Abstract
The Lennard-Jones potential approach is used to investigate the effect of pressure on the ultrasonic and elastic properties of the rare-earth ternary TbNiAl intermetallic compound. The second- and third-order elastic constants of TbNiAl are considered using the potential model. The pressure-dependent higher-order elastic constants are studied, and it is observed that the elastic constants of the TbNiAl compound increased monotonously with pressure. The hexagonal TbNiAl compound is mechanically stable up to the pressure 20 GPa according to the Born elastic stability criteria. The Voigt–Reuss–Hill approach is used to compute such elastic parameters as Young’s modulus, bulk modulus, Poisson’s ratio, and shear modulus in the pressure range 0–45 GPa. Hardness, melting temperature, and anisotropy are also determined for the intermetallic TbNiAl compound. The pressure-dependent velocities and attenuation of ultrasonic waves in this ternary compound are evaluated. The computation results are also satisfactory in estimating the Debye temperature and thermal conductivity Kmin under different pressure. It is observed that TbNiAl has a significant anisotropy at zero pressure, which becomes stronger as the pressure increased. This ternary compound behaves as its purest form at higher pressure and is more ductile, which is demonstrated by the minimum attenuation.
Similar content being viewed by others
REFERENCES
Cable, J.W., Koehlar, W.C., and Wollan, E.O., Magnetic Order in Rare-Earth Intermetallic Compound, Phys. Rev., 1964, vol. 136, pp. 240–242. https://doi.org/10.1103/PhysRev.136.A240
Javorsky, P., Burlet, P., Shekovsky, P., Arons, R.R., Ressouche, E., and Lapertot, G., Neutron Diffraction Study of Magnetic Ordering in RNiAl Compounds, Phys. B. Condens. Matter, 1997, vol. 234, pp. 665–666. https://doi.org/10.1016/S0921-4526(96)01080-0
Kitazawa, H., Donni, A., Keller, L., Tang, J., Fauth, F., and Kido, G., Magnetic Structures of the Rare-Earth Platinum Aluminides RPtAl (R = Ce, Pr, Nd), J. Solid Chem., 1998, vol. 140, pp. 233–241. https://doi.org/10.1006/jssc.1998.7881
Soderberg, O., Brown, D., Aaltio, I., Oksanen, J., Syren, J., Pulkkinen, H., Hannula, S.P., Microstructure and Properties of Ni–Mn–Ga Alloys Produced by Rapid Solidification and Pulsed Electric Current Sintering, J. Alloys Compnd, 2011, vol. 509, pp. 5981–5987. https://doi.org/10.1016/j.jallcom.2011.02.16
Klicpera, M., Javorský, P., and Puente Orench, I., Development of Magnetic Order in the TbNi(Al, In) Series and Magnetocrystalline Anisotropy in TbTX Compounds, Phys. Rev. B, 2011, vol. 84, pp. 224414–8. https://doi.org/10.1103/PhysRevB.84.224414
Javorsky, P., Prchal, J., Klicpera, M., Kastil, J., and Misek, M., Pressure Influence on Magnetic Properties of TbNiAl, Acta Phys. Polon. A, 2014, vol. 126, pp. 280–281. https://doi.org/10.12693/APhysPolA.126.280
Mao, H.K., Bell, P.M., Shaner, J.W., and Steinberg, D.J., Specific Volume Measurements of Cu, Mo, Pd, and Ag and Calibration of the Ruby R1 Fluorescence Pressure Gauge from 0.06 to 1 Mbar, J. Appl. Phys., 1978, vol. 49, pp. 3276–3282. https://doi.org/10.1063/1.325277
Ishii, Y., Kosaka, M., Uwatoko, Y., Andreev, A.V., and Sechovský, V., Ferromagnetism Induced in UCoAl under Uniaxial Pressure, Phys. B. Condens. Matter, 2003, vol. 334, pp. 160–166. https://doi.org/10.1016/S0921-4526(03)00041-3
Prchal, J., Javorsky, P., Rusz, J., de Boer, F., Divis, M., Kitazawa, H., Donni, A., Danis, S., and Sechovsky, V., Structural Discontinuity in the Hexagonal RtAl Compounds: Experiments and Density-Functional Theory Calculations, Phys. Rev. B, 2008, vol. 77, p. 134106. https://doi.org/10.1103/PhysRevB.77.134106
Prchal, J., Klicpera, M., Dolezal, P., Kastil, J., Misek, M., and Javorsky, P., Pressure Effect on the Isostructural Transition in RNiAl Compounds (R = Tb and Gd), J. Phys. Conf. Ser., 2014, vol. 500, p. 032013. https://doi.org/10.1088/1742-6596/500/3/032013
Jha, A.R., Applications of Rare Earth Intermetallic Compounds, Hydrides, and Ceramics, New York: Taylor & Francis Group, 2014.
Singh, N.K., Suresh, K.G., Nirmala, R., Nigam, A.K., Malik, S.K., Magnetic and Magnetocaloric Properties of the Intermetallic Compound TbNiAl, J. Magnetism Magnetic Mater., 2006, vol. 302(2), pp. 302–305. https://doi.org/10.1016/j.jmmm.2005.09.023
Jaiswal, A.K., Yadawa, P.K., and Yadav, R.R., Ultrasonic Wave Propagation in Ternary Intermetallic CeCuGe Compound, Ultrasonics, 2018, vol. 89, pp. 22–25. https://doi.org/10.1016/j.ultras.2018.04.009
Panday, D.K., Yadawa, P.K., and Yadav, R.R., Ultrasonic Properties of Hexagonal ZnS at Nanoscale, Mater. Lett. 2007, vol. 61, pp. 5194–5198. https://doi.org/10.1016/j.matlet.2007.04.028
Yadawa, P.K., Singh, D., Panday, D.K., and Yadav, R.R., Elastic and Acoustic Properties of Heavy Rare-Earth Metals, Open Acoustics J., 2009, vol. 2, pp. 61–67. https://doi.org/
Donald, T.M. and Glen, A.S., High Lattice Thermal Conductivity Solids in High Thermal Conductivity of Materials, Springer, 2006, pp. 37–43.
Voigt, W., Lehrbuch der Kristallphysik (Mitausschluss der Kristalloptik), Leipzig–Berlin: B.G. Teubner, 1928.
Reuss, A., Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle, ZAMM–J. Appl. Math. Mech., 1929, vol. 9, p. 49. http://dx.doi.org/10.1002/zamm.19290090104
Hill, R., The Elastic Behaviour of a Crystalline Aggregate, Proc. Phys. Soc. A, 1952, vol. 65, pp. 349–354. https://doi.org/10.1088/0370-1298/65/5/307
Turkdal, N., Deligoz, E., Ozisik, H., and Ozisik, H.V., First-Principles Studies of the Structural, Elastic, and Lattice Dynamical Properties of ZrMo2 and HfMo2, Phase Transit., 2017, vol. 90, pp. 1–12. https://doi.org/10.1080/01411594.2016.1252979
Weck, P.F., Kim, E., Tikare, V., and Mitchell, J.F., Mechanical Properties of Zirconium Alloys and Zirconium Hydrides Predicted from Density Functional Perturbation Theory, Dalton Trans., 2015, vol. 44, pp. 18769–18779. https://doi.org/10.1039/C5DT03403E
Yadav, N., Singh, S.P., Maddheshiya, A.K., Yadawa, P.K., and Yadav, R.R., Mechanical and Thermophysical Properties of High-Temperature IrxRe1–x Alloys, Phase Transit., 2020, vol. 93, pp. 883–894. https://doi.org/10.1080/01411554.20201813290
Singh, D., Panday, D.K., Yadawa, P.K., and Yadav, A.K., Attenuation of Ultrasonic Waves in V, Nb and Ta at Low Temperatures, Cryogen, 2009, vol. 49. pp. 12–16. https://doi.org/10.1016/j.cryogenics.2008.08.008
Yadawa, P.K., Computational Study of Ultrasonic Parameters of Hexagonal Close-Packed Transition Metals Fe, Co, and Ni, Arab. J. Sci. Eng., 2012, vol. 37, pp. 255–262. https://doi.org/10.1007/s13369-011-0153-6
Pillai, S.O., Solid State Physics: Crystal Physics, New Age International Publisher, 2005, pp. 100–102.
Fine, M.E., Brown, L.D., and Marcus, H.L., Elastic Constants Versus Melting Temperature in Metals, Scripta Metallurg., 1984, vol. 18, pp. 951–956. https://doi.org/10.1016/0036-9748(84)90267-9
Panday, D.K. and Panday, S., Ultrasonics: A Technique of Material Characterization, Sciyo Croatia: Sciyo Publisher, 2010, pp. 397–430.
Yadawa, P.K., Elastic and Acoustic Properties of Hexagonal Intermetallic Ternary Compound, J. Pure Appl. Ultrasonics, 2018, vol. 40, pp. 16–21.
Rai, S., Chaurasiya, N., and Yadawa, P.K., Elastic, Mechanical and Thermophysical Properties of Single-Phase Quaternary ScTiZrHf High-Entropy Alloy, Phys. Chem. Solid State, 2021, vol. 22, pp. 687–696. https://doi.org/10.15330/pcss.22.4.687-696
Havela, L., Divis, M., Sechovsky, V., Andreev, A.V., Honda, F., Oomi, G., Meresse, F., and Heathman, S., U Ternaries with ZrNiAl Structure–Lattice Properties, J. Alloys Compnd, 2001, vol. 322, pp. 7–13. https://doi.org/10.1016/S0925-8388(01)01176-8
Zhang, G., Zhao, Y.X., Hao, Y.J., and Zhang, L., Structural, Elastic, Electronic and Thermodynamic Properties of ZrB2 under High-Pressure: First-Principle Study, World Sci., 2018, vol. 32, pp. 1–15. https://doi.org/10.1142/S0217979218502004
Suetin, T.V. and Shien, I.R., Electronic and Mechanical Properties, Phase Stability, and Formation Energies of Point Defects of Niobium Boronitride Nb2BN, Phys. Solid State, 2017, vol. 59, pp. 1459–1469. https://doi.org/10.1134/S1063783417080285
Guechi, A., Merabet, A., Chegaar, M., Bouhemadou, A., and Guechi, N., Pressure Effect on the Structural, Elastic, Electronic and Optical Properties of the Zintl Phase KAsSn, First Principles Study, J. Alloys Compnd, 2015, vol. 623, pp. 219–228. https://doi.org/10.1016/j.jallcom.2014.10.114
Ranganathan, S.I. and Ostoja-Starzewski, M., Universal Elastic Anisotropy Index, Phys. Rev. Lett., 2008, vol. 101, pp. 1–4. https://doi.org/10.1103/PhysRevLett.101.055504
Panda, K.B. and Ravi Chandran, K.S., Determination of Elastic Constants of Titanium Diboride (TiB2) from First Principles Using FLAPW Implementation of the Density Functional Theory, Comput. Mater. Sci., 2006, vol. 35, pp. 134–150. https://doi.org/10.1103/PhysRevLett.101.055504
Yadawa, P.K., Ultrasonic Characterization of Ceramic Material Titanium Diboride, Ceramics-Silikaty, 2011, vol. 55, pp. 127–133.
Singh, S.P., Singh, G., Verma, A.K., Yadawa, P.K., and Yadav, R.R., Ultrasonic Wave Propagation in Thermoelectric ZrX2 (X = S, Se) Compounds, Pramana. J. Phys., 2019, vol. 93, pp. 1–9. https://doi.org/10.1007/s12043-019-1846-8
Yadawa, P.K., Behaviour of Ultrasonic Velocities and Elastic Constants in Ag-Zn Alloys, Adv. Mater. Lett., 2011, vol. 2, pp. 157–162. https://doi.org/
Yadawa, P.K., Effect of Temperature Dependence Ultrasonic Velocities and Attenuation of GaP Nanowires, J. Theor. Appl. Phys., 2016, vol. 10, pp. 1–7. https://doi.org/10.1007/s40094-016-0216-x
Funding
The work was performed within the Veer Bahadur Singh Purvanchal University Grant (133/VBSPU/ IQAC/2022, date 23-03-2022, code 50) and the R&D Grant of the Uttar Pradesh Department of Higher Education as well as with financial support from the Council for Scientific and Industrial Research and University Grants Commission of India (Junior Research Fellowship 1500/CSIR-UGC NET, December 2017), India.
Author information
Authors and Affiliations
Corresponding authors
Ethics declarations
The authors declare that they have no conflicts of interest.
Rights and permissions
About this article
Cite this article
Rai, S., Prajapati, A.K. & Yadawa, P.K. Effect of Pressure on Elastic Constants and Related Properties of Rare-Earth Intermetallic Compound TbNiAl. Phys Mesomech 26, 495–504 (2023). https://doi.org/10.1134/S1029959923050028
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1029959923050028