L X-Rays RYIEDOscillations and Proton-NMRD of Gd 2 O 3 Nanoparticles

Recently, it was shown that relative yields of X-rays induced by ion impact are not constant but depend on beam energy. In the framework of this problem, pellets of Gd2O3 and a Gd chelate, Gd-DOTA, as well as a 5 nm in diameter Gd2O3 nanoparticles dispersion on a polycarbonate Nuclepore filter, were studied. In this work, it is shown that after subtraction of known matrix effects, relative yield variations still present different patterns for Gd2O3 pellet and Gd2O3 nanoparticles. Proton NMRD T1(ω) data for Gd2O3 nanoparticles and Gd-DOTA water solutions published by Bridot et al. and Toth et al., respectively, were reproduced using a model for paramagnetic substances in water solutions and identical electronic relaxation times. The analysis of both techniques results points collective electron behaviour as the explanation for the different observations on X-ray data of Gd2O3 nanoparticles and bulk material.


Introduction
In Particle Induced X-Ray Emission (PIXE), it is usually assumed that the ratio between two X-ray lines of the same element is an atomic parameter independent of the chemical environment surrounding the emitting ion.That this in detail is not exactly the case is also a well-known fact, shown by several authors [1][2][3][4][5][6][7][8][9][10].Furthermore, recently, effects due to an applied external magnetic field have been reported on the fluorescence yield of L 3 sub-shell of Gd, Dy, Hg, and Pb by Demir and S ¸ahin [11].
Taking into account that, in a PIXE experiment, the X-ray emitting ion is located in a condensed matter environment and is therefore subjected to strong local magnetic and electric fields, the result from Demir may be seen as a clear demonstration that the solid state environment may well affect electronic transition rates as well as it affects details on the valence electronic configuration of the emitting ion [8,9].Furthermore, it is important to realise that in parallel to the main process of ionisation of the inner-shells and first-order processes of reorganisation of the electron cloud, namely, the emission of X-rays or Auger electrons, the collision between the incident ions and the sample atoms also induces other secondary processes such as multi-ionisation, electrons shake-up and shake-off, polarisation of atomic orbitals and multiparticle and collective processes such as the emission of Radiative Auger Emission X-rays (RAE) [12,13] and production of intrinsic and extrinsic plasmons [14,15].The result of all these is that the relative intensity of Xray lines corresponding to transitions to the same subshell ends up being apparently or even in fact dependent on the chemical (or electronic) environment of the emitting ion as well as on the incident ion beam energy.This effect has been named RYIED-Relative Yield Ion Energy Dependence and has been under study by the authors since several years now [1,16,17].
In the case of proton Nuclear Magnetic Resonance Dispersion (NMRD), the longitudinal relaxation time T 1 and the transverse relaxation time T 2 are measured for a broad range of Larmor frequencies (ω).The obtained T 1 (ω) or T 2 (ω) curves are called nuclear magnetic relaxation dispersion curves, and NMRD is particularly interesting in the study of paramagnetic and superparamagnetic systems.The fitting of the T 1 (ω) curves, using appropriate models, provides an important insight into the paramagnetic centre environment [18], including also parameters relative to the paramagnetic centre itself.In a preliminary work [19], a possible resemblance between the magnetic field in NMRD experiments and the ion beam energy in RYIED, as well as between the T 1 (ω) curves in NMRD and the intensity ratio variation curves in RYIED, was put forward by the first time.Taking into account, for the RYIED case, that (i) the impact of an incident ion on a target, as well as the emission of the scattered electrons, corresponds to electromagnetic pulses, (ii) the duration of the electromagnetic pulse corresponding to the incident ion is roughly proportional to the inverse of the speed of the impinging ion, (iii) the ionisation of the target converts a closed, ideally momentless shell, into an asymmetric shell with a magnetic and electric moments that are not null, (iv) the emission of an electron by an initially neutral atom generates plasmons in the material where the ion is embedded, the links between RYIED and NMRD become clear, because the electromagnetic pulses associated to the ion beam can be seen as perturbations comparable to the RF pulses used to obtain NMRD T 1 (ω) data.
Regarding NMRD data, 1/T 1 (ω) measures the rate at which the protons in a water solution of a magnetically active substance align with a magnetostatic field once taken out of that condition by an RF pulse in the resonance condition.Now, different X-rays correspond to different transitions of the whole ion between two different excited (ionic) states, each transition having its own characteristic partial half-life.Calculating the relative intensity of two different atomic transitions is, therefore, among other things, a way of calculating the ratio of intensity of transitions (between ionic states) that take place in two different times after collision.This is much the same as saying that it is a way to measure the rate at which beam-induced ion states precess, loose alignment or, are otherwise time affected by an essentially nonsymmetric electrostatic and magnetostatic local field and other electronic collective phenomena, in a close similarity to 1/T 1 (ω) measurements.Furthermore, it is here quite important to realise that what controls atomic processes is the combination of fields and not the classical positions of atomic or molecular electrons.Since changes in sources of fields (e.g., the ionisation process) propagate at the speed of light and not at the speed of electrons or protons, in detail the whole process should not be seen as frozen relative to the protons speed, as usually it is.
In the present paper, it is shown that a similarity observed between NMRD curves for the Gd chelate Gd-DOTA and Gd 2 O 3 nanoparticles solutions and similarities observed between Gd-DOTA and Gd 2 O 3 nanoparticles in RYIED can be explained by a similarity between effective values for the longitudinal and transverse electronic spin relaxation times of Gd electrons in both environments, a result that strongly supports both the above stated view upon the resemblance between RYIED and proton NMRD, as well as the existence of a collective behaviour of electrons in Gd 2 O 3 nanoparticles, different from those present in bulk pressed powder Gd 2 O 3 pellets.

Materials and Methods
After studying the relative intensity variations on W and Mo L X-rays in previous works [1,2,17], a decision was made to study an element allowing the easy measurement of the L shell as well as the K and the M shells X-rays.Gd was selected, among other reasons also because Gd is an important technological element, namely, for biomedical applications, being used as paramagnetic contrast agent (CA) for nuclear magnetic resonance imaging (MRI), due to its large magnetic moment [20].Regarding RYIED, Gd L-shell spectra were obtained using a Gresham Scientific Instruments Lda 150 eV resolution LN-cooled Scirus Si(Li) detector.As irradiation targets, a Gd 2 O 3 pellet, a Gd 2 O 3 5 nm particles dispersion on a polycarbonate membrane filter, and a Gd-DOTA pellet were used.Gd-DOTA (gadolinium-tetraazacyclododecanetetraacetic acid complex) is a Gd chelate used in the production of MRI contrast agents [21].Pure materials, namely, 99.99% pure Gd 2 O 3 powder from Alfa Aeser and 99.9% pure Gd 2 O 3 nanoparticles and 97.5% pure Gd-DOTA from Sigma-Aldrich Co., were used to avoid problems in data interpretation due to sample contamination.Further, to avoid problems due to the sample preparation, irradiation targets were made in a glove chamber and in an inert dry atmosphere to prevent for sample degradation.Once ready, the samples were placed in the irradiation chamber under vacuum, to assure that no degradation or contamination would arise from atmospheric exposure, which was thus limited to a very few minutes necessary for closure and evacuation of the irradiation chamber.The experimental facilities details can be found elsewhere [22].High statistics spectra were collected (roughly 200 000 counts in the L α ) for proton energies from 700 keV to 1450 keV in steps of 50 keV, and for 1700 keV and 1950 keV.Spectra deconvolution was carried out using the new DT2 program fitting core [23].This includes a Bayesian inference algorithm by Barradas [24], for determination of the error levels associated to the fitted line areas.The precision of the Bayesian inference algorithm plays an important role in this work, allowing for errors below 5% in most cases.
A Python routine specifically written for the purpose was used to calculate the experimental line intensity ratios.The theoretical values of X-ray line intensities and intensity ratios were calculated using the C calculation routine DT2simul [25].
The NMRD data for the gadolinium oxide nanoparticles of three different sizes was obtained from the work of Bridot et al. [26].Data for the Gd-DOTA was obtained from the work of Toth et al. [20].The 1/T 1 (ω) data fitting was performed using the commercial software SigmaPlot.

Results and Discussion
3.1.RYIED.Figure 1 shows the ratios of intensity determined for lines corresponding to transitions to the same sub-shell, namely, , for the three different Gd environments, and as function of the incident proton beam energy, after being normalised to the expected theoretical values.
It can be seen that the intensity ratios variation curves obtained are different not only for the three samples: the Gd-DOTA pellet, the Gd 2 O 3 5 nm particles dispersed on a filter, and the Gd 2 O 3 pellet, but more than that, the experimental ratios are significantly different from the the-oretical expectations, mainly at low energy.Apart from the amplitude, the oscillations seen are not new and were observed in previous works on the K X-rays RYIED of a Gd 2 O 3 pellet sample [17] as well as in studies made on L and K X-rays of Mo [2,16,17] and W samples [1,16,27].
Figure 1, nevertheless, presents a very surprising result.The patterns obtained for the Gd 2 O 3 pellet and the Gd 2 O 3 5 nm particles are different.This is a striking result because it means that the oscillating pattern is not only dependent on the local chemical composition (which is the same for the pellet and for the nanoparticles), but also in some property related to the size of the nanoparticles.It is important to realise here that "normal" matrix effects are already excluded by normalisation to theoretical (simulated) values, which include these "normal" effects [28,29].The second amazing result in Figure 1 is the resemblance between the patterns for the Gd 2 O 3 5 nm particles and those for the Gd-DOTA pellet, in the Lβ 2,15 /Lα 1 plot.

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The question is what resemblance can be found between Gd 2 O 3 5 nm particles and a Gd-DOTA chelate that may justify these results.One detail that can be observed is the fact that in all ratios, one of the transitions considered involves electrons originating from the N-shell and, therefore, close enough to the valence shell of Gd.
Finally, it is important to realise that all these ratios correspond to ratios between transitions to the same L subshell (as pointed out initially), and therefore conditions such as strong variations in the L 3 /L 1 ionisation cross-section ratios do not apply here.
Since the most striking result is observed for the 750 keV irradiations, some specific attention may be put into these spectra.In Figure 2, the overlap of Gd 2 O 3 nanoparticles spectra and those of Gd-DOTA (top graph) and Gd 2 O 3 powder pellet (bottom graph) are presented.Gd 2 O 3 nanoparticles spectra were normalised to the others to simplify the comparison.
In the case of the overlap with the Gd-DOTA spectra, the similitude is such that if it were not for the differences in the Lγ group around channel 500, it could be thought that the spectra were the same.This is definitely not seen in the overlap with the Gd 2 O 3 powder pellet spectrum, since the low-energy tail region is impressively different.Furthermore, and strange enough, the highest tail corresponds to the Gd 2 O 3 nanoparticles and not to the powder pellet.
Since the low energy tail may contain contributions from Radiative Auger Emission (RAE) satellites [12,13] as well as other satellites due to collective electron behaviours [14,15], this is another result suggesting that collective or second-order phenomena may be behind the strange results displayed in Figure 1.
Endorem (or AMI-25) and Gd-DOTA are contrast agents used in Magnetic Resonance Imaging (MRI).Endorem (or AMI-25) is an aqueous colloidal suspension of superparamagnetic iron oxide (Fe 2 O 3 and Fe 3 O 4 mixture) nanoparticles, while Gd-DOTA is a paramagnetic chelate.
Paramagnetic and superparamagnetic contrast agents are expected to have strikingly different signatures in the nuclear magnetic resonance dispersion profiles as shown in Figure 3 for Endorem and Gd-DOTA.
Given that Gd 2 O 3 is a material expected to have a specific magnetic moment higher than Fe 2 O 3 or Fe 3 O 4 , the Gd 2 O 3 nanoparticles NMRD 1/T 1 (ω) curves should at first behave like Endorem and not like Gd-DOTA.Still, as shown in Figure 3, they do behave like Gd-DOTA for Larmor frequencies between 0.01 MHz and 100 MHz.Furthermore, as stated by Bridot et al. [26], the magnetic behaviour of these gadolinium oxide nanoparticles is not yet fully elucidated.Now, given the resemblance between the NMRD curves of Gd 2 O 3 nanoparticles and Gd-DOTA, as well as RYIED patterns, one may consider that, in the range of proton Larmor frequencies of interest, Gd 2 O 3 nanoparticles behave like a paramagnetic substance in respect to their effect on nuclear relaxation of water protons.2)) as a function of proton Larmor frequency between the three sizes of gadolinium oxide (Gd 2 O 3 ) nanoparticles [26], a superparamagnetic nanoparticles suspension (Endorem) [30], and a paramagnetic chelates solution (Gd-DOTA) [20].

Theoretical Approach.
The use of the theory of solvent nuclear relaxation in the presence of paramagnetic substances developed by Bloembergen [31], Solomon [32], and others was therefore considered in its version specially developed for studying the effect of paramagnetic chelates in water relaxation [20].Here it is important to realise that the system to be studied is not a single paramagnetic ion surrounded by a molecule (a chelate) but instead a Gd 2 O 3 crystal core coated with a 2 nm Polysiloxane shell [26], as presented schematically in Figure 4.
This leads to two important facts.
(i) Water protons do not have access to sites near the Gd core, the inner sphere in the Bloembergen-Solomon model, and therefore only the second-and outer-sphere terms may be considered, making the longitudinal relaxation rate be given by [20] 1 1 where r 1 is the longitudinal relaxivity, [M] is the concentration of the paramagnetic element (in this case Gd), and (1/T 1 ) medium is the longitudinal relaxation rate of the medium where the paramagnetic chelates are suspended.
(ii) There is a need to consider a set of effective terms by assuming both a pure mechanical spherical symmetry of the particle and a coherent, or at least highly correlated, collective behaviour of the Gd 2 O 3 nanoparticles electrons.
The second-sphere term, (1/T 1 ) 2nd , can be expressed as [20] 1 where P m is the mole fraction of bound water nuclei in the second-sphere, with N H2O being the number of specially bound water molecules in the second-sphere, τ m, j the lifetime of a specific water molecule j in the second shell, and 1/T 1, j the longitudinal proton relaxation rate of molecule j for water protons in the second sphere.Assuming a spherical symmetry geometry for the particles leads to the definition of effective parameters and to rewriting (3) as where N = qN H2O /55.5, with q being the number of bound water nuclei per Gd and c the molal concentration of the paramagnetic element.T eff 1 is assumed to be given by 1 where the subscript I refers to the water proton nuclear spin and the subscript S refers to the gadolinium nanoparticle electron spin.All the parameters in the right-hand side of the equation are to be taken as effective parameters.In (5), the following was considered: (1) r GdH is the distance between the water proton and the centre of the crystal core, (2) S was assumed to be 198 μ B by considering a spin density of 3.86 μ B /nm 3 , calculated from a lattice constant of 1.0812 nm determined by Niinistö for a cubic body-centred crystalline structure Gd 2 O 3 nanoparticles [33], (3) the τ ck are effective times characteristic of relaxation times defined as , where the right hand terms are effective values for the rotational correlation time τ R , the longitudinal and transverse electron spin relaxation times of Gd, T 1e and T 2e , respectively, and τ eff m the mean lifetime of a water molecule in the second-sphere, (4) based on the similarity between the Gd 2 O 3 nanoparticles response and that of Gd-DOTA for both NMRD and RYIED, it was decided to take, as effective electronic relaxation times, the electronic relaxation times determined by Powell et al. [34] for Gd-DOTA: T 1e = 5.0 × 10 −10 s and T 2e = 1.08 × 10 −9 s.
The diffusion coefficient for relative diffusion D was taken equal to the one obtained for Endorem in a previous work [30,36], since Gd 2 O 3 nanoparticles may be seen as mechanically similar to Endorem nanoparticles.The distance of closest approach of the Gd electron spin and the water proton spin in the outer-sphere d was fitted assuming that it could not be smaller than the hydrodynamic radius of the nanoparticles, namely, 8.9 nm for the nanoparticles with a crystal core of 4.6 nm [26].This value was also considered as a rough value for r GdH for fitting the d parameter.Once the value for d is obtained, the following parameters for the second sphere were fitted: r GdH , τ R , τ eff m , and N .

NMRD Curves and Fitting Results
. Figure 5 presents the experimental NMRD data for the Gd 2 O 3 nanoparticles [26] as well as the results of the fit of (1) to these.The experimental longitudinal relaxation rates data, 1/T 1 , shown in Figure 5, for the nanoparticles with a Gd 2 O 3 crystal core having a diameter of 4.6 nm, were calculated from the r 1 values in Bridot et al. [26] using the known relation between relaxation rates and relaxivity expressed in (2).The medium was assumed to be water at 25 • C, (1/T 1 ) medium ≈ 0.333 s −1 , and the concentration of gadolinium, [M], was taken as 0.6 mM based on the information in page 5079 of [26].
It can be seen that the fitted curve follows closely the experimental points extracted from the literature.
The fitted values for the model parameters are shown in Table 1.Errors associated with these are not presented because they are irrelevant for the present discussion.In fact, what this result points out is that, by using the electronic longitudinal and transverse relaxation times of Gd-DOTA as effective electronic longitudinal and transverse relaxation times of the Gd 2 O 3 nanoparticles, it is possible to reproduce its NMRD experimental data, which is a valid result, independent of the precision of the values obtained for the fitting parameters.

Summary and Conclusions
This last result in the previous section shows that electrons in Gd 2 O 3 nanoparticles present an effective electronic relaxation behaviour identical to that reported in the literature for Gd-DOTA electrons.On the other hand, RYIED oscillation patterns for Gd-DOTA and for Gd 2 O 3 nanoparticles also show a very similar structure for a ratio involving the valence transitions Lβ 2,15 .Besides, the low energy tail of spectra collected during irradiations at the ion beam energy where this effect is more striking also points out to a similar electronic behaviour at an atomic or nanoparticle scale.The conjugation of all these results allows us to conclude that RYIED oscillation patterns are most probably linked to collective electronic properties of materials under analysis either directly or through its effect on second-order phenomena.In fact, in the case of Gd 2 O 3 nanoparticles, the existence of a collective coherent behaviour is clearly compatible with the NMRD curves, and, in the case of the RYIED and spectra resemblances (and differences) for the most critical ion beam energy, results are also strongly in favour of this interpretation.
The possibility of accessing information regarding electronic collective behaviour in materials such as Gd 2 O 3 nanoparticles is a very important result since this is an information hard to access and frequently only available by the use of large infrastructures whoes effective beam time available is always limited.In the specific case of Gd, the importance is enhanced due to its relevance in technological applications, namely, for biomedical applications such as paramagnetic contrast agent in nuclear magnetic resonance imaging (MRI), or even as a possible basis for therapeutic methodologies under development (like diathermy therapy).The preliminary results here reported should thus lead to further studies allowing a complete clarification of the full potential of the present analytical approach, part of which should include high-resolution X-rays spectrometry using either standard crystal spectrometers of, preferably, microcalorimeter EDS detectors, in order to be able to resolve low energy tail contributions [37] and thus become in possession of better and richer X-ray data that is not strongly affected by the detectors response function.
The holistic analysis of X-ray and NMRD data is also of the utmost importance both for a positive demonstration that electrons collective behaviour is indeed affecting X-ray data, as well as for robustness of the analysis of unknown samples, once the above demonstration has been achieved.

Figure 2 :
Figure2: Overlap of spectra collected during irradiation of Gd 2 O 3 nanoparticles, Gd-DOTA pellets (a), and Gd 2 O 3 powder pellets (b), using 750 keV proton beams.The Gd 2 O 3 nanoparticles spectrum was normalised in order that the peak counts in the Lα peak are the same as that of the overlapping spectra.It can be seen that while the tail region of the Lα peak is identical for the Gd 2 O 3 nanoparticles and for the Gd-DOTA pellet, the same is not true for the Gd 2 O 3 nanoparticles and the Gd 2 O 3 bulk pellet.

Figure 4 :
Figure 4: Schematic illustration of the Gd 2 O 3 nanoparticles model considered.The thin layer on top of the Polysiloxane shell is considered to be the second sphere.The outer sphere is considered as fully outside to the particles structure.

Figure 5 :
Figure 5: Longitudinal relaxation rates as a function of proton Larmor frequency and fitting curve to the 4.6 nm diameter Gd 2 O 3 crystal core nanoparticles data from Bridot et al. [26] using the paramagnetic model of nuclear relaxation described above.

Table 1 :
[34]ing parameters for the 4.6 nm diameter Gd 2 O 3 crystal core nanoparticles and for the Gd-DOTA chelates found in the literature[34].