Studies on the structural, quantitative and semi-quantitative analyses of NiO – GDC nanocomposites

A simultaneous analysis of the crystallite size and strain of x NiO $ (1 (cid:1) x )GDC nanopowders prepared in stoichiometric proportions of x ¼ 0, 0.1, 0.2 . to 1 was performed by a self-sustained combustion (SC) process and calcination of the thus-synthesized nanopowders at 600 (cid:3) C. The nanopowders were examined by powder X-ray di ﬀ raction (XRD) pattern using two approaches: integral breadth of multiple peaks (multi-line) with Pearson VII (PVII), and pattern analysis of powders through total adjustment of the di ﬀ raction peaks with the double-Voigt (V – V) method. The synthesis route and stoichiometric variation allowed a quantitative study using the global setting pro ﬁ le with Rietveld re ﬁ nement and semi-quantitative analysis by X-ray ﬂ uorescence (XRF) of nickel oxide (NiO) and gadolinium doped ceria (GDC) phases in the as-prepared and the calcined samples. The investigation of the microstructures of the nanopowders was further supported by high-resolution transmission electron microscopy (HR-TEM) and scanning electronic microscopy (SEM) with energy dispersive X-ray spectroscopy (EDS).


Introduction
The development of X-rays in the twentieth century is a cornerstone of evolution in the eld of solid-state sciences and also in understanding chemical bonds. Although Roentgen discovered X-rays (1898), several other pioneers, such as Moseley (1912) and Bragg (1913), have paved the way for improvement in many essential techniques for the characterization of metals, ceramics, semiconductors, glasses, minerals and biological materials. Diffraction studies, along with uorescence and absorption studies, provide qualitative and quantitative information on the structure and composition, which are indispensable elements to understanding the nature of materials. 1 Recently, nanostructured ceramic materials have received signicant attention because they demonstrate better returns or possess unique properties compared to conventional ceramic materials. Cerium based materials such as cerium doped gadolinium (GDC) and compounds of nickel oxide (NiO) with GDC are considered to be promising candidates as electrolytes and anodes, respectively, in the design of intermediatetemperature solid oxide fuel cells. GDC, a mixed conductor, possesses higher ionic conductivity than yttrium stabilized zirconia (YSZ) at intermediate temperatures (between 400 C and 700 C); therefore, the difficulties arising from degradation of the materials can be minimized by using high temperatures (z1000 C). In addition, the usage of GDC reduces manufacturing costs and increases production. 2 NiO-GDC powder can be synthesized by a self-sustaining citrate-nitrate combustion technique (SC), which has emerged as a facile and inexpensive method to facilitate the formation of nanoceramics with homogeneous microstructures at low temperature and with short reaction times. This SC technique is based on the principles of chemical propellants, 3 which involve a redox reaction between a thermal-induced oxidant and a fuel. 4 Theoretical and experimental procedure Stoichiometric quantities of cerium nitrate (Ce(NO 3 ) 3 $6H 2 O, Sigma Aldrich, $99.5%), gadolinium nitrate (Gd(NO 3 ) 3 $6H 2 O, Sigma Aldrich, $99.5%), and nickel nitrate (Ni(NO 3 ) 2 $6H 2 O, Sigma Aldrich, $99.5%) were mixed with a calculated amount of citric acid (Sigma Aldrich, ACS reagent, $99.5%). This mixture was dissolved in the amount of distilled water required to achieve a clear homogeneous solution and was then stirred for three hours using a magnetic stirrer. The amount of citric acid was calculated by the chemical propellant principle, i.e. the ratio of the oxidizing and reducing valences must be equal to 1. The resulting solution obtained aer stirring was poured into an alumina crucible, and the crucible was maintained for 10 minutes in an oven preheated to 500 C while the self-sustained combustion process occurred. The high exothermic energy generated during the combustion process releases many gases, such as N 2 , CO 2 and water vapor, to form a foam with a fragile, porous and irregular nature; this was powdered using an agate mortar. 5 To remove the organic residues, the thus-obtained ne powder was nally calcined at 600 C for 2 hours. 6 The chemical reaction that leads to SC is given by where x ¼ 0, 0.1, 0.2,., 0.9, 1 (in mol%), and y is obtained from the chemical propellant; z 1 , z 2 and z 3 are constants arising from the combustion process. 7,8 The total sum of the products of the cation and anion valences by the stoichiometric coefficients should be zero: These valences must be balanced by the total valence of the fuel; therefore, the composition requires the determination of the y value for each case in order to release the maximum energy of the reaction. 9 XRD analysis was used to characterize the phases of the asprepared and calcined samples. These measurements were carried out using a Bruker AXS D8 diffractometer equipped with an X-ray tube with a copper target (CuK a wavelength l ¼ 1.54 A), a nickel lter and a point detector. The operating conditions of current ¼ 30 mA and voltage ¼ 40 kV in the tube were selected for high quality XRD proles as well as for good statistical analysis, narrow peaks and detection of small peaks. The XRD data was collected over the 2q range from 10 to 70 , with a step size of 0.02 and a counting time of 1 second per step, which was sufficient for the intensity obtained (usually, if the peaks are weak, more time is required to acquire data 10 ).
In this work, Rietveld analysis using TOPAS version 4.2 (Bruker AXS) and XRD renement were used. The Rietveld method of nonlinear least-squares t is the best t between the experimental prole and the prole calculated based on the peak intensities aer an entire renement of the parameters given by the method. 11 For the application of the Rietveld method, the instrumental function was empirically parameterized from the prole shape of a corundum standard sample (NIST 676 a ) and measured under the same conditions. The renement protocol also included major parameters such as background, zero displacement, scale factors, peak breadth and unit cell parameters. On the other hand, line broadening effects that arose due to crystallite size and lattice strain were analyzed in this renement with the double-Voigt approach, in which both comprise a convolution of Lorentzian and Gaussian with varying 2q as a function of 1/cos q and tan q, respectively. [12][13][14] The quality and reliability of the Rietveld analysis was quantied by the corresponding gures of merit: adjusting the weighted sum of least squares (R w ), adjusting the statistically expected sum of least squares, (R exp ), the residual prole (R p ), and the goodness of t (GoF, oen referred to as chi-square). 15 Since GoF ¼ R w /R exp , a value of one GoF equal to 1 indicates a perfect tting.
The XRF dispersion wavelength to quantify the phases of the synthesized and calcined samples was carried out with a ZSX Primus II Rigaku spectrometer. The semi-quantitative analysis was performed with SQX soware. This program is based on spectral series sweeps which are optimized for spectral resolution (choice of collimator glass) rather than sensitivity. The peaks of the elements are identied by automatically subtracting the background rate accounts. The program applies theoretical approaches of "basic parameters" using information from the physics of the X-rays to calculate matrices (correction) individually for each element detected in the sample. This procedure is an iterative process which ultimately provides the concentrations of the elements.
The XPHS program, which allows the peak of each line in position to be distinguished, was used. The phases of the powders were identied with the soware database. The information processed by XPHS was resolved with Origin 8.0 soware to mathematically adjust each peak at a PVII distribution within the multi-line approach. 16 For the b width, the value w (or Full Width at Half Maximum ¼ FWHM), is corrected to the mathematical prole adjustment of a Lorentz [L] or Gauss [G] instrument. This FWHM, which computes PVII, is included in the relationship described in terms of b, w and gamma function (G), i.e., the shape coefficient for a PVII.
w b The peak shape is subjected to adjustment of the parameter m, which effectively combines functions [L] and [G] to describe the prole. 17 Individual contributions to the broadening occurring due to crystallite size and deformation can be determined only aer subtracting the effect of peak broadening due to the instrument. 18 The peak width and shape vary with respect to 2q. It is fundamental to examine the variation in 2q FWHM regarding the instrument. 19 Polynomials describing the instrumental resolution function (IRF) were proposed by Cagliotti et al. 20 in the Rietveld renement to explain the broadening behavior [G] or [L] due to the instrument.
U, V, W and/or X, and Y are renable parameters. For multi-line analysis, the change in FWHM ins (w ins ) for the sweep interval is smooth and does not change signicantly. Therefore, it can be considered to be a linear model for the IRF with three measuring points: 35.16 , 43.36 and 57.51 . The effects of the instrument are described by the mathematical relationship w ins ¼ 6.532 Â 10 À5 (2q) + 8.457 Â 10 À4 .
The FWHM correction (w obs ) due to the instrument was conducted with three mathematical approaches: [L], [G] and parabolic [P]. If the peak has a [L] or [G] prole, the instrumental inuence is removed in eqn (3) to obtain the b value. Accordingly, Wagner and Aqua 21 suggested the parabolic relationship of integral breadths given by In eqn (8), all the instrumental effects on the Gaussian prole are calculated in accordance with the assumption of b ins ¼ [O(p/2 ln (2))] Â w ins /2. 17 The microstructural features of the 0.5NiO-0.5GDC nanocomposite were examined for both the as-prepared and calcined nanopowders. High-resolution transmission electron (HR-TEM) micrographs and selected area of electron diffraction patterns (SAED) were obtained with a FEI TITAN G2 80-300 microscope and were examined with GATAN soware. Also, scanning electron micrographs (SEM) were acquired with QUANTA QEMS-CAN 650 equipment, and elemental chemical identication was conducted using energy dispersive X-ray spectroscopy (EDS).

Results and discussion
In broadening line analysis, the generalization of the approximation in adjustments to Lorentz and Gaussian has been experimentally justied. 22 Therefore, if it is not assumed with the conviction of a mathematical adjustment to the diffraction peak prole, a convolution of functions [L] and [G] is the best way to describe the structural peak. 13,23,24 The mathematical structure of b enables approximation of the pattern diffraction prole in the analytic functions [L] and [G].
The PVII distribution is a function ranging from [G] (broadens towards the tip and narrows at the base) to [L] (opposite to Gaussian) with the selection of an adjustable parameter m to accommodate the shape of the diffraction prole of each peak. 16,19 It should be noted that Voigt (V), pseudo-Voigt (p-V) and PVII provide descriptions of the shape of the peaks with the same approximate degree of accuracy . 25,26 However, PVII does not confer the ability to solve (analytically) the convolution of functions [L] and [G]. In addition, while providing high reliability in the setting, there is no function V that enables extraction of the microstructural physical information. Fig. 1 shows the clear differences between the adjustments V, p-V and PVII. It is clear that both V and p-V lose precision throughout the prole; however, the presence of disagreement is evident from the magnied image of the inection zone where the queues originate. PVII ts properly at the top, agrees with the contour and even stands out for the queues. The proximity between the precision values of the adjustment proles did not limit the categorical decision that PVII gives the best mathematical representation of the peaks.

Crystallite size and microdeformation
Imperfections modify the intensity distribution of the Bragg reection and the peak shape of polycrystalline materials. This modication of peak shape, which denes the microstructure, in turn strongly indicates the physical, mechanical and chemical properties of materials. 19 Among the major existing methods for extracting the sizes of coherent domains from the diffraction peak, the Scherrer equation is the most widely used. Thus, for incident monochromatic radiation on a mono-dispersed powder of cubeformed crystallites, 27 the expression derived by Scherrer (except for a constant that arises from the Gaussian representation of the peak) for the crystallite size 28 is Fig. 1 Comparative graph of the adjustments V, p-V and PVII for the NiO (200) (left) and GDC (111) (right) peaks of the calcined sample.
In other words, t hkl is the "apparent" crystallite size in the perpendicular direction to the network planes, hkl are the Miller indices of the planes under consideration, b f hkl is the integral width of the peak at 2q radians of adjustment f, q hkl is the Bragg angle and l is the wavelength of the X-rays used.
Crystal lattice deformations are represented by multiple displacements of atoms from their positions into an idealized structure due to dislocations, vacancies, interstitial and substitutional defects. It should be noted that the distances between planes are continually changing according to d 0 À Dd and d 0 + Dd (where d 0 and Dd are the interplanar distances of an ideal crystal and the average change in the distance between hkl planes in the crystal volume, respectively). The derivation of 3 from the Bragg equation is If all values are assumed with equal likely stress values between 0 and a maximum value, then 43 corresponds to the maximum deformation limit. 29 If the crystallite size and deformation are simultaneously present, microstructure analysis naturally involves a competition between the contributions of the crystallite size and the deformation to the width of the diffraction peak.
Schoenin suggested that size-broadening is represented by the [L] prole and deformation-broadening by the [G] prole and proposed a graphical method for the separation of each contribution to the broadening of each peak. 30 However, much earlier, Williamson and Hall assumed that the width originates from a relationship of type [L]. Based on the above, the following equations are used in the analysis of multiple lines: 13 For Hall, 31 both proles are described by [L] functions: Meanwhile, Kurdyumov et al. 32 proposed that both proles are described by [G] functions: However, Schoenin 30 and Halder and Wagner 33 showed that the prole describing the crystallite size is given by the [L] function and the deformation is represented by the [G] function. Thus, Halder and Wagner 33 developed the equation where b f T is the width of the prole, b f C is the contribution to the prole width due to crystallite size and b f S is the contribution to the prole width due to deformation.
Eqn (11) is called the Williamson-Hall equation. Eqn (13) is similar to the approach of Halder and Wagner 24 for the integral width of a function V, and expression (12) is valid for a Gaussian presumption.
Corrections to the observed width using eqn (6)-(8) are applied in their order of relations with eqn (11)-(13) under the assumption of the mathematical proles that represent the crystallite size and the microstrain, respectively.
Microstructure analysis of crystallite size and the microstrain multi-line comes from an extensive study supported by propagation error theory.

Identication of phases of NiO-GDC composites
XPHS is a rst step to conrm the polycrystalline nature as well as the nanosize of both the as-prepared and calcined powders. With regard to the synthesis route and the calcination temperature, the powders showed imperceptible amounts of carbon, nitrogen and hydrogen. In short, during the calcination process, all the waste obtained from combustion was eliminated. Also, this thermal treatment promoted the complete oxidation of nickel. 34 The XRD patterns of the xNiO$(1 À x)GDC nanopowders (Fig. 2) were identied with JCPDS (Joint Committee on Powder Diffraction Standards) standards. The cubic phases of nickel oxide (78-0423), gadolinium doped ceria (75-0161) and metallic nickel (87-0712) belong to the space group Fm 3m. The crystalline phases of NiO and GDC (which indicates that there was no solid solution between them) remained unchanged even aer calcination, without the appearance of new diffraction peaks.
An increase in peak intensity accompanied by a decrease in peak width is indicative of crystallite growth by the calcination process. Changes in the conditions of thermal treatment, an important step in structural formation, not only determine the nal shape but also ensure the formation of high-dispersion material. 35

XRF
The intensity of the energy associated with each electron transition is proportional to the concentration of the elements present. Based on this principle, XRF analysis can be dened as a spectrum, showing the radiation intensity as a wavelength function. The results obtained from the XRF analysis (Fig. 3) of the as-prepared and calcined samples suggest that the amounts of NiO and GDC are not consistent with the theoretically predicted results obtained using the starting stoichiometry.
The tted impurities percentage, obtained using the soware, remained in the range of 0 to 0.67; this can be attributed to semi-quantication error because the metallic nickel has been assumed to be nickel oxide in the uorescence analysis.
The exothermic reaction of the SC can generate an intense amount of heat because the critical temperature produced during the reaction is between 2000 K and 3000 K. 36,37 This intense amount of heat manifests the ability to melt or volatilize the reagents as well as the products; sometimes, both melting and volatilizing will occur. Therefore, the adiabatic ame temperatures of combustion were calculated as a possible cause of divergence between the theoretical expected values and the outcomes obtained from both Rietveld and XRF.
The thermodynamic data of reagents and products include the enthalpies of reaction for combustion, 38-41 while the amounts of gases generated were calculated based on eqn (1). It is assumed that GDC z CeO 2 ¼ À260 kcal mol À1 and Gd(NO 3 ) 3 $6H 2 O z À700 kcal mol À1 . Therefore, the ame temperatures as a function of the fuel/oxidant ratio were estimated: where DH prod and DH reag are the enthalpies of formation of the products and reagents, respectively, T C is the critical temperature of the theoretical adiabatic ame and C p is the molar heat capacity at constant pressure. 39,41 Despite the complexity of the combustion thermal behavior, eqn (14) assumes an ideal thermodynamic process in which there will be no heat exchange with the environment. The adiabatic argument is under the rst law of thermodynamics, which allows a maximum temperature that can be generated during the combustion process. Thus, for the as-prepared samples, the maximum range of temperatures calculated according to the nickel content was 1189.5 K # T C # 1301.8 K. These temperatures are consistent with the measurements made in image analysis by Chinarro et al. 42 to study the synthesis of ceramic and ceramic-metal materials using combustion. However, it can be suggested that the temperatures during the synthesis were not solely responsible for the differences found between the expected results and the results obtained by Rietveld and XRF. The deviation from linearity shows that SC is rarely a complete reaction, and as a result, the products are highly heterogeneous in nature.

Rietveld renement
Within modern X-ray diffraction analysis, the TOPAS program is distinguished by the denition of new standard sets for prole and structural analysis by an efficient method where all the proles use convergence and apply it to tting techniques. In fact, among the most important applications, it excels at the incorporation of a modied Rietveld renement that increases precision and avoids the deconvolution of overlapping peaks. As shown in Fig. 4, even aer applying the Rietveld method, the amounts of NiO and GDC do not match the theoretically predicted amounts. The amounts of NiO and GDC found in the calcined sample are the same as those found in the starting sample. The areas of the diffraction peaks of the two phases coincide with each other, which indicates that during calcination, crystallization of the amorphous phase has not occurred in the starting material. During calcination, the nickel in the starting material is only oxidized, without any crystallization of the amorphous phase; this is evident from the identical baselines of the diffractograms and the doubled peak areas of the calcined sample compared with those of the starting material. The goodness interval of the as-prepared samples was 1.06 # GoF # 1.33 and that of the calcined samples was 1.05 # GoF # 1.10. The lattice parameter of the phases was independent of x and had a marginal error of 0.0002 (lattice parameter JCPDS a NiO ¼ 4.1790 A, a GDC ¼ 5.4180 A, and a Ni ¼ 3.5238 A) due to the absence of nickel in the asprepared sample (x ¼ 0.1).

Size-microdeformation analysis with V-V
A precise description of powder pattern shape proles is critical to the success of any adjustment application. The V-V approach    employed by TOPAS 43 allows the calculation of L Vol according to eqn (9) for an intermediate crystallite size and according to eqn (10) for deformation, which are modeled by a function V. The approach with the TOPAS fundamental parameters assumes the calculation of h with distortion Dd/d and a network with 50% probability of being related to the distortion. 44 The obtained crystallite sizes conrmed their nanosized natures. The crystallite growth obeys the thermo-chemical events involved in their synthesis and subsequent calcination. As shown in Fig. 5 and 6, GDC has a tendency toward crystallite growth (both in preparation and calcination of the samples) irrespective of the nickel concentration. Furthermore, NiO growth was intrinsically linked to the increase in nickel concentration during both the preparation and the calcination process.
Although the XRD patterns did not show signicant peak shiing, the lines are broadened slightly with respect to the diffraction angle, which indicates the minimal presence of microstrain (see Table 1). In many cases, the difference between the coefficients of thermal expansion is responsible for the deformation. 45 Consequently, the physical meaning of the results can be related to the proximity between the thermal expansion coefficients of GDC (12 Â 10 À6 K À1 ) and NiO (14 Â 10 À6 K À1 ).

Size-microdeformation multi-line analysis
Usually, the crystallites in a sample have the same shape and dimensions; therefore, the apparent size is inuenced by variations in the crystallite shape and size, and it is thus difficult to evaluate the apparent size. These restrictions are also implicitly included in the graphical method, which essentially combines eqn (9) with an apparent strain relation derived from Bragg's law, i.e., eqn (10). 46 Single-line analysis requires adjustment proles that allow deconvolution into analytic functions, whereas multi-line analysis requires any distribution that is used as an adjustment which will allow separation of the contributions to the broadening of the peak, crystallite size and microstrain, without deconvolution by means of interpreting the specic parameters for the linear t.
The graphical method [L]-[L] shows the importance of the sign of the microstrain value. GDC shows compressive strain and NiO shows tensile strain for both the as-prepared and calcined samples. The Gaussian shape assumption for the deformation results in a positive elongation for the nanocomposites. An atom such as gadolinium within cerium oxide is seen as a substitutional defect which can induce microstrain by compression of the neighboring crystals, while nickel oxide can cause microstrain due to stress. 45 There is no possibility of resolving the overlap between the background diffractogram baseline and the low intensity NiO peaks (x ¼ 0.1, 0.2, 0.3 for the as-prepared and x ¼ 0.1, 0.2 for the calcined samples) in accordance with the results of Chavan et al. 45 The standard error adjustment parameter (m) presented at GDC peaks (222) and (400) and the three NiO peaks for x ¼ 0.4 and 0.5 for the as-prepared and x ¼ 0.2, 0.5 for the calcined samples was high. The magnitude of the plastic deformation was very small, on the order of 10 À3 , 10 À4 and 10 À5 . 47  Multi-line analysis considers the intrinsic contribution of the deformation to the broadening of the diffraction peak; therefore, it indicates a strain signicantly larger than or less than zero, and also confers an increase of the average crystallite size for all the crystallographic directions, 48 as shown in Fig. 7. However, the microstrain resulting from multi-line analysis allows dismissal of the microstrain effect in both the as-prepared and calcined samples. Indeed, these results are comparable with the microstrain value of silicon powder (considering the microstrain value of silicon, which is almost free of dust, 0.01%). 49

SEM and HR-TEM analyses
Particle size is a critical parameter in processing materials and ne crystallites from nanopowders, and this parameter generally improves the mechanical, thermal, electrical and magnetic properties of ceramics, sintered metals and composites. 50 The SEM images of the calcined nanocomposites (Fig. 8) showed homogeneity and less agglomeration compared to the asprepared nanopowders. The spectrograms (inset) of the elemental chemical analysis conrmed the presence of nickel, oxygen, cerium and gadolinium along with the chemical composition of the as-prepared and calcined samples, respectively.
The nanocrystalline nature and the arrangement of the network of planes with atomic resolution is shown in Fig. 9. Also, the SAED images conrmed the electron diffraction from the network planes of the respective phases of the nanocomposites. The crystallographic planes of GDC (yellow) and the crystallographic planes of NiO (green) were identied. Unfortunately, the measurement accuracy has limited the identication (red) of nickel (220), GDC (331) and NiO (311), due to their measurements of 8.03 nm À1 and 8.08 nm À1 ; these match the measurements of GDC (420) and NiO (222), which are 8.25 nm À1 and 8.35 nm À1 , respectively. Fig. 9 AP1 and CA1 clearly show the appearance of aggregates of nanoparticles with internal crystalline structures. A size distribution of nanoparticles between 5 and 10 nm is observed in AP1, whereas in the case of CA1, a size distribution of nanoparticles between 10 nm and 20 nm is observed due to their crystallite growth during the heat treatment. Both the as-

Conclusions
The self-sustained combustion (SC) route is an effective and lowcost method for the production of materials on an industrial scale. This synthesis technique ensures the preparation of xNiO$(1 À x)GDC nanomaterials. However, the reaction rarely goes to completion, and the end product is highly heterogeneous.
Heat treatment by calcination is a versatile technique that promotes the complete oxidation of nickel, removes organic residues, reduces heterogeneity, releases stress within the composites and also increases the crystallite size.
PVII is a simple and convenient mathematical function to represent XRD patterns with the highest precision, even without physical justication for the choice of an adjustment prole.
The behavioral inspection of the XRD patterns with respect to x showed a strange tendency regarding the peak intensities. In fact, the quantitative analysis by Rietveld renement and XRF conrmed that the amounts of NiO and GDC phases in the asprepared samples do not match those of the subsequently calcinated samples.
The maximum theoretical adiabatic ame temperatures calculated for the combustion process were not as high as those for melting and/or volatilizing reagents or products of the synthesis.
To apply the appropriate correction for instrumental broadening, the peak shape is mandatory, since the Gaussian form appropriately demonstrated the effects arising due to the instrument.
The crystallite size behavior with respect to the concentration of nickel in both the preparation as well as the calcination is similar in both the approaches proposed in this study. The V-V analysis resulted in a minimum margin of error with a maximum of 5% only.
It is possible to correct the difference in the results obtained from the crystallite size between the V-V and graphical methods by subtracting the "noise" background baseline with the XPHS soware tool and the application of the basic parameters of TOPAS soware.
The non-zero values of microstrain obtained from the graphical methods are due to the deformation effects in the diffraction line and, hence, to the highest crystallite size. The V-V method did not detect the deformation; thus, a smaller crystallite size was observed.
Graphical methods differ in the expansion or compression of the network, giving a positive or negative sign for the linear t parameter which interprets the microdeformation. In general, the results obtained from The quasi-imperceptible values of the microdeformation allow us to infer them to be the cause of the proximity of the thermal expansion coefficients of NiO and GDC. The results obtained for the crystallite size with XRD are in agreement with the HR-TEM results.