Theoretical Investigations on Structural Stability and Elastic Properties of MoNbTaW-X (=Ti/V) High Entropy Alloys
Journal of Materials Science Research and Reviews,
Page 1-9
Abstract
A refractory high entropy alloy based on MoNbTaW, with varying amounts of Ti and V, has been studied to elucidate the effect of the alloy composition on the electronic structure, phase stability, thermodynamic properties and the elastic properties. A synergistic approach has been adopted, employing empirical parameters, CALPHAD, and first principles calculations, to verify phase stability and single-phase solid solution formation for this alloy system. First-principles calculations are based on density functional theory, and employ the supercell method for modeling random alloys. The calculated lattice parameter for equiatomic MoNbTaW is in good agreement with available experimental data. The effect of Ti and V in various compositions on the electronic structure of the host alloy has been elucidated via the density of states spectra. Elastic constants of C11, C12, and C44 of 9 alloys based on MoNbTaW with varying amounts of Ti and V, are reported by the stress-strain method and the Voigt-Reuss-Hill approximation. Elastic properties including Young’s modulus, bulk modulus, Poisson’s ratio and Debye temperature of polycrystalline alloys have been reported. All the alloys show mechanical isotropy for bulk modulus and Young's modulus. Addition of Ti and V in increasing amounts shows improved in ductility in the base alloy.
Keywords:
- Refractory high entropy alloys
- CALPHAD
- density functional theory
- elastic constants
- phase stability.
How to Cite
Mishra, A., Priyadarshan, G., Clark, D., Lu, Y., & Shi, R. (2019). Theoretical Investigations on Structural Stability and Elastic Properties of MoNbTaW-X (=Ti/V) High Entropy Alloys. Journal of Materials Science Research and Reviews, 4(2), 1-9. Retrieved from https://journaljmsrr.com/index.php/JMSRR/article/view/30112
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Soven P. Coherent-potential model of substitutional disordered alloys. Phys. Rev; 1967.
Zaddach AJ, Niu C, Koch CC, Irving DL. Mechanical properties and stacking fault energies of NiFeCrCoMn high-entropy alloy. JOM; 2013.
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Yao HW, Qiao JW, Hawk JA, Zhou HF, Chen MW, Gao MC. Mechanical properties of refractory high-entropy alloys: Experiments and modeling. J. Alloys Compd; 2017.
Han ZD, et al. Effect of Ti additions on mechanical properties of NbMoTaW and VNbMoTaW refractory high entropy alloys. Intermetallics; 2017.
Sundman B, Jansson B, Andersson JO. The Thermo-Calc databank system Le système de banque de données Thermo-Calc. Calphad; 1985.
King DJM, Middleburgh SC, McGregor AG, Cortie MB. Predicting the formation and stability of single phase high-entropy alloys. Acta Mater; 2016.
Middleburgh SC, King DM, Lumpkin GR, Cortie M, Edwards L. Segregation and migration of species in the CrCoFeNi high entropy alloy. Journal of Alloys and Compounds; 2014.
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Voigt W. Lehrbuch der Kristallphysik; 2013.
Reuss A. Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle. ZAMM ‐ J. Appl. Math. Mech. / Zeitschrift für Angew. Math. und Mech; 1929.
Pugh SF. XCII. Relations between the elastic moduli and the plastic properties of polycrystalline pure metals. London, Edinburgh, Dublin Philos. Mag. J. Sci; 1954.
Pettifor DG. Theoretical predictions of structure and related properties of intermetallics. Mater. Sci. Technol; 2014.
Yeh JW, et al. Nanostructured high-entropy alloys with multiple principal elements: Novel alloy design concepts and outcomes. Adv. Eng. Mater; 2004.
Cantor B, Chang ITH, Knight P, Vincent AJB. Microstructural development in equiatomic multicomponent alloys. Mater. Sci. Eng. A; 2004.
Zhang Y, Zhouc YJ, Lin JP, Chen GL, Liaw PK. Solid-solution phase formation rules for multi-component alloys. Adv. Eng. Mater; 2008.
Takeuchi A, Amiya K, Wada T, Yubuta K, Zhang W. High-entropy alloys with a hexagonal close-packed structure designed by equi-atomic alloy strategy and binary phase diagrams. JOM; 2014.
Zhang Y, et al. Microstructures and properties of high-entropy alloys. Progress in Materials Science; 2014.
Youssef KM, Zaddach AJ, Niu C, Irving DL, Koch CC. A novel low-density, high-hardness, high-entropy alloy with close-packed single-phase nanocrystalline structures. Mater. Res. Lett; 2014.
Zhao K, Xia XX, Bai HY, Zhao DQ, Wang WH. Room temperature homogeneous flow in a bulk metallic glass with low glass transition temperature. Appl. Phys. Lett; 2011.
Gao XQ, Zhao K, Ke HB, Ding DW, Wang WH, Bai HY. High mixing entropy bulk metallic glasses. J. Non. Cryst. Solids; 2011.
Li HF, et al. In vitro and in vivo studies on biodegradable CaMgZnSrYb high-entropy bulk metallic glass. Acta Biomater; 2013.
Highmore RJ, Greer AL. Eutectics and the formation of amorphous alloys. Nature; 1989.
Li Y. Bulk metallic glasses: Eutectic coupled zone and amorphous formation. JOM; 2005.
Gludovatz B, Hohenwarter A, Catoor D, Chang EH, George EP, Ritchie RO. A fracture-resistant high-entropy alloy for cryogenic applications. Science. 2014;80.
Zou Y, Ma H, Spolenak R. Ultrastrong ductile and stable high-entropy alloys at small scales. Nat. Commun; 2015.
Zhang ZJ, et al. Nanoscale origins of the damage tolerance of the high- entropy alloy CrMnFeCoNi. Nat. Commun; 2015.
Liu WH et al. Ductile CoCrFeNiMox high entropy alloys strengthened by hard intermetallic phases. Acta Mater; 2016.
Koželj P, et al. Discovery of a superconducting high-entropy alloy. Phys. Rev. Lett; 2014.
Huo J, et al. The magnetocaloric effect of Gd-Tb-Dy-Al-M (M = Fe, Co and Ni) high-entropy bulk metallic glasses. Intermetallics; 2015.
Huo J, et al. High-entropy bulk metallic glasses as promising magnetic refrigerants. J. Appl. Phys; 2015.
Chen YY, Duval T, Hung UD, Yeh JW, Shih HC. Microstructure and electrochemical properties of high entropy alloys-a comparison with type-304 stainless steel. Corros. Sci; 2005.
Senkov ON, Wilks GB, Miracle DB, Chuang CP, Liaw PK. Refractory high-entropy alloys. Intermetallics; 2010.
Senkov ON, Wilks GB, Scott JM, Miracle DB. Mechanical properties of Nb25Mo25Ta25W25 and V20Nb20Mo20Ta20W20 refractory high entropy alloys. Intermetallics; 2011.
Senkov ON, Scott JM, Senkova SV, Miracle DB, Woodward CF. Microstructure and room temperature properties of a high-entropy TaNbHfZrTi alloy. J. Alloys Compd; 2011.
Juan CC, et al. Enhanced mechanical properties of HfMoTaTiZr and HfMoNbTaTiZr refractory high-entropy alloys. Intermetallics; 2015.
Chen H, et al. Microstructure and mechanical properties at elevated temperatures of a new Al-containing refractory high-entropy alloy Nb-Mo-Cr-Ti-Al. J. Alloys Compd; 2016.
Senkov ON, Senkova SV, Woodward C, Miracle DB. Low-density, refractory multi-principal element alloys of the Cr-Nb-Ti-V-Zr system: Microstructure and phase analysis. Acta Mater; 2013.
Gorr B, Azim M, Christ HJ, Mueller T, Schliephake D, Heilmaier M. Phase equilibria, microstructure, and high temperature oxidation resistance of novel refractory high-entropy alloys. J. Alloys Compd; 2015.
Senkov ON, Semiatin SL. Microstructure and properties of a refractory high-entropy alloy after cold working. J. Alloys Compd; 2015.
Juan CC, et al. Solution strengthening of ductile refractory HfMoxNbTaTiZr high-entropy alloys. Mater. Lett; 2016.
Senkov ON, Woodward C, Miracle DB. Microstructure and Properties of Aluminum-Containing Refractory High-Entropy Alloys. JOM; 2014.
Senkov ON, Senkova SV, Woodward C. Effect of aluminum on the microstructure and properties of two refractory high-entropy alloys. Acta Mater; 2014.
Huhn WP, Widom M. Prediction of A2 to B2 phase transition in the high-entropy alloy Mo-Nb-Ta-W. JOM; 2013.
Yeh JW. Recent progress in high-entropy alloys. Eur. J. Control. 2006;31:633–648.
Wertz KN, Miller JD, Senkov ON. Toward multi-principal component alloy discovery: Assessment of CALPHAD thermodynamic databases for prediction of novel ternary alloy systems. J. Mater. Res; 2018.
Hohenberg P, Kohn W. Inhomogeneous electron gas. Phys. Rev; 1964.
Kresse G. Ab initio molecular dynamics for liquid metals. J. Non. Cryst. Solids; 1995.
Ganesh P, Widom M. Ab initio simulations of geometrical frustration in supercooled liquid Fe and Fe-based metallic glass. Phys. Rev. B - Condens. Matter Mater. Phys; 2008.
Chizmeshya AVG, Bauer MR, Kouvetakis J. Experimental and theoretical study of deviations from Vegard’s law in the SnxGe1-x system. Chem. Mater; 2003.
Soven P. Coherent-potential model of substitutional disordered alloys. Phys. Rev; 1967.
Zaddach AJ, Niu C, Koch CC, Irving DL. Mechanical properties and stacking fault energies of NiFeCrCoMn high-entropy alloy. JOM; 2013.
Bellaiche L, Vanderbilt D. Virtual crystal approximation revisited: Application to dielectric and piezoelectric properties of perovskites. Phys. Rev. B-Condens. Matter Mater. Phys; 2000.
Guo S, Ng C, Lu J, Liu CT. Phase equilibria, microstructure, and high temperature oxidation resistance of novel refractory high-entropy alloys. J. Alloys Compd. in Journal of Applied Physics. 2011;624(2015):270e278.
Troparevsky MC, Morris JR, Kent PRC, Lupini AR, Stocks GM. Criteria for predicting the formation of single- phase high-entropy alloys. Phys. Rev. X; 2015.
Zhang F, Zhang C, Chen SL, Zhu J, Cao WS, Kattner UR. An understanding of high entropy alloys from phase diagram calculations. Calphad Comput. Coupling Phase Diagrams Thermochem; 2014.
Senkov ON, Miller JD, Miracle DB, Woodward C. Accelerated exploration of multi-principal element alloys with solid solution phases. Nat. Commun; 2015.
Senkov ON, Miller JD, Miracle DB, Woodward C. Accelerated exploration of multi-principal element alloys for structural applications. Calphad Comput. Coupling Phase Diagrams Thermochem; 2015.
Gorsse S, Senkov ON. About the reliability of CALPHAD predictions in multi component systems. Entropy; 2018.
Yao HW, Qiao JW, Hawk JA, Zhou HF, Chen MW, Gao MC. Mechanical properties of refractory high-entropy alloys: Experiments and modeling. J. Alloys Compd; 2017.
Han ZD, et al. Effect of Ti additions on mechanical properties of NbMoTaW and VNbMoTaW refractory high entropy alloys. Intermetallics; 2017.
Sundman B, Jansson B, Andersson JO. The Thermo-Calc databank system Le système de banque de données Thermo-Calc. Calphad; 1985.
King DJM, Middleburgh SC, McGregor AG, Cortie MB. Predicting the formation and stability of single phase high-entropy alloys. Acta Mater; 2016.
Middleburgh SC, King DM, Lumpkin GR, Cortie M, Edwards L. Segregation and migration of species in the CrCoFeNi high entropy alloy. Journal of Alloys and Compounds; 2014.
Blaha JLP, Schwarz K, Madsen GKH, Kvasnicka D. An augmented plane wave+local orbitals program for calculating crystal properties. Techn. Univ. Wien, Austria; 2001.
Hill R. The elastic behaviour of a crystalline aggregate. Proc. Phys. Soc. Sect. A; 1952.
Voigt W. Lehrbuch der Kristallphysik; 2013.
Reuss A. Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle. ZAMM ‐ J. Appl. Math. Mech. / Zeitschrift für Angew. Math. und Mech; 1929.
Pugh SF. XCII. Relations between the elastic moduli and the plastic properties of polycrystalline pure metals. London, Edinburgh, Dublin Philos. Mag. J. Sci; 1954.
Pettifor DG. Theoretical predictions of structure and related properties of intermetallics. Mater. Sci. Technol; 2014.
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