Home Search Collections Journals About Contact us My IOPscience Free-standing silicene obtained by cooling from 2D liquid Si: structure and thermodynamic properties This content has been downloaded from IOPscience Please scroll down to see the full text 2014 J Phys D: Appl Phys 47 495303 (http://iopscience.iop.org/0022-3727/47/49/495303) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 137.30.242.61 This content was downloaded on 25/02/2015 at 07:44 Please note that terms and conditions apply Journal of Physics D: Applied Physics J Phys D: Appl Phys 47 (2014) 495303 (9pp) doi:10.1088/0022-3727/47/49/495303 Free-standing silicene obtained by cooling from 2D liquid Si: structure and thermodynamic properties Vo Van Hoang1,2 and Huynh Thi Cam Mi2 Computer Physics Lab, Institute of Technology, Vietnam National University-HCM City, 268 Ly Thuong Kiet Street, District 10, HochiMinh City, Vietnam Department of Physics, College of Natural Science, Can Tho University, 3/2 Street, Ninh Kieu District, Can Tho City, Vietnam E-mail: vvhoang2002@yahoo.com and cammi0809@gmail.com Received 14 September 2014, revised 18 October 2014 Accepted for publication 23 October 2014 Published 17 November 2014 Abstract The structure and various thermodynamic properties of free-standing silicene have been studied by computer simulation Models are obtained by cooling from buckling twodimensional (2D) liquid Si via molecular dynamics (MD) simulation with Stillinger–Weber interatomic potential The temperature dependence of total energy, heat capacity, mean ring size and mean coordination number shows that silicenization of 2D liquid Si exhibits a first-order-like behavior The evolution of radial distribution function upon cooling from the melt also shows that solidification occurs in the system The final configuration of silicene is analyzed via coordination, bond-angle, interatomic distance and ring distributions or distribution of buckling in the system 2D visualization of atomic configurations clearly demonstrated that silicene obtained ‘naturally’ by cooling from the melt exhibits various structural previously unreported behaviors We find the formation of polycrystalline silicene with clear grain boundaries containing various defects including various vacancies, Stone– Wales defects or skew rings and multimembered rings unlike those proposed in the literature However, atoms in the obtained silicene are mostly involved in six-fold rings, forming a buckling honeycomb structure like that found in practice We find that buckling is not unique for all atoms in the models although the majority of atoms reveal buckling of the most stable low-buckling silicene found in the literature The buckling distribution is broad and symmetric Our comprehensive MD simulation of a relatively large silicene model containing 104 atoms and obtained ‘naturally’ by cooling from the melt provides original insights into the structure and thermodynamics of this important 2D material Keywords: silicene, silicenization, structure and properties of silicene, molecular dynamics simulation of silicenization (Some figures may appear in colour only in the online journal) 1. Introduction silicene possesses graphene-like properties such as massless Dirac fermions that carry charge and the quantum Hall effect in addition to its own specific properties due to its buckling atomic configuration as opposed to flat graphene [1–3] The synthesis of free-standing one-atom-thick silicene sheets is a big challenge and so far, it has not been successfully synthesized and characterized in practice Note that the interlayer Silicene, the 2D silicon counterpart of graphene, has attracted great interest in the scientific and technological community in recent years since this material can be easily integrated into Si-based devices in the semiconductor and electronics industry (see reviews [1–4]) It is found theoretically that 0022-3727/14/495303+9$33.00 © 2014 IOP Publishing Ltd Printed in the UK V V Hoang and H T Cam Mi J Phys D: Appl Phys 47 (2014) 495303 Si–Si bond in bulk Si is covalent in nature and that the graphitic form of Si is not known to exist; therefore, one cannot use the exfoliation method to extract free-standing silicene as in the case of graphene In practice, silicene has often been produced on substrate experimentally using different techniques Although the existence of silicene was predicted a long time ago, experimental evidence of this material has only been reported recently (see more details in [1–9]) In particular, a silicene monolayer has been successfully grown on certain metal substrates such as Ag [5–8] or Ir [9] It is found that all structures studied are buckled with the Si–Si bond length ranging between 2.28 and 2.50 Å, while the lateral Si-Si distance can be as low as 1.89 Å due to buckling of the silicene sheet [8] In addition, the growth of silicene layers on Ag(1 1 0) and Ag(1 1 1) surfaces can be seen in [10–12] The existence of 2D silicon was predicted theoretically in 1994 [13] and then it was reinvestigated by Guzman-Verri et al who named it silicene in 2007 [14] An increasing amount of research into silicene by computer simulations can be found recently [15–36] The formation of single- and double-layer silicon (i.e silicene) in slit pores was studied by molecular dynamics (MD) simulation using the Tersoff potential, and the structure of these layers is honeycomb, similarly to that of graphene [15] It is found by ab initio calculations that a low-buckled honeycomb structure of silicene with buckling equal to 0.44 Å and a bond length of 2.28 Å are the most stable properties [16] Monolayer honeycomb structures of group IV elements and III–V binary compounds have been studied by first-principles calculations as an extended research in this direction [17] Moreover, various aspects of silicene nanoribbons have been studied, including thermal stability, electronic structure and nanoribbon width dependence of the band gap or effects of hydrogen termination by ab initio calculations [18, 19] The size, shape and edge effects on the structure and properties of Si nanoribbons are of great interest and it is easily investigated in the same way as was done for graphene nanoribbons Similarly, the electronic properties of bulk silicene are studied using first-principles calculations [20–22] It is found that silicene is able to change from a metallic to a semiconducting or even a 2D piezomagnet material as one desires by using appropriate hydrogenation and/or substitutional doping [20, 22] Structural defects play an important role in various performances of silicene in the same way as that found for graphene, and comprehensive study of structural defects in silicene is desired It is found by MD simulation with reactive force field (ReaxFF) that buckling free-standing silicene is stable up to 1500 K before transition into 3D amorphous configuration, and vacancy defects reduce the thermal stability of silicene [23] However, the stability of silicene can be improved by saturating the dangling bonds at the edge by foreign atoms [23] In addition, it is found by density functional theory (DFT) that armchair silicene nanoribbons, but not zigzag ones, are stable 2D structures [24] Moreover, it is predicted that electron and hole-doped armchair silicene nanoribbons may be potential ferromagnetic semiconductors [24] Ab initio calculations also show that the band gap of silicene can be changed by surface adsorption of alkali atoms or using a vertical electric field [25, 26] The origin of the buckling of silicene has been discussed and analyzed; i.e strong coupling between the unoccupied molecular orbitals with occupied molecular orbitals leads to pseudo-Jahn–Teller distortion and the characteristic buckling in silicene [27] Vibrational properties of silicene have been studied via first-principles calculations [28] Stability and electronic properties of silicene/graphene systems have also been calculated and discussed [29] As noted above, silicene is often prepared on substrate, and the substrate effects on its structure and properties should be significant This problem is studied by ab initio calculations; i.e the substrate induces symmetry breaking in silicene and the band structure is drastically modified by the hybridization between Si and Ag atoms, the latter belonging to the substrate [30, 31] Moreover, the effects of substrate and strain on the stability and electronic structure of silicene have also been studied by first-principles calculations [32] Point defects in silicene have attracted much attention again [33, 34] The formation, stability and reactivity of Stone– Wales (S–W) defects in silicene have been studied by the DFT method [33], finding that the formation energy of S–W defects in silicene is lower than that in graphene On the other hand, the buckling of silicene provides a large energy for the healing of S–W defects, leading to stability of the sample even at high temperature and silicene with S–W defects as a semiconductor with the band gap depending on their concentration [33] The structure, mobility, electronic and magnetic properties of various point defects in silicene including S–W defects, single and double vacancies (SV and DV) and adatoms have been studied in detail using the DFT method [34] Various mechanical properties and the thermal conductivity of silicene are studied by MD simulations using ReaxFF or modified Stillinger–Weber (SW) potentials, respectively [35, 36] So far, our understanding of the structure and thermodynamics of silicene is still poor There is no simulation work related to the formation, structure and thermodynamics of free-standing silicene obtained by cooling from the melt It motivates us to carry out the study in this direction 2. Calculations Initially, the pristine buckling silicene model containing 104 Si atoms with the same buckling of 0.44 Å and a bond length of 2.28 Å (i.e the most stable low-buckling silicene [16]) is relaxed at zero pressure and at 3500 K for 106 MD steps in order to obtain an equilibrium 2D liquid state Periodic boundary conditions (PBCs) are applied only in the x and y Cartesian directions while in the z direction a fixed boundary with an elastic reflection behavior is applied The initial size of the model is LX × LY × L Z = 335.571 × 193.742 × 0.44 (unit of the length, L, is in Å) We fixed the length of the model in the z direction to be equal to buckling of 0.44 Å, i.e equal to 0.22 Å above and below z = 0, in order to form a 2D buckling structure Atoms in the model are interacted via SW potential [37], which contains two-body and three-body terms with a dimensionless parameter λ that controls their relative strength as follows: U = ∑ ∑ U2 (rij ) + λ ∑ ∑ ∑ U3 (rij, rik , θijk ) i j>i i j≠i k>j (1) V V Hoang and H T Cam Mi J Phys D: Appl Phys 47 (2014) 495303 The two-body term consists of a steep repulsion at very short separations and a short-range attraction: ⎡ ⎛ σ ⎞ p ⎛ σ ⎞q ⎤ ⎛ σ ⎞ ⎟; U2 (r ) = Aε ⎢B⎜ ⎟ − ⎜ ⎟ ⎥ exp ⎜ ⎝r ⎠ ⎦ ⎝ r − aσ ⎠ ⎣ ⎝r ⎠ (2) The second term is a sum over all triplets of a three-body interaction of the form: ⎛ γσ ⎞ ⎟ U3 (rij, rik , θijk ) = ε⎡⎣cos θijk − cos θ0 ⎤⎦ exp ⎜ ⎝ rij − aσ ⎠ ⎛ γσ ⎞ exp ⎜ ⎟ ⎝ rik − aσ ⎠ (3) All parameters of SW potential are taken from the original version performed in 1985 and details of the SW potential can be seen in [37]; we shall not discuss potential further here since it has been widely used for the simulation of Si or Si-based systems for the last 30 years After a careful test we found that upon cooling from a high temperature, 2D liquid Si with this SW potential spontaneously solidifies into a 2D solid with a honeycomb structure, i.e a silicene or graphene-like structure On the other hand, this potential gives a melting/ freezing temperature which is close to that found experimentally for bulk Si These are two reasons why the SW potential from the original version is adopted for the simulation of silicenization of 2D liquid Si in the present work, although some modified versions of SW or other potentials for Si can be found in the literature We use the classical MD method with the Verlet algorithm and a time step of 1.0 fs Zero-pressure NPT ensemble simulation is used for the whole simulation procedure under the same boundary conditions described above Temperature is corrected via simple velocity rescaling After melting at 3500 K, the model is cooled down to 300 K at a cooling rate as low as × 1010 K s−1 in order to obtain crystalline silicene Note that the same cooling rate has been used for study on the formation of single- and double-layer silicon in slit pores [15] The final configuration obtained at 300 K is relaxed for 105 MD steps before analyzing its characteristics We use LAMMPS software for MD simulations [38], ISAACS software for calculating ring statistics [39] and VMD software (Illinois University) for 2D visualization of atomic configurations [40] We use a cutoff radius of 3.0 Å in order to calculate coordination number, bond angle and interatomic distance distributions in the system This cutoff radius is equal to the position of the first minimum after the first peak in the radial distribution function (RDF) of models obtained at 300 K For the calculation of rings, the ‘shortest path’ rule is applied [39] Figure 1. Temperature dependence of total energy The inset shows heat capacity energy per atom and heat capacity is shown in figure 1 The former contains two linear parts; the high-temperature part is related to the liquid region and the low-temperature part is related to the solid region The latter exhibits a sharp peak at TX = 1775 K which should be located at the freezing temperature of the system (see the inset) Total energy has a sudden drop at the freezing temperature, TX = 1775 K, exhibiting a first-order-like phase transition Note that the thermodynamic melting point found experimentally for bulk Si equaled 1683 K as opposed to the 1691 ± 20 K found by MD simulation of bulk Si with the same SW potential used in the present work (see [41] and references therein) This means that the freezing temperature found for silicene has a reasonable value Constraints in the z direction of the silicene model increase the melting/freezing point compared to that found for bulk Si Interestingly, freezing (and/or melting) of 2D real materials such as silicene also exhibits a first-order behavior like that found for 3D bulk materials Note that a similar tendency of potential energy of a similar system with Tersoff potential, i.e a sudden drop at transition temperature, has been found, and the freezing temperature is found to be around 1700 K, which is close to our result [15] It is a big challenge for experimentalists to determine a melting/freezing point for one-atom-thick 2D materials such as graphene or silicene using a traditional calorimetric method Therefore, the order of freezing/melting transition of actual 2D materials is still unclear and our MD simulation highlights the situation Note that heat capacity is calculated approximately via the simple relation: CP = ΔE / ΔT Here, ΔE = E2 − E1 is the discrepancy of total energy for temperature change ΔT = T2 − T1 = 4 K In addition, the total energy per atom in the model obtained at 300 K is equal to around −3.08 eV, which is close the value for binding energy in silicene presented in [34] The evolution of the structure of the system upon cooling from the melt can be seen below As shown in figure 2, the RDF of the system at 3500 K is rather smooth and has almost only one peak indicating a liquid behavior This means that the initial configuration is an equilibrium liquid state Further cooling leads to the occurrence of additional peaks in RDF, indicating a solidification/crystallization process Additional 3. Results and discussions 3.1. Thermodynamics and evolution of structure upon cooling from the melt The evolution of the structure and some thermodynamic quantities of the system upon cooling from the melt can be seen in figures 1–3 First, temperature dependence of the total V V Hoang and H T Cam Mi J Phys D: Appl Phys 47 (2014) 495303 Figure 2. Evolution of RDF upon cooling from the melt The bold line is for T = 1700 K, which is close to TX = 1775 K Figure 3. Temperature dependence of mean coordination number The inset shows mean ring size peaks in RDF start growing clearly at around 1700 K (see the bold line in figure 2) which is close to the freezing point of 1775 K Finally, the RDF of a room temperature model has sharp peaks which appear over a large distance, clearly indicating that the final configuration is indeed a crystalline one The position of the first peak in the RDF of the model obtained at 300 K is located at around 2.36 Å, which is considered as the mean interatomic distance of the crystalline silicene It is a bit larger than the 2.28 Å obtained by DFT calculation for pristine silicene [28]; however, it is very close to the value of 2.35 Å of the bulk Si and almost coincides with the range from 2.28 to 2.50 Å proposed for silicene [8] More details of the evolution of the structure of the system upon cooling from the melt can be seen via the temperature dependence of the mean ring size and mean coordination number (figure 3) The mean coordination number (CN) of the system has a tendency to decrease with decreasing temperature, like that found for the graphene-like model [42] In contrast, the mean ring size has a tendency to increase with decreasing temperature (see the inset of figure 3) A sudden decrease in the mean CN or a sudden increase in the mean ring size at around TX = 1775 K exhibits a first-order behavior of phase transition For pristine silicene, the coordination number is the same for all atoms in the system (Z = 3) while all atoms are involved in 6-fold rings The same tendency is found for our silicene models obtained at low temperature; however, we found a small fraction of defects in our models (figures and 4) Note that we not use PBCs for the x and y Cartesian directions when the coordination number (and bond angle, see below) is calculated in order to see what happens at the edge Therefore, the mean CN of the model at low temperatures is slightly lower than 3.0, i.e it contains a small fraction of atoms with undercoordination The decrease in the mean CN upon cooling is related to the negative thermal expansion of honeycomb structure 2D materials in general [43, 44] However, unlike that found for graphene-like models in [42], the mean CN in silicene does not decrease for the whole temperature range studied (figure 3) Note that for graphene, negative thermal expansion is also found experimentally only for some temperature intervals, and not for the whole temperature range studied [44, 45] On the other hand, the mean ring size was around 4.0 at temperatures above 2000 K, indicating that the honeycomb structure has been destroyed and that the configuration in this region is indeed liquid (see the inset of figure 3) Upon cooling from the melt, the honeycomb structure is spontaneously formed in the system; i.e below freezing temperature (TX = 1775 K) almost all atoms in the system are involved in 6-fold rings and have Z = 3.2. Structure of silicene model obtained at 300 K We pause here for a detailed discussion of the structure of the silicene model obtained at 300 K Note that the model has been relaxed for 105 MD steps before analyzing the structure We found that 97% of atoms have a coordination number Z = and only 3% of atoms have Z = 1, or 4, indicating a nearly perfect crystalline honeycomb structure (figure 4) Undercoordinated atoms, i.e those with Z = 1, 2, are mainly located at the edge of the silicene sheet (see 2D visualization of atomic configuration given below) These dangling bonds at the edge are highly reactive sites for attraction of impurities which may lead to the modification of the atomic and electronic structure of silicene nanoribbons Moreover, it is found that the stability of silicene can be improved by saturating the dangling bonds at the edge by foreign atoms including H (hydrogenation [23]) Similarly, we found that 98% of the rings are 6-fold and the ring distribution is broad-ranged from 3-fold to 7-fold (see the inset of figure 4) Rings other than 6-fold can be considered as structural defects which often exhibit a higher chemical reactivity compared to that of 6-fold rings [46] Although we found the existence of small membered 3-fold and 4-fold rings, their fraction is very small In contrast, the fraction of 5-fold and 7-fold rings is significant and they can be considered as defects originating from the adjacent two 6-fold rings, i.e they are related to S–W defects Note that the existence of 4-membered rings has been found in silicene formed in slit pores [15] Unlike in graphene, the issue of rings in silicene has not been well investigated yet and so cannot be discussed However, due to close nature of the bonds in the two materials, the rings should play a similar role The presence of 4-fold rings in graphene V V Hoang and H T Cam Mi J Phys D: Appl Phys 47 (2014) 495303 Figure 5. Bond-angle and interatomic distance distributions (inset) in the model obtained at 300 K Figure 4. Coordination number and ring distributions (inset) in the model obtained at 300 K has been highlighted by a transmission electron microscopy study, in which these rings were proposed to be the result of overlapping of the two pentagons of the adjacent di-vacancies [47] In contrast, the existence of 3-fold rings in graphene has been rarely mentioned in the literature, although one can see them in MD simulation models [48] Bond-angle and interatomic distance distributions in the silicene model obtained at 300 K can be seen in figure 5 One can see that bond-angle distribution has a single peak located at around 119° which is very close to the value of 120° of a flat perfect honeycomb structure Some important points can be listed as follows: (i) Bond-angle distribution is relatively broad-ranged from 102° to 135°, indicating a significant degree of distortion of silicene obtained by cooling from the melt compared to that of the pristine one; for the latter, the bond-angle is unique and equal to 116.3° due to buckling; (ii) Interatomic distance distribution is also relatively broad-ranged from around 2.22–2.55 Å and close to the range of 2.28–2.50 Å proposed for silicene [8], which also indicates the distortion of the honeycomb structure of silicene obtained by cooling from the melt (see the inset of figure 5) Note that the interatomic distance distribution also has a single peak located at around 2.375 Å, which is close to the bond length of 2.35 Å for the bulk Si Broad bond-angle and interatomic distance distributions also indicate the existence of skew rings and rings of various sizes including small membered and multimembered ones in the silicene obtained by cooling from the melt (see 2D visualization of atomic configuration given below) This information has not yet been reported in the literature In addition, a relatively broad bond-angle distribution indicates an sp3 / sp hybridization of the silicene model [4] 2D visualization of the atomic configuration of the silicene model obtained at 300 K provides good insights into the structure of the material (figure 6) It is clear that the atomic configuration exhibits a honeycomb structure However, some important points can be drawn as follows: some grain boundaries: one is almost vertical and located in the center of the configuration presented in figure 6, two other shorter ones are located in the corners of the right-hand side edge region and the last one is located in the center of the left-hand side edge region (figure 6) Polycrystalline silicene has not yet been reported in the literature but it should be if the size of the sample is large enough and the sample is obtained by the appropriate technique Note that polycrystalline graphene has been found in practice, and polycrystalline graphene has been considered as a patchwork of coalescing graphene grains of varying lattice orientations and size, resulting from the chemical vapor deposition growth at random nucleation sites on the metallic substrates [49] (b) Silicene obtained by cooling from the melt indeed also exhibits a buckling behavior (figure 7) The presence of buckling indicates a clear preference for sp3 rather than sp hybridization of Si atoms However, the buckling is not unique for all atoms in the model (figure 7) Although it is also mentioned somewhere that the buckling is not unique in silicene, i.e the value of buckling decreases near the edge [16] or not all Si atoms are lying on the Ag surface at the same height [8], buckling distribution has not yet been reported in the literature That is, although atoms mostly have a maximal buckling of 0.44 Å setup in the simulation, the distribution of buckling is broad-ranged from to 0.44 Å, indicated by the inhomogeneous buckling of the system (figure 7) First-principles calculations show that the band structure is sensitive towards the buckling in silicene; i.e silicene structures found in recent experiments were calculated to have a finite band gap, unlike the planar or low-buckled silicene [50] Note that although the distribution of buckling is broad, it exhibits a symmetrical behavior (figure 7) It would be very interesting if our silicene obtained by cooling from the melt was taken for further DFT calculations in order to highlight the situation (c) We find a large number of vacancies including mono- and di-vacancies The silicene model obtained by cooling (a) The obtained silicene is not a monocrystalline honeycomb structure but a polycrystalline one which contains V V Hoang and H T Cam Mi J Phys D: Appl Phys 47 (2014) 495303 Figure 6. 2D visualization of atomic configuration of the crystalline silicene model obtained at 300 K various structural defects including the dangling bonds Dangling bonds at the edge are reactive sites Indeed, it is found that the oxidation process takes place only at the silicene nanoribbon terminations where the dangling bonds are abundant [51] Various aspects of typical point defects in silicene have been studied comprehensively by DFT and MD methods in [23, 33, 34, 52] The most common defects observed in 2D graphene-like structures are missing atoms (e.g vacancies), S–W defects and adatoms Due to the buckling structure, the formation of defects in silicene is easier compared to that in graphene DFT calculations show that the formation of energy of adatoms is very small or negative [34] For other defects, the formation energy is smallest for S–W defects followed by DV-2, SV-1, DV-1 and SV-2 (see more details in [34]) It is found that S–W defects in silicene are not stable and they can be recovered by thermal annealing S–Ws defects can induce a small band gap and limit the number of possible doping sites for nitrogen atoms in silicene [33, 34] SVs are the most mobile, and two SVs have a tendency to coalesce into one DV in order to lower energy Moreover, SVs may transform semimetallic silicene into metallic silicene [34] It is found that vacancies may induce a small band gap in silicene while adatoms are the most stable among point defects and may strongly affect the electronic structure of the material [34] Moreover, Si adatoms in silicene can induce long-range spin polarization as well as a significant band gap, leading to the formation of magnetic semiconductor silicene; i.e Si adatoms induce a magnetic moment of 2μB in silicene [34] Note that the atomic configuration of silicene obtained above can be reconstructed by various factors such as that found recently for both graphene and silicene [53–55] Indeed, the self-healing of vacancy defects in single-layer silicene has been found by first-principles calculations [53] It is found that the electronic and magnetic properties of suspended silicene are modified by reconstructed vacancy defects [53] It is of great interest to carry out the study in this direction for our silicene model, and research is ongoing In addition, a new 2D material—single-layer silica, similar to silicene—has been predicted theoretically and found recently in experiments (see Figure 7. Distribution of atoms with a given coordinate in the z direction of the crystalline silicene model obtained at 300 K (buckling) The dotted lines are the edges of the buckling from the melt contains vacancies of various sizes and shapes, unlike the vacancies of simple forms proposed in literature (figures and 8) Among the four common types of defects in silicene (single-vacancy, di-vacancy, S–W defects and adatoms), adatoms have not been found in our model and this is simply due to the artificial boundary conditions used in simulation (figures and 8) Due to constraints in the z direction, i.e the length of the model in the z direction being fixed equal to 0.44 Å with an elastic reflection behavior, the space is too small to allow atoms to move out from one site to form an adatom on the other site of the silicene sheet (d) It is often thought that grain boundaries of polycrystalline honeycomb structures predominantly consist of 5- and 7-fold rings [49] However, we found that they contain various types of structural defects including 5- and 7-fold rings, vacancies of various sizes/shapes, and rings of various sizes/shapes (see figures 6 and 8(d)) Therefore, grain boundaries may act as a center for attracting impurities and exhibit a highly physico–chemical performance (e) One can see in figure that the silicene nanoribbons obtained by cooling from the melt have a complicated edge containing not only armchair or zigzag parts but also V V Hoang and H T Cam Mi J Phys D: Appl Phys 47 (2014) 495303 Figure 8. Specific defects in the silicene obtained at 300 K by cooling from 2D liquid Si: (a) SV with three dangling bonds inside a multimembered ring; (b) SV with two dangling bonds inside a multimembered ring; (c) Stone–Wales defect; (d) part of grain boundary of polycrystalline silicene containing various types of defects for example, [56, 57]) It is found that 2D silica also exhibits a honeycomb-like structure [56, 57] Bilayer silica has also been the focus of much attention [58, 59] However, the details of the structure and thermodynamic properties of 2D silica obtained by cooling from the melt have not been studied yet and it is of great interest to carry out MD simulation for this new 2D material in the same way we have done in the present work for silicene As stated in the Introduction, our main aim here is studying free-standing silicene obtained by cooling from the melt; substrate effects on the structure and properties of supported silicene will be left for future work However, both free-standing and supported silicene should have a honeycomb structure and our results for free-standing silicene can provide useful information about the structure of this 2D material Depending on the behavior of the interaction between 2D materials and their substrates, substrate effects should vary Our results for free-standing silicene are more appropriate for silicene, which has a weak interaction with substrate Figure 9. Temperature dependence of a fraction of atoms with Z = and atoms involved in 6-fold rings rings are the mail building blocks in the honeycomb structure of silicene in which atoms have 3-fold coordination, it is interesting to analyze spatio-temporal arrangements of atoms involved in 6-fold rings and/or atoms with Z = in the system occurring upon cooling from the melt As shown in figure 9, the fraction of atoms involved in 6-fold rings is rather small in the high temperature region and then it strongly increases at around the freezing point, reaching almost 100% at lower temperature A similar tendency is found for the fraction of atoms with Z = Again, the sudden increase in the fraction of atoms involved in 6-fold rings and/or atoms with Z = at 3.3. Atomic mechanism of formation of silicene from the melt It is of great interest to analyze the atomic mechanism of formation of silicene upon cooling from 2D liquid Si Although the solidification of 2D systems has been studied in the past, the studies have mostly been performed for simple or colloidal systems No work related to the solidification of actual 2D materials has been found in the literature yet Since 6-fold V V Hoang and H T Cam Mi J Phys D: Appl Phys 47 (2014) 495303 solid phase occur/grow locally in the same manner throughout the system As shown in figure 10(b), atoms with Z = form various local configurations including hexagons, open chains of various sizes, rings of various sizes/shapes and free atoms This means that the formation of the new crystalline honeycomb phase does not follow the classical nucleation theory; i.e according to this theory, nucleation clusters should have the same density and the same structure as the new phase (see [60] and references therein) This problem should be analyzed in more detail 4. Conclusions We have carried out MD simulation of the formation of freestanding buckling silicene from 2D liquid Si with S–W interatomic potential Some conclusions can be drawn, as follows: • Crystalline buckling 2D silicene with a honeycomb structure formed from 2D buckling liquid Si with S–W interatomic potential has structural characteristics which are in good accordance with experiments or with the data predicted by DFT calculations However, this silicene also exhibits specific behaviors which have not been reported yet; i.e the broad bond-angle and interatomic distance distributions indicated a significant order of distortion in the structure, unlike that in pristine silicene proposed in literature Although 97–98% of atoms in silicene obtained in the present work are involved in 6-fold rings or have coordination number Z = 3, a significant amount of defects were detected • We found that the buckling of silicene obtained by cooling from the melt is not unique for all atoms in the system The distribution of buckling is broad, as indicated by the inhomogeneity in the buckling structure of the material, and the problem has not been drawn to attention until now The buckling of silicene can drastically affect the atomic and electronic structure of material; therefore, a comprehensive study in this direction is needed • Atomic mechanism of the formation of 2D buckling silicene: (i) Upon cooling from the melt, atoms involved in the 6-fold rings occur locally and homogeneously throughout the system Close to the freezing temperature their number has a sudden growth with further cooling; (ii) Atoms involved in 6-fold rings have a tendency to form clusters, including those with a hexagonal order, which may act as crystalline nucleation sites These clusters grow fast with decreasing temperature and then merge into a single percolation cluster, leading to the formation of a final rigid honeycomb configuration • Silicene obtained by cooling from the melt contains a significant amount of structural defects which have not been previously reported, including grain boundaries, vacancies of various sizes/shapes, rings of various size/ shapes and dangling points at the edges We find that the edges of silicene cannot be considered as simple zigzag or armchair edges but are more complicated; i.e they contain zigzag and armchair parts plus various defects including dangling bonds Figure 10. 2D visualization of occurrence/growth of atoms with Z = upon cooling from the melt around TX = 1775 K indicates a first-order-like phase transition In addition, we found that at freezing temperature about 55% of atoms are involved in 6-fold rings compared with 76% atoms with Z = 3; i.e atoms mostly participate in the formation of a new phase More details of the formation of silicene from 2D liquid Si can be seen in figure 10; i.e atoms with Z = are distributed homogeneously throughout the system at temperatures as high as 3500 K (figure 10(a)) At 3500 K, these atoms should be liquid since, although they have Z = 3, their distribution exhibits a diverged behavior—they not form clusters of hexagons of the honeycomb structure of silicene Further cooling to 2100 K (figure 10(b)) leads to the formation of clusters of hexagons of the honeycomb structure of silicene; these clusters can be considered as nucleation sites for subsequent growth of a new, solid phase At around the freezing point (figure 10(c)), the honeycomb structure is formed and spans throughout the 2D system This means that the formation of the rigid 2D honeycomb structure from a 2D liquid under PBCs exhibits a homogeneous behavior; i.e atoms of the V V Hoang and H T Cam Mi J Phys D: Appl Phys 47 (2014) 495303 [29] Cai Y, Chuu C P, Wei C M and Chou M Y 2013 Phys Rev B 88 245408 [30] Lin C L, Arafune R, Kawahara K, Kanno M, Tsukahara N, Minamitani E, Kim Y, Kawai M and Takagi N 2013 Phys. Rev Lett 110 076801 [31] Chen L, Li H, Feng B, Ding Z, Qiu J, Cheng P, Wu K and Meng S 2013 Phys Rev Lett 110 085504 [32] Lee C C, Fleurence A, Friedlein R, Yamada-Takamura Y and Ozaki T 2013 Phys Rev B 88 165404 [33] Sahin H, Sivek J, Li S, Partoens B and Peeters F M 2013 Phys. Rev B 88 045434 [34] Gao J, Zhang J, Liu H, Zhang Q and Zhao J 2013 Nanoscale 5 9785 [35] Roman R E and Cranford S W 2014 Comp Mater Sci 82 50 [36] Zhang X, Xie H, Hu M, Bao H, Yue S, Qin G and Su G 2014 Phys Rev B 89 054310 [37] Stillinger F H and Weber T A 1985 Phys Rev B 31 5262 [38] Plimpton S 1995 J Comp Phys 117 [39] Le Roux S and Petkov V 2010 J Appl Cryst 43 181 [40] Humphrey W, Dalke A and Schulten K 1996 J Mol Graph 14 33 [41] Broughton J Q and Li X P 1987 Phys Rev B 17 9120 [42] Hoang V V 2014 J Phys.: Condens Matter 26 205101 [43] Zkharchenko K V, Katsnelson M I and Fasolino A 2009 Phys Rev Lett 102 046808 [44] Yoon D, Son Y W and Cheong H 2011 Nano Lett 11 3227 [45] Bao W, Miao F, Chen Z, Zhang H, Jang W, Dames C and Lau C N 2009 Nat Nanotechnol 562 [46] Boukhvalov D W and Katnelson M I 2008 Nano Lett 4373 [47] Kotakoski J, Krasheninnikov A V, Kaiser U and Meyer J C 2011 Phys Rev Lett 106 105505 [48] Ranjbartoreh A R, Wang G and Nanosci J 2012 Nanotechnology 12 1398 [49] Tuan D V, Kotakoski J, Louvet T, Ortmann F, Meyer J C and Roche S 2013 Nano Lett 13 1730 [50] Huang S, Kang W and Yang L 2013 Appl Phys Lett 102 133106 [51] De Padova P, Leandri C, Vizzini S, Quaresima C, Perfetti P, Olivieri B, Oughaddou H, Aufray B and Le Lay G 2008 Nano Lett 2299 [52] Li R, Han Y, Hu T, Dong J and Kawazoe Y 2014 Phys Rev B 90 045425 [53] Ozcelik V O, Gurel H H and Ciraci S 2013 Phys Rev B 88 045440 [54] Zan R, Ramasse Q M, Bangert U and Novoselov K S 2012 Nano Lett 12 3936 [55] Robertson A W, Montanari B, He K, Allen C S, Wu Y A, Harrison N M, Kirkland A I and Warner J H 2013 ACS Nano 4495 [56] Ozcelik V O, Cahangirov S and Ciraci S 2014 Phys Rev Lett 112 246803 [57] Huang P Y et al 2012 Nano Lett 12 1081 [58] Björkman T, Kurasch S, Lehtinen O, Kotakoski J, Yazyev O V, Srivastava A, Skakalova V, Smet J H, Kaiser U and Krasheninnikov A V Sci Rep 3482 [59] Kumar A, Sherrington D, Wilson M and Thorpe M F 2014 J. Phys.: Condens Matter 26 395401 [60] Kelton K F 1991 Crystal nucleation in liquids and glasses Solid State Physics vol 45, ed H Ehrenreich and D Turnbull (New York: Academic) p 75 Acknowledgments This research is funded by Vietnam National University— Ho Chi Minh City (VNU-HCM) under grant number B2014-20-01 References [1] Kara A, Enriquez H, Seitsonen A P, Lew Yan Voon L C, Vizzini S, Aufray B and Oughaddou H 2012 Surf Sci Rep 67 [2] Xu M, Liang T, Shi M and Chen H 2013 Chem Rev 113 3766 [3] Jose D and Datta A 2014 Acc Chem Res 47 593 [4] Le Lay G, Aufray B, Leandri C, Oughaddou H, Biberian J P, De Padova P, Davila M E, Ealet B and Kara A 2009 Appl. Surf Sci 256 524 [5] Vogt P, De Padova P, Quaresima C, Avila J, Frantzeskakis E, Asensio M C, Resta A, Ealet B and Le Lay G 2012 Phys Rev Lett 108 155501 [6] Chiappe D, Grazianetti C, Tallarida G, Fanciu M and Molle A 2012 Adv Mater 24 5088 [7] De Padova P et al 2010 Appl Phys Lett 96 261905 [8] Enriquez H, Vizzini S, Kara A, Lalmi B and Oughaddou H 2012 J Phys.: Condens Matter 24 314211 [9] Meng L et al 2013 Nano Lett 13 685 [10] Jamgotchian H, Colignon Y, Hamzaoui N, Ealet B, Hoarau J Y, Aufray B and Biberian J P 2012 J Phys.: Condens Matter 24 172001 [11] Lalmi B, Oughaddou H, Enriquez H, Kara A, Vizzini S, Ealet B and Aufray B 2010 Appl Phys Lett 97 223109 [12] Aufray B, Kara A, Vizzini S, Oughaddou H, Leandri C, Ealet B and Le Lay G 2010 Appl Phys Lett 96 183102 [13] Takeda K and Shiraishi K 1994 Phys Rev B 50 14916 [14] Guzman-Verri G G and Lew Yan Voon L C 2007 Phys Rev B 76 075131 [15] Morishita T, Nishio K and Mikami M 2008 Phys Rev B 77 081401(R) [16] Cahangirov S, Topsakal M, Akturk E, Sahin H and Ciraci S 2009 Phys Rev Lett 102 236804 [17] Sahin H, Cahangirov S, Topsakal M, Bekaroglu E, Akturk E, Senger R T and Ciraci S 2009 Phys Rev B 80 155453 [18] Cahangirov S, Topsakal M and Ciraci S 2010 Phys Rev B 81 195120 [19] Song Y L, Zhang Y, Zhang J M and Lu D B 2010 Appl Surf Sci 256 6313 [20] Morishita T, Russo S P, Snook I K, Spencer M J S, Nishio K and Mikami M 2010 Phys Rev B 82 045419 [21] Houssa M, Pourtois G,Afanas’ev V V and Stesmans A 2010 Appl Phys Lett 97 112106 [22] Dzade N Y et al 2010 J Phys.: Condens Matter 22 375502 [23] Berdiyorov G R and Peeters F M 2014 RSC Adv 1133 [24] Miller M and Owens F J 2011 Chem Phys 381 [25] Quhe R et al 2012 Sci Rep 853 [26] Ni Z, Liu Q, Tang K, Zheng J, Zhou J, Qin R, Gao Z, Yu D and Lu J 2012 Nano Lett 12 113 [27] Jose D and Datta A 2012 J Phys Chem C 116 24639 [28] Scalise E, Houssa M, Pourtois G, van den Broek B, Afanas’ev V and Stesmans A 2013 Nano Res 19 ... (9pp) doi:10.1088/0022-3727/47/49/495303 Free-standing silicene obtained by cooling from 2D liquid Si: structure and thermodynamic properties Vo Van Hoang1,2 and Huynh Thi Cam Mi2 Computer Physics... still poor There is no simulation work related to the formation, structure and thermodynamics of free-standing silicene obtained by cooling from the melt It motivates us to carry out the study... comprehensive MD simulation of a relatively large silicene model containing 104 atoms and obtained ‘naturally’ by cooling from the melt provides original insights into the structure and thermodynamics