The thermodynamic properties of elementary phosphorus The heat capacities of two crystalline modifications of red phosphorus, of α and β white phosphorus, and of black phosphorus from 15 to 300 K

Stephenson, C. C.; Potter, Robert; Maple, T.G.; Morrow, Joe

doi:10.1016/0021-9614(69)90037-8

Cited by 39 publications

(38 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Roth et al [23] reported that besides the amorphous red phosphorus (form I), at least three other crystalline forms of red phosphorus exist with triclinic, hexagonal and tetragonal structure. The so-called Hittorf′s phosphorus or violet phosphorus (form V) is believed the most common crystalline form of red phosphorus with a monoclinic structure [24][25][26], accepted as red-P in this work. Ruck et al [26] identified a new fibrous form of red phosphorus with triclinic structure.…”

Section: Solid Phasesmentioning

confidence: 99%

Thermodynamic assessment of the Al–P system based on original experimental data

Liang

Schmid–Fetzer

2013

Calphad

View full text Add to dashboard Cite

Section: Solid Phasesmentioning

confidence: 99%

Thermodynamic assessment of the Al–P system based on original experimental data

Liang

Schmid–Fetzer

2013

Calphad

View full text Add to dashboard Cite

“…Elemental phosphorous can exist in a variety of allotropic forms including white, red, black and their modifications, 1 and the interest in this rich chemistry has not diminished over the last century. [2][3][4][5][6][7][8][9][10][11] Today, the exfoliated 2D form of black P, phosphorene, is emerging as a unique semiconducting material for electronic applications. [12][13][14][15] The fundamental question of which form of elemental phosphorus is most stable at low temperatures and pressures has long been under debate, sparked by the discovery of black phosphorus under high pressures by Bridgman in the first half of the 20 th century.…”

Section: Introductionmentioning

confidence: 99%

“…2,3 This orthorhombic phase of P was found to be more stable at room temperature and pressure than red phosphorus on the basis of both vapor pressure and the relative heats of reaction with bromine as early as in 1914 and 1937. 2,3 These findings were later criticized by Stephenson et al 4 based on the fact that the entropies calculated from any reasonable high-temperature extrapolation of the heat capacities measured up to roomtemperature for red and black P could not reproduce the P(black)→P(red) transformation observed at 820 K 16 when the enthalpy of this transformation is taken from Jacobs, 3 and therefore they reported that there was no conclusive evidence for the stability of black P over red under ambient conditions. Later, O'Hare et al 11 used combustion calorimetry to show black P is more stable than red at low temperatures and pressures.…”

Section: Introductionmentioning

confidence: 99%

“…However, in all such calorimetric experiments, fully isolating a single and uncontaminated form of P is known to be a major challenge limiting the accuracy of measurements. 1,4,17 Today, black P is therefore accepted as probably the most stable phase at room temperature and pressure. 4,18 Allotropes of P with known crystal structures reported in the Inorganic Crystal Structure Database (ICSD) 19 are shown in Fig.…”

Section: Introductionmentioning

confidence: 99%

“…8,9 β-white is often accepted as the low temperature reference state for P. 20 Red P can be synthesized in many modifications numbered from I to V, 1 where only IV and V are known to exist in crystalline form. 4 Violet phosphorus, also known as Hittorf's phosphorus, is a monoclinic crystal comprised of linked pentagonal tubes of P. Recently Ruck et al 7 showed that the crystal structure of violet P can be ascribed to what is historically known as the red-V form, whereas the fibrous-red crystal structure is identical to the red-IV form of P.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Phosphorus allotropes: Stability of black versus red phosphorus re-examined by means of the van der Waals inclusive density functional method

2017

View full text Add to dashboard Cite

We evaluate the energetic stabilities of white, red and black allotropes of phosphorus using density functional theory (DFT) and hybrid functional methods, van der Waals (vdW) corrections (DFT+vdW and hybrid+vdW), vdW density functionals and random phase approximation (RPA). We find that stability of black phosphorus over red-V (i.e violet) is not ubiquitous among these methods, and the calculated enthalpies for the reaction P(red-V)→P(black) are scattered between-20 and 40 meV/atom. With local density and generalized gradient approximations, and hybrid functionals, mean absolute errors (MAEs) in densities of P allotropes relative to experiments are found to be around 10%-25%, whereas with vdW-inclusive methods, MAEs in densities drop below ∼5%. While the inconsistency among the density functional methods could not shed light on the stability puzzle of black versus red P, comparison of their accuracy in predicting densities and the supplementary RPA results on relative stabilities indicate that opposite to the common belief, black and red-P are almost degenerate, or the red-V (violet) form of P might even be the ground state.

show abstract

Anisotropic Thermal Conductivity of Exfoliated Black Phosphorus

et al. 2015

View full text Add to dashboard Cite

We ascertain the anisotropic thermal conductivity of passivated black phosphorus (BP), a reactive 2D nanomaterial with strong in-plane anisotropy. We measure the room temperature thermal conductivity by time-domain thermoreflectance for three crystalline axes of exfoliated BP. The thermal conductivity along the zigzag direction (86 ± 8 W m −1 K −1 ) is ~2.5 times higher than that of the armchair direction (34 ± 4 W m −1 K −1 ). TOC Figure 2Black phosphorus (BP), a stable phosphorus allotrope at ambient temperature and pressure, [1] is a two-dimensional electronic material with desirable properties for transistor, [2, 3] thermoelectric, [4] and optical sensing [5] applications. Few-layer BP flakes can be exfoliated from bulk crystals due to weak interlayer bonding. [2, 3,6] In contrast to the planar character of graphite and transition metal dichalcogenides, BP has a puckered, honeycomb structure, leading to heightened chemical reactivity [7] and pronounced in-plane anisotropy.Experimental and theoretical examinations of the electrical, [3, 4,6] optical, [3,8] mechanical, [9] and thermal [4,10,11,12] properties reveal distinct anisotropy along BP's two high-symmetry, inplane directions. These symmetry axes are commonly referred to as the zigzag and armchair directions, with lattice constants of a = 3.314 Å and c = 4.376 Å, respectively. [1] Understanding an electronic material's thermal conductivity is critical for the thermal management of small-scale devices and for exploring potential thermoelectric applications.Despite extensive electrical characterization of exfoliated BP, experimental measurements of BP's thermal properties are few. [12,13] First-principles calculations of the anisotropic thermal conductivity of monolayer BP, that is, phosphorene, predict that the thermal conductivity along the zigzag direction is two-or three-fold higher [10,11] than along the armchair direction; for example, ref. 11 finds 110 and 36 W m −1 K −1 , respectively, in the two directions. Of this, the electronic contribution to the thermal conductivity is markedly small, less than 3 W m −1 K −1 , even at a high carrier concentration of ~10 12 cm −2 . [11] Experimentally, Slack found the thermal conductivity of bulk, polycrystalline BP to be 10 W m −1 K −1 at room temperature, [13] but no anisotropic effects were examined. Only mechanically exfoliated BP flakes, with defined symmetry axes, allow an assessment of anisotropic thermal properties in all three high symmetry directions of the crystal. A recent preprint [12] reports the in-plane, anisotropic thermal transport for exfoliated, few-layer BP using micro-Raman spectroscopy; still, the extracted values were much smaller than theoretically predicted for phosphorene. For thinner (<15 nm) BP samples, the measured BP thermal conductivity is modified by phonon scattering from oxidized regions, substrates, and surface imperfections. By contrast, thermal measurements on thicker (>100 nm) BP flakes, especially those protected against ambient oxidation, provide an intrinsic ...

show abstract

The thermodynamic properties of elementary phosphorus The heat capacities of two crystalline modifications of red phosphorus, of α and β white phosphorus, and of black phosphorus from 15 to 300 K

Cited by 39 publications

References 21 publications

Thermodynamic assessment of the Al–P system based on original experimental data

Thermodynamic assessment of the Al–P system based on original experimental data

Phosphorus allotropes: Stability of black versus red phosphorus re-examined by means of the van der Waals inclusive density functional method

Anisotropic Thermal Conductivity of Exfoliated Black Phosphorus

Contact Info

Product

Resources

About