When x-rays alter the course of your experiments^*

The interaction of electromagnetic radiation with matter is a complex process and it is dependent on the photon energy and the nature of the material. This section is not intended as a comprehensive treatise on absorption, but instead to provide understanding for the large group of synchrotron radiation users whom are non-specialists in this field, of which effects are likely most relevant in the context of radiation induced sample interference. For comprehensive details there are several textbooks available [15, 16].

The different energy dependent absorption cross sections of processes that play a role when Iron is exposed to radiation are shown in figure 2. For synchrotron radiation-based effects, the energy range of 5–30 keV is most relevant and important, and here the photo-electric effect is the dominant interaction. This is similar for all other elements as well. For absorption calculations in the 50–30 000 eV range one can use the data from the Henke tables [17]. Most web-based applications are based upon these tables.

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An important fact to realize is that photon absorption triggers a cascade of secondary processes. The initial absorption of a photon with energy E_ph = hν, in the 5–30 keV range, will mainly result in the creation of a photoelectron with an energy E_el = hν − E₀, where E₀ is the energy level of the excited electron. The absorption cross section is maximum for electrons whose level is close, but lower, to the energy of the impinging photon. The emitted electrons have an energy high enough to create a cascade of secondary electrons [21]. There are three aspects that then require attention: (i) the distance that electrons can travel in matter; (ii) the effects of sample heating due to absorption; and (iii) the life-time of defects or excited states that have been created.

The mean free path of electrons between inelastic scattering events in matter is energy dependent but in general below 50 nm [18, 19]. Figure 3 shows the mean free electron path in water as a function of electron energy, which can be considered close to a universal curve valid for most matter.

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In the solid state, such as crystalline diamond, and with energies of up to 250 eV, this corresponds to ranges of around 0.2 nm and a lifetime of about 100 fs [20], increasing to 10 nm at around 1 keV [21]. However, the mean free path is not the travel range of an electron, but rather the average path length between consecutive interactions. The total path length can be calculated, using for instance the continuous slow down approximation. For electrons of 10 keV the total path length corresponds to the order of microns. Detailed modelling studies of the interaction between high energy electrons and matter have been made [22].

Since the interaction is not a single step process and a photoelectron with sufficient energy can create a cascade of secondary and higher generation electrons the aggregate volume affected by a temporary excess of free electrons will extend to several microns. A simulation of this process in a protein crystal is shown in figure 4.

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The extent of the photo-electron 'cloud' and the lifetime depends on material constants and the state of matter. For micro focus beamlines, the important fact is to realize that the effects can be found even outside the direct x-ray beam.

The relevance in the context of this manuscript, is that x-ray photo absorption is a complicated and multi-step cascade process. Excess electrons will exist; for a limited time after photon absorption; in a limited volume larger than a single free photoelectron distance; in an initially increasing number but with time, reduced energy; and until they reach energy levels where they will be reduced to the source of local heating and for instance couple with phonons. Depending on the medium, radiolysis products may also exist for a longer time and will temporarily change the local environment and thus can influence time-resolved experiments.

When absorbed, electromagnetic radiation will increase the temperature of materials. The questions 'how much is the temperature increased' and 'is this relevant for the experiment?' must then be considered.

The first approximation is to calculate the maximum temperature increase under the assumption that there is no heat exchange between the irradiated volume and its surroundings. If that calculation causes concern, one can attempt to model the temperature increase.

For the adiabatic thermal increase one can use:

$$\begin{equation}{\Delta}T=A\frac{{\Delta}Q}{M{C}_{\mathrm{p}}}=A\frac{NE{\times}1.6{\times}{10}^{-16}}{{V}_{\text{irr}}\rho {C}_{\mathrm{p}}}\enspace (\mathrm{K}\enspace {\mathrm{s}}^{-1}),\end{equation} \tag{ 1 }$$

ΔT is thermal increase, A the fraction of photons absorbed by the sample, N number of photons in the beam, E the photon energy (keV), V_irr the irradiated volume, ρ the specific mass density and C_p the materials heat capacity.

A practical remark is that in real experiments, the beam is generally smaller that the sample. If a temperature-controlled sample environment is used in which the thermal sensor does not measure the temperature at the position where the sample intercepts the x-ray beam and hence there might be an erroneous reading of the sample temperature of the material probed by the x-ray beam.

In modern macromolecular crystallography, to limit radiation damage effects, the sample is rapidly cooled to around 100 K in order to create amorphous ice around the protein crystal. A transition from amorphous to crystalline ice, which can occur around 130–140 K will be detrimental to the crystal. Finite element modelling (FEA) on thermal effects have extensively been explored in this research community but the methodology is to be considered for materials science applications as well.

Assuming forced cooling (FEA) [24], a crystal of 100 micron exposed to a 50 micron beam of 10¹⁵ ph s⁻¹ mm⁻² would heat the crystal by ΔT = 4.1–5.6 K, with a temperature gradient of <0.2 K over the total crystal volume and that steady state was approached 100–400 ms after the start of the exposure. Another paper [25] also considered the same problem but now using different photon energies and crystal configurations. The conclusion of these calculations is that a thin (50 μm) crystal exposed to 10¹³ ph s⁻¹ mm⁻² would increase in temperature by 6 K within 4.5 s, but that a thicker (>100 μm) crystal exposed to the same beam would increase 18 K over 52 s before reaching steady state. In view of the factor of 100 difference in flux the authors remarked [26]. 'The calculated temperature increase appears to be very sensitive to the simulation parameters'. Experimental data obtained using glass balls and an imaging infra-red camera showed that a maximum increase in temperature, with respect to the coolant gas temperature (100 K), of 20 K occurred [27]. Similar experiments attempted [28] using ruby spheres (Al₂O₃) found an increase of 70 K over 25 s.

It is difficult to distill a comprehensive picture from such modelling and empirical methods since, unfortunately, different authors include or omit different details. However, the global picture appears to be that with cryo-stream cooling, it is feasible to limit the temperature increase in the sample portion exposed to the direct beam to 20–40 K (authors estimate) with beams up to 10¹³ ph s⁻¹ mm⁻².

In more complicated sample configurations, the modelling complexity increases. A modelling study of room temperature study of gold nanoparticles [26] sandwiched between Kapton sheets and exposed to 6.3 × 10¹³ ph s cm⁻² (12.4 keV photons) showed an increase of 30 K in temperature—but the measured increase was just 4 K. The effects of thermal contact between the sample and a heat sink have also been investigated by the thermal increase of a 100 nm diameter semiconducting InP wire. The simulations showed an increase of 8 K when in contact with a heat sink and 55 K without contact, when exposed to 10¹² ph s⁻¹. When a realistic SR pulse train, instead of a continuous exposure, is simulated it is possible to see thermal decay between pulses, i.e., the reaction time is very fast [29]. Similar conclusions with respect to the maximum temperature increase of Bi₂Sr₂CaCu₂O₈₊ nanocrystals when exposed to SR pulse trains were reached by using a combination of finite element analysis and Monte Carlo simulations [30].

A special case is the situation where nanoparticles with a large absorption cross section (Pb) are embedded in a poor heat conducting matrix of lighter elements [31]. Here one has to take the particle size and the extent of the photoelectron cloud into consideration. If the latter is larger than the particle dimension most of the energy, independent of the particle absorption cross section, will be deposited in the matrix. Taking dimensional considerations into account a still considerable gradient of 33 K between the Pb and the matrix exists at a temperature of about 600 K when exposed to a relatively low bending magnet flux [31].

Direct measurements of beam heating have been possible using on-line differential calorimeters (DSC). A relatively small increase of ΔT = 0.2 K was found when a Sn particle was exposed to a micro focus beam (0.02 μm², 15 keV, flux unknown) [32]. Incorporation of an on-line DSC for powder diffraction measurements on an undulator beamline enabled in-beam heating to be observed and taken into account when interpreting the phase transition data [33]. Here there were no absolute temperatures given but instead the heat flux dH/dt (mW). In diffraction experiments on PbMgNbO, Chernyshov [34] noted differences of 100 K in sample temperature between an undulator and a bending magnet beamline, even whilst the sample was actively cooled in a cryostream. This appears to be a rather extreme case.

As shown above both modelling as well as direct temperature measurements can also be fraught with issues. A priori knowledge of the sample's thermal behaviour without exposure to an x-ray beams is therefore required to detect and distinguish heating effects. For example, in a time-resolved experiment during a phase transition it was noticed that the transition occurred 8–10 degrees below the transition temperature when compared to the controller set temperature [35]. In another experiment [36], shedding light on the difficult problem of beam induced thermal gradients in liquids used SAXS to observe the de-mixing in a binary liquid and used the Ornstein–Zernike formalism to determine the temperature of the solution. A rise of 0.45 K in the spot exposed to the direct beam of 10¹³ ph s⁻¹ mm⁻² was observed.

The tentative conclusion that can be drawn from the literature is that for experiments above ambient temperature and pressure, in-beam temperature increases are measurable but probably limited to several degrees. This is especially true with thermally insulating samples, like polymers or ceramics, where the local temperature can be some degrees off. The main issue is that when accurate temperature control is required, the temperature should be measured at the position where the beam hits the sample. It is also then important to verify that the temperature sensor is not also influenced by exposure to the x-ray beam or to the surrounding photoelectrons that result. At cryogenic temperatures in vacuum, when using a highly focused undulator, one can expect substantial thermal heating if the sample is not mounted on a heat sink of some sort. The thermal read-out could be rather different from the real sample temperature.

Absorbed radiation has different effects depending on the medium that absorbs it. Intuitively one can expect that effects in liquids will be much more-short lived than some of those that can exist in the solid state. There are questions of mobility and life time to consider. That radiation induced excited states can exist for long times is evidenced by the fact that latent images in exposed photographic film can exist for up to 50 years and that thermal photo luminesce, due to absorbed cosmic radiation, is used to determine the age of archeological artefacts and even rocks [37]. In daily life the self-darkening sun glasses point to reversibility and the need for continued exposure to remain in one or the other state [38].

2.4.1. Soft matter

Radiation processing of polymers is a common process that finds various applications, as reviewed by Makuuchi and Cheng [39]. Schnabel explains effects in polymers exposed to both non-ionizing as well as ionizing radiation [12]. In reality, the most used radiation sources are γ-rays but this is a more practical than fundamental choice. The higher penetration power allows larger objects to be irradiated with a more uniform deposition of energy. A commonly used materials parameter is the 'G value', which is defined as the 'chemical yield of radiation in number of molecules per 100 eV of absorbed radiation' [39] (although other definitions are also in use [8]; 1 molecule/100 eV = 1.036 × 10⁻⁷ mol J⁻¹ (or 0.1036 μmol J⁻¹)). Values for cross linking and scission for high density polyethylene (HDPE) are respectively G_cl = 0.96 and G_sc = 0.48. For isotactic polypropylene (iPP) the values are G_cl = 0.2 and G_sc = 0.3 but surprisingly for the chemically similar atactic polypropylene one finds G_cl = 0.3 and G_sc = 0.45. Values for polystyrene are <0.02. (See [39]). Whatever the values are, it will be clear that each absorbed 10 keV x-ray photon can cause up to 100 events. To place this in context, an order of magnitude calculation shows that on a 10 keV, 10¹³ ph s⁻¹, 0.1 × 0.1 × 0.2 mm³ irradiated HDPE sample, every chain of 5000 monomers sees a cross linking event every 0.02 s. Hence it should be no surprise that after a 10 min exposure to a focused undulator beam the sample behaves more like a thermoset cross-linked polymer instead of showing thermoplastic behavior.

An example of a relation between the change in average molecular weight as function of radiation dose can be found [12]:

$$\begin{equation}\frac{1}{{M}_{\mathrm{w},D}}=\frac{1}{{M}_{\mathrm{w},\mathrm{0}}}+\left(\frac{{G}_{\mathrm{s}\mathrm{c}}}{2}-2{G}_{\mathrm{c}\mathrm{l}}\right)\frac{{D}_{\text{abs}}}{{N}_{\mathrm{A}}}\end{equation} \tag{ 2 }$$

Here M_w,D is the average of the molecular weight distribution after a radiation dose D_abs, whilst M_w,0 is the original average. The example above is for vinyl polymers with an initial random molar mass distribution, i.e., a rather special case, but it illustrates the danger of sample modification during an experiment when one realizes that D_abs is a time dependent parameter.

The chemical structure of polymers has a bearing on how they respond to radiation. Methyl groups and halogens tend to increase the degradation while aromatic rings in the main chain tend to reduce the effects [39].

It is surprising that while most soft matter researchers using synchrotron radiation are familiar with radiation damage, there is little common literature or overlap with the community that use radiation as a tool. Most more quantitative manuscripts relate to γ- or VUV-radiation. However, to our knowledge there are few manuscripts that examine the activated sites themselves and most deal with macroscopic effects and use mechanical testing to assess how the material properties have changed. The lack of fundamental expertise is surprising since it is well known that most polymers suffer from exposure to light and there are many manufacturers that use additives (e.g., Irganox™) to prolong the life time of polymers exposed to light.

In electron paramagnetic resonance experiments on cross linked polyethylene exposed to γ-rays, it was found that the main issue was scission of the C–H bonds, and consequently the creation of a free radical and paired electrons that were mobile along the backbone of the polymer [40]. At non-cryogenic temperatures these phenomena were all rather short lived (<minutes).

By using electron spin resonance and thermally stimulated luminescence on ultra-high molecular weight polyethylene (UHMWPE), polyetheretherketone (PEEK) and polycarbonateurethane (PCU) samples exposed to broadband x-rays (maximum energy 50 keV), it was found that in UHMWPE an order of magnitude more free radicals were formed than in PEEK [41]. These were eliminated on two different time scales. While 40% of radials decayed within several hours, the remainder decayed to oxygen centered radicals over a period of months. In PEEK the decay time was on the order of weeks.

Using x-ray spectroscopy around the C-absorption edge (≈300 eV) to examine the effect on individual bonds, it was shown that the NEXAFS spectrum changed as a consequence of the radiation [42]. In such cases, a cross correlation is sometimes possible by checking if there is any mass loss in the sample, which is a clear indication of damage. However, there are cases where here is no mass loss but still a change in the NEXAFS spectrum. If one is not aware of this effect one could draw erroneous conclusions regarding the structure. See figure 5.

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The authors of this study also showed that irradiation in the presence of atmospheric O₂ resulted in a larger amount of damage. This is probably related to the amorphous component since O₂ has more difficulty penetrating crystalline parts.

The main conclusion, based upon a limited number of manuscripts, is that the main damage caused by irradiation is the scission of C–H bonds and cross linking. There is also a variety of electronic defects, but these are temperature sensitive and do not play a large role in the processing of polymers and in general have limited life times and/or do not alter the structure much. Experiments by Goderis [43] have shown that the damage can lead to changes in the glass transition temperature, which can be measured by differential scanning calorimetry, though the structural evidence of which was hard to find in the SAXS patterns.

2.4.2. Liquids and solutions

Empirically, it is known that the interaction of high energy radiation with super-heated liquids can generate macroscopic effects. This is the principle of the cloud and bubble chambers, the long time work horse detectors for high energy physics research, which generated Nobel prizes for Charles Wilson (1927) and Donald Glaser (1960). These devices enable not only the primary interactions of very high energy particles to be observed, but also many other secondary high energy particles that act as sources for the nucleation of gas bubbles along their path in the liquids.

In the 1960's, Swallow produced a monograph detailing the interactions of several forms of radiation with a variety of liquids and solutions, including which intermediaries could be formed and gave estimates of their life-times [44]. In 1975, Roots and Okada [45] did an exhaustive study on H₂O/DNA solutions to estimate the damage and provided a list of radiation induced solvent intermediates, their life time and their diffusion coefficients, which allows an estimate of the extent of the radiation influence around the point of photo absorption. It should be noted that this work did not take into account the paths of the small fraction of scattered photons inside the sample, which extends the range of the interactions to a much larger volume, although with a much lower radiation product yield. While this fraction is low, it can influence the sample as will be discussed later [46]. A more recent manuscript details reactions and lifetimes in a variety of solutions and in aqueous solutions at different pH values [47] (figure 6).

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The principal radicals are the hydrated electron (e_aq ⁻) which is a reductant (reduction potential E_o = −2.87 V) and the hydroxyl radical (OH) which is an oxidant (E_o(OH/OH⁻) = 1.90 V in neutral solution. In different pH regions these values change [47]. The situation can be quite complex in real solutions, since different components can have differing effects on the life time of individual radiolysis radicals [8]. This is especially true in aqueous solutions, since the local chemical environment around the point of photon absorption can temporarily be changed, generating for instance changes in pH which can last up to 4 ms and diffuse over a distance of 4 μm around the point of absorption. With a high enough flux, chemical reactions inside the beam might therefore show different kinetics or be inhibited [48]. Electron/liquid interactions are also important in environmental electron microscopy cells [49–51] and it is likely that there are similarities in the observed phenomena.

It is perhaps ironic to note that while some research groups use radiolysis products to create nanoparticles in solution [52, 53], others use very intense x-ray beams to follow the kinetics of the formation of nanoparticles in solution scattering experiments. A brief survey on the application of radiation to form nanoparticles reveals that in the case of organics, cross linking is the main driving force, whilst in the case of inorganic nanoparticles the change of chemical environments and the creation of free radicals will drive particle formation [54]. Apart from the direct effects of the radiation itself, it is also possible that the presence of a solid/liquid interface plays a role. An example where a synchrotron beam was used to induce particle formation without being the experimental probe beam uses this solid/liquid interface [55]. The particles were subsequently analyzed by SEM etc. Although the authors do not provide an exact dose estimate it could be noted that these irradiations were performed on a superbend magnet beamline with a critical energy of around 3 keV using a polychromatic beam (1–20 keV). Depending on the photon beam size the photo-electron production rate is comparable to a monochromatic undulator beamline.

Further information on radiolysis products in a variety of hydro carbons and chlorinated hydrocarbons [47] and on reaction products and reaction rate constants for both polymers as well as bio-based polymers can be found in a monograph by Schnabel [12].

2.4.3. Solid state

Although radiation damage and deterioration in protein crystals has been studied extensively [11, 23, 71–75] less attention has been given to radiation effects that do not destroy the crystals but change them. This is especially the case in redox-active metalloproteins where the redox state of the active center can be changed by irradiation, and thus can lead to erroneous interpretations of their catalytic activity. This is unlikely to be specific for protein crystals but can act as a model for inorganic crystals as well.

Many proteins rely upon high-valent 3d transition-metal ions (such as copper or iron) for function, where the oxidation and coordination state of the metal determines the redox properties and molecular interactions of the protein [76]. Such metal centers are prone to photoreduction, whereby photo-electrons reduce the high-valent active metal site(s), thereby altering their electronic structure and bonding interactions. These electrons are still mobile at the cryogenic temperatures where most protein diffraction experiments are carried out and propagate rapidly to electrophilic centers [77]. The formation rate of photoelectrons is fast (10's of fs) and these x-ray induced effects accumulate rapidly (on the seconds to minutes long duration of a typical x-ray data collection), and can give rise to mixed redox and structural states that complicate interpretation of the underlying chemistry. Thus, in addition to being subject to the same radiation induced issues of local chemical modification and global changes that limit diffraction, analysis can be directly impacted and compromised by x-ray driven changes in the valence and oxidation state of the metal centers.

Such x-ray induced effects are manifold in heme [78, 79] and copper [77] containing metallo-proteins, not even more exemplified in studies of photosystem II (PS-II), a key component of the photosynthetic apparatus. Light captured by the reaction center drives water oxidation and oxygen generation through a bound Mn₄CaO₅ cluster that forms the redox center of the oxygen-evolving complex (OEC) [80]. The redox chemistry is complex, involving cycling through five intermediate S-states (S0-S4s) [81]—and unravelling the structural basis of the O–O bond formation though the cycle presents a particular challenge. Complicating this, PS-II is very radiation sensitive and x-ray induced photoreduction of Mn ions in the OEC has significantly complicated interpretation of the mechanism involved [68, 82–84]. Specifically, x-ray induced reduction of the OEC Mn(III) and Mn(IV) ions to Mn (II) by solvated electrons has been shown to disrupt the bridged Mn₄CaO₅ structure, breaking the Mn di-µ-oxo units, and giving rise to a mixture of metal bound sub-states in the resulting x-ray crystal structures.

While these x-ray photoreduction effects are essentially unescapable, they can also be harnessed in experiments designed to use x-rays to control and drive redox reactions within the crystals. An early, striking example of this approach used x-rays at different wavelengths (0.9 and 1.4 Å) to capture intermediate states of the heme iron-oxygen complex in the hydroxylation reaction of camphor by P450cam [85]. As another example; x-ray-induced photoreduction enabled a catalytically relevant Michaelis complex structure of ferrous aldoxime dehydratase to be captured from crystals of the inactive ferric aldoxime complex [86].

Photographic materials, silver halogenides embedded in gelatin and deposited on a plastic film, have played an enormous role in the 20th century. It is rather ironic that only near the tail end of the mass use of this technology one has developed tools that can show in real time what actually happens in the AgBr grains when exposed to radiation. In this case the x-ray beam is both the irradiation tool as well as the probe beam, for XRD, used for the experiment. The photo chemistry of AgBr is well known. Br⁻ + hν → Br + e⁻ and e⁻ + Ag⁺ → Ag⁰. On the nanoscale this has as consequence that the AgBr lattice will distort due to the buildup of Ag crystalline regions. The resulting stress will cause the AgBr crystalline grains to break up in several smaller grains which can rotate due to the stress relaxation taking place [87]. The time scale with which this occurs is on the order of 10–30 s. The authors showed that this is a mechanical effect taking place due to the photo chemistry, since under similar conditions Ce and Ti oxide particles did not show this kind of behavior.

3.2.1. Induced phase transitions

3.2.2. Particle growth in matrix

3.2.3. Electronic/conductivity effects

Current generation due to absorbed x-rays has been used as a tool to characterize single nanowire solar cells [97]. See figure 8. For this, a nano-focus x-ray beam was aimed at such a solar cell in order to measure the spatial variations in the charge collection probability. Whereas many experimenters do not take creation electron–hole pairs into account when assessing the effects that radiation may have on their samples, these experimenters effectively harnessed this current as a tool.

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That the conductivity of materials can be influenced by exposure to radiation is well known in semiconductor and photovoltaic research and industries but less well studied in other materials. A phase transition in an antiferromagnetic manganese oxide insulator irradiated at T < 40 K has been observed to change to a metallic ferro magnetic state when exposed to x-rays [98]. Neutron diffraction showed a doubling of the crystalline unit cell. This conducting state persisted after irradiation was stopped but was sensitive to thermal cycling and high magnetic fields. The authors assume that the effect was due to photoelectron interaction with the samples. In a later paper, the conductivity is suggested to be due to electron tunneling between metallic islands [99].

The thin MoO₃ films used in solar cells undergo a reduction from Mo⁴⁺ to Mo⁵⁺ when exposed to 1.2 keV photons, even at relatively low doses, which the authors attributed to oxygen vacancies created by irradiation [100]. This can clearly be seen as a case of radiation induced damage, but when studying the performance of the solar cells, these damage effects can easily be convoluted with other damage effects. The role that these layers have in solar cells as electronic hole extraction layers means that any damage will have an effect on the performance of the cell.

In Pt/TiO₂/Pt cells, where a 40 nm TiO₂ layer is sandwiched between two platinum slabs with a bias of 0.2 V, a multitude of effects can be found as function of both beam intensity as well as exposure time [101]. For short exposures, an induced current four orders of magnitude above the base level was observed (beam parameters 8.3 keV, 2 × 10¹³ ph (mm⁻² s⁻¹). However, for exposures up to 24 h, the current increased by several orders of magnitude and persisted even after cessation of irradiation. The low dose behavior can be explained since TiO₂ is a well-known photocatalyst. The authors appear to neglect the fact that the TiO₂ layer of 40 nm is thinner than the range of the induced electron avalanche, which might explain an increase in the current. The increase of current after long exposures is attributed to defect formation and induced phase transition.

By using a very high x-ray dose (17 keV, 2 × 10¹¹ ph s⁻¹ in 1.3 × 10⁻² mm²) it has shown to be possible to change the critical temperature for superconductivity, T_c, in a Bi₂Sr₂CaCu₂O_8+δ (Bi2212) superconductor [102]. An elongation of one of the crystalline axes was explained as a consequence of radiation induced change of O-content. Here, the O atoms are being displaced by the knock-on effect of secondary electrons. It should be noted that the dimensions of the elongated crystals were less than the expected extent of the photoelectron and secondary electron cloud. Hence to calculate a real dose dependence would be complicated. It should be pointed out that this effect could also be classified as radiation damage but since the change in T_c takes place gradually and the elongation of the crystalline unit cell is rather difficult to observe.

In glasses, events around the glass transition temperature do not show up as structural changes. However, the structural relaxations, or microscopic motion, as probed by XPCS measurements, are considerably faster when exposed to high doses of x-rays [103, 104]. The authors observe that the magnitude of these effects are beam intensity dependent and appear well below the energy levels required for atomic knock-on effects [104]. Attempts to distinguish between the natural glass dynamics and the beam induced dynamics rely on computational methods with, obviously, the complications involved in such an approach [103]. It is also interesting to note that this effect is observed in oxide glasses but not in metallic glasses.

Radiation induced chemical reactions rates in solids have been discussed in a monograph on reaction kinetics [105].

The issue of radiation interference at interfaces is even more complicated, since one is dealing with solid–liquid or solid/gas combinations where the radiation can have effects on both media. This is especially relevant in operando catalysis studies. X-ray spectroscopy techniques like EXAFS and XANES often require extended exposure due to variations in catalyst gas loading and repeated reaction cycles. A systematic study, dealing not with structural or electronic defects but instead focusing on the relation between x-ray dose and the conversion rate of methane to methanol by a Cu catalyst has indeed shown a significant effect [106]. The working hypothesis is that the radiation reduces Cu²⁺ to Cu⁺ and that this has a negative effect on the conversion rate of the methane. To paraphrase the authors: 'the comparative results obtained from this study show that a considerable misrepresentation of the behavior of the Cu catalyst at numerous levels may be arrived at when using a high intensity focused x-ray beam'. Noteworthy is that these effects were not radiation dose dependent but were already present from the start of the experiment. To avoid issues as experienced on high intensity beamlines (10¹²–10¹⁴ ph (mm⁻² s⁻¹), the incident beam intensity had to be reduced by a factor of around 1000 using amorphous carbon filters. The unfortunate truth in this case is that the beam intensity was attenuated back to the level of bending magnets at third generation synchrotrons, before any upgrades.

The above study focuses on the effect of radiation on the metallic particles and leaves unanswered the question of whether the photoelectrons could interfere in the catalytic process itself. For this, we only have anecdotal evidence in that in some cases the catalytic reactions on the beamline proceeded much faster than in the home laboratories [48, 107].

That photon absorption can lead to interference in catalytic processes was also found when a white beam was used to enhance the electrolytic deposition of Ni–P alloys from solution. This process is pH sensitive and autocatalytic, and takes place regardless of the presence of x-rays. However, exposure to x-rays speeds up the process considerably and has similar effect to increasing the pH [108]. This could indicate an increase in the pH due to irradiation, but the authors also provide evidence of another pathway through which x-rays generate hydrogen radicals that then help to reduce the Ni ions. This would imply two parallel processes with similar result. Similar experiments were reported for the deposition at room temperature of Cu layers from solution [48, 55, 109–111]. The formation of metallic particles, however, is not limited to white beam irradiation and focused monochromatic undulator beams have also been shown to affect the growth kinetics of Au particles from solution at lower intensity beamlines [112].

A modification of the surface due to desorption of oxygen from a Pt surface covered with a thin water layer has been reported and is attributed to the radiolytic water products enabling the desorption process [113]. In a control experiment, in a high vacuum environment, this effect was not observed.

To our knowledge, no systematic study has yet been performed to examine the effect of the directionality of the x-ray beam, i.e., at right angles or parallel to the interface. One can imagine that when the x-ray beam is orthogonal to the interface, there will be a gradient of photoelectrons in the solvent layer which might be relevant in coating studies.

A combination of x-ray scattering, imaging and modelling was used to examine radiation effects on a calcite-water interface [114]. Here the equilibrium dissolution rate was enhanced due to exposure to 10 keV photons from a focused undulator beam. The dissolution rate at steady state was observed to be 2.2 monolayers s⁻¹, in close agreement with modelling where the assumption was that the radiolysis products caused an acidification from pH = 8.3 → 5.2. There was a marked difference between the initial stages and steady state. In light of the many bio-crystallization studies performed in the last decade, this is the first somewhat more quantified results that takes the effect of radiation into account and indicates that such pH dependent results have to be approached with caution and the lowest radiation dose and larger beam dimensions should be used.

The water–air interface is also not immune to radiation influence. In an experiment in a closed capillary, it was shown that the evaporation rate of H₂O increased due to exposure to radiation. Both thermal effects as well as chemical hydrolysis reactions, e.g., gas formation, could be ruled out and the authors explain the increased evaporation rate as being due to changes in the surface tension [115], even though no changes in the shape of the meniscus were observed. The radiation dose in this case was expressed in the number of ph Å⁻² and was calculated to be 0.1 ph Å⁻² (13 keV), well below the limit of 200 ph Å⁻² were the authors claim Coulomb explosions can occur.

The glass transition temperature, T_g, is an important parameter in polymer physics and is related to the polymer molecular weight via the Flory–Fox relation:

$$\begin{equation}{T}_{\mathrm{g}}={T}_{\mathrm{g},\infty }-\frac{K}{{M}_{\mathrm{w}}}\end{equation} \tag{ 3 }$$

The effects of ionizing radiation on long chain molecules are a combination of chain scission and cross linking. Whilst chain scission will reduce the average molecular weight, M_w, which in turn will decrease the glass transition temperature, cross linking will increase this. Figure 9 shows the schematic development of the M_w as function of radiation doses in the different scenarios. The numerical values are different for each polymer and have to be determined empirically. The parameters G(x) and G(s) have been defined before in this text.

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As previously mentioned, Goderis [43] has examined the effects of the radiation dose using differential scanning calorimetry (DSC). A systematic study on polymethylmethylacrylate (PMMA) using monochromatic x-rays showed a decrease of the T_g from 119 °C to 95 °C as function of radiation dose (E = 8.5 keV). The empirically determined relation was T_g (°C) $\approx 118.0-8.0{\times}1{0}^{-3}\varepsilon \left(\mathrm{m}\mathrm{J}\enspace \mathrm{m}{\mathrm{m}}^{3}\right)$, where ε is the absorbed dose expressed in Gray units [116]. The maximum dose administered was about 2000 kGy. For comparison, it is noted that in industrial processing, doses in the range of 50–2000 kGy are within the normal range to transform semicrystalline thermoplasts to thermosets [39]. Tools to perform cross correlations to assess the degree of cross linking can be ¹³C-NMR and photoelectron spectroscopy [39].

The lowering of the T_g can be seen as radiation damage, but was also shown to influence the coalescence behavior of PMMA colloids [117] deposited onto Kapton films and imaged with 8 keV photons with a dose rate of 2 × 10¹¹ ph s⁻¹ and a beam size of 15 × 15 μm². Coalescence generally requires elevated temperatures, but was observed to occur here upon radiation at ambient temperature. Further, when using different monodisperse samples (radii R = 100, 550, 1000 and 1800 nm), it was found that smaller radii samples coalesced faster. The process resembled viscoelastic coalescence, but was not observed in non-irradiated materials. The authors attribute this effect to polymeric scission, which reduces the T_g, surface tension and viscosity of the colloids.

Chemical reactions that involve radicals are likely candidates for radiation-induced interference. This has indeed been observed in the polymerization-induced self-assembly of poly(stearyl methacrylate)–poly(benzyl methacrylate) (PSMA–PBzMA) diblock copolymer via reversible addition-fragmentation chain transfer (RAFT) dispersion polymerization [118]. SAXS experiments, designed to follow the reaction kinetics, showed a fourfold increased reaction rate compared to off-line experiments. This increase was explained by presence of radiation induced free radicals.

In protein solution scattering experiments radiation damage is recognized by the aggregation of proteins. It is less well known that for synthetic polymers similar effects can occur. An extensive study of the radiation induced aggregation of [6,6]-phenyl-C71-butyric acid methyl ester (PC71BM) in chlorobenzene with and without addition of 1,8-diiodooctane indeed showed such aggregation effects, which were not observed in parallel neutron scattering experiments on the same material. The effect was less when 1,8-diiodooctane (C₈H₁₆I₂) was present. One would expect that with the presence of the heavier iodine, more absorption and photoelectrons would be created. Alternatively, it could be that the Iodine acts as electron scavenger [119].

While the aggregation described above is permanent, reversible effects have also been found in solutions containing self-assembling stiff supramolecular peptide filaments [120]. Here, when radiation is applied during the growth phase, crystalline bundles are formed that then loose regular ordering when exposure ceases. The changes of the surface charge density induced by radiolysis products are the likely cause. It is noteworthy that the radiation has to be applied during the growth phase to observe this effect. This is reminiscent of the orientation of bundles of stiff biological macromolecules grown under an applied force field. Here, bundling should take place before the molecules are too long and steric hindering inhibits the reorientation required for bundle formation [121, 122].

Dynamic events at the very local level, as measured by XPCS, can also be influenced by radiation. In stretched elastomers, filled with either Si or carbon black, it was observed that the Si particle mobility was reduced as function of the radiation dose. In this case, the authors speculated that radiation damage caused crosslinking and hence a slowing down of the Si particles by the increase in stiffness of the polymer network [123], but could not verify the same behavior for the carbon black filled sample. However, this system is somewhat confusing. Experiments on samples of the same material swollen in a solvent using an estimated 300-fold increase in incident flux, showed a breaking from the crosslinks which allowed the Si particles to diffuse out of the beam [124]. As these authors state: 'however, even if there is no obvious change in the scattering intensity profiles, the dynamics suffer from the radiation damage as shown in this study'. The real problem here, as noted before, lies in distinguishing the radiation induced effects from the real physics. The uncertainty in interpretation of the results in the examples above illustrate the difficulties of making accurate predictions of how polymeric materials will react to exposure to radiation.

In the section on interfaces, several examples of metallic nanoparticle synthesis in irradiated solvents were given with specific emphasis on how this could be used to produce coatings. It is thus interesting to compare the radiation doses used in this type of manufacturing with the radiation doses used on beamlines for characterization. For radiation induced/assisted polymerization of dissolved synthetic polymers, values of an absorbed 30 kGy total dose with a dose rate of 1.8 kGy h⁻¹ have been reported [125]. Gel formation in polymer solutions is reported for 2 kGy total dose [126]. A non-exhaustive survey of the radiation induced formation of different metallic (colloidal Au, core shell bimetallic Cu–Al, etc) nanoparticles shows that, depending on the solvent conditions, dose rates 8–60 kGy h⁻¹ and total dose of 40–250 kGy are being used [54, 127–129].

As comparison, consider the radiation dose on a modern microfocus synchrotron beamline. A water sample of 2 mm thick will absorb approximately 70% of 10 keV photons. We assume that the absorption is distributed evenly over the irradiated volume. Mounted on a microfocus beamline with a size of 10 × 10 μm² and 10¹³ ph s⁻¹ this sample receives 500 kGy s⁻¹, which is considerably higher than the doses used in the industrial contexts. Mitigating circumstances will be that material can diffuse out of the volume exposed to the synchrotron beam. This, however, also indicates that viscosity can play a role.

In this context it is not surprising that in pink beam energy dispersive XAFS experiments [48], where the absorbed x-ray dose will again be considerably higher, it was found that the reaction rate of the oxidation of benzyl alcohol to benzaldehyde using a copper bipyridine (1:1) complex was considerably increased. See figure 10.

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A further investigation on Cu salt solutions with different ligands but without the presence of a catalyst showed that the ligands could influence the rate at which the Cu ions were reduced [48, 110]. These effects were observed on both polychromatic as well as monochromatic bending magnet beamlines, with differences of 0.38 kGy versus 41.5 kGy. Reduction of the Cu allowed the formation of 2–3 nm sized Cu nanoparticles, as well as the formation of gas bubbles. Gas formation in solutions has also been observed over a range of intensities in monochromatic beamline experiments, in solutions to which LiBr was added [1].

Similar experiments have followed the formation of Ag particles in a polymer/water/AgClO₄ solution. Here, x-ray experiments were performed after exposure of samples to a 500 W mercury lamp [130]. The effects of the exposure to two different photon sources are difficult to disentangle.

While the examples above use polychromatic beams, it is clear that lower intensity monochromatic beams could induce the same effects over a longer time-scale [48]. This is confirmed by the observation that Au nanoparticles form under the influence of a monochromatic irradiation [112]. In contrast, however, the growth rate of Bi₂O₂CO₃ crystals from a solution was slowed down considerably under irradiation compared to off-line experiments [131]. In this case, the growth process was shown to be pH dependent which could explain why the on- and off-line results differ.

With simple solutions containing a single additive, it is relatively simple to deduce which reaction(s) may occur upon exposure to x-rays. In a previous section, it was noted that the presence of an interface can complicate matters and this is also the case with more complex solutions in which different particles are grafted to each other. An elaborate example can be found in the reduction of graphene oxide attached to TiO₂ particles in an acidic environment [132].

In low concentration solutions of long stiff supramolecular peptide filaments, it was observed that exposure to monochromatic x-rays (dose 4.4 kGy s⁻¹) induced the formation of highly ordered hexagonal bundles [133]. Although the bundle formation was reversible, it was found that these bundles could remain stable for many hours after irradiation had ceased. Induced charges, rather than chemical crosslinking, was found to be the cause of the bundle formation. The stability of such bundles has also been observed in other rigid rod systems [121] and is not necessarily related to irradiation, since steric hindering of the rotational diffusion should also be taken into account. At higher peptide concentrations the bundle formation was spontaneous, and irradiation played a minor role. See figure 11.

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The rotation of ordered domains of microtubules towards the beam position in low viscosity pipes buffers has also been found. (Bras, Diakun, Diaz unpublished data.) This was not observed in higher viscosity glycerol containing buffer solutions.

If we consider for a moment how the numbers mentioned above compare to a modern x-ray source with a metal jet generator, 1 mm thick water or polymer sample, we find that samples on these instruments absorb about 2 Gy s⁻¹. A 15 min experiment will therefore render a dose similar to that reported for the purposeful cross linking of polymer gels [126].