Jump to main content
Jump to site search
Access to RSC content Close the message box

Continue to access RSC content when you are not at your institution. Follow our step-by-step guide.

Issue 46, 2018
Previous Article Next Article

Atomic structure of boron resolved using machine learning and global sampling

Author affiliations


Boron crystals, despite their simple composition, must rank top for complexity: even the atomic structure of the ground state of β-B remains uncertain after 60 years’ study. This makes it difficult to understand the many exotic photoelectric properties of boron. The presence of self-doping atoms in the crystal interstitial sites forms an astronomical configurational space, making the determination of the real configuration virtually impossible using current techniques. Here, by combining machine learning with the latest stochastic surface walking (SSW) global optimization, we explore for the first time the potential energy surface of β-B, revealing 15 293 distinct configurations out of the 2 × 105 minima visited, and reveal the key rules governing the filling of the interstitial sites. This advance is only allowed by the construction of an accurate and efficient neural network (NN) potential using a new series of structural descriptors that can sensitively discriminate the complex boron bonding environment. We show that, in contrast to the conventional views on the numerous energy-degenerate configurations, only 40 minima of β-B are identified to be within 7 meV per atom in energy above the global minimum of β-B, most of them having been discovered for the first time. These low energy structures are classified into three types of skeletons and six patterns of doping configurations, with a clear preference for a few characteristic interstitial sites. The observed β-B and its properties are influenced strongly by a particular doping site, the B19 site that neighbors the B18 site, which has an exceptionally large vibrational entropy. The configuration with this B19 occupancy, which ranks only 15th at 0 K, turns out to be dominant at high temperatures. Our results highlight the novel SSW-NN architecture as the leading problem solver for complex material phenomena, which would then expedite substantially the building of a material genome database.

Graphical abstract: Atomic structure of boron resolved using machine learning and global sampling

Back to tab navigation

Supplementary files

Article information

02 Aug 2018
11 Sep 2018
First published
11 Sep 2018

This article is Open Access
All publication charges for this article have been paid for by the Royal Society of Chemistry

Chem. Sci., 2018,9, 8644-8655
Article type
Edge Article

Atomic structure of boron resolved using machine learning and global sampling

S. Huang, C. Shang, P. Kang and Z. Liu, Chem. Sci., 2018, 9, 8644
DOI: 10.1039/C8SC03427C

This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. Material from this article can be used in other publications provided that the correct acknowledgement is given with the reproduced material and it is not used for commercial purposes.

Reproduced material should be attributed as follows:

  • For reproduction of material from NJC:
    [Original citation] - Published by The Royal Society of Chemistry (RSC) on behalf of the Centre National de la Recherche Scientifique (CNRS) and the RSC.
  • For reproduction of material from PCCP:
    [Original citation] - Published by the PCCP Owner Societies.
  • For reproduction of material from PPS:
    [Original citation] - Published by The Royal Society of Chemistry (RSC) on behalf of the European Society for Photobiology, the European Photochemistry Association, and RSC.
  • For reproduction of material from all other RSC journals:
    [Original citation] - Published by The Royal Society of Chemistry.

Information about reproducing material from RSC articles with different licences is available on our Permission Requests page.

Social activity

Search articles by author