Periodic Segregation of Solute Atoms in Fully Coherent Twin Boundaries

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Science  24 May 2013:
Vol. 340, Issue 6135, pp. 957-960
DOI: 10.1126/science.1229369

The Strength of Impurities

The practical strength of a material (rather than its theoretical strength) is influenced by the presence of defects between crystalline domains and the inclusion of impurities. In some cases, synergistic effects may arise where the impurity atoms segregate to the domain boundaries, although kinetic barriers may limit the extent to which the impurity atoms can order. Nie et al. (p. 957) show the segregation of oversized and undersized solute atoms at coherent twin boundaries in a magnesium alloy. The minimization of strain energy drives the differently sized impurities to different twin boundaries, strengthening the material.


The formability and mechanical properties of many engineering alloys are intimately related to the formation and growth of twins. Understanding the structure and chemistry of twin boundaries at the atomic scale is crucial if we are to properly tailor twins to achieve a new range of desired properties. We report an unusual phenomenon in magnesium alloys that until now was thought unlikely: the equilibrium segregation of solute atoms into patterns within fully coherent terraces of deformation twin boundaries. This ordered segregation provides a pinning effect for twin boundaries, leading to a concomitant but unusual situation in which annealing strengthens rather than weakens these alloys. The findings point to a platform for engineering nano-twinned structures through solute atoms. This may lead to new alloy compositions and thermomechanical processes.

Interfaces such as twin and grain boundaries play a critical role in plastic deformation and ultimately in controlling the formability and mechanical properties of many engineering materials (15); notable examples are lightweight magnesium (Mg) alloys, which have received considerable attention for applications leading to fuel efficiency and green environment (6). Like other commonly used metals such as titanium (Ti), zirconium (Zr), and zinc (Zn), Mg has a hexagonal structure with fewer slip systems than those of cubic materials. To readily form Mg products requires the activation of twinning modes for plastic deformation. As an emerging class of engineering materials, Mg alloys are less strong than the counterpart aluminum alloys, implying the need for more efficient barriers in order to impede the motion of dislocations and twin boundaries. The control of deformation twinning during thermomechanical processes and applications is a major technical barrier to the wider application of Mg (7). Twinning occurs predominantly in the 1¯011{101¯2} system (where {101¯2} is the twinning plane and 1¯011 is the twinning direction in the twinning plane), although 1¯012{101¯1} and 3¯032{101¯3} have also been observed (813). The formability, yield strength, and tension–compression yield-strength asymmetry of wrought Mg products are all intimately related to twinning; hence, there have been considerable efforts to gain a fundamental understanding of the nucleation, growth, and thermal stability of such deformation twins and of the factors that dictate their development under different loading conditions. However, gaining fundamental insights from experimental observations of the effects of solute, second-phase particles, grain size, and sample size on deformation twinning in Mg (1416) has proved elusive. This has also been the case more broadly in engineering materials (1719). Specifically, we need atomic-scale experimental evidence and an understanding of the structure and chemistry of twin boundaries in alloys.

In contrast with partially coherent interfaces such as high-angle grain boundaries and symmetrical tilt boundaries with arrays of misfit dislocations, for which segregation of alloying elements is well established (2022), fully coherent twin boundaries have low interfacial energies, and solute segregation in such boundaries is therefore not expected. We studied this issue using high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) to observe the migration and segregation of randomly distributed solute atoms to fully coherent terraces of deformation twin boundaries in Mg alloys. Solutes consisted of gadolinium (Gd) (which is larger than Mg and represents rare-earth elements that are major alloying additions in many commercial Mg alloys), Zn (which is smaller than Mg and a major alloying element in some commonly used Mg alloys), and mixtures of Gd and Zn (table S1). We also analyzed the experimental observations using first-principles calculations (fig. S1) and continuum estimates and the impact of the solute segregation on mechanical properties using compression tests. Alloy compositions, the preparation and testing conditions and characterizations, and the details of the computations are available in the supplementary materials.

Microstructural examination of the deformed samples of all alloys indicated the existence of many twins—generally {101¯2}, but {101¯1} and {101¯3} were also present in samples subjected to larger compression strains. Inspection of HAADF-STEM images in 12¯10 suggested that the boundary terraces were free of apparent solute segregation (fig. S2). However, twin boundaries in samples that have been plastically compressed and subsequently heat-treated were quite different (fig. S3). Shown in Fig. 1 are the atomic-resolution HAADF-STEM images of retained {101¯1},{101¯2}, and {101¯3} twin boundaries in two binary Mg–Gd alloys that have been plastically compressed at room temperature and annealed for either 5 or 60 min at 275°C. We found that all twin boundary images were decorated by a periodic distribution of bright dots. Because the brightness of individual columns of atoms in HAADF-STEM approximates the square of Z (23, 24)—the averaged atomic number—each bright dot represents a column rich in Gd atoms. The Gd-rich and Mg columns were distributed alternately along the boundaries, with a Mg column between the two adjacent Gd-rich columns. Careful examination of the HAADF-STEM images (Fig. 1, C, E, and G) indicated that the Gd-rich columns were invariably located in the apparently dilated sites of the twin boundaries, irrespective of the type of twin—that is, whether the twin was{101¯1},{101¯2}, or {101¯3}.

Fig. 1 Periodic segregation of Gd in various twin boundaries (TBs).

(A) Schematic illustration and (B) Embedded Image-perspective view of α-Mg lattice. TheEmbedded Image,Embedded Image, and Embedded Image planes are blue, red, and purple, respectively. (C, E, and G) HAADF-STEM images showingEmbedded Image,Embedded Image, and Embedded Image twin boundaries (TBs) in Mg–0.2 atomic % Gd [(C) and (G)] and Mg–0.8 atomic % Gd (E) solid solution alloys. (D, F, and H) Close-ups of (C), (E), and (G), schematically illustrated in (I to K). In (B) and (I) to (K), atoms in the A layer are blue (in the paper plane) or purple (out of the paper plane) and yellow (in) or orange (out) in the B layer. Sample details are available in table S1.

Shown in Fig. 2 are {101¯2} twin boundaries in a Mg–Zn binary alloy and a Mg–Gd–Zn ternary alloy. Again, a periodic segregation of solute atoms was visible in the twin boundaries. However, in the Mg–Zn alloy, Zn atoms occupied the compressed sites of the twin boundary (Fig. 2E), whereas in the Mg–Gd–Zn alloy, the Gd and Zn atoms took the extension sites (Fig. 2F). In the Mg–Gd–Zn alloy, energy-dispersive x-ray spectra such as the one in fig. S4 indicated an enrichment of Gd and Zn within the {101¯2} boundary, and the absence of bright dots at the compressed sites of the boundary suggested that Zn atoms had most likely joined the Gd atoms to occupy the extended sites of the boundary, in contrast with the Zn atoms’ occupancy of compressed sites in the Mg–Zn alloy.

Fig. 2 Periodic segregation of solutes in TBs.

HAADF-STEM images showing Embedded Image TBs in (A and B) Mg–1.9 atomic % Zn and (C and D) Mg–1.0 atomic % Gd–0.4 atomic % Zn–0.2 atomic % Zr alloys. (E) and (F) are schematic illustrations of (B) and (D). Sample details are available in table S1.

The in-plane atomic local strain hydrostatic invariant (ALSHI) in {101¯1},{101¯2}, and {101¯3} twin boundaries of pure Mg are shown in Fig. 3, A to C, and were obtained by means of density functional theory (DFT) computations. We observed periodic distribution of extension (positive) and compression (negative) strains in each case. The strains in the{101¯2} boundary were reduced (Fig. 3, D to F) after the periodic segregation of Gd atoms into the extension sites (Fig. 1J), of Zn atoms into the compression sites (Fig. 2E), or of both Gd and Zn atoms into the extension sites (Fig. 2F). The segregation of Gd, Zn, or both significantly reduces the elastic strain of the twin boundary. The atomic radii of Gd, Zn, and Mg are 0.180, 0.133, and 0.160 nm, respectively. Substituting a Mg atom with a Gd atom leads to a large negative misfit (–0.125) and compression strain, whereas substitution with Zn causes a slightly larger but positive misfit (0.169) and extension strain. Therefore, Gd or Zn atoms in the Mg solid solution tended to segregate into twin boundaries to minimize the elastic strains associated with individual Gd or Zn atoms and different types of twin boundaries, which in turn reduced the twin boundary energy and the total energy of the system (Fig. 3G, figs. S5 and S6, and table S2). When both Gd and Zn atoms were available, the segregation of Zn atoms into Gd-rich columns led to a greater reduction in system energy, particularly when each Gd-rich column has more than three consecutively packed Gd atoms (Fig. 3, H to J, fig. S7, and table S3).

Fig. 3 Strain energy minimization induced periodic segregation of solute atoms in TBs.

(A to C) In-plane ALSHI inEmbedded Image,Embedded Image, and Embedded Image TBs of pure Mg, respectively, and inEmbedded Image after segregation of (D) Gd into extension sites, (E) Zn into compression sites, and (F) Gd and Zn into extension sites. The color strip at the left shows the strain magnitude. (G) System total energy reduction with solute concentration in aEmbedded Imageboundary. (H and I) ALSHI inEmbedded Image boundary with Gd in the extension sites, and with Zn segregated into (H) extension and (I) compression sites. (J) System total energy reduction with various Gd and Zn segregations inEmbedded Image boundary. The viewing direction is parallel to Embedded Image for (A) to (F) and perpendicular toEmbedded Image for (H) and (I). ∆EA and ∆EV represent the reductions in system total energy normalized by TB area and volume, respectively. A detailed explanation is available in the supplementary materials.

Thermodynamically, the segregation or aggregation of Gd or Zn atoms (or both) is not expected to occur within the Mg solid solution, particularly when the concentration of added solute atoms is below the equilibrium solid solubility at the annealing temperature. However, when elastic strains associated with twin boundaries were introduced into the solid solution matrix, the segregation of Gd or Zn atoms, or both, into the strained sites led to reduced elastic strain energies associated with Gd or Zn atoms and twin boundaries. The DFT computations and continuum estimates both indicated that the ordered segregation of solute atoms in twin boundaries was driven by the minimization of the total energy (fig. S5) and elastic strain energy (table S4) in the system and did indeed reach equilibrium. These periodic solute segregation patterns can be considered as grain boundary “complexions” (4, 25, 26): They are thermodynamically stable only in twin boundaries.

We examined the effects of this phenomenon on the mobility of twin boundaries in and the deformation behavior of Mg alloys, finding that the ordered distribution of solute atoms exerted a stronger pinning effect on any further migration of the twin boundary than expected for individual solute atoms and, hence, a larger strengthening effect. Experimentally, we studied the pinning effect with two identical specimens of a Mg–Gd solid solution alloy. Both samples were unloaded immediately after compressed to 0.025 strain. After unloading, one specimen was compressed again to an accumulated strain of 0.045, whereas the other was annealed at 150°C for 3 hours and compressed again to an accumulated strain of 0.045. We observed twins in both samples after the first compression (Fig. 4, A and C). For the sample without annealing, we detected further growth of twins generated during the first compression (Fig. 4B, red arrow). The boundaries of most twins were noticeably expanded by the second compression. For the annealed specimen, the size and shape of most preexisting twins remained almost unchanged (Fig. 4, C and D), but some new, small-sized twins also formed (Fig. 4D, red arrow). Analogous experiments on a Mg–0.4 atomic % Zn solid solution alloy yielded a similar but less thermally stable pinning effect (Fig. 4, E to H, and fig. S8).

Fig. 4 Pinning effect on TBs and annealing strengthening.

(A to D) Optical micrographs showing twins in Mg–0.2 atomic % Gd alloy. (A) Sample compressed to a strain of 0.025, and (B) unloaded and immediately recompressed to an accumulated strain of 0.045. (C) Sample compressed to a strain of 0.025 and (D) unloaded, immediately annealed at 150°C for 3 hours, and recompressed to an accumulated strain of 0.045. (E to H) Electron back-scatter diffraction (EBSD) maps showing microstructure changes. (E) Mg–0.2 atomic % Gd alloy compressed to 0.080 strain, and (F) unloaded, annealed at 300°C for 20 min. (G) Mg–0.4 atomic % Zn alloy compressed to 0.080 strain, and (H) unloaded, annealed at 300°C for 20 min. For each sample, EBSD maps were obtained from exactly the same location after the heat treatment. (I) Engineering stress–strain curves of three samples of the same alloy from compression tests. Curve 1 is the same test as for (A) and (B). Curve 2 is the same test as for (C) and (D). Curve 3 is the same as for curve 1 but heat treated at 150°C for 3 hours before first loading. Sample details are available in table S1.

The pinning effect on the mechanical properties of a binary Mg–Gd solid solution alloy is shown in Fig. 4I. Three identical samples were compression tested at room temperature. The first sample was loaded, unloaded, and immediately reloaded; we observed little strength change from the testing interruption. The second specimen was annealed at 150°C for 3 hours after unloading and before reloading, which led to an appreciable strengthening effect, rather than the weakening that would be expected according to conventional understanding. Before the first loading of the third specimen, it was given the same heat treatment, but this caused neither a weakening nor the strengthening that was observed in the second specimen.

The findings are expected to lead to new insights into the structure and chemistry of fully coherent twin boundaries in other hexagonal materials and cubic materials, as well as strategies for engineering the design of alloy compositions and thermomechanical processes in order to achieve desired formability and mechanical properties.

Supplementary Materials

Materials and Methods

Supplementary Text

Figs. S1 to S8

Tables S1 to S4

References (2746)

References and Notes

  1. Acknowledgments: The authors are grateful for the support of the Australian Research Council and for access to the facilities of the Monash Centre for Electron Microscopy and the National Computational Infrastructure at Australian National University. Further information on the alloys, experimental procedures, and computation details can be found in the supplementary materials.
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