Solid Solutioning in CoCrFeNiMx (M= 4d transition metals) High-Entropy Alloys Sheng Guo Department of Industrial and Materials Science Chalmers University of Technology, Gothenburg, Sweden 21 September 2017, Thessaloniki, Greece
Outline high entropy alloys (HEAs): what & why phase selection in HEAs solid solution strengthening? the molecular orbital approach (Md) conclusions
HEAs: new strategy for alloy design Traditional alloys have only 1 (steels, Al alloys, Cu alloys, etc.) or 2 principal elements (NiAl, FeAl, etc.) High entropy alloys have at least 5 (4?) principal metallic elements, and have equal or close to equal compositions Example, Al Co Cr Cu Fe Ni system Equimole: AlCoCrCuFeNi Non equimole: AlCo 0.5 CrCuFe 1.5 Ni 1.2 Minor element addition: AlCo 0.5 CrCuFe 1.5 Ni 1.2 B 0.1 C 0.15
why are they called high entropy alloys? they have high configuration entropy N R ciln c i 1 i
why high entropy? high entropy stabilizes the formation of solid solution phases G mix = H mix T S mix single phase solid solution co existence of two solid solution phases
why bother? high entropy alloys open up vast unexplored compositional space (Murty, Yeh and Ranganathon, High Entropy Alloys, Elsevier, 2014) in the middle
binary solid solution and Hume Rothery rules an alloy is a mixture of metals, or a mixture of metals and other elements (C, Si, etc.). an alloy may be a solid solution of alloying elements (a single phase), or a mixture of multiple phases. a solid solution is a solid state solution of one or more solutes in a solvent. Such a mixture is considered a solution, rather than a compound, when the crystal structure of the solvent remains unchanged by addition of the solutes, and when the mixture remains in a single homogeneous phase. (substitutional) solid solutions, in accordance with the Hume Rothery rules, may form if the solute and solvent have: o similar atomic radii (< 15%) o same crystal structure o similar electronegativities (< 0.4) o similar valency William Hume Rothery
opposite side of H R rules melt spinning volume 80*85 mm (1990) Inoue s three empirical rules to prepare BMGs (>1 mm): at least 3 alloying elements; large mismatching atomic sizes of constituent elements large negative heat of mixing among major alloying elements Pd 42.5 Cu 30 Ni 7.5 P 20 BMG 3.4 Kg! (Nishiyama, Intermetallics, 2012)
2 parameter map for phase selection in HEAs atomic size difference n 2 ci(1 ri / r), r i 1 mixing enthalpy m i x n H i 1, i j 4 H ij n ciri ij AB m ix i 1 c c i j (Guo et al., Intermetallics, 2013) Solid solution phases form when is small, and H mix is either slightly positive or insignificantly negative; Amorphous phases form when is large, and H mix is noticeably negative; In the intermediate conditions (in terms of and H mix ), intermetallic compounds compete with both amorphous phases & solid solution phases. (Guo et al., Prog Nat Sci: Mater Int, 2011; Guo et al., Intermetallics, 2013)
strength ductility trade off in high entropy alloys (Tong et al., Metall Mater Trans A, 2005)
(Gludovatz et al., Science, 2014) CoCrFeMnNi
fcc solid solutions forming HEAs in CoCrFeNiM x (M=Zr, Nb, Mo; Ti, Mn, Cu) HEAs 3d 4d 5d 22 Ti 1.462 40 Zr 1.603 72 Hf 1.578 23 V 1.316 41 Nb 1.429 73 Ta 1.430 24 Cr 1.249 42 Mo 1.363 74 W 1.367 25 Mn 1.350 43 Tc 75 Re 26 Fe 1.241 44 Ru 76 Os 27 Co 1.251 45 Rh 77 Ir 28 Ni 1.246 46 Pd 78 Pt 29 Cu 1.278 47 Ag 79 Au (Sheikh et al., J Appl Phys, 2017)
solid solubility of Zr in CoCrFeNi (Sheikh et al., J Appl Phys, 2017) Zr0.05 Zr0.3 Zr0.4 Zr0.5
solid solubility of Zr in CoCrFeNi (Sheikh et al., J Appl Phys, 2017)
here is the issue: can solid solutions be predicted more accurately, without being bothered by the formation of intermetallic compounds? Finding solid solubility limit. (Morinaga et al., Phil Mag A, 1985) (Guo et al., Intermetallics, 2013) here is the motivation: other parameters? even better, one parameter? an Md parameter, correlating well with electronegativity and atomic size
Md, d orbital energy level of alloying transition metals Md originates from the d orbitals of the alloying transition metal (so including both the alloying effect and the type of the secondary phase) when a transition element is added into Ni 3 Al, new energy levels due to the d orbitals of additive elements, appear above E f each value of Md is the average of e g and t 2g levels Md can be obtained by DV X cluster (molecular orbital) calculation (Morinaga et al., J Phys Soc JPN, 1984) crystal structure of Ni3Al and the cluster (MNi12Al6) used in the calculation energy level structure of pure and alloyed Ni3Al with 3d transition metals
Md, d orbital energy level of alloying transition metals Md for an alloy is defined by the compositional average Bo, measure for strength of covalent bonding (Morinaga et al., Phil Mag A, 1985) M Md for M in fcc Ni Md for M in bcc Cr (Matsumoto et al., J Phys Cond Mater, 1996)
using Md to predict solid solubility when Md increases beyond a certain value, the phase instability will occur and a secondary phase appears in terminal solid solutions in other words, a critical Md determines the solubility limit of the terminal solid solution, and it depends on the type of the secondary phase (Morinaga et al., Phil Mag A, 1985) /( + ) phase boundary in Ni Co Cr (left) and /( + ) phase boundary in Co Ni Mo (right) alloys
Md for fcc solid solutions forming HEAs containing 4d elements? phase boundary in CoCrFeNiM x (M=Zr, Nb, Mo; Ti, Mn, Cu) HEAs 3d 4d 5d 22 Ti 1.462 40 Zr 1.603 72 Hf 1.578 23 V 1.316 41 Nb 1.429 73 Ta 1.430 24 Cr 1.249 42 Mo 1.363 74 W 1.367 25 Mn 1.350 43 Tc 75 Re 26 Fe 1.241 44 Ru 76 Os 27 Co 1.251 45 Rh 77 Ir 28 Ni 1.246 46 Pd 78 Pt 29 Cu 1.278 47 Ag 79 Au (Sheikh et al., J Appl Phys, 2017)
Conclusions substitutional solid solution strengthening in CoCrFeNiMx (M=4d transition metals) high entropy alloys seems to be difficult 4d transition metals, Zr, Nb and Mo, have quite limited solid solubility in fcc CoCrFeNi a single parameter, Md, the average d orbital energy level, previously used to describe solid solubility in transition metal based terminal solid solutions, was applied to predict solubility limit in HEAs Md can possibly also describe the solubility in fcc solid solution forming HEAs containing 4d elements, at least for CoCrFeNiM x (M=Zr, Nb, Mo) alloys