8. XAFS Measurements and Errors

Transcription

1 8. XAFS Measurements and rrors

2 XAFS Measurements X-ray detectors: Ionization chamber detectors Solid state detectors lectron yield detectors Scintillation detectors µ ) = µ 1 + χ )) 0

3 Transmission Measurement I t Total absorption is given as I I e µ x = 0 µx = lni 0 /I) µ ) = µ 1 + χ )) 0 Important points: 1. Uniform thickness. 2. Absorption edge step size is about The sample should fully cover the beam cross section. 4. Particle size should be uniform and less than 2~3 absorption length.

4 X-ray Absorption Length

5 XAFS Transmission Measurement µt = lni 0 /I), µ) = µ 0 [1 + χ)] µ k) χ k) = 1 µ 0 XAFS, χ, is obtained without depending on the sample thickness. µ 0

6 XAFS Transmission Measurements Sample I 0 I t % absorption % absorption The x-ray absorption can be controlled by gas in the ionization chamber. In general, He, N 2, Ar or a mixed gas of any two is used. To avoid statistical error, the total x-ray counts should be more than 100,000. Than the error is less than 0.3 % of the signal.

7 Gas Absorption Calculation

8 XAFS Fluorescence Measurement I t Important points: 1. Sample thickness of the region where x-rays hit should be uniform or less than couple of absorption lengths. 2. Take enough fluorescence counts, more than several tens of thousands. 3. Avoid background noisy as much as possible.

9 Principle of Fluorescence I 0 f If t θ i sample θ f z dz k α2 k α1 k β

10 Theory of Fluorescence XAFS i t z f f dz e I z di I f f T i T θ µ ε θ µ θ µ sin / ) ) ) ] )/sin )/sin [ + = = 0 0 [ ] t f i f T T f f f T i T e I I ] )/sin )/sin [ sin / )sin ) ) ) θ µ θ µ θ θ µ µ µ ε + + = 1 0 µ T ) = µ) + µ B ), where µ B ) is the absorption coefficient of the x-rays of which energy is not. In general, µ) >> µ T f ) and µ) >> µ B ). I f /I 0 = ε){1-[1- µ)t / sinθ i ]}= ε)µ)t / sinθ i For a small t / sinθ i, after normalizing the data, µ) = I f /I 0 Ref: Japanese Journal of Applied Physics 49, ).

11 Fluorescence and Transmission XAFS In general transmission XAFS measurements give better information than fluorescence XAFS does. However, sometimes we cannot make transmission XAFS measurements due to the specimens, thin films on substrates and dilute materials, for examples. Transmission XAFS TiO 2 Fluorescence XAFS

12 Fluorescence XAFS SABCOR) If t / sinθ i is larger than 2 ~ 3 absorption length 1/µ=1absorption length), self absorption may distort the χ and µ) = I f /I 0 is no longer good.therefore, the the χ and µ) should be properly corrected. XAFS from copper foil XAFS self-absorption correction software was developed by Corwin Booth. C. H. Booth and F. Bridges, Physica Scripta, T115, ).

13 Fluorescence XAFS FLUO) S K-edge NH 4 ) 2 SO 4 Self-absorption correction software of XANS fluorescence was developed by Daniel Haskel.

14 X-ray Self-absorption Corrections in Athena

15 XANS Self-Absorption Correction FLUO)

16 XAFS Self-Absorption Correction SABCOR)

17 rrors in XAFS 1. Statistical error: Counting x-rays by a detector can be treated as a Poisson distribution. For the Poisson distribution, the uncertainty is N. Therefore, the portion of the error in a signal is 1/ N. To reduce the statistical error, one should take the counts as much as possible. In general I 0 is larger than 10 6 the incident x-rays of a synchrotron source are ~ photons/sec.), and I t or I f is more than 10 5 photons/sec. Since XAFS data are analyzed in r-space after the absorption data are taken as a function of the incident x-ray energy, the statistical error cannot be counted in the analysis. The Fourier transformed data with the error will be further distorted. 2. Systematic error: this error is occurring from equipments and/or other environments. Systematic error can be a background noisy in XAFS signal in r-space. However, it is still difficult to eliminate this error. 3. Random error: unexpected circumstance curses the random noisy. To reduce the random noisy, do not change experimental setting during a scan. Take several sans and compared them if there is any difference among scans.

18 Remind Points 1. Sample thickness should be uniform less then 1 absorption length) 2. Take enough counts more then 100,000 counts). If count is low, take many scans and average over χ XAFS) values in k-space. 3. Measure a standard sample as a counterpart. 4. Try to avoid any error during measurements as much as possible because the error cannot be distinguished from signals in r-space scan more then three times). 5. In XAFS measurement set up, the x-ray should be hit the region with a uniform thickness, not with a maximum intensity. 6. Very carefully analyze the XAFS data.

19 Find further information of XAFS at Korean XAFS Society homepage: The next XAFS School may be held in January, In order to obtain the information of the next XAFS School, check the Korean XAFS homepage in Dec