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Density functional study of small cobalt–platinum nanoalloy clusters
Journal of Magnetism and Magnetic Materials 324 (2012) 588–594
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Density functional study of small cobalt–platinum nanoalloy clusters Ali Sebetci n Computer Engineering Department and Nanotechnology Applications and Research Center (ZUNAM), Zirve University, Gaziantep 27260, Turkey
a r t i c l e i n f o
a b s t r a c t
Article history: Received 4 December 2010 Received in revised form 15 August 2011 Available online 3 September 2011
The structural, energetic, electronic and magnetic properties of small bimetallic ConPtm (n þ m r 5) nanoalloy clusters are investigated by density functional theory within the generalized gradient approximation. A plausible candidate for the ground state isomer and the other possible local minima, binding energies, relative stabilities, magnetic moments, the highest occupied and the lowest unoccupied molecular orbital energy gaps have been calculated. It is found as a general trend that average binding energies of Co–Pt bimetallic clusters increase with Pt doping. Planar structures of pure Co clusters become 3D with the addition of Pt atoms. CoPt2, Co2Pt2, Co3Pt2, and CoPt4 nanoalloys are identified as the most stable species since they have higher second finite difference in energy than the others. Pt doping decreases the total spin magnetic moment gradually. A rule for the prediction of the total spin moments of small Co–Pt bimetallic clusters is derived. & 2011 Elsevier B.V. All rights reserved.
Keywords: Cobalt Platinum Clusters Density functional theory Electronic properties
1. Introduction While transition metal clusters, in general, have many potential applications in different areas of nanotechnology such as heterogeneous catalysis [1], magnetic recording media [2], medicine and biochemistry [3], magnetic CoPt nanoalloy clusters, in particular, have been attracted much attention during the last decade [4–30] due to the consideration that they are the best candidates for ultra-high density magnetic storage applications [31]. The main physical limitation of such a technology for permanent nanomagnets is related to their superparamagnetic behavior, as the magnetization direction of a nanoparticle usually fluctuates at room temperature which is incompatible with longtime recording [32]. One of the most promising routes to maintain the thermal stability of the nanoparticles’ magnetization is to employ bimetallic nanoalloys composed of 3d magnetic elements and 5d or 4d transition metals, such as CoPt, CoRh, FePt, FePd and so on [25]. Since the anisotropy energy arises from the spin–orbit interaction [33] which increases with atomic number, these materials have a magnetocrystalline anisotropy constant one order of magnitude larger than CoCr-based alloys used in magnetic devices [34]. The magnetocrystalline anisotropy constant of the nanoalloys depends on the size and the structure of the nanoparticles [25]. Another important motivation for the study of CoPt bimetallic nanoclusters is that one of the key objectives of the lowtemperature polymer electrolyte membrane fuel-cell technology
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is to improve and reduce Pt loading as the oxygen-reduction catalyst [35]. Many investigations [36–39] such as the series of binary PtM alloys (M ¼Cr, Mn, Co, Ni) supported on carbon [40] have been carried out to determine the role of alloying in the electrocatalytic activity of Pt for the oxygen-reduction reaction. All these studies have shown that the intrinsic activity of nanoparticles depends particle size, shape and composition. A recent synthesis of CoPt nanoparticles in MgO and amorphous carbon matrices with a mean diameter of 3 nm and their characterization by using X-ray magnetic circular dichroism and superconducting quantum interference device are reported by Tournus et al. [30]. They have shown that embedded clusters undergo a transition from a chemically disordered phase, labeled A1 to the chemically ordered L10 phase upon annealing, even for clusters with a 2 nm diameter, without cluster coalescence and that the magnetic anisotropy of chemically ordered nanoparticles increases with respect to the chemically disordered A1 phase. 1D and 2D CoPt nanostructures have been successfully synthesized in solution-phase process [8,13,14] and in thermal decomposition of an organometallic precursor [5,7]. CoPt nanorods were synthesized in ionic liquids [15]. Tzitzios et al. [14] described the synthesis of a 3D ferromagnetic CoPt polypod-like nanostructure. Hyun An et al. [27] have synthesized monodisperse CoPt nanoparticles possessing high crystallinity with a particle size of 5.3 nm and a tight size distribution by a modified polyol process. On the theoretical side, the Metropolis Monte Carlo (MC) sampling method with an isotropic semi-empirical Embedded Atom Model (EAM) and a modified (angle dependent) EAM potentials were used to investigate structural properties of free CoPt nanoclusters [26]. Both potentials predicted partially ordered L10 phase for CoPt nanoparticles. Rossi et al. [28] have
A. Sebetci / Journal of Magnetism and Magnetic Materials 324 (2012) 588–594
investigated the structure and chemical ordering of CoPt nanoclusters in the size range of 1–3 nm by global optimization methods and MC simulations using a many body potential derived from the tight binding model and reported that for the smaller systems (number of atoms N o 100), the optimized clusters display a polyicosahedral-like atomic structure and that a transition to the decahedral symmetry occurs at about N ¼100 atoms, with a pseudo L10 ordered phase in each tetrahedral unit. Gruner et al. [29] have performed large-scale Density Functional Theory (DFT) calculations on FePt and CoPt clusters with diameters of up to 2.5 nm by selecting so-called magic cluster sizes (13, 55, 147, 309, 561, etc.). They have found that CoPt core-shell segregated morphologies predominate with considerably increased energy differences to the L10 structure. In order to understand the mechanism and elucidate more details on the formation of CoPt nanoparticles, it is worthy to investigate small CoPt nanoclusters systematically. To the best of our knowledge, the only theoretical study of small CoPt clusters in the literature is by Feng et al. [41]. They investigated the geometrical and magnetic properties of (CoPt)n (n r5) clusters where the numbers of Co and Pt atoms in each cluster are the same. They found that the magnetism per (CoPt) unit increases with the size of the cluster. Wu and coworkers [42] have investigated the electronic and magnetic properties of small ConMnm and ConVm (n þ mr 6) clusters using DFT and shown that Co and V atoms prefer to aggregate in Co–Mn and Co–V clusters, respectively. They found significant magnetic moment enhancement in Co–Mn clusters with Mn doping and reduction in Co–V clusters with V doping consistent with experimental results for larger clusters [43]. Lv et al. [44] have studied (CoRh)n (n r 5) clusters in the framework of DFT and reported that the most stable structures of (CoRh)n (n r5) clusters are similar to those of corresponding pure Co2n and Rh2n clusters. Parida and coworkers [45] have presented a systematic DFT study of NinCom and NinFem (n þ m r6) clusters and found that with increase in substitution of Co and Fe atoms in Ni cluster, while NinCom becomes more stable, NinFem clusters become less stable. Du and coworkers [46] have studied the magnetic states including collinear and noncollinear magnetic coupling in bimetallic Co6 nMnn clusters. They reported that the ground state of Co6 nMnn clusters displays collinear magnetic ordering for n r 3, whereas a magnetic transition to noncollinear ordering occurs at n ¼4 and the noncollinear magnetic structure remains to be energetically favored afterwards. We have previously studied pure Con and Ptn (n r 6) clusters and reported their properties [47]. In the present study, we have investigated the structural, energetic, electronic and magnetic properties of small bimetallic ConPtm (n þm r 5) nanoclusters by employing DFT within the generalized gradient approximation and collinear magnetic coupling formalism. Spin–orbit and noncollinearity effects may be investigated in a future study. The putative ground state isomers and the other possible local minima, binding energies (BE), relative stabilities, magnetic moments, the highest occupied and lowest unoccupied molecular orbital (HOMO–LUMO) energy gaps have been calculated. Vibrational frequency calculations of the lowest energy structures have been carried out to differentiate minima from transition states. Above mentioned questions emerged for the properties of Co containing small nanoalloy clusters have been discussed for the Co–Pt bimetallic clusters.
2. Computational details NWChem 5.1.1 program package [48] has been used to perform geometry optimizations and total energy calculations by DFT. The default convergence criteria, which are 1 10 6 Hartree
589
for energy, and 5 10 4 Hartree/a0 for energy gradient, are used. CRENBL [49] basis sets and effective core potentials (ECP) for both of the elements have been employed where the outer most 17 electrons of free Co atom (3s2 3p6 3d7 4s2 ) and the outer most 18 electrons of free Pt atom (5s2 5p6 5d9 6s1 ) are treated explicitly. The corresponding Gaussian basis functions of Co and Pt are (7s6p6d) and (5s5p4d), respectively. The ECPs were computed using the relativistic Dirac–Fock equation. The reliability of the basis sets and the ECPs were determined by comparing atomic excitation energies with accurate all-electron calculations where the maximum errors were found to be less than 0.05 eV for Co, and 0.12 eV for Pt [49]. The generalized gradient approximation (GGA) of Becke’s exchange functional [50] and Lee–Yang–Parr correlation functional [51] (BLYP) has been employed in the calculations. Justification of the choice of the xc-functional is discussed in the next section by giving a comparison between the results for Co2 and Pt2 dimers with the following functionals: Perdew–Burke– Ernzerhof (PBE96) [52] GGA, B3LYP [50], and PBE0 [53] hybrid, and Slater-Vosko–Wilk–Nusair (SVWN5) [54] local density approximation (LDA). As the number of atoms in a homonuclear cluster increases, the number of locally stable isomers increases very fast [55] and the identification of the ground state structure becomes much more difficult. For the case of alloy clusters the situation is worse since the interchange of the two types of atoms for a given morphology creates new structures called homotops and they need to be considered separately in the geometry optimizations. We have performed several geometry relaxation calculations starting from different morphologies such as linear and various triangular arrangements for trimers, linear, planar Y-like, square, rhombus structures, and 3D tetrahedron for tetramers, and bipyramid, pyramid, bridge-side-capped tetrahedron, planar W-like, X-like, V-like structures, and pentagon for pentamers. For each initial geometry, all possible homotops were subject to individual geometry optimizations. The structures have been relaxed without imposing any symmetry constraints. Spin-polarized calculations have been done for at least five different spin multiplicities.
3. Results and discussion 3.1. Diatomic ConPtm (nþm ¼2) nanoalloys To validate the reliability of the present calculations, we first compare our results with available experimental data and previous reports on pure Co and Pt dimers. Table 1 presents the BEs, bond lengths, vibrational frequencies, and adiabatic ionization potentials (IP). The results on CoPt with different xc-functionals have also been included in the table to provide the reader a sense about what could be the values with other xc approximations. The BE of a given cluster is defined as the absolute value of the difference between the total energy of the cluster and the sum of the ground state energies of free atoms which are the Co atom quartet and Pt atom triplet states. The ground state spin multiplicities of Co2, Pt2, and CoPt are quintet, triplet, and quartet, respectively for all xc-functionals employed in this study except PBE0 which gives a doublet for CoPt. Co2þ , Pt2þ , and CoPt þ cations’ spin multiplicities calculated for IPs are sextet, quartet, and quintet, respectively. The exceptions are PBE which results in a doublet state for Pt2þ and B3LYP which results in a triplet state for CoPt þ . Table 1 shows that BLYP calculations are the closest results to the experimental values of Co dimer in three categories: BE, bond length, and IP. The vibrational frequency value is also in the range of a reasonable scaling factor. For Pt dimer, again BLYP
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Table 1 Comparisons of the present results for Co2 and Pt2 with those of the previous experimental and theoretical works and comparison of the present results for CoPt with different xc-functionals. Cluster Type of work
Co2
Experimental Ref. [56] Literature Ref. [57] Ref. [58] Theoretical Ref. [59] Literature Ref. [60] Present SVWN5 Work BLYP PBE96 PBE0 B3LYP
Pt2
Experimental Ref. [61] Literature Ref. [62] Ref. [63] Theoretical Ref. [64] Literature Ref. [65] Present SVWN5 Work BLYP PBE96 PBE0 B3LYP
CoPt
a b c
Binding Ref. No. energy or xcfunctional (eV)
Theoretical Literature Present Work
Bond length ˚ (A)
Vibrational frequency (cm 1)
Ionization potential (eV)
1.69 7 0.26 2.31 6.26 7 0.16 2.35 2.26 3.70 1.73 2.04 0.08 0.15
1.99 2.01 1.93 2.13 2.10 2.08 2.09
296.8 75.4 373 342 440 329 271 366 357
3.14 7 0.02
7.49 7.48 7.46 6.84 6.97 8.18 8.27 8.68 7 0.02
222 2.44 3.29 4.46 3.21 3.50 2.58 2.59
2.33 2.39 2.39 2.33 2.41 2.38 2.35 2.38
Ref. [41]
5.40
2.37
SVWN5 BLYP PBE96 PBE0 B3LYP
4.72 2.97 3.31 1.82b 1.60
2.17 2.24 2.22 2.35 2.21
223 253 215 228 247 235
8.87 8.54 8.61 8.62a 8.60
381 337 319 235 237
8.03 7.78 7.89 7.20 7.81c
Cation is a doublet. Doublet. Cation is a triplet.
produces the nearest BE calculation to the experimental estimation. Although there are slightly better values for the other three properties of Pt2, overall performances of the other functionals are not as good as that of BLYP. Generally, LDA functionals overestimate the BEs of transition metal clusters, while hybrid functionals underestimate them. The hybrid PBE0 even resulted in a negative BE for Co dimer in our study. In addition, all the exceptions for the spin multiplicities reported in Table 1 are calculated with the two hybrid functionals. Thus, GGA functionals are more favorable than both LDA and hybrid functionals for the present purposes. Since BLYP has slightly better performance than PBE96, we have employed it in the rest of our calculations. We can compare our results on CoPt with those of Feng et al. [41]. They performed DFT calculations by using the code DMol [66] and by employing PW91 [67] GGA xc-functional at allelectron level and double numerical basis set with polarization functions. They reported CoPt BE as 5.40 eV and its bond length as ˚ whereas our calculated BLYP results are 2.97 eV and 2.37 A, ˚ respectively. We believe that the substantial discrepancy 2.24 A, between the two BEs is related to the possibility that they directly extracted CoPt energy from the output of DMol where the correct Co atomic ground state may not be referred. When one use the correct reference state of 3d7 4s2 Co atom as in the case of Wu and coworkers’ study [42], one would get a more similar value to ours with that package as well. The calculated bond length of CoPt obeys the general trend that interatomic distances of alloy clusters are between the corresponding values for the pure clusters: Co–Pt bond length 2.24 A˚ is between Co–Co bond length ˚ Similarly, CoPt BE is between 2.13 A˚ and Pt–Pt bond length 2.41 A. Co2 and Pt2 BEs. CoPt Mulliken population analysis gives charge
distributions of 3d7:68 4s1:05 4p0:02 and 5d9:22 6s1:02 for Co and Pt, respectively. The spin density population analysis reveals that Co contribution to the magnetic moment is 2:32mB whereas that of Pt is 0:68mB which can be compared to that of Feng and coworkers’ [41] results (2:75mB for Co and 0:25mB for Pt). Almost all of the magnetic contributions of both of the atoms are due to their d orbitals. The atomic charge distributions indicate that 68% of one of the Co 4s electron is transferred to Co 3d orbital and 22% of it is transferred to Pt 5d orbital. Since 0.68 of the three unoccupied spindown d orbitals of neutral Co atom is now occupied, its magnetic moment becomes 30:68 ¼ 2:32mB . Similarly, due to the new 0.22 electron on Pt 5d orbital and 0.1 electron on the other orbitals, Pt atom magnetic moment becomes 10:32 ¼ 0:68mB . The electrons on Co 4s and Pt 6s orbitals are coupled antiferromagnetically. 3.2. Triatomic ConPtm (nþm¼ 3) nanoalloys Putative lowest energy structures of ConPtm (3 rn þ m r 5) nanoalloys are illustrated in Fig. 1. The point group symmetries, spin moments, BEs per atom, HOMO–LUMO gaps, the lowest and the highest vibrational frequencies of ConPtm (n þ m r5) clusters are given in Table 2. The ground state geometry of Co trimer has been identified as a linear structure with a BE of 1.20 eV/atom. Both of the bond lengths are 2.21 A˚ and the spin moment is 7mB . As one of the Co atoms is replaced by a Pt atom, the lowest energy structure of Co2Pt becomes an isosceles triangle with 2.23 A˚ Co-Co and 2.39 A˚ Co–Pt bond lengths. Its BE is 1.62 eV/atom in the quintet magnetic state (4mB spin moment). As Pt doping increases, triangular structures maintain to be the lowest energy structures with increasing BEs: CoPt2 is an isosceles triangle with 2.35 A˚ Co–Pt and 2.59 A˚ Pt–Pt bond length, while Pt3 is an ˚ However, the equilateral triangle with a bond length of 2.53 A. difference of average BE (BE per atom) between CoPt2 and Pt3 (about 0.07 eV) is much smaller than that of Co2Pt–CoPt2 (0.42 eV) and Co3–Co2Pt (0.42 eV). Successive doping of Pt to Co2Pt decreases the spin moment monotonically from 4mB to 2mB . The b-spin HOMO– LUMO gap of Co trimer (1.04 eV) is significantly higher than that of the other Co–Pt trimers (0.78 eV for Co2Pt, 0.65 eV for CoPt2, and 0.15 eV for Pt3) indicating that it is chemically more inert than the others. 3.3. Tetratomic ConPtm (n þm¼4) nanoalloys All four-atom Co–Pt clusters favor planar rhombic structures except the Pt tetramer which is a distorted tetrahedron. The Co– Co diagonal bond length of Co4 is 2.78 A˚ whereas edge bond ˚ The diagonal bond lengths of Co3Pt, lengths are 2.25 A˚ and 2.21 A. ˚ 2.59 A, ˚ and 2.45 A, ˚ Co2Pt2, and CoPt3 rhombuses are 2.35 A, respectively. Co–Pt interatomic distances at Co3Pt and Co2Pt2 are the same which is 2.38 A˚ whereas they are 2.42 A˚ and 2.44 A˚ ˚ while Pt–Pt distance at at CoPt3. Co–Co distance at Co3Pt is 2.25 A, ˚ One of the faces of the Pt4 tetrahedron is CoPt3 is 2.54 A. ˚ approximately equilateral triangle with a bond length of 2.67 A. The distance between the fourth Pt atom and each of these three ˚ Feng et al. [41] has also investigated the lowest atoms is 2.59 A. energy structure of Co2Pt2 and identified it as a distorted tetrahedron with a total magnetic moment of 4mB which is not consistent with the present results. They reported a rhombic structure as the second isomer in the quintet state which is 0.25 eV higher in energy than the ground state. However, it is not clear whether they have examined the septet magnetic state for the rhombic structure or not. In addition, the initial interatomic distances for a given morphology in a geometry optimization calculation may have important consequences. For instance, the second low lying isomer of Co2Pt2 in our calculations is also a rhombic structure with different bond lengths (diagonal Co–Co
A. Sebetci / Journal of Magnetism and Magnetic Materials 324 (2012) 588–594
591
˚ Fig. 1. (Color online) lowest energy structures of ConPtm clusters (3 r n þ mr 5). Distances are given in A.
˚ That structure is 0.12 eV higher in energy and distance is 2.24 A). more similar to Feng and coworkers’ second isomer. In general, as the number of Pt atoms in the Co–Pt nanoalloys increases, the average BEs increase with a decreasing amount of change. The situation is similar for Co–Pt tetramers as well (see Table 2). The interesting thing is that the average BE of the Pt4 tetramer (2.32 eV/atom) is less than that of CoPt3 (2.37 eV/atom). Thus, CoPt3 is more stable than Pt4. The higher binding energy of CoPt3 compared with Pt4 is consistent with the quite strong exothermic mixing of Co and Pt as evidenced by the formation of several ordered phases in the bulk and by the tetragonal ordering in CoPt nanoparticles. This also shows up in the dimer, where the Co–Pt binding energy is much closer to the Pt–Pt than the Co–Co binding energy (see Table 2). When the spin magnetic moments are considered, it is seen that there is an initial abrupt decrease from 10mB to 7mB in the transition from Co4 to Co3Pt. Then, the addition of Pt atoms to the tetramers decreases the
magnetic moment monotonically one by one up to 5mB for CoPt3. Finally, the spin moment of Pt4 is 2mB . The highest HOMO–LUMO gap (0.94 eV) belongs to the pure Co tetramer once again. 3.4. Pentatomic ConPtm (n þm¼5) nanoalloys The putative lowest energy structure of Co5 is a planar trapezoid ˚ When a where the bond lengths are between 2.24 A˚ and 2.35 A. single Co atom is replaced by a Pt, the lowest energy morphology does not change (see Fig. 1). Co–Pt bond lengths at Co4Pt are 2.35 A˚ and 2.39 A˚ whereas Co–Co bond lengths are between 2.21 A˚ and ˚ The ground state structure of Co3Pt2 is a bipyramid. Three Co 2.41 A. atoms constitute an isosceles triangle in the equatorial plane of the ˚ 2.48 A, ˚ and 2.48 A. ˚ bipyramid with the bond lengths of 2.38 A, ˚ ˚ The apex Pt atoms are 2.45 A and 2.49 A away from the Co atoms. The lowest energy structure of Co2Pt3 is a bridge-side capped tetrahedron (see Fig. 1). A Pt atom is capped the Co–Co bridge of
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the tetrahedron. Co–Co bond distance is 2.52 A˚ whereas the capping Pt atom is 2.38 A˚ away from these Co atoms. Pt–Pt and Co–Pt bond ˚ respectively. We lengths on the tetrahedron are 2.55 A˚ and 2.52 A, have identified two different morphologies as the lowest energy structure of CoPt4 with almost the same BE: a nearly planar, capped rectangle and a pyramid (see Fig. 1). Co–Pt bond length in the capped rectangle is about 2.36 A˚ while Pt–Pt bond lengths are ˚ The base of the pyramid structure is between 2.52 A˚ and 2.60 A. ˚ The composed of Pt atoms with an average separation of 2.59 A. apex Co atom is 2.50 A˚ away from each of these Pt atoms. We have presented the two structures of pure Pt pentamer having the lowest two energies since the ground state structure which is a bridge side capped tetrahedron has only 0.02 eV/atom lower energy than the second isomer which is a pyramid. Pt–Pt bond lengths of the capped tetrahedron are between 2.53 A˚ and 2.95 A˚ whereas the bond length at the base of the pyramid is 2.64 A˚ and the distance between the ˚ apex atom and a base atom is 2.62 A. The average BEs of the Pt pentamers are less than that of the CoPt4 structures as in the case of tetramers. The highest amount of change in the average BE (0.39 eV/atom) occurs at the transition from Co4Pt to Co3Pt2. Thus we expect Co3Pt2 to be observed Table 2 Properties of ConPtm (n þ mr 5) clusters. Cluster Structure
Symmetry Spin moment (mB )
BE per atom (eV)
HOMO– LUMO gap (eV)a
Lowest and highest vibrational frequencies (cm 1)
Co2 CoPt Pt2
Linear Linear Linear
D1h C1h D1h
4 3 2
0.87 1.49 1.61
0.41 0.55 0.19
329 337 215
Co3 Co2Pt CoPt2 Pt3
Linear Triangle Triangle Triangle
D1h C2v C2v D3 h
7 4 3 2
1.20 1.62 2.04 2.11
1.04 0.78 0.65 0.15
80, 237 191, 298 149, 296 57, 212
Co4 Co3Pt Co2Pt2 CoPt3 Pt4
Rhombus Rhombus Rhombus Rhombus Tetrahedron
Cs Cs Cs Cs C1
10 7 6 5 2
1.37 1.82 2.29 2.37 2.32
0.94 0.80 0.65 0.35 0.19
16, 69, 48, 42, 70,
260 289 287 262 205
Co5 Co4Pt Co3Pt2 Co2Pt3
Trapezoid Trapezoid Bipyramid Capped tetrahedron Capped rectangle Pyramid Capped tetrahedron Pyramid
Cs C1 C1 Cs
11 10 7 6
1.54 1.89 2.28 2.34
0.81 0.66 0.87 0.59
98, 72, 70, 38,
297 328 279 281
C1
5
2.56
0.31
27, 326
C4 C2v
7 4
2.56 2.55
0.06 0.36
59, 266 34, 200
C4
6
2.53
0.14
41, 201
CoPt4
Pt5
a
b-spin.
more abundantly in a mass spectroscopy experiment. Co3Pt2 has also the highest HOMO–LUMO gap (0.87 eV) which contributes to its stability. We discuss particularly the stability of the Co–Pt nanoalloys in the next section. The spin moments decrease as the number of Pt atoms increases in the alloy clusters. However, pyramidal CoPt4 has higher spin moment (7mB ) than Co2Pt3 (6mB ) which can be related to the fact that pyramidal Pt5 magnetic moment is higher than that of tetrahedral Pt pentamer. 3.5. Stability of ConPtm (3 rn þm r 5) nanoalloys The second finite difference in energies Dn,m ¼ En þ 1,m1 þEn1,m þ 1 2En,m where En,m is the total energy of the cluster ConPtm, is generally correlated with the magic numbers observed in mass spectra. Clusters are particularly abundant at magic number sizes in mass spectra as they are the most stable ones. We have given the average BEs and the average second finite differences in energies (D per atom) for ConPtm tetramers and pentamers in Fig. 2. For the triatomic Co–Pt nanoclusters, CoPt2 has much higher D energy (0.35 eV/atom) than Co2Pt (0.00 eV). Thus, it is found to be more stable than the latter species. For tetramers, the peak in Fig. 2(a) indicates that Co2Pt2 is more stable than CoPt3 and Co3Pt. For pentamers, there are two peaks in the graph Fig. 2(b) at Co3Pt2 and CoPt4. Thus, these two species are expected to be more abundant in mass spectra than the other pentamers. Our results show that the optimal path of dissociation for bimetallic Co–Pt clusters involves the evaporation of a single Co atom with a single exception that CoPt4 cluster prefers a Pt atom removal. 3.6. Total spin moments of ConPtm (n þ m r5) nanoalloys Generally, the ground state total spin moment of a Co–Pt bimetallic cluster is equal to the spin moment of CoPt dimer times the number of CoPt units involved in the cluster plus the spin moment of the remaining part of the cluster if the remaining part is not a single atom. For instance, the spin moment of CoPt3 (5mB ) is equal to the spin moment of CoPt (3mB ) plus the spin moment of Pt2 (2mB ), or the spin moment of Co4Pt (10mB ) is equal to the spin moment of CoPt (3mB ) plus the spin moment of Co3 (7mB ). When a single Co atom remains after the extraction of CoPt units, that single Co atom contributes 1mB to the spin moment of the cluster as an addition to the total spin moments of the CoPt units. For example, the spin moment of Co2Pt (4mB ) is equal to the spin moment of CoPt (3mB ) plus the contribution of the Co atom (1mB ), or the spin moment of Co3Pt2 (7mB ) is equal to two times the spin moment of CoPt (2 3 ¼ 6mB ) plus the contribution of the Co atom (1mB ). If the remaining single atom is Pt, no contribution to the total spin moment occurs. For instance, the spin moment of CoPt2 (3mB ) is equal to the spin moment of CoPt, or the spin moment of Co2Pt3 (6mB ) is equal to two times the spin moment of
Fig. 2. (a) BE and second finite difference in energies (D) of ConPtm tetramers (b) those of ConPtm pentamers.
A. Sebetci / Journal of Magnetism and Magnetic Materials 324 (2012) 588–594
CoPt (2 3 ¼ 6mB ). Therefore, we may speculate about the total spin moments of Co–Pt hexamers: it may be expected that Co5Pt has 13mB (3þ10), Co4Pt2 has 10mB (2 3 þ4), Co3Pt3 has 9mB (3 3), Co2Pt4 has 8mB (2 3þ2), and CoPt5 has 5mB (3þ2) spin moments in their ground magnetic states. However, this empirical rule of the additivity of CoPt unit magnetism presumably become not to work for much bigger nanoparticles.
4. Conclusions In the present article, we have carried out systematic DFT study for bimetallic ConPtm (n þm r 5) clusters within the generalized gradient approximation to understand the mechanism and elucidate more details on the formation of CoPt nanoparticles. The ground geometric, electronic, and magnetic states of these clusters have been identified. It is found that as Pt doping to Co clusters increases the initial planar structures become 3D. In general, average BE increases with increase in substitution of Pt atoms. CoPt2, Co2Pt2, Co3Pt2, and CoPt4 species are identified as the most stable ones, since they have higher second finite difference in energy than their neighboring sizes. Total magnetic moments are decreased with doped Pt. Generally, the ground state total spin moment of a Co–Pt bimetallic cluster is equal to the spin moment of CoPt dimer times the number of CoPt units plus the spin moment of the remaining part of the cluster if the remaining part is not a single atom. When a single Co atom remains after the extraction of CoPt units, that Co atom contributes 1mB to the spin moment of the cluster. If the remaining single atom is Pt, no contribution to the total spin moment occurs. HOMO–LUMO gaps, and the lowest and the highest vibrational frequencies are reported to guide further experimental studies.
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Density functional study of small cobalt–platinum nanoalloy clusters Ali Sebetci n Computer Engineering Department and Nanotechnology Applications and Research Center (ZUNAM), Zirve University, Gaziantep 27260, Turkey
a r t i c l e i n f o
a b s t r a c t
Article history: Received 4 December 2010 Received in revised form 15 August 2011 Available online 3 September 2011
The structural, energetic, electronic and magnetic properties of small bimetallic ConPtm (n þ m r 5) nanoalloy clusters are investigated by density functional theory within the generalized gradient approximation. A plausible candidate for the ground state isomer and the other possible local minima, binding energies, relative stabilities, magnetic moments, the highest occupied and the lowest unoccupied molecular orbital energy gaps have been calculated. It is found as a general trend that average binding energies of Co–Pt bimetallic clusters increase with Pt doping. Planar structures of pure Co clusters become 3D with the addition of Pt atoms. CoPt2, Co2Pt2, Co3Pt2, and CoPt4 nanoalloys are identified as the most stable species since they have higher second finite difference in energy than the others. Pt doping decreases the total spin magnetic moment gradually. A rule for the prediction of the total spin moments of small Co–Pt bimetallic clusters is derived. & 2011 Elsevier B.V. All rights reserved.
Keywords: Cobalt Platinum Clusters Density functional theory Electronic properties
1. Introduction While transition metal clusters, in general, have many potential applications in different areas of nanotechnology such as heterogeneous catalysis [1], magnetic recording media [2], medicine and biochemistry [3], magnetic CoPt nanoalloy clusters, in particular, have been attracted much attention during the last decade [4–30] due to the consideration that they are the best candidates for ultra-high density magnetic storage applications [31]. The main physical limitation of such a technology for permanent nanomagnets is related to their superparamagnetic behavior, as the magnetization direction of a nanoparticle usually fluctuates at room temperature which is incompatible with longtime recording [32]. One of the most promising routes to maintain the thermal stability of the nanoparticles’ magnetization is to employ bimetallic nanoalloys composed of 3d magnetic elements and 5d or 4d transition metals, such as CoPt, CoRh, FePt, FePd and so on [25]. Since the anisotropy energy arises from the spin–orbit interaction [33] which increases with atomic number, these materials have a magnetocrystalline anisotropy constant one order of magnitude larger than CoCr-based alloys used in magnetic devices [34]. The magnetocrystalline anisotropy constant of the nanoalloys depends on the size and the structure of the nanoparticles [25]. Another important motivation for the study of CoPt bimetallic nanoclusters is that one of the key objectives of the lowtemperature polymer electrolyte membrane fuel-cell technology
n
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is to improve and reduce Pt loading as the oxygen-reduction catalyst [35]. Many investigations [36–39] such as the series of binary PtM alloys (M ¼Cr, Mn, Co, Ni) supported on carbon [40] have been carried out to determine the role of alloying in the electrocatalytic activity of Pt for the oxygen-reduction reaction. All these studies have shown that the intrinsic activity of nanoparticles depends particle size, shape and composition. A recent synthesis of CoPt nanoparticles in MgO and amorphous carbon matrices with a mean diameter of 3 nm and their characterization by using X-ray magnetic circular dichroism and superconducting quantum interference device are reported by Tournus et al. [30]. They have shown that embedded clusters undergo a transition from a chemically disordered phase, labeled A1 to the chemically ordered L10 phase upon annealing, even for clusters with a 2 nm diameter, without cluster coalescence and that the magnetic anisotropy of chemically ordered nanoparticles increases with respect to the chemically disordered A1 phase. 1D and 2D CoPt nanostructures have been successfully synthesized in solution-phase process [8,13,14] and in thermal decomposition of an organometallic precursor [5,7]. CoPt nanorods were synthesized in ionic liquids [15]. Tzitzios et al. [14] described the synthesis of a 3D ferromagnetic CoPt polypod-like nanostructure. Hyun An et al. [27] have synthesized monodisperse CoPt nanoparticles possessing high crystallinity with a particle size of 5.3 nm and a tight size distribution by a modified polyol process. On the theoretical side, the Metropolis Monte Carlo (MC) sampling method with an isotropic semi-empirical Embedded Atom Model (EAM) and a modified (angle dependent) EAM potentials were used to investigate structural properties of free CoPt nanoclusters [26]. Both potentials predicted partially ordered L10 phase for CoPt nanoparticles. Rossi et al. [28] have
A. Sebetci / Journal of Magnetism and Magnetic Materials 324 (2012) 588–594
investigated the structure and chemical ordering of CoPt nanoclusters in the size range of 1–3 nm by global optimization methods and MC simulations using a many body potential derived from the tight binding model and reported that for the smaller systems (number of atoms N o 100), the optimized clusters display a polyicosahedral-like atomic structure and that a transition to the decahedral symmetry occurs at about N ¼100 atoms, with a pseudo L10 ordered phase in each tetrahedral unit. Gruner et al. [29] have performed large-scale Density Functional Theory (DFT) calculations on FePt and CoPt clusters with diameters of up to 2.5 nm by selecting so-called magic cluster sizes (13, 55, 147, 309, 561, etc.). They have found that CoPt core-shell segregated morphologies predominate with considerably increased energy differences to the L10 structure. In order to understand the mechanism and elucidate more details on the formation of CoPt nanoparticles, it is worthy to investigate small CoPt nanoclusters systematically. To the best of our knowledge, the only theoretical study of small CoPt clusters in the literature is by Feng et al. [41]. They investigated the geometrical and magnetic properties of (CoPt)n (n r5) clusters where the numbers of Co and Pt atoms in each cluster are the same. They found that the magnetism per (CoPt) unit increases with the size of the cluster. Wu and coworkers [42] have investigated the electronic and magnetic properties of small ConMnm and ConVm (n þ mr 6) clusters using DFT and shown that Co and V atoms prefer to aggregate in Co–Mn and Co–V clusters, respectively. They found significant magnetic moment enhancement in Co–Mn clusters with Mn doping and reduction in Co–V clusters with V doping consistent with experimental results for larger clusters [43]. Lv et al. [44] have studied (CoRh)n (n r 5) clusters in the framework of DFT and reported that the most stable structures of (CoRh)n (n r5) clusters are similar to those of corresponding pure Co2n and Rh2n clusters. Parida and coworkers [45] have presented a systematic DFT study of NinCom and NinFem (n þ m r6) clusters and found that with increase in substitution of Co and Fe atoms in Ni cluster, while NinCom becomes more stable, NinFem clusters become less stable. Du and coworkers [46] have studied the magnetic states including collinear and noncollinear magnetic coupling in bimetallic Co6 nMnn clusters. They reported that the ground state of Co6 nMnn clusters displays collinear magnetic ordering for n r 3, whereas a magnetic transition to noncollinear ordering occurs at n ¼4 and the noncollinear magnetic structure remains to be energetically favored afterwards. We have previously studied pure Con and Ptn (n r 6) clusters and reported their properties [47]. In the present study, we have investigated the structural, energetic, electronic and magnetic properties of small bimetallic ConPtm (n þm r 5) nanoclusters by employing DFT within the generalized gradient approximation and collinear magnetic coupling formalism. Spin–orbit and noncollinearity effects may be investigated in a future study. The putative ground state isomers and the other possible local minima, binding energies (BE), relative stabilities, magnetic moments, the highest occupied and lowest unoccupied molecular orbital (HOMO–LUMO) energy gaps have been calculated. Vibrational frequency calculations of the lowest energy structures have been carried out to differentiate minima from transition states. Above mentioned questions emerged for the properties of Co containing small nanoalloy clusters have been discussed for the Co–Pt bimetallic clusters.
2. Computational details NWChem 5.1.1 program package [48] has been used to perform geometry optimizations and total energy calculations by DFT. The default convergence criteria, which are 1 10 6 Hartree
589
for energy, and 5 10 4 Hartree/a0 for energy gradient, are used. CRENBL [49] basis sets and effective core potentials (ECP) for both of the elements have been employed where the outer most 17 electrons of free Co atom (3s2 3p6 3d7 4s2 ) and the outer most 18 electrons of free Pt atom (5s2 5p6 5d9 6s1 ) are treated explicitly. The corresponding Gaussian basis functions of Co and Pt are (7s6p6d) and (5s5p4d), respectively. The ECPs were computed using the relativistic Dirac–Fock equation. The reliability of the basis sets and the ECPs were determined by comparing atomic excitation energies with accurate all-electron calculations where the maximum errors were found to be less than 0.05 eV for Co, and 0.12 eV for Pt [49]. The generalized gradient approximation (GGA) of Becke’s exchange functional [50] and Lee–Yang–Parr correlation functional [51] (BLYP) has been employed in the calculations. Justification of the choice of the xc-functional is discussed in the next section by giving a comparison between the results for Co2 and Pt2 dimers with the following functionals: Perdew–Burke– Ernzerhof (PBE96) [52] GGA, B3LYP [50], and PBE0 [53] hybrid, and Slater-Vosko–Wilk–Nusair (SVWN5) [54] local density approximation (LDA). As the number of atoms in a homonuclear cluster increases, the number of locally stable isomers increases very fast [55] and the identification of the ground state structure becomes much more difficult. For the case of alloy clusters the situation is worse since the interchange of the two types of atoms for a given morphology creates new structures called homotops and they need to be considered separately in the geometry optimizations. We have performed several geometry relaxation calculations starting from different morphologies such as linear and various triangular arrangements for trimers, linear, planar Y-like, square, rhombus structures, and 3D tetrahedron for tetramers, and bipyramid, pyramid, bridge-side-capped tetrahedron, planar W-like, X-like, V-like structures, and pentagon for pentamers. For each initial geometry, all possible homotops were subject to individual geometry optimizations. The structures have been relaxed without imposing any symmetry constraints. Spin-polarized calculations have been done for at least five different spin multiplicities.
3. Results and discussion 3.1. Diatomic ConPtm (nþm ¼2) nanoalloys To validate the reliability of the present calculations, we first compare our results with available experimental data and previous reports on pure Co and Pt dimers. Table 1 presents the BEs, bond lengths, vibrational frequencies, and adiabatic ionization potentials (IP). The results on CoPt with different xc-functionals have also been included in the table to provide the reader a sense about what could be the values with other xc approximations. The BE of a given cluster is defined as the absolute value of the difference between the total energy of the cluster and the sum of the ground state energies of free atoms which are the Co atom quartet and Pt atom triplet states. The ground state spin multiplicities of Co2, Pt2, and CoPt are quintet, triplet, and quartet, respectively for all xc-functionals employed in this study except PBE0 which gives a doublet for CoPt. Co2þ , Pt2þ , and CoPt þ cations’ spin multiplicities calculated for IPs are sextet, quartet, and quintet, respectively. The exceptions are PBE which results in a doublet state for Pt2þ and B3LYP which results in a triplet state for CoPt þ . Table 1 shows that BLYP calculations are the closest results to the experimental values of Co dimer in three categories: BE, bond length, and IP. The vibrational frequency value is also in the range of a reasonable scaling factor. For Pt dimer, again BLYP
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Table 1 Comparisons of the present results for Co2 and Pt2 with those of the previous experimental and theoretical works and comparison of the present results for CoPt with different xc-functionals. Cluster Type of work
Co2
Experimental Ref. [56] Literature Ref. [57] Ref. [58] Theoretical Ref. [59] Literature Ref. [60] Present SVWN5 Work BLYP PBE96 PBE0 B3LYP
Pt2
Experimental Ref. [61] Literature Ref. [62] Ref. [63] Theoretical Ref. [64] Literature Ref. [65] Present SVWN5 Work BLYP PBE96 PBE0 B3LYP
CoPt
a b c
Binding Ref. No. energy or xcfunctional (eV)
Theoretical Literature Present Work
Bond length ˚ (A)
Vibrational frequency (cm 1)
Ionization potential (eV)
1.69 7 0.26 2.31 6.26 7 0.16 2.35 2.26 3.70 1.73 2.04 0.08 0.15
1.99 2.01 1.93 2.13 2.10 2.08 2.09
296.8 75.4 373 342 440 329 271 366 357
3.14 7 0.02
7.49 7.48 7.46 6.84 6.97 8.18 8.27 8.68 7 0.02
222 2.44 3.29 4.46 3.21 3.50 2.58 2.59
2.33 2.39 2.39 2.33 2.41 2.38 2.35 2.38
Ref. [41]
5.40
2.37
SVWN5 BLYP PBE96 PBE0 B3LYP
4.72 2.97 3.31 1.82b 1.60
2.17 2.24 2.22 2.35 2.21
223 253 215 228 247 235
8.87 8.54 8.61 8.62a 8.60
381 337 319 235 237
8.03 7.78 7.89 7.20 7.81c
Cation is a doublet. Doublet. Cation is a triplet.
produces the nearest BE calculation to the experimental estimation. Although there are slightly better values for the other three properties of Pt2, overall performances of the other functionals are not as good as that of BLYP. Generally, LDA functionals overestimate the BEs of transition metal clusters, while hybrid functionals underestimate them. The hybrid PBE0 even resulted in a negative BE for Co dimer in our study. In addition, all the exceptions for the spin multiplicities reported in Table 1 are calculated with the two hybrid functionals. Thus, GGA functionals are more favorable than both LDA and hybrid functionals for the present purposes. Since BLYP has slightly better performance than PBE96, we have employed it in the rest of our calculations. We can compare our results on CoPt with those of Feng et al. [41]. They performed DFT calculations by using the code DMol [66] and by employing PW91 [67] GGA xc-functional at allelectron level and double numerical basis set with polarization functions. They reported CoPt BE as 5.40 eV and its bond length as ˚ whereas our calculated BLYP results are 2.97 eV and 2.37 A, ˚ respectively. We believe that the substantial discrepancy 2.24 A, between the two BEs is related to the possibility that they directly extracted CoPt energy from the output of DMol where the correct Co atomic ground state may not be referred. When one use the correct reference state of 3d7 4s2 Co atom as in the case of Wu and coworkers’ study [42], one would get a more similar value to ours with that package as well. The calculated bond length of CoPt obeys the general trend that interatomic distances of alloy clusters are between the corresponding values for the pure clusters: Co–Pt bond length 2.24 A˚ is between Co–Co bond length ˚ Similarly, CoPt BE is between 2.13 A˚ and Pt–Pt bond length 2.41 A. Co2 and Pt2 BEs. CoPt Mulliken population analysis gives charge
distributions of 3d7:68 4s1:05 4p0:02 and 5d9:22 6s1:02 for Co and Pt, respectively. The spin density population analysis reveals that Co contribution to the magnetic moment is 2:32mB whereas that of Pt is 0:68mB which can be compared to that of Feng and coworkers’ [41] results (2:75mB for Co and 0:25mB for Pt). Almost all of the magnetic contributions of both of the atoms are due to their d orbitals. The atomic charge distributions indicate that 68% of one of the Co 4s electron is transferred to Co 3d orbital and 22% of it is transferred to Pt 5d orbital. Since 0.68 of the three unoccupied spindown d orbitals of neutral Co atom is now occupied, its magnetic moment becomes 30:68 ¼ 2:32mB . Similarly, due to the new 0.22 electron on Pt 5d orbital and 0.1 electron on the other orbitals, Pt atom magnetic moment becomes 10:32 ¼ 0:68mB . The electrons on Co 4s and Pt 6s orbitals are coupled antiferromagnetically. 3.2. Triatomic ConPtm (nþm¼ 3) nanoalloys Putative lowest energy structures of ConPtm (3 rn þ m r 5) nanoalloys are illustrated in Fig. 1. The point group symmetries, spin moments, BEs per atom, HOMO–LUMO gaps, the lowest and the highest vibrational frequencies of ConPtm (n þ m r5) clusters are given in Table 2. The ground state geometry of Co trimer has been identified as a linear structure with a BE of 1.20 eV/atom. Both of the bond lengths are 2.21 A˚ and the spin moment is 7mB . As one of the Co atoms is replaced by a Pt atom, the lowest energy structure of Co2Pt becomes an isosceles triangle with 2.23 A˚ Co-Co and 2.39 A˚ Co–Pt bond lengths. Its BE is 1.62 eV/atom in the quintet magnetic state (4mB spin moment). As Pt doping increases, triangular structures maintain to be the lowest energy structures with increasing BEs: CoPt2 is an isosceles triangle with 2.35 A˚ Co–Pt and 2.59 A˚ Pt–Pt bond length, while Pt3 is an ˚ However, the equilateral triangle with a bond length of 2.53 A. difference of average BE (BE per atom) between CoPt2 and Pt3 (about 0.07 eV) is much smaller than that of Co2Pt–CoPt2 (0.42 eV) and Co3–Co2Pt (0.42 eV). Successive doping of Pt to Co2Pt decreases the spin moment monotonically from 4mB to 2mB . The b-spin HOMO– LUMO gap of Co trimer (1.04 eV) is significantly higher than that of the other Co–Pt trimers (0.78 eV for Co2Pt, 0.65 eV for CoPt2, and 0.15 eV for Pt3) indicating that it is chemically more inert than the others. 3.3. Tetratomic ConPtm (n þm¼4) nanoalloys All four-atom Co–Pt clusters favor planar rhombic structures except the Pt tetramer which is a distorted tetrahedron. The Co– Co diagonal bond length of Co4 is 2.78 A˚ whereas edge bond ˚ The diagonal bond lengths of Co3Pt, lengths are 2.25 A˚ and 2.21 A. ˚ 2.59 A, ˚ and 2.45 A, ˚ Co2Pt2, and CoPt3 rhombuses are 2.35 A, respectively. Co–Pt interatomic distances at Co3Pt and Co2Pt2 are the same which is 2.38 A˚ whereas they are 2.42 A˚ and 2.44 A˚ ˚ while Pt–Pt distance at at CoPt3. Co–Co distance at Co3Pt is 2.25 A, ˚ One of the faces of the Pt4 tetrahedron is CoPt3 is 2.54 A. ˚ approximately equilateral triangle with a bond length of 2.67 A. The distance between the fourth Pt atom and each of these three ˚ Feng et al. [41] has also investigated the lowest atoms is 2.59 A. energy structure of Co2Pt2 and identified it as a distorted tetrahedron with a total magnetic moment of 4mB which is not consistent with the present results. They reported a rhombic structure as the second isomer in the quintet state which is 0.25 eV higher in energy than the ground state. However, it is not clear whether they have examined the septet magnetic state for the rhombic structure or not. In addition, the initial interatomic distances for a given morphology in a geometry optimization calculation may have important consequences. For instance, the second low lying isomer of Co2Pt2 in our calculations is also a rhombic structure with different bond lengths (diagonal Co–Co
A. Sebetci / Journal of Magnetism and Magnetic Materials 324 (2012) 588–594
591
˚ Fig. 1. (Color online) lowest energy structures of ConPtm clusters (3 r n þ mr 5). Distances are given in A.
˚ That structure is 0.12 eV higher in energy and distance is 2.24 A). more similar to Feng and coworkers’ second isomer. In general, as the number of Pt atoms in the Co–Pt nanoalloys increases, the average BEs increase with a decreasing amount of change. The situation is similar for Co–Pt tetramers as well (see Table 2). The interesting thing is that the average BE of the Pt4 tetramer (2.32 eV/atom) is less than that of CoPt3 (2.37 eV/atom). Thus, CoPt3 is more stable than Pt4. The higher binding energy of CoPt3 compared with Pt4 is consistent with the quite strong exothermic mixing of Co and Pt as evidenced by the formation of several ordered phases in the bulk and by the tetragonal ordering in CoPt nanoparticles. This also shows up in the dimer, where the Co–Pt binding energy is much closer to the Pt–Pt than the Co–Co binding energy (see Table 2). When the spin magnetic moments are considered, it is seen that there is an initial abrupt decrease from 10mB to 7mB in the transition from Co4 to Co3Pt. Then, the addition of Pt atoms to the tetramers decreases the
magnetic moment monotonically one by one up to 5mB for CoPt3. Finally, the spin moment of Pt4 is 2mB . The highest HOMO–LUMO gap (0.94 eV) belongs to the pure Co tetramer once again. 3.4. Pentatomic ConPtm (n þm¼5) nanoalloys The putative lowest energy structure of Co5 is a planar trapezoid ˚ When a where the bond lengths are between 2.24 A˚ and 2.35 A. single Co atom is replaced by a Pt, the lowest energy morphology does not change (see Fig. 1). Co–Pt bond lengths at Co4Pt are 2.35 A˚ and 2.39 A˚ whereas Co–Co bond lengths are between 2.21 A˚ and ˚ The ground state structure of Co3Pt2 is a bipyramid. Three Co 2.41 A. atoms constitute an isosceles triangle in the equatorial plane of the ˚ 2.48 A, ˚ and 2.48 A. ˚ bipyramid with the bond lengths of 2.38 A, ˚ ˚ The apex Pt atoms are 2.45 A and 2.49 A away from the Co atoms. The lowest energy structure of Co2Pt3 is a bridge-side capped tetrahedron (see Fig. 1). A Pt atom is capped the Co–Co bridge of
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A. Sebetci / Journal of Magnetism and Magnetic Materials 324 (2012) 588–594
the tetrahedron. Co–Co bond distance is 2.52 A˚ whereas the capping Pt atom is 2.38 A˚ away from these Co atoms. Pt–Pt and Co–Pt bond ˚ respectively. We lengths on the tetrahedron are 2.55 A˚ and 2.52 A, have identified two different morphologies as the lowest energy structure of CoPt4 with almost the same BE: a nearly planar, capped rectangle and a pyramid (see Fig. 1). Co–Pt bond length in the capped rectangle is about 2.36 A˚ while Pt–Pt bond lengths are ˚ The base of the pyramid structure is between 2.52 A˚ and 2.60 A. ˚ The composed of Pt atoms with an average separation of 2.59 A. apex Co atom is 2.50 A˚ away from each of these Pt atoms. We have presented the two structures of pure Pt pentamer having the lowest two energies since the ground state structure which is a bridge side capped tetrahedron has only 0.02 eV/atom lower energy than the second isomer which is a pyramid. Pt–Pt bond lengths of the capped tetrahedron are between 2.53 A˚ and 2.95 A˚ whereas the bond length at the base of the pyramid is 2.64 A˚ and the distance between the ˚ apex atom and a base atom is 2.62 A. The average BEs of the Pt pentamers are less than that of the CoPt4 structures as in the case of tetramers. The highest amount of change in the average BE (0.39 eV/atom) occurs at the transition from Co4Pt to Co3Pt2. Thus we expect Co3Pt2 to be observed Table 2 Properties of ConPtm (n þ mr 5) clusters. Cluster Structure
Symmetry Spin moment (mB )
BE per atom (eV)
HOMO– LUMO gap (eV)a
Lowest and highest vibrational frequencies (cm 1)
Co2 CoPt Pt2
Linear Linear Linear
D1h C1h D1h
4 3 2
0.87 1.49 1.61
0.41 0.55 0.19
329 337 215
Co3 Co2Pt CoPt2 Pt3
Linear Triangle Triangle Triangle
D1h C2v C2v D3 h
7 4 3 2
1.20 1.62 2.04 2.11
1.04 0.78 0.65 0.15
80, 237 191, 298 149, 296 57, 212
Co4 Co3Pt Co2Pt2 CoPt3 Pt4
Rhombus Rhombus Rhombus Rhombus Tetrahedron
Cs Cs Cs Cs C1
10 7 6 5 2
1.37 1.82 2.29 2.37 2.32
0.94 0.80 0.65 0.35 0.19
16, 69, 48, 42, 70,
260 289 287 262 205
Co5 Co4Pt Co3Pt2 Co2Pt3
Trapezoid Trapezoid Bipyramid Capped tetrahedron Capped rectangle Pyramid Capped tetrahedron Pyramid
Cs C1 C1 Cs
11 10 7 6
1.54 1.89 2.28 2.34
0.81 0.66 0.87 0.59
98, 72, 70, 38,
297 328 279 281
C1
5
2.56
0.31
27, 326
C4 C2v
7 4
2.56 2.55
0.06 0.36
59, 266 34, 200
C4
6
2.53
0.14
41, 201
CoPt4
Pt5
a
b-spin.
more abundantly in a mass spectroscopy experiment. Co3Pt2 has also the highest HOMO–LUMO gap (0.87 eV) which contributes to its stability. We discuss particularly the stability of the Co–Pt nanoalloys in the next section. The spin moments decrease as the number of Pt atoms increases in the alloy clusters. However, pyramidal CoPt4 has higher spin moment (7mB ) than Co2Pt3 (6mB ) which can be related to the fact that pyramidal Pt5 magnetic moment is higher than that of tetrahedral Pt pentamer. 3.5. Stability of ConPtm (3 rn þm r 5) nanoalloys The second finite difference in energies Dn,m ¼ En þ 1,m1 þEn1,m þ 1 2En,m where En,m is the total energy of the cluster ConPtm, is generally correlated with the magic numbers observed in mass spectra. Clusters are particularly abundant at magic number sizes in mass spectra as they are the most stable ones. We have given the average BEs and the average second finite differences in energies (D per atom) for ConPtm tetramers and pentamers in Fig. 2. For the triatomic Co–Pt nanoclusters, CoPt2 has much higher D energy (0.35 eV/atom) than Co2Pt (0.00 eV). Thus, it is found to be more stable than the latter species. For tetramers, the peak in Fig. 2(a) indicates that Co2Pt2 is more stable than CoPt3 and Co3Pt. For pentamers, there are two peaks in the graph Fig. 2(b) at Co3Pt2 and CoPt4. Thus, these two species are expected to be more abundant in mass spectra than the other pentamers. Our results show that the optimal path of dissociation for bimetallic Co–Pt clusters involves the evaporation of a single Co atom with a single exception that CoPt4 cluster prefers a Pt atom removal. 3.6. Total spin moments of ConPtm (n þ m r5) nanoalloys Generally, the ground state total spin moment of a Co–Pt bimetallic cluster is equal to the spin moment of CoPt dimer times the number of CoPt units involved in the cluster plus the spin moment of the remaining part of the cluster if the remaining part is not a single atom. For instance, the spin moment of CoPt3 (5mB ) is equal to the spin moment of CoPt (3mB ) plus the spin moment of Pt2 (2mB ), or the spin moment of Co4Pt (10mB ) is equal to the spin moment of CoPt (3mB ) plus the spin moment of Co3 (7mB ). When a single Co atom remains after the extraction of CoPt units, that single Co atom contributes 1mB to the spin moment of the cluster as an addition to the total spin moments of the CoPt units. For example, the spin moment of Co2Pt (4mB ) is equal to the spin moment of CoPt (3mB ) plus the contribution of the Co atom (1mB ), or the spin moment of Co3Pt2 (7mB ) is equal to two times the spin moment of CoPt (2 3 ¼ 6mB ) plus the contribution of the Co atom (1mB ). If the remaining single atom is Pt, no contribution to the total spin moment occurs. For instance, the spin moment of CoPt2 (3mB ) is equal to the spin moment of CoPt, or the spin moment of Co2Pt3 (6mB ) is equal to two times the spin moment of
Fig. 2. (a) BE and second finite difference in energies (D) of ConPtm tetramers (b) those of ConPtm pentamers.
A. Sebetci / Journal of Magnetism and Magnetic Materials 324 (2012) 588–594
CoPt (2 3 ¼ 6mB ). Therefore, we may speculate about the total spin moments of Co–Pt hexamers: it may be expected that Co5Pt has 13mB (3þ10), Co4Pt2 has 10mB (2 3 þ4), Co3Pt3 has 9mB (3 3), Co2Pt4 has 8mB (2 3þ2), and CoPt5 has 5mB (3þ2) spin moments in their ground magnetic states. However, this empirical rule of the additivity of CoPt unit magnetism presumably become not to work for much bigger nanoparticles.
4. Conclusions In the present article, we have carried out systematic DFT study for bimetallic ConPtm (n þm r 5) clusters within the generalized gradient approximation to understand the mechanism and elucidate more details on the formation of CoPt nanoparticles. The ground geometric, electronic, and magnetic states of these clusters have been identified. It is found that as Pt doping to Co clusters increases the initial planar structures become 3D. In general, average BE increases with increase in substitution of Pt atoms. CoPt2, Co2Pt2, Co3Pt2, and CoPt4 species are identified as the most stable ones, since they have higher second finite difference in energy than their neighboring sizes. Total magnetic moments are decreased with doped Pt. Generally, the ground state total spin moment of a Co–Pt bimetallic cluster is equal to the spin moment of CoPt dimer times the number of CoPt units plus the spin moment of the remaining part of the cluster if the remaining part is not a single atom. When a single Co atom remains after the extraction of CoPt units, that Co atom contributes 1mB to the spin moment of the cluster. If the remaining single atom is Pt, no contribution to the total spin moment occurs. HOMO–LUMO gaps, and the lowest and the highest vibrational frequencies are reported to guide further experimental studies.
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