high entropy alloys, J. Alloys Compd. 774 (2019) 856–864, https://doi.org/10.1016/j.jallcom.2018.09.342. [30] K. Christofidou, T. McAuliffe, P. Mignanelli, H.J. Stone, N.G. Jones, On the prediction and the formation of the sigma phase in CrMnCoFeNix high entropy alloys, J. Alloys Compd. 770 (2019) 285–293, https://doi.org/10.1016/j.jallcom.2018.08. 032. [31] Y. Ikeda, B. Grabowski, F. Körmann, Ab initio phase stabilities and mechanical properties of multicomponent alloys: a comprehensive review for high entropy alloys and compositionally complex alloys, Mater. Charact. 147 (2018) 464–511, https://doi.org/10.1016/j.matchar.2018.06.019. [32] T. Jayakumar, M. Mathew, K. Laha, R. Sandhya, Materials development for fast reactor applications, Nucl. Eng. Des. 265 (2013) 1175–1180, https://doi.org/10. 1016/j.nucengdes.2013.05.001. [33] N. Saunders, U. Guo, X. Li, A. Miodownik, J.-P. Schillé, Using JMatPro to model materials properties and behavior, JOM 55 (2003) 60–65, https://doi.org/10.1007/ s11837-003-0013-2. [34] Y. Wang, J. Lv, L. Zhu, Y. Ma, Crystal structure prediction via particle-swarm optimization, Phys. Rev. X 82 (2010) 094116, , https://doi.org/10.1103/PhysRevB. 82.094116. [35] A.R. Oganov, C.W. Glass, Crystal structure prediction using ab initio evolutionary techniques: principles and applications, J. Chem. Phys. 124 (2006) 244704, , https://doi.org/10.1063/1.2210932. [36] W. Kohn, L.J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140 (1965) A1133, https://doi.org/10.1103/PhysRev.140. A1133. [37] P.E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50 (1994) 17953, , https://doi.org/10.1103/PhysRevB.50.17953. [38] G. Kresse, J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci. 6 (1996) 15–50, https://doi.org/10.1016/0927-0256(96)00008-0. [39] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77 (1996) 3865, https://doi.org/10.1103/PhysRevLett.77. 3865. [40] X. Zhang, X. Liu, G. Liang, R. Li, H. Xu, B. Yan, Theoretical study on the low-lying excited states of the phosphorus monoiodide (PI) including the spin–orbit coupling, J. Quant. Spectrosc. Radiat. Transf. 168 (2016) 66–77, https://doi.org/10.1016/j. jqsrt.2015.09.006. [41] J.L. Walker, B. Chalmers, B. Chalmers (Ed.), Principles of Solidification, 1964 Boston. [42] K. Momma, F. Izumi, VESTA: a three-dimensional visualization system for electronic and structural analysis, J. Appl. Crystallogr. 41 (2008) 653–658, https://doi. org/10.1107/S0021889808012016. [43] F. Birch, Finite elastic strain of cubic crystals, Phys. Rev. 71 (1947) 809, https://doi. org/10.1103/PhysRev.71.809.
Acknowledgements Authors sincerely acknowledge Dr. Arup Dasgupta, Head, Structural and Analytical Microscopy Section, Dr. S. Raju, Head, Physical Metallurgy Division, Dr. G. Amarendra, Director, Metallurgy and Materials Group and Dr. A. K. Bhaduri, Director, Indira Gandhi Centre for Atomic Research for their sustained support and encouragement during this work. The authors also thank UGC-DAE-CSR facility at Kalpakkam for extending their experimental facility. Mr. Saikumaran sincerely acknowledge HBNI-IGCAR for the fellowship. Data availability The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study. References [1] S.J. Mary, N. Rajan, R. Epshiba, High entropy alloys properties and its applications–an over view, Eur. Chem. Bull 4 (2015) 279–284, https://doi.org/10.17628/ ecb.2015.4.279-284. [2] M.-H. Tsai, J.-W. Yeh, High-entropy alloys: a critical review, Mater. Res. Lett 2 (2014) 107–123, https://doi.org/10.1080/21663831.2014.912690. [3] Y. Qiu, S. Thomas, M.A. Gibson, H.L. Fraser, N. Birbilis, Corrosion of high entropy alloys, npj Mater, Degrad 1 (2017) 1–18, https://doi.org/10.1038/s41529-0170009-y. [4] P. Chen, C. Lee, S.-Y. Wang, M. Seifi, J.J. Lewandowski, K.A. Dahmen, H. Jia, X. Xie, B. Chen, J.-W. Yeh, Fatigue behavior of high-entropy alloys: a review, Sci China Technol Sc 61 (2018) 168–178, https://doi.org/10.1007/s11431-017-9137-4. [5] S. Gorsse, M. Nguyen, O. Senkov, D. Miracle, Database on the mechanical properties of high entropy alloys and complex concentrated alloys, Data Brief 21 (2018) 2664–2678, https://doi.org/10.1016/j.dib.2018.11.111. [6] J.-P. Couzinié, O. Senkov, D. Miracle, G. Dirras, Comprehensive data compilation on the mechanical properties of refractory high-entropy alloys, Data brief 21 (2018) 1622–1641, https://doi.org/10.1016/j.dib.2018.10.071. [7] W.-Y. Chen, X. Liu, Y. Chen, J.-W. Yeh, K.-K. Tseng, K. Natesan, Irradiation effects in high entropy alloys and 316H stainless steel at 300 °C, J. Nucl. Mater. 510 (2018) 421–430, https://doi.org/10.1016/j.jnucmat.2018.08.031. [8] J. Chen, X. Zhou, W. Wang, B. Liu, Y. Lv, W. Yang, D. Xu, Y. Liu, A review on fundamental of high entropy alloys with promising high–temperature properties, J, Alloys Compd. (2018) 15–30, https://doi.org/10.1016/j.jallcom.2018.05.067. [9] W. Zhang, P.K. Liaw, Y. Zhang, Science and technology in high-entropy alloys, Sci. China Mater 61 (2018) 2–22, https://doi.org/10.1007/s40843-017-9195-8. [10] J.W. Yeh, S.K. Chen, S.J. Lin, J.Y. Gan, T.S. Chin, T.T. Shun, C.H. Tsau, S.Y. Chang, Nanostructured high-entropy alloys with multiple principal elements: novel alloy design concepts and outcomes, Adv. Eng. Mater. 6 (2004) 299–303, https://doi. org/10.1002/adem.200300567. [11] J.-W. Yeh, Alloy design strategies and future trends in high-entropy alloys, JOM 65 (2013) 1759–1771, https://doi.org/10.1007/s11837-013-0761-6. [12] Y. Ye, Q. Wang, J. Lu, C. Liu, Y. Yang, High-entropy alloy: challenges and prospects, Mater. Today 19 (2016) 349–362, https://doi.org/10.1016/j.mattod.2015.11.026. [13] R. Devanathan, W. Jiang, K. Kruska, M.A. Conroy, T.C. Droubay, J.M. Schwantes, Hexagonal close-packed high-entropy alloy formation under extreme processing conditions, J. Mater. Res. 34 (2019) 1–11, https://doi.org/10.1557/jmr.2018.438. [14] J. Qiao, M. Bao, Y. Zhao, H. Yang, Y. Wu, Y. Zhang, J. Hawk, M. Gao, Rare-earth high entropy alloys with hexagonal close-packed structure, J. Appl. Phys. 124 (2018) 195101, , https://doi.org/10.1063/1.5051514. [15] 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) 2628–2638, https://doi.org/10.1016/j.actamat.2013.01.042. [16] N.E. Koval, J.I. Juaristi, R.D. Muiño, M. Alducin, Elastic properties of the TiZrNbTaMo multi-principal element alloy studied from first principles, Intermetallics 106 (2019) 130–140, https://doi.org/10.1016/j.intermet.2018.12. 014.
457
Contents lists available at ScienceDirect
Materials Characterization journal homepage: www.elsevier.com/locate/matchar
Experimental and theoretical study of microstructural characteristics and phase stability in equiatomic CrFeMoV alloy
T
⁎
A. Saikumarana, Jaiganeshb, Chanchal Ghoshc, R. Mythilic,e, , D. Sornaduraib, N. Subramanianb,e, S. Mathi Jayab,e, Saroja Saibabad a
Homi Bhabha National Institute, Indira Gandhi Centre for Atomic Research, Kalpakkam, India Materials Science Group, IGCAR, Kalpakkam, India c Metallurgy and Materials Group, IGCAR, Kalpakkam, India d Formerly with IGCAR, HBNI, Kalpakkam 603102, India e HBNI, IGCAR, Kalpakkam, India b
A R T I C LE I N FO
A B S T R A C T
Keywords: High entropy alloys Microstructure Density functional theory Micro-segregation Scheil cooling XRD
Multi-principal elemental or high entropy alloys are viewed as promising class of materials with enhanced performance in a variety of environments. Study of microstructure of these alloys is essential to understand its influence on various properties. This study is aimed at the synthesis of an equiatomic Cr-Fe-Mo-V alloy by conventional casting method and its microstructural characterization. For the first time, crystal structure of this alloy has been predicted by ab-initio density functional approach and found to be in close agreement with the experimental results. Micro-segregation observed during solidification is also predicted by Scheil cooling model and is attributed to the higher melting point and partition coefficient of Molybdenum. This alloy may be a potential radiation resistant alloy, in view of the possibility of formation of a single BCC solid solution, shown experimentally and theoretically.
1. Introduction Alloy design recipe has been gradually changing from single principal element based alloys to multi-principal elemental alloys (MPEAs) also called as High Entropy Alloys (HEAs), since they offer promising engineering properties [1–9] and myriad of microstructures by fine tuning the composition. Initially, it was proposed that [10–12], HEAs formed single-phase solid solutions with simple crystal structures, of predominantly bodycentered cubic (BCC) and face-centered cubic (FCC), and quite less frequently hexagonal closed-packed (HCP) [13,14], mainly due the high configurational entropy, achieved by increasing the number of alloying elements. However, it has been realized by recent experiments that the high configurational entropy is neither a sufficient nor an essential condition to form single-phase solid solution in all MPEAs [15,16]. Most of the MPEAs constituting four or more elements form multiphase structures. Experimentally, to explore immense compositional space spanned by these HEAs will be a nightmare. Hence, it will be promisingly practical to predict the phase stability of HEAs through some reliable theoretical criteria. In the early days of the HEA development, several
⁎
proposals for stability of high entropy alloys are reported in literature, which are an extension of Hume-Rothery rules like empirical relations about difference in atomic size, electro-negativity, entropy of mixing, e/a ratio, enthalpy of mixing using Midemma approach, Valence electron concentration, etc. [9,17–24]. Later Yiping Lu et al. [25] proposed a quantity called average value of d-orbital energy level (Md ) which quite successfully predicted the formation of topological close packed phases in Ni based Superalloys and further validated in HEAs [26]. Calphad based techniques were also employed by several researchers to determine the phases in HEAs of particular composition [27–30]. However, none of these methods can successfully predict the phases experimentally observed in many alloys. Recently, ab initio calculations have emerged as a powerful approach that complements experiment and serves as a predictive tool for the identification and characterization of promising alloys. Such calculations are based only on quantum mechanical laws and natural constants and hence offers an advantage of the prediction and investigation of materials structure and properties without empirical input [31]. In this work, an equiatomic CrFeMoV alloy has been characterized through extensive X-Ray diffraction and electron microscopy techniques. Employment of various theoretical tools mentioned above also
Corresponding author at: Metallurgy and Materials Group, IGCAR, Kalpakkam, India. E-mail address: [email protected] (R. Mythili).
https://doi.org/10.1016/j.matchar.2019.06.027 Received 4 May 2019; Received in revised form 13 June 2019; Accepted 14 June 2019 Available online 15 June 2019 1044-5803/ © 2019 Elsevier Inc. All rights reserved.
Materials Characterization 154 (2019) 449–457
A. Saikumaran, et al.
Fig. 1. (a, b, c) Optical, SE, BSE micrographs of as cast CrFeMoV alloy showing dendritic morphology (d) EDX spectra of dendrites and interdendrites showing Mo and Fe enrichment respectively.
diffractometer (STOE, Darmstadt, GmbH) operated in Bragg - Brentano geometry and in θ–θ mode. Room temperature Powder - XRD measurements were carried out on a 10 mm diameter pellet of CrFeMoV alloy mounted on the Si(911) single crystal sample holder. The Si (911) single crystal was employed as it does not give any Bragg peak in the 2θ range 10 – 100° with Cu Kα radiation (1.54060 Å). XRD data was collected at a step size of 0.05° 2θ, with a counting time of 7 s per step with spinning of the sample holder. The diffracted X-rays were detected with a NaI:Tl point detector attached with a secondary monochromator. The as cast alloy sample surfaces were sequentially polished down to the 1 μm grit diamond paste, and then chemically etched using a solution containing 95% nitric acid and 5% hydrofluoric acid for microstructural analysis. Preliminary microstructural and microchemical analysis of the as cast alloy was carried out using Zeiss Optical microscope and Helios Nanolab 600i Dual beam FESEM equipped with EDX spectrometer. Specimens for Transmission Electron Microscopy (TEM) were prepared by mechanical grinding and thinning up to ~40 μm,
showed a close correspondence with the experimental results. The composition of this alloy has been chosen from the major alloying elements in ferritic steels, which exhibit good irradiation resistance due to their more open BCC structure, less dislocation bias and higher defect sink strength than FCC structured alloys [32]. 2. Materials and methods Equiatomic CrFeMoV alloy was synthesized by vacuum arc melting technique from high purity raw materials of Cr, Fe, Mo and V (each 25 at.%) using a tungsten electrode tri-arc furnace with water cooled copper hearth. The alloys were re-melted 5 to 8 times due to the large difference in melting points and densities of the pure elements and also flipped between two melting processes to obtain chemical homogeneity. Further some of these pellets of the melted alloy were subjected to suction casting as a rod of 3 mm diameter. X-ray diffraction (XRD) patterns were recorded using a STOE X-ray 450
Materials Characterization 154 (2019) 449–457
A. Saikumaran, et al.
followed by ion milling using a Technoorg Linda IV4/H ion miller. Detailed investigations on microstructure, chemistry and phase analyses were carried out using Philips CM200 Analytical Transmission Electron Microscope (ATEM) equipped with Oxford X-Max SDD detector for EDX analysis 3. Computational methods In the present work, phase stability calculations have been made through empirical equations reported in literature [17,25] and also Calphad based thermodynamic calculations using JMatpro software [33] under the Stainless steel module with an alloy of Cr-Fe-Mo-V of equiatomic composition and also to predict the phases formed during non-equilibrium cooling from the liquid. Also, detailed theoretical calculations have been made to predict the possible structure of the CrFeMoV alloy based on global minimization of free energy surfaces by using the particle-swarm optimization method, which is implemented in the CALYPSO (Crystal structure AnaLYsis by Particle Swarm Optimization) package [34] and using the evolutionary algorithm based tool USPEX (Universal Structure Predictor: Evolutionary Xtallography) [35]. USPEX and CALYPSO techniques need no prior information on the system and these methods utilize ab-initio free energies for predicting the crystal structure. For structural search, calculations are carried out from one formula unit to four formula units per simulation cell. All the structural relaxations and the electronic property calculations are achieved in the framework of density functional theory [36] within the projector augmented wave (PAW) method [37], by using the Vienna Ab-initio Simulation Package (VASP) [38]. Herein, the Fe 3d74s1 electrons, Cr 3d54s1, Mo 4d55s1 and the V 3d44s1 electrons are treated as valence electrons. The exchange and correlation interactions are considered within the GGA approach by adopting the Perdew-Burke-Ernzerhof functional [39]. To ensure that the total energy calculations are well converged, a kinetic energy cutoff of 750 eV and the (8 × 8 × 8) Monkhorst-Pack (MP) [40] k-point mesh has been chosen with uniform spacing of 2π × 0.03 Å−1. The convergence for the energy and force is chosen as 10−6 eV and 0.01 eV/Å, respectively.
Fig. 2. EDX maps of as cast CrFeMoV alloy showing distribution of (a) Mo (b) Fe (c) Cr (d) V from region marked in Fig. 1(c). Table 1 Variation of concentrations of constituent elements of the as cast alloy during solidification. Concentrations and partition coefficients
Mo
V
Cr
Fe
Nominal alloy composition Co (at.%) Average dendritic composition, CSexp (at.%) Average inter-dendritic composition, CLexp (at. %) Partition coefficient, kexp = CSexp/CLexp Solid composition, CScal (at.%) Liquid composition, CLcal (at.%) Partition coefficient, kcal = CScal/CLcal ΔC = CSexp − C0 (at.%)
25 33.31 17.91
25 25.83 24.43
25 22.6 23.06
25 18.25 34.6
1.85 25.49 8.17 3.12 8.31
1.05 25.01 25.57 0.98 0.83
0.98 25.36 16.88 1.50 −2.40
0.52 24.14 49.38 0.49 −6.75
consisting of columnar grains along the edges with central equiaxed grains. Further, it is observed that the average dendritic arm spacing in this case is ~1–2 μm, which is much lower than in the as cast pellets (~10 μm), suggesting that the cooling rate is higher during suction casting. However, the EDX maps clearly reveal the enrichment of Mo to the dendrites, indicating that micro-segregation cannot be suppressed even at a high cooling rate. In order to understand this segregation effect, solidification under non- equilibrium conditions was simulated by Scheil cooling model, using JMatpro software. The liquidus and solidus of the alloy is predicted to be 1900 and 1605 °C respectively using the Scheil cooling model, though the equilibrium solidus temperature would be higher, since this model assumes no diffusion in the solid in contrast to a fast diffusion in the liquid. The variation of concentration of different alloying elements in the liquid and solid on cooling is shown in Fig. 4. It is observed that during the initial stages of solidification, there is a depletion of Mo and an enrichment of Fe in the liquid, while in the solid depletion of Fe and an enrichment of Mo is predicted. It is also clearly observed that the liquid to finally solidify is enriched with Fe and depleted in Mo. However, the concentration of V in the liquid and solid does not show a significant change with cooling, though there is a slight depletion of Cr in the liquid at the end of solidification. Micro-segregation of solute elements between the liquid and the solid during solidification can be explained by the partition coefficient [41] of the solute defined by the following equation:
4. Results and discussion 4.1. Microstructural characterization Fig. 1(a) shows the optical micrograph of the as cast alloy, where the presence of a dendritic microstructure is observed. Such microstructures are commonly observed in castings [41]. Fig. 1(b) shows the Secondary Electron (SE) image of as cast alloy which shows the presence of columnar grain structure with dendrites along the solidification direction. The average inter-dendritic arm spacing in the as cast alloy was determined to be ~10 μm. The contrast in BSE image of the alloy in Fig. 1(c) suggests a difference in composition between the dendrites and inter-dendrites as revealed in EDX spectra in Fig. 1(d). Further EDX maps from several regions of the specimen were acquired and a typical one from region marked in Fig. 1(c) is shown in Fig. 2. It is clearly observed that Mo and Fe are enriched in the dendrites and interdendrites respectively, while Cr and V are distributed more or less uniformly in both dendrites and interdendrites, which is also evident from quantitative analysis of the composition in Table 1. It is well known that instabilities at the solid liquid interface due to constitutional supercooling leads to a dendritic solidification, which is strongly influenced by the cooling rate from the melting temperature of the alloy. The dendrites are the first to solidify, while the inter-dendritic region represents the liquid at the instant of solidification. In order to check if a high cooling rate can suppress the microsegregation, few molten pellets were also subjected to suction casting into rods of 3 mm diameter. The SEM images of the alloy after suction casting are shown in Fig. 3 (a and b) along with the EDX maps (Fig. 3(e–f)). The SE micrograph shows a typical cast microstructure
k = CS /CL
(1)
where, CS and CL are the concentration of the solute in solid and liquid respectively. k < 1 implies the segregation of solute to the liquid, 451
Materials Characterization 154 (2019) 449–457
A. Saikumaran, et al.
Fig. 3. (a, b) SE micrograph of suction cast CrFeMoV alloy; EDX maps of (c) Mo; (d) Fe; (e) Cr; (f) V showing micro-segregation of Mo and Fe along dendrites and interdendrites respectively.
accounts for the segregation of Mo in the dendrites that solidify first, leaving the surrounding liquid to be enriched with Fe. Additionally, the excess concentration of an alloying element i inside the dendritic arm is calculated as ΔC = Cda − Cavg, where Cda is the concentration of an alloying element i inside the dendritic arm and Cavg is the average concentration of an alloying element i. The difference in melting point is calculated as ΔTi = Tmi − Tmalloy. The melting point of CrFeMoV alloy is calculated using the rule of mixtures.
while k > 1 implies the segregation of solute to the solid. With a large difference in the melting point of the alloying elements, the solidus temperature is further depressed during non-equilibrium cooling. The partition coefficient determined experimentally and reported in Table 1 is from the measured composition of the dendritic and interdendritic regions of the as cast pellet, which has comparatively a larger dendritic arm spacing by both SEM and TEM – EDX analysis. These compositions are compared with the theoretically calculated compositions of liquid and solid (using Scheill cooling model) at the end of solidification, as per Eq. (1) in Table 1. These observations suggest that the partition coefficients (k) of the alloying elements are as follows: Mo ≫ 1; Fe < 1; V and Cr ≈ 1, which
n
Tmalloy =
∑ Ci Tmi i=1
(2)
where, Ci and Tmi is the concentration and melting temperature of 452
Materials Characterization 154 (2019) 449–457
A. Saikumaran, et al.
4.2. Structural characterization From the XRD spectrum of the as cast CrFeMoV alloy, it was observed that it consists of 2 BCC phases with close by lattice parameters, which could be due to the Mo rich and Fe rich regions observed in the microstructure. In order to confirm this point, Rietveld analysis has been carried out (Fig. 6) and the refined lattice parameters of the two phases are determined to be 3.0094 ± 0.0003 and 2.9696 ± 0.0005 Å. Further TEM analysis of the as cast alloy, whose results are shown in Fig. 7(a,b,d,e) confirmed the BCC structure of dendritic and inter-dendritic regions with lattice parameters of 2.99 ± 0.2 and 2.97 ± 0.2 Å. The enrichment of Mo (Fig. 7(c)) and Fe (Fig. 7(f)) in the dendrites and inter-dendrites respectively was also observed similar to the SEM observations. Typical HRTEM image from a dendritic region is shown in Fig. 8(a), with the inset showing the Fast Fourier Transform (FFT) from the region marked, the analysis of which confirmed a BCC structure with a lattice parameter of 3 ± 0.2 Å, which is in line with above analysis. Fig. 8(b) shows the inverse FFT of the region marked in Fig. 8(a). Fig. 8(c) shows the lattice imaging of (211) planes with an interplanar distance of 0.129 nm. From the above analysis, it is clear that equiatomic CrFeMoV alloy forms two BCC phases with very close lattice parameters. This very small difference in lattice parameters can be due to the micro-segregation effect of Mo and Fe in the dendrites and interdendrites respectively. A comparison of atomic size shows that the Mo has much larger atomic size (190 pm) than that of Fe (126 pm). Hence, it can be understood that the lattice parameter of dendrites enriched with Mo is slightly higher than that of the interdendrites enriched with Fe.
Fig. 4. Simulated concentration profile in the solid and liquid during cooling from the liquidus. Table 2 Calculation of Tm of alloy and ΔTi. Element
Melting temperature (°C)
ΔTi (°C) = Tmi − Tmalloy
Fe Cr Mo V Tm of alloy
1538 1907 2617 1890 1988
−450 −81 629 −98
4.3. Thermodynamic phase stability Many theoretical means of prediction of possible phases in high entropy alloys have been reported including the empirical relations, Calphad based approaches, ab-initio density functional theoretical calculations though none of them satisfactorily predict or match with the experimental observations. This could be due to the metastability of some of the phases formed in these alloys stemming from the prevailing non-equilibrium conditions during processing of the alloy. In this study, an attempt has been made to compare the experimental observations to theoretical predictions from empirical relations, thermodynamic calculations using JMatpro software and also an ab-initio DFT based calculations, which are explained in the following sections. a. Empirical analysis Various empirical equations have been reported in literature to predict the phase stability like difference in atomic size, VEC, electronegativity, enthalpy and entropy of mixing through Midemma relations, Ω parameter based on average melting point of the alloy, etc. These values obtained for this alloy are listed in Table 3, which are calculated using standard well established empirical equations which are given in references [9, 17, 25]. From these values the formation of single BCC solid solution is predicted for this composition. However, a high value of the average d-orbital energy (Md ) suggests the possibility of formation of an intermetallic compound.
Fig. 5. Dependence of excess concentration of a particular element i (Fe, Cr, V, Mo) inside the dendritic arm on the temperature difference (between Tm of element i and that of the alloy).
b. Calphad approach
element i respectively. The computed values are shown in Table 2. The dependence of ΔC on ΔTi plotted in Fig. 5 clearly shows that, the segregation of an element in the dendritic arm increases with an increase in ΔT, which explains the enrichment of Mo inside the dendrites.
Thermodynamic equilibrium phase stability calculations have been carried out using JMatpro software and the results are shown in Fig. 9. It is observed that a stable BCC solid solution exists in the temperature range of 1180 to 1778 °C, while Sigma and Laves phase are predicted at lower temperatures up to 1180 and 266 °C respectively. Though the formation of Sigma and Laves phases is predicted in this alloy, 453
Materials Characterization 154 (2019) 449–457
A. Saikumaran, et al.
Fig. 6. Rietveld refined XRD spectrum (wRp = 0.19; Rp = 0.13; χ2 = 1.829) of as cast CrFeMoV alloy showing the presence of two BCC phases with near-by lattice parameters.
Fig. 7. (a) BF image of dendrite with SAD pattern confirming BCC structure along [−111] zone axis in inset (b) DF image of dendrite with (0−11) reflection (c) EDX spectrum of dendrites showing enrichment of Mo (d) BF image of inter-dendrite with SAD pattern confirming BCC structure along [−113] zone axis in inset (e) DF image of interdendrite with (110) reflection (f) EDX spectrum of dendrites showing enrichment of Fe.
may be noted that the equilibrium solidus temperature is higher than that estimated during cooling from the liquidus, which is 1605 °C. In the light of the above empirical and thermodynamic predictions, it is inferred that a single BCC solid solution is possible in this alloy. However, the experimental observations show the presence of two BCC
experimental observations did not show any signature for the existence of these phases. This is attributed to the fact that these calculations are carried out at equilibrium conditions, while during arc melting nonequilibrium cooling conditions prevail. The equilibrium liquidus and solidus of the alloy are estimated to be 1900 and 1778 °C respectively. It 454
Materials Characterization 154 (2019) 449–457
A. Saikumaran, et al.
Fig. 8. (a) HRTEM image from the dendritic region with FFT in the inset from the region marked; (b) Inverse FFT from the region marked in (a); (c) Fourier filtered inverse FFT showing lattice imaging of (211) planes with an interplanar distance of 0.129 nm.
c. Ab-initio structure prediction
Table 3 Empirically calculated parameters for phase prediction in CrFeMoV alloy. Parameter
Value in CrFeMoV alloy
Phase predicted
δ
3.88
BCC + Intermetallics
ΔSmix
11.52
ΔHmix
-3
Ω
7.637
VEC
1.25
Md
1.27
There are few literature reports available on first principle calculations of phase stability in high entropy alloys [31]. Since such calculations are based on quantum mechanical laws, the predictions require only the atomic number of the constituent elements and no other empirical input. To explore the stable structure for this alloy, an extensive structural search has been performed by both particle swarm optimization [34] and evolutionary algorithm techniques [35]. Using the above-said techniques, the enthalpy of formation per atom of this CrFeMoV alloy was calculated through the following relation:
ΔH (CrFeMoV ) =
1 ⎡H (CrFeMoV ) − a. H (Fe ) − a. H (Cr ) − a a + b + c + d⎢ ⎣ . H (Mo) − a. H (V )
(3)
where, ΔH is the enthalpy of formation per atom and H is the calculated enthalpy per chemical unit for each system at their respective groundstate structure and a, b, c, d are number of atoms per unit cell of respective elements. Although, it is true that Gibb's free energy dictates the stability of different phases at equilibrium, enthalpy of formation has been used to predict the crystal structure of this alloy. The DFT calculations for structure prediction reported in the current study have been carried out using USPEX and CALYPSO packages, where the enthalpy of formation only are computed at absolute zero Kelvin [34, 35]. Hence the enthalpy of formation represents the Gibb's free energy. Also, since the configurational entropy of the alloy is high, even at high temperatures, it is expected to aid the stability of the phase with low enthalpy of formation. This is evident from the Calphad calculations, which predict a BCC solid solution at high temperatures. The computed results using both the techniques predicted that the enthalpy of formation for this alloy is −10.543 eV/atom for two structures, namely tetragonal P4mm (Space Group: 99) and cubic F43 m (Space Group: 216) with lattice parameter of 5.7594 Å. This suggests that if sufficient energy is supplied to overcome the reaction barrier, CrFeMoV alloy can be formed at ambient conditions with a face centred cubic or a primitive tetragonal structure. The BCC structure of the alloy from experimental observation and other computations, may be seemingly contradict the DFT prediction of an FCC structure. However, the underlying topology of F-43 m FCC can be understood to be made up as a supercell of 2 × 2 × 2 BCC crystals, which has been shown in Fig. 10(a,b), demonstrated using the crystal visualization program VESTA [42]. These structural features can further be explained as follows: Close-packed Fe layers in c stacking; Cr in octahedral voids, Mo and V in tetrahedral voids. Fe4(Mo,V) tetrahedra
Fig. 9. JMatPro simulation of variation of phases in CrFeMoV alloy with temperature.
structures with close lattice parameters. This could be attributed to the micro-segregation effects formed in the casting during non-equilibrium cooling and proper homogenization is expected to yield a homogeneous BCC alloy. The presence of sigma and Laves predicted at low temperatures has not been experimentally observed when cooled from the liquid state. This suggests the sluggish kinetics of these transformations, which may be observed if the alloy is subjected to long term aging in these temperature ranges. 455
Materials Characterization 154 (2019) 449–457
A. Saikumaran, et al.
Fig. 10. Crystal structure of CrFeMoV alloy along [100] with 2 × 2 × 2 supercells of BCC lattice (a) 3D view (b) in plane view (c) Structural features of CrFeMoV showing Fe4(Mo,V) tetrahedra sharing vertices to form a 3D-framework (d) Predicted variation of energy with volume of the BCC unit cell.
5. Conclusions
share vertices to form a 3D-framework as shown in Fig. 10(c). Substitution derivative of W, which is the prototype for a BCC atomic arrangement, with a sequence along 〈111〉 forms the Fe-Cr-Mo-V alloy. Hence the BCC structure is considered for further computations for analyzing the stability of the optimized structure. To obtain optimized volume or lattice constants of this alloy in ground state, first, the total energy of the system was computed at different volume or lattice constants around the relaxed value. Then energy-volume data was fitted to the second order Birch-Murnaghan equation of state (EOS) [43] to give the theoretical equilibrium volume and minimum energy. The obtained energy versus volume results are plotted in Fig. 10(d). The optimized computed lattice constant is 2.87 Å, which is in good agreement with the experimental results. To summarise, the empirical parameters, Calphad and DFT calculations suggest a single BCC solid solution except for the high Md values, which only indicates a possibility for formation of an intermetallic phase. However, the experimental observation of 2 BCC phases is due to the micro-segregation effects and the very close lattice parameters also reflect this. Hence an appropriate homogenization treatment can remove such segregations.
The present study is on evaluation of phase stability in an equiatomic Cr-Fe-V-Mo alloy by experimental observations and theoretical calculations. The important conclusions drawn from this work are as follows: 1. As cast alloy showed a dendritic structure with enrichment of Mo, which is understood to be due to the higher partition coefficient and melting point of Mo. 2. Microstructure of the as cast alloy is found to consist of two BCC phases with close lattice parameters, though thermodynamic phase stability calculations show the possibility of getting a single BCC solid solution for the alloy at high temperatures. Hence the presence of two BCC phases is attributed to the segregation Mo to dendrites and Fe to interdendrites. 3. For the first time, energetically stable crystal structure of the alloy has been predicted using DFT calculations, as a 2 × 2 × 2 super cell of BCC unit cell of lattice parameter of 2.87 Å, which is in close agreement with the experimentally determined value. The above analysis and predictions suggest that, it is possible to 456
Materials Characterization 154 (2019) 449–457
A. Saikumaran, et al.
obtain a stable BCC solid solution in this equiatomic Cr-Fe-Mo-V alloy. Since the current alloy composition is based on alloying elements in ferritic steels and possesses similar crystal structure, it is expected to exhibit good irradiation resistance, which is an important criterion for a good candidate core structural material for nuclear applications [32].The evaluation of mechanical and irradiation properties of this alloy are currently in progress.
[17] G. Sheng, C.T. Liu, Phase stability in high entropy alloys: formation of solid-solution phase or amorphous phase, Pro Nat Sci-Mater 21 (2011) 433–446, https://doi.org/ 10.1016/S1002-0071(12)60080-X. [18] Y. Zhang, Y.J. Zhou, J.P. Lin, G.L. Chen, P.K. Liaw, Solid-solution phase formation rules for multi-component alloys, Adv. Eng. Mater. 10 (2008) 534–538, https://doi. org/10.1002/adem.200700240. [19] D. King, S. Middleburgh, A. McGregor, M. Cortie, Predicting the formation and stability of single phase high-entropy alloys, Acta Mater. 104 (2016) 172–179, https://doi.org/10.1016/j.actamat.2015.11.040. [20] S. Guo, Q. Hu, C. Ng, C. Liu, More than entropy in high-entropy alloys: forming solid solutions or amorphous phase, Intermetallics 41 (2013) 96–103, https://doi. org/10.1016/j.intermet.2013.05.002. [21] Y. Ye, Q. Wang, J. Lu, C. Liu, Y. Yang, Design of high entropy alloys: a singleparameter thermodynamic rule, Scr. Mater. 104 (2015) 53–55, https://doi.org/10. 1016/j.scriptamat.2015.03.023. [22] M.C. Troparevsky, J.R. Morris, P.R. Kent, A.R. Lupini, G.M. Stocks, Criteria for predicting the formation of single-phase high-entropy alloys, Phys. Rev. X 5 (2015) 011041, , https://doi.org/10.1103/PhysRevX.5.011041. [23] S. Guo, C. Ng, J. Lu, C. Liu, Effect of valence electron concentration on stability of fcc or bcc phase in high entropy alloys, J. Appl. Phys. 109 (2011) 103505, , https:// doi.org/10.1063/1.3587228. [24] K. Guruvidyathri, B. Murty, J. Yeh, K.H. Kumar, Gibbs energy-composition plots as a tool for high-entropy alloy design, J. Alloys Compd. 768 (2018) 358–367, https:// doi.org/10.1016/j.jallcom.2018.07.264. [25] Y. Lu, Y. Dong, L. Jiang, T. Wang, T. Li, Y. Zhang, A criterion for topological closepacked phase formation in high entropy alloys, Entropy 17 (2015) 2355–2366, https://doi.org/10.3390/e17042355. [26] A. Saikumaran, R. Mythili, S. Saroja, V. Srihari, Microstructural characterization of Equiatomic CrFeNbNiV alloy, T Indian I Metals 72 (2019) 111–121, https://doi. org/10.1007/s12666-018-1466-x. [27] F. Zhang, C. Zhang, S.-L. Chen, J. Zhu, W.-S. Cao, U.R. Kattner, An understanding of high entropy alloys from phase diagram calculations, CALPHAD 45 (2014) 1–10, https://doi.org/10.1016/j.calphad.2013.10.006. [28] M. Gao, D. Alman, Searching for next single-phase high-entropy alloy compositions, Entropy 15 (2013) 4504–4519, https://doi.org/10.3390/e15104504. [29] M. Vaidya, K. Guruvidyathri, B. Murty, Phase formation and thermal stability of CoCrFeNi and CoCrFeMnNi equiatomic high entropy alloys, J. Alloys Compd. 774 (2019) 856–864, https://doi.org/10.1016/j.jallcom.2018.09.342. [30] K. Christofidou, T. McAuliffe, P. Mignanelli, H.J. Stone, N.G. Jones, On the prediction and the formation of the sigma phase in CrMnCoFeNix high entropy alloys, J. Alloys Compd. 770 (2019) 285–293, https://doi.org/10.1016/j.jallcom.2018.08. 032. [31] Y. Ikeda, B. Grabowski, F. Körmann, Ab initio phase stabilities and mechanical properties of multicomponent alloys: a comprehensive review for high entropy alloys and compositionally complex alloys, Mater. Charact. 147 (2018) 464–511, https://doi.org/10.1016/j.matchar.2018.06.019. [32] T. Jayakumar, M. Mathew, K. Laha, R. Sandhya, Materials development for fast reactor applications, Nucl. Eng. Des. 265 (2013) 1175–1180, https://doi.org/10. 1016/j.nucengdes.2013.05.001. [33] N. Saunders, U. Guo, X. Li, A. Miodownik, J.-P. Schillé, Using JMatPro to model materials properties and behavior, JOM 55 (2003) 60–65, https://doi.org/10.1007/ s11837-003-0013-2. [34] Y. Wang, J. Lv, L. Zhu, Y. Ma, Crystal structure prediction via particle-swarm optimization, Phys. Rev. X 82 (2010) 094116, , https://doi.org/10.1103/PhysRevB. 82.094116. [35] A.R. Oganov, C.W. Glass, Crystal structure prediction using ab initio evolutionary techniques: principles and applications, J. Chem. Phys. 124 (2006) 244704, , https://doi.org/10.1063/1.2210932. [36] W. Kohn, L.J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140 (1965) A1133, https://doi.org/10.1103/PhysRev.140. A1133. [37] P.E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50 (1994) 17953, , https://doi.org/10.1103/PhysRevB.50.17953. [38] G. Kresse, J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci. 6 (1996) 15–50, https://doi.org/10.1016/0927-0256(96)00008-0. [39] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77 (1996) 3865, https://doi.org/10.1103/PhysRevLett.77. 3865. [40] X. Zhang, X. Liu, G. Liang, R. Li, H. Xu, B. Yan, Theoretical study on the low-lying excited states of the phosphorus monoiodide (PI) including the spin–orbit coupling, J. Quant. Spectrosc. Radiat. Transf. 168 (2016) 66–77, https://doi.org/10.1016/j. jqsrt.2015.09.006. [41] J.L. Walker, B. Chalmers, B. Chalmers (Ed.), Principles of Solidification, 1964 Boston. [42] K. Momma, F. Izumi, VESTA: a three-dimensional visualization system for electronic and structural analysis, J. Appl. Crystallogr. 41 (2008) 653–658, https://doi. org/10.1107/S0021889808012016. [43] F. Birch, Finite elastic strain of cubic crystals, Phys. Rev. 71 (1947) 809, https://doi. org/10.1103/PhysRev.71.809.
Acknowledgements Authors sincerely acknowledge Dr. Arup Dasgupta, Head, Structural and Analytical Microscopy Section, Dr. S. Raju, Head, Physical Metallurgy Division, Dr. G. Amarendra, Director, Metallurgy and Materials Group and Dr. A. K. Bhaduri, Director, Indira Gandhi Centre for Atomic Research for their sustained support and encouragement during this work. The authors also thank UGC-DAE-CSR facility at Kalpakkam for extending their experimental facility. Mr. Saikumaran sincerely acknowledge HBNI-IGCAR for the fellowship. Data availability The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study. References [1] S.J. Mary, N. Rajan, R. Epshiba, High entropy alloys properties and its applications–an over view, Eur. Chem. Bull 4 (2015) 279–284, https://doi.org/10.17628/ ecb.2015.4.279-284. [2] M.-H. Tsai, J.-W. Yeh, High-entropy alloys: a critical review, Mater. Res. Lett 2 (2014) 107–123, https://doi.org/10.1080/21663831.2014.912690. [3] Y. Qiu, S. Thomas, M.A. Gibson, H.L. Fraser, N. Birbilis, Corrosion of high entropy alloys, npj Mater, Degrad 1 (2017) 1–18, https://doi.org/10.1038/s41529-0170009-y. [4] P. Chen, C. Lee, S.-Y. Wang, M. Seifi, J.J. Lewandowski, K.A. Dahmen, H. Jia, X. Xie, B. Chen, J.-W. Yeh, Fatigue behavior of high-entropy alloys: a review, Sci China Technol Sc 61 (2018) 168–178, https://doi.org/10.1007/s11431-017-9137-4. [5] S. Gorsse, M. Nguyen, O. Senkov, D. Miracle, Database on the mechanical properties of high entropy alloys and complex concentrated alloys, Data Brief 21 (2018) 2664–2678, https://doi.org/10.1016/j.dib.2018.11.111. [6] J.-P. Couzinié, O. Senkov, D. Miracle, G. Dirras, Comprehensive data compilation on the mechanical properties of refractory high-entropy alloys, Data brief 21 (2018) 1622–1641, https://doi.org/10.1016/j.dib.2018.10.071. [7] W.-Y. Chen, X. Liu, Y. Chen, J.-W. Yeh, K.-K. Tseng, K. Natesan, Irradiation effects in high entropy alloys and 316H stainless steel at 300 °C, J. Nucl. Mater. 510 (2018) 421–430, https://doi.org/10.1016/j.jnucmat.2018.08.031. [8] J. Chen, X. Zhou, W. Wang, B. Liu, Y. Lv, W. Yang, D. Xu, Y. Liu, A review on fundamental of high entropy alloys with promising high–temperature properties, J, Alloys Compd. (2018) 15–30, https://doi.org/10.1016/j.jallcom.2018.05.067. [9] W. Zhang, P.K. Liaw, Y. Zhang, Science and technology in high-entropy alloys, Sci. China Mater 61 (2018) 2–22, https://doi.org/10.1007/s40843-017-9195-8. [10] J.W. Yeh, S.K. Chen, S.J. Lin, J.Y. Gan, T.S. Chin, T.T. Shun, C.H. Tsau, S.Y. Chang, Nanostructured high-entropy alloys with multiple principal elements: novel alloy design concepts and outcomes, Adv. Eng. Mater. 6 (2004) 299–303, https://doi. org/10.1002/adem.200300567. [11] J.-W. Yeh, Alloy design strategies and future trends in high-entropy alloys, JOM 65 (2013) 1759–1771, https://doi.org/10.1007/s11837-013-0761-6. [12] Y. Ye, Q. Wang, J. Lu, C. Liu, Y. Yang, High-entropy alloy: challenges and prospects, Mater. Today 19 (2016) 349–362, https://doi.org/10.1016/j.mattod.2015.11.026. [13] R. Devanathan, W. Jiang, K. Kruska, M.A. Conroy, T.C. Droubay, J.M. Schwantes, Hexagonal close-packed high-entropy alloy formation under extreme processing conditions, J. Mater. Res. 34 (2019) 1–11, https://doi.org/10.1557/jmr.2018.438. [14] J. Qiao, M. Bao, Y. Zhao, H. Yang, Y. Wu, Y. Zhang, J. Hawk, M. Gao, Rare-earth high entropy alloys with hexagonal close-packed structure, J. Appl. Phys. 124 (2018) 195101, , https://doi.org/10.1063/1.5051514. [15] 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) 2628–2638, https://doi.org/10.1016/j.actamat.2013.01.042. [16] N.E. Koval, J.I. Juaristi, R.D. Muiño, M. Alducin, Elastic properties of the TiZrNbTaMo multi-principal element alloy studied from first principles, Intermetallics 106 (2019) 130–140, https://doi.org/10.1016/j.intermet.2018.12. 014.
457