Journal articles: 'Voigt-Reuss-Hill'

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Villalobos-Portillo, Edgar E., Luis Fuentes-Montero, María E. Montero-Cabrera, Diana C. Burciaga-Valencia, and Luis E. Fuentes-Cobas. "Polycrystal piezoelectricity: revisiting the Voigt-Reuss-Hill approximation." Materials Research Express 6, no. 11 (October 2, 2019): 115705. http://dx.doi.org/10.1088/2053-1591/ab46f2.

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Zuo, L., M. Humbert, and C. Esling. "Elastic properties of polycrystals in the Voigt-Reuss-Hill approximation." Journal of Applied Crystallography 25, no. 6 (December 1, 1992): 751–55. http://dx.doi.org/10.1107/s0021889892004874.

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Gnäupel-Herold, Thomas. "ISODEC: software for calculating diffraction elastic constants." Journal of Applied Crystallography 45, no. 3 (May 4, 2012): 573–74. http://dx.doi.org/10.1107/s0021889812014252.

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A program is introduced that calculates diffraction elastic constants for the Reuss, modified Voigt, Hill, Kröner and inverse Kröner models. For materials with preferred orientation it uses the orientation distribution function (ODF) to calculate the anisotropic stress factors. The ODF is read in text format as output from the freely available texture programspopLAandMTEX. The software also calculates the orientation-dependent mixing ratios of intensities of overlapped reflections, anisotropic bulk constants, and stress from lattice strain andvice versa.

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Liu, Jide, Xiaoming Du, Xue Wang, Ming Xie, Jinguo Li, Shangqiang Zhao, Yizhou Zhou, Qiao Zhang, and Jiheng Fang. "First-Principles Calculations of Elasticity Properties of AgW₂₀ Alloy." Journal of Physics: Conference Series 2459, no. 1 (March 1, 2023): 012008. http://dx.doi.org/10.1088/1742-6596/2459/1/012008.

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Abstract In this paper, the first-principles calculations based on DFT were employd to investigate the elasticity characteristics of AgW20 alloy. The elasticity constants of the single crystals are calculated using the finite strain method and Voigt – Reuss – Hill (VRH) approach. The universal anisortropic index (AU ), shear anisortropic index, orientation dependency of Young’s modulus, bulk modulus were used to characterize elasticity anisortropy behaviors. The calculated elasticity properties of AgW20 alloy show a remarkable elasticity anisortropy for AgW20 alloy.

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Ishaje, Michael E., Kseniia Minakova, Valentyna Sirenko, and Ivan Bondar. "Study of structural and mechanical properties of the C2CaNa half-Heusler alloy using density functional theory approach." Low Temperature Physics 50, no. 6 (June 1, 2024): 467–71. http://dx.doi.org/10.1063/10.0026085.

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The mechanical properties of the half-Heusler alloy C2CaNa using density functional theory approach as installed in Quantum Espresso software was examined. We observed that C2CaNa will be easily compressed due to the small value of its bulk modulus. The values of the lattice constant a0, elastic constants (C11, C12, C14), Young’s modulus E, Piosson’s ratio ν, Shear modulus G, Zener anitropy A, pressure derivative B′, and band-gap Eg were obtained. Also the Voigt approximation, Reuss approximation and the Voigt–Reuss–Hill average of the approximation were gotten. Calculated values of G/B ratio is 0.581; this shows that C2CaNa has low resistance opposed to shear deformation. The B/G ratio evaluated for C2CaNa is 1.72. This implies that C2CaNa is “brittle” in nature at ambient condition. Our calculated elastic constants (C11, C12, and C44) for C2CaNa satisfied the following mechanical stability conditions for cubic structure: C11 – C12 > 0, C44 > 0, and C11 + 2C12 > 0. The value of C12 is an indication that C2CaNa is mechanically stable. This examination gives important experiences into the primary dependability and mechanical way of behavior of this material, this will empower advance material plan and application.

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Svetashkov, Alexander, Nikolay Kupriyanov, and Kayrat Manabaev. "Modifications of the Mathematical Crisher Model for Effective Moduli of Two-Component Elastic Isotropic Composite." Key Engineering Materials 685 (February 2016): 206–10. http://dx.doi.org/10.4028/www.scientific.net/kem.685.206.

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The problem of determining the effective properties of composite materials is actual problem for deformable body mechanics. The model, proposed by Crisher for modeling effective values of the coefficient of thermal conductivity, has been considered. Modifications of this mathematical model for two-component elastic composite were built. Model of Hill-Budiansky compresses classic fork of Voigt-Reuss, if it is added by Voigt component. Expressions of hybrid effective characteristics through the use of effective Hashin-Shtrikman moduli are built. The accuracy is estimated depending on the type of modification of the effective characteristics for the calculation of the stress-strain state of bodies (two-layer shell and three-layer plate) made from composite materials. The results are compared with the exact classical solutions, and admissible concordance is achieved.

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Li, Ang, Liyan Zhang, Jianguo Yang, Shichao Li, Fei Xiao, Yulai Yao, Yiming Huang, Bo Liu, and Longsheng Li. "Study on Anisotropic Petrophysical Modeling of Shale: A Case Study of Shale Oil in Qingshankou Formation in Sanzhao Sag, Songliao Basin, China." Geofluids 2023 (April 27, 2023): 1–21. http://dx.doi.org/10.1155/2023/6236986.

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Seismic petrophysics is an important link between seismic elastic properties and reservoir physical properties. Based on the petrological and microstructure characteristics of shale in the Qingshankou formation of Sanzhao sag in the north of Songliao Basin, this paper presents an anisotropy petrophysical model with complex pore structure suitable for organic shale constructed with the use of the Voigt-Reuss-Hill average model, an anisotropy self-consistent approximation+differential effective medium model, and the layering of clay and kerogen is simulated by using the Voigt-Reuss-Hill average and bond transform to achieve the simulation of shale anisotropy. Based on the proposed model, the effects of the organic volume fraction, porosity, and pore aspect ratio on rock elastic properties are discussed. The result shows that with the increase of matrix porosity, all elastic parameters show a decreasing trend; with the increase of the organic volume fraction, except shear modulus, other elastic parameters show an increasing trend. Through comparative analysis, the elastic parameters (Lamé impedance and Shear impedance) sensitive to the organic volume fraction and porosity are optimized; the seismic petrophysical cross-plot template with core calibration is constructed. The application shows that the predicted S-wave velocity based on the proposed model is in good agreement with the S-wave velocity derived from dipole source logging. Combined with the high-precision prestack elastic parameter inversion, the “sweet spot” characteristics can be well described, and the research could contribute to a better “sweet spot” description and provide a better support for shale exploration in Sanzhao sag.

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Huang, Bo, Yong Hua Duan, Sun Yong, and Ming Jun Peng. "Elastic Properties and Electronic Structures of L1₂-TiAl₃ and L1₂-Ti(Al,Pt)₃: A Density Functional Theory Investigation." Materials Science Forum 817 (April 2015): 816–25. http://dx.doi.org/10.4028/www.scientific.net/msf.817.816.

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First-principles calculations have been carried out to investigate the elastic properties and electronic structures of L12-TiAl3and L12-Ti (Al, Pt)3. The optimized structural parameters were largely consistent with the experimental values. The electronic density of states (DOS) and the differences of charge density distribution were given. The independent single-crystal elastic constants and polycrystalline elastic parameters such as bulk modulusB, Young’s modulusE, shear modulusG, Poisson’s ratioνand anisotropy valueAhave been calculated by Voigt-Reuss-Hill averaging scheme. The results indicate that the L12-Ti (Al, Pt)3exhibits larger anisotropy and more ductile than L12-TiAl3.

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Wang, H. Y., F. Y. Xue, Nai Hui Zhao, and De Jun Li. "First-Principles Calculation of Elastic Properties of TiB₂ and ZrB₂." Advanced Materials Research 150-151 (October 2010): 40–43. http://dx.doi.org/10.4028/www.scientific.net/amr.150-151.40.

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Based on Density Functional Theory (DFT), using first-principles pseudopotential plane wave method, elastic properties and electronic structure of TiB2 and ZrB2 were calculated. The elastic constants of these compounds were calculated by Voigt-Reuss-Hill method. The results show that the elastic modulus of TiB2 and ZrB2 are 594 and 520 GPa, and the shear modulus are 268 and 229 GPa, respectively. Pugh empirical criterion and Poisson's ratio show that the two compounds are very brittle, and the brittleness of TiB2 is higher than ZrB2. Finally, the differences in elastic properties between TiB2 and ZrB2 result form their electronic structures.

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Vermeulen, Arnold C., Christopher M. Kube, and Nicholas Norberg. "Implementation of the self-consistent Kröner–Eshelby model for the calculation of X-ray elastic constants for any crystal symmetry." Powder Diffraction 34, no. 2 (April 30, 2019): 103–9. http://dx.doi.org/10.1017/s088571561900037x.

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In this paper, we will report about the implementation of the self-consistent Kröner–Eshelby model for the calculation of X-ray elastic constants for general, triclinic crystal symmetry. With applying appropriate symmetry relations, the point groups of higher crystal symmetries are covered as well. This simplifies the implementation effort to cover the calculations for any crystal symmetry. In the literature, several models can be found to estimate the polycrystalline elastic properties from single crystal elastic constants. In general, this is an intermediate step toward the calculation of the polycrystalline response to different techniques using X-rays, neutrons, or ultrasonic waves. In the case of X-ray residual stress analysis, the final goal is the calculation of X-ray Elastic constants. Contrary to the models of Reuss, Voigt, and Hill, the Kröner–Eshelby model has the benefit that, because of the implementation of the Eshelby inclusion model, it can be expanded to cover more complicated systems that exhibit multiple phases, inclusions or pores and that these can be optionally combined with a polycrystalline matrix that is anisotropic, i.e., contains texture. We will discuss a recent theoretical development where the approaches of calculating bounds of Reuss and Voigt, the tighter bounds of Hashin–Shtrikman and Dederichs–Zeller are brought together in one unifying model that converges to the self-consistent solution of Kröner–Eshelby. For the implementation of the Kröner–Eshelby model the well-known Voigt notation is adopted. The 4-rank tensor operations have been rewritten into 2-rank matrix operations. The practical difficulties of the Voigt notation, as usually concealed in the scientific literature, will be discussed. Last, we will show a practical X-ray example in which the various models are applied and compared.

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Muñoz-Romero, Alejandro, L. Fuentes-Montero, M. E. Montero-Cabrera, U. Trivedi, and Luis E. Fuentes-Cobas. "Textured Multiferroics: 2-D Diffraction and Properties Prediction." Materials Science Forum 702-703 (December 2011): 1007–10. http://dx.doi.org/10.4028/www.scientific.net/msf.702-703.1007.

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A description of recent work performed by collaboration among the CIMAV Crystal Physics Group, the ILL Diffraction Group and the GEC Nanotechnology Education and Research Centre (NERC), regarding structure-electromagnetic properties relationships, is given. Structure analysis puts emphasis on thin films texture characterization. The new software package ANAELU, for texture analysis via two-dimensional (2-D) diffraction detection, is described. Crystallographic texture plays a significant role on ferroic and multiferroic bulk and nano-structured materials properties. With the objective of estimating effective values for polycrystal dielectric, piezoelectric, elastic and magnetoelectric coefficients, the Voigt, Reuss and Hill approximations are systematized in an extended version of program SAMZ.

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León-Flores, J., M. Romero, J. Rosas-Huerta, and R. Escamilla. "Ab Initio study of the crystal structure and the elastic properties of the Mo0.85Nb0.15B3 compound under pressure." MRS Advances 4, no. 63 (2019): 3453–61. http://dx.doi.org/10.1557/adv.2019.420.

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ABSTRACTThe elastic constants, elastic modulus, anisotropy, Debye temperature, and sound velocity properties of Mo0.85Nb0.15B3 were investigated by first-principles calculations under pressure based on the generalized gradient approximation (GGA) proposed by Perdew–Burke-Ernzerhof (PBE). Employing the stress-strain method and the Voigt-Reuss-Hill approximations, were calculated the elastic properties of single and polycrystalline crystals; Bulk modulus (B), Young modulus (E), Poisson ratio (ν), Pugh ratio (G/B), Debye temperature and the Cauchy pressure terms. The calculated ν, Cauchy pressure, and Pugh ratio G/B values indicate that Mo0.85Nb0.15B3 shows a transition from brittle to ductile under pressure. Finally, the Density of States decreases as pressure increases.

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Park, N. J., H. J. Bunge, H. Kiewel, and L. Fritsche. "Calculation of Effective Elastic Moduli of Textured Materials." Textures and Microstructures 23, no. 1 (January 1, 1995): 43–59. http://dx.doi.org/10.1155/tsm.23.43.

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Effective elastic constants of polycrystalline materials were determined with a recently developed method. This method bases on the modelation of the actual material by a cluster of 100 to 500 single crystals. In the present version of the scheme parallelepipeds are used. The ODF was calculated with the series expansion method. The transformation of this ODF into a finite sum of single orientations permits to assign any grain an individual orientation.Reliable results for the effective elastic moduli of textured materials are reported. They lie always within the bounds of Voigt and Reuss. The very high anisotropic substances, e.g. shape-memory-alloys, show a significant deviation from the Hill values.

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Mengmeng Wu, Mengmeng Wu, Rongkai Pan Rongkai Pan, Jilei Liang Jilei Liang, Guohai Zhou Guohai Zhou, and Li Ma and Chunyu Zhang Li Ma and Chunyu Zhang. "Structural, Elastic and Electronic Properties of γ˝ Phase Precipitate in Mg-Gd-Zn Alloy." Journal of the chemical society of pakistan 41, no. 6 (2019): 932. http://dx.doi.org/10.52568/000826/jcsp/41.06.2019.

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The γ˝ phase (Mg4GdZn) precipitate in Mg-Gd-Zn alloy was calculated via ﬁrst-principle density functional theory within the generalized gradient approximation. Through structure optimization of full relaxation, the lattice parameters were theoretically obtained, and the calculated Mg4GdZn is the most energetically stable in view of the formation energy. Independent elastic constants were also calculated, illustrating the calculated Mg4GdZn is mechanically stable. The shear modulus, polycrystalline bulk modulus, Poisson ratio, and Young’s modulus of Mg4GdZn were calculated via the Voigt-Reuss-Hill approximation. Elastic anisotropy and ductility were analyzed in details. Seen from their charge density distribution and electronic density of states, both metallic bond and covalent bond were found in Mg4GdZn.

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Yao, Qiang. "Elastic Properties and Electronic Structure of L1₂ (Al,Si)₃Sc." Advanced Materials Research 284-286 (July 2011): 1987–90. http://dx.doi.org/10.4028/www.scientific.net/amr.284-286.1987.

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The method of ultrasoft pseudopotential within the generalized gradient approximation has been employed to study the elastic constants and electronic structure of (Al,Si)3Sc precipitate with L12structure in Al-base alloys. Based on the calculated results, the elastic properties of (Al,Si)3Sc precipitate were investigated. The Young’s and shear modulus of the polycrystals for (Al,Si)3Sc precipitate were calculated using Voigt-Reuss-Hill averaging scheme. The calculated results of elastic properties showed that the (Al,Si)3Sc precipitate has a strengthening effect in the Al matrix, owing to the larger shear modulus differences between (Al,Si)3Sc and Al matrix. The calculated results also showed that (Al,Si)3Sc precipitate is brittle in nature.

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Shi, Zuhao, Kaiyi Weng, and Neng Li. "The Atomic Structure and Mechanical Properties of ZIF-4 under High Pressure: Ab Initio Calculations." Molecules 28, no. 1 (December 20, 2022): 22. http://dx.doi.org/10.3390/molecules28010022.

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The effects of pressure on the structural and electronic properties and the ionic configuration of ZIF-4 were investigated through the first-principles method based on the density functional theory. The elastic properties, including the isotropic bulk modulus K, shear modulus G, Young’s modulus E, and Poisson’s ratio ν of the orthorhombic-type structure ZIF-4 were determined using the Voigt–Reuss–Hill averaging scheme. The results show that the ZIF-4 phase is ductile according to the analysis of K/G and Cauchy pressure. The Debye temperatures obtained from the elastic stiffness constants increase with increasing pressure. Finally, the pressure-dependent behaviors of the density of states and ionic configuration are successfully calculated and discussed.

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Howard, C. J., and E. H. Kisi. "Measurement of single-crystal elastic constants by neutron diffraction from polycrystals." Journal of Applied Crystallography 32, no. 4 (August 1, 1999): 624–33. http://dx.doi.org/10.1107/s0021889899002393.

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The relationships of diffraction averaged elastic compliances for an ideally random polycrystal to the single-crystal elastic compliances are given, within the Reuss approximation, for crystal systems with orthorhombic and higher symmetry. For anisotropic materials, these diffraction elastic compliances are dependent on the reflection indexhkl. Expressions for the conventional elastic constants (Young's modulus, Poisson's ratio) are also given. A connection is made to the `X-ray elastic constants' used for diffraction-based measurements of residual stress. The relationships are used to calculate diffraction averaged constants for comparison with neutron diffraction data recorded from samples under applied uniaxial stress. The Reuss approximation works well for materials with the capacity for plastic deformation, such as metals and transformation toughening ceramics, whereas for other materials the Voigt–Reuss–Hill approximation gives better results. Based on the given relationships and experimental determinations of the diffraction elastic compliances for polycrystalline materials, a method is developed for determining the single-crystal elastic constants. The method for estimating single-crystal compliances is demonstrated here by application to extant data on Ni–Cr–Fe and Ti–6 wt% Al–4 wt% V alloys, and new measurements on cubic zirconia. It has been applied very recently [Kisi & Howard (1998).J. Am. Ceram. Soc.81, 1682–1684] to determine the previously unknown elastic constants for a tetragonal zirconia.

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Wang, Lan Xin, Shan Yao, and Bin Wen. "First-Principle Studies of a High Entropy Solid Solution of AlCoCrCuFeNi_x with Different Mole Fractions of Ni." Materials Science Forum 809-810 (December 2014): 419–25. http://dx.doi.org/10.4028/www.scientific.net/msf.809-810.419.

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The structural properties, elastic properties, and heat of formation of a high entropy alloy (HEA) of AlCoCrCuFeNi containing different mole fraction of Ni. The calculated results indicate that the lattice parameter decreased and the mass density increased as the mole fraction of Ni increased. The high entropy solid solutions AlCoCrCuFeNixusing the FCC model are mechanically stable. The elastic properties have been deduced by Voigt-Reuss-Hill (VRH) approximations, and the calculated ratio of shear modulus to bulk modulus indicated that When the mole fraction of Ni was 0 in the FCC model, or 0.5 in both the BCC and FCC models, the high entropy solid solutions were considered ductile materials. All the HEAs are thermodynamically stable due to their negative heats of formation.

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Fu, Jia, Jukui Guo, Hao Bai, and Weihui Lin. "Structural and elastic properties of CaMg2 Laves phase by Y-parameter and Reuss-Voigt-Hill methods." IOP Conference Series: Materials Science and Engineering 423 (November 6, 2018): 012052. http://dx.doi.org/10.1088/1757-899x/423/1/012052.

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Alhan, Preeti, Suresh Kumar, and Ranjan Kumar. "Structure Optimization and Electronic Properties of Co₂tix(X=Si, Ge) Heusler Alloys: A DFT Study." ECS Transactions 107, no. 1 (April 24, 2022): 13815–22. http://dx.doi.org/10.1149/10701.13815ecst.

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A theoretical study of structural, electronic, magnetic, mechanical and vibrational properties of Co-based heusler alloys, namely Co2TiX(X=Si,Ge); have been studied by the first principle calculations with the Generalized Gradient approximation(GGA) based on Density functional theory(DFT). The total spin magnetic moments per unit cell is 2µB, obeying the Slater-Pauling rule. The electronic band structure along the high symmetry points reveal that majority spin states have metallic character and minority spin states have a band gap at the Fermi level. There are no imaginary phonon mode which illustrate the dynamical stability. The Bulk modulus, young’s modulus, shear modulus, Pugh’s ratio, sound velocities, Debye temperature in accordance with the Voigt-Reuss-Hill approximation. The elastic constant results show that these alloys are mechanically stable.

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Heldmann, Alexander, Markus Hoelzel, Michael Hofmann, Weimin Gan, Wolfgang W. Schmahl, Erika Griesshaber, Thomas Hansen, Norbert Schell, and Winfried Petry. "Diffraction-based determination of single-crystal elastic constants of polycrystalline titanium alloys." Journal of Applied Crystallography 52, no. 5 (September 20, 2019): 1144–56. http://dx.doi.org/10.1107/s1600576719010720.

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Single-crystal elastic constants have been derived by lattice strain measurements using neutron diffraction on polycrystalline Ti-6Al-4V, Ti-6Al-2Sn-4Zr-6Mo and Ti-3Al-8V-6Cr-4Zr-4Mo alloy samples. A variety of model approximations for the grain-to-grain interactions, namely approaches by Voigt, Reuss, Hill, Kroener, de Wit and Matthies, including texture weightings, have been applied and compared. A load-transfer approach for multiphase alloys was also implemented and the results are compared with single-phase data. For the materials under investigation, the results for multiphase alloys agree well with the results for single-phase materials in the corresponding phases. In this respect, all eight elastic constants in the dual-phase Ti-6Al-2Sn-4Zr-6Mo alloy have been derived for the first time.

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Le Bourdais, Florian, Audrey Gardahaut, and Nicolas Leymarie. "Characterization of effective elastic constants and anisotropy directions for Wire Arc Additive Manufactured steel samples using RUS." Journal of the Acoustical Society of America 155, no. 3_Supplement (March 1, 2024): A157. http://dx.doi.org/10.1121/10.0027145.

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In recent years, Resonant Ultrasound Spectroscopy (RUS) has been extensively applied to objects produced by additive manufacturing to characterize elastic material properties, detect defects or geometrical deviations. In this talk, we analyze samples that were produced using the wire-arc additive manufacturing (WAAM) process using different grades of steel wires. Resonance spectra were obtained and allowed to classify samples as either elastically isotropic or anisotropic. Detailed investigation on anisotropic samples (produced with 316L wire) under an orthotropy hypothesis showed that the samples were markedly softer along the layer deposition direction. Subsequent investigation using EBSD confirmed the results obtained with RUS. They also allowed to quantitatively model the elastic constants using the Voigt-Reuss-Hill averaging theory, which were in good agreement with the ones obtained using the RUS inverse problem.

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Rahaman, Md Zahidur, and Md Atikur Rahman. "Investigation of the physical properties of two Laves phase compounds HRh2 (H = Ca and La): A DFT study." International Journal of Modern Physics B 32, no. 12 (May 3, 2018): 1850149. http://dx.doi.org/10.1142/s0217979218501497.

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By using the first-principle calculations, the structural, elastic, electronic and optical properties of Laves phase intermetallic compounds CaRh2 and LaRh2 prototype with MgCu2 are investigated. The evaluated lattice parameters are consistent with the experimental values. The important elastic properties, such as bulk modulus B, shear modulus G, Young’s modulus Y and the Poisson’s ratio v, are computed by applying the Voigt–Reuss–Hill (VRH) approximation. The analysis of Pugh’s ratio exhibits the ductile nature of both the phases. Electronic conductivity is predicted for both the compounds. Most of the contribution comes from Rh-4d states. The study of bonding characteristics reveals the existence of ionic and metallic bonds in both intermetallics. The study of optical properties indicates that CaRh2 is a better dielectric material than LaRh2. Absorption quality of both the phases is good in the ultraviolet region.

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Wang, Hui-Yuan, Wen-Ping Si, Shi-Long Li, Nan Zhang, and Qi-Chuan Jiang. "First-principles study of the structural and elastic properties of Ti5Si3 with substitutions Zr, V, Nb, and Cr." Journal of Materials Research 25, no. 12 (December 2010): 2317–24. http://dx.doi.org/10.1557/jmr.2010.0293.

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The formation enthalpy, electronic structures, and elastic moduli of the intermetallic compound Ti5Si3 with substitutions Zr, V, Nb, and Cr are investigated by using first-principles methods based on the density-functional theory. Our calculation shows that the site occupancy behaviors of alloying elements in Ti5Si3, determined by their atom radius, are consistent with the available experimental observations. Furthermore, using the Voigt–Reuss–Hill (VRH) approximation method, we obtained the bulk modulus B, shear modulus G, and the Young’s modulus E. Among these four substitutions, the V, Nb, and Cr substitutions can improve the ductility of Ti5Si3 effectively, while Zr substitution has little effect on the elastic properties of Ti5Si3. The elastic property variations of Ti5Si3 due to different substitutions are found to be correlated with the Me4d–Me4d antibonding and the strengthened Me4d–Si bonding in the solids.

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Ali, Md Lokman, and Md Zahidur Rahaman. "Investigation of different physical aspects such as structural, mechanical, optical properties and Debye temperature of Fe2ScM (M=P and As) semiconductors: A DFT-based first principles study." International Journal of Modern Physics B 32, no. 10 (April 13, 2018): 1850121. http://dx.doi.org/10.1142/s0217979218501217.

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By using first principles calculation dependent on the density functional theory (DFT), we have investigated the mechanical, structural properties and the Debye temperature of Fe2ScM (M=P and As) compounds under various pressures up to 60 GPa. The optical properties have been investigated under zero pressure. Our calculated optimized structural parameters of both the materials are in good agreement with other theoretical predictions. The calculated elastic constants show that Fe2ScM (M=P and As) compounds are mechanically stable under external pressure below 60 GPa. From the elastic constants, the shear modulus G, the bulk modulus B, Young’s modulus E, anisotropy factor A and Poisson’s ratio [Formula: see text] are calculated by using the Voigt–Reuss–Hill approximation. The Debye temperature and average sound velocities are also investigated from the obtained elastic constants. The detailed analysis of all optical functions reveals that both compounds are good dielectric material.

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Fu, Jia, Hao Bai, Zhaoyuan Zhang, and Weihui Lin. "Elastic constants and homogenized moduli of manganese carbonate structure based on molecular dynamics and Reuss-Voigt-Hill methods." IOP Conference Series: Materials Science and Engineering 423 (November 6, 2018): 012046. http://dx.doi.org/10.1088/1757-899x/423/1/012046.

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Satta, Niccolò, Hauke Marquardt, Alexander Kurnosov, Johannes Buchen, Takaaki Kawazoe, Catherine McCammon, and Tiziana Boffa Ballaran. "Single-crystal elasticity of iron-bearing phase E and seismic detection of water in Earth's upper mantle." American Mineralogist 104, no. 10 (October 1, 2019): 1526–29. http://dx.doi.org/10.2138/am-2019-7084.

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Abstract The elastic properties of Mg2.12(2)Fe0.21(2)Ni0.01Si1.15(1)O6H2.67(8) phase E single crystals with Fe3+/ΣFe = 0.25(3) have been determined by Brillouin spectroscopy at ambient conditions. We find that that the elasticity of iron-bearing phase E is described by the six independent stiffness tensor components (all in units of GPa): C11 = 192.2(6), C12 = 56.4(8), C13 = 43.5(8), C14 = –4.3(3), C33 = 192.1(7), C44 = 46.4(3). The Voigt-Reuss-Hill averages of bulk and shear moduli are 95.9(4) and 59.6(2) GPa, respectively. The aggregate velocities of iron-bearing phase E are νP = 7.60(2) and νS = 4.43(1) km/s, markedly lower than those of major mantle minerals at ambient conditions. Modeling based on our results suggests that the presence of iron-bearing phase E may reduce the sound wave velocities in upper mantle and transition zone rocks, making it a possible target for future seismological investigations aiming to map hydration in subducting slabs.

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Wang, Lan Xin, Shan Yao, and Bin Wen. "First-Principle Studies Al-Fe-Ti-Cr-Zn-Cu High Entropy Solid Solutions with Pressure-Induced." Materials Science Forum 809-810 (December 2014): 333–47. http://dx.doi.org/10.4028/www.scientific.net/msf.809-810.333.

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The structural properties, elastic properties, mechanical stability, and phase transition of equiatomic Al-Fe-Ti-Cr-Zn-Cu high entropy solid solutions from binary (Al-Fe) to hexanary (Al-Fe-Ti-Cr-Zn-Cu) composition with pressure-induced have been analyzed using density functional theory calculations. The results indicate that the lattice parameters decrease, the mass densities increase with the pressure-increased. The mechanically stability may improve with the pressure increased appropriately for ternary Al-Fe-Ti and quaternary Al-Fe-Ti-Cr. The Young’s modulus has nothing to do with the pressure-induced, but the bulk modulus increases with the pressure increased. The elastic properties were also calculated using Voigt-Reuss-Hill (VRH) approximations. The brittle and ductile properties were studied by Poisson’s ratios and the ratios of shear modulus to bulk modulus. The calculated results of the enthalpy indicate that the binary to hexanary high entropy solid solutions transform the FCC structure to the BCC structure at a certain pressure.

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Li, Bo, Yonghua Duan, Mingjun Peng, Li Shen, and Huarong Qi. "Anisotropic Elastic and Thermal Properties of M2InX (M = Ti, Zr and X = C, N) Phases: A First-Principles Calculation." Metals 12, no. 7 (June 28, 2022): 1111. http://dx.doi.org/10.3390/met12071111.

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First-principles calculations were used to estimate the anisotropic elastic and thermal properties of Ti2lnX (X = C, N) and Zr2lnX (X = C, N) M2AX phases. The crystals’ elastic properties were computed using the Voigt-Reuss-Hill approximation. Firstly, the material’s elastic anisotropy was explored, and its mechanical stability was assessed. According to the findings, Ti2lnC, Ti2lnN, Zr2lnC, and Zr2lnN are all brittle materials. Secondly, the elasticity of Ti2lnX (X = C, N) and Zr2lnX (X = C, N) M2AX phase are anisotropic, and the elasticity of Ti2lnX (X = C, N) and Zr2lnX (X = C, N) systems are different; the order of anisotropy is Ti2lnN > Ti2lnC, Zr2lnN > Zr2lnC. Finally, the elastic constants and moduli were used to determine the Debye temperature and sound velocity. Ti2lnC has the maximum Debye temperature and sound velocity, and Zr2lnN had the lowest Debye temperature and sound velocity. At the same time, Ti2lnC had the highest thermal conductivity.

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Yao, Qiang, Tong Lu, Qiong Wang, Yan Wang, and Yu Hong Zhu. "First-Principles Investigation of Phase Stability, Elastic and Thermodynamic Properties in L1₂ Co₃(Al,Mo,Ta) Phase." Materials Science Forum 898 (June 2017): 438–45. http://dx.doi.org/10.4028/www.scientific.net/msf.898.438.

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First-principles calculations have been performed to investigate the phase stability, elastic, and thermodynamic properties of Co3(Al,Mo,Ta) with the L12 structure. Calculated elastic constants showed that Co3(Al,Mo,Ta) is mechanically stable and possesses intrinsic ductility. Young’s and shear moduli of polycrystalline Co3(Al,Mo,Ta) were calculated using the Voigt-Reuss-Hill approach. It was found that the shear and Young’s moduli of Co3(Al,Mo,Ta) were smaller than those of Co3(Al,W). States density indicated the existence of covalent-like bonding in Co3(Al,Mo,Ta). Temperature-dependent thermodynamic properties of Co3(Al,Mo,Ta) could be described satisfactorily using the Debye-Grüneisen approach, including entropy, enthalpy, heat capacity and linear thermal expansion coefficient, showing their significant temperature dependences. Furthermore the obtained data could be employed in the modeling of thermodynamic and mechanical properties of Co-based alloys to enable the design of high temperature alloys.

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Chowdhury, Uttam Kumar, and Tapas Chandra Saha. "An ab-initio Investigation: The physical properties of ScIr-=SUB=-2-=/SUB=- Superconductor -=SUP=-*-=/SUP=-." Физика твердого тела 61, no. 4 (2019): 659. http://dx.doi.org/10.21883/ftt.2019.04.47408.332.

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AbstractUsing ab initio technique the physical properties of ScIr_2 superconductor have been investigated with T _c 1.03 K with a MgCu_2-type structure. We have carried out the plane-wave pseudopotential approach within the framework of the first-principles density functional theory (DFT) implemented within the CASTEP code. The calculated structural parameters confirm a good agreement with the experimental and other theoretical results. Using the Voigt-Reuss-Hill (VRH) averaging scheme the most important elastic properties including the bulk modulus B, shear modulus G , Young’s modulus E and Poisson’s ratio ν of ScIr_2 are determined. At ambient condition, the values of Cauchy pressure and Pugh’s ratio exhibit ductile nature of ScIr_2. The electronic and optical properties of ScIr_2 were investigated for the first time. The electronic band structure reveals metallic conductivity and the major contribution comes from Ir-5 d states. In the ultraviolet region the reflectivity is high up to 50 eV as evident from the reflectivity spectrum.

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Schoderböck, Peter, Peter Leibenguth, and Michael Tkadletz. "Pattern decomposition for residual stress analysis: a generalization taking into consideration elastic anisotropy and extension to higher-symmetry Laue classes." Journal of Applied Crystallography 50, no. 4 (June 14, 2017): 1011–20. http://dx.doi.org/10.1107/s1600576717006616.

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The residual stress state of ion-conducting layers (yttria stabilized zirconia) and protective hard coatings (α-aluminium oxide, titanium carbonitride) was investigated using X-ray diffraction techniques. Its evaluation within the tetragonal, trigonal and cubic phases present was performed by a whole powder pattern decomposition procedure according to Pawley. Going beyond previous work, the applied refinements directly include the influence of elastic anisotropy on the residual stress results. Starting from the single-crystal elastic coefficients, the X-ray elastic constants according to the Voigt and Reuss models were calculated. Finally, the Neerfeld–Hill model as a generalization was implemented to introduce thehkl-specific X-ray elastic constants for calculating the residual stress magnitude within the least-squares minimization routine. It was possible to resolve the residual stress state in stacked layers of different chemical and phase composition and to reproduce the results obtained by the classical χ- and ω-inclination sin2Ψ techniques.

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Wohlschlögel, M., W. Baumann, U. Welzel, and Eric J. Mittemeijer. "Mechanical Stress Gradients in Thin Films Analyzed Employing X-Ray Diffraction Measurements at Constant Penetration/Information Depths." Materials Science Forum 524-525 (September 2006): 19–24. http://dx.doi.org/10.4028/www.scientific.net/msf.524-525.19.

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Stress gradients have been investigated employing a measurement strategy for diffraction measurements at constant penetration/information depths. Two examples have been considered: (i) sputter-deposited copper thin films on silicon wafers and (ii) γ’-Fe4N1-x layers on α-Fe substrates obtained by gaseous nitriding. In the Cu thin films rather low tensile stresses, increasing in magnitude with increasing penetration/information depth have been found. An evaluation of the measured lattice strains has been performed on the basis of the f(ψ) method, where the X-ray elastic constants (XEC’s) have been calculated as weighed averages of the corresponding Voigt and Reuss XEC’s and the weighing parameter has been taken as a fitting parameter. This evaluation reveals that the grain interaction changes with increasing penetration/information depth from near-Reuss type towards Neerfeld-Hill type. In the γ’-Fe4N1-x layers stress gradients occur due to surface relaxation near the surface and deeper in the layer due to a nitrogen concentration gradient which is built up during nitriding. First measurements in a laboratory diffractometer show the effect of surface relaxation on the stress-depth profile near the surface. As no single-crystal elastic constants are available for γ’-Fe4N1-x, the mechanical elastic constants have been employed in diffraction stress analysis. The results indicated that single-crystal elastic anisotropy occurs. From the measured data also a concentration – depth profile has been deduced.

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Man, Chi-Sing, and Mojia Huang. "A Simple Explicit Formula for the Voigt-Reuss-Hill Average of Elastic Polycrystals with Arbitrary Crystal and Texture Symmetries." Journal of Elasticity 105, no. 1-2 (February 1, 2011): 29–48. http://dx.doi.org/10.1007/s10659-011-9312-y.

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Radjai, R., N. Guechi, and D. Maouche. "An ab initio study of structural, elastic and electronic properties of hexagonal MAuGe (M = Lu, Sc) compounds." Condensed Matter Physics 24, no. 1 (March 2021): 13706. http://dx.doi.org/10.5488/cmp.24.13706.

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In this paper, we performed a detailed theoretical study of structural, elastic and electronic properties of two germanides LuAuGe and ScAuGe by means of first-principles calculations using the pseudopotential plane-wave method within the generalized gradient approximation. The crystal lattice parameters and the internal coordinates are in good agreement with the existing experimental and theoretical reports, which proves the reliability of the applied theoretical method. The hydrostatic pressure effect on the structural parameters is shown. The monocrystalline elastic constants were calculated using the stress-strain technique. The calculated elastic constants of the MAuGe (M = Lu, Sc) compounds meet the mechanical stability criteria for hexagonal crystals and these constants were used to analyze the elastic anisotropy of the MAuGe compounds through three different indices. Polycrystalline isotropic elastic moduli, namely bulk modulus, shear modulus, Young's modulus, Poisson's ratio, and the related properties are also estimated using Voigt-Reuss-Hill approximations. Finally, we studied the electronic properties of the considered compounds by calculating their band structures, their densities of states and their electron density distributions.

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Hutami, Harnanti Yogaputri, Fitriyani Fitriyani, Tiara Larasati Priniarti, and Handoyo Handoyo. "Analisis Model Kecepatan Gelombang-P pada Coal-Seam Gas Studi Kasus Cekungan Sumatera Selatan, Indonesia." Jurnal Geofisika Eksplorasi 6, no. 2 (July 16, 2020): 113–20. http://dx.doi.org/10.23960/jge.v6i2.74.

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The rock physics model is one effective yet challenging way to investigate the coal-seam gas potential in Indonesia. However, because of the complex conditions of the Coal-Seam Gas Reservoirs, it is difficult to establish models. Despite the scarce modeling, this study aims to estimate the relation of gas-saturated within pores of coal seam to the elastic properties of rock, which is P-wave velocity. First, the coal seam minerals are applied to quantify matrix moduli using the Voigt-Reuss-Hill Average method. Pride’s simple equation is used to estimate the elastic properties of the coal seam at dry condition (zero gas saturation). Finally, Biot-Gassmann’s theory is applied to determine the elastic properties of coal seam with fully gas saturated. As the result, the proposed model showed that there is a significant negative correlation between gas content with both density and P-wave velocity of the coal seam. Finally, this P-wave velocity model of gas-saturated coal seams should be properly useful as the quick look for identifying coal seam gas potentials.

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Li, Yingzhe, and Jay D. Bass. "Single Crystal Elastic Properties of Hemimorphite, a Novel Hydrous Silicate." Minerals 10, no. 5 (May 10, 2020): 425. http://dx.doi.org/10.3390/min10050425.

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Hemimorphite, with the chemical formula Zn4Si2O7(OH)2·H2O, contains two different types of structurally bound hydrogen: molecular water and hydroxyl. The elastic properties of single-crystal hemimorphite have been determined by Brillouin spectroscopy at ambient conditions, yielding tight constraints on all nine single-crystal elastic moduli (Cij). The Voigt–Reuss–Hill (VRH) averaged isotropic aggregate elastic moduli are KS (VRH) = 74(3) GPa and μ (VRH) = 27(2) GPa, for the adiabatic bulk modulus and shear modulus, respectively. The average of the Hashin–Shtrickman (HS) bounds are Ks (HS) = 74.2(7) GPa and and μ (HS) = 26.5(6) GPa. Hemimorphite displays a high degree of velocity anisotropy. As a result, differences between upper and lower bounds on aggregate properties are large and the main source of uncertainty in Ks and μ. The HS average P wave velocity is VP = 5.61(4) km/s, and the HS S-wave velocity is VS = 2.77(3) km/s. The high degree of elastic anisotropy among the on-diagonal longitudinal and pure shear moduli of hemimorphite are largely explained by its distinctive crystal structure.

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Ba, Jing, Peng Hu, Wenhui Tan, Tobias M. Müller, and Li-Yun Fu. "Brittle mineral prediction based on rock-physics modelling for tight oil reservoir rocks." Journal of Geophysics and Engineering 18, no. 6 (December 2021): 970–83. http://dx.doi.org/10.1093/jge/gxab062.

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Abstract The reservoir rocks from Chang-7 member of Yanchang Formation of Ordos Basin are characterised with heterogeneous fabric structures at the pore scale, and low porosity/permeability is exhibited at the macro scale. Precise prediction of reservoir brittleness is of great significance to oil production. Ultrasonic experiments are performed on tight sandstones collected from the target formation. A rock-physics model (RPM) is presented based on the Voigt–Reuss–Hill average (VRH), self-consistent approximation (SCA) and differential effective medium (DEM) theory. The brittleness characteristics relying on mineral composition, porosity and microcrack properties are explored by using the RPM. The Young's modulus increases and Poisson ratio decreases with increasing quartz content. Based on experimental, log and seismic data, brittle mineral analysis of rock physical model is performed at multiple scales. The model accuracy is verified by experimental data and well log data. The brittleness distribution is predicted on the basis of log and seismic data, which can be instructive for the reservoir rock fracturing in actual engineering operations.

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Handoyo, Handoyo, M. Rizki Sudarsana, and Restu Almiati. "Rock Physics Modeling and Seismic Interpretation to Estimate Shally Cemented Zone in Carbonate Reservoir Rock." Journal of Geoscience, Engineering, Environment, and Technology 1, no. 1 (December 1, 2016): 45. http://dx.doi.org/10.24273/jgeet.2016.11.6.

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Carbonate rock are important hydrocarbon reservoir rocks with complex texture and petrophysical properties (porosity and permeability). These complexities make the prediction reservoir characteristics (e.g. porosity and permeability) from their seismic properties more difficult. The goal of this paper are to understanding the relationship of physical properties and to see the signature carbonate initial rock and shally-carbonate rock from the reservoir. To understand the relationship between the seismic, petrophysical and geological properties, we used rock physics modeling from ultrasonic P- and S- wave velocity that measured from log data. The measurements obtained from carbonate reservoir field (gas production). X-ray diffraction and scanning electron microscope studies shown the reservoir rock are contain wackestone-packstone content. Effective medium theory to rock physics modeling are using Voigt, Reuss, and Hill. It is shown the elastic moduly proposionally decrease with increasing porosity. Elastic properties and wave velocity are decreasing proporsionally with increasing porosity and shally cemented on the carbonate rock give higher elastic properties than initial carbonate non-cemented. Rock physics modeling can separated zones which rich of shale and less of shale.

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Startt, Jacob K., and Chaitanya S. Deo. "First Principles Study of the Structure and Elastic Properties of Thorium Metal." MRS Advances 1, no. 35 (2016): 2447–52. http://dx.doi.org/10.1557/adv.2016.500.

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ABSTRACTThorium has long been considered a possible source of fuel for use in power generating nuclear reactors. While much attention and interest have focused on thorium oxide, metallic thorium alloys were investigated in the past as fuel candidates for fast and thermal breeder reactors. In this work, thorium’s two solid allotropes (face centered cubic α and body centered cubic β) are modelled using Density Functional Theory (DFT). The Vienna Ab Initio Simulation Package (VASP) is used to determine structural and elastic properties, as well as the density of states. The Voigt-Reuss-Hill approximations are used to predict the phases’ bulk moduli, shear moduli, Young’s moduli, and Poisson’s ratios. Four exchange-correlation potentials are used and compared. These are the LDA, the PBE-GGA, the RPBE, and the PBEsol. All potentials showed relatively good accuracy when predicting the lattice constant. The RPBE was the most accurate, slightly over predicting by < 0.2%. The RPBE and the PBE-GGA were the most accurate in predicting elastic properties, performing almost equally, while slightly over predicting most values.

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Prazyan, Tigran L., and Yuri N. Zhuravlev. "Ab initio study of naphthalene and anthracene elastic properties." International Journal of Modern Physics C 29, no. 03 (March 2018): 1850024. http://dx.doi.org/10.1142/s0129183118500249.

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A study of the crystal structure, mechanical and acoustic properties of two [Formula: see text] and [Formula: see text] monoclinic phases of naphthalene and anthracene was performed using ab initio method of linear combination of atomic orbitals (LCAO) and basis sets: C_6-21G*, H_3-1p1G. The method was implemented in the CRYSTAL[Formula: see text]14,[Formula: see text]17 software package using electron density functional theory including van der Waals interactions (DFT-D2 and DFT-D3 (BJ)), in the local density approximation (LDA) with VWN exchange-correlation potential, gradient approximation PBE exchange-correlation functional and B3LYP hybrid functional. The calculated elastic constants for the first time are in moderate agreement with experimental data. Bulk modulus [Formula: see text], shear modulus [Formula: see text], Young’s modulus [Formula: see text] and the Poisson’s ratio [Formula: see text], as well as acoustic properties (average velocity of sound [Formula: see text], the Debye temperature [Formula: see text], and acoustic Grüneisen parameter [Formula: see text]) were obtained using the Voigt–Reuss–Hill model.

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Scardi, P., and Y. H. Dong. "Residual stress in fiber-textured thin films of cubic materials." Journal of Materials Research 16, no. 1 (January 2001): 233–42. http://dx.doi.org/10.1557/jmr.2001.0036.

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The effect of fiber texture on the x-ray residual stress analysis in thin films of cubic materials is discussed according to different mechanical models. The x-ray elastic constants (XECs) were calculated from single-crystal elastic constants for Cu, cubic ZrO2, and TiN, in the case of a typical [111] fiber texture with different spread of orientations [expressed by the half-width at half-maximum of the (111) pole figure]. Calculations were performed according to Reuss, Voigt, and Hill models, considering different crystallographic directions in cubic structures, in order to underline the effect of the mechanical anisotropy and fiber texture. The results clearly indicated the dependence of the XECs on the sample tilting angle, with the notable exception of [111] and [200], which were texture oscillation-free directions. Profiting from this condition the residual stress gradient in a fiber-textured TiN thin film deposited on stainless steel was determined by the simultaneous analysis of texture and residual strain for the (111) and (200) reflections. Advantages and limits of the procedure are discussed together with the experimental results.

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Aligholi, Saeed, and Manoj Khandelwal. "Computing Elastic Moduli of Igneous Rocks Using Modal Composition and Effective Medium Theory." Geosciences 12, no. 11 (November 10, 2022): 413. http://dx.doi.org/10.3390/geosciences12110413.

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Elastic constants of rock materials are the basic parameters required for modeling the response of rock materials under mechanical loads. Experimental tests for determining these properties are expensive, time-consuming and suffer from a high uncertainty due to both experimental limitations and the heterogeneous nature of rock materials. To avoid such experimental difficulties, in this paper a method is suggested for determining elastic constants of rock materials by determining their porosity and modal composition and employing effective medium theory. The Voigt–Reuss–Hill average is used to determine effective elastic constants of the studied igneous rocks according to the elastic moduli of their mineral constituents. Then, the effect of porosity has been taken into account by considering rock as a two-phase material, and the Kuster–Toksoz formulation is used for providing a close estimation of different moduli. The solutions are provided for different isotropic igneous rocks. This sustainable method avoids destructive tests and the usage of energy for performing time-consuming and expensive tests and requires simple equipment.

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Linton, Nathan, and Dilpuneet S. Aidhy. "A machine learning framework for elastic constants predictions in multi-principal element alloys." APL Machine Learning 1, no. 1 (March 1, 2023): 016109. http://dx.doi.org/10.1063/5.0129928.

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On the one hand, multi-principal element alloys (MPEAs) have created a paradigm shift in alloy design due to large compositional space, whereas on the other, they have presented enormous computational challenges for theory-based materials design, especially density functional theory (DFT), which is inherently computationally expensive even for traditional dilute alloys. In this paper, we present a machine learning framework, namely PREDICT (PRedict properties from Existing Database In Complex alloys Territory), that opens a pathway to predict elastic constants in large compositional space with little computational expense. The framework only relies on the DFT database of binary alloys and predicts Voigt–Reuss–Hill Young’s modulus, shear modulus, bulk modulus, elastic constants, and Poisson’s ratio in MPEAs. We show that the key descriptors of elastic constants are the A–B bond length and cohesive energy. The framework can predict elastic constants in hypothetical compositions as long as the constituent elements are present in the database, thereby enabling property exploration in multi-compositional systems. We illustrate predictions in a FCC Ni-Cu-Au-Pd-Pt system.

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Zaki, Shrouk E., Mohamed A. Basyooni, Mohammed Tihtih, Walid Belaid, Jamal Eldin F. M. Ibrahim, Mohamed Mostafa Abdelfattah, Amina Houimi, and A. M. Abdelaziz. "Tin diselenide/zirconium disulfide terahertz acoustic multi-layer superlattice for liquid sensing applications of acetonitrile; reconsidering Voigt-Reuss-Hill schemes." Results in Physics 42 (November 2022): 106041. http://dx.doi.org/10.1016/j.rinp.2022.106041.

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Sarioglu, C. "ANALYSIS OF XRD STRESS MEASUREMENT DATA OF NATURALLY GROWN OXIDE FILMS Al2O3AND Cr2O3BASED ON EXISTING REUSS, VOIGT, AND HILL MODELS." Surface Engineering 18, no. 2 (April 28, 2002): 105–11. http://dx.doi.org/10.1179/026708402225002767.

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Ghellab, T., H. Baaziz, Z. Charifi, K. Bouferrache, Ş. Uğur, G. Uğur, and H. Ünver. "Structural, elastic, electronic and thermoelectric properties of XPN2 (X = Li, Na): First-principles study." International Journal of Modern Physics B 33, no. 21 (August 20, 2019): 1950234. http://dx.doi.org/10.1142/s0217979219502345.

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Based on the density functional theory (DFT) implemented by the wien2k code which uses the full potential linearized augmented plane wave plus local orbitals (APW + lo) method, we have been able to study different physical properties of X[Formula: see text]PN2 (X = Li, Na) chalcopyrite such as structural, electronic, elastic and thermoelectric properties. According to our calculations, we have found that our structural and electronic parameters, such as the lattice parameter, energy bandgap, the tetragonal ratio, the displacement of the anions, are in very good agreement with the previous experimental and theoretical results. Based on the Voigt–Reuss–Hill approximations, we were able to compute the elastic constants: the compressibility, Young’s and the shear’s moduli, the average velocity of the elastic waves, the Debye temperature and the Poisson’s coefficient of the chalcopyrite LiPN2 and NaPN2. The elastic anisotropy is estimated and further illustrated by the three-dimensional (3D) direction of Young’s and Bulk’s moduli. Finally, using the semi-classical Boltzmann theory implemented in the BolzTraP code, we calculated the transport properties such as the Seebeck coefficient, the thermal electrical conductivity and the figure of merit of these materials.

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Gueddouh, A., B. Bentria, Y. Bourourou, and S. Maabed. "Anisotropic elastic properties of FexB (x = 1, 2, 3) under pressure. First-principles study." Materials Science-Poland 34, no. 3 (September 1, 2016): 503–16. http://dx.doi.org/10.1515/msp-2016-0078.

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AbstractSpin-polarization (SP) and pressure effects have been used to better clarify and understand anisotropic elastic properties of Fe-B intermetallic compounds using the first-principles calculation with generalized gradient approximation (GGA) within the plane-wave pseudopotential density functional theory. Elastic properties, including bulk, shear and Young’s moduli as well as Poisson ratio were obtained by Voigt-Reuss-Hill approximation. All studied Fe-B compounds were mechanically stable. The brittle and ductile properties were discussed using bulk to shear moduli ratio (B/G) of the studied structures in the pressure range of 0 GPa to 90 GPa in order to predict the critical pressure of phase transition from ferromagnetic (FM) to nonmagnetic (NM) state. Mechanical anisotropy in both cases was discussed by calculating different anisotropic indexes and factors. We have plotted three-dimensional (3D) surfaces and planar contours of the bulk and Young’s moduli of FexB (x = 1, 2, 3) compounds for some crystallographic planes, (1 0 0), (0 1 0) and (0 0 1), to reveal their elastic anisotropy. On the basis of anisotropic elastic properties the easy and hard axes of magnetization for the three studied compounds were predicted.

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Fu, Jia, Tian Hou, and Jing Rui Chen. "First-Principles Calculations of Thermoelectric PbSe₂ Compound to Predict its Elastic Properties." Materials Science Forum 956 (June 2019): 46–54. http://dx.doi.org/10.4028/www.scientific.net/msf.956.46.

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The influencing effect of pressure on structural stability and elastic properties of PbSe2 compound is mainly investigated by first-principles method and homogenization method of the Y parameter. The optimized structural parameters at zero pressure are a=b=6.446Å, c=7.887Å (GGA method) and a=b=6.316Å, c=7.651Å (LDA method), which has good agreement with the experimental and theoretical values. Our calculated lattice parameters and Se-Se bond length are in excellent agreement with experimental data. PbSe2 compound is energetically stable with a good alloying ability. The elastic constants are calculated, and then the bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio and anisotropy factor are determined. Besides, Y parameter method is used to investigate changes of the Poisson ratio, Young’s and shear moduli of PbSe2 within different normal orientation crystal planes. Results show that: 1) Young’s modulus is about 48.37 GPa from GGA and 58.87 GPa from LDA by Reuss-Voigt-Hill estimation, which is averaged about 53.62 GPa; 2) The PbSe2 compound is ductile according to B/G ratio. The universal anisotropic index AU shows that PbSe2 exhibits a fairly high elastic anisotropy.

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Zhu, Wenjie, Chaoyong Wang, Wei Li, and Xingtao Ma. "Computational study on the mechanical properties of lotus-type nanoporous magnesium under uniaxial tension and compression." Materials Express 12, no. 6 (June 1, 2022): 839–47. http://dx.doi.org/10.1166/mex.2022.2205.

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In this work, molecular dynamics (MD) simulation was performed to study the mechanical property of lotus-type nanoporous magnesium (Mg) under uniaxial tension and compression. Initial structure was treated by simulated annealing to obtain the stable state of surface atoms around the pore. After annealing, the porosity decreases and the atoms on the surface are in a disordered state due to rearrangement. Using the Voigt-Reuss-Hill (VRH) formula, we have deduced the elastic moduli based on calculated elastic constants for the annealed structure. The structure was declared as ductile according to Pugh criterion. Uniaxial tension and compression simulations were used to study the relationship among the stress–strain curves, the atomic crystalline phases and the vacancies-strain curves. For lotus-type nanoporous Mg, the main crystalline phases were also studied, combined with disordered atoms. The evolution of pore morphology is also different in the three directions. The shapes of pores after tension or compression are mainly cylindrical, elliptical and rhombic. The results of uniaxial tension and compression show that the faster the vacancy increases, the faster the stress decreases, and the number of vacancies is closely related to the change of atomic crystalline phases.

Journal articles on the topic 'Voigt-Reuss-Hill'

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