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South African Journal of Science

versión On-line ISSN 1996-7489
versión impresa ISSN 0038-2353

S. Afr. j. sci. vol.109 no.5-6 Pretoria ene. 2013




Nanoscience and the Scherrer equation versus the 'Scherrer-Gottingen equation'



R.E. (Ted) Kroon

Department of Physics, University of the Free State, Bloemfontein, South Africa




Keywords: Scherrer; X-ray diffraction; nanoscience; nanotechnology; citation



Interest in nanoscience and nanotechnology in South Africa is strong1 and has received further momentum with the recent launch of the National Nanoscience Postgraduate Teaching and Training Programme. Nanotechnology is generally considered to be a relatively new field and so it may surprise some that the year 1912 has recently been proposed for the birth of modern nanotechnology, to coincide with the invention of the immersion ultramicroscope by Zsigmondy.2 Although modern microscopes have atomic resolution, the average size of nanoparticles is routinely estimated from the width of X-ray diffraction pattern peaks using a simple equation first published by Scherrer in 1918.3 In fact, the size of gold nanoparticles determined by Scherrer substantially confirmed the pioneering work of Zsigmondy.4

A recent note by Holzwarth and Gibson5 gives some historical background and motivates why the equation should be associated with Scherrer alone, instead of incorrectly being referred to as the 'Debye-Scherrer equation'. They urge those working in the field to review the basic physics involved, to note the various factors that contribute to the broadening of X-ray diffraction peaks and to cite Scherrer's original paper where appropriate. Therefore it is of interest that a significant and growing number of recent articles attribute the original paper to two authors: P Scherrer and N.G.W. Gottingen,6-14 although it is clear from a digitised version of the original article (Figure 1)15 that Scherrer is the only author. The original paper is in German and a clue to the identity of the enigmatic co-author N.G.W. Gottingen is obtained from the name of the journal, as printed on its title page: 'Nachrichten von der Koniglichten Gesellschaft der Wissenschaften zu Gottingen. Mathematisch-physikalische Klasse aus der Jahre 1918'. Confusion regarding the abbreviated journal title has resulted in part of the title being misinterpreted as a second author.



Having clarified the issue of authorship, to cite correctly the original article one must still consider the most appropriate journal title abbreviation. For the years 1894-1922, during which the journal retained a consistent format, the Scholarly Societies Project website lists 97 variations of the journal's abbreviated name as cited in other journals.16 Among the data one finds six variations used to cite this particular journal in Science, and the abbreviation recently used by Holzwarth and Gibson7 is different to all of those listed. After deciding on the appropriate journal title abbreviation, one must determine the volume number, which is often given as either 2 or 26.

A volume number could not be found in the journal itself - only the year - which is how the volumes are described on the website from which the paper was downloaded.15 A number of citations from articles published in the first half of the 20th century also do not give a volume number. Of particular interest is the citation17 given in the influential Chemistry Abstracts journal Chemisches Zentralblatt: 'Nachr. K. Ges. Wiss. Gottingen 1918. 98-100. 26/9. 1918.' Here the volume number and the year are both given as 1918, together with the mysterious numbers 26/9 (from where it is speculated that the incorrect volume number 26 may have originated; possibly the 6 was later truncated to give the incorrect volume 2, as used by Holzwarth and Gibson5). The numbers 26/9 can be interpreted as a date (26 September). Consulting the original article, one finds that it was presented by P Debye in a meeting on 26 July 1918 (Figure 1). This contribution by Debye in the history of the Scherrer equation was not mentioned by Holzwarth and Gibson5. The date translates to 26/7 instead of 26/9, but comparing other citations to the journal proves that the date was intended. Finally, although the page numbers are certainly 98-100, the incorrect starting page 96 is used in all but one of the papers cited here.610,12-14

It is clear that from the outset, Scherrer's paper was cited with errors and these errors were copied from paper to paper. This situation has culminated in the 'birth' of a fictitious co-author - N.G.W. Gottingen. Scientists should show the same attention to detail in reporting their sources as they do in reporting their results, and only cite papers that they have personally consulted. Tracing inaccurate references can be a time-consuming and frustrating, albeit interesting, task.



1. Cele LM, Ray SS, Coville NJ. Nanoscience and nanotechnology in South Africa. S Afr J Sci. 2009;105:242.

2. Mappes T, Jahr N, Csaki A, Vogler N, Popp J, Fritzsche W. The invention of immersion ultramicroscopy in 1912 - the birth of nanotechnology? Angew Chem Int Ed. 2012;51:11208-11212.

3. Scherrer P Bestimmung der Grosse und der inneren Struktur von Kolloidteilchen mittels Rontgensrahlen [Determination of the size and internal structure of colloidal particles using X-rays]. Nachr Ges Wiss Goettingen, Math-Phys Kl. 1918;1918:98-100. German.         [ Links ]

4. Baker A, Usher FL. Nuclear gold sols. III Lower limit of particle size. Trans Faraday Soc. 1940;35:549-557.

5. Holzworth U, Gibson N. The Scherrer equation versus the 'Debye-Scherrer equation'. Nature Nanotech. 2011;6:534.

6. Azira AA, Zainal NFA, Nik SF, Rusop M. Optimization of Fe/Ni/Mg trimetallic catalyst for carbon nanotubes growth by using fluidized floating catalyst method. AIP Conf Proc. 2009;1136:740-744.

7. Sumi H, Ogawa S, Sato M, Saikubo A, Ikenaga E, Nihei M, et al. Effect of carrier gas (Ar and He) on the crystallographic quality of networked nanographite grown on Si substrates by photoemission-assisted plasma-enhanced chemical vapour deposition. Jpn J Appl Phys. 2010;49:076201(7 pages).

8. Qi Z, Geng H, Wang X, Zhao C, Ji H, Zhang C, et al. Novel nanocrystalline PdNi alloy catalyst for methanol and ethanol electro-oxidation in alkaline media. J Power Sources 2011;196:5823-5828. jpowsour.2011.02.083

9. Park H, Youn H, Lee S, Bang H, Oh I. Consolidation of ultra fine WC-Co hard materials by a spark plasma sintering method and their mechanical properties. J Ceram Process Res. 2001;12:304-309.

10. Nezamzadeh-Ejhieh A, Badri A. Perchloate selective membrane electrode based on surfactant-modified zeolite Y nanocluster. Anal Bioanal Electrochem. 2011;3:565-568.

11. Paul R, Dey A, Mukherjee AK, Sarangi SN, Pal AK. Effect of nanocrystalline silver impregnation on mechanical properties of diamond-like-carbon films by nano-indentation. Indian J Pure Appl Phys. 2012;50:252-259.

12. Liu K, He D, Wang H, Lu T, Li F, Zhou X. High-pressure sintering mechanism of yttrium aluminium garnet (Y3Al5O12) transparent nanoceramics. Scr Mater. 2012;66:319-322.

13. Zhang H, Hu C, Chen S, Zhang K, Wang X. Synthesis of SnO2 nanostructures and their application for hydrogen evolution reaction. Catal Lett. 2012;142:809-815.

14. Chatterjee M, Ishizaka T, Suzuki T, Suzuki A, Kawanami H. In situ synthesized Pd nanoparticles supported on B-MCM-41: An efficient catalyst for hydrogenation of nitroaromatics in supercritical carbon dioxide. Green Chem. 2012;14:3415-3422.

15. Center for Retrospective Digitization, Gottingen (GDZ) [database on the Internet]. No date [cited 2012 Jul 27]. Available from:        [ Links ]

16. Scholarly Societies Project [database on the Internet]. No date [cited 2012 Jul 27]. Available from:        [ Links ]

17. Chem Zentralbl. 1919;I:322-323. German.         [ Links ]



Ted Kroon
Department of Physics, University of the Free State
PO Box 339, Bloemfontein 9300, South Africa

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