EXAFS. Extended X-Ray Absorption Fine Structure. Santiago J. A. Figueroa Researcher Beamline coordinator XAFS2

Transcription

1 EXAFS Santago J. A. Fgueroa Researcher Beamlne coordnator XAFS Extended X-Ray Absorpton Fne Structure EXAFS 5 th School on X-Ray Spectroscopy Methods Campnas, 3 de Agosto de 16

2 Overvew 1.Interacton of X-rays wth matter.bascs aspects about XAFS 3.Understandng the EXAFS equaton

3 Interacton of X-rays wth matter Par producton h > 1M ev Photoelectrc absorpton h MATTER h Transmsson X-rays h' h Scatterng h Decay processes h f Compton Thomson Fluorescence Auger electrons Prmary competng processes and some radatve and non-radatve decay processes

4 Cross secton (barns/atom) Interacton of X-rays wth matter Photoelectrc effect s the domnatng process at the x-ray energy range (-1 kev) X-ray attenuaton : Thomson Compton Cu Z=9 Absorpton Observed data Par producton Photonuclear absorpton 1 ev 1 KeV 1 MeV 1 GeV Energy

5 mt Bascs aspects about XAFS What s XAFS? XAFS studes the detals of the x-ray absorpton coeffcent around an absorpton edge. It reveals a wealth of nformaton regardng the geometrc and electronc structure of materals Energa(keV)

6 Bascs aspects about XAFS

7 Coefcente de atenuação (cm /g) Bascs aspects about XAFS 1 4 L II L I Ge (Z=3) L III mt K Energa(keV) Energa (ev) XAFS: Study the detals of the varaton on the absorpton coeffcent (fne structure) after the edge. Absorpton edges K 1s p L 1 L L 3 s p p 1/ s, d p 3/ s, d

8 Bascs aspects about XAFS X-ray attenuaton Absorpton coeffcent: h di t m Idt I I 1 h µ : lnear absorpton coeffcent t : thckness µt: absorbance amostra I 1 I t exp( m ) Includes contrbutons from all scatterng and absorpton precesses Mass absorpon coeffcent: m j g j m j unts (cm /g) Atomc absorpton coeffcent: m a j m j A j N Mass fracton of el. j Unts: 1-4 cm (1 barn)

9 Bascs aspects about XAFS Basc XAFS experment sequental mode detectors monochromator I o sample I Radaton source mt I log I 1

10 Bascs aspects about EXAFS SAMPLE Incdent X-rays Transmtted X-rays Vsble lght XEOL h e - TEY h Fluorescence X-rays EXAFS spectrum m X-ray energy

11 Bascs aspects about XAFS Whch method for whch applcaton? h fluor. I e- h The most mportant crteron: The best sgnal to nose rato for the element of nterest h e - h lumn. Always transmsson, f possble Most accurate method, best overall S/N countng statstcs of about 1-4 from beamlnes wth more than 1 8 photons/s) Fluorescence for very dluted samples A specfc sgnal reduces the large background (but maxmum tolerable detector count-rate can result n very long measurng tmes). Total electron yeld (TEY) for surface senstvty and surface XAFS (adsorbates on surfaces) TEY for thck samples that cannot be made unform. XEOL X-ray excted optcal lumnescence VIS/UV detecton from lumnescent samples

12 mt Bascs aspects about XAFS X-ray Absorpton Near Edge Strucuture hgh Z elements XANES.6.5 XAFS = XANES + EXAFS InAs - As K-Edge Extended X-ray Absorpton Fne Strucuture EXAFS.4.3 low Z elements NEXAFS..1 Near Edge X-ray Absorpton Fne Strucuture E = kev Photon Energy (kev) XANES s the regon ~5 ev around the edge

13 Bascs aspects about XAFS XANES : transtons to unoccuped states (localzed and contnuum) low energy photoelectron multple scatterng (MS) Informaton content Ferm energy Projected densty of unoccuped states Oxdaton states Coordnaton symmetry EXAFS: hgh energy photoelectron sngle scatterng + some mportant MS Informaton content nteratomc dstances dsorder coordnaton numbes Bond-angle dstrbutons Partal par dstrbuton Vbratonal propertes.

14 Bndng Energy Bascs aspects about XAFS Contnuum XANES Unnocuped states Ferm Energy 4s, 4p, 4d, 4f N fóton 3s, 3p, 3d s, p M L Ocupped states 1s K

15 E XANES: pre edge structure Ferm Golden rule m f > > E E a b f f > m Arctangent curve Inflecton pont > E E m > E

16 Bndng Energy Bascs aspects about XAFS Contnuum EXAFS Unnocupped states Ferm Energy 4s, 4p, 4d, 4f N Informaton obtaned: Coordnaton number Interactomc dstances Dsorder fóton 3s, 3p, 3d s, p M L Ocupped states 1s K

17 Bascs aspects about XAFS

18 mt Bascs aspects about XAFS XAFS = XANES + EXAFS InAs - As K-Edge Extended X-ray Absorpton Fne Strucuture.6.5 EXAFS.4.3 Fne Strucuture..1 E = kev Photon Energy (kev) EXAFS s the regon from 5 1 ev after the edge

19 Understandng the XAFS equaton Photon energy (E) > Bndng Energy (E l ): Photoelectrc effect. Knetc energy of the photoelectron (E c )= E - E L Wave-Partcle dualty: The photoelectron travel as a esferc wave: E c = h Wavevector of the photoelectron: K k m ( E e E L ) Quantcal state of the photoelectron: superposton of the propagatng wave wth the retrodspersed waves on the neghtbourgs Phase dfference of the ncomng and outgong waves: Δ kr R Interference n between propagatng waves and retrodspersed ones. Ths moduls the absorpton coeffcent. Osclaton frequence: R Osclaton ampltudes: number of neghtbourgs and dsorder

20 mx Understandng the XAFS equaton m (k) m m m m Vetor de onda do fotoelétron: k(å -1 ) Energa(eV) Here we add (superpose) osclatons of dfferent frequences (radal dstances), one for each coordnaton shell Coordnaton shell: Refers to the aggrupaton's of atoms at the same dstance to the absorber atom. Coordnaton Number: amount of atoms n a coordnaton shell

21 Understandng the XAFS equaton Prncpal hypothess: Fnal states are plane waves Gaussan dsorder Dpolares transtons One actve electron Photoelectron dsperson s sngle Sayers et al.,prl 7, 14 (1971) E f F m( E) f ê r f E ( E f ) (k) N kr S F ( k) e k e R sn[ kr ( k)] Estructural parameters Atomc parameters: Absopton and dsperson of the Photoelectron R N F(k) (k) S ab nto

22 Understandng the XAFS equaton TF( R) 1 k k max mn ( k)e Rk dk

23 Understandng the XAFS equaton TF( R) 1 k k max mn ( k)e Rk dk

24 (k) Módulo da TF Understandng the XAFS equaton TF( R) 1 k k max mn ( k)e Rk dk sn(*r*k) R=3 R=.5 R= R= k(å -1 ) R(Å)

25 (k) Módulo da TF Understandng the XAFS equaton TF( R) 1 k k max mn ( k)e Rk dk 1. *sn(*r *k) =6 =4 3 =5 4 = k(å -1 ) R(Å) (k) N kr S F ( k) e k e R sn[ kr ( k)]

26 Understandng the XAFS equaton 1 Fourer Transform (FT) (k) x k Sgnal at Ge-K edge k(å -1 ) FT: s not a Radal Dstrbuton functon but have some resemblance Módulo da TF R(Å) 4 a shell: R = 5.66 N=4 1 a shell: R =.45 Å N=4 ok a shell: R = 4. Å N=1 3 a shell: R = 4.69 Å N=1 (k) N kr S F ( k) e k e R sn[ kr ( k)]

27 Módulo da TF Understandng the XAFS equaton Changes on the EXAFS sgnal wth varatons on the Coordnaton number 3 1 N=4 N=3 N= N= N=4 N=3 N= N=1 x k k(å -1 ) R(Å)

28 3 R R + R Módulo da TF Understandng the XAFS equaton 1 8 R R + R x k k(å -1 ) R R - R Changes on the EXAFS sgnal wth a varaton on the Módulo da TF R.1Å R(Å) R R - R x k k(å -1 ) R(Å)

29 3 Sem desordem Com desordem 1 8 Sem desordem Com desordem x k k(å -1 ) Changes on the EXAFS wth a varaton on the structural dsorder Módulo da TF R(Å) Gaussan Dsorder: σ =.3 Å

30 absorbânca (E) Understandng the XAFS equaton 1 background extracton Data treatment. 1.5 CdSe - Borda K do Se xm bkg Vctoreen.1.5 m m m 1. m m Energa(eV) Energa (ev)

31 Understandng the XAFS equaton Converson Ek k m ( E e E L ).3..1 K-wegthng k k(å -1 ) k)*k k(å -1 )

32 FT((k)) FT((k)) Understandng the XAFS equaton R(Å) Structural parameters: Mnmal Square fttng k)*k Phases and ampltudes of the retrodsperson k(å -1 )

33 Understandng the XAFS equaton Prncpal hypothess: Fnal states are plane waves Gaussan dsorder Dpolares transtons One actve electron Photoelectron dsperson s sngle E f F m( E) f ê r f E ( E f ) Sayers et al.,prl 7, 14 (1971) (k) N kr S F ( k) e k e R sn[ kr ( k)] Estructural parameters Atomc parameters: Absopton and dsperson of the Photoelectron R N F(k) (k) S ab nto

34 But remeber...

35 Obrgado pela sua atenção! More nfo about XAFS: Questons, please emal me: Acknowlegments: To Gustavo Azevedo, Valmor Mastelaro, Anatoly Frenkel por some sldes