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

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Experiments

_{Kα}radiation was used. A white and clean hydroxyapatite was obtained. Then, samples were grinded in a rotary ball mill with some volume ratios of fired grogs, steel balls, and empty space. The model of the ball mill was planetary Fritsch Pulverisette-5 (Kaunas, Lithuania). The particle sizes were micron scale, while the crystal sizes inside the particles were nanosize, as it is known in the literature [5]. The powder X-ray diffractions were taken at 40 kV and 40 mA, and recorded from 20 to 50 degrees for 2θ at a scanning speed of 2.5 degrees/minute and a step size of 0.02 degrees. The resulting patterns were studied by version 4.9 of High Score X’Pert software analysis, which uses the fundamental parameter procedure implemented in ASC suffix files. In addition, the specific surface area of the samples was measured by desorption isotherms of nitrogen (N

_{2}) gas through the use of a Brunauer–Emmett–Teller (BET) apparatus Gemini V analyzer, micrometrics GmbH, (Isfahan, Iran) For chemical elements of the samples, an energy dispersive X-ray (EDX) spectrometer Phillips/FEI Quanta 200 was utilized. In addition, for thin layers of the samples, the transmission electron microscopy (TEM), CM 10-Philips (Tehran, Iran) with acceleration voltage between 50 and 80 KV, was used.

#### 2.1. Preparation of Hydroxyapatite Powders

#### 2.2. XRD Analysis of Samples

## 3. Results and Discussions

#### 3.1. Scherrer Method

_{m}is the measured broadening, β

_{i}is the instrumental broadening, and β

_{d}was introduced as the corrected broadening responsible for crystal size. Furthermore, in this case, crystalline silicon was used as the reference material for calibration of instrumental error. The instrumental broadening and physical broadening of the sample measured through the full width half maximum (FWHM) and with utilizing the correction of physical broadening, it will be possible to follow up calculation on the crystal size with the Scherrer equation, such as cited in [16,17]. There are several publications that used calculation of the Scherrer equation only for the sharpest peak and they were not considering calculations for all or selected peaks.

#### 3.1.1. Straight Line Model in Scherrer Method

#### 3.1.2. Model of Straight Line Passing the Origin in Scherrer Method

#### 3.1.3. Average Model in Scherrer Equation

#### 3.2. Modified Scherrer Equation (Monshi–Scherrer Method)

^{(intercept)}gives $\frac{\mathrm{K}\mathsf{\lambda}}{\mathrm{L}}$, from which a single value of L is obtained from all of the available peaks. Lnβ versus ln(1/cosθ) is demonstrated in the plots of Figure 4, together with the equations of the linear least squares method obtained from the linear regression of data in plots. According to the Monshi–Scherrer equation, for finding the size of the crystals, Equation (6) is employed. When using X’Pert software, it is better for making and using an ASC file of peaks data (with suffix ASC) and obtain the peak list including FWHM, which is related to the fit profile icon (right click on the peak and select fit profile in X’Pert software) to create full fitting in finding β (FWHM). After plotting Equation (5) and obtaining the linear equation for the least squares method of all or some selected peaks, then,

^{(−6.0921)}= 0.00227, e

^{(−6.0826)}= 0.00228, and e

^{(−6.0285)}= 0.00240, respectively. Therefore, $\frac{\mathrm{K}\text{}\lambda}{\mathrm{L}}$ = 0.00227, $\frac{\mathrm{K}\text{}\lambda}{\mathrm{L}}$ = 0.00228 and $\frac{\mathrm{K}\text{}\lambda}{\mathrm{L}}$ = 0.00240 for cow, pig, and chicken tandemly. After the calculations, the values of crystal sizes were obtained as 60, 60, and 57 nm for cow, pig, and chicken, respectively.

#### 3.3. Williamson–Hall Method of Analysis

#### 3.3.1. Uniform Deformation Model (UDM)

_{2}is the broadening of the width of the peaks due to strain, while the broadening due to nanocrystal size β

_{1}comes from the Scherrer equation.

_{hkl}cosθ) corresponds to (4 sinθ) for the preferred orientation peaks of hydroxyapatite with the hexagonal lattice and considers the isotropic nature of the crystals. Figure 5 shows the 4 sinθ as an X-axis and β cosθ term along the Y-axis. Mostly, UDM is related to an isotropic (perfect) crystal system in all (hkl) planes. Apparently, slope and intercept of the fitted line correspond to the strain and crystal size, respectively. The intercept values equal $\frac{\mathrm{K}\mathsf{\lambda}}{\mathrm{L}}$. The $\frac{\mathrm{K}\mathsf{\lambda}}{\mathrm{L}}$ reported was 0.0021 for cow, 0.0022 for pig, and 0.0021 for chicken. These quantities are estimated from the intercept of the vertical axis and slope, from the plot of β

_{hkl}cosθ as a function of 4 sinθ. After calculations, the crystal size values were obtained as 65, 62, and 65 nm for cow, pig, and chicken, respectively. In this plot, the units of 4 sinθ and β cosθ are degree and radian degree tandemly. In addition, several defects influence to the lattice structure via size restriction and it will be caused to the strain lattice. Herein, the slope values (positive values) are represented to the intrinsic strain, therefore, 0.0003 for cow, 0.0002 for pig, and 0.0004 for chicken have been reported. The positive values of intrinsic strain can prove tensile strain and if values were negative, they will be related to the compressive strain.

#### 3.3.2. Uniform Stress Deformation Model (USDM)

_{11}S

_{33}, S

_{13}, and S

_{44}are introduced as elastic compliances and C

_{11}, C

_{12}, C

_{33}, and C

_{44}are elastic stiffness constants of hexagonal hydroxyapatite. The values of S

_{11}, S

_{33}, S

_{13}, and S

_{44}for hydroxyapatite are presented in Table 7 and the values are cited in reference [26]. In addition, the values of crystallography parameters and Young’s modulus (E) of each individual XRD pattern related to the hydroxyapatite obtained from cow, pig, and chicken are presented in Table 8. In fact, Young’s modulus (E

_{hkl}) is in the direction perpendicular to the set of crystal lattice planes (hkl).

_{hkl}.cosθ along the Y-axis are related to the peaks in the XRD pattern of the samples and are presented in Figure 6.

^{−4}, 1.59 × 10

^{−4}, and 3.81 × 10

^{−4}for cow, pig, and chicken, respectively.

#### 3.3.3. Uniform Deformation Energy Density Model (UDEDM)

^{3}for cow, pig, and chicken tandemly. For strain values also, states have been noted. According to Equation (14), the strain values were calculated as 0.87 × 10

^{−3}, 0.73 × 10

^{−3}, and 0.70 × 10

^{−3}(E ~ average Young’s modulus) for cow, pig, and chicken, respectively.

#### 3.4. Halder–Wagner Method (H-W)

_{L}and β

_{G}are full width at half maximum of the Lorentzian and Gaussian function tandemly. The important observation is the calculation and values of lattice distance between the (hkl) planes (d

_{hkl}). Hexagonal lattice (hydroxyapatite) is associated with Equation (18), but for cubic crystal lattice distance between the (hkl) planes, (d

_{hkl}) are corresponded to the Equation (19). The values of d

_{hkl}for hydroxyapatite obtained from cow, pig, and chicken bones are presented in Table 1, Table 2 and Table 3.

_{hkl}is the lattice distance between the (hkl) planes for the hexagonal crystal, as well as the term of $\frac{{\mathsf{\beta}}_{\mathrm{hkl}}^{*}}{{\mathrm{d}}_{\mathrm{hkl}}^{*}{}^{2}}$ for the X-axis and the term of ${\left(\frac{{\mathsf{\beta}}_{\mathrm{hkl}}^{*}}{{\mathrm{d}}_{\mathrm{hkl}}^{*}}\right)}^{2}$ for the Y-axis illustrated in Figure 8.

#### 3.5. Size Strain Plot Method (SSP)

_{hkl}= β

_{L}+ β

_{G}

_{L}and β

_{G}are the peak broadening via Lorentz and Gaussian functions tandemly. Equation (24) is the submitted formula of the SSP method [27].

^{−4}and 4.48 × 10

^{−4}for pig and chicken, respectively.

#### 3.6. Specific Surface Area by Gas Adsorption (BET Method)

^{−7}atmosphere) for around 15 to 20 h before each measurement. The amount of nitrogen was by volume adsorption at −197 °C. The reported surface area for a bone-derived hydroxyapatite is much lower and the value is around 0.1 m

^{2}/g [32]. However, one synthetic hydroxyapatite (not sintered or deproteinized bone) is 17 to 82 m

^{2}/g [33]. Theoretical particle size can be calculated from adsorption specific surface area data by using Equation (25).

^{2}/g. As explained, a theoretical particle size can be calculated from these data and the values of crystal size for hydroxyapatite calcined at 950 °C obtained from cow, pig, and chicken were 56, 52, and 49 nm, respectively.

#### 3.7. Study of TEM Analysis

^{2}), where there are differences between values of R

^{2}in each method. According to the calculation, R

^{2}allows it to be negative for some methods such as UDM (cow). It is intended to approximate the actual percentage variance, therefore, if the actual R

^{2}is close to zero, the R

^{2}can be slightly negative. However, the nanopowder was not dispersed perfectly, and the reason may be related to the agglomeration of powders created through the Van der Waals attraction [36]. In Figure 10, there is spacing (d

_{hkl}) with interplanar of less than 50 nm and the existence of hexagonal hydroxyapatite can be confirmed, according to the d

_{hkl}reported in Table 1, Table 2 and Table 3. The results obtained from the methods and models are summarized in Table 9 and Table 10. In addition, the crystal size of hydroxyapatite obtained from different natural sources in several studies are presented in Table 11.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Images of production route of hydroxyapatite obtained from cow, pig, and chicken bones (steps

**1**–

**4**).

**Figure 3.**Pattern of XRD analysis of hydroxyapatite obtained from (

**a**) cow, (

**b**) pig, and (

**c**) chicken bones.

**Figure 4.**Linear plots of the modified Scherrer (Monshi–Scherrer) equation and gained intercepts for different hydroxyapatites obtained from (

**a**) cow, (

**b**) pig, and (

**c**) chicken bones.

**Figure 8.**Halder–Wagner plot of hydroxyapatite obtained from (

**a**) cow, (

**b**) pig, and (

**c**) chicken bones.

**Figure 10.**TEM images and stoichiometric composition of hydroxyapatite nanocrystals obtained from. (

**a**) cow, (

**b**) pig, and (

**c**) chicken bones.

**Table 1.**Crystallographic parameters of the XRD pattern related to the hydroxyapatite obtained from cow.

Cow | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

2θ (Degree) | β = FWHM (Degree) | θ (Degree) | cosθ (Degree) | 1/cosθ (Degree) | Ln(1/cosθ) (Degree) | β = FWHM (Radian) | Ln β (Radian) | 4 sinθ (Degree) | β(Radian).cosθ (Degree) | hkl | ${\mathbf{d}}_{\mathbf{hkl}}\phantom{\rule{0ex}{0ex}}\left(\mathbf{\AA}\right)$ |

26.15 | 0.14 | 13.07 | 0.9740 | 1.02669 | 0.02634 | 0.00244 | −6.0174 | 0.9045 | 0.00238 | 002 | 3.46500 |

28.32 | 0.2 | 14.16 | 0.9696 | 1.03135 | 0.03087 | 0.00348 | −5.66072 | 0.9785 | 0.00337 | 102 | 3.17485 |

29.18 | 0.1 | 14.59 | 0.9677 | 1.03338 | 0.03283 | 0.00174 | −6.35387 | 1.007 | 0.00168 | 210 | 3.07687 |

31.96 | 0.15 | 15.98 | 0.9613 | 1.04026 | 0.03947 | 0.00261 | −5.94841 | 1.1012 | 0.00251 | 211 | 2.81215 |

32.54 | 0.14 | 16.27 | 0.9599 | 1.04178 | 0.04093 | 0.00244 | −6.0174 | 1.1206 | 0.00234 | 112 | 2.78900 |

32.98 | 0.15 | 16.49 | 0.9588 | 1.04297 | 0.04207 | 0.00261 | −5.94841 | 1.1353 | 0.0025 | 300 | 2.71354 |

33.97 | 0.14 | 16.98 | 0.9564 | 1.04559 | 0.04458 | 0.00244 | −6.0174 | 1.1681 | 0.00233 | 202 | 2.63845 |

40.03 | 0.15 | 20.01 | 0.9396 | 1.06428 | 0.0623 | 0.00261 | −5.94841 | 1.3687 | 0.00245 | 310 | 2.26285 |

46.94 | 0.16 | 23.47 | 0.9172 | 1.09027 | 0.08643 | 0.00278 | −5.88387 | 1.5930 | 0.00255 | 222 | 1.94339 |

48.35 | 0.2 | 24.17 | 0.9123 | 1.09613 | 0.09179 | 0.00348 | −5.66072 | 1.6377 | 0.00317 | 320 | 1.87176 |

49.73 | 0.15 | 24.86 | 0.9073 | 1.10217 | 0.09728 | 0.00261 | −5.94841 | 1.6816 | 0.00237 | 213 | 1.84732 |

**Table 2.**Crystallographic parameters of the XRD pattern related to the hydroxyapatite obtained from pig.

Pig | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

2θ (Degree) | β = FWHM (Degree) | θ (Degree) | cosθ (Degree) | 1/cosθ (Degree) | Ln(1/cosθ) (Degree) | β = FWHM (Radian) | Ln β (Radian) | 4 sinθ (Degree) | β(Radian).cosθ (Degree) | hkl | ${\mathbf{d}}_{\mathbf{hkl}}\phantom{\rule{0ex}{0ex}}\left(\mathbf{\AA}\right)$ |

26.12 | 0.13 | 13.06 | 0.9741 | 1.02659 | 0.02624 | 0.00226 | −6.09151 | 0.9038 | 0.0022 | 002 | 3.46500 |

29.20 | 0.14 | 14.60 | 0.9677 | 1.03338 | 0.03283 | 0.00244 | −6.0174 | 1.0082 | 0.00236 | 210 | 3.07687 |

32.04 | 0.14 | 16.02 | 0.9611 | 1.04047 | 0.03968 | 0.00244 | −6.0174 | 1.1038 | 0.00235 | 211 | 2.81215 |

32.44 | 0.13 | 16.22 | 0.9601 | 1.04156 | 0.04072 | 0.00226 | −6.09151 | 1.1173 | 0.00217 | 112 | 2.78900 |

33.07 | 0.14 | 16.53 | 0.9586 | 1.04319 | 0.04228 | 0.00244 | −6.0174 | 1.1380 | 0.00234 | 300 | 2.71354 |

34.02 | 0.14 | 17.01 | 0.9562 | 1.04581 | 0.04479 | 0.00244 | −6.0174 | 1.1701 | 0.00233 | 202 | 2.63845 |

40.07 | 0.18 | 20.03 | 0.9395 | 1.0644 | 0.06241 | 0.00313 | −5.76608 | 1.3700 | 0.00294 | 310 | 2.26285 |

46.96 | 0.15 | 23.48 | 0.9171 | 1.09039 | 0.08654 | 0.00261 | −5.94841 | 1.5937 | 0.00239 | 222 | 1.94339 |

48.34 | 0.14 | 24.17 | 0.9123 | 1.09613 | 0.09179 | 0.00244 | −6.0174 | 1.6377 | 0.00223 | 320 | 1.87176 |

49.73 | 0.15 | 24.86 | 0.9073 | 1.10217 | 0.09728 | 0.00261 | −5.94841 | 1.6816 | 0.00237 | 213 | 1.84732 |

**Table 3.**Crystallographic parameters of the XRD pattern related to the hydroxyapatite obtained from chicken.

Chicken | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

2θ (Degree) | β = FWHM (Degree) | θ (Degree) | cosθ (Degree) | 1/cosθ (Degree) | Ln(1/cosθ) (Degree) | β = FWHM (Radian) | Ln β (Radian) | 4 sinθ (Degree) | β(Radian).cosθ (Degree) | hkl | ${\mathbf{d}}_{\mathbf{hkl}}\text{}\phantom{\rule{0ex}{0ex}}\left(\mathbf{\AA}\right)$ |

26.20 | 0.14 | 13.10 | 0.9739 | 1.0268 | 0.02645 | 0.00244 | −6.0174 | 0.9066 | 0.00238 | 002 | 3.46500 |

28.39 | 0.16 | 14.19 | 0.9694 | 1.03157 | 0.03108 | 0.00278 | −5.88387 | 0.9805 | 0.00269 | 102 | 3.17485 |

29.19 | 0.15 | 14.59 | 0.9677 | 1.03338 | 0.03283 | 0.00261 | −5.94841 | 1.0076 | 0.00253 | 210 | 3.07687 |

32.03 | 0.16 | 16.01 | 0.9612 | 1.04037 | 0.03957 | 0.00278 | −5.88387 | 1.1032 | 0.00267 | 211 | 2.81215 |

32.45 | 0.15 | 16.22 | 0.9601 | 1.04156 | 0.04072 | 0.00261 | −5.94841 | 1.1173 | 0.00251 | 112 | 2.78900 |

33.16 | 0.15 | 16.58 | 0.9584 | 1.04341 | 0.04249 | 0.00261 | −5.94841 | 1.1414 | 0.0025 | 300 | 2.71354 |

34.21 | 0.16 | 17.10 | 0.9557 | 1.04635 | 0.04531 | 0.00278 | −5.88387 | 1.1761 | 0.00266 | 202 | 2.63845 |

40.05 | 0.17 | 20.02 | 0.9395 | 1.0644 | 0.06241 | 0.00296 | −5.82324 | 1.3693 | 0.00278 | 310 | 2.26285 |

46.95 | 0.18 | 23.47 | 0.9172 | 1.09027 | 0.08643 | 0.00313 | −5.76608 | 1.5930 | 0.00287 | 222 | 1.94339 |

48.34 | 0.17 | 24.17 | 0.9123 | 1.09613 | 0.09179 | 0.00296 | −5.82324 | 1.6377 | 0.0027 | 320 | 1.87176 |

49.74 | 0.18 | 24.87 | 0.9072 | 1.10229 | 0.09739 | 0.00313 | −5.76608 | 1.6822 | 0.00284 | 213 | 1.84732 |

**Table 4.**Crystallographic parameters related to the hydroxyapatite structure resulting via X’Pert software.

Bone | Crystal System | a $\left(\mathbf{\AA}\right)$ | c $\left(\mathbf{\AA}\right)$ | c/a $\left(\mathbf{\AA}\right)$ | Cell Volume (Å^{3}) | Crystal Density (g/cm^{3}) |
---|---|---|---|---|---|---|

Cow | Hexagonal | 9.4000 | 6.9300 | 0.7340 | 530.30 | 3.14 |

Pig | Hexagonal | 9.4210 | 6.8930 | 0.7316 | 529.83 | 3.14 |

Chicken | Hexagonal | 9.4210 | 6.8800 | 0.7302 | 528.83 | 3.18 |

**Table 5.**The (x,y) points extracted by the plots in Figure 3.

Cow | Pig | Chicken | |||
---|---|---|---|---|---|

x | y | x | y | x | y |

409.83 | 0.974 | 442.47 | 0.9741 | 409.83 | 0.9739 |

287.35 | 0.9696 | 409.83 | 0.9677 | 359.71 | 0.9694 |

574.71 | 0.9677 | 409.83 | 0.9611 | 383.14 | 0.9677 |

383.14 | 0.9613 | 442.47 | 0.9601 | 359.71 | 0.9612 |

409.83 | 0.9599 | 409.83 | 0.9586 | 383.14 | 0.9601 |

383.14 | 0.9588 | 409.83 | 0.9562 | 383.14 | 0.9584 |

409.83 | 0.9564 | 319.48 | 0.9395 | 359.71 | 0.9557 |

383.14 | 0.9396 | 383.14 | 0.9171 | 337.83 | 0.9395 |

359.71 | 0.9172 | 409.83 | 0.9123 | 319.48 | 0.9172 |

287.35 | 0.9123 | 383.14 | 0.9073 | 337.83 | 0.9123 |

383.14 | 0.9073 | - | - | 319.48 | 0.9072 |

$\frac{\mathbf{K}\mathsf{\lambda}}{\mathsf{\beta}\mathbf{c}\mathbf{o}\mathbf{s}\mathsf{\theta}}\text{}\mathbf{of}\text{}\mathbf{Cow}$ | $\frac{\mathbf{K}\mathsf{\lambda}}{\mathsf{\beta}\mathbf{c}\mathbf{o}\mathbf{s}\mathsf{\theta}}\text{}\mathbf{of}\text{}\mathbf{Pig}$ | $\frac{\mathbf{K}\mathsf{\lambda}}{\mathsf{\beta}\mathbf{c}\mathbf{o}\mathbf{s}\mathsf{\theta}}\text{}\mathbf{of}\text{}\mathbf{Chicken}$ |
---|---|---|

57.60 | 62.32 | 57.60 |

40.68 | 58.09 | 50.96 |

81.60 | 58.34 | 54.19 |

54.62 | 63.18 | 51.35 |

58.59 | 58.59 | 54.62 |

54.84 | 58.84 | 54.84 |

58.84 | 46.63 | 51.54 |

55.96 | 57.36 | 49.31 |

53.76 | 61.48 | 47.77 |

43.25 | 57.85 | 50.77 |

57.85 | - | 48.27 |

56 | 58 | 52 |

**Table 7.**Elastic compliances and stiffness constants of hydroxyapatite [26].

Elastic Compliances (GPa) | Stiffness Constants (GPa) | ||||||||
---|---|---|---|---|---|---|---|---|---|

C_{11} | C_{12} | C_{13} | C_{33} | C_{44} | S_{11} | S_{12} | S_{13} | S_{33} | S_{44} |

137 | 42.5 | 54.9 | 172 | 39.6 | 0.88 | −0.18 | −0.22 | 0.72 | 2.52 |

**Table 8.**Young’s modulus (E) of each individual XRD pattern related to the hydroxyapatite obtained from cow, pig, and chicken bones.

Cow | Pig | Chicken | |||
---|---|---|---|---|---|

2θ (Degree) | E (GPa) | 2θ (Degree) | E (GPa) | 2θ (Degree) | E (GPa) |

26.15 | 138.889 | 26.12 | 138.889 | 26.20 | 138.889 |

28.32 | 123.935 | 29.20 | 113.636 | 28.39 | 124.121 |

29.18 | 113.636 | 32.04 | 108.694 | 29.19 | 113.636 |

31.96 | 108.734 | 32.44 | 113.02 | 32.03 | 108.684 |

32.54 | 112.887 | 33.07 | 113.636 | 32.45 | 113.054 |

32.98 | 113.636 | 34.02 | 110.706 | 33.16 | 113.636 |

33.97 | 110.598 | 40.07 | 113.636 | 34.21 | 110.733 |

40.03 | 113.636 | 46.96 | 107.155 | 40.05 | 113.636 |

46.94 | 107.161 | 48.34 | 113.636 | 46.95 | 107.154 |

48.35 | 113.636 | 49.73 | 112.702 | 48.34 | 113.636 |

49.73 | 112.571 | - | - | 49.74 | 112.734 |

**Table 9.**Nanosize of hydroxyapatite crystallites obtained from cow, pig, and chicken bones extracted by some calculation methods and experimental methods (BET, TEM) in this study.

Size of Crystallites | Scherrer (All Peaks/New Model/Average Model) | Monshi–Scherrer | Williamson–Hall (UDM/USDM/UDEDM) | H-W | SSP | BET | TEM |
---|---|---|---|---|---|---|---|

L_{cow} (nm) | 1371/60/56 | 60 | 65/60/62 | 4 | 43 | 56 | ~ 50 |

L_{pig} (nm) | 457/60/58 | 60 | 62/62/62 | 4 | 62 | 52 | ~ 50 |

L_{chicken} (nm) | 196/53/52 | 57 | 65/62/65 | 4 | 57 | 49 | ~ 50 |

Williamson–Hall | SSP | |||||
---|---|---|---|---|---|---|

UDM | USDM | UDEDM | ||||

Strain (ε) × 10 ^{−4} | Stress $\left(\mathsf{\sigma}\right)$ (MPa) | Strain (ε) × 10 ^{−4} | Strain (ε) × 10 ^{−3} | LED (KJ/m ^{3}) | Strain (ε) × 10 ^{−4} | |

cow | 3 | 22 | 1.89 | 0.87 | 43.67 | - |

pig | 2 | 18 | 1.59 | 0.73 | 29.70 | 2.83 |

chicken | 4 | 44 | 3.81 | 0.70 | 28.28 | 4.48 |

**Table 11.**Reports of some studies on the nanocrystallite size of hydroxyapatite prepared at high temperature.

Number | Source | Method of Preparation | Temperature of Heat Treatment | Crystallite Phases | Size of Crystal (L) (nm) | Shape | Reference |
---|---|---|---|---|---|---|---|

1 | Bovine bone | Thermal treatment | 800 °C | hydroxyapatite | <100 (58 and 62) | Needle | [35] |

2 | Bovine bone | Thermal treatment | 800 °C | hydroxyapatite | 70–180 | Irregular | [37] |

3 | Fish scale | Thermal treatment | 800 °C | hydroxyapatite | 30 | Irregular | [38] |

4 | Bovine bone | Thermal treatment | 900 °C | hydroxyapatite | 30 | - | [39] |

5 | Bovine bone | Thermal treatment | 900 °C | hydroxyapatite | 70–80 | Spherical | [40] |

6 | Pig bone | Thermal treatment | 1000 °C | hydroxyapatite | 38–52 | Rod like | [41] |

7 | Fish scale | Thermal treatment | 1000 °C | hydroxyapatite | 76 | Nearly spherical | [42] |

8 | Clam shell | Thermal treatment | 1000 °C | hydroxyapatite | 53–67 | Agglomerate | [43] |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Rabiei, M.; Palevicius, A.; Monshi, A.; Nasiri, S.; Vilkauskas, A.; Janusas, G. Comparing Methods for Calculating Nano Crystal Size of Natural Hydroxyapatite Using X-Ray Diffraction. *Nanomaterials* **2020**, *10*, 1627.
https://doi.org/10.3390/nano10091627

**AMA Style**

Rabiei M, Palevicius A, Monshi A, Nasiri S, Vilkauskas A, Janusas G. Comparing Methods for Calculating Nano Crystal Size of Natural Hydroxyapatite Using X-Ray Diffraction. *Nanomaterials*. 2020; 10(9):1627.
https://doi.org/10.3390/nano10091627

**Chicago/Turabian Style**

Rabiei, Marzieh, Arvydas Palevicius, Ahmad Monshi, Sohrab Nasiri, Andrius Vilkauskas, and Giedrius Janusas. 2020. "Comparing Methods for Calculating Nano Crystal Size of Natural Hydroxyapatite Using X-Ray Diffraction" *Nanomaterials* 10, no. 9: 1627.
https://doi.org/10.3390/nano10091627