Comment | Published:

Interatomic force laws that evade dynamic measurement

Nature Nanotechnologyvolume 13pages10881091 (2018) | Download Citation



Measurement of the force between two atoms is performed routinely with the atomic force microscope. The shape of this interatomic force law is now found to directly regulate this capability: rapidly varying interatomic force laws, which are common in nature, can corrupt their own measurement.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Change history

  • 09 January 2019

    In the version of this Comment originally published, equation (4) was incorrect; see the correction notice for details. This has now been corrected in the online versions of the Comment.


  1. 1.

    Garcia, R. & Perez, R. Surf. Sci. Rep. 47, 197–301 (2002).

  2. 2.

    Giessibl, F. J. Rev. Mod. Phys. 75, 949–983 (2003).

  3. 3.

    Dürig, U. Appl. Phys. Lett. 76, 1203–1205 (2000).

  4. 4.

    Giessibl, F. J. Appl. Phys. Lett. 78, 123–125 (2001).

  5. 5.

    Sader, J. E. & Jarvis, S. P. Appl. Phys. Lett. 84, 1801–1803 (2004).

  6. 6.

    Lantz, M. A. et al. Science 291, 2580–2583 (2001).

  7. 7.

    Sugimoto, Y. et al. Nature 446, 64–67 (2007).

  8. 8.

    Gross, L., Mohn, F., Moll, N., Liljeroth, P. & Meyer, G. Science 325, 1110–1114 (2009).

  9. 9.

    Gross, L. et al. Science 324, 1428–1431 (2009).

  10. 10.

    Welker, J. & Giessibl, F. J. Science 336, 444–449 (2012).

  11. 11.

    Weymouth, A. J., Hofmann, T. & Giessibl, F. J. Science 343, 1120–1122 (2014).

  12. 12.

    Ternes, M., Lutz, C. P., Hirjibehedin, C. F., Giessibl, F. J. & Heinrich, A. J. Science 319, 1066–1069 (2008).

  13. 13.

    Kawai, S. et al. Science 351, 957–961 (2016).

  14. 14.

    Albrecht, T. R., Grütter, P., Horne, D. & Rugar, D. J. Appl. Phys. 69, 668–673 (1991).

  15. 15.

    Giessibl, F. J. Phys. Rev. B 56, 16010–16015 (1997).

  16. 16.

    Phillips, D. L. J. ACM 9, 84–97 (1962).

  17. 17.

    Tikhonov, A. N. & Arsenin, V. Y. Solutions of Ill Posed Problems (Winston, Washington, 1977).

  18. 18.

    Hansen, P. C. Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion (SIAM, Philadelphia, 1998).

  19. 19.

    Vogel, C. R. Computational Method for Inverse Problems (SIAM, Philadelphia, 2002).

  20. 20.

    Welker, J., Illek, E. & Giessibl, F. J. Beilstein J. Nanotechnol. 3, 238–248 (2012).

  21. 21.

    Sader, J. E., Hughes, B. D., Huber, F. & Giessibl, F. J. Preprint at (2017).

Download references


We acknowledge support from the Australian Research Council Centre of Excellence in Exciton Science (CE170100026), the Australian Research Council Grants Scheme and Deutsche Forschungsgemeinschaft within SFB 689, project A9, and CRC 1277, project A02. The referees are thanked for their comments.

Author information


  1. ARC Centre of Excellence in Exciton Science, The University of Melbourne, Victoria, Australia

    • John E. Sader
  2. School of Mathematics and Statistics, The University of Melbourne, Victoria, Australia

    • John E. Sader
    •  & Barry D. Hughes
  3. Institute of Experimental and Applied Physics, University of Regensburg, Regensburg, Germany

    • Ferdinand Huber
    •  & Franz J. Giessibl


  1. Search for John E. Sader in:

  2. Search for Barry D. Hughes in:

  3. Search for Ferdinand Huber in:

  4. Search for Franz J. Giessibl in:


J.E.S. supervised the project. F.H. and F.J.G. performed initial measurements on the Cu–Cu atomic system in which an anomaly between the matrix and Sader–Jarvis methods was observed. This was communicated to J.E.S. who explored with B.D.H. various theories to explain the anomaly. J.E.S. identified ill-posedness in the inverse problem, formulated the inflection point test and performed all calculations. F.H. and F.J.G. devised and performed further measurements using the Cu–CO system to validate the inflection point test. All authors analysed the data and contributed to the writing of the paper.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to John E. Sader.

About this article

Publication history



Newsletter Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing