First-Principles Investigation of Black Phosphorus Synthesis - The

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Cite This: J. Phys. Chem. Lett. 2018, 9, 1759−1764

First-Principles Investigation of Black Phosphorus Synthesis Pola Shriber, Atanu Samanta, Gilbert Daniel Nessim, and Ilya Grinberg* Department of Chemistry, Bar-Ilan University, Ramat Gan, Israel 52900

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S Supporting Information *

ABSTRACT: Black phosphorus (BP) is a layered semiconductor with outstanding properties, making it a promising candidate for optoelectronic and other applications. BP synthesis is an intriguing task largely due to the insufficient understanding of the synthesis mechanism. In this work, we use density functional theory calculations to examine BP and its precursor red phosphorus as they are formed from P4 building blocks. Our results suggest that, without external effects such as pressure or addition of a catalyst, the precursor is energetically favored in the initial steps of the synthesis, even though BP is the more stable allotrope. The higher energy of BP is dictated by its 2D geometry that gives rise to the higher number of high-energy strained bonds at the edge compared to the 1D geometry of red phosphorus. The elucidated BP formation pathway provides a natural explanation for the effectiveness of the recently discovered Sn/I catalyst used in BP synthesis.

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rthorhombic black phosphorus (BP) is a high density,1−5 stable,6,7 2D layered material with eight atoms per unit cell with layers separated by 3.21−3.73 Å and stabilized by vdW interactions.8−10 Recently, the successful exfoliation11−14 of BP has been used to obtain the phosphorus analogue of graphene (phosphorene), which has attracted intense research interest15,16 due to its numerous intriguing properties, many of which depend on the number of layers. For example, phosphorene shows high carrier mobility with exceptionally high hole mobility and anisotropy between electrons and holes across x and y directions,11,12,17,18 phonon anisotropy,19 and anisotropic optical responses of a few-layer material.20 Additionally, few-layer phosphorene possesses a tunable, thicknessdependent bandgap.20−26 These qualities make it a promising candidate for various applications27 such as lithium ion batteries,13,28 field effect transistors,11,14 and optoelectronic devices.9,27 Nevertheless, the practical use of phosphorene in devices is hindered by its oxidation upon exposure to air and by the extremely high cost of the BP material synthesis. BP is traditionally prepared at high temperatures29−32 and/or high pressures33,34 from its precursor red phosphorus (RP), from violet phosphorus,35 or from white phosphorus.1 Less common methods involve the use of shear stress,36,37 mercury catalysis,38 and bismuth flux.3,39,40 Unfortunately, these procedures are complicated, time-consuming, costly, and suffer from low yield. Both first-principles studies6,7 and experimental results1−5 indicate that BP is the lowest-energy phosphorus allotrope that is slightly lower in energy than the RP allotrope. While BP is a 2D planar material, RP consists of 1D phosphorus tubes and is found in either amorphous or crystalline forms with both structures obeying the rule that each P atom bonds to three neighboring P atoms. Upon melting, both BP and RP transition to the liquid phosphorus state consisting of P4 molecules. The cooling of the liquid at ambient conditions leads to the © 2018 American Chemical Society

formation of RP, while BP is obtained under high pressure or at ambient pressure in the presence of Sn and I catalysts.47 The greater thermodynamic stability of BP relative to RP indicates that the lack of BP formation at ambient conditions in the absence of the catalyst is due to kinetic barriers. These barriers are removed by the Sn/I catalyst, leading to the synthesis of BP from the RP precursor. Here, we use dispersion-corrected density functional theory (DFT-D2)41 calculations to understand the formation of BP and RP allotropes and to elucidate the microscopic origin of the kinetic barriers to BP formation. We find that the difficulties in the synthesis of BP can be easily understood by considering the polymerization process that leads to the formation of RP and BP from the P4 molecule liquid state.42 The mechanism of the BP formation process also indicates that both Sn and I play a crucial role in the BP synthesis and provides guidance for the use of other possible catalysts and more efficient BP synthesis. All calculations were performed using the Quantum Espresso package.41,43,44 For bulk RP and BP, we have used the crystal structure coordinates of fibrous RP45 and BP, respectively.2 Because both black and fibrous RP are stabilized by vdW interactions,6 these interactions must be included in the theoretical calculations. Therefore, we have performed DFTD2 calculations that account for the dispersion forces of vdW interactions. To perform the calculations, we used the PBE exchange−correlation functional, plane wave cutoff of 30 Ry, GBRV P46 pseudopotential and 3 × 5 × 1 and 2 × 2 × 1 Monkhorst−Pack k-point sampling for bulk BP and RP. For the large supercells used for calculations on the finite-size BP and RP structures, Γ point k-point sampling was found to be converged. Received: January 7, 2018 Accepted: March 20, 2018 Published: March 20, 2018 1759

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Figure 1. Competing synthesis pathways of BP and RP: (a) Breaking-up of RP tubes to P4 molecules upon heating is followed by their assembly to either BP or RP when the temperature is lowered again; (b) P4 molecules are added in a polymerization-like reaction to form either BP or RP.

We attribute this difference in stability to the existence of unsaturated bonds and P4 strained groups on the edges of the BP and RP nuclei. A close inspection of the large BP structures (Figure 3) shows that the bonds between the P atoms inside of the cluster are essentially identical to those in the bulk BP sheet. However, at the edge, some atoms form highly strained bonds (P4 groups) to satisfy the requirement of three bonds per P atom, and some only have two bonds. This leads to a higher energy of the surface region of the BP growth nucleus. Accordingly, as is seen in Figure 2b, the energetic profile of the BP growing sheets is correlated with the number of unsaturated bonds and strained P4 group bonds on the sheet edges. The overall increase in the material stability is accompanied by irregularities that follow the existence of the unsaturated bonds (Figure 2b, blue line) found in several of the examined structures. The only exceptions to this rule are the 12- and 3units structures, where the energy is lower despite the presence of unsaturated bonds. For the 12-unit structure, this may be explained by the smaller number of strained P4 groups (Figure 2b, green line) on the edges (5 instead of 6 for the 11- and 13unit structures, Figure 3). For the RP tubes shown in Figure 3, there are no unsaturated P atoms and the strained P4 groups are present only at the two ends of the tube, while all other P atoms have three P bonds that are very similar to those found in bulk fibrous RP. The much smaller surface area and therefore a much smaller number of strained or unsaturated P bonds allow a rapid decrease in the energy per atom for RP, making the RP synthesis pathway kinetically preferred. We note that the effect of the strained bonds is much more important as even in the absence of any unsaturated bonds (number of P4 units = 4, 6, 8, 10, 14) the BP energy is higher than that of RP. We find that the BP and RP energies can be expressed as simple functions of the number of P4 units based on the separation of the RP and BP nuclei into the bulk-like and edge regions. For the 2D BP with the total number of N P4 units, the number of P atoms in the bulk-like region is proportional to N, while the number of P atoms at the edge is proportional to √N. We can therefore write

Bulk BP preparation traditionally involves heating a sealed ampule containing amorphous RP to approximately 600 °C.29−32 Following controlled cooling, BP is obtained with a conversion ratio of 8 this expression captures the trend quite well. For smaller BP-like clusters, the strong changes in the cluster shape give rise to different values of E*edge,BP. For a RP-like cluster containing N P4 units, the number of the P atoms in the bulk-like regions is proportional to N, while the number of the P atoms at the edges of the tube is fixed. Therefore, the total energy of the RP cluster is given by E RP(N ) = 4NE*bulk,RP + Eedge,RP

(3)

Aand the energy per atom E*RP(N) is given by E*RP (N ) = E*bulk,RP + (N /4)Eedge,RP

(4)

The fit of the RP DFT data to eq 4 shows that this inverse linear relationship is valid for N > 3. Extrapolation to 1/N = 0 results in the energy that is higher than the calculated energy of crystalline fibrous RP. This because the tube-like clusters examined in our study do not necessarily correspond to the lowest possible energy RP structures but are rather sample structures that can be found in amorphous (higher-energy) RP. Comparison of the extrapolations of RP and BP energies to small 1/N (large N) shows that the crossover in the relative RP−BP stability occurs at around N = 75. Our results show that the difficulty in the synthesis of BP originates from the fundamental differences in dimensionality between the 1D RP and the 2D BP. The much smaller surface area of the 1D RP tubes leads to the much more rapid decrease in energy with cluster size. This kinetically favors the growth of RP-like nuclei that are too large to be transformed to BP at the sizes (N > 75) where BP is energetically favored. 1762

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Among metals, only Sn and to lesser degree Pb have been found to be suitable for BP synthesis catalysis.47 The melting point of Sn is lower than that of RP and BP so that the growth/ polymerization of BP occurs in the presence of molten Sn consisting of Sn clusters. It is likely that the small vertical size and 2D nature of BP preserves the vdW interactions between such clusters (similar to vdW transparency of graphene found recently),51 while the bulkier tubular structure and 1D nature of RP pushes the Sn clusters apart and reduces or eliminates their attractive vdW interactions. This provides further stabilization for the BP nuclei, enabling the synthesis of BP at ambient pressure. To prove the hypothesized catalytic mechanism of Sn/I, we have performed calculations of the RP and BP polymerization pathways in the presence of I2, Sn, and Sn−I2 (see the Supporting Information). The results for the energetics of the RP and BP pathways in the presence of Sn only and I only are shown in Figure 2a, while the results for the RP and BP pathways in the presence of Sn and I are shown in Figure S5. It can be seen that the introduction of I2 leads to relief of the strained bonding of the strained edge P4 groups, making the energies of RP and BP much closer to each other. Nevertheless, RP is still slightly preferred. Similarly, in the presence of 48atom Sn clusters, the stronger vdW interactions between Sn and BP lead to a smaller energy that leads to the preference for BP over RP for all cluster sizes. The calculated binding energy also shows that BP is more stable with Sn cluster compared to the RP, as shown in Supplementary Figures S6(a) and S6(b), due the higher number of P and I atoms in contact with Sn. In addition, the interaction between I and Sn increase P−I bond length, as shown in Supplementary Figure S3, which will reduce the required energy for breaking P−I bonds and helps for preferable P4 molecule attachment to the sheet. Such an energetic preference for the BP pathways would lead to the synthesis of BP only. We have used DFT-D2 calculations to model the growth of BP and RP nuclei from liquid phosphorus. Growth of RP and BP was modeled as a 1D and 2D polymerization process, respectively, consisting of successive addition of P4 molecules. We have found that the much larger edge area of BP leads to its higher energy in the initial growth stage, strongly favoring the growth of 1D RP nuclei. Once formed, these nuclei will be trapped in the RP structure local minimum even at sizes at which BP is energetically preferred (N > 75 at ambient pressure). The application of pressure shifts the relative energetics of RP and BP pathways, destabilizing the bulkier RP allotrope and enabling the synthesis of BP even without catalysts. Our results suggest that both Sn and I play a crucial role in BP synthesis, with I atoms saturating the P atoms at the edge of the BP nucleus and obviating the need for the formation of strained bonds in P4 edge groups and with Sn atoms stabilizing the flat BP sheets due to their transparency to the attractive vdW interactions between the Sn atoms. We hope that our work will stimulate further research into the synthesis and applications of BP-based materials.

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Description of the DFT methodology and additional results of the calculations for BP and RP reaction pathways in different conditions (PDF)

AUTHOR INFORMATION

ORCID

Pola Shriber: 0000-0003-3540-4796 Gilbert Daniel Nessim: 0000-0003-0738-5436 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors wish to thank the Israel National Research Center for Electrochemical Propulsion (INREP) for funding this work under contract by the Israeli Committee for Higher Education and the Israel Prime Minister’s Offices Fuel Choices and Smart Mobility Initiative. The authors would like to thank Prof. Javier Junquera for his assistance in SIESTA code calculations.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.8b00055. 1763

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