On the exfoliation and anisotropic thermal expansion of black phosphorus

Research output: Contribution to journalArticle


  • Giuseppe Sansone
  • Antti Karttunen

  • Denis Usvyat
  • Martin Schütz
  • Jan Gerit Brandenburg
  • Lorenzo Maschio

Research units

  • University of Turin
  • Humboldt-Universität zu Berlin
  • University College London
  • University of Göttingen


Black phosphorus is a bulk solid allotrope of elemental phosphorus and can be seen as an infinite stack of phosphorene sheets. It is interesting from a technological point of view as well as from an electronic structure perspective due to the importance of electron correlation effects. In a recent paper [M. Schütz, L. Maschio, A. J. Karttunen and D. Usvyat, J. Phys. Chem. Lett., 2017, 8, 1290-1294] a highly accurate exfoliation energy has been computed. Building upon these results we carefully benchmark various dispersion-corrected density functional approximations. The choice of the range-separating function that suppresses London dispersion at short interatomic distances apparently has a substantial influence on the results. Having chosen the suitable functional, we have computed the thermal expansion coefficients of black phosphorous via a quasi-harmonic approximation. The computed coefficients manifest a strong anisotropy between the two in-plane directions. Our calculations, however, do not support the existence of negative thermal expansion in black phosphorus, as reported in some theoretical studies.


Original languageEnglish
Pages (from-to)9793-9796
Number of pages4
JournalChemical Communications
Issue number70
Publication statusPublished - 1 Jan 2018
MoE publication typeA1 Journal article-refereed

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