First-Principles Investigation of Black Phosphorus Synthesis - The

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First-Principles Investigation of Black Phosphorus Synthesis Pola Shriber, Atanu Samanta, Gilbert Daniel Nessim, and Ilya Grinberg J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b00055 • Publication Date (Web): 20 Mar 2018 Downloaded from http://pubs.acs.org on March 21, 2018

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The Journal of Physical Chemistry Letters

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

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. Keywords: Black phosphorus, BP, Black phosphorus synthesis, Black phosphorus energy Orthorhombic black phosphorus (BP) is a high density,1–5 stable,6,7 2D layered material with 8 atoms per unit cell with layers separated by 3.21-3.73 Å and stabilized by vdW 1

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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 few layer material.20 Additionally, few-layer phosphorene possesses a tunable, thickness-dependent 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 devices9,27. 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. Black phosphorus 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 phosphorus1. 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 formation of RP, while BP is obtained under high pressure or at ambient pressure in the presence of Sn and 2


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I catalysts. 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 black phosphorous 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 red phosphorus45 and black phosphorus, respectively.2 Since both black and fibrous red phosphorus are stabilized by vdW interactions,6 these interactions must be included in the theoretical calculations. Therefore, we have performed DFT-D2 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 3x5x1 and 2x2x1 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. Bulk black phosphorus preparation traditionally involves heating a sealed ampoule containing amorphous red phosphorus to approximately 600°C.29–32 Following controlled cooling, black phosphorus 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 an 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: (Eq. 3) ERP(N) = 4N E*bulk,RP +Eedge,RP And the energy per atom E*RP(N) is given by: (Eq. 4) E*RP(N) = E*bulk,RP +(1/4N) Eedge,RP 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 7



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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.

Figure 3. Structures of black phosphorus and red phosphorus (A) Top left to bottom right: final relaxed structures for black phosphorus constructed from 11,12,13 and 14 P4 molecules that are the building blocks of BP and RP. Unsaturated bonds and strained P4 groups can be seen on sheet edges. Green arrows indicate unsaturated bonds. (B) Top to bottom: final relaxed structures of red phosphorus constructed from 8,9,10 and 11 P4 molecules. Strained P4 groups are found on the two opposite ends of the growing tubes.

To study the effect of the pressure on the BP synthesis, we performed DFT-D2 calculations for bulk RP and bulk BP at different pressures. As expected, the larger volume of the RP allotrope leads to the increase of the energy difference between RP and BP at higher 8


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pressures, with BP becoming increasingly favored (Fig. 4). Such a change in the relative energies of bulk P atoms of RP and BP (destabilization of the RP allotrope) will also lead to an earlier crossover between RP and BP nuclei stabilities.

Figure 4. Pressure and catalyst effect on BP synthesis (A) Enthalpy (H=U+PV) of both allotropes increases with growing pressure, as expected, due to the force exerted on the phosphorus atoms. The effect of pressure on red phosphorus enthalpy is more prominent than on black phosphorus enthalpy, resulting in increasing difference ∆H = HRED – HBLACK between the two allotropes. Inset: Absolute values of BP and RP enthalpy with growing pressure. (B) Pressure and temperature conditions required for black phosphorus synthesis are inversely related. The zero pressure reactions are executed without a catalyst and are found on the same line with other reactions. (C) Iodine atoms (yellow) will saturate the dangling bonds on the black phosphorus surface while tin atoms (purple) on both sides of the black phosphorus sheets will interact via vdW forces, increasing black phosphorus stability.

Experimentally, higher temperatures are required for BP synthesis at lower pressures and vice versa.48 Interestingly, the plot of synthesis temperature versus pressure shows the same linear dependence regardless of whether a catalyst is present (lower P) or absent (higher P). 32,48,49

29-

We attribute this to the fact that the synthesis temperature is essentially equivalent to the

temperature necessary to melt RP. At higher pressures, the slow cooling following such melting leads to the formation of BP due to the destabilization of the RP nuclei. At lower pressure, cooling in the absence of catalyst will lead to the reassembly of RP while in the presence of catalyst BP is obtained.29,32,34,47,48,50

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The BP growth pathway and the chemical bonding of the BP nuclei discussed above naturally suggest a mechanism for the action by the Sn/I catalysts used for the synthesis of BP at ambient pressure. The unfavorability of small BP nuclei relative to the RP nuclei is due to the large number of P4 groups with strained P bonds present at the perimeter of the 2D BP nucleus. The presence of I is likely to lead to the formation of P-I bonds (because PI3 enthalpy of formation is negative) for the P atoms at the edges that are forced to make the strained bonds in the edge

P4

groups in the absence of catalyst. Such P-I bonds will drastically reduce the energy cost of the capping groups and will shift the energies of the BP nuclei down making BP synthesis pathways competitive and preferred relative to the RP pathways. As the BP nucleus grows, the P-I bonds will be replaced by the P-P bonds of the added P4 units. This is enabled by the relatively weak energy of the P-I bond. The much stronger P-X (X=Br,Cl,F) bonds make other halogens unsuitable for use as catalysts because once formed, the P-X bonds will not be easily broken. By contrast, the enthalpy of formation of PI3 is quite small (-46 kJ/mol) so that the P-I bonding is close to the ideal neither too strong nor too weak (∆G =0) for the catalyst. Among metals, only Sn and to lesser degree Pb have been found to be suitable for BP synthesis catalysis47. 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 of BP preserves the vdW interactions between such clusters (similar to vdW transparency of graphene found recently),51 while the more bulky tubular structure of RP pushes the Sn clusters apart and reduces or eliminates their attractive vdW interactions. This provides a further stabilization for the BP nuclei, enabling the synthesis of BP at ambient pressure.

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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 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 Fig. 2a while the results for the RP and BP pathways in the presence of Sn and I are shown in Fig. S5. It can be seen that the introduction of I2 leads to the 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 48-atom Sn clusters the stronger vdW interactions between Sn and BP lead to a smaller energy leads to the preference for BP over RP for all cluster sizes. 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. 11



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ACKNOWLEDGEMENTS 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. ASSOCIATED CONTENT Supporting information Description of the DFT methodology, additional results of the calculations for BP and RP reaction pathways in different conditions.

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First-Principles Investigation of Black Phosphorus Synthesis - The

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