Effect of Cyclic Martensitic γ-ε-γ Transformations on Diffusion Characteristics of Carbon in an Iron–Manganese Alloy
Carbon-diffusion characteristics in metastable Г18C2 iron–manganese alloy after the cyclic γ-ε-γ (f.c.c.–h.c.p.–f.c.c.) martensitic transitions were investigated using the radioactive-isotope method. As shown, the process of carbon transport acceleration in the alloy phase-hardened by means of the γ...
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Інститут металофізики ім. Г.В. Курдюмова НАН України
2018
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irk-123456789-1679042020-04-15T01:25:56Z Effect of Cyclic Martensitic γ-ε-γ Transformations on Diffusion Characteristics of Carbon in an Iron–Manganese Alloy Bondar, V.Y. Danilchenko, V.E. Mazanko, V.F. Filatov, O.V. Iakovlev, V.E. Carbon-diffusion characteristics in metastable Г18C2 iron–manganese alloy after the cyclic γ-ε-γ (f.c.c.–h.c.p.–f.c.c.) martensitic transitions were investigated using the radioactive-isotope method. As shown, the process of carbon transport acceleration in the alloy phase-hardened by means of the γ-ε-γ transformations was caused by two independent mechanisms. Методом радиоактивных изотопов исследованы диффузионные характеристики углерода в метастабильном железомарганцевом сплаве Г18С2, наклёпанном циклическими мартенситными превращениями γ-ε-γ (ГЦК–ГПУ–ГЦК). Методою радіоактивних ізотопів досліджено дифузійні характеристики Карбону у метастабільному залізоманґановому стопі Г18С2, наклепаному циклічними мартенситними перетвореннями γ-ε-γ (ГЦК–ГЩП–ГЦК). 2018 Article Effect of Cyclic Martensitic γ-ε-γ Transformations on Diffusion Characteristics of Carbon in an Iron–Manganese Alloy / V.Y. Bondar, V.E. Danilchenko, V.F. Mazanko, O.V. Filatov, V.E. Iakovlev // Progress in Physics of Metals. — 2018. — Vol. 19, No 1. — P. 70-94. — Bibliog.: 35 titles. — eng. 1608-1021 PACS: 64.60.Bd, 64.70.kd, 66.10.cd, 66.30.Lw, 81.16.Hc, 81.30.Kf DOI: https://doi.org/10.15407/ufm.19.01.070 http://dspace.nbuv.gov.ua/handle/123456789/167904 en Успехи физики металлов Інститут металофізики ім. Г.В. Курдюмова НАН України |
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Carbon-diffusion characteristics in metastable Г18C2 iron–manganese alloy after the cyclic γ-ε-γ (f.c.c.–h.c.p.–f.c.c.) martensitic transitions were investigated using the radioactive-isotope method. As shown, the process of carbon transport acceleration in the alloy phase-hardened by means of the γ-ε-γ transformations was caused by two independent mechanisms. |
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Bondar, V.Y. Danilchenko, V.E. Mazanko, V.F. Filatov, O.V. Iakovlev, V.E. |
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Bondar, V.Y. Danilchenko, V.E. Mazanko, V.F. Filatov, O.V. Iakovlev, V.E. Effect of Cyclic Martensitic γ-ε-γ Transformations on Diffusion Characteristics of Carbon in an Iron–Manganese Alloy Успехи физики металлов |
| author_facet |
Bondar, V.Y. Danilchenko, V.E. Mazanko, V.F. Filatov, O.V. Iakovlev, V.E. |
| author_sort |
Bondar, V.Y. |
| title |
Effect of Cyclic Martensitic γ-ε-γ Transformations on Diffusion Characteristics of Carbon in an Iron–Manganese Alloy |
| title_short |
Effect of Cyclic Martensitic γ-ε-γ Transformations on Diffusion Characteristics of Carbon in an Iron–Manganese Alloy |
| title_full |
Effect of Cyclic Martensitic γ-ε-γ Transformations on Diffusion Characteristics of Carbon in an Iron–Manganese Alloy |
| title_fullStr |
Effect of Cyclic Martensitic γ-ε-γ Transformations on Diffusion Characteristics of Carbon in an Iron–Manganese Alloy |
| title_full_unstemmed |
Effect of Cyclic Martensitic γ-ε-γ Transformations on Diffusion Characteristics of Carbon in an Iron–Manganese Alloy |
| title_sort |
effect of cyclic martensitic γ-ε-γ transformations on diffusion characteristics of carbon in an iron–manganese alloy |
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Інститут металофізики ім. Г.В. Курдюмова НАН України |
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2018 |
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http://dspace.nbuv.gov.ua/handle/123456789/167904 |
| citation_txt |
Effect of Cyclic Martensitic γ-ε-γ Transformations on Diffusion Characteristics of Carbon in an Iron–Manganese Alloy / V.Y. Bondar, V.E. Danilchenko, V.F. Mazanko, O.V. Filatov, V.E. Iakovlev // Progress in Physics of Metals. — 2018. — Vol. 19, No 1. — P. 70-94. — Bibliog.: 35 titles. — eng. |
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70 ISSN 1608-1021. Prog. Phys. Met., 2018, Vol. 19, No. 1
https://doi.org/10.15407/ufm.19.01.070
PACS numbers: 64.60.Bd, 64.70.kd, 66.10.cd, 66.30.Lw, 81.16.Hc, 81.30.Kf
V.Y. bondar, V.e. danIlChenko,
V.F. Mazanko, o.V. FIlaToV, and V.e. IakoVleV
G.V. Kurdyumov Institute for Metal Physics, NAS of Ukraine,
36 Academician Vernadsky Blvd., UA-03142 Kyiv, Ukraine
effect of cyclic Martensitic
γ – ε – γ transforMations on diffUsion
characteristics of carbon
in an iron–Manganese alloy
Carbon-diffusion characteristics in metastable Г18C2 iron–manganese alloy after
the cyclic γ–ε–γ (f.c.c.–h.c.p.–f.c.c.) martensitic transitions were investigated using
the radioactive-isotope method. As shown, the process of carbon transport accelera-
tion in the alloy phase-hardened by means of the γ–ε–γ transformations was caused
by two independent mechanisms. They are as follow: athermal one realized via the
stress field occurrence under the cyclic martensitic transitions and thermoactivated
one realized during subsequent diffusion annealing due to low-angle subboundaries
as well as the one-dimensional and two-dimensional crystal structure defects in
f.c.c. austenite and h.c.p. ε-martensite generated during these transitions. After the
cyclic γ−ε−γ martensitic transformations, the diffusion coefficient of carbon at low
temperatures (100–350 °C) increased by more than three orders of magnitude. In
this case, the diffusion coefficient at 325 °C corresponds to the stationary diffusion
coefficient at 900 °C. Maximum carbon-diffusion coefficient rising was observed
when number of thermal cycles was increased up to 100 and maximum structure
defects density increasing was fixed. Phase composition variation was as an addi-
tional cause of carbon-diffusion characteristics changing during the γ–ε–γ cycling
and subsequent diffusion annealing.
Keywords: diffusion, martensite, austenite, radioisotope, dislocation, stacking fault
defect.
introduction
Different phase transformations can efficiently affect the diffusive mo-
bility of substitutional and interstitial atoms in metastable alloys. The
degree and quality of such an influence depend on the structural state
ISSN 1608-1021. Usp. Fiz. Met., 2018, Vol. 19, No. 1 71
Effect of Martensitic Transformations on Diffusion in Fe–Mn
of the alloys that formed due to the phase transformations [1–3]. A
significant acceleration of diffusion is found in nanocrystalline materi-
als with a structure splintered due to severe plastic deformation [4–8].
Phase and structural transformations occurring in metals and alloys
with a bulk effect and therefore forming a certain system of defects in
the crystalline structure cause an amplification of diffusion processes
and stimulate the mass transport of atoms on macroscopic distances.
Martensitic transformations that can be realized via the shear diffu-
sionless mechanism significantly accelerate diffusion of substitutional
and interstitial atoms in the reversible parent phase [9–14]. Diffusive
mobility of alloying atoms substantially depends on cooling and heating
regimes necessary for realization of direct and reversible martensitic
transformation. A considerable change in the diffusion coefficient in
iron and thallium was observed only when a certain critical thermal
cycling rate was reached [2, 3].
Due to the atomic γ–α (f.c.c.–b.c.c.) restructuring of original crys-
tal lattice into the martensitic one in alloy with an explosive transfor-
mation kinetics without additional annealing the atomic mass transport
on a large distance (up to 60–100 µm) was observed [12, 13]. Behaviour
of concentration dependence of diffusing atoms on a penetration depth
indicates about the bulk character of diffusion at the cryogenic tem-
peratures.
Because of γ−α−γ (f.c.c.–b.c.c.–f.c.c.) martensitic transformations
in austenite phase of iron–nickel alloys, the dislocation density was in-
creased by more three orders of magnitude [14, 15], which resulted to
enhanced diffusion of substitutional atoms as well as carbon atoms at
low temperatures [16, 17]. Particularly, diffusion coefficients of Fe and
Ni atoms at 400 °С corresponded to coefficients of stationary diffusion
at 900 °С [17]. The enhanced diffusion was affected by two factors: high
dislocation density and additional low-angle subboundaries of disorien-
tated nanofragments together with subboundaries of deformation twins
formed due to the γ–α–γ cycles. The low-temperature diffusion anomaly
in iron–nickel alloys after the cyclic γ–α–γ transformations is similar to
that described in the literature diffusion anomaly in nanocrystal mate-
rials obtained by the gas-condensate, electrodeposition, and severe plas-
tic deformation methods [4]. Due to the γ–α–γ transformations, the
diffusive mobility of carbon atoms was also appreciably enhanced.
The γ–ε–γ martensitic transformations in iron–manganese alloys re-
sult to one order increasing of dislocation density in reversible austenite
phase [18]. The difference in increase of dislocation density in compari-
son with γ–α–γ transformations is caused by different degree of the
volume effect γ–α and γ–ε transformations (3 % and 1.75 %, respec-
tively). The γ–ε–γ transformations in iron–manganese reversible austen-
ite with low stacking fault energy cause accumulation of random stack-
72 ISSN 1608-1021. Prog. Phys. Met., 2018, Vol. 19, No. 1
V.Y. Bondar, V.E. Danilchenko, V.F. Mazanko, O.V. Filatov, and V.E. Iakovlev
ing faults, but do not result to significant structural fragmentation and
formation of additional subboundaries. A considerable difference of the
structural state and imperfection degree in the crystal lattice of phase
components, generated due to the γ–α–γ and γ–ε–γ transformations,
stimulate further investigations of effect of martensitic γ–ε–γ transfor-
mations on diffusion characteristics in alloys with a low stacking fault
energy. Authors of Ref. [10] studied an effect of γ–ε–γ transformations
in cobalt and iron–manganese alloys on diffusion characteristics of sub-
stitutional (Fe and Co) atoms and revealed a significant enhancement of
their diffusive mobility.
Experimental studies of effect of γ–ε–γ martensitic transformations
on diffusion characteristics of interstitial atoms still were not carried
out. That is why the purpose of this work is to investigate the effect of
the cyclic γ–ε–γ martensitic transformations on the diffusion character-
istics of carbon in the iron–manganese alloys using the method of radio-
active isotopes.
Мaterials and experimental technique
The studies were performed for a metastable Г18С2 alloy (18.3 mas.%
Мn; 2.1 mas.% Si), where a large amount of martensitic ε-phase was
generated due to the thermal cycling and γ–ε–γ transformations. This
allowed to reach a high degree of the phase hardening from the γ–ε–γ
transformations. Cyclic γ–ε straight lines and reversible γ–ε transforma-
tions were sequentially realized in alloys during cooling in the liquid
nitrogen and subsequent heating in the salt bath at a temperature of
800 °C. In this case, the cooling rate within the range of direct transfor-
mations and the heating rate in the range of reversible transformation
were reached: 20 °C/s and 80 °C/s, respectively. Such a thermal cycling
regime resulted to deceleration of relaxation processes and provided an
effective accumulation of structural defects (due to both direct and re-
versible transformations) that can strongly affect diffusion processes in
the phase-hardened alloys. Indeed, a considerable increasing of diffusion
coefficients in Ni and Tl were observed as long ago as 1962 [19] only when
a certain critical thermal cycling rate was reached. After the γ–ε–γ trans-
formations, a diffusion annealing (homogenization) of the phase hard-
ened alloys was carried out at the temperatures of 100 °С and 200 °С.
X-ray studies were performed using the automated diffractometer
DRON-3 in the radiation of iron anode monochromatized with a lithium
fluoride. The amount of ε-phase was measured via the ratio of integral in-
tensity of (111)γ and (002)ε diffraction reflexes [18]:
ε
γ
ε
=
+ (111)
(002)
100%
1 0.27
M
I
I
.
ISSN 1608-1021. Usp. Fiz. Met., 2018, Vol. 19, No. 1 73
Effect of Martensitic Transformations on Diffusion in Fe–Mn
Using of these reflexes from the austenite and ε-martensite crystal-
lographic planes, which were parallel in accordance with orientation
relations between f.c.c. and h.c.p. lattices, enabled to calculate an
amount of ε-phase without decrease in accuracy of the measurement in
case of the appearance of texture during the thermal cycling process.
In order to characterize structural state of the phase-hardened alloy
and crystal lattice defectiveness degree of the phase components, the
maximal angle disorientation ψ of austenite lattice and ε-martensite as
well as concentration of random stacking faults were measured. The ψ
value, which characterizes formation possibility for low-angle disloca-
tion subboundaries, was measured by the value of azimuth smearing of
(200)γ and (101)ε reflexes at the diffraction pattern from the single
crystal samples [15].
The concentration (α) of random stacking faults in f.c.c. lattice was
measured via the change of Bragg angles of certain diffraction reflexes
[18, 20–23] or via the value of their physical broadening [24]. Accord-
ing to Refs. [20, 21], for f.c.c. structure that contains stacking faults
in {111} planes, the Bragg angle remains invariable for that reflexes,
the Miller indexes for which satisfy the conditions (in cubic coordi-
nates):
(h + k + l) = 3N, (2h − k − l) = 6N′,
where N and N′ are integers.
The value of α for austenite of Г18С2 alloy was determined by the
mutual shift of Bragg angles of (200)γ and (111)γ reflexes,
200 111
200 111 2
45 3(2tg tg )
(2 2 )
2
Σα θ − θ
∆ θ − θ = −
π
, (1)
where θ is a Bragg angle, and αΣ denotes concentration of random stack-
ing faults.
The value of αΣ was determined using the reflex half-width [18]:
3 1 [(1 3 (1 )]
1 [(1 3 (1 )]
B Σ Σ
Σ Σ
− − α − α
=
+ − α − α
, (2)
where В denotes a half-width of the reflex in radians.
The value of αΣ for h.c.p. lattice can be determined via the physical
broadening of the reflexes that meet conditions H − K = 3N ± 1 and L ≠
≠ 0 (N—integers) [22, 23, 25, 26]. In this case, we have to take into ac-
count that random stacking faults do not cause broadening of (hk0) re-
flexes.
Concentration of random stacking faults within the {001}ε crystal-
lographic planes was calculated using the formula [20]
1 [(1 3 (1 )]
1 [(1 3 (1 )]
B Σ Σ
Σ Σ
− − α − α
=
+ − α − α
; (3)
74 ISSN 1608-1021. Prog. Phys. Met., 2018, Vol. 19, No. 1
V.Y. Bondar, V.E. Danilchenko, V.F. Mazanko, O.V. Filatov, and V.E. Iakovlev
here, В denotes a half-width of (hkl) reflex. The value of αΣ in this ex-
pression denotes concentration of random stacking faults without their
separation into deformed and twinned.
Diffusion characteristics of carbon were determined by the radioac-
tive isotope method. Radioactive isotope of carbon 14С was deposited on
the alloy surface of 10 × 10 × 5 mm3 in size during the cementation pro-
cess at a temperature of 800 °С using the carburizer containing impuri-
ties of ВаСО3 compound with a radioactive isotope of carbon 14С. During
the cementation of the samples for X-ray investigation, the carburizer
ВаСО3 was used without 14С isotope. Thereby, the radiation safety dur-
ing the X-ray diffraction procedure was attained.
The depth distribution of carbon atoms was determined via the lay-
er skimming with a measurement of β-activity radioisotope 14С. Diffu-
sion coefficient of carbon (D) was calculated as
1
4 tg
D = −
τ α
, (4)
where τ is a diffusion annealing time, α is a slope angle of a straight
line to the abscissa axis at the graphs of dependences of lnI on x2, where
I is a specific β-activity of a sample residue after skimming of a layer
of x in depth.
effect of the cyclic γ–ε–γ Martensitic transformations
and cementation of alloy surface
on its Phase composition
The alloy of Г18С2 grade had a temperature of direct martensitic γ–ε
transformation higher than a room temperature, therefore the alloy
contained a considerable amount of martensite ε-phase in an initial
state. An amount of ε-martensite did not decrease after the reversible
ε−γ transitions and subsequent cooling in a liquid nitrogen. The phase-
hardened alloy contained more than 90% of ε-martensite after the hun-
dredth γ–ε–γ cycle. The microstructure of the alloy phase-hardened dur-
ing 100 γ–ε–γ transformations is represented in a metallographic image
in Fig. 1. The microstructure resembles Widmanstätten patterns (also
known as Thomson structures) which are typical for alloy with a large
amount of ε-phase.
One can see in Fig. 1 that ε-martensite occupy practically all field
of image. Observed (via an optical microscope) straight lines on the
Widmanstätten pattern of iron–manganese alloys sometimes are consid-
ered in the literature [27–30] as the boundaries that separate austenite
and ε-martensite. The content of ε-phase reached under 100%, which
indicated that the mentioned straight lines were not boundaries between
ISSN 1608-1021. Usp. Fiz. Met., 2018, Vol. 19, No. 1 75
Effect of Martensitic Transformations on Diffusion in Fe–Mn
the γ- and ε-phase. They should be considered as effect of crystallo-
graphic orientation shift during the γ–ε reconstruction.
Thus, there were no a stabilization of reversible austenite due to the
increase in degree of phase hardening as it has place for some other
iron–manganese alloys [26, 29]. The established fact of increase in
ε-martensite content as a result of sequential γ–ε–γ transformations in-
dicated a considerable decrease in the stacking fault energy during an
increase in a degree of phase hardening of the reversible austenite.
Fig. 2. The diffraction patterns of the alloy in the initial state (1), after cementation
(2) and at a depth of 0.05 mm from the cemented surface (3)
Fig. 1. Microstructure of the alloy after 100 γ–ε–γ cycles
76 ISSN 1608-1021. Prog. Phys. Met., 2018, Vol. 19, No. 1
Fig. 3. Concentration distribution of radioisotope
14С by the depth after one (1), 10 (2),
and 200 (3) γ–ε–γ cycles (a) and 10 (1), 100 (2), and 500 (3) γ–ε–γ cycles and additional
diffusion annealing at 200°С during 2500 hours (b)
V.Y. Bondar, V.E. Danilchenko, V.F. Mazanko, O.V. Filatov, and V.E. Iakovlev
Cementation of the alloy led to the carbon saturation of near-surface
layer and resulting change in the phase composition. In an initial state,
the alloy contained the ε-martensite and residual austenite (Fig. 2, curve 1),
whereas after the cementation the diffraction pattern of near-surface car-
burized layer contained reflexes of the residual austenite and intense
reflexes of α-martensite (Fig. 2, curve 2). There were already no reflexes
of ε-martensite fixed for the alloy in an initial state. From the value of
the parameter аγ for austenite, it was calculated that 0.38 mass percent
of carbon dissolved in the γ-phase of near-surface layer. The ε-martensite
was observed at a depth of 0.05 mm and more (Fig. 2, curve 3). The
content of ε-martensite increased along the depth from 0.05 to 0.5 mm.
The penetration of carbon atoms into the ε-solid solution along the sam-
ple depth in a process of diffusion annealing occurred from the residual
austenite and α-martensite of near surface carburized layer via through
the γ–ε and α–ε interphase boundaries. Such boundaries can serve as
diffusion barrier for the movement of carbon atoms. Evidently that the
effectiveness of barriers differed for boundaries between different phas-
es, since in one case carbon atoms are transported into the lattice with
a more close-packed structure (α–ε barrier), whereas, in another case,
into the lesser close-packed lattice (γ–ε barrier). The analysis of diffu-
sion transport of carbon atoms from the α-phase into the ε-one became
more complicated because α-solid solution decomposed and depleted with
a carbon to the state of equilibrium solubility in the α-phase at the dif-
fusion annealing temperatures (100–200 °C). In this case, when carbon
leaves the α-solid solution, it can occupy crystal-lattice defects (disloca-
tions, stacking faults), enter into the carbide content or form graphite
globules. The diffusion path of carbon into the sample depth can sig-
nificantly differ and differently affect the integral diffusion character-
istics of carbon in phase-hardened alloys. A role of interphase boundar-
ISSN 1608-1021. Usp. Fiz. Met., 2018, Vol. 19, No. 1 77
Effect of Martensitic Transformations on Diffusion in Fe–Mn
ies in the change of diffusion characteristics of carbon in iron–manga-
nese alloys with γ–ε transformation deserves additional investigations.
Еffect of cyclic γ–ε–γ Martensitic transformations
on the diffusion characteristics of carbon
Measurements of diffusion profiles for carbon in alloys, phase-hardened
with the γ–ε–γ transformations, were carried out for two cases: after the
cementation and transformation cycles, and after subsequent additional
diffusion annealing at 100 °С and 200 °С. It turned out that transport
of carbon, as a result of γ–ε–γ cycles, occurred on the macroscopic depth
without additional diffusion annealing. After the first transformation
cycle, the penetration depth (x) of carbon (without diffusion annealing),
amounted 127 µm. As the cycle number increased up to 100, the depth
increased up to 200 µm. Figure 3 represents typical distributions of
β-activity of radioisotope 14С along the depth in the alloys with different
phase hardening degree. Subsequent diffusion annealing has led to a
significant increase in the x-value (Fig. 3, b). The difference in the in-
crease in the depth of total carbon penetration via two different diffu-
sion mechanisms increased significantly with increasing number of cy-
cles as Fig. 4 shows. For instance, after 10 cycles, the mentioned differ-
ence was 97 µm, whereas, after 100 cycles, it reached 204 µm. In addition
to experimental results in Fig. 4, we carried out 500 γ−ε−γ cycles and
corresponding diffusion annealing. We revealed that an increment of
the penetration depth (due to such a treatment as compared to the treat-
ment with 200 γ–ε–γ cycles) was 27 µm, i.e., 6%. A small increase in
depth for a significant number of thermocycles showed that the active
penetration of carbon atoms occur during the first 100–200 γ–ε–γ trans-
formations, whereas the penetration process gradually attenuate during
the next cycling.
The dependence lnI(x2) for all cycling regimes was found to be close
to the linear one as Fig. 5 demonstrates. This indicates about predomi-
nately bulk character of diffusion.
Calculation of carbon diffusivity from the corresponding curves in
Fig. 4. Penetration depth vs. number of γ–ε–γ
cycles for 14С atoms without annealing (1)
and after additional diffusion annealing at
200 °C during 2500 hours (2)
78 ISSN 1608-1021. Prog. Phys. Met., 2018, Vol. 19, No. 1
V.Y. Bondar, V.E. Danilchenko, V.F. Mazanko, O.V. Filatov, and V.E. Iakovlev
Fig. 3, a is impossible due to impossibility of correct determination of
diffusion process time, which evidently is commensurable with time
of martensitic transformation elapse. Actually, transport mechanism
for carbon atoms is connected with the structural f.c.c.–h.c.p. recon-
struction and accompanying resulting propagation of the stress force
field as a result of the transformation-induced change in crystal volume
and shape. Apparently, movement over the interstitial sites is the most
probable diffusion mechanism for carbon atoms in the field of stresses.
The increase of the penetration depth in case of the cycle repetition
(Fig. 3, а) is indicative of possibility to accumulate internal stresses
that sequentially stimulate an additional carbon transport. Apparently,
this carbon transport mechanism should be athermal. It was shown
earlier that an athermal mechanism of mass transport of substitutional
and interstitial atoms was realized under the explosive kinetics of
the martensitic f.c.c.–b.c.c. transformation in the iron–nickel alloys
[12, 13].
During the γ–ε–γ transformations in the local regions of the alloy,
internal structural tensile and compressive stresses appeared in accor-
dance with a sign of the bulk effect of direct γ–ε (increase in specific
volume) and reverse ε–γ (decrease in specific volume) transformations.
Stretched regions appeared due to direct γ–ε transformation at low tem-
peratures when relaxation processes were decelerated and internal stres-
ses were conserved. This created conditions for the movement of carbon
atoms in such areas. We can assume that the inverse ε–γ transformation
contributed lesser to conditions for the migration of carbon atoms via
the athermal mechanism.
The penetration depth for carbon atoms in alloy phase-hardened at
100 °С and 200 °С significantly increased as the number of previous
Fig. 5. The estimated dependence of lnI x2) for two cases: (a) after one (1), 10 (2), 100
(3), and 200 (4) γ–ε–γ cycles; (b) after 10 (1), 100 (2), and 500 (3) γ–ε–γ cycles and addi-
tional diffusion annealing at 200 °C during 2500 hours
ISSN 1608-1021. Usp. Fiz. Met., 2018, Vol. 19, No. 1 79
Effect of Martensitic Transformations on Diffusion in Fe–Mn
transformation cycles increased (Fig. 3, b). Thermoactivated character
of transport process enabled calculation of carbon diffusion characteris-
tics. After the first γ ↔ ε transformations, calculated carbon diffusion
coefficient was equal to 1.7 ∙ 10−11 і 2.3 ∙ 10−11 cm2/sec for 100 °C and
200 °C, respectively. Increase in number of γ–ε–γ cycles up to 100,
caused increase in diffusivity by 2.5 and 3.2 times. Further increase in
number of cycles induced an additional, lesser significant, increase in D
value and deviation of D (N) dependence from the linear one. After 500
γ–ε–γ cycles, diffusion coefficient (D) increased by 3.2 and 4.2 times at
100 °С and 200 °С, respectively (Fig. 6, curves 1 and 2).
Difference between the diffusivity D at 100 °С and 200 °С was suf-
ficient for determination of diffusion activation energy Е. The value of
Е decreased monotonically as the number of γ–ε–γ transformations in-
creased (Fig. 6, curve 3). The main change of E (by 4 times approxi-
mately) occurred when number of cycles was increased up to 100.
For comparison, it should be noted that, for titanium, the increase
in the self-diffusion coefficient D in both the low-temperature α-modi-
fication and high-temperature β-modification approximately linearly
depends on the number of cycles during martensitic transformations [2,
3]. Note that we observed deviation from the linearity for ∆D(N) depen-
dence at high number (more than 100) of cycles. The above-mentioned
differen ce in ∆D value for γ ↔ ε and α ↔ β transformations in iron–
nickel alloys and titanium, respectively, is attributed to different na-
ture of structural defects generated by different types of martensite
transformations.
The revealed experimental dependence of the phase composition of
the alloy at hand on number of γ–ε–γ cycles, i.e., on phase hardening
degree, allowed to separate carbon diffusion coefficients in austenite
and martensite. After 100 γ–ε–γ cycles in the reversible austenite, the
sufficiently active direct γ–ε transformation took place. Further ther-
mal cycling resulted to observation of the traces of austenite only on the
diffraction pattern. It means that, starting from 100 cycles, the value
of D should be referred to ε-martensite. From the dependence of carbon
concentration on the penetration depth (Fig. 4, curves 1 and 2), we cal-
Fig. 6. The dependences of the dif-
fusion coefficient of carbon D at the
diffusion annealing tempe ratures
of 100 °C (1) and 200 °C (2) and
diffusion activation energy E (3)
on the number of γ–ε–γ cycles
80 ISSN 1608-1021. Prog. Phys. Met., 2018, Vol. 19, No. 1
V.Y. Bondar, V.E. Danilchenko, V.F. Mazanko, O.V. Filatov, and V.E. Iakovlev
culated coefficients D for 100 °С and 200 °С (Fig. 6, curves 1 and 2) and
diffusion activation energy (Fig. 6, curve 3). The value of D was found
to be higher for ε-martensite in comparison with austenite.
Thus, the intensification of the transport of carbon by the γ–ε–γ
transformations occurred via the two independent mechanisms: ather-
mal one, which was realized in the process of martensitic transforma-
tion, and thermoactivated one, which was realized in the process of the
subsequent diffusion annealing.
In connection with this, the conditions for the formation and accu-
mulation of certain structural defective elements of the phase-hardened
alloy, which can accelerate the diffusion processes via the thermoacti-
vated mechanism, were investigated.
characteristics of disorientation
accumulation in the crystal lattices of austenite
and ε -martensite due to the Phase hardening
As a result of reverse ε–γ transformation in the iron–manganese alloys,
the dislocation density in reversible austenite increased approximately
by one order of magnitude [18, 26]. Electron microscopic investigations
showed that further enhancement of the number of γ–ε–γ transforma-
tions up to hundreds does not induce an appreciable increase in disloca-
tion density [14]. It means that intensification of the carbon diffusion
after the first circle of γ–ε–γ transformations in Г18С2 alloy is mainly
attributed to the enhancement of dislocation density in the reversible
γ-phase and ε-martensite. Dislocation contribution to the further in-
crease of D value due to many thermal cycles was already insignificant
in accordance with an insignificant growth of the dislocation density.
For the iron–manganese alloys, there were no observed formations
of large-angle boundaries of austenite grains analogously to iron–nickel
alloys [18]. However, due to the many γ–ε–γ transformations in this al-
loy, the small-angle dislocation subboundaries, which can be character-
ized by the angle ψ denoting maximal disorientation of the crystal lat-
tice, appeared.
The ψ angle increased monotonically with increase in the number of
γ–ε–γ transformations and reached value of 6.4° and 8.7° for ε- and
γ-phase, respectively, as a result of 70 thermal cycles (Fig. 7, curves 1
and 2). After the first 5 γ–ε–γ cycles, the ψ angle for martensite was
found to be higher as compared with it was found for austenite. In this
range of the cycling, there were no appreciable disorientation accumula-
tion for f.c.c. and h.c.p. lattices because of high crystallographic revers-
ibility of direct γ–ε and reverse ε–γ transformations. However, after the
tenth transformation cycle, the ability to accumulate disorientation in
the lattice of austenite, as well as in the lattice of martensite, began to
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Effect of Martensitic Transformations on Diffusion in Fe–Mn
manifest itself. In this case, the possibil-
ity to compare ψ angle for γ- and ε-phase
in the cycling range up to 100 cycles ap-
peared. As the number of cycles increased
up to 100, we fixed by means of diffrac-
tion only ε-phase, since during the cooling from the end of reverse ε–γ
transformation to the room temperature, direct γ–ε transformation in
the phase-hardened alloy occurred practically completely. Due to this
circumstance, already there were no a possibility to measure ψ angle for
the γ-phase lattice at room temperature after 100 cycles (Fig. 7, curve
2). The disorientation accumulation for ε-martensite lattice, continued
develop continuously with increase of the γ–ε–γ cycles up to 500 (Fig. 7,
curve 1). In this case, the growth of diffusion coefficient was also ob-
served.
Above-mentioned regularity of disorientation accumulation for
ε-martensite lattice indicated on a substantial difference between depen-
dence of degree of the phase hardening and strengthening reached via
the γ–α–γ transition recycles in one case and γ–ε–γ recycles in another
one. Authors of Ref. [14] found that strengthening of the metastable
iron–nickel alloys can grow only when an additional volume fraction of
austenite will take part in each subsequent circle of γ–α–γ transforma-
tions. For a studied iron–manganese alloy, the phase hardening degree
continued to grow after 100 of γ–ε–γ transformations, when austenite
phase with a practically 100% volume fraction contributed. This was
seen from a considerable increase in the ψ angle value for ε-phase lattice
at an increase in number of γ–ε–γ cycles up to 500, whereas the diffrac-
tion pattern of the phase-hardened alloy at a room temperature already
did not contain reflexes of the γ-phase.
Disorientation of the austenite lattice after the first 5–7 cycles ex-
ceeded disorientation of the ε-martensite lattice. Larger ψ angle of aus-
tenite lattice indicated about deceleration of γ–ε martensitic transfor-
mation in the maximally disoriented fragments of the reversible austen-
ite. It is known that barrier action of subboundaries of fragmented
structure for growth of martensitic crystal is always lesser than action
of grain boundaries and is determined, except the fragment sizes, by the
angle of the mutual disorientation of adjacent fragments [29]. It was
shown earlier by the electron microscopic studies that α-martensite
crystals passed through several weakly disoriented subboundaries of the
fragments and stopped by meeting with subboundaries overcritical de-
formation [29]. Subboundaries of overcritical disorientation affected
Fig. 7. The maximum orientation angle ψ of
the crystalline lattice of ε-martensite (1) and
austenite (2) vs. the number of γ–ε–γ cycles
82 ISSN 1608-1021. Prog. Phys. Met., 2018, Vol. 19, No. 1
V.Y. Bondar, V.E. Danilchenko, V.F. Mazanko, O.V. Filatov, and V.E. Iakovlev
the martensitic crystal growth already as grain boundaries. Barrier
effect of disorientated subboundaries for α-martensite crystals [18]
was stronger as compared with action for ε-martensite crystals. Really,
after 3–5 γ–α–γ cycles, the difference of the lattice disorientation for
γ- and α-phase reached 3° [18], whereas after 100 γ–ε–γ cycles, the dif-
ference of the lattice disorientation for γ- and ε-phase was 6° only. This
dif ference defined also difference in dislocation structure of low-angle
subboundaries generated by the cyclic γ–α–γ and γ–ε–γ martensitic
transformations. This, in turn, can determine the different impact de-
gree of such subboundaries on the diffusion characteristics in phase-
har dened alloys.
As a result of multiple cycles, the magnitude of the angle was sig-
nificantly lower than that achieved as a result of cycles in iron–nickel
alloys [15, 16]. This is caused by much more higher structural revers-
ibility of direct γ−ε and reverse ε−γ transitions. Note that ψ angle even
for intensive γ–ε–γ cycling (1000 cycles) did not exceed value of 9° for
austenite, though large-angle grain boundaries possess a disorientation
angel of 14–15°. It means that cyclic γ–ε–γ transformations can gener-
ate only low-angle subboundaries of the fragments and it is impossible
to form new grains of reversible austenite, which would differ from the
initial grain orientation, due to the accumulation of the lattice disorien-
tations, as was the case for iron–nickel alloys due to the multiple mar-
tensitic transformations.
The subfragments with accumulated disorientation should be con-
sidered as a factor in the intensification of the diffusion mobility of
carbon. Indeed, it was established earlier that the intensity of diffusion
processes significantly increased with increasing angle of disorientation
of grain fragments [28]. For example, in the study of the grain bound-
ary diffusion, it was revealed that the self-diffusion coefficient of the
silver increased by 500 times with changing ψ from 9° to 28°. Such de-
pendence can be attributed to the dependence of surface energy of grain
boundaries on the disorientation angle. Experimental findings showed
that surface energy of grain boundaries for germanium grew sharply
for small values of ψ (up to 14–16°), whereas the surface energy of
grain boundaries remained constant in case of large ψ values [28]. The
ψ-dependences of surface energy of grain boundaries and diffusion coef-
ficient agree with dislocation model for low-angle grain subboundaries.
Сharacteristics of the formation of random stacking
faults in the Phase-hardened austenite and ε-martensite
As a result of cyclic γ–ε–γ transformations in a reversible austenite and
ε-martensite of the iron–manganese alloys with a low stacking fault
energy, the random stacking faults along the {001}ε crystallographic
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Effect of Martensitic Transformations on Diffusion in Fe–Mn
plane were found to be generated. The random stacking faults in f.c.c.
and h.c.p. structures showed ability to the accumulation [18, 22, 26].
Therefore, we studied the regularities of the formation and accumula-
tion of the random stacking faults in the austenite and ε-martensite of
Г18С2 alloy due to γ–ε–γ cycles.
It was revealed that the Bragg angle difference ∆θ = θ(200)γ − θ(111)γ of
austenite reflexes decreased due to their mutual shift, whereas the half-
depth of β reflex (200)γ increased with increasing number of the γ−ε−γ
cycles. According to the Paterson theory [20, 22, 23], it indicated about
enhancement of the random stacking fault concentration. The value of
β grew appreciably for the (102)ε reflex (Fig. 8), physical broadening of
which (in accordance with a theory in Ref. [25]) was the most sensitive
to the presence of the twin stacking faults. For the (101)ε reflex, which
is sensitive to the presence of deformation stacking faults, the value of
β varied much more slightly. To calculate physical broadening of the
ε-martensite reflexes, as a standard, we used the (100)ε reflex, the half-
width of which was practically independent on the random stacking
faults. Some changes in the diffusion pattern characteristics of the
phase-hardened Г18С2 alloy indicated on accumulation during thermal
cycling of the random stacking faults in the (111)γ and (001)ε planes of
austenite and ε-martensite, respectively.
Using values of ∆θ and β, we calculated concentration of the stack-
ing fault defects in austenite and ε-martensite. After the first cycle of
γ–ε–γ transformations, concentration of the random stacking faults in
austenite was circa 0.015. The value of α grew with increasing N up to
10. After 50 such cycles, the value of α reached value of 0.02, and due
to the further increasing N up to 100, grew in insignificantly (Fig. 9).
There was obtained quantitatively the same α (N) dependence for calcu-
lation via the value of ∆θ (curve 1) and value of β (curve 2).
Concentration of the random stacking faults in ε-martensite also
grew as the N increased (Fig. 9, curve 3). Total concentration of the
random stacking faults (without their separation on the twin and defor-
mation ones) calculated via Eq. (3) reached a significant value of 0.033
(curve 3).
The presence of random stacking faults in austenite and martensite
phases enabled to assume [18] that because of the rapid cooling and sub-
sequent rapid heating cycles, thermal-stress-induced disordered (ran-
domly located) stacking faults were generated and accumulated in aus-
tenite f.c.c. lattice. They tended to ordering in some regions of the f.c.c.
structure (as in Refs. [31–33]), where critical concentration of the ran-
dom stacking faults was reached. In this case, austenite region trans-
formed into ε-martensite one. Electron-microscopic studies [26] showed
that austenite matrix between the ε-martensite wafers is filled with
stacking faults in [111]γ planes, which contributed to the mutual orien-
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V.Y. Bondar, V.E. Danilchenko, V.F. Mazanko, O.V. Filatov, and V.E. Iakovlev
tation of the stacking faults and hexagonal phase wafers, and made
easier reconstruction of f.c.c. structure, which contained accumulated
random stacking faults, into h.c.p. structure.
Authors of Ref. [26] pointed out that concentration of stacking
faults in the residual austenite increased as the temperature or stresses
varied. Thus, characteristics and regularities of generation of the ran-
dom stacking faults revealed in this work and electron-microscopic ob-
servations in Ref. [26] made possible to explain activation of direct γ–ε
transformation effect due to γ–ε–γ cycles by a decrease in the stacking
fault energy.
Сorrelation of the change in the structural defect
concentration and carbon diffusion characteristics
in a Phase-hardened alloy
The change in concentration of the random stacking faults correlates
with the growth of the carbon diffusion coefficient (Fig. 6). Increase in
the random stacking faults’ concentration up to 0.033 (Fig. 9) accompa-
nied with accumulation of other defects (dislocations, low-angle grain
subboundaries) resulted to increase in the carbon diffusion coefficient
by 3.3 times at 100 °С.
In order to analyse effect of random stacking faults on the diffusion
characteristics, we have to take into account local structure within the
stacking fault regions. This is due to the prevailing ideas about the
splitting of complete dislocations into the partial ones with the forma-
tion of the stacking faults. For the close-packed metals, the ability to
split dislocations and the formation of the stacking faults [22] lies in
the possibility of slipping along the planes of the slightest displacement.
Fig. 9. Concentration of the random stacking faults in austenite, calculated via the ∆θ
(1) і β (2) values, and in ε-martensite (3), where 1, 2, and 3 are deformation α, twin β,
and total αΣ random stacking faults, respectively
Fig. 8. The change of the diffraction reflex (102)ε depending on the number of γ–ε–γ
cycles: 1—the initial state, 2 and 3—after 5 and 100 cycles
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Effect of Martensitic Transformations on Diffusion in Fe–Mn
There are different dislocation reactions proposed for the formation of
the stacking faults in the f.c.c. and h.c.p. [18, 22, 34] as well as b.c.c.
[35] structures. In accordance with this scheme, it was experimentally
observed that the formation of a hexagonal structure in the Г20 alloy
cooled from 400 °C occurred with the formation of the stacking faults
bounded by partial dislocations. For the austenite Г19М6 alloy quenched
in water 1100 °С there were observed initial splitting stages for disloca-
tions and wide stacking faults bounded by partial dislocations [26]. Au-
thors of Ref. [34] showed that depending on the energy of the stacking
faults, the degree of dislocations’ splitting can vary, and therefore their
ability to multiplication can vary as well. Taking into account local
structural reconstruction related with generation of random stacking
faults, they can be considered as the complexes of ‘stacking faults–
partial dislocations’. Both partial dislocations and actually stacking
faults can contribute to the acceleration of diffusion processes. The
component of the diffusion intensification due to the random stacking
faults in the f.c.c. and h.c.p. structures was implemented during the
thermal cycling regime, when maximum number of random stacking
faults accumulated, i.e., during the first 30–40 γ–ε–γ cycles.
At the temperatures lower than half of the melting point, diffusion
occurs mainly in dislocations, grain boundaries, fragment subboundar-
ies, and other crystal structure defects [1–3]. Results of the present
work show that the phase hardening from the γ–ε–γ transformations in
the Г18С2 alloy appreciably accelerate diffusion of carbon atoms due to
effect of dislocations, random stacking faults, and subboundaries of
disoriented fragments of austenite and ε-martensite crystal lattices.
To separate the contribution of various defects into the change of
diffusion characteristics, it does not seem to be feasible based on the
obtained results. However, one can conclude qualitatively about ranges
of γ–ε–γ cycling with the maximal contribution of different defects into
the diffusion intensification during subsequent diffusion annealing.
Analysis of the characteristics of accumulation of each type of struc-
tural defects (Fig. 9) showed thermal hardening ranges with predomi-
nant contribution of certain defect type. Effect of dislocations gener-
ated via reverse ε−γ transformation was observed after the first trans-
formation cycle. Such dislocations can be randomly distributed in lattice
of each of the phase components. Their spatial distribution may have
the character of a dislocation network. Dislocation distribution depends
on the degree of intensification of diffusion processes. In the case of the
dislocation network formation, carbon atoms diffuse predominantly
along dislocation tubes, which compose a continuous diffusion pathway,
and there is no C diffusion in dislocation-free bulk regions. In this case,
the diffusivity significantly exceeds diffusion coefficient at a random
distribution of dislocations. Electron microscopic studies of the disloca-
86 ISSN 1608-1021. Prog. Phys. Met., 2018, Vol. 19, No. 1
V.Y. Bondar, V.E. Danilchenko, V.F. Mazanko, O.V. Filatov, and V.E. Iakovlev
tion distributions in austenitic and martensitic lattices of the phase-
har dened alloy can resolve this problem. The exponential dependence of
the carbon concentration on the squared penetration depth indicates
about the bulk character of diffusion. Due to bulk diffusion (over the
crystal lattice), the parameters of the crystal lattice of austenite and
martensite became higher (Fig. 10). Using these parameters, we can
calculate the depth distribution of carbon in austenitic and martensitic
phases. The carbon dissolution in γ- and ε-solid solution of the phase-
hardened alloy indicated that the dislocations and the low-angle frag-
ment subboundaries, generated by the γ–ε–γ transformations, did not
form a continuous dislocation network capable to create continuous dis-
location tubes along which the carbon atoms could diffuse.
An increase in the contribution of the random stacking faults took
place during the first 30–40 cycles. This fact concerns the contribution
of the random stacking faults in both austenite and martensite. Disori-
ented low-angle subboundaries, which began to accumulate after the
first 5–7 cycles, acted during all term of the thermal cycling interval.
Analysing the formation of a concentration profile, it is necessary
to take into account the segregation effects of dissolved carbon atoms
on subboundaries, dislocations and stacking faults, and, consequently,
to estimate the corresponding contribution to the diffusivity value. In-
deed, as far back as 1963 [28], it was reported that the equilibrium
concentration of dissolved metal atoms at the boundaries depends on the
disorientation angle; at the same time, the degree of atomic segregation
increased rapidly after 16°. For some diffusers, a nonmonotonic depen-
dence of the diffusion coefficient along subboundaries on the disorienta-
tion angle was observed [1, 28]. Due to high diffusion mobility of car-
bon atoms, they formed saturated atmospheres at the dislocations in the
b.c.c. martensite of the quenched steel. Approximately 0.2 wt.% C was
required for atmospheric saturation [36]. The nature of the segregation
effects in the phase-hardened Г18С2 alloy may be different. Diffusion
annealing created favourable conditions for atomic chains of C to be
generated along an extra plane of the edge dislocations (Cottrell atmo-
sphere) and for diffusion in the stacking fault regions (Suzuki atmo-
Fig. 10. The dependence of crystalline
lattice parameter for austenite (1) and
the c/a ratio for ε-martensite (2) on the
penetration depth x after 500 γ–ε–γ cy-
cles and subsequent annealing at 200 °C
during 1000 hours
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Effect of Martensitic Transformations on Diffusion in Fe–Mn
sphere). Carbon atoms segregated on the structural defects did not give
a contribution into the diffusion path value and consequently into the
diffusion coefficient.
Except the described structural defective elements, an important
factor for changing diffusion characteristics is also a change of the
phase composition of the phase-hardened alloy during the thermal cy-
cling process and subsequent diffusion annealing. The increase in the of
ε-martensite content as a result of γ–ε–γ cycling can be considered as a
factor that increases the diffusion mobility of the substitution and in-
terstitial atoms, since diffusion processes in the bulk of martensite pos-
sessing h.c.p. crystalline lattice are more intensive as compared with
austenite that has an f.c.c. lattice with a closer atomic packing. As a
result, the contribution of carbon diffusion over the residual austenite
f.c.c. lattice to the integral diffusion flux decreased as the number of
cycles increased, which corresponded to decreasing its volume fraction.
For comparison, let us note that for some iron–manganese alloys, be-
haviour of N-dependent ε-martensite content differed. With increasing
of N, there was observed a stabilization of austenite with respect to the
subsequent γ–ε transformation, and, accordingly, the ε-martensite con-
tent decreased due to the multiple transformation cycles [18, 26]. In
such alloys, the contribution of carbon bulk diffusion over the residual
austenite reduced the integral diffusion flow.
As the number of transformation cycles increased, the contribution
of the D coefficients in austenite and martensite to the magnitude of
the effective coefficient D for the two-phase γ + ε alloy (Fig. 6) con-
tinuously changed in accordance with the change in phase composi -
tion.After the first cycle, the contribution of the coefficients for
austenite and martensite to the value of D was commensurate. As for
100 cycles, the D coefficient at 100 °С, equal to 5.5 ∙ 10−11 сm2/s, can be
practically related to the ε-martensite. Due to the further cycling up to
500 γ−ε−γ transformations, the D coefficient in ε-martensite grew up to
6.85 ∙ 10−11 m2/s, i.e., circa by 25%. The above-mentioned increase in the
value of D, in case of a diffusion annealing within the range of
the existence of martensite, prior to the inverse ε–γ transformation,
should be attributed only to the effect of the dislocations that formed
the polygonal walls of the low-angle subboundaries in the f.c.c. ε-phase
lattice (Fig. 7).
It is known that random stacking faults in austenite were generated
simultaneous with formation of ε-martensite. They disappeared (were
‘healed’) at a temperature slightly higher than the temperature of re-
verse ε–γ transformation [27]. Therefore, we can believe that the ran-
dom stacking faults in the austenite, formed due to the γ↔ε-martensitic
transformations, are more thermally stable in case of annealing than
the ε-martensite. That is why, after the completion of the ε–γ transfor-
88 ISSN 1608-1021. Prog. Phys. Met., 2018, Vol. 19, No. 1
V.Y. Bondar, V.E. Danilchenko, V.F. Mazanko, O.V. Filatov, and V.E. Iakovlev
mation, the diffusion of atoms in the reversible austenite was lesser
accelerated than it was in the ε-martensite containing a certain content
of random stacking faults. Therefore, in order to determine the diffu-
sion characteristics of carbon, the diffusion annealing of the alloy was
carried out within the temperature range of the ε-phase existence: 100–
200 °C. Being subjected to such annealing conditions, the random stack-
ing faults contributed as much as possible into the changing the diffu-
sion characteristics.
During the annealing of a phase-hardened alloy, a partial isothermal
inverse ε–γ transformation may occur in the ε-phase existence range
(Fig. 11). Such a transformation occurred more intensively when a de-
gree of phase hardening grew; this is evident from the increase in the
Fig. 11. The diffraction pattern changing of the phase-hard-
ened alloy after its diffusion annealing at 200 °C during 430
(1) and 1000 (2) hours after 10 (a) and 50 (b) γ–ε–γ cycles
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Effect of Martensitic Transformations on Diffusion in Fe–Mn
intensity of the reflexes of reversible austenite during annealing for the
alloy, in which 50 cycles of γ–ε–γ transformation were implemented, as
compared with alloy after 10 γ–ε–γ transformations. Indeed, as a result
of annealing during 1000 hours, the content of ε-martensite decreased
by 18% for alloy after 50 cycles, whereas it decreased only by 5% for
alloy after 10 cycles.
Within the range of reverse ε–γ transformation, simultaneously with
decrease in the content of ε-martensite, there was observed a decrease in
concentration of the random stacking faults in the austenite and marten-
site phases. In order to establish regularities in the changing concentra-
tion of the random stacking faults during the annealing of the phase-
hardened alloy, we chose an alloy, where there were accumulated a consid-
erable (up to 0.025) content of the random stacking faults due to 150 γ–ε–γ
transformations. The change in the Bragg angles of austenite reflexes and
the half-widths of austenite and martensite reflexes indicated a change in
the concentration of random stacking faults (Fig. 12). Heating of such an
alloy up to the temperatures lower the temperature of onset of the ε–γ
transformation, did not result to decrease in the concentration of the ran-
dom stacking faults (Fig. 13). During the progress in the ε–γ transforma-
tion, concentration of the random stacking faults significantly decreased
and reached the level in the initial state of the alloys after the first cooling
in the liquid nitrogen. Such a heating
withdrew phase hardening from γ–ε–γ
transformations concerning accumula-
tion of the random stacking faults. Re-
sults of these experiments showed that
Fig. 12. Change in the difference of the Bragg angles of the (111) γ and (200) γ re-
flexes (1) as well as the half-width of the (200) γ reflex (2) for austenite (a), and the
half-width of the (100)ε (1), (101)ε (2), and (102)ε (3) reflexes for ε-martensite (b)
depending on the temperature of annealing during 30 min (150 γ–ε–γ cycles)
Fig. 13. Concentration of the random stacking
faults vs. the temperature of annealing during
30 min for austenite (1) and ε-martensite (2)
90 ISSN 1608-1021. Prog. Phys. Met., 2018, Vol. 19, No. 1
V.Y. Bondar, V.E. Danilchenko, V.F. Mazanko, O.V. Filatov, and V.E. Iakovlev
maximal amplification of diffusion processes takes place when annealing
of the ε-martensite occurs in the range of its existence.
Contribution of the random stacking faults to the change of diffusion
characteristics during a reverse transformation dropped due to decreasing
amount of ε-martensite and thus concentration of the random stacking
faults. Annealing at the higher temperatures, resulted to the ‘healing’ (dis-
appearance) of the random stacking faults in the austenite (Fig. 13) and
elimination of effect of the random stacking faults on diffusion character-
istics of carbon.
Сonclusions
Significant acceleration of carbon transport due to the cyclic γ–ε–γ mar-
tensitic transformations in the iron–manganese Г18С2 alloy was deter-
mined via two independent mechanisms: athermal one, which was real-
ized in the process of martensitic transformations, and thermoactivated
one, which was realized during the subsequent diffusion annealing. The
difference in the increase in the penetration depth of carbon via two
different diffusion mechanisms increased with an increase in the phase
hardening degree of the alloy, i.e., with an accumulation of the struc-
tural defects in the austenite and ε-martensite.
Transport of carbon atoms to macroscopic distances by the athermal
mechanism occurred in the field of stresses, which appeared and were
accumulated during γ–ε–γ retransformations, apparently, via the inter-
stitial diffusion mechanism. Appearance of extended regions as a result
of direct γ–ε transformation at low temperatures, when relaxation pro-
cesses were decelerated, whereas internal stresses were conserved, cre-
ated conditions for transport of carbon atoms to such regions without
thermal activation.
As a result of the annealing, subsequent after cycle transformations,
diffusion mobility of carbon atoms additionally increased due to the ef-
fect of the one-dimensional and two-dimensional defects of the crystal
structure of the residual austenite and ε-martensite being forming during
these transformations (dislocations, low-angle dislocation fragment sub-
boundaries, random stacking faults). The maximal enhancement of car-
bon diffusion coefficient was found as a thermal cycle number increased
up to one hundred, when the main increase in the defect density was
observed in the f.c.c. and h.c.p. crystal structures.
After the first γ–ε–γ transformation cycle, the diffusion coefficient
of carbon was found to be equal to 1.7 ∙ 10−11 and 2.3 ∙ 10−11 cm2/s at the
temperatures of 100 °С and 200 °С, respectively. Further increase in
number of γ–ε–γ cycles up to 500 induced additional enhancement of
diffusion coefficient by 3.2 and 4.2 times, respectively.
Contribution of different defects into the diffusion intensification-
ISSN 1608-1021. Usp. Fiz. Met., 2018, Vol. 19, No. 1 91
Effect of Martensitic Transformations on Diffusion in Fe–Mn
during the diffusion annealing manifests itself within the different
ranges of γ–ε–γ cycling. Analysing characteristics and regularities in a
process of accumulation of different types of structural defects enabled
to determine a certain succession of their effect on diffusion:
(i) dislocation effect was observed after the first γ–ε–γ transition
cycle;
(ii) enhancement of contribution of the random stacking faults oc-
curred during the first 30–40 cycles;
(iii) disoriented low-angle subboundaries did not strongly affect the
diffusion after the first 5–7 cycles, however, they were found to be con-
tinuously accumulated and effectively influenced on the diffusion pro-
cesses already in a whole thermal cycling range.
An increase of the value of D after 100 cycles of transitions during
the diffusion annealing in the range of existence of ε-martensite, up to
the onset of the reverse ε–γ transformation, should be attributed only to
the effect of dislocations, which formed polygonal networks of the low-
angle subboundaries in the h.c.p. lattice of the ε-phase.
An additional factor in changing the diffusion characteristics of
carbon in a phase-hardened alloy is the change in the phase composition,
in one case, in the process of thermal cycling and, in another case, due
to the subsequent diffusion annealing. The annealing of the phase-hard-
ened alloy in the temperature range of existence of ε-martensite induced
a partial reverse ε–γ transformation. When a degree of the phase hard-
ening increased, the reverse ε–γ transformation occurred more actively.
Because of decreasing amount of ε-martensite and accordant content of
the random stacking faults during the partial ε–γ transformation, the
effect of amplification of diffusion processes became weaker. That is
why, in order to increase impact of defects on the diffusion processes,
the alloy should be annealed at the temperatures when ε-martensite ex-
ists (onset of the reverse ε–γ transformation). In case of the annealing
temperatures higher the temperature of the completion of ε–γ transfor-
mation, the random stacking faults do not contribute to the amplifica-
tion of diffusion processes.
An exponential dependence of the content of carbon on the squared
penetration depth indicated about the bulk character of carbon diffu-
sion at the low temperatures. Effect of the bulk diffusion resulted to
the enhanced crystal lattice parameters for austenite and ε-martensite;
using these parameters, we can calculate the depth distribution of dis-
solved carbon atoms in both austenite and martensite phases. The dis-
solution of carbon in γ- and ε-phases of the phase-hardened alloy indi-
cated that randomly distributed dislocations and low-angle dislocation
subboundaries of the fragments, generated by the γ–ε–γ transformations,
did not form continuous dislocation network capable to create continu-
ous dislocation tubes for a diffusion of carbon atoms along them.
92 ISSN 1608-1021. Prog. Phys. Met., 2018, Vol. 19, No. 1
V.Y. Bondar, V.E. Danilchenko, V.F. Mazanko, O.V. Filatov, and V.E. Iakovlev
The revealed fundamental regularity for acceleration of carbon dif-
fusion via the cyclic γ–ε–γ martensitic transformations has a practical
importance. It is expedient to use it to intensify the technological pro-
cesses of cementation of metastable iron–manganese alloys, as well as to
accelerate the processes of decomposition of carbon-based solid solutions
and dispersion hardening in martensite-aging alloys. Accelerated diffu-
sion of carbon and, apparently, nitrogen will allow realization of the
processes of cementation and nitriding at the temperatures that are
hundreds of degrees lower as compared with those used in the practice
of surface chemical and thermal treatments of metal devices.
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Received February 2, 2018;
in final version, March 30, 2018
В.Й. Бондар, В.Ю. Данільченко,
В.Ф. Мазанко, О.В. Філатов, В.Є. Яковлев
Інститут металофізики ім. Г.В. Курдюмова НАН України,
бульв. Академіка Вернадського, 36, 03142 Київ, Україна
ВПЛИВ ЦИКЛІЧНИХ МАРТЕНСИТНИХ
ПЕРЕТВОРЕНЬ γ−ε−γ НА ДИФУЗІЙНІ ХАРАКТЕРИСТИКИ
КАРБОНУ В ЗАЛІЗОМАНґАНОВОМУ СТОПІ
Методою радіоактивних ізотопів досліджено дифузійні характеристики Карбону
у метастабільному залізоманґановому стопі Г18С2, наклепаному циклічними
мар тенситними перетвореннями γ−ε−γ (ГЦК–ГЩП–ГЦК). Показано, що інтен си-
фікація процесу транспорту Карбону у стопі, фазонаклепаному γ−ε−γ-перет во-
реннями, визначалася двома незалежними механізмами: атермічним, який реа-
лізовувався за рахунок ґенерації поля напружень у процесі мартенситних пере-
творень, і термоактивованим, який реалізовувався в процесі наступного ди-
фузійного відпалення за рахунок дії малокутових субмеж та одновимірних і
94 ISSN 1608-1021. Prog. Phys. Met., 2018, Vol. 19, No. 1
V.Y. Bondar, V.E. Danilchenko, V.F. Mazanko, O.V. Filatov, and V.E. Iakovlev
двовимірних дефектів кристалічної будови ГЦК-аустеніту і ГЩП-ε-мартенситу,
що формувалися в результаті цих перетворень. Після багаторазових циклів
γ−ε−γ-пе ретворень коефіцієнт дифузії Карбону за низьких температур (100–
350 °С) підвищувався на понад три порядки. При цьому коефіцієнт за темпера-
тури у 325 °С відповідав коефіцієнту стаціонарної дифузії при 900 °С. Макси-
мальний приріст коефіцієнта дифузії Карбону спостерігали при збільшенні
кількости термоциклів до ста, коли фіксували основний приріст густини дефектів
будови. Додатковим чинником зміни дифузійних характеристик Карбону у фа-
зонаклепаному стопі є зміна фазового складу як у результаті γ−ε−γ-циклування,
так і в процесі наступного дифузійного відпалення.
Ключові слова: дифузія, мартенсит, аустеніт, радіоізотоп, дислокація, дефект
пакування.
В.Й. Бондар, В.Ю. Данильченко,
В.Ф. Мазанко, О.В. Филатов, В.Є. Яковлев
Институт металлофизики им. Г.В. Курдюмова НАН Украины,
бульв. Академика Вернадского, 36, 03142 Киев, Украина
ВЛИЯНИЕ ЦИКЛИЧЕСКИХ МАРТЕНСИТНыХ
ПРЕВРАЩЕНИЙ γ−ε−γ НА ДИФУЗИОННыЕ ХАРАКТЕРИСТИКИ
УГЛЕРОДА В жЕЛЕЗОМАРГАНЦЕВОМ СПЛАВЕ
Методом радиоактивных изотопов исследованы диффузионные характеристики
углерода в метастабильном железомарганцевом сплаве Г18С2, наклёпанном ци-
клическими мартенситными превращениями γ−ε−γ (ГЦК–ГПУ–ГЦК). Показано,
что интенсификация процесса транспорта углерода в сплаве, фазонаклёпанном
γ−ε−γ-превращениями, определялась двумя независимыми механизмами: атер-
мическим, который реализовывался за счёт генерирования поля напряжений
в процессе мартенситных превращений, и термоактивированным, который реа-
лизовывался в процессе последующего диффузионного отжига за счёт действия
малоугловых субграниц, а также одномерных и двухмерных дефектов кристал-
лического строения ГЦК-аустенита и ГПУ-ε-мартенсита, сформированных в про-
цессе этих превращений. После многократных циклов γ−ε−γ-превращений коэф-
фициент диффузии углерода при низких температурах (100–350 °C) повышался
более чем на три порядка. При этом коэффициент диффузии при температуре
325 °C соответствовал коэффициенту стационарной диффузии при температуре
900 °C. Максимальный прирост коэффициента диффузии углерода наблюдали
при увеличении количества термоциклов до ста, когда фиксировали основной
прирост плотности дефектов строения. Дополнительным фактором изменения
диффузионных характеристик углерода в фазонаклёпанном сплаве было изме-
нение фазового состава как в процессе γ−ε−γ-циклирования, так и последующего
диффузионного отжига.
Ключевые слова: диффузия, аустенит, мартенсит, радиоизотоп, дислокация, де-
фект упаковки.
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