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‘Colorful’ Polyline Grain Boundaries in Two-dimensional Transition Metal Dichalcogenides

Grain boundaries (GBs) are vital to crystal materials and their applications. Although the GBs in bulk and two-dimensional materials have been extensively studied, the polyline GBs prevalently forming in transition metal dichalcogenide monolayers by a sequence of folded segments remain a mystery. We visualize the large-area distribution of the polyline GBs in MoSe 2 monolayers by means of a strain mapping method and unravel their structural origin using ab initio calculations combined with high-resolution atomic characterizations. Unlike normal GBs in two-dimensional materials with one type of dislocation cores, the polyline GBs consist of two basic elements—4|8 and 4|4|8 cores, whose alloying results in structural diversity and distinctly high stability due to relieved stress fields nearby. The defective polygons can uniquely migrate along the polyline GBs via the movement of single molybdenum atoms, unobtrusively giving the GBs their chameleon-like ‘colorful’ appearances. Furthermore, the polyline GBs can achieve useful functionalities such as intrinsic magnetism and highly active electrocatalysis.

Crystal materials are typically polycrystalline, with distinct grains of varying orientation stitched by grain boundaries (GBs). The average grain size and microstructures of the GBs are critical to material properties. Elemental and alloyed metals can exhibit greatly enhanced yield strength by optimizing grain sizes and boundaries [1][2][3] , while strong covalent crystals can be continuously hardened by decreasing grain sizes down to a few nanometers [4][5][6] . The GB effects become more significant in two-dimensional (2D) materials [7][8][9] , where the crystalline order is highly vulnerable to various types of disorder and can be directly disrupted by a line defect.
These issues are of special significance in 2D transition metal dichalcogenides MX2 (M = Mo, W; X = S, Se, etc.), a large family of three-atom-thick 2D materials that have attracted keen current interest [10][11][12][13] . The MX2 monolayers can now be fabricated by chemical vapor deposition (CVD) 11,14-17 on scales up to centimeters 18,19 , such that GBs are almost unavoidable and even ubiquitous in these materials. GBs in MX2 are unique for their extension into a third dimension, forming series-connected, dreidel-shaped polyhedra 12 . They likewise present a fertile ground for exploring new phenomena [20][21][22][23][24] through the fascinating interplay they afford between local chemistry and far-field mechanics.
GBs in graphene are mostly a string of pentagon-heptagon (5|7) dislocation cores, which have low elastic strain energy. These GBs generally follow straight or wiggle lines [25][26][27] . In contrast, the 5|7 cores in 2D MX2 introduce extra chemical energy due to local nonstoichiometric compositions 12,13,28 , such that square-octagon (4|8) cores, which meet the stoichiometry but have high strain energy, can be favored by high-angle GBs where the high linear density of dislocations alleviate stress fields 12,29 . The rich mechanochemical coupling at dislocations in 2D MX2 would cause distinct behaviors for the corresponding GBs. Indeed, experimentally observed GBs in 2D MX2 often exhibit a fine-polyline topology with a sequence of alternately folded segments 11,14,24 . Despite extensive study of GBs in the flatland, the polyline GBs (p-GBs) are yet to be understood, hampered by the fact that the characteristic size spans several orders of magnitude, from grains, via GB segments, to atoms. In this work, we perform a cross-scale study to unravel the structural origin of the p-GBs by combining a large-scale strain mapping method, atomistic computations and annular dark-field scanning transmission electron microscope (ADF-STEM) characterizations. The p-GBs are distinguished by their 'colorful' appearances due to exceptional variability of component dislocation cores and rich functionalities because of the diverse sequences of defects. The results may bridge the relatively monotone GB structures in truly planar graphene and h-BN and the rich 'complexions' [30][31][32] and phase transformations 33 of GBs in bulk systems.

Results and discussion
We conduct the CVD growth of MoSe2 monolayers by merging numerous grains. This results in rich GBs. To rapidly locate the GBs in the process of STEM characterization, we introduce the substitution reaction of Se by S atoms within the MoSe2 matrix for a short time and at ~700 °C. The concentrated stress field along the GBs makes the nearby atomic sites more active than those in the perfect region, so that the substitution reaction preferentially starts from the GBs and then proceeds to extend the MoS2 domains along the GBs. As a result, the shorttime reaction generates hybrid MoS2 channels within the MoSe2 matrix that strictly follow the GB shapes. Our early work has verified that this substitution can well preserve the morphology of GBs in 2D MoSe2 24 . S and Se atoms show distinct brightness in the STEM images according to their sizes. This enables easy recognition of the hybrid channels and large-scale characterization of the microscopic structures of GBs.
The global GB morphology can be visualized by mapping the nominal lattice rotation with respect to the MoSe2 lattice obtained from our geometric phase analysis ( Fig. 1a and Supplementary Fig. S1). The distinguished intensity of rotation in the maps reveals a significant number of p-GBs in the same matrix. Compared with straight GBs as have been focused in previous reports 12,34 , the p-GBs exhibit unexpected structural diversity, with a series of segments alternately folded at various angles θf. These segments differ in length l and angle θf.
96% of these segments are shorter than 15 nm, with a highest distribution of 33% in the range of 3-6 nm (Fig. 1b, right). The angle exhibits a wide range of distribution, from 79.1° to 149.1°.
By distributing all the measured θf into a sequence of intervals spaced by 10°, we find θf exhibits an outstandingly high probability distribution of 58.2% in 107±5°, followed by a distribution of 19.4% in 117±5°, while the distributions in other intervals appear to be much lower (Fig. 1b, left). Atomic-resolution ADF imaging for the GB regions in the MoS2 channels displays two grains stitched seamlessly by each p-GB, with the Mo atoms being brighter than the S atoms ( Fig. 1c). The two grains are Mo-oriented toward each other so that all the p-GBs have a uniform tilt angle of θT = 60°. The GB segments are composed of a string of mixed squares and octagons, consistent with previous experiments on 2D MX2 11,13,28,29 . Yet, we find that the p-GBs of distinct θf differ significantly in polygon sequences, suggesting a correlation of their morphology with the defect structures. It has been deemed that the overall orientations of GBs are not determined by energy but by growth history 35 . While this viewpoint may hold for straight GBs, the following analysis suggests distinction for the p-GBs.
To unravel the origin of polyline morphology and understand the structural diversity of p-GBs, we resort to first-principles calculations. Owing to the similarity in atomic structures and bonding characteristics in 2D MX2, we take MoSe2 as an example. Two 60° tilted domains with inverse lattice orientations are stitched by either a straight GB or a p-GB denoted by the white band in Fig. 2a. Instead of only one type of dislocation core for building the GB, we here identify two types of cores as two basic elements from our experiments-the 4|8 and 4|4|8 dislocation cores 11,12,24,29 , which can be mixed to fill the interstice between the two domains.
According to the content of dislocation cores, the p-GBs can be expressed as AxB1-x, where A = 4|8, B = 4|4|8. The three-fold symmetry of the 2D MoSe2 dictates that the octagons in A and B are either aligned or misoriented by 120° (right, Fig. 2a).

Fig.2 | Structures and energetics of p-GBs in 2D MoSe 2 . a,
A schematic model of a 60° tilted GB stitching two inversely oriented domains, following a polyline shape as indicated by the white band. The GB is made of two basic elements-4|8 and 4|4|8 cores which are slanted at different angles. The octagons in these dislocation cores can be either aligned or misoriented by 120°. b, In the aligned case, the 4|8 and 4|4|8 cores can be alloyed to form a set of relaxed p-GB structures, depicted as A x B 1-x , where A and B denote the 4|8 and 4|4|8 cores, respectively. The octagons in A and B are aligned. A straight Mo-4|8 structure of GB is given on the rightmost for comparison. c, The relative energy of these p-GBs to the one with x = 0.5' as a function of the chemical potential of Se, μ Se . The shaded area indicates the range of μ Se corresponding to our experiments. d, A set of relaxed p-GB structures, A x B 1-x , in which octagons in two segments are misoriented by 120°. Calculated folding angles, θ f , from the structures of distinct x are marked with numbers.
We first considered the aligned case. With a periodic boundary condition, we build a set of p-GBs with varying x in AxB1-x (Fig. 2b). Note that the periodicity does not exist in practical GBs and is adopted here to facilitate computations. Calculated θf from fully relaxed structures of p-GBs for distinct x in AxB1-x is marked in Fig. 2b, showing an almost linear relationship with x. The p-GB with x = 0 has a minimum of θf = 98°, since each 4|4|8 core is slanted at an angle of ~49°, whereas the p-GB with x = 1 has a maximal θf = 121°, enabled by a larger slant angle of ~60.5° of the 4|8 core (middle, Fig. 2a). All other p-GBs with mixed A and B cores have θf stayed in-between. Interestingly, when the A and B cores are mixed equally (i.e. x = 0.5), the p-GBs have a constant θf = 107°, regardless of the detailed arrangement of the two types of cores.
For comparison, we also build a straight GB structure with densely packed 4|8 cores, ever reported to be one of the most favorable high-angle GB structures 34 .
We then examine the relative stability of these p-GBs by their relative energies ∆E, where Etar and Eref are the total energies of targeted and referenced p-GBs, respectively, ni is the number of excessive Mo or Se atoms, μi is the corresponding chemical potential, and ∆Sconf is the configurational entropy difference, as detailed in the Methods section below. We take the structure x = 0.5' with equally mixed A and B cores as the point of reference. The energy unit is normalized by the GB length, L. μMo and μSe satisfy μMoSe2 = μMo + 2μSe at equilibrium, where μMoSe2 is the chemical potential of a MoSe2 unit in a pristine sheet.
The calculated ∆E of p-GBs at T = 973 K as a function of μSe are summarized in Fig. 2c.
The straight Mo-4|8 structure, albeit with a shorter length, has a much higher energy than the p-GBs across the whole range of μSe. This is attributed to the higher stress concentration caused by densely stacked 4|8 cores. In contrast, the dislocation cores in p-GBs are more linearly connected, which relieves the stress fields of dislocations to lower the energy. This contrast is supported by the calculated maps of stress distribution around the GBs (Supplementary Fig.   S2). Under a Mo-rich condition, the GB with θf = 98° is preferred, and its ∆E increases with θf.
Relative stabilities of the p-GBs with different θf are blurred as μSe increases. Our experiment corresponds to a Se-rich condition, indicated by the shaded area in Fig. 2c, in which the p-GB with θf = 107° is the most favorable. This energetic preference agrees with the experimental abundance of the p-GBs in the interval of 107±5° (Fig. 1b).
We next consider the case in which the octagons in two segments are misoriented by 120°.
A set of AxB1-x with varying x can then be built as shown in Fig. 2d, where segments in p-GBs are joined by squares at the corner. This set of p-GBs exhibit apparently larger θf than those GBs with aligned octagons. Calculated θf from relaxed structures of these GBs decreases from 140° at x=0 to 118° at x=1. It is noteworthy that all these p-GBs are Se-oriented and are less stable than the straight counterpart composed of aligned rhombs (Supplementary Fig. S3) 34 .
These features may account for their relatively less frequency in our experimental observation (Fig. 1b). The stability ranking of p-GBs depends also on other factors such as temperature and lattice stress. For example, an applied tensile stress of 200 MPa decreases the free energy difference between the p-GBs with x=0.5 and 0.8 by 90% at μSe = -3.7 eV. Hence, different p-GBs could stably coexist under given conditions, as observed in our experiments.
Aside from the standard combination of 4|8 and 4|4|8 cores, the p-GBs strike us more by unusual structural evolution. Scrutinizing STEM images of p-GBs shows strings of successive squares or octagons, such as the 4|4|4 and 8|8 motifs ( Fig. 1c and Supplementary Fig. S4). These new dislocations can be rationalized by structural evolution of the p-GBs via polygon migrations, like the dislocation motions observed in MX2 sheets 36 . For example, the connected square and octagon in p-GBs may swap positions, turning a 4|4|8|4|4|8 segment into a 4|8|4|4|4|8 or a 4|8|4|8 segment into a 4|4|8|8, and further (Fig. 3a). To deepen our understanding of the structural evolution, we calculate the minimum energy pathways in the process of polygon migrations. Surprisingly, the polygon migrations can be easily realized by merely moving one Mo atom shared by both a square and an octagon, as indicated by the red circle in Fig. 3b. Taking the p-GB composed of 4|4|8 cores for example, the migration starts from the break of a Se-Mo bond in the square, transforming the squareoctagon into a paired heptagon-heptagon at the transition state. Finally, the Mo atom bonds to a Se atom on the opposite side of the second heptagon, transforming the original 44|8|4|4|8 sequence to 4|8|4|4|4|8 (black line, Fig. 3b). This migration mechanism does not require collective movement of multiple atoms, which is in sharp contrast to the glide of 6|8 cores in 2D WS2 through concerted bond breaking and reconnection 36,37 . This new mechanism can explain the structural evolution of other p-GBs, such as the p-GB composed of 4|8 cores whose evolution features 8|8 motifs (red line, Fig. 3b).  Fig. 3c). Fig. 3d presents a similar structural evolution of another p-GB with θf = 115°, where the polygon migrations occur in two segments of the elbow to form structures composed of 4|8, 4|4|4|8, and 4|4|8|8 cores. The successive change of the polygon sequence gradually reduces θf from 115° to 111°; the evolved structure exactly reproduces the structure from our atomic-resolution ADF characterization (right, Fig. 3d).
In contrast to the migration of squares toward the folding point that sharpens the elbow, the accumulation of octagons at this point tends to increase θf.  Fig. S6). These defect states result in a weak ferromagnetic ground state for the p-GBs and evolved forms (inset, Fig. 4a), benefitting from the semiconducting bulk state that localizes the defect states. Magnetism was also predicted in the GBs composed of 5|7 cores in 2D MX2 29 . However, experimental confirmation of such magnetism remains unavailable, probably due to the low areal density of spins and the high sensitivity to carrier concentrations in the samples. The results for a perfect 2D MoSe 2 and the Mo-4|8 GB are also provided. c, A contour plot of G around the p-GBs. d, Optical images of micro-electrochemical devices, where the HER process occurs at the exposed windows on the p-GBs in a MoSe 2 matrix as indicated by a dark frame. e-f, Polarization curves and Tafel plots of current density for catalytic devices based on the p-GBs, edges, and basal planes of MoS 2 , respectively. The plot of Pt is also provided for comparison.
Since the p-GBs create rich states near the Fermi level in an otherwise semiconductor, they should be chemically active for catalysis. We use the hydrogen evolution reaction (HER) as a test to demonstrate this potential. We first take p-GB segments composed solely of 4|8 and 4|4|8, respectively, as model systems. The Gibbs free energy G of hydrogen atoms is calculated by first-principles, scanning all possible adsorption sites. The results suggest high intrinsic per-site activity at the GBs, with G = -0.15 and -0.19 eV for the 4|8 and 4|4|8 cores, respectively, compared with 0.25 eV of the Mo-4|8 GB (Fig. 4b). Following the decay of the stress field, G rises sharply as the reaction site moves away from the GB, until there is a convergence in the bulk region. A contour plot of G around a p-GB with x=0.5' shown in Fig. 4c displays a zigzaglike distribution of catalytic sites, offering a higher density of active sites than straight GBs.
Notably, the sites over the hollow octagons of the folding corners in this p-GB have G as small as 0.03 eV, nearly as perfect as that of Pt.
To verify the enhanced catalytic performance of the p-GBs experimentally, we manage to fabricate a micro-electrochemical device to selectively examine the HER on the p-GBs (Fig.   4d). Similar devices are also fabricated to examine HER on the edges and basal plane of a MoS2 sheet ( Supplementary Fig. S7). The polarization curves and corresponding Tafel slopes recorded with these devices in a 0.5 M H2SO4 solution are shown in Fig. 4e-f, where the result of Pt is also provided for comparison. Compared to previously focused MX2 edges, the p-GBs exhibit a markedly higher catalytic performance, manifested as having a lower onset potential and a higher current density, in agreement with our calculations. While the activity of p-GBs remains inferior to that of Pt, which is due to the small fraction of GBs in our 2D system, it should be amenable to improvement if the areal density of GBs is increased. Fabrication of micro-electrochemical devices. The HER catalytic performance of MoS2 was measured by assembling them into micro-electrochemical devices. A set of Au electrodes were first patterned on standard SiO2/Si substrates using photolithography. Then, high-quality graphene monolayers were transferred onto pre-patterned substrates with the aid of PMMA, followed by another transfer procedure of as-synthesized MoS2 onto the graphene. After that, a further annealing at 200 °C in a high-vacuum environment (1×10 -5 torr) was carried out to optimize their contact for better electron transport during reaction. Finally, a layer of PMMA (1 μm) was deposited on the sample, and a reaction window on a target area (plane, edge or grain boundary) was opened by e-beam lithography to expose the reaction region of MoS2. A fourelectrode micro-electrochemical measurement system was applied in the electrocatalytic experiment. 0.5 M H2SO4 was used as the electrolyte solution, and the scan rate was set to 5 mv/step. During the measurements, only the exposed region of the sample (reaction window area) was available for HER. The electrocatalytic current (Ic) and conductance current (Ids) could be simultaneously obtained for monitoring the electric conductivity of devices. nanoribbons to isolate the grain boundaries from the edges. A kinetic energy cutoff was set to 300 eV for the plane-wave expansion, and a vacuum region of 15 Å was adopted to isolate neighboring periodic images. Structures were fully relaxed until the force on each atom was less than 0.01 eV/Å −1 . The Brillouin zone integration was sampled by five k-points along the GB direction. The minimum-energy paths of polygon migration for p-GBs were mapped out with the climbing image-nudged elastic-band method 43 .