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X-ray Diffraction Analysis and Williamson-Hall Method in USDM Model for Estimating More Accurate Values of Stress-Strain of Unit Cell and Super Cells (2 × 2 × 2) of Hydroxyapatite, Confirmed by Ultrasonic Pulse-Echo Test
Taking into account X-ray diffraction, one of the well-known methods for calculating the stress-strain of crystals is Williamson-Hall (W–H). The W-H method has three models, namely (1) Uniform deformation model (UDM); (2) Uniform stress deformation model (USDM); and (3) Uniform deformation energy de...
Autores principales: | , , , , , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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MDPI
2021
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8198306/ https://www.ncbi.nlm.nih.gov/pubmed/34070721 http://dx.doi.org/10.3390/ma14112949 |
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author | Rabiei, Marzieh Palevicius, Arvydas Dashti, Amir Nasiri, Sohrab Monshi, Ahmad Doustmohammadi, Akram Vilkauskas, Andrius Janusas, Giedrius |
author_facet | Rabiei, Marzieh Palevicius, Arvydas Dashti, Amir Nasiri, Sohrab Monshi, Ahmad Doustmohammadi, Akram Vilkauskas, Andrius Janusas, Giedrius |
author_sort | Rabiei, Marzieh |
collection | PubMed |
description | Taking into account X-ray diffraction, one of the well-known methods for calculating the stress-strain of crystals is Williamson-Hall (W–H). The W-H method has three models, namely (1) Uniform deformation model (UDM); (2) Uniform stress deformation model (USDM); and (3) Uniform deformation energy density model (UDEDM). The USDM and UDEDM models are directly related to the modulus of elasticity (E). Young’s modulus is a key parameter in engineering design and materials development. Young’s modulus is considered in USDM and UDEDM models, but in all previous studies, researchers used the average values of Young’s modulus or they calculated Young’s modulus only for a sharp peak of an XRD pattern or they extracted Young’s modulus from the literature. Therefore, these values are not representative of all peaks derived from X-ray diffraction; as a result, these values are not estimated with high accuracy. Nevertheless, in the current study, the W-H method is used considering the all diffracted planes of the unit cell and super cells (2 × 2 × 2) of Hydroxyapatite (HA), and a new method with the high accuracy of the W-H method in the USDM model is presented to calculate stress (σ) and strain (ε). The accounting for the planar density of atoms is the novelty of this work. Furthermore, the ultrasonic pulse-echo test is performed for the validation of the novelty assumptions. |
format | Online Article Text |
id | pubmed-8198306 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-81983062021-06-14 X-ray Diffraction Analysis and Williamson-Hall Method in USDM Model for Estimating More Accurate Values of Stress-Strain of Unit Cell and Super Cells (2 × 2 × 2) of Hydroxyapatite, Confirmed by Ultrasonic Pulse-Echo Test Rabiei, Marzieh Palevicius, Arvydas Dashti, Amir Nasiri, Sohrab Monshi, Ahmad Doustmohammadi, Akram Vilkauskas, Andrius Janusas, Giedrius Materials (Basel) Article Taking into account X-ray diffraction, one of the well-known methods for calculating the stress-strain of crystals is Williamson-Hall (W–H). The W-H method has three models, namely (1) Uniform deformation model (UDM); (2) Uniform stress deformation model (USDM); and (3) Uniform deformation energy density model (UDEDM). The USDM and UDEDM models are directly related to the modulus of elasticity (E). Young’s modulus is a key parameter in engineering design and materials development. Young’s modulus is considered in USDM and UDEDM models, but in all previous studies, researchers used the average values of Young’s modulus or they calculated Young’s modulus only for a sharp peak of an XRD pattern or they extracted Young’s modulus from the literature. Therefore, these values are not representative of all peaks derived from X-ray diffraction; as a result, these values are not estimated with high accuracy. Nevertheless, in the current study, the W-H method is used considering the all diffracted planes of the unit cell and super cells (2 × 2 × 2) of Hydroxyapatite (HA), and a new method with the high accuracy of the W-H method in the USDM model is presented to calculate stress (σ) and strain (ε). The accounting for the planar density of atoms is the novelty of this work. Furthermore, the ultrasonic pulse-echo test is performed for the validation of the novelty assumptions. MDPI 2021-05-30 /pmc/articles/PMC8198306/ /pubmed/34070721 http://dx.doi.org/10.3390/ma14112949 Text en © 2021 by the authors. https://creativecommons.org/licenses/by/4.0/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 (https://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Rabiei, Marzieh Palevicius, Arvydas Dashti, Amir Nasiri, Sohrab Monshi, Ahmad Doustmohammadi, Akram Vilkauskas, Andrius Janusas, Giedrius X-ray Diffraction Analysis and Williamson-Hall Method in USDM Model for Estimating More Accurate Values of Stress-Strain of Unit Cell and Super Cells (2 × 2 × 2) of Hydroxyapatite, Confirmed by Ultrasonic Pulse-Echo Test |
title | X-ray Diffraction Analysis and Williamson-Hall Method in USDM Model for Estimating More Accurate Values of Stress-Strain of Unit Cell and Super Cells (2 × 2 × 2) of Hydroxyapatite, Confirmed by Ultrasonic Pulse-Echo Test |
title_full | X-ray Diffraction Analysis and Williamson-Hall Method in USDM Model for Estimating More Accurate Values of Stress-Strain of Unit Cell and Super Cells (2 × 2 × 2) of Hydroxyapatite, Confirmed by Ultrasonic Pulse-Echo Test |
title_fullStr | X-ray Diffraction Analysis and Williamson-Hall Method in USDM Model for Estimating More Accurate Values of Stress-Strain of Unit Cell and Super Cells (2 × 2 × 2) of Hydroxyapatite, Confirmed by Ultrasonic Pulse-Echo Test |
title_full_unstemmed | X-ray Diffraction Analysis and Williamson-Hall Method in USDM Model for Estimating More Accurate Values of Stress-Strain of Unit Cell and Super Cells (2 × 2 × 2) of Hydroxyapatite, Confirmed by Ultrasonic Pulse-Echo Test |
title_short | X-ray Diffraction Analysis and Williamson-Hall Method in USDM Model for Estimating More Accurate Values of Stress-Strain of Unit Cell and Super Cells (2 × 2 × 2) of Hydroxyapatite, Confirmed by Ultrasonic Pulse-Echo Test |
title_sort | x-ray diffraction analysis and williamson-hall method in usdm model for estimating more accurate values of stress-strain of unit cell and super cells (2 × 2 × 2) of hydroxyapatite, confirmed by ultrasonic pulse-echo test |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8198306/ https://www.ncbi.nlm.nih.gov/pubmed/34070721 http://dx.doi.org/10.3390/ma14112949 |
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