# Why natural monazite never becomes amorphous:
Experimental evidence for alpha self-healing

Anne-Magali Seydoux-Guillaume, Xavier Deschanels, Cédric Baumier, Stefan

Neumeier, William John Weber, Sylvain Peuget

► To cite this version:

Anne-Magali Seydoux-Guillaume, Xavier Deschanels, Cédric Baumier, Stefan Neumeier, William John Weber, et al.. Why natural monazite never becomes amorphous: Experimental evidence for alpha self-healing. The American Mineralogist, 2018, 103 (5), pp.824-827. 10.2138/am-2018-6447. hal-01783590

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Why natural monazite never becomes amorphous: experimental evidence for alpha self-healing.

Anne-Magali Seydoux-Guillaume<fnref n="1" />,<fnref n="2" />*, Xavier Deschanels<fnref n="3" />, Cédric Baumier<fnref n="4" />, Stefan Neumeier<fnref n="5" />, William John Weber<fnref n="6" />,<fnref n="7" />, and Sylvain Peuget<fnref n="8" />.

ABSTRACT:

Monazite, a common accessory rare-earth orthophosphate mineral in the continental crust widely used in U-Pb geochronology, holds promise for (U-Th)/He thermochronology, and for the immobilization of Pu and minor actinides (MA) coming from spent nuclear fuel

<footnote n="1">¹ CNRS, Université Clermont Auvergne, IRD, UJM, Laboratoire Magmas et Volcans, F-63000 Clermont-Ferrand, France</footnote>

<footnote n="2">² Univ Lyon, UJM-Saint-Etienne, UCA, CNRS, IRD, LMV UMR 6524, F-42023 SAINT-ETIENNE, France</footnote>

<footnote n="3">³ ICSM, CEA, CNRS, ENSCM, Univ Montpellier, Marcoule, France</footnote>

<footnote n="4">⁴ CSNSM, JANNuS-Orsay/SCALP, Univ Paris-Sud, CNRS/IN2P3, Orsay, France</footnote>

<footnote n="5">⁵ Forschungszentrum Jülich GmbH, Institute of Energy and Climate Research, Nuclear Waste Management and Reactor Safety (IEK-6), D-52425 Jülich, Germany</footnote>

<footnote n="6">⁶Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN 37996, USA</footnote>

<footnote n="7">⁷ Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA</footnote>

<footnote n="8">⁸ CEA, DEN, DE2D, SEVT, LMPA BP 17171, 30207 Bagnols-sur-Ceze Cedex, France.</footnote>

<footnote>*Corresponding author.</footnote>

<footnote>E-mail address:anne.magali.seydoux@univ-st-etienne.fr (A.-M. Seydoux-Guillaume).</footnote>
reprocessing. Previous results obtained on natural and plutonium-doped monazite have
demonstrated the ability of this structure to maintain a crystalline state despite high radiation
damage levels. However, the low critical temperature (180°C), above which amorphization
cannot be achieved in natural monazite under ion irradiation, does not explain this old and
unsolved paradox: why do natural monazites, independent of their geological history, remain
crystalline even when they did not experience any thermal event that could heal the defects?
This is what the present study aims to address. Synthetic polycrystals of LaPO₄-monazite
were irradiated sequentially and simultaneously with alpha particles (He) and gold (Au) ions.
The use of Au²⁺ ions at 1.5 MeV allows the simulation of the nuclear energy loss of the recoil
nucleus and He⁺ ions at 160 keV simulate the electronic energy loss of the α-particle released
in α-decay. *In situ* irradiation experiments were performed at room temperature conditions on
the JANNuS-Orsay/SCALP platform, which couples two accelerators with a Transmission
Electron Microscope. Our results demonstrate experimentally for the first time in monazite,
the existence of the defect recovery mechanism, called alpha-healing, acting in this structure
due to electronic energy loss of alpha particles, which explains the absence of amorphization
in natural monazite samples. This mechanism is critically important for monazite geo and
thermochronology and to design and predictively model the long-term behavior of ceramic
matrices for nuclear waste conditioning.

**Keywords:** monazite; alpha self-healing; *in situ* TEM irradiation; dual-ion beam irradiation; Helium; geo and thermochronology; nuclear waste

INTRODUCTION

Monazite (APO₄, A = LREE, Th, U, Ca; Clavier et al., 2011), is a common accessory
rare-earth orthophosphate mineral in the continental crust widely used in U-Pb geochronology
(Parrish, 1990). It is also a promising candidate for the immobilization of Pu (for countries that are not actively reusing Pu in MOX fuel) and minor actinides (MA) coming from spent nuclear fuel reprocessing (Boatner et al., 1988; Weber et al., 1998), due to its high structural flexibility that can accommodate high concentrations of actinides in its structure, its high chemical durability, and its apparent high-radiation resistance (e.g. Ewing and Wang, 2002; Seydoux-Guillaume et al., 2004; Lumpkin, 2006; Oelkers and Montel, 2008; Dacheux et al., 2013). However, this last point, demonstrated in natural crystals (Seydoux-Guillaume et al., 2004), is still not understood. During an α-decay event, an α-particle (4-8 MeV) and a recoil nucleus (70-165 keV) are released. The kinetic energy of these two particles is deposited in the host material by two distinct processes, ballistic (S<sub>nucl</sub>) and electronic (S<sub>elec</sub>). The ballistic process correspond to elastic collisions between atom nuclei, and the electronic process to ionization and electronic processes resulting in a temperature rise in the material. Most of the atomic displacements that can result in amorphization of the crystal lattice are caused by the recoil nuclei (e.g. 1000-2000 atomic displacements) due to intense elastic collision cascades (Ewing et al., 2000). In contrast to its U-Pb geochronological concurrent zircon, which commonly contains U in the hundreds of parts per million range, has received alpha-decay doses on the order of 10<sup>18</sup>–10<sup>19</sup> α/g, and is easily amorphized (Ewing et al., 2000), even very old (up to 2 Ga) monazite crystals, containing high concentrations of actinides (up to 10 wt. % ThO<sub>2</sub> and ~1 wt. % UO<sub>2</sub>), and thus sustaining high irradiation doses (up to 1.7 x 10<sup>20</sup> α/g, which should induce up to 14 displacements per atom – dpa), are not amorphous; evidence of radiation damage is limited to isolated nm-sized domains within the crystal, corresponding to strain in the lattice (Seydoux-Guillaume et al., 2004). Similarly, Pu-doped monazite remains crystalline even after an irradiation dose of 7.5x10<sup>18</sup> α/g (0.8 dpa; Deschanels et al., 2014), which is well above the critical amorphization doses (~0.3 dpa) determined using external heavy-ion irradiation experiments (Meldrum et al., 1996). The reason for this apparent
resistance has remained an enigma until today. It is well known that the critical amorphization
temperature, for natural monazite under ion irradiation is relatively low (180°C; Meldrum et
al., 1997a) compared to other minerals (e.g. 830°C for zircon, 1130°C for quartz, 440°C for
zirconolite; Ewing et al., 2000), and the temperature and activation energy associated with
thermal recrystallization of the amorphous state is much lower for monazite (~300°C, 2.7 eV;
Karioris et al., 1981; Ehlert et al., 1983; DeschANELS et al., 2014) than for zircon (1200°C, 5.3
to 6.6 eV; Weber, 1990). Furthermore, the large differences in dose rates between ion
irradiation and Pu-doped or natural monazite are insufficient to explain the amorphization
resistance (DeschANELS et al., 2014). In monazite, the transition between amorphous and
crystalline states is also very sensitive to electron beams and to the ratio of electronic-to-
nuclear energy loss (S<sub>elec</sub>/S<sub>nucl</sub>) of the accelerated ions (Meldrum et al., 1997b; DeschANELS et
al., 2014). More generally, other phosphates (F-apatite, berlinite, xenotime) exhibit similar
behavior, which is generally attributed to the presence of tetrahedrally coordinated
phosphorous and to the higher binding energy of the P-O bond compared to Si-O (Meldrum et
al., 1999; Luo and Liu, 2001). However, these results cannot explain the behavioral
differences (amorphization, swelling) observed for equivalently damaged monazite resulting
from external heavy ion irradiation compared to α-decay self-irradiation (natural monazite or
<sup>238</sup>Pu doped monazite; Fig. 1 in Supp. Data). Finally, the mechanism called α-healing,
experimentally demonstrated for apatite (Ouchani et al., 1998; Soulet et al., 2001; Gerin et al.,
2017; Li et al., 2017) and borosilicate glasses (Mir et al., 2015), but only suggested for
monazite (Soulet et al., 2001; Seydoux-Guillaume et al., 2002; DeschANELS et al., 2014), could
be another possibility and remains to be demonstrated. The present experimental study solves
the old paradox of the apparent resistance of monazite samples to amorphization, and
demonstrates for the first time in monazite the existence and efficiency of α-particles for
recovering radiation damage in this mineral.
SAMPLE AND METHODS (MORE DETAILS IN SUPPLEMENTARY DATA)

Several Focused Ion Beam (FIB)-foils (12 x 6 x 0.1 µm) were cut perpendicular to the surface of the polycrystalline sample of sintered monazite (LaPO₄) ceramic, by the *in situ* lift-out technique for the Transmission Electron Microscope (TEM) *in situ* irradiation experiments performed at room temperature conditions on the JANNuS-Orsay/SCALP platform, which allows coupling two accelerators with a Transmission Electron Microscope (Figure 5 in Suppl data). We used Au²⁺ ions at 1.5 MeV to simulate the nuclear energy loss of the recoil nucleus of an α-decay (S<sub>nucl.</sub> ~ 4.5 keV/nm) and He⁺ ions at 160 keV to simulate the electronic energy loss of the α-particle released in α-decay (S<sub>elec.</sub> ~ 0.254 keV/nm). To evaluate the recovery effect of α-particles on the damage state induced by heavy recoil nuclei, three irradiation configurations were investigated: two were sequential, and the third simultaneous (Figs. 2-3). All three used the same ions and accelerating energy: 1.5 MeV Au²⁺ ions (ARAMIS accelerator) to induce ballistic damage and 160 keV He⁺ ions (IRMA accelerator) to induce electronic excitations without implanting He atoms in the lamella. (For further details see in Supplementary Materials)

RESULTS AND DISCUSSION

In the first experiment (Fig. 2), Au irradiation up to 2x10<sup>14</sup> Au/cm<sup>2</sup> (1.13 dpa) is used
to fully amorphize the monazite sample (Picot et al., 2008; DeschANELS et al., 2014), and ten
He irradiation steps are subsequently performed up to a fluence of 5x10<sup>16</sup> He/cm<sup>2</sup> to evaluate
the recovery of the fully amorphized material due to electronic energy loss of He ions (Table
1 in Supplementary Material). The second experiment (Fig. 3) is similar to the first and aims
at evaluating the He-induced recovery of a partially damaged material (0.2 dpa),
corresponding to a monazite with a strained lattice (DeschANELS et al., 2014), and structurally
similar to natural monazite samples (Seydoux-Guillaume et al., 2004). The third experiment
(Fig. 4) involve simultaneous irradiation by Au and He ions, up to fluences of 2x10¹⁴ Au/cm² and 3.4x10¹⁶ He/cm², performed in 4 steps. All these experiments were performed without continuous TEM observation to avoid artefacts (e.g. recrystallization; see Figs. 6-7 in Suppl. Mat.) from the electron beam (Meldrum et al., 1997b; Deschanels et al., 2014). Therefore, Bright-Field images (BF) and Selective Area Electron Diffraction (SAED) were done rapidly after each irradiation step under conditions carefully chosen (Suppl. Mat.) to avoid any recrystallization of amorphous areas (0.17 nA at x25500 magnification).

The first experiment (#2; Fig. 2) confirms that monazite is completely amorphous at a fluence of 2x10¹⁴ Au/cm² (1.13 dpa), consistent with previous work (Deschanels et al., 2014). At 10¹⁴ Au/cm² (0.56 dpa), the foil is almost completely amorphous, only a few phantoms of grain boundaries remain (compare Fig. 2A-B). This result is confirmed both by the diffuse rings in the SAED pattern and the homogeneous contrast in the BF image (Fig. 2C). After amorphization, successive steps of He-irradiation were performed. A first modification in the crystallinity of the amorphized monazite appears at 4x10¹⁶ He/cm², where nanometer size nuclei formed in the sample (Suppl. Mat. Fig. 7). Significant changes are observed at 5x10¹⁶ He/cm² with the presence of a greater amount of crystallized nuclei (arrows in Fig. 2D), corresponding to spots in the diffraction pattern (circle in SAED Fig. 2D). This nucleation process is similar to that due to an electron beam (Meldrum et al., 1997b; Deschanels et al., 2014), suggesting an effect of the electronic energy loss from α-particles, since the electron beam contribution in our experiment is negligible (Suppl. Mat. Fig. 7). This observation is confirmed by the achievement of another Au+He sequential irradiation experiment (#5; Fig. 8 in Suppl. Mat.) with 1.5 MeV He (factor of 4 lower S<sub>nucl.</sub> with similar S<sub>elec.</sub> than for #2), during which the same recrystallization was observed at similar fluence levels (Suppl. Mat. Fig. 8), ruling out a recovery mechanism involving nuclear energy loss. In contrast, He-irradiation of the partially damaged sample (#3; Fig. 3) induces immediate recovery of the crystallinity at
low He-fluence (from 10<sup>14</sup> He/cm<sup>2</sup>; Fig. 3C) with a very efficient recrystallization process (Fig. 3D-E), as attested by the disappearance of amorphous rings and appearance of Bragg diffraction lines, with well-defined bend contours at the end of the He-irradiation cycle (5x10<sup>15</sup> He/cm<sup>2</sup>; Fig. 3E). These results are a first demonstration that the electronic energy deposited in the sample during helium irradiation is responsible for the recrystallization of monazite, either inducing nucleation and growth (Fig. 2D) when starting with an amorphized material, or inducing a recovery of the defected structure when starting with a partially damaged monazite (Fig. 3B-E).

Results from the dual-ion beam experiment (Fig. 4) distinctly demonstrate that simultaneous irradiation with He and Au prevents monazite from undergoing amorphization, as the sample remains crystalline at Au fluences that induced full amorphization in experiment 1 (Figs. 4C-D). The only visible changes are modifications in the bright field contrasts, corresponding to small lattice distortion and presence of strains (i.e. Bragg lines are different in Figs. 4B-C-D); however, the global orientation is approximately the same in both SAED patterns when the doses increase from 10<sup>14</sup> to 2x10<sup>14</sup> Au/cm<sup>2</sup> (Figs. 4C-D). Another modification corresponds to the formation of mottled diffraction contrasts (Fig. 4D), typical of point defect formation due to ballistic process, which are commonly observed in natural monazite samples (e.g. Seydoux-Guillaume et al., 2003, 2004, 2018) or in monazite samples irradiated at lower Au-fluences (~ 0.05 dpa in Deschamps et al., 2014). The last proof that helium irradiation prevents monazite amorphization is shown in Figs. 4E-F. The bottom right area of the foil (Fig. 4E) corresponds to a region where the helium beam was masked (only irradiated by Au ions) and that is completely amorphous, as shown by the homogeneous BF-contrast and the diffuse rings in SAED pattern (Fig. 4E-F).

IMPLICATIONS
From our results, it can be concluded that during α-decay self-irradiation of monazite
a competition takes place between (1) damage creation by ballistic processes induced by
recoil nuclei, resulting in atomic displacements and defect formation, and (2) electronic
processes from α-particle ejection, from which the electronic energy deposited in the material
is sufficient to heal the displaced atoms and prevents the structure amorphization. This
mechanism, called α-healing, finally explains why monazite is never amorphous in nature,
independent from its thermal history: the α-particles are able to heal the damage generated by
the recoil nuclei, via a thermal spike induced by the electronic energy loss (Weber et al.,
2015; Zhang et al., 2015) and prevent amorphization.

Our results have different implications, especially in geochronology (U-Pb and Th-Pb), thermochronology (fission tracks and U-Th/He), and for the containment of actinides in monazite matrix. First, this mechanism explains what is long known about monazite U-Pb and Th-Pb dating, i.e. disturbance of the geochronological systems is not due to Pb diffusion (Seydoux-Guillaume et al., 2002). Pb diffusion coefficient obtained from experimental studies performed in synthetic monazite crystals (Cherniak et al., 2004; Gardès et al., 2006) must be very close to the Pb diffusion coefficient that would be measured from natural monazite samples. With the help of alpha-healing mechanisms, monazite can be continuously maintained in a crystalline state during its geological history even at low temperature. Our results confirm then, that, in contrast to zircon where amorphization is very common and in which Pb loss by diffusion can be enhanced, significant Pb loss in monazite will not happen via diffusion; the U-Pb and Th-Pb systems will remain closed at the µm scale, and thus grain size scale, and disturbance of U-Pb and Th-Pb systems can only happens via dissolution-precipitation mechanisms (Seydoux-Guillaume et al., 2018). However, at the nanoscale, Pb mobility could be locally and temporary enhanced due to defect formation before defect healing, and may be responsible for Pb segregation into nanophases observed at the nanoscale
in monazite (e.g. Seydoux-Guillaume et al., 2003; Fougerouse et al., 2018); this should be
studied in details, taking into account this new alpha-healing mechanism active in monazite.

Secondly, the knowledge of He diffusivity is crucial in (U-Th/He) thermochronology
for the estimation of closure temperature (Tc), to give correct interpretation of thermal history
(e.g. Farley and Stockli, 2002; Cherniak and Watson, 2013). In apatite, it has been
demonstrated that vacancies can efficiently trap He atoms, thus reducing diffusivity (Gerin et
al., 2017). In monazite, the differences in He diffusivities, and therefore in Tc (~100°C
difference according to authors; Peterman et al., 2014), depending on the type of samples
(natural vs synthetic) and the type of experiments (step heating vs ³He implantation) may be a
consequence of the amount of radiation damage in monazite, which depends on the healing
effect of He, as demonstrated in our study. Furthermore, ³He implantation (100 keV, 5 x 10¹⁵
He/cm²) used for He diffusivity measurements in natural monazite (Cherniak and Watson,
2013) may induce some recovery of radiation damage as these conditions are very similar to
those used in our present study (160 keV, recovery from 10¹⁴ He/cm²; Fig. 3) and may explain
discrepancies between authors using step heating (see Fig. 3 in Peterman et al., 2014), and a
much less pronounced difference in He-diffusivities between natural and synthetic monazite
for Cherniak and Watson (2013) than for Farley (2007). Our results have therefore
demonstrated the necessity to consider α-healing in experimental set-up and models used for
U-Th/He thermochronology. Length measurements of confined fission tracks in monazite
should also be taken with care because the efficiency of the α-healing is not considered in the
thermal annealing models. Even at ambient temperature, healing of tracks may reduce the
track length and make interpretation of thermochronological data difficult (Weise et al.,
2009). Furthermore, to correlate the amount of radiation damage in natural monazite samples
to the temperature at which they were exposed, should be avoided, as α-healing proceeds
independently from thermal history; low-temperature damage annealing has to be excluded as
an explanation of radiation resistance of natural monazite samples.

Finally, our results have important implications for the Pu and MA immobilization in
monazite matrices because it implies that the α-particles produced by α-decays are sufficient
to heal the structure damaged by self-irradiation due to recoil nuclei. Such a mechanism
acting in the monazite structure should prevent the matrix from amorphization and
microcracking as a consequence of swelling. The benefit is evident for the long-term behavior
of monazite as a nuclear waste matrices, because the leaching rate would not be altered by
radiation damage since the atomic structure and the specific surface area of the material
would be conserved.

ACKNOWLEDGMENTS:

Experiment performed at the CSNSM facility: JANNuS-Orsay/SCALP platform (CSNSM
Univ Paris-Sud / CNRS, Orsay, France). We thank V. Picot-Magnin (ISTerre, CNRS, France)
for the synthesis of monazite samples. This experiment was supported by the EMIR French
accelerator network. This work was partly supported by the french RENATECH network.
Two of the authors were supported by the U.S. Department of Energy, Office of Basic Energy
Sciences, Materials Science and Engineering Division (WJW) and the German Federal
Ministry of Education and Research (BMBF), grant no. 02NUK021A (SN), respectively.
NEEDS-CNRS is thanked for financial support. E. Gardès is thanked for the long and exciting
discussion on diffusion. Two anonymous reviewers are thanked for their constructive
comments. The associated editor, Ian Swainson, is also thanked for his helpful editorial
handling.

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FIGURES CAPTIONS

**Figure 2.** Bright-Field Transmission Electron Microscope images (BF-TEM) of a sequence of *in situ* irradiation in LaPO₄ monazite polycrystal - first experiment: complete amorphization (2x10¹⁴ Au/cm²). **A**- Part of the TEM focused ion beam (FIB) foil before irradiation. **B**- Same area as in A *in situ* irradiated up to 1x10¹⁴ Au/cm². The sample is amorphous with some phantoms of grain boundaries. **C**- Same area as in A *in situ* irradiated up to 2x10¹⁴ Au/cm². The sample is completely amorphous as shown by the homogenous contrast on the BF image and the presence of diffuse rings in the selected area electron diffraction (SAED) pattern (inset). **D**- Same area irradiated up to 5x10¹⁶ He/cm². Note the
presence of nuclei (arrows) that formed in the sample, and the corresponding diffraction spots
circle) reflecting recrystallization in the SAED pattern.

**Figure 3.** *Bright-Field Transmission Electron Microscope images (BF-TEM) of a sequence of in situ irradiation in LaPO₄ monazite polycrystal - second experiment: intermediate irradiation dose (5x10¹³ Au/cm²).* **A-** Part of the TEM foil before irradiation with SAED pattern (inset). Note that some amorphous material is present in the sample due to the FIB preparation (diffuse ring in SAED). **B-** Same area as in A after one irradiation and annealing cycle (see Table in sup data) followed by this second cycle, which start with in situ irradiation up to 5x10¹³ Au/cm². The sample is still crystalline as demonstrated by the SAED pattern (inset) but contains more radiation damage as shown by the presence of diffuse rings in the SAED and the disappearance of Bragg diffraction lines in the BF image. **C to E-** Annealing cycle starting with irradiation of helium from 1x10¹⁴ He/cm² (C), 1x10¹⁵ He/cm² (D) to 5x10¹⁵ He/cm² (E). Note the progression of recrystallization with the disappearance of amorphous rings and appearance of Bragg diffraction lines, with well-defined bend contours at the end (E). After the last He-irradiation the sample is perfectly crystalline and the orientation has changed and is close to a zone axis (compare the SAED patterns). The presence of mottled diffraction contrasts attest for He irradiation. **F-** The entire foil after irradiation; the bottom-left part correspond to the previous observed areas. Note the upper right part masked to Au-irradiation (arrow), which testifies to original crystallinity of the sample.

**Figure 4.** *BF-TEM of a sequence of *in situ* dual-beam (Au+He) irradiation in LaPO₄ monazite polycrystal.*
**A-** The entire foil before irradiation. **B-** Zoom in the left-bottom side area before irradiation. Note the Bragg diffraction lines (bend contours) witness of the crystallinity of the sample and depending on the orientation of the sample, and grain boundaries (sharp lines in the image). **C-** Simultaneous irradiation step with 1x10¹⁴ Au/cm² and 1.67x10¹⁶ He/cm². The sample is still crystalline (confirmed by SAED pattern), but with different bend contours resulting from slight orientation modification. **D-** Simultaneous irradiation step with 2x10¹⁴ Au/cm² and 3.40x10¹⁶ He/cm². The sample is still crystalline (confirmed by SAED pattern), with different bend contours. Note the presence of mottled diffraction contrasts in the upper part of the foil, which corresponds to few atomic displacements. **E-** The entire foil after dual-irradiation (2x10¹⁴ Au/cm² and 3.40x10¹⁶ He/cm²). **F-** Zoom in the bottom-right area of the foil showing a large zone completely masked to He irradiation. A large part of this area is completely amorphous: homogeneous contrast in BF and diffuse rings in the SAED pattern performed inside the circle (inset in E).
<figure><img src="image_2.png" /><figcaption>Before Au irradiation</figcaption></figure>

<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /></figure>
<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /></figure>
Before (Au+He) irradiation

Before (Au+He) irradiation

<figure><img src="image_12.png" /></figure>

A

500 nm

B

<figure><img src="image_13.png" /></figure>

1 x 10¹⁴ Au/cm²
1.67 x 10¹⁶ He/cm²

<figure><img src="image_14.png" /></figure>

2 x 10¹⁴ Au/cm²
3.40 x 10¹⁶ He/cm²

<figure><img src="image_15.png" /></figure>

C

500 nm

D

<figure><img src="image_16.png" /></figure>

2 x 10¹⁴ Au/cm²
3.40 x 10¹⁶ He/cm²

<figure><img src="image_17.png" /></figure>

E

<figure><img src="image_18.png" /></figure>

2 x 10¹⁴ Au/cm²
3.40 x 10¹⁶ He/cm²