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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. Thanks a e also due o he OEAD o suppo ia he bi-
la e al WTZ CZ02 and o he MEYS CR ia he bila e al Mobili y
8J19AT011. Compu a ional esou ces we e supplied by he p ojec
"e-In as uc u e CZ" (e-INFRA CZ LM2018140) p o ided wi hin he
p og am “La ge In as uc u es o Resea ch, Expe imen al
De elopmen and Inno a ions“ suppo ed by he Minis y o
Educa ion, You h and Spo s o he Czech Republic.
Appendix A. Suppo ing in o ma ion
Supplemen a y da a associa ed wi h his a icle can be ound in
he online e sion a doi:10.1016/j.jallcom.2021.158715.
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