Materials Chemistry and Physics 127 (2011) 489–494
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Materials Chemistry and Physics
journa l homepage: www.e lsev ier .com/ locate /matchemphys
tructural and electronic properties of lead nanowires: Ab-initio study
nurag Srivastavaa,∗, Neha Tyagia, R.K. Singhb
Advance Materials Research Lab, Indian Institute of Information Technology & Management, Gwalior, Madhya Pradesh, IndiaSchool of Basic Sciences, ITM University, Gurgaon 122017, Haryana, India
r t i c l e i n f o
rticle history:eceived 31 August 2010eceived in revised form 21 January 2011ccepted 17 February 2011
ACS:3.22.−f1.15.Mb
a b s t r a c t
Ab-initio self-consistent study has been performed to analyze the stability of lead nanowires in its sixstable configurations like linear, zigzag, triangular, ladder, square and dumbbell. In the present study,the lowest energy structures have been analyzed under the revised Perdew-Burke-Ernzerhof (revPBE)parameterization of generalized gradient approximation (GGA) potential. The two-atom zigzag shapedatomic configuration with highest binding energy and lowest total energy has been confirmed as themost stable structure out of the six atomic configurations. The electronic band structure and density ofstates have been discussed in detail with a remarkable observation in case of three-atom triangular lead
8.67.Uh1.15.Nc
eywords:. Metals, nanostructures. ab initio calculations, computer modeling
nanowire having a very small band gap while other configurations are found to be metallic. Bulk modulus,pressure derivatives and lattice parameters for different lead nanowires have also been computed anddiscussed.
Since last one decade materials at nano dimensions, partic-larly their novel physical, chemical and electrical propertiesave attracted a large number of researchers and engineers tonderstand its behavior and possible applications. Properties ofanomaterials are not determined exclusively by their chemicalomposition but also on other characteristics such as the structure,orphology, the form, size and spatial distribution of the individual
articles. We are well aware of the fact that the reduction in sizef a sample causes quantum confinement, which leads to quan-um wire in two dimensions. To obtain various exotic propertiesf metallic nanowires, one must consider them within a quite lowiameter, large aspect ratio and uniform orientation [1]. Nanowiresave been studied intensively and showed a distinct behavior thatrises due to unique confinement of electrons in two-dimension2D) [2–4]. Metal nanowires exhibit unique physical behavior that
eads to a large number of experimental and theoretical researches5–8,21]. Lead has been used in number of applications for thou-ands of years, reason being it is widespread, easy to extract, dense,uctile, very soft, highly malleable metal with poor conductivity
∗ Corresponding author at: Advance Materials Research Lab, Indian Institute ofnformation Technology & Management, E-110, First Floor, IIITM Campus, Morenaink Road, Gwalior 474010, Madhya Pradesh, India. Tel.: +91 751 2449826.
and very low melting point. One of the most prominent and poten-tial application of individual nanostructures is in the processing of(optical, electrical, magnetic, chemical and biological) signals. Sur-vey of literature reveals that only a very few studies have beenperformed on lead nanowires by using different experimental andtheoretical techniques but the basic comprehension of differentnanostructures, based on their structural and electronic propertiespertaining to the size and shape is very rare. Recently, Tsai et al.[9] have reported that the extended metal-atom chain is a promis-ing candidate to be the smallest molecular electrical wire for futuretechnological applications, where the electron can move throughcore metals, while the internal current is insulated from outside bythe surrounding �-conjugated functional group.
A number of experimental techniques have been adopted forthe fabrication and analysis of nanowires. Using scanning tunnel-ing microscope (STM), Pb nanowires have been analyzed betweenthe macroscopic electrodes and reports that Pb nanowire remainsin the superconducting state even when the magnetic field destroysthe superconductivity of electrodes [10]. In an experiment onthe transport properties of lead nanowires, it was found thatlead nanowire had a non zero resistance in superconducting statewhich varies by fluctuations of the superconducting order param-
eters [11]. Arrays of mesoscopic superconducting lead nanowireswith high aspect ratio and diameter ranging from 40 to 270 nmhave been grown successfully. Pb nanowires of different diame-ters have been grown in nanoporous polycarbonate membranesby electrodeposition and pressure casting [12,13]. Structural phase
ransition in the superconducting state has also been analyzedn Pb nanowires at a temperature very close to that of bulk lead14]. Cuenot et al. [15] have reported the effect of reduced sizen the elastic properties of Pb nanowires by using atomic forceicroscopy (AFM). The effects of temperature on the penetration
nd coherence lengths in Pb nanowire have been discussed bytenuit et al. [16], whereas Shen and Yan [17] discovered a cost-ffective method for producing ordered nanostructures of lead onarge scale at room temperature under atomic pressure. Romanovn his article [18] has explained the fabrication process of someuantum wires, including lead, inside the zeolite mordenite andeported the conductivity data as well as optical absorption spec-ra, where he proposed the occurrence of double zigzag chains of Bin his sample but could not propose the structure for Pb nanowire.he optical responses of the Pb nanowires by means of polarizednfrared spectroscopy have been analyzed recently by Chung et al.19]. Besides the experimental research the theoreticians have alsoevoted their efforts in understanding the behavior of nanowires.ith the same intension Batra and coworkers [20] have performed
he ab-initio studies on pentagonal shaped nanowires of variety ofetals including Pb and concluded that staggered pentagons have
table structure, but could not give any remark about other pos-ible structures like zigzag, ladder, square and dumbbell. Tossatind coworkers [21] have done a remarkable work on the com-arative analysis of cluster with wire and particularly in case of
ead nanowire, where they have simulated the ultrathin metalanowire to observe the effect of thickness variation on the sta-
ility of structure of nanowire. Another ab-initio study has beenerformed by Schmidt and Springborg [24] on the structural andlectronic properties of three types of atomic configurations of lead;ne atom linear chain, single zigzag chain and double zigzag, usingP-LMTO method. However most of their structures were found
ig. 1. The structures of Pb nanowires (a) one-atom linear wire, (b) two-atom zigzag wiire, and (f) five-atom dumbbell wire.
and Physics 127 (2011) 489–494
unstable and these unstable geometries of Pb nanowires have beentaken as a challenge in the present work. Besides this, technolog-ical importance of metal nanowires, success of ab-initio methodsas a means of producing startup information and our recent workon electronic and structural properties of bulk semiconductor [22]and Si nanowire [23] have boosted us to explore the possibility ofreanalyzing the stability of different atomic configurations of Pbnanowires.
2. Computational method
For the present study on the structural and electronic proper-ties of lead nanowires, Atomistix ToolKit (ATK) [25] has been used.ATK is a further development of TranSIESTA-C [26,27] which, inturn, is based on the technology, models and algorithms devel-oped in the academic code TranSIESTA and, in part, McDCal [28],employing localized basis sets as developed in SIESTA [29]. Wehave used Perdew Zunger type parameterized local density approx-imation (LDA-PZ) [30], Perdew, Burke and Ernzerhof (PBE) [31]and Zhang and Yang [32,33] revised PBE (revPBE) type generalizedgradient approximation (GGA) exchange correlation functional.In self consistent manner the calculations have been performedusing steepest descent geometric optimization technique withPulay algorithm [34] for iteration mixing and diagonal mixingparameter value as 0.1. The energy cut-off is taken as 40 Ryd with1 × 1 × 50 Monkhorst-Pack grid in one dimensional Brillouin zone.The nanowires are placed in the supercell along the wire length in
z-direction while the supercell lengths in the x-and y-directions arechosen big enough to avoid interaction between nanowire and itsperiodic image. The LDA-PZ potential computes total energy muchhigher than that of GGA-revPBE and GGA-PBE. The total energyfor bulk lead using LDA-PZ potential is −629.10 eV and with GGA-
evPBE −641.20 eV, which indicates that GGA-revPBE potential isuitable for the present computation. For better understandingf fundamental physics associated with different structures, theinding energies of Pb nanowire have also been calculated usingGA-revPBE potential. Bulk modulus and pressure derivatives haveeen analyzed using Murnaghan’s equation of state [35] and tonderstand the nature of material, localization and delocalizationf states near the Fermi level, we have analyzed the electronic bandtructure and density of states for all the six stable configurationsf lead nanowires.
. Results and discussions
.1. Structural properties
The atomic configurations of the six stable Pb nanowires con-aining 1–5 atoms are presented in Fig. 1a–f. It may be cautionedhat these figures are schematic and separations between thetoms are not to scale. As these figures depicts the structures quitelearly and hence have not been discussed separately in the text.he stability energetic in the various nanostructures of lead haseen performed under the GGA scheme with the revised PBE typexchange correlation functional and shown in Fig. 2 by total energyer atom as a function of volume curve. The computed bindingnergy per atom and total energy per atom for all the Pb nanowiretructures have been reported in Table 1, where a comparative lookn the total energy per atom indicates that out of all the six stabletomic configurations, the two-atom zigzag shaped structure withowest value can be confirmed as the most stable structure, how-ver the one-atom linear shaped nanowire is next stable structure,
s its energy is higher than the zigzag but comparatively lower thanhat of the other structures. In reference to the computed bindingnergies of various Pb nanowires, the zigzag shaped configurationith highest value can be confirmed as the most stable structure
Fig. 2. Energy/atom vs. volume curve for bulk lead and nanowires.
able 1alculated binding energy and total energy for various Pb atomic configurations.
among all the other atomic configurations taken into considera-tion. The calculated lattice parameter for the bulk Pb material is5.10 A, which is in close agreement with its experimental (4.91 A,4.92 A) [36,37] as well as theoretical counterpart as reported byothers [38]. For different Pb nanowires, the lattice constant has alsobeen calculated and shown in Table 2, which is defined as the dis-tance between two nearest neighbor atoms in minimum energyconfiguration, hence the lattice constants for different nanowirescan be explained through their geometries. The bulk modulus (Bo)and its pressure derivative (Bo
′) for bulk lead have been com-puted using Murnaghan’s equation of state [35] and are in goodagreement with the other reported results [36,37]. These mechan-ical properties have been computed for different Pb nanowirestaken into consideration and are compared in Table 2, where itis observed that the two-atom ladder shaped nanowire, due tohighest bulk modulus among all the six structures, can be consid-ered as high mechanical strength. However in absence of any otherreported data on mechanical properties for Pb nanowires our cal-culated results needs verification with experimental or theoreticalfindings.
3.2. Band structure analysis
To understand the material behavior of the stable geometriesof Pb nanowires, electronic band structures analysis have beenperformed and their band structures are compared in Fig. 3a–gwith bulk lead. On the basis of number of conducting channelscrossing the Fermi level, conductivity of various Pb nanowireshas been explained. The band structure of bulk lead as shown inFig. 3a, few conduction bands are crossing the Fermi level whichdefends its metallic behavior. The band structure of one-atom lin-ear wire shown in Fig. 3b, reveals the occurrence of free electronlike parabolic bands, where there are number of conduction bandscrossing the Fermi level which defends its metallic nature. In Fig. 3c,the band structure of two-atom zigzag wire shows crossing of fewvalence bands as well as few conduction bands to the Fermi level,which indicates that zigzag wire is also metallic in nature. In Fig. 3dthe band structure of two-atom ladder wire is shown, where manybands are crossing the Fermi level, which again defends this atomicconfiguration too as metallic. Fig. 3e represents the band structureof three-atom triangular wire, where a remarkable small band gapof the order of 0.03 eV can be seen, which defends this structureas semiconducting in nature. In an another geometry, four-atomsquare wire as shown in Fig. 3f, only a single conduction band istouching the Fermi level and a valence band is crossing the Fermilevel. In Fig. 3g the band structure of five-atom dumbbell wireshows that there are many conduction bands crossing the Fermilevel and again defends this structure as metallic.
3.3. Density of states (DOS) analysis
The DOS profile for all the stabilized structures have been shownin Fig. 4a–g along with that of bulk lead. In case of bulk lead onlya single peak in the valence band region and few distorted peaks
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Fig. 3. (a) Band structure for bulk lead (Fermi level is set at 0 eV), (b) band structure for one-atom linear wire (Fermi level is set at 0 eV), (c) band structure for two-atomzigzag wire (Fermi level is set at 0 eV), (d) band structure for two-atom ladder wire (Fermi level is set at 0 eV), (e) band structure for three-atom triangular wire (Fermi levelis set at 0 eV), (f) band structure for four-atom square wire (Fermi level is set at 0 eV), and (g) band structure for five-atom dumbbell wire (Fermi level is set at 0 eV).
A. Srivastava et al. / Materials Chemistry and Physics 127 (2011) 489–494 493
Fig. 4. (a) DOS for bulk lead, (b) DOS for one-atom linear wire, (c) DOS for two-atom zigzag wire, (d) DOS for two-atom ladder wire, (e) DOS for three-atom triangular wire,(f) DOS for four-atom square wire, and (g) DOS for five- atom dumbbell wire.
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n the conduction band region have been observed, which showshat the allowed states are near the Fermi level. The highest peaks around 3.3 eV and a weak peak appears near the Fermi level atround −0.7 eV. For one-atom linear wire, a number of peaks cane seen in the valence band region but the highest magnitude peakppears at −2.1 eV and a peak around 0.1 eV very close to the Fermievel, shows that allowed states are near the Fermi level. In theOS profile of most stable two-atom zigzag wire, one prominenteak appears at −0.7 eV near the Fermi level in the valence bandegion and few peaks in the conduction band region indicates theocalization of states near the Fermi level. In case of two-atom lad-er wire, there is one prominent peak in the valence band regionround −4.3 eV and also one at 0.6 eV in conduction band, indi-ates that the allowed states are near the Fermi level. The DOS forhree-atom triangular wire shows few strong peaks in the valenceand region, out of them the highest one appears at −2.6 eV and atrong peak also appears in the conduction band region at 2.9 eV,hich defends less localization of states near the Fermi level. In case
f four-atom square wire, there is one prominent peak at −1.5 eVn valence band region along with number of weak peaks in theonduction band region, out of which the highest magnitude peakppears at around 1.7 eV. In case of five-atom dumbbell shapedire, the highest peak appears at around −2.3 eV near the Fermi
evel and a prominent peak at around 4 eV in the conduction bandegion clearly defends less localization of states near the Fermievel.
. Conclusion
On the basis of above findings, it may be concluded thathe investigation of electronic properties and structural sta-ility of various ordered and disordered structures of Leadanowires has successfully been performed by using ab-initiopproach. The calculation of binding energy per atom, totalnergy per atom, density of states and band structures haveeen demonstrated in large energy intervals. Out of six atomiconfiguraions of Pb nanowires, the two-atom zigzag geome-ry with its lowest total energy and highest binding energyas been predicted as the most stable among all the studiedtructures. In the present work the study also reveals that the
wo-atom ladder shaped nanowire with highest bulk modulus,efends its mechanical strength. The electronic band structuretudy of Pb nanowires exhibit semiconducting as well as pureetallic behavior, which are useful for the quantum conduc-
ion.
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and Physics 127 (2011) 489–494
Acknowledgments
Authors gratefully acknowledge the support from ABV-IIITM,Gwalior for providing the financial support under the faculty initi-ation grant RP-001/2008.
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