Measurement Modulus of Elasticity Related to the Atomic Density of Planes in Unit Cell of Crystal Lattices
- PMID: 33019629
- PMCID: PMC7579002
- DOI: 10.3390/ma13194380
Measurement Modulus of Elasticity Related to the Atomic Density of Planes in Unit Cell of Crystal Lattices
Abstract
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.
Keywords: X-ray diffraction; Young’s modulus; crystalline materials; elastic compliances; modified W–H.; planar density.
Conflict of interest statement
The authors declare no conflict of interest.
Figures
Similar articles
-
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.Materials (Basel). 2021 May 30;14(11):2949. doi: 10.3390/ma14112949. Materials (Basel). 2021. PMID: 34070721 Free PMC article.
-
Relationship between Young's Modulus and Planar Density of Unit Cell, Super Cells (2 × 2 × 2), Symmetry Cells of Perovskite (CaTiO3) Lattice.Materials (Basel). 2021 Mar 6;14(5):1258. doi: 10.3390/ma14051258. Materials (Basel). 2021. PMID: 33800951 Free PMC article.
-
Mechano-acoustic determination of Young's modulus of articular cartilage.Biorheology. 2004;41(3-4):167-79. Biorheology. 2004. PMID: 15299250
-
Young's modulus of trabecular bone at the tissue level: A review.Acta Biomater. 2018 Sep 15;78:1-12. doi: 10.1016/j.actbio.2018.08.001. Epub 2018 Aug 4. Acta Biomater. 2018. PMID: 30081232 Review.
-
Anisotropy, Anatomical Region, and Additional Variables Influence Young's Modulus of Bone: A Systematic Review and Meta-Analysis.JBMR Plus. 2023 Oct 31;7(12):e10835. doi: 10.1002/jbm4.10835. eCollection 2023 Dec. JBMR Plus. 2023. PMID: 38130752 Free PMC article. Review.
Cited by
-
Investigation of Minerals Extracted during Seawater Desalination Using Two-Dimensional Correlation Spectroscopy.Molecules. 2023 Nov 29;28(23):7852. doi: 10.3390/molecules28237852. Molecules. 2023. PMID: 38067581 Free PMC article.
-
Crystal plasticity simulations with representative volume element of as-build laser powder bed fusion materials.Sci Rep. 2023 Nov 21;13(1):20372. doi: 10.1038/s41598-023-47651-2. Sci Rep. 2023. PMID: 37989841 Free PMC article.
-
Shedding light on rechargeable Na/Cl2 battery.Proc Natl Acad Sci U S A. 2023 Sep 26;120(39):e2310903120. doi: 10.1073/pnas.2310903120. Epub 2023 Sep 20. Proc Natl Acad Sci U S A. 2023. PMID: 37729201 Free PMC article.
-
FT-IR Analysis of P. aeruginosa Bacteria Inactivation by Femtosecond IR Laser Radiation.Int J Mol Sci. 2023 Mar 7;24(6):5119. doi: 10.3390/ijms24065119. Int J Mol Sci. 2023. PMID: 36982184 Free PMC article.
-
Phase Transformations and Subsurface Changes in Three Dental Zirconia Grades after Sandblasting with Various Al2O3 Particle Sizes.Materials (Basel). 2021 Sep 16;14(18):5321. doi: 10.3390/ma14185321. Materials (Basel). 2021. PMID: 34576556 Free PMC article.
References
-
- Ma Y.Z., Sobernheim D., Grazon J.R. Unconventional Oil and Gas Resources Handbook. Elsevier; Amsterdam, The Netherlands: 2016. Glossary for Unconventional Oil and Gas Resource Evaluation and Development; pp. 513–526. Chapter 19. - DOI
-
- Ravindran P., Fast L., Korzhavyi P.A., Johansson B. Density functional theory for calculation of elastic properties of orthorhombic crystals: Application to TiSi2. Appl. Phys. 1998;84:4891. doi: 10.1063/1.368733. - DOI
-
- Fine M.E., Brown L.D., Marcus H.L. Elastic constants versus melting temperature in metals. Scr. Metall. 1984;18:951–956. doi: 10.1016/0036-9748(84)90267-9. - DOI
-
- Nakamura M. Elastic constants some transition metal-disilicide-single crystals. Met. Mater. Trans. A. 1994;25:331–340. doi: 10.1007/BF02647978. - DOI
-
- Brich F. Finite Elastic Strain of Cubic Crystals. Phys. Rev. 1947;71:809. doi: 10.1103/PhysRev.71.809. - DOI
LinkOut - more resources
Full Text Sources