X-ray microstructural analysis of nanocrystalline TiZrN thin films by diffraction pattern modeling
Introduction
Microstructure is considered the most important feature, other than chemical composition, for defining material properties and performance due to its strong effect on all physical properties [1], [2], [3]. Suitable characterization techniques and models for extracting information regarding physical properties on the atomic scale, comprise a very important field of study for microstructural analysis and act as a bridge for establishing the relationship between synthesis processes and the performance of materials in particular applications.
The microstructure in a specific material can be described in terms of the atomic arrangement and the imperfections such as dislocations, small crystallite size, and faults. These imperfections are due to the synthesis process parameters used to growth the material. One method that is widely used for extracting microstructural information from materials is the X-ray diffraction technique (XRD), either based on the line profile analysis (LPA) generally extracted from the integral breadths of reflections or the Fourier analysis of diffraction lines. Using this technique, microstructural imperfections such as lattice distortions, dislocations, faults, crystallite size and microstrain distributions can be obtained. The possibility of obtaining the distributions of different microstructural parameters, according to the statistical representation of these features, is an important and possibly unique characteristic of the XRD technique, allowing for a connection to be made between the micro and macroscale in materials [4], [5], [6]. This technique is also accessible and offers convenient sample preparation, demonstrating the advantages of XRD over electron microscopy [7].
One of the most relevant problems concerning the microstructural characterization of materials by XRD is the poor physical meaning of the parameters extracted. Methods such as Williamson–Hall and Warren–Averbach analysis provide quantities that are difficult to interpret, making such techniques burdensome to use in engineering applications. One such application is determining the size of crystallites composing a material, considering that real polycrystals exhibit a distribution of size rather than one weighted average size; thus, errors in the information extracted from diffraction patterns are inevitable [6]. To more precisely interpret another important parameter such as lattice microstrain, the strain must be related to a real physical parameter, such as dislocation density. Dislocations are the most common sources of local lattice distortion, and a study that has successfully exploited this feature has been reported [8], [9], [10]. Thus, the interpretation of parameters that are directly related to industrial processing variables is required. To fulfill this goal, a variety of methods have been widely studied over the past two decades to improve the quantification and extraction of meaningful physical parameters from XRD patterns. One of the most successful methods is the Whole Powder Pattern Modeling (WPPM) method developed by Matteo Leoni, Paolo Scardi and others [8], [11], [12], [13]. This method, unlike the methods previously mentioned, directly relates a material's microstructure with its diffraction pattern, without having to extract parameters such as the full width at half maximum (FWHM) or integral breadth. This concept presents an advantage in the field of diffraction pattern analysis of microstructure considering that WPPM makes no use of arbitrary a priori analytical profile functions and directly models the experimental data by means of suitable microstructural model, avoiding systematic errors and no real values in microstructure parameters. Due to the straightforward modeling of experimental data of the diffraction patterns by means of microstructural models, WPPM is not considered a fitting procedure. This method is based on the concept of diffraction exposed by Ewald, where the diffraction signal can be described as the integral of the diffraction intensity in reciprocal space over the intersection surface between the diffraction sphere and the reciprocal space points. For this reason, the intensity distribution I(d⁎) can be described in terms of Fourier transforms of diffraction profile contribution aswhere d⁎ corresponds to the diffraction vector in reciprocal space and k(d⁎) represents geometrical and structural contributions to the diffracted intensity like Lorentz polarization factor, structure factor, absorption, and extinction, among others. L is called the Fourier length and is inverserly proportional to the diffraction vector d⁎. C(L) is the convolution of contributions from the sample (size and strain) and the instrument (with exception to absorption) and can be written in terms of suitable models aswhere TIP and AS are the Fourier transform contributions of instrument (IP) and crystallite size (S) respectively. The expressions in brackets are average phase factors related to lattice distortions (ψ) and faulting (φ). A detailed description of this method is presented in [6].
Ternary transition-metal nitride nanocrystalline coatings have been widely studied and have gained great attention due to their interesting properties, such as oxidation resistance, high hardness, high thermal and chemical stability, wear resistance, and low resistivity, among others [14], [15], [16], [17]. In this group of materials, one of the most interesting is titanium–zirconium nitride (TiZrN), which exhibits some features described above with the incorporation of additional Zr metallic atoms in the TiN lattice, allowing a variety of stoichiometric proportions of the components and hence different properties to be obtained [18], [19], [20].
One of the most widely used techniques in the industry to obtain these materials is the cathodic arc technique in the pulsed mode. This technique is very advantageous compared with others such as continuous cathodic arc and sputtering due to the limited spot displacement which prevents the movement of spots to specific zones of the cathode such as boundaries, the ability to adjust the power consumption during the duty cycle of the arc, the high ionization energy of the plasma chemical ions, the high deposition rate and a wide range of obtainable thicknesses, among others [21], [22], [23]. In this process, several important factors such as adatom mobility, the lattice inter-diffusion of material deposited on the substrate, nucleation and crystallization, among others, depend on TS. These processes are induced by the displacement of the thermodynamic equilibrium between reactive species in the substrate during growth [24], [25]. One effect of this process is the competition between adatom mobility and the desorption processes that occur during deposition [26], [27]. These factors have a strong effect on film microstructure. Moreover, the study of the critical temperatures affecting this competition is important for establishing the final properties of materials.
According to the above discussion, real microstructure information extraction from the mentioned thin film materials is an important challenge in the field. Despite other techniques based on powder microstructure that have been developed [6], [28], [29], [30], WPPM method can be used to study non-textured films as well, so its adaptation to hard thin films may be very useful in determining the synthesis–properties relationship and ultimately improving the performance of these materials.
In this study, a detailed characterization of the microstructure of nanocrystalline TiZrN thin films was performed by X-ray diffraction pattern modeling in order to obtain more meaningful microstructural parameters. This analysis was performed based on the variation in substrate temperature during the deposition of thin films, and the physical phenomena of the pulsed cathodic arc technique were elucidated as functions of WPPM microstructural parameters.
Section snippets
TiZrN Thin Film Production
Titanium–zirconium nitride thin films were produced in a non-commercial system by the cathodic pulsed vacuum arc technique. The system consisted of a reaction chamber with two electrodes: an anode (A), where the substrate was placed, and a cathode (K), which was composed of a titanium–zirconium alloy (50%–50%) 6N target. The distance between the electrodes was 4 mm, and substrates composed of 316L stainless steel and measuring 1.27 cm in diameter and 3 mm in thickness were used. The system was
Results and Discussion
From the diffraction patterns of the five samples, peaks corresponding to the (111), (200), (220), (311) and (222) planes for the TiZrN phase grown, depending on the substrate temperature (TS), were identified (Fig. 1). The last reflection was not taken into account for the microstructural analysis due to its overlap with a peak corresponding to the substrate phase and its low intensity, which does not provide a reliable broadening measurement. Phases corresponding to TiN, ZrN and TiZrN have
Conclusions
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TiZrN thin films were obtained by the pulsed cathodic arc technique showing a nanostructured growth. No evident texture was found in the material as a consequence of the high energy applied during the deposition process. Also slight microstructure anisotropy related to the local strain could be observed. This result was incorporated into the model implemented using the PM2K software.
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The competition between mobility and desorption generates a critical point in the substrate temperature (TS ~ 100
Acknowledgments
The authors gratefully acknowledge the financial support of the Dirección Nacional de Investigaciones under the project “Grupo PCM Computational Applications” and to the scholarship program “Estudiantes Sobresalientes de Posgrado” both from the National University of Colombia. The authors are also grateful to Laboratório Nacional de la Luz Síncrotron and XRD Beamline Group for the support under research proposal D12A-XRD1-11659.
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