Status of NIST Nanocrystallite Size SRM 1979.

N. Armstrong¹, J. P. Cline², W. Kalceff¹, J. Ritter² & J. Bonevich³

¹Department of Applied Physics,University of Technology Sydney, AUSTRALIA.

² Ceramics & ³Metallurgy Divisions, National Institute of Standards and Technology (NIST), USA.

The NIST nanocrystallite size Standard Reference Material (SRM) 1979 will provide a standard for both scientific and commercial laboratories to quantify the size distribution and shape of nanocrystallites using X-ray line profile and electron microscopy techniques. It will also apply a Bayesian/Maximum entropy (MaxEnt) method of X-ray diffraction data analysis especially developed for certifying the SRM. It is expected that SRM 1979 will play a pivotal role in the rapidly developing nanotechnology industry by providing uniformity in the measurement of crystallite size and shape data, while clarifying the underlying assumptions of many existing line profile techniques.

In this paper we discuss the preparation and analysis of the two proposed SRM 1979 candidate materials. An outline of the procedure is given, together with a detailed discussion of the X-ray line profile analysis used to determine both the size and shape information of the SRM 1979 specimens.

SRM 1979 will consist of two material specimens prepared in 1kg batches from bulk feedstock. The specimens have been produced to minimize the presence of structural defects that may result in strain broadening in the line profiles. The first material sample is ceria (cerium (IV) oxide, CeO₂) with an (approximate) average spherical crystallite size of 20 nm over a size range of 5–35 nm. The SRM is produced from a precipitation reaction between cerium (IV) sulfate solution and an ammonium hydroxide solution, conducted in a fixed-element flow reactor. Ceria has a cubic symmetry resulting in well-spaced diffraction lines. This allows rapid and simplified analysis techniques to be used to determine the shape and dimensions of the crystallites, while minimizing systematic error arising from overlapping peaks. Moreover, the spherical morphology ensures that the size broadening will be isotropic in hkl. This enables models for simple shapes to be applied.

The second SRM 1979 specimen is zinc oxide (ZnO) which is also prepared in a fixed-element flow reactor, by a precipitation reaction between zinc acetate and an ammonium hydroxide solution. This SRM specimen has a cylindrical crystallite morphology with an approximate length of 80 nm and a size range of 60–100 nm. ZnO has a hexagonal symmetry, producing a large number of (overlapped) lines. Consequently, this specimen requires more complex size and shape models to be applied in order to extract the necessary information from the X-ray diffraction data. Specifically, the anisotropic broadening for various hkl provides a direct indication of the crystallite morphology, while the size distribution reveals the spread in the cylinder heights and diameters.

The analysis technique essentially involves two steps [1,2]. The first step applies MaxEnt/Fuzzy pixel deconvolution methods simply to remove the instrumental broadening, and produce the specimen profile. Using this data, simple microstructural models for the crystallite size/shape (and if necessary defect content) can be developed. This data serves as the a priori information for the full Bayesian/MaxEnt analysis constituting the second step. Moreover, this approach provides a basis for developing a series of models from which the most probable model can be determined using Bayesian model selection theory. This analysis takes full account of the form of the instrumental, background and statistical noise contributions embedded in the diffraction data. As well as providing the most probable solution, the second step also produces a full error analysis of the size distribution— a critical element in certifying SRM 1979.

The X-ray analysis presented here will be compared with the results of direct observations of SRM 1979 using TEM imaging, and a discussion based on this comparison will be presented.

[1] N. Armstrong, W. Kalceff, J. P. Cline and J. Bonevich (2004), “Bayesian inference of nanoparticle-broadened line profiles”, J. Res. NIST. Accepted for publication 11 April 2003.

[2] N. Armstrong, W. Kalceff, J. P. Cline and J. Bonevich (2003), “A Bayesian/maximum entropy method for certification of a nanocrystalline-size NIST Standard Reference Material”, in Chapter 8, Diffraction Analysis of the Microstructure of Materials (eds. E. J. Mittemeijer & P. Scardi), Springer, Berlin, pp.187–227.