Temperature and Doping Effect on Thermal Conductivity of Copper

Article pubs.acs.org/JPCC

Temperature and Doping Effect on Thermal Conductivity of Copper− Gold Icosahedral Bimetallic Nanoclusters and Bulk Structures Farid Taherkhani,*,†,‡ Zohreh Parviz,† Hamed Akbarzadeh,§ and Alessandro Fortunelli‡ †

Department of Physical Chemistry, Razi University, 67149-67346 Kermanshah, Iran CNR-ICCOM, Istituto per la Chimica dei Composti Organometallici del CNR, Pisa, Italy § Department of Chemistry, Faculty of Basic Sciences, Hakim Sabzevari University, 96179-76487 Sabzevar, Iran ‡

ABSTRACT: Molecular dynamics simulations based on analytic potentials are performed to investigate the coefficient of thermal conductivity (CTC) of gold−copper (Au−Cu) nanoclusters with 55 atoms and icosahedral (Ih) structure at different compositions via a Green−Kubo formalism, and the results are compared with the corresponding quantities for bulk systems. The temperature dependence of CTC is considered for both AuCu nanoclusters and bulk systems in the 40 K < T < 273 K temperature range. For bulk systems, our results are in excellent agreement with the experiment and show that thermal conductivity decreases with temperature in the range of 40 K < T < 273 K, whereas it increases with temperature in the same range for Au−Cu alloys. The dependence of CTC for bulk AuCu on Cu mole fraction at 273 K is investigated, and a plateau is found as a function of copper doping. Heat transfer for pure copper and gold bulk systems occur mostly via a phonon mechanism, whereas for bulk copper−gold alloys a diffusion mechanism is prevalent, explaining the difference in behavior as a function of temperature. For the 55-atom Ih AuCu nanoclusters, the CTC as a function of temperature and copper doping exhibits a nonmonotonous peak at about 80% Cu molar content, with the CTC value for the pure copper nanoparticles in good agreement with the experiment. The CTC values for Au, Cu, and Au−Cu alloys in nanoform tend to be much lower than the corresponding values in bulk structures with heat transfer occurring also via a convection mechanism that is absent in the bulk.

1. INTRODUCTION Metal clusters and nanoparticles are aggregates of atomic or molecular units, starting with the diatomic molecule and reaching, with an indistinctly defined upper bound of several hundred thousand atoms, the mesoscopic size range.1−5 A significant reason for the interest in metal clusters is the sizedependent evolution of their properties,1−5 such as their structural properties. Metal nanoparticles can in fact be found in different shapes such as cubic, spherical, octahedral, tetrahedral, decahedral, dodecahedral, or even tetrahedral,6−13 some of which have no counterpart in the bulk. From the point of view of applications, there is a traditional interest in metal cluster due to their potential use in fields such as electronics, engineering, and catalysis.14−24 Bimetallic nanoparticles composed of two metallic elements have also received great attention in addition to monometallic nanoparticles; in particular, recent theoretical25 and experimental26−31 works demonstrated that core−shell structures show physical and chemical properties different from those of the separate metals. Mixing with a second metal (Ag, Pd, or Cu) has shown to improve catalytic activity28,32−35 of Au-based bimetallic catalysts. Bimetallic clusters can be produced by a diversity of techniques, such as chemical reduction, cluster beam generation, electrochemical synthesis, etc.17,36−41 Ther© XXXX American Chemical Society

mal analysis of bulk Au−Cu alloy shows that high thermal stability is expected for the gold−copper structures.42 Apart from the extensive studies on the Cu−Au bulk alloy,43−45 there has been a steady growth of interest in Cu−Au bimetallic clusters both in the experiment46 and theory.47,48 López et al.47 simulated the 13-atom and 14-atom Cu−Au bimetallic clusters with different atomic structures using classical molecular dynamics simulations. Johnston and co-workers investigated Cu−Au bimetallic clusters by using energy calculations49 and genetic algorithm with up to 56 atoms50 and showed that Au atoms sit on the surface and Cu atoms in the core on sometimes highly symmetric icosahedra. Recent investigations have shown that Au−Cu bimetallic clusters are novel catalysts for propene epoxidation, CO oxidation, 5-hydroxymethyl-2furfural, and benzyl alcohol oxidation.51−54 Gold and copper nanoparticles construct atomic structures which are either icosahedral (Ih), decahedral (Dh), or octahedral (Oh), depending on the particle size.55 For many metals or metal alloy clusters, icosahedral clusters are stable due to high-symmetry in comparison with other structure. Since icosahedral metal Received: December 23, 2014 Revised: March 11, 2015

A

DOI: 10.1021/jp512832b J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

2. METHODOLOGY Following the Green−Kubo formalism in linear response theory, the lattice TC of a solid λ is calculated by integrating the heat-current correlation function J:65,66 ∞ 1 λ= ⟨J(0)J(t )⟩ dt 2 ∫ 3VkBT 0 (1)

clusters have more low-coordinated atomic sites than other low-symmetry isomers, they have special catalytic properties.56 Low-coordinated Au atoms are better than high-coordinated atoms for catalytic active site reaction.57 More unusual properties such as thermal conductivity (TC) have been much less investigated. Being small objects, nanoclusters have a very favorable surface/volume ratio so that the surface effect on TC cannot be neglected.1 Unusual, unpredictable and high values of TC in nano materials have opened a new field of study. The TC of solid argon in the classical limit has been studied using the Green−Kubo formalism by equilibrium molecular dynamic simulations (EMD), employing Lennard−Jones interatomic potential.58 Temperature and size dependency of TC of aluminum nanocluster has also been investigated by using the EMD method via the Green−Kubo formalism with Sutton−Chen (SC)-type potentials.1 Previous literature investigated impurity and vacancy effects on the lattice TC of solid argon with MD method. Argon with vacancy defects is thus found to have a lower TC than argon with krypton impurities at the same defect concentration.59 Many investigations have been done about TC of bimetallic clusters in the bulk limit. There is no specific trend for the TC of bulk bimetallic alloy. For instance, Bi-43 wt % Sn and Zn0.15 wt % Mg exhibit monotonic trends.60 On the contrary, for pure nickel and a number of dilute Ni−Co, Ni−Pd, Ni−Fe, and Ni−Cu alloys, one finds an extremum in TC.61 Heat transfer of some water-based Al2O3, SiO2, and MgO nanofluids shows that spherical and smooth particles are suitable for improvement of heat transfer.62 Few studies have been done on the TC of bimetallic nanoclusters; however, there are a lot of investigations on TC of bimetallic nanofluids. Previous literature has investigated the TC enhancement of bimetallic nanofluids with a range of volume fractions of 0.2−1% at temperatures ranging from 20 to 60 °C and for different metallic/metallic ratios of 3/1, 1/1, and 1/3. The TC enhancement increases with temperature and volume percentage of Cu nanoparticles in the Cu/Zn ratio.63 Mechanism of heat conduction in copper−argon nanofluids was studied by MD simulations and the TC was obtained by using the Green−Kubo method with Lennard−Jones interatomic potential between argon atoms and a more accurate embedded atom method (EAM) potential between copper atoms.64 Thermal conductivity was investigated for nanostructured material via a quantum mechanical approach.65 Here we explore, to the best of our knowledge for the first time, the heat transfer process in AuCu nanoclusters via computational simulations. TC for AuCu nanoclusters as well as for the corresponding bulk structures is investigated as a function of doping and temperature in 55-atom Ih-symmetry configurations. We investigate the trend of the interaction parameter (k′) as a function of temperature. Finally, the TC for pure gold, copper, and alloys in nanostructure is compared with the bulk limit. The mechanism of heat transfer is also explored. In particular, we find a nonmonotonic behavior of TC as a function of composition in these systems which seems promising in view of novel effects (e.g., in the field of thermoelectrics). In section 2, we detail our approach. In section 3, we report results and discuss them, while in section 4, we summarize conclusions.

where V, T, and kB are the volume, temperature, and the Boltzmann constant, respectively. t is the time and the angular brackets denote the ensemble average, or, in the case of a MD simulation, the average over time. The microscopic heat current is given by65 J(t ) =

∑ νεi i + i

1 2

∑

ri , j(Fi , j. νi) (2)

i ,j,i≠j

where νi is the velocity of particle i and Fi, j is the force on atom i due to its neighbor j from the pair potential. The energy of particle i, εi, is defined as58 εi =

1 1 mi |vi|2 + 2 2

∑ ϕ(rij) (3)

j

where mi, φij are the mass of atom i and potential interaction between particle i and j, respectively. The total simulation time for calculating the heat current is finite. Since the simulations are performed for discrete MD steps of length Δt (1), calculating TC can be rewritten as58 λ=

Δt 3VkBT 2

M

∑ m=1

1 (N − M )

N−M

∑

J(m + n)J(n) (4)

n=1

where N is the number of MD steps after equilibration, M is the number of steps over which the time average is calculated, and J(m + n) is the heat current at MD time step m + n. Thermal conductivity of an intermetallic compound can be expressed as67 λ=

1 (1 − x)/λA + x /λB + k′x(1 − x)

(5)

where λA and λB are the thermal conductivity of the elements A and B, x represents the composition of element B, and k′ is the interaction parameter. For metals, the electronic contribution to thermal conductivity is very important. The electronic thermal conductivity is estimated via the Wiedemann−Franz (WF) relation for simple metals as a κele ≈ TL0σ.68−70 In the WF relation κele, T, L0, and σ are the electronic thermal conductivity, temperature, universal constant and electrical conductivity, respectively. The value for the universal constant L0 is L0 = (π2kB2/3) = 2.44 × 10−8 (WΩ2/K2). On the basis of the experimental result, the electrical conductivity of gold metal is 4.52 × 107 (1/Ωm),71 as a result, at T = 300 K, the electronic thermal conductivity of gold metal is estimated as κele ≈ 300 K × 4.52 × 107 (1/Ωm) × 2.44 × 10−8 (WΩ/K2) = 330.86 (W/ mK). In accordance with the experimental value for electrical conductivity of bulk copper,71 electronic contribution in thermal conductivity for copper in the bulk structure can be estimated as κele ≈ 300 K × 5.98 × 107 (1/Ωm) × 2.44 × 10−8 (WΩ/K2) = 437.73 (W/mK). Estimation of electronic contribution in thermal conductivity can be extended for metallic nanoparticle. For the gold nanoparticle with size 2−4 nm similar to our calculated cluster size, on the basis of its experimental value for electrical conductivity,72 electronic B


Article


1 Au 1 (n + nCu), m = (m Au + mCu) (10) 2 2 the values of these parameters for the pure metals are taken from ref 80. Previous literature shows that different results can be found for the shear viscosity of n-decane compound by using NVE microcanonical and canonical NVT ensembles via the Green Kubo formalism.81 The effects of integration time step, potential cutoff, ensemble, and system size have been studied on thermal conductivity, shear viscosity, and diffusion of linear and branched alkanes in the gas phase and in the liquid phase via the Green Kubo formalism and have been shown to be small compared to the computational precision except for diffusion in gaseous n-butane.82

contribution in thermal conductivity of gold nanoparticle can be estimated as a κele ≈ 300 K × 7.14 × 106 (1/Ωm) × 2.44 × 10−8 (WΩ/K2) = 52.26 (W/mK). Experimental result shows that the electrical conductivity for copper nanoparticle73 is 5 × 106 (1/Ωm) . As a result, electronic contribution in thermal conductivity can be done for copper nanoparticle as follows: κele ≈ 300 K × 5 × 106 (1/Ωm) × 2.44 × 10−8 (WΩ/K2) = 36.6 (W/mK). From what has been discussed regarding the electronic contribution in thermal conductivity, the value of thermal conductivity for copper and gold in the bulk structure is greater than the copper and gold nanostructures. In all calculations, electronic contribution has been involved for thermal conductivity. 2.1. MD Simulations. The MD simulations for AuCu bulk were done in the constant temperature ensemble (NVT) with a constant number of atoms N, volume V, and temperature T with periodic boundary conditions, while those on AuCu nanoclusters were carried out in a NVE ensemble without any periodic boundary conditions at 1 atm pressure. The Verlet Leapfrog algorithm was used for the integration of Newton’s equations of motion, with a time step of 1−2 fs. The system was equilibrated for 500 ps, and averages were computed after 400 ps. Evans thermostat is used for controlling the temperature.74 For obtaining the global minimum structure of nanoclusters here considered, first the system has been heated above its melting temperature, and then the system have been slowly cooled according to a simulated annealing technique.75 In this study, we have used the DL-POLY-2.20 program.76 In the MD simulations, we have applied the quantum SuttonChen (Q-SC) potential to describe interatomic interaction. This potential has a many-body form and is similar to the Embedded Atom Model (EAM).77 The potential is given by78 N

N i

3. RESULTS AND DISCUSSION 3.1. Thermal Conductivity Calculation. Molecular dynamics simulations have been performed to calculate Au and Cu thermal conductivity in the bulk via a Green−Kubo formula. Quantities extracted from MD simulations (at the pressure of 1 atm) such as velocity, force, and position are used to calculate the coefficient of thermal conductivity for Au and Cu via eqs 2 and 4. The Q-SC potential is used for calculating the force between the particles. To obtain the thermal conductivity for Au and Cu, the heat current is calculated via eq 2 and then the coefficient of thermal conductivity is obtained via eq 4. Thermal conductivity for alloy Au−Cu is calculated on the basis of eq 5. For the calculation of the heat current, positions, velocities, and forces are calculated from step 499800 to 500000 with a time step of 2 fs. To obtain the coefficient thermal conductivity, the value and correlation function of the heat current in eq 4 are taken into account. The following strategy gives more detail on the calculation of coefficient thermal conductivity of bulk AuCu alloy. Q-SC potential parameters on the basis of Table 1 were chosen. First,

N

∑ Ui = ∑ ε[1/2 ∑ V (rij) − c i=1

n=

ρi ] (6)

j≠i

Table 1. Quantum Sutton−Chen Potential Parameter for Copper and Gold Atom

here rij is the distance between atoms i and j, c, a positive dimensionless parameter and ε a parameter with the dimensions of energy, where V(rij) is a pair interaction function defined by the following equation ⎛ a ⎞n V (rij) = ⎜⎜ ⎟⎟ ⎝ rij ⎠

(7)

(8)

a is a length parameter scaling all spacing (leading to dimensionless V and ρ); n and m are both positive integer parameters, that n > m. Given the exponents (n, m), c is determined by the equilibrium lattice parameter. This formalism had been extended to the study of fcc binary alloys by RaffiTabar and Sutton.79 The parameters for the AuCu alloy are obtained through the following mixing rules79 ε AuCu =

ε AuεCu ,

a AuCu =

1 Au (a + aCu) 2

C

ε (eV)

m

n

metal

4.07830 3.61530

34.4280 39.75500

1.27940 × 10−2 1.23860 × 10−2

8 5

11 10

Au Cu

the force has been calculated from the negative gradient of QSC potential, namely, Fij = −∇iuj. Second, MD simulations have been done for periodic boundary conditions with the facecenter cubic structure with 500 ps as a total time of simulation and ensemble averaging after 400 ps. Third, the output of MD provides coordination and velocity of each particle as a function of time. Trajectories including position and velocity of the particles were saved from steps 499800 to 500000 with a time interval of 2 fs. It is important to notice that the analytical force obtained in the first step is a function of displacement. After substitution of displacement of particle that is obtained from MD simulation into force function, force is obtained as a function of time. Fourth, after obtaining force, velocity and positions of all atoms as a function of time, we used eqs 2 and 3 to calculate heat current versus time. Fifth, from the calculation of heat current and correlation function of heat current as a function of time and using eq 4, the thermal conductivity of bulk pure and bimetallic nanostructure AuCu is obtained. All the mentioned processes have been repeated to get thermal

accounting for the repulsion between the i and j atomic cores; ρi is a local electron density accounting for cohesion associated with atom i defined by ⎛ a ⎞m ρ = ∑ ⎜⎜ ⎟⎟ r j ≠ i ⎝ ij ⎠

a (A0)

(9) C


Article

The Journal of Physical Chemistry C conductivity at different temperatures and doping compositions. 3.2.Thermal Conductivity As a Function of Temperature for Au and Cu Bulk with Q-SC Potential. The Green−Kubo approach has been applied for computing the CTC of bulk Au and bulk Cu in the 40 K < T < 273 K and 70 K < T < 300 K temperature range, respectively. The result of CTC for bulk Au and Cu is shown in Figure 1 (panels a and b,

respectively). CTC decreases as a function of temperature for pure gold and copper in the bulk. Increase of temperature leads to a decrease in the correlation function of the heat current. Atoms move in a random way at high temperature, so that the correlation of force vectors are reduced: thus, the F contributions (second term) in eq 4 are reduced.1 At a high temperature, more phonons in each vibration mode are excited. As a result, the collisions between the phonons become more intense, which is disadvantageous to the transport of energy.83 Temperature dependence and decreases of phonon distribution of copper bulk with temperature has been determined from the neutron inelastic scattering method.84 Molecular dynamics simulation shows that the self-diffusion coefficient of copper and gold increases with temperature.85 On the basis of Figure 1, the trend of our simulation results and the value of CTC for Au and Cu in bulk as a function of temperature are in excellent agreement with the experimental results.86−88 Our result shows that thermal conductivity of pure gold in bulk decreases with temperature due to a decreased phonon contribution to the transport of energy. Tight bonding molecular dynamics simulation confirms the decrease of phonon distribution function with temperature for pure Au bulk.87 Thermal conductivity of pure copper has been calculated at 273 K as well. Thermal conductivity of Cu metal is greater than Au metal due to the smaller mass of Cu. Our result for CTC value of pure bulk copper versus temperature agrees with the experimental result completely.88 Previous literature shows that theoretical simulations can predict CTC values for bulk gold two-order magnitude smaller than experimental values89 and in all cases lower than its experimental result.90,91 Due to lack of electronic excitations in gold metal, the QSC and related embedded atom method (EAM) models for gold are known to predict unreasonably low values for bulk conductivity.89−92 3.3. Thermal Conductivity as a Function of Temperature for AuCu Bulk with Q-SC Potential. By using eq 4, the TC of bimetallic AuCu has been computed in the bulk as a function of temperature. On the basis of our simulation result, the thermal conductivity increases monotonically for the AuCu alloy as a function of temperature in the range of 40 K ≤ T ≤ 273 K (Figure 2a). Heat transfer in bimetallic AuCu occurs via a diffusion mechanism. Diffusion increases with temperature, and at high temperatures, the interatomic distances increase and AuCu atoms move with a larger mean free path. Our result for the mean−square displacement (MSD) versus time for copper and gold atoms in the bulk Au0.5Cu0.5 alloy is presented in Figure 2 (panels b and c) at two different temperatures: 70 and 273 K. Our calculations show that for both copper and gold atom, the self-diffusion coefficient increases with temperature. Experimental results regarding trace diffusion for other composition of gold−copper alloy shows that for copper and gold atoms, tracer diffusion coefficients increase with temperature.93 It is important to note that our results for CTC as a function of temperature for bulk AuCu alloy at 75% Cu molar fraction are in excellent agreement with the experimental result94 (see Figure 1c). Results for 50% Cu mole fraction as a function of temperature are similar to 75% Cu mole fraction. A comparison of the two plots as reported in Figure 2a shows that the thermal conductivity for 75% mole fraction of Cu is greater than 50% Cu mole fraction due to smaller mass of the copper atom. A comparison between the thermal conductivity of Au and Cu with AuCu alloys shows that the trend of thermal conductivity for pure metals is quite different. In the mixed

Figure 1. (a) Coefficient of thermal conductivity of bulk Au as a function of temperature with Q-SC potentials (blue) and experimental coefficient of thermal conductivity of Au74 as a function of temperature (green). (b) Coefficient of thermal conductivity of bulk Cu as a function of temperature with Q-SC potentials (blue) and experimental coefficient of thermal conductivity of Cu75 as a function of temperature (green). (c) Coefficient of thermal conductivity of bulk AuCu alloy for 75% Cu mole fraction as a function of temperature with Q-SC potentials (blue) and experimental CTC of AuCu as a function of temperature (green)75. D


Article


Figure 2. (a) Coefficient of thermal conductivity of bulk AuCu alloy for 75% (blue) and 50% (red) Cu mole fraction as a function of temperature with Q-SC potentials. (b) Mean square displacement as a function of time in picoseconds at two different temperatures 70 K and 273 K for gold atom in the bulk Au0.5Cu0.5 alloy. (c) Mean square displacement as a function of time in picoseconds at two different temperatures 70 K and 273 K for the copper atom in bulk Au0.5Cu0.5 alloy. (d) Coefficient of thermal conductivity of bulk AuCu alloy as a function of Cu mole fraction with Q-SC potentials at 273 K (blue) and experimental coefficient of thermal conductivity of AuCu as a function of Cu mole fraction (green) at 273 K75.

since thermal conductivity of Cu is greater than Au, thermal conductivity increases again with increasing Cu mole fraction. Our simulation results are in excellent agreement with the experimental result94 (see Figure 2d). 3.5. Interaction Parameter as a Function of Temperature. The interaction parameter (k′) is a positive constant, which depends on the alloy system and is calculated on the basis of eq 5. Results for the interaction parameter for 0.75 and 0.50 copper mole fractions as a function of temperature are reported in Figure 3 (panels a and b, respectively). The interaction parameter decreases as a function of temperature for the copper−gold alloy. As shown in the Figure 3, the trend of the interaction parameter as a function of temperature is opposite to the thermal conductivity result versus temperature. Atomic distance at a high temperature increase and interaction range diminishes, therefore the interaction parameter decreases versus temperature, and its contribution decreases in the thermal conductivity value. Trends of our simulation results and the value of the interaction parameter for AuCu alloy in bulk as a function of temperature are in excellent agreement with the experimental result:94 the discrepancy is really small and further decreases at higher temperatures. 3.6. Thermal Conductivity as a Function of Temperature for Cu55 Nanocluster with Icosahedral (Ih) Structure. Molecular dynamics simulations have been extended to be applied to nanostructures within microcanonical ensemble and without periodic boundary conditions as

systems, the heat transfer mechanism occurs via atom selfdiffusion and the self-diffusion coefficient of copper and gold increases with temperature in the copper−gold alloy.93 For the pure gold bulk structure, heat is transferred via a phonon mechanism and the phonon mean-free path decreases via temperature. As a result, CTC of pure gold and copper bulk has an opposite behavior with that of the mixed Au−Cu systems. 3.4. Thermal Conductivity of Bulk AuCu Alloy with Doping Effect. MD simulation results for CTC of AuCu versus Cu mole fraction are shown in Figure 2d. CTC decreases with increasing Cu mole fraction; afterward, there is a plateau in the range from 0.25 to 0.75 Cu mole fraction, and finally, CTC increases with further copper content. The self-diffusion coefficient of gold decreases with the increase of Cu percent in gold−copper alloy,93 and therefore, TC decreases with Cu content at a low Cu mole fraction. In the range from 0.25 to 0.75 mole fraction of Cu, instead, two factors compete with each other for the value of thermal conductivity. The first factor is the reduction in self-diffusion and the second factor is the concentration of Cu, which should lead to an increase, due to the larger value for thermal conductivity of Cu with respect to Au. These two contrasting factors cause that the thermal conductivity to become constant as a function of the Cu molar fraction in the range from 0.25 to 0.75% Cu. Inserting a little doping of gold atom in copper, namely Au9.3 Cu90.7 lead to asymmetric, smaller, broader phonon mode in comparison with the pure copper phonon mode.95 At high Cu mole fraction, E


Article


Figure 3. (a) Theoretical Interaction parameter of bulk AuCu alloy for 75% Cu mole fraction as a function of temperature with Q-SC potentials (blue) and experimental interaction parameter of AuCu as a function of temperature (green)75. (b) Theoretical interaction parameter of bulk AuCu alloy for 50% Cu mole fraction as a function of temperature with Q-SC potentials (blue) and experimental interaction parameter of AuCu as a function of temperature (green).

Figure 4. (a) Coefficient of thermal conductivity of Cu55 nanocluster as a function of temperature with Q-SC potentials with two different ensembles NVE and NVT. (b) Snapshots of Cu55 nanocluster at (a) 500 and (b) 800 K.

simulation results for the coefficient thermal conductivity of a Au49Cu6 nanocluster (11% Cu atom fraction) versus temperature are shown in Figure 5a. The thermal conductivity increases significantly with temperature at low temperature due to coupling of self-diffusion and low-frequency phonon modes; afterward, it increases with a smaller slope. The increase of temperature leads to enhancement of self-diffusion and the diffusion coefficient of metallic nanoparticles.98−103 In Au49Cu6, the gold atoms (in yellow) prefer to stay at the surface due to lower surface energy of Au with respect to Cu in agreement with previous simulations. The order of calculated thermal conductivity for gold−copper bimetallic nanocluster is the same as in bimetallic nanofluids ZnCu.63 Figure 5b shows snapshots of Cu6Au49 at three temperatures: (a) 300, (b) 500, and (c) 630 K. At low temperature the Cu6Au49 cluster has an icosahedral core−shell structure with an Au-enriched surface and a Cuenriched core in agreement with literature results:96 Cu6Au49 at 300 K exhibits a icosahedral symmetry. In this structure, a single Cu atom occupies the central site, and 12 Au atoms are in the middle shell covering the central single Cu atom completely, while the remaining 5 Cu atoms lie in the surface shell. The Cu atoms on the surface are surrounded by 6 Au atoms. Increasing the temperature further at 500 K, the bimetallic gold−copper nanocluster becomes disordered. The melting temperature of copper−gold bimetallic nanocluster as a function of copper atom fraction as obtained in the present simulations is shown in Figure 6: the melting temperature increases with the fraction of copper in copper−gold bimetallic nanocluster. Our result regarding the melting temperature with Q-SC potential for copper gold bimetallic nanocluster with 55 atoms is consistent with those obtained using a Monte Carlo method and a semiempirical potential model.96

described in section 2. The Green−Kubo approach has been applied for calculating the CTC of a Cu55 nanocluster as a function of temperature with microcanonical ensemble NVE. At low-temperature (below 70 K) for Cu55 the thermal conductivity decreases with temperature a little (See Figure 4a). Here, copper self-diffusion is an increasing factor and phonon free path as a reducing factor compete with each other. Instead, the thermal conductivity increases with temperature significantly at higher temperature for Cu55 due to diffusion mechanism. It is worthwhile to note that Cu has a high surface energy, so Cu atoms tend to adopt a compact icosahedral structure.96 The dominant mechanism of heat transfer in Cu55 is convection leading to a significantly lower CTC value in comparison with the bulk. Calculation of CTC for the Cu55 nanocluster has been repeated with a canonical ensemble, NVT, via Green Kubo formalism to investigate the effect of the thermostat on the CTC value. Result of the CTC value with NVT ensemble on Cu55 nanocluster is presented in Figure 4a. On the basis of Figure 4a, the order of magnitude for CTC value with two different ensembles, microcanonical and canonical (NVE and NVT), are the same and trend of CTC versus temperature within two different ensembles is roughly the same. Figure 4b shows snapshots of Cu55 at (a) 500 and (b) 800 K, respectively. At the lower temperature, the cluster remains in the compact icosahedral structure. At the higher temperature, the Cu55 cluster deforms due to melting phenomena. The order of magnitude of thermal conductivity for this copper nanocluster is consistent with experimental results.97 3.7. Thermal Conductivity of Au49Cu6 Nanocluster with Temperature. By assuming a Ih structure, MD F


Article


Figure 5. (a) Coefficient of thermal conductivity of nano Au49Cu6 as a function of temperature. (b) Snapshots of Au49Cu6 nanocluster at (a) 300, (b) 500, and (c) 630 K (brown atoms, Cu; yellow atoms, Au).

Figure 6. Melting temperature of gold−copper bimetallic nanocluster with 55 total atoms with copper atom fraction.

3.8. Thermal Conductivity of AuCu Nanocluster with Doping Effect. The effect of doping on thermal conductivity has been studied for different compositions: Au37Cu18, Au28Cu27, Au6Cu49, Cu55 for Au−Cu nanoclusters of Ih symmetry and the results are shown in Figure 7a at a temperature of 500 K. What is most striking is the peak in thermal conductivity versus the Cu mole fraction. These large changes in thermal conductivity with doping can be interpreted as a disorder effect. A little doping changes significantly the structure in nanoclusters, which then has significant effect on the thermal conductivity. The thermal conductivity of copper is greater than that of gold, but in binary structures with not too much Au, the heat transfer mechanism via convection is favored by gold positioning at the surface of the cluster and contributing to the heat transfer via diffusion. Thus, removing all the gold atoms and eliminating the diffusion contribution to the heat current entails that CTC diminishes significantly from

Figure 7. (a) Coefficient of thermal conductivity of Au−Cu nanostructure with 55 atoms versus Cu mole fraction at 500 K. (b) Mean−square displacement versus time in picoseconds for the Au6Cu49, Cu55 nanostructure.

G


Article

The Journal of Physical Chemistry C Au6Cu49 to Cu55. Mean−square displacement (MSD) versus time in picoseconds has been calculated for Au6Cu49 and Cu55 nanostructures, and these results are presented in Figure 7b. On the basis of Figure 7b, MSD for copper atom in Au6Cu49 nanostructure is greater than the Cu55 nanostructure. Snapshots of Au49Cu6, Au28Cu27, Au6Cu49, Cu55 nanoclusters at 500 K are presented in Figure 8. It is interesting to note that the

Figure 9. Copper phonon density of state [S(w)-Cu], versus frequency (THz) for the Au6Cu49, Cu55 nanostructure.

decreases as a function of temperature. On the contrary, for bulk AuCu alloys, the thermal conductivity increases with temperature in the range of 40 K < T < 273 K. This opposite behavior for the alloy is interpreted as due to the fact that heat transfer occurs via a diffusion mechanism rather than a phonon mechanism as in the pure phases. Comparison between the thermal conductivity for pure Cu and Au with AuCu alloys shows that CTC in general decreases in alloys, with a plateau of CTC as a function of copper mole fraction at room temperature. It is worthwhile to note that our results for CTC as a function of temperature and Cu mole fraction are in excellent agreement with the experimental results. The effect of temperature on the interaction parameter in the CTC value of bulk gold−copper is also examined. At low temperatures, the interaction parameter diminishes very fast, whereas at high temperature, its value decreases linearly, with our predicted values for the interaction parameter practically coincident with the experimental result. MD simulations have also been used for investigating the effect of chemical composition on the thermal conductivity of AuCu nanoclusters within the Green−Kubo approach for the first time here to the best of our knowledge. The behavior of CTC in terms of the Cu atom fraction and temperature for AuCu nanocluster has been investigated. CTC values for pure metals and alloys in bulk structure are much larger than in nanostructures. The small CTC values in copper−gold nanocluster shows that heat transfer occurs via a dominant convection mechanism in nanoclusters. Moreover, our results show that there is an extremum in thermal conductivity of Au− Cu nanoclusters at a given temperature as a function of copper content. The existence of a peak in thermal conductivity as a function of Cu composition in AuCu nanocluster can be put in correspondence with experimental result for AgCu nanoparticles within nanofluids and seems promising in view of applications of these systems in the field of thermoelectrics.

Figure 8. Snapshots of (a) Au49Cu6, (b) Au28Cu27, (c) Au6Cu49, and (d) Cu55 nanocluster at 500 K (yellow atoms, Au; brown atoms, Cu).

trend of gold−copper CTC calculated values versus doping resembles the experimental behavior of CTC for Ag−Cu nanoparticles in nanofluids.104 The phonon densities of states can be computed from the Fourier transform of the velocity autocorrelation function as per the following equation105 ⎯⎯⎯→ ⎯⎯⎯→ iwt ⟨v(t )• v(0)⟩ dt S(w) = e ⎯⎯⎯→

Temperature and Doping Effect on Thermal Conductivity of Copper

Recommend Documents