Anisotropic Thermal Expansion and Compressibility of Black Phosphorus

Riedner, R. J.; Srinivasa, S. R.; Cartz, L.; Worlton, T.G.; Klinger, R.; Beyerlein, R. A.

doi:10.1063/1.2945940

Cited by 11 publications

(16 citation statements)

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“…However, this work was cited as "private communication" in reference 19 and, to our knowledge, never published so far. This α v value is also in close agreement with the one obtained by Sansone et al 19 (α v = 20.•10 -6 K -1 ) using ab-initio computer simulations, but strongly deviates from the values reported by Keyes et al 21 and Riedner et al 20 which, however, are both affected by large uncertainties due to the few collected data points. This journal is © The Royal Society of Chemistry 20xx…”

Section: Resultssupporting

confidence: 90%

“…We have excluded the 2θ region between 6 and 7° due to the overlap of the (021) reflection of bP and (002) reflection of hBN which leads to a broad and asymmetric peak. The resulting unit-cell parameters and volume that are in excellent agreement with previous works 20,27 are listed in Table 1.…”

Section: Experimental Methodssupporting

confidence: 85%

“…To experimentally validate this scenario, accurate thermal expansion measurements are needed but, so far, very few and limited data have been made available in the literature. 20,21,22…”

Section: Introductionmentioning

confidence: 99%

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Anisotropic thermal expansion of black phosphorus from nanoscale dynamics of phosphorene layers

et al. 2020

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Section: Resultssupporting

confidence: 90%

Section: Experimental Methodssupporting

confidence: 85%

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Anisotropic thermal expansion of black phosphorus from nanoscale dynamics of phosphorene layers

et al. 2020

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“…The thermal properties of bulk BP were originally observed to be anisotropic in 1974 when greater thermal expansion was measured along the armchair direction . More recently, several reports have demonstrated higher thermal conductivity along the zigzag direction compared to the armchair direction in exfoliated BP .…”

Section: Thermal and Mechanical Anisotropymentioning

confidence: 99%

Resolving the In‐Plane Anisotropic Properties of Black Phosphorus

et al. 2017

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which provides opportunities for fundamental studies and applications that are otherwise not possible with highersymmetry materials. [9] As the prototypical 2D nanomaterial with in-plane anisotropy, BP also serves as a model system that is informing investigations of other emerging anisotropic 2D nanomaterials including ReS 2 , [10,11] GeS, [12] and borophene. [13,14] However, a review of BP anisotropic properties with an emphasis on the experimental techniques capable of resolving such anisotropy has not yet been performed. Herein, starting from the highly anisotropic atomic structure of BP, we review methods for characterizing the anisotropic properties of exfoliated BP including optical, vibrational, electronic, thermal, and mechanical anisotropy. We also provide insight into potential applications that are derived from 2D in-plane anisotropy and suggest how the results for BP can be generalized to other anisotropic 2D materials. Structural AnisotropyBP is the most stable phosphorus allotrope, and exists as a layered van der Waals crystal with an orthorhombic structure at room temperature and pressure. As shown in Figure 1a, the two in-plane directions are defined as a and c, and the out-ofplane direction is defined as b. The unit cell dimensions of bulk BP are a = 3.314 Å, b = 10.478 Å, and c = 4.376 Å, with the interlayer distance being 5.239 Å. [5] Similar to graphene, each phosphorus atom is bound to three neighbors. However, unlike graphene, BP displays out-of-plane distortion resulting in a ridge structure along the zigzag direction (i.e., the a direction) and a puckered structure along the armchair direction (i.e., the c direction), and thus non-equal bond lengths (d 1 = 2.244 Å, d 2 = 2.224 Å) and bond angles (α = 96.34°, β = 102.09°). This structure leads to substantial in-plane anisotropy and resembles the hinge-like structure seen in artificially engineered auxetic materials. [15] As a result, monolayer BP exhibits a negative Poisson ratio. [16,17] The anisotropic in-plane structure of BP can be visualized via microscopy and diffraction methods. By cleaving a bulk crystal to expose the a-c plane, scanning tunneling micro scopy (STM) images reveal atomic chains of BP along the zigzag direction as demonstrated in the left portion of Figure 1b. [18][19][20] Exfoliated BP layers can also be visualized with high-resolution transmission electron microscopy (HRTEM) (right portion of Figure 1b). [21][22][23][24] The in-plane orientation of BP sheets is Two-dimensional (2D) black phosphorus (BP) has recently attracted significant attention due to its favorable semiconducting properties and promise for nanoscale devices. Additionally, BP possesses distinctive anisotropic physical properties, which stem from the non-equal bond angles and bond strengths in its crystal structure along its orthogonal in-plane directions. Here, the anisotropic properties of BP are summarized, along with the methods to characterize them and the opportunities they present for novel technological applications. This survey of the pro...

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“…For the out-of-plane B mode of few-layer BP, which is solely due to interlayer coupling, the contribution to the Raman shift from the second term ( ) ∆ depends on the thermal expansion along the out-of-plane direction. Since the interlayer distance will not change much with the temperature, the thermal expansion along the out-of-plane direction can be ignored 69,70 . Therefore, the contribution from the crystal thermal expansion can be ignored for the B mode, as confirmed 18 by our calculations (Fig.…”

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confidence: 99%

Low-Frequency Interlayer Breathing Modes in Few-Layer Black Phosphorus

et al. 2015

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As a new two-dimensional layered material, black phosphorus (BP) is a promising material for nanoelectronics and nano-optoelectronics. We use Raman spectroscopy and first-principles theory to report our findings related to low-frequency (LF) interlayer breathing modes (<100 cm -1 ) in few-layer BP for the first time. The breathing modes are assigned to Ag symmetry by the laser polarization dependence study and group theory analysis. Compared to the high-frequency (HF) Raman modes, the LF breathing modes are much more sensitive to interlayer coupling and thus their frequencies show much stronger dependence on the number of layers. Hence, they could be used as effective means to probe both the crystalline orientation and thickness for fewlayer BP. Furthermore, the temperature dependence study shows that the breathing modes have a harmonic behavior, in contrast to HF Raman modes which are known to exhibit anharmonicity. 2 Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, Troy, New York 12180, USA.3 Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA. 2Orthorhombic black phosphorus (BP) is the most stable allotrope of phosphorus. It features a layered structure with puckered monolayers stacked by van der Waals (vdW) force 1 . Few-or single-layer BP can be mechanically exfoliated from bulk BP [2][3][4][5] . Due to BP's intrinsic thicknessdependent direct bandgap (ranging from 0.3 eV to 2.0 eV) and relatively high carrier mobility (up to ~1,000 cm 2 V -1 s -1 at room temperature) 2,4,[6][7][8][9] , it is expected to have promising applications in nanoelectronic devices [2][3][4]10 , and near and mid-infrared photodetector [11][12][13][14][15][16][17][18][19] . Recently, high performance thermoelectric devices were also predicted based on BP thin films [20][21][22] . With the surge of interest in two-dimensional (2D) materials (such as graphene and transition metal dichalcogenides (TMDs)) 23,24 , BP has become a new attraction since 2014 because it bridges the gap between graphene and TMDs, and offers the best trade-off between mobility and on-off ratio 3 . Moreover, the unique anisotropic puckered honeycomb lattice of BP leads to many novel in-plane anisotropic properties, which could lead to more applications based on BP 3,9,25,26 .Phonon behaviors play an important role in the diverse properties of materials 27 , which has been intensively studied in vdW layered materials, such as graphene and TMDs [28][29][30][31][32][33][34][35] . Raman spectroscopy is a powerful non-destructive tool to investigate the phonons and their coupling to electrons, and has been successfully applied to vdW layered materials [36][37][38][39][40] . Due to the lattice dynamics of vdW layered compounds, the phonon modes in these materials can be classified as high-frequency (HF) intralayer modes and low-frequency (LF) interlayer modes 27 . Intralayer modes involve vibrations from the intralayer chemical bonds (Fig. 1c), and the associated frequencies ...

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Anisotropic Thermal Expansion and Compressibility of Black Phosphorus

Cited by 11 publications

References 0 publications

Anisotropic thermal expansion of black phosphorus from nanoscale dynamics of phosphorene layers

Anisotropic thermal expansion of black phosphorus from nanoscale dynamics of phosphorene layers

Resolving the In‐Plane Anisotropic Properties of Black Phosphorus

Low-Frequency Interlayer Breathing Modes in Few-Layer Black Phosphorus

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