Ab Initio Studies of Segregation, Ordering, and Magnetic Behavior in

Subscriber access provided by University of Ulster Library

Article

Ab Initio Studies of Segregation, Ordering, and Magnetic Behavior in (Fe-Pt)n, n = 55 and 147: Design of Fe75Pt72 Nanoparticle Bheema Lingam Chittari, and Vijay Kumar J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp511741f • Publication Date (Web): 07 Feb 2015 Downloaded from http://pubs.acs.org on February 18, 2015

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 47

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Ab Initio Studies of Segregation, Ordering, and Magnetic Behavior in (Fe-Pt)n, n = 55 and 147: Design of Fe75Pt72 Nanoparticle Bheema Lingam Chittari‡1 and Vijay Kumar‡*1,2 1

Dr. Vijay Kumar Foundation, 1969 Sector 4, Gurgaon 122001, Haryana, India

2

Center for Informatics, School of Natural Sciences, Shiv Nadar University, NH91, Tehsil

Dadri, Gautam Budh Nagar - 201314, U.P., India KEYWORDS: Fe-Pt nanoparticles, Nanoalloys, Ferromagnetism, Charge transfer, Heat of formation, Surface segregation, Ordering, Core-shell icosahedral structure, Electronic density of states;

ABSTRACT.

We report results of a systematic study on atomic and electronic structure of 55-atom and 147-atom Fe-Pt nanoparticles with different compositions using ab initio calculations. Our results on 55-atom nanoparticles suggest icosahedral structure and segregation of Pt on the surface to be favourable. Also there is a tendency for Fe-Pt ordering on the surface and maximization of the unlike bonds similar to bulk while the core is made of pure Fe13 giving it a core-shell structure. Using these considerations we designed a unique 147-atom icosahedral Fe75Pt72 nanoparticle in which 55-atom core is made of Fe atoms and 72 Pt atoms are on the outer shell of the icosahedron. Twenty Fe atoms are on the centers of the Pt hexagons on the 1

ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

faces of the icosahedron. This nanoparticle has 260 µ B magnetic moments and the local magnetic moments on Fe and Pt atoms are higher compared with the values in bulk FePt. Free Fe55 cluster has a distorted icosahedral structure to be most favorable with large magnetic moments (~3 µ B/atom) which we also find in the core of the nanoalloy particle, but the surface Fe atoms have higher magnetic moments of about 3.4 µ B/atom. All the Pt atoms are on the surface with Fe-Pt ordering in a nearly symmetric icosahedral structure and the heat of formation is the highest which makes it an optimal nanoparticle. The overall composition of this nanoparticle is FePt-like, but it decomposes in to Fe core and Fe-Pt shell. (*Corresponding Author: [email protected] and [email protected]; Tel/Fax.: +91-1244079369) 1. Introduction The L10 ordered FePt nanoparticles are one of the most promising materials for ultrahigh-density magnetic recording media applications1-6 due to their high magnetic crystalline anisotropy (MCA) and coercivity compared to other materials7. The size reduction of the nanoparticles may affect the atomic structure as well as the magnetic behaviour because the MCA of FePt originates from the long range ordering of alternately stacked Fe and Pt layers along the c-axis8-9. FePt nanoparticles smaller than the critical grain size of about 2.5 nm are not ordered to L10 structure10. Experiments suggest that complete ordering to bulk structure sets in above 7 nm10,11. Surface effects and twin boundary formation below 7 nm at room temperature vanishes the high coercivity and MCA rapidly12-14. However, small nanoparticles of FePt are much better catalyst for oxygen reduction reactions (ORR)15,16 compared with pure Pt nanoparticles. The activity and durability of these nanoparticles are not only dependent on their composition but also on the surface structure17,18. Surface disorder could lead to significant modification in the atomic structure of the nanoparticles. 2


Page 2 of 47

Page 3 of 47

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Also, the surface energy difference between constituents namely Fe and Pt as well as its variation on different facets may lead to surface segregation of a species and its variation on different facets that could also lead to a change in the shape of the nanoparticles. Therefore, FePt nanoparticles below the size of 7 nm have a considerable competition between ordering, twinning, and segregation since these nanoparticles are driven more by the consideration of size dependent surface affects and geometry. The evolution of the atomic structure and order in these nanoparticles before they form complete ordering is of fundamental interest to develop the designing strategy of specific nanoparticles as a function of size and composition. In this paper we present design of an optimally structured alloy nanoparticle which has interesting magnetic properties. Our results provide insight in to alloying and segregation behaviour at the nanoscale which may also lead to useful information for understanding the catalytic behaviour of FePt nanoparticles. Further, we have explored charge transfer and hybridization effects to understand the physical properties of Fe-Pt nanoalloy clusters. We performed calculations on bulk fragments of Fe-Pt nanoparticles that transform to icosahedral structure for the intermediate size of 55-atom clusters as discussed here. Also we find segregation of Pt atoms to be favourable on the surface as well as there is ordering of Fe and Pt on the surface. Following these results of the preference for icosahedral structure, we considered a 147-atom nanoparticle which is the next size of Mackay icosahedral structure and which is often found to be energetically favourable for many systems19. We designed an icosahedral alloy nanoparticle Fe75Pt72 in which the Fe and Pt compositions are nearly equal but there is a formation of core-shell structure with icosahedral Fe55 core and Fe20Pt72 ordered shell. This nanoparticle combines many preferred features, namely, icosahedral 55-atom Fe cluster, triangular faces of Pt as favored by pure Pt nanoparticles20, as well as ordering of FePt and segregation of Pt on the surface. All these make this nanoparticle unique and 3



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

interesting as Fe atoms are isolated on the surface and we reduce Pt content by making all of them available on the surface. We discuss these results as well as the magnetic properties in the following sections. 2. Method of calculation The calculations have been performed within the framework of density functional theory21 using Vienna Ab-initio Simulation Package (VASP)22,23. We considered fourteen valence electrons (including the 3p semi-core states) for Fe and ten valence electrons for Pt atoms. The electron-ion interactions have been treated using pseudopotentials within the projector augmented wave method24,25. The valence electron wave functions have been expanded in terms of a plane wave basis set using medium precision in VASP code. We use spin-polarized generalised gradient approximation for the exchange-correlation functional following the formulation of Perdew-Burke-Ernzerhof26. The nanoparticles were placed in a large cubic supercell so that the separation between the surfaces of the nanoparticle and its periodic images was at least 12 Å to minimize interactions between them. The Brillouin zone is represented by the Γ point. We considered bulk fragments as well as icosahedral structures for a given number of atoms in the cluster and explored different spin isomers. Also decahedral isomers have been considered. Further, the magnetic moments and charge variations on each atom have been calculated by performing Bader charge analysis. All the structures are fully optimized without any symmetry constraint by using conjugate gradient method. The convergence criterion for force on each ion is taken to be less than 0.005 eV/Å. 3. Results and Discussion 3.1. Bulk fragments and 55-atom nanoparticles of Fe3Pt and FePt type

4


Page 4 of 47

Page 5 of 47

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


To begin with we considered 2x2x2 cubic fragments of bulk Fe3Pt and FePt and optimized their atomic structures (see Figs.1a & 2a). The 2x2x2 fragment of Fe3Pt bulk with Fe51Pt12 composition instantaneously transformed into an icosahedral structure with a few Pt atoms in the core (below the surface of the cluster) and eight corner Fe atoms of the cube sticking out as shown in Fig. 1b. We removed the eight corner atoms to have Fe43Pt12 cluster and reoptimized it. The optimization interestingly leads to a 55-atom Mackay icosahedral structure with the binding energy (B.E.) of 4.262 eV/atom (see Fig. 1c). Subsequently we brought the Pt atoms in the core to the surface by exchanging with surface Fe atoms. Reoptimization of this nanoparticle led to a lower energy structure (B.E. of 4.373 eV/atom) compared to the one in which Pt atoms were in the core (see Fig.1d). Therefore for this nanoparticle, all Pt atoms are favoured on the surface. A similar behaviour has been obtained in the case of FePt bulk fragment for which the initial composition was Fe39Pt24 and the final composition was Fe28Pt27 as shown in Fig. 2. The Fe39Pt24 bulk fragment transforms to cuboctahedral structure with eight Fe atoms at the corners coming out. The B.E. of this nanoparticle is 4.314 eV/atom (see Fig. 2b). We removed these eight Fe atoms at the corners and reoptimized the atomic structure. This leads to a cuboctahedron with Fe31Pt24 composition and the B.E. is 4.316 eV/atom (see Fig. 2c). Further, we exchanged all the Pt atoms of the core with Fe atoms on the surface. Upon further re-optimization, the cuboctahedron structure instantaneously transformed to icosahedral structure with a large gain in the B.E. which is 4.631 eV/atom (see Fig. 2d). Since Fe-Pt alloys prefer equiatomic composition, we replaced a few Fe atoms with Pt atoms on the surface in Fe31Pt24 nanoparticle to obtain Fe28Pt27 and Fe27Pt28 nanoparticles. The optimized Fe28Pt27 and Fe27Pt28 nanoparticles remain in icosahedral structures and there is a further increase in the B.E. to 4.686 eV/atom and 4.692 eV/atom, respectively, as shown in Figs. (2e) and (2f).

5



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

In order to further check the stability, we also optimized a 55-atom decahedral structure of Fe28Pt27 nanoparticle and found it to have a lower B.E. of 4.605 eV/atom (see Fig. 2i). From the above, it is concluded that these nanoparticles have a tendency to form icosahedral structure and segregation of Pt atoms on the surface is favourable as it leads to higher B.E. of the nanoparticles. Therefore, we further considered different arrangements of Fe and Pt atoms on the surface in order to understand surface alloying within icosahedral structure. We considered a configuration in which the 12 vertex sites on the surface are occupied by Fe atoms to have the Fe25Pt30 composition and the optimized structure (see Fig.2g) has increased B.E. to 4.730 eV/atom. We also considered another isomer in which 10 Fe atoms are substituted on edges symmetrically so that they have six Pt atoms as neighbours while two Fe atoms are substituted on vertices so that there is 5-fold symmetry (see Fig. 2h). Its B.E. is found to be 4.732 eV/atom and it is very slightly better than the former case. Among the two isomers of Fe25Pt30, the isomer having Fe at vertex sites has higher symmetrical bonding arrangement than the other one with Fe at the edges (which we use to calculate the physical properties of this cluster) but energetically both are nearly degenerate. We also considered a core-shell nanoparticle having 42 Pt atoms on the surface and 13 Fe atoms in the core (Fe13Pt42) of an icosahedral structure and it has a higher B.E. of 4.835 eV/atom. When one Pt atom on the surface is replaced with a Fe atom (Fe14Pt41), the B.E. is reduced to 4.820 eV/atom. This again supports that Pt is favourable on the surface. On the other hand when Pt atoms occupy only 12 vertices of 55-atom icosahedron (Fe43Pt12) on the surface, then the B.E. is reduced to considerably lower value of 4.370 eV/atom due to higher Fe content. The B.E. and the corresponding magnetic moments of all the 55-atom icosahedral structures are compared in Fig. 3. It is noted that the B.E. (magnetic moments) decreases (increase) as the fraction of Fe atoms increases in the nanoparticle.

6


Page 6 of 47

Page 7 of 47

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


We further calculated the heat of formation (∆H) of Fe-Pt nanoparticles of different sizes and different compositions. If E(AmBn) is the energy of a AmBn nanoparticle of size N = m+n, then the heat of formation (∆H) is defined as:

∆H ( Am Bn ) = E ( Am Bn ) − m

E ( AN ) E ( BN ) −n N N

Here E(AmBn) and E(XN) are the energies of the alloy nanoparticle and the pure reference nanoparticle (XN = AN and BN) of the same size. We optimized pure Fe55 nanoparticle with icosahedral structure and it becomes distorted (see Fig. 4a) with the B.E of 3.98 eV/atom and 160 µ B magnetic moments. In the case of pure Pt55, we followed the work on Pt nanoparticles by Kumar and Kawazoe20 who have reported octahedral growth to be most favourable and that the 55-atom icosahedral structure has higher binding energy than the simple cubic, decahedral, and cuboctahedral isomers. The most symmetric and stable octahedral structures near to the 55-atom size have been reported to be Pt44 and Pt79. But they have not suggested any particular arrangement for 55-atom octahedral structure. We have optimized Pt55 nanoparticle with octahedral structure by adding 11 atoms to Pt44 in different ways. The lowest energy structure is shown in Fig. 4c and the calculated binding energy is 4.67 eV/atom. The heat of formation (∆H) for the core-shell structure (Fe13Pt42) nanoparticle is -18.28 eV. It is less exothermic than the value of -21.29 eV for Fe25Pt30 whereas in the case of almost equiatomic composition (Fe28Pt27) the value is -21.39 eV. The ∆H value for the nanoparticle having Pt atoms at the vertices (Fe43Pt12) is -14.89 eV. These results indicate that similar to the bulk behaviour, the nanoparticles with near equiatomic composition have the largest heat of formation. The nanoparticles tend to maximize the number of unlike bonds but symmetry and structure are also important. The composition of the Fe25Pt30 is slightly off from equiatomic and its heat of formation is only slightly lower (see inset in Fig.3), but its 7



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

atomic structure is more symmetric. In general symmetry and structure play an important role in nanoparticles. As we discussed, in the case of bulk FePt alloys the equiatomic composition always has the highest heat of formation. This is because the Fe-Pt bonds are strongest compared to Fe-Fe and Pt-Pt bonds. In the case of nanoparticles, the surface energy dominates the ordering energy in FePt nanoalloys leading to the segregation of Pt on the surface and complete change in the atomic structure. As we found, these nanoparticles arrange themselves with Pt on the surface and core being Fe with maximum Fe-Pt bonding. The maximum Fe-Pt bonding is achieved only with equiatomic composition. In the case of Fe25Pt30, surface Fe atom at vertex makes one Fe-Fe bond with a Fe atom in the core and five Fe-Pt bonds on the surface. On the other hand, a Fe atom at the edge of icosahedron makes two Fe-Fe bonds and six Fe-Pt bonds. The later arrangement improves the binding energy as well as the heat of formation. So, these results lead us to conclude that the maximization of “unlike bonds”, the symmetry, and equiatomic composition affect the heat of formation of the nanoparticles. The magnetic moments and bond lengths of the core-shell nanoparticle, Fe13Pt42 and highly symmetric near equiatomic Fe25Pt30 nanoparticle are summarized in Table.1. For the core-shell Fe13Pt42 nanoparticle, the bond lengths between the 13 core Fe atoms are 2.520 Å (center to inner shell) and 2.652 Å (for atoms on the inner shell). The bond lengths from the inner shell to the surface (outer shell) are 2.478 Å for Fe-Pt (vertex) and 2.664 Å for Fe-Pt (edge) while the bond lengths between surface atoms are 2.636 Å for Pt (edge)-Pt (vertex) and 2.754 Å for Pt (edge)-Pt (edge). In the case of Fe25Pt30 nanoparticle the Fe-Fe bond lengths in the core are 2.534 Å (center to inner shell) and 2.663 Å and 2.657 Å (in the inner shell). The bond lengths from inner shell to the surface are 2.407 Å for Fe (core)-Fe (vertex) and 2.614 Å for Fe (core)-Pt (edge) while the bond lengths between atoms on the surface are 8


Page 8 of 47

Page 9 of 47

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2.600 Å for Pt (edge)-Fe (vertex) and 2.721 Å for Pt (edge)-Pt (edge). The bond lengths from extended X-ray absorption fine structure (EXAFS) experiments on FePt nanoparticles having sizes of more than 4 nm27 are Pt-Pt = 2.72±0.02 Å, Fe-Pt = 2.67±0.02 Å and Fe-Fe = 2.74±0.02 Å. These nanoparticles are larger than the sizes we considered in the present calculations and are likely to have bulk structure as also indicated from the nearly equal FeFe and Pt-Pt bond lengths. In our case in both the nanoparticles the bond lengths between the center and the inner shell Fe atoms in the core are slightly shorter than between the shell atoms due to the icosahedral structure. Also the vertex (outer shell) to the core (Fe-Fe) bond lengths are shorter compared with the bond lengths between core atoms because at the vertex sites the coordination of atoms is the lowest and it leads to inward relaxation of the vertex atoms. Overall our Fe-Pt and Pt-Pt bond lengths are similar to the values obtained from EXAFS27-30. The magnetic moments of these nanoparticles increase very significantly as a function of the number of Fe atoms with ferromagnetic coupling. The Fe13Pt42 nanoparticle has 48 µ B magnetic moments and the addition of one Fe atom on the surface (Fe14Pt41) increases the magnetic moment to 52 µ B. The surface alloyed ordered nanoparticle Fe25Pt30 with 13 Fe atoms in the core and 12 Fe atoms on the surface vertices has 88 µ B magnetic moments. This is large as the substitution of 12 Fe atoms in place of Pt atoms increases the magnetic moment by 40 µ B. For Fe28Pt27 with 13 Fe atoms in the core and 15 Fe atoms on the edges of the icosahedron, the magnetic moments increase to 96 µ B, while for the Fe43Pt12 nanoparticle with 12 Pt atoms on the vertices, the magnetic moments increase to 126 µ B. All these results are summarized in Fig. 3. However, the average magnetic moments on Fe atoms decrease as the number of Fe atoms in a nanoparticle increases. In the Fe13Pt42 core-shell nanoparticle, the magnetic moments on Fe atoms in the core are close to the value in small free Fe clusters 9



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

which is about 3.0 µ B/atom. The Fe atom at the center has slightly lower value of 2.75 µ B while the magnetic moments on Pt atoms have the value of about 0.21 µ B (see Table.1). In the case of Fe25Pt30 nanoparticle the calculated magnetic moments on the Fe atom at the center is 2.71 µ B and the Fe atoms in the inner shell have 3.0 µ B similar to Fe13Pt42 (see Table.1). However, the Fe atoms at the vertices on the surface have enhanced magnetic moments of 3.25 µ B. This is significantly higher compared with the value of 2.2 µ B for bulk Fe and about 2.95 µ B for bulk FePt. The magnetic moment on Pt atoms is enhanced to 0.34 µ B. The Bader charge analysis shows that there is charge transfer from Fe to Pt atoms on the surface. We calculated the difference of the charge by subtracting the sum of the charges of Fe atoms alone and Pt atoms alone at the same positions as in the nanoparticle from the total charge density of Fe13Pt42 as shown in Fig. 5. For the core-shell Fe13Pt42 nanoparticle, the charge on the 12 Fe atoms in the core is 13.42 e while the charge on the center Fe atom is 14.16 e. On the other hand Pt atoms have 10.10e. For Fe25Pt30 nanoparticle, the charge on the inner 12 Fe atoms is 13.50 e while the center Fe atom has 14.10 e. The Fe atoms on the surface of the nanoparticle have 13.40 e and the charge on Pt atoms is 10.40 e. In this case more charge is transferred to Pt atoms compared to the case of Fe13Pt42 and this is indicative of larger magnetic moments on Fe atoms. But in spite of the higher charge transfer to Pt atoms in Fe25Pt30, the magnetic moments on them are increased compared with the values for Fe13Pt42. This is due to hybridization between Fe and Pt states. The charge transfer from Fe to Pt is more significant to Pt atoms on the edges. The density of states (DOS) for the Fe13Pt42 nanoparticle (Fig. 6) shows that the occupied spin-up and spin-down states are unbalanced leading to net magnetic moments on Fe and Pt atoms. There are two types of Fe atoms which have different interactions: (1) Fe atom at the center of the icosahedron in the core which interacts with all the 12 Fe atoms 10


Page 10 of 47

Page 11 of 47

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


surrounding it and (2) the 12 Fe atoms (inner shell) below the surface which interact with Pt atoms on the surface and the Fe atom at the center. Also there are two types of Pt atoms on the outer shell: (1) Pt atoms on twelve vertices which have interaction with one Fe atom and five neighbouring Pt atoms and (2) Pt atoms on the thirty edges of the outer icosahedral shell that interact directly with two Fe atoms below the surface and have six Pt atoms as neighbours. We have shown the partial DOS for these Fe/Pt atoms separately in Fig. 6. From all these plots it is found that the spin-up states of Fe atoms are almost fully occupied and lie significantly below the highest occupied molecular orbital (HOMO). The unoccupied states are primarily from the spin-down 3d states of Fe. The 3d states of the central Fe atom hybridize with those of the twelve Fe atoms and this as well as short bonds leads to a reduction in the magnetic moments on the central Fe atom to 2.75 µ B. But there is a delta function like distribution of the states because of the symmetry at the center. However, each one of the twelve Fe atoms below the surface interact with three Pt atoms as well as with the Fe atom at the center and five Fe atoms on the inner icosahedron of Fe atoms. These Fe atoms do not have high symmetry and the distribution of states is more spread. There is charge transfer from these twelve Fe atoms to the surface Pt atoms as well as to the Fe atom at the center. On the other hand the Pt atoms show nearly balanced up-spin and down-spin occupied electronic states which lead to small (0.21 and 0.22 µ B) magnetic moments on vertex and edge sites, respectively. If we consider only the shell of Pt surface atoms, then the vertex and edge sites have 0.50 µ B and 0.46 µ B magnetic moments, respectively. This clearly indicates that the reduction in the magnetic moment of Pt atoms in the nanoalloy is due to charge transfer from Fe atoms to the unoccupied states of Pt atoms. The density of states of Fe25Pt30 nanoparticle is plotted in Fig. 7. In this case we have only edge Pt atoms on the surface and the vertices are Fe atoms. The density of states of 11



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Fe25Pt30 is also dominated by d-states of Fe and Pt atoms and the peaks are sharper suggesting more symmetric structure. The up-spin states of Fe25Pt30 are found to lie deeper with respect to the HOMO whereas the down-spin states move towards the HOMO compared to the coreshell structure of Fe13Pt42. A similar behaviour is also observed for the partial density of states of Fe and Pt atoms. This leads to larger magnetic moments on Fe25Pt30 over Fe13Pt42. The density of states of the surface Fe atoms is quite different and has narrower distribution compared with that of the Fe atoms on the inner shell or at the center. The significant enhancement in the magnetic moment of Fe and Pt on the surface is due to the charge transfer and hybridization between the Fe and Pt d states.

3.2. Designing 147-atom Fe75Pt72 nanoparticle Following the results of the 55-atom Fe-Pt nanoparticles, we constructed a 147-atom icosahedral Fe-Pt nanoalloy particle with core-shell (i.e Fe55Pt92) and surface alloyed structure (i.e Fe75Pt72). We started with a 55-atom Fe core and 92-atom Pt shell in an icosahedral structure. The surface alloyed structure is obtained by optimizing the number of Fe-Pt bonds by replacing Pt atoms from the centers of the twenty hexagons on the faces of the icosahedral surface shell with Fe atoms. This structure has three shells: 1) the inner shell of 12 Fe atoms in the core (Fig. 8a), 2) the 42 Fe atoms outer shell in the core (Fig. 8b), and 3) surface shell having 20 Fe and 72 Pt atoms as shown in Fig. 8c. All these shells are aligned in a way that the vertices of all the shells are on top of each other31 to form a Mackay icosahedron (Fig. 8d). The B.E. of this nanoparticle is 4.921 eV/atom whereas it is 5.020 eV per atom for the core-shell Fe55Pt92 nanoparticle. We interchanged a surface Pt atom and a sub-surface Fe atom in Fe75Pt72 and it leads to reduced B.E. of 4.916 eV/atom, suggesting that Pt atoms are favourable on the surface.

12


Page 12 of 47

Page 13 of 47

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


The 146-atom decahedron (Fe71Pt75) with Fe atoms in the core and Fe-Pt ordered shell and 147-atom cuboctahedron (Fe75Pt72) with L10 structures have been also optimized and the B.E. is found to be 4.82 eV/atom and 4.83 eV/atom, respectively. These are significantly lower compared to the value (4.921 eV/atom) for the 147-atom (Fe75Pt72) icosahedral structure. Further, we replaced Pt atoms on twelve vertices on the surface with Fe atoms in Fe75Pt72 icosahedral structure to obtain Fe87Pt60 nanoparticle. This has a reduced binding energy of 4.83 eV/atom compared to the Fe75Pt72. We also studied a Fe115Pt32 nanoparticle in which the centers of hexagons on the triangular faces of the icosahedron and also the twelve vertices are occupied by Pt atoms and the rest of the atoms are Fe. The binding energy of Fe115Pt32 is further reduced (4.61 eV/atom) compared to Fe75Pt72 icosahedral structure. To calculate the heat of formation for these nanoalloys, we optimized pure Fe147 nanoparticle with body centered cubic structure and its binding energy is 4.21 eV/atom (see Fig. 4b) having magnetic moment of 442 µ B. The B.E. of the icosahedral structure of Fe147 (4.16 eV/atom) is found to be lower than that of the BCC cubic isomer. For the pure Pt147 nanoparticle we considered octahedral Pt146 from the earlier calculations20 and added one Pt atom on it (see Fig. 4d). This has the B.E. of 4.95 eV/atom. The calculated heat of formation for the core-shell Fe55Pt92 nanoparticle is -50.55 eV whereas the value for Fe75Pt72 is -50.76 eV. Further, the calculated heat of formation for Fe87Pt60 and Fe115Pt32 is -47.05 eV and 34.88 eV, respectively. This suggests that the nanoparticle with nearly equiatomic Fe75Pt72 composition has the lowest heat of formation as also seen for the 55-atom nanoparticles. The atomic structure of the Fe75Pt72 nanoparticle has significant distortions. The bond length between Fe atom at the centre and its 12 neighbours in the core (centre to core inner shell) of Fe75Pt72 is short (2.474 Å) and this leads to lower magnetic moments on the Fe atom at the centre. The bond lengths between the 12 Fe atoms on the inner shell have significant 13



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

variation (2.490 Å, 2.536 Å, 2.552 Å, 2.565 Å, 2.601 Å, 2.652 Å, and 2.661 Å). The bond length between Fe atoms on the core vertex (outer shell) and Fe atoms on the inner shell vertex is 2.585 Å. The bond lengths between the edge atoms in the outer shell Fe atoms of the core and inner shell of Fe atoms are 2.432 Å, 2.517 Å, 2.643 Å, and 2.662 Å. The bond lengths between the atoms in the outer shell of the core are: Fe (vertex) – Fe (edge) 2.652 Å and 2.594 Å; Fe (edge) – Fe (edge) 2.605 Å, 2.665 Å, 2.671 Å, and 2.684 Å. The bond lengths between Fe atoms on the vertex of the outer shell of the core to Pt (vertex on the surface) is 2.588 Å and Fe atoms on the edges of the outer shell of the core to Pt (surface edge) are 2.562 Å and 2.569 Å whereas for Fe atoms on the edge of the outer shell of the core to Fe atoms on the centers of the hexagons on the faces of the surface shell are 2.674 Å, 2.711 Å, 2.734 Å. The bond length between Pt (edge)-Pt (vertex) is 2.705 Å, and for Pt (edge)-Pt (edge) on the surface the values are 2.596 Å, 2.737 Å. This shows significant variations in the bond lengths and these have been also given in Table.1. As we mentioned above for the 55atom nanoparticles, these bond lengths are comparable with the experimental values27-30 on larger nanoparticles. The total magnetic moments on the nanoparticles are 175 µ B for Fe55Pt92 and 260 µ B for Fe75Pt72. The magnetic moments on the center Fe atom is 2.27 µ B for Fe55Pt92 and for Fe75Pt72 it is 2.19 µ B. The 12 Fe atoms in the inner shell of the core have 2.45 µ B for Fe75Pt72 nanoparticles while the value for Fe55Pt92 has variations namely, 2.37, 2.44, 2.50, and 2.56 µ B. Therefore, for the 55-atom Fe core, the inner shell also has reduced magnetic moments. The magnetic moments on the sub-surface 12 Fe atoms at the vertices are 3.07 µ B for both Fe55Pt92 and Fe75Pt72 since these atoms interact with the core and surface atoms in a similar way. The 30 Fe atoms at the edge sites of the outer shell of the core (sub-surface) have 2.85 and 2.90 µ B magnetic moments for Fe75Pt72 and Fe55Pt92, respectively. The slightly higher 14


Page 14 of 47

Page 15 of 47

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


magnetic moments for Fe55Pt92 are due to larger charge transfer from the sub-surface Fe atoms to Pt atoms on the surface whereas in the case of Fe75Pt72, the Pt atoms get charge transfer from the surface Fe atoms as well as from the sub-surface Fe atoms. The magnetic moments on the surface Fe atom are enhanced to 3.35 µ B for Fe75Pt72. The magnetic moments on Pt atoms are small and the values lie in the range of 0.118-0.238 µ B for Fe55Pt92 and 0.520.62 µ B for Fe75Pt72. The magnetic moments on different positions are illustrated in Fig. 9 for Fe75Pt72. The recent X-ray circular magnetic dichroism (XCMD) studies5,32 on Fe50Pt50 nanoparticles for the sizes of 6 nm reported 2.58±0.28 µ B spin magnetic moments per Fe atom. This is close to the value for bulk FePt. A higher value in our case is expected as our nanoparticles are much smaller. The charge on the 13 Fe atoms in the inner core of Fe75Pt72 (Fe55Pt92) nanoparticle is 14.31 (14.34) e for the center Fe and 14.05 (14.00) e for Fe atoms in the inner shell. This shows a slight increase in the charge on the inner core Fe atoms compared with the value on a free Fe atom. While the charge on Fe atoms at the vertices in the sub-surface region are 13.32 (13.45) e and for Fe atoms at the edges in the sub-surface are 13.75 (13.64) e for Fe75Pt72 (Fe55Pt92). Therefore, there is depletion of charge on these Fe atoms. The charge on Pt atoms has the value of 10.20 e and 10.40 e for Fe55Pt92 and Fe75Pt72, respectively. Accordingly there is excess charge on Pt atoms. The difference of the sum of the charge densities of Fe atoms alone and Pt atoms alone at the same positions as in the nanoparticle and the total charge density of the nanoparticle shows that there is excess of charge along the Fe-Pt bonds and it is more located near the Pt atoms as shown in Fig. 10. Some rearrangement of charge is also found on Fe atoms. Overall charge is transferred to Pt atoms from Fe atoms that lie just below the Pt shell and also from the Fe atoms on the surface in the case of Fe75Pt72. The charge transfer to Pt atoms is expected to affect their catalytic properties.

15



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The density of states of Fe75Pt72 nanoparticle is shown in Fig. 11. The occupied spinup and spin-down electronic states are unbalanced and it leads to net magnetic moments on Fe and Pt atoms. There are five types of Fe atoms which have different interactions: (1) Fe atom at the center of the icosahedron in the core which interacts with all the 12 Fe atoms surrounding it, (2) the 12 Fe atoms below the sub-surface which interact with Fe atoms in the sub-surface and the Fe atom at the center, (3) the 30 Fe atoms at the edges in the sub-surface interacting with neighboring Fe atoms on the sub-surface as well as inner shell of the core, and the Pt atoms at the edge sites of the surface, (4) the 12 Fe atoms at the vertices in the subsurface interacting with the vertex Pt atoms on surface as well as Fe atoms in the shells of the core, and (5) the 20 Fe atoms on the surface that interact with six Pt atoms on the surface and two Fe atoms in the sub-surface. Also there are two types of Pt atoms on the surface: (1) Pt atoms on twelve vertices which have interaction with one Fe atom in the sub-surface and five neighbouring Pt atoms on the surface and (2) sixty Pt atoms on the 30 edges of the outer icosahedral shell that interact directly with two Fe atoms on surface as well in sub-surface and have four Pt atoms as neighbours. We have shown the partial DOS for these Fe/Pt atoms separately in Fig. 10. From all these plots it is found that the up-spin states of Fe/Pt atoms are almost fully occupied. The partial DOS of Fe atoms show that the spin-up states lie below the HOMO while the partial DOS of Pt atoms show some unoccupied spin-up states. The unoccupied states are primarily from the spin-down d states of Fe/Pt. As we discussed earlier, a sharp peak appears in the DOS for the Fe atom at the center because of the icosahedral environment at the center. The Fe atoms in the inner shell of the core and the sub-surface do not have high symmetry and the distribution of states is more spread. The Fe atoms at the vertices in the sub-surface and on the surface also have wide distribution of states, but their down-spin states are mostly un-occupied and this leads to higher magnetic moments on these atoms. On the other hand the Pt atoms show nearly balanced spin-up and spin-down occupied 16


Page 16 of 47

Page 17 of 47

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


electronic states and have magnetic moments of 0.52 and 0.62 µ B on vertex and edge sites, respectively. Our results show that there is charge transfer to Pt atoms and some hybridization between the d states of Fe and Pt atoms that leads to higher magnetic moments on Fe and Pt atoms.

4. Summary We have systematically investigated Fe-Pt nanoparticles of different sizes and with different initial structures including bulk fragments, icosahedral, and decahedral structures as well as by considering different compositions. Our results suggest segregation of Pt atoms on the surface along with Fe-Pt ordering as unlike bonds are most favourable. For 55- and 147atom nanoparticles, icosahedral structure is preferred. We found a unique 147-atom icosahedral Fe-Pt nanoparticle in which 55-atom core is made of Fe atoms and 72 Pt atoms are on the outer shell of a Mackay icosahedron along with 20 Fe atoms on the centers of the Pt hexagonal faces of the icosahedron giving it Fe75Pt72 stoichiometry. This has 260 µ B magnetic moments. In this structure the magnetic moments on Fe and Pt atoms are higher compared with the values in bulk FePt. Note that Fe55 cluster has icosahedral structure to be most favorable with large magnetic moments of about 3 µ B per atom. Also the tendency for surface segregation of Pt as well as ordering of FePt on the surface leads to this optimal nanoparticle. It is interesting for magnetic as well as catalytic applications. The overall composition of this nanoparticle is FePt-like, but it decomposes in to a Fe core and Fe-Pt shell. AUTHOR INFORMATION

Corresponding Author *[email protected] and [email protected], Email addresses for correspondence. 17



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Author Contributions ‡These authors contributed equally.

Funding Sources Asian Office of Aerospace Research and Development (AOARD) under project grant No. FA2386-13-1-4034. ACKNOWLEDGMENT We are thankful to the staff of the Centre for Development of Advanced Computing (CDAC) for supercomputing resources and their excellent support. Also we thankfully acknowledge the use of the high performance computing facility Magus of Shiv Nadar University. Financial support from Asian Office of Aerospace Research and Development (AOARD) is gratefully acknowledged. REFERENCES (1) Ferrando, R.; Jellinek, J.; Johnston, R. L. Nanoalloys: From Theory to Applications of Alloy Clusters and Nanoparticles, Chem. Rev. 2008, 108, 845-910. (2) Zeng, H.; Li, J.; Liu, J. P.; Wang, Z. L.; Sun, S. Exchange-Coupled Nanocomposite Magnets by Nanoparticle Self-Assembly, Nature. 2002, 420, 395-398. (3) Qiu, J.-M.; Wang, J.-P. Tuning the Crystal Structure and Magnetic Properties of FePt Nanomagnets, Adv. Mater. 2007, 19, 1703-1706. (4) Wang, C.; Hou, Y.; Kim, J.; Sun, S. A General Strategy for Synthesizing FePt Nanowires and Nanorods, Angew. Chem. Int. Ed. 2007, 46, 6333-6335. (5) Antoniak, C.; Gruner, M. E.; Spasova, M.; Trunova, A. V.; Römer, F. M.; Warland, A.; Krumme, B.; Fauth, K.; Sun, S.; Entel, P.; Farle, M.; Wende, H. A Guideline for Atomistic Design and Understanding of Ultrahard Nanomagnets, Nat. Commun. 2011, 2, 528(1)-528(7). 18


Page 18 of 47

Page 19 of 47

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(6) Zeng, H.; Li, J.; Wang, Z. L.; Liu, J. P.; Sun, S. Bimagnetic Core/Shell FePt/Fe3O4 Nanoparticles, Nano. Lett. 2004, 4, 187-190. (7) Rutledge, R. D.; Morris III, W. H.; Wellons, M. S.; Gai, Z.; Shen, J.; Bentley, J.; Wittig, J. E.; Lukehart, C. M. Formation of FePt Nanoparticles Having High Coercivity, J. Am. Chem. Soc., 2006, 128, 14210–14211. (8) Lyubina, J.; Opahle, I.; Müller, K.; Gutfleisch, O.; Richter, M.; Wolf, M.; Schultz, L. Magnetocrystalline Anisotropy in L10 FePt and Exchange Coupling in FePt/Fe3Pt Nanocomposites, J. Phys.: Condens. Matter, 2006, 17, 4157-4170. (9) Entel, P.; Gruner, M. E.; Rollmann, G.; Hucht, A.; Sahoo, S.; Zayak, A.T.; Herper, H.C.; Dannenberg, A. First-Principles Investigations of Multimetallic Transition Metal Clusters, Philo. Mag. 2008, 88, 2725-2738. (10) Delalande, M.; Guinel, M. J.-F.; Allard, L. F.; Delattre, A.; Bris, R. L.; Samson, Y.; BayleGuillemaud, P.; Reiss, P. L10 Ordering of Ultra Small FePt Nanoparticles Revealed by TEM In Situ Annealing. J. Phys. Chem. C, 2012, 116 6866–6872. (11) Miyazaki, T.; Kitakami, O.; Okamoto, S.; Shimada, Y.; Akase, Z.; Murakami, Y.; Shindo, D.; Takahashi, Y. K.; Hono K. Size Effect on the Ordering of L10 FePt Nanoparticles, Phys. Rev. B, 2005, 72, 144419. (12) Nandwana, V.; Elkins, K. E.; Poudyal, N.; Chaubey, G. S.; Yano, K.; Ping Liu, J. Size and Shape Control of Monodisperse FePt Nanoparticles, J. Phys. Chem. C, 2007, 111, 4185–4189. (13) Lu, L. Y.; Wang, D.; Xu, X. G.; Zhan, Q.; Jiang, Y. Enhancement of Magnetic Properties for FePt Nanoparticles by Rapid Annealing in a Vacuum, J. Phys. Chem. C, 2009, 113, 19867–19870. (14) Vajda, S.; Pellin, M. J.; Greeley, J. P.; Marshall, C. L.; Curtiss, L. A.; Ballentine, G. A.; Elam, J. W.; Catillon-Mucherie, S.; Redfern, P. C.; Mehmood, F.; Zapol, P. Subnanometre Platinum Clusters

19



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

as Highly Active and Selective Catalysts for the Oxidative Dehydrogenation of Propane, Nat. Mater. 2009, 8, 213-216. (15) Guo, S.; Sun, S. FePt Nanoparticles Assembled on Graphene as Enhanced Catalyst for Oxygen Reduction Reaction, J. Am. Chem. Soc. 2012, 134, 2492-2495. (16) Rongming, W.; Olga, D.; Michael, F.; Günter, D.; Mehmet, A.; Sergio, M.-R.; Eduardo, P.-T.; Miguel, J. Y.; Christian, K. FePt Icosahedra with Magnetic Cores and Catalytic Shells, J. Phys. Chem. C, 2009, 113, 4395–4400 (17) Zhang, L.; Iyyamperumal, R.; Yancey, D. F.; Crooks, R. M.; Henkelman, G. Design of Pt-Shell Nanoparticles with Alloy Cores for the Oxygen Reduction Reaction, ACS Nano, 2013, 7, 9168–9172. (18) Zhang , S.; Zhang , X.; Jiang , G; Zhu, H.; Guo, S.; Su, D.; Lu, G.; Sun, S. Tuning Nanoparticle Structure and Surface Strain for Catalysis Optimization, J. Am. Chem. Soc., 2014, 136, 7734–7739. (19) Kumar, V.; Esfarjani, K.; Kawazoe, Y. Ab Initio Computer Simulations on Microclusters: Structures and Electronic Properties; Kawazoe, Y.; Kondow, T.; Ohno, T. Eds.; Clusters and Nanomaterials: Theory and Experiment; Springer Series in Cluster Physics; Springer-Verlag: New York, 2002. (20) Kumar, V.; Kawazoe, Y. Evolution of Atomic and Electronic Structure of Pt clusters: Planar, Layered, Pyramidal, Cage, Cubic, and Octahedral Growth, Phys. Rev. B. 2008, 77, 205418. (21) Kohn, W.; Sham, L. J. Self-Consistent Equations Including Exchange and Correlation Effects, Phys. Rev. 1965, 140, A1133-A1138. (22) Kresse, G.; Hafner, J. Ab Initio Molecular Dynamics for Liquid Metals, Phys. Rev. B. 1993, 47, 558-561. (23) Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations using a Plane-Wave Basis set, Phys. Rev. B. 1996, 54, 11169-11186. 20


Page 20 of 47

Page 21 of 47

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(24) Blöchl, P. E. Projector Augmented-Wave Method, Phys. Rev. B. 1994, 50, 17953-17979. (25) Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method, Phys. Rev. B. 1999, 59, 1758-1775. (26) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple, Phys. Rev. Lett. 1996, 77, 3865-3868. (27) De la Presa, P.; Rueda, T.; Hernando, A.; Ramallo-López, J. M.; Giovanetti L. J.; Requejo, F. G. Spontaneous Oxidation of Disordered Fcc FePt Nanoparticles, J. App. Phys, 2008, 103, 103909. (28) Figueroa, S.J.A.; Stewart, S.J.; Rueda, T.; Hernando, A.; De la Presa, P. Thermal Evolution of PtRich FePt/Fe3O4 Heterodimers Studied Using X-ray Absorption Near-Edge Spectroscopy. J. Phys. Chem. C, 2011, 115, 5500-5508. (29) Antoniak, C. Extended X-ray Absorption Fine Structure of Bimetallic Nanoparticles, Beilstein J Nanotechnol, 2011, 2, 237-251. (30) Antoniak, C.; Spasova, M.; Trunova, A.; Fauth, K.; Wilhelm, F.; Rogalev, A.; Minar, J.; Ebert, H.; Farle, M.; Wende, H. Inhomogeneous Alloying in FePt Nanoparticles as A Reason for Reduced Magnetic Moments., J. Phys.:Cond. Matt. 2009, 21, 336002. (31) Kuo K.H. Mackay, Anti-Mackay, Double-Mackay, Pseudo-Mackay and Related Icosahedral Shell Clusters; Struct. Chem. 2002, 13, 221-230. (32) Antoniak, C.; Lindner, J.; Spasova, M.; Sudfeld, D.; Acet, M.; Farle, M.; Fauth, K.; Wiedwald, U.; Boyen, H.-G.; Ziemann, P.; Wilhelm, F.; Rogalev, A.; Sun, S. Enhanced Orbital Magnetism in Fe50Pt50 Nanoparticles, Phys. Rev. Lett. 2007, 99, 117201.

21



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 47

Table.1 The bond lengths and magnetic moments on different atoms of Fe75Pt72, Fe25Pt30, and Fe13Pt42 nanoparticles in the optimised structures. Bond lengths (Å) Fe75Pt72

Center to 2.474 core Core – 2.490, 2.536, 2.552, 2.565, 2.601, inner shell 2.652, 2.661 Core inner shell to 2.585 (vertex-vertex), sub2.432, 2.517, 2.643, 2.662 surface/ Surface 2.652, 2.594, (edge-vertex), Sub2.605, 2.665, 2.671, 2.684 (edgesurface edge) Sub2.588 (vertex-vertex), surface to 2.562, 2.569 (Fe-Pt), surface 2.674, 2.711 Å, 2.734 (Fe-Fe) Surface 2.596, 2.705, 2.737

Center Coreinner shell SubSurface Surface

Fe25Pt30

Fe13Pt42

2.534

2.520

2.660

2.652

2.407(vertexvertex, Fe-Fe), 2.614

2.478 (vertexvertex, Fe-Pt), 2.664

-

-

-

-

2.600, 2.721

2.636, 2.754

Magnetic moments (µB) Fe75Pt72 Fe25Pt30 2.19 (Fe) 2.71 (Fe)

Fe13Pt43 2.75 (Fe)

2.45 (Fe)

3.00 (Fe)

3.00 (Fe)

-

-

3.25 (Fe) 0.34 (Pt)

0.22 (Pt-edge) 0.21 (Pt-vertex)

2.88 (Fe-edge) 3.07 (Fe-vertex) 3.35 (Fe) 0.62 (Pt-vertex) 0.52 (Pt-edge)

22


Page 23 of 47

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 1. (a) The 2x2x2 bulk fragment of Fe3Pt having the composition Fe51Pt12. (b) After optimization, the bulk fragment instantaneously transforms to a spherical-like structure with eight Fe atoms coming out at the corners. (c) The re-optimized structure after removing those eight corner atoms. It is an icosahedral structure with the composition Fe43Pt12. (d) The optimized structure after the Pt atoms in the core have been exchanged with some Fe atoms on the surface without disturbing the composition. The binding energy per atom is given for the structures (c) and (b). Red (blue) balls show Fe (Pt) atoms.

23



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 2. (a) The 2x2x2 bulk fragment of FePt having the composition Fe39Pt24. (b) The optimized structure is a cuboctahedron with eight atoms coming out at the corners. (c) The optimized structure after removing the eight Fe atoms at the corners. It remains a cuboctahedron with the composition of Fe31Pt24. (d) The Pt atoms in the core are brought on the surface by exchanging some Fe atoms on the surface. The optimized structure completely transforms to an icosahedral structure. (e) The optimized atomic structure after a few Fe 24


Page 24 of 47

Page 25 of 47

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


atoms on the surface are replaced with Pt atoms to make a nearly equiatomic composition Fe27Pt28 and (f) Fe28Pt27. This leads to an increase in the binding energy which is given below the figure. (g) By making an ordered surface alloying we obtained the composition of Fe25Pt30 in which Fe atoms are at the vertices on the surface. (h) Ten Fe atoms are at the centres of Pt hexagons and two occupy opposite vertices to make a nearly 5-fold symmetric structure. This leads to further increase in the binding energy. (i) We also optimized a decahedral isomer in which all the Pt atoms were placed on the surface. This, however, has a lower binding energy. An arrow is shown to guide the evolution of nanoparticle structure and binding energy per atom. Red (blue) balls show Fe (Pt) atoms.

Figure 3: Plots of the binding energy per atom and the total magnetic moments of different 55-atom Fe-Pt nanoparticles with increasing number of Fe atoms namely Fe13Pt42, Fe14Pt41, Fe25Pt30, Fe28Pt27, and Fe43Pt12 lowest energy isomers. Brown (blue) balls represent Fe (Pt) atoms. Each isomer is indicated by the arrows with their respective binding energy in eV/atom and the magnetic moments. Inset shows the heat of formation (∆H) of nanoparticles with different compositions. The Fe28Pt27 nanoparticle with nearly equiatomic composition has the largest ∆H whereas the nanoparticle Fe25Pt30 has a slightly less value.

25



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 4: (a) The optimized icosahedral structure of Fe55 which is distorted from the regular icosahedra, whereas (b) is optimised Fe147 having body centered cubic arrangement structure. The cuboctahedral arrangement of (c) Pt55 is obtained by adding 11 atoms to Pt44 and (d) Pt147 is by adding one atom to Pt146 cuboctahedral structure from the work of Kumar and Kawazae25.

26


Page 26 of 47

Page 27 of 47

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 5: Excess and depletion of charge for the core-shell Fe13Pt42 nanoparticle with Fe13 forming the core. These are calculated by subtracting the sum of the charge densities of only Fe atoms and only Pt atoms separately at the same positions as in the nanoparticle from the total charge density of the nanoparticle. Red (blue) balls show Fe (Pt) atoms. Excess charge is seen around Pt atoms while depletion (rearrangement) of charge occurs near Fe atoms. Some rearrangement of charge also occurs near Fe and Pt atoms.

27



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 6: The spin-polarized total and angular momentum decomposed partial densities of states for the core-shell structure of Fe13Pt42. In the top right corner, we have given the magnetic moments on the isomer as well as on different atoms. Vertical line shows the HOMO.

28


Page 28 of 47

Page 29 of 47

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 7: Spin-polarized total and angular momentum decomposed partial densities of states for the core-shell Fe25Pt30 nanoparticle. In the top right corner, we have given the magnetic moments on the isomer as well as on different atoms. Vertical line shows the HOMO.

29



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 8: Three shell structure of the 147-atom Fe75Pt72 nanoparticle. The core has an inner icosahedral shell of Fe12 and an outer icosahedral shell of Fe42 while the surface icosahedral shell has Fe20Pt72 composition. The Red (blue) balls show the Fe (Pt) atoms.

30


Page 30 of 47

Page 31 of 47

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 9: The magnetic moments on different Fe and Pt atoms in Fe75Pt72 nanoparticle for the lowest energy isomer.

31



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 10: The excess and depletion of charge for core-shell structure of Fe75Pt72 nanoparticle. These are calculated by subtracting the sum of the charge densities of Fe atoms alone and Pt atoms alone at the same positions as in the isomer from the total charge density of the nanoparticle. Red (blue) balls show Fe (Pt) atoms. Some rearrangement of charge also occurs near Fe and Pt atoms.

32


Page 32 of 47

Page 33 of 47

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 11: Spin-polarized total and angular momentum decomposed partial densities of states for the core-shell Fe75Pt72 nanoparticle. In the top right corner, we have given the magnetic moments on the isomer as well as on different atoms. Vertical line shows the HOMO.

33



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

TOC (Table of Content)

34


Page 34 of 47

Page 35 of 47

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Coverart

35



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

32x37mm (600 x 600 DPI)


Page 36 of 47

Page 37 of 47

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


392x454mm (72 x 72 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

581x396mm (72 x 72 DPI)


Page 38 of 47

Page 39 of 47

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


443x535mm (72 x 72 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

536x420mm (72 x 72 DPI)


Page 40 of 47

Page 41 of 47

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


184x200mm (72 x 72 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

184x227mm (72 x 72 DPI)


Page 42 of 47

Page 43 of 47

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


386x388mm (72 x 72 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

566x315mm (72 x 72 DPI)


Page 44 of 47

Page 45 of 47

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


232x88mm (72 x 72 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

182x200mm (72 x 72 DPI)


Page 46 of 47

Page 47 of 47

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


299x179mm (72 x 72 DPI)


Ab Initio Studies of Segregation, Ordering, and Magnetic Behavior in

Recommend Documents