High-dose temperature-dependent neutron irradiation effects on the optical transmission and dimensional stability of amorphous fused silica

Journal of Non-Crystalline Solids 525 (2019) 119668

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High-dose temperature-dependent neutron irradiation effects on the optical transmission and dimensional stability of amorphous fused silica☆

T

Christian M. Petriea, , Anthony Birrib, Thomas E. Blueb ⁎

a b

Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831, USA The Ohio State University, 281 W. Lane Ave., Columbus, OH 43210, USA

ARTICLE INFO

ABSTRACT

Keywords: Irradiation Fiber optic Transmission Compaction Silica

The primary concern for implementing amorphous fused silica (a-SiO2) fiber optic sensors in a nuclear environment is the radiation-induced attenuation (RIA) of the light signal due to the formation of radiation-induced color centers. In addition, Bragg grating sensors drift under irradiation due to radiation-induced compaction of the a-SiO2 structure. This work provides new data regarding RIA and radiation-induced compaction of a-SiO2 samples irradiated to a fast neutron fluence of 2.4 × 1021 n/cm2 at temperatures of 95, 298, and 688 °C. Results show that RIA may be approaching saturation for the range of photon energies evaluated in this paper and that the hydroxyl content has a significant impact on RIA when the irradiation temperature is increased to 688 °C. A model was developed for predicting radiation-induced compaction, and the resulting signal drift for Bragg grating sensors, as a function of neutron fluence and temperature.

1. Introduction Instrumentation for process monitoring and control of nuclear reactors must be able to provide reliable measurements under extremely harsh conditions. Depending on the specific reactor design, the sensor must survive extended exposure to high temperatures (300–1000 °C), high pressures (up to tens of MPa), radiation damage (on the order of tens to hundreds of displacements per atom, or dpa), and chemically aggressive media. The sensor must provide adequate signal strength with minimal drift over a period of months to years. Most reactor designs require monitoring of temperature, pressure, coolant flow rate, and neutron flux within the primary system [1]. Some instrumentation currently being used for process monitoring in light water reactors (LWRs) is not suitable for advanced reactor applications because of concerns related to high temperatures, chemical compatibility, or increased radiation damage dose [2]. Other nuclear applications include in situ performance monitoring of nuclear fuels and materials during irradiation in test reactors, which requires monitoring of temperature, neutron flux, dimensional changes, and thermal and mechanical properties [3–5]. Compact cores in some reactor designs limit the quantity and size of vessel penetrations for instrumentation and place increased

importance on small sensors that are capable of multimodal measurements. Even in larger core designs, vessel penetrations are minimized because they increase the risk of coolant leaks from the primary containment vessel. Fiber optic sensors have long been considered as candidate technologies for nuclear applications given (1) their small diameter, (2) their immunity to electromagnetic interference, (3) their capability to withstand high temperatures, and (4) their ability to perform spatially distributed sensing and/or multimodal measurements. Fiber optic–based sensors have been demonstrated for measuring temperature [6–9], pressure [7,10,11], flow [12–14], and liquid level [15–17]. Measurements of neutron and gamma flux have been demonstrated for low dose applications [18–20]. The primary concern for deploying any of these fiber optic–based sensors for nuclear applications is radiationinduced attenuation (RIA) of the light signal due to color center formation during exposure to ionizing radiation. 1.1. RIA in amorphous fused silica Amorphous fused silica (a-SiO2) optical fibers are known to suffer from RIA, particularly in the ultraviolet (UV) and visible ranges. Much

☆ Notice: This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan). ⁎ Corresponding author. E-mail address: [email protected] (C.M. Petrie).

https://doi.org/10.1016/j.jnoncrysol.2019.119668 Received 30 May 2019; Received in revised form 30 August 2019; Accepted 6 September 2019 Available online 19 October 2019 0022-3093/ © 2019 Elsevier B.V. All rights reserved.

Journal of Non-Crystalline Solids 525 (2019) 119668

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work has been devoted to determining the defects in a-SiO2 that are responsible for RIA and the dependence of RIA on ionizing dose, dose rate, temperature, wavelength, fiber stoichiometry, and dopants [21–25]. Most studies generally agree that the most radiation-resistant a-SiO2 optical fibers are those with a pure silica core and F-doped silica cladding. Dopants such as Cl and Ge are known to result in increased defect absorption [26,27]. Hydrogen loading can passivate radiationinduced defect centers in the UV to visible range at the expense of increased intrinsic absorption in the infrared [28]. However, most sources that discuss the effect of hydrogen loading on RIA are based on gamma irradiations or low-fluence neutron irradiations. While most defect centers have peak absorption in the UV-to-visible range, which is far from typical operating sensor wavelengths near 1300 and 1550 nm, these absorption bands can extend into the infrared after high dose irradiation. There is also evidence of increased infrared absorption in aSiO2 that is not fully understood but could be due to increased vibrational absorption after metamictization that occurs after accumulation of significant fast neutron fluence [29–31]. Despite the significant amount of previous research investigating RIA in a-SiO2, questions remain regarding performance at extremely high displacement damage dose caused by neutron irradiation. Moreover, the data regarding RIA and radiation-induced dimensional change at temperatures above 100 °C is very limited. Cheymol et al. tested a variety of a-SiO2 fibers and monitored broadband RIA in situ during irradiation up to a maximum fast neutron fluence of 1.3 × 1020 n/cm2 [29]. Although the temperature was not specified, the fibers were in contact with an aluminum plate that was cooled by the reactor coolant, so the temperature was likely not significantly higher than the reactor's coolant temperature (38–47 °C). Cheymol et al. observed prohibitively large RIA in the UV-to-visible range, as well as increased infrared absorption that was earlier attributed to radiation-induced compaction of the glass [32]. The minimum RIA was observed in the range of 800–1100 nm, with some a-SiO2 fibers showing attenuation as low as ~5 dB (10 dB/m, assuming an active fiber length of 50 cm within the high neutron flux region) at the end of the irradiation. Hollow core photonic band gap fibers showed significantly lower RIA—with one fiber exhibiting RIA < 1 dB—before they abruptly failed after accumulating a fast neutron fluence of ~9 × 1020 n/cm2. Increased temperatures are generally expected to reduce RIA, and a few experiments have confirmed this by monitoring RIA in a-SiO2 fibers in situ during low-dose, temperature-controlled neutron and/or gamma irradiation [33–37]. However, the maximum fast neutron fluence achieved during this in situ testing was only 4.5 × 1015 n/cm2. Zaghloul et al. tested Type II, femtosecond fiber Bragg grating sensors (center wavelength near 1550 nm) during irradiation at temperatures in the range of 600 °C to a total fast neutron fluence of ~1 × 1020 n/cm2 [38]. The gratings showed only ~5 dB signal reduction over the entire experiment that seemed to be approaching saturation. With an irradiated fiber length of ~60 cm, the attenuation per unit length was ~8.3 dB/m. For comparison, Cheymol et al. observed RIA > 35 dB/m at 1550 nm during irradiation at a temperature < 100 °C to a much lower fast neutron fluence of 3.2 × 1019 n/cm2 [29]. While this improvement at high temperatures is encouraging, additional data regarding broadband temperature-dependent RIA at high neutron dose is required before a-SiO2 fiber optic sensors can be reliably deployed for in-core applications in advanced nuclear reactors or in-pile applications in materials test reactors.

equilibrium volumetric compaction following irradiation at temperatures < 60 °C was 2.5–2.9%. Later efforts showed no temperature dependence of radiation-induced compaction in the range of 0–100 °C [40]. A more recent study showed that when the irradiation temperature is increased to 291 °C, the radiation-induced compaction in a-SiO2 after accumulating fast neutron fluence levels of 2.8 × 1019 n/cm2 and 4.8 × 1019 n/cm2 is reduced to 0.7–1.0% [41]. While post-irradiation annealing studies of radiation-induced compaction suggest that higher irradiation temperatures would further reduce radiation-induced compaction [39], there are no data regarding radiation-induced compaction following neutron irradiation at temperatures beyond 300 °C. 1.3. Scope of this paper This paper discusses measurements of RIA and radiation-induced dimensional changes in a-SiO2 samples subjected to high-dose neutron irradiation at nominal temperatures of 100, 300, and 700 °C. The doses and temperatures to which the specimens were exposed are relevant to both LWRs and some advanced high-temperature reactor concepts. The irradiation temperatures are higher than those of previous works to allow for quantification of the temperature-dependence of compaction. Understanding radiation-induced compaction as a function of dose and temperature is important for estimating radiation-induced drift of sensors such as Bragg gratings during operation. Silica samples with low and high hydroxyl (OH) content are tested to evaluate the influence of OH on RIA after high-dose neutron irradiation at various temperatures. Ultimately, these results seek to improve the fundamental understanding of radiation effects on a-SiO2 to determine the suitability of fiber optic sensors for high-temperature nuclear applications. 2. Experimental methodology 2.1. Samples Amorphous SiO2 samples were obtained from Heraeus with both low (Infrasil 301) and high (Spectrosil 2000) OH content. The nominal OH contents specified by Heraeus are < 8 weight parts per million (wppm) for Infrasil 301, and ~1350 wppm for Spectrosil 2000. The nominal sample dimensions were 16 mm length × 5 mm width × 0.85 mm thickness. Optical transmission was measured through the sample thickness. The pre-irradiation densities were measured to be 2.194 ± 0.005 g/cm3, which is consistent with the nominal density of 2.20 g/cm3 specified by the vendor. Four specimens of each material were included in each irradiation capsule, each of which was designed for a unique temperature, as described in Section 2.2. 2.2. Irradiation testing The capsules were irradiated in the flux trap of the High Flux Isotope Reactor (HFIR). The capsules were exposed to an average thermal (neutron energy < 0.5 eV) neutron flux of 1.9 × 1015 n/cm2/s and an average fast (neutron energy > 0.1 MeV) neutron flux of 1.1 × 1015 n/cm2/s over 25.7 effective full power (85 MW) days of irradiation. The resulting thermal and fast neutron fluences were 4.2 × 1021 and 2.4 × 1021 n/cm2, respectively. The calculated displacement damage dose is 5.2 dpa, assuming values of 15 and 28 eV for the threshold displacement energies in Si and O, respectively [42]. The specimen temperatures were estimated using thermal finite element simulations. Neutron and gamma heating of the experiment components was evaluated using the Monte Carlo N-Particle (MCNP) radiation transport code [43] and the ORIGEN module of the SCALE code package [44]. Simulation of heat transport from the specimens through an insulating inert gas gap to the reactor coolant was performed using three-dimensional finite element analyses in the ANSYS software package, similar to other previous material irradiations [45,46]. Passive silicon carbide temperature monitors (TMs) were

1.2. Radiation-induced dimensional changes In addition to RIA, some sensors such as Bragg gratings are known to drift under irradiation due to radiation-induced dimensional changes that cannot be distinguished from changes in temperature or strain. Primak quantified the compaction of a-SiO2 and the resulting metamict phase formation that appears to approach an equilibrium after accumulation of a fast neutron fluence on the order of 1019 n/cm2 [39]. The 2

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Table 1 Summary of calculated specimen and passive TM temperatures and TM temperatures measured post-irradiation. Nominal design temperature

Specimen material

Calculated average [min − max] specimen temperature (°C)

Calculated average [min − max] TM temperatures (°C)

Measured average [min − max] TM temperatures (°C)

Adjusted average specimen temperature

100 °C

Low-OH a-SiO2 High-OH a-SiO2

99 [78–131] 99 [76–131]

104 [91–129] 127 [113–138]

95 °C

300 °C

Low-OH a-SiO2 High-OH a-SiO2

306 [271–346] 295 [246–342]

316 [281–354] 331 [296–354]

600 °C

Low-OH a-SiO2 High-OH a-SiO2

617 [585–649] 594 [540–637]

626 [570–658] 627 [588–654]

125 115 108 110 307 292 330 360 705 717 708

pressed against the specimens during irradiation and evaluated postirradiation using dilatometry to confirm the irradiation temperatures [47]. Table 1 summarizes the calculated temperatures of the specimens and the passive temperature monitors, as well as the experimental temperatures determined using dilatometry. For the nominally 100 °C specimens, all the measured average TM temperatures fall in between the calculated average temperatures for the two sets of TMs included in the analyses. For the nominally 300 °C specimens, there is more variation in the measured TM temperatures, but three of the four experimentally determined average TM temperatures (292–360 °C) fall within the range of temperatures (281–354 °C) predicted by the thermal analysis. The passive TMs for the nominally 600 °C specimens showed measured average temperatures that were approximately 80–100 °C higher than those predicted by the thermal analyses. The best estimate of the specimen temperature can be determined by taking the average of the measured TM temperatures and compensating by the calculated difference in average temperature between the specimens and the TMs. When including the calculated temperatures of the a-SiO2 specimens and the single-crystal sapphire specimens that were also included in these experiments (to be discussed in a future paper), the average specimen temperatures are 95, 298, and 688 °C for nominal design temperatures of 100, 300, and 600 °C, respectively. These average specimen temperatures are used for the remainder of the paper.

[116–132] [102–125] [95–119] [98–120] [259–330] [257–316] [303–352] [330–382] [672–736] [683–747] [694–717]

298 °C

688 °C

uses deuterium (StellarNet SL3) and tungsten halogen (StellarNet SL1) light sources, coupled via a multimode fiber optic Y cable into a cuvette holder (ThorLabs CVH100). Inside the cuvette holder, the samples are held in a custom sample holder (see Fig. 1b) that keeps the samples vertically oriented so that the light is perpendicularly incident on the samples. Aspheric condenser lenses in the cuvette holder focus the incident light onto the sample and collect the transmitted light into a second multimode fiber optic Y cable. The two output ends of the second Y cable are coupled to a UV/visible spectrometer (StellarNet SILVER-Nova, 190–1100 nm range) and a near infrared spectrometer (StellarNet DWARF-Star, 900–1700 nm range). Because there is some overlap in the wavelength range of the two spectrometers, the UV/ visible spectrometer was used to measure transmission for wavelengths up to 1020 nm and the infrared spectrometer was used for wavelengths > 1020 nm. The RIA in the sample is expressed in units of optical density (OD), which is calculated from the ratio of the spectral intensities (proportional to the photon flux) measured by the spectrometers with (the active scan) and without (the reference scan) the specimen inserted into the container. This calculation is shown in Eq. (1):

OD(E) =

I (E) 1 log10 A T IR (E)

(1)

where T is the sample thickness and IA and IR are the intensities for the active and reference scans, respectively, as a function of photon energy hc E= (where h and c and Planck's constant and the speed of light, respectively), or alternatively, wavelength λ. Five measurements were taken for each active and reference scan. These measurements are evaluated to determine mean intensities and statistical uncertainties as a function of energy. While RIA in optical fibers is typically expressed in logarithmic units such as dB/m, RIA in thin slab samples like the ones tested in this work is often expressed as an OD in units of cm−1. OD data in cm−1 can be converted to units of dB/cm by multiplying by a factor of 10. To improve signal-to-noise ratios at higher energies (lower

2.3. Post-irradiation measurements After irradiation, the samples were extracted from the irradiation capsules in a hot cell, cleaned, and transferred to a separate low-activation facility for dimensional inspection using a micrometer. The same dimensional measurements were performed pre-irradiation to allow for quantification of radiation-induced compaction. Because the SiO2 samples are amorphous, the radiation-induced compaction is expected to be isotropic. The samples were then interrogated using a broadband optical transmission system shown schematically in Fig. 1a. This system

Fig. 1. (a) Schematic of optical transmission measurement system, and (b) picture showing sample inside sample holder. 3

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C.M. Petrie, et al.

wavelengths) where there was significant light attenuation, additional active scan measurements were performed with increased detector integration times. The intensities that were measured with shorter and longer integration times are denoted as IS(E) and IL(E), respectively. However, increasing the integration time can result in detector saturation for photon energies at which the sample attenuation is lower. Consequently, IA(E) is formed by combining the two spectrometer output data sets IS(E) and IL(E) without including the intensity data for which the spectrometers' output was saturated. For the photon energies that require increased integration times, the reference intensities must also be compensated because the integration time is not the same for the reference vs. active scans. Reference scans cannot be performed with the increased integration times because the detectors would become saturated for most energies and would not accurately represent the true photon flux. Instead, the reference intensities for the photon energies that require increased integration time are artificially increased by a scalar constant to preserve the true spectral absorption curve across the transition in the data sets from longer integration time for higher energies to shorter integration time for lower energies. To distinguish between the compensated reference intensity data—denoted as IR(E) to be consistent with Eq. (1) —and the uncompensated intensities measured by the spectrometer with no sample inserted, the uncompensated intensities are denoted as IRU(E). A mathematical description of the determination of IA(E) and IR(E) from the measured values IS(E), IL(E) and IRU(E) is shown in Eq. (2) and Eq. (3). The active intensities IA(E) are simply set equal to the values of IS(E) or IL(E), depending on the photon energy relative to Etrans. The values of Etrans were chosen for each sample such that IS(Etrans) was maximized without IL(Etrans) reaching saturation. The value of Etrans varies for each specimen, but it is generally in the range of 3.54–4.96 eV (250–350 nm). The reference intensities IR(E) are equal to IRU(E) for photon energies less than Etrans. For E ≥ Etrans, the values of IRU(E) are scaled by the ratio to ensure that the optical density has a smooth transition between data sets made with different integration times.

IA (E) = IS (E)forE < Etrans IA (E) = IL (E)forE Etrans IR (E) = IRU (E)forE < Etrans , IR (E) = K × IRU (E)forE Etrans I (E ) whereK = L trans IS (Etrans)

Fresnel reflection losses occurring at the interfaces between the samples and the surrounding air. Pre-irradiation measurements show minimal sample attenuation, particularly for photon energies < 3 eV, and they remain below 2 cm−1 for all energies. Vendor-supplied, wavelengthdependent Fresnel reflection losses range from ~9% at 200 nm to ~6% at 1600 nm. While the Fresnel reflection losses are independent of specimen thickness, they are manifested as an increase in the optical density, which is expressed per unit thickness. Converting these Fresnel reflection losses to an optical density and dividing by a nominal specimen thickness of 0.85 mm gives a contribution of 0.3–0.5 cm−1 to the measured optical density. For photon energies < 1.5 eV (wavelength > 827 nm), all pre-irradiation measurements showed optical densities within the range of the expected Fresnel reflection losses, which indicates that the pre-irradiation absorption is negligible over this energy range. All samples show a maximum post-irradiation optical density in the range of 4.5–6.0 eV (207–276 nm) and a general decrease in optical density with decreasing photon energy (or increasing wavelength) for energies less than the peak absorption energy. For photon energies < 1.9 eV (wavelength > 653 nm), the measured optical density in all samples irradiated at 95 and 298 °C were equal to the preirradiation optical density data within the measurement uncertainties. The low-OH and high-OH a-SiO2 samples have similar behavior after irradiation at temperatures of 95 and 298 °C. The increase in irradiation temperature from 95 to 298 °C caused a slight increase in the maximum optical density, a positive shift in the energy corresponding to the maximum optical density, and a reduction in optical density for photon energies below ~4.9 eV. Increasing temperature from 298 to 688 °C resulted in a decrease in the maximum optical density, with more significant decreases occurring in the high-OH sample vs. the low-OH sample. Both the low-OH and high-OH a-SiO2 samples show a broadband 1–2 cm−1 increase in optical density after irradiation at a temperature of 688 °C. There is some discrepancy in the measured optical density for the low-OH sample irradiated at 688 °C near 1.22 eV (1020 nm), where there is a transition between the data measured by the two spectrometers. It is unclear what may have caused this discrepancy.

(2)

4. Discussion 4.1. Radiation-induced compaction in a-SiO2

(3)

Amorphous SiO2 is known to compact under neutron irradiation, and the amount of compaction approaches an equilibrium after accumulating enough fast neutron fluence. Primak found that the amount of compaction (C) with respect to dose (or fast neutron fluence, Φ) follows Eq. (4) [40]:

3. Results 3.1. Dimensional changes Table 2 summarizes the dimensional changes in all specimens measured after irradiation. All specimens compacted under irradiation and the magnitude of the radiation-induced compaction decreased monotonically with increasing temperature. Post-irradiation measurements of specimen width and thickness were also performed. The postirradiation thickness measurements were used to determine optical density per unit thickness. However, because the width and thickness were considerably smaller than the length, reliable measurements of the change in these dimensions could not be made. One high-OH sample was broken during post-irradiation handling.

C( ) = C

1

e

s

,

(4)

where C∞ is the equilibrium compaction and ΦS is the characteristic fast neutron fluence for saturation of the radiation-induced compaction. Eq. (4) does not account for the slight recovery of the compaction observed prior to reaching an equilibrium. Primak et al. suggest that a small portion of the compaction following neutron irradiation is locked in by adjacent damage cascades, which the authors compare to two springs stressing against each other [48,49]. They theorize that the recovery of compaction at higher fast neutron fluence seems to be related to ionization-induced rearrangement of overlapping long-range strain fields caused by these adjacent damage cascades, which are most vulnerable to radiation annealing. Most previous irradiation tests were performed at low temperatures (< 100 °C) with a total accumulated fast neutron fluence on the order of 1020 n/cm2 or lower [39,50,51]. Primak found that radiation-induced compaction has a small temperature dependence in the range of 30–90 °C [48]. There are some limited data [41,50] indicating that the

3.2. Optical transmission Fig. 2 and Fig. 3 show optical density as a function of photon energy and wavelength with irradiation temperature (T) as a parameter for low-OH and high-OH a-SiO2 samples, respectively. The optical density data are divided by the measured sample thickness to give units of cm−1. The measurements include the effects of absorption, as well as 4

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Table 2 Summary of dimensional measurements before and after neutron irradiation to a fast neutron fluence of 2.4 × 1021 n/cm2. Irradiation temperature

Specimen material

Pre-irradiation length (mm)

Post-irradiation length (mm)

Linear dimensional change

Average linear compaction

Average volumetric compactiona

95 °C

Low-OH a-SiO2

15.738 15.725 15.718 15.714 15.729 15.727 15.741 15.741 15.735 15.731 15.732 15.724 15.736 15.718 15.731 15.722 15.740 15.733 15.732 15.731 15.722 15.729 15.726 15.723

15.626 15.624 15.599 15.596 15.613 15.603 15.628 15.623 15.647 15.633 15.632 15.636 15.634 15.621 15.637 15.623 15.704 15.706 15.702 15.702 15.700 Broken 15.708 15.696

−0.71% −0.64% −0.76% −0.75% −0.74% −0.79% −0.72% −0.75% −0.56% −0.62% −0.64% −0.56% −0.65% −0.62% −0.60% −0.63% −0.23% −0.17% −0.19% −0.18% −0.14%

0.73 ± 0.04%

2.20 + 0.13%

0.61 ± 0.03%

1.83 + 0.10%

0.17 ± 0.04%

0.52 + 0.11%

High-OH a-SiO2

298 °C

Low-OH a-SiO2

High-OH a-SiO2

688 °C

Low-OH a-SiO2

High-OH a-SiO2

a

−0.11% −0.17%

Calculated from linear dimensional change, assuming isotropic behavior.

Fig. 2. Optical density vs. photon energy and wavelength with irradiation temperature (T) as a parameter for the low-OH a-SiO2 samples.

Fig. 3. Optical density vs. photon energy and wavelength with irradiation temperature (T) as a parameter for the high-OH a-SiO2 samples.

amount of compaction could be significantly lower at temperatures in the range of 300 °C. These findings are consistent with the significant thermal annealing of the radiation-induced compaction that has been observed during post-irradiation isochronal annealing [39]. The dimensional measurements described in this paper can be combined with previous measurements to obtain a more complete picture of radiationinduced compaction in a-SiO2. The measurements performed in this paper can help to determine (1) whether the radiation-induced compaction is indeed approaching an equilibrium at temperatures of ~100 and 300 °C by providing data at a higher neutron fluence than what was tested previously, and (2) the extent to which further increases in temperature during irradiation decrease radiation-induced compaction. Fig. 4 summarizes the compaction measurements performed in this work, along with those from previous works. In addition to the experimental measurements, Fig. 4 also shows compaction predicted by a model for radiation-induced compaction, which is described below. The compaction model is a modified version of Primak's original model,

where both the equilibrium compaction C∞ and the characteristic fast neutron fluence ΦS are assumed to have a temperature dependence (see Eq. (5)). The temperature dependence of C∞ is arbitrarily determined by fitting a second-order polynomial (Eq. (6)) to the temperature-dependent compaction data in Table 2. This assumes that the compaction in all samples has reached an equilibrium. The characteristic fast neutron fluence ΦS is assumed to have an Arrhenius dependence on temperature (Eq. 7), where k is the Boltzmann constant. The pre-exponential parameter Φ0 and the activation energy Ea are determined using two sets of compaction data: (1) Primak's measurements for Φ < 1019 n/cm2 (below the saturation point) and T = 60 °C [39], and (2) Cheymol's measurements for 1019 n/cm2 ≤ Φ ≤ 3 × 1019 n/cm2 and T = 250 °C [52]. The experimental data used in the fitting of C∞(T) cover a temperature range from 368 to 961 K, although the model appears to show reasonable agreement with previous experimental data at a lower temperature of 60 °C (333K). Caution should be used when 5

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Fig. 4. Comparison of previous measurements [39,41,50–52] of radiation-induced compaction in a-SiO2 with the experimental results from this paper and the model that is proposed.

extending this model to higher temperatures.

C( , T) = C (T) 1

e

S(T)

C (T) = 0.023 + 6.30 × 10 6T S (T)

=

0 exp

equilibrium. Because the annealing of overlapping strain fields is a thermally activated process, an Arrhenius temperature dependence is assumed in this work for ΦS(T), the characteristic fluence for reaching saturation of the radiation-induced compaction. The compaction C(Φ, T) predicted by the model generally agrees with most of the available experimental data on radiation-induced compaction in a-SiO2. However, there are still very limited data for model verification, particularly for temperatures above 100 °C. The compaction measurements reported by Remy et al. [41] and plotted in Fig. 4 show clear inconsistencies with the proposed model. Remy's measurements had no active temperature monitoring and no passive evaluations of temperature were performed. Therefore, the actual irradiation temperature could have been different than the reported temperature. Regarding C∞(T), increasing the irradiation temperature beyond 100 °C clearly reduces the radiation-induced compaction for an equivalent fast neutron fluence. If the neutron fluence required to achieve saturation of the radiation-induced compaction, ΦS(T), is also temperature-dependent, then the samples previously irradiated by Remy et al. may not have reached saturation, as was originally suggested in their work [41]. Future work should include (1) measuring the compaction of samples irradiated to additional neutron fluences at temperatures in the range of 300–700 °C to confirm the fluence at which the compaction reaches an equilibrium, and (2) measuring the compaction of samples irradiated to a wide range of neutron fluences at various temperatures in the range of 100–1000 °C to provide more data over a larger temperature range. Testing beyond 1000 °C may provide additional fundamental data regarding compaction of a-SiO2, but those data would not be very relevant to determining the suitability of fiber optics for high-temperature nuclear applications, as optical transmission in a-SiO2 fibers is known to severely degrade beyond 1000 °C due to devitrification [56].

(5) (6)

2.60 × 10 8T2 ,

Ea n = 3.42 × 1019 2 exp KT cm

0.036eV kT

(7)

The structural model for the compaction process during neutron irradiation was originally proposed by Primak [40,53] and later refined by Piao et al. [54]. In Primak's proposed process, incident neutrons collide with Si and O atoms (primary knock-on atoms), causing a displacement damage cascade and movement of oxygen atoms into void spaces. At low temperatures, the ballistic energy from the damage cascade is rapidly dissipated as it diffuses from the damaged volume. It is during this rapid quenching from temperatures beyond a critical transition temperature (as defined by Piao [54]) that the compaction occurs and the locally rearranged atomic structure is stabilized, a process similar to that observed in thermal quenching of vitreous silica [55]. The local rearrangement of the quenched structure remains disordered like the amorphous structure, but with a closer average atomic spacing and a shift in the inter-tetrahedral bond angles (Si-O-Si). Eventually, with increasing neutron fluence, the damage cascades from individual neutron scattering events start to overlap, which reduces the rate at which the structure compacts, ultimately leading to a saturation effect. Increasing the irradiation temperature can drive thermal annealing of long-range overlapping strain fields from adjacent damage cascades. For example, Primak et al. showed that a-SiO2 samples that were first irradiated in a reactor at low temperatures and then subsequently exposed to ionizing radiation at higher temperatures showed significant recovery of the initial compaction [48,49]. The authors suggest that the compaction caused by overlapping strain fields is annealed much more easily as compared to the compaction caused by isolated damage cascades. Increasing the irradiation temperature would reduce the equilibrium compaction by relieving the overlapping strain fields, and in the process, it would reduce the volume occupied by the compacted atomic structure for each damage cascade. As a result, irradiations performed at higher temperatures would require increased displacement damage dose, or higher neutron fluence, before the compaction reaches an

4.2. Optical density measurements It can be seen in Fig. 2 and Fig. 3 that the optical density data have a prominent absorption peak in the range of 4.98–5.06 eV after irradiation at 95 °C. This peak appears to increase in intensity and shift to energies of 5.17–5.26 eV after irradiation at 298 °C. After irradiation at 688 °C, the low-OH a-SiO2 specimens show only a slight reduction in the intensity of this peak, and the peak absorption energy remains in the range of 5.2–5.3 eV. For the high-OH a-SiO2 specimens, the 6

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absorption peak shows a much more significant reduction after irradiation at 688 °C, and the peak absorption energy shifts to ~5.5 eV. There is also some evidence for an absorption band in the 5.7–6.3 eV range, with varying width and peak absorption energy depending on the irradiation temperature. The broadband increases in optical density that occurred after irradiation at 688 °C may have been caused by introduction of Cr into the samples at high temperatures. The samples were in direct contact with a vanadium alloy holder, which contained 4 wt% Cr and 4 wt% Ti. Previous studies have shown that 23–69 wppm of Cr was volatilized in VCr-Ti alloys after 5 h at a temperature of ~700 °C [57]. Furthermore, Schultz estimated the absorption spectra for Cr impurities in a-SiO2 and found that (1) the spectrum is relatively constant over a wavelength range from ~800–1600 nm (0.77–1.55 eV), (2) the absorption generally increases with decreasing wavelength (or increasing energy), and (3) there is a very small absorption band located in the range of 600–700 nm (1.77–2.07 eV). These spectral features are consistent with the observed broadband increases in optical density after irradiation at 688 °C and the small peaks that can be observed in Fig. 2 and Fig. 3 near 2 eV. To quantitatively evaluate the spectral features of the measured optical density, two approaches can be used: (1) fitting the absorption to several discrete Gaussian absorption bands with no restrictions on the peak absorption energies, magnitudes, or widths, or (2) fitting the magnitudes of the known defect centers in a-SiO2 using peak absorption energies and widths established in the literature. The first approach was used to provide initial unbiased predictions for peak absorption energies and widths. The optical density data in the range of 3.54–6.2 eV were fit to three Gaussian peaks after subtracting the measured optical density at 3.54 eV. This subtraction was performed to ignore the contributions from Fresnel reflection losses and the aforementioned broadband increases in optical density that were observed after irradiation at 688 °C. Table 3 summarizes the peak absorption energies, magnitudes, and full widths at half maximum (FWHM) for unbiased fitting of the a-SiO2 optical density data. Fits for all data sets resulted in a coefficient of determination (R2) > 0.999. Some of the fitting parameters in Table 3, particularly those for specimens irradiated at 95 °C, can be related to known defect centers in a-SiO2. For example, the largest absorption peak for the samples irradiated at 95 °C has a peak absorption energy in the range of 5.09–5.16 eV and a FWHM of 1.30–1.34 eV. These parameters are similar to the reported peak absorption energy (5.3 eV) and FWHM (1.3 eV) for the peroxy radical (POR) defect center, which consists of a dangling bond terminating a broken Si-O bond in a peroxy linkage (interstitial oxygen) [25]. This is often expressed as ≡Si − O − O•, where Si and O refer to silicon and oxygen atoms, respectively, ≡ denotes three Si-O bonds, − denotes individual Si-O bonds, and • denotes an unpaired electron. Further evidence supporting the assignment of this prominent absorption band to PORs is the previous finding that PORs are created in a-SiO2 due to generation of interstitial oxygen during the Frenkel process [58,59]. The fact that the peak absorption

occurs at energies slightly lower than the reported peak absorption of 5.3 eV for PORs could be caused by well-known overlapping of absorption due to non-bridging oxygen hole centers (NBOHCs), which have maximum absorption near 4.7 eV [60]. For example, Morimoto et al. observed an absorption band near 5 eV after oxygen ion implantation that they ascribed to POR absorption [61]. However, they concluded that there are likely contributions from other defect centers that affect the 5 eV absorption band. The other well-known Frenkel defects in a-SiO2 are the oxygen-deficiency centers (ODCs). The most prominent ODC is a neutral silicon vacancy—termed ODC(I) and denoted as ≡Si − Si≡—which has a peak absorption energy of 7.6 eV and a narrow FWHM of 0.5 eV. With such a narrow width, it is unlikely that the ODC(I) center would have significant impact over the range of energies evaluated in this paper [24]. However, the ODC(II) center, which is presently modeled as a divalent silicon atom, has an absorption band at 5.0 eV with a FWHM of 0.3 eV [24,60]. These parameters are consistent with the smallest absorption band (4.89–4.96 eV with 0.29–0.33 eV FWHM) determined from the fitting of the optical density data for samples irradiated at 95 °C. There are no known defect centers that could explain the absorption bands calculated to be in the range of 6.18–6.22 eV (FWHM varying from 0.83–0.84 eV). The Eγ′ center, which is one of several variants of the generic E′ defect centers, is characterized by dangling silicon bonds (≡Si•) and has a well-known absorption band centered at 5.8 eV with a 0.8 eV FWHM [24]. While the FWHM of the Eγ′ center matches the results of the fitting, the peak absorption energy is far enough away that the Eγ′ center alone is unlikely to be responsible for the 6.23–6.32 eV absorption band identified by the fitting. The fitting of the optical density data for specimens irradiated at higher temperatures resulted in similar values for R2, but the peak absorption energy and FWHM data do not match the literature data for known defect centers in a-SiO2. The explanation for this discrepancy could be that (1) the higher experiment temperatures resulted in chemical interactions between the samples and the surrounding materials that increased extrinsic impurity absorption, (2) the irradiations at higher temperatures resulted in defect centers that have not yet been identified in the literature, or (3) the fitting produced effective absorption bands that contain a combination of multiple known defect centers. The first explanation is possible and perhaps even likely for the samples irradiated at 688 °C based on the evidence presented earlier in this section. Attempts were made to subtract the measured optical density at 3.54 eV before fitting to compensate for what appears to be Cr-induced impurity absorption. However, if the Cr-induced absorption is significant for energies > 3.54 eV, then this contribution would still affect the results of the fitting. Explanation 2 is possible but unlikely based on the extensive database for defect centers in a-SiO2. Explanation 3 can be evaluated by fitting the measured optical density data using peak absorption energies and FWHM data from the literature. 4.3. Estimation of defect center concentrations A second fit was performed using peak absorption energies and FWHM data for Eγ′, POR, NBOHC, and ODC(II) centers. Including the ODC(I) center in the fitting did not change the results of the fitting due to the absorption from ODC(I) centers being outside the energy range over which the measurements were made. Data for the peak absorption energies, FWHM, and absorption cross sections, which can be used to determine defect concentrations from the peak absorption, were mostly taken from Skuja's paper [24]. Data from more recent papers were used for PORs [25] and NBOHCs [60,62], which are treated as a combination of five Gaussian absorption bands. For the case of PORs and ODC(II) defects, the absorption cross sections were calculated from the reported oscillator strengths using Smakula's equation. Fig. 5 and Fig. 6 show examples comparing measured optical density spectra with the results of the fitting for high-OH samples irradiated at 95 and 298 °C, respectively. Table 4 summarizes the values of R2 and the calculated defect

Table 3 Summary of peak absorption energies, magnitudes, and full widths at half maximum (FWHM) for un-biased Gaussian fitting to the optical density data. Low-OH a-SiO2

Peak absorption energy (eV) Magnitude (1/cm) FWHM (eV)

Band Band Band Band Band Band Band Band Band

1 2 3 1 2 3 1 2 3

High-OH a-SiO2

95 °C

298 °C

688 °C

95 °C

298 °C

688 °C

6.18 5.09 4.89 5.70 17.22 1.78 0.83 1.30 0.29

6.23 5.45 5.05 3.47 19.31 4.85 0.50 1.54 0.45

5.81 5.14 4.32 8.04 9.98 2.12 1.54 0.77 0.72

6.22 5.16 4.96 5.82 17.43 1.87 0.84 1.34 0.33

6.25 5.52 5.14 2.47 19.71 4.85 0.44 1.61 0.45

5.97 5.45 4.61 6.63 3.70 2.90 1.71 0.71 1.02

7

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Smakula's equation for a Gaussian absorption band (see Eq. 6.4 of [63], derived from [64]), which depends on the defect oscillator strength (0.05 for the POR [25]), the FWHM of the absorption center (1.3 eV for the POR [25]), and the refractive index (calculated to be 1.52 for a-SiO2 at the peak absorption energy of 5.3 eV). The resulting absorption cross section is calculated to be 5.4 × 10−18 cm2, which compares well with Skuja's early estimate of ~5 × 10−18 cm2 for bulk PORs [24]. Dividing the optical density by the absorption cross section gives a POR concentration of 1.98 × 1018 cm−3. Fig. 5 shows an example in which the fit provided a relatively high coefficient of determination. After irradiation at 95 °C, the optical density spectra are dominated by defect absorption from PORs and NBOHCs, with a small contribution from ODC(II) centers and a very minor contribution from Eγ′ centers. For the samples irradiated at 298 and 688 °C, the fits do not match the experimental data quite as well (R2 ≤ 0.985), particularly for energies > 5 eV. Fig. 6 shows one example of the difficulty in matching the measured peak optical density. The reason that the data for energy > 5 eV cannot be fit using optical properties obtained from the literature could be that the optical properties that were assumed are incorrect or that the fit does not include a defect center that is responsible for a significant percentage of the measured optical density for energies > 5 eV. One example of the latter is the potential for extrinsic impurity absorption (see earlier discussion). Because a reasonable fit is obtained for lower energies for which absorption from PORs and NBOHCs is dominant, the calculated concentrations of PORs and NBOHCs may provide some insight into the behavior of these defect concentrations at high fast neutron fluence and as a function of temperature during irradiation. Previously, Lagomacini et al. directly measured the concentrations of NBOHCs, PORs, and Eγ′ centers in low-OH a-SiO2 (Infrasil 301) using electron paramagnetic resonance (EPR) techniques after irradiation to a neutron fluence up to 1018 n/cm2 at a temperature of 50 °C [65]. They report POR and NBOHC defect concentrations of 4 × 1018 cm−3 and 1.3 × 1018 cm−3, respectively, which are of the same order of magnitude as the concentrations estimated in this work for low-OH a-SiO2 irradiated to a much higher fast neutron fluence (2.4 × 1021 n/cm2) at a temperature of 95 °C. In a separate work, Leon et al. measured the optical density of the same samples tested by Lagomacini [66]. The optical density measured by Leon et al. increases with increasing photon energy from 0.9 cm−1 at 3.78 eV to 20 cm−1 at 4.96 eV, which compares well with the data in this work for low-OH a-SiO2 irradiated at a temperature of 95 °C (see Fig. 7). Because the measured optical densities are similar and the defect concentrations predicted by the fitting match the EPR measurements made by Lagomacini, the POR and NBOHC defect concentrations determined from fitting the optical density data appear to be reasonable. In addition, because the RIA in this work agrees well with that measured by Leon, despite the samples tested in this work being irradiated to a neutron fluence that is > 2000 higher, the RIA may be approaching saturation, at least for the range of photon energies that can be compared. Takemoto et al. reported similar evidence of saturation of PORs, NBOHCs, and Eγ′ centers following ion irradiation [67]. If the POR and NBOHC concentrations determined from fitting the optical density data can be trusted, the temperature dependence of the calculated defect concentrations can be evaluated. The NBOHC concentrations decrease monotonically with increasing temperature, whereas the POR concentrations increase when the irradiation temperature is increased from 95 to 298 °C. These findings are consistent with previous measurements made after post-irradiation isochronal annealing [23]. The POR concentrations decrease when the irradiation temperature is increased from 298 to 688 °C, which is also consistent with previous isochronal annealing studies. However, the magnitude of the change in POR concentration appears to be highly dependent on the OH concentration, as evidenced by the large difference in POR concentration after irradiation at 688 °C in low- vs. high-OH a-SiO2. Therefore, it is possible that hydrogen plays some role in the thermal

Fig. 5. Optical density (OD) vs. energy comparing measured data in a high-OH a-SiO2 sample after irradiation at 95 °C with the results of fitting using the optical properties of various absorption bands identified in the literature.

Fig. 6. Optical density (OD) vs. energy comparing measured data in a high-OH a-SiO2 sample after irradiation at 298 °C with the results of fitting using the optical properties of various absorption bands identified in the literature. Table 4 Summary of R2 and predicted defect concentrations from fitting optical density data using literature data for defect optical properties. Low-OH a-SiO2 95 °C R2 Defect center Eγ′a POR NBOHC ODC(II)

298 °C

High-OH a-SiO2 688 °C

0.993 0.983 0.980 Defect concentration (1018 cm−3) 0.00 0.29 0.06 1.49 2.40 2.26 3.80 1.58 0.32 0.05 0.08 0.03

95 °C

298 °C

688 °C

0.997

0.976

0.985

0.02 1.98 3.00 0.05

0.34 2.63 1.12 0.05

0.19 0.57 1.44 0.00

a

Calculated Eγ′ concentrations cannot be trusted due to the poor fitting obtained near the peak absorption (5.8 eV) for Eγ′centers.

concentrations for all data sets. One example of how a defect concentration is calculated from the optical density is provided here for the case of the POR defect concentration in the high-OH sample after irradiation at 95 °C. The peak optical density due to POR absorption is 10.7 cm−1 (see Fig. 5). The absorption cross section for the POR defect is calculated using 8

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Fig. 8. Predicted shift in Bragg wavelength and the resulting temperature drift, calculated using the radiation-induced compaction model developed in this work and a previous density-dependent model for a-SiO2 refractive index [71], as a function of irradiation temperature (T) and fast-neutron fluence.

Fig. 7. Increases in optical density after irradiation of low-OH a-SiO2 samples in this work vs. the data from Leon et al. [66] after irradiation to a lower neutron fluence (Φ). The red curve in this figure was obtained by subtracting the green curve (pre-irradiation OD) from the blue curve (post-irradiation OD) in Fig. 2. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

temperature monotonically reduces the Bragg wavelength shift and the associated temperature drift. For temperatures as high as 700 °C, the temperature drift is ~20 °C. For comparison, Cheymol et al. report and ΔT after irradiation of Bragg gratings to fast neutron values for fluences of 1019 and 3 × 1019 n/cm2 at a nominal temperature of 250 °C [52]. While there is considerable scatter in the reported data, two of the samples that were irradiated to a fast neutron fluence of 1019 n/cm2 were found to have = 0.029%, which compares well with the value (−0.03%) predicted by the model. There is certainly much additional work required to validate this model for radiation-induced compaction and the resulting effect on temperature drift, but the results presented in this paper raise serious questions regarding the feasibility of using Bragg grating sensors for accurate temperature monitoring for applications with high fast neutron fluence. For any sensor that would utilize fiber optics either as part of the sensing medium or simply for signal delivery, the fiber must be able to provide adequate signal transmission despite the RIA. Because highfluence irradiation of a-SiO2 produces significant RIA due to the formation of defect centers with peak absorption at energies > 2 eV (wavelength < 620 nm), most sensors utilize wavelengths that are further into the near infrared. Following neutron irradiation, infrared losses have been shown to increase with increasing wavelength, and it has been suggested that this loss could be related to radiation-induced compaction [32]. If that is the case, then the compaction model developed in this work can be used to estimate infrared RIA and to compare these estimates with previous results from the literature. For this, the RIA data from Cheymol et al. (Φ = 3.2 × 1019 n/cm2, T = 50 ° C) [29] were digitized and fit to a Gaussian (with respect to wavelength) absorption band that is assumed to be a result of radiationinduced compaction. All RIA data in the wavelength range of 900–1650 nm were used except for the regions from 1225 to 1285 nm and 1330–1480 nm, where there are clear OH absorption peaks that are unrelated to radiation-induced compaction. The fitting (R2 = 0.996) predicts a peak absorption wavelength of 3529 nm, a FWHM of 2459 nm, and a magnitude of 229 dB/m at the peak absorption wavelength. Assuming that the magnitude of this Gaussian absorption is linearly proportional to the amount of compaction allows for an estimation of infrared RIA using the temperature- and neutron fluence–dependent model for radiation-induced compaction described in Section 4.1. Fig. 9 shows the RIA measured by Cheymol et al. [29] and Brichard et al. [32] as a function of wavelength, as well as the RIA predicted using the fit to Cheymol's high fluence measurement and the radiation-

annealing of PORs. 4.4. Implications for signal drift of in-core fiber optic sensors The model developed to predict the dependence of radiation-induced compaction on fast neutron fluence and temperature can be used to estimate signal drift in different types of in-core fiber optic sensors. For simple extrinsic Fabry-Perot interferometric temperature sensors formed by fusing two optical fibers inside a SiO2 capillary [68], the cavity length will change proportionally to the linear compaction strain C( , T) = . Because the compaction strain is typically much larger 3 than the thermal strain in a-SiO2, these sensors would suffer prohibitively large signal drift during irradiation unless the fiber is bonded to a metal that is dimensionally stable under irradiation [69,70]. For fiber Bragg grating temperature sensors, the Bragg wavelength is equal to λB = 2nΛB, where n and ΛB are the effective refractive index and the period of the grating, respectively. If the percent change in the grating period is equal to ε, then the percent change in the Bragg wavelength is n equal to = + n . The volumetric compaction is in the range of 0.5% to 2.8% (see Fig. 4), corresponding to linear strains ranging from −0.17 to −0.93% assuming isotropic compaction. However, the compaction results in a positive increase in refractive index that is as large as 0.7% [39]. The relationship between refractive index and density can be approximated using correlations developed by Kitamura et al. for evaluating densified silica glass based on extended point dipole theory [71]. Using the model presented in Section 4.1 to calculate the linear strain ε caused by compaction and using Kitamura's model for the dependence of refractive index on density, the resulting Bragg wavelength shifts can be calculated as a function of the nominal sensor temperature and the fast neutron fluence. The corresponding temperature drift (ΔT) can be calculated assuming that T 6.7 × 10 6 C 1 [72].

(

)

Values for and ΔT are calculated in Fig. 8 as a function of fast neutron fluence up to 1022 n/cm2 for nominal temperatures ranging from 100 to 700 °C (the approximate temperature range over which the model was developed) in increments of 100 °C. The refractive index was calculated assuming a nominal Bragg grating wavelength of 1550 nm. Fig. 8 shows that the magnitude of the Bragg wavelength shifts approach ~0.07% after the radiation-induced compaction reaches saturation at a temperature of 100 °C. This shift corresponds to > 100 °C drift in the temperature estimated by a Bragg grating sensor. Increasing

9

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defect center absorption and radiation-induced compaction. However, sensors such as Bragg gratings will likely suffer from prohibitively large signal drift, even at higher temperatures, due to compaction of a-SiO2 under fast neutron irradiation. 5. Conclusions This work provides new information regarding RIA and radiationinduced compaction of a-SiO2 samples with low- and high-OH content after irradiation to a high fast neutron fluence at multiple temperatures. The RIA measured in low-OH samples after irradiation to a fast neutron fluence of 2.4 × 1022 n/cm2 at 95 °C was only slightly larger than previous measurements made in the same type of low-OH a-SiO2 glass after accumulating a fast neutron fluence of 1018 n/cm2, indicating that RIA may be approaching saturation. The RIA measured after irradiation at temperatures of 95 and 298 °C was similar for the low- and high-OH samples. Increasing temperature from 95 to 298 °C caused the peak absorption band to increase in magnitude and shift to higher photon energies. Fitting of the RIA provided evidence that the spectral changes were caused by increasing POR defect concentrations and decreasing NBOHC concentrations, which is consistent with previous isochronal annealing studies of irradiated a-SiO2 samples. When the irradiation temperature was increased to 688 °C, significant differences were observed between the low- and high-OH samples. Both sets of samples showed a broadband increase in optical density, which may have been caused by the introduction of Cr impurities from the surrounding experiment materials, which caused increased extrinsic absorption. Despite the increased impurity absorption, the high-OH samples clearly showed much lower RIA compared to the low-OH samples after irradiation at 688 °C, which suggests that hydrogen may play a role in the thermal annealing of POR defects, which were found to be the primary contributor to RIA after irradiation at these temperatures. The irradiated samples were also used to determine the temperature-dependence of radiation-induced compaction after high neutron fluence irradiation. The compaction was found to monotonically decrease with increasing irradiation temperature. Comparing the measured compaction to previous measurements, a model was developed to predict radiation-induced compaction as a function of temperature and neutron fluence. By combining this model with a previous model for the dependence of refractive index on density, the signal drift for Bragg grating sensors was estimated as a function of neutron fluence for various temperatures. For a fast neutron fluence as high as 1022 n/cm2, the estimated Bragg wavelength shift is as high as ~0.07%, which corresponds to a temperature drift of ~100 °C. Increasing temperature reduces the signal drift, but the drift remains as high as ~20 °C for an irradiation temperature of 700 °C. The compaction model was also combined with previous infrared RIA data to provide additional evidence supporting the previous claim that infrared RIA is correlated with radiation-induced compaction. Future work should test a-SiO2 samples irradiated to a wider range of temperatures and fast neutron fluence to refine the compaction model and the implications for a-SiO2 fiber optic sensors for nuclear applications.

Fig. 9. RIA measured by Cheymol et al. [29] and Brichard et al. [32] as a function of wavelength, as well as the RIA predicted using the fit to Cheymol's high fluence measurement and the radiation-induced compaction model developed in this paper.

induced compaction model developed in the work described herein. The data predicted by the fitting were also scaled so that the fit matches the experimental measurements at 900 nm, because the fit does not account for effects of RIA from defect centers at lower wavelengths. While it is no surprise that the fit matches the data from Cheymol for Φ = 3.2 × 1019 n/cm2 (these data were used to develop the fit), the fact that the fit accurately predicts the RIA from Cheymol at a lower neutron fluence and the data from Brichard et al. supports the theory that radiation-induced compaction is responsible for the infrared RIA. If radiation-induced compaction is indeed the primary source of infrared RIA, then a similar calculation can be performed to predict broadband RIA as a function of temperature after the compaction has reached saturation. Fig. 10 shows the predicted contribution to RIA due to compaction effects after irradiation to a fast neutron fluence of 1022 n/cm2 at various temperatures. These results show that for higher temperatures of 500–700 °C, the RIA could be < 10 dB/m, depending on the sensor wavelength, which is consistent with the findings of Zaghloul et al. [38]. Combining this finding with the findings reported earlier in this paper, the general conclusion is that RIA in a-SiO2 could be greatly reduced at higher temperatures due to the reduction in both

Declaration of Competing Interest The authors declare no conflict of interest. Acknowledgments This research is sponsored by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory (ORNL), managed by UT-Battelle, LLC, for the US Department of Energy (DOE). A portion of this research used the irradiation capabilities of the HFIR, a DOE Office of Science User Facility operated by ORNL. Post-irradiation measurements were made using the ORNL Irradiated Materials Examination and Testing hot cell facility and the Low Activation

Fig. 10. Predicted compaction-induced attenuation at various temperatures after irradiation to a fast neutron fluence of 1022 n/cm2 using the radiationinduced compaction model developed in this paper and a fit to Cheymol's data following high fluence neutron irradiation [29]. 10

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Materials Development and Analysis facility using funding provided by the US DOE Office of Nuclear Energy through a Nuclear Science User Facilities Program rapid turnaround experiment. Travis Dixon, Alicia Raftery, and Kory Linton assisted in the execution of the post-irradiation examination.

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