by Prof. Jenő Gubicza

Nanostructured materials are in the forefront of materials science due to their unique properties, such as improved mechanical and magnetic performances. The properties of nanomaterials can be tuned by changing the chemical composition and/or the microstructure, such as the size of grains, as well as the type and density of crystal defects inside the grains. Defects disrupt the ideal periodic arrangement of atoms in crystallites. This disruption is known as lattice strain. For instance, dislocations and planar faults are frequently formed crystal defects for which considerable lattice strain is observed in one and two dimensions, respectively. In other words, dislocations are line defects and planar faults are defects that extend along a crystal plane. Both defects have a significant influence of the deformation behavior of materials [1]. Crystal defects in nanomaterials form naturally during their processing. However, their types, amount and spatial arrangement can be modified by changing the processing conditions. This route of tailoring the properties of nanomaterials is called as “crystal defect engineering”.

For improving the performance of nanostructured materials by “crystal defect engineering”, it is essential to possess experimental techniques for a reliable characterization of crystal defects. Microscopic methods, such as transmission electron microscopy (TEM), give direct observation of the microstructure as it is. However, the studied volume is usually very small, resulting in an uncertainty whether the information deduced from the images characterize the whole sample. Alternatively, there are indirect methods which study much larger volumes but in these cases the features of the defect structure are extracted from the analysis of the recorded signals without seeing the real microstructure. 

X-ray line profile analysis (XLPA) is a very effective indirect method for the characterization of the nanocrystalline microstructure. XLPA analyses the diffraction peak shape and yields the crystallite size distribution and the type and density of crystal defects with a good statistics and in a non-destructive way [2]. Special instrumentation is not needed for XLPA, since commercial diffractometers are capable of measuring good quality X-ray diffraction (XRD) patterns. However, the extraction of the microstructural parameters from the diffraction peak shapes requires special care and knowledge. In addition, there is a concern whether the information about defect structure obtained by XLPA is reliable, since this method evaluates the XRD peak shape instead of taking pictures on the real microstructure. Due to this indirect nature of XLPA, the reliability of the microstructural parameters determined by this technique is worth to check by comparing them with the results obtained by direct methods, such as TEM.


X-ray diffraction

A schematic showing that the analysis of the shape of the X-ray diffraction peaks can reveal the crystallite size as well as the type and density of crystal defects.


In a recent study [3], the reliability and the interpretation of the microstructural parameters measured by XLPA have been analysed and instructions were given for a correct application of this method on nanomaterials. In addition, the microstructures determined indirectly through XLPA were compared with those obtained by direct techniques, such as TEM. It was shown that the evaluation of the diffraction peak breadth solely is not suitable for the determination of the defect density. Rather, an analysis of the full diffraction profile is necessary. 

It was revealed in Ref. [3] that the density of crystal defects evaluated from the full profile shape are in a reasonable agreement with the values obtained by other methods, such as TEM or positron annihilation spectroscopy (PAS). On the other hand, the crystallite sizes determined by TEM and XLPA are usually different; however, this difference decreases when the microstructures become finer and at about 20 nm the sizes determined by the two methods agree well. This result indicates that below this critical size the grains or particles are not fragmented into sub-grains. Through the study of hundreds of different nanomaterials, it was revealed that although nanomaterials with smaller grain size usually contain a higher density of crystal defects, there is no strict correlation between the crystallite size and the density of crystal defects (dislocations).

Nanomaterials can be produced either by bottom-up or top-down techniques. In the former case, the material is built up from elemental units, such as atoms or particles, while in the latter case the pre-existing coarse grains are refined in bulk materials using severe plastic deformation (SPD). During SPD procedures, bulk coarse-grained metallic materials are deformed plastically for very high strains without changing the size and shape of the specimens. This methodology requires special instruments. During the production of nanomaterials using SPD, a very high defect density forms and the grains are fragmented simultaneously. Finally, a nanocrystalline microstructure can be achieved [1].  

The study published in Ref. [3] revealed that the defect density can be similar or even higher in nanomaterials processed by bottom-up methods in comparison with the samples having similar chemical composition but processed by SPD. This is a surprising result since plastic deformation during SPD induces the formation of many crystal defects while there is no deformation during bottom-up processing of nanomaterials. In nanomaterials processed by bottom-up techniques, the crystal defects are grown-in faults which reduce the mismatch stresses between the neighboring grains in the as-processed materials. Thus, in these samples the type and density of crystal defects are determined by the processing conditions, and the defect structure cannot be predicted from the properties of the basic material. For instance, a considerable amount of planar faults can be observed even in those nanomaterials for which the formation energy of planar faults is high. On the other hand, for nanocrystalline metals processed by SPD, the defect density is determined mainly by the properties of materials, such as the melting point, the elastic modulus (the measure of the elastic stiffness) and the formation energy of planar faults. 

Alloying either in the form of solute atoms or precipitates refines the microstructure and increases the defect density in nanomaterials. The highest defect density and the smallest grain size can be achieved in highly alloyed nanomaterials such as multi-principal element alloys, containing three or more constituents with equal quantities. It was also revealed in [3] that short (less than one hour) post-processing heat-treatment at moderate temperatures (about one-third of the melting point in Kelvin degrees) can yield improvement of the mechanical performance of nanomaterials due to the relaxation of the defect structure. Therefore, this anneal-hardening is suggested to apply in “crystal defect engineering” of nanomaterials. 

An important conclusion of the overview presented in Ref. [3] is that fine-tuning of the properties of nanomaterials can be carried out by controlling the type and density of crystal defects via an appropriate selection of the processing conditions of nanomaterials. XLPA can be effectively used for the characterization of crystal defects in nanostructured materials – but special care is required for the application. The overview published in Ref. [3] provides researchers with useful guidance on how and when XLPA should be applied.

It is noted that recently a novel machine learning-based X-ray line profile analysis (ML-XLPA) was developed for the characterization of nanocrystalline microstructures [4]. The new method was tested on a combinatorial Co-Cr-Fe-Ni alloy film where the elemental concentrations vary in a wide range on the surface. The most important benefit of the combinatorial sample is that it can be used for the study of the correlation between the chemical composition and the microstructure on a single specimen. The new ML-XLPA method was able to produce maps of the characteristic parameters of the nanostructure (crystallite size, lattice defect densities) on the film surface. The following figure shows a map for the spatial variation of the crystallite size on the combinatorial Co-Cr-Fe-Ni alloy film.


Map of the crystallite size on the surface of a Co-Cr-Fe-Ni allow film

Map of the crystallite size on the surface of a Co-Cr-Fe-Ni alloy film processed by physical vapor deposition. The notations Co, Cr, Fe and Ni at the perimeter of the disk indicate the approximate positions of Co, Cr, Fe and Ni sputtering sources, respectively. Due to the different positions of the sources, the chemical composition of the sample is different in the various points of the film surface. Only a part of the film with face-centered cubic structure was studied while the rest is indicated by grey color.




1. J. Gubicza: Defect Structure and Properties of Nanomaterials, 2nd and Extended Edition, Woodhead Publishing, an imprint of Elsevier, Duxford, UK, ISBN: 9780081019177 (2017).

2. J. Gubicza: X-ray line profile analysis in Materials Science, IGI-Global, Hershey, PA, USA, ISBN: 978-1-4666-5852-3 (2014).

3. J. Gubicza, Reliability and interpretation of the microstructural parameters determined by X-ray line profile analysis for nanostructured materials, Eur. Phys. J. Spec. Top. (2022) https://doi.org/10.1140/epjs/s11734-022-00572-z

4. P. Nagy, B. Kaszás, I. Csabai, Z. Hegedűs, J. Michler, L. Pethö, J. Gubicza, Machine learning-based characterization of the nanostructure in a combinatorial Co-Cr-Fe-Ni compositionally complex alloy film, Nanomaterials 12 (2022) 4407. https://doi.org/10.3390/nano12244407

Biography of the author

Jenő Gubicza is a professor at Eötvös Loránd University in Budapest, Hungary. He received his PhD and Dr.habil degrees in 1997 and 2005, respectively. Prof. Gubicza’s main research field is the study of microstructure of nanomaterials. He was awarded the scientific title of Doctor of the Hungarian Academy of Sciences, the Schmid Rezso Prize of Roland Eotvos Physical Society and the Bolyai-plaquette of Hungarian Academy of Sciences. He has published three books and about 300 papers that have been cited more than 10,000 times (on the basis of Google Scholar). His h-index is 51. Prof. Gubicza has supervised 10 PhD students. He served as the heads of the Department of Materials Physics and the Doctoral School of Physucs at Eotvos Lorand University in Budapest, Hungary.


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