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Thermodynamics-Based Selection and Design of Creep-Resistant Cast Mg Alloys

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Abstract

Atomic level thermodynamics arguments that account for the generally weak age hardening response while suggesting that extending the athermal regime through short-range order (SRO) is a most feasible path to increasing the creep strength of many current alloys are presented. The tendency, or otherwise, of many solutes to develop SRO in dilute solid solutions rationalizes a number of observations in current multicomponent Mg alloys, and in particular the retention of linear strain hardening at high temperatures, while it disputes the viability of several micromechanisms often considered active, such as pinning of edge dislocations by mobile solute clouds, dynamic precipitation of thermally stable precipitates, or atomic size effects on the diffusivity. Potential solutes are sorted out and ranked based on the sign and value of the enthalpy of mixing of binary solid solutions using the Miedema phenomenological scheme. Due to their large negative energy of mixing and reasonable solubility (>1 at. pct) at ~473 K (~200 °C), Y and Gd appear as the best candidates to increase the creep strength through SRO, followed by Nd and Ca, in close agreement with data reported in the literature. The feasibility of enhancing the age hardening response through homogeneously nucleated, coherent precipitates, in some cases despite the negative energy of mixing of the alloy, or via internally ordered precipitates mimicking those present in Mg-Th alloys is considered by making parallels with the Al-Zn and the Al-Cu alloy systems. The possible optimization of the strengthening of high pressure die cast alloys combining SRO and intergranular eutectics or of heat-treatable cast alloys through internally ordered precipitates and SRO is discussed.

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Notes

  1. The alleged valence mechanism is supposed to increase the yield strength of Mg-RE solutions through the introduction of a covalent component in the atomic bonding. This model, however, also predicts that Zn should harden Mg at the same (low) rate of Al, in contradiction with the experimental results of Figure 3.

  2. SRO is expected in Mg-Al as well, but its strength is bounded by the low melting point of the Mg17Al12 intermetallic.[31]

  3. The low values of the Hall-Petch friction stress in Mg-Zn,[48] and which are also accounted for by SRO effects on twinning, led some authors[32,37] to conclude that solid solution by Zn is below that of the RE, also against what Figure 3 shows.

  4. It has been recently pointed out [49] that the RE increase the ductility more than Zn, which is not correct as can be seen by comparing the data of References 31–33. That the alloys are more ductile than the pure Mg metal is yet another classic conclusion,[50–53] stemming in this case from the solid solution softening of the prism planes, which being a general solid solution effect should apply equally well to all kinds of solutes, including the RE.

  5. Mg-Sn is known to develop SRO,[42] hence its hardening rate should match that of Mg-Zn, but recent experiments[34] suggest otherwise, as shown by Figure 3. It is noted however that the specimens used in those experiments had only 4 to 5 grains across the cross sections, questioning the validity of the data for polycrystals.

  6. A number of studies, e.g., Refs. [86], [90], [91] based their conclusions on specimens tested in the (gravity) as-cast condition. Cast microstructures are strongly geometry dependent, and since coring creates concentration gradients and disproportionate amounts of interdendritic eutectics, as-cast specimens seem hardly suitable to properly quantify solid solution strengthening, or any other micromechanisms, for that matter. This criticism does not apply to studies based on HPDC specimens, since in those cases what is measured, rather than material properties, are the properties of the casting cross section.[54]

  7. The formation of the so called RE texture in Mg-RE Mg-Y and Mg-Ca alloys has also been ascribed to atomic size/solute segregation effects.[55,105,106]

  8. This criticism can also be levered to the hypothesis that co-segregation of Gd and Zn atoms to form dimers in dilute Mg-Gd-Zn alloys blocks the edge components of mobile dislocations on the basal plane.[39] Alternatively, it may be argued that the co-segregation of Zn and Gd reinforces the SRO of the dilute Mg-Gd alloy, hence the hardening effect on both the screw and the edge components of mobile dislocations. (It is noted that Zn additions have no effects in concentrated Mg-Gd alloys.[1])

  9. Using the Miedema-Niessen model, Bakker[110] showed that for solutes much smaller than the host, the reduction of effective atomic volume due to the charge transfer enables a significant fraction of the solute atoms to fast-diffuse as interstitials, i.e., the solute exhibits on average a faster than expected diffusion rate. However, when the difference in size between solute and host is less than the Hume-Rothery limit of ±15 pct the solute behaves strictly as substitutional and the diffusion is normally slow and size independent. Considering the similar atomic radius and c/a ratio of Mg and Zr[111] the diffusivity behavior of any solutes can in principle be expected to be similar for both hosts. Tendler and Abriata’s results also suggest that for solutes larger than the 15 pct limit, increased rather than decreased diffusivity can be expected, further denying the possibility of slower diffusivity of the larger RE, or any other larger substitutional solute, for that matter.

  10. Solutes that lower the stacking fault energy are expected to have similar effects.[119,129] Possible RE effects on the SFE of Mg at the nano-scale have also been considered in recent work.[49,130]

  11. Deep eutectics and the development of SRO already in the liquid correlate with the tendency to form metallic glasses in many Mg alloys.[40]

  12. Pettifor’s Quantum Mechanics analysis[142] identified some contradiction in the fundamentals, but those do not detract from the practical value of the scheme as a (powerful) sorting and ranking tool.

  13. For consistency with the original formulation, non-SI units (eV and d.u.) are used for the scheme.

  14. Diagrams similar to that of Fig. 8 can be seen in Reference 144 for Fe, in Reference 28 for Mg and a generic one in Reference 138.

  15. Save for Ni and B, the sorting of solutes in Figure 8 is consistent with the respective phase diagrams as per Figures 6(a) through (c). The mismatching cases are discussed in the Appendix.

  16. Note that elements on the south sector are larger in size than Mg, something that led to the assumptions concerning atomic size effects on texture formation (see footnote ¶) and diffusivity at high temperature.

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Acknowledgments

The authors are indebted to Yanlu Huang (South China University of Technology) and Uday Chakkingal (IIT Madras) for useful comments and suggestions.

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  1. ARC Centre of Excellence for Design in Light Metals, Materials Engineering, School of Engineering, The University of Queensland, Brisbane, QLD, 4072, Australia

    Saeideh Abaspour (Postdoctoral Fellow) & Carlos H. Cáceres (Reader in Casting Technology)

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Correspondence to Carlos H. Cáceres.

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Manuscript submitted December 5, 2014.

Appendix

Appendix

1.1 The Miedema Scheme for R ≠ 0

In alloys of a transition metal (d-electron-type) and one of the polyvalent non-transition (p-electron-type) metals, the solutes can be sorted out in the same way as non-transition elements. However, in this case, the lines which separate the positive enthalpy of mixing regions from negative ones are not straight through the origin, but take a hyperbolic shape because of an additional, negative term, R. This term indicates that a large negative energy stemming from hybridisation between the valence d and p electrons contributes to the heat of formation. Using Eq. [2], Figure A1 was created for different R values according to the solutes, listed in Table A1.

Fig. A1
figure 14

The Miedema scheme for Mg alloys, for different R values (given as R/P ratios) in Eq. [2]. Co-ordinates data from Ref. [27]. R = 0 corresponds to Fig. 8

Full size image
Table A1 R Values for Different Elements[27]
Full size table

Replacing the diagonal lines of Figure 8 by the lines for different R/P values shifts a few elements as borderline elements, e.g., Th and Sc, from the East sector to the North-South. In those cases, examination of the phase diagrams determines to which sector the element actually belongs to. Thus, Th and Sc, both with a single-eutectic phase diagram, belong in the West-East sector, consistently with assuming R = 0 for Figure 8.

The Mg-Ni phase diagram, with two eutectics, belongs in the North sector, which is correct according to the R/P = 0.4 line. On the other hand, B, with a single-eutectic phase diagram is expected to sit on the West sector while it appears on the North sector.

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Abaspour, S., Cáceres, C.H. Thermodynamics-Based Selection and Design of Creep-Resistant Cast Mg Alloys. Metall Mater Trans A 46, 5972–5988 (2015). https://doi.org/10.1007/s11661-015-3128-5

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