Comparing Methods for Calculating Nano Crystal Size of Natural Hydroxyapatite Using X-Ray Diffraction
Abstract
:1. Introduction
2. Materials and Experiments
2.1. Preparation of Hydroxyapatite Powders
2.2. XRD Analysis of Samples
3. Results and Discussions
3.1. Scherrer Method
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)
3.3. Williamson–Hall Method of Analysis
3.3.1. Uniform Deformation Model (UDM)
3.3.2. Uniform Stress Deformation Model (USDM)
3.3.3. Uniform Deformation Energy Density Model (UDEDM)
3.4. Halder–Wagner Method (H-W)
3.5. Size Strain Plot Method (SSP)
3.6. Specific Surface Area by Gas Adsorption (BET Method)
3.7. Study of TEM Analysis
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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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 | |
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 |
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 | |
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 |
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 | |
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 |
Bone | Crystal System | a | c | c/a | Cell Volume (Å3) | Crystal Density (g/cm3) |
---|---|---|---|---|---|---|
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 |
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 |
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 |
Elastic Compliances (GPa) | Stiffness Constants (GPa) | ||||||||
---|---|---|---|---|---|---|---|---|---|
C11 | C12 | C13 | C33 | C44 | S11 | S12 | S13 | S33 | S44 |
137 | 42.5 | 54.9 | 172 | 39.6 | 0.88 | −0.18 | −0.22 | 0.72 | 2.52 |
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 |
Size of Crystallites | Scherrer (All Peaks/New Model/Average Model) | Monshi–Scherrer | Williamson–Hall (UDM/USDM/UDEDM) | H-W | SSP | BET | TEM |
---|---|---|---|---|---|---|---|
Lcow (nm) | 1371/60/56 | 60 | 65/60/62 | 4 | 43 | 56 | ~ 50 |
Lpig (nm) | 457/60/58 | 60 | 62/62/62 | 4 | 62 | 52 | ~ 50 |
Lchicken (nm) | 196/53/52 | 57 | 65/62/65 | 4 | 57 | 49 | ~ 50 |
Williamson–Hall | SSP | |||||
---|---|---|---|---|---|---|
UDM | USDM | UDEDM | ||||
Strain (ε) × 10−4 | Stress (MPa) | Strain (ε) × 10−4 | Strain (ε) × 10−3 | LED (KJ/m3) | 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 |
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] |
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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
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 StyleRabiei, 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