Investigation of the electronic properties of the surface and bulk forms of gold and palladium
U.N. Kurelchuk, P.V. Borisyuk, O.S. Vasilyev, Yu. Yu. Lebedinsky
IInvestigation of the electronic properties of the surfaceand bulk forms of gold and palladium
U.N. Kurelchuk, P.V. Borisyuk , O.S. Vasilyev, Yu. Yu. Lebedinsky
National Research Nuclear University MEPhI, Kashirskoye sh., 31, Moskva, 115409E-mail: [email protected]
Abstract.
The density of electronic states for bulk metals Au and Pd, their surfaces in the formof polycrystalline surface layers of nanometer thickness is investigated. The calculations wereperformed using density functional theory with pseudopotential in full relativistic approximation.Approximations have been found that provide calculations the density of electronic states of noblemetal surfaces that describe the experimentally observed features of XPS spectra of the valence bandof these metals.
Introduction
Nanoporous films made of noble metallic nanoclusters are promising materials for high-efficiency thermoelectric elements. Modern computational modeling and numeric methods allowsolving such problems as: prediction of stable nanoclusters from, predetermined materials with certaindimensions, theoretical study of their electronic, thermal, magnetic and other properties;computational experiments for planning and optimizing physical experiments and interpreting theirresults. In this article we consider the features of the experimental and theoretical investigation of thedensity of electron states (DOS), and we develop an approach to the analysis of DOS obtainedtheoretically and experimentally for noble transition metals, for example, the surfaces ofpolycrystalline samples of d-metals Au, Pd. In the future, it is planned to develop an approach toimplement for the analysis of metallic nanoclusters and porous nanocluster films.One of the most common and informative experimental methods for studying electronicproperties is X-ray photoelectron spectroscopy (XPS) [1]. Its essence is in obtaining the distribution ofthe number of emitted photoelectrons depending on their binding energy, and this distributiondescribes the density of occupied electronic states in the material. It should be noted thatphotoelectrons can be collected from the depth no more than 2-3 nm or 10-20 monoatomic layers, sothe method is sensitive only to the upper surface layer [1]. The analysis of publications concerningDOS, started from the earliest studies of the bulk state, and up to the modern calculations ofnanoclusters, shows that the comparison of theoretical DOS with XPS spectra has for the most part aqualitative similarity. Generally, the comparison of volumetric DOS and XPS spectrum is not aomparison of two identical systems, since XPS is dealing with a surface, whose state is changed incomparison with the bulk structure of the material, even the idealy prepared surface – avoidingadsorption, oxidation, etc. It is necessary to compare with the experimental spectrum the theoreticallycalculated surface spectrum of the investigated material of that thickness and with those surfacefeatures specific for the sample and experiment.A feature of nanoscale material modeling techniques is presence of both quantum (ab initio)and many-body approaches. For structures with a big (>10^3) number of atoms very powerfulapproach is density functional theory (DFT) with pseudopotential. In this work we use plane-wavebasis set and pseudopotential DFT technique, with geometric optimization, implemented in PW DFTcode Quantum Espresso [2]. Calculations was performed using resources of NRNU MEPhI high-performance computing center.
1. DFT DOS calculation for d nobble metals, particularly Au and Pd.
The properties of noble metals are due to their d-band filled and localized near the Fermi level.The width of the d-band, it position relative to the Fermi level, spin-orbit splitting is DOScharacteristics which cause physical properties, and it all can be measured experimentally by the XPSspectrum [4].-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1Au PDOS d5/2Energy (E - Ef), eV s t a t e s / e V -8 -7 -6 -5 -4 -3 -2 -1 0 1 2Pd DOSPd PDOS d5/2Energy (E - Ef), eV s t a t e s / e V Fig. 1a.
Total and d-DOS of bulk Au
Fig. 1b.
Total and d-DOS of bulk PdThe DFT study of the electronic structure of bulk gold and palladium was provided in DFTGGA (PBE) approximation [3] of the Ex, for the noncollinear spin orientation with the spin-orbitinteraction and nonmagnetic state. The interaction of valence electrons with the core is described withthe full-relativistic ultrasoft Vanderbild pseudopotentials [5]. The obtained DOS show a more accuratecorrespondence to the experimental data, spin-orbit splitting, rather than the results of DOS fromdatabases for bulk metals [6,7]. Figures 1a, 1b show the calculated total and d-projected DOS.
PBE) .,This approximation of the DFT correctly describes the valence band, its distance to the Fermi levelnd the position of the peaks, the spin-orbit splitting of d , d on atomistic scale, and was thereforealso used for modeling nanoscaled surfaces.
2. Metal Au, Pd surfaces modeling
The structure with which photoelectrons are analyzed in XPS of these noble metals is apolycrystalline surface with a thickness of about 1 nm [1]. An arbitrarily cleaved surface consists ofsections of surfaces of different crystalline faces. Like the growth of fcc clusters and spontaneoussurface formation, it is most likely that the most closely packed faces with the lowest surface energyare [111], 100 ([200]). Analysis of diffraction patterns of polycrystalline gold shows that the greatestintensity is given by the faces [111]: [200]: [220] in the ratio ~ 2:1:0.8. Similar pictures are observedfor thin films, surfaces, fcc-nanoclusters Au, Pt, Pd. [8].In the XPS, the shape of the spectral line is related to the density of electronic states n (E) as: I ( E )= I ∫ I DS ( E − E ' ) n ( E ' ) G ( E ' , σ ) dE ' (1) G (E'; σ ) is the total instrumental broadening, which is described by the Gaussian function, and theDonsSchünich I DS function [9]. The fluxes of photoelectrons from each part of the surface (withinformation on the occupied electronic states in it) are summed in the detector, therefore, because ofthe transformation (1) is linear, the spectrum can be represented as a superposition of the spectra I (n i (E)) from the sites of the most probable hkl configuration [111], [200], [220] weighed with Cicorresponding to the peaks of Xray diffraction. I ( E )= ∑ i = [ hkl ] i C i ∙ I ( n i ( E ) ) (2) An infinite film with a thickness of 1 nm, cut in the [hkl] direction in a fcc crystal, isconsidered. To solve the periodic problem for such a structure, such a Bravais pseudo-lattice isconstructed so that the periodicity in all directions is preserved, but the films do not interact. At thesame time, the upper surface of the film remains free, and the lower surface is part of the bulk. In theabsence of part of the bonds, the atoms on the surface are rearranged so as to minimize the energy ofthe system, on the other hand, the position of the atoms inside the film must be equal to the bulk one. The Bravais pseudo-lattice primitive cell is composed of 2 XY planeand 5 atomic layers in Z to provide a layer thickness of 1 nm and the motion of atoms relative to eachother during geometric optimization, the interatomic distances in the first 2 layers are fixed, the filmsare separated by a 1.5 nm. Hexagonal and tetragonal Bravais lattices were constructed for [111] and[200] [220] films, respectively. Geometric optimization of these structures was performed using theBFGS algorithm (Broyden-Fletcher-Goldfarb-Shanno) [10] implemented in the Quantum Espressocode. 12 -10 -8 -6 -4 -2 0Energy (E Ef), eV I ~ s t a t e s / e V -10 -8 -6 -4 -2 0Au (XPS)Au bulk (smeared DOS)Energy (E Ef), eV I ~ s t a t e s / e V Fig. 2a . Smeared DOS of Au model surfaces.
Fig. 2b. . Au valence band lines: experimentalXPS, calculated from model surface DOS, andfrom bulk DOS..-7 -6 -5 -4 -3 -2 -1 0 1[111] Energy(E Ef), eV I ~ s t a t e s / e V -7 -6 -5 -4 -3 -2 -1 0 1Pd XPSPd surface (smeared DOS)Energy (E-Ef), eV I ~ s t a t e s / e V Fig. 3a . Smeared DOS of Pd model surfaces.
Fig. 3b . Pd valence band lines: experimentalXPS, calculated from model surface DOS, andfrom bulk DOS.In Fig. 2a showed the smeared DOS of model areas of the surface I [hkl]i and in Fig. 2b theirsuperposition according to rule (2) with instrumental broadening, describing the XPS of the valenceband of gold. The same for palladium is shown in Fig. 3a, 3b. It can be seen that the model of asurface more accurately describes the filled electronic states of the valence band (XPS) than the modelof a bulk sample. hus, this approach reveals the suitability for modeling the surface DOS in the aggregate withan experimental study, and will be used for the analysis of nanoclusters and porous films formed fromthem.
Acknowledgements
This work was financial supported by the Russian Federation President Grant to supportyoung scientists (№ 14.Y30.17.2948-MK)