Self-Assembly of Two Unit Cells into a Nanodomain Structure

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Surfaces, Interfaces, and Catalysis; Physical Properties of Nanomaterials and Materials

Self-Assembly of Two Unit Cells into a Nanodomain Structure Containing Five-Fold Symmetry Hongbo Xie, Hucheng Pan, Yuping Ren, Shineng Sun, Liqing Wang, Hong Zhao, Boshu Liu, Song Li, and Gaowu Qin J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b01526 • Publication Date (Web): 20 Jul 2018 Downloaded from http://pubs.acs.org on July 22, 2018

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The Journal of Physical Chemistry Letters

Self-Assembly of Two Unit Cells into a Nanodomain Structure Containing Five-Fold Symmetry Hongbo Xie, Hucheng Pan, Yuping Ren*, Shineng Sun, Liqing Wang, Hong Zhao, Boshu Liu, Song Li, Gaowu Qin* Key Laboratory for Anisotropy and Texture of Materials (Ministry of Education), School of Materials Science and Engineering, Northeastern University, Shenyang 110819, China

ABSTRACT: Five-fold symmetry is forbidden for the periodic crystals until the discovery of the Al-Mn icosahedral quasicrystal. Here, we reported a kind of precipitated rod-shaped nanophase containing five-fold symmetry but not belonging to any either crystals or quasicrystals discovered so far. These metastable nanodomain phases, which precipitated in Mg-6Zn alloy during isothermal ageing at 200 ºC, contain two separate unit cells in the two-dimensional plane perpendicular to five-fold axis but periodic atom arrangement along the five-fold axis, i.e., 72° rhombus structure and 72° equilateral hexagon structure. The selfassembly of two unit cells under some geomotrical constraints into a nanodomain contains the 2D five-fold, C14 and C15 structures. This finding confirms the existence of solid matters in a special structure between the crystals and quasicrystals, and it is expected to provide a way for understanding the atomic arrangement and stacking behavior in condensed matters.

KEYWORDS: Magnesium alloys; Precipitation; Nanodomain; Five-fold symmetry; Self-assembly; HAADF-STEM

Solid matters can be classified simply into three groups by the difference of the order and rotational symmetry of their atomic arrangements. Amorphous solids have disordered atomic arrangements and without any exact rotational symmetry. Crystals have atomic structure with long-range periodic order that can be described simply by the repetition of a single atom or atomic cluster. And thus, the rotational symmetries of crystals are highly restricted: two-fold, threefold, four-fold, and six-fold symmetry axes are allowed, but five-fold, seven-fold, and all higher-fold symmetry axes are forbidden. Quasicrystals (QCs) are long-range ordered structures but with no lattice periodicty1, 2, whose atomic arrangements have symmetries that are forbidden for traditional crystals, such as 3D icosahedral QCs (five-fold)1, 3, 4, 2D octagonal (eight-fold)5, decagonal (ten-fold)6-8, and dodecagonal (twelve-fold)9 QCs. Therefore, the square or hexagonal tilings are commonly used as geometric analogs for periodic crystals, the Penrose tiling10 is used as an analog for QCs. The five-fold symmetric tiling consists of 36° and 72° rhombic tiles that repeat along each symmetry direction with frequencies whose quotient is τ = (1+√5)/2 = 1.618, the golden ratio. After the discovery of the QCs in 19841, some metallic solids precipitated in superalloys or in the rapidly solidified alloys have been proposed as the intermediate states between the QCs and crystals11-13. These intermediate phases also exhibit five-fold (or ten-fold) symmetry electron diffraction patterns similar to those of the QCs, but they are, actually, all the microdomain structures that composed of many Frank-Kasper phases with multiple orientational orders11-13. It is still a chanllenge to confirm and well interpret whether another structure of condensed matters exist between traditional crystals and QCs. We reported herein the discovery of a new type of rod-shaped nanophase containing five-fold symmetry, directly

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precipitated in a Mg-Zn binary alloy during isothermal ageing at 200 ºC. The meta-stable phase behaves like a QC of the structure self-assembled by two unit cells without any translational symmetry on the normal plane but periodically arranged along the normal direction, therefore, it doesn’t belong to either any icosahedral 3D QCs or decagonal 2D QCs discovered so far. In this work, based on the spherical aberration corrected scanning transmission electron microscopy (Cs-STEM) results, the structure and atomic coordinates of the specially structured precipitate-rod have been systematically analyzed.

Figure. 1. TEM images and corresponding selected-area electron diffraction (SAED) patterns of the Mg-6Zn alloy after 0]α and (c) [1100]α. (a to c) Bright-field isothermally aged at 200 ºC for 8 h. The electron beam is parallel to: (a and d) [0001]α, (b) [112 images. (d) High-resolution TEM image. The insets are the corresponding SAED patterns. A minor of precipitates, marked by yellow circle in Fig.1a-c, is the β2’ MgZn2 Laves nanoplate, which lies on the (0001)α basal plane.

The Mg-6Zn (wt.%) alloy was induction melted and solution treated at 400 ºC for 12 h, followed by aging at 200 ºC for 8 h (the materials and methods in the detail in the Supporting Information). The TEM bright-field images and 0]α, corresponding selected-area electron diffraction (SAED) patterns of the sample, viewed along the [0001]α, [112 and 1100 α zone axis, respectively, are shown in Figs. 1a-c. The majorities of rod-shaped precipitates are observed to be parallel to the [0001]α direction. The SAED patterns, as shown in the insets, exhibit extra diffraction streaks or spots between {1100}α and {1120}α diffraction spots (as shown in yellow arrows in Figs. 1b and c), but no diffraction intensity were be detected between in the {0002}α, implying the precipitate-rods with periodic arrangements along the normal vector. Corresponding HRTEM image of a precipitate-rod viewed along [0001]α direction is displayed in Fig. 1d, under this imaging condition, the structural characteristics of this precipitate would not be well represented. Additionally, the [001]P SAED pattern for the precipitate-rod presented in the inset in Fig. 1d indicates the diffraction


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information is diffuse distribution around the α-Mg diffraction spots. It should be noted that besides the majority of precipitate-rods, there are also a small amount of precipitate-plates in the peak-aged microstructure (as marked by yellow circle in Figs. 1a-c), which have been identified as MgZn2 Laves phase that formed on the (0001)α basal planes14.

Figure. 2. STEM images of the Mg-6Zn alloy after isothermally aged at 200 ºC for 8 h, viewed along the [0001]α / [001]P direction. (a) Low-magnification HAADF-STEM image. (b to e) Some precipitate-rods circled in Fig. 2a are enlarged and shown in Figs. 2b-e. (f) Local part of a precipitate-rod is further enlarged, the atomic-scale HAADF-STEM image indicates the structure in the observed 2D containing two separate unit cells, whose lattice images are labeled as H and R, respectively, the top-right inset is the corresponding Fast Fourier Transformation (FFT) image. (g) Interface structure between the precipitate-rod and α-Mg matrix. (h) Two precipitate-rods bond together, and the phase boundary is described by yellow curve, and this area is also enlarged in the inset. (i) An atomic-scale ABF-STEM image of the precipitate-rod. The unique characteristics of the 2D five-fold nanodomain structure, five orientation rhombi variants bonding together to form a star pattern and five orientation equilateral hexagon variants bonding together to form a petal pattern, are marked by red star and yellow petal, respectively.



Fig. 2a provides a low-magnification HAADF-STEM image from the [0001]α direction showing the precipitaterods with bright contrast precipitation in the α-Mg matrix, which is consistent with the BF-TEM image show in Fig. 1a. In order to reveal the crystal structure and atomic coordinates of the precipitate-rod, atomic imaging by STEM was be used. High-resolution HAADF-STEM images of the precipitate-rods, circled in Fig. 2a, are enlarged and shown in Figs. 2b-e. These precipitate-rods with different sizes exhibit an ellipse-like shape on the normal plane. The atomic arrangement on the 2D is of an nanodomain structure containing unusual five-fold symmetry, which is neither the crystals nor belongs to any already discovered icosahedral 3D QCs or decagonal 2D QCs. Local part of a precipitaterod is further enlarged, as shown in Fig. 2f, the atomic-scale HAADF-STEM image shows two kinds of bright dots with different contrasts inside the precipitate. Each bright dot represents a column rich in Zn atoms because the brightness of individual atomic-columns in HAADF-STEM image approximates the square of the average atomic numbers (the atom number is 12 for Mg, and 30 for Zn)15, 16. The corresponding fast fourier transformation (FFT) image of the precipitate is shown in the top-right inset of Fig. 2f. It can be seen that the Zn-rich columns are uniformly arranged to distribute along ten regular directions, considering that the FFT pattern can only reflect crystal structure information of the brightdotted Zn-rich columns. On the other hand, the Zn-rich columns are arranged to form two kinds of minimum unit cells, i.e., 72° rhombus (marked with R) and 72° equilateral hexagon (marked with H), in which the bright contrast Zn-rich columns locate at the apexes, and the weak contrast Zn-rich columns in the midpoints. Careful measurment of the HAADF-STEM images (Fig. 2f) indicate that the value of lattice parameter a is ~ 4.54 Å. The most unique feature of the five-fold nanodomain structure, i.e., five orientation rhombi variants bonding together to form a star pattern, and five orientation equilateral hexagon variants bonding together to form a petal pattern, are traced with red stars or yellow petal in Figs. 2b-g and Fig. 2i. Fig. 2g shows the interface structure between the precipitate-rod and α-Mg matrix, and the orientation relationship between them is determined to be (100)P // (1210)α and 001 P // 0001 α, and the corresponding schematic of the orientation coordinate is shown in Supplementary Fig. S2. In addition, it can be seen that the Zn atoms (as shown in the yellow arrow in Fig. 2g) diffuse to the phase interface, leading to the growth of precipitate-rod by “expanding” in a manner of inside-out. Fig. 2h shows a case of two precipitate-rods bonding together, and the phase boundary is marked by yellow curve. More details of this area are enlarged in the inset, and it exhibits some angular differences between them, and eventually, they would form a single precipitate-rod with a certain orientation with the matrix. Fig. 2i provides an atomic-scale ABF-STEM image, and the Mg-rich columns in 72° equilateral hexagons are detected (as shown in the blue arrow in the Fig. 2i). To determine the structure and atomic coordinate of the precipitate-rod via modeling and image simulation, the atomic icosahedral clusters be taken into considered12, 13. Based on which, together with the atomic-scale STEM results, a 2D nanodomain structure model containing the five-fold symmetry is created, and the corresponding atomic arrangement simulation viewed along the 001 P direction (five-fold axis) is shown in Fig. 3a. It can be seen that all the apexs Zn atoms (red circles) are surrounded by ten atoms, combined with one Zn atom above and the other one Zn atom below, and thus, formed is a icosahedral atomic clusters structure with coordination number of 12. As shown in Fig. 3b, it exhibits a 3D view of the icosahedral chain structure model with an atomic number of “ …1-5-1-5-1… ”, which means that the central Zn atom is in contact with two sets of five atoms and with one Zn atom on its left and the other Zn atom on its right. In addition, it can be found six kinds of chain structures of icosahedral clusters in this precipitate-rod. They include the type Ⅰ with bonding angles of “ 72° + 72° + 72° + 72° + 72° ”, in which all 5 Zn


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atoms on one side (Fig. 3b-1); type Ⅱbonding angles of “ 72° + 108° + 72° + 108° ”, in which 2 Zn atoms on the left and another 2 Zn atoms on the right (Fig. 3b-2); type Ⅲ bonding angles of “ 72° + 72° + 108° + 108° ”, in which 3 Zn atoms on the left and another 1 Zn atoms on the right (Fig. 3b-3); type Ⅳ bonding angles of “ 72° + 72° + 72° + 144° ”, in which all 4 Zn atoms on the left (Fig. 3b-4); type Ⅴ bonding angles of “ 108° + 108° + 144° ”, in which 2 Zn atoms on the left and another 1 Zn atoms on the right (Fig. 3b-5), and type Ⅵ bonding angles of “ 72° + 144° + 144° ”, in which all 3 Zn atoms on the left (Fig. 3b-6). The six kinds of icosahedral columns with differents atomic stacking manners are arranged to form the present strcucture containing two unit cells.

Figure. 3. Atomic schematic diagrams of the precipitate-rod. (a) Modeled atomic arrangement of the precipitate-rod, viewed along [001]P direction (five-fold axis). (b) The six kinds of icosahedral clusters models in the precipitate-rod. (c) Modeled atomic structure of the 72° rhombus unit cell. (d) Modeled atomic structure of the 72° equilateral hexagon unit cell.

Shown in Fig. 3c and 3d are the structures of the two kinds of unit cells. From the atomic arrangements of [100]P and [010]P directions, it can be concluded that the precipitate-rod with a stacking sequence of “ …ABAC… ” along the five-fold axis, and the c value is matching with α-Mg matrix, of ~ 5.22 Å. From Fig. 3c, it can be seen that the 72° rhombus contains two Mg atoms, and the plane distance between every Mg atom and adjacent apex Zn atom is 0.618 a, perfectly following the golden section distance of the side length. Besides, the chemical composition of the 72° rhombus is be determined as MgZn2. As shown in Fig. 3d, the 72° equilateral hexagon can be divided into two intersecting 72° rhombus structures, and it contains 6 Mg atoms, the plane distance also is 0.618 a, thus, the



coordination number of all apexs Zn atoms would be guaranteed to 12. In addition, the chemical composition of the 72° equilateral hexagon structure can also be determined, i.e., MgZn. Fig. 4a shows orientation mapping of the two separate unit cells about local part of a precipitate-rod (corresponding in Fig. 3a). The structural characteristic is clearly demonstrated by recognizing the colors, where the same color means the same orientation. The two tiling patterns exhibit the most five variants in distributing orientations, as shown in Fig. 3b and 3c, represented by red, yellow, green, blue and purple, respectively. The two tiling patterns randomly assemble together under the specific five-orientation constraint, and finally constitute the nanodomain structure containing five-fold, C14 and C15 structures. Due to the randomness of bonding, there is no translational symmetry on the normal plane. Shown in Figs. 4d-i are the schematic diagrams of nucleation and growth mechanism for the structure. As it is well-known, the nucleation and growth of precipitated phases are realized by diffusion of the solute atoms in supersaturated solid solution at isothermal ageing14, 17. We consider that solute segregation first forms the icosahedral clusters by atoms diffusion (Fig. 4d), then the precipitate takes the cluster as the nucleation point, and followed by the inside-out growth under some geometrical rules (Fig. 4e), and finally forms the present structure containing two unit cells with star characteristic (Fig. 4g) and / or petal characteristic (Fig. 4i). Although the present structure has not any translational symmetry on the normal plane, it is self-assembled by two unit cells of 72° rhombus and 72° equilateral hexagon, constrained by the Penrose geometry rule. And thus, some area contains the five-fold rotational symmetry (five-fold star pattern and five-fold petal pattern) on the normal plane, while the other area contains the short-range ordered structures (including C14, C15 Laves structure), as schematically shown in Figs. 3a and 4a. These periodic and aperiodic structures bond together to form the nanodomain structure, which is totally different from the 3D icosahedral QCs or 2D decagonal QCs with long-range five-fold (or ten-fold) rotational symmetry. Therefore, the nanodomain phase confirmed in this experiment belongs to a new structure, an intermediate state between the QCs and crystals. Recently, a similar structure was found to precipitate along dislocations in the cold-rolled Mg-Zn binary alloys, and it was interpreted as a new structured QC18. However, the short-range ordered structures (including C14 and C15 Laves phase structures, as well as the µ and K7Cs6 type structures) were still found in the domain, and thus it is completely different from QC structure. By the geometrical rules, we also expect a hypothetical perfect 2D five-fold rotational symmetry structure, as shown in Fig. 4j, although the morphology has not been confirmed by HAADF-STEM observation in this study. We believe that such structure would be formed if the initial petal cluster continues to grow up by the inside-out manner in five directions to maintan the orientational order. The rod-shaped precipitates in Mg-Zn alloys were initially reported to have an order hexagonal structure (MgZn2 Laves phase, a = 5.20 Å, c = 8.57 Å), which were refer to as β1’ phase 19, 20, and they are key strengthening precipitates in Mg-Zn based alloys. However, the crystal structures of these precipitate-rods are yet controversial and have not been clarified. Another hexagonal structure (a = 5.56 Å, c = 5.21 Å) for the Mg-Zn precipitate-rod was also reported by L. L. Rokhlin although the structure has not been confirmed21. Later, X. Gao and co-workers characterized the precipitaterod in a Mg-8 wt.% Zn alloy using electron micro-diffraction, and reported that the precipitate-rod didn’t have the MgZn2 structure, but has a base-centered monoclinic structure (a = 25.96 Å, b = 14.28 Å, c = 5.24 Å, γ = 102.5°) similar to that of the Mg4Zn7 phase22. More recently, a mixture of the MgZn2 and Mg4Zn7 for the precipitate-rod in the Mg-Zn alloy system was also reported23. In the present work, however, we unambiguously confirm the precipitate-rod is a new type nanodomain structure containing 2D five-fold symmetry locally on the normal plane and periodically arranges along the normal direction at initial ageing, and can transform into the MgZn2 Laves structure with a


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prolonged ageing, as evidenced by TEM in Supplementary Fig. S3. In other words, the present nanodomain structure found in the Mg-Zn alloy is one meta-stable phase.

Figure. 4. Schematic diagrams of the precipitate-rod, viewed along the [001]P direction (five-fold axis). (a) Orientation mapping of the two tiling patterns about the local part of a precipitate-rod (corresponding in Fig. 3a). (b and c) Five orientation variants of the two kinds of unit cells, which are represented by red, yellow, green, blue, purple 72° rhombus (R) and 72° equilateral hexagon (H), respectively. (d → e → f → g) and (d → e → h → i) The schematic diagram of nucleation and growth mechanism of the precipitate-rod. (j) A hypothetical 2D nanodomain structure with five-fold rotational symmetry.



In conclusion, we have discovered a new type of nanodomain structure, containing 2D five-fold symmetry locally and short-range ordered C14 and C15 Laves structure on the normal plane while periodical arrangement along the normal direction, precipitated in the Mg-6Zn binary alloy during isothermal ageing at 200 ºC. On the normal plane, it contains two unit cells of 72° rhombus structure (MgZn2，a = 4.54 Å，c = 5.22 Å) and 72° equilateral hexagon structure (MgZn，a = 4.54 Å，c = 5.22 Å), and the two separate unit cells self-assemble under some geometrical constraints to fully maintan five orientational orders, and thus to generate the present nanodomain phase. The precipitate-rod has a stacking sequence of “…ABAC…” along the five-fold axis (or the normal direction), and would transform into the MgZn2 Laves phase with much longer ageing time. On the other hand, this work has verified that the β1’ precipitate-rod precipitated in Mg-Zn based alloys is not the previously reported MgZn2 with hexagonal structure, Mg4Zn7 with monoclinic structure, or the mixture of two phases. It is a new nanodomain structure with complex structures. This result is expected to lead to new insights into the structure and formation mechanism in the condensed matters, especially into a special structure between quasicrystals and traditional crystals, and also to provide a practical guidance for design novel high-strength Mg-Zn based alloys by the nanodomain structure strengthening.

ASSOCIATED CONTENT Supporting Information: Sample preparation, TEM/STEM experimental procedures, ageing-hardening response curve, schematic diagram of orientation coordinates, and supplemental TEM results (PDF)

AUTHOR INFORMATION Corresponding author. Email: * [email protected] (Y. P. Ren); * [email protected] (G. W. Qin). Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS The authors acknowledge the National Key Research and Development Program of China (No.2016YFB0701202), the financial support from the National Natural Science Foundation of China (Grant No. 51371046, No. 51525101, No. 51501032, No. U1610253), Fundamental Research Funds of the Central Universities (No. N141008001). The authors extend their gratitude to Prof. X. L. Ma (Institute of Metal Research, Chinese Academy of Sciences) and Prof. C. Dong (Dalian University of Technology) for constructive discussions, Prof. Y. H. Sun and Dr. Y. Dong (Northeastern University) for their help in Cs-corrected STEM technique.

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Self-Assembly of Two Unit Cells into a Nanodomain Structure

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