Nanocrystalline Materials Studied by Powder Diffraction

 

Tamás Ungár

 

Department of General Physics, Eötvös University Budapest, H-1518, POB 32, Budapest Hungary

 

Crystalline materials can be defined, in a broader sense, as nanocrystalline if the average grain size is smaller than a micron. It can be either in the form of loose powder or in the form of polycrystalline bulk materials. Since nanocrystalline materials is one of the major buzz-words in the present decade, the procedures to produce tham vary from single atom or cluster condensation [1], through different chemical reactions [2] down to crystallisation from the bulk amorphous phase [3] or fragmentation by ball milling and different techniques of severe plastic deformation [4]. Latter are, in particular, the methods of equal channel angular pressing (ECAP) [5], high pressure torsion (HPT) [6] or corrugated cold rolling (CCR) [7]. Depending on the way the material was produced the grain size and size distribution and the strain or stress state, frozen into the crystallites, are varying over vide scales. The average crystallite size in inert-gas condensed metals like copper or palladium can vary between 5 to 20 nm together with dislocation densities at the order of magnitude of several times 1015 m-2 [8,9]. Nanocrystalline foils produced by electrodeposition can contain extremely high densities of stacking faults [10]. Stacking faults can become one of the major type of lattice defects in materials with very high stacking fault energy, e.g. in aluminium [11,12], in which under conventional circumstances stacking faults can not be observed. Powder specimens produced by the chemical precursor method can be as small as 5 to 10 nm without even a single dislocation [13]. Hexagonal materials like titanium can be produced by the ECAP method to have an average grain size of about 50 nm and dislocation densities as high as 1016 m-2 [14]. The stregth of this material can exceed the strength of its conventional grain size counterpart by one order of magnitude [14].

Depending on the purpose for what the material has been prepared and the procedure by which it has been produced the microstructure can be very different. Due to constantly improving diffractometers [15] and sometimes sophisticated X-ray optical devices in the home laboratories [16] and high intensities and high angular resolution at powder diffraction beam lines at synchrotrons [17], powder diffraction has become one of the most powerful tools to determine the microstructure of nanocrystalline materials.

Acording to the kinematical theory of powder diffraction if the crystallites are free from lattice defects and the average crystallite size is larger than a few microns, however, not much larger than about 10 microns, the physical line profiles of the diffraction peaks are delta functions [18]. In the measured powder patterns these delta functions are convoluted with the instrumental functions of the diffractometer. To the best knowledge of the present EPDIC community such a powder pattern is realised by the mesurement of a good LaB6 standard specimen, e.g. the LaB6 standard specimen provided by one of the laboratories of NIST. If the crystallites become smaller than about a micron or the lattice becomes distorted by any kind of lattice defects the physical line profiles will no longer remain delta functions. The deviations from the ideal delta function type can be very different. The diffraction peaks can be: (i) shifted, (ii) can broaden, (iii) can become asymmetric, (iv) the broadening can be anisotropic with hkl and (v) any combination of the former cases can occure. In recent years it has been shown that the physical origin of strain anisotropy is the extremely anisotropic strain field of dislocations [19-22]. The effect of dislocation on the broadening of different hkl reflections, especially in polycrystalline materials, can be summarized in a fairly simple form of average dislocation contrast factors [23]. The fundamental parameters in determining the contrast factors can be determined by whole profile fitting numerical procedures. The physical interpretation of these parameters can reveal several details about the dislocation structure in nanocrystalline materials. The same whole profile fitting procedures provide size distribution density functions of the coherently diffracting domains [24,25]. The interpretation of the this size distribution either in terms of crystallite size distribution or in terms of other physical units in the material is the virtue of the experimentator.

 

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