Prediction of 2D IV–VI semiconductors: auxetic materials with direct bandgap and strong optical absorption

Abstract

Auxetic materials are highly desirable for advanced applications because of their negative Poisson's ratios, which are rather scarce in two-dimensional materials. Motivated by the elemental mutation method, we predict a new class of monolayer IV–VI semiconductors, namely, δ-IV–VI monolayers (GeS, GeSe, SiS and SiSe). Distinctly different from the previously predicted IV–VI monolayers, the newly predicted δ-MX (X = Ge and Si; M = S and Se) monolayers exhibit a puckered unit cell with a space group of Pca2₁. Their stabilities were confirmed by first-principles lattice dynamics and molecular dynamics calculations. In particular, all these MX monolayers possess a large bandgap in the range of 2.08–2.65 eV and pronounced anisotropic mechanical properties, which are demonstrated by direction-dependent in-plane Young's moduli and Poisson's ratios. Furthermore, all these 2D MX monolayers possess negative Poisson's ratios (even up to about −0.3 for SiSe). Strong optical absorption is observed in these δ-IV–VI monolayers. These interesting physical properties will stimulate the development of 2D flexible devices based on IV–VI semiconductor monolayers.

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1. Introduction

Graphenes are considered as the horizon of two-dimensional (2D) materials, as they inspire intense research activity on 2D layered materials,^1,2 which have fantastic mechanical,^3–5 electronic,⁶ thermal^7–10 and magnetic¹¹ properties. The Dirac cone in graphenes induces ultrafast dynamics for the charge carrier, but their zero bandgap characteristics also impede some applications in field-effect transistors, impelling the further investigation of other 2D semiconductor materials.¹² Black phosphorus (BP) is an ideal alternative for 2D electronics because of its high charge carrier mobility and high on–off ratio in field-effect transistor application. Duo to the puckered honeycomb structure, the physical properties of BP exhibit pronounced anisotropy. For example, the thermal conductivity of BP is about 20 and 40 W m⁻¹ K⁻¹ along armchair and zigzag directions with a thickness of 15 nm, which can be further decreased by reducing the thickness,¹³ mainly contributed by strong anisotropy in phonon group velocities.¹⁴ Furthermore, the BP-based nanophononic heterostructure shows novel thermal management ability with tunable interfacial thermal resistance.¹⁵ The electronic band structure of 2D semiconductors can be further tuned,^16,17 which opens prospects for the design of various innovative devices for applications in flexible electronics, spintronics, photocatalysis, and artificial synapses.^18–22 Inspired by the successful demonstration of these 2D materials, extensive effort has been conducted to expand the family of 2D materials.^23,24 Since the synthesis of new 2D materials is time-consuming and costly, the theoretical calculation is of great utility. Some new 2D materials such as 2D magnetic MSi₂C_xN_4−x (M = Cr, Mo, and W; x = 1 and 2),²⁵ anisotropic MBs (M = Cr, Mn or Fe; B = boron),²⁶ CrX₃ (X = I, Br, and Cl),²⁷ tetragonal and hexagonal boron nitride,²⁸ graphene-like Si_1−xGe_x,²⁹ α′-boron sheet,³⁰ and B₂X₃ (X = Se and Te) photocatalysts³¹ are theoretically predicted by different theoretical schemes, which present a set of unique functional properties.^32–34

Recently, auxetic materials characterized by negative Poisson's ratios (NPRs) have attracted tremendous research attention from both fundamental science and practical application points of view.^35–37 Poisson's ratio is defined as the ratio of the lateral contraction strain to the longitudinal extension strain. Negative Poisson's ratio reveals that the material would expand laterally when stretched longitudinally. This is totally opposite to most of the conventional materials, which tend to shrink laterally when subjected to strain in the longitudinal direction.³⁸ Bulk auxetic materials have been studied for some applications. For example, a NPR copper foam was synthesized experimentally, which displays enhanced toughness.³⁹ To explore the effect of the chondrocyte proliferation on the cartilage regeneration by a compress, polyurethane materials with NPRs were used for such tissue engineering.⁴⁰ The NPR fastener was designed using ceramic aerogels via 3D graphene structures, which possesses novel mechanical properties.⁴¹ For metals, a correlation between the NPR and work function was demonstrated based on the electron-gas model, which enables a promising application in highly sensitive detectors because negative Poisson's ratios of the metal electrodes can amplify the response of strain on sensor sheets.⁴² A hierarchical tube was proposed with a NPR characteristic that it will extend along the transverse direction by the vertical force as harder composites.⁴³ Some other studies also demonstrated that bulk materials with NPRs have fantastic properties for a muffler and a shock absorber.^44,45

In particular, nanomaterials with NPRs have more advantages because of their particular unique structure,^46–48 which also inspired tremendous prediction from both theoretical and computational efforts.⁴⁹ The puckered structure in BP has proven to induce anisotropic characteristics and a NPR in the out-of-plane direction,⁵⁰ which is also demonstrated in the experiment.⁵¹ Besides, δ-phosphorene has a remarkable NPR (−0.267) along the grooved direction, excellent flexibility and critical crack strain showing a potential usage for electromechanical devices.⁵² B₄N monolayers were predicted to have dynamic and thermal stabilities and excellent mechanical properties with a maximal NPR of −0.032, which can be considered as future nanomechanical devices.⁵³ GaPS₄ monolayers were reported to exhibit a NPR of −0.033 in the in-plane and −0.62 in the out-of-plane direction. Combined with its ultralow cleavage energy (about 0.23 J m⁻²), 2D GaPS₄ is expected to be a promising candidate for nanoelectronics and electromechanical devices.⁵⁴ The NPR characteristic in 2D blue phosphorus oxide was also reported, and the mechanism is attributed to the competition between attractive P–P bonding and repulsive P–O bonding, respectively.⁵⁵ For other 2D NPR materials, orbital coupling and hybridization of the electron are also possible origin of negative Poisson's ratios.^56,57 It is worth noting that auxetic materials are especially appropriate in the application of flexible or bio-electronics. Because most biological materials have a negative Poisson ratio, in such applications, the substrate made of non-auxetic materials may result in a mismatch in deformation and cause irritation.⁵⁸

Very recently, IV–VI-based monolayers^59,60 such as GaS,⁶¹ GaSe,⁶² GeS^63,64 and InSe⁶⁵ monolayers have aroused tremendous attention, shown as Fig. 1(a), which were synthetized in the experiment as high-performance photodetectors. In detail, the IV–VI compounds have been proposed with different structures such as the monolayer Pcnm-GeSe, Pmma-SiS and Pma2-SiS.^66,67 The SiSe monolayer was also predicted to have Pmma and Pma2 structures.^68,69 Puckered SiS and SiSe were suggested in previous reports.^70,71 In this work, we predict a family of 2D group δ-IV–IV monochalcogenide materials, XM (X = Ge and Si; M = S and Se), using the first-principles calculation and ab initio molecular dynamics (AIMD) method. The XM monolayers possess pronounced direction-dependent NPR characteristics. Besides, the electronic band structure and direction-dependent Young's modulus are discussed. The ultra-strong optical absorption property of those layered materials is characterized as well. These multi-functional features support promising applications in nanoelectronics, nanomechanical and optoelectronic devices.

Fig. 1 (a) Synthesized IV–VI monolayers in a previous experiment and (b) crystal structure of the newly predicted δ-IV–VI monolayers XM (X = Ge and Si; M = S and Se). The yellow and red balls are M and X atoms, respectively.

2. Computational methodology

Based on density functional theory (DFT), the first-principles method was explored using the Vienna Ab initio Simulation Package (VASP)⁷² with the projector-augmented wave method. The Perdew–Burke–Ernzerhof functional was adopted. Besides, the hybrid Heyd–Scuseria–Ernzerhof (HSE06) functional was considered by the standard screening and the standard mixing parameter of 0.2 Å⁻¹ and 0.25, respectively.⁷³ The cutoff energy was set at 500 eV for plane-wave, and the k-mesh was demonstrated by 8 × 8 × 1. The Brillouin zone was explored with the convergence criteria of the energy by 10⁻⁸ eV and force by 10⁻⁴ eV Å⁻¹ in a vacuum layer thickness of about 20 Å. The minimum energy pathways of different phase transitions were determined by a climbing image nudged elastic band method (NEB)⁷⁴ based on the interatomic forces and total energies acquired from the DFT calculations. The Brillouin zone (BZ) was sampled by the gamma method with 7 × 7 × 1 k-point sampling; meanwhile, the criteria for energy convergence and force convergence are 10⁻⁶ eV per cell and 0.01 eV Å⁻¹, respectively. Furthermore, the density functional perturbation theory calculation was conducted to investigate the phonon dispersion of the materials, which was realized using the PHONOPY package.^75,76

3. Results and discussion

3.1 Structure and stability

The anisotropic crystal structure of the XM (X = Ge and Si; M = S and Se) monolayers is presented in Fig. 1(b), which shows a puckered unit cell with a space group of Pca2₁, constructed by elemental mutation based on the prototype of δ-CS structures,⁷⁷ different from the well-known orthorhombic layered structure with space group Pcmn of GeS and GeSe.^66,78 The optimized unit cell of the XM monolayer contains 4 X and 4 M atoms and the obtained lattice constants, a (or b), of the GeS, GeSe, SiS and SiSe monolayers are 5.58, 5.83, 5.50 and 5.69 Å (5.76, 5.81, 5.67 and 5.73 Å), respectively. The cohesive energy of the XM system was calculated using (4E_X + 4E_M − E_XM)/8, where E_X, E_M and E_XM are the total energies of a X atom, a M atom and the XM, respectively. The cohesive energies of the monolayer GeS, GeSe, SiS and SiSe are 3.61, 3.37, 3.81, 3.51 eV per atom (as shown in Table 1), respectively, which are comparable with that of germanene (about 3.24 eV per atom), phosphorene (about 3.48 eV per atom) and silicene (about 3.91 eV per atom).⁷⁹ Furthermore, the obtained cohesive energy of SiS is larger than that of puckered SiS (3.16 eV per atom),⁸⁰ and the calculated cohesive energy of GeS and GeSe monolayers in our work is also similar to some reported GeS, GeSe with other phases, as presented in Table 2. The predicted new IV–VI monolayers can be synthesized in the experiment by a chemical vapour deposition method, and then be isolated by mechanical, sonicated or liquid-phase exfoliation, which have been adopted to synthesize few-layer GaSe⁶² and GeS.⁶⁴ In addition, the δ-IV–IV monolayers can also be obtained by shifting X atoms in puckered IV–IV monolayer structures.⁸¹ Furthermore, the X–M bond lengths in the GeS, GeSe, SiS and SiSe monolayers are 2.42, 2.54, 2.32 and 2.44 Å, respectively. We also take GeS as an example to estimate the stability by the structural transition barrier between δ-GeS and α-GeS in Table 2. The NEB calculated energy barrier is about 61.0 meV, which is far higher than the thermal kinetic energy of about 13 meV at room temperature (1/2k_BT, T = 300 K), avoiding such structural transformation, as shown in Fig. 2.

Fig. 2 Structural transition barrier between δ-GeS and α-GeS obtained by NEB calculations.

Table 1 Cohesive energy (E, eV), ratio of lattice constants (b/a) along different directions, bandgap (E_g, eV) and elastic constants (N m⁻¹) of the monolayer XM system

	E	b/a	C 11	C 22	C 12	C 66	E ^PBEg	E ^HSEg
GeS	3.61	1.01	41.21	22.83	−4.38	7.64	1.920	2.65
GeSe	3.37	1.01	42.79	32.56	−7.51	7.41	1.60	2.20
SiS	3.81	1.03	50.29	24.75	−4.10	7.67	1.42	2.15
SiSe	3.51	1.01	50.35	33.68	−9.78	7.77	1.46	2.08

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Table 2 Symmetry groups, cohesive energy (E, in eV) and bandgap (E_g, HSE, in eV) of the investigated GeS and GeSe monolayers in this work compared with the previous structures

	Space group	E	E g	Ref.
δ-GeS	Pca21	3.61	2.65	This work
δ-GeSe	Pca21	3.37	2.20	This work
α-GeS	Pmn21	3.76	1.72	82–84
β-GeS	P3m1	3.74	2.47	83 and 85
γ-GeS	Pmn21	3.74	1.77	83 and 86
α-GeSe	Pmn21	3.88	1.75	87 and 88
β-GeSe	P3m1	3.85	3.01	85 and 88
γ-GeSe	Pmn21	3.83	2.53	59 and 88

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The phonon dispersion of the GeS, GeSe, SiS and SiSe monolayers was calculated, as shown in Fig. 3, characterized by 3 acoustic branches and 21 optical branches. Importantly, no imaginary frequency is found in these phonon dispersions showing a dynamic stability of these newly predicted XM monolayers. Besides, the maximum frequencies of the phonon dispersion for the GeS, GeSe, SiS and SiSe monolayers are 325, 232, 397 and 324 cm⁻¹, respectively. Furthermore, the AIMD calculation was employed to explore the thermal stability of those layered materials using a Nosé–Hoover heat bath scheme.⁸⁹ Taking the lattice translational constraints into consideration, the unit cell of the XM monolayer was expanded by an 8 × 8 × 1 supercell, which includes 128 atoms within the AIMD simulation. After a relaxation time of 5 ps, the structures of GeS, GeSe, SiS and SiSe monolayers were still undamaged at an ambient temperature of 300 K, as shown in the inset in Fig. 4(a)–(d), respectively. The temperature and total energy fluctuations versus simulation time are also presented in Fig. 4, which exhibits a convergence for the AIMD results.

Fig. 3 Phonon dispersion of the (a) GeS, (b) GeSe, (c) SiS and (d) SiSe monolayers, respectively.

Fig. 4 Total energy and the temperature fluctuation of the (a) GeS, (b) GeSe, (c) SiS and (d) SiSe monolayers during the AIMD simulation, the insets are the atomic structure after 5 ps at 300 K. The red, yellow, cyan and blue marks represent the Ge, S, Se and Si atoms, respectively; the red and gray lines represent the system total energy and temperature calculated by the AIMD simulation.

3.2 Electronic and mechanical properties

The HSE06 functional was used to calculate the band structure of the GeS, GeSe, SiS and SiSe monolayers, as shown in Fig. 5(a)–(d), respectively. It is worth noting that all those 2D materials are semiconductors. In detail, the GeS monolayer has a direct band structure with a bandgap of 2.65 eV, and the valence band maximum (VBM) and conduction band minimum (CBM) are at Γ point. In contrast, the GeS monolayer with a honeycomb hexagonal structure is an indirect bandgap semiconductor, with a bandgap of 2.47 eV.⁸³ The band structure of GeSe and SiS monolayers have an almost direct bandgap (2.20 eV and 2.15 eV) with the CBM and VBM located near the Y (GeSe) point and Γ (SiS) point, respectively. While the GeSe monolayer with a hexagonal structure possesses an indirect bandgap (bandgap of 2.92 eV obtained by HSE06 calculation).⁹⁰ The bandgaps of the IV–VI monolayer with different structures are summarized in Table 2. In contrast, the SiSe monolayer exhibits an indirect bandgap with VBM at the Y point, while the CBM is on the M–Y path. The PBE calculated density of states of the GeS, GeSe, SiS and SiSe monolayers is presented in Fig. 5(e)–(h), respectively. It is clear that the CBM and VBM of the GeS are mainly contributed from Ge_p_x, Ge_p_y and Ge_s, S_p_y, respectively. While the CBM and VBM of the GeSe are mainly contributed by Ge_p_y and Ge_s, S_p_x, respectively. Similar orbital contribution is also observed in the partial density of states (PDOS) of the SiS and SiSe monolayers.

Fig. 5 Band structure of the monolayer (a) GeS, (b) GeSe, (c) SiS and (d) SiSe calculated by the HSE06 method, and the partial density of states of the monolayer (e) GeS, (f) GeSe, (g) SiS and (h) SiSe calculated by PBE. In (a–d), the locations of the CBM and VBM are marked by grey dots.

Next, the orientation dependence of in-plane Young's moduli and Poisson's ratios for those four layered materials were calculated as follows:⁵³

where E_2D(θ) and v(θ) are Young's moduli and Poisson's ratios, respectively; the angle θ is between the considered direction and a-direction. Fig. 6(a)–(d) show direction-dependent Young's moduli of the GeS, GeSe, SiS and SiSe monolayers. Obviously, these monolayer materials are anisotropy with maximal Young's moduli located at θ = 0° with 40, 41, 50 and 47 N m⁻¹, respectively, while minimal Young's moduli are 19, 20, 20 and 21 N m⁻¹, respectively, at θ values of about 51°, 46°, 47° and 45°. In the b-direction, Young's moduli of the GeS, GeSe, SiS and SiSe monolayers were calculated to be 22, 31, 24 and 32 N m⁻¹, respectively. However, such anisotropic characteristic of Young's moduli does not exist in the honeycomb hexagonal IV–VI monolayer.⁸³ Furthermore, Poisson's ratios (as shown in Fig. 6(e)–(h)) also reveal remarkable direction dependence. The GeS, GeSe, SiS and SiSe monolayers possess a maximal Poisson ratio of about 0.248, 0.333, 0.320 and 0.331 along the 45° direction, respectively. The calculated NPRs of the GeS, GeSe, SiS and SiSe monolayers along the a-direction are −0.192, −0.231, −0.165 and −0.290, respectively, and the obtained NPRs along b-direction are −0.106, −0.176, −0.081 and −0.194. It should be noted that the GeSe and SiSe monolayers possess pronounced NPR characteristics, which are larger than other reported 2D materials such as δ-phosphorene (−0.267),⁵² PtI₂ (−0.24),⁹¹ and Ag₂S (−0.12).⁹² It is worth noting that the puckered IV–VI monolayers were also reported to possess NPRs such as GeS (−0.208), GeSe (−0.433)⁹³ and Pma2-SiS monolayers (−0.19).⁶⁸ In particular, the puckered SiS has a maximal in-plane Poisson ratio of 1.025,⁹⁴ which is larger than that of SiS (0.320) reported in this work. The maximal in-plane Poisson ratio for puckered SiSe is 0.330,⁹⁴ almost the same as the Poisson ratio of the SiSe structure (0.331) in this work. Interestingly, the puckered SiS and SiSe monolayers possess out-of-plane Poisson's ratios of −0.073 and −0.466, respectively.⁹⁴

Fig. 6 Young's modulus of the (a) GeS, (b) GeSe, (c) SiS and (d) SiSe monolayers; the Poisson ratios of the (e) GeS, (f) GeSe, (g) SiS and (h) SiSe monolayers, respectively. The blue and red lines represent the positive and negative values.

In addition, the strain in the b-direction was calculated under different uniaxial a-direction strains, as shown in Fig. 7(a), which further prove the auxetic characteristic of 2D GeS, GeSe, SiS and SiSe monolayers. Meanwhile, by fitting the results, the obtained Poisson ratios of the GeS, GeSe, SiS and SiSe monolayers are −0.193, −0.264, −0.184 and −0.294, respectively, which are comparable with the results from eqn (2). Similarly, the fitted Poisson ratios of the GeS, GeSe, SiS and SiSe monolayers in the b-direction are −0.108, −0.181, −0.089 and −0.121, respectively, as shown in Fig. 7(b).

Fig. 7 (a) Strain in the b-direction under the external uniaxial a-direction strain and (b) the strain in the a-direction under the external uniaxial b-direction strain of the GeS, GeSe, SiS and SiSe monolayers; the schematic diagram of thickness deformation by the strain along the (c) a-direction and (d) b-direction of the MX monolayers; here the loading strain is shown in blue, while the induced strain is shown in grey.

When the tensile stress is applied along the a-direction, as shown in Fig. 7(c), the deformation in the c-direction (h) is from the initial configuration (black rectangle) to the blue one, demonstrating a compressed deformation in the c-direction. While along the b-direction, the cross section of the MX monolayer can be considered as two cantilevers with a connecting rod, as shown in Fig. 7(d). When the tensile stress is applied along the b-direction, the length of the connecting rod (l) has little change, and the angle (α) of the cantilever beam increases obviously, showing a transformation from black lines (initial structure) to blue ones (structure under stress), which also decreases the deformation in the c-direction of the MX monolayers. Therefore, these MX monolayers possess an intrinsic in-plane NPR characteristic, which is different from the out-of-plane half-NPR reported in graphene+.⁹⁵

3.3 Optical properties

All these investigated 2D materials possess a decent bandgap of about 2.08–2.65 eV, which falls in the visible light region (the energies of the visible light spectrum vary from about 1.5 to 3.0 eV). Thus, it is necessary to evaluate the optical properties of these 2D XM to access its potential in optoelectronic devices. We calculated the optical absorption as follows:⁹⁶where α, ω and c are the absorption coefficient, angular frequency and the speed of light respectively. ε₁(ω) and ε₂(ω) are the real and imaginary parts of the dielectric constant, respectively. ε₂(ω) can be obtained as follows:⁹⁷where Ψ_k, E_k and û are the wave function, energy and unit vector of the electric field of the incident light. The superscripts (v and c) in Ψ_k, E_k, label the conduction bands and valence bands, respectively. The complex dielectric function is ε(ω) = ε₁(ω) + iε₂(ω), and the real part ε₁ can be obtained from ε₂ by using the Kramers–Kronig relation. Considering the characteristic of 2D materials, we just investigated the in-plane light absorption properties (a-polarized and b-polarized light). Fig. 8 shows the absorption spectrum of the monolayer XM, which indicates that all these four XM materials strongly absorb a-polarized and b-polarized light around an energy of 3–5 eV. The areas below the adsorption profiles in the visible light region (about 1.64–3.19 eV) are 54.56 eV cm⁻¹ (or 54.27 eV cm⁻¹), 58.87 eV cm⁻¹ (or 58.21 eV cm⁻¹), 51.05 eV cm⁻¹ (or 50.83 eV cm⁻¹) and 55.53 eV cm⁻¹ (or 55.20 eV cm⁻¹) for GeS, GeSe, SiS and SiSe monolayers in the a-direction (or b-direction), respectively. Importantly, the GeSe and SiSe monolayers strongly absorb a-polarized and b-polarized light at around 2 eV but is transparent for GeS and SiS monolayers in this energy region. The optical absorption peak frequency is lower than that of δ-CTe.⁹⁸ GeSe (or SiSe) monolayers have ultra-strong optical absorption, the maximal absorption coefficients are 7.69 × 10⁵ cm⁻¹ (or 7.8 × 10⁵ cm⁻¹) and 8.34 × 10⁵ cm⁻¹ (or 6.77 × 10⁵ cm⁻¹) for a-polarized and b-polarized light, respectively, and the positions of absorption peaks are 3.68 eV (or 2.91 eV) and 3.72 eV (or 3.30 eV). The characteristic that monolayer XM possesses different light absorption performances in different polarization directions is induced by the anisotropic crystal structure, which also raises up promising applications in ultraviolet region linear polarizers. Besides, the calculated optical absorption of GeS, GeSe, SiS and SiSe monolayers covers the entire solar spectrum, which suggests the potential importance in the application of solar photovoltaics. Furthermore, it is worth noting that the calculated optical absorption values are similar to that of monolayer MoS₂, which has been reported to possess more than 5% solar power conversion efficiency in previous experimental investigation.⁹⁹ The obtained light absorption coefficient is also higher than other commonly studied 2D materials such as MoSSe (about 5.5 × 10⁵ cm⁻¹),¹⁰⁰ Hf₂CO₂ (about 4.8 × 10⁵ cm⁻¹),¹⁰¹ arsenene (about 2.7 × 10⁵ cm⁻¹),¹⁰² WSSe (about 2.1 × 10⁵ cm⁻¹)¹⁰³ and δ-CS (about 5.8 × 10⁵ cm⁻¹),⁷⁷ which were calculated using the similar method. In addition, it is worth noting that the GW + BSE method has been considered as an effective means to include the electron–hole interaction in the calculation of optical properties, which has been adopted in previous reports.^104,105 However, the optical calculations with the GW method for our studied system are computationally expensive, and hence, we adopted the HSE06 calculation, which has also been adopted to explore the optical properties of 2D materials.^106–108

Fig. 8 Absorption spectrum of (a) GeS, (b) GeSe, (c) SiS and (d) SiSe monolayers, respectively. The red and black lines denote the absorption of a-polarized and b-polarized light, respectively.

4. Conclusions

In summary, based on DFT calculations, GeS, GeSe, SiS and SiSe monolayers were investigated to possess a puckered structure. The dynamic and thermal stability proves by AIMD simulations for those layered materials, and they also have a desirable bandgap of about 2.08–2.65 eV. The anisotropy mechanical properties were explored by in-plane Young's moduli and Poisson's ratios, and the novel NPR was obtained by −0.081 to −0.290 especially. Furthermore, the ultra-strong light absorption performance was addressed, and all those suggest that the studied δ-IV–VI monolayers can be considered as promising candidates for future nanoelectronic, nanomechanical and optoelectronic devices.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This investigation was supported by the Open Fund Project of Maanshan Engineering Technology Research Center of Advanced Design for Automotive Stamping Dies (grant number: QMSG202105). We thank Dr Minglei Sun for fruitful discussions.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d2nr00818a

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