Corresponding author: S. Anand ( anandnapoleon@gmail.com ) © 2019 H. Irfan, K Mohamed Racik, S. Anand.
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Citation:
Irfan H, Mohamed Racik K, Anand S (2018) X-ray peak profile analysis of CoAl2O4 nanoparticles by Williamson-Hall and size-strain plot methods. Modern Electronic Materials 4(1): 31-40. https://doi.org/10.3897/j.moem.4.1.33272
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CoAl2O4 nanoparticles were prepared by a sol-gel process using citric acid as chelating agent with different calcination temperatures of 600 to 900 °C. The crystalline spinel cubic phase was confirmed by X-ray diffraction results. High-resolution scanning electron microscopy (HRSEM) revealed that nanoparticles of CoAl2O4 morphology showed spherical forms with a certain degree of agglomeration. The Williamson-Hall (W-H) method and size-strain method to evaluate the size of crystallites and strain in the CoAl2O4 nanoparticles peak broadening were applied. Physical parameters such as strain and stress values were calculated for all XRD reflection peaks corresponding to the cubic spinel phase of CoAl2O4 in the range of 20 to 70° from the modified plot shape by W-H plot assuming a uniform deformation model (UDM), uniform stress deformation model (USDM), uniform deformation energy density model (UDEDM) and by the size-strain plot method (SSP). The CoAl2O4 NPs crystal size calculated on the W-H plots and the SSP method are in good agreement with the HRSEM Scherrer method.
CoAl2O4, sol-gel synthesis, strain analysis, W-H analysis, SSP method
Spinel oxide type AB2O4, where A and B represent two different sites tetrahedral and octahedral and the oxygen ions form a cubic closed structure, are a class of chemically and thermally stable materials that are suitable for a wide-ranging applications such as catalyst and magnetic materials [
In the class of nanomaterials, cobalt aluminate nanocrystalline spinel (CoAl2O4) is known as blue Thenard, commonly used as a catalyst, color filter for automotive lamps and pigment layer on luminescent materials due to their optical properties, thermal chemical, peculiar stability and photochemistry [
It is known that the crystallite size and strain are of a pattern that the two main key factors lead to the expansion of XRD diffraction peaks [
In this study, CoAl2O4 nanoparticles were prepared by the sol-gel method. X-ray diffraction analysis (XRD) and high resolution scanning electron microscopy (HRSEM) to examine nanoparticles Structural and morphological behavior of CoAl2O4 have been used. X-ray peak profile (XPPA) analysis was determined to calibrate the size of the crystallites and strain of CoAl2O4 nanoparticles based on UDM, USDM and UDEDM models. This work discussed the importance of W-H models and SSP method in calibration of crystalline size and strain parameters for CoAl2O4 nanoparticles.
CoAl2O4 nanoparticles were synthesized using Co(NO3)2 . 6H2O (LOBA chemie Ltd), Al (NO3)3× 9H2O (Merck), citric acid and deionized water. All of the chemicals above were of analytical grade and were used directly without further purification.
CoAl2O4 were prepared by a sol-gel method using citric acid as a chelating agent. First, a certain amount of cobalt nitrate (Co(NO3)2 . 6H2O) and aluminum nitrate (Al(NO3)3 . 9H2O) dissolved in deionized water. After that, appropriate amount of citric acid was added to the solution above with magnetic stirring. The molar ratio of metal ions to citric acid was 1:2. The mixed solution was continuously stirred for 1 hour and then heated to 80 °C until a highly viscous gel was formed. Then the gels were dried in a 110 °C oven and then calcined at desired temperatures (600-900 °C) for 5 h.
X-ray diffraction pattern powder (XRD) was performed on a Bruker D8 Advance X-ray diffractometer. Morphological analysis and energy dispersion X-ray analysis was performed using EDAX attached to the high resolution scanning electron microscope (HRSEM, FEI, Quanta 200F).
The crystalline structure of the prepared samples was determined by XRD models reached between 2θ of (20) to (70°). Fig.
In general, X-ray diffraction analysis by peak width is due to instrumental amplification, increase in crystallite size and lattice strain due to dislocation [
β2D = [(β2measured) - (β2instrumental)]1/2 (1)
It is well known that the Scherrer formula provides only the lower limit of crystallite size. The size of crystalline nanoparticles is estimated by the Scherrer formula,
Where, D is the volume weighted crystallite size (nm), k is the shape factor (k = 0.94), λ is the X-ray wavelength (1.54056 Å), θ is the diffraction angle of Bragg and β is the expanded diffraction peak measured at FWHM (in radians). The size of crystallites of CoAl2O4 nanoparticles are shown in Table
Geometric parameters of the CoAl2O4 nanoparticles
Sample | Scherrer method | Williamson-Hall method | Size-Strain method | HRSEM | ||||||||||
UDM | USDM | UDEDM | ||||||||||||
D (nm) | D (nm) | ε no unit x10-3 | D (nm) | ε no unit x10-3 | σ (MPa) | D (nm) | ε no unit x10-3 | σ (MPa) | U (KJm-3) | D (nm) | ε no unit x10-3 | σ (MPa) | D (nm) | |
600 | 19.98 | 21.07 | 0.0236 | 21.07 | 0.0576 | 228.3 | 21.23 | 0.1152 | 231.9 | 108.6 | 20.11 | 0.00278 | 135.3 | 18.76 |
700 | 21.71 | 23.76 | 0.0827 | 24.58 | 0.1394 | 259.6 | 24.70 | 0.2788 | 264.3 | 138.5 | 21.39 | 0.00485 | 165.9 | 20.93 |
800 | 22.50 | 25.44 | 0.0010 | 25.58 | 0.2419 | 286.2 | 25.49 | 0.0483 | 216.2 | 98.6 | 23.79 | 0.01916 | 263.4 | 22.34 |
900 | 23.08 | 29.91 | 0.0016 | 30.04 | 0.0852 | 237.6 | 30.22 | 0.0172 | 102.8 | 56.8 | 24.79 | 0.01991 | 268.3 | 24.95 |
In many cases, X-ray diffraction patterns are influenced not only by the size of crystallites, but possibly also by lattice strain and lattice defects. Williamson-Hall analysis is a simplified integral breath method, clearly differentiates the armature size and strain induced deformation peak considering the broadening of the peak width as a function of 2 theta. Individual contribution to the line broadening of a Bragg reflection line can be expressed as:
βhkl = βs + βD (3)
Where βhkl represents the full width at half maximum (FWHM) of a radiant peak, and βs βD are the width due to the size strain, respectively. In the W-H relation it is assumed that the strain is uniform throughout the crystallographic direction, is given by βhkl
βhkl = (kλ/Dcosθ) + 4ε tanθ (4)
Rearranging Eq. (4) gives
βhklcosθ = (kλ/D) + 4εsinθ (5)
Here D and ε correspond to the value of the crystallite size and the value of the microstrain respectively. By potting 4sinθ, the average size of the crystallites and the strain can be estimated by the Y-intercept extrapolation and the slope of the line; See fig. 2.
According to Hooke’s law, within the elastic limit, there exists a linear proportionality relation between the stress (σ) and strain (ε)
σ = E ε (6)
where E is the elasticity modulus or Young’s modulus. This equation is an approximation that is valid for the significantly small strain. Hence, by assuming that the lattice deformation stress is uniform in the second term of equation signifying UDM and is replaced by ε = (σ/E) and the modified Eq. (5) is given by
βhklcosθ = (Kλ/D) + (4σsinθ/Ehkl) (7)
Here Ehkl is Young’s modulus in the direction normal to the set of (hkl) planes. The slope of the straight line between 4sinθ/Ehkl and βhklcosθ gives the uniform stress and the crystallite size D easily determined from the intercept (Fig.
1/Ehkl = S11 - 2(S11 - S12 - 0.5S44) (m12 m22 + m22m32 + m32m12) (8)
where,
m1 = h (h2 + k2 + l2)-0.5,
m2 = k (h2 + k2 + l2)-0.5 and
m3 = l (h2 + k2 + l2)-0.5.
The Young’s modulus Ehkl value for cubic CoAl2O4 NPs was calculated as 2.44 TPa. Fig.
The following model that can be used to find the energy density of a crystal called Uniform Deformation Energy Density Model (UDEDM). Previously, it is assumed that crystals are homogeneous and isotropic. Although in many cases, the assumption of homogeneity and isotropy is not justified. In addition, the proportional constants for strain stress relationship are not widely independent when studying deformation energy density (u). For an elastic system that follows Hooke’s law, the energy density (unit energy) can be calculated from the relation u=(ε2Ehkl)/2. Thus, the equation (9) can be rewritten according to the energy and strain relationship, that is,
βhklcosθ =(Kλ/D) + [4sinθ(2u/Ehkl)1/2] (9)
Plot of βhklcosθ versus 4sinθ(2u/Ehkl)1/2 is shown in Fig.
The Williamson-Hall plot showed that the line brosening was essentially isotropic. This indicates that the diffraction domains were isotropic and there was also a MicroStrain contribution. However, in the case of isotropic line broadening, it is possible to obtain a better evaluation of the size-strain considering an average ‘‘size-strain plot” (SSP), which has relatively less weight gain, is given to high-angle reflections where Accuracy is generally lower. In this approach, the “crystalline dimension” profile is assumed to be described by a Lorentz function and the “strain profile” of a Gaussian function. As a result, we have:
(dhkl βhkl cosθ)2 = (d2hkl βhkl cosθ) + (ε/2)2 (10)
where K is a constant dependent on the shape of the particles; For spherical particles is given as 03/04. In Fig.
Variation of crystallite size (D) with calcination temperature obtained from Scherrer method.
The morphology of cobalt aluminate synthesized nanoparticles was studied by high-resolution scanning electron microscopy (HRSEM). From Fig.
CoAl2O4 nanoparticles have been prepared by the sol gel method and are characterized by powder XRD and HRSEM analysis. From the XRD powder analysis, the peak line broadening of CoAl2O4 nanoparticles due to finite crystallite size and strain were analyzed by Scherrer’s formula, Williamson-Hall method based on UDM, UDSM and UDEDM models and Size strain plot method. W-H plot has been worked out and established to determine the crystallite size and strain-induced broadening due to lattice deformation. The W-H analysis based on the UDM, UDSM and UDEDM models are very helpful in calculating the estimation of crystallite size and strain. W-H has been developed and established to determine the size of crystallites and the elongated induced deformation due to deformation of the network. UDM-based U-DMS, UDSM and UDEDM analyzes are useful for calculating dimension estimation and deformation of crystallites. The size of crystallites and strain evaluated by the XRD powder measurements are in good agreement with HRSEM results. The elastic properties of the Young Sij (Ehkl) module were estimated by the values of the plane of the lattice (h, k, l). The methods discussed above were very useful in determining the average size of deformation crystals, stress and energy density value, including the size-strain method; it is highly preferable to set crystal perfection.
The Authors are thankful to Dept. of Nuclear Physics, University of Madras, Chennai for XRD facility.