On the constitution and thermodynamic modeling of the phase diagrams Nb-Mn and Ta-Mn

Con en s lis s a ailable a ScienceDi ec Jou nal o Alloys and Compounds jou nal homepage: www.else ie .com/loca e/jalcom On he cons i u ion and he modynamic modeling o he phase diag ams Nb-Mn and Ta-Mn ☆ Xinlin Yan a,1 , Pa el B ož b , Jan Vřešťál b , Jiří Vlach b , Jiří Bu šík c , Ma ina Mazalo á b , Jana Pa lů b , Bedřich Sme ana d , Ge da Rogl a , Ma kus Eibe ge a , And iy G y si a , He wig Micho e , He be Mülle e , Ge ald Gies e , Pe e Rogl a,⁎ a Ins i u e o Ma e ials Chemis y, Uni e si y o Vienna, Waeh inge s asse 42, A-1090 Wien, Aus ia b Depa men o Chemis y, Facul y o Science, Masa yk Uni e si y, Ko lářská 2, 611 37 B no, Czech Republic c Ins i u e o Physics o Ma e ials, Czech Academy o Sciences, Žižko a 22, 6160 00 B no, Czech Republic d Facul y o Ma e ials Science and Technology, VSB-TU Os a a, 17. lis opadu 15, 708 33 Os a a, Czech Republic e Ins i u e o Solid S a e Physics, TU-Wien, Wiedne Haup s asse 8-10, A-1040 Wien, Aus ia Ins i u e o Mine alogy and C ys allog aphy, Uni e si y o Vienna, Al hans asse 14, A-1090 Wien, Aus ia a icle in o A icle his o y: Recei ed 3 No embe 2020 Recei ed in e ised o m 5 Janua y 2021 Accep ed 9 Janua y 2021 A ailable online 22 Janua y 2021 Keywo ds: In e me allics C ys al s uc u e Phase diag ams The modynamic modeling Magne ic measu emen s The mal analysis abs ac The cons i u ion o he wo phase diag ams Nb-Mn and Ta-Mn has been de e mined om ligh op ical and ansmission and scanning elec on mic oscopy (LOM, TEM and SEM) wi h ene gy dispe si e (EDX) as well as wa eleng h dispe si e (WDX) X- ay spec oscopy, X- ay powde (XPD) and single c ys al di ac ion (XSCD), di e en ial he mal analysis (DTA) and/o di e en ial scanning calo ime y (DSC). The La es phases NbMn 2 and TaMn 2 a e he only bina y compounds in hese sys ems. High- empe a u e di e en ial he mal analyses e ealed cong uen mel ing o NbMn 2 wi h T m (NbMn 2 ) = 1515 ± 15 °C, whe eas TaMn 2 mel s in- cong uen ly wi h T m (TaMn 2 ) = 1797 ± 40 °C close o a deple ed pe i ec ic eac ion. Bo h La es phases engage in eu ec ic eac ions ℓ ↔ (Mn) + Nb(Ta)Mn 2 (T eu = 1220 ± 10 °C a 4.9 a % Nb and T eu = 1234 ± 10 °C a 0.7 a % Ta, espec i ely). NbMn 2 also o ms a eu ec ic wi h (Nb): ℓ ↔ (Nb) + NbMn 2 a T eu = 1493 ± 15 °C and 53.2 a % Nb. Mn shows ema kably la ge maximum solid solubili ies o 19.4 a % Mn in (Nb) as well as o 21.3 a % Mn in (Ta). De ailed a om si e dis ibu ion has been es ablished o he La es phases by means o empe a u e dependen X- ay single c ys al da a (bo h C14 - MgZn 2 - ype). Combined da a om XPD, EDX/WDX and SEM mic os uc u e indica e ha o bo h La es phases ex ended homo- genei y egions exis : Nb 1+x Mn 2−x (62.5–73.0 a % Mn a 950°C: −0.19≤x≤0.125) and Ta 1+x Mn 2−x (59.5–68.5 a % Mn: −0.055≤x≤0.215). Densi y unc ional heo y (DFT) calcula ions a o Nb(Ta)/Mn an isi e occupa ion a he han de ec s. The phases, “NbMn” and “TaMn”, adop ed ea lie in he li e a u e as bina y sys em inhe en compounds, we e shown (TEM, WDX elec on mic op obe da a and X- ay Rie eld e inemen s) o be oxygen s abilized phases o he Ti 4 Ni 2 O ype (so-called e a(η)-phases) wi h modi ied Nb(Ta)/Mn si e subs i u ion o comply wi h he o mula Nb(Ta) 3−x Mn 3+x O 1−y (de ec η-W 3 Fe 3 C- ype). F om magne ic sus- cep ibili y and magne iza ion measu emen s, bo h oxide s abilized e a phases η-Nb 3 Mn 3 O 1−y and η-Ta 3 Mn 3 O 1−y we e ound o o de e omagne ically below T c ~ 77 K, bu he La es phases NbMn 2 , TaMn 2 e eal weakly empe a u e dependen pa amagne ism. No ace o he hombohed al μ-phase (W 6 Fe 7 - ype) has been encoun e ed in ou in es iga ion o he wo bina y phase diag ams. The modynamic and anspo p ope ies (speci ic hea , elec ical esis i i y and magne ic suscep ibili y/magne iza ion) classi y he La es phases wi h me allic beha io whils mechanical p ope ies (elas ic moduli om DFT and nanoinden a ion as well as ha dness and he mal expansion) g oup bo h La es phases among a he ha d and b i le in- e me allics. Based on (i) he expe imen ally de i ed cons i u ion o he Nb-Mn and Ta-Mn sys ems, and h ps://doi.o g/10.1016/j.jallcom.2021.158715 0925-8388/© 2021 The Au ho s. Published by Else ie B.V. CC_BY_4.0 ☆ The pape is dedica ed o P o . D . Wol gang Jei schko, in memo iam. ]]]] ]]]]]] ⁎ Co esponding au ho . E-mail add ess: pe e [email p o ec ed] (P. Rogl). 1 Cu en add ess: Ins i u e o Solid S a e Physics, TU-Wien, Wiedne Haup s asse 8-10, A-1040 Wien, Aus ia. Jou nal o Alloys and Compounds 865 (2021) 158715 (ii) on new own DFT da a o he ene gy o o ma ion o he La es phases, a CALPHAD (CALcula ion o PHAse Diag ams) calcula ion o bo h sys ems was made p o iding a comple e se o op imized he modynamic da a. Fu he mo e, he DFT calcula ions p o ided in o ma ion on he ins abili y o he η-Ta 3 Mn 3 s uc u e and he a om-si e speci ic s abiliza ion e ec o oxygen. © 2021 The Au ho s. Published by Else ie B.V. CC_BY_4.0 1. In oduc ion In di e se echnological applica ions Nb, Ta and Mn a e playing an impo an ole such as o ins ance: (i) addi ions o Mn a e able o inc ease he yield s eng h o Ti-Nb-Ta-Mn alloy oams o biome- dical implan s [1,2], (ii) niobium-manganese composi e elec odes we e ound o be mo e sui able in supe capaci o s han niobium elec odes [3]; (iii) Mn, Nb and bo on addi ions maximize s eng h and oughness in ma ensi ic mic o-alloyed s eels o hea y-du y engine connec ing ods [4]; acili a e he p oduc ion o seamless s eel ubes [5]; Ta inc eases he pi ing co osion in supe duplex s ainless s eels o ming (Ta,Mn) - oxysul ide [6], and (i ) Ha ano [7] s udied he coun e ac ing e ec s o Nb and Mn on mic os uc u e and oughness o 590 MPa class low ca bon baini ic s eels. Nb(Ta)- o Mn-doping has been employed o imp o e he he moelec ic beha io o pe o ski e mangani es [8,9], o NbFe 2−x Mn x Al Heusle alloys [10] and o highe manganese silicides (Nowo ny chimney ladde s uc u es) [11]. Al hough he knowledge o phase diag ams and he modynamic p ope ies is essen ial in de ining p ocessing condi ions o op imal enginee ing p ope ies, eliable phase diag am in o ma ion on he basic bina y sys ems Nb-Mn and Ta-Mn is s ill sca ce. Fo a de ailed summa y o he expe imen al indings, see he compila ion o bina y phase diag ams in Massalski [12]. The limi ed expe imen al da a a ailable wi hin he pa ial phase diag am Nb-Mn conce n he e- gion a ound he La es phase (50–80 a % Mn [13]) and he Mn- ich liquidus/solidus, which has been de i ed om he mal analysis in he egion om 88 o 100 a % Mn [14]. In e es ingly he in es iga ion o he sys em Nb-Mn-B a 800 °C e ealed a bina y NbMn phase a 45–50 a % Mn (s uc u e unde e mined, W 6 Fe 7 - ype assumed [15]). Such a phase was la e bu unknowingly accoun ed o as a μ-phase (Nb 6 Mn 7 ) in he he modynamic modeling o he Nb-Mn bina y as pa o he Nb-Fe-Mn sys em [16]. F om he phase diag am o he Ta-Mn sys em hi he o only he egion om 67 o 100 a % Mn has been expe imen ally de i ed [17] wi h some addi ional da a on he ha dness o he TaMn 2 -La es phase [13]. Being unawa e o an expe imen al diag am, Kau man [18] p oduced a i s he modynamic calcula ion o he en i e phase diag am Ta-Mn using s uc u e-insensi i e hea o o ma ion da a de i ed om Miedema’s model [19] and ea ly ab ini io da a by Co- line [20]: besides TaMn 2 , also a compound TaMn was shown o exis . Howe e , he Gibbs ene gies o phases we e no based on s anda d SGTE una y da a [21]. Al hough expe imen al da a a e only a ailable o he Mn- ich pa and he ype and empe a u e o mel ing o TaMn 2 emained unclea [17], he modynamic modeling o he en i e phase diag am was pe o med by C. Wang e al. [22] esul ing in a Mn- ich and a Ta- ich eu ec ic besides cong uen ly mel ing TaMn 2 (T m = 1670 °C). A phase “TaMn” was no conside ed. The La es phases in bo h sys ems ecei ed mo e a en ion: om high- empe a u e di ec syn hesis calo ime y measu emen s Meschel e al. [23] claimed a s anda d en halpy o o ma ion o NbMn 2 o −31.2 ± 8.1 kJ/mol. .u. and −43.5 ± 7.5 kJ/mol. .u. o TaMn 2 . This expe imen al alue o NbMn 2 , howe e , appea s signi ican ly lowe han he Δ 298 H ° = −45.05 ± 3.64 kJ/mol. .u. ex ac ed om d op isope ibolic calo ime y in a Ni ba h [24], which p o ed o be consis en wi h a densi y unc ional heo y (DFT) calcula ion by Yan e al. [24], who a i ed a −46.5 kJ/mol. .u. These alues compa e well wi h olde ab ini io da a by Coline e al. (−42 kJ/mol. .u. o NbMn 2 and −24 kJ/mol. .u. o TaMn 2 [20]), which we e e alua ed wi hin a igh -binding scheme o he d band – an app oxima e model calcula ion o es ima e he en halpies o o ma ion no dealing wi h s uc u e and magne ic e ec s. Mo e ecen ab ini io calcula ions o Yan e al. on NbMn 2 also p o ided an eDOS ( om which a gamma alue o γ = 10.5 mJ/mol.K 2 is de i ed), as well as a ull se o elas ic moduli [24] ( o de ails see Sec ion 4.4. Ha dness and mechanical p ope ies). Wi h espec o (a) he absence o eliable phase diag am da a in bo h sys ems Nb-Mn and Ta-Mn as well as (b) conce ning he in- consis encies on he exis ence o he phases "Nb 7 Mn 6 " and "TaMn", and (c) inconsis encies in he hea o o ma ion and he lack o physical p ope y da a o he La es phases, he aim o he p esen pape is mani old: (i) o check on he c ys al s uc u e, he o ma ion and s abili y o he sys em inhe en phases pa icula ly on he "NbMn" (Nb 7 Mn 6 ) and "TaMn" phases, (ii) o es ablish eliable phase ela ions o he en i e phase diag ams Nb-Mn and Ta-Mn, (iii) o p o ide physical p ope y da a o a de ailed cha ac e iza ion o he La es phases, (i ) o calcula e ia ab ini io me hods he ene gy o o ma ion o he La es phases, and ( ) o check on he DFT s abili y o he "Nb(Ta)Mn" phases (pa icula ly on η-Ta 3 Mn 3 O 1−x ), as well as ( i) o p o ide a eliable se o he modynamic da a ia CALPHAD modeling o bo h sys ems. 2. Expe imen al de ails 2.1. Syn hesis and cha ac e iza ion o physical p ope ies The s a ing ma e ials we e o a minimal pu i y o 99.9 mass%: Ta and Nb in he o m o ingo , oil o wi e om Good ellow, UK, and elec oly ically deposi ed Mn pla ele s (>99.95%, Al a Aesa , D), which we e su ace cleaned in concen a ed HNO 3 immedia ely p io o use. Sample specimens (1–2 g each) we e p epa ed om elemen al pieces by ei he a gon a c mel ing on a wa e -cooled coppe hea h o on a wa e -cooled Hukin c ucible o a high e- quency (HF) u nace in Ti-ge e ed a gon. To ensu e homogeniza ion, all alloys we e e-mel ed se e al imes. A sligh excess o Mn was used o allow o e apo a ion du ing usion in o de o keep he o al mass loss o he sample a e mel ing below 0.5 mass%. Each alloy was weighed ca e ully a e mel ing and, i necessa y, Mn was added un il he nominal composi ion was achie ed a e inal mel ing. Due o he high di e ences in he mel ing poin s o Nb(Ta) and Mn in combina ion wi h he high apo p essu e o Mn, some o he spe- cimens a e mel ing and annealing s ill u ned ou o be in- homogeneous. The e o e, alloy specimens wi h mo e han 90% Mn and a o al weigh o 2 g we e p epa ed om well blended powde mix u es, which we e compac ed in s eel dies (Φ = 10 mm, wi hou lub ican ) a a p essu e o 50 kg/cm 2 (~5 MPa). Nb(Ta) powde s o 99.9 mass% we e pu chased om Sigma-Ald ich, D; Mn powde was ob ained om clean Mn-pieces eshly c ushed in a WC mo a (see abo e). A pa o each sample (wi hin an Al 2 O 3 c ucible) was sealed in a silica capsule unde 280 mba A and hea - ea ed a 950 °C o abou 120 h and quenched. A maximum annealing empe a u e he A -p essu e inside he silica capsule eached abou 1 ba and X. Yan, P. B ož, J. Vřešťál e al. Jou nal o Alloys and Compounds 865 (2021) 158715 2 e icien ly supp essed Mn-e apo a ion. Fo annealing a 750 °C, 700 °C and 650 °C he ampullae we e kep a empe a u e o 1 mon h. X- ay powde di ac ion (XPD) da a om as-cas and annealed alloys we e collec ed employing a Guinie -Hube image pla e sys em wi h monoch oma ed Fe K α1 o Cu K α1 adia ion (8°≤2θ≤100°). P ecise la ice pa ame e s we e calcula ed by leas -squa es i s o he indexed θ- alues wi h Ge as in e nal s anda d (a Ge = 0.5657906 nm). Rie eld e inemen s we e made wi h he FULLPROF p og am [25]. Single c ys als (SC) we e mechanically isola ed om a c ushed alloy. Inspec ion on an AXS D8-GADDS ex u e goniome e assu ed high c ys al quali y, uni cell dimensions and Laue symme y o he single c ys al specimens p io o X- ay in ensi y da a collec ion on a ou -ci cle APEX II di ac ome e equipped wi h a CCD a ea de ec o and an Incoa ec Mic o ocus Sou ce IμS (30 W, mul ilaye mi o , Mo-K α ; λ = 0.071069 nm; de- ec o dis ance o 3 cm; ull sphe e; 2°≤2θ ≤72°). Whe eas he SC o TaMn 2 was s udied a oom empe a u e (RT), o NbMn 2 we col- lec ed X- ay da a a ou empe a u es: 100 K, 150 K, 200 K and 300 K, cooled by a con inuous s eam o ni ogen gas enclosing he c ys al a p ese empe a u e. Besides he gene al ea men o ab- so p ion e ec s using he mul i-scan echnique (SADABS; e- dundancy o in eg a ed e lec ions >8) [26], no indi idual abso p ion co ec ion was necessa y because o he a he egula c ys al shape and small dimensions o he in es iga ed specimens (40 × 45 × 60 µm³). The c ys al s uc u e was sol ed applying di ec me hods (P og am SHELXS-97) and e ined agains F 2 (P og am SHELXL-97-2) wi hin he p og ams OSCAIL o WINGX [27]. Finally, he c ys al s uc u e was s anda dized wi h he p og am S uc u e Tidy [28]. All as-cas and annealed samples we e g ound on SiC pape s and polished wi h Al 2 O 3 powde s (down o 0.3 µm) ia s anda d p oce- du es and ha e been examined by ligh op ical me allog aphy (LOM) and scanning elec on mic oscopy (SEM). The mic os uc u e and chemical composi ion o he alloys we e analyzed by SEM on a Zeiss Sup a 55 VP equipped wi h an ene gy dispe si e X- ay (EDX) de ec o ope a ed a 20 kV. The non-me al con en in oxygen/ni ogen/ca bon s abilized impu i y phases was de e mined om wa eleng h dis- pe si e X- ay (WDX) analyses in a Jeol JSM-6460 scanning elec on mic oscope ope a ed a 20 kV equipped wi h an Ox o d Ins umen s mic oanalyse using Nb/Ta-L α , Mn-K α , O-K α , C-K α , Ν-K α and Si-K α a- dia ion and spec ome e c ys als LiF ( o Mn), PET (Nb/Ta), LSM60 (O, C) and LSM80N (N) (PET = Pen ae y h i ol, LSM60 = W-Si supe - la ice, LSM80N = Ni-C supe la ice). Quan i a i e e alua ion o com- posi ions was pe o med wi h he INCA - so wa e [29]. Thin lamellae (la e al dimensions abou 10 × 7 µm 2 ) o he TEM s udy we e p epa ed om he Ta45Mn55 alloy a e long annealing (2 mon hs a 1000 °C) using a ocused ion beam (FIB) echnique in a TESCAN LYRA 3 XMU FEG/SEM×FIB scanning elec on mic oscope. A Philips CM12 ansmission elec on mic oscope ope a ed a 120 kV was used namely in di ac ion mode. Elec ical esis i i y was measu ed om 4.2 K o oom empe a- u e in a con en ional 4 He c yos a , elying on an in-house equip- men (e o <3%). The speci ic esis ance was ob ained ia a dc ou - poin echnique using a Lake Sho e Resis ance B idge 370 AC. Fo speci ic hea measu emen s, we employed a Quan um Design PPMS in he empe a u e ange om 2 o 300 K using Apiezon-N g ease o ensu e a good he mal con ac be ween sample and sample pla o m. Tempe a u e and ield dependen magne iza ion da a we e collec ed a empe a u es anging om 3 o 298 K using a 6T CRY- OGENIC SQUID magne ome e . Tempe a u e dependen ac suscep - ibili y measu emen s we e ca ied ou om 4.2 o 150 K wi h a e ised Lakesho e 7000 AC Suscep ome e [30], applying an ac ield wi h an RMS ampli ude o 400 A/m and a equency o 200 Hz. The mal expansion om 4.2 K o 300 K was measu ed in a min- ia u e capaci ance dila ome e , using he il ed pla e p inciple [31]. Th ee di e en ypes o equipmen se ed o ob ain ha dness da a (HV): (i) a mic oha dness es e , AD Paa MHT-4 moun ed on a Zeiss Axioplan op ical mic oscope, employing loads o 0.1, 0.5, 1, 1.5 and 2 N, applying a a e o 0.1 N s −1 and a loading ime o 10 s, e e ed o as HV s a ic, (ii) a mic oinden e MHT4 wi h a Zeiss mic oscope, e e ed o as HV dynamic (MI), using loads o 0.1, 0.5, 1, 1.5, 2, 3, 5 N and a a e o 0.1 N s −1 p o iding in pa allel o HV he Young’s mod- ulus, E, om he inden a ion expe imen s, using he Poisson’s a io ν (ν = 0.36 was aken om DFT calcula ions o NbMn 2 [32]) and (iii) a nanoinden e ASMEC Una wi h QCSM module (Vicke s Ha dness Tes V1, ISO 14577 s anda d me hod), e e ed o as HV dynamic (NI), measu ing he inden a ions (a leas 30 imp in s pe load and sample) wi h a load o 100 mN, a load a e o 100 mN/20s, an un- loading a e o 10 mN/15s and p o iding in addi ion he Young’s modulus o a gi en ν. To e alua e he ha dness da a o (i), he di- agonal leng h, 2ℓ is measu ed and HV is calcula ed acco ding o: = × = ° HV 0.102 2Fsin (2 ) 0.1891F (2 ) 136 2 2 2 (1) wi h F as inden a ion load. To ge eliable esul s, a leas 10 di e en imp essions pe load we e e alua ed and he e o was calcula ed. The e o o (ii) and (iii) was abou 5%. 2.2. Di e en ial he mal analysis (DTA) and di e en ial scanning calo ime y (DSC) measu emen s DTA and DSC measu emen s we e pe o med on annealed sam- ples in a Ne zsch STA 409 CD/3/403/5/G appa a us wi hin sealed qua z and/o Al 2 O 3 c ucibles, espec i ely, unde a s eam o 6 N a gon. Sealed qua z ampules we e used o p e en e apo a ion o ola ile Mn om he samples du ing he measu emen ( echnique discussed, e.g. in [33]). The equipmen was calib a ed in he em- pe a u e ange om oom empe a u e o 1400 °C agains pu e me al s anda ds supplied by Ne zsch wi h he accu acy o be wi hin ± 1 °C. The measu emen s we e pe o med a hea ing and cooling a es o 10 K/min o which he bes signals s. hei se- pa a ion we e ound. As a negligible in luence o Mn e apo a ion on measu ed da a was ound and consis ency be ween DTA and DSC da a was obse ed, he DSC echnique allowing measu emen up o 1400 °C was p e e ed. Sample specimens, o which mel ing was an icipa ed abo e 1400 °C, we e measu ed in Al 2 O 3 and/o Z O 2 c ucibles co e ed by a hin sp ayed-on laye o Y 2 O 3 unde high pu i y a gon (6 N) a a hea ing a e o 15 K/min in ei he a DTA Se- a am SETSYS 18 TM , a 3D DSC Se a am MHTC Line 96, o a DTA NETZSCH STA 449 F3 Jupi e . 2.3. DFT s abili y calcula ions The ab ini io calcula ions we e pe o med using he Vienna ab ini io Simula ion Package (VASP) [34,35] wi hin he amewo k o DFT. The pseudopo en ials we e cons uc ed acco ding o he p o- jec o augmen ed wa e me hod [36,37], whe e he Pe dew, Bu ke and E nze ho app oxima ion was used o ea he exchange-co - ela ion e m [38,39]. The alence s a e con igu a ion o he con- s uc ion o he pseudopo en ials included he 3d and 4s s a es o Mn, 4p, 5s, 4d o Nb, 6s, 5d o Ta and 2s, 2p o O. In case o he con igu a ions NbMn 2 , Nb 2 Mn, TaMn 2 , and Ta 2 Mn o he C14 La es phase, he op imiza ion calcula ions we e made wi h he e imag- ne ic (FIM) a angemen o magne ic momen s (he e, he magne ic momen s o Nb and Ta ha e opposi e di ec ion and smalle alues han hose o Mn), as his a angemen o magne ic momen s is mo e s able in compa ison wi h he nonmagne ic (NM) a angemen [40]. The cu -o ene gy es ic ing he numbe o plane wa es in he basis se was 550 eV o TaMn 2 , Ta 2 Mn, Ta 3 Mn 3 , Ta 48 Mn 48 O 8 , Ta 48 Mn 48 O and he co esponding pu e elemen s, i.e. body-cen e ed X. Yan, P. B ož, J. Vřešťál e al. Jou nal o Alloys and Compounds 865 (2021) 158715 3 e agonal Mn (bc , being equi alen o ace-cen e ed e agonal), body-cen e ed cubic (bcc) Ta and he dimolecule o oxygen. Fo NbMn 2 and Nb 2 Mn, bcc Nb and bc Mn (used o he e alua ion o ene gies o o ma ion in he Nb-Mn sys em), a cu -o alue was se a 650 eV. He e, he bc s uc u e co esponds o he bcc one wi h he c la ice pa ame e sho e han a and b. The con e gence es s o o al ene gies wi h espec o he numbe o k-poin s showed ha he 21 × 21 × 21 k-poin g id in he i educible pa o he B illouin zone is op imal o TaMn 2 and Ta 2 Mn, whils a g id 13 × 13 × 7 is app op ia e o NbMn 2 and 23 × 23 × 13 o Nb 2 Mn. Fo Ta 3 Mn 3 , Ta 48 Mn 48 O 8 and Ta 48 Mn 48 O, he k-poin g id was 6 × 6 × 6. Fo pu e elemen s, he g id o k-poin s 31 × 31 × 31 was used o bcc Ta and 19 × 19 × 19 o bc Mn, bo h in he Ta-Mn sys em, and he g id 35 × 35 × 37 and 29 × 29 × 29 we e used o bc Mn and bcc Nb in he Nb-Mn sys em. Fo oxygen, he k-poin g id was 8 × 8 × 8. This e- sul ed in well-con e ged o al ene gies and equilib ium s uc u al pa ame e s, i.e. la ice pa ame e s and in e nal a omic posi ions. The ene gies o o ma ion we e calcula ed as he di e ence be ween he DFT o al ene gy o he co esponding compounds and he weigh ed a io o o al ene gies o pu e elemen s in hei s an- da d elemen e e ence (SER) s a es, i.e. αMn, bcc Nb, bcc Ta and O 2 . In o de o a oid he ab ini io calcula ion o he complex magne ic s uc u e o αMn, we used he o al ene gy o he bc Mn s uc u e wi h an an i e omagne ic a angemen (an ipa allel o ien a ion o magne ic momen s) plus he o al ene gy di e ence be ween α and bc Mn (1.82 kJ/mol), as calcula ed by Chen e al. [41], o e alua e he o al ene gy o he SER s a e o αMn. 2.4. CALPHAD modeling Fo he modynamic and phase diag am calcula ions as well as o op imiza ion o he modynamic pa ame e s based on he CALPHAD me hod, he Panda so wa e package [42] was used. The mo- dynamic modeling o phases exis ing in he bina y sys ems Nb-Mn and Ta-Mn elies on he well-known Compound Ene gy Fo malism (CEF) enabling us o espec he eal c ys allog aphic s uc u e o a phase by means o a subla ice desc ip ion [43]. Fo he he mo- dynamic desc ip ion o elemen s i in he phase ϕ, he commonly used polynomial o m was applied: = = + + + = G (T) G (T) H (298.15 K) A BT CT ln T D T , i 0 ii SER0 n 2 nn (2) whe e A, B, C, D n and n ( ypically equal o 2, 3, and −1) a e cons an s cha ac e is ic o he pa icula s uc u e o he elemen i in a gi en empe a u e in e al in Kel in [21]. The Gibbs ene gy o a gi en e na y phase ϕ is he e exp essed as a sum o se e al con- ibu ions: = + + + = G x H (298.15 K) G G G G , mi Mn,Nb,Ta ii SER0 m e mm id m ex (3) whe e Gm e is he e e ence le el o he mola Gibbs ene gy o a gi en phase ϕ, Gm means Gibbs ene gy o o ma ion, Gm id desc ibes he mola Gibbs ene gy o ideal mixing o componen s (non- s oichiome ic case) and Gm ex is he mola excess Gibbs ene gy de- sc ibing a non-ideal beha io o componen s due o hei mu ual in e ac ions [44]. The Gibbs ene gy o o ma ion o he phase ϕ is exp essed by he equa ion =G H T S, m (4) which is used o he desc ip ion o he Gibbs ene gies o com- pounds. The alue o ΔH was based on DFT alues o ene gy o o - ma ion o he phase and op imized on phase equilib ium da a, simila ly as ΔS. The la ice s abili ies o me as able o uns able phases a e calcula ed om i s -p inciples now; his idea was p e- sen ed i s in 2001 in pape s [45,46]. Fo he desc ip ion o solu- bili ies o componen s in phases, he subs i u ional model o he Compound Ene gy Fo malism (CEF) Eq. (3) is used. The o mula o ideal mixing: = = G RT x ln(x ) m id k i,j k k (5) and he Redlich-Kis e polynomial o excess con ibu ion om in e ac ion o componen s o he Gibbs ene gy: =G RT L (x x) m ex nnijn (6) a e used. In Eqs. (5) and (6) x i , x j , a e he mola ac ions o componen s and n is he summa ion index o pa ame e s L, which may be empe a u e dependen . 3. Resul s and discussion 3.1. C ys al s uc u e o he La es phases NbMn 2 and TaMn 2 Bo h La es phases NbMn 2 and TaMn 2 a e known o c ys allize wi h he hexagonal MgZn 2 - ype s uc u e (C14- ype). A summa y o all XPD da a a ailable in he li e a u e can be ound in he compi- la ion by P. Villa s and K. Cenzual [47], howe e , ecen single c ys al X- ay wo k on NbMn 2 and Nb 0.87 Mn 2.13 (Nb29Mn71 a %) by D. G üne [48] was no included (de ails will be discussed below). So a , no de ailed single c ys al s uc u e de e mina ion has been published o TaMn 2 . Fo he p esen wo k, small single c ys als we e b oken om a c mel ed alloys wi h he s oichiome ic nominal composi ion {Nb,Ta} Mn 2 . The X- ay in ensi y pa e ns in bo h cases we e ully indexed and we e unambiguously consis en wi h hexagonal symme y wi h space g oup P6 3 /mmc and la ice pa ame e s: a = 0.48898(1) nm, c = 0.79970(1) nm o he Nb-c ys al and sligh ly smalle alues a = 0.48708(1) nm and c = 0.79718(1) nm o he Ta-c ys al. S uc u e solu ion by di ec me hods yielded a ully o de ed a om a ange- men o MgZn 2 - ype o NbMn 2 , whe eas a mino bu signi ican andom dis ibu ion o 0.96(1) Mn1 + 0.04 Ta1 in he 2a si e was obse ed o Ta(Ta x Mn 1−x ) 2 (x = 0.01). The e inemen s wi h aniso opic a om displacemen pa ame e s (ADPs) con e ged o R F2 = 0.0110 wi h esidual elec on densi ies smalle han ± 0.51 e - /10 −3 nm 3 o NbMn 2 (a RT) and R F2 = 0.0244 wi h esidual elec on densi ies < ± 2.40 e - /10 −3 nm 3 o Ta(Ta x Mn 1−x ) 2 ; x = 0.01, espec- i ely. C ys allog aphic da a o bo h single c ys als a e summa ized in Tables 1 and 2. In e a omic dis ances a e shown in Fig. 1 o Ta(Ta x Mn 1−x ) 2 wi h 0.2970 ≤ d Ta-Ta ≤0.2990 nm, 0.2848 ≤ d Ta-Mn ≤0.2858 nm, 0.2360 ≤ d Mn-Mn ≤ 0.2510 nm and a e a he consis en wi h he sum o CN12 me al a om adii (R Nb = 0.1468 nm, R Ta = 0.1467 nm and R Mn = 0.1304 nm [49]). Whe eas dis ances Ta-Ta a e sligh ly longe han he sum o adii, dis ances Mn-Mn o si e 6h a e sho e by abou 10% and o Mn-Mn (2a o 6h) a e sho e by abou 5% indica ing a s ong Mn-Mn in e ac ion. Such a beha io is also inhe en o NbMn 2 . Ou oom empe a u e a om pa ame e s o NbMn 2 a e essen ially consis en wi h he indings o G üne [48], al hough his a om pa ame e s a e sligh ly highe and his la ice pa ame e s a e somewha lowe . E alua ion o he empe a u e dependen X- ay single c ys al in ensi y da a se s in Table 2 clea ly documen ha NbMn 2 adop s he MgZn 2 -La es ype a all he ou empe a u es measu ed, namely: 100 K, 150 K, 200 K and 300 K. In combina ion wi h XPD da a up o he mel ing poin we obse e ha no phase ansi ion appea s wi hin he en i e empe a u e in e al (100–1788 K). TaMn 2 displays analogous beha io (298–2070 K). The empe a u e dependence o he la ice pa ame e s o NbMn 2 o he empe a u e ange om 100 o 300 K, as depic ed in Fig. 2 ( op), shows a a he smoo h a ia ion wi hin ~2 pe mille. Fig. 2 X. Yan, P. B ož, J. Vřešťál e al. Jou nal o Alloys and Compounds 865 (2021) 158715 4 (middle) deno es he a ia ion wi h T o he a om pa ame e s in he a ious Wycko si es o NbMn 2 . Al hough he z pa ame e o he Nb-a oms in 4 seems o cons an ly ise wi h empe a u e, he x pa ame e o he Mn-a oms in he 6h si e passes h ough a max- imum a 150 K. Fig. 2 (bo om) (100–300 K) po ai s he empe a u e depen- dence o he in e a omic dis ances in NbMn 2 , which me ely e lec s he a ia ion o la ice pa ame e s in combina ion wi h he a om pa ame e a ia ion s. T. Consequen ly, all dis ances be ween Mn a oms ise a he mono onically wi h empe a u e wi hin 2 pe mille. Fo he e alua ion o he Debye empe a u e om he empe a u e dependen ADPs see Sec ion 4.2. Speci ic hea . In his con ex , i is in e es ing o no e ha D. G üne [47] ob- se ed a weak 2a×2a×2c supe s uc u e o he MgZn 2 - ype on polyc ys alline esidues, which we e ex ac ed by dilu ed HCl om a c mel ed Mn- ich alloys Nb10Mn90 (in a %), sealed in Nb- essels and annealed a 1100 °C. No s uc u al de ails we e epo ed, bu i was said ha single c ys als Nb 0.87 Mn 2.13 (Nb29Mn71 a %), ex ac ed in he same way om Mn- ich alloys, did no show any supe - s uc u e e lec ions and clea ly e ealed iso ypism wi h he MgZn 2 - ype. The andom dis ibu ion o (3.48Nb+0.52Mn) in he 4 -si es in he Mn- ich single c ys al Nb 0.87 Mn 2.13 [48] is in line wi h andom dis ibu ions o (0.1Nb+1.9Mn) in he 2a si es and (0.22Nb+5.78Mn) in he 6h si es o he Nb- ich alloy Nb 1.08 Mn 1.92 (Rie eld e inemen da a in Table 2). I should be men ioned he e, ha ou XPD nei he in Nb-Mn no he Ta-Mn sys em de ec ed any supe s uc u e e lec ions. 3.2. The oxygen-s abilized phases "NbMn" (^ Nb 3 Mn 3 O 1-y ) and "TaMn" (^ Ta 3−x Mn 3+x O 1-y ) Ou ecen a emp s o ge a phase-pu e compound NbMn 2 [24], e ealed ha in Nb- ich samples small amoun s o a second com- pound iche in Nb caused he appea ance o weak e omagne ism. EDX measu emen s yielded a phase composi ion close o NbMn. Fu he expe imen s ga e clea hin s ha he pe cen age o his phase in Nb-Mn and also in Ta-Mn alloys inc eases wi h he non-me al impu i y con en ( om WDX p edominan ly oxygen, no ni ogen, no ca bon) in he aw elemen s (such as Mn o Nb/Ta-powde ). The e- o e, he new seconda y phase was concluded o be an impu i y s abilized e na y phase. Indeed, pains aking a emp s o educe he oxygen-le el o he s a ing ingo ma e ials as well as in he p e- pa a ion (mel ing unde high pu i y a gon, handling ma e ials ex- clusi ely in a <3 ppm (O+H 2 O) glo e box sys em) we e inally success ul yielding phase pu e and pa amagne ic La es phases NbMn 2 [24] and TaMn 2 ( his wo k). La es phase samples wi hou any ace- able amoun s o he magne ic phase ha e been ob ained wi h an addi ion o 1–2 mass% o lan hanum me al as an in e nal oxygen ge e ob iously cap u ing he oxygen and o ming a „nonmagne ic“ LaMn x O y phase, which did no dis u b he magne ic cha ac e iza ion o he La es phases (see below Sec ion 4.1 Suscep ibili y). In his pape we adop ed a “di y way” o inc ease he amoun o his impu i y s abilized phase by mel ing powde compac s in he egion Nb o NbMn (and Ta o TaMn) in an a gon a c-mel e wi h in e mi en c ushing he bu ons in ai and adding Mn o com- pensa e usion losses. Va ious oxygen con en s we e in oduced by adding p ope amoun s o MnO 2 o Nb 2 O 5 and Ta 2 O 5 . In a ew cases, we also ied o s a om ine powde compac s ha we e eac ed in a sealed qua z ube o 3 × 36 h a 950 °C wi h in e mi en c ushing in ai and e-compac ing. Al hough he new phase o med in la ge quan i ies, we we e unable o syn hesize a single-phase sample in bo h sys ems. The spec a usually con ained he La es phase as he dominan phase and he “impu i y phase” in addi ion. A his s age, a se ies o selec ed a ea elec on di ac ion (SAED) pa e ns in Fig. 3 we e ob ained ia TEM om hin lamellae p epa ed in SEM by FIB om he whi e phase in he cas alloy Ta50Mn50, which was annealed o 2 mon hs a 1000 °C. Thei analyses p omp ed a ace-cen e ed cubic ( cc) la ice wi h a la ice pa ame e a ~ 1.12 nm (a e aged om a se o axes, [100], [110], [111], [210], [310] and [510]). On he basis o his in o ma ion, he indexa ion o he X- ay powde in ensi y pa e n o he new phases in bo h sys- ems was success ul. A sea ch o he s uc u e ype in c ys al da- abases such as in Pea son’s C ys al Da a [47] and in ICSD [50], employing cc c ys al symme y wi h a ange o la ice pa ame e s a = 1.13 ± 0.1 nm p omp ed di ec ly he CdNi- ype (o H Mn), which in ac is an occupa ion a ian o he Ti 2 Ni- ype (e a(η)-phase). The mode o a om si e occupa ion and illing he oc ahed al oids in he a ious composi ion a ian s o he so-called η-phases de- i ing om he pa en Ti 2 Ni- ype was al eady ex ensi ely discussed by Rogl e al. [51]. Re e ing o his analysis, he phases Nb ~1 Mn ~1 O y and Ta ~1 Mn ~1 O y ha e o be classi ied as a illed me al hos la ice s uc u e whe e he manganese a oms in 16c o space g oup Fd 3 m (o igin a cen e o symme y) ill he cen e s o me al icosahed a (each o med by six Nb(Ta)/Mn a oms om he si es 48 and 32e) yielding a o mula Nb(Ta) ~3 Mn ~3 O y . Gene ally in e a-phases, non- me al a oms such as C, N o O a e assumed o occupy he oc ahed al oids in 16d, bu may also en e a second se o oc ahed al oids in Wycko si e 8b (⅜,⅜,⅜). I may be no ed he e ha Wycko si e 8b changes o si e 8a (⅛,⅛,⅛) in he non-s anda dized s uc u e (using Fd 3 m wi h he o igin a −43m). We used his s anda dized s a ing model o Rie eld e inemen s o elucida e he inal a om dis- ibu ion in he no el compounds Nb ~1 Mn ~1 O y and Ta ~1 Mn ~1 O y . As he si ua ion is qui e simila o bo h sys ems Nb(Ta)-Mn, we may u he on ocus he e on he alloys om he Ta-Mn sys em. Table 1 S uc u al da a o Ta(Ta x Mn 1−x ) 2 (x = 0.01) om X- ay single c ys al measu emen a 300 K. Pa ially o de ed MgZn 2 - ype; space g oup P6 3 /mmc; No. 194; s uc u e s an- da dized wi h p og am S uc u e Tidy [28]. Aniso opic a omic displacemen pa a- me e s U ij in [10 2 nm 2 ]. Pa ame e /compound C ys al da a Phase composi ion (EDX, a %) Ta35Mn65 ^Ta 1.05 Mn 1.95 Re inemen composi ion (a %) Ta 1.02 Mn 1.98 ^Ta(Ta x Mn 1−x ) 2 ; x = 0.01 S uc u e ype MgZn 2 - ype θ ange (deg) 5.1 ≤ 2θ≤ 72.5 C ys al size 65 × 70 × 80 µm 3 a = b (nm) 0.487077(7) c (nm) 0.797175(11) Re lec ions in e inemen 182 ≥ 4σ(F o ) o 182 Numbe o a iables 12 Mosaici y <0.49 R F2 = Σ|F 2 o -F 2 c |/ΣF 2 o 0.0244 wR2 0.0582 R In 0.069 GOF 1.278 Ex inc ion (Zacha iasen) 0.0011(8) M1 in 2a (0,0,0); occ. 0.96(1) Mn1 + 0.04 Ta1 U 11 = U 22 ; U 33 ; U 12 ; U 23 = U 13 = 0 0.0029(8); 0.0028(9); 0.0015(4) Ta2 in 4 (⅓, ⅔, z); occ. z = 0.56376(6); 1.00(1) U 11 = U 22 ; U 33 ; U 12; U 23 = U 13 = 0 0.0027(2); 0.0036(3); 0.0014(1) Mn2 in 6h (x, 2x, ¼); occ. x = 0.1718(2); 1.00(1) U 11 ; U 22 ; U 33 ; U 12 ; U 23 = U 13 = 0 0.0009(4); 0.0005(5); 0.0025(5); 0.0003(3) Residual elec on densi y; max; min in (elec on/nm 3 ) × 10 3 2.40 (0.134 nm om Mn2); −1.76 In e a omic dis ances < 0.3 nm (s anda d de ia ion <0.0004) Ta – 3 Mn2 0.2848 Ta – 6 Mn2 0.2853 Ta – 3 Mn1 0.2858 Mn1 – 6 Mn2 0.2464 Mn1 – 6 Ta 0.2858 Mn2 – 2 Mn2 0.2360 Mn2 – 2 Mn1 0.2464 Mn2 – 2 Mn2 0.2510 Mn2 – 2 Ta 0.2848 Mn2 – 4 Ta 0.2853 Ta – 1 Ta 0.2970 Ta – 3Ta 0.2990 X. Yan, P. B ož, J. Vřešťál e al. Jou nal o Alloys and Compounds 865 (2021) 158715 5 Rie eld e inemen o an a c mel ed alloy Ta43Mn57 (see Fig. 4) clea ly showed ha he composi ion o he new phases appea s close o a a io (Nb,Ta):Mn ~ 1:1 a he han o a a io (Nb,Ta):Mn ~ 4:2 such as is ypical o many oxygen-s abilized compounds de i ing om he Ti 2 Ni- ype (Ti 4 Ni 2 O) (e a(η)-phase; o ep esen a i es see Pea son’s C ys al Da a [47]). Al hough he hexagonal La es phase Ta 0.9 Mn 2.1 (MgZn 2 - ype) wi h 85 ol% is he dominan phase in he X- ay powde di ac ion pa e n, he sec- onda y phase o his pa e n can clea ly be indexed on an cc la ice (a = 1.14546(1) nm), ully consis en wi h he s uc u e model discussed abo e. The esul s o he e inemen a e lis ed in Table 3. These esul s e eal only sligh de ia ions om a ull a om o de wi h a andom a om dis ibu ion o (43.6 Ta+4.4 Mn) a oms in he 48 si e, (1.0 Ta+31.0 Mn) a oms in he 32e si e and exclusi ely Mn in he 16c si e. In e es ingly he e inemen e uses any oxygen in he Wycko si es 8a and 8b bu eadily accep s 5.34 O a oms in he 16d si e o he space g oup Fd 3 m (o igin a cen e ). F om his a om dis ibu ion, we a i e a a chemical o mula Ta 2.78 Mn 3.22 O 0.33 (Ta 3−x Mn 3+x O 1−y ; x = 0.22, y = 0.67), which di ec ly complies wi h he p o o- ype o W 3 Fe 3 C as one o he s uc u e a ian s o he Ti 4 Ni 2 O amily [47,51]. The small de ia ions om ull s oichio- me y (Ta 2.78 Mn 3.22 O 0.33 ^ Ta43.9Mn50.9O5.2 in a %, i.e. a a a io Ta:Mn = 46.3:53.7) a e well e lec ed in he EDX/WDX-composi- ions de i ed by he X- ay mic oanalyses. The in ensi y simula- ions o he SAED-pa e ns, calcula ed o he s uc u e model o Ta 2.78 Mn 3.22 O 0.33 (plo ed in Fig. 3 in he JEMS so wa e [52,53]) a e ully consis en wi h he obse ed pa e ns. I should be men ioned he e ha he appea ance o oxygen exclusi ely in Wycko si e 16d ules ou he s uc u e ype o W 6 Fe 6 C (whe e he nonme al a om only en e s he 8b si e bu lea es he 16d si e emp y). Table 2 S uc u al da a o NbMn 2 om X- ay single c ys al measu emen a ou di e en empe a u es. Pa ially o de ed MgZn 2 - ype; space g oup P6 3 /mmc; No. 194; o igin a cen e ; s uc u e s anda dized wi h p og am S uc u e Tidy [28]. Aniso opic a omic displacemen pa ame e s U ij in [10 2 nm 2 ]. In e a omic dis ances < 0.3 nm. Pa ame e /Alloy composi ion NbMn 2 Tempe a u e Room empe a u e 200 K 150 K 100 K a=b (nm); c (nm) 0.48898(1); 0.79970(1) 0.48834(1); 0.79853(2) 0.48824(1); 0.79823(1) 0.48801(1); 0.79798(1) Da a collec ion, 2Θ ange 2 < 2Θ < 72.73 2 < 2Θ < 72.39 2 < 2Θ < 72.41 2 < 2Θ < 72.44 Re lec ions in e inemen 173 F o > 4σ(F o ) o 184 172 F o > 4σ(F o ) o 182 175 F o > 4σ(F o ) o 181 170 F o > 4σ(F o ) o 182 Mosaici y < 0.43 < 0.43 < 0.43 < 0.43 Numbe o a iables 11 11 11 11 R F2 = Σ|F 02 -F c2 |/ΣF 02 0.0110 0.0210 0.0158 0.0118 R In 0.0265 0.0296 0.0299 0.0269 GOF 1.901 2.072 2.178 2.183 Ex inc ion (Zacha iasen) 0.014(1) 0.015(1) 0.015(1) 0.016(1) Nb1 in 4 (1/3,2/3,z); occ. z = 0.56349(3); 1.00 Nb z = 0.56347(4); 1.00 Nb z = 0.56339(4); 1.00 Nb z = 0.56337(4); 1.00 Nb U 11 = U 22 ; U 33 ; U 12 0.0051(1); 0.0051(1); 0.0025(1) 0.0038(1); 0.0036(2); 0.0019(1) 0.0031(1); 0.0030(1); 0.0015(1) 0.0027(1); 0.0025(1); 0.0014(1) Mn1 in 2a (0,0,0); occ. 1.00 Mn 1.00 Mn 1.00 Mn 1.00 Mn U 11 = U 22 ; U 33 ; U 12 0.0051(2); 0.0043(3); 0.0026(1) 0.0038(2); 0.0029(3); 0.0019(1) 0.0030(2); 0.0023(3); 0.0015(1) 0.0026(2); 0.0022(3); 0.0013(1) Mn2 in 6h (x,2x,¼); occ. x = 0.17128(4); 1.00 Mn x = 0.17136(5); 1.00 Mn x = 0.17139(5); 1.00 Mn x = 0.17133(4); 1.00 Mn U 11; U 22 ; U 33 ; U 12 0.0048(1); 0.0045(2); 0.0051(3); 0.0023(1) 0.0036(2); 0.0035(2); 0.0034(2); 0.0017(1) 0.0030(2); 0.0030(2); 0.0029(2); 0.0015(1) 0.0026(2); 0.0026(2); 0.0025(2); 0.0013(1) Residual elec on densi y; max; min in (e/nm 3 ) x 1000 0.51; − 0.50; 0.097 nm om Mn1 1.11; − 1.12; 0.135 nm om Mn2 0.98; − 0.79; 0.149 nm om Nb1 0.72; − 0.67; 0.160 nm om Mn2 Nb1 – 3 Mn2 0.2858 0.2854 0.2852 0.2851 Nb1 – 6 Mn2 0.2864 0.2860 0.2860 0.2859 Nb1 – 3 Mn1 0.2868 0.2865 0.2864 0.2862 Mn1 – 6 Mn2 0.2470 0.2467 0.2466 0.2465 Mn1 – 6 Nb1 0.2868 0.2865 0.2864 0.2862 Mn2 – 2 Mn2 0.2377 0.2373 0.2372 0.2372 Mn2 – 2 Mn1 0.2470 0.2467 0.2466 0.2465 Mn2 – 2 Mn2 0.2513 0.2510 0.2510 0.2508 Mn2 – 2 Nb1 0.2858 0.2854 0.2852 0.2851 Mn2 – 4 Nb1 0.2864 0.2860 0.2860 0.2859 Nb1 – 2 Nb1 0.2983 0.2979 0.2979 0.2979 Nb1 – 2 Nb1 0.3000 0.2996 0.2995 0.2994 Fig. 1. C ys al s uc u e o TaMn 2 (Ta 1.02 Mn 1.98 ) in h ee-dimensional iew wi h bond dis ances (in Å). A oms a e displayed wi h hei aniso opic he mal displacemen ellipsoids as de i ed om X- ay single c ys al e inemen (see Table 1). Mn1 a oms in si e 2a a e yellow (0.96 Mn1 + 0.04 Ta1); Mn2 a oms in si e 6h a e oche ; Ta2 a oms in si e 4 a e ed. (Fo in e p e a ion o he e e ences o colou in his igu e legend, he eade is e e ed o he web e sion o his a icle.) X. Yan, P. B ož, J. Vřešťál e al. Jou nal o Alloys and Compounds 865 (2021) 158715 6 A e annealing a 950 °C o 4 days he XPD pa e n o he cas alloy Ta43Mn57 has changed, i.e. besides he La es phase as he dominan phase, we now encoun e wo o he cc e a-phases in he SEM analysis as well as om Rie eld e inemen (see Table 3). In- e es ingly he La es phase (~81 ol%) appea s p ac ically s oichio- me ic bu wi h sligh ly lowe la ice pa ame e s. The seconda y phases can bo h be desc ibed wi h he W 3 Fe 3 C- ype bu con ain a he small con en s o oxygen: Ta 2.84 Mn 3.16 O 0.23 (14 ol%, a = 1.14088(1) nm) and Ta 3.01 Mn 2.99 O 0.13 (4 ol%, a = 1.12859(2) nm). Random dis ibu ions o Ta/Mn a oms only appea in he 48 si e and a e o smalle ex en , he e o e he o mulae a e close o ull o de ; he main di e ence is he oxygen con en e lec ed also by he di - e en uni cell dimensions. I is unclea i he sample e eals a ansi ion s a e o inal equilib ium o i he wo e a-phases a e equilib ium phases o he Ta-Mn-O sys em. The e omagne ic impu i y phase, which appea ed in small quan i ies du ing he a emp s o p epa e single phase NbMn 2 was equally well desc ibed by a W 3 Fe 3 C- ype e a-phase ( o de ails see he Rie eld e inemen o alloy Nb40Mn60, annealed a 900 °C, in Table 3 and Fig. S1 o Supplemen a y Ma e ial). Rie eld and EDX analyses ag ee on a o mula Nb 2.86 Mn 3.14 O 0.31 (Nb 3−x Mn 3+x O y ; x = 0.14, y ~ 0.69) wi h a la ice pa ame e a = 1.13415(2) nm. Finally, a sea ch o ep esen a i es o he W 3 Fe 3 C ype in Pea son’s C ys al Da a [47] indeed e ealed he e a-phase Ta 3 Mn 3 O, as epo ed by Schönbe g [54]. Al hough Schönbe g in es iga ed he Ta-Mn-O sys em (<50 a % O), he was unable o ob ain he e a-phase in a pu e condi ion bu a he “in he p esence o ai ly la ge amoun s o o he phases”. Howe e , nei he he Ta-Mn-O phase equilib ia no a s uc u e e inemen o he e a-phase ha e been gi en; only he ange o la ice pa ame e s was lis ed om 1.115 o 1.118 nm [54], which, howe e , is much smalle han he uni cells de i ed om ou samples. In e es ingly, Schönbe g’s in es iga ion o he Ta-Mn-N sys em [55] did no yield any η-phase, in con as o indings o Holleck e al. [56], who was able o syn- hesize bo h e a-ni ides: Nb 3.5 Mn 2.5 N (a = 1.142 nm) and Ta 3 Mn 3 N (a = 1.135 nm). He e i should be emphasized ha ou WDX es on N in ou e a-phases was always nega i e. The o ma ion o e a-phases in Ta-Mn alloys can be bes seen in Fig. 5 om an HF mel ed alloy TaMn 2 , p epa ed om Ta- oil and pieces o Mn. The e alua ion o he mic os uc u e by means o SEM- EDX and WDX e ealed a pa ially mel ed Ta- oil su ounded by li- quid Mn, which solidi ied in laye s o e a-phases and inally he La es phase ( o de ails see Fig. 5). 3.3. Cons i u ion o he sys ems Nb-Mn and Ta-Mn In o de o p o ide a ho ough cons i u ional basis o p ope he modynamic modeling, we ha e s a ed wi h DTA/DSC in- es iga ions. As he hi he o known in o ma ion sugges ed mel ing empe a u es o he sec ions T - TMn 2 (T = Nb,Ta) abo e 1400 °C, we applied high- empe a u e DTA wi h Al 2 O 3 and/o Y 2 O 3 -su ace coa ed Z O 2 c ucibles om which we de ined he ollowing cha ac e is ics: cong uen mel ing o NbMn 2 a T m (NbMn 2 ) = 1515 ± 15 °C, incong uen mel ing o TaMn 2 a T m (TaMn 2 ) = 1797 ± 40 °C and a p ac ically iden ical mel ing empe a u e o alloy Ta40Mn60, whe eas alloy NbMn displayed la ge p ima y dend i es o NbMn 2 and a eu ec ic ℓ = (Nb) + NbMn 2 a T eu . = 1493 ± 15 °C. Some o he high- empe a u e DTA uns a e summa ized in Fig. S2 and Fig. S3 o Supplemen a y Ma e ial. This in o ma ion on he li- quidus cu es, complemen ed by SEM mic og aphs and EDX/WDX analyses (see Fig. 6 and Tables 4 and 5), con i med (i) cong uen mel ing o NbMn 2 (S echniko e al. ga e T m = 1500 °C [13]) and (ii) a a he deple ed pe i ec ic mel ing o TaMn 2 a 1797 °C, consis en wi h (a) he no e o Sa i skii e al. ha TaMn 2 “mel s abo e 1670 °C” [17] and (b) S echniko [13], who simply lis ed (wi hou commen ) he mel ing o TaMn 2 a 1800 °C. I should be emphasized, ha in none o ou samples om bo h sys ems (Nb-Mn and Ta-Mn) we obse ed any ace o he hombohed al μ-phase (W 6 Fe 7 - ype; space g oup R m3 ; hex. axes: a ~ 0.47 nm, c ~ 2.58 nm). The e o e, and om he discussion (i) in Sec ion 3.2. on he oxygen s abilized e a-phases as well as (ii) on he DFT-ins abili y o e a-Ta 3 Mn 3 , (iii) he Rie eld e inemen s o he alloys Nb40Mn60 (as-cas a e anneal a 900 °C) and Ta43Mn57 (as-cas and a e anneal a 1000 °C), and (i ) he Fig. 2. S uc u e pa ame e s o NbMn 2 in he empe a u e ange om 100 o 300 K ( om X- ay single c ys al da a, Table 2). Top: he mal expansion o he la ice pa a- me e s; middle: a om pa ame e s o he a ious Wycko si es; bo om: in e a omic dis ances. The dis ance d Mn2–2Mn2 = 0.25130 nm ( owa ds he neighbo ing uni cell) a 300 K wi h almos no a ia ion is no shown he e. X. Yan, P. B ož, J. Vřešťál e al. Jou nal o Alloys and Compounds 865 (2021) 158715 7 solidi ica ion mic os uc u es in Fig. 6 (Nb-Mn) and Fig. 6l (Ta-Mn), we may sa ely exclude he phases “NbMn” [16] and “TaMn” [18] om he co esponding bina y phase diag ams. Whils he homogenei y egions o he wo La es phases will be ea ed below, he maximum solubili y o Mn in (Nb) and (Ta), as de i ed om he cas alloys and he alloys om DTA (see also he mic os uc u es in Fig. 6 and Tables 4 and 5) we e 19.4 a % Mn in (Nb) and e en 21.3 a % Mn in (Ta). In addi ion, i should be men- ioned ha o he (Nb/Ta)- ich pa o he phase diag ams, DTA did no e eal any ans o ma ions om RT o he mel ing. Con en ional DTA (alloys sealed in qua z) and DSC (Al 2 O 3 -c u- cibles unde a gon) we e chosen o elucida e he Mn- ich pa o he phase diag ams, o which liquidus empe a u es we e all expec ed o eside below 1250 °C. Whe eas he cas alloy Nb5Mn95 u ned ou o be ully eu ec ic (T eu = 1220 ± 10 °C), he si ua ion is less s aigh o wa d in he sys em Ta-Mn e ealing an almos deple ed eu ec ic a abou 0.7 a % Ta ((δ-Mn) + TaMn 2 a T eu = 1234 ± 10 °C) (see Fig. 6). The maximal solid solubili y o (Nb) and (Ta) in δ-Mn appea s o be small and is abou 0.5 a % Mn o bo h Nb and Ta. In con as o ha , Hellawell [14] (on he basis o mic os uc u es, TA and XPD da a; bu no EPMA) epo ed he eu ec ic a 3.6 a % Nb (1224 °C) and a maximum solubili y o 2.4 a % Nb in δ-Mn, a alue which in iew o ou in es iga ions (see Fig. 6a and Table 4) seems o be exagge a ed. In con as o ou indings, he da a o he Ta-Mn sys em by Sa i skii [17] exclude δ-Mn om he eu ec ic, which was claimed a 2.6 a % Ta a 1175 °C and o med by (γ-Mn) + TaMn 2 . Ou DTA and DSC analyses in combina ion wi h SEM-EDX/WDX on a se ies o alloys wi h 1, 2, 3, 4, 5 and 10 a % o he T-me al se ed o de ine he phase ela ions in he Mn- ich pa o bo h sys ems Nb- Mn and Ta-Mn, which a e cha ac e ized by he 4 c ys al s uc u e modi ica ions o pu e Mn and hei phase ansi ions [12]: ° ° ° ° liquid Mn Mn Mn Mn. C C C C1246 1138 1100 727 Al hough he highe ansi ion empe a u es a e alike, he lowe wo ansi ion empe a u es in he compila ion om A. Dinsdale [21] ( he modynamic da a o una y phases) show a disc epancy as high as abou 20 °C (707 °C and 1087 °C). EXD and WDX da a in e ed ha o bo h phase diag ams he solubili ies o he T-me al a e below ~0.8 a % T o all modi ica ions excep o (γMn) and (αMn), he la e yielding a signi ican inc ease o i s T-solubili y close o i s pe i ec oid decomposi ion on hea ing (see Fig. 6 and Tables 4 and 5), hand in hand wi h a p onounced inc ease o he (αMn) o (βMn) ans o ma ion empe a u e on solu ion ( o de ails see he phase diag ams below in Figs. 8 and 9). I should be men ioned he e, ha also Sa i skii e al. [17] om he mal analyses concluded a pe i ec oid decomposi ion on hea ing o (αMn) a ~1.5 a % Ta and 750 °C, qui e simila o ou DTA and EPMA da a. DTA/DSC cu es o selec ed Mn- ich alloys a e p esen ed in Fig. S4 and Fig. S5 o Supplemen a y Ma e ial. 3.3.1. The homogenei y egions o he La es phases NbMn 2 and TaMn 2 The expe imen ally de i ed homogenei y egion o he La es phase Nb 1+x Mn 2−x (62.5–73.0 a % Mn a 950 °C: −0.19 ≤x≤ 0.125) (see Fig. 7a) is ai ly consis en wi h he epo s by D ys [57] (64–69 a % Mn ^ −0.07 ≤x ≤ 0.08 a 800 °C), S echniko e al. [13] (62–70 a % Mn a 1000 °C) and Blazina [58] (62–69 a % Mn a 1000°C), which was Fig. 3. SAED pa e ns o he cubic “TaMn” e a(η)-phase a a ious sample il s (uppe panel) oge he wi h esul s o kinema ic simula ion (lowe panel). Weake e lec ions 00k o k = 4n + 2 obse ed in he cen al ho izon al line o he [110] pa e n (compa e he SAED and i s simula ion below) a e caused by dynamic e ec s (double di ac ion). Fig. 4. Rie eld e inemen o as-cas alloy Ta43Mn57. The excluded egion a ound 2θ≈ 22° belongs o a small peak s emming om he sample ca ie oil. X. Yan, P. B ož, J. Vřešťál e al. Jou nal o Alloys and Compounds 865 (2021) 158715 8 also used by Gup a e al. [59] o he Nb-Mn-Ni sys em a 1000 °C. Ou s udy o he la ice pa ame e s con i med he homogenei y e- gion ob ained om EDX measu emen s wi hin a small ma gin o ± 0.5 a % Mn (see Fig. 7a). A simila ly wide homogenei y egion was ound om XPD o Ta 1+x Mn 2−x (59.5–68.5 a % Mn o 900 °C and cas alloys: −0.055 ≤x ≤ 0.215; see Fig. 7b), which is ai ly consis en wi h he EPMA alues. A his poin , i should be emphasized ha bo h sys ems Nb-Mn and Ta-Mn a e cha ac e ized by only one bina y compound, a La es phase wi h MgZn 2 - ype wi hou any o he s uc u e modi ica ions in he en i e composi ion/ empe a u e ange o exis ence. Fo NbMn 2 his has been p o en by empe a u e dependen XPD (4.2–300 K), X- ay SC di ac ome y om 100 o 300 K and by XPD up o he mel ing ange on quenched alloys. Fig. 7a and b display he la ice pa ame e s o Nb 1+x Mn 2−x and Ta 1+x Mn 2−x as a unc ion o compo- si ion and o a se o empe a u es. Fo compa ison, all da a a ail- able in he li e a u e a e plo ed ( aken om [47]), al hough many o hem lack a de ined composi ion and can only be placed a s oi- chiome ic TMn 2 . I is in e es ing o see ha he wid h o he homogenei y egion Nb 1+x Mn 2−x is p ac ically in a ian om 950 °C o he mel ing ange: − 0.19 ≤ x ≤ 0.125. Simila beha io is also en- coun e ed o Ta 1+x Mn 2−x . F om he ene ge ics o poin de ec o ma ion in a DFT supe cell app oach o he la ge homogenei y egion o he Z Mn 2 La es phase, Chen e al. [41] clea ly de i ed ha an isi e occupa ion is mo e a o able han acancy o ma ion. Pa icula ly he low ene gy o Mn a Z si es in e s a b oad nons oichiome y ange owa d he Mn- ich side and wi h inc easing empe a u e he minimum o he ee ene gy o he La es phase is shi ed owa d Mn- iche compo- si ions (a 32.8 a % Z ) concomi an wi h he occu ence o he cong uen mel ing poin no a he s oichiome ic bu a a sligh ly Mn- iche composi ion [41]. Simila a gumen s may also hold o bo h La es phases NbMn 2 and TaMn 2 . 3.4. DFT s abili y o in e me allic phases The ab ini io calcula ed equilib ium la ice pa ame e s o he FIM a angemen o he a ious con igu a ions o C14 La es phases a e p o ided below. This ype o magne ic a angemen was chosen, as i shows o be he mos s able (a de ailed s udy o his opic can be ound in Re . [40]). The la ice pa ame e s o NbMn 2 (a = 0.48087 nm, c = 0.79061 nm) and TaMn 2 (a = 0.47899 nm, c = 0.78874 nm) ag ee Table 3 XPD Rie eld e inemen ( oom empe a u e da a) o alloys Nb40Mn60 (as-cas a e anneal a 900 °C) and Ta43Mn57 (as-cas and a e anneal a 1000 °C); he a ange 14 ≤ 2Θ≤ 95°); all s uc u es s anda dized wi h p og am S uc u e Tidy [28]. Iso opic a omic displacemen pa ame e s B iso in [10 2 nm 2 ]. Pa ame e /sample (a %) Nb40Mn60; 900 °C Ta43Mn57; a c Ta43Mn57; 1000 °C P o ile pa ame e s Numbe o a iables 24 24 26 R P = Σ|y oi -y ci |/Σ|y 0i | 0.0150 0.0348 0.0638 R wP = [Σw i |y oi -y ci | 2 /Σw i |y oi | 2 ] ½ 0.0198 0.0459 0.0871 R e = [(N-P + C)/Σw i y 2 oi )] ½ 0.0132 0.0085 0.0081 La es phase Nb 1.08 Mn 1.92 ; 86 ol% Ta 0.9 Mn 2.1 ; 85 ol% TaMn 2 ; 81 ol% Space g oup, P o o ype P6 3 /mmc, MgZn 2 P6 3 /mmc, MgZn 2 P6 3 /mmc, MgZn 2 a; c (nm) 0.489376(4); 0.800616(9) 0.491376(4); 0.803961(8) 0.48680(1); 0.79713(2) R F = Σ|F o -F c |/ΣF o 0.0654 0.0322 0.0435 R I = Σ|I o -I c |/ΣI o 0.0826 0.0450 0.0464 Si e 2a (0,0,0); B iso 0.36(2); 0.10(2) Nb + 1.90 Mn 0.20(3); 0.09(1) Ta + 1.91 Mn 0.21 2 Mn Si e 4 (⅓,⅔,z); z; B iso 0.56276(5); 0.49(3); 4 Nb 0.56381(2); 0.42(4); 3.51(1) Ta + 0.49 Mn 0.56483(3); 0.41(4); 4 Ta Si e 6h (x,2x,¼); x; B iso 0.1733(3); 0.57(4); 0.22(2) Nb + 5.78 Mn 0.1697(1); 0.21(4); 6 Mn 0.1778(2); 0.40(6); 6 Mn η (e a) phase #1 Nb 2.86 Mn 3.14 O 0.31 ; 14 ol% Ta 2.78 Mn 3.22 O 0.33 ; 15 ol% Ta 2.84 Mn 3.16 O 0.23 ; 14 ol% Space g oup, P o o ype Fd 3 m, W 3 Fe 3 C Fd 3 m, W 3 Fe 3 C Fd 3 m, W 3 Fe 3 C a (nm) 1.13415(2) 1.14546(1) 1.14088(3) R F = Σ|F o -F c |/ΣF o 0.096 0.0985 0.0980 R I = Σ|I o -I c |/ΣI o 0.114 0.0995 0.1041 Si e 48 (x,⅛,⅛); x; B iso 0.4308(2); 0.63; 42.6(3) Nb + 5.4 Mn 0.4325(1); 0.55; 43.6(1) Ta + 4.4 Mn 0.4288(2), 0.2; 45.4(1) Ta + 2.6 Mn Si e 32e (x,x,x), x; B iso 0.2064(3); 0.56; 3.1(2) Nb + 28.9 Mn 0.2120(3); 0.12; 1.0(1) Ta + 31.0 Mn 0.2038(3), 0.4; 32 Mn Si e 16c (0,0,0) B iso 16 Mn; 0.51 16 Mn; 0.12 16 Mn; 0.4 Si e 16d (½,½,½) B iso 5.0(1) O; 0.61 5.34(8) O; 0.41 3.61(1) O; 0.55 η (e a) phase #2 no no Ta 3.01 Mn 2.99 O 0.13 ; 4 ol% Space g oup, P o o ype – – Fd 3 m, W 3 Fe 3 C a (nm) – – 1.12859(2) R F = Σ|F o -F c |/ΣF o – – 0.1020 R I = Σ|I o -I c |/ΣI o – – 0.1141 Si e 48 (x,⅛,⅛); x; B iso – – 0.4288(-); 0.2; 48 Ta Si e 32e (x,x,x), x; B iso – – 0.2038(-); 0.4; 0.2 Ta + 31.8 Mn Si e 16c (0,0,0) B iso – – 16 Mn; 0.4 Si e 16d (½,½,½) B iso – – 2.05(6) O; 0.55 Fig. 5. SEM-BSE mic og aph o HF mel ed alloy Ta39.8Mn60.2 (o e all EDX): b igh Ta99.7Mn0.3, ligh g ay band adjacen o b igh (un eac ed) oil: Ta48Mn52 (Ta44.8Mn52.0O3.2 ≡ η-phase Ta 3−x Mn 3+x O 1−y om WDX), da k g ay band second nex o Ta- oil: Ta46Mn54 (second η-phase) and da k La es phase Ta40.6Mn59.4. X. Yan, P. B ož, J. Vřešťál e al. Jou nal o Alloys and Compounds 865 (2021) 158715 9 E = 233.9 ± 16 GPa, espec i ely, e alua ed om he nanoinden e measu emen s as well as wi h he DFT alue E H = 197 calcula ed o NbMn 2 [32] ( o de ails see Table 7). Fo he calcula ions o he bulk modulus, B, and he shea mod- ulus, G, he ollowing equa ions we e applied: = = + BE 3(1 2 ) , G E 2( 1) . (8) The esul s o TaMn 2 , B ~ 277 GPa, G ~ 86 GPa, a e sligh ly highe han hose o NbMn 2 wi h B ~ 242 GPa, G ~ 75 GPa ( o de ails see Table 7). This bulk modulus alue o NbMn 2 is ai ly consis en wi h he alues ob ained om DFT calcula ions o a p e ious wo k o he au ho s [24] wi h B ~ 250 GPa o he pa amagne ic and B = 200–220 GPa o e omagne ic and an i e omagne ic NbMn 2 . Acco ding o he c i e ion o Pugh [65] ha ma e ials wi h <G/B 1.75 a e b i le, bo h compounds NbMn 2 and TaMn 2 wi h =G/B 0.309 classi y as b i le. Fo iso opic compounds, i is possible o de e mine he Debye empe a u e, θ D om he sound eloci y, using Ande son’s Eq. (9) [66]: = h k 3nLd 4M , D B 1/3 m (9) whe e h is he Plank’s cons an , k B is he Bol zmann’s cons an , L is Loschmid ’s numbe , d is he densi y, M is he molecula weigh , and n is he numbe o a oms. The mean sound eloci y m ollows om ela ions (10) [66]: = + = + = 1 3 2 1 wi h 3B 4G 3d and G d m T 3L 3 1/3 L 1/2 T 1/2 (10) Whe eas o NbMn 2 Debye empe a u es o θ D = 423 K (MI) and θ D = 424 K (NI), we e calcula ed, we a i e o TaMn 2 a somewha smalle alues o θ D = 378 K (MI) and θ D = 377 K (NI), espec i ely. F ac u e oughness is a measu e o he esis ance o a ma e ial o c ack p opaga ion. As can be seen in he inse o Fig. 17, c acks we e p oduced om he imp in , om which we calcula e he inden a ion ac u e oughness K IC using Eq. (11): =KE HV F c, IC 1/2 3/2 (11) whe e E is he Young’s modulus, HV is he ha dness, F is he in- den a ion load, c is he adial c ack leng h om he cen e o he Vicke s inden a ion and β is a unc ion o he inden e angle, which o Vicke s inden a ion is β = 0.016(4). The inden a ion ac u e oughness usually is subs i u ed o ac u e oughness in case o b i le ma e ials, o o samples no big enough o quali y o he s anda d me hods o de e mine ac u e oughness (like he Che on No ched Flexu e Specimen me hod, he Single-Edge P ec acked Beam me hod o he sha p ‘V′ no ch beam me hod). The esul s a e Fig. 15. Tempe a u e dependen elec ical esis i i y, ρ(T), o NbMn 2 (Nb34Mn66) and TaMn 2 (Ta33Mn67). Solid lines indica e en a i ely assigned esidual esis i i y plus Bloch-G üneisen elec on-phonon sca e ing con ibu ions (see ex ). Fig. 16. Es ima ed esis i i y con ibu ions, Δρ(T), due o elec on-elec on and elec- on-pa amagnon sca e ing ob ained by sub ac ing o he con ibu ions as en a- i ely indica ed by dashed lines in Fig. 15. Solid lines a e powe law i s o he low- empe a u e beha io (see ex ). Fig. 17. S a ic and dynamic (MI) ha dness, HV, o NbMn 2 and TaMn 2 s. load. The solid lines a e guides o he eyes. The scale on he y-axis ( igh ) ans e s HV alues o GPa. Inse : Imp in wi h c ack p opaga ion lines. X. Yan, P. B ož, J. Vřešťál e al. Jou nal o Alloys and Compounds 865 (2021) 158715 16 almos alike o hose o measu ed ac u e oughness da a. E alu- a ing many c ack leng hs o a ious loads om s a ic and dynamic ha dness imp in s, yields a K IC = 1.1 ± 0.5 MPa m 1/2 o NbMn 2 and K IC = 1.5 ± 0.2 MPa m 1/2 o TaMn 2 . F om σ ≈ E 1/2 a ough es ima ion o he ac u e s eng h can be de i ed, which e eals o NbMn 2 σ ≈ 14 GPa 1/2 and o TaMn 2 σ ≈ 15 GPa 1/2 . The mal expansion o NbMn 2 was measu ed in he empe a u e ange o 4.2–300 K (Fig. 19). The co esponding T( ) 0 s. T cu e shows a s ic ly linea beha io abo e 150 K. Consequen ly, a linea i in he empe a u e ange o 150–300 K e eals a he mal expansion coe icien α = 10.9 × 10 −6 Κ −1 . Besides ex ac ing he he mal expan- sion coe icien , he semi-classical ea men by Mukhe jee e al. [67] was applied o analyze he he mal expansion as a unc ion o em- pe a u e, aking in o accoun he Debye model o acous ic phonons and he Eins ein app oxima ion o he op ical modes. The leng h change T( ) 0 is gi en by: = = + = + ( ) ( ) ( ) , x T [ G F ] 3k T , T x( ) x x T2 23g 4c 2 3 3 pBT3 0 z dz e 1 p 3 p k e 1 T T 0 0 02 D D T3 zB E D/T (12) whe e δ is he elec onic con ibu ion o he a e age la ice dis- placemen , θ D is he Debye empe a u e, θ E is he Eins ein em- pe a u e, and p is he a e age numbe o phonon b anches ac ually exci ed o e he empe a u e ange. G, F, c, and g a e u he ma e ial dependen cons an s. The Debye and Eins ein empe a u e, ex- ac ed ia a leas -squa es i o he expe imen al da a we e θ D = 413 K and θ E = 87 K, wi h θ D in e y good ag eemen wi h he da a gained ia elas ic moduli and elec ical esis i i y. 5. Summa y/conclusion Based on a de ailed e-in es iga ion, he cons i u ion o he wo phase diag ams Nb-Mn and Ta-Mn has been es ablished om 600 °C o he mel ing ange: he sys ems a e cha ac e ized by MgZn 2 - ype La es phases (C14), which a e he only bina y compounds in hese sys ems bu e eal ex ended homogenei y egions (each in- cluding he s oichiome ic composi ion): Nb 1+x Mn 2−x (62.5–73.0 a % Mn a 950 °C: −0.19 ≤ x ≤ 0.125) and Ta 1+x Mn 2−x (59.5–68.5 a % Table 7 Elas ic cons an s c ij o NbMn 2 (all in GPa; densi y d = 8.15 g/cm 3 ) and o TaMn 2 (d = 11.86 g/cm 3 ; c 66 = (c 11 -c 12 )/2); shea modulus G; bulk modulus B; Young’s modulus E; subsc ip s V, R, H e e o Voig , Reuss limi s and Hill a e age; Poisson’s a io ν; mean sound eloci y m in ms −1 ; Debye empe a u e θ D in K; e e ences ( .w. = his wo k); alues in cu si e sc ip we e comple ed in his wo k om he C ij ma ix o he au ho [24,32]. c 11 E (010) c 12 c 13 c 33 E (001) c 44 G V G R G H B V B R B H E V E R E H ν m θ D Re . NbMn 2a 346 218 180 384 68 73 71 72 248 248 248 200 194 197 0.36 3214 410 [24,32] 341# 75# 75# 242# 203# 3407# 423# .w. TaMn 2 391# 86# 86# 277# 233# 0.36 3025# 378# .w. a Fo pa amagne ic C14- ype; # da a ex ac ed om mic oinden a ion and nanoinden a ion measu emen s. Table 8 P ope ies (s a ic ha dness (HV 0.1 (s a .) in GPa), dynamic ha dness ia mic oinden e (HV 0.1 (MI) in GPa), dynamic ha dness ia nanoinden e (HV 0.01 (NI) in GPa), Bulk modulus B (DFT) in GPa, Debye empe a u e calcula ed wi h E (MI) (θ D (MI)) in K, ac u e esis ance, (K IC ) in MPam 1/2 , Debye empe a u e calcula ed wi h E (NI) (θ D (MI)) in K, Debye empe a u e ia Mukhe jee- i (θ D (MUK)) in K, Eins ein empe a u e ia Mukhe jee- i (θ E ) in K, he mal expansion coe icien (α)*10 −6 in K −1 . P ope ies NbMn 2 TaMn 2 Re . HV 0. 1 (s a .) 823 (9.2) 900 (10.1) w. HV 0.1 (MI) 735 (7.5) 815 (7.9) w. HV 0.01 (NI) 724.7 (7.1) 815.9 (8.0) w. HV – 730 [17] HV 1040–1250 1020 [13] B (DFT), pa amagne ic 250 – [24] B (DFT), e omagne ic 200–220 – [24] B (DFT), an i e omagne ic 220 – [24] θ D (C p ) ~430 ~370 w. θ D (U ij ) 397 – w. θ D ( he m. exp.) 413 – w. θ E ( he m. exp.) 87 – w. θ E (C p ) ~166 ~135 w. α 10.9 – w. K IC 1.1 1.5 w. Fig. 18. Elas ic modulus, E, s. load o NbMn 2 and TaMn 2 . The solid lines a e guides o he eye. Fig. 19. Tempe a u e dependen dila ome ic he mal expansion o NbMn 2 . S a s e- p esen SC X- ay da a om Table 2. Fo he i see ex . X. Yan, P. B ož, J. Vřešťál e al. Jou nal o Alloys and Compounds 865 (2021) 158715 17 Mn: −0.055 ≤ x ≤ 0.215). Abou 20 samples ha e been p epa ed in each sys em, mainly by a c- o high equency mel ing elemen al ingo s, in some cases also cold compac ed powde blends. The in- es iga ion o he cons i u ion comp ised ligh op ical and ans- mission and scanning elec on mic oscopy (TEM and SEM) wi h ene gy dispe si e (EDX) as well as wa eleng h dispe si e (WDX) X- ay spec oscopy, X- ay powde (XPD) and single c ys al (XSCD) di ac ion, di e en ial he mal analysis (DTA) and/o di e en ial scanning calo ime y (DSC). Whe eas NbMn 2 mel s cong uen ly a T m (NbMn 2 ) = 1515 ± 15 °C, TaMn 2 mel s incong uen ly wi h T m (TaMn 2 ) = 1797 ± 40 °C close o a deple ed pe i ec ic eac ion. Bo h La es phases engage in eu ec ic eac ions wi h manganese: ℓ ↔ (Mn) + TMn 2 (T eu = 1220 ± 10 °C a 4.9 a % Nb and T eu = 1234 ± 10 °C a 0.7 a % Ta, espec i ely). NbMn 2 also o ms a eu ec ic wi h (Nb): ℓ ↔ (Nb) + NbMn 2 a T eu = 1493 ± 15 °C a 53.2 a % Nb. In bo h sys ems, Mn e eals e- ma kably la ge maximum solid solubili ies (a he eac ion iso- he ms 1493 °C (Nb) and 1797 °C o (Ta)): 19.4 a % Mn in (Nb) and 21.3 a % Mn in (Ta). De ailed in es iga ion (SEM-WDX, TEM, Rie eld-XPD) on he s abili y and s uc u e o he phases, “NbMn” and “TaMn”, adop ed ea lie in he li e a u e as bina y sys em inhe en compounds, clea ly e ealed hese phases o be oxygen-s abilized adop ing he Ti 4 Ni 2 O ype (so-called e a(η)-phases) wi h modi ied Nb(Ta)/Mn si e subs i u ion o comply wi h he o mula Nb(Ta) 3−x Mn 3+y O 1−y (W 3 Fe 3 C- ype). We also emphasize ha no hin s we e ound in ou analyses o he exis ence o a μ-phase Nb 6 Mn 7 o Ta 6 Mn 7 (W 6 Fe 7 - ype; space g oup R 3 m). Magne ic suscep ibili y and magne iza ion measu emen s documen ed ha bo h e a-phases η-Nb 3 Mn 3 O 1−y and η-Ta 3 Mn 3 O 1−y a e e omagne ic below T c ~ 77 K, whe eas he La es phases NbMn 2 , TaMn 2 a e empe a u e independen pa amagne ic. Fu he mo e, ou DFT calcula ions de ine ins abili y o he e a-phase Ta 3 Mn 3 wi hin he bina y sys em (wi h espec o he weigh ed a io o he C14 La es phase TaMn 2 and pu e bcc Ta). Addi ionally, he ab ini io calcula ions con i med (i) he s abilizing e ec o oxygen on he e a-phase and (ii) he p e e ence o oxygen a oms o subla ices in he sequence 16d (W 3 Fe 3 C- ype)> 8b> 8a (W 6 Fe 6 C- ype) in space g oup Fd 3 m. The expe imen ally de i ed cons i u ion o he Nb-Mn and Ta- Mn sys ems se ed as he basis o CALPHAD calcula ions esul ing in a comple e se o op imized he modynamic da a o each sys em. The CALPHAD op imiza ion was suppo ed by DFT calcu- la ed hea s o o ma ion o a ious con igu a ions o he C14 La es phases. Tempe a u e dependen X- ay single c ys al da a (100–300 K) o NbMn 2 as well as oom empe a u e SC da a o Ta 1.05 Mn 1.95 p o ided de ails on a om si e dis ibu ion and he mal expansion (CTE-NbMn 2 = 10.9 × 10 −6 K −1 ). The modynamic and anspo p ope ies (speci ic hea , elec ical esis i i y and magne ic sus- cep ibili y/magne iza ion, om 2 o 300 K) classi y bo h La es phases wi h me allic beha io whils mechanical p ope ies (elas ic moduli om DFT and nanoinden a ion as well as ha dness and he mal expansion) g oup bo h La es phases among a he ha d (HV-NbMn 2 = 800, HV-TaMn 2 = 900) and b i le in e me allics (K IC = 1.1 ± 0.5 MPa m 1/2 o NbMn 2 and K IC = 1.5 ± 0.2 MPa m 1/2 o TaMn 2 ). CRediT au ho ship con ibu ion s a emen All au ho s ha e con ibu ed equally o he wo k. Decla a ion o Compe ing In e es The au ho s decla e ha hey ha e no known compe ing i- nancial 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 . Acknowledgemen This esea ch was suppo ed by he Czech Science Founda ion unde p ojec s GA 17-12844S and CZ.02.1.01/0.0/0.0/17_049/ 0008399. 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