Comparing Methods for Calculating Nano Crystal Size of Natural Hydroxyapatite Using X-Ray Diffraction

Abstract

We report on a comparison of methods based on XRD patterns for calculating crystal size. In this case, XRD peaks were extracted from hydroxyapatite obtained from cow, pig, and chicken bones. Hydroxyapatite was synthesized through the thermal treatment of natural bones at 950 °C. XRD patterns were selected by adjustment of X-Pert software for each method and for calculating the size of the crystals. Methods consisted of Scherrer (three models), Monshi–Scherrer, three models of Williamson–Hall (namely the Uniform Deformation Model (UDM), the Uniform Stress Deformation Model (USDM), and the Uniform Deformation Energy Density Model (UDEDM)), Halder–Wanger (H-W), and the Size Strain Plot Method (SSP). These methods have been used and compared together. The sizes of crystallites obtained by the XRD patterns in each method for hydroxyapatite from cow, pig, and chicken were 1371, 457, and 196 nm in the Scherrer method when considering all of the available peaks together (straight line model). A new model (straight line passing the origin) gave 60, 60, and 53 nm, which shows much improvement. The average model gave 56, 58, and 52 nm, for each of the three approaches, respectively, for cow, pig, and chicken. The Monshi–Scherrer method gave 60, 60, and 57 nm. Values of 56, 62, and 65 nm were given by the UDM method. The values calculated by the USDM method were 60, 62, and 62 nm. The values of 62, 62, and 65 nm were given by the UDEDM method for cow, pig, and chicken, respectively. Furthermore, the crystal size value was 4 nm for all samples in the H-W method. Values were also calculated as 43, 62, and 57 nm in the SSP method for cow, pig, and chicken tandemly. According to the comparison of values in each method, the Scherrer method (straight line model) for considering all peaks led to unreasonable values. Nevertheless, other values were in the acceptable range, similar to the reported values in the literature. Experimental analyses, such as specific surface area by gas adsorption (Brunauer–Emmett–Teller (BET)) and Transmission Electron Microscopy (TEM), were utilized. In the final comparison, parameters of accuracy, ease of calculations, having a check point for the researcher, and difference between the obtained values and experimental analysis by BET and TEM were considered. The Monshi–Scherrer method provided ease of calculation and a decrease in errors by applying least squares to the linear plot. There is a check point for this line that the slope must not be far from one. Then, the intercept gives the most accurate crystal size. In this study, the setup of values for BET (56, 52, and 49 nm) was also similar to the Monshi–Scherrer method and the use of it in research studies of nanotechnology is advised.

Relationship between Young’s Modulus and Planar Density of Unit Cell, Super Cells (2 × 2 × 2), Symmetry Cells of Perovskite (CaTiO3) Lattice

“…In addition, crystallographic parameters ( Table S1 ) of CaTiO 3 and analyzed data by X’Pert [ 24 ] nasiri are recorded as the cell volume = 54.44 3 and crystal density = 4.14 ± 0.01 g/cm 3 , and the space group is Pm-3m. In addition, the crystal size of CaTiO 3 was calculated by the Monshi–Scherrer equation ( Figure S2 ) [ 25 ] and BET analysis. The crystal size values were registered at ~59.10 and 63.02 nm, respectively.…”

Biologically Compatible Lead-Free Piezoelectric Composite for Acoustophoresis Based Particle Manipulation Techniques

“…In previous research, the polymorphic rhombohedra–tetragonal phase transition temperature was found shifted toward room temperature with the Li doping for BCZT [ 26 ]. The study showed that BCZT lead-free piezoelectric ceramic with improved performance properties at room temperature can be achieved by shifting the polymorphic phase transition point nearer to room temperature through the addition of LiF [ 9 , 26 ].…”

“…The lattice constant a can be calculated using the equation [ 9 ]: where, h , k , and l are indexes of the XRD reflection peak, and d is the interplaner spacing.…”

“…Further, calculations of the average BT crystallite diameter D XRD can be estimated from the equation [ 9 ] below, using the data of most intense (110) peak. where, C —constant; B 1/2 —the full width of the half maximum in 2 θ ; θ —corresponding Bragg angle.…”

“…The aim of this research paper is to propose a technology based on the principle of bulk acoustic wave generation. It is related to the development of lead-free piezoceramics [ 8 , 9 , 10 ] which may be applied in the process of acoustophoresis [ 3 , 4 , 5 ]. Acoustophoresis is a noncontact and label-free mode of manipulation process separating the particles using high intensity sound waves and eliminating the necessity of earlier mentioned exclusion filters or membranes in microfluidic devices.…”