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Effect of the electron mean free path in small particles on the evaluation of coordination numbers
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PhysicaB158(1989)405-406 North-Holland, Amsterdam 405 EFFECT OF THE ELECTRON MEAN FREE PATH IN SMALL PARTICLES ON THE EVALUATION OF COORDINATION NUMBERS J.Zhaol and P.A.montanol" I-Department of Physics,West Virginia University,Morgantown,WV. 2-Department of Physics,Brooklyn College of CUNY,Brooklyn,NY. Abstract.It is a common practice in EXAFS analysis to transfer the electron mean free path (MFP) value from the bulk standard to the small particles samples.We show that such a procedure can lead to an incorrect evaluation of coordination numbers.The electron MFP in small particles can be significantly different from the bulk value.We performed a detailed analysis of Al small particles to illustrate this point.We discuss the implications of assuming transferability of the electron MFP . Introduction.It is a common practice in EXAFS analysis to transfer the amplitude and phase shifts from a standard to the sample under study. The transferability of the amplitudes and phase shifts requires similar chemical environments for the standard and sample.For example, in analyzing the EXAFS spectra of small particles and supported catalysts one usually transfer the phase shifts and normalized amplitude,Aj(k)=Fj(k)exp(-2rj/h)exp(-2k202), from the j-shell of the bulk metal standard to the corresponding small particle sample[l].For small particles,a large amount of atoms are on or near the surface.The electronic properties of the surface atoms are quite different from those of the bulk.The photoelectron MFP is strongly sensitive to changes in the band structure and collective excitations of the electrons in the material.In small particles the contribution from the surface atoms to the inelastic scattering of the photoelectrons is enhanced with respect to the bulk. In the following paragraphs we calculate the electron MFP for small particles of Al,and show that h is substantially shorter than in the bu1k.A brief qualitative discussion is given for other metal particles on the effect of MFP changes in the determination coordination numbers . Results.We calculate the total transition probabilities for the inelastic scattering of electrons by small spherical particles using Fujimoto and Komaki [21 equations.These calculations are performed using a free electron model for the metal.In Fig. 1 we show the total transition probability vs radius for Al particles.One can observe the emergence of the surface plasmon peak as the radius of the particle decreases. It is clear from the figure that the loss processes are dominated by surface effects in the smallest particles.When the radius is larger than 100 A the contribution from the surface losses is negligible .We calculate the electron MFP ,h,from the total transition probability.The results of these calculations are shown in Fig.2.It is noted that h for a particle of 10 A radius is about 60 % of the bulk value. This variation in the electron MFP value raises serious questions about the transferability of i from the bulk to small particles. The main effect of transferring the bulk value of h to the small particles will be an incorrect evaluation of the coordination number.We ilustrate this point using a simple model.If we take the average h 0921-4526/89/$03.50 @ El sevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Transcript of Effect of the electron mean free path in small particles on the evaluation of coordination numbers
PhysicaB 158(1989)405-406 North-Holland, Amsterdam
405
EFFECT OF THE ELECTRON MEAN FREE PATH IN SMALL
PARTICLES ON THE EVALUATION OF COORDINATION NUMBERS J.Zhaol and P.A.montanol" I-Department of Physics,West Virginia University,Morgantown,WV. 2-Department of Physics,Brooklyn College of CUNY,Brooklyn,NY.
Abstract.It is a common practice in EXAFS analysis to transfer the electron mean free path (MFP) value from the bulk standard to the small particles samples.We show that such a procedure can lead to an incorrect evaluation of coordination numbers.The electron MFP in small particles can be significantly different from the bulk value.We performed a detailed analysis of Al small particles to illustrate this point.We discuss the implications of assuming transferability of the electron MFP . Introduction.It is a common practice in EXAFS analysis to transfer the amplitude and phase shifts from a standard to the sample under study. The transferability of the amplitudes and phase shifts requires similar chemical environments for the standard and sample.For example, in analyzing the EXAFS spectra of small particles and supported catalysts one usually transfer the phase
shifts and normalized amplitude,Aj(k)=Fj(k)exp(-2rj/h)exp(-2k202),
from the j-shell of the bulk metal standard to the corresponding small particle sample[l].For small particles,a large amount of atoms are on or near the surface.The electronic properties of the surface atoms are quite different from those of the bulk.The photoelectron MFP is strongly sensitive to changes in the band structure and collective excitations of the electrons in the material.In small particles the contribution from the surface atoms to the inelastic scattering of the photoelectrons is enhanced with respect to the bulk. In the following paragraphs we calculate the electron MFP for
small particles of Al,and show that h is substantially shorter than
in the bu1k.A brief qualitative discussion is given for other metal particles on the effect of MFP changes in the determination coordination numbers . Results.We calculate the total transition probabilities for the inelastic scattering of electrons by small spherical particles using Fujimoto and Komaki [21 equations.These calculations are performed using a free electron model for the metal.In Fig. 1 we show the total transition probability vs radius for Al particles.One can observe the emergence of the surface plasmon peak as the radius of the particle decreases. It is clear from the figure that the loss processes are dominated by surface effects in the smallest particles.When the radius is larger than 100 A the contribution from the surface losses is negligible .We calculate the electron MFP
,h,from the total transition probability.The results of these
calculations are shown in Fig.2.It is noted that h for a particle of
10 A radius is about 60 % of the bulk value. This variation in the electron MFP value raises serious questions about the
transferability of i from the bulk to small particles. The main
effect of transferring the bulk value of h to the small particles
will be an incorrect evaluation of the coordination number.We
ilustrate this point using a simple model.If we take the average h
0921-4526/89/$03.50 @ El sevier Science Publishers B.V. (North-Holland Physics Publishing Division)
406 J. Zhao, P.A. Montana/Evaluation of coordination numbers
Figure 1. Transition probability for inelatic scattering in Al particles.
RADIUS: 1000 i
a-l / 30 i
,20 i
200 300 500 1000
ENERGY (a")
Figure 2 .Electron MFP in A3 particles.
for Al bulk to be 10 A and for 20 A particles to be 6 A ( from 100-1000 eV) , assuming a 2 A interatomic distance,we obtain that the coordination number will be 0.72 of the true value.
It is clear that such a reduction in coordination number is the result of using incorrect values for the MFP.The situation is not improved when dealing with transition metals ,where such effects are more evident.In the literature there are many examples of reduced coordination number for small particles, which are inconsistent with the number of shells observed and with the interatomic distances measured[3,4].We believe that such results are due to the incorrect transfer of the electron MFP from the bulk to the small clusters.It is observed that in noble metals this effect is less noticeable [5,6] Great care is recommended in the evaluation of coordination numbers for small particles and in inferring structural modifications based upon coordination number values obtained
assuming the transferability of hfrom the bulk.
Bibliography.
l.J.H.Sinfelt,G.H.Via and F.W.Lytle,Catal.Rev. Sci.Eng.26,81(1984) and references there in. 2.F.Fujimoto and K.Komaki,J.Phys.Soc.Jpn.,23,1168(1967). 3.J.H.Sinfelt,G.H.Via and F.W.Lytle,J.Chem.Phys.,68,2009(1979). 4.G.H.Via,G.Meitzner,F.W.Lytle and J.H.Synfelt,J.Chem.Phys.,79,1527 (1983). S.P.A.Montano,W.Schulze,B.Tesche,G.K.Shenoy and T.I.Morrison, Phys Rev. B30,672(1984). 6.A.Balerna,E.Bernieri,P.Picozzi,A.Reale,S.Santucci,E.Burattini and S.Mobilio,Phys. Rev. B31,5058(1985).
