Beamline Alignment

 Figure 1.  Basic Components

The basic components of a typical XAFS experiment are shown above (Figure 1).  X-rays are produced in the source (bending magnets, wigglers, or undulators) and pass through an aperture before striking the monochromator.  This aperture, a pair of slits, can be adjusted to control the size and energy resolution of the beam.  Most monochromators at SSRL XAFS beam lines are double crystal designs.  The first crystal of the pair can be detuned (rotated off of the Bragg condition) for precise alignment and for harmonic rejection.  After entering the hutch, the beam passes through another defining aperture (Huber Ta slits).  The beam passes through the gas in the gas ionization chambers, and its intensity is measured.  These gas ionization chambers are typically used to measure the incident beam when filled with appropriate gas mixtures.  Lytle or Germanium detectors are then used to measure fluorescent x-rays from the samples.

The first step in an XAFS experiment is to align the beam line so that the most intense part of the beam is directed toward the hutch.  The beam alignment procedure is as follow:

Gas Ionization Chambers
 
SSRL has two standard sizes of gas ionization chambers: 15 cm and 30 cm in length.  In a typical EXAFS experiment, the first ion chamber should be filled with a gas mixture to absorb about 20 to 40% of the incident beam.  A second ion chamber is placed after the sample to detect the transmitted beam, and its gas mixture is also chosen to absorb about 20 to 40% of the transmitted beam.  An appropriate gas mixture fills the third ion chamber to absorb as much of the remaining beam as is possible.  Table 1 below lists the useful gases, densities, absorption edge energies, and absorption coefficients.  The ratios of beam transmitted for ion chambers of length 15 cm and 30 cm for different energy ranges are also listed.  These ratios can be calculated using the following expression:

Gain Settings For Ionization Chambers

The voltage-to-frequency (V/F) converters are most linear between values of 0.5 V and 10 V.  Hence, the gain for each Keithley amplifier for I_o, I₁, and I₂ should be adjusted such that the V/F Converters give results in this range.  The same also applies for Lytle detectors.  Also, when working with Keithley amplifiers, it is essential to remember to set the suppression equal to the inverse of the gain.

The Lytle Detector

The Lytle detector, or the fluorescent ion chamber detector, measures fluorescent x-ray emission.  Fluorescence arises from the de-excitation of electrons into the core hole produced by x-ray photon absorption and is proportional to the probability of x-ray photon absorption.  Hence, fluorescence can be used to measure XAFS.  Fluorescence measurement has the greatest utility when using samples that are dilute, have low K-edge energies, or are very small.  Depending upon the system being studied, it can be effective for concentrations down to one part per million.  Typically, the Lytle dectector is used for samples having greater than 1000 parts per million of the metal ion of interest.  For more dilute samples, it is often necessary to use a germanium detector.  The advantages of the Lytle detector are its much larger solid angle of acceptance and its ability to measure photons at much higher count rates than germanium detectors.  The use of germanium detectors are not covered in this document due to their complexity.

When using a Lytle detector, most samples should be positioned such that the angle of incidence and exit are equal to 45^o, which minimizes elastic scattering into the detector and maximizes the signal from the sample.  The standard Lytle detector sample holder provides the 45^o geometry.  The sample should be mounted on the back of the holder. Additionally, one must insure that the Soller slits are positioned so that the fan of blades points in the direction of the x-ray beam (refer to Figure 2).  For information on x-ray filters, refer to the section How to Select X-ray Filters.

An important consideration for fluorescence measurements is what gas to use in the ion chamber of the Lytle detector. In general, it is desirable to use nitrogen for x-ray energies below 3 KeV, argon between 3-7 KeV, and krypton (or heavier gases) for energies above 7 KeV.  For greater detail, refer to Table 2. Also, refer to the section Gas Ionization Chambers.  When selecting gases for the Lytle detector, the theory is the same as for ion chambers, except that the Lytle chamber thickness is 3 cm and calculations should be based upon the energy of the fluorescence peak of the element of interest rather than the incident beam.  The gas should absorb 90-95% of the radiation passing through the 3 cm distance of the Lytle chamber.  Therefore, it is undesirable to use too heavy of a gas.

To adjust the gain on the Lytle detector, simply move the knob mounted on the front of the detector to the desired setting.  For concentrated samples, the typical setting is 1.  For dilute samples, the typical setting is 10 or higher, depending upon the concentration.  Refer to the section Gas Ionization Chambers for gain settings of ion chambers.

Transmission Measurements

In a transmission measurement, the absorption spectrum of the sample is measured directly, as opposed to fluorescence or electron yield experiments.  Key advantages to the transmission method are its simplicity and the absence of self absorption (nonlinear amplitude reduction effects), which is an inherent problem for fluorescence measurements of concentrated samples.  Hence,  transmission measurements are typically used for concentrated samples.  Transmission data are plotted as Ln (I_o/I₁), which expresses absorption amplitude as a linear function of absorber concentration (and thickness).  For transmission measurements, it is important that the gas ionization chambers be filled with appropriate gas mixtures (see Table 1 in Gas Ionization Chambers for useful gases and percentages of beam transmitted at various energy ranges).  For a typical transmission measurement, the first gas ionization chamber should be filled with a gas mixture that will absorb about 22% of the incident beam.  The second gas ionization chamber should then be filled with a gas mixture that will absorb as much of the remaining beam as possible in order to obtain the best counting statistics.

The following procedure can be used as a guide to preparing transmission samples.  It is based on the assumption that the absorption coefficient (m_metal) of the metal is much larger than the absorption coefficient of the matrix (m_matrix).  If m_metal of the sample is comparable with m_matrix, the matrix will contribute substantially to background noise.  For example, in a sample with two types of metal ions and both present in significant concentration (e.g. PbFe₄O₇), both metal ions will be dominant absorbers.  Hence, the optimum sample mass may be different from the one obtained using the procedure that follows.

The absorption by a sample with absorption coefficient m_s and thickness L is related to the ratio of I_o and I₁ as exp (-m_srL) = (I₁/I₀).  Consideration of counting statistics in a transmission measurement has shown that the optimum product of  m_srL is 2.6, that is when the sample absorbs about 96% of the beam (Stern & Heald (1983), Brown, et. al.).  However, the samples are often prepared in sample holders with standard sizes of 1 or 2 mm.  Therefore, it is practical to achieve this optimum value by adjusting the sample's density instead of its thickness.  In practice, best results have been obtained when the sample is prepared with a density that will absorb about 90% of the beam, that is, when m_srx = 2.3.  For a sample with known composition and density, m_s can be calculated using the following summation:

where f_i is the mole fraction of each element i presents in the sample and m_i is the absorption coeffient of that element at a particular x-ray energy.  For most cases, the metal will be a dominant absorber.  So, for simplicity, the absorption coeffient of the metal is often used as m_s.  Since the effective density of the sample is defined as the mass of the absorber divided by the total volume of the sample, the mass of the absorber can be found using the following expression

where m_a is the mass of the absorber and V_t is the total volume of the sample.  Take m_s to be equivalent to m of the metal of interest.  Since V_t  and L are fixed, the optimum mass of the metal of interest in the sample can be found.  From this, one can directly calculate the mass of the sample to use.  The sample is then mixed with enough inert matrix to fill the sample holder.
 
It is often necessary to mix the sample with an inert matrix such as BN, B₂O₃ or LiCO₃ to obtain the required sample volume.  A good transmission XAFS sample must be uniform, with the compound of interest grounds to a size smaller than its characteristic absorption length, typically less than 4 mm.

How to Select X-ray Filters 

With the fluorescent method of detection one of the chief concerns is noise generated by the scattering of elastic plus Compton radiation by the sample.  X-ray filters may be used to reduce the scattering radiation that enters the detector, making the choice of an x-ray filter an important consideration.

When selecting a filter, the K-edge (or L-edge) energy of the filter should be such that it absorbs much of the elastic plus Compton radiation scattered by the sample, while simultaneously transmitting the desired Ka radiation.  For elements from titanium (Ti) to ruthenium (Ru), it is preferable to select a x-ray filter with element that has an atomic number of one less than the sample – that is, Z-1.  Beyond Ru, either Z-1 or Z-2 elements may be used.  However, if the L-edge of a sample is be measured, it may be difficult to find an element that satisfies the Z-1 or Z-2 condition for the filter.  For example, consider a uranium sample, whose La, Compton, and elastic peaks are illustrated in Figure 4.  The elements satisfying the Z-1 or Z-2 condition are protactinium and thorium, both of which are unavailable to use as filter elements.  Therefore, the periodic table must be searched to find an element that is both suitable and available.  That is, an element must be found with a K-edge energy that will absorb the Compton and elastic radiation from the uranium sample.  A search reveals that strontium is an excellent candidate, with a K-edge energy that will absorb much of the scattering radiation going towards the detector.
 

The x-ray filter should be positioned so that it covers the Soller slits.

One consideration when choosing a filter is its thickness.  For dilute samples, it is often preferable to use a filter of 3 absorption lengths.  For more concentrated samples, a filter of 6 absorption lengths probably will be optimal.  However, each should be tried to ascertain which is best.  Included is a table of selected elements to illustrate this (Table 3).

Resolution and Slit Dimensions

The energy resolution of an XAFS beamline is controlled primarily by the monochromator and the vertical divergence of the beam.  On many SSRL XAFS beam lines, the vertical beam divergence, described by the vertical opening angle of the beam, is defined by the vertical slits upstream of the monochromator.  The vertical opening angle can be calculated trigonometrically from the source-slit distance and the vertical opening of the slits:

where Dq is the angular opening of the slits, s is the monochromator slit dimension, and d is the distance between the source and the monochromator entrance slit.  Distances from sources to monochromator slits for selected beam lines are provided in Table 4 below.
 

Once the angular opening is known, the dispersion of the incident beam can be calculated using the differential form of the Bragg's law
 

where DE is the energy width (FWHM) due to the beam divergence, E is the incident beam energy (eV), q_Bragg is the Bragg angle for the monochromator and Dq is the angular opening of the monochromator slits.  q_Bragg can be calculated from Bragg's law, expressed in terms of energy:

For details on energy resolution obtained when focussing mirrors or other optics are inserted into a beam line, see Sean Brennan's "Flux Calculations for SPEAR."

Monochromator Calibration

Energy calibration of monochromators is needed because their calibration drifts over time due to missed steps by the driving motor, computer problems, or changes in the synchrotron orbits.  Therefore, energy calibration should be checked frequently, at least once a day after new fills.  Reference materials (e.g. metal foils that can be checked out from the SSRL store room) are used as energy calibration for the position of the absorption edge.  Absorption edges for other elements should be found near their tabulated energies after this calibration.  The procedure for monochromator calibration is as follow:
 

Monochromator Calibration 1. Place the reference metal foil between Io and I1 or between I1 and I2. 2. Do a scan to collect an edge on the foil using the same resolution in the edge region for the foil as you are using for samples  3. Plot Ln (Io/I1) or Ln (I1/I2) 4. Check the inflection point of the foil edge. 5. Record the inflection energy.  6. Move monochromator to the inflection energy.  7. Reset monochromator to the reference energy of the metal that you are using.

Taking Offsets

Before data collection may begin, the electronic background signal should be measured.  This is accomplished by taking offsets.  The computer will then be able to subtract the background of electronic noise from the data during collection.  The procedure is both simple and brief:
 

Taking Offsets 1.  Close the shutters. 2.  Collect offsets.

Detuning

Synchrotron radiation may simultaneously satisfy the Bragg condition for multiple orders of diffraction (multiple n).  Bragg's Law is given by
 

nl = 2d sin q

where l is the wavelength, d is the lattice plane spacing (the d-spacing), and q is the Bragg angle.  The fundamental mode is such that n=1, and the harmonics are n such that n>1.  X-rays corresponding to harmonics (n>1) have energies that may interfere with data collection.  These should be removed prior to gathering data.  The angular widths of the diffraction conditions (rocking curves) for higher n are smaller than for the fundamental (n=1).  That is, reducing the parallelism of – or detuning – the crystals of the monochromator will significantly diminish the intensity of higher orders of diffraction, while having minimal impact upon the intensity of the first order.  Detuning causes the first monochromator crystal to be rotated off of the Bragg condition enough to greatly reduce the intensity of higher n, while maintaining much of the intensity of n=1.

How to Determine The Proper Amount of Detuning

To measure the amount of detuning required, a strong sample or foil of the element being investigated is placed in front of the Lytle detector.  The monochromator is then set to an energy below the binding energy of the element.  Thereby, most of the fluorescence emitted by the sample should result from harmonics in the beam, since they lie in higher energies than the fundamental.  Create a table similar to Table 5 that has the following columns: percent detuned, I₀, I_F, and I_F/I₀.  Make rows beginning with the monochromator fully tuned, 5% detuned, 10% detuned, and so on.  Record the values for I₀ and I_F in the table.  Then plot the ratio I_F/I₀ as a function of percent detuning.  When the ratio of I_F/I₀ exhibits asymptotic behavior as it approaches a constant value, the desired amount of detuning has been achieved.

As an example of the procedure for detuning, consider the actual detuning data collected for Uranium at beamline 4-3 of SSRL shown in Table 5 and Figure 5.  The ratio I_F/I₀ becomes asymptotic at 40%.  Therefore, as indicated in Table 5, the optimal detuning is 40%.  However, the experimenter should verify that this level of detuning is actually necessary by comparing the noise levels of scans with different amounts od detuning.

Once the amount of detuning is determined, the direction of detuning must also be determined: whether to detune up or down in Piezo voltage.  The direction of detuning can effect the severity of "glitches" (i.e. intensity spikes in I₀) in data.  Detuning in one direction may reduce or even eliminate glitches present when tuned in the other direction.  A sample of the desired element should be run once with the monochromator tuned in one direction and once in the other.  Qualitative comparison will then yield the best direction to detune.  To measure glitches, determine the positions of the top and bottom glitch, which represent the counts per second of the data.  Then calculate its percent size.  It is undesirable to have glitches with a magnitude greater than 1%.
 

Before collecting data, the detuning should be checked at the lower and upper extremes of the energy region being scanned.  For example, suppose that Uranium is being scanned from 17,166eV to 18,040eV, and it is determined that 20% down is the optimal detuning.  The tuning is then set to 20% at 17,600eV.  The detuning is then checked at the extrema, with results summarized in Table 6.  At the upper end of the region, the tuning is only at 13%.  Therefore, the tuning should be adjusted as to insure that its value is 20% at the upper end.

Detuning should be checked often, and one should be mindful that the detuning may change as the temperature of the monochromator changes with variations in x-ray flux.