X-ray diffraction analysis by Williamson-Hall, Halder-Wagner and size-strain plot methods of CdSe nanoparticles- a comparative study
Graphical abstract
Introduction
Semiconductor nanoparticles, in the dimension of 1–100 nm, possess unique size-dependent many physical properties, different from their bulk counterpart [1,2]. It is reported that elastic properties is one of the important physical properties, tuning of which, can modify many physical properties such as optical properties and surface properties and because of which, many semiconductor nanoparticles find enormous application in different branches of science such as in the field of optoelectronics devices as light-emitting diodes [3], solar cells [4].
Cadmium selenide (CdSe) is one of the important group II-VI semiconductor nanoparticles having a direct band gap of 1.74 eV, with an exciton Bohr radius of 6 nm [[5], [6], [7]]. CdSe nanocrystals reported to exhibit cubic (zinc blende) and hexagonal (wurtzite) lattice structure [8], which can be prepared by many suitable synthesis methods [[9], [10], [11]]. In nanocrystals, there exists intrinsic strain because of size confinement and this important elastic property can be tuned by varying synthesis parameters, such as pH and concentration, which in turn affects the optical and other properties [12]. X-ray Diffraction (XRD) analysis of a nanocrystal can confirm the crystallinity of the sample, which shows different peaks, related to different reflection planes [13]. It is well known that because of size confinement in nanocrystals and presence of intrinsic strain, which originates due to size confinement, broaden the XRD peaks. Thus, a physical peak broadening primarily consists of two parts; size-dependent broadening and strain induced broadening [14]. The most common sources of the lattice strain are dislocation density, point defects, grain boundary junction, contact or sinter stress, and stacking faults [[15], [16], [17], [18]]. So, from the XRD peak broadening analysis, the size of the nanocrystals as well as the value of the intrinsic strain, including other elastic properties such as stress, energy density, which are related to strain, can be determined indirectly. There are many methods for this, such as Williamson-Hall Method, Warren-Averbach Method and Balzar Method. Warren-Averbach and Balzar method consider Stokes fourier de-convolution method [[27], [28], [29], [30], [31]], whereas Williamson-Hall method uses the FWHM of the diffraction peak and hence, it is very easy and suitable one for determination of different elastic properties including strain, along with average size calculation.
Here, our interest lies in the determination of different elastic properties of the wet chemically synthesized CdSe nanocrystals, from their X-ray diffraction data, using Williamson-Hall (W–H) analysis, Size-Strain Plot (SSP) and Halder-Wagner (H–W) Method. Williamson-Hall analysis comprises of uniform deformation model (UDM), uniform stress deformation model (USDM), and uniform deformation energy density model (UDEDM) to calculate the various elastic parameters such as strain, stress and energy density respectively. Again, size-strain plot considers the size broadened part as Lorentzian function and the strain broadened part as Gaussian function of the XRD peak profile. The advantage of SSP model is that, it gives more importance to the low angle XRD reflection peak, where the accuracy and precession of the XRD data are high. Due to this, size estimation from the SSP model is more accurate than W–H method [[23], [24], [25]]. Halder-Wagner Method, on the other-hand, assumes the physical peak broadening as voigt function and considering that, average size and strain can be estimated from the XRD peak broadening [26].
In the present work, we have done a comparative study of various elastic parameters of chemically prepared CdSe nanocrystals based on the XRD peak broadening using different models of the W–H plot, along with SSP method and H–W method. Subsequently, their morphological analysis has been performed on high resolution Transmission electron microscopy (HR-TEM), atomic force microscopy (AFM) and field emission scanning electron microscopy (FE-SEM), where the average size obtained from these methods matches very well with the obtained results from XRD analysis.
Section snippets
Chemical synthesis
For the preparation of CdSe nanocrystals, selenium precursor has been prepared by dissolving 0.2 mmol of selenium powder and 0.5 mmol of sodium borohydride in 10 mL of distilled water, which is constantly stirred for 1 h at 600 rpm [27]. Under this vigorous reaction, selenium is reduced within a few minutes by forming a colorless sodium hydrogen selenide (NaHSe). Again, in another beaker, containing 10 mL of distilled water, 0.2 mmol of cadmium chloride and 1 mmol of 3-mercaptoacetic acid (MPA)
X-ray diffraction analysis
The X-ray diffraction (XRD) profile of chemically prepared CdSe nanoparticles, in the range of 20° < 2θ < 60° with a step size of 0.02° is shown in Fig-1, which has been taken in Bruker D8 diffractometer, using CuKα1 radiation with the wavelength of 1.5406 Å, having the accelerating voltage of 40 kV. Diffraction pattern shows peaks at 25.41°, 30.11°, 42.44° and 50.18°, corresponding to the planes (111), (200), (220), and (311), which matches with the stick pattern of the Joint Committee on
Conclusion
MPA capped CdSe nanoparticles have been prepared by chemical route, which is further studied through X-ray diffraction analysis for their crystallinity and structural properties. XRD peak broadening analysis has been performed to calculate the various elastic properties of the CdSe nanocrystals such as intrinsic strain, stress, energy density, using Scherrer plot, different models of Williamson-Hall plot, Size-Strain Plot and Halder-Wagner Method, along with the determination of the average
Acknowledgement
The authors are also thankful to Inter University Accelerator Centre (IUAC), New Delhi, India, for providing the financial support for this work under UFR funds (ref: IUAC/XIII.3A/dated 28.12.2018). The authors are thankful to SAIF NEHU, Shillong, India, for providing the TEM data and to Central Instrumentation Centre (CIC), Tripura University for AFM and SEM analysis. Authors are also thankful to Krishna Deb, Department of Physics, NIT Agartala, for providing XRD data. The authors are grateful
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