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Measurement Modulus of Elasticity Related to the Atomic Density of Planes in Unit Cell of Crystal Lattices

Young’s modulus (E) is one of the most important parameters in the mechanical properties of solid materials. Young’s modulus is proportional to the stress and strain values. There are several experimental and theoretical methods for gaining Young’s modulus values, such as stress–strain curves in com...

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Autores principales: Rabiei, Marzieh, Palevicius, Arvydas, Dashti, Amir, Nasiri, Sohrab, Monshi, Ahmad, Vilkauskas, Andrius, Janusas, Giedrius
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7579002/
https://www.ncbi.nlm.nih.gov/pubmed/33019629
http://dx.doi.org/10.3390/ma13194380
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author Rabiei, Marzieh
Palevicius, Arvydas
Dashti, Amir
Nasiri, Sohrab
Monshi, Ahmad
Vilkauskas, Andrius
Janusas, Giedrius
author_facet Rabiei, Marzieh
Palevicius, Arvydas
Dashti, Amir
Nasiri, Sohrab
Monshi, Ahmad
Vilkauskas, Andrius
Janusas, Giedrius
author_sort Rabiei, Marzieh
collection PubMed
description Young’s modulus (E) is one of the most important parameters in the mechanical properties of solid materials. Young’s modulus is proportional to the stress and strain values. There are several experimental and theoretical methods for gaining Young’s modulus values, such as stress–strain curves in compression and tensile tests, electromagnetic-acoustic resonance, ultrasonic pulse echo and density functional theory (DFT) in different basis sets. Apparently, preparing specimens for measuring Young’s modulus through the experimental methods is not convenient and it is time-consuming. In addition, for calculating Young’s modulus values by software, presumptions of data and structures are needed. Therefore, this new method for gaining the Young’s modulus values of crystalline materials is presented. Herein, the new method for calculating Young’s modulus of crystalline materials is extracted by X-ray diffraction. In this study, Young’s modulus values were gained through the arbitrary planes such as random (hkl) in the research. In this study, calculation of Young’s modulus through the relationship between elastic compliances, geometry of the crystal lattice and the planar density of each plane is obtained by X-ray diffraction. Sodium chloride (NaCl) with crystal lattices of FCC was selected as the example. The X-ray diffraction, elastic stiffness constant and elastic compliances values have been chosen by the X’Pert software, literature and experimental measurements, respectively. The elastic stiffness constant and Young’s modulus of NaCl were measured by the ultrasonic technique and, finally, the results were in good agreement with the new method of this study. The aim of the modified Williamson–Hall (W–H) method in the uniform stress deformation model (USDM) utilized in this paper is to provide a new approach of using the W–H equation, so that a least squares technique can be applied to minimize the sources of errors.
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spelling pubmed-75790022020-10-29 Measurement Modulus of Elasticity Related to the Atomic Density of Planes in Unit Cell of Crystal Lattices Rabiei, Marzieh Palevicius, Arvydas Dashti, Amir Nasiri, Sohrab Monshi, Ahmad Vilkauskas, Andrius Janusas, Giedrius Materials (Basel) Article Young’s modulus (E) is one of the most important parameters in the mechanical properties of solid materials. Young’s modulus is proportional to the stress and strain values. There are several experimental and theoretical methods for gaining Young’s modulus values, such as stress–strain curves in compression and tensile tests, electromagnetic-acoustic resonance, ultrasonic pulse echo and density functional theory (DFT) in different basis sets. Apparently, preparing specimens for measuring Young’s modulus through the experimental methods is not convenient and it is time-consuming. In addition, for calculating Young’s modulus values by software, presumptions of data and structures are needed. Therefore, this new method for gaining the Young’s modulus values of crystalline materials is presented. Herein, the new method for calculating Young’s modulus of crystalline materials is extracted by X-ray diffraction. In this study, Young’s modulus values were gained through the arbitrary planes such as random (hkl) in the research. In this study, calculation of Young’s modulus through the relationship between elastic compliances, geometry of the crystal lattice and the planar density of each plane is obtained by X-ray diffraction. Sodium chloride (NaCl) with crystal lattices of FCC was selected as the example. The X-ray diffraction, elastic stiffness constant and elastic compliances values have been chosen by the X’Pert software, literature and experimental measurements, respectively. The elastic stiffness constant and Young’s modulus of NaCl were measured by the ultrasonic technique and, finally, the results were in good agreement with the new method of this study. The aim of the modified Williamson–Hall (W–H) method in the uniform stress deformation model (USDM) utilized in this paper is to provide a new approach of using the W–H equation, so that a least squares technique can be applied to minimize the sources of errors. MDPI 2020-10-01 /pmc/articles/PMC7579002/ /pubmed/33019629 http://dx.doi.org/10.3390/ma13194380 Text en © 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/).
spellingShingle Article
Rabiei, Marzieh
Palevicius, Arvydas
Dashti, Amir
Nasiri, Sohrab
Monshi, Ahmad
Vilkauskas, Andrius
Janusas, Giedrius
Measurement Modulus of Elasticity Related to the Atomic Density of Planes in Unit Cell of Crystal Lattices
title Measurement Modulus of Elasticity Related to the Atomic Density of Planes in Unit Cell of Crystal Lattices
title_full Measurement Modulus of Elasticity Related to the Atomic Density of Planes in Unit Cell of Crystal Lattices
title_fullStr Measurement Modulus of Elasticity Related to the Atomic Density of Planes in Unit Cell of Crystal Lattices
title_full_unstemmed Measurement Modulus of Elasticity Related to the Atomic Density of Planes in Unit Cell of Crystal Lattices
title_short Measurement Modulus of Elasticity Related to the Atomic Density of Planes in Unit Cell of Crystal Lattices
title_sort measurement modulus of elasticity related to the atomic density of planes in unit cell of crystal lattices
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7579002/
https://www.ncbi.nlm.nih.gov/pubmed/33019629
http://dx.doi.org/10.3390/ma13194380
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