1
Assessmen o he composi ional equi emen s o o m Fe-Mn-C
aus eni e-ma ensi e composi es
Ma cel Muencha, Reza Gholizadehb, Myeong-heom Pa kb, Nobuhi o Tsujib, Ma in Pe e lechne c, Yoli a
M. Eggele c, Jan L. Riedela, Michael K. Eus e holza,d, Ma in Heilmaie a and Alexande Kau mann*e
a Ins i u e o Applied Ma e ials (IAM-WK), Ka ls uhe Ins i u e o Technology (KIT), Kaise s aße
12, 76131 Ka ls uhe, Ge many
b Depa men o Ma e ials Science and Enginee ing, Kyo o Uni e si y, Sakyo-kyu, Kyo o 606-8501,
Japan
c Labo a o y o Elec on Mic oscopy (LEM), Ka ls uhe Ins i u e o Technology (KIT), Engesse s . 7,
76131 Ka ls uhe, Ge many
d Ka ls uhe Nano Mic o Facili y (KNMFi), Ka ls uhe Ins i u e o Technology (KIT), He mann- on-
Helmhol z-Pla z 1, 76344 Eggens ein-Leopoldsha en, Ge many
e Ins i u e o Ma e ials (IM), Ruh Uni e si y Bochum (RUB), Uni e si ä ss aße 150, 44780
Bochum, Ge many
* co esponding au ho
mail: alexande .kau mann@ ub.de (A. Kau mann)
phone: +49 234 32 18430
Abs ac
Recen ly, a new gene a ion o high s eng h s eels was in oduced by u ilizing a la e al chemical pa e n
1
o an aus eni e s abilize o c ea e mic os uc u es o aus eni e γ and ma ensi e α’ a e quenching. A
2
e na y Fe-Mn-C pea li e is a sui able ini ial s a e o his i Mn e ec i ely pa i ions in o he cemen i e.
3
In he p esen s udy, wo model Fe-Mn-C alloys we e pea li e ea ed ou side he well-es ablished local
4
equilib ium, Mn pa i ioning egime (P-LE). A comple e pea li e o ma ion was achie ed no only o
5
Fe-3.0Mn-3.0C (a .%, Alloy A) a high pea li e o ma ion empe a u e bu also o Fe-6.9Mn-3.2C
6
(a .%, Alloy B) a low ans o ma ion empe a u e. The mo phology o he pea li e included ine-scaled
7
ibe s and lamellae. E en hough ou side he P-LE egion, signi ican Mn pa i ioning in o cemen i e
8
was ob ained o bo h alloys. Pea li e was o med a app oxima ely he o e all Mn con en , while
9
g owing ei he en iched o deple ed in C o mos o he eac ion. The success ul applica ion o a sho
10
ime aus eni iza ion ea men was p o en o bo h alloys ans o ming he pea li e in o α’ + γ
11
mic os uc u es while e aining he ini ial pea li e mo phology. Thus, ine-s uc u ed α’ + γ can be
12
syn hesized om pea li e p ocessed well ou side he es ablished Mn pa i ioning egimes, opening a
13
much la ge composi ional and p ocessing space.
14
Keywo ds
Pea li e, Aus eni e, Ma ensi e, Fe-Mn-C, T ans o ma ion
15
2
1 In oduc ion
In 2018, Sun e al. [1] in oduced a p omising p ocessing ou e o achie e an ou s anding combina ion
16
o s eng h and duc ili y in Mn con aining s eels by ine-scaled aus eni e-ma ensi e mic os uc u es.
17
The basic p emise is o o m a chemical Mn pa e n in aus eni e γ-(Fe,Mn,C) p io o quenching. The
18
Mn pa e n ge s in oduced ia an ini ial pea li e o ma ion, whe e Mn is s ongly en iched in he
19
cemen i e θ-(Fe,Mn)3C compa ed o he e i e α-(Fe,Mn,C). These phases will be abb e ia ed as γ, θ
20
and α, espec i ely. In a subsequen sho ime aus eni iza ion (STA) ea men , he chemical Mn pa e n
21
emains s able unde sui able p ocessing condi ions, e en a e he comple e ans o ma ion o γ. Rapid
22
cooling a e comple ion o he γ ans o ma ion esul s in a mic os uc u e simila in mo phology and
23
dimensions o he ini ial pea li e, consis ing o ma ensi e α’-(Fe,Mn,C) (Mn deple ed egions,
24
abb e ia ed wi h α’) and aus eni e γ (Mn en iched egions). By addi ional empe ing ea men s,
25
ema kable ul ima e ensile s eng h and s ain o ailu e combina ions o 1.6-2.1 GPa and 7-10 % we e
26
achie ed [1].
27
These esul s we e achie ed wi h a hypo-eu ec oid alloy composi ion o Fe-4.3Mn-2.3C (a .%, Fe-
28
4.4Mn-0.5C in w .%) [1]. To es he limi s o his scheme, one ob ious possibili y would be he
29
manipula ion o he alloy composi ion. As he inal mic os uc u e and he e o e also he esul ing
30
mechanical p ope ies s ongly depend on he Mn pa e n, a a ia ion o he o e all Mn con en would
31
be a easible objec i e o ailo ing he mechanical p ope ies. Howe e , he ecen endea o s on his
32
opic [1–5], including he o iginal wo k, s ic ly ocus on Mn con en s in a ange o only 2-5 a .% Mn
33
and a C con en ha esul s in an o e all hypo-eu ec oid composi ion. This na ow composi ional ange
34
migh be a ionalized by wha was sugges ed in he ea ly wo k o Hu chinson e al. [6] on he g ow h
35
kine ics and local equilib ium (LE) condi ions o Fe-Mn-C pea li e. Thei wo k p esen s wo di e en
36
design p inciples o p edic he LE a he eac ion on o pea li e o ma ion: one o ans o ma ions
37
occu ing in he h ee-phase egion o α + θ + γ, and ano he o he wo-phase egion o α + θ.
38
The design p inciples in Re . [6] a e s ic ly limi ed by he cons uc ion o wo Mn pa i ioning
39
bounda ies ha o igina e om a sepa a e LE design app oach o p o-eu ec oid α and θ o ma ion. The
40
app oach is based on he as ly di e en di usion coe icien s o in e s i ial, as -di using C compa ed
41
o subs i u ional, slow-di using Mn. The di usi i y a io is abou 104 – 106 [7]. The bounda ies ma k
42
he composi ional and empe a u e ansi ion o a eac ion whe e Mn pa i ioning is no longe
43
he modynamically necessa y be ween α/γ and θ/γ, espec i ely. These undamen als ha e i s been
44
ans e ed quali a i ely om he p o-eu ec oid eac ions o pea li e o ma ion by Coa es and Hille [7,
45
8], as he co esponding eac ion on exhibi s LEs o bo h α/γ and θ/γ. Wi h he simul aneous
46
applica ion o bo h pa i ioning bounda ies, wo majo egimes we e de i ed: (i) a pa i ioning egime
47
(P-LE) whe e he pa i ioning c i e ia wi h γ a e ul illed o bo h α and θ and (ii) a negligible-
48
pa i ioning egime (NP-LE) whe e he c i e ia a e no sa is ied o ei he o he wo. As he pea li e
49
o ma ion wi h a su icien ly s ong Mn pa i ioning is a p e equisi e o he a o emen ioned p ocessing
50
ou e, he in oduc ion o hese egimes hea ily es ic s he applicable ange o alloy composi ions and
51
ans o ma ion empe a u es, as s aying inside he P-LE egime seemed easonable [6].
52
Wha has no been expe imen ally add essed in li e a u e hus a is he exis ence o an addi ional hi d
53
and ou h egime besides P-LE and NP-LE. In hese egimes, only one o he wo pa i ioning c i e ia
54
is ul illed, ei he o α o θ. The egime o in e es o his wo k is he one ha ul ills he Mn pa i ioning
55
c i e ion o α, bu no o θ. I includes a la ge ange o empe a u es and composi ions, especially a
56
highe Mn and C con en s, which ha e ye o be es ed o Mn pa i ioning and he possibili y o apply
57
he in ended STA p ocessing. Howe e , wi h inc easing Mn con en he eu ec oid line as well as he
58
3
h ee-phase ield ha sepa a es he γ single-phase ield and he α + θ wo-phase ield, shi o lowe
59
empe a u es [9]. A lowe ans o ma ion empe a u e as well as high con en s o he slow-di using Mn
60
will esul in a cu en ly unknown e a da ion o he pea li e ans o ma ion. Ano he aspec ha needs
61
o be conside ed a such e a ded eac ion eloci ies is he o ma ion o me as able phases o o he
62
mic os uc u es besides α + θ pea li e. In case o Fe-Mn-C, po en ial o ma ion o M5C2 [10] and M23C6
63
ca bides needs o be conside ed, wi h M ep esen ing me allic elemen s. Thei o ma ion has been
64
epo ed o example in C - ich and Al- ich, Mn-con aining s eels [10, 11].
65
Thus, he ollowing esea ch ques ions will be add essed in he p esen s udy:
66
1. Does a pea li e ea men o a low Mn con aining Fe-3.0Mn-3.0C (a .%) a 600 °C and o a
67
high Mn con aining Fe-6.9Mn-3.2C (a .%) a 540 °C esul in an en i ely ans o med
68
mic os uc u e comp ising pea li e ha only consis s o α and θ?
69
2. Does pea li e in hese Fe-Mn-C alloys exhibi conside able Mn pa i ioning in o θ and how does
70
i compa e o global equilib ium (GE) and LE condi ions?
71
3. Is i possible o achie e a α’ + γ mic os uc u e by sho - ime aus eni iza ion om hese pea li e
72
condi ions?
73
2 Expe imen s and Simula ions
The design o he Mn pa i ioning bounda ies was i s de eloped o p o-eu ec oid α and θ o ma ion [7,
74
12] and quan i a i ely applied o Fe-Mn-C pea li e o ma ion by Hu chinson e al. [6]. Thei applica ion
75
o gi en iso he mal sec ions is shown in Fig. 1. I di ides he pa ame e space, desc ibed by 𝑋C and
76
𝑋Mn as he mola ac ion o C and Mn, espec i ely, in o ou egions. The ep esen a ion in Fig. 1,
77
howe e is gi en by using he de i ed quan i ies 𝑈C=𝑋C/(1−𝑋C) and 𝑈Mn =𝑋Mn/(1−𝑋C)
78
acco ding o he ea men by Hille [8, 12] as well as Coa es [7] and Hu chinson [6]. A de ailed
79
explana ion o he physical meaning and p ac ical usage o hese a iables can be ound in he
80
Supplemen a y Ma e ial o his a icle. The empe a u es o 600 (Fig. 1 a)) and 540 °C (Fig. 1 b)) we e
81
selec ed o cap u e a po en ially as ans o ma ion a low Mn con en s and a e a ded one a high Mn
82
con en s, espec i ely. The design o he pa i ioning bounda ies (do -dashed, pu ple lines in Fig. 1) a e
83
adop ed om Re . [7] and comp ehensi ely desc ibed o he p esen cases in he Supplemen a y
84
Ma e ial, Fig. S1. The he modynamic da a was ob ained using he 2023 PanHEA da abase in he Panda
85
so wa e p o ided by CompuThe m (USA). The heo e ical da a on he phase ield posi ions o he Fe-
86
Mn-C sys em a e in good ag eemen wi h expe imen al li e a u e da a in he ele an composi ional
87
ange [1, 9, 13–21]. All addi ional he modynamic LE conside a ions ha a e no cap u ed by Panda
88
we e ob ained using sel -de eloped Ma lab sc ip s which a e published public domain [22].
89
As men ioned in Sec. 1, ou o he ou egimes o med by he use o he wo pa i ioning bounda ies,
90
only wo ha e been add essed in li e a u e hus a [6–8]: The P-LE egime (highligh ed in pu ple) and
91
he NP-LE egime (highligh ed in g ay). Fo he pea li e ans o ma ion, hese wo egimes a e uniquely
92
de ined by he ul illmen o he wo independen Mn pa i ioning c i e ia be ween α and γ as well as θ
93
and γ (see Supplemen a y Ma e ial Fig. S1).
94
The egime o he igh o he in e sec ion o he wo do -dashed pu ple lines in Figs. 1 a) and b) is he
95
scope o he p esen a icle. I includes high o e all Mn con en s which hold he po en ial o s abilizing
96
la ge ac ions o γ in he inal mic os uc u e a e STA. He e, he pa i ioning c i e ia a e ul illed o
97
α, bu no o θ o ma ion.
98
Inside his egime wo model alloys, Alloy A and Alloy B, we e selec ed. They lie inside he α + θ wo-
99
phase ield as well as inside he me as able ex ensions o he α + γ and γ + θ phase ield bounda ies o
100
4
a oid p o-eu ec oid α o θ o ma ion. The nominal composi ions o he Mn-lean Alloy A and he Mn-
101
ich Alloy B a e Fe-3.0Mn-3.0C and Fe-6.9Mn-3.2C (a .%, Fe-3.0Mn-0.7C and Fe-7.0Mn-0.7C in
102
w .%), espec i ely.
103
Fig. 1: Fe-Mn-C iso he mal sec ions a a) 600 °C and b) 540 °C. Black bold lines illus a e he phase ields in GE. Black do ed
lines indica e he me as able ex apola ions o he α + γ and γ + θ phase ield bounda ies. The pu ple do -dashed lines ep esen
Mn pa i ioning bounda ies o α (nea ho izon al) and θ (nea e ical). P-LE and NP-LE egions a e ma ked pu ple and g ay,
espec i ely. Alloys A and B, bo h lie ou side hese egions. The expe imen ally de e mined composi ions lis ed in Tabs. 1 and
2 a e displayed.
Alloy manu ac u ing was done by a c mel ing high pu i y bulk elemen s as well as an in-house
104
syn hesized Fe3C ob ained by he same me hod. The elemen s Mn (e ched nominal pu i y 99.8 %) and
105
g aphi e (nominal pu i y 99.999 %) we e p o ided by chemPUR GmbH (Ge many). Fe (nominal pu i y
106
99.99 %) was p o ided by Al a Aesa (Uni ed S a es). A c mel ing was conduc ed in an AM/0.5 u nace
107
p o ided by Edmund Bühle GmbH (Ge many). The u nace chambe was e acua ed o 5∙10−2 mba
108
and illed wi h A . This p ocess was epea ed o h ee imes in o al in o de o pu i y he mel ing
109
a mosphe e. Then, a acuum o less han 1∙10−4 mba was es ablished. The p ocessing chambe was
110
hen illed wi h A once mo e o a p essu e o 600 mba . Residual O2 wi hin he u nace chambe was
111
ge e ed by lique ying a Z g anule be o e mel ing he bulk elemen s. E e y manu ac u ed ingo was
112
lipped and e-mel ed a leas i e imes. The alloy ingo s we e homogenized u ilizing a STF15/450 21-
113
601449 ube u nace by Ca boli e Ge o GmbH & Co. KG (Ge many) wi h lowing high pu i y A
114
a mosphe e. The hea ea men empe a u e was 1100 °C o a dwell ime o 96 h. Hea ing and cooling
115
we e conduc ed a a a e o 115 K/h. The chemical composi ion was de e mined h ough op ical emission
116
spec oscopy (OES) by analyzing bo h, he op and bo om side a e he las e-mel ing s ep. The esul s
117
a e displayed in Tabs. 1 and 2 o Alloys A and B, espec i ely. The s anda d de ia ion o all elemen s
118
was de e mined o be < 0.07 a .% (0.07 w .%). Samples o u he in es iga ions we e cu om he
119
alloy ba ches using a high-speed o a o y cu ing de ice (S ue s, F ance).
120
Pea li e o ma ion was ca ied ou in ai a a mosphe ic p essu e using wo p e-hea ed box u naces.
121
A e comple ion o he p io aus eni iza ion s ep a 910 °C o 1 h, an immedia e u nace ans e was
122
pe o med. Pea li e in Alloy A and Alloy B was o med a 600 °C o 16 h and 540 °C o 96 h,
123
espec i ely, based on ini ial ials o ob ain ele an empe a u e/ ime combina ions. The hea
124
ea men s we e concluded by oil quenching.
125
The STA ea men s we e done in a p e-hea ed box u nace a 770 °C o 150 s and also concluded by
126
oil quenching. To ensu e a high hea ing a e, he samples we e co e ed by p e-hea ed Al2O3 powde a
127
he s a o he ea men .
128
5
The samples o mic os uc u e cha ac e iza ion we e p epa ed by wa e -cooled g inding wi h SiC pape
129
ollowed by s anda d me allog aphic polishing s eps wi h 3 and 1 µm polyc ys alline diamond
130
suspensions. As a inishing s ep, polishing wi h Mas e Me -2 by Buehle (USA) was pe o med o
131
5 min. Samples we e subsequen ly e ched in a 1 % Ni al solu ion o 5 s. The g inding p ocess was
132
ca ied ou o emo e any deca bu ized laye ha has o med du ing he hea ea men s. Mic os uc u e
133
cha ac e iza ion was pe o med by scanning elec on mic oscopy (SEM). Fo seconda y elec on (SEM-
134
SE) as well as backsca e ed elec on (SEM-BSE) con as imaging, a Leo Gemini 1530 ield-emission
135
SEM by Zeiss (Ge many) was u ilized. Low magni ica ion, wide ield o iew mic og aphs wi h high
136
esolu ion we e ob ained by au oma ed s i ching in Mic oso Image Composi e Edi o . The
137
quan i ica ion o mic os uc u al de ails including he a ea ac ions o he cons i u ing phases and
138
mo phologies was ca ied ou using he ImageJ so wa e. Es ima es o he ac ions o egions o simila
139
mo phology we e done by manually selec ing and asse ing egions wi h θ aspec a ios close o one as
140
ib ous. Fibe s o ien ed pa allel o he sample su ace we e he e o e iden i ied as lamellae. Mic og aphs
141
o all analysis we e selec ed andomly and a di e en magni ica ion o enable bo h a la ge o e all a ea
142
o in es iga ion as well as high accu acy o he imaging. The di e ence in o al a ea mapped be ween
143
di e en magni ica ion mic og aphs was conside ed. The de e mined a ea ac ions we e con e ed in o
144
olume ac ions unde he assump ion o isome y and iso opy. A mo e de ailed assessmen o
145
pa ame e s like θ spacing o θ mo phology ac ion would equi e 3D me hods o mic os uc u e
146
analysis, e.g. FIB omog aphy, and was no scope o he p esen s udy.
147
Phase iden i ica ion was done by means o ansmission synch o on X- ay di ac ion (XRD) a
148
beamline BL13XU, SP ing-8 o he Japan Synch o on Radia ion Resea ch Ins i u e (JASRI). The
149
di ac ion expe imen s we e pe o med using monoch oma ic synch o on adia ion a an ene gy o
150
30 keV (
λ
= 0.0413 nm) and 30 s exposu e ime. The calib a ion o he 2θ ze o-shi and sample
151
displacemen was done wi h a s anda d specimen o ce ia (CeO₂). Addi ionally, local analysis o he
152
cons i u ing phases was pe o med ia selec ed a ea elec on di ac ion (TEM-SAED) wi h a JEM-
153
2100F by Jeol (Japan) and a Ti an3 by FEI (USA) ansmission elec on mic oscope (TEM) ope a ed a
154
200 kV and 300 kV, espec i ely. Fo de e mining he local composi ion o he phases, bo h ene gy
155
dispe si e X- ay spec oscopy in scanning TEM (STEM-EDS) as well as a om p obe omog aphy (APT)
156
we e conside ed. Howe e , due o signi ican inaccu acies in oduced by quan i ying he C con en , APT
157
was selec ed as he supe io me hod bo h in e ms o da a accu acy and spa ial esolu ion [23]. The
158
expe imen s we e pe o med on bo h alloys a e pea li e o ma ion wi h a LEAP 4000X HR by Cameca
159
(F ance). Da a p esen ed in he main a icle we e gene a ed in ol age mode, while addi ional da a
160
depic ed in he Supplemen a y Ma e ial we e gene a ed in lase mode. Tip p epa a ion was done ia
161
ocused ion beam (FIB) milling wi h an Au iga 60 by Zeiss (Ge many). Tips p esen ed in he
162
Supplemen a y Ma e ial we e coa ed wi h C o inc ease ip s abili y, ollowing he ou ine used in
163
Re . [24]. Peak decomposi ion was equi ed o he θ egions, which was applied by he in eg a ed
164
ea u e o he AP Sui e 6.3 so wa e (Cameca, F ance). The so wa e decomposes o e lapping peaks by
165
conside ing he emaining unique peak(s) o he species o in e es o he same cha ge and applies he
166
ela i e na u al abundances o weigh he con ibu ion o ha species o he ini ial peak. An example o
167
his would be C2
1+ and C4
2+ in θ. Bo h species exhibi peaks a 24 and 25 Da. Howe e , C4
2+ possesses a
168
unique peak a 24.5 Da as well. Conside ing he na u al abundances o he di e en C4
2+ iso opes, he
169
con ibu ion o he peak a 24 Da and 25 Da can be de i ed, which lea es he emaining coun s o he
170
peaks o C2
1+.
171
6
3 Resul s and Discussion
3.1 Pea li e Fo ma ion
To answe he esea ch ques ions om Sec. 1, i is essen ial o de elop an unde s anding o he
172
in icacies o a comple e Fe-Mn-C pea li e o ma ion and he Mn pa i ioning beha io . Hille [12]
173
p oposed ha o simul aneous Mn and C pa i ioning, he d i ing o ce o C di usion in γ ahead o he
174
eac ion on mus be educed o compensa e o he o de s o magni ude di e ence in di usion
175
coe icien s o he elemen s. A p ac ical way o achie e his condi ion was shown by Hu chinson
176
e al. [6], i.e. γ in con ac wi h ei he g owing θ o α a e equi ed o sha e he same C ac i i y aC
γ. This
177
can be elegan ly applied quan i a i ely o iso he mal sec ions o he e na y phase diag am, as depic ed
178
in Fig. 2. The composi ions o γ ahead o g owing θ and α a e loca ed on he same C iso-ac i i y line in
179
Fig. 2 (blue do s on he C iso-ac i i y line a he in e sec ions wi h he do ed, me as able ex ensions).
180
The o ming θ and α a e ob ained om ollowing he ie lines (blue, solid lines) connec ed o hese γ
181
composi ions. As Hu chinson e al. [6] ob ained a s eady-s a e g ow h o pea li e wi hin he α + θ wo-
182
phase ield wi h cons an g ow h a e and in e phase spacing, an addi ional bounda y condi ion ega ding
183
he o e all composi ion o he g owing pea li e was in oduced. Namely, i s composi ion mus be
184
consis en wi h he alloy composi ion. This can only be achie ed when he connec ing line (blue, dashed
185
line) be ween he g owing θ and α in e sec s he alloy composi ion. This connec ing line does no
186
ep esen a ie line as he wo g owing phases a e no in equilib ium wi h each o he . In wha ollows,
187
his design p inciple is e e ed o as s eady-s a e, C ac i i y-based local equilib ium condi ion (SCA-
188
LE). As depic ed in Fig. 2, he applica ion o he SCA-LE design indica es an en ichmen o Mn in θ
189
du ing pea li e o ma ion e en hough i is being applied o Alloys A and B ou side he P-LE egime.
190
Fig. 2: Schema ic design acco ding o SCA-LE in iso he mal sec ions: a) Alloy A a 600 °C and b) Alloy B a 540 °C. The
illus a ion o he iso he mal sec ion is he same as o Fig. 1. The blue solid lines indica e ie lines while he blue dashed line
is he line connec ing θ and α o ming du ing s eady-s a e pea li e g ow h. The p edic ed en ichmen o Mn in θ is: a) 8.0 a .%
( s. 2.8 a .% in Alloy A) and b) 35.0 a .% ( s. 6.9 a .% in Alloy B).
In Fig. 3, mic og aphs o bo h alloys a e shown a e hei espec i e pea li e ea men s: 600 °C/16 h
191
o Alloy A and 540 °C/96 h o Alloy B. A comple e ans o ma ion was achie ed o bo h alloys. High
192
esolu ion, wide ield o iew mic og aphs ob ained om s i ching p o ing he s a emen a e p o ided
193
ia a public eposi o y [25]. Despi e he lowe ans o ma ion empe a u e, which is usually associa ed
194
wi h a dec ease in lamella spacing [26], Alloy B does no show a clea ly e ined mic os uc u e
195
compa ed o Alloy A. Wi h espec o pea li e mo phology, a no able di e ence be ween he wo alloys
196
is ob ained. Bo h exhibi ex ended egions o ib ous mo phology, comp ising a olume ac ion o
197
(0.91 ± 0.08) and (0.32 ± 0.12) o he pea li e in Alloys A and B, espec i ely. The olume-speci ic
198
phase ac ion o θ is (0.06 ± 0.01) o Alloy A and (0.21 ± 0.02) o Alloy B. Alloy B equen ly
199
7
exhibi s egions o inc easing in e ace spacing owa ds he colony bounda ies, hus, a po en ially la e
200
s ages o he ans o ma ion be o e comple ion. Due o hei low o e all ac ion o (0.02 ± 0.01), hese
201
egions we e no included in he andomly selec ed mic og aphs o de e mine he olume-speci ic phase
202
ac ions.
203
Fig. 3: SEM-SE mic og aphs (Ni al e ching) a e comple ion o pea li e o ma ion: a) Alloy A, 600 °C/16 h and b) Alloy B,
540 °C/96 h. No un ans o med egions we e ound. θ appea s ligh , α appea s da k. Lamella mo phology is indica ed by
yellow, ib ous by ed a ows. High esolu ion, wide ield o iew mic og aphs ob ained om s i ching a e a ailable ia
Re . [25].
To iden i y he cons i u ing phases o bo h alloys a e he pea li e ea men , ansmission XRD
204
expe imen s we e pe o med. Due o la ge pea li e colony size, p e e ed o ien a ion and in ensi ies
205
di e en om powde di ac ion pa e ns we e ob ained. All analyzed peaks we e exclusi ely a ibu ed
206
o ei he α o θ, as shown in Fig. 4 and no e idence o any o he ca bide han θ o un ans o med γ was
207
ound. The (211)θ and (112)θ peaks we e conside ed o uniquely iden i y he ca bide as θ.
208
Fig. 4: T ansmission XRD pa e ns o : a) Alloy A and b) Alloy B. The in ensi y is plo ed as a unc ion o 2Θ. Cha ac e is ic
di ac ion peaks co esponding o α a e ma ked in ed, while peaks associa ed wi h θ a e highligh ed in blue. All ele an peaks
o θ a e highligh ed below he spec a, while he (211)θ and (112)θ peaks we e used o uniquely iden i y he ca bide
Fu he cha ac e iza ion o he pea li e was done ia TEM imaging and elec on di ac ion. Due o he
209
la ge pea li e colony size, TEM specimens we e aken om ep esen a i e egions, i.e. a ib ous colony
210
o Alloy A and a lamella colony o Alloy B. Bo h li ou s we e aken in egions o nea cons an
211
in e ace spacing (73 ± 26 nm) and (104 ± 19 nm), espec i ely. B igh ield mic og aphs as well as he
212
TEM-SAED pa e ns a e shown in Fig. 4. The zone axes in bo h Fig. 4 a) and d) a e pa allel o he
213
[100]θ di ec ion ollowing he la ice pa ame e con en ion, 𝑏 > 𝑎 > 𝑐 o θ. The li ou s we e
214
chosen pe pendicula o he long ibe axes o Alloy A (Fig. 4 a)) and he lamella plane o Alloy B
215
8
(Fig. 4 c)). In such a scena io, ib ous and lamella colonies o in e es canno be dis inguished om one
216
ano he as bo h appea simila a he sample su ace. They can only be dis inguished a e cu ing a FIB
217
ench and subsequen c oss-sec ional imaging. Fo bo h samples, he ansmission XRD esul s
218
ega ding he cons i u ing α and θ phases we e con i med by TEM-SAED pa e ns in Figs. 4 b) and d),
219
espec i ely. Fu he mo e, he o ien a ion ela ionship (OR) was de e mined. The in es iga ed colonies
220
o Alloy A and Alloy B bo h exhibi a ian s o he Isaiche OR wi h 〈111〉α || 〈100〉θ and
221
{12
1}α || {011}θ, which is well es ablished o pea li e [27]. Please no e ha Fig. 4 a) o Alloy A
222
exhibi s a win si e o he OR wi h a (011
)θ habi plane ins ead o (011)θ as o Fig. 4 b). The θ win
223
a ian is o compound cha ac e wi h he habi plane (011)θ, shea di ec ion [011
]θ and shea plane
224
(100)θ. Fu he mo e, he win o ien a ion can be achie ed ia a o a ion o he θ ma ix c ys al a ound
225
he [100]θ di ec ion by 111.8°. This equa es o he angle be ween (011)θ and (011
)θ in he θ uni cell.
226
The Isaiche OR migh al e na i ely be exp essed di e en ly by de ining he habi plane acco ding o
227
{01
1}α || {031}θ. This can be a ibu ed o he e y small angula misma ch (0.3°) be ween he se s o
228
la ice planes in ol ed. Howe e , he angula misma ch becomes mo e appa en o high indexed spo s.
229
Fig. 5: TEM b igh ield mic og aphs (a),c)) and co esponding TEM-SAED pa e ns (b), d)) o : a), b) ib ous egions om
Alloy A and c),d) lamella egion om Alloy B. The zone axes (ZA) in bo h b) and d) a e [111]α || [100]θ.
Samples o APT we e selec ed in simila ashion like he TEM specimens, i.e., li ou ia FIB in a
230
ib ous colony o Alloy A and in a lamella colony o Alloy B, bo h wi hin egions o nea ly cons an
231
in e ace spacing. In o al, ou ips we e analyzed wi h wo o Alloy A s emming om he same colony
232
and wo o Alloy B om di e en colonies. One o each alloy is discussed as an example. The
233
emaining da a ag ees wi h he s a emen s and discussion. The da a is included in Fig. S2, Fig. S3 and
234
Tab. S2 o he Supplemen a y Ma e ial. To allow o a mo e de ailed assessmen o he chemical
235
composi ion, he local phase ac ions we e de e mined a he li ou posi ion om SEM-SE
236
mic og aphs. The local θ olume ac ion o Alloy A is 0.05, while i is 0.19 o Alloy B. These alues
237
we e hen con e ed o he local mola phase ac ions 𝑓m which a e p o ided oge he wi h he alues
238
o α in Tabs. 1 and 2 o Alloys A and B, espec i ely.
239
9
Tab. 1: Composi ions 𝑋, C ac i i y in γ
a
C
γ, mola phase ac ions 𝑓m and 𝑈 o Alloy A acco ding o he modynamic
calcula ions (GE, SCA-LE), expe imen al (exp.) esul s om APT analyses and econs uc ions. + deno es expe imen al da a.
# deno es expe imen al da a adjus ed acco ding o he he modynamic da ase . The o he da a was de i ed om he
he modynamic da ase .
Condi ion
Phase
Posi ion
𝑋C
𝑋Mn
𝑈C
𝑈Mn
a
C
γ
𝑓m
Alloy A
–
–
0.029 +
0.028 +
0.030
0.029
–
–
GE
α
–
1 · 10-4
0.011
1 · 10-4
0.011
–
0.88
θ
–
0.250
0.163
0.333
0.217
–
0.12
SCA-LE
α
γ
1 · 10-4
0.021
1 · 10-4
0.021
–
0.88
θ
γ
0.250
0.080
0.333
0.106
–
0.12
γ
α
0.031
0.114
0.032
0.118
0.29
–
θ
0.020
0.027
0.020
0.027
0.29
–
Exp.
α
–
1 · 10-4 +
0.020 +
1 · 10-4
0.020
–
0.95 +
θ
–
0.262 +
0.218 +
0.355
0.295
–
0.05 +
Recons .
α
γ
1 · 10-4 +
0.020 +
1 · 10-4
0.020
–
0.95 +
θ
γ
0.250 #
0.222 #
0.333
0.296
–
0.05 +
γ
α
0.034
0.111
0.035
0.115
0.33
–
θ
0.017
0.089
0.017
0.091
0.16
–
Tab. 2: Composi ions 𝑋, C ac i i y in γ
a
C
γ, mola phase ac ions 𝑓m and 𝑈 o Alloy B acco ding o he modynamic
calcula ions (GE, SCA-LE), expe imen al (exp.) esul s om APT analyses and econs uc ions. + deno es expe imen al da a.
# deno es expe imen al da a adjus ed acco ding o he he modynamic da ase . The o he da a was de i ed om he
he modynamic da ase .
Condi ion
Phase
Posi ion
XC
XMn
UC
UMn
a
C
γ
𝑓m
Alloy B
–
0.029 +
0.069 +
0.030
0.071
–
–
GE
α
–
1 · 10-5
0.029
1 · 10-5
0.029
–
0.88
θ
–
0.250
0.375
0.333
0.500
–
0.12
SCA-LE
α
γ
1 · 10-5
0.032
1 · 10-5
0.032
–
0.88
θ
γ
0.250
0.350
0.333
0.466
–
0.12
γ
α
0.013
0.179
0.013
0.181
0.09
–
θ
0.010
0.147
0.010
0.148
0.09
Exp.
α
–
2 · 10-4 +
0.020 +
2 · 10-4
0.020
–
0.80+
θ
–
0.221 +
0.293 +
0.284
0.376
–
0.20 +
Recons .
α
γ
1 · 10-4 #
0.020 +
1 · 10-4
0.020
–
0.80 +
θ
γ
0.250 #
0.282 #
0.333
0.376
–
0.20 +
γ
α
0.054
0.158
0.058
0.167
0.76
–
θ
0.011
0.106
0.011
0.107
0.14
–
Two econs uc ed ips a e depic ed in Fig. 6. Bo h show Mn and C en ichmen coinciding in he same
240
egion, a θ ibe (Fig. 6 a)) o Alloy A and lamella (Fig. 6 b)) o Alloy B. The de e mined C con en
241
o θ in all ips (Tab. 1, Tab. 2 and Tab. S2 in he Supplemen a y Ma e ial) de ia es om he
242
s oichiome ic expec a ion, which may be explained by di e en phenomena. Possible scena ios a e
243
discussed in Re . [28, 29]. An addi ional aspec ha could ha e a ec ed he e apo a ion and, he e o e,
244
16
[8] Hille , M.: Phase Equilib ia, Phase Diag ams and Phase T ans o ma ions: Thei The modynamic
446
Basis. In: Phase Equilib ia, Phase Diag ams and Phase T ans o ma ions: Thei The modynamic
447
Basis. Camb idge: Camb idge Uni e si y P ess, 2007, p. 358–366.
448
[9] Benz, R. e al.: The modynamics o he solid phases in he sys em Fe−Mn−C. Me all T ans, 4 (8),
449
1973, p. 1975–1986.
450
[10] Shen, Y.Z. e al.: M5C2 Ca bides in a High-Ch omium Fe i ic/Ma ensi ic S eel. Me all Ma e
451
T ans A, 45 (7), 2014, p. 2950–2962.
452
[11] Cheng, W.-C. e al.: On he Eu ec oid Reac ion in a Qua e na y Fe-C-Mn-Al Alloy:
453
Aus eni e → Fe i e + Kappa-Ca bide + M23C6 Ca bide. Me all Ma e T ans A, 45 (3), 2014, p.
454
1199–1216.
455
[12] Hille , M.: Swedish Ins i u e o Me al Resea ch, 1953.
456
[13] Eckel, J.F., K i obok, V.N.: Alloys o i on, manganese and ca bon-pa VIII. T ans. Am. Soc. S .
457
T ., 21, 1933, p. 846–864.
458
[14] Gensame , M.: Alloys o i on and manganese-pa XII. T ans. Am. Soc. S . T ., 21, 1933, p. 1028–
459
1034.
460
[15] Hille , M., Waldens öm, M.: A he modynamic analysis o he Fe-Mn-C sys em. Me all T ans A,
461
8 (1), 1977, p. 5–13.
462
[16] S e anescu, D., Ka z, S.: The modynamic P ope ies o I on-Base Alloys. In: Cas ing (Edi o s: S.
463
Viswana han e al.). Ohio: ASM In e na ional, 2008, p. 41–55.
464
[17] Bain, E.C. e al.: The equilib ium diag am o i on-manganese-ca bon alloys o comme cial pu i y.
465
T an. Am. Ins . Min. Me all. Eng., (100), 1932, p. 228–256.
466
[18] To au e, W., Linden, K.: Die Umwandlung im es en Zus ande bei Mangans ählen mi Gehal en bis
467
1,2% C und 17% Mn. A chi ü das Eisenhü enwesen, 10 (11), 1937, p. 515–524.
468
[19] Vogel, R., Dö ing, W.: Das Sys em Eisen-Zemen i -Manganka bid-Mangan. A chi ü das
469
Eisenhü enwesen, 9 (5), 1935, p. 247–252.
470
[20] Wal e s, F.M., Wells, C.: Alloys o i on and manganese-pa XIII. T ans. ASM, 23 (3), 1935, p.
471
727–750.
472
[21] Wal e s, F.M., Wells, C.: Alloys o i on, manganese and ca bon-pa XIV. T ans. ASM, 23 (3),
473
1935, p. 751–760.
474
[22] Muench, M., Kau mann, A.: Ma lab code o ‘Assessmen o he composi ional equi emen s o
475
o m Fe-Mn-C aus eni e-ma ensi e composi es’. Ka ls uhe Ins i u e o Technology, 2025.
476
[23] Gaul , B. e al.: A om p obe omog aphy. Na Re Me hods P ime s, 1 (1), 2021, p. 1–30.
477
[24] Schwa z, T.M. e al.: In Si u Me allic Coa ing o A om P obe Specimen o Enhanced Yield,
478
Pe o mance, and Inc eased Field-o -View. Mic oscopy and Mic oanalysis, 30 (6), 2024, p. 1109–
479
1123.
480
[25] Muench, M., Kau mann, A.: Comple ion o Pea li e T ans o ma ion in Fe-Mn-C Alloys wi h 3 and
481
7 w .% Mn. Zenodo, 2025.
482
[26] Mehl, R.F., Hagel, W.C.: The aus eni e: Pea li e eac ion. P og ess in Me al Physics, 6, 1956, p.
483
74–134.
484
17
[27] Zhou, D.S., Shi le , G.J.: Fe i e: Cemen i e c ys allog aphy in pea li e. Me all T ans A, 23 (4),
485
1992, p. 1259–1269.
486
[28] Peng, Z. e al.: Un a eling he Me as abili y o Cn2+ (n = 2–4) Clus e s. J. Phys. Chem. Le ., 10
487
(3), 2019, p. 581–588.
488
[29] Takahashi, J. e al.: S udy on Quan i a i e Analysis o Ca bon and Ni ogen in S oichiome ic θ-
489
Fe3C and γ′-Fe4N by A om P obe Tomog aphy. Mic oscopy and Mic oanalysis, 26 (2), 2020, p.
490
185–193.
491
492
