Structural calculation and properties of one-dimensional Pt materials

Chemical Physics Letters 381 (2003) 94–101 www.elsevier.com/locate/cplett

Structural calculation and properties of one-dimensional Pt materials Li Hui b

a,b,*

, F. Pederiva a, Wang Guanghou b, Wang Baolin

b

a Physics Department, Trento University, I-38050 Povo, Trento, Italy National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China

Received 26 May 2003; in final form 29 July 2003 Published online: 15 October 2003

Abstract The structures of free-standing platinum nanowires are systematically investigated by using genetic algorithm simulation with an EAM potential. The magnetic properties are also studied. Several helical multi-shell cylindrical and pentagonal packing structures are observed. These multi-shell structures are composed of coaxial atomic shells with the three and four strand helical, centered pentagonal, and hexagonal, and parallel double chain-core curved surface epitaxy. Under the same growth sequence, the numbers of atomic strands in inner and outer shells exhibit even–odd coupling. Ó 2003 Published by Elsevier B.V.

1. Introduction Material structures with spatial dimensions reduced to the nanometer-scale regime often exhibit unique structural, electronic, spectral, transport and mechanical properties. The metallic nanostructures have attracted great attention. Early predictions pertaining to formation mechanisms, energetic, mechanical response, and structural evolution of three-dimensional crystalline nanowires generated upon elongation of a contact be*

Corresponding author. Present address: Department of Computer Science and Informatics Systems, University of Hong Kong, Pokfulam Road, Hong Kong, China. Fax: +8522559-8447. E-mail address: [email protected] (L. Hui). 0009-2614/$ - see front matter Ó 2003 Published by Elsevier B.V. doi:10.1016/j.cplett.2003.08.110

tween material bodies led to intensive theoretical and experimental investigations of such systems [1,2]. One experimental approach is the study of the structure and conductance by scanning tunneling microscope [3,4] or mechanically controllable break junctions [5–7]. Another attempt to produce very thin wires and to study the structure are the electron-beam irradiation of a Au(1 0 0)oriented thin film [8,9]. Recent experiments have revealed the formation of well-defined and longlived gold nanowires [10]. In recent years, there has been tremendous interest in metallic nanowires from both fundamental low dimensional physics and potential applications as molecular electronic devices [11,12]. Understanding a formation of multi-shell nanowires is an important practical issue in

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physical and material sciences. However, some important questions about formation of nanowires have remained unanswered. Several studies have shown that icosahedra are preferred structures for small metallic nanoparticles [13]. Metallic nanowires do not form spontaneously under cluster preparation conditions. But in fact nanowires prepared in laboratory seem to be rather stable. Depending on the number of atoms, the most stable structure is either a fcc crystal or an icosahedral nanoparticle. Therefore, it is important to study effects of an imposed cylindrical geometry on their stability. Experiments have not allowed us to directly study these microstructures of nanowires or to observe which local structures are prone to reorganization. Therefore, stability and formation mechanism of nanowire determined by experiment is hardly possible. In contrast, computer simulations provided an opportunity for such investigation at an atomic level. Recently, Takayanagi has successfully fabricated stable gold wires with various diameters (0.58–2.8 nm) of sufficient length suspended in vacuum between two tips, and the helical multi-shell structures are observed [8,9]. On the theoretical side, the non-crystalline structures, melting behavior, and electronic properties of ultra-thin free-standing Pb, Al nanowires have been investigated [14,15]. Ab initio calculations for infinite wires based on density functional theory have been reported for Al, Au, and recently for pentagonal metallic nanowires [16,17]. However, until now, the present knowledge on the detailed structural characters and growth sequences of the metal nanowires is still limited. In this Letter, we report on systematical multi-shell structural growth sequence of platinum nanowires and their properties.

2. Simulation method In this Letter, we have systematically studied the structures and properties of platinum nanowires with diameters from 0.157 to 2.10 nm by a genetic algorithm (GA). This GA method had ever been used by us to get the lowest energy structures of clusters successfully [18]. We had also used this method to study the novel structure and properties

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of gold nanowire [19]. A given cutoff distance is chosen to equal the position of the first minimum in the appropriate pair correlation function, in this simulation, the cutoff distance used to define the neighbor is 0.34 nm. The interaction between Pt atoms is described by an EAM potential [20]. Some EAM parameters were given in [21]. EAM had been used to study the structures of clusters [22,23] and surface [24].

3. Results and discussions In Fig. 1, we introduce the indices R3-x, R4-x, R5-x, R6-x (x ¼ 1–2) to characterize the multi-shell (x is number of shells) growth patterns based on trigonal(R3-x), tetragonal(R4-x), centered pentagonal(R5-x), and centered hexagonal(R6-x), respectively. We use the index n–n1–n2–n3–n4 to describe the closed-shell magic nanowires consisting of coaxial shells. As shown in Fig. 1, wires R31(3) and R3-2(8-3) constitute the sequence of trigonal multi-shell packing. The thinnest wire R3-1 (diameter of wire D ¼ 0:568 nm) has threestrand structure. Wire R3-2 (D ¼ 1:213 nm) is formed by double-walled shells, i.e., the outer shell contains nine strands and the inner shell has three strands. Similarly, wires R4-1(4) and R4-2(9-4) constitute growth patterns with one- and two-shell tetragonal packing. Wire R4-1 (D ¼ 0:649 nm) has four strands, while R4-2 (D ¼ 1:863 nm) is composed of nine strands in the outer shell and four strands in the inner shell. In both the trigonal and tetragonal multi-shell growth sequences, the outer and inner shells differ by five helical atomic strands. In contrast to the helical structures observed in R3-x and R4-x wires, the wires R5-1, R5-2 under the centered pentagonal multi-shell sequence are not helical. R5-1 (D ¼ 0:825 nm) and R5-2 (D ¼ 1:345 nm) wires in Fig. 1 represent growth patterns with two-shell and three-shell centered pentagonal structures. The innermost shell of these wires consists of a single row of atoms. The wires R6-1 (D ¼ 0:906 nm) and R6-2 (D ¼ 1:417 nm) in Fig. 1 show the centered hexagonal growth patterns with two-shell and three-shell. They are the most ideal cylindrical configurations in all the structures studied.

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Fig. 1. Structures of platinum nanowires with diameters from 0.568 to 1.417 nm in growing patterns of trigonal (R3-1, R3-2), tetragonal (R4-1, R4-2), centered pentagonal (R5-1, R5-2) and centered hexagonal (R6-1, R6-2) packings are presented.

All multi-shell structures of nanowire shown in Fig. 1 are composed of coaxial cylindrical atomic shells. Each shell is usually formed by a number of atomic strands winding up helically side-by-side. The pitches of the helix for the outer and inner shells are different. The lateral surface of the cylindrical shell forms a nearly triangular atomic network. Such helical multi-shell structures have been theoretically predicted for Al, Pb [14] and observed in recent experiment [25]. The helical multi-shell structures obtained from our present simulations agree well with the experiment [25]. This experiment is also a validation test to our model. The experimental result further demonstrates the accuracy of our simulation result. It is also worthy to note that, in most growth sequence of Pt nanowires, the number of atomic strands that form the inner and outer shells typically have even–odd coupling. These behaviors are similar to those obtained from previous experiment on suspended Pt nanowire. In this experiment, the number of atomic strands in inner and outer shells also exhibit even–odd coupling. Interestingly, the

nanowire with D ¼ 0:5–0:9 nm obtained from our simulation has a single-walled structure and nanowire with D > 1:2 nm has a multi-shell structure, while multi-walled wires with D ¼ 0:5–0:9 nm have been observed in this experiment [25]. Also, same helical multi-walled structures are observed in an opportune simulation work [14] . Icosahedral and non-crystalline structures appeared in lead nanowire, this behavior is familiar with R5-1 and R5-2 obtained in our simulation. However, single atomic chain is not observed in our simulation which appeared in previous work [14]. To illustrate the structural characters of platinum nanowires, the angular correlation functions (ACFs) of these nanowires are calculated and presented in Fig. 2. For most structures, two major peaks in the ACFs are found to be located around 90° and 120°, which are related to the fcc packing. The broad distributions of ACFs in addition to the two major peaks demonstrate that non-crystalline multi-shell structures do not have any definite bond angle. It is clearly seen from Fig. 2 that

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Fig. 2. Angular correlation function of platinum nanowires.

discrete feature of the ACF peaks gradually disappear with the diameter increases and the bulk character gradually comes out. On the other hand,

there are considerable differences between the angular correlation functions for the different growth sequences in Fig. 2. For instance, the features

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related to deformed icosahedron can be observed in R5-x (x ¼ 1–2) sequence, while perfect icosahedral bond angles are 63.4°, 116.6°, and 180° [14]. Based on the optimized structures of platinum nanowires, vibrational properties of nanowires are obtained [26]. The vibrational densities of states of platinum nanowires in Fig. 3 exhibit remarkable dependence on the wire diameters and the corresponding growth classes. Except wires R3-1 and

R4-1, the position and shape of the major vibrational peak located around 2.1–2.7 THz do not sensitively change with the size and growth sequence of wires. Although the positions of second peak (
5 THz) do not substantially change, its shape and height sensitively vary with the size and growth sequence. Such differences might be understood by the different vibrational couplings between the atomic shells for the nanowires with

Fig. 3. Vibrational densities of states of platinum nanowires.

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various sizes and growth classes. In other words, the vibrational modes of platinum nanowires sensitively depend on the specific growth patterns of the constituent atomic strands and diameters of nanowires. The vibrational bands of the thinner wires (R3-1, R4-1) are rather discrete and molecule-like. Some high-frequency modes around 7.5 THz are observed in some sequences (R3-2, R5-1, R6-1). These high-frequency vibration modes may be due to the contraction of inter-atomic distance in those wires. In general lower symmetry normally possesses higher magnetic moments because it looks more like an atomic state. Small platinum nanowire may possess permanent magnetic moment although bulk platinum is non-magnetic. In the following, we investigate the electronic and magnetic properties by parameterized unrestricted Hartee–Fock approximation [27,28]. Fig. 4 gives the magnetic moment per atom as a function of shell number form inner to outer. The magnetic moments decrease from 0.34lb to 0.08lb from inner to outer. Radius seems to have a ÔscreeningÕ effect on the magnetic moments. However, the contribution to the magnetism of nanowires mainly comes from the electronic effects far away from the symmetry [29,30]. It may be due to the large transfer of charge between inner and outer atoms. In fact, electronic effects are non-negligible and they are responsible for magnetic moments. The inner of

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wire possess a large magnetic moment, but small magnetic moment of outer. When comparing these magnetic moments for inner and outer of wires, a remarkable trend is observed: the large magnetic moment is shifted from outer to inner. In general, when charge moving from the 3d to 4d and 5d series, the localization of valence d wave functions decrease. Consequently, an increase of the d-band width and a reduction of LDOS n3d > n4d > n5d , at Fermi energy are observed. Together with the fact that the exchange integral also decreases as I3d > I4d > I5d 5d magnetism becomes extremely unlikely and is never considered. Certainly, symmetry effect should not be neglected because the symmetric structure would lead to the changes of electronic distribution. Symmetry effect is finally exhibited by the electronic effects. The magnetism of the nanowire in Table 1 is found to be related with the radius of nanowires. For example, the magnetic moment of R3-1 with diameter 0.568 nm is much larger than those of R5-2 and R6-2. The main reason is due to the large charge distribution. Obviously, the number of bonds in R3-1 is much more than that of R5-2 and R6-2. In general, the larger the charge transfer, the higher magnetic moment. The reduced radius may also arouse smaller magnetic moment. This effect can be understood by the ZabalaÕs theory [31] which showed that certain radius favor the occurrence of ferromagnetism with in oscillatory dependence.

Fig. 4. Magnetic moment (lb ) versus shell number (from inner to outer).

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Table 1 The diameter D (nm), average bond length hRi, average coordination numbers hCNi, average magnetic moments ln (lb ) and calculated binding energy E (eV/atom) for Pt nanowires Wires

R3-1

R3-2

R4-1

R4-2

R5-1

R5-2

R6-1

R6-2

D (nm) hRi ðAÞ hCNi ln ðlb Þ E

0.568 2.624 6.12 0.18 4.567

1.213 2.634 9.005 0.07 5.342

0.649 2.658 7.05 0.19 4.773

1.863 2.649 9.089 0.04 5.435

0.825 2.668 8.763 0.26 5.129

1.345 2.663 9.798 0.09 5.531

0.906 2.675 8.864 0.23 5.241

1.417 2.639 9.124 0.08 5.573

However, the magnetic moment of R5-1 and R6-1 is anomalous. The structures maybe possess spinorder in two kinds of nanowires. Although the average magnetic moment of bulk Pt is zero, high magnetic moments are found in some nanowires (R5-1 and R6-1). These may be due to the different charge transfer. For Pt atoms, the charges are transferred from sp orbitals to d orbital. Further, the charge transfer takes place from inner to outer atoms. It is also worthy to note that some researchers found non-magnetic mono-atomic free Pt wires [32] and zero magnetic moment was observed in low dimensional Pt [33]. In our present simulation, the magnetic moments of wires are rather small. With the radius increase, the magnetism would disappear finally. More accurate investigation can be carried out by ab initio method, which requires significantly larger computational time. To explore the origin of the peculiar magnetic properties, we study the total density of states (DOS) and sp, d DOS of the nanowires (not shown here). In general, the DOS near to Fermi level play a primary role in determining the magnetism of the nanowires. Obviously, the contribution of d electrons is found dominantly, while the sp electrons contribution is low. The contribution of d electrons leads to an occurrencee of magnetic moment of nanowire [34,35]. Similarly, the distribution of d electrons is different for various symmetries, thus their corresponding magnetism are different from each other. For R5-1 and R6-1, may be the contribution of d electrons is relatively closer to Fermi level compared with other cases, which leads to particular high magnetic moments. In summary, the geometrical and magnetic properties of ultra-thin platinum nanowires have been researched by using empirical genetic algo-

rithm and a spin polarized tight binding Hamiltonian. The main conclusions can be made as follows. (1) Helical multi-shell cylindrical structure with different growing patterns such as trigonal, tetragonal, centered pentagonal, and centered hexagonal packings are found. (2) All these nanowires we studied are magnetic. (3) The number of atomic strands in outer and inner shells exhibit even–odd coupling. (4) The angular correlation functions and vibrational properties are related to the wire diameter and growth pattern. In this work, the geometrical properties are in good agreement with OshimaÕs experimental result, but its magnetic properties are not identical to the previous work [32,33]. The magnetic properties of Pt nanowire are our next step to study by experiments and simulations in the future.

Acknowledgements Li Hui would like to acknowledge support from the Natural Science Foundation of China, Grant Nos. 29890210, 10023001, 50231040 and this work is also supported in part by natural science foundation (NSF) of Shandong province, Grant No. L2000F01.

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