Predicting Solid Solubility Limit in High-Entropy Alloys using the Molecular Orbital Approach

Transcription

1 Predicting Solid Solubility Limit in High-Entropy Alloys using the Molecular Orbital Approach Sheng Guo Department of Industrial and Materials Science Chalmers University of Technology, Gothenburg, Sweden 12 July 2017, Bordeaux, France

2 Outline High entropy alloys solid solutions Hume Rothery rules Phase selection in HEAs: parametric approaches The molecular orbital approach (Md) Using Md to predict solid solubility limit in HEAs Conclusions

3 what we talk about when we talk about high entropy alloys (Miracle et al., Entropy, 2014) It is more convenient to define HEAs by the magnitude of configuration entropy in the high temperature (ideal or regular solution) state: Smix > 1.5R

4 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

5 why bother? high entropy alloys open up vast unexplored compositional space (Murty, Yeh and Ranganathon, High Entropy Alloys, Elsevier, 2014) in the middle

6 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

7 breaking of H R limit? (MG to SS) (Zeng et al., PNAS, 2009) (random fcc Ce Al solid solution) ( Ce3Al to SS) (From Ce3Al) Intermetallic compounds solid solution XRD patterns of Ce3Al at high pressure Atomic structure models of Ce Al alloy

8 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)

9 high entropy effect: stabilization of solid solutions or amorphous phase? (Nature, 1993) S R c ln c N mix i i i 1 when N elements are mixing in equiatomic ratio (c 1 =c 2 = =c N ), the mixing entropy reaches the maximum: S Rln N mix Based on the confusion principle, we can easily understand that random solid solutions tend to be stablized in HEAs. but, why not form a glassy (amorphous) phase then?

10 high entropy metallic glasses do exist (Ma et al., Mater Trans, 2002) (1.5mm) (Takeuchi et al., Intermetallics, 2011) (Gao et al., J Non-Crys. Solids, 2011)

11 intermetallic compounds can certainly form in equiatomic multi component alloys For example: XRD patterns of the CoCrCuFeNiTi x samples (x = 0, 0.5, 0.8, and 1) (Wang et al., Intermetallics, 2007) (Yang et al., Mater Chem Phys, 2007) So, can we predict the phase selection (solid solution, amorphous phase and intermetallic compound) in equiatomic multi component alloys?

12 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)

13 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

14 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

15 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)

16 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

17 can Md work for HEAs, mainly containing TM elements? (Sheikh et al., J Appl Phys, 2015) assume as the condition of solid solutioning in fcc CoCrFeNi solute elements fcc CoCrFeNi solvent (Wang et al., Entropy, 2013) phase formation in fcc solid solutions forming HEAs containing 3d elements only

18 improvement of Hmix map using one parameter, Md (Sheikh et al., J Appl Phys, 2015) Md=0.97 this overlapping is the concern solid solution strengthening precipitation strengthening phase formation in fcc solid solutions forming HEAs containing 3d elements only (Sheikh et al., J Appl Phys, 2015)

19 the case for bcc solid solutions the choice of base elements (bcc Fe or Cr here) is only a matter of the threshold Md assume as the condition of solid solutioning in bcc AlCoCrFeNi (Sheikh et al., J Appl Phys, 2015)

20 Md for fcc solid solutions forming HEAs containing 4d elements? phase boundary in CoCrFeNiM x (M=Zr, Nb, Mo; Ti, Mn, Cu) HEAs (Sheikh et al., J Appl Phys, 2017)

21 Conclusions 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 reasonably describe the solubility in fcc solid solution forming HEAs containing 3d elements only, and also in bcc solution forming 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 Bo not touched upon yet (Kuroda et al., MSEA, 1998)

22 Thanks for your attention! Sheng Guo Industrial and Materials Science Department Chalmers University of Technology Gothenburg, Sweden E mail: sheng.guo@chalmers.se