One of the strengths of the X-ray absorption fine-structure (XAFS) technique is that it is applicable to a vast range of materials and systems, and spectra can be measured under a great variety of sample conditions. The optimal forms of XAFS samples are correspondingly diverse. Additional material on samples and experimental design can be found in Heald (1988), Bunker (2010), Iwasawa et al. (2017) and references therein.

XAFS samples can consist of solids (single crystals, polycrystalline materials, nanoparticles, glasses or amorphous solids), liquids (pure substances, solutions, suspensions or eutectics), atomic or molecular gases, combinations of these, such as fluids adsorbed on solids, and composite structures. Because of the wide range of materials that can be studied, and the strong dependence of X-ray absorption coefficients on energy E, it is necessary to design samples and their containment cells as part of an integrated experimental system. Careful thought and attention to the preparation of XAFS samples is important if one wishes to obtain accurate data. Inadequate planning and execution of sample preparation can easily lead to distorted and noisy spectra, leading to incorrect interpretation of the data and to systematic errors in the numerical parameters that are determined from data analysis.

The physical form of samples can consist of deposited thin films or multilayers, powders deposited on substrates or in pellets, or slabs of material, including solid biological samples, fluids such as protein solutions or catalysts with adsorbed gases that are contained in a sample cell, oriented single crystals and partially oriented films. These are normally encapsulated in a sample cell with windows that are partially transparent to X-rays at the relevant energy.

X-ray absorption coefficients of any material μ(E) decrease roughly as 1/E³ at energies between the absorption edges; because the absorption depends exponentially on μ(E), the absorption increases dramatically as the incident X-ray beam energy is lowered. This is illustrated in Fig. 1. For example, the absorption coefficient increases by about a factor of eight if the X-ray energy is halved (assuming that there is no absorption edge in this range), and the fraction of X-rays transmitted depends exponentially on the absorption coefficient. Depending on the thickness of the material, this can result in a very large changes in absorption with energy, which has profound implications for the suitable choice of thickness of the sample, window materials, ambient gases etc. For this reason it is good practice to calculate the absorption coefficients for the sample and the containment cell windows in the actual energy range of interest. Computer programs are readily available (built into the commonly used XAFS data-analysis program suites, and Mathematica from Wolfram Research) to calculate the absorption for various materials, or it can be performed by elementary means (for example a spreadsheet) using atomic cross sections per mass (`mass attenuation coefficients') accessed from servers such as http://www.csrri.iit.edu/mucal.html or http://physics.nist.gov/PhysRefData/FFast/html/form.html .

Figure 1 Log–log plot of mass attenuation coefficients for platinum: photoelectric absorption (solid line), elastic plus inelastic scattering (dotted line) and total (dashed line). The approximately straight lines between the edges indicate approximate power-law behaviour: approximately 1/E3. Data from http://physics.nist.gov/PhysRefData/FFast/html/form.html .

When preparing samples for XAFS, special care must be taken not to degrade the nature of the chemical sample during sample preparation. Grinding can induce heating, which can alter some samples; chemical reactions with window materials or adhesives can alter some solution samples. Some standard methods of sample preparation for X-ray fluorescence spectrometry, such as fusion (making a solid solution of the sample in lithium borate), are mostly inapplicable for XAFS because heating and dissolution will generally chemically alter the sample. This is not a concern for X-ray spectrometry if elemental concentrations are all that are sought, but it is a problem for XAFS and the determination of chemical speciation, and other sample-preparation methods are needed.

Especially hazardous substances such as highly toxic materials, radioactive materials or biohazards may require additional levels of containment, as do extreme environments: cryogenic, vacuum, high pressure, high voltage etc. Safety Data Sheets should always be consulted before handling materials or designing containment cells, which may themselves make use of hazardous materials.

The various experimental modes (transmission, fluorescence and electron yield) impose their own requirements on sample characteristics. These are described in detail elsewhere in this volume.

In transmission mode one measures, as a function of energy E, the fraction of the incident X-rays (I_o) that are transmitted through the sample (I), and the desired signal μ(E) is obtained from the natural logarithm of I_o/I. The sample may consist of self-supporting foils, materials deposited on a substrate, for example sputtered films, or small particles that are either uniformly deposited on a supporting film of low absorption or mixed into a material of low absorption (for example boron nitride, cellulose or polymers such as polyethylene) that is enclosed or compressed into a pellet.

The most basic requirement is that the sample must be sufficiently thick that there is sufficient absorption contrast (a large enough edge step) to accurately measure the variations in intensity as a function of energy, but thin enough that the sample transmits sufficient photons to obtain an adequate signal-to-noise ratio from the transmitted beam I. It is also important that the transmitted beam flux is much larger than the flux of spurious undesired photons that may be measured by the transmitted beam detector owing to air scatter around the sample, harmonics transmitted through the sample, fluorescence emitted by the sample, transmitted photons of lower energy from the tails of the monochromator resolution function and similar small but non-negligible effects. These small effects (which can be measured and can be calculated without great effort) are always present to some degree, and the goal is to reduce them to acceptable levels relative to the signal. These errors become more important when the sample thickness is increased and so are called `thickness effects'. Although there is a theoretical optimum thickness for optimizing the signal-to-noise ratio, practical factors indicate that somewhat smaller sample edge steps Δμx ≃ 1 are preferable in order to reduce systematic errors.

It is important to minimize `thickness effects' in transmission mode and also `self-absorption' (or `over-absorption') effects in fluorescence measurements. Both of these have the consequence that the measured spectra depend nonlinearly on the true absorption spectrum. Some materials have strong absorption features (`white lines') at the edge which can have a peak absorption several times the size of the edge itself. Thickness effects and self-absorption effects will depress the apparent absorption of these features and they will also reduce the measured EXAFS amplitudes, reducing the apparent coordination numbers or otherwise interfering with data analysis.

Normal data-analysis methods assume that the measured spectra have a linear dependence on the true spectrum, although numerical corrections can be applied in some cases when this assumption is invalid. Specifically, the measured spectrum is assumed to be some function A(E) times the true spectrum plus a background B(E): μ_measured = A(E)μ_true + B(E) + noise, where A(E) is a function that is smoothly dependent on energy (or is constant) over the range of interest and the energy dependence of B(E) is smooth enough that it can unambiguously be removed by numerical background subtraction without significantly altering the data.

Many of these issues are moot when preparing samples for electron-yield measurements because they only detect electrons that are emitted from within ∼100 nm of the sample surface, so the sample is always effectively thin. Electron yield has its own concerns, however: if the sample is not sufficiently conductive, local charging of the sample can cause systematic errors and artefacts, especially in a high-intensity beam. Mixing conductive particles such as graphite into the sample or applying a thin conductive coating, and performing measurements with a lower intensity beam, can mitigate this kind of problem.

If the composition of a sample is known to be very homogeneous, and the sample contains a well isolated `reporter' fluorescence emission line at lower energy than the edge of interest, it may be possible to sidestep self-absorption effects by using inverse partial fluorescence yield (IPFY; Achkar et al., 2011).

X-ray beams always have some spatial variation in intensity due to optics and partial beam coherence, for example from an undulator. This does not cause a problem if the spatial frequency of beam variation is either much larger or much smaller than the spatial frequency of inhomogeneities in the sample. However, if the spatial frequencies of the beam and the sample are comparable, any beam motion over the sample can create large spurious variations in signal. For example, if the beam has variations on a 100 µm length scale, and the sample also does, spurious artefacts in the data may occur. This is one reason why spatially uniform samples are important. Other reasons are given below.

As mentioned above, although transmission measurements are conceptually simple, if the sample is nonuniform in thickness then the measured spectrum will depend nonlinearly on the true spectrum. Particularly damaging are thin regions, or `pinholes', in the sample. The variation in sample thickness over a sample can be described with a probability distribution P(x), where P(x)dx is the proportion of the sample area presented to the beam that has a thickness between x and x + dx. The nonlinear terms are directly related to the second-order and higher order cumulants of the sample-thickness distribution; if P(x) were a Dirac delta function (i.e. of zero width) the measurement would be ideal. For a Gaussian P(x) we obtain (exactly) , where and σ² are the average thickness and the variance of the thickness distribution, respectively. For a uniform distribution between and , .

More generally (and exactly, for any distribution for which cumulants exist), where C_n are the cumulants (specific combinations of power moments) of the thickness distribution. These expressions (Bunker, 1984, 2010) can be used to quantify the errors associated with sample-thickness variation and, with some effort, to correct for them. Since the second cumulant of the distribution is always positive, thickness variations always tend to reduce the apparent absorption relative to the true absorption.

Variations in sample thickness can and should be checked visually, preferably by measuring the signal versus position on the sample. It is important to realize that optical absorption lengths and X-ray absorption lengths may be very different, so this visual test is not foolproof. Visually monitoring variations in transmitted intensity as a means of checking sample inhomogeneity may not be reliable for a sample that absorbs weakly in the UV–visible spectrum compared with the X-ray spectrum. The cumulant analysis mentioned above could be used in the UV–visible range to characterize the cumulants of the thickness distribution, which could then be used to estimate errors or apply corrections to the X-ray data.

The samples for transmission and fluorescence measurements are often composed of small particles, but the meaning of `small' depends on the material being measured and on the energy. Particles for measurement should be small in size compared with the absorption length 1/μ of the material in the energy range of interest. This should be calculated. The resulting particles should then be dispersed as uniformly as possible over the cross-sectional area of the sample. There are several ways to do this, as described below.

A classic but somewhat less well controlled way to separate particles by size exploits the tendency of small particles to adhere better to an adhesive surface compared with larger particles. It is possible to make surprisingly good samples by brushing particles onto adhesive tape (Scotch Magic Tape is suitable for many purposes) and then mechanically removing the larger particles by rubbing. Uniformity can be judged visually, with the caveats mentioned above; particle size can be judged approximately by its texture (grittiness) or by more sophisticated means such as microscopy.

The simplest way to prepare sufficiently small particles for some samples is to generate them under conditions in which they naturally form, for example through precipitation from solutions; nanoparticles can often be prepared this way. Other materials may require mechanical grinding using laboratory mills (for example a rotor or ball) or simply by using a porcelain or (better) alumina or agate mortar and pestle. It is important to ensure (or test) that the heat of grinding does not alter the molecular structure of the sample. Even a few percent of damaged sample can pose problems of interpretation in data analysis, although it may be possible to subtract the effect numerically if the spectrum and quantity are known well enough. This damage can be checked by complementary methods such as powder diffraction or UV–visible or other spectroscopies, but it is still possible to obtain false-negative results using such tests.

Commercial sieves are readily available for sequentially separating particles by size. As seen in Fig. 2, a useful simple approximation is that the maximum particle size in micrometres is ∼15 000/S, where S is the sieve-mesh wire density in wires per inch (a common specification in the US). This implies that even an apparently fine mesh sieve of S = 300 wires per inch still lets through particles as large as ∼50 µm which, in the Fe₃O₄ example above, is still an order of magnitude too large. In such cases a simple sedimentation method can often be used. In a small beaker, the sieved particles are suspending by stirring into a liquid that is chosen to be nonreactive with the sample (for example acetone for Fe₃O₄) over the several minute timescale of sedimentation. The larger particles sediment to the bottom of the beaker, while the desired smaller particles remain suspended. Assuming approximately spherical particles, the sedimentation rate is easily calculated from Stokes's law (see, for example, Bunker, 1984, 2010); it depends on the size of the particles, the densities and viscosity of the liquid and the density of the sample material. Explicitly, the time for which it necessary to wait to ensure a maximum (roughly spherical) particle size R is T = 9ηh/[5gR²(ρ − ρ₀)], where h is the drop height, g is the gravitational acceleration, η and ρ₀ are the viscosity and density of the liquid and ρ is the density of the material. After stirring, one waits for a time that is calculated from the desired maximum particle size (Fig. 3); the particles that are still suspended in the liquid are then decanted and the particles separated from the liquid by evaporation or vacuum filtration are then further dried and dispersed in the sample. If necessary, to speed up the process (for example for particles that have a density that is not much greater than the liquid) the particles can be sedimented in a centrifuge.

Figure 2 Maximum particle size (µm) versus sieve mesh (wires per inch).

Figure 3 Required sedimentation time for a 5 cm height in acetone as a function of desired particle size and sample density.

The resulting particles may tend to spontaneously aggregate, which should be prevented. Adhesive tape tends to reduce this effect because the particles may adhere better to the tape than to each other. Good samples can be made by the mechanical mixing of particles into diluent particles of another, usually less absorbing, material such as boron nitride or a polymer, followed by pelletization in a press. The key objective is to obtain approximately the desired areal density of the material of interest, which should be calculated (it does not have to be exact), and to mix the sample constituents thoroughly. An inexpensive dentist's amalgamator can be useful to mix the sample. It is also possible to make samples containing particles suspended in a liquid, which is then rapidly cooled to form a solid. The key objective is to disperse the particles in a uniform manner. Another subtle effect can be an undesired de-randomization of the orientations of plate-like particles when pressed into a pellet, which can give rise to unintended orientation (called `texture' in crystallography) of particles and undesired X-ray polarization dependence in samples. This potential problem can be tested for by varying the sample orientation or can be eliminated by magic angle spinning (for a simple explanation, see Bunker, 2010).

Solutions (solid and liquid) are described in more detail in Bunker (2023). The considerations for making liquid solution measurements, and the choice of using transmission versus fluorescence mode, are essentially the same as solid samples except that X-ray windows are used to contain the liquid, and liquids are more prone to spatial inhomogeneities if precipitation from solution occurs. Such windows should not contain significant quantities of the element of interest (which should be checked), should not react with the sample and should be minimally absorbing of X-rays to an extent consistent with their required mechanical properties. As in all experiments, design compromises must be made. We note in passing that it is possible to measure a free horizontal liquid surface without using an entrance window by deflecting the incident beam downwards onto the liquid using an X-ray mirror or a diffracting optic.

A typical example of an XAFS solution sample is a highly concentrated metalloprotein solution suspended in buffer. Metalloproteins are typically large molecules, and a protein solution of high concentration may still only be in the parts per million range of concentration for the element of interest. The most appropriate detection mode in this case is normally fluorescence detection, although effective concentrations can be increased by adsorption onto a surface. Mitigation of radiation damage usually requires the measurements to be made on frozen solutions at cryogenic temperatures, to inhibit the mobility of radical species and hydrated electrons, but if care is taken to replace the samples before they become too damaged, room-temperature measurements can be performed on liquid solutions. This is described further elsewhere in this volume.

Radiation damage is a potential problem not only for proteins but for other systems, even some solids. Undulator beams may be of sufficient intensity to photolyze water in the buffer, creating small bubbles in the liquid, which are holes in the sample as far as X-rays are concerned. These inhomogeneities can strongly interfere with measurement. Radiation damage to solid samples also may be a significant problem. Remote visual observation of the sample with an inexpensive camera can be helpful in monitoring its state.