{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T19:39:56Z","timestamp":1776281996026,"version":"3.50.1"},"reference-count":48,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2016,5,19]],"date-time":"2016-05-19T00:00:00Z","timestamp":1463616000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.mdpi.com"],"crossmark-restriction":true},"short-container-title":["Entropy"],"abstract":"<jats:p>Guided by CALPHAD (Calculation of Phase Diagrams) modeling, the refractory medium-entropy alloy MoNbTaV was synthesized by vacuum arc melting under a high-purity argon atmosphere. A body-centered cubic solid solution phase was experimentally confirmed in the as-cast ingot using X-ray diffraction and scanning electron microscopy. The measured lattice parameter of the alloy (3.208 \u00c5) obeys the rule of mixtures (ROM), but the Vickers microhardness (4.95 GPa) and the yield strength (1.5 GPa) are about 4.5 and 4.6 times those estimated from the ROM, respectively. Using a simple model on solid solution strengthening predicts a yield strength of approximately 1.5 GPa. Thermodynamic analysis shows that the total entropy of the alloy is more than three times the configurational entropy at room temperature, and the entropy of mixing exhibits a small negative departure from ideal mixing.<\/jats:p>","DOI":"10.3390\/e18050189","type":"journal-article","created":{"date-parts":[[2016,5,19]],"date-time":"2016-05-19T20:43:57Z","timestamp":1463690637000},"page":"189","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":146,"title":["MoNbTaV Medium-Entropy Alloy"],"prefix":"10.3390","volume":"18","author":[{"given":"Hongwei","family":"Yao","sequence":"first","affiliation":[{"name":"Laboratory of Applied Physics and Mechanics of Advanced Materials, College of Materials Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, China"}]},{"given":"Jun-Wei","family":"Qiao","sequence":"additional","affiliation":[{"name":"Laboratory of Applied Physics and Mechanics of Advanced Materials, College of Materials Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, China"}]},{"given":"Michael","family":"Gao","sequence":"additional","affiliation":[{"name":"National Energy Technology Laboratory, Albany, OR 97321, USA"},{"name":"AECOM, P.O. Box 1959, Albany, OR 97321, USA"}]},{"given":"Jeffrey","family":"Hawk","sequence":"additional","affiliation":[{"name":"National Energy Technology Laboratory, Albany, OR 97321, USA"}]},{"given":"Sheng-Guo","family":"Ma","sequence":"additional","affiliation":[{"name":"Institute of Applied Mechanics and Biomedical Engineering, Taiyuan University of Technology, Taiyuan 030024, China"}]},{"given":"Hefeng","family":"Zhou","sequence":"additional","affiliation":[{"name":"Laboratory of Applied Physics and Mechanics of Advanced Materials, College of Materials Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, China"}]}],"member":"1968","published-online":{"date-parts":[[2016,5,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Donachie, M.J., and Donachie, S.J. (2002). Superalloys: A Technical Guide, ASM International.","DOI":"10.31399\/asm.tb.stg2.9781627082679"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"361","DOI":"10.2514\/1.18239","article-title":"Nickel-based superalloys for advanced turbine engines: Chemistry, microstructure and properties","volume":"22","author":"Pollock","year":"2006","journal-title":"J. Propuls. Power"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1002\/adem.200300567","article-title":"Nanostructured High-Entropy Alloys with Multiple Principal Elements: Novel Alloy Design Concepts and Outcomes","volume":"6","author":"Yeh","year":"2004","journal-title":"Adv. Eng. Mater."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"534","DOI":"10.1002\/adem.200700240","article-title":"Solid\u2014Solution phase formation rules for multi-component alloys","volume":"10","author":"Zhang","year":"2008","journal-title":"Adv. Eng. Mater."},{"key":"ref_5","unstructured":"Ye, Y.F., Wang, Q., Lu, J., Liu, C.T., and Yang, Y. (2015). High-entropy alloy: Challenges and prospects. Mater. Today, in press."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/j.msea.2003.10.257","article-title":"Microstructural development in equiatomic multicomponent alloys","volume":"375","author":"Cantor","year":"2004","journal-title":"Mater. Sci. Eng. A"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1758","DOI":"10.1016\/j.intermet.2010.05.014","article-title":"Refractory high-entropy alloys","volume":"18","author":"Senkov","year":"2010","journal-title":"Intermetallics"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1984","DOI":"10.1007\/s11837-014-1085-x","article-title":"High-entropy alloys with a hexagonal close-packed structure designed by equi-atomic alloy strategy and binary phase diagrams","volume":"66","author":"Takeuchi","year":"2014","journal-title":"JOM"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Gao, M.C., Zhang, B., Guo, S.M., Qiao, J.W., and Hawk, J.A. (2016). High-entropy alloys in hexagonal close-packed structure. Metall. Mater. Trans. A.","DOI":"10.1007\/s11661-015-3091-1"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.matdes.2016.01.149","article-title":"A hexagonal close-packed high-entropy alloy: The effect of entropy","volume":"96","author":"Zhao","year":"2016","journal-title":"Mater. Des."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Gao, M.C., Yeh, J.W., Liaw, P.K., and Zhang, Y. (2016). Design of High-Entropy Alloys. High-Entropy Alloys: Fundamentals and Applications, Springer.","DOI":"10.1007\/978-3-319-27013-5"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"633","DOI":"10.3166\/acsm.31.633-648","article-title":"Recent progress in high entropy alloys","volume":"31","author":"Yeh","year":"2006","journal-title":"Ann. Chim. Sci. Mat."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.pmatsci.2013.10.001","article-title":"Microstructures and properties of high-entropy alloys","volume":"61","author":"Zhang","year":"2014","journal-title":"Prog. Mater. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Murty, B.S., Yeh, J.W., and Ranganathan, S. (2014). High Entropy Alloys, Butterworth-Heinemann.","DOI":"10.1016\/B978-0-12-800251-3.00002-X"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1153","DOI":"10.1126\/science.1254581","article-title":"A fracture-resistant high-entropy alloy for cryogenic applications","volume":"345","author":"Gludovatz","year":"2014","journal-title":"Science"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.mser.2015.12.001","article-title":"Metallic glass matrix composites","volume":"100","author":"Qiao","year":"2016","journal-title":"Mater. Sci. Eng. R."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"6043","DOI":"10.1016\/j.jallcom.2011.02.171","article-title":"Microstructure and room temperature properties of a high-entropy TaNbHfZrTi alloy","volume":"509","author":"Senkov","year":"2011","journal-title":"J. Alloys Compd."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.jallcom.2014.01.237","article-title":"Ab initio design of elastically isotropic TiZrNbMoVx high-entropy alloys","volume":"599","author":"Tian","year":"2014","journal-title":"J. Alloys Compd."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1016\/j.proeng.2012.03.043","article-title":"Microstructure and compressive properties of NbTiVTaAlx high entropy alloys","volume":"36","author":"Yang","year":"2012","journal-title":"Procedia Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2653","DOI":"10.1007\/s11837-015-1617-z","article-title":"Design of Refractory High-Entropy Alloys","volume":"67","author":"Gao","year":"2015","journal-title":"JOM"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Gao, M.C., Zhang, B., Yang, S., and Guo, S.M. (2016). Senary Refractory High-Entropy Alloy HfNbTaTiVZr. Metall. Mater. Trans. A.","DOI":"10.1007\/s11661-015-3105-z"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"698","DOI":"10.1016\/j.intermet.2011.01.004","article-title":"Mechanical properties of Nb25Mo25Ta25W25 and V20Nb20Mo20Ta20W20 refractory high entropy alloys","volume":"19","author":"Senkov","year":"2011","journal-title":"Intermetallics"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/s11837-008-0092-1","article-title":"The first-principles design of ductile refractory alloys","volume":"60","author":"Gao","year":"2008","journal-title":"JOM"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"075402","DOI":"10.1088\/0953-8984\/25\/7\/075402","article-title":"Phase Stability and Elastic Properties of Cr-V Alloys","volume":"25","author":"Gao","year":"2013","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_25","unstructured":"Goodfellow. Available online: http:\/\/www.goodfellow.com."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/0364-5916(85)90021-5","article-title":"The thermo-calc databank system","volume":"9","author":"Sundman","year":"1985","journal-title":"Calphad"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1207","DOI":"10.1179\/1743284715Y.0000000031","article-title":"Senary Refractory High-Entropy Alloy MoNbTaTiVW","volume":"31","author":"Zhang","year":"2015","journal-title":"Mater. Sci. Technol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/j.calphad.2015.09.007","article-title":"Senary Refractory High-Entropy Alloy CrxMoNbTaVW","volume":"51","author":"Zhang","year":"2015","journal-title":"Calphad"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Gao, M.C., Yeh, J.W., Liaw, P.K., and Zhang, Y. (2016). CALPHAD Modeling of High-Entropy Alloys. High-Entropy Alloys: Fundamentals and Applications, Springer.","DOI":"10.1007\/978-3-319-27013-5"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Yao, H.W., Qiao, J.W., Gao, M.C., Hawk, J.A., Ma, S.G., Zhou, H.F., and Zhang, Y. (2016). NbTaV-(Ti, W) Refractory High Entropy Alloys. Mater. Sci. Eng. A, submitted.","DOI":"10.1016\/j.msea.2016.07.102"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"839","DOI":"10.1007\/s11837-012-0365-6","article-title":"Computational thermodynamics aided high-entropy alloy design","volume":"64","author":"Zhang","year":"2012","journal-title":"JOM"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"4504","DOI":"10.3390\/e15104504","article-title":"Searching for next single-phase high-entropy alloy compositions","volume":"15","author":"Gao","year":"2013","journal-title":"Entropy"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.calphad.2013.10.006","article-title":"An understanding of high entropy alloys from phase diagram calculations","volume":"45","author":"Zhang","year":"2014","journal-title":"Calphad"},{"key":"ref_34","first-page":"17","article-title":"Die konstitution der mischkristalle und die raumf\u00fcllung der atome","volume":"5","author":"Vegard","year":"1921","journal-title":"Z. Phys. A Hadron. Nucl."},{"key":"ref_35","first-page":"120","article-title":"The quantitative effect of rapid cooling upon the constitution of binary alloys","volume":"9","author":"Gulliver","year":"1913","journal-title":"J. Inst. Met."},{"key":"ref_36","first-page":"70","article-title":"Comments on the layer crystal formation","volume":"34","author":"Scheil","year":"1942","journal-title":"Z. Metallkd."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/j.matchemphys.2011.11.021","article-title":"Prediction of high-entropy stabilized solid-solution in multi-component alloys","volume":"132","author":"Yang","year":"2012","journal-title":"Mater. Chem. Phys."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Martienssen, W., and Warlimont, H. (2005). Springer Handbook of Condensed Matter and Materials Data, Springer.","DOI":"10.1007\/b137475"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2817","DOI":"10.2320\/matertrans.46.2817","article-title":"Classification of bulk metallic glasses by atomic size difference, heat of mixing and period of constituent elements and its application to characterization of the main alloying element","volume":"46","author":"Takeuchi","year":"2005","journal-title":"Mater. Trans."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"830","DOI":"10.1007\/s11837-012-0366-5","article-title":"Alloy design and properties optimization of high-entropy alloys","volume":"64","author":"Zhang","year":"2012","journal-title":"JOM"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1557\/mrc.2014.11","article-title":"Guidelines in predicting phase formation of high-entropy alloys","volume":"4","author":"Zhang","year":"2014","journal-title":"MRS Commun."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"103505","DOI":"10.1063\/1.3587228","article-title":"Effect of valence electron concentration on stability of fcc or bcc phase in high entropy alloys","volume":"109","author":"Guo","year":"2011","journal-title":"J. Appl. Phys."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1016\/S1002-0071(12)60080-X","article-title":"Phase stability in high entropy alloys: Formation of solid-solution phase or amorphous phase","volume":"21","author":"Guo","year":"2011","journal-title":"Prog. Nat. Sci."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/j.intermet.2014.04.001","article-title":"Effects of electro-negativity on the stability of topologically close-packed phase in high entropy alloys","volume":"52","author":"Dong","year":"2014","journal-title":"Intermetallics"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Gao, M.C., Yeh, J.W., Liaw, P.K., and Zhang, Y. (2016). Applications of Special Quasi-Random Structures to High-Entropy Alloys. High-Entropy Alloys: Fundamentals and Applications, Springer.","DOI":"10.1007\/978-3-319-27013-5"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1002\/pssb.19700410221","article-title":"A statistical theory of solid solution hardening","volume":"41","author":"Labusch","year":"1970","journal-title":"Phys. Status Solidi B"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.actamat.2014.11.014","article-title":"Modelling solid solution hardening in high entropy alloys","volume":"85","year":"2015","journal-title":"Acta Mater."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"1028","DOI":"10.1007\/BF00540987","article-title":"Multi-component solid solution hardening","volume":"12","author":"Gypen","year":"1977","journal-title":"J. Mater. Sci."}],"updated-by":[{"DOI":"10.3390\/e18080289","type":"correction","label":"Correction","source":"publisher","updated":{"date-parts":[[2016,5,19]],"date-time":"2016-05-19T00:00:00Z","timestamp":1463616000000}}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/18\/5\/189\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,3]],"date-time":"2025-08-03T23:09:17Z","timestamp":1754262557000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/18\/5\/189"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,5,19]]},"references-count":48,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2016,5]]}},"alternative-id":["e18050189"],"URL":"https:\/\/doi.org\/10.3390\/e18050189","relation":{"correction":[{"id-type":"doi","id":"10.3390\/e18080289","asserted-by":"object"}]},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,5,19]]}}}