X-ray peak profile analysis of Sb2O3-doped ZnO nanocomposite semiconductor

In the present work, nanostructured ZnO doped with (2, 4, 6, 8 and 10 ) is prepared by conventional solid state reaction method. X-ray diffraction peak intensities are sharp and narrow, confirming that the sample is of high quality with good crystallinity. The intensity and full width at half-maximum of x-ray diffraction peaks of (100) and (101) decreases with the increase of dopant in ZnO. X-ray peak profile analysis was used to evaluate the crystallite size and lattice strain by the Williamson-Hall (W-H) method. Using the models namely uniform deformation model (UDM), uniform stress deformation model (USDM) and uniform deformation energy density model (UDEDM) of W-H method, the physical parameters such as strain, stress, and energy density values were calculated. The surface morphology and elemental composition of the samples were characterized by scanning electron microscope and energy dispersive spectroscopy.


Introduction
Zinc oxide (ZnO) has been considered as one of the most promising materials for optoelectronic applications due to its wide energy band gap of 3.37 eV, large exciton binding energy of 60 meV, high optical gain, and high radiation and temper ature stability [1]. In order to extend the application possibility of ZnObased devices, several doping elements have been studied and reported, such as Ga, N, In, and Sn. However, it is difficult to achieve p-type doping in ZnO. Recently, there were reports indicating that doping with group V elements, such as phosphorous (P), arsenic (As), and antimony (Sb) was achieved, and the p-type materials exhibited super ior electrical properties [2]. Among the group V elements, anti mony has similar ionic radius to that of Zn ion [3]. Some reports suggested that doping with antimony might produce more stable p-type conductivity and higher carrier concentra tion [4,5]. Antimony oxide (Sb 2 O 3 ) had a wide band gap of 3.4 eV, which is widely used in various applications as cata lyst, flame retardant, optoelectronic and photoelectric devices [6]. The photocatalytic activity of pure Sb 2 O 3 is low due to high band gap (E g = 3.4 eV) [7]. The coupling of Sb 2 O 3 with other metal oxides can effectively improve the photocatalytic activity. Recently, Sb 2 O 3 doped ZnO microflowers have been deposited onto tiny µ−chip to fabricate a smart chemical sensor for toxic ethanol [8]. The present work is devoted to understand the microstructural properties of Sb 2 O 3 doped ZnO. However, the xray peak profile analysis of Sb 2 O 3 with ZnO has not yet been reported. Xray peak profile analysis (XPPA) is used to estimate the microstructural quantities and correlate them to the material properties. It is a simple and powerful tool to estimate the crystallite size and lattice strain [9]. The lattice strain and crystallite size affect the Bragg peak in different ways and both these effects increase the Bragg peak width, peak intensity and shift the 2θ peak position accordingly. The pseudoVoigt function, Rietveld refinement, and WarrenAverbach analysis are used to estimate the lattice strain and crystallite size [10][11][12]. However, the Williamson Hall (WH) analysis is a simplified integral breadth method employed for estimating crystallite size and lattice strain, considering the peak width as a function of 2θ [13,14]. In the present work, XPPA is carried out to estimate the crys tallite size, strain, stress and strain energy density of Sb 2 O 3 doped ZnO nanoparticles based on modified WH plots using uniform deformation model (UDM), uniform stress deforma tion model (USDM), and uniform deformation energy den sity model (UDEDM). A detailed study using these models on ZnO doped with different concentrations of Sb 2 O 3 samples is not reported yet. This study reveals the importance of WH models in the determination of crystallite size and strain of Sb 2 O 3 doped ZnO nanocomposite semiconductors.

Experimental details
Nanostructured ZnO doped with 2%, 4%, 6%, 8% and 10% of Sb 2 O 3 were synthesized by conventional solidstate reaction method. The appropriate ratio of the constituent oxides, i.e. ZnO and Sb 2 O 3 (99.99% Aldrich Chemicals, USA) were milled in a planetary ball miller (Retsch PM 200) with tung sten carbide milling media (10 mm diameter balls) at a ballto powder weight ratio of 10:1 and at a speed of 350 rpm for 12 h. These mixed powders was calcined at 900 • C for 10 h and finally sintered in a programmable SiC furnace at 1100 • C for 3 h with a heating and cooling rate of 10 • C min −1 . The xray diffraction (XRD) patterns of the prepared samples were recorded at room temperature using Philips: PW 1830 with Cu-K α radiation λ = 1.5418Å in a wide range of Bragg angles 2θ (20 • < 2θ < 70 • ) with scanning rate of 2 • C × min −1 . The pseudoVoigt function which is a linear combination of a Lorentzian and Gaussian function was used in order to obtain the information about the shapes and inte grated intensities of Bragg reflections for the investigated samples. The diffraction lines were modelled by pseudoVoigt functions and the background by a fifthorder polynomial. The following parameters were refined: the overall scale factor; the background (six parameters of the 5 th order polynomial); 2θ-Zero; the unit cell parameters; the specimen displacement; the Adv. Nat. Sci.: Nanosci. Nanotechnol. 9 (2018) 035018 halfwidth parameters; the peak shape; the reflectionprofile asymmetry; the Lorentzian isotropic strain; the isotropic thermal parameters. Also the preferred orientation parameters were refined in order to obtain a good fit of the calculated diffraction pattern. The surface morphology of the samples has been carried out by scanning electron microscope (SEM) (Model: Carl Zeiss, EVO MA15) instrument operated at 15 kV with a resolution of 3.5 nm. The elemental composition of ZnO doped with Sb 2 O 3 was determined from energy dis persive xray spectroscopy (EDS) which is attached to SEM.  (103), corresponding to ZnO (space group p63mc, JCPDS no. 361451) indicating that the phase of the sample was wurtzite structure. XRD peaks corresponding to the Zn 7 Sb 2 O 12 (JCPDS no. 741858) phase were observed, which indicates that the structure shift from mono phase to hetero phase. The intensity of these peaks increased with the increase of doping concentration of Sb 2 O 3 in ZnO. The second phase α-Zn 7 Sb 2 O 12 plays an important role in the microstructure development [15]. The intensity of the diffraction peaks (100) and (101) decreased and their full width at halfmaximum (FWHM) increased with the increase of Sb 2 O 3 doping con centration in ZnO. Such changes in crystallinity might be the result of changes in the atomic environment due to impurity doping on ZnO samples. No change in the crystalline struc ture was noticed, which suggests that the most Sb atoms were incorporated in ZnO wurtzite lattice. Sb dopant in ZnO lattice was expected to substitute Zn atom and connect two vacancies of Zn to form a Sb Zn -2V Zn complex [16]. According to Xiu et al [17] the complex Sb Zn -2V Zn could be the explanation of strong p-type conductivity in Sb doped ZnO films. This result is attributed to a small lattice mismatch between radii of Zn 2+ (0.074 nm) and Sb 3+ (0.076 nm), and it indicates that Sb ions systematically substituted Zn ions without deteriorating its crystal structure.

Results and discussion
The average crystallite size (D) was calculated using Scherrer's formula [18] where D is crystallite size, K (= 0.94) is shape factor and λ (= 0.154 nm) is the wavelength of Cu-K α radiation. The crystallite size estimated from Scherrer formula is found to be decreased from 56 to 32 nm with the increase of Sb 2 O 3 content in ZnO. The decrease of crystallite size correlates with a large developed surface of grain boundaries, thus leading to a larger scattering effect. Another reason for the decreased crystallite size values may be due to the drag force exerted by the dopant ions on boundary motion and grain growth. The increase of Sb 2 O 3 doping progressively reduces the concentration of zinc in the system. Thus the diffusivity is decreased in ZnO, which results in a suppressed grain growth of Sb 2 O 3 doped ZnO samples. At the same time, the substituted Sb ions pro vide a retarding force on the grain boundaries. If the retarding force generated is more than the driving force for grain growth due to Zn, the movement of the grain boundary is impeded [19,20]. This in turn gradually decreases crystallize size with increasing Sb 2 O 3 concentration. There exist reports of similar trend in some Mn doped ZnO systems [21,22]. The lattice parameters a and c of ZnO doped with different concentrations of Sb 2 O 3 were calculated from the positions of the (100) and (002) peaks, respectively using the formulas as reported in our previous work [23]. The lattice constants calculated from XRD data for Sb 2 O 3 doped ZnO composite samples are close to the lattice constants given in the standard data (JCPDS no. 792205, 800075). The change in the lattice parameters of ZnO host material depends on the ionic radii of the impurity that substitute the Zn ions at the lattice site [24]. In case of Sb doping the ionic radii of the Sb 3+ (0.076 nm) is larger than Zn 2+ (0.074 nm). If Sb 3+ ion substitutes Zn 2+ ion in ZnO host lattice, then the variation in the lattice constants is expected due to ionic radii difference which has also been reported in the previous literature [25]. The increase in lattice constant values with increasing Sb 2 O 3 concentration in ZnO is due to interstitial position of Sb ions in ZnO lattice.
The volume of the ZnO hexagonal cell was calculated using the formula The Zn-O bond length was calculated from the formula [26,27] In wurtzite structure, the parameter u is given by u = a 2 3c 2 + 0.25. The degree of crystallinity X c was calculated using the fol lowing equation where β 002 is the full width at half maximum (in degrees) of (002) Miller's plane. The unit cell volume is calculated for all samples using lattice parameters. The values of the unit cell volume are increasing with increasing Sb 2 O 3 concentration in ZnO which led to increase the bond length. The parameter u represents the relative position of two hexagonal closepacked sublattices i.e. the position of the anion sublattice with respect to the cation sublattice. The enhancement of parameter u rep resents the softer ZnO bond along the c-axis direction. The specific surface area of the crystallites of the samples was determined from XRD data. The specific surface area is a material property of solids which measures the total surface area of the crystallites present in per unit of mass. It is par ticularly significant for adsorption, heterogeneous catalysis, and reactions on surfaces. The specific surface area can be calculated by Sauter formula [28] where S is the specific surface area, D p is the size of the particle and ρ is the density of bulk ZnO which equals to 5.606 g cm −3 . The specific surface area of the samples increases with the increase of Sb 2 O 3 concentration in ZnO. The increase in specific surface area is due to presence of pores (as we noticed in SEM images) which leads to decrease in particle size. The structural param eters of different concentrations of Sb 2 O 3 doped ZnO estimated from xray diffraction data are given in table 1.

Williamson-Hall (W-H) methods
The broadening of XRD pattern is attributed to the crystallite sizeinduced or strain induced broadening. The significance of peak broadening of the sample evidence the large strain asso ciated with the powder and grain refinement. The instrumental broadening (β hkl ) of the diffraction peak was corrected using the equation The strain induced in powders due to crystal imperfection and distortion was calculated using the formula [29] The strain and particle size contributions to xray peak broadening are independent to each other and both have a Cauchylike profile, the observed line breadth is simply the sum of equations (1) and (8) By rearranging the above equation The above equations (9) and (10) are WilliamsonHall equations.
To make WilliamsonHall analysis, a plot is drawn with 4 sin θ along the x-axis and β hkl cos θ along the y-axis for all orientation peaks of Sb 2 O 3 doped ZnO nanoparticles as shown in figure 2. The crystalline size (D) was estimated from the y-intercept and the slope of the linear fit to the data gives the value of strain (ε). Equation (10) represents the uniform In the uniform stress deformation model (USDM) there is a linear proportionality between stress and strain given by σ = Yε which is known as the Hook's law within the elastic limit. In this relation, σ is the stress of the crystal and Y is the Young's modulus. Hook's law is a reasonable approximation to estimate the lattice stress. In USDM, the WilliamsonHall equation is modified by substituting the value of strain (ε) in the second term of equation (5) which yields Y hkl is the Young's modulus in the direction perpendicular to the set of crystal lattice plane (hkl). The uniform deformation stress is estimated from the slope of the line plotted between 4sinθ/Y hkl and β hkl cosθ, and crystallite size (D) from the yintercept as shown in figure 3.
The strain can be measured if Y hkl of hexagonal ZnO nano particles is known. The Young's modulus Y hkl for hexagonal crystal phase is related to their elastic compliances S ij as [30,31]     When the strain energy density (u) is considered, all the constants of proportionality associated with the stressstrain relation are independent. According to Hooke's law, the energy density u (energy per unit volume) as a function of strain is u = ε 2 Y hkl /2. Thus the equation (11) can be modified to the form The slope of the line plotted between β hkl cos θ and 4 sin θ(2/Y hkl ) 1/2 gives the value of uniform deformation energy density. The lattice strain can be evaluated by knowing the Y hkl values of the sample. The value of u was calculated from the slope and the crystallite size (D) is estimated from the y-intercept of linear fit WH equations modified assuming UDEDM and the corresponding plots are shown in figure 4. From equations (11) and (13), the deformation stress and deformation energy density are related as u = σ 2 /Y hkl . It is to be note that though both equations (11) and (13) are taken into account in the anisotropic nature of the elastic constant, they are essentially different. This is because in equation (7), it is assumed that the deformation stress has the same value in all crystallo graphic directions allowing u to be anisotropic, while equa tion (12) is developed by assuming the deformation energy to be uniform treating the deformation stress (σ) to be anisotropic. The scattering of the points away from the linear expres sion is lesser for figure 2 as compared with figures 3 and 4. The results obtained from WH models (UDM, USDM and UDEDM) are summarized in table 2. It can be noted that the values of the average crystallite size obtained from the UDM, USDM and UDEDM are in good agreement with the values obtained from Scherrer's formula. It was observed that the strain and stress values increased with decreasing average crystallite size. This study reveals the importance of models in the determination of crystallite size of Sb 2 O 3 doped ZnO nanoparticles. Thus all the three models are found to be suit able for the determination of crystallite size. It is also observed that the surface of the sample is dense up to 6% doped Sb 2 O 3 in ZnO, as Sb 2 O 3 content is increased up to 10 at%, the surface is bumpy and rough. Figures 6(a)-(e) shows the EDX spectra of different concentrations of Sb 2 O 3 doped ZnO. The spectra revealed the presence of Zn, Sb and O elements along with their atomic percentage composition. The presence of O K α peak at 0.56 keV, Zn L α peak at 1.01 keV, Zn K α peak 8.68 keV, Sb L α peak at 3.64 keV was observed.

Surface morphology and elemental analysis
To study the distribution of Sb in the nanostructures, we performed elemental mapping for the samples. It is noticed that the distribution of zinc in the sample was homogeneous, oxygen and antimony remained inhomogeneously distrib uted. With the increase of Sb concentration, the concentration of zinc decreased significantly. We believe the incorporated Sb atoms substitute Zn atoms from their lattice sites in ZnO nanostructures.

Conclusions
ZnO doped with different concentrations of Sb 2 O 3 samples were prepared by solid state reaction method. Structure analysis indicates that Sb ions substitute for Zn ions without changing the wurtzite structure. The xray peak profile analysis is performed for the estimation of crystallite size and lattice strain. The peak broadening was analyzed by the Scherrer's equation and modified forms of WH models viz. UDM, UDSM, and UDEDM. Hence these models are highly preferable to define the crystal perfection. A modified WH plot has been used to determine the crystallite size, strain induced broadening due to lattice deformation and energy density value with a certain approximation. The average crystallite size estimated from Scherrer's formula and WH analysis shows a small variation because of the difference in averaging the particle size distribution. The strain values obtained from the graphs plotted for various forms of WH analysis, i.e. UDM, USDM, and UDEDM were found to be accurate and comparable.