First Shell EXAFS Analysis

Transcription

1 EXAFS Data Collection and Analysis Workshop, NSLS, July, First Shell EXAFS Analysis Anatoly Frenkel Physics Department, Yeshiva University, New York, NY 116 General strategy: -Collect good data -Come up with a physically reasonable, constrained model -Test your model on a reference compound -Fit it to the unknown sample data -Be conservative with the number of fitting parameters

2 Bottom-up approach the preferred strategy of the First Shell Analysis: (You will avoid going in the wrong direction too early ) Implementation Analysis Strategy Conceptual Modeling Find the best analysis software that can implement your strategy. Not all packages are universally good. -Plan on doing reality checks; -Reference compounds should be measured and analyzed first; -Try to maximize the number of degrees of freedom in the fits (use constraints, experimental/theoretical info etc.) Linear fit is better than nonlinear fit! -Start with the crude picture first, then refine it; -Homogeneous or heterogeneous environment? (bulk or nano, eq. or ineq. unit cell positions, solution or separate phases etc.)

3 Test case: supported Pt nanoparticles What are we after? -Size, -Structure, -Thermal properties. (Beamline: X16C, NSLS) Raw absorption coefficient What relevant info can be found from EXAFS? -Model of atomic packing, -Average CN, -Average distances, -Average disorder Photon energy, ev

4 EXAFS data measured of particles of ~ Å in size: 1. K K 47 K 67 K.5 k χ(k), Å k, Å -1 Can we tell what is the particle s structure? Whether particles agglomerate at high T? Whether the changes are dominated by atomic rearrangements or by thermal disorder?

5 Can we answer the same questions if a reference compound is measured as well? 1. Pt particles (~ Å) K K 47 K 67 K Bulk Pt K K 47 K 67 K.5 1. k χ(k), Å - k χ(k), Å χ( k) = k, Å -1 NS kr f eff ( k) e σ k sin k, Å -1 [ ( )] 4 kr C k + δ k Can we tell what is the particle s structure? -Yes, consistent with fcc Whether particles agglomerate at high T? - Most likely no, the size effect is not evident Whether the changes are dominated by atomic rearrangements or by thermal disorder?

6 How to tell size dependence from temperature dependence? T= K; Size is varied Bulk Pt; Temperature is varied Bulk Pt 8 Å 45 Å Å K K 47 K 67 K k χ(k), Å k χ(k), Å χ( k) ~ N e σ k k, Å -1 k, Å -1 As a function of size, EXAFS amplitude is scaled uniformly throughout the k-range As a function of temperature, EXAFS amplitude is scaled nonuniformly

7 How to model metal (Pt) foil data:.5 K. # Pt foil, T= K guess S =.9 guess ss1 = guess dr1 = guess th1 = guess e = χ( k) = sin NS kr ( k) e [ ( )] 4 kr C k + δ k f eff σ k k χ(k), Å data = ptfoil-avk.chi out = ptfoil-avk rmin =.1 rmax =. kmin = kmax= w = dk= k, Å K!% 1st path: eshift 1 e amp 1 S path 1 p1.dat id 1 SS Pt-Pt(1), r=.7719 delr 1 dr1 sigma 1 abs(ss1) third 1 th1 k χ(k), Å k, Å -1

8 5 4 S = ss1 = dr1 = th1 = - 19 e = Fit Results This is not physically reasonable What caused S to be different at K and 67 K? S = ss1 = dr1 = th1 = e = χ( k) = sin - correlation with other fit variables: NS kr ( k) e [ ( )] 4 kr C k + δ k f eff σ k

9 χ( k) = NS kr f eff ( k) k χ(k) of Pt foil: temperature dependence How to break the correlation? e σ k sin [ ( )] 4 kr C k + δ k One possible solution: a multiple-data-set (mds) fit K K 47 K 67 K What variables are not expected to change at different temperatures? k χ(k), Å σ σ E, N d = σ = s + σ d σ s, ΘE h 1+ exp( Θ ωµ 1 exp( Θ E E T ) T ) k, Å -1

10 title = Pt L-edge, foil data = ptfoil-avk.chi out = ptfoil-avk rmin =.1 rmax =. kmin = kmax= w = dk = path 1 p1.dat id 1 SS Pt-Pt1 eshift 1 e amp 1 S delr 1 dr11 sigma 1 abs(ss11) third 1 th11 next data set data = ptfoil-avk.chi out = ptfoil-avk rmin =.1 rmax =. kmin = kmax= w = dk = path 1 p1.dat id 1 SS Pt-Pt1 eshift 1 e amp 1 S delr 1 dr1 sigma 1 abs(ss1) third 1 th1 Multiple-Data-Set Fit next data set.. ptfoil-47avk.chi. next data set.. ptfoil-67avk.chi. set ss11 = abs(ss11) + eins(, theins1) set ss1 = abs(ss11) + eins(, theins1) set ss1 = abs(ss11) + eins(47, theins1) set ss14 = abs(ss11) + eins(67, theins1) guess e =. guess s =.9 guess ss11 = guess theins1 = guess th11 = guess th1 = guess th1 = guess th14 = σ d = guess dr11 = guess dr1 = guess dr1 = guess dr14 = σ = σ s + σ d h 1+ exp( Θ ωµ 1 exp( Θ E E T ) T )

11 MDS fit results K K K K ss11 = 5 9 theins1 = s = dr11 = dr1 = dr1 = dr14 = th11 = -5 1 th1 = -17 th1 = 11 th14 = 67 6 e = Physical (chemical, engineering, mat.science, life science etc.) reality checks: 1) Debye temperature: 4 K for Pt As obtained (through ): 5() K Θ E σ s ) Static disorder : ~ ) Corrections to model distances: ~ 4) Thermal expansion: evident 5) S: reasonable (between.7 and 1.)

12 χ( k) = NS kr How to tell right from wrong? f eff ( k) e σ k sin [ ( )] 4 kr C k + δ k Pretend, we do not believe in third cumulants. With C Without C ss11 = 5 9 theins1 = s = dr11 = dr1 = dr1 = dr14 = th11 = -5 1 th1 = -17 th1 = 11 th14 = 67 6 ss11 = theins1 = s = dr11 = dr1 = dr1 = dr14 = e = e =

13 How to model XAFS data in nanoparticles? A priori knowledge or a working hypothesis must exist (the zero approximation) otherwise: the transferability of amplitude/phase will not work!) 1) Hemispherical ) Crystal order ) Size: about Å What information can be obtained from 1 st shell EXAFS analysis? 1) Size of the particle (via N) ) Distances, thermal vibration, expansion ) Static disorder (icosahedral? surface tension?) Average First-Shell Coordination Average CN Nanoparticle Diameter (A) (Å) Relative Abundance

14 MDS fit (1shell) to the nanoparticles EXAFS - Coordination number is now guessed (a variable) S - is fixed to be equal to that in Pt foil EXAFS - E is fixed to be equal to that in Pt foil EXAFS K K K K ss11 = theins1 = n1 = dr11 = dr1 = dr1 = dr14 = th11 = -17 th1 = th1 = th14 = 41 79

15 To get the most out of the data, the Multiple-Scattering Analysis is often needed. What are the limitations of the 1 st Shell Analysis in the case of nanoparticles? -Shape, Size, Surface orientation are not revealed through the 1NN CN -Short Range Order in nanoparticle alloys:

16 Another example: Giant inorganic molecules, Polyoxomolybdates (POMs): [Mo 1 O 7 (HCOO) ] {Mo 1 } [Mo 7 Fe O 5 ] {Mo 7 Fe } Fe +.9 nm.5 nm

17 {Mo 7 Fe } {Mo 1 } Modeling pair distribution functions using XRD results g AB ( r) = dn dr AB

18 K K Mo K-edge K K Fe K-edge 1 Mo-O Å shift Mo-O Mo-O Å shift Mo-Fe Mo-Mo -. Å shift Mo-Mo Å shift Fe-Mo Fe-O Å shift Fe-O 1

19 Mo K-edge T=14 K 1. Fe K-edge T=14 K Mo K-edge T= K Fe K-edge T= K Mo-O 1 Mo-O Mo-O Fe-O Mo-Mo Mo-Fe Mo-Mo Bond N 14 K K Mo-O 1.67 r (Å) 1.75(1) 1.75(1) σ (Å ) 6(5) 8() Mo-O.5 r (Å).5(1).5(1) σ (Å ) 4(9) 51(7) Mo-O 1. r (Å).7().7() σ (Å ) 5(7) 67() Fe-O 6. r (Å).(1).(1) σ (Å ) 18(14) 4(17) Mo-Mo 1.67 r (Å).1(1).1(1) σ (Å ) 7(5) 7(4) Fe-Mo 4. r (Å).58().61() σ (Å ) 1(1) 14(1) Mo-Fe 1.67 r (Å).58 f.61 f σ (Å ) 1 f 14 f Mo-Mo 1.67 r (Å).89().9() σ (Å ) 5(14) 9(19)

20 4 Mo-O Mo 1 1 Mo-O 1 Mo-O O Mo 1 -Mo 1 O Mo -Mo Mo -Mo O 4 Mo-Mo 1 Mo-Mo 1 Mo-Mo

21 k χ(k), Å K.6 K Mo K 47 K Mo-O 1 k, Å -1 Mo-O Mo-O Å shift -. Å shift Mo-Mo 1 Mo-Mo 14 K K 7 K 47 K Mo-Mo

22 T=14 K T= K.5 T=7 K T=47 K Mo-Mo Mo-O 1 Mo-O Mo-O Mo-Mo 1 1 Mo-Mo O Mo 1 -Mo 1 Mo -Mo O O Asymmetric distortion of MoO 6 octahedron Mo -Mo

23 References (send reprint requests to: 1) A. I. Frenkel, C. W. Hills, and R. G. Nuzzo, Feature Article, J. Phys. Chem. B, 15, (1). ) A. I. Frenkel, M. S. Nashner, C. W. Hills, R. G. Nuzzo, and J. R. Shapley, Science Highlights, NSLS Activity Report 1999, NSLS, Brookhaven National Laboratory,. ) A. I. Frenkel, J.Synchrotron Rad., 6, 9 (1999). 4) C. W. Hills, M. S. Nashner, A. I. Frenkel, J. R. Shapley, and R. G. Nuzzo, Langmuir, 15, 69-7 (1999). 5) M. S. Nashner, A. I. Frenkel, D. Somerville, C. W. Hills, J. R. Shapley, and R. G. Nuzzo, J. Am. Chem. Soc., 1, (1998). 6) M. S. Nashner, A. I. Frenkel, D. L. Adler, J. R. Shapley, and R. G. Nuzzo, J. Am. Chem. Soc., 119, 776 (1997)