Two-Dimensional Disorder in Black Phosphorus and Monochalcogenide Monolayers

Mehrshad Mehboudi, Alex M. Dorio, Wenjuan Zhu, Arend Van Der Zande, Hugh O.H. Churchill, Alejandro A. Pacheco-Sanjuan, Edmund O. Harriss, Pradeep Kumar, Salvador Barraza-Lopez

Research output: Contribution to journalArticle

Abstract

Ridged, orthorhombic two-dimensional atomic crystals with a bulk Pnma structure such as black phosphorus and monochalcogenide monolayers are an exciting and novel material platform for a host of applications. Key to their crystallinity, monolayers of these materials have a 4-fold degenerate structural ground state, and a single energy scale EC (representing the elastic energy required to switch the longer lattice vector along the x- or y-direction) determines how disordered these monolayers are at finite temperature. Disorder arises when nearest neighboring atoms become gently reassigned as the system is thermally excited beyond a critical temperature Tc that is proportional to EC/kB. EC is tunable by chemical composition and it leads to a classification of these materials into two categories: (i) Those for which EC ≥ kBTm, and (ii) those having kBTm > EC ≥ 0, where Tm is a given material's melting temperature. Black phosphorus and SiS monolayers belong to category (i): these materials do not display an intermediate order-disorder transition and melt directly. All other monochalcogenide monolayers with EC > 0 belonging to class (ii) will undergo a two-dimensional transition prior to melting. EC/kB is slightly larger than room temperature for GeS and GeSe, and smaller than 300 K for SnS and SnSe monolayers, so that these materials transition near room temperature. The onset of this generic atomistic phenomena is captured by a planar Potts model up to the order-disorder transition. The order-disorder phase transition in two dimensions described here is at the origin of the Cmcm phase being discussed within the context of bulk layered SnSe.

Original languageEnglish (US)
Pages (from-to)1704-1712
Number of pages9
JournalNano letters
Volume16
Issue number3
DOIs
StatePublished - Mar 9 2016

Fingerprint

Phosphorus
phosphorus
Monolayers
disorders
Order disorder transitions
melting
Potts model
room temperature
Temperature
crystallinity
critical temperature
chemical composition
platforms
Ground state
Melting point
Melting
Phase transitions
Switches
ground state
temperature

Keywords

  • 2D atomic materials
  • black phosphorus
  • layered monochalcogenides
  • molecular dynamics
  • phase transitions
  • structural degeneracies

ASJC Scopus subject areas

  • Bioengineering
  • Chemistry(all)
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanical Engineering

Cite this

Mehboudi, M., Dorio, A. M., Zhu, W., Van Der Zande, A., Churchill, H. O. H., Pacheco-Sanjuan, A. A., ... Barraza-Lopez, S. (2016). Two-Dimensional Disorder in Black Phosphorus and Monochalcogenide Monolayers. Nano letters, 16(3), 1704-1712. https://doi.org/10.1021/acs.nanolett.5b04613

Two-Dimensional Disorder in Black Phosphorus and Monochalcogenide Monolayers. / Mehboudi, Mehrshad; Dorio, Alex M.; Zhu, Wenjuan; Van Der Zande, Arend; Churchill, Hugh O.H.; Pacheco-Sanjuan, Alejandro A.; Harriss, Edmund O.; Kumar, Pradeep; Barraza-Lopez, Salvador.

In: Nano letters, Vol. 16, No. 3, 09.03.2016, p. 1704-1712.

Research output: Contribution to journalArticle

Mehboudi, M, Dorio, AM, Zhu, W, Van Der Zande, A, Churchill, HOH, Pacheco-Sanjuan, AA, Harriss, EO, Kumar, P & Barraza-Lopez, S 2016, 'Two-Dimensional Disorder in Black Phosphorus and Monochalcogenide Monolayers', Nano letters, vol. 16, no. 3, pp. 1704-1712. https://doi.org/10.1021/acs.nanolett.5b04613
Mehboudi, Mehrshad ; Dorio, Alex M. ; Zhu, Wenjuan ; Van Der Zande, Arend ; Churchill, Hugh O.H. ; Pacheco-Sanjuan, Alejandro A. ; Harriss, Edmund O. ; Kumar, Pradeep ; Barraza-Lopez, Salvador. / Two-Dimensional Disorder in Black Phosphorus and Monochalcogenide Monolayers. In: Nano letters. 2016 ; Vol. 16, No. 3. pp. 1704-1712.
@article{b2b2137c5e74469885a92bc9b59e24b0,
title = "Two-Dimensional Disorder in Black Phosphorus and Monochalcogenide Monolayers",
abstract = "Ridged, orthorhombic two-dimensional atomic crystals with a bulk Pnma structure such as black phosphorus and monochalcogenide monolayers are an exciting and novel material platform for a host of applications. Key to their crystallinity, monolayers of these materials have a 4-fold degenerate structural ground state, and a single energy scale EC (representing the elastic energy required to switch the longer lattice vector along the x- or y-direction) determines how disordered these monolayers are at finite temperature. Disorder arises when nearest neighboring atoms become gently reassigned as the system is thermally excited beyond a critical temperature Tc that is proportional to EC/kB. EC is tunable by chemical composition and it leads to a classification of these materials into two categories: (i) Those for which EC ≥ kBTm, and (ii) those having kBTm > EC ≥ 0, where Tm is a given material's melting temperature. Black phosphorus and SiS monolayers belong to category (i): these materials do not display an intermediate order-disorder transition and melt directly. All other monochalcogenide monolayers with EC > 0 belonging to class (ii) will undergo a two-dimensional transition prior to melting. EC/kB is slightly larger than room temperature for GeS and GeSe, and smaller than 300 K for SnS and SnSe monolayers, so that these materials transition near room temperature. The onset of this generic atomistic phenomena is captured by a planar Potts model up to the order-disorder transition. The order-disorder phase transition in two dimensions described here is at the origin of the Cmcm phase being discussed within the context of bulk layered SnSe.",
keywords = "2D atomic materials, black phosphorus, layered monochalcogenides, molecular dynamics, phase transitions, structural degeneracies",
author = "Mehrshad Mehboudi and Dorio, {Alex M.} and Wenjuan Zhu and {Van Der Zande}, Arend and Churchill, {Hugh O.H.} and Pacheco-Sanjuan, {Alejandro A.} and Harriss, {Edmund O.} and Pradeep Kumar and Salvador Barraza-Lopez",
year = "2016",
month = "3",
day = "9",
doi = "10.1021/acs.nanolett.5b04613",
language = "English (US)",
volume = "16",
pages = "1704--1712",
journal = "Nano Letters",
issn = "1530-6984",
publisher = "American Chemical Society",
number = "3",

}

TY - JOUR

T1 - Two-Dimensional Disorder in Black Phosphorus and Monochalcogenide Monolayers

AU - Mehboudi, Mehrshad

AU - Dorio, Alex M.

AU - Zhu, Wenjuan

AU - Van Der Zande, Arend

AU - Churchill, Hugh O.H.

AU - Pacheco-Sanjuan, Alejandro A.

AU - Harriss, Edmund O.

AU - Kumar, Pradeep

AU - Barraza-Lopez, Salvador

PY - 2016/3/9

Y1 - 2016/3/9

N2 - Ridged, orthorhombic two-dimensional atomic crystals with a bulk Pnma structure such as black phosphorus and monochalcogenide monolayers are an exciting and novel material platform for a host of applications. Key to their crystallinity, monolayers of these materials have a 4-fold degenerate structural ground state, and a single energy scale EC (representing the elastic energy required to switch the longer lattice vector along the x- or y-direction) determines how disordered these monolayers are at finite temperature. Disorder arises when nearest neighboring atoms become gently reassigned as the system is thermally excited beyond a critical temperature Tc that is proportional to EC/kB. EC is tunable by chemical composition and it leads to a classification of these materials into two categories: (i) Those for which EC ≥ kBTm, and (ii) those having kBTm > EC ≥ 0, where Tm is a given material's melting temperature. Black phosphorus and SiS monolayers belong to category (i): these materials do not display an intermediate order-disorder transition and melt directly. All other monochalcogenide monolayers with EC > 0 belonging to class (ii) will undergo a two-dimensional transition prior to melting. EC/kB is slightly larger than room temperature for GeS and GeSe, and smaller than 300 K for SnS and SnSe monolayers, so that these materials transition near room temperature. The onset of this generic atomistic phenomena is captured by a planar Potts model up to the order-disorder transition. The order-disorder phase transition in two dimensions described here is at the origin of the Cmcm phase being discussed within the context of bulk layered SnSe.

AB - Ridged, orthorhombic two-dimensional atomic crystals with a bulk Pnma structure such as black phosphorus and monochalcogenide monolayers are an exciting and novel material platform for a host of applications. Key to their crystallinity, monolayers of these materials have a 4-fold degenerate structural ground state, and a single energy scale EC (representing the elastic energy required to switch the longer lattice vector along the x- or y-direction) determines how disordered these monolayers are at finite temperature. Disorder arises when nearest neighboring atoms become gently reassigned as the system is thermally excited beyond a critical temperature Tc that is proportional to EC/kB. EC is tunable by chemical composition and it leads to a classification of these materials into two categories: (i) Those for which EC ≥ kBTm, and (ii) those having kBTm > EC ≥ 0, where Tm is a given material's melting temperature. Black phosphorus and SiS monolayers belong to category (i): these materials do not display an intermediate order-disorder transition and melt directly. All other monochalcogenide monolayers with EC > 0 belonging to class (ii) will undergo a two-dimensional transition prior to melting. EC/kB is slightly larger than room temperature for GeS and GeSe, and smaller than 300 K for SnS and SnSe monolayers, so that these materials transition near room temperature. The onset of this generic atomistic phenomena is captured by a planar Potts model up to the order-disorder transition. The order-disorder phase transition in two dimensions described here is at the origin of the Cmcm phase being discussed within the context of bulk layered SnSe.

KW - 2D atomic materials

KW - black phosphorus

KW - layered monochalcogenides

KW - molecular dynamics

KW - phase transitions

KW - structural degeneracies

UR - http://www.scopus.com/inward/record.url?scp=84960533183&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84960533183&partnerID=8YFLogxK

U2 - 10.1021/acs.nanolett.5b04613

DO - 10.1021/acs.nanolett.5b04613

M3 - Article

C2 - 26866878

AN - SCOPUS:84960533183

VL - 16

SP - 1704

EP - 1712

JO - Nano Letters

JF - Nano Letters

SN - 1530-6984

IS - 3

ER -