INTERACTION OF THE ELECTROMAGNETIC RADIATION WITH THE SURFACE OF PALLADIUM HYDRIDE CATHODES

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1 Material Characterization Session 10 O_4 INTERACTION OF THE ELECTROMAGNETIC RADIATION WITH THE SURFACE OF PALLADIUM HYDRIDE CATHODES E. Castagna,S. Lecci, M. Sansovini, F. Sarto and V. Violante RdA ENEA, C. R. Frascati Nuclear Fusion and Fission and Related Technologies Department Via Enrico Fermi, Frascati (Rome) ITALY The change of the electronic density of metallic Pd due to the hydride formation and to the build-up of the double layer, rising at the metal-dielectric interface hen an electric field is applied, is involved in the variation of the metal dielectric function. A model including also metal surface roughness has been developed to take into account such modifications. ICCF-15 81

3 Introduction The dissolution of hydrogen ithin a metal lattice and the formation of a metal hydride greatly perturb the electrons and phonons of the host material. Several are the relevant observed effects The generally observed epansion of the lattice, often including a change in the crystal structure, involves a modification of the symmetry of the states and a reduction of the band idth. The attractive potential of the protons affects those metal avefunctions hich have a finite density at the H site and leads to the so called metal hydrogen bonding band belo the metal d- band. The additional electron brought by the H atoms into the unit cell produces a shift of the Fermi level.

4 Consequently, the electronic Density of State of Palladium changes as deuterium solubilized inside metal lattice increase. Fig. 1 - Total Density of States at the Fermi level plotted versus hydrogen concentration in PdH 3

5 Model of the Electrochemical Interface The electrochemical interface is ell represented by a double layer structure in contact ith a space of charges V capacitor electrolyte Cation Solvent molecule Specifically absorbed anion Potential drop d ( nm) 4

6 d d 1 8KTn0 0 sinh ze KT KT ze 1 e ln 1 e ~ k ~ k d 0 d m 1 ze 8 KT n sinh 0 0 KT ~ k n0z e kt 0 1 E dl d d tanh( ze0 4KT) 0 50mV m C / m E dl 10 8 V / m 5

PdH Dielectric Function Estimation The purpose is to obtain a reasonable, consistent dielectric function value suitable to be used in our model PdH PdH -6 16-8 14-10 r -1 =0.7 =0.8 1 i =0.7 =0.8-14 =0.

7 PdH Dielectric Function Estimation The purpose is to obtain a reasonable, consistent dielectric function value suitable to be used in our model PdH PdH r -1 =0.7 =0.8 1 i =0.7 = =0.99 (etrapolated) 10 =0.99 (etrapolated) E+15 3E+15 4E+15 5E+15 rad/s) Fig.- Dielectric function real component, palladium hydride 6 E+15 3E+15 4E+15 5E+15 rad/s) Fig. 3- Dielectric function imaginary component, palladium hydride Double layer is characterized by a high density of charges: it is necessary to describe a metal foil having on its surface a very high charge density, hich results in an intense electrostatic field 6

8 The dielectric function variation related to surface charge density is N m q d 1 PdH free Ne e PdH DOS KT Pd PdH Ne PdH Ry Ne PdH PdH V cell d c PdH TOT PdH PdH PdH0.99 PdH0.99 r No Charge Charge i No Charge Charge -0 E+15.5E+15 3E E+15 4E E+15 5E+15 (rad/s) Fig. 4- PdH0.99 dielectric function real component versus angular frequency. The shift to negative values due to surface charge is shon 6 E+15.5E+15 3E E+15 4E E+15 5E+15 (rad/s) Fig. 5- PdH0.99 dielectric function imaginary component versus angular frequency. The shift to higher values due to surface charge is shon 7

d y z Surface Plasmons Wave Vector component dispersion relation is epressed by Under certain conditions one could use the

9 ˆ ˆ d d c K 1) ( ) ( p d p d c K 0 eff p m Ne 8 Surface plasmons (polaritons) are quanta of plasma oscillations created by the collective oscillation of electrons on a solid surface. d y z Surface Plasmons Wave Vector component dispersion relation is epressed by Under certain conditions one could use the simplified epression: Surface plasmons may be generated by mechanisms able to produce charge separation beteen Fermi level electrons and a background of positive charges (i.e. lattice atoms) i

Surface Plasmons Ecitation Conditions - Prism Coupling - Roughness Coupling K p p p K K c c d d

010 16 sp,a 110 16 Pd-air interface K ' =/c K ' =/c n g sin 1.510 16 K' =/c n g =45 0 0 0.

6 - Matching condition given by intercept

10 Surface Plasmons Ecitation Conditions - Prism Coupling - Roughness Coupling K p p p K K c c d d sin p K sin K c K sp p p (rad/s) sp,a (rad/s) sp,a Pd-air interface K ' =/c K ' =/c n g sin K' =/c n g = K K ' (m-1 ) K I (m -1 ) Fig.6 - Matching condition given by interception beteen s.p. and laser beam dispersion la, achievable using a prism coupler Fig.7 - Matching condition given by laser beam ave vector increment due to a corrugation lattice 9

11 Surface Plasmons resonance could give rise to a huge local field enhancement, due to a focusing effect: a broad e.m. ave is confined in a surface. This phenomenon could be understood considering the ave vector component perpendicular to the interface beteen the to media: K z c ˆ ˆ 1 K z 1 c 1 ˆ 1 The field enhancement could be in a phenomenological ay epressed as E E j 0 K K zj 10

12 Enhancement of about 10 factor could be obtained in this classical calculation. On appropriate structures and by quantum mechanical computation the enhancement factor could be equal to several magnitude orders Fig.8 - Electromagnetic Field due to SP ecitation, arbitrary units 11

13 L7a(07-5)RA_4.jpg L68(0-0)RAE_5.jpg L68(0-40)RAE_3.jpg L51(43-81)RAE_5.jpg 1

Length (m) L7a(07-5)RA 0.04 L68(0-0) 0.109.

14 L55(15-54)RAE_7.jpg L56(6-6)RAE_5.jpg Sample Roughness (m) Surface Profile Average Wave Length (m) L7a(07-5)RA 0.04 L68(0-0) L68(0-40) L51(43-81)RAE L55(15-54)RAE L56(6-6)RAE

15 A surface Plasmon can not be ecited by direct impinging of an electromagnetic radiation on a smooth surface A rough surface increases incoming electromagnetic ave momentum Modelling: Laser Angular Reflectance from gratings Deepenings S10_O3 Roughness=0.04m A.W.L.= m Roughness=0.109m A.W.L.=.3m 14

16 Roughness=0.175m A.W.L.= 3m Roughness=0.11m A.W.L.= 1.8m Roughness=0.13m A.W.L.= 1.6m Roughness=0.05m A.W.L.= 1.5m 15

17 Previous Model: No information on Electromagnetic Field localization Source terms can not be included in the Analytical Model FEM implemented to solve differential Maell equations. Adequate boundary conditions are needed: Perfectly Matched Boundary Conditions (PML) ig. 9- Electromagnetic Wave propagation in free space Fig. 10- Plane ave propagating in a to semi-infinite media domain Fig. 11- The domain of interest is surrounded by outer PML elements. 16

18 Fig. 1- Magnetic field originated by a surface current flu Fig. 13- Electric field distribution originated by an alternate surface current density floing on a corrugated interface beteen air and PdH 17

19 Description of Pd samples surface under cathodic polarization has been performed by including the effects of high charge density at the inter-phase On suitable surfaces electron plasma oscillation may occur. Their frequency is depending on the material electronic properties and surface profile properties The models developed sho that under adequate conditions strong electromagnetic field localization and magnification arises. Advanced modelling of process occurring at the interface and into the bulk is the first step toards material engineering 18

Usama Anwar. June 29, 2012

Usama Anwar. June 29, 2012 June 29, 2012 What is SPR? At optical frequencies metals electron gas can sustain surface and volume charge oscillations with distinct resonance frequencies. We call these as plasmom polaritons or plasmoms.