Tracer Diffusion of Cobalt in High-Entropy Alloys AlxFeNiCoCuCr
The Co diffusion in the as-cast high-entropy alloys AlxFeNiCoCuCr (x = 1, 1.5, 1.8) is studied by means of the tracer-diffusion method using the ⁶⁰Cо isotope. As shown, the Co diffusion in the high-entropy alloys occurs by means of the vacancy mechanism and the diffusion coefficient decreases approx...
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Інститут металофізики ім. Г.В. Курдюмова НАН України
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Nadutov, V.M. Mazanko, V.F. Makarenko, S.Yu. 2017-09-05T16:56:02Z 2017-09-05T16:56:02Z 2017 Tracer Diffusion of Cobalt in High-Entropy Alloys AlxFeNiCoCuCr / V.M. Nadutov, V.F. Mazanko, S.Yu. Makarenko // Металлофизика и новейшие технологии. — 2017. — Т. 39, № 3. — С. 337-348. — Бібліогр.: 22 назв. — англ. 1024-1809 DOI: 10.15407/mfint.39.03.0337 PACS: 61.66.Dk, 61.72.S-, 65.40.gd, 66.30.Fq, 66.30.J-, 68.37.Hk, 81.70.Pg https://nasplib.isofts.kiev.ua/handle/123456789/123468 The Co diffusion in the as-cast high-entropy alloys AlxFeNiCoCuCr (x = 1, 1.5, 1.8) is studied by means of the tracer-diffusion method using the ⁶⁰Cо isotope. As shown, the Co diffusion in the high-entropy alloys occurs by means of the vacancy mechanism and the diffusion coefficient decreases approximately in three times (from 3.21•10⁻¹⁶ to 0.98•10⁻¹⁶ m⁻¹⁶s⁻¹) with the increasing Al concentration. The decelerated Co diffusion is explained in terms of relatively large and negative enthalpy of mixing. Методом радиоактивных изотопов изучена диффузия ⁶⁰Cо в литых высокоэнтропийных сплавах AlxFeNiCoCuCr (х = 1, 1,5, 1,8). Показано, что диффузия Сo в высокоэнтропийных сплавах происходит по вакансионному механизму, и с увеличением концентрации Al значение коэффициента диффузии уменьшается примерно в три раза (от 3,21•10⁻¹⁶ до 0,98•10⁻¹⁶ м⁻¹⁶с⁻¹). Замедленная диффузия Co объясняется за счёт относительно большой и отрицательной энтальпии смешения. Методою радіоактивних ізотопів досліджено дифузію ⁶⁰Cо у литих високоентропійних стопах AlxFeNiCoCuCr (х = 1, 1,5, 1,8). Показано, що дифузія Сo у високоентропійних стопах відбувається за вакансійним механізмом, і зі збільшенням концентрації Al значення коефіцієнта дифузії зменшується приблизно втричі (від 3,21•10⁻¹⁶ до 0,98•10⁻¹⁶ м⁻¹⁶с⁻¹). Уповільнена дифузія Co пояснюється за рахунок відносно великої і неґативної ентальпії змішання. This work was carried out with financial support of the Project 22/15-H of the Goal-Oriented Complex Program of Fundamental Research ‘Fundamental Problems of Fabrication of the Nanomaterials and Nanotechnologies’ of the N.A.S. of Ukraine, and partially, the budget program 022/11B of Department of the Structure and Properties of Solid Solutions at the G. V. Kurdyumov IMPh of the N.A.S. of Ukraine. The authors enclose gratitude to V. P. Zalutskii for X-ray measurements. en Інститут металофізики ім. Г.В. Курдюмова НАН України Металлофизика и новейшие технологии Дефекты кристаллической решётки Tracer Diffusion of Cobalt in High-Entropy Alloys AlxFeNiCoCuCr Диффузия меченых атомов кобальта в высокоэнтро-пийных сплавах AlxFeNiCoCuCr Дифузія значених атомів Кобальту у високоентропійних стопах AlxFeNiCoCuCr Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Tracer Diffusion of Cobalt in High-Entropy Alloys AlxFeNiCoCuCr |
| spellingShingle |
Tracer Diffusion of Cobalt in High-Entropy Alloys AlxFeNiCoCuCr Nadutov, V.M. Mazanko, V.F. Makarenko, S.Yu. Дефекты кристаллической решётки |
| title_short |
Tracer Diffusion of Cobalt in High-Entropy Alloys AlxFeNiCoCuCr |
| title_full |
Tracer Diffusion of Cobalt in High-Entropy Alloys AlxFeNiCoCuCr |
| title_fullStr |
Tracer Diffusion of Cobalt in High-Entropy Alloys AlxFeNiCoCuCr |
| title_full_unstemmed |
Tracer Diffusion of Cobalt in High-Entropy Alloys AlxFeNiCoCuCr |
| title_sort |
tracer diffusion of cobalt in high-entropy alloys alxfenicocucr |
| author |
Nadutov, V.M. Mazanko, V.F. Makarenko, S.Yu. |
| author_facet |
Nadutov, V.M. Mazanko, V.F. Makarenko, S.Yu. |
| topic |
Дефекты кристаллической решётки |
| topic_facet |
Дефекты кристаллической решётки |
| publishDate |
2017 |
| language |
English |
| container_title |
Металлофизика и новейшие технологии |
| publisher |
Інститут металофізики ім. Г.В. Курдюмова НАН України |
| format |
Article |
| title_alt |
Диффузия меченых атомов кобальта в высокоэнтро-пийных сплавах AlxFeNiCoCuCr Дифузія значених атомів Кобальту у високоентропійних стопах AlxFeNiCoCuCr |
| description |
The Co diffusion in the as-cast high-entropy alloys AlxFeNiCoCuCr (x = 1, 1.5, 1.8) is studied by means of the tracer-diffusion method using the ⁶⁰Cо isotope. As shown, the Co diffusion in the high-entropy alloys occurs by means of the vacancy mechanism and the diffusion coefficient decreases approximately in three times (from 3.21•10⁻¹⁶ to 0.98•10⁻¹⁶ m⁻¹⁶s⁻¹) with the increasing Al concentration. The decelerated Co diffusion is explained in terms of relatively large and negative enthalpy of mixing.
Методом радиоактивных изотопов изучена диффузия ⁶⁰Cо в литых высокоэнтропийных сплавах AlxFeNiCoCuCr (х = 1, 1,5, 1,8). Показано, что диффузия Сo в высокоэнтропийных сплавах происходит по вакансионному механизму, и с увеличением концентрации Al значение коэффициента диффузии уменьшается примерно в три раза (от 3,21•10⁻¹⁶ до 0,98•10⁻¹⁶ м⁻¹⁶с⁻¹). Замедленная диффузия Co объясняется за счёт относительно большой и отрицательной энтальпии смешения.
Методою радіоактивних ізотопів досліджено дифузію ⁶⁰Cо у литих високоентропійних стопах AlxFeNiCoCuCr (х = 1, 1,5, 1,8). Показано, що дифузія Сo у високоентропійних стопах відбувається за вакансійним механізмом, і зі збільшенням концентрації Al значення коефіцієнта дифузії зменшується приблизно втричі (від 3,21•10⁻¹⁶ до 0,98•10⁻¹⁶ м⁻¹⁶с⁻¹). Уповільнена дифузія Co пояснюється за рахунок відносно великої і неґативної ентальпії змішання.
|
| issn |
1024-1809 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/123468 |
| citation_txt |
Tracer Diffusion of Cobalt in High-Entropy Alloys AlxFeNiCoCuCr / V.M. Nadutov, V.F. Mazanko, S.Yu. Makarenko // Металлофизика и новейшие технологии. — 2017. — Т. 39, № 3. — С. 337-348. — Бібліогр.: 22 назв. — англ. |
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2025-11-26T19:07:39Z |
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2025-11-26T19:07:39Z |
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| fulltext |
PACS numbers: 61.66.Dk, 61.72.S-, 65.40.gd, 66.30.Fq, 66.30.J-, 68.37.Hk, 81.70.Pg
Tracer Diffusion of Cobalt in High-Entropy Alloys
AlхFeNiCoCuCr
V. M. Nadutov, V. F. Mazanko, and S. Yu. Makarenko
G. V. Kurdyumov Institute for Metal Physics, N.A.S. of Ukraine,
36 Academician Vernadsky Blvd.,
UA-03142 Kyiv, Ukraine
The Co diffusion in the as-cast high-entropy alloys AlxFeNiCoCuCr (x = 1,
1.5, 1.8) is studied by means of the tracer-diffusion method using the
60Cо
isotope. As shown, the Co diffusion in the high-entropy alloys occurs by
means of the vacancy mechanism and the diffusion coefficient decreases ap-
proximately in three times (from 3.21⋅10−16
to 0.98⋅10−16
m
2⋅s−1) with the in-
creasing Al concentration. The decelerated Co diffusion is explained in terms
of relatively large and negative enthalpy of mixing.
Keywords: high-entropy alloys,
60Cо diffusion coefficient, structure, activa-
tion energy, melting temperature.
Методою радіоактивних ізотопів досліджено дифузію
60Cо у литих висо-
коентропійних стопах AlxFeNiCoCuCr (х = 1, 1,5, 1,8). Показано, що ди-
фузія Сo у високоентропійних стопах відбувається за вакансійним меха-
нізмом, і зі збільшенням концентрації Al значення коефіцієнта дифузії
зменшується приблизно втричі (від 3,21⋅10−16
до 0,98⋅10−16
м
2⋅с−1). Упові-
льнена дифузія Co пояснюється за рахунок відносно великої і неґативної
ентальпії змішання.
Ключові слова: високоентропійний стоп, коефіцієнт дифузії
60Cо, струк-
тура, енергія активації, температура топлення.
Методом радиоактивных изотопов изучена диффузия
60Co в литых высоко-
энтропийных сплавах AlxFeNiCoCuCr (х = 1, 1,5, 1,8). Показано, что диф-
фузия Сo в высокоэнтропийных сплавах происходит по вакансионному ме-
Corresponding author: Sergiy Yuriyovych Makarenko
E-mail: serg_makar@ukr.net
Please cite this article as: V. M. Nadutov, V. F. Mazanko, and S. Yu. Makarenko,
Tracer Diffusion of Cobalt in High-Entropy Alloys AlхFeNiCoCuCr, Metallofiz.
Noveishie Tekhnol., 39, No. 3: 337–348 (2017), DOI: 10.15407/mfint.39.03.0337.
Ìåòàëëîôèç. íîâåéøèå òåхíîë. / Metallofiz. Noveishie Tekhnol.
2017, т. 39, № 3, сс. 337–348 / DOI: 10.15407/mfint.39.03.0337
Îттиски доступны непосредственно от издателя
Ôотокопирование разрешено только
в соответствии с лицензией
2017 ÈМÔ (Èнститут металлофизики
им. Ã. Â. Курдюмова ÍÀÍ Украины)
Íапечатано в Украине.
337
338 V. M. NADUTOV, V. F. MAZANKO, and S. Yu. MAKARENKO
ханизму, и с увеличением концентрации Al значение коэффициента диф-
фузии уменьшается примерно в три раза (от 3,21⋅10−16
до 0,98⋅10−16
м
2⋅с−1).
Замедленная диффузия Co объясняется за счёт относительно большой и
отрицательной энтальпии смешения.
Ключевые слова: высокоэнтропийный сплав, коэффициент диффузии
60Cо, структура, энергия активации, температура плавления.
(Received December 16, 2016)
1. INTRODUCTION
Development of new engineering materials with the high properties is
a requirement of the present time. The high-entropy alloys (HEAs),
which attracted attention of a number of scientists, can be attributed
to these materials [1–5]. These alloys belong to multicomponent metal-
lic systems containing constituents in equimolar or nearly equimolar
relationship being between 5 and 35 at.%. According to Yeh et al. [2],
the HEAs do not have the element as host and are characterized by high
configurational entropy of mixing (∆Smix) providing formation of sim-
ple solid solutions. Subsequent studies were followed this determina-
tion, however, the name HEA was unchanged.
The HEA possess unique practically important properties, for in-
stance, high heat resistance, corrosion resistance [6], low electrical
conductivity and thermal conductivity [7, 8]. The low growth of grains
[9] and high thermal stability [10] are attributed also to the HEA. One
can assume that sluggish diffusion kinetics even at high temperatures
is an important contributor to the outstanding properties of the HEA.
Nevertheless, currently there is no enough diffusion data for HEAs.
For example, M. H. Tsai et al. [11] have applied the diffusion pair method
and measured the diffusion parameters in the CoCrFeMnNi HEA, and
the obtained data were compared with the self-diffusion. It was found
that the diffusion rates of each element in the CoCrFeMnNi HEA were
low, which was attributed to a higher activation energy of diffusion. To
explain the sluggish diffusion in the HEA, the quasi-chemical model was
proposed in which the essential fluctuations of the lattice potential ener-
gy (LPE) in different matrixes create the effect of trap and obstacles for
atomic mobility resulting in high diffusion-activation energy.
Recently M. Dabrowa et al. [12] have studied interdiffusion parame-
ters in non-equimolar HEA AlCoCrFeNi and determined the tracer dif-
fusion coefficients of the components using two methods of optimisa-
tion. The results confirmed the theory of sluggish diffusion in HEAs.
Very recently, M. Vaidya et al. [13] have reported the results upon
tracer (
63Ni) diffusion obtained for the first time in CoCrFeNi and
CoCrFeMnNi alloys by the radiotracer technique in the temperature
range of 1073–1373 K. A tendency to a successive slow down on the
TRACER DIFFUSION OF COBALT IN HIGH-ENTROPY ALLOYS AlхFeNiCoCuCr 339
tracer diffusion rate with an increased number of components in the
HEAs was established. They concluded that diffusion in HEAs is not
inevitably decelerated.
Taking into account the limited number of works upon diffusion in
HEA as well as the fact that the knowledge upon diffusion and kinetic
parameters are the key data in study of crystallization processes, phase
transformations, and atomic ordering, the new studies in this direc-
tion are required. At the same time, in order to enhance the reliability
of the diffusion data, it is necessary to extend a set of the experimental
methods. Therefore, the diffusion processes in the AlхFeNiCoCuCr
HEA with the third chemical compositions х = 1, 1.5, 1.8 has been
studied by means of the tracer-diffusion method using the
60Co isotope.
2. MATERIAL AND METHODS
The as-cast high-entropy alloys AlхFeNiCoCuCr with the Al concentra-
tions х = 1 (А1), х = 1.5 (А2), and х = 1.8 (А3) were studied (Table 1). The
samples of the HEA were the 10×10×1.2 mm plates. To study the diffu-
sion of cobalt in HEA, the tracer diffusion method was applied, which
is more effective to study the diffusion processes in metals and alloys.
The radioactive isotope
60Co was chosen as diffusant which was depos-
ited on the plate surface at room temperature. This isotope has the
∼ 5.3 years half-life time and irradiates electrons (β) resulting from β
decay. The plates with the deposited layer of the radioactive isotope
were aged in vacuum (p = 10−5
Pa) at 1473 K during 10 hrs.
The phase composition and the microstructure of the as-cast HEA
were studied by means of the X-ray diffraction (XRD) analysis using
diffractometer DRON-3M with the CoKα irradiation and the scanning
electron microscope Jeol JCM-5000 (Neoscope). All the X-ray powder
diffractograms of the HEA in initial as-cast state were measured with
the same exposure of 0.05°/2′′. The surface layer of the 0.2–0.25 µm in
thickness was removed by etching before measurements in order to ex-
clude the effect of stresses appeared after mechanical treatment.
In order to estimate the tracer diffusion coefficient of Co, the meth-
odology described in [14] was applied. The concentration distribution of
TABLE 1. Chemical composition of the high-entropy alloys AlxFeCoNiCuCr.
Alloy x Element, [wt.%]/[at.%]
Al Fe Co Ni Cu Cr
A1 1 8.8/17.2 18.1/17.1 18.3/16.3 18.9/16.9 19.7/16.3 16.0/16.2
A2 1.5 12.2/23.0 17.4/15.9 17.3/14.9 18.6/16.1 19.4/15.5 14.9/14.6
A3 1.8 14.9/27.3 16.8/14.9 17.1/14.4 17.7/14.8 18.7/14.6 14.7/14.0
340 V. M. NADUTOV, V. F. MAZANKO, and S. Yu. MAKARENKO
the
60Co isotope in the studied sample was determined by layer-by-layer
analysis. This methodology is used in case of diffusion from a thin layer
(1–3 µm) into infinite body at stationary isothermal ageing. In this
method, the concentration of the radioactive isotope penetrated in a
sample is detected upon irradiation intensity In (a number of pulses per
minute) from n-th layer. Generally, the dependence of irradiation inten-
sity In on a coordinate after n-th layer stripping is expressed by formula:
( ) [ ]
∞
= τ −µ −∫ 0, exp ( ) d ,
n
n n
d
I c d d d d (1)
where dn is the coordinate of n-th layer, c(d, τ) is the function ex-
pressed the dependence of a radioactive isotope concentration on coor-
dinate, µ is the absorption coefficient of an isotope irradiation by a
sample material; τ is the durability of diffusion annealing.
If to accept the premise that solution of the Fick’s second equation
for the above-mentioned conditions is as follows:
( )
2
, exp
4
A d
c d
DD
τ = − τp τ
, (2)
and, moreover, substituting Eq. (2) in Eq. (1), after transformations,
one obtains:
∂
µ + = − ∂ τp τ
2
exp .
4
n n
n
n
I dA
I
d DD
(3)
After taking a logarithm of the expression (3) and neglecting µIn
(through a smallness of µ for this case), one obtains:
21
ln .
4
n
n
n
I
d A
d D
∂
= − + ∂ τ
(4)
Since ln( / )n nI d∂ ∂ is linear function of
2
nd Eq. (4), the tgα equals to
1/(4 )Dτ (α is the angle between this dependence and coordinate d
2) that
characterises a bulk diffusion. Deviation from linear dependence
∂ ∂ = 2ln( / ) ( )n n nI d f d is an attribute of existence of other contributions
into diffusion process from grain boundaries, dislocations, interphase
boundaries, etc. [15].
Thus, according to Eq. (4), the following relationship for diffusion
coefficient determination is obtained:
= −
τ α
1
4 tg
D , (5)
or, in decimal logarithm:
TRACER DIFFUSION OF COBALT IN HIGH-ENTROPY ALLOYS AlхFeNiCoCuCr 341
= −
τ α
0.1086
.
tg
D (6)
This approach is usually used in diffusion studies at isothermal age-
ing of an alloy with the accuracy in diffusion coefficient determination
of approximately 5%.
3. RESULTS
The XRD analysis at room temperature has shown that one bcc (α) and
two f.c.c. (γ1 and γ2) phases were identified in the as-cast equimolar
AlFeCoNiCuCr alloy (A1) (Fig. 1), which is consistent with the data of
works [1–3, 16]. The lattice parameters of these phases are àα = 0.2871
nm, àγ1 = 0.3624 nm and àγ2 = 0.3592 nm, respectively. The phases α
and the γ1 were detected in the as-cast HEA having a higher concentra-
tion of Al (x = 1.8), whereas the γ2 phase was not revealed. The lattice
constants of the α and γ1 phases grow to the values of 0.2882 nm and
0.3648 nm, respectively, with increasing concentration of Al, which
suggests dissolution of Al in both phases and is consistent with the
concentration dependences of the lattice parameter of the b.c.c. and
f.c.c. phases in the AlxFeCoNiCuCr HEA shown in [2, 3]. At the same
time, the width of diffraction lines of α-phase increases approximately
by 13%. As there is no evidence for dispersion of crystal structure, the
broadening of the linewidth is attributed to growing microstresses.
The linewidth of diffraction lines from the γ-phase, particularly for
the HEA with the higher Al concentration, has been not estimated cor-
rectly through its weak intensity because of the low content of this
phase. According to the X-ray diffraction data, the concentration of the
Fig. 1. XRD patterns of the as-cast AlxFeCoNiCuCr HEAs for x = 1 (A1) (a) and x =
= 1.8 (A3) (b).
342 V. M. NADUTOV, V. F. MAZANKO, and S. Yu. MAKARENKO
γ-phase was reduced from 35% to 8% by opposite to that of the α-phase,
which increases from 65% to 92% with the increasing Al content.
Figure 2 represents the SEM images of the as-cast AlxFeCoNiCuCr
HEA. The typical dendrite (DR) structure with the interdendrite (ID)
zones is observed in the HEA that is consistent with works [3, 16]. The
dimensions and morphology of the DRs and IDs are diverse in these al-
loys and the sizes of individual DR reach of 100–500 nm and ID zones of
1–10 µm. This indicates on inhomogeneity of the crystallization reac-
tion through a difference in local composition and inhomogeneous dis-
tribution of atoms in the melt and, as a result, in the solid solution.
Moreover, with it, the increase of Al content results in refinement of
DRs and IDs, excepting for individual large ID zones (Fig. 2, b). The in-
homogeneous atomic distribution in the AlxFeCoNiCuCr HEA was de-
tected in [16–18]. Particularly Cu tends to segregate in ID–DR bounda-
ries [16, 18], which results from a high positive enthalpy of mixing of
Cu in the mixture with the other elements [16, 19]. Taking into account
the spatial inhomogeneities in the as-cast AlxFeCoNiCuCr HEA [16–
18], their multiphase composition and dendritic microstructure [1–3]
(see Fig. 1 and Fig. 2) as well as the competing affinity of each element
with other ones (negative and positive enthalpy of mixing in binary sys-
tems A–B, where A, B = Cu, Ni, Cr, Al, Co, Fe [19]), one can assume ab-
normal behaviour of the diffusion characteristics.
The concentration profiles of the
60Со tracer diffusion in the
equimolar AlFeNiCoCuCr HEA are presented in Fig. 3. The pro-
nounced exponential behaviour of the concentration profiles for this
alloy points to the fact that the Co tracer diffusion at 1473 K occurs in
the bulk due to the vacancy mechanism. The diffusant
60Co penetrates
on the depth of 50 µm. At this temperature, the diffusion coefficient of
Fig. 2. SEM images of microstructures of the as-cast AlxFeCoNiCuCr HEAs
with different aluminium contents (x-value): 1.0 (A1) (a) and 1.8 (A3) (b).
TRACER DIFFUSION OF COBALT IN HIGH-ENTROPY ALLOYS AlхFeNiCoCuCr 343
cobalt in the equimolar HEA, as estimated upon (6), is equal to
3.21⋅10−16
m
2⋅s−1
(Table 2).
In order to correct compare the obtained value with the Co diffusion
coefficient in CoCrFeMnNi HEA obtained by M. H. Tsai et al. [11], the
melting point Tm of the equimolar A1 HEA was measured by means of
the DTA analysis (Tm = 1600 K; Fig. 4, a) and the inverse homologous
temperature was determine Tm/T ≅ 1.1. Extrapolating the data of
M. H. Tsai et al. on this homologous temperature, the Co diffusion co-
efficient for CoCrFeMnNi HEA,
HEA
CoD ≅ 10−14
m
2⋅s−1, differs from that
obtained in our experiment and higher by two orders of magnitude.
One can assume that this difference results from effect of Al.
The increase of Al concentration confirms this hypothesis. The dif-
fusion curve for the Al1.5FeNiCoCuCr HEA (A2) is near the exponential
shaped one, although it differs from that for the equimolar HEA (A1)
by abrupt decreasing depth (≅ 11 µm) of the
60Со penetration at 1473 K
(Fig. 3). The exponential behaviour of the curve means also the bulk
diffusion of Co in the A2 HEA and, at the same time, this diffusion pro-
cess is slower than in the equimolar A1 alloy. The estimated Co diffu-
sion coefficient in this case is 1.1⋅10−16
m
2⋅s−1, which approximately
Fig. 3. The concentration profiles of the
60Со isotope tracer diffusion in the
equimolar (x = 1.0) high-entropy alloy AlxFeNiCoCuCr (А1) and in the HEAs
with x = 1.5 (А2) and x = 1.8 (А3) after diffusion ageing at Т = 1473 K during
τ = 3.6⋅104
sec. Insert shows the diffusion curve for А1 in coordinates
∂ ∂ = 2ln( / ) ( )n n nI d f d (x = 1).
344 V. M. NADUTOV, V. F. MAZANKO, and S. Yu. MAKARENKO
three times of magnitude smaller than in the equimolar HEA (Table 2).
The melting point of this alloy increases by 16 K (Tm = 1616 K) and does
not change essentially the Tm/T ≅ 1.1 value. Therefore, the comparison
of D values for A1 and A2 alloys is correct.
In case of the Al1.8FeNiCoCuCr HEA (A3) with the higher Al content
(x = 1.8), the
60Co penetration depth at the same temperature (1473 K) is
approximately by one order smaller than in equimolar HEA (A1) and does
not exceed 6 µm (Fig. 3). This one points onto a still smaller Co diffusion
rate in the alloy. The diffusion curve shows also exponential behaviour
(Fig. 3), although its slope is greater than that for the AlFeNiCoCuCr
(A1) and the Al1.5FeNiCoCuCr (A2) HEAs. The estimated diffusion coeffi-
cient in the Al1.8FeNiCoCuCr HEA (A3) is smaller and equal to 0.98⋅10−16
m2⋅s−1
(Table 2). This
HEA
CoD value should be still smaller since the melting
of the A3 HEA occurs at higher temperature, 1638 K (Fig. 4, b) (the cor-
responding inverse homologous temperature Tm/T is increased). Conse-
quently, the addition of Al reduces the tracer diffusion rate.
Thus, in accordance with the data obtained by M. H. Tsai et al. [11],
the Co diffusion coefficient for Al free CoCrFeMnNi HEA at identical
Fig. 4. Heat flow for the AlxFeCoNiCuCr HEA: х = 1 (А1) (a) and х = 1.8 (А3) (b).
TABLE 2. Diffusion characteristics of the AlхFeNiCoCuCr HEAs for 1473 K.
Alloy х
HEA
CoD ,
[m2⋅s−1]
shield
CoD ,
[m2⋅s−1]
shield
CoD / HEA
CoD
D0,
[m2⋅s−1]
Q,
[kJ⋅mol−1]
A1 1 3.21⋅10−16 – 18 – 351.4
A2 1.5 1.1⋅10−16 – 52 – 364.5
A3 1.8 0.98⋅10−16 – 59 – 365.9
CoCrFeMnNi
[11]
–
∼ 10−14
(1473 K) – – 9.26⋅10−4 306.9
Co [14] – –
57.6⋅10−16 m2⋅s−1
(1448 K) – – –
TRACER DIFFUSION OF COBALT IN HIGH-ENTROPY ALLOYS AlхFeNiCoCuCr 345
temperature conditions (the same inverse homologous temperature) is
higher by approximately two orders in magnitude. Moreover, the
HEA
CoD
values determined in our tracer diffusion experiment (Table 2) are ap-
proximately by one order of magnitude smaller than Co self-diffusion
coefficient at 1448 K,
self
CoD = 57.6⋅10−16
m
2⋅s−1, in [14] (Table 2). Thus, it
can be concluded that aluminium decelerates diffusion process in as-cast
high-entropy alloys AlхFeNiCoCuCr (x = 1, 1.5, 1.8).
The activation enthalpy of the diffusion Q was estimated by means of
the Arrhenius equation:
0 exp ,
Q
D D
RT
= −
(7)
where D0 is the pre-exponential factor, RT has its usual meaning. We
are aware that diffusion experiment at different temperatures is re-
quired, which will be fulfilled in the near future. However, just to esti-
mate Q value and its change with the Al increase, the pre-exponential
factor, D0 = 9.26⋅10−4
m
2⋅s−1, as obtained for Co in the multicomponent
CoCrFeMnNi alloy, was taken from [11]. The estimated activation en-
thalpy for the studied equimolar AlFeNiCoCuCr HEA equals
Q = 351.4 kJ⋅mol−1. The enthalpy of activation for the studied HEA
equals Q = 333.6 kJ⋅mol−1
in case of pre-exponential factor,
D0 = 2.16⋅10−4
m
2⋅s−1, as obtained by J. Dabrowa et al. for the Co tracer
diffusion in AlCoCrFeNi system [12]. The obtained Q values are by 15%
higher than those reported in [11, 12]. The differences between Q value
obtained in the present work and those reported in [11, 12] can be ex-
plained by the effect of Al, except for proximity in D0 for studied values.
The presence of Mn in the multicomponent CoCrFeMnNi alloy [11] and
the considerable deviation from equimolar composition of HEA [12] may
also have an impact upon differences between Q values.
4. DISCUSSION
The activation enthalpy for studied HEAs estimated in the same way
using the pre-exponential factor taken from [11] turned out an increas-
ing value with the increasing Al content to x = 1.5 and x = 1.8 (Table 2).
The higher diffusion activation enthalpy, the slower is diffusion pro-
cess [14]. This one supports a statement that Al suppresses diffusion in
the AlxFeNiCoCuCr HEAs, and this process is sluggish.
One can assume that such an essential effect of Al on tracer diffu-
sion of Co is due to significant interaction between Al and Co atoms.
The calculation results of the mixing enthalpy of different binary sys-
tems [19] support this assumption. The negative enthalpy of mixing
∆Hmix of the Al–Co binary system (−19 kJ⋅mol−1) is larger in contrast to
other binary systems (−1 kJ⋅mol−1
for Al–Cu; −10 kJ⋅mol−1
for Al–Cr;
346 V. M. NADUTOV, V. F. MAZANKO, and S. Yu. MAKARENKO
−11 kJ⋅mol−1
for Al–Fe). An exception is only for the Al–Ni system
where ∆Hmix = −22 kJ⋅mol−1
[19]. One can expect also the sluggish dif-
fusion of Ni in the AlхFeNiCoCuCr HEA. It correlates with the
EDS/TEM data regarding the existence of the dendritic Al–Ni zones
with the B2 crystal structure enriched principally with Co in the as-
cast equimolar AlCoCrCuFeNi HEA [20].
Possible mechanisms of the diffusion of Co in the HEAs were consid-
ered in [11–13]. A quasi-chemical model for calculation of fluctuations
of the lattice potential energy (LPE) in different principle metals and
particularly Al-free CoCrFeMnNi HEA was proposed by M. H. Tsai et
al. [11]. Greater LPE fluctuation between the lattice sites produces
more significant atomic traps and leads to higher activation enthalpy,
which accounts for the decelerated diffusion in HEA [11]. However, it
could be noted that the single phase in CoCrFeMnNi HEA did not con-
tain Al, which essentially distorts crystal lattice [2, 3], and the ap-
proach [11] does not take into consideration the possible different in-
teraction in pairs of atoms.
According to [21], the grain-boundary diffusion in polycrystals is
the main contribution to mass transfer only within the temperature
interval (0.5–0.7)Тm. At temperatures higher than denoted interval,
the bulk tracer diffusion is dominated. The grain-boundary contribu-
tion at 0.85Tm in
63Ni tracer diffusion in homogeneous equimolar
HEAs CoCrFeNi and CoCrFeMnNi (with relatively developed grain
structure at room temperature) was studied in [13], although, the au-
thors underlined a need of more detailed investigation of this point at
relatively high temperatures as the subject of a separate study.
Our experiment has been done at even greater temperature 1473 K
that corresponds to (0.90–0.92)Tm and excludes grain-boundary con-
tribution. Moreover, the as-cast Al-containing AlxFeNiCoCuCr HEAs
(x = 1, 1.5, 1.8) represent the dendrites formed during crystallization
of the melt and do not contain grain boundaries (Fig. 2). Thus, a grain
boundary diffusion mechanism in the studied HEAs with Tm = 1600–
1638 K can be excluded.
In addition, in case of two-phase system [15], the second phase exists
as an isolated inclusion and phase boundaries do not form the uniform
system similar to grain boundary one. Therefore, the whole mass
transfer upon phase boundaries at high temperature should be still
lower than along grain boundaries. A contribution of DR–ID bounda-
ries to diffusion process remains open, although, taking into account
high temperature (1473 K) and linear dependence ∂ ∂ = 2ln( / ) ( )n n nI d f d
Eq. (4) (Fig. 3, insert), the contributions to diffusion process from
boundaries of different structural elements, particularly from DR–ID
boundaries, are not sufficient [15].
According to [14], the exponential-like concentration curves (Fig. 3)
and linear dependence Eq. (4) mean that diffusion of Co in the as-cast
TRACER DIFFUSION OF COBALT IN HIGH-ENTROPY ALLOYS AlхFeNiCoCuCr 347
AlxFeNiCoCuCr HEA at high temperature occurs preferably in the
bulk by a vacancy mechanism. The vacancies in their sufficient concen-
tration for diffusion in HEAs can be generated at high temperatures by
a theoretically forecasted mechanism based on local distortion of the
interatomic distances due to considerable differences of the atomic ra-
dii [22]. In the studied HEAs, the atomic radius of Al (0.143 nm) is
higher than that for the rest metals (for example, 0.125 nm of Co).
5. CONCLUSIVE REMARKS
The
60Co tracer diffusion in the as-cast AlхFeNiCoCuCr (х = 1, 1.5, 1.8)
HEAs at the temperature of 1473 K ((0.90–0.92)Tm) turned out to be
abnormally low more than one order as compared to the Co self-
diffusion process.
Increase in the concentration of Al in the as-cast AlхFeNiCoCuCr
HEAs from х = 1 to x = 1.8 decreases the
60Co tracer diffusion coeffi-
cient
HEA
CoD by three times from 0.98⋅10−16
m
2⋅s−1
to 3.21⋅10−16
m
2⋅s−1
and
increases the activation enthalpy of the diffusion approximately by
4% (from 351.4 to 365.9 kJ⋅mol−1). The tracer diffusion of Co in the Al
containing HEAs at given homologous temperatures (0.90–0.92)Tm is
decelerated one provided by Al that is explained in terms of relatively
high and negative enthalpy of mixing of the Al and Co system.
The exponentially shaped
60Со concentration profiles correspond
certainly to the bulk tracer diffusion in the as-cast AlхFeNiCoCuCr
HEAs via more probable vacancy mechanism.
ACKNOWLEDGEMENTS
This work was carried out with financial support of the Project 22/15-H
of the Goal-Oriented Complex Program of Fundamental Research ‘Fun-
damental Problems of Fabrication of the Nanomaterials and Nanotech-
nologies’ of the N.A.S. of Ukraine, and partially, the budget program
022/11B of Department of the Structure and Properties of Solid Solu-
tions at the G. V. Kurdyumov IMPh of the N.A.S. of Ukraine. The au-
thors enclose gratitude to V. P. Zalutskii for X-ray measurements.
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