least two components of comparable amplitude will be required to reproduce the kspace data. The first attempt using a fixed number of 3 Mo–S refined to a distance of
2.36 Å and σ = 0.045 Å (Fig. 6.20a).
A second component representing 3 Mo–Fe interactions was then added to
capture the beat pattern (not shown). Finally, a third component representing 3
Mo–O interactions was added to fill in the largest residual. The Mo–Fe and Mo–O
components are shown in Fig. 6.20b, and the final fit is shown in Fig. 6.20c. The
results illustrate the strengths and weaknesses of the curve-fitting procedure. Without
fitting it would be hard to demonstrate the presence of a weaker shell of Mo–O/N
interactions. However, the true distances are Mo–O = 2.16 and 2.19 Å and Mo–
N = 2.33 Å, so the fitting has its limits in defining the structure. Furthermore, in this
example we have not tried to untangle the multiple scattering contributions to the
long Mo–Fe distances shown in Fig. 6.19 and we have also ignored the weak
contributions from the outer shell histidine imidazole ligand. EXAFS curve-fitting
is often a solid technique for refining structures that have crystallographic data or
other evidence for constraining the proposed structure being refined. It has a less
than glorious history for prediction of structures out of whole cloth.
6.10 Suggested Exercises
1. Mass Absorption Coefficients. Using tabulated mass absorption coefficients
(http://www-cxro.lbl.gov), calculate:
(a) The fraction of X-rays absorbed at 8 keV by Fe for a 10 mM solution of Fe in
H 2 O.
(b) The fraction of X-rays absorbed at 800 eV by Fe for a 10 mM solution of Fe in
H 2 O.
(c) Which experiments is easier: Fe K-edge or Fe L-edge?
2. Detection Modes. Using tabulated mass absorption coefficients and fluorescence
yields and assuming a 10% solid angle for fluorescence collection, calculate the
concentration where Fe Kα fluorescence has the same S/N as a transmission
experiment.
3. First Shell EXAFS. Suppose you are planning an EXAFS experiment and you
want to estimate how hard you will have to work. Assume you have prepared FeS
molecules isolated in a noble gas matrix at 10 K. Assume a bond length of 2.3 Å,
a stretching frequency of 500 cm
À1 , S 0
2 ~ 0.9, and a mean free path of 10 Å.
(a) Estimate the rms σ for the Fe–S distance using: σ ab ¼ 4:106
1
μv coth
1:44v
2T
1=2
where μ is the reduced mass in atomic mass units, T is the temperature in
Kelvin, h is Planck’s constant, and ν is the vibrational frequency in wave
numbers.
162
6 X-ray Absorption and EXAFS
2.36 Å and σ = 0.045 Å (Fig. 6.20a).
A second component representing 3 Mo–Fe interactions was then added to
capture the beat pattern (not shown). Finally, a third component representing 3
Mo–O interactions was added to fill in the largest residual. The Mo–Fe and Mo–O
components are shown in Fig. 6.20b, and the final fit is shown in Fig. 6.20c. The
results illustrate the strengths and weaknesses of the curve-fitting procedure. Without
fitting it would be hard to demonstrate the presence of a weaker shell of Mo–O/N
interactions. However, the true distances are Mo–O = 2.16 and 2.19 Å and Mo–
N = 2.33 Å, so the fitting has its limits in defining the structure. Furthermore, in this
example we have not tried to untangle the multiple scattering contributions to the
long Mo–Fe distances shown in Fig. 6.19 and we have also ignored the weak
contributions from the outer shell histidine imidazole ligand. EXAFS curve-fitting
is often a solid technique for refining structures that have crystallographic data or
other evidence for constraining the proposed structure being refined. It has a less
than glorious history for prediction of structures out of whole cloth.
6.10 Suggested Exercises
1. Mass Absorption Coefficients. Using tabulated mass absorption coefficients
(http://www-cxro.lbl.gov), calculate:
(a) The fraction of X-rays absorbed at 8 keV by Fe for a 10 mM solution of Fe in
H 2 O.
(b) The fraction of X-rays absorbed at 800 eV by Fe for a 10 mM solution of Fe in
H 2 O.
(c) Which experiments is easier: Fe K-edge or Fe L-edge?
2. Detection Modes. Using tabulated mass absorption coefficients and fluorescence
yields and assuming a 10% solid angle for fluorescence collection, calculate the
concentration where Fe Kα fluorescence has the same S/N as a transmission
experiment.
3. First Shell EXAFS. Suppose you are planning an EXAFS experiment and you
want to estimate how hard you will have to work. Assume you have prepared FeS
molecules isolated in a noble gas matrix at 10 K. Assume a bond length of 2.3 Å,
a stretching frequency of 500 cm
À1 , S 0
2 ~ 0.9, and a mean free path of 10 Å.
(a) Estimate the rms σ for the Fe–S distance using: σ ab ¼ 4:106
1
μv coth
1:44v
2T
1=2
where μ is the reduced mass in atomic mass units, T is the temperature in
Kelvin, h is Planck’s constant, and ν is the vibrational frequency in wave
numbers.
162
6 X-ray Absorption and EXAFS