The role of P 3s2 lone pair (E) in structure, properties and phase transitions of black phosphorus. Stereochemistry and ab initio topology analyses
Graphical abstract
Introduction
Black phosphorus is at the center of active research owing to its particular layer structure made of phosphorene layers, partly analogous to graphene ones. The stable solid form crystallizes in the orthorhombic system (space group Cmce) as reported by Hultgren et al. in 1935 [1], here designed by O-P (A17 in literature). Brown & Rundqvist published refined structural data in 1965 [2] confirming its original layered packing. A little bit earlier, in 1963, Jamieson reported that under ~5 GPa O-P develops a phase transition to the rhombohedral (trigonal) system exhibiting a distinct layered structure after a rearrangement of atoms, R–P (A7) [3,4]. Applying higher pressures, ~10 GPa [4] or ~11 GPa [5], a new transition occurs giving a simple cubic form C-P isostructural with polonium Po. Important to note are the large electrical conductivity changes with phase transitions from semiconductor O-P [1,3] to semi-metallic R–P and finally metallic C-P [3]. This has been confirmed in a study by Kikegawa et al. who locate this transition at 5.5 GPa; they also report the transformation of semi-metallic R–P into a metallic cubic phase C-P occurring at ~11 GPa [3,6]. More recently a systematic study has been made by Scelta et al. using synchrotron radiation (ESRF) at up to 30 GPa [7]; it shows the evolution of R–P structure up to 27.6 GPa indicating the presence of a pseudo cubic sub-lattice in its X-ray data; finally an ultimate transition to the cubic form is reported at pressures >~30 GPa. A study at low temperature and high pressure allowed Shirotani et al. [4] to show that the minimal pressures to produce the phase transitions were higher at 21 K than those at 77 K. Li et al. [8] studied resistivity, magnetoresistivity and Hall resistivity at low temperatures and high pressures, accompanying the phase transitions and confirming the onset of superconductivity at very low temperatures (7 K or below) in black phosphorus single crystal.
Our deep interest for lone pair stereochemistry covering a large panel of atoms, a systematic work supported by Density Functional Theory (DFT) Electron Localization Function (ELF) [[9], [10], [11]], pushed us to reinvestigate this P element in these O-P to R–P and finally C-P allotropes, showing interesting behavior at high pressure and room temperature.
It has been shown in previous papers [[9], [10], [11]] that lone pairs, designed by E, possess some pertinent structural data attached to each ns2 element as demonstrated by Electron Localization Function (ELF) maps from DFT computations, briefly recalled hereafter.
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Three dimensional electronic density data show an excess concentration of electronic density in a small volume, close to some atom M*, having an intensity maximum, the so called centroid Ec of a lone pair, the coordinates of which can be determined;
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the atom-lone pair distance M*-Ec can be calculated;
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Ec is accompanied by a larger electron cloud E appreciated by its volume, roughly an ellipsoid, which corresponds to a sphere of influence (radius rE) a volume often compared to the one of an oxygen or a fluorine atom [12]. Its center is often slightly displaced from Ec, the electronic cloud being sensitive to its environment and showing a certain degree of plasticity;
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in all circumstances, E also shows a resistance to compression.
The purpose of the present article is to bring new elements of understanding about the structure of the black phosphorus allotropes and to the transitions between them under pressure increase at ambient temperature, based on the identification of lone pairs, their positions, their steric occupation, and their reactivity upon pressure underlying the phase transformations, for which we propose network rebuilding mechanisms.
In the following part, we will briefly recall our investigation methods; the rest of this document features five more parts, devoted to O-P, R–P and C-P, respectively, and in between to the transitions from one structure to another.
Section snippets
X-ray data
We start from well-known and established structural data for phosphorus allotropes. Black P structures in the first pressure domain up to 2,66 GPa were taken from the results of investigations by Cartz et al. [13], in the orthorhombic system and Cmce space group corresponding to the O-P phase. For higher pressures (6,05 up to 27,55 GPa) corresponding to rhombohedral R–P structures, we have used the data of Jamieson [3], Kikegawa et al. [6] and Scelta et al. [7]. Finally, cubic P
Classical description of the black phosphorus crystal structure
A refinement of black phosphorus crystal structure was reported by Brown and Rundqvist in 1965 [2]. This O-P variety crystallizes in the orthorhombic system with a base centered space group Cmce. X-ray data are reported in Table 1 of Appendix. The P atom x,y,z coordinates occupy the peculiar 8f (0,y,z) Wyckoff position which corresponds to a mirror plane perpendicular to [100].
In Fig. 1 a perspective view of O-P structure is given according to X-ray investigations. The drawing respects exactly
Description of the crystal structure
The chosen cell representation of R-PE is hexagonal (with a = b, c, α = β = 90° and γ = 120°): it is the most common representation of a rhombohedral system and also the easiest to grasp and to describe features of the three dimensional network.
The R–P structure, isostructural with the As type, has been studied in the same way as the O-P phase using the data of Scelta et al. in the 6.05–27.55 GPa pressure range, completed by a lone pair search with systematic Ec (x,y,z) coordinates
R2-[PE] → C-[PE] phase transition mechanism
The phase transition from the layered R2-[PE] structure, to the three dimensional cubic C-[PE] is latent in the network architecture of the former. Upon increasing pressure there is a slip of the [P] layers and a flattening of the double E layers. The zigzag layer … P4P7P6P8 … slips toward the … P2PP0P1P9 … one formed by P-P bonds (black sticks), these two layers being still separated by the double layer of split lone pairs Ed with P-P distances marked by red sticks as illustrated in Fig. 12a
About pseudo-cubic phase presence in R2-[PE] according to X-Ray data
Scelta et al. [7] report in their X-ray study under increased pressures the presence of a pseudo-cubic phase (pC-[PE]). Recalling our description of the phase transition R2-[PE] to C-[PE] we can make a proposal concerning this pC-[PE] phase.
The calculated powder XRD patterns of R1-[PE] (blue) at 6.05 GPa, R2-[PE] (red) at 27.55 GPa and C-[PE] (black) one at 32 GPa [6] are drawn in Fig. A2 in Appendix. Comparing R1 and R2 peaks we mostly observe a shift towards higher Bragg angles from R1 to R2
Recapitulation of black P allotropes and phase transitions
To get a global view of black phosphorus structure evolution at room temperature and various pressures in the range 0 up to 32 GPa a diagram of the reduced volume vs. pressure V(Å3) = f (p) is given in Fig. 14. rV is the reduced volume of [PE] obtained by the cell volume divided by the number Z of [PE] in the cell, rV = V/Z.
Data points are available for some pressure ranges: from 0.1 to 2.66 GPa [5] and to 5.5 GPa [13] for O-[PE], from 5.5 GPa to 9.7 GPa [13] and from 6.05 to 27.55 GPa [14] for
Concluding notes
Orthorhombic black phosphorus exhibits in its crystalline network wide empty space between its puckered [P]n layers. Such peculiar puckered network architecture is also the case of Ga but in the latter case the layers are firmly associated by a Ga–Ga bond resulting in a much shorter parameter perpendicular of the layers. The difference resides in the existence of lone pairs in the case of phosphorus. These lone pairs play a major role in black phosphorus structure and transformations under high
Acknowledgements
J. Galy wishes to thank LCTS - CNRS for providing laboratory facilities. Thanks also to G. Couégnat (LCTS) for his efficient support in post-processing computations.
Dr. Jean GALY, Emeritus Senior Director of CNRS. Obtained his PhD in Structural Physico-Chemistry in 1966 at LCI of Bordeaux University. Stayed 1975-88 at LCC-CNRS (Toulouse), then was Founder and Director of CNRS research laboratory CEMES 1988–1996. Also founded the technical platform PNF2 (SPS) in Toulouse University (2004). Former Chairman of Scientific Program committees of ILL, ESRF (Grenoble) and LURE (Orsay). His main research topics are: Solid state chemistry (Vanadium oxides and lone
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Dr. Jean GALY, Emeritus Senior Director of CNRS. Obtained his PhD in Structural Physico-Chemistry in 1966 at LCI of Bordeaux University. Stayed 1975-88 at LCC-CNRS (Toulouse), then was Founder and Director of CNRS research laboratory CEMES 1988–1996. Also founded the technical platform PNF2 (SPS) in Toulouse University (2004). Former Chairman of Scientific Program committees of ILL, ESRF (Grenoble) and LURE (Orsay). His main research topics are: Solid state chemistry (Vanadium oxides and lone pair stereochemistry in crystalline compounds), X-ray diffraction & diffusion, Electron Microscopy, Fast Sintering. He is the author of ~400 papers (h-index 44), and has directed ~50 PhD theses. In 1998 he received the Alexander von Humboldt award (Solid State Chemistry).
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