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Abstract
Upcoming space instrumentation, such as LUMOS (LUVOIR Ultraviolet Multi-Object Spectrograph) in LUVOIR (Large Ultraviolet Optical Infrared Surveyor) mission, demands efficient narrowband coatings centered in the far UV (FUV). Narrowband FUV coatings can be prepared with all-dielectric multilayers (MLs) based on two fluorides. This research evaluates the performance of AlF3/LaF3 FUV MLs prepared by thermal evaporation and compares this performance with MgF2/LaF3 MLs, which were previously investigated. FUV reflectance, stress, and the influence of substrate materials have been investigated, along with ML stability over time when stored in a desiccator. Coatings were deposited both on fused silica and on CaF2 crystals, two common optical substrates. AlF3/LaF3 MLs exhibited reduced stress compared with MgF2/LaF3 MLs, resulting in a larger thickness threshold before crack generation. This enables preparing MLs with more layers and hence with higher performance. AlF3/LaF3 MLs underwent lower reflectance decay over time compared with MgF2/LaF3 MLs. Fresh MLs centered at ∼160 nm displayed a peak reflectance close to 100%, and most of the AlF3/LaF3 MLs kept a reflectance of 99% after several months of storage. The bandwidth of AlF3/LaF3 MLs for a given number of layers was found to be somewhat larger than for MgF2/LaF3 MLs.
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1. Introduction
Astrophysics, solar physics, and atmosphere physics can benefit from space observations in the far ultraviolet (FUV: λ = 100-200 nm) since the FUV contains an abundance of spectral lines which can help to increase the knowledge of the local Universe [1]. LUMOS (LUVOIR Ultraviolet Multi-Object Spectrograph) is an instrument in the LUVOIR – NASA mission concept, with science targets that include tomography of circumgalactic halos, exoplanet characterization, and water plumes in outer solar system satellites [2]. LUMOS will operate with narrow- and medium-band filters in a FUV imaging channel. The science requirements of LUMOS include exploring very faint objects in the FUV, which will need an enhancement on the optical performance of FUV narrowband coatings compared to pioneer instruments, such as the International Solar-Terrestrial Physics (ISTP) [3]. Other recently funded spatial instruments, that might benefit from narrowband FUV coatings, are GLIDE (Global Lyman-alpha Imagers of the Dynamic Exosphere) [4] and SIHLA (Spatial/Spectral Imaging of Heliospheric Lyman Alpha) [5], which are tuned at 121.6 nm. FUV narrowband coatings are also useful for many other fields. These include high-order harmonics, as the fifth harmonic of 800 nm emission of Ti:sapphire lasers is placed at ∼160 nm [6–10], or excimer laser optics [11], with, for example, F2 laser operation at 157 nm [12], and Xe2 at 172 nm [13]. Petawatt-laser beamlines [14], thermonuclear fusion reactors [15], or the semiconductor industry, including lithography on the sub-200 nm range [16], can also benefit from the use of tuned reflectors in the FUV. Yet, coating optical performance is somewhat limited in this part of the spectrum, due to the high absorption of materials and the need of an accurate knowledge of their optical constants.
FUV narrowband coatings typically consist of multilayers (MLs) with two materials with low absorption and contrasting refractive indices in Bragg configuration [17,18]. Fluorides are the materials that keep their transparency deeper in the FUV, so they have been typically chosen as the materials for FUV MLs. Lithium fluoride (LiF), magnesium fluoride (MgF2), and aluminum fluoride (AlF3) are the fluorides with the shortest FUV cutoffs, from which LiF has the shortest; however, its hygroscopic nature and the lack of knowledge of its optical constants complicate its application as a coating material. Nevertheless, LiF has been exceptionally used as a broadband mirror protection [19,20] and also in narrowband FUV MLs [21]. MgF2 and AlF3 have next shorter cutoffs at around ∼113 nm and ∼110 nm, respectively, and have been used in MLs as low-index materials along with, typically, lanthanum fluoride (LaF3), which is transparent down to a relatively short FUV wavelength and has a good contrasting refractive index with both low-index materials. AlF3 has still received limited attention, probably because of the relatively long successful experience with MgF2/LaF3 MLs, that has been reported in the literature for the last decades [3,22–28] and also due to the slightly hydrophilic nature of AlF3 [29]. Yet, various encouraging results regarding AlF3/LaF3 MLs have been reported on MLs, mostly tuned at long FUV wavelengths [24,30–33] and successful AlF3 protective coatings for Al have been reported [34–37]. Alternatives to LaF3, such as gadolinium fluoride (GdF3), and lutetium fluoride (LuF3) have been also attempted [38,39], but these materials are expected to have a longer cutoff compared with LaF3 and/or higher absorption and stress [40].
Fluorides with highest FUV transparency are deposited by vacuum evaporation. This transparency is enhanced when the coating is deposited on a heated substrate [41]. The latter is related with a reduced porosity, and hence with an increase of the packing density. This increase of the packing density will reduce the room for water or contaminant molecules, which could diminish the coating performance over time.
Fluorides deposited by thermal evaporation typically develop tensile stress, which can alter the figure of the substrate, and can also induce cracks and/or coating delamination. Most of this stress has a thermal origin when the fluoride coating is deposited on a heated low-expansion substrate, such as fused silica (FS). This is due to the large difference in thermal expansion coefficient (CTE) between substrate and film materials, which results in a larger contraction of the coating when cooling down from deposition temperature to room temperature (RT). The deleterious effect of stress increases with accumulated coating thickness and hence with the number of layers. A trade-off between temperature and the number of layers in the ML was determined for high-reflecting MgF2/LaF3 MLs at 160 nm [28]. AlF3 has been reported to have a somewhat lower CTE than MgF2 [32], so stress on AlF3/LaF3 MLs is expected to be lower than on MgF2/LaF3 MLs, and hence the crack thickness threshold is expected to be higher. An alternative procedure to reduce stress is the choice of the substrate material with reduced CTE difference with respect to the coating materials, such as crystalline calcium fluoride (CaF2) or MgF2.
This research investigates the performance of narrowband AlF3/LaF3 MLs and compares them with MgF2/LaF3 ML coatings that were investigated in a previous research [28]. Section 2 presents the main experimental techniques used. Section 3 presents the performance of AlF3/LaF3 MLs in terms of FUV reflectance, thickness threshold, stress, and the presence of cracks. MLs deposited both on FS and on CaF2, two commonly used substrate materials with very different CTEs, were also investigated.
2. Experimental
Fluoride MLs with LaF3 as the high-index material, and AlF3 as the low-index material were deposited in a high-vacuum chamber pumped with a turbo-Roots pump system and a titanium sublimation pump with a shroud that is cooled down with liquid nitrogen. Some MgF2/LaF3 MLs were also deposited in this system for comparison purposes. 99.99% pure AlF3 and LaF3 and VUV-grade MgF2 were evaporated from tungsten boats with deposition rates of ∼0.7 nm/s for AlF3, ∼0.6 nm/s for LaF3, and ∼0.8 nm/s for MgF2. Chamber base pressure was ∼3×10−5 Pa and it increased to ∼4×10−4 Pa during deposition. Substrates were cleaned with several rinses in organic solvents and cleaning was completed with a glow discharge in the deposition chamber. The total coating thickness was measured a posteriori with contact profilometry.
Substrates in the vacuum chamber were placed in contact with a resistance heater and a K thermocouple was used to measure substrate temperature. Substrate temperature was left to stabilize for ∼3 h before deposition to favor uniformity. Once deposition was finished, the coating was cooled down at a slow rate, as it has proven to be successful in slightly reducing stress in MgF2/LaF3 mirrors [26].
2 inch-diameter, 0.5 mm-thick, FS and CaF2 wafers were used as substrates. CaF2 wafers were (111) oriented monocrystals. The cut orientation of the CaF2 wafers was measured with Bragg-Brentano X-ray diffractometry through θ–2θ scans and was used to calculate the biaxial modulus of CaF2 [42,43]. Additional silicon or float glass substrates were also coated in the same vacuum cycle as witness samples. FUV reflectance was measured in GOLD’s reflectometer (GOLD is the Spanish acronym for Thin Films Optics Group, Madrid, Spain [44], which operates in ultra-high vacuum (UHV) conditions. The reflectometer has a grazing-incidence, toroidal-grating monochromator, with entrance and exit arms 146° apart and covers the 12.5-200 nm spectral range. A deuterium lamp was used to cover the range of 113 to 185 nm. A channel-electron-multiplier with a cesium iodide (CsI)-coated photocathode was used as a light detector. Reflectance was obtained by alternately measuring the incident intensity and the intensity of the light beam reflected at the sample. Near-normal reflectance measurements at GOLD reflectometer were performed at 5°. Reflectance measurements that were made at angles of 15° and above were performed using a Rochon prism polarizer in s and p polarization. FUV reflectance was initially measured after ∼one-hour sample contact with the atmosphere and it was also measured after various months of storage in a desiccator operating with silica gel. Hygrometers displayed a humidity below 20% in the desiccator at all times. To verify some high reflectance values, some aged samples were measured at NASA Goddard Space Flight Centre (GSFC) with a McPherson Vacuum Ultraviolet (VUV) 225 spectrophotometer. This spectrometer has a one-meter length, high-vacuum monochromator with a 1200 lines/mm grating at near-normal incidence operating in the spectral range from 30 nm to 325 nm. The spectrometer is equipped with a windowless hydrogen-purged light source, which provides discrete H2 emission lines between 90 nm and 161 nm and a continuum above these wavelengths. The detector, which is placed inside a sample-holder compartment, consists of a photomultiplier cathode tube connected to a light-pipe for feeding the light signal coming out of the monochromator. The light pipe has a fluorescence and high quantum efficiency coating of sodium salicylate that is used to convert the FUV radiation into visible light. The measurement error for the McPherson instrument is estimated to be 1%. Reflectance measurements with the latter spectrophotometer were performed at 10° from normal incidence; a negligible reflectance difference from normal incidence to 10° is calculated for the present MLs. Reflectance in the near UV to the near infrared (NIR) was measured with a lambda-900 Perking–Elmer, double-beam spectrophotometer, which operated at 8°.
Stress was measured ex situ at RT by the curvature method using a contact profilometer adapted to guarantee sample relocation after deposition. The radius of curvature was measured in two perpendicular directions before and after deposition. Stress was calculated by averaging both measurements. A “free-tension” holder was designed to place the wafers in contact with the heating element while minimizing external loads, specifically high tensions on small areas of the substrate, because we previously observed that cracks were like to start on those. A scheme of the fixture can be found on Fig. 1. The fixture consists of two pieces: a stainless-steel frame, which is in thermal contact with the heating element, and a copper holder, placed inside the frame. The substrate is held in a cavity, made in the holder, with a depth equal to the substrate thickness. To minimize tensions on the substrate, the latter is not directly clamped; instead, the clamps are placed between the frame and the holder.
Fig. 1. Front, and cross view of the fixture for the substrate during deposition. The holder was designed to minimize external loads on small areas of the substrate.
To evaluate coating surface quality, an optical microscope with different magnifications in dark field mode was used.
3. Results and discussion
3.1 FUV reflectance
A quarterwave (QW) periodic ML design of two fluorides of high (H) and low refractive index (L), (H/L)m, where m is the number of bilayers, was chosen to make narrowband reflectors nominally tuned in the FUV around 160 nm. The nominal layer thicknesses were ∼29 nm and ∼28 nm for the low-index materials (AlF3 and MgF2, respectively), and ∼21 nm for the high-index material (LaF3). All samples were deposited at ∼250°C, as stated as the optimal deposition temperature for MgF2/LaF3 MLs tuned at ∼160 nm to increase the transparency of the fluoride layers while maintaining acceptable stress levels [28]. This temperature was also reported as the fluoride optimal deposition temperature for broadband Al/MgF2 [45] and Al/AlF3 mirrors [36].
Seven AlF3/LaF3 ML coatings were prepared; the number of layers, deposition rates, and the substrate materials are presented in Table 1. Various MgF2/LaF3 MLs were also prepared for the sake of comparison.
Table 1. Design and deposition parameters.
Table 2. Central wavelength λ0, reflectance at central wavelength R(λ0), bandwidth in FWHM, and stress of samples over time.
Figure 2 compares the reflectance measured for AlF3/LaF3 MLs with 10, 12, 15, and 18 bilayers, which were deposited on the same FS substrate; measurements were performed after four months of ageing. To deposit various numbers of layers on a single sample, a shutter was progressively moved to mask some areas while the remaining areas were let to overcoat with further layers.
Fig. 2. Reflectance as a function of wavelength of (AlF3/LaF3)m multilayers with m = 10, 12, 15, and 18 (samples A_FS_10, A_FS_12, A_FS_15, and A_FS_18 in Table 1) deposited on a common FS substrate during the same vacuum cycle. Measurements were performed after 4 months of ageing in a desiccator.
The measured peak reflectance was close to ∼100% for the whole interval of 10 to 18 bilayers. Hence the number of bilayers required for high-reflectance (AlF3/LaF3) MLs at 160 nm is around 10. (AlF3/LaF3) MLs with additional bilayers were deposited to evaluate thicker MLs that could be useful for MLs tuned at longer wavelengths and also for the sake of comparison with similar (MgF2/LaF3) MLs reported on [28].
The influence of the substrate material on the ML performance was also investigated. Figure 3 shows the FUV reflectance of aged AlF3/LaF3 MLs deposited onto FS and CaF2 substrates. A high performance was obtained with either substrate material. Additionally, we present the aged reflectance of a (MgF2/LaF3)20 ML deposited on CaF2; the performance of (MgF2/LaF3) MLs deposited on FS were presented in [28]. While both (AlF3/LaF3)m and (MgF2/LaF3)m MLs presented very high FUV-peak fresh reflectances of, typically, ∼99% and ∼98%, respectively, they displayed bandwidth differences: the FWHM of (AlF3/LaF3) ML coatings was about 3 nm larger than for (MgF2/LaF3) MLs for the same number of bilayers. This is attributed to the refractive index of AlF3, which is expected to be somewhat smaller than for MgF2, and hence it would be more contrasting with LaF3. These differences in bandwidth can be taken advantage of for specific bandwidth targets.
Fig. 3. Reflectance as a function of wavelength of aged (AlF3 /LaF3)m MLs deposited on FS or CaF2 (CF) substrates; m = 13 and 20, (samples A_FS_13, A_FS_20, A_CF_13 in Table 1). Additionally, we present the aged reflectance of a (MgF2/LaF3)20 ML deposited on CaF2 (M_CF_20 in Table 1). Ageing period in months is shown in parenthesis. ªAged samples that were measured at NASA/GSFC.
Figure 4 presents the evolution over time of an (AlF3 /LaF3)13 ML on FS. The figure also presents the evolution of a (MgF2/LaF3)13 ML on FS, both aged in a desiccator. Most of the (AlF3/LaF3)m MLs kept their high reflectance of about 99% after several months of storage in a desiccator. On the other hand, many of the (MgF2/LaF3)m MLs, either prepared here or reported in [28], typically showed a trend to decay during the first months of storage.
Fig. 4. Evolution over time of the reflectance as a function of wavelength of (AlF3 /LaF3)13 (A_FS_13) (a) and (MgF2 /LaF3)13 (M_FS_13) filters (b) deposited on FS substrates. Ageing period in months is shown in parenthesis. Solid (dotted) lines correspond to fresh (aged) measurements. ªSamples that were measured at NASA/GSFC.
Another ageing phenomenon observed both on (AlF3/LaF3)m and (MgF2/LaF3)m MLs, regardless of the substrate material used, is that the reflectance band shifts ∼2 nm towards longer wavelengths. This shift usually occurs during the first months of ageing. The evolution over time of the central wavelength λ0, reflectance at central wavelength R(λ0), bandwidth in FWHM, and stress of the presented samples is presented on Table 2.
The dependence of the band with the angle of incidence is important for instrumentation with a large aperture. The FUV reflectance of an (AlF3 /LaF3)13 ML was measured at 4 incidence angles with both s and p polarization and is plotted in Fig. 5. As expected, the band shifted with the angle towards shorter wavelengths. The coating kept a high performance at an angle as large as 45° and the band shifted ∼15 nm from normal incidence. This behavior could enable band tuning upon filter tilting. For optics that work at angles different than the normal, for example at 45°, quarterwave coatings can be designed to peak at the desired wavelength (160 nm in this case) by properly increasing the optical thicknesses of both materials. Calculations predict that a periodic ML tuned at 160 nm at 45° for unpolarized radiation would reflect about ∼ 2% less, and would have a bandwidth about ∼1.5 nm narrower than a ML tuned at normal incidence.
Fig. 5. Reflectance as a function of wavelength at four angles of incidence for s and p polarization of an 8-month aged (AlF3 /LaF3)13 ML deposited on FS (sample A_FS_13 in Table 1).
Sample A_FS_13 in Table 1 was measured at longer wavelengths up to the NIR. Measurements were performed after 1 year of ageing in a desiccator. The full spectrum is plotted in Fig. 6. In the out-of-band, reflectance is kept under 10% for the visible and NIR. Measured reflectance includes the contribution from the back substrate surface, and no attempt was made to reduce such contribution.
Fig. 6. Near-normal reflectance as a function of wavelength extended to the visible and the near IR of a 1-year aged (AlF3 /LaF3)13 ML deposited on FS (sample A_FS_13 in Table 1). The x-axis is scaled linearly up to 180 nm, and then logarithmically up to 2500 nm.
3.2 Surface quality
To evaluate the quality of the coating surfaces, and/or the presence of cracks, coatings were inspected in the optical microscope. Images were taken after a few days of contact with the atmosphere and they were taken again several months after deposition on similar sample areas. Microscope pictures of some samples are presented in Fig. 7. No cracks were observed on fresh (AlF3/LaF3)m MLs deposited on FS for the investigated values of m between 10 and 20, (∼500 to ∼1000 nm total thickness, respectively). This wide thickness range without cracks suggests that MLs with high reflectance at longer wavelengths, which require thicker coatings, can be prepared below the cracking threshold.
Fig. 7. Dark-field images of (AlF3/LaF3)m MLs, with m = 13 (a, b) and 20, (c, d) deposited on FS taken a few days (fresh) and after several months (aged) of contact with the atmosphere.
In [28,46] it was observed that crack generation is a dynamic process, and fluoride coatings with higher initial stress tend to develop cracks over time. After several months of ageing, an (AlF3/LaF3)20 ML deposited on FS displayed marginal cracks in the limit of detection, so that the bilayer number m limit for 160-nm peaked (AlF3/LaF3)m MLs must be in the ∼18-20 range (∼1000 nm total thickness). This contrasts with the thickness threshold to avoid cracks observed for hot-deposited (MgF2/LaF3)m MLs on FS also tuned at 160 nm, which was about 13 bilayers (∼650 nm total thickness) [28].
Regarding coatings deposited on CaF2 substrates, Neither (MgF2/LaF3)m nor (AlF3/LaF3)m MLs presented cracks for any of the bilayer number evaluated in this research. The presence of cracks on the two sorts of MLs both on FS and CaF2 are summarized in Table 3, which includes some additional witness samples that were deposited during the same vacuum cycle on different substrates, such as silicon or float glass.
Table 3. Crack density on (AlF3/LaF3)m MLs deposited on FS, CaF2, Silicon, and glass substrates compared with (MgF2/LaF3)m MLs.
3.3 Stress
Crack generation is attributed to coating stress. Among the various contributions to the total stress of a coating [52], thermal stress is expected to be predominant in fluoride MLs deposited on low-expansion substrates, such as FS [53]. Thermal stress, σtherm, is caused by the difference in CTE between the substrate (αsub) and the film (αfilm) and by the temperature difference between deposition (Td) and stress measurement (T) [46,54] according to:
Stress was evaluated using Stoney’s equation [55]. The application of Stoney’s equation in MLs assumes that each individual layer contributes to the total deformation of the substrate regardless of its position and neighbors [56,57]. Total stress of AlF3/LaF3 MLs was measured a few days after deposition and again a few months later, and it is shown in Figs. 8 and 9; some MgF2/LaF3 MLs were also measured to extend the comparison with AlF3/LaF3 MLs [28]. Figure 8 indicates that MLs with AlF3 grow with smaller stress than MLs with MgF2, of about 70 MPa for an (AlF3/LaF3)13 ML compared with 170 MPa for the equivalent (MgF2/LaF3)13 ML. This is correlated with the reported lower CTE of bulk AlF3 compared to MgF2 [32]. The generation of cracks does not only depend on stress, but also on thickness (or hence on the number of bilayers), through the Force Per Unit Width (FPUW), which equals stress times thickness. Hence, increasing thickness will increase FPUW, eventually leading to crack formation.
Fig. 8. Total stress vs number of bilayers, m, for (AlF3/LaF3)m and (MgF2/LaF3)m MLs deposited on a) FS, or b) CaF2.
Fig. 9. Stress relaxation over storage time in a desiccator for samples plotted in Fig. 8: a) deposited on FS, and b) deposited on CaF2; solid (dotted) lines denote 13 (20) bilayers.
Regarding substrate nature, for a given number of bilayers, samples deposited on CaF2 of both (AlF3/LaF3) and (MgF2/LaF3) MLs show lower stress than samples deposited on FS, as expected for the lower CTE contrast of CaF2 with the coating.
On stress evolution over time, MLs with MgF2 display a clear decreasing trend, whereas MLs with AlF3 display a slight or even null decay, which correlates with the observed evolution of peak reflectance of (AlF3/LaF3)m and (MgF2/LaF3)m MLs. In contrast, their band shifts in a similar way for both fluoride combinations. Some possible phenomena that might be at the origin of band shift over time are thickness expansion, and/or material interdiffusion at the interfaces. The absorption of water, or other contaminants, in the porous structure of the coating, might also lead to band shifts or band shape changes, and also to some stress relaxation over time [26,32,58]. Coating porosity and the presence of contaminants is expected to depend to some extent on specific deposition rates and on the partial pressure of gases in the chamber during deposition, and it cannot be discarded that unintentional differences on such parameters might be at the origin of part of the ageing differences observed over the two sorts of ML coatings.
4. Conclusions
(AlF3/LaF3)m MLs centered at ∼160 nm were deposited by thermal evaporation at 250°C and their FUV reflectance, stress, and the presence of cracks were investigated, as well as their optical and mechanical stability over time. Additional (MgF2/LaF3)m MLs were prepared to extend the comparison between both material combinations.
Most of the (AlF3/LaF3)m MLs presented a FUV peak reflectance of ∼99% and kept this reflectance after several months of ageing. While most (MgF2/LaF3)m MLs also presented high initial peak reflectance of, typically, ∼98%, reflectance decayed during the first months of storage. The band of both fluoride combinations shifted about ∼3 nm towards longer wavelengths over time.
The bandwidth was about 3 nm (FWHM) larger for (AlF3/LaF3) ML coatings compared with (MgF2/LaF3) MLs. Such difference is attributed to the refractive index of AlF3, which is expected to be somewhat smaller than the refractive index of MgF2. These bandwidth differences can be taken advantage to select the material pair that better matches the specific bandwidth requirements. By increasing the angle of incidence, the band shifted towards shorter wavelengths; at an angle as large as 45°, the coating kept high performance with a shift of ∼15 nm. Such shift could enable band tuning upon filter tilting.
The top number of bilayers before crack generation for 160-nm MLs deposited on FS was found to be ∼18-20 for (AlF3/LaF3) MLs (∼1000 nm), which is considerably larger than the number for (MgF2/LaF3) MLs that was evaluated in a previous research, which was ∼13 (∼650 nm). This was correlated with the reduced stress that was measured for (AlF3/LaF3) MLs on FS compared to (MgF2/LaF3) coatings.
An effective way to decrease stress on fluoride coatings, and thus, to prevent crack generation, is the use of substrates with lower CTE contrast with the coating, such as CaF2 instead of FS, which resulted in a reduced stress for an (AlF3/LaF3) ML with 13 bilayers from 73 to 27 MPa. Other than crystalline fluorides, such as CaF2 or MgF2, substrates with medium CTE contrast with the fluoride films, such as BK7 or quartz, are expected to enable coatings with an intermediate stress, and such substrates could be a good choice when the fluoride crystal substrates could not be used. This would enable a higher deposition temperature and/or coatings with a larger number of bilayers compared with the use of low-CTE substrates like FS.
Funding
Agencia Estatal de Investigación (BES-2017-081909, ESP2016- 76591-P, PID2019-105156GB-I00); Ministerio de Economía, Industria y Competitividad, Gobierno de España (BES-2017-081909).
Acknowledgments
We gratefully acknowledge José L. Bris and Joaquín Campos for spectrophotometer measurements, Ignacio Carabias and “Centro de Asistencia a la Investigación”, Universidad Complutense de Madrid (UCM), for performing XRD measurements, and M. Quijada (NASA/GSFC) for aged reflectance measurements. LRM acknowledges CRESST II cooperative agreement supported by NASA under award number 80GSFC21M0002.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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