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Alloy Design

Alloy Design Based on Combining First-Principles and TEM Methods

S. Sandlöbes 1, S. Zaefferer 1, M. Friák 2, A. Dick 2, D. Raabe 1, J. Neugebauer 2

1 Department of Microstructure Physics and Metal Forming
2 Department of Computational Materials Design

Fig. 1: Stress-strain curves of tensile test results obtained at room temperature for pure Mg and Mg–3 wt.% Y.

Pure magnesium and most commercial wrought magnesium alloys exhibit a low room temperature ductility which can be significantly increased by the addition of rare earth elements in solid solution (Fig. 1). Understanding the mechanisms causing this ductility enhancement on an atomistic and electronic-structure level would provide a systematic approach to identify further favourable alloying elements. We have therefore performed complementary investigations byexperimental and ab initio methods.

Mechanical testing of pure Mg and a single-phase solid solution Mg–3 wt.% Y alloy showed that the addition of yttrium increases the room temperature ductility about 5 times and leads to a well-balanced work-hardening during deformation [1-2].

The main deformation modes in pure Mg are limited to basal dislocation slip and {1012}<1011> tensile twinning. Consequently, the strain is localized in few shear bands and crack formation starts early. Contrarily, in the Mg-Y alloy additionally {1011}<1012> compression twinning, {1011}{1012} secondary twinning and pyramidal <c+a> dislocation slip are frequently observed [1,2]. In particular, the activity of <c+a> slip systems enables interaction of different slip systems resulting in a homogeneous deformation [1,2]. As grain refinement, precipitation hardening, shear banding, decreased c/a ratio, and changed Peierls potentials cannot be responsible for the higher activity of compression, secondary twinning and <c+a> dislocation slip [2], it is commonly assumed, that the addition of yttrium changes the stacking fault energies (SFE). A modified SFE would also affect the critical resolved shear stresses (CRSS) associated with the competing shear mechanisms and, hence, would influence their relative contributions to the overall deformation.

Detailed Burgers vector (b) and displacement vector (R) analysis according to the g*b resp. g*R visibility criterion of these stacking faults was performed and is exemplary shown in Fig. 2 (next page). From the analysis it can be concluded that both intrinsic stacking faults are formed in Mg–3Y. The corresponding stacking fault energies are calculated based on the dissociation width of the partial dislocations according to the equation

Here, γ is the stacking fault energy, G the shear modulus, ν the Poisson`s ratio, b the Burgers vector of the partials, β the angle between the partials, and d the splitting width of the partials.

 

Fig. 2: Stacking faults in 1.5 % cold deformed Mg-3Y: (a) the intrinsic stacking fault I1, (b) the intrinsic stacking fault I2 and (c) after 5 % cold deformation; P1 and P2 are the partial dislocations bounding the stacking faults.

In the case of I1 (Fig. 2(a)) the average splitting of the partials is 40-80 nm, which corresponds to an I1 stacking fault energy of 0.482-0.964 mJ·m-2. For I2 (Fig. 2(b)) the stacking fault energy amounts to 0.964-1.964 mJ·m-2 with an average dissociation width of 20-40 nm.

In order to obtain a deeper insight into the mechanisms responsible for the increased ductility observed in the Mg-Y alloys, the above described experimental studies have been complemented by a quantummechanical study of the compositional dependence of intrinsic stacking fault (ISF) energies. Employing DFT calculations, the ISF energies have been determined within the axial next-nearest-neighbour Ising (ANNNI) model [4], which has already been successfully applied to austenitic stainless steels [5] and Fe-Mn alloys [6].

Fig. 3: Schematic representation of the ideal hcp and intrinsic stacking fault geometries.

The ANNNI model provides a reasonable energetic description of the faulted crystal. It uses as input a few simple structures with different stacking sequences (Fig. 3). This allows to avoid explicit DFT calculations of the stacking faults, and to focus instead on computationally efficient supercells containing only a moderate set of atoms. The energies of the stacking faults I1, I2, and E are computed considering the energies of the fcc (ABCABC stacking), hcp (ABAB stacking), and double-hcp (ABACABAC) sequences.

The resulting intrinsic stacking fault energies of Mg-Y alloys possess a strong  non-linear compositional dependence: Despite the fact that pure yttrium has higher ISF energies than pure Mg for both basal-plane stacking faults I1 and I2, small additions of yttrium into Mg (exactly Mg15Y and Mg14Y2) result in a significant reduction of the I1 intrinsic stacking fault energy in excellent agreement with experimental data.

From a phenomenological point of view the ductility increase is related to higher activities of compression, secondary twinning and <c+a> dislocation slip in Mg-Y alloys. These higher shear activities can be easily explained by the significantly decreased stacking fault energy through the addition of Y. At the same time a lower basal stacking fault energy causes a less mobile basal dislocation substructure so that <c+a> slip can yield a higher shear contribution.

An in-depth analysis of the theoretical data shows that the reduced ISF energy is a direct consequence of the dramatically reduced thermodynamic stability of hexagonal Mg–Y solid solution when the yttrium concentration approaches its solubility limit in Mg. The deduced lowering of the thermodynamic stability is supported by the Mg–Y phase diagram where for yet higher concentrations of Y in Mg two-phase alloys containing Mg24Y5 cubic-structure precipitates are formed.

In conclusion, combining ab initio with advanced experimental dislocation characterization approaches provides an efficient and accurate toolset to determine and understand critical microstructure parameters as needed for materials design of complex structural engineering materials.

References

  1. Sandlöbes, S.; Zaefferer, S.; Schestakow, I.; Yi, S.; Gonzales-Martinez, R.: Acta Mater. (2010) in press.
  2. Schestakow, I.; Sandlöbes, S.; Yi, S.; Zaefferer, S.: in: Agnew, S. et al. (eds.): Magnesium Technology 2010 -Late News (Proc. TMS 2010, Seattle, USA, February 14-18), TMS, 2010, pp. 115.
  3. Smith, A.E.: Surf. Sci. 601 (2007) 5762.
  4. Denteneer, P.J.H.; van Haeringen, W.: J. Phys. C 20 (1087) L883.
  5. Vitos, L.; Nilsson, J.-O.; Johansson, B.: Acta Mater. 54 (2006) 3821.
  6. Dick, A.; Hickel, T.; Neugebauer, J.: Steel Res. Int. 80 (2009) 603.