Abstract
Materials with a negative Poisson’s ratio, also known as auxetic materials, exhibit unusual and counterintuitive mechanical behaviour—becoming fatter in crosssection when stretched. Such behaviour is mostly attributed to some special reentrant or hinged geometric structures regardless of the chemical composition and electronic structure of a material. Here, using firstprinciples calculations, we report a class of auxetic singlelayer twodimensional materials, namely, the 1Ttype monolayer crystals of groups 6–7 transitionmetal dichalcogenides, MX_{2} (M=Mo, W, Tc, Re; X=S, Se, Te). These materials have a crystal structure distinct from all other known auxetic materials. They exhibit an intrinsic inplane negative Poisson’s ratio, which is dominated by electronic effects. We attribute the occurrence of such auxetic behaviour to the strong coupling between the chalcogen p orbitals and the intermetal t_{2g}bonding orbitals within the basic triangular pyramid structure unit. The unusual auxetic behaviour in combination with other remarkable properties of monolayer twodimensional materials could lead to novel multifunctionalities.
Introduction
The Poisson’s ratio of a material characterizes its response to uniaxial load and is given by ν_{ab}=−ɛ_{b}/ɛ_{a}, where ɛ_{a} is an applied strain in the a axis direction and ɛ_{b} is the resulting strain in a transverse b axis direction. Counterintuitively, negative Poisson’s ratio (auxetic) materials^{1} expand laterally when stretched and contract laterally when compressed. They can lead to enhanced mechanical properties, such as shear modulus^{2}, indentation resistance^{3} and fracture toughness^{4}. The unusual auxetic effect itself and concomitant enhancements in other material properties offers enormous potential in many technologically important applications^{5,6,7}, such as biomedicine^{8}, sensors^{9}, fasteners^{10} and protective equipments^{11}.
Auxetic effect has been reported in a number of natural and manmade materials and structures in bulk form^{5,6,12,13}, for example, cubic metals^{14,15}, αcristobalite (SiO_{2})^{16}, αTeO_{2} (ref. 17), the zeolite mineral natrolite^{18}, honeycombs^{19}, foams^{7}, microporous polymers^{20,21}, composites^{22,23}, ceramics^{24}, molecular auxtics^{25}, metalorganic frameworks^{26}, bucklicrystals^{27} and origami structures^{28,29,30}. Geometric considerations dominate the literature in understanding such auxetic effects and designing new auxetic materials. For most of these auxetic materials, the auxetic effect is explained by some special reentrant structure or the crystal structure that can be viewed as being made up of rigid building blocks linked by flexible hinges^{1,19,31,32,33}, independent of their chemical composition and electronic structure.
Auxetic effect has also been recently reported in several monolayer twodimensional (2D) materials. For example, the outofplane negative Poisson’s ratio was discovered in phosphorene^{34,35}, GeS^{36} and monolayer arsenic^{37}. The inplane negative Poisson’s ratio was also predicted in borophene^{38} and three theoretically proposed but notyetsynthesized materials (that is, the pentagraphene^{39,40}, hαsilica^{41} and Be_{5}C_{2} (ref. 42)). Similar to that in the bulk auxetic materials, the auxetic behaviour in these 2D materials is also considered to originate mainly from the puckered or buckled crystal structure.
In this study, using quantum mechanical firstprinciples calculations (see Methods section), we report a class of auxetic singlelayer 2D materials with an intrinsic inplane negative Poisson’s ratio. They differ from other known auxetic materials not only in their crystal structure but also in the microscopic origin of auxetic behaviour. These materials are the 1Ttype crystalline monolayers of groups 6–7 transition metal dichalcogenides, 1TMX_{2} (M=Mo, W, Tc, Re; X=S, Se, Te). In contrast to those known bulk or 2D auxetic materials, the inplane auxetic behaviour discovered in groups 6–7 1TMX_{2} cannot be explained merely from their geometric structure because the nonauxetic behaviour is also found in other groups of MX_{2} compounds with the same 1Ttype structure. This dichotomy between auxetic and nonauxetic behaviour in the 1TMX_{2} compounds is explained by their distinct electron structures. The inplane stiffness of those 1TMX_{2} materials is predicted to be order of 10^{2} GPa, at least three orders of magnitude higher than manmade auxetic materials. The high inplane stiffness and the auxetic behaviour in combination with other remarkable electronic and optoelectronic properties of the singlelayer 2D materials^{43} could lead to novel multifunctionalities, such as nanoscale auxetic electrodes and sensors.
Results
Crystal structure
The single layers of 2D transition metal dichalcogenides are formed by a hexagonally packed layer of metal (M) atoms sandwiched between two layers of chalcogen (X) atoms (Fig. 1). Each chalcogen atom forms the apex of a triangular pyramid that has three metal atoms at its base. The symmetry of the chalcogen array about each metal atom is either octahedral or trigonal prismatic. The former is often referred to as the 1T phase, whereas the latter as the 1H phase. Depending on the combination of the metal and chalcogen elements, one of the two phases is thermodynamically preferred. Most group6 MX_{2} compounds thermodynamically prefer the 1H phase^{44}, but the metastable 1T phase is also observed^{45,46,47}. For other groups of layered MX_{2} compounds, most crystallize in the highsymmetry 1T or lowsymmetry distorted 1T phase^{44,48}. The 1HMX_{2} compounds are known to be nonauxetic in the plane due to their hexagonal inplane crystalline structure. We hence focus on 42 monolayer MX_{2} compounds in the highsymmetry 1T phase (Table 1).
Poisson’s ratio results
Figure 2a shows our calculated Poisson’s ratio results (ν_{ab}) for 42 1TMX_{2} compounds in the b axis direction subjected to a 5% tensile strain applied along the a axis direction. Remarkably, we find that the sign of Poisson’s ratio strongly depends on the delectron count. All 12 1TMX_{2} compounds from group 6 (d^{2}) and group 7 (d^{3}) exhibit negative Poisson’s ratios, ranging from −0.03 to −0.37. Seven of them (that is, TcTe_{2}, ReTe_{2}, WTe_{2}, WSe_{2}, MoSe_{2}, ReS_{2} and TcS_{2}) have a Poisson’s ratio <−0.1, higher in magnitude than that of borophene (−0.04 along a and −0.02 along b)^{38}, rendering them more promising candidates for specific applications in mechanical nanodevices. For other groups of 1TMX_{2} compounds, we find positive Poisson’s ratios ranging from 0.09 to 0.53.
Figure 2b,c shows our calculated Poisson’s ratios (ν_{ab} and ν_{ba}) as a function of applied strain in two example compounds, nonauxetic ZrS_{2} and auxetic MoS_{2}. For both compounds, Poisson’s ratio varies slowly as applied strain goes from −5% to 5%, suggesting a dominant linear elastic behaviour within the strain range considered. (Note the Poisson’s ratio at a large strain (that is, >5% or <−5%) may strongly depend on the strain. This behaviour is not pursued in this work since such large strains are often experimentally inaccessible.) The small differences between ν_{ab} and ν_{ba} reflect a nearly isotropic auxetic or nonauxetic behaviour inside the 1Tstructure plane. Therefore, the delectron count dependence of the sign of Poisson’s ratio as shown in Fig. 2a does not change with respect to the amount of the applied strain within the linear elastic range and the loading direction inside the plane.
Stiffness
To compare the stiffness (Young’s modulus) of a singlelayer material with bulk materials, we calculate its 3D inplane stiffness (Y_{3D}) from 2D inplane stiffness (Y_{2D}) and effective layer thickness (t) via Y_{3D=}Y_{2D}/t. The Y_{2D} is directly derived from firstprinciples total energies as a function of uniaxial strain. The effective layer thickness t can also be uniquely determined from firstprinciples calculated bending energy^{49}. Here for simplicity, we approximate t as t=t_{0}+0.8 Å, where t_{0} is the distance between the top and bottom chalcogen atom layers and the 0.8 Å is the total effective decay length (0.4 Å in each layer side) of electron density into the vacuum. The 0.8 Å is derived from the firstprinciples calculated layer thickness for 1HMoS_{2} (ref. 49). MSe_{2} and MTe_{2} may have different decay lengths than MS_{2}. However, such difference should be less than one time of magnitude. Hence, using a different decay length does not induce one time of magnitude difference in the calculated 3D inplane stiffness.
Table 1 shows that the 3D inplane stiffness of almost all 1TMX_{2} compounds lies in between 100 and 300 GPa. Among the auxetic d^{2}–d^{3} 1TMX_{2} compounds, WS_{2} and ReSe_{2} are the stiffest, having a stiffness of ∼290 GPa; TcTe_{2} is the softest, having a stiffness of ∼80 GPa. Manmade auxetic materials typically have a stiffness in the range from ∼10^{−5} to ∼1 GPa, and naturally occurring auxetic bulk solids exhibit a stiffness of ∼10^{1}–10^{2} Pa (ref. 50). Therefore, even considering the uncertainty of our calculated 3D stiffness (less than one order of magnitude) that may be caused by using different approximations for effective layer thickness, the 3D stiffness values predicted for 1TMX_{2} compounds are among the highest in the naturally occurring crystalline solids and are at least three orders of magnitude higher than manmade auxetic materials.
The fact that both auxetic and nonauxetic materials are found in the same 1Tstructure type implies that the auxetic effect is not a purely geometric property. The delectron count dependence of electronic structure must be involved. In the 1T structure, the d orbitals of the octahedrally coordinated transition metal split into two groups, d_{xy,yz,zx} (t_{2g}) and (e_{g}). In what follows, we shall show that (i) transition metals interact with each other through t_{2g}orbital coupling, and (ii) the coupled t_{2g} orbitals are further coupled with the lonepair electrons of chalcogen atoms. It is the gradual filling of such t_{2g}phybridized bands that leads to the different behaviour of Poisson’s ratio.
Intermetal t_{2g}orbital coupling
In the ideal 1T phase, the Mcentred octahedra share edges, forming three onedimensional Mchains along the directions of lines y=x, y=z, and z=−x, respectively, within the local reference frame of the octahedra (Fig. 1b). The metal atoms can interact with each other through the coupling between their t_{2g} orbitals. This coupling gives rise to t_{2g}bonding states and t_{2g}antibonding states, with no energy gap in between due to the weak coupling nature. The t_{2g} states are mostly located within the gap between the bonding and antibonding bands of the M–X bonds (Fig. 1c).
The progressive filling of these t_{2g} bands from group 4 (d^{0}) to group 10 (d^{6}) species leads to different M–M bonding or antibonding character at the Fermi level. In d^{1}d^{3} 1TMX_{2}, the Fermi level crosses the t_{2g}bonding states; the highest occupied bands close to the Fermilevel thus exhibit a stronger bonding character as we go from d^{1} to d^{3}. This bonding character attracts the metal atoms towards each other, leading to an intermetal distance shorter than that in the ideal 1T structure. In d^{5}–d^{6} 1TMX_{2}, since the t_{2g} bonding states can accommodate up to six electrons (three from each metal), all t_{2g}bonding states are filled and the Fermi level crosses the t_{2g}antibonding states. Hence the highest occupied bands in the vicinity of the Fermi level exhibit antibonding character, repelling metal atoms from each other.
The existence of the intermetal t_{2g}orbital interactions is reflected by the delectron count dependence of the M–X–M bond angles (∠MXM) as illustrated in Fig. 1d. The ideal 1T phase has regular octahedra with ∠MXM=90°. In the d^{0} 1TMX_{2} compounds, the ∠MXM deviates least from 90°. This is expected since all t_{2g} states are almost completely unoccupied and the intermetal d–d interaction is marginal. For the d^{1}–d^{3} 1TMX_{2}, all have acute ∠MXM, decreasing with the increasing delectron count. This trend arises from the increasing intermetal t_{2g}bonding character in going from d^{1} to d^{3}, which shortens the intermetal distance. In the d^{5}–d^{6} 1TMX_{2}, the ∠MXM jumps up to over 90°, consistent with the intermetal t_{2g}antibonding character.
Figure 1d also shows that the chalcogen atoms have minor effect on ∠MXM compared with the transition metals with different delectron counts, but a trend can still be observed: the ∠MXM decreases with increasing atomic number of the chalcogen. For example, the ∠MXM of TiS_{2}, TiSe_{2} and TiTe_{2} decreases from 89.6° to 88.2° to 86.0°. This trend is not associated with the intermetal t_{2g}orbital interaction; instead it is intrinsic to the spatial distribution of the lonepair charge density relative to that of the M–X bonds around the chalcogen.
t_{2g}–porbital coupling
The intermetal t_{2g} orbitals are further coupled with chalcogen p orbitals in 1TMX_{2}. It can be seen from their projected density of states (DOS) as shown in Fig. 3. In the 4d transition metal disulfides with the ideal 1T structure, we find that the DOS of sulfur 3p and metal t_{2g} states overlap, as manifested by their similar DOS peak shapes and positions in energy. The t_{2g}–porbital overlap is marginal in d^{0} ZrS_{2}, but it increases quickly in going from d^{1} NbS_{2} to d^{6} PdS_{2}. This trend is clear not only in the energy range from −12 to −7 eV, where the major peaks of 3p DOS are located, but also near the Fermi level.
The t_{2g}–porbital interaction is attractive because the X ligand has one lone electron pair and acts as a sigma donor. In d^{1}–d^{3} MX_{2}, the t_{2g}–p coupling force draws atom X towards the intermetal bond centres, because the t_{2g} states are the intermetal bonding states spreading over the M–M bond centers. In d^{5}–d^{6} MX_{2}, the t_{2g}–p coupling force attracts atoms M and X towards each other, because the t_{2g} states are antibonding and localized near the metal atoms. The delectron count dependence of t_{2g}–p interaction direction plays a key role in determining the structure deformation presented below.
Deformation mechanism
To understand the microscopic origin of Poisson’s ratios, let us now look into the resulting structural relaxation subjected to a tensile strain applied along the a axis. Due to the centrosymmetric nature of the 1T phase, the whole relaxation process manifests itself in the triangular pyramid unit as illustrated in Fig. 4. For the stretch along the M_{1}–M_{3} axis (that is, axis a), the resulting relaxation involves only atoms M_{2} and X moving inside the Q–X–M_{2} plane. Hence, two relations always hold during relaxation: {d}_{{\text{M}}_{1}{\text{M}}_{2}}={d}_{{\text{M}}_{2}{\text{M}}_{3}} and ∠M_{1}XM_{2}=∠M_{3}XM_{2}.
We analyse the relaxation process by decomposing it into three consecutive steps: (i) atom X relaxes along the line Q–X, (ii) atom X rotates around the M_{1}–M_{3} axis, and (iii) atom M_{2} relaxes along the line Q–M_{2}. In the first two steps, the lattice constant b is fixed to the value found in the relaxed strainfree 1T structure. In the third step, b varies as atom M_{2} moves along the Q–M_{2} line, leading to different Poisson’s ratio behaviour.
Figure 4 shows the detailed structural relaxation in the three consecutive steps described above for 1TMX_{2} with ∠QXM_{2}<90° (Fig. 4a) and with ∠QXM_{2}>90° (Fig. 4b) separately. Each step can be understood in the way that atom X (or atoms X and M_{2}) relaxes to conserve the M–X bond length (d_{MX}) since d_{MX} is energetically dominant. After the first two steps of the relaxation, it can be seen that (i) both {d}_{{\text{M}}_{1}{\text{M}}_{2}} (also {d}_{{\text{M}}_{2}{\text{M}}_{3}}) and ∠M_{1}XM_{2} and ∠M_{3}XM_{2} (Supplementary Fig. 1) increase in all 1TMX_{2} compounds no matter whether ∠QXM_{2} is larger or smaller than 90°, and (ii) ∠XQM_{2} increases in the 1TMX_{2} with ∠QXM_{2}<90° but decreases in the 1TMX_{2} with ∠QXM_{2} >90° (Supplementary Fig. 1). The changes in {d}_{{\text{M}}_{1}{\text{M}}_{2}} and {d}_{{\text{M}}_{2}{\text{M}}_{3}}, ∠M_{1}XM_{2} and ∠M_{2}XM_{3} and ∠XQM_{2} thus store the strain energy, which will be partially released in the subsequent third step relaxation.
The thirdstep relaxation determines the sign of Poisson’s ratio. The negative Poisson’s ratio of d^{2}–d^{3} MX_{2} can be attributed to the strong t_{2g}–porbital coupling. Such strong coupling implies a large amount of strain energy stored in the decreased ∠XQM_{2} after the second step. This part of strain energy will be released in this third step through atom M_{2} relaxing along the increased blattice direction, leading to a negative Poisson’s ratio. The strength of t_{2g}–porbital coupling depends not only on the delectron count of the transition metal but also on the chalcogen atom. This dependence explains why the Poisson’s ratio of the compounds from same d^{2} or d^{3} group also differs from one another as shown in Fig. 2a.
For d^{0}–d^{1} MX_{2}, the positive Poisson’s ratio results from the marginal or weak intermetal t_{2g} coupling and t_{2g}–p coupling. Such weak couplings imply that the strain energy stored in {d}_{{\text{M}}_{1}{\text{M}}_{2}} and {d}_{{\text{M}}_{2}{\text{M}}_{3}} and ∠XQM_{2} is also marginal or small. The major strain energy that can be released in the third step is thus stored in the increased ∠M_{1}XM_{2} and ∠M_{2}XM_{3}. Therefore, it is energetically favourable that atom M_{2} relaxes in the bdecreasing direction, reducing the increase in ∠M_{1}XM_{2} and ∠M_{2}XM_{3}, and resulting in a positive Poisson’s ratio. For d^{5}–d^{6} MX_{2}, the positive Poisson’s ratio originates from the fact that the t_{2g}–p coupling aligns along the M–X bond and does not energetically affect the change in ∠XQM_{2}. In other words, the strain energy stored in the decreased ∠XQM_{2} is small. Since the t_{2g} antibonding is also generally weak, the relaxation of atom M_{2} is energetically favourable in the bdecreasing direction, giving rise to a positive Poisson’s ratio. This deformation mechanism is similar to that in d^{0}–d^{1} compounds.
Simply saying, the negative Poisson’s ratio in d^{2}–d^{3} MX_{2} results from the strong attractive coupling between the intermetal t_{2g}bonding states and the X p states, which prevents atoms X and M_{2} relaxing toward the ∠XQM_{2}increasing direction. The positive Poisson’s ratio arises from lack of such strong t_{2g}–p coupling in other groups of 1TMX_{2}.
Discussion
The monolayer MX_{2} materials involve transition metals where strong correlation effects may be not well captured by the new strongly constrained and appropriately normed (SCAN) metaGGA functional. To check the robustness of our results, we also calculated the Poisson’s ratio for 12 d^{2}–d^{3} MX_{2} by using the HSE06 hybrid functional^{51}. The results are summarized in Supplementary Table 1. It shows that the Poisson’s ratio of eight 1TMX_{2} compounds (that is, MoSe_{2}, MoTe_{2}, WSe_{2}, WTe_{2}, TcTe_{2}, ReS_{2}, ReSe_{2}, ReTe_{2}) remains negative, whereas for other four compounds (that is, MoS_{2}, WS_{2}, TcS_{2}, TcSe_{2}) their Poisson’s ratio changes the sign from negative to slightly positive, which is still very interesting and useful for applications. Although it is found that the SCAN lattice constants agree better with experiment than the HSE06 ones for most of the compounds listed in this table, it is uncertain whether SCAN predicts a more accurate Poisson’s ratio than HSE06 since the semilocal SCAN functional could make larger densitydriven error in the energy than HSE06 does for the system under stretching^{52}. This uncertainty calls for experimental validation and further theoretical study. Nevertheless, the auxetic behaviour we find is robust in most of the d^{2}–d^{3} MX_{2} compounds. The less negative Poisson’s ratio predicted by HSE06 (Supplementary Table 1) further indicates that the auxetic behaviour originates from the strong p–d coupling. In general, compared with the semilocal SCAN functional, HSE06 yields more localized metal d and chalcogen p orbitals and hence the weaker hybridization between them, which leads to less negative Poisson’s ratios in HSE06.
Our predicted inplane auxetic behaviour is intrinsic in the 1T structure without any external engineering and occurs in the elastic region. This is different from the extrinsic auxetic behaviour reported in the epitaxial oxide thinfilm^{53,54} and the engineered 2D materials, such as the wrinkled graphene^{55}, graphane^{56} and borophane^{57}. Recently, the negative Poisson’s ratio was also reported in metal nanoplates^{58}, pristine graphene^{59} and semifluorinated graphene^{60}. The negative Poisson’s ratio claimed there corresponds to the ratio calculated from ν_{ab}=−∂ɛ_{a}/∂ɛ_{b} under large stains, differing from that calculated from ν_{ab}=−ɛ_{a}/ɛ_{b} (the original definition of Poisson’s ratio) as we followed here. The Poisson’s ratios calculated from ν_{ab}=−ɛ_{a}/ɛ_{b} for pristine graphene^{59} and semifluorinated graphene^{60} are actually both positive under a strain <∼15%, and for metal nanoplates, it is also positive under a strain <∼4%.
Finally, it is noteworthy that the auxetic behaviour of d^{2}–d^{3} MX_{2} compounds is predicted in the highsymmetry 1T phase. This phase is known to be metastable or dynamically unstable in both d^{2} and d^{3} MX_{2} compounds^{44,61,62,63}. However, experimentally, relevant phase diagrams of monolayer materials differ from those of bulk materials. The kinetic barriers between the different phases of monolayers may arise and be affected by many external factors, such as interfaces, underlying substrate, temperature, strain and impurities. Therefore, it is not uncommon to observe the undistorted 1T phase synthesized experimentally. For instance, although no kinetic barrier is found from firstprinciples calculations between the unstable 1T phase and dynamically stable distorted 1T phase, the undistorted 1T monolayer structures of MoS_{2}, MoSe_{2}, WS_{2} and WSe_{2} are observed from the exfoliation using Liintercalation method^{45,64}. For MoS_{2}, the coexistence of 1T and 1H domains is also observed in the same monolayer^{46,47}. Such heterogeneous monolayers with auxetic and nonauxetic domains are particularly intriguing since they could lead to novel functionality.
Methods
All calculations were performed using density functional theory and the planewave projector augmentedwave^{65} method as implemented in the VASP code^{66}. The new SCAN metageneralized gradient approximation was used^{67,68}. SCAN is almost as computationally efficient as PBEGGA functional, yet it often matches or exceeds the accuracy of the more computationally expensive hybrid functionals in predicting the geometries and energies of diversely bonded systems^{68}. Supplementary Table 2 shows our calculated lattice constants for 1TMX_{2} compounds. They agree very well with available experimental data^{44}, especially for groups 4–7 1TMX_{2} whose errors are within 1%. An energy cutoff of 500 eV was used. The monolayer structure is modelled in an orthorhombic supercell that contains two formula units (Fig. 1a) and a 20 Å vacuum space inserted in the outofplane direction. A 24 × 14 × 1 kpoint grid was used to sample the Brillouin zone during structure relaxation. All atoms were fully relaxed until their atomic forces were <0.005 eV Å^{−1}. The effects of spinorbit coupling on the structural deformation are considered to be minor and hence not included in our study.
The Poisson’s ratio is calculated from the engineering strain (ɛ), which is defined as the change in length ΔL per unit of the original length L, that is, ɛ=ΔL/L. The applied uniaxial strain is realized in our calculations by fixing the lattice parameter to a value different from its equilibrium value during structural relaxation. The resulting strain in the transverse direction is extracted from the fully relaxed structure subjected to an applied strain.
Data availability
The authors declare that the data supporting the findings of this study are available within the paper and its Supplementary Information files.
Additional information
How to cite this article: Yu, L. et al. Negative Poisson’s ratio in 1Ttype crystalline twodimensional transition metal dichalcogenides. Nat. Commun. 8, 15224 doi: 10.1038/ncomms15224 (2017).
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Acknowledgements
We thank John P. Perdew for valuable scientific discussions and comments on the manuscript. We also thank Richard C. Remsing and Jefferson E. Bates for the comments on the manuscript. This research was supported as part of the Center for the Computational Design of Functional Layered Materials (CCDM), an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under Award #DESC0012575. This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DEAC0205CH11231. This research was also supported in part by the National Science Foundation through major research instrumentation grant number CNS0958854.
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L.Y. designed the project, performed the calculations and wrote the manuscript. Q.Y. and A.R. contributed to analysing the results and writing the manuscript.
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Yu, L., Yan, Q. & Ruzsinszky, A. Negative Poisson’s ratio in 1Ttype crystalline twodimensional transition metal dichalcogenides. Nat Commun 8, 15224 (2017). https://doi.org/10.1038/ncomms15224
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DOI: https://doi.org/10.1038/ncomms15224
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