Prog. Theor. Exp. Phys. 2015, 043I01 (12 pages)
DOI: 10.1093/ptep/ptv048
Doping effect on the Janus-like structure of a
copper–iron bimetallic nanocluster and its
solid–liquid phase transition
Farid Taherkhani∗ and Pegah Freshteh Seresht
Department of Physical Chemistry, Razi University, Kermanshah 67149-67346, Iran
∗
E-mail: [email protected]
Received November 26, 2014; Revised February 17, 2015; Accepted March 3, 2015; Published April 30 , 2015
...............................................................................
A molecular dynamics simulation with a new-application potential model has been explored for
melting temperature, radial distribution of iron–copper bimetallic nanoclusters, and their bulk
for the first time. At low copper weight percentages, the melting temperature changes a little
for the bulk structures; however, for nanostructures, the variation of melting temperature is significant. At medium copper-doping values, there is a melting-temperature plateau in bimetallic
nanoclusters. For many catalysis applications, Janus-like structures are considered, which occur
at around 53% iron weight in copper at room temperature, when copper–iron bimetallic nanoclusters clearly consist of two distinct faces. Our result for the melting temperature of the bulk
alloy confirms the experimental result.
...............................................................................
Subject Index
1.
I10, I14
Introduction
In commercial steels, copper can be a common element; it can be measured as an added alloying
species or as an impurity [1]. Determination of the solid–liquid phase diagram for iron body center
cubic (bcc) and copper face center cubic (fcc) structures is difficult via experimental methods [2,3].
Fe-rich Fe–Cu alloys are of technological interest as admixtures of copper strengthen steel [4–8].
An iron–copper system is often used for prevailing such microstructures because the immiscibility
of these metals produces an ultrafine microstructure [4–8].
Bimetallic nanoclusters may form multishell chemical ordering patterns [9–11]. Bimetallic nanoalloys (Fe–Ni, Fe–Cu) and coated iron nanoalloys (chitosan–Fe0 , sodium oleate–Fe0 ) have been utilized
to support autotrophic denitrification [12]. Fe–Cu catalysts are used to synthesize the alcohols from
CO hydrogenation [13]. Iron–copper (Fe–Cu) alloys have practical applications in improving surface
heat conduction and corrosion resistance [14]. Synthesis of monodispersed carboxymethyl cellulose
stabilized Fe–Cu bimetal nanoparticles is used to reduce dechlorination of 1, 2, 4-trichlorobenzene
[15]. Fe–Cu catalysts are used for the hydrogenation of CO2 and are being applied to slurry reactors [16]. Iron, iron–copper, and iron–silver are Fischer–Tropsch catalysts [17]. The use of classical
potentials (hard spheres, Lennard–Jones (LJ), etc.) is more common at present. More complex and
more accurate potentials work to correct many deficiencies of simple pair potentials. However, it is
always a challenge to choose adequate models. On the one hand, the empiricism required often makes
the applicability to real materials somewhat questionable; on the other hand, the complex methods
and potentials also demand certain assumptions and leave the question about the applicability of
© The Author(s) 2015. Published by Oxford University Press on behalf of the Physical Society of Japan.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/),
which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
PTEP 2015, 043I01
F. Taherkhani and P. F. Seresht
the model and potentials open [18]. Previous simulations of film growth using the LJ potential concentrated only on the dependence on the size-mismatch of the two different atoms in the structure
[19–22]. Binary mixtures of Lennard–Jones (BLJ) atoms have been used extensively to simulate
glassy materials in recent years [19–22], owing to their reluctance to crystallize on the timescale of
molecular dynamics (MD) simulations. Some researchers have studied crystalline structures for 60-,
256-, and 320-atom supercells of binary Lennard–Jones solids [23]. The many-body Sutton–Chen
[24] potential is used for metal–metal interactions, and Lennard–Jones potentials describe the interaction between nanoclusters and substrates. The interatomic potentials are of Finnis–Sinclair type for
some bcc and fcc metals, as well as alloys such as the Fe–Cu system [25–31]. The Fe–Fe potential
is fitted to the elastic constant of iron and the calculated dependence of the lattice parameter on the
concentration of copper in solution is close to the experimental value [25–31].
The Finnis–Sinclair model has successfully predicted many properties of bcc metals, but it has not
proven very reliable for a few applications, such as modeling thermal expansion [32] or surface relaxation [33]. The Janus and Janus-like patterns individuate nanoparticles that exhibit two well defined
subunits, found during melting simulations from the theoretical and experimental points of view for
AgNi [34] and AgCu [35], respectively. The surface and interface energies are crucial quantities of
nanostructures because, as the surface-to-volume ratio increases with decreasing size, these quantities will greatly affect the physical properties of nanostructures, as in the case of nanostructures with
negative curvature, for which a clear and detailed understanding of surface energy is still lacking
[36]. Scanning tunneling microscopy can be used to investigate the solid surface structure experimentally [37]. Single-impurity metals influence the melting temperature of bimetallic nanoclusters
[38]. Different pathways leading to core–shell and bicompartmentalized configurations, reminiscent
of Janus geometry, have been shown in cobalt- and silver-rich alloys, and silver–nickel and silver–
gold alloys, respectively [39,40]. The present study focuses on the trend of the melting-point curve in
the presence of doping on bimetallic Fe–Cu nanoclusters and its alloy with the new potential model.
The radial distribution function near the melting temperature and the effect of doping on the radial
distribution function has been investigated for the present case of study. The core–shell structure of
copper–iron bimetallic nanoclusters is the other aim of the present case of study.
2.
Potential model for molecular dynamics simulation
In molecular dynamic simulations, we chose the quantum-corrected Sutton–Chen (Q-SC)-type
potentials for the copper atom. The Q-SC potential model describes interatomic interactions for metal
nanoparticles, because Q-SC potential is able to estimates static and transport properties such as the
lattice parameter, cohesive energy, bulk modulus, elastic constants, phonon dispersion, vacancy formation energy, self-diffusion coefficient, surface energy, and thermal transport properties [36–45].
The parameters of the Q-SC-type potential for pure Cu for the present case of study are taken from
Ref. [46]. For the Sutton–Chen-type force field, the total potential energy for an atomic system can
be written as
⎤
⎡
N
N
N
1
√
Ui =
ε⎣
V Ri j − c ρi ⎦ ,
(1)
U=
2
i
i
j=i
where V Ri j is a pair interaction function, which is defined by the following equation:
a n
V Ri j =
,
Ri j
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(2)
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accounting for the repulsion between the i and j atomic cores; ρi is the local electron density,
accounting for the cohesion associated with atom i, defined by
N
N a m
ϕ Ri j =
.
(3)
ρi =
Ri j
j=i
j=i
In Eqs. (1)–(3), Ri j , a, c, ε, n, and m are the distance between atoms i and j, a length parameter
scaling all spacing (leading to dimensionless V and ρ), a dimensionless parameter scaling the attractive terms, the overall energy scale, and integer parameters such that n > m, given the exponents
(n, m), respectively [41]. Parameter c is determined by the equilibrium lattice parameter, and ε is
determined by the total cohesive energy [41]. The Lennard–Jones potential has been extended for
interatomic interactions in bimetallic systems via the Lorentz–Berthelot rules for our present case
of study [47,48]. Lennard–Jones potential parameters can be investigated for bimetallic nanoclusters such as Fe, Cu [49]. The Lennard–Jones potential parameters for hetero interactions of Fe, Cu
between copper and iron for our simulation study are taken from Ref. [49]. The experimental result
for the mean square displacement of copper and iron metal shows that the Lennard–Jones potential is
able to predict the thermal lattice vibration properties and the temperature dependence very well [49].
A Finnis–Sinclair (FS) potential model has been applied for bcc metals such as Fe, V, Nb, Ta, Mo,
W [50,51]; as a result, the FS potential model has been used between iron atoms in our simulation.
The FS potential can be explained as
⎡
⎤1
2
1
2
⎣
⎦
V ri j −
A ϕ ri j
,
(4)
Utot =
2
ij
i
j=i
where the first term is a normal pairwise energy consisting of a repulsive part, the second term is the
n-body term taking a sum form over all atoms for a “cohesive function,” and A is a positive constant
to be fitted. In Eq. (4), V ri j is the pair potential between atoms i and j, taking the quadratic
polynomial, and φ ri j is the cohesive potential between atoms i and j, taking the parabolic form,
as follows:
(r − c)2 c0 + c1r + c2r 2 r ≤ c,
(5)
V (r ) =
0,
r > c,
(r − d)2 , r ≤ d,
ϕ(r ) =
(6)
0,
r > d,
where c and d are two disposable parameters assumed to be between the second- and third-neighbor
distances, and c0 , c1 , and c2 are three parameters to be fitted [51]. In fact, the FS potential model is
able to describe the cohesion energy on large atomic scales for metal compounds and give correct
descriptions of relaxation at free surface metals. From what has been discussed, it can be concluded
that the new potential application model yields accurate thermodynamics properties.
3.
Method of simulation
Molecular dynamics (MD) simulations of the bulk structure of bimetallic iron–copper are carried out
using the NVT ensemble and periodic boundary conditions. In the case of bimetallic nanoclusters,
simulations are carried out in an NVT ensemble without periodic boundary conditions. Temperature
is controlled by an Evans thermostat [52] and the equations of motion are integrated using the Verlet
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F. Taherkhani and P. F. Seresht
leapfrog algorithm [53] with a time step of 0.001 ps. The systems were equilibrated for 400 ps, and
then the averages of structures were computed over the following 500 ps. The DL-POLY-2.20 package
was used to conduct the MD simulations [54]. In order to obtain starting structures, a block of fcc
bimetallic was constructed from an fcc unit cell, and then replicated in three dimensions. To obtain
the optimum structure of all components, the system was first heated to the upper melting temperature
(1800 K) then, using the annealing technique, it was slowly cooled [55].
4. Results and discussion
4.1. Solid–liquid phase transition in bulk bimetallic Fe–Cu
A density functional calculation has been applied for optimization of iron nanoclusters [56].
A molecular dynamics (MD) simulation with the new-extension potential model has been done
for investigation of the solid–liquid phase transition of iron–copper bimetallic nanoclusters with
a total of 256 atom numbers. The periodic boundary condition was applied for calculation of the
thermodynamic properties of copper–iron alloys in the canonic NVT ensemble in the bulk limit. bcc
structure has been applied for pure iron in the bulk structure.
The MD simulation can be extended for calculation of the thermodynamic properties with the
NVT ensemble in nano systems. The MD simulations were done with an Evans thermostat and
time steps of 1 fs, a total time step of 500 ps, and ensemble averaging of 400 ps. The configurational
energy and radial distribution function were calculated via MD simulation. Many techniques can be
extended for determination of melting temperature, such as diffusion coefficients [57,58], Lindeman
indexes [59,60], phase-field-crystal models [61], configurational energy versus temperature [38,62],
and distortion parameters [63]. Surface curvature and nanoparticle size have an effect on melting
temperature [64,65]. The magnetic properties of bimetallic nanoparticles completely change near
the melting temperature [66].
Heat capacity [67] has been used for investigation of the solid–liquid phase transition of
nanostructures. On the basis of the heat capacity results from the MD simulation, there is a peak
in heat capacity as a function of temperature due to the solid-to-liquid phase transition. For example,
the heat capacity results for Cu3 Fe13 , CuFe3 , Cu7 Fe bimetallic copper–iron nanoclusters as a function of temperature are presented in Figs. 1(a)–(c), respectively. There is a relatively good agreement
between our MD results regarding melting temperature and the experimental results [68,69] for different amounts of doping of iron–copper bulk alloys. On the basis of the MD simulation results, the
melting temperature shows that there is a melting-temperature plateau as a function of the copper
weighting percentage. Our simulation result, Fig. 2, shows that the trend of melting temperature as a
function of the copper weight percentage doping for the copper–iron bulk alloy is in agreement with
the experimental result. On the basis of Fig. 2, the melting temperature for pure iron is greater than
that for pure copper metals in bulk structure. An increase of copper doping in iron causes a decrease in
the melting temperature because the stability of iron metal is decreased. The melting temperature for
the fcc structure of pure iron with the Q-SC-type potential is lower than that for the FS potential for
iron in the bcc structure [70]. For the bulk iron–copper alloy, copper doping in iron does not change
the melting temperature significantly. The melting temperature for bulk copper–iron alloys for the
new potential model just shows a maximum deviation of five relative percentages from the experimental data. The melting temperature for bimetallic copper–iron nanoclusters is shown in Fig. 3.
At low weight percentages of copper doping, the melting temperature decreases significantly and
there is a melting-temperature plateau at medium values of copper weight percentage. The melting
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CV
(a)
T
CV
(b)
T
CV
(c)
T
Fig. 1. Heat capacity versus temperature for Cu3 Fe13 , CuFe3 , Cu7 Fe1 bimetallic nanostructures.
temperature for all copper weight percentages in copper–iron bimetallic nanoclusters is lower than
the bulk-structure values.
Our result regarding melting temperature for copper bulk, 1400 K, is consistent with the firstprinciples molecular dynamics simulation result, 1460 K [71].
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Tm
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Tm
Fig. 2. Theoretical and experimental results for melting temperature versus weight copper percentage for
copper–iron alloy.
Fig. 3. Melting temperature for a copper–iron bimetallic nanocluster versus copper weight percentage and its
bulk structure.
Our results for the formation energy for the bulk structure of FeCu and CuFe3 are 0.252 eV/atom
and 0.179 eV/atom, respectively; these values are consistent with the DFT results, 0.275 eV/atom and
0.162 eV/atom, via the projected augmented wave (PAW) and generalized gradient approximation
(GGA) with exchange correlation PW91 [1]. Our results for the atomic volumes of pure Cu and
pure iron are 13.63 A3 and 13.69 A3 , respectively. The DFT calculation results with GGA and the
PW91 exchange correlation for the atomic volumes of pure iron and copper are 11.8 A3 and 12.2 A3 ,
respectively, which confirms our result [1]. Our calculation shows that the atomic volumes for Fe–Cu
and CuFe3 are 13.05 and 13.06 A3 , respectively. The DFT results with PAW and GGA for the atomic
volumes of FeCu and CuFe3 in bulk structure are 12.1 and 12 A3 , which confirms our calculation
result as well [1]. The phase diagram for Fe–Cu alloys, including the magnetic properties of iron as
a quantum property, has been reported in the previous literature, and confirms our phase diagram
regarding the melting point for the bulk structure of Fe–Cu alloys [72].
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g(r)
PTEP 2015, 043I01
r
Fig. 4. Radial distribution of a copper–copper atom for a Cu7 Fe1 bimetallic nanostructure at 400 K, 800 K,
1800 K, respectively.
Our calculations for the lattice parameter of CuFe3 with a bcc structure are 2.44 Ao and, for a FeCu
composition, the lattice parameter is 2.42 Ao . The DFT results for the lattice parameters of FeCu and
the bcc structure of CuFe3 are 2.89 Ao and 2.88 Ao , respectively, which approximately confirm our
calculated lattice parameters [51]. As a result, by using the new potential model, physical quantities
such as lattice parameter, atomic volume, and formation energy show good consistency with firstprinciples results. Including the magnetization effect in iron as a quantum property due to find phase
diagram of Fe–Cu alloys shows good consistency with our calculated phase diagram with application
of the new potential model.
Structural analysis of nanostructures has been performed via a radial distribution function calculation [73–75]. The radial distribution function (RDF) can be defined by the following equation
[73–75]:
1 δ(r − ri j ) .
(7)
g(r ) =
Nn
i
j
In Eq. 7, N , n, and ri j are the total number of copper and gold atoms, density, and distance between
atom i and atom j.
Structural analysis for the solid-to-liquid phase transition can be done from a radial distribution
quantity such as copper–iron alloy as well. The radial distribution function results for copper–copper
atoms in Cu7 Fe1 , namely, a compound of 224 copper atoms and 32 iron atoms, is represented in
Fig. 4. On the basis of Fig. 4, the peak of the radial distribution function at the first shell after melting temperature decreases significantly. RDF peaks for a long-range distance, namely the third and
fourth peaks, gradually vanish after melting temperature. The structure of bimetallic nanoparticles
for Cu7 Fe1 is shown at 400 K, 800 K, and 1100 K in Figs. 5(a), (b), and (c), respectively. For all figures, the green and blue atoms are iron and copper, respectively. Structural analysis shows that the
copper atoms are set in the shell of the bimetallic nanocluster; however, the iron atoms are set in the
core of the cluster. On the basis of Fig. 5, the surface energy [76] of copper atoms is lower than that
of iron atoms, meaning that the copper atoms prefer to stay in the shell of the nanocluster. Melting
phenomena occur from copper atoms on the surface or in the shell of the cluster, as they have lower
interaction energy with other atoms.
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(a)
(b)
(c)
Fig. 5. Structural configuration for a Cu7 Fe1 bimetallic nanostructure at (a) 400 K, (b) 800 K, (c) 1800 K.
Fig. 6. Radial distribution function for a copper–copper atom as a function of distance from the center of the
cluster for Cu3 Fe13 , Cu3 Fe5 , Cu7 Fe1 at 400 K.
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Fig. 7. RDF result for an iron–iron atom for Cu3 Fe13 , Cu3 Fe5 , Cu7 Fe1 compositions at 400 K.
(a)
(b)
(d)
(c)
(e)
(g)
(f)
(h)
Fig. 8. Structural configurations for different amounts of iron doping within copper at room temperature for
(a) Cu3 Fe13 , (b) Cu5 Fe11 , (c) Cu3 Fe5 , (d) Cu7 Fe9 , (e) Cu5 Fe3 , (f) Cu3 Fe1 , (g) Cu7 Fe1 , (h) Cu15 Fe1 .
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F. Taherkhani and P. F. Seresht
Doping effect on radial distribution function
RDF has been calculated for structural analysis of iron–copper bimetallic nanoparticles. On the basis
of Fig. 6, an increase in the copper weight percentage in bimetallic copper–iron nanoalloys causes
the RDF peak height of copper–copper in the first shell to decrease significantly. The RDF value
for copper–copper atoms slowly decreases with increasing copper doping in the second shell. On
the basis of Fig. 6, there is a long-range interaction for copper–copper atoms at low weight percentages of copper doping in iron. The long-range structural order between copper atoms vanishes with
increasing copper weight percentage within copper–iron bimetallic nanoclusters. At low iron weight
percentages, the value of the peak for the radial distribution function of copper–copper atoms in the
first shell decreases significantly. The results of the radial distribution function for iron–iron atoms
are presented in Fig. 7. On the basis of Fig. 7, there is no regular trend for the peak height of the
radial distribution function versus iron weight percentage as doping for the first shell of iron–copper
bimetallic nanoclusters. Janus-like structures have been investigated for iron–copper bimetallic nanoclusters at room temperature. Structural configurations for different copper weight percentages in
iron in bimetallic nanoclusters, namely, Cu3 Fe13 (i.e., 48 copper atoms and 208 iron atoms), Cu5 Fe11 ,
Cu3 Fe5 , Cu7 Fe9 , Cu5 Fe3 , Cu3 Fe1 , Cu7 Fe1 , Cu15 Fe1 , are represented in Figs. 8(a)–(h), respectively,
at 300 K. On the basis of Fig. 8, for the Cu5 Fe11 and Cu3 Fe5 structures, the iron atoms (green) are
set on the shell of the cluster and the copper atoms (blue) are set on the core of the cluster. In the
Cu7 Fe9 nanostructure as 53% iron weight in copper, there are two distinct faces, which are occupied with iron and copper atoms separately. At lower than 53% iron weight in copper, there is an
exchange of copper and iron atoms in the surface structure. According to Fig. 8, for the Cu5 Fe3 ,
Cu3 Fe1 , Cu7 Fe1 , Cu15 Fe1 nanostructures, iron and copper atoms are arranged in the cores and shells
of the nanostructures, respectively. Janus-like structures appear at around 53% iron weight in copper at room temperature and, in this composition, copper–iron bimetallic nanoclusters consist of two
distinct faces.
5.
Conclusion
A molecular dynamics simulation has been performed for melting temperature, structural configuration, and radial distribution function for bimetallic iron–copper nanostructures and their bulk
alloys for many catalysis applications. A new-application potential model has been proposed for the
investigation of solid–liquid phase transitions for different copper weight percentages as doping in
iron for bimetallic copper–iron nanostructures and their bulk structure for the first time. Our result
regarding melting temperature shows that a little doping with copper atoms decreases the melting
temperature significantly and, at medium values of copper doping within iron, there is a plateau for
copper–iron bimetallic nanoclusters. The RDF result shows that, for low copper weight percentages within iron, there is a long-range structural order for copper atoms. The value of the peak
height of the first shell for copper–copper atoms at low copper weight percentages is more than
the other RDF peak with a higher copper-doping atom fraction. There is no regular trend for the
value of the peak height of iron in the first shell versus copper doping in copper–iron bimetallic
nanostructures. Due to many catalysis applications, structural analysis for copper–iron bimetallic
nanostructures shows that the copper atoms are set in the shell of the cluster and the iron atoms
are set in the core of the cluster. Structural analysis shows that the melting temperature starts at the
copper surface atoms due to the small surface energy of copper atoms in bimetallic copper–iron
nanoclusters.
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F. Taherkhani and P. F. Seresht
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