Design of Fe-containing GdTbCoAl high-entropy-metallic-glass composite microwires with tunable Curie temperatures and enhanced cooling efficiency

Design o Fe-con aining GdTbCoAl high-en opy-me allic-glass composi e mic owi es wi h unable Cu ie empe a u es and enhanced cooling e iciency Hangboce Yin a,b , Jiayan Law b , Yongjiang Huang a, ⇑ , Vic o ino F anco b , Hongxian Shen a, ⇑ , Sida Jiang c, ⇑ , Ying Bao a , Jian ei Sun a a School o Ma e ials Science and Enginee ing, Ha bin Ins i u e o Technology, Ha bin 150001, China b Dp o. Física de la Ma e ia Condensada, ICMS-CSIC, Uni e sidad de Se illa, Se illa 41080, Spain c Space En i onmen Simula ion Resea ch In as uc u e, Ha bin Ins i u e o Technology, Ha bin 150001, China highligh s Nanoc ys alline Fe-con aining GdTbCoAl high-en opy-me allic- glass we e a ained. Cu ie empe a u e is uned by Fe- doping in a wide empe a u e ange o 81–108 K. Magne ic en opy change 7.6– 8.9 J kg 1 K 1 o 5 T we e achie ed. The dual-phase s uc u e wi h T C dis ibu ion enhances he cooling e iciency. g aphical abs ac a icle in o A icle his o y: Recei ed 26 Janua y 2021 Re ised 6 May 2021 Accep ed 10 May 2021 A ailable online 12 May 2021 Keywo ds: Fe-doping Dual-phase mic os uc u e Cooling e iciency Mic owi es Magne ocalo ic e ec abs ac Th ough designing he composi ion and p ocessing app oach, he non-equia omic (Gd 36 Tb 20 Co 20 Al 24 ) 100- x Fe x (x = 0, 1, 2 and 3 a .%) high-en opy-me allic-glass (HE-MG) alloy mic owi es we e success ully ab- ica ed by mel -ex ac ion echnique. The mic os uc u e and magne ocalo ic p ope ies o he mic o- wi es we e sys ema ically in es iga ed. The mic owi es possess unable Cu ie empe a u es, i.e. 81– 108 K, abo e he ypical a e-ea h (RE) con aining HE-MG epo s. The high Cu ie empe a u es a e a ibu ed o he designed composi ion. Magne ocalo ic esponse peak alues o Fe-con aining GdTbCoAl alloy mic owi es ange 7.6–8.9 J kg 1 K 1 (5 T), which a e compa able o hose o many ou - s anding RE-con aining magne ocalo ic HE-MGs. The cha ac e is ics o he mel -ex ac ion me hod, com- bining wi h composi ional e ec s, a o he o ma ion o amo phous and nanoc ys alline phases. The inc ease in he cooling e iciency o mic owi es wi h highe Fe con en can be a ibu ed o he b oad- ening o he Cu ie empe a u e dis ibu ion induced by he composi ion di e ence be ween nanoc ys- alline phase and amo phous ma ix. The designed composi ion and he mel -ex ac ion p ocessing app oach o Fe-con aining GdTbCoAl alloys can une hei Cu ie empe a u es owa ds a empe a u e ange o na u al gas lique ac ion and imp o e hei magne ocalo ic p ope ies. This demons a es ha Fe-con aining GdTbCoAl HE-MG composi e mic owi es ha e g ea po en ial as high-pe o mance mag- ne ic e ige an s. Ó2021 The Au ho (s). Published by Else ie L d. This is an open access a icle unde he CC BY-NC-ND license (h p://c ea i ecommons.o g/licenses/by-nc-nd/4.0/). h ps://doi.o g/10.1016/j.ma des.2021.109824 0264-1275/Ó2021 The Au ho (s). Published by Else ie L d. This is an open access a icle unde he CC BY-NC-ND license (h p://c ea i ecommons.o g/licenses/by-nc-nd/4.0/). ⇑ Co esponding au ho s. E-mail add esses: [email p o ec ed] (Y. Huang), [email p o ec ed] (H. Shen), [email p o ec ed] (S. Jiang). Ma e ials & Design 206 (2021) 109824 Con en s lis s a ailable a ScienceDi ec Ma e ials & Design jou nal homepage: www.else ie .com/loca e/ma des 1. In oduc ion Magne ic e ige a ion based on he magne ocalo ic e ec (MCE) o solid s a e ma e ials has been widely conside ed as a p omising candida e o he con en ional gas comp ession- expansion e ige a ion, due o i s excellen cooling e iciency and en i onmen al iendliness [1]. Magne ocalo ic ma e ials (MCMs) exploi he adiaba ic empe a u e change when subjec ed o an applied a ying magne ic ield whe e hey can ac as solid e ige an s. The MCE p ope y can be cha ac e ized by he mag- ne ic en opy change ( D S M ). Typically, he MCE pe o mance can be op imized by wo ways, i.e., i) composi ional design and ii) design o p ocessing app oach. Wi h an app op ia e composi ional design, desi ed phase selec ion could op imize MCE pe o mance and aid he T C unabili y. As an example, MCMs wi h amo phous and nanoc ys alline phases ha e been epo ed showing enhanced cooling e iciency wi h app op i- a ely la ge maximum magne ic en opy change ( D S max M )inan ex ended empe a u e ange [2,3]. These cha ac e is ics ha e g ea po en ial o E icsson cycle e ige a ion [4]. Fo he second app oach o op imize MCE pe o mance, i has been epo ed ha MCMs wi h educed dimensions could acili a e he design o mag- ne ic e ige a o s, especially in hea ans e abili y [5–7]. In pa - icula , MCMs p ocessed in o wi e o ms show g ea sui abili y among o he educed dimensions (such as lamina o pa icles) due o i s high su ace- o- olume a io, supe io mechanical s abil- i y, la ge deg ee o packing, g ea empe a u e span be ween ends, and high p essu e d op [7,8]. Using he mel -ex ac ion echnique, high quali y me allic mic owi es (mic o-size diame e s) can be easily ob ained. As he MCM wi e dimensions educe o mic o- sized diame e s, i can u he os e an inc ease in he cooling load, cooling e iciency o he sys em and p essu e d op o he MCMs [7]. This indica es ha i is o g ea signi icance o s udy MCM mic owi es as his o m can g ea ly acili a e he design o magne ocalo ic e ige a o s. In addi ion, amo phous/nanoc ys- alline dual-phase s uc u e could be de eloped in mel -ex ac ed mic owi es wi hou addi ional pos hea ea men . This is acili- a ed by he g ea cooling a e di e ence be ween he egion in con ac wi h he wheel and he ee su ace o he mel du ing he mel -ex ac ion p ocess, which has been p o en by he p e i- ous wo k o ou g oup [9,10]. High-en opy-alloys (HEAs), as a highly ega ded new class o ma e ials, a e designed wi h mul iple p incipal alloying elemen s o yield high con igu a ional en opy, unlike he adi ional ma e- ials whose designs a e based on one o wo main elemen s. Since HEAs we e i s ly epo ed in 2004 [11,12], hey ha e e ol ed om he i s -gene a ion quina y equimola single-phase amilies o he second-gene a ion HEAs, ex ending composi ions o ou o mo e p incipal componen s in non-mola concen a ions and/o wi h mul i-phases [13]. MCE HEAs mainly ocus on a e-ea h (RE) con- aining high-en opy-me allic-glasses (HE-MGs), which possess ex emely low magne ic hys e esis and excellen MCE p ope ies [14–17]. Analogous o HEAs, MCE RE-con aining HE-MGs also epo an e olu ion end o i s ?second gene a ion composi- ions, s a ing wi h equia omic composi ions (e.g. GdTbDyAl(Fe/ Co/Ni) [16], HoE CoAl(Gd/Dy/Tm) [17]) o non-equia omic compo- si ions (e.g. Gd 36 Y 20 Co 20 Al 24 [15]). Howe e , bo h gene a ions end o exhibi low ansi ion empe a u es, mainly anging <60 K whe e hey exhibi  D S max M alues, ypical o he MCE cha ac e is- ics. Hence, MCE RE-con aining HE-MGs a e s ill a an eme ging s age and i is essen ial o op imize hem wi h unable ansi ion empe a u es, like Cu ie empe a u es (T C ), and ex end o highe empe a u e ange o his new class o magne ocalo ic alloys. Xue e al. [14] designed he qua e na y equimola GdHoCoAl and GdTbCoAl HE-MGs and ound ha T C can be g ea ly uned om 50 K o 73 K when subs i u ing o Tb. In addi ion, he equimola GdTbCoAl HE-MG possesses ou s anding MCE pe o mance:  D S max M o 8.88 J kg 1 K 1 and ela i e cooling powe (RCP)o 577 J kg 1 o l 0 D H= 5 T. One possible way o u he op imize MCE RE-con aining HE-MGs o highe empe a u e ange is Fe- doping, which has been epo ed o e ec i ely inc ease T C and imp o e he MCE p ope ies o Gd-based me allic glasses [18– 20]. Fu he mo e, he hea o mixing ( D H mix AB ), which can a ec he ype o phase o ma ion, is ound o be nega i e al hough small o a om pai s be ween Fe and RE/ ansi ion elemen s: 1, 3 and 1 kJ mol 1 o Fe-Gd, Fe-Tb and Fe-Co, espec i ely [21]. La ge nega i e D H mix AB alues be ween he dopan and main elemen s would a o he glass o ming abili y (GFA) [9,22,23]. The e o e, he esul an small alues o D H mix AB indica e ha designing compo- si ions o GdTbCoAl wi h Fe-doping could enable he o ma ion o dual-phase mic os uc u e consis ing o amo phous and nanoc ys- alline phases. Hence, he pu pose o his pape is o design and p epa e RE- con aining HE-MG composi e mic owi es wi h widely unable T C abo e he ypical limi (<60 K), wi h amo phous and nanoc ys- alline phases and enhanced MCE p ope ies. Fo ha , we selec ed he composi ional design which is ul illed as he second- gene a ion MCE RE-con aining HE-MG wi h mino Fe addi ions: (Gd 36 Tb 20 Co 20 Al 24 ) 100-x Fe x whe e x = 0 o 3 a .%. These alloys we e p ocessed in o mic owi es wi h s uc u e e olu ion om single phase (amo phous phase) o wo phases (amo phous and nanoc ys alline phases), which show unable T C om 81 o 100 K wi h ela i ely la ge MCE p ope ies. The success ul MCE op imiza- ion o hese mic owi es demons a e ha app op ia e composi- ional design and p ocessing echnique can pa e a new pa hway o design and ab ica e high-pe o mance MCMs as well as o he HEA communi y. 2. Expe imen al me hods The mas e alloys wi h nominal composi ions o (Gd 36 Tb 20 Co 20 - Al 24 ) 100-x Fe x (x = 0, 1, 2 and 3 a .%) we e i s ly ab ica ed by a c- mel ing a mix u e o cons i uen elemen s (each wi h pu i y highe han 99.9 w %) unde a Ti-ge e ed high-pu i y A a mosphe e. Acco ding o he Fe addi ion con en s, samples s udied in his wo k a e deno ed he ea e as Fe0, Fe1, Fe2 and Fe3. The alloy ingo s we e e-mel ed a leas i e imes o ensu e chemical homogenei y, ollowed by suc ion cas ing in o a coppe mold o o m cylind ical ods wi h 10 mm in diame e and 50 mm in leng h. Subsequen ly, he alloy mic owi es we e p epa ed by using a mel -ex ac ion acili y wi h a molybdenum (Mo) wheel. The line speed o Mo wheel was 30 m s 1 . The mel -ex ac ion p ocess was unde an A a mosphe e. Fo alloys wi h Fe con en highe han 3 a .%, e.g. 4 and 5 a .%, hei mic owi es could no be p epa ed wi hin he limi s o he mel -ex ac ion equipmen . The de ails can be ound in Supplemen a y In o ma ion Documen and Fig. S1. The su ace mo phology o he mic owi es was examined by a scanning elec on mic oscope (SEM, FEI Quan a 200FEG). Fig. 1(a) shows he smoo h su ace o he Fe3 mic owi es. The mac oscopic iew and he c oss-sec ional SEM image o Fe3 mic owi es a e shown in Fig. S2. The c oss-sec ional SEM image shows ha he diame e o Fe3 mic owi e is ~30 l m. The he mal s abili y o he samples was s udied by di e en ial scanning calo ime e (DSC, Ne zsch STA449F3 Jupi e ) a a hea ing a e o 10 K min 1 . The mic os uc u e and composi ional in o ma ion we e examined by ansmission elec on mic oscope (TEM, FEI Talos F200X) equipped wi h ene gy-dispe si e X- ay spec oscopy (EDS). Tem- pe a u e dependence o magne iza ion (MT) and magne ic ield dependence o magne iza ion (MH) we e measu ed by using a Physical P ope y Measu emen Sys em (PPMS, Quan um Design Dynacool-14 T). Fo a la ge signal o noise a io, a bundle o mic o- H. Yin, J. Law, Y. Huang e al. Ma e ials & Design 206 (2021) 109824 2 wi es we e used o he magne ic measu emen s. The mic owi es we e a anged pa allel o each o he in a non-magne ic polyme ic ubula sample holde wi h 1 mm in inne diame e , 2.5 mm in ou e diame e , and 3 mm in leng h. 3. Resul s and discussion DSC cu es o Fe0, Fe1, Fe2, and Fe3 mic owi es a e p esen ed in Fig. 1(b) and (c). These cu es show he he mophysical pa ame- e s including he glass ansi ion empe a u es (T g ), he onse em- pe a u e o he i s c ys alliza ion peak (T x ), and he liquidus empe a u es (T l ). I is obse ed ha wi h inc easing Fe con en , T g and T l inc ease whe eas T x dec eases. Thei de ailed in o ma ion is summa ized in Table 1, oge he wi h he supe -cooled liquid egion ( D T x =T x T g ) and c =T x /(T g +T l ). D T x and c indica e he he mal s abili y, i.e. esis ance o c ys alliza ion [24,25], and he GFA [26] o he supe cooled liquid, espec i ely. As seen in Table 1, he alues o D T x and c mono onically dec ease wi h inc easing Fe con en , acili a ing he p ecipi a ion o c ys alli es on mic owi es. I should be no ed ha he la ges dec ease o D T x and c akes place be ween Fe1 and Fe2, sugges ing he possibili y o mic os uc u al change be ween hese samples. The GFA is a ec ed by hese pa ame e s: a omic size di e ence (d), he mixing en halpy ( D H mix ) and he mixing en opy ( D S mix ). These a e also widely used o p edic he phase o ma ion in HEAs, including HE-MGs [23,27– 29]. Hence, hese pa ame e s o Fe0, Fe1, Fe2 and Fe3 mic owi es a e calcula ed and lis ed in Table 1. Fo all he s udied mic owi es, hese pa ame e s a e in ag eemen o he c i e ia epo ed o HE- MG (d9, 49  D H mix 5.5 kJ mol 1 and 7  D S mix 16 J K 1 mol 1 )[23]. The au ho s [23] u he epo ha he o ma ion o amo phous phase is a o ed by la ge d, smalle D S mix and mo e nega i e D H mix alues in compa ison wi h solid solu ion phases. In ou case, d alues e ol e e y sligh ly wi h inc easing Fe con en , while he changes o D S mix and D H mix a e ela i ely la ge. The el- a i ely small e ec o Fe-doping on dis o li le help o he a omic packing densi y, which does no aid he enhancemen o GFA. The e olu ions o D S mix and D H mix a e in ag eemen o ha o c . The e- o e, he de e io a ion o he GFA should be asc ibed o he ela- i ely la ge change o D H mix and D S mix induced by Fe-doping. TEM obse a ions we e pe o med in o de o in es iga e he mic os uc u es o Fe-con aining GdTbCoAl mic owi es a he nano-scale. The homogeneous maze-like pa e ns o he high- esolu ion TEM (HRTEM) images in Fig. 2(a) and (b) indica e he ully amo phous s uc u e o Fe0 and Fe1 mic owi es, espec i ely [30]. Thei ully amo phous s uc u es a e also con i med by he a he ain and di used halo ings o he selec ed a ea elec on di ac ion (SAED) pa e ns wi hou any dis inguishable di ac ion spo (see inse s o Fig. 2(a) and (b)). Fig. 2(c) shows he HRTEM, he co esponding as Fou ie ans o m (FFT)-in e se as Fou ie ans o m (IFFT) and SAED images o Fe2 mic owi e. The FFT-IFFT image wi h c ys alline inges, co esponding o he ed dashed squa e ma ked by he numbe 1, indica es he exis ence o nanoc ys alline phase wi h a g ain size o ~3nm[31]. The amo - phous ma ix is con i med by he bo om- igh FFT-IFFT image which shows he comple ely andom a omic a angemen and co - esponds o he ed dashed squa e ma ked by he numbe 2. As shown in he op- igh inse o Fig. 2(c), a ligh c ys alline- ing SAED pa e n can be obse ed besides he s ong halo ing co e- sponding o he amo phous ma ix, con i ming he dual-phase mic os uc u e. The b igh - ield TEM image o he su ace a ea o Fe3 mic owi e is shown in Fig. 2(d). A dual-phase s uc u e can be ob iously obse ed in his image. The p esence o he nanoc ys- als in he amo phous ma ix can be con i med by he co espond- ing SAED esul s wi h he ligh c ys alline di ac ion spo s and s ong halo ing (Fig. 2(e)). The c ys alline di ac ion spo s indica e he nanoc ys alline phase is ace-cen e ed cubic (FCC) s uc u e. The asymme ic spo s can be also obse ed in he SAED esul s. To u he con i m he s uc u e o he nanoc ys alline phase, HRTEM along h ee di e en zone axes we e ob ained, as shown in he op images o Fig. 2( )–(h). The HRTEM images indica e he nanoc ys alline phase wi h an a e age g ain size o ~27 nm. The FFT images co esponding o he ed dashed squa es in he HRTEM images con i m FCC s uc u e o he nanoc ys alline phase [32],as shown in he bo om images o Fig. 2( )–(h). O e all, he single amo phous s uc u es o he Fe0 and Fe1 mic owi es e ol e in o a dual-phase mic os uc u e wi h inc easing Fe-doping, whe e nanoc ys als a e obse ed ( hough a he ew) o Fe2 and Fe3. This is in line wi h he e olu ion o D T x and c . Fo he mic owi es wi hou Fe-doping, he composi ion is e y close o he ideal glass- o ming composi ion acco ding o Lu’s empi ical concep [33]. This composi ion no mally means he bes glass- o ming composi ion o an alloy. Wi h he inc ease o Fe Fig. 1. (a) SEM image o he Fe3 mic owi e, (b) and (c) DSC esul s o he Fe0, Fe1, Fe2 and Fe3 mic owi es. Table 1 The he mophysical pa ame e s o Fe0, Fe1, Fe2 and Fe3 mic owi es. Sample T g (K) T x (K) T l (K) D T x (K) c d D H mix (kJ mol 1 ) D S mix (J K 1 mol 1 ) Fe0 586 638 1064 52 0.386 14.31 34.63 11.25 Fe1 588 637 1065 49 0.385 14.44 34.08 11.61 Fe2 590 624 1155 34 0.357 14.56 33.53 11.84 Fe3 592 622 1162 30 0.354 14.68 32.99 12.02 H. Yin, J. Law, Y. Huang e al. Ma e ials & Design 206 (2021) 109824 3 con en , he he mal s abili y and GFA o Fe-con aining GdTbCoAl mic owi es de e io a e. Du ing he mel -ex ac ion p ocess, he mel su ace can be di ided in o wo egions, i.e., he egion in con- ac wi h he wheel and he ee su ace. The cooling a e o he egion in con ac wi h he wheel eaches a high alue o o e 10 6 Ks 1 , a o ing he o ma ion o amo phous phase. Con a ily, o he ee su ace, he cooling a e is much lowe , acili a ing he o - ma ion o nanoc ys als i he GFA o he alloy is no high enough [9,10]. Due o he de e io a ed GFA and ela i ely low cooling a e a he ee su ace, nanoc ys als could be c ea ed in he case o Fe- con aining GdTbCoAl mic owi es. Two pa ame e s can a o he g ow h o nanoc ys al in he liquid, i.e. he ema kable long- dis ance a omic di usion [34] and he high mobili y o a oms [27,35]. In supe cooled liquids o Fe-con aining GdTbCoAl mic o- wi es, he a omic di usion is kine ically e a ded by he high deg ee o dense andom packing, which is a ibu ed o he ela- i ely la ge absolu e alues o dand D H mix [34,36,37]. The inc eased mel iscosi y o GdTbCoAlFe liquids, which is induced by Fe-doping [37], kine ically es ic s he mobili y o he a oms [35,38]. Acco dingly, he nanoc ys alline phase which exis s in he liquid is e ained in Fe-con aining GdTbCoAl mic owi es. Fig. 3 shows he empe a u e dependence o he ield cooling magne iza ion (M FC ) o Fe0, Fe1, Fe2 and Fe3 mic owi es, mea- su ed unde a ield o 200 Oe. An ex apola ion me hod o he lin- ea pa o he MTcu e is used o con i m he T C, which is he Fig. 2. HRTEM images and co esponding SAED esul s (inse s) o (a) Fe0, (b) Fe1 and (c) Fe2 mic owi es, espec i ely. Co esponding FFT-IFFT esul s o he ed dashed squa es ma ked by numbe s 1 and 2 a e also shown in he inse s o (c). (d) and (e) show he b igh - ield TEM image and he co esponding SAED esul s o Fe3 mic owi e, espec i ely. ( ), (g) and (h) show HRTEM images ( op) and FFT esul s (bo om) co esponding o he ed dashed squa es in HRTEM images o Fe3 mic owi e along h ee di e en zone axes. Fig. 3. Tempe a u e dependence o M FC cu es o Fe0, Fe1, Fe2 and Fe3 mic owi es unde an applied magne ic ield o 200 Oe. Fig. 4. Magne ic en opy changes o Fe0, Fe1, Fe2 and Fe3 mic owi es unde l 0 D H o 2 T (solid symbols) and 5 T (open symbols). H. Yin, J. Law, Y. Huang e al. Ma e ials & Design 206 (2021) 109824 4 in e cep o he ex apola ed line and he empe a u e axis. The T C o he Fe-con aining GdTbCoAl mic owi es inc eases wi h inc eas- ing Fe con en : 81, 94, 100 and 108 K o Fe0, Fe1, Fe2 and Fe3 mic owi es, espec i ely. The a e age inc ease o T C is 9 K pe Fe a .%. The inc eased T C is due o he s ong exchange in e ac ions o RE-Fe and Fe-Fe pai s [39,40]. The - D S M as a unc ion o he empe a u e o Fe-con aining GdTbCoAl mic owi es unde l 0 D H= 2 and 5 T a e plo ed in Fig. 4. Fo bo h ield changes,  D S max M mono onically dec eases whe eas hei co esponding peak empe a u es inc ease wi h inc easing Fe con en . Fo  D S max M , i dec eases om 8.9 o 7.6 J kg 1 K 1 unde l 0 D H= 5 T o Fe0 o Fe3 as shown in Fig. 5 (a). The a e age educ ion o  D S max M is 0.43 J kg 1 K 1 pe Fe a . %. This small educ ion in  D S max M wi h inc easing Fe con en is a ibu ed o he eplacemen o he RE-elemen s wi h high mag- ne ic momen s by Fe. TEC(10) is he empe a u e a e aged - D S M ecen ly p oposed by G i i h e al. [41], which e e s o he maximum a e age o - D S M o e a 10 K empe a u e span. I is ega ded as an al e na i e igu e me i o e alua ing MCE ma e ials. I can a oid a i icially la ge alues o e ige an capaci y o MCMs in he cases o exhibi ing shallow and wide peaks. TEC(10) can be calcula ed as ollows [41]: TECð10Þ¼ 1 10max Z T mid þ5 T mid 5 S M ðTÞdT () ð2Þ whe e T mid is chosen by sweeping o e he  D S M (T) cu e o ob ain maximum alue o TEC(10) a he empe a u e span o 10 K. In he Fig. 5. The Fe con en dependence o (a)  D S max M and FWHM, (b) TEC(10), TEC (app ox.) ,RC and RCP o l 0 D H=5T. Fig. 6. A o plo s o (a) Fe0, (b) Fe1, (c) Fe2 and (d) Fe3 mic owi es. H. Yin, J. Law, Y. Huang e al. Ma e ials & Design 206 (2021) 109824 5 case ha he a ailable da a o he  D S M (T) cu es a e limi ed (e.g. li e a u e da a), his exp ession can be app oxima ed as ollows [42]: TEC ðapp ox:Þ  D S M ðT peak 5Þþ D S M ðT peak Þþ D S M ðT peak þ5Þ  3ð3Þ The TEC(10) and app oxima e alue o TEC(10), TEC (app ox.) , dec ease wi h inc easing Fe con en , as shown in Fig. 5(b). The sim- ila i y o bo h alues shows he alidi y o he app oxima ion. They a e in he ange o  D S max M alues, con i ming he ela i ely b oad peaks o  D S M (T) cu es o Fe-con aining GdTbCoAl mic owi es. Fo alloys wi h ela i ely high  D S max M , e ige a ion capaci y (RC) and RCP a e usually employed o e alua e cooling e iciency, and a e calcula ed by using he ollowing o mulas [43–45]: RCP ¼ D S max M dT FWHM ¼ D S max M ðT 2 T 1 Þð4Þ RC ¼Z T 2 T 1 D S M ðTÞdTð5Þ whe e T 1 and T 2 ep esen he endpoin s o ull-wid h a hal - maximum (FWHM, i.e. wo king empe a u e ange) o  D S M (T) cu es. Fig. 5(a) shows FWHM o  D S M (T) cu es. The esul s show ha FWHM inc eases wi h inc easing Fe con en . Al hough a single ma e ial in a e ige a o de ice will no ope a e in such b oad em- pe a u e span, he la ge  D S M exis ing in such b oad empe a u e ange will acili a e he ope a ion o he ma e ials in he empe a- u e anges wi hin he FWHM. The esul s o RCP and RC o Fe- con aining GdTbCoAl mic owi es a e shown in Fig. 5(b) o l 0 D H=5T.RCP and RC inc ease wi h he inc ease o Fe con en due o he enla ged FWHM o  D S M (T) cu es. The alues o RCP and RC inc ease o 684 J kg 1 and 520 J kg 1 , espec i ely, o Fe3 mic owi es unde l 0 D H=5 T. The inc ease o FWHM could be asc ibed o he appea ance o nanoc ys als. To de e mine he o de o magne ic phase ansi ion o he s udied mic owi es, wo me hods we e used: 1) A o plo s (M 2 s. H/M) and 2) he quan i a i e c i e ion based on he magne ic ield dependence o MCE [46].Fig. 6 shows he A o plo s o all s udied mic owi es. All he cu es show posi i e angen slopes o he whole measu emen empe a u e ange, indica ing second-o de o phase ansi ion (SOPT) o all he s udied mic o- wi es acco ding o Bane jee’s c i e ion [47]. Fo he nex me hod, he exponen o he magne ic ield dependence o MCE, ep e- sen ed as n, is calcula ed and analyzed. The ela ionship be ween  D S M and l 0 D H ollows a powe law [48]:  D S M / l 0 D H n ð6Þ whe e nis a local exponen ha depends on bo h magne ic ield and empe a u e. The local calcula ion o ob aining nis: n¼dln D S M jj dln l 0 D Hð7Þ The empe a u e dependence o he calcula ed nis shown in Fig. 7(a), which shows he ypical beha io o SOPT ma e ials in he absence o o e shoo o nla ge han 2. This ag ees well wi h he obse a ions o Fig. 6. Usually, mul iple phases would appea as sepa a ed peaks in he  D S M (T) cu es unless he phase ansi- ion empe a u es a e a he close o he ac ions o he addi ional phase a e oo low. In such cases, he n(T) da a can be used o ana- lyzing he exis ence o addi ional phase ansi ions [48] whe e he exis ence o mul iple phases would show addi ional minima in n (T). This is no he case in Fig. 7(a) whe e no addi ional minimum is obse ed despi e Fe2 and Fe3 a e ound wi h dual-phase mic os uc u e. Fig. 7(b) p esen s he wid hs o n(T) cu es as a unc ion o Fe con en . The wid hs a e ob ained a n= 0.85, as shown in he inse o Fig. 7(b). The signi ican inc ease o he wid h is obse ed o he Fe3, in ag eemen o he wides FWHM and la - ges nanoc ys al ac ion o Fe3 mic owi es. The absence o addi- ional ea u es bo h in n(T) and  D S M (T) cu es could be ela ed o p oximi y o he T C o wo phases o he low ac ion o nanoc ys alline phase. The composi ional di e ences be ween nanoc ys alline phase and amo phous ma ix (see Fig. S3 and Fig. 7. (a) The empe a u e dependence o he exponen n. (b) Fe con en dependence o he wid h o n, wi h inse showing how he wid h o nwas ob ained. Bo h g aphs a e unde l 0 D H=5T. Fig. 8. MCE pe o mance o RE-con aining HE-MGs o l 0 D H=5 T. Da a o he li e a u e a e collec ed om Re s. [14,15,49–51]. H. Yin, J. Law, Y. Huang e al. Ma e ials & Design 206 (2021) 109824 6 Table S1) lead o a b oad T C dis ibu ion, b oadening he FWHM. The wide FWHM coun e ac s he small  D S max M educ ion and he e o e inc eases he cooling e iciency. Fig. 8 shows he ansi ion empe a u e dependence o  D S max M o ou s udied mic owi es in compa ison wi h hose o non- equia omic RE-con aining HE-MGs and equia omic GdTbCoAl HE- MG. I is obse ed ha ou HE-MG alloy mic owi es exhibi a wide ange o ansi ion empe a u es beyond he ypical limi , <60 K. Fu he mo e,  D S max M is main ained in a ela i ely la ge alue ange as compa ed wi h hose o o he epo ed non-equia omic RE- con aining HE-MGs and equia omic GdTbCoAl HE-MG. This demons a es ha Fe-con aining GdTbCoAl HE-MG composi e mic owi es ha e g ea applica ion p ospec s as high-pe o mance magne ic e ige an s. 4. Conclusion Wi h mino Fe addi ions, (Gd 36 Tb 24 Co 20 Al 20 ) 100-x Fe x (x = 0, 1, 2 and 3 a .%) high-en opy-alloy mic owi es enabled unable Cu ie empe a u es up o 108 K, which is beyond he ypical limi o RE-con aining magne ocalo ic HEAs (<60 K). The T C inc eases a an a e age a e o 9 K pe Fe a .%, asc ibed o he s ong exchange in e ac ions o RE-Fe and Fe-Fe pai s. Fu he mo e, he Fe addi ions acili a e he o ma ion o amo phous/nanoc ys alline dual-phase s uc u e ha leads o inc eased cooling e iciency, keeping ela- i ely la ge  D S max M alues (7.6–8.9 J kg 1 K 1 o 5 T) in an ex ended wo king empe a u e span. Compa ed o epo ed p omising magne ocalo ic HEAs, hese mic owi es exhibi compa- able MCE p ope ies ye a much highe wo king empe a u es. The la ge MCE pe o mance enhanced by he app op ia e composi- ional design and p ocessing echnique opens ano he di ec ion o op imizing HEAs as high-pe o mance MCMs. Decla a ion o Compe ing In e es The au ho s decla e ha hey ha e no known compe ing inan- cial in e es s o pe sonal ela ionships ha could ha e appea ed o in luence he wo k epo ed in his pape . Acknowledgmen s The au ho s would like o acknowledge he inancial suppo om he Na ional Na u al Science Founda ion o China unde G an Nos. 51871076, 51671070, 51801044, and 51827801, and he 66 h China Pos doc o al Science Founda ion unde G an No. 2019M661275. 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