The origins of high hardening and low ductility in magnesium


Magnesium is a lightweight structural metal but it exhibits low ductility—connected with unusual, mechanistically unexplained, dislocation and plasticity phenomena—which makes it difficult to form and use in energy-saving lightweight structures. We employ long-time molecular dynamics simulations utilizing a density-functional-theory-validated interatomic potential, and reveal the fundamental origins of the previously unexplained phenomena. Here we show that the key 〈c + a〉 dislocation (where 〈c + a〉 indicates the magnitude and direction of slip) is metastable on easy-glide pyramidal II planes; we find that it undergoes a thermally activated, stress-dependent transition to one of three lower-energy, basal-dissociated immobile dislocation structures, which cannot contribute to plastic straining and that serve as strong obstacles to the motion of all other dislocations. This transition is intrinsic to magnesium, driven by reduction in dislocation energy and predicted to occur at very high frequency at room temperature, thus eliminating all major dislocation slip systems able to contribute to c-axis strain and leading to the high hardening and low ductility of magnesium. Enhanced ductility can thus be achieved by increasing the time and temperature at which the transition from the easy-glide metastable dislocation to the immobile basal-dissociated structures occurs. Our results provide the underlying insights needed to guide the design of ductile magnesium alloys.

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Figure 1: Transitions of the easy-glide pyramidal II edge 〈c + a〉 dislocation.
Figure 2: Comparison of the 〈c + a〉 dislocation core structure in MD and experiments.
Figure 3: Thermally activated mean transition time and energy barrier for the pyramidal II to basal plane transformation.
Figure 4: Dislocation energy versus dislocation structure.
Figure 5: Glide behaviour of the various dislocations under applied resolved shear stresses (directions indicated) at 300 K.


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Z.W. acknowledges financial support from the Agency for Science, Technology and Research (A*STAR), Singapore. W.A.C. acknowledges support of this work through a European Research Council Advanced Grant, ‘Predictive Computational Metallurgy’, ERC grant agreement no. 339081 – PreCoMet. W.A.C. also acknowledges earlier long-term support of Mg research from General Motors Corporation that provided the basis for research reported here.

Author information




Z.W. and W.A.C. designed the research, analysed the data, developed the model, discussed the results, and wrote the paper. Z.W. performed the molecular dynamics simulations.

Corresponding author

Correspondence to W. A. Curtin.

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The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Dislocation core structures.

Pyramidal II c + a edge dislocation (top) and screw dislocation (bottom) core structures predicted by the modified embedded-atom method (MEAM) potential and DFT as visualized by the component of the Nye tensor and differential displacement plots26. The circles depict atoms projected onto the plane perpendicular to the dislocation line direction with the crystallographic orientation of the x and y axes shown (a is the lattice parameter of the hcp unit cell). In each image, the distribution of colour represents the distribution of the Nye tensor component (in units of Å−1), that is, the distribution of infinitesimal dislocation Burgers vector; the arrows represent the relative displacement component between two neighbouring atoms. At the dislocation cores, similarities in the distributions of colour and patterns of arrows between MEAM and DFT suggest similarities in atomic structures predicted by the two models. Figure from ref. 26 (, copyright IOP Publishing. Reproduced with permission. All rights reserved.

Extended Data Figure 2 Distribution of pyramidal 〈c + a〉 edge dislocation transition type at different applied stresses.

At zero or low applied stresses, basal c + a is dominant (blue), while partial 〈a〉 and 〈c〉 (orange) or full 〈a〉 and 〈c〉 (red) dislocations are dominant at high applied stresses.

Extended Data Figure 3 Atom trajectories during transition from pyramidal II 〈c + a〉 to basal 〈c + a〉 at 500 K.

Each white line traces individual atom trajectory during the transition. No vacancy/interstitial diffusion from the bulk is involved during the transition. Atoms and trajectories are projected onto the plane perpendicular to the dislocation line direction (see Fig. 1 caption for colour representation).

Extended Data Figure 4 Schematics and coordinate system for 〈c + a〉 dislocation transition.

The c + a edge dislocation dissociated with a stacking fault (shown pink) on the pyramidal II plane (shown green) climb-dissociates into the basal plane with an I1 stacking fault (shown blue). The pink solid arrow and blue dashed arrows indicate the relevant c + a Burgers vectors before and after climb-dissociation. ξ indicates the dislocation line direction and x1, x2, and x3 are the Cartesian coordinate system used for calculating dislocation elastic energy.

Extended Data Figure 5 Pyramidal II 〈c + a〉 edge dislocation dissociation.

Shown are details of the dissociation of the easy-glide pyramidal II c + a into basal-dissociated products as observed during long-time MD simulations, for a, zero, b, moderate, and c, high compressive stresses normal to the pyramidal II plane. Dislocation cores are indicated by the symbol ‘’. See Supplementary Information V for details of the dislocation reactions and Burgers vectors.

Extended Data Figure 6 Transition probability distribution for the random 〈c + a〉 transition processes.

P is the cumulative transition probability, is the mean transition time, and ti indicates the ordered transition times from smallest to largest, t1 < t2 < < tN. See Supplementary Information VII for details.

Extended Data Figure 7 Energy of 〈c + a〉 dislocations calculated within a cylindrical region of radius r.

a, Schematic showing the total dislocation energy consisting of near-core energy Estruc and far-field elastic energy Kln(r/rmin), where rmin ≈ 6b = 6|c + a|. b, The four dislocation energies (dashed lines, top to bottom) correspond respectively to the c + a edge dislocation on the pyramidal II plane, edge 〈c〉 and 〈a〉 in close proximity, c + a edge dislocation climb-dissociated on the basal plane, and the c + a screw dislocation on the pyramidal II plane. The edge dislocations with different core configurations have different energy density within rmin but the same far-field elastic energy scaling K. The screw dislocation has both lower energy within rmin and lower elastic energy scaling than do all the edge dislocations. The analytical energy prefactors K (the slope) from the anisotropic elastic solution are also shown (solid lines).

Extended Data Figure 8 Glide behaviour of the various dislocations under resolved shear stresses (directions indicated) at 300 K.

a, Easy-glide pyramidal II c + a at 13 MPa and 11 MPa with a distinct directional dependence. b, Glide of the basal-dissociated c + a but at very high stresses, 330 MPa. c, Glide of the 〈a〉 dislocation away from the remaining c + a product at 119 MPa, leaving an immobile 〈c〉, and reaction of 〈a〉 and 〈c〉 forming the basal c + a dislocation. d, Nucleation of partial 〈a〉 dislocations at 400–600 MPa from the immobile basal-dissociated 〈c〉 dislocation.

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Wu, Z., Curtin, W. The origins of high hardening and low ductility in magnesium. Nature 526, 62–67 (2015).

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