{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T09:48:08Z","timestamp":1782985688843,"version":"3.54.5"},"reference-count":63,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2019,3,19]],"date-time":"2019-03-19T00:00:00Z","timestamp":1552953600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004663","name":"Ministry of Science and Technology, Taiwan","doi-asserted-by":"publisher","award":["MOST 106-2218-E-002-025 and MOST 107-2218-E-002-019"],"award-info":[{"award-number":["MOST 106-2218-E-002-025 and MOST 107-2218-E-002-019"]}],"id":[{"id":"10.13039\/501100004663","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The recrystallization behavior, grain growth kinetics, and corresponding hardness variation of homogenized and 80% cold-rolled FeCoNiCrPd, FeCoNiCrMn, and their quaternary\/ternary FCC-structured high\/medium entropy alloys (H\/MEAs) annealed under different conditions were investigated. Experimental results indicate that the grain size and hardness of these H\/MEAs follow the Hall\u2013Petch equation, with the Hall\u2013Petch coefficient KH value being mainly dominated by the alloy\u2019s stacking fault energy and shear modulus. The FeCoNiCrPd alloy exhibits the highest hardness of the H\/MEAs at the same grain size due to the largest Young\u2019s modulus difference between Cr and Pd. The grain growth exponent n, kinetic constant k, and activation energy for grain growth QG of all H\/MEAs are calculated. The k can be expressed by the Arrhenius equation with QG, which is attributed to the diffusion rate. The results demonstrate that the QG values of these H\/MEAs are much higher than those of conventional alloys; most notable is FeCoNiCrPd HEA, which has an unusually lattice distortion effect that hinders grain growth.<\/jats:p>","DOI":"10.3390\/e21030297","type":"journal-article","created":{"date-parts":[[2019,3,19]],"date-time":"2019-03-19T12:12:25Z","timestamp":1552997545000},"page":"297","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":95,"title":["A Study on the Hall\u2013Petch Relationship and Grain Growth Kinetics in FCC-Structured High\/Medium Entropy Alloys"],"prefix":"10.3390","volume":"21","author":[{"given":"Yung-Chien","family":"Huang","sequence":"first","affiliation":[{"name":"Department of Materials Science and Engineering, National Taiwan University, Taipei 106, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Che-Hsuan","family":"Su","sequence":"additional","affiliation":[{"name":"Department of Materials Science and Engineering, National Taiwan University, Taipei 106, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shyi-Kaan","family":"Wu","sequence":"additional","affiliation":[{"name":"Department of Materials Science and Engineering, National Taiwan University, Taipei 106, Taiwan"},{"name":"Department of Mechanical Engineering, National Taiwan University, Taipei 106, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chieh","family":"Lin","sequence":"additional","affiliation":[{"name":"Department of Materials Science and Engineering, National Taiwan University, Taipei 106, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,19]]},"reference":[{"key":"ref_1","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_2","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_3","doi-asserted-by":"crossref","first-page":"494","DOI":"10.3390\/e16010494","article-title":"Exploration and development of high entropy alloys for structural applications","volume":"16","author":"Miracle","year":"2014","journal-title":"Entropy"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"448","DOI":"10.1016\/j.actamat.2016.08.081","article-title":"A critical review of high entropy alloys and related concepts","volume":"122","author":"Miracle","year":"2017","journal-title":"Acta Mater."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1080\/21663831.2014.912690","article-title":"High-entropy alloys: A critical review","volume":"2","author":"Tsai","year":"2014","journal-title":"Mater. Res. Lett."},{"key":"ref_6","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. Mater."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2254","DOI":"10.1007\/s11837-015-1583-5","article-title":"Physical metallurgy of high-entropy alloys","volume":"67","author":"Yeh","year":"2015","journal-title":"JOM"},{"key":"ref_8","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_9","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/j.intermet.2013.03.018","article-title":"Tensile properties of high- and medium-entropy alloys","volume":"39","author":"Gali","year":"2013","journal-title":"Intermetallics"},{"key":"ref_10","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_11","doi-asserted-by":"crossref","first-page":"548","DOI":"10.1016\/j.jallcom.2015.05.129","article-title":"Microstructural evolution of a CoCrFeMnNi high-entropy alloy after swaging and annealing","volume":"647","author":"Laplanche","year":"2015","journal-title":"J. Alloys Compd."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"526","DOI":"10.1016\/j.scriptamat.2012.12.002","article-title":"Grain growth and the Hall\u2013Petch relationship in a high-entropy FeCrNiCoMn alloy","volume":"68","author":"Liu","year":"2013","journal-title":"Scr. Mater."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"5743","DOI":"10.1016\/j.actamat.2013.06.018","article-title":"The influences of temperature and microstructure on the tensile properties of a CoCrFeMnNi high-entropy alloy","volume":"61","author":"Otto","year":"2013","journal-title":"Acta Mater."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.intermet.2014.05.014","article-title":"Microstructural evolution after thermomechanical processing in an equiatomic, single-phase CoCrFeMnNi high-entropy alloy with special focus on twin boundaries","volume":"54","author":"Otto","year":"2014","journal-title":"Intermetallics"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.intermet.2015.10.005","article-title":"Effect of heavy cryo-rolling on the evolution of microstructure and texture during annealing of equiatomic CoCrFeMnNi high entropy alloy","volume":"69","author":"Sathiaraj","year":"2016","journal-title":"Intermetallics"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1016\/j.intermet.2014.12.004","article-title":"Effect of cryo-deformation on structure and properties of CoCrFeNiMn high-entropy alloy","volume":"59","author":"Stepanov","year":"2015","journal-title":"Intermetallics"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1016\/j.msea.2015.03.097","article-title":"High temperature deformation behavior and dynamic recrystallization in CoCrFeNiMn high entropy alloy","volume":"636","author":"Stepanov","year":"2015","journal-title":"Mater. Sci. Eng. A"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"428","DOI":"10.1016\/j.actamat.2014.08.026","article-title":"Temperature dependence of the mechanical properties of equiatomic solid solution alloys with face-centered cubic crystal structures","volume":"81","author":"Wu","year":"2014","journal-title":"Acta Mater."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/j.intermet.2014.06.015","article-title":"Steady state flow of the FeCoNiCrMn high entropy alloy at elevated temperatures","volume":"55","author":"He","year":"2014","journal-title":"Intermetallics"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1016\/j.scriptamat.2015.10.025","article-title":"Precipitation in the equiatomic high-entropy alloy CrMnFeCoNi","volume":"113","author":"Pickering","year":"2016","journal-title":"Scr. Mater."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/j.intermet.2017.02.010","article-title":"Deformation stimulated precipitation of a single-phase CoCrFeMnNi high entropy alloy","volume":"85","author":"Zhou","year":"2017","journal-title":"Intermetallics"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/j.intermet.2013.10.024","article-title":"Recovery, recrystallization, grain growth and phase stability of a family of FCC-structured multi-component equiatomic solid solution alloys","volume":"46","author":"Wu","year":"2014","journal-title":"Intermetallics"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"254","DOI":"10.1016\/j.matdes.2017.02.072","article-title":"Optimizing the coupled effects of Hall\u2013Petch and precipitation strengthening in a Al0.3CoCrFeNi high entropy alloy","volume":"121","author":"Gwalani","year":"2017","journal-title":"Mater. Des."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/j.jallcom.2018.12.300","article-title":"Demystifying the sluggish diffusion effect in high entropy alloys","volume":"783","author":"Zajusz","year":"2019","journal-title":"J. Alloys Compd."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1080\/21663831.2018.1446466","article-title":"Influence of compositional complexity on interdiffusion in ni-containing concentrated solid-solution alloys","volume":"6","author":"Jin","year":"2018","journal-title":"Mater. Res. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1016\/j.jallcom.2016.04.248","article-title":"Structure of some CoCrFeNi and CoCrFeNiPd multicomponent HEA alloys by diffraction techniques","volume":"681","author":"Dahlborg","year":"2016","journal-title":"J. Alloys Compd."},{"key":"ref_27","unstructured":"ASTM Standard E112-12 (2014). Standard Test Methods for Determining Average Grain Size, ASTM International."},{"key":"ref_28","unstructured":"Su, C.H. (2018). A Study on Hall\u2013Petch Relationship and Grain Growth of Ternary to Quinary FCC-Structured Medium\/High Entropy Alloys. [Master\u2019s Thesis, National Taiwan University]."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"747","DOI":"10.1088\/0370-1301\/64\/9\/303","article-title":"The deformation and ageing of mild steel: III discussion of results","volume":"64","author":"Hall","year":"1951","journal-title":"Proc. Phys. Soc. Sect. B"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/j.scriptamat.2012.09.025","article-title":"Grain-boundary strengthening in nanocrystalline chromium and the Hall\u2013Petch coefficient of body-centered cubic metals","volume":"68","author":"Wu","year":"2013","journal-title":"Scr. Mater."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1016\/j.intermet.2013.05.002","article-title":"More than entropy in high-entropy alloys: Forming solid solutions or amorphous phase","volume":"41","author":"Guo","year":"2013","journal-title":"Intermetallics"},{"key":"ref_32","first-page":"311","article-title":"Plasticity of 2-phase materials with a coarse microstructure","volume":"68","author":"Fischmeister","year":"1977","journal-title":"Z. Met."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1016\/0026-0800(80)90001-4","article-title":"Effect of prestrain and stacking-fault energy on the application of the Hall\u2013Petch relation in FCC metals and alloys","volume":"13","author":"Wang","year":"1980","journal-title":"Metallography"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2429","DOI":"10.1007\/BF03038370","article-title":"The influence of alloying, temperature, and related effects on the stacking fault energy","volume":"1","author":"Gallagher","year":"1970","journal-title":"Metall. Trans."},{"key":"ref_35","first-page":"1275","article-title":"The effects of solute additions on the stacking fault energy of a nickel-base superalloy","volume":"245","author":"Kotval","year":"1969","journal-title":"Trans. Metall. Soc. AIME"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1016\/j.intermet.2017.10.004","article-title":"Stacking fault energy of face-centered-cubic high entropy alloys","volume":"93","author":"Liu","year":"2018","journal-title":"Intermetallics"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"505403","DOI":"10.1088\/0953-8984\/24\/50\/505403","article-title":"Effects of alloying element and temperature on the stacking fault energies of dilute Ni-base superalloys","volume":"24","author":"Shang","year":"2012","journal-title":"J. Phys.-Condens. Matter"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"35863","DOI":"10.1038\/srep35863","article-title":"Size effect, critical resolved shear stress, stacking fault energy, and solid solution strengthening in the CrMnFeCoNi high-entropy alloy","volume":"6","author":"Okamoto","year":"2016","journal-title":"Sci. Rep."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"42742","DOI":"10.1038\/srep42742","article-title":"High-velocity deformation of al0.3cocrfeni high-entropy alloy: Remarkable resistance to shear failure","volume":"7","author":"Li","year":"2017","journal-title":"Sci. Rep."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1259","DOI":"10.1179\/1743284715Y.0000000050","article-title":"Lattice strain framework for plastic deformation in complex concentrated alloys including high entropy alloys","volume":"31","author":"Mishra","year":"2015","journal-title":"Mater. Sci. Technol."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1016\/j.actamat.2017.02.036","article-title":"Reasons for the superior mechanical properties of medium-entropy CrCoNi compared to high-entropy CrMnFeCoNi","volume":"128","author":"Laplanche","year":"2017","journal-title":"Acta Mater."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"19","DOI":"10.2320\/matertrans.MA201310","article-title":"Hall-Petch relationship and dislocation model for deformation of ultrafine-grained and nanocrystalline metals","volume":"55","author":"Kato","year":"2014","journal-title":"Mater. Trans."},{"key":"ref_43","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_44","unstructured":"Greenwood, N.N., and Earnshaw, A. (1997). Chemistry of the Elements, Butterworth-Heinemann. [2nd ed.]."},{"key":"ref_45","unstructured":"Kaye, G.W., and Laby, T.H. (1993). Tables of Physical and Chemical Constants, Longman. [15th ed.]."},{"key":"ref_46","unstructured":"James, A.M., and Lord, M.P. (1992). Macmillan\u2019s Chemical and Physical Data, Macmillan."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"8600","DOI":"10.1038\/s41598-018-26830-6","article-title":"High throughput discovery and design of strong multicomponent metallic solid solutions","volume":"8","author":"Coury","year":"2018","journal-title":"Sci. Rep."},{"key":"ref_48","first-page":"73","article-title":"Some factors affecting the rate of grain growth in metals","volume":"180","author":"Burke","year":"1949","journal-title":"Trans. Am. Inst. Min. Metall. Eng."},{"key":"ref_49","first-page":"372","article-title":"Grain growth in high-purity aluminum and in an aluminummagnesium alloy","volume":"175","author":"Beck","year":"1948","journal-title":"Trans. Am. Inst. Min. Metall. Eng."},{"key":"ref_50","first-page":"162","article-title":"Grain growth in 70-30 brass","volume":"175","author":"Beck","year":"1948","journal-title":"Trans. Am. Inst. Min. Metall. Eng."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1016\/0502-8205(52)90009-9","article-title":"Recrystallization and grain growth","volume":"3","author":"Burke","year":"1952","journal-title":"Prog. Met. Phys."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"1387","DOI":"10.1016\/0001-6160(68)90035-7","article-title":"The impurity-drag effect on grain growth","volume":"16","author":"Drolet","year":"1968","journal-title":"Acta Metall. Mater."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"1113","DOI":"10.1557\/JMR.1999.0147","article-title":"Computer simulation of grain growth kinetics with solute drag","volume":"14","author":"Fan","year":"1999","journal-title":"J. Mater. Res."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"4882","DOI":"10.1007\/s11661-014-2459-y","article-title":"On the effect of atoms in solid solution on grain growth kinetics","volume":"45","author":"Hersent","year":"2014","journal-title":"Metall. Mater. Trans. A"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"1374","DOI":"10.1016\/j.actamat.2007.11.042","article-title":"An experimentally quantifiable solute drag factor","volume":"56","author":"Dillon","year":"2008","journal-title":"Acta Mater."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/S0921-5093(00)00731-0","article-title":"Behaviour of normal grain growth kinetics in single phase titanium and titanium alloys","volume":"283","author":"Gil","year":"2000","journal-title":"Mater. Sci. Eng. A"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"1219","DOI":"10.1007\/s11661-009-9803-7","article-title":"Low-temperature sensitization behavior of base, heat-affected zone, and weld pool in AISI 304LN","volume":"40","author":"Singh","year":"2009","journal-title":"Metall. Mater. Trans. A"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/j.jallcom.2012.03.006","article-title":"Grain growth kinetics of bulk AZ31 magnesium alloy by hot pressing","volume":"527","author":"Wang","year":"2012","journal-title":"J. Alloys Compd."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"920","DOI":"10.1016\/j.jallcom.2017.10.108","article-title":"Studies of \u201csluggish diffusion\u201d effect in Co-Cr-Fe-Mn-Ni, Co-Cr-Fe-Ni and Co-Fe-Mn-Ni high entropy alloys; determination of tracer diffusivities by combinatorial approach","volume":"731","author":"Kucza","year":"2018","journal-title":"J. Alloys Compd."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"4887","DOI":"10.1016\/j.actamat.2013.04.058","article-title":"Sluggish diffusion in Co-Cr-Fe-Mn-Ni high-entropy alloys","volume":"61","author":"Tsai","year":"2013","journal-title":"Acta Mater."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1179\/msc.1974.8.1.143","article-title":"Grain-boundary migration and grain growth","volume":"8","author":"Higgins","year":"1974","journal-title":"Met. Sci."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1146\/annurev.pc.14.100163.001225","article-title":"Kinetics of solids","volume":"14","author":"Gill","year":"1963","journal-title":"Annu. Rev. Phys. Chem."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"981","DOI":"10.1016\/S0025-5408(01)00578-5","article-title":"Grain growth and kinetics for nanocrystalline magnesium alloy produced by mechanical alloying","volume":"36","author":"Cao","year":"2001","journal-title":"Mater. Res. Bull."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/3\/297\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:39:02Z","timestamp":1760186342000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/3\/297"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,19]]},"references-count":63,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2019,3]]}},"alternative-id":["e21030297"],"URL":"https:\/\/doi.org\/10.3390\/e21030297","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,3,19]]}}}