Abstract

Sapphire should be highly transparent for photon energies less than the band gap, but residual, weak absorption and scattering losses in the near infrared occur as a result of extrinsic and intrinsic defects. Lattice disorder, impurities, and point defects have all been implicated as being the origin of loss phenomena but very little experimental evidence exists to quantitatively establish the relationships that might exist between these defects and optical loss. In this study, three synthetic, c-axis sapphire samples manufactured under similar conditions were characterized using UV-VIS spectroscopy, photothermal common-path interferometry, and positron annihilation lifetime spectroscopy. Model-based interpretation of optical measurements indicated that vacancy-type defects were partially responsible for absorption loss from the ultraviolet to the near-infrared and that the population densities differed among the samples. Positron annihilation lifetime spectroscopy measurements also indicated a higher concentration of cationic vacancy defects near the sample surface which correlates with a higher surface optical loss. This work establishes the use of positron annihilation techniques as a characterization tool for optical materials that could be useful for investigating the origin of weak surface absorption in the transparent region of sapphire.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Synthetic, single-crystal sapphire has been studied as a promising high energy laser (HEL) window material candidate due to its high melting point, strength, and large range of optical transparency from the UV to the near-infrared region [1,2]. However, the future generation of HEL will likely have power outputs as high as 1 megawatt under continuous wave (cw) operation near 1 μm, and under these operational conditions, commercially-available sapphire likely cannot be used owing to optical losses even though these losses might be quite low [2,3]. Absorption and scattering, are related to materials defects such as lattice disorder, impurities, and point defects that originate from sapphire growth and post-growth treatment processes [4], and, at the projected laser power levels, these losses lead to effects such as thermal lensing and light scattering that degrade laser beam quality and reduce the overall operating efficiency [5]. It is important to investigate the underlying sources of the optical losses so they can be reduced or eliminated during the manufacturing process [6].

Point defects in crystalline materials, including anionic and cationic vacancies in different charge states, are inevitably introduced during crystal growth and post-growth treatment [4]. They are known for causing absorption loss at different wavelengths in crystalline semiconductors and insulators through electron/hole trapping, and interactions with impurities and dislocations [2,7]. In the case of sapphire, both aluminum (VAl) and oxygen vacancies (VO) exist in either neutral form or in charged states. The latter are commonly known to cause formation of F (two electrons trapped due to $\textrm{V}_\textrm{O}^{ + 2}$) and F+ centers (one electron trapped due to $\textrm{V}_\textrm{O}^{ + 1}$), which are associated with well-known absorption bands in sapphire in the UV and visible wavelength regions [8,9], but relatively little is known about the effects of aluminum vacancies on the optical properties [4]. More importantly, no previous experimental studies have investigated how vacancy-type defects contribute to the optical losses in sapphire observed in the region near 1 μm. Establishing the populations of both anionic and cationic vacancy-type defects in sapphire can only enhance our understanding of optical loss phenomena in this material.

In this work, correlations between sapphire vacancy-type defect concentrations and surface optical loss are established. Optical absorption measurements were made on three sapphire samples having different optical absorption losses. Standard UV-VIS spectroscopy measurements were made to establish characteristic absorption bands (associated with both bulk and surface contributions but the bulk dominates in the case of sapphire) due to different types of vacancy defects in the UV and visible wavelength regions while photothermal common-path interferometry (PCI) measurements provided both surface and bulk absorption losses (bulk and surface losses can be distinguished) in the near-infrared wavelength region. Both types of absorption losses were measured to investigate possible defect mechanisms. Positron annihilation lifetime spectroscopy (PALS) measurements were made on polished sample surfaces to identify cationic vacancy-related defect content. A two-component lifetime model was used to fit the PALS data and model parameters were extracted to perform a subsequent defect concentration analysis. Results of these measurements indicate that higher surface absorptions losses of sapphire samples were associated with higher concentrations of cationic vacancy-related defects that were detected by PALS.

2. Materials and methods

Three single-crystal, c-axis sapphire disks with diameters of 25.4 mm and thicknesses of 10 mm (GT Advanced Technologies) were characterized. All samples were synthesized with the heat exchange method (HEM) in a reducing environment and were polished to an optical finish with a scratch/dig specification of 60/40. Optical transmittance was measured in the wavelength region from 190 to 600 nm using a PerkinElmer Lambda 950 integrating-sphere spectrometer with a step size of 1 nm and 0° angle of incidence. PCI measurements (Stanford Photo-Thermal Solutions) at 355 nm, 532 nm, and 1064 nm were performed using a pump-probe approach to assess surface and bulk absorption of the samples. Originally, six sapphire samples were produced under similar growth conditions and cut to the same geometry, but only three samples were chosen for this study because their bulk and surface absorption spectra had relatively large differences. PALS measurements were performed at the Oak Ridge National Laboratory on the polished surfaces of all samples. A conventional sample-source-sample geometry was prepared by directly evaporating a 20$\mu L$ Na22Cl solution (∼3.7${\times} $105 Bq) onto the surface of one of the two disk samples, after the water evaporated, then covering that disk with the other disk sample. This ‘sandwich’ was then wrapped into 10$\; \mu m$ thick aluminum foil. The PALS system operates in a double-stop mode and has a calculated system time resolution of ∼160 ps. Each recorded lifetime spectrum contained a total of 1million counts and was analyzed by fitting the exponential decay of two lifetime components, after deconvolution of the resolution function, which was approximated as a weighted sum of three Gaussians.

3. Results

The measured UV-VIS transmittance and the calculated Fresnel reflectance for each sapphire sample were used to calculate extinction coefficients at each wavelength. A frequency-dependent scattering model that takes the form of $A{\mathrm{\nu }^4} + B{\mathrm{\nu }^p}$ (where A, B, p are coefficients used for fitting purposes) was used to remove the scattering component from the total loss for purposes of isolating the absorption coefficient. The fitting parameters were identified empirically with the following values being used: A = 4.5 × 10−21 cm3, B = 10−9 cm-0.3, and p = 1.3. Details about the scattering model have been reported previously [5]. The results are shown in Fig. 1 where the bulk absorption coefficients are plotted on a logarithmic scale as a function of the wavelength. Various absorption bands centered at different wavelengths appear in all three samples and are labeled to indicate the species associated with absorption. Among these bands, the one at 206 nm (6.1 eV) has been reported to be related to F centers associated with the neutral oxygen vacancies,$\textrm{V}_\textrm{O}^0$ [4,10]. The bands at 225 nm (5.5 eV) and 255 nm (4.8 eV) are likely related to F+ centers that are linked to $\textrm{V}_\textrm{O}^{ + 1}$[4,9]. In Sample A, the band at 206 nm is narrower compared to that of Sample B and has a slightly decreased amplitude, suggesting a reduced overall $\textrm{V}_\textrm{O}^0$ content. The 225 nm band feature is not detected in Sample A by a visual examination of the enlarged view of that region as seen in Fig. 1, but it becomes more apparent in the absorption spectrum for Sample B, indicating a decreased $\textrm{V}_\textrm{O}^{ + 1}$ concentration in Sample A compared to that in Sample B. Sample C also has a missing band at 225 nm, but its band at 206 nm is relatively broad. This indicates a small $\textrm{V}_\textrm{O}^{ + 1}$ content but a moderately large $\textrm{V}_\textrm{O}^0$ concentration compared to Sample B. Both types of F centers indicate oxygen deficiency during the growth process, and this is consistent with the growth conditions for the sapphire since all samples were produced in reducing environments. Furthermore, both the reducing growth condition and subsequent cooling process could result in a non-equilibrium vacancy concentration which could be much higher than the thermodynamic equilibrium state [4]. Additionally, previous experimental studies have shown that a cationic vacancy in sapphire may form V-2 and V-1 centers that cause absorption near 3 eV [11,12]. According to Fig. 1, Sample B exhibits a wide absorption band near 3.1 eV and a partial absorption loss could be attributed to charged VAl-induced color centers in addition to the well-known impurity band caused by Cr3+. However, these centers were less noticeable in either Sample A or C indicating a reduced defect concentration of charged VAl.

 figure: Fig. 1.

Fig. 1. Bulk absorption in sapphire Samples A, B, and C as a function of wavelength (blue, orange, and yellow broken lines respectively). Absorption bands are labeled with associated vacancy defects.

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The total concentration of VO associated with the F centers can be estimated using Smakula’s equation

$$[{{\textrm{V}_\textrm{O}}} ]= [\textrm{F} ]+ [{{\textrm{F}^ + }} ]= ({1.86{\mathrm{\alpha }_{206}} + 0.292{\mathrm{\alpha }_{225}} + 0.167{\mathrm{\alpha }_{255}}} )\; {\times}\; {10^{16}}$$
where $\alpha $ represents the optical absorption coefficient (at the wavelength indicated by the subscript) while the numerical coefficients for the absorptions are related to oscillator strengths obtained empirically for sapphire [4,7].

The calculated concentrations of VO defects of each type are shown in Table 1. Note that Eq. (1) gives the number density of different VO defects and the number of atoms per unit volume of sapphire must be used to obtain the defect concentration. These results suggest that the concentrations of $\textrm{V}_\textrm{O}^0$are at similar levels in Sample A and B while Sample C has a relatively higher $\textrm{V}_\textrm{O}^0$ content, but all have concentrations at levels of approximately 0.1 ppm. For $\textrm{V}_\textrm{O}^{ + 1}$content, calculations for Sample A and C were based only on the absorption band at 255 nm since the band at 225 nm was not present. Sample B appears to have the largest concentration of $\textrm{V}_\textrm{O}^{ + 1}$among all samples. At all other wavelengths, where no defect and impurity-related absorption bands are present, Sample B shows a higher absorption loss than either Sample A or C, suggesting that charged VO and VAl defects and impurities may form additional defect states in the material. Previous computational studies have reported the formation energy of intrinsic $\textrm{V}_\textrm{O}^0$ to be in the range of 2 to 5 eV at 0 K [4,13,14]. Using these formation energy values, an equilibrium concentration of $\textrm{V}_\textrm{O}^0$ under the room temperature conditions was estimated to be in the 10−60 to 10−30 cm-3 range which was much lower than the experimentally observed values. The higher concentrations of $\textrm{V}_\textrm{O}^0$ indicate a non-equilibrium point defect concentration in these sapphire samples due to their growth and post-growth treatments. It should be noted that $\textrm{V}_\textrm{O}^{ + 2}$ was not considered in Smakula’s equation but likely exists in the form of Schottky pairs in sapphire [13,15] and has been reported to cause small optical attenuation around the 200 nm wavelength region [16].

Tables Icon

Table 1. Concentrations of Anionic Vacancy Defects in Sapphire

PCI results of all samples obtained at three wavelengths are shown in Table 2. At 355 nm and 532 nm, bulk absorption values measured by PCI are in good agreement with the absorption values based on the UV-VIS measurements shown in Fig. 1. The bulk absorption losses for Sample B and C at 355 nm and 532 nm from Table 2 indicate the existence of Ti3+ and Ti4+ impurities in these samples [17]. While Ti3+ is an isovalent impurity, Ti4+ appears as a heterovalent impurity that likely causes the formation of cationic vacancies and hole trapping centers to compensate for the higher valence charge state [4]. It is likely that a relatively higher concentration of cationic vacancies exists in both Sample B and C. At 1064 nm, Sample B has a bulk absorption that is 4 times greater than absorption in Sample A and is over 7 times higher than in Sample C.

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Table 2. Optical absorption coefficients obtained from PCI measurements

In the region between 600 and 1200 nm, previous studies on sapphire have indicated an exponentially decreasing bulk absorption known as the weak absorption tail that is likely related to states in the bandgap caused by lattice disorder and impurities [18], [19]. Defects such as vacancies, dislocations, and impurities are the main contributors to the optical absorption loss in this region and can trap holes or electrons generating localized changes to the optical properties [7]. Previous density-functional theory (DFT)-based computational studies have shown that both neutral and negatively charged VAl result in optical attenuation in the near-infrared wavelength region at room and elevated temperatures [16].

In contrast to the bulk measurements, surface absorbance measured using PCI yields a different story that is indicated by Table 2. Although Sample C has a lower bulk absorption loss at all three wavelengths compared to Sample A, its surface absorbance becomes approximately two to three times larger than that of Sample A at both 532 nm and 1064 nm. Furthermore, at 1064 nm, bulk and surface absorption losses for Sample C are at the same level indicating a relatively large population of absorbing species near the surface. Similar to the bulk absorption loss, Sample B has the largest surface absorption loss at all the measured wavelengths. The different bulk absorption spectra in all three samples indicate a varied impurity concentration in these samples as trace element impurities mainly contribute to the absorption losses at different wavelengths [4], [9], [20], [21]. Although all three samples were grown by the same manufacturer under a similar set of growth conditions, these samples were obtained from different boules. It is known that the homogeneity of the crystalline microstructure is difficult to maintain from boule to boule because a small change in the growth parameters can result in very different microstructural content. Indeed, sapphire obtained from the same boule can display a range of impurities and structural defects since variations occur as a result of uneven temperature profiles at the crystallization front [4], [20]. Beyond the bulk, defect populations in the near surface region include a range of extrinsic defects because sapphire used for optical components undergoes post-growth processing steps such as grinding and polishing [2224]. These processes often result in an increased level of vacancy and dislocation concentrations in the sub-surface of sapphire; and these concentrations are directly related to polishing conditions such as lapping rate, rotation speed, applied pressure level, and polishing solution types which are critical during the chemical-mechanical polishing [4], [24]. Again, although all samples have undergone a similar post-growth treatment process, their sub-surface structures differ as the treatment conditions are not exactly matched. Related differences in surface absorption loss can be studied using PALS.

Results from the PALS measurements provided positron lifetime spectra, shown in Fig. 2, that were analyzed using a two-component lifetime model. The fitting parameters used in this model include: ${\tau _1}$, the bulk sapphire positron annihilation lifetime;$\; {\tau _2}$, the defect-related lifetime; and ${I_i}$, the intensity associated with each lifetime component [25]. In this study, ${\tau _1}$ was fixed at 140 ps because this is the positron lifetime that is reported for bulk sapphire having no extrinsic defects (including vacancy-type defects) [2629]. However, ${\tau _1}$can also be calculated using ${\tau _2}$ and the bulk positron lifetime in sapphire, ${\tau _b}$, through ${\tau _1} = \frac{1}{{\tau _b^{ - 1} + \; \frac{{{\textrm{I}_2}}}{{{\textrm{I}_1}}}({\mathrm{\tau }_\textrm{B}^{ - 1} - \mathrm{\tau }_2^{ - 1}} )}}$ ; however, in this study, a fixed ${\tau _1}$was chosen to enable a direct comparison of the positron lifetimes of the defect features in sapphire samples. The calculated ${\tau _1}$ has been confirmed to be within 10% of the fixed value (140 ps) assumed for each sample. The mean lifetime <$\mathrm{\tau }$>, represents the geometric mean of the measured lifetime components and is calculated from <$\mathrm{\tau }$>= ${\tau _1}{I_1} + {\tau _2}{I_2}$, where ${I_1} + {I_2} = 1$ [25]. The list of all parameters along with the calculated mean positron lifetime for each sample can be found in Table 3. Note that the fitting error associated with ${\tau _2}$ is approximately 5%.

 figure: Fig. 2.

Fig. 2. Positron lifetime spectra for single crystal sapphire samples used in this study. Data points indicate measured counts while the solid curves represent fits to the data using a two-component lifetime model (a) Sample A, (b) Sample B, (c) Sample C.

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Tables Icon

Table 3. PALS analysis results of the studied samples

Results in Table 3 indicate that Sample C has a longer ${\tau _2}$ component as well as an increased intensity associated with it contributing to an overall longer mean positron lifetime. Longer average lifetimes are associated with a larger average defect size (associated with ${\tau _2}$) and/or a higher average defect concentration (associated with I2) [25]. Among different vacancy-type defects, positively charged defects do not interact strongly with positrons due to repulsive Coulombic interactions between the positron and the local charge density. For sapphire, this suggests that aluminum vacancy-type defects are more likely to be measured by PALS compared to oxygen-related vacancies [25], [30,31]. Furthermore, previous studies reported the positron annihilation lifetime of a single Al vacancy was 165 ps [29]. Since ${\tau _2}$ of all samples are larger than 165 ps, all samples are likely to have divacancy or small vacancy clusters. Indeed, divacancy-related defects have been shown to have a lifetime in the range of 194 ps to 220 ps in Al2O3 thin films [29]. Results obtained from PALS indicate that Sample C has a comparable cationic vacancy-type defect concentration to that of Sample B while also having a larger average defect size. Since PALS measurements were performed on the polished surfaces of each sample and the positron penetration depths can be hundreds of micrometers, the measured results should most closely relate to the defect states in the near-surface region. Indeed, PCI results show that Sample B and C have a relatively large surface absorbance at all wavelengths. Although loss in Sample C appeared to be lower than that of Sample B, the UV-VIS measurements indicated a relatively larger $\textrm{V}_\textrm{O}^0$ concentration in Sample C. In an ionic crystal, the creation of an anionic vacancy is typically accompanied by the creation of a cationic vacancy to achieve the overall charge conservation. At 1064 nm where Sample C’s surface absorption loss is comparable to its bulk loss, a larger quantity of cationic vacancies could correlate with such optical attenuation [32].

Previous work has suggested that Schottky defects (aluminum and oxygen vacancies generated in a stoichiometric ratio) are more likely to form compared to Frenkel defects (aluminum or oxygen vacancy/interstitial pairs) under the equilibrium condition since the former have smaller formation energies [13,15]. Additionally, Schottky defects are known to form near the surface where they could arise from elevated dislocation concentrations that result from grinding and polishing [4]. Furthermore, a recent computational study suggested there are two more types of Schottky defect that could form in sapphire under the oxygen-deficient growth environments, $\left(2 \mathrm{~V}_{0}^{+1}: \mathrm{V}_{\mathrm{Al}}^{-2}\right)$ and $\left(3 \mathrm{~V}_{\mathrm{O}}^{+1}: \mathrm{V}_{\mathrm{Al}}^{-3}\right)$, owing to their lowered formation energies [13]. Also, other cationic vacancy-associated clusters, including $\left(\mathrm{V}_{\mathrm{O}}^{+2}: \mathrm{V}_{\mathrm{Al}}^{-3}\right)^{-1}$, $\left(2 \mathrm{V}_{\mathrm{O}}^{+2}: 2 \mathrm{V}_{\mathrm{Al}}^{-3}\right)^{-2}$, $\left(3 \mathrm{Ti}_{\mathrm{Al}}^{+1}: \mathrm{V}_{\mathrm{Al}}^{-3}\right)$, $\left(2 \mathrm{Ti}_{\mathrm{Al}}^{+1}: \mathrm{V}_{\mathrm{Al}}^{-3}\right)^{-1}$, and $\left(2 \mathrm{Ti}_{\mathrm{Al}}^{+1}: \mathrm{V}_{\mathrm{Al}}^{-3}\right)^{-1}$ could also be found in sapphire [15]. Since PALS results for all samples indicated large defect sizes that were likely associated with vacancy clusters, the neutral and negatively-charged vacancy-related defect structures noted here were likely among the positron trapping centers in the sapphire samples studied in this work.

The vacancy defect concentration can be estimated using a two-state trapping model that takes into account positron trapping both in the bulk and at defect sites [25,33]. In this model, the net positron trapping rate for defects, $\mathrm{\kappa }$, can be found by using I1, I2, and ${\mathrm{\tau _2}}$ along with the following expression:

$$\mathrm{\kappa } = \frac{{{\textrm{I}_2}}}{{{\textrm{I}_1}}}({\mathrm{\tau }_\textrm{B}^{ - 1} - \mathrm{\tau }_2^{ - 1}} )$$
where ${\mathrm{\tau _B}}$is the positron lifetime in the bulk [25]. The trapping rate is directly proportional to the concentration of defects, C, through
$$\mathrm{\kappa } = \mathrm{\mu }\textrm{C}$$
where $\mu $ is the trapping coefficient associated with a specific defect type [25,33]. At room temperature, this coefficient typically is in the range of 5 × 1014 to 5 × 1015 s-1 for semiconductors [25,28]. Unfortunately, no available information has been reported experimentally or theoretically for Al-related trapping coefficients in sapphire. Based on the studies of different semiconductors, the trapping coefficients of neutral, singly negative, and doubly negative VAl-associated defects could be estimated as 6 × 1014, 2.5 × 1015, and 5 × 1015 s-1, respectively [28]. Additionally, similar data were also reported on VAl-associated defects for aluminum alloys at room temperature [34]. For a small vacancy cluster with n vacancies, Hu et al. have proposed a specific trapping coefficient as ${\mu _{{V_n}}} = {(\frac{{{r_{{v_n}}}}}{{{r_v}}})^2}{\mu _v}$, where ${r_{{v_n}}}$is the radius of the defect cluster containing n vacancies, ${r_v}$ is the trapping radius of a single vacancy-type defect, and ${\mu _v}$ is the trapping coefficient associated with a specific defect type (neutral or charged as mentioned previously) [25]. In this work, atomic volumes of both Al and O atoms were approximated using Voronoi tessellation. The defect cluster volume was estimated based on the addition of individual atomic volumes to obtain the ratio of $\frac{{{r_{{v_n}}}}}{{{r_v}}}$. The trapping rate of each sample was calculated based on the PALS result using Eq. (2) and the values are 3.53 × 108 s-1, 8.23 × 108 s-1, and 8.88 × 108 s-1, for Sample A, B, and C, respectively. These values were used to obtain an estimate of the cationic vacancy-type defect concentrations.

It is difficult to identify which VAl-related defect clusters dominate in the sapphire samples but simple estimations are possible using information extracted from the optical measurements presented here along with results from computational studies in the literature. Only three types of VAl-related clusters (neutral, singly, and doubly negative charged) that were previously mentioned are considered because aluminum-related point defects such as interstitials and antisites are less likely to trap positrons. Therefore, all three types of VAl -associated small vacancy clusters (i.e. $\left(2 \mathrm{~V}_{0}^{+1}: \mathrm{V}_{\mathrm{Al}}^{-2}\right)$, $\left(3 \mathrm{~V}_{0}^{+1}: \mathrm{V}_{\mathrm{Al}}^{-3}\right)$, $\left(3 \mathrm{~V}_{\mathrm{O}}^{+2}: 2 \mathrm{~V}_{\mathrm{Al}}^{-3}\right)$, $\left(\mathrm{V}_{\mathrm{O}}^{+2}: \mathrm{V}_{\mathrm{Al}}^{-3}\right)^{-1}$, ($2 {\mathrm{V}}_{\mathrm{O}}^{ + 2}:2{ \mathrm V}_{ \mathrm {Al}}^{ - 3}{)^{ - 2}}$, (3$\mathrm{Ti_{Al}}^{ + 1}:\mathrm{V_{Al}}^{ - 3})$, (2$\mathrm{Ti_{Al}}^{ + 1}:\mathrm{V_{Al}}^{ - 3}{)^{ - 1}}$, ($\mathrm{Ti_{Al}}^{ + 1}:\mathrm{V_{Al}}^{ - 3}{)^{ - 2}}$) could contribute to the defect-related lifetime component, ${\tau _2}$. Assuming they share a similar positron lifetime, Eq. (2) could be expressed as follows:

$$\; \mathrm{\kappa } = {\mathrm{\mu }_{{\textrm{V}_{\textrm{Al}}}}}{\textrm{C}_{{\textrm{V}_{\textrm{Al}}}}} + {\mathrm{\mu }_{\textrm{V}_{\textrm{Al}}^ - }}{\textrm{C}_{\textrm{V}_{\textrm{Al}}^ - }} + {\mathrm{\mu }_{\textrm{V}_{\textrm{Al}}^{ - 2}}}{\textrm{C}_{\textrm{V}_{\textrm{Al}}^{ - 2}}}.$$
Using the concentration of $\textrm{V}_\textrm{O}^{ + 1}$ from UV-VIS data (10−5 to 10−2 ppm level according to Table 1), concentrations of ($2 \mathrm{V_O}^{ + 1}:\mathrm{V_{Al}}^{ - 2})$ and ($3 \mathrm{V_O}^{ + 1}:\mathrm{V_{Al}}^{ - 3})$ could be estimated. Given the concentration level of $\textrm{V}_\textrm{O}^{ + 1}$ was at the 10−10 and 10−11 for Sample A and C respectively, the maximum concentration level of ($2 \mathrm{V_O}^{ + 1}:\mathrm{V_{Al}}^{ - 2})$ and (3$\mathrm{V_O}^{ + 1}:\mathrm{V_{Al}}^{ - 3})$ in Sample A and C would also be at ∼10−11 to 10−10 as $\textrm{V}_\textrm{O}^{ + 1}$ acts as the limiting factor. In Sample B, the maximum concentration level of both clusters would be around 10−8. The trapping coefficient of both clusters was estimated to be at the level of 1015 s-1 based on the defect cluster volume approximated using Voronoi tessellation as mentioned previously. By combining the defect concentration and trapping coefficient for each sample, the contribution from both types of vacancy clusters (105 s-1 and 104 s-1 for Sample A and C and 107 s-1 for Sample B) to the trapping rate,$\textrm{\; }\mathrm{\kappa }$, could be estimated and was very small, suggesting other VAl -related vacancy clusters may contribute more to the longer positron lifetime. The remaining possible vacancy clusters include $\left(3 \mathrm{~V}_{\mathrm{O}}^{+2}: 2 \mathrm{~V}_{\mathrm{Al}}^{-3}\right)$, $\left(\mathrm{V}_{\mathrm{O}}^{+2}: \mathrm{V}_{\mathrm{Al}}^{-3}\right)^{-1}$, ($\mathrm{2V_O}^{ + 2}:\mathrm{2V_{Al}}^{ - 3}{)^{ - 2}}$, (3$\mathrm{Ti_{Al}}^{ + 1}:\mathrm{V_{Al}}^{ - 3})$, (2$\mathrm{Ti_{Al}}^{ + 1}:\mathrm{V_{Al}}^{ - 3}{)^{ - 1}}$, ($\mathrm{Ti_{Al}}^{ + 1}:\mathrm{V_{Al}}^{ - 3}{)^{ - 2}}$. Since Sample A did not exhibit a noticeable optical attenuation due to Ti4+ compared to the other two samples, it is reasonable to exclude Ti-related vacancy clusters. Among three vacancy clusters of $\left(3 \mathrm{~V}_{\mathrm{O}}^{+2}: 2 \mathrm{~V}_{\mathrm{Al}}^{-3}\right)$, $\left(\mathrm{V}_{\mathrm{O}}^{+2}: \mathrm{V}_{\mathrm{Al}}^{-3}\right)^{-1}$, $\left(2 \mathrm{~V}_{0}^{+2}: 2 \mathrm{~V}_{\mathrm{Al}}^{-3}\right)^{-2}$, the specific trapping coefficient associated with each was calculated to be 2.0 × 1015 s-1, 4.4 × 1015 s-1, and 1.4 × 1016 s-1. The minimum and maximum coefficient values can be used to estimate the upper and lower bounds of VAl -related defect cluster concentration. For Sample B and C, Ti-associated vacancy clusters need to be considered. However, it is difficult to obtain the atomic volume associated with the substitutional defect $\left(3 \mathrm{Ti}_{\mathrm{Al}}^{+1}: \mathrm{V}_{\mathrm{Al}}^{-3}\right)$so it was treated as having the same volume of an Al atom in sapphire. The real volume associated with a Ti atom sitting at an Al site should be slightly larger compared to that of an Al atom due to the larger atomic radius of Ti. For Sample B and C, the minimum and maximum trapping coefficients from all possible VAl-related vacancy clusters were estimated to be 1.5 × 1015 s-1 (from $\left(3 \mathrm{Ti}_{\mathrm{Al}}^{+1}: \mathrm{V}_{\mathrm{Al}}^{-3}\right)$) and 1.4 x1016 s-1 (from ($\left.\left(2 \mathrm{~V}_{0}^{+2}: 2 \mathrm{~V}_{\mathrm{Al}}^{-3}\right)^{-2}\right)$.

Using values for the trapping coefficients, the VAl-related defect cluster concentration in each sample could be estimated along with the upper and lower limits depending on the defect type, and the results are shown in Table 4. Since the calculated trapping coefficients were based on the estimated values for different VAl-related defects (which could differ considerably from actual values), a large uncertainty exists in the estimated defect concentrations (factor of two to three) [25]. One observation from the estimated defect concentrations shown in Table 4 is that charged vacancy clusters tend to have a smaller concentration due to a relatively higher trapping coefficient value, which is reasonable since the locally-unbalanced charge is not favored by the overall system. The results in Table 4 indicate that the positron trapping rates of Sample B and C are twice that of Sample A since both have larger ${\mathrm{\tau }_2}$ and ${\textrm{I}_2}$ values. Similarly, based on the specific trapping coefficient value associated with VAl -related divacancy defect, the VAl-related defect cluster concentrations are higher in Sample B and C by a factor of two or three compared to Sample A. Note that other vacancy-impurity complexes or negatively charged dislocations, which could potentially contribute to positron trapping in sapphire, were not considered. Additionally, $\textrm{V}_\textrm{O}^0$ could possibly be present in any of the vacancy clusters due to its neutral charge state and this would produce a larger defect size.

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Table 4. Estimated Vacancy Defect Concentrations in Sapphire

4. Discussion

The results in this work for vacancy-related defect concentrations in sapphire were obtained using techniques that are complementary in many ways. PALS is sensitive to defect structures that carry a negative or a neutral charge while many features in the optical absorption spectrum in the visible and near infrared are associated with defects that are either neutral or positively charged. PALS is likely more sensitive to defects near the surface owing to the finite penetration depth of positrons into the sample surface. Total concentrations for VAl (based on PALS) and VO (based on optical absorption) were found to be in the 0.01 to 1 ppm range with the concentration of defects in Sample A and C being higher than in Sample A. Different VO defects along with different trace impurities are optically active in the UV and visible wavelength regions, while both neutral and charged VAl-related defects are more influential in the near-infrared and infrared regions [16].

Since PALS measurements were done on the polished surfaces of all samples and the typical penetration depth of the positron is on the order of hundreds of micrometers, the measured lifetime results should provide better information of defects (i.e. size and concentration) residing near the sapphire surface compared to those in the bulk. Sample A and C had a similar, low-level bulk absorption across all wavelengths, and UV-VIS results indicated that these samples had fewer impurities and charged color centers. However, the surface absorption losses proved to be significantly different owing to defect structures likely introduced during grinding and polishing. PALS results for Sample C included larger ${\mathrm{\tau }_2}$ and I2 values compared to those of Sample A, suggesting a higher cationic vacancy-related defect concentration as well as larger defect sizes near the surface. Moreover, Sample C had a longer defect-related lifetime (about 26 ps higher) than that of Sample A. Surface absorbance measurements at 355 nm and 532 nm differed by a factor of 1.5 to 2 whereas at 1064 nm this factor increases to 3 (see Table 2). Note that the smaller difference at 355 nm could be caused by a higher concentration of F+ centers in Sample A which would contribute less when moving to the longer wavelength regions. At longer wavelengths, cationic vacancy defects likely play a more important role. The positron lifetimes measured by PALS indicated that the near-surface, cationic vacancy-related defect concentrations in Sample B and C are at a similar level while defect sizes are likely larger in Sample C. This is supported by the somewhat higher defect-related mean lifetime component in Sample C and the comparable I2 values for Sample B and C which only differed by 0.6% (within the 5% fitting uncertainty). The larger defect size could result either from larger vacancy clusters or vacancy-decorated dislocations that could be introduced by grinding and polishing processes [4,24]. It is useful to note that increased cationic defect concentrations resulting from polishing-generated dislocations have been detected by PALS in both ZnO and GaN [3537]. In these materials, both cationic vacancy-related clusters as well as vacancy-dislocation complexes acted as the positron trapping centers. In the case of sapphire, even though no previous studies have measured the positron lifetimes associated with dislocations, values have been reported for single-crystal aluminum that are in the range of 210 to 240 ps, comparable to the measured defect lifetimes of Sample B and C [38]. When examining the surface absorbance of these samples at 355 nm and 532 nm from Fig. 3, loss is higher in Sample B by factors of 3 and 2.5, respectively. These differences could be due to higher populations of point defects in Sample B beyond the VAl-related ones (i.e. single anionic vacancies, positively charged vacancy clusters, and additional impurities). Interestingly, at 1064 nm, the surface absorbance of both samples was very close. Since the average concentrations of VAl-related clusters measured by PALS were comparable and these defects tend to be more optically active in sapphire in the near-infrared wavelength region, the higher surface absorbances recorded at 1064 nm indicate higher cationic vacancy-related defect concentrations in these samples.

 figure: Fig. 3.

Fig. 3. A Bar plot shows the total surface absorbance of each sample at each wavelength. The defect associated mean lifetime as a product of ${\mathrm{\tau }_2}\textrm{\; and\; \; }{\textrm{I}_2}$ is labeled for each sample.

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5. Conclusion

In this study, it was shown that higher vacancy-type defect concentrations correlate with higher optical absorption loss in sapphire. Measurements of absorption in the UV-VIS were used to identify different vacancy-type defects along with impurity concentration levels in all samples. The neutral VO concentration in the bulk was found to be at the level of 10−1 ppm for all samples while the one of $\textrm{V}_\textrm{O}^{ + 1}$was found to be in the range of 10−3 to 10−5 ppm depending on different samples. PALS measurements suggest that in the near-surface region, the VAl-related defect cluster concentration level among all samples was approximately 10−2 to 10−1 ppm depending on the defect chemistry. While the overall defect concentrations from the two methods seem to correlate, surface-specific optical absorbance measurements more closely relate to PALS measurements. It was shown that samples with both higher levels of VO and VAl-related defects also had a higher surface absorbance at three different wavelengths where PCI measurements were performed. Defect complexes in the near-surface region composed of vacancy clusters as well as dislocations that are introduced during surface grinding and polishing operations affect both optical absorbance and positron lifetimes. This correlation indicates that PALS measurements could be useful for assessing surface-induced damage produced during optical component fabrication.

Funding

Directed Energy Professional Society; Applied Physics Laboratory, Johns Hopkins University.

Disclosures

The authors declare that there are no conflicts of interest related to this article.

References

1. B. S. Patel and Z. H. Zaidi, “The suitability of sapphire for laser windows,” Meas. Sci. Technol. 10(3), 146–151 (1999). [CrossRef]  

2. M. E. Thomas, “Low-level background absorption in durable window materials,” Proc. SPIE 10179, 101790B (2017). [CrossRef]  

3. J. Ma, M. B. Airola, M. E. Thomas, and J. Spicer, “Measurements of weak scattering and absorption in spinel and sapphire from the near infrared to the visible,” Proc. SPIE 10985, 1098502 (2019). [CrossRef]  

4. E. R. Dobrovinskaya, L. A. Lytvynov, and V. Pishchik, Sapphire: Material, Manufacturing, Applications. 2009.

5. J. Ma, M. E. Thomas, P. McGuiggan, and J. Spicer, “Weak absorption and scattering losses from the visible to the near infrared in single-crystal sapphire materials,” Opt. Eng. 59(8), 087101 (2020). [CrossRef]  

6. P. Pellegrino, “Trace chemical vapor detection by photothermal interferometry,” Proc. SPIE4205, 2001.

7. D. L. Dexter, “Theory of the Optical Properties of Imperfections in Nonmetals,” Solid State Phys. 6, 353–411 (1958). [CrossRef]  

8. M. E. Innocenzi, R. T. Swimm, M. Bass, R. H. French, A. B. Villaverde, and M. R. Kokta, “Room-temperature optical absorption in undoped α-Al2O 3,” J. Appl. Phys. 67(12), 7542–7546 (1990). [CrossRef]  

9. B. D. Evans, “Optical transmission in undoped crystalline α-Al2O 3 grown by several techniques,” J. Appl. Phys. 70(7), 3995–3997 (1991). [CrossRef]  

10. B. D. Evans and M. Stapelbroek, “Optical properties of the F+ center in crystalline Al2O3,” Phys. Rev. B 18(12), 7089–7098 (1978). [CrossRef]  

11. R. T. Cox, “Electron spin resonance studies of holes trapped at Mg2+, Li+ and cation vacancies in Al2O3,” Solid State Commun. 9(22), 1989–1992 (1971). [CrossRef]  

12. K. H. Lee, G. E. Holmberg, and J. H. Crawford, “Optical and ESR studies of hole centers in γ-irradiated Al2O3,” Phys. Status Solidi 39(2), 669–674 (1977). [CrossRef]  

13. X. Xiang, G. Zhang, X. Wang, T. Tang, and Y. Shi, “A new perspective on the process of intrinsic point defects in α-Al2O3,” Phys. Chem. Chem. Phys. 17(43), 29134–29141 (2015). [CrossRef]  

14. G. Zhang, Y. Lu, and X. Wang, “Hydrogen interactions with intrinsic point defects in hydrogen permeation barrier of α-Al2O3: A first-principles study,” Phys. Chem. Chem. Phys. 16(33), 17523–17530 (2014). [CrossRef]  

15. K. P. D. Lagerlo and R. W. Grimes, “The Defect Chemistry of Sapphire (a-Al2O3),” Acta Mater. 46(16), 5689–5700 (1998). [CrossRef]  

16. T. Blue, F. Goldner, F. Poc, J. Greene, and R. Fielder, “Testing of Sapphire Optical Fiber and Sensors in Intense Radiation Fields, when Subjected to Very High Temperatures Proposal,” NEUP Final Rep., 2012.

17. G. Molnár, M. Benabdesselam, J. Borossay, D. Lapraz, P. Iacconi, V. S Kortov, and A. I Surdo, “Photoluminescence and thermoluminescence of titanium ions in sapphire crystals,” Radiat. Meas. 33(5), 663–667 (2001). [CrossRef]  

18. W. J. Chung, B. J. Park, H. S. Seo, J. T. Ahn, M. H. Lee, and Y. G. Choi, “Effects of the weak absorption tail on the transmission loss of Ge-Sb-Se optical fibers,” J. Am. Ceram. Soc. 88(5), 1205–1208 (2005). [CrossRef]  

19. D. L. Wood and J. Tauc, “Weak absorption tails in amorphous semiconductors,” Phys. Rev. B 5(8), 3144–3151 (1972). [CrossRef]  

20. M. Marchiò, M. Leonardi, M. Bazzan, and R. Flaminio, “3D characterization of low optical absorption structures in large crystalline sapphire substrates for gravitational wave detectors,” Sci. Rep. 11(1), 2654 (2021). [CrossRef]  

21. E. Hirose, D. Bajuk, G. Billingsley, T. Kajita, B. Kestner, N. Mio, M. Ohashi, B. Reichman, H. Yamamoto, and L. Zhang, “Sapphire mirror for the KAGRA gravitational wave detector,” Phys. Rev. D: Part., Fields, Gravitation, Cosmol. 89(6), 062003 (2014). [CrossRef]  

22. S. E. Kulkova, L. Y. Zagorskaya, and I. R. Shein, “Electronic structure of α-Al 2O 3 in the bulk and on the surface,” Russ. Phys. J. 48(11), 1127–1133 (2005). [CrossRef]  

23. J. Carrasco, J. R. B. Gomes, and F. Illas, “Theoretical study of bulk and surface oxygen and aluminum vacancies in α-Al2O3,” Phys. Rev. B: Condens. Matter Mater. Phys. 69(6), 064116 (2004). [CrossRef]  

24. T. Saito, T. Hirayama, T. Yamamoto, and Y. Ikuhara, “Lattice strain and dislocations in polished surfaces on sapphire,” J. Am. Ceram. Soc. 88(8), 2277–2285 (2005). [CrossRef]  

25. X. Hu, T. Koyanagi, Y. Katoh, and B. D. Wirth, “Positron annihilation spectroscopy investigation of vacancy defects in neutron-irradiated 3C-SiC,” Phys. Rev. B 95(10), 104103 (2017). [CrossRef]  

26. G. Moya, J. Kansy, A. Si Ahmed, J. Liebault, F. Moya, and D. Gæuriot, “Positron lifetime measurements in sintered alumina,” Phys. Status Solidi A 198(1), 215–223 (2003). [CrossRef]  

27. H. E. Schaefer and M. Forster, “As-grown metal oxides and electron-irradiated Al2O3 studied by positron lifetime measurements,” Mater. Sci. Eng., A 109, 161–167 (1989). [CrossRef]  

28. N. Djourelov, Y. Aman, K. Berovski, P. Nédélec, N. Charvin, V. Garnier, and E. Djurado, “Structure characterization of spark plasma sintered alumina by positron annihilation lifetime spectroscopy,” Phys. Status Solidi A 208(4), 795–802 (2011). [CrossRef]  

29. J. Xu, B. Somieski, L. Hulett, B. Pint, P. Tortorelli, R. Suzuki, and T. Ohdaira, “Microdefects in Al2O3 films and interfaces revealed by positron lifetime spectroscopy,” Appl. Phys. Lett. 71(21), 3165–3167 (1997). [CrossRef]  

30. J. C. Han, H. L. Zhang, M. F. Zhang, B. Y. Wang, Z. X. Li, C. H. Xu, and H. X. Guo, “Neutron irradiation and post annealing effect on sapphire by positron annihilation,” Appl. Radiat. Isot. 68(9), 1699–1702 (2010). [CrossRef]  

31. K. P. Muthe, K. Sudarshan, P. K. Pujari, M. S. Kulkarni, N. S. Rawat, B. C. Bhatt, and S. K. Gupta, “Positron annihilation and thermoluminescence studies of thermally induced defects in α-Al2O3 single crystals,” J. Phys. D: Appl. Phys. 42(10), 105405 (2009). [CrossRef]  

32. M. Hornak, “Energetics, Kinetics, and Optical Absorption of Point Defects in Sapphire,” The Ohio State University, 2016.

33. M. Eldrup and B. N. Singh, “Studies of defects and defect agglomerates by positron annihilation spectroscopy,” J. Nucl. Mater. 251, 132–138 (1997). [CrossRef]  

34. G. Dlubek, “Positron Studies of Decomposition Phenomena in Al Alloys,” Mater. Sci. Forum 13-14, 11–32 (1987). [CrossRef]  

35. F. A. Selim, M. H. Weber, D. Solodovnikov, and K. G. Lynn, “Nature of native defects in ZnO,” Phys. Rev. Lett. 99(8), 085502 (2007). [CrossRef]  

36. V. Quemener, L. Vines, E. V. Monakhov, and B. G. Svensson, “Electronic properties of vacancy related defects in ZnO induced by mechanical polishing,” Appl. Phys. Lett. 99(11), 112112 (2011). [CrossRef]  

37. C. H. Qiu, C. Hoggatt, W. Melton, M. W. Leksono, and J. I. Pankove, “Study of defect states in GaN films by photoconductivity measurement Study of defect states in GaN films by photoconductivity measurement,” Appl. Phys. Lett. 66(20), 2712–2714 (1995). [CrossRef]  

38. C. Hidalgo, G. González-Doncel, S. Linderoth, and J. San Juan, “Structure of dislocations in Al and Fe as studied by positron-annihilation spectroscopy,” Phys. Rev. B 45(13), 7017–7021 (1992). [CrossRef]  

References

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  • |
  • |

  1. B. S. Patel and Z. H. Zaidi, “The suitability of sapphire for laser windows,” Meas. Sci. Technol. 10(3), 146–151 (1999).
    [Crossref]
  2. M. E. Thomas, “Low-level background absorption in durable window materials,” Proc. SPIE 10179, 101790B (2017).
    [Crossref]
  3. J. Ma, M. B. Airola, M. E. Thomas, and J. Spicer, “Measurements of weak scattering and absorption in spinel and sapphire from the near infrared to the visible,” Proc. SPIE 10985, 1098502 (2019).
    [Crossref]
  4. E. R. Dobrovinskaya, L. A. Lytvynov, and V. Pishchik, Sapphire: Material, Manufacturing, Applications. 2009.
  5. J. Ma, M. E. Thomas, P. McGuiggan, and J. Spicer, “Weak absorption and scattering losses from the visible to the near infrared in single-crystal sapphire materials,” Opt. Eng. 59(8), 087101 (2020).
    [Crossref]
  6. P. Pellegrino, “Trace chemical vapor detection by photothermal interferometry,” Proc. SPIE4205, 2001.
  7. D. L. Dexter, “Theory of the Optical Properties of Imperfections in Nonmetals,” Solid State Phys. 6, 353–411 (1958).
    [Crossref]
  8. M. E. Innocenzi, R. T. Swimm, M. Bass, R. H. French, A. B. Villaverde, and M. R. Kokta, “Room-temperature optical absorption in undoped α-Al2O 3,” J. Appl. Phys. 67(12), 7542–7546 (1990).
    [Crossref]
  9. B. D. Evans, “Optical transmission in undoped crystalline α-Al2O 3 grown by several techniques,” J. Appl. Phys. 70(7), 3995–3997 (1991).
    [Crossref]
  10. B. D. Evans and M. Stapelbroek, “Optical properties of the F+ center in crystalline Al2O3,” Phys. Rev. B 18(12), 7089–7098 (1978).
    [Crossref]
  11. R. T. Cox, “Electron spin resonance studies of holes trapped at Mg2+, Li+ and cation vacancies in Al2O3,” Solid State Commun. 9(22), 1989–1992 (1971).
    [Crossref]
  12. K. H. Lee, G. E. Holmberg, and J. H. Crawford, “Optical and ESR studies of hole centers in γ-irradiated Al2O3,” Phys. Status Solidi 39(2), 669–674 (1977).
    [Crossref]
  13. X. Xiang, G. Zhang, X. Wang, T. Tang, and Y. Shi, “A new perspective on the process of intrinsic point defects in α-Al2O3,” Phys. Chem. Chem. Phys. 17(43), 29134–29141 (2015).
    [Crossref]
  14. G. Zhang, Y. Lu, and X. Wang, “Hydrogen interactions with intrinsic point defects in hydrogen permeation barrier of α-Al2O3: A first-principles study,” Phys. Chem. Chem. Phys. 16(33), 17523–17530 (2014).
    [Crossref]
  15. K. P. D. Lagerlo and R. W. Grimes, “The Defect Chemistry of Sapphire (a-Al2O3),” Acta Mater. 46(16), 5689–5700 (1998).
    [Crossref]
  16. T. Blue, F. Goldner, F. Poc, J. Greene, and R. Fielder, “Testing of Sapphire Optical Fiber and Sensors in Intense Radiation Fields, when Subjected to Very High Temperatures Proposal,” NEUP Final Rep., 2012.
  17. G. Molnár, M. Benabdesselam, J. Borossay, D. Lapraz, P. Iacconi, V. S Kortov, and A. I Surdo, “Photoluminescence and thermoluminescence of titanium ions in sapphire crystals,” Radiat. Meas. 33(5), 663–667 (2001).
    [Crossref]
  18. W. J. Chung, B. J. Park, H. S. Seo, J. T. Ahn, M. H. Lee, and Y. G. Choi, “Effects of the weak absorption tail on the transmission loss of Ge-Sb-Se optical fibers,” J. Am. Ceram. Soc. 88(5), 1205–1208 (2005).
    [Crossref]
  19. D. L. Wood and J. Tauc, “Weak absorption tails in amorphous semiconductors,” Phys. Rev. B 5(8), 3144–3151 (1972).
    [Crossref]
  20. M. Marchiò, M. Leonardi, M. Bazzan, and R. Flaminio, “3D characterization of low optical absorption structures in large crystalline sapphire substrates for gravitational wave detectors,” Sci. Rep. 11(1), 2654 (2021).
    [Crossref]
  21. E. Hirose, D. Bajuk, G. Billingsley, T. Kajita, B. Kestner, N. Mio, M. Ohashi, B. Reichman, H. Yamamoto, and L. Zhang, “Sapphire mirror for the KAGRA gravitational wave detector,” Phys. Rev. D: Part., Fields, Gravitation, Cosmol. 89(6), 062003 (2014).
    [Crossref]
  22. S. E. Kulkova, L. Y. Zagorskaya, and I. R. Shein, “Electronic structure of α-Al 2O 3 in the bulk and on the surface,” Russ. Phys. J. 48(11), 1127–1133 (2005).
    [Crossref]
  23. J. Carrasco, J. R. B. Gomes, and F. Illas, “Theoretical study of bulk and surface oxygen and aluminum vacancies in α-Al2O3,” Phys. Rev. B: Condens. Matter Mater. Phys. 69(6), 064116 (2004).
    [Crossref]
  24. T. Saito, T. Hirayama, T. Yamamoto, and Y. Ikuhara, “Lattice strain and dislocations in polished surfaces on sapphire,” J. Am. Ceram. Soc. 88(8), 2277–2285 (2005).
    [Crossref]
  25. X. Hu, T. Koyanagi, Y. Katoh, and B. D. Wirth, “Positron annihilation spectroscopy investigation of vacancy defects in neutron-irradiated 3C-SiC,” Phys. Rev. B 95(10), 104103 (2017).
    [Crossref]
  26. G. Moya, J. Kansy, A. Si Ahmed, J. Liebault, F. Moya, and D. Gæuriot, “Positron lifetime measurements in sintered alumina,” Phys. Status Solidi A 198(1), 215–223 (2003).
    [Crossref]
  27. H. E. Schaefer and M. Forster, “As-grown metal oxides and electron-irradiated Al2O3 studied by positron lifetime measurements,” Mater. Sci. Eng., A 109, 161–167 (1989).
    [Crossref]
  28. N. Djourelov, Y. Aman, K. Berovski, P. Nédélec, N. Charvin, V. Garnier, and E. Djurado, “Structure characterization of spark plasma sintered alumina by positron annihilation lifetime spectroscopy,” Phys. Status Solidi A 208(4), 795–802 (2011).
    [Crossref]
  29. J. Xu, B. Somieski, L. Hulett, B. Pint, P. Tortorelli, R. Suzuki, and T. Ohdaira, “Microdefects in Al2O3 films and interfaces revealed by positron lifetime spectroscopy,” Appl. Phys. Lett. 71(21), 3165–3167 (1997).
    [Crossref]
  30. J. C. Han, H. L. Zhang, M. F. Zhang, B. Y. Wang, Z. X. Li, C. H. Xu, and H. X. Guo, “Neutron irradiation and post annealing effect on sapphire by positron annihilation,” Appl. Radiat. Isot. 68(9), 1699–1702 (2010).
    [Crossref]
  31. K. P. Muthe, K. Sudarshan, P. K. Pujari, M. S. Kulkarni, N. S. Rawat, B. C. Bhatt, and S. K. Gupta, “Positron annihilation and thermoluminescence studies of thermally induced defects in α-Al2O3 single crystals,” J. Phys. D: Appl. Phys. 42(10), 105405 (2009).
    [Crossref]
  32. M. Hornak, “Energetics, Kinetics, and Optical Absorption of Point Defects in Sapphire,” The Ohio State University, 2016.
  33. M. Eldrup and B. N. Singh, “Studies of defects and defect agglomerates by positron annihilation spectroscopy,” J. Nucl. Mater. 251, 132–138 (1997).
    [Crossref]
  34. G. Dlubek, “Positron Studies of Decomposition Phenomena in Al Alloys,” Mater. Sci. Forum 13-14, 11–32 (1987).
    [Crossref]
  35. F. A. Selim, M. H. Weber, D. Solodovnikov, and K. G. Lynn, “Nature of native defects in ZnO,” Phys. Rev. Lett. 99(8), 085502 (2007).
    [Crossref]
  36. V. Quemener, L. Vines, E. V. Monakhov, and B. G. Svensson, “Electronic properties of vacancy related defects in ZnO induced by mechanical polishing,” Appl. Phys. Lett. 99(11), 112112 (2011).
    [Crossref]
  37. C. H. Qiu, C. Hoggatt, W. Melton, M. W. Leksono, and J. I. Pankove, “Study of defect states in GaN films by photoconductivity measurement Study of defect states in GaN films by photoconductivity measurement,” Appl. Phys. Lett. 66(20), 2712–2714 (1995).
    [Crossref]
  38. C. Hidalgo, G. González-Doncel, S. Linderoth, and J. San Juan, “Structure of dislocations in Al and Fe as studied by positron-annihilation spectroscopy,” Phys. Rev. B 45(13), 7017–7021 (1992).
    [Crossref]

2021 (1)

M. Marchiò, M. Leonardi, M. Bazzan, and R. Flaminio, “3D characterization of low optical absorption structures in large crystalline sapphire substrates for gravitational wave detectors,” Sci. Rep. 11(1), 2654 (2021).
[Crossref]

2020 (1)

J. Ma, M. E. Thomas, P. McGuiggan, and J. Spicer, “Weak absorption and scattering losses from the visible to the near infrared in single-crystal sapphire materials,” Opt. Eng. 59(8), 087101 (2020).
[Crossref]

2019 (1)

J. Ma, M. B. Airola, M. E. Thomas, and J. Spicer, “Measurements of weak scattering and absorption in spinel and sapphire from the near infrared to the visible,” Proc. SPIE 10985, 1098502 (2019).
[Crossref]

2017 (2)

M. E. Thomas, “Low-level background absorption in durable window materials,” Proc. SPIE 10179, 101790B (2017).
[Crossref]

X. Hu, T. Koyanagi, Y. Katoh, and B. D. Wirth, “Positron annihilation spectroscopy investigation of vacancy defects in neutron-irradiated 3C-SiC,” Phys. Rev. B 95(10), 104103 (2017).
[Crossref]

2015 (1)

X. Xiang, G. Zhang, X. Wang, T. Tang, and Y. Shi, “A new perspective on the process of intrinsic point defects in α-Al2O3,” Phys. Chem. Chem. Phys. 17(43), 29134–29141 (2015).
[Crossref]

2014 (2)

G. Zhang, Y. Lu, and X. Wang, “Hydrogen interactions with intrinsic point defects in hydrogen permeation barrier of α-Al2O3: A first-principles study,” Phys. Chem. Chem. Phys. 16(33), 17523–17530 (2014).
[Crossref]

E. Hirose, D. Bajuk, G. Billingsley, T. Kajita, B. Kestner, N. Mio, M. Ohashi, B. Reichman, H. Yamamoto, and L. Zhang, “Sapphire mirror for the KAGRA gravitational wave detector,” Phys. Rev. D: Part., Fields, Gravitation, Cosmol. 89(6), 062003 (2014).
[Crossref]

2011 (2)

N. Djourelov, Y. Aman, K. Berovski, P. Nédélec, N. Charvin, V. Garnier, and E. Djurado, “Structure characterization of spark plasma sintered alumina by positron annihilation lifetime spectroscopy,” Phys. Status Solidi A 208(4), 795–802 (2011).
[Crossref]

V. Quemener, L. Vines, E. V. Monakhov, and B. G. Svensson, “Electronic properties of vacancy related defects in ZnO induced by mechanical polishing,” Appl. Phys. Lett. 99(11), 112112 (2011).
[Crossref]

2010 (1)

J. C. Han, H. L. Zhang, M. F. Zhang, B. Y. Wang, Z. X. Li, C. H. Xu, and H. X. Guo, “Neutron irradiation and post annealing effect on sapphire by positron annihilation,” Appl. Radiat. Isot. 68(9), 1699–1702 (2010).
[Crossref]

2009 (1)

K. P. Muthe, K. Sudarshan, P. K. Pujari, M. S. Kulkarni, N. S. Rawat, B. C. Bhatt, and S. K. Gupta, “Positron annihilation and thermoluminescence studies of thermally induced defects in α-Al2O3 single crystals,” J. Phys. D: Appl. Phys. 42(10), 105405 (2009).
[Crossref]

2007 (1)

F. A. Selim, M. H. Weber, D. Solodovnikov, and K. G. Lynn, “Nature of native defects in ZnO,” Phys. Rev. Lett. 99(8), 085502 (2007).
[Crossref]

2005 (3)

T. Saito, T. Hirayama, T. Yamamoto, and Y. Ikuhara, “Lattice strain and dislocations in polished surfaces on sapphire,” J. Am. Ceram. Soc. 88(8), 2277–2285 (2005).
[Crossref]

W. J. Chung, B. J. Park, H. S. Seo, J. T. Ahn, M. H. Lee, and Y. G. Choi, “Effects of the weak absorption tail on the transmission loss of Ge-Sb-Se optical fibers,” J. Am. Ceram. Soc. 88(5), 1205–1208 (2005).
[Crossref]

S. E. Kulkova, L. Y. Zagorskaya, and I. R. Shein, “Electronic structure of α-Al 2O 3 in the bulk and on the surface,” Russ. Phys. J. 48(11), 1127–1133 (2005).
[Crossref]

2004 (1)

J. Carrasco, J. R. B. Gomes, and F. Illas, “Theoretical study of bulk and surface oxygen and aluminum vacancies in α-Al2O3,” Phys. Rev. B: Condens. Matter Mater. Phys. 69(6), 064116 (2004).
[Crossref]

2003 (1)

G. Moya, J. Kansy, A. Si Ahmed, J. Liebault, F. Moya, and D. Gæuriot, “Positron lifetime measurements in sintered alumina,” Phys. Status Solidi A 198(1), 215–223 (2003).
[Crossref]

2001 (1)

G. Molnár, M. Benabdesselam, J. Borossay, D. Lapraz, P. Iacconi, V. S Kortov, and A. I Surdo, “Photoluminescence and thermoluminescence of titanium ions in sapphire crystals,” Radiat. Meas. 33(5), 663–667 (2001).
[Crossref]

1999 (1)

B. S. Patel and Z. H. Zaidi, “The suitability of sapphire for laser windows,” Meas. Sci. Technol. 10(3), 146–151 (1999).
[Crossref]

1998 (1)

K. P. D. Lagerlo and R. W. Grimes, “The Defect Chemistry of Sapphire (a-Al2O3),” Acta Mater. 46(16), 5689–5700 (1998).
[Crossref]

1997 (2)

M. Eldrup and B. N. Singh, “Studies of defects and defect agglomerates by positron annihilation spectroscopy,” J. Nucl. Mater. 251, 132–138 (1997).
[Crossref]

J. Xu, B. Somieski, L. Hulett, B. Pint, P. Tortorelli, R. Suzuki, and T. Ohdaira, “Microdefects in Al2O3 films and interfaces revealed by positron lifetime spectroscopy,” Appl. Phys. Lett. 71(21), 3165–3167 (1997).
[Crossref]

1995 (1)

C. H. Qiu, C. Hoggatt, W. Melton, M. W. Leksono, and J. I. Pankove, “Study of defect states in GaN films by photoconductivity measurement Study of defect states in GaN films by photoconductivity measurement,” Appl. Phys. Lett. 66(20), 2712–2714 (1995).
[Crossref]

1992 (1)

C. Hidalgo, G. González-Doncel, S. Linderoth, and J. San Juan, “Structure of dislocations in Al and Fe as studied by positron-annihilation spectroscopy,” Phys. Rev. B 45(13), 7017–7021 (1992).
[Crossref]

1991 (1)

B. D. Evans, “Optical transmission in undoped crystalline α-Al2O 3 grown by several techniques,” J. Appl. Phys. 70(7), 3995–3997 (1991).
[Crossref]

1990 (1)

M. E. Innocenzi, R. T. Swimm, M. Bass, R. H. French, A. B. Villaverde, and M. R. Kokta, “Room-temperature optical absorption in undoped α-Al2O 3,” J. Appl. Phys. 67(12), 7542–7546 (1990).
[Crossref]

1989 (1)

H. E. Schaefer and M. Forster, “As-grown metal oxides and electron-irradiated Al2O3 studied by positron lifetime measurements,” Mater. Sci. Eng., A 109, 161–167 (1989).
[Crossref]

1987 (1)

G. Dlubek, “Positron Studies of Decomposition Phenomena in Al Alloys,” Mater. Sci. Forum 13-14, 11–32 (1987).
[Crossref]

1978 (1)

B. D. Evans and M. Stapelbroek, “Optical properties of the F+ center in crystalline Al2O3,” Phys. Rev. B 18(12), 7089–7098 (1978).
[Crossref]

1977 (1)

K. H. Lee, G. E. Holmberg, and J. H. Crawford, “Optical and ESR studies of hole centers in γ-irradiated Al2O3,” Phys. Status Solidi 39(2), 669–674 (1977).
[Crossref]

1972 (1)

D. L. Wood and J. Tauc, “Weak absorption tails in amorphous semiconductors,” Phys. Rev. B 5(8), 3144–3151 (1972).
[Crossref]

1971 (1)

R. T. Cox, “Electron spin resonance studies of holes trapped at Mg2+, Li+ and cation vacancies in Al2O3,” Solid State Commun. 9(22), 1989–1992 (1971).
[Crossref]

1958 (1)

D. L. Dexter, “Theory of the Optical Properties of Imperfections in Nonmetals,” Solid State Phys. 6, 353–411 (1958).
[Crossref]

Ahn, J. T.

W. J. Chung, B. J. Park, H. S. Seo, J. T. Ahn, M. H. Lee, and Y. G. Choi, “Effects of the weak absorption tail on the transmission loss of Ge-Sb-Se optical fibers,” J. Am. Ceram. Soc. 88(5), 1205–1208 (2005).
[Crossref]

Airola, M. B.

J. Ma, M. B. Airola, M. E. Thomas, and J. Spicer, “Measurements of weak scattering and absorption in spinel and sapphire from the near infrared to the visible,” Proc. SPIE 10985, 1098502 (2019).
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N. Djourelov, Y. Aman, K. Berovski, P. Nédélec, N. Charvin, V. Garnier, and E. Djurado, “Structure characterization of spark plasma sintered alumina by positron annihilation lifetime spectroscopy,” Phys. Status Solidi A 208(4), 795–802 (2011).
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E. Hirose, D. Bajuk, G. Billingsley, T. Kajita, B. Kestner, N. Mio, M. Ohashi, B. Reichman, H. Yamamoto, and L. Zhang, “Sapphire mirror for the KAGRA gravitational wave detector,” Phys. Rev. D: Part., Fields, Gravitation, Cosmol. 89(6), 062003 (2014).
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M. Marchiò, M. Leonardi, M. Bazzan, and R. Flaminio, “3D characterization of low optical absorption structures in large crystalline sapphire substrates for gravitational wave detectors,” Sci. Rep. 11(1), 2654 (2021).
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G. Molnár, M. Benabdesselam, J. Borossay, D. Lapraz, P. Iacconi, V. S Kortov, and A. I Surdo, “Photoluminescence and thermoluminescence of titanium ions in sapphire crystals,” Radiat. Meas. 33(5), 663–667 (2001).
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N. Djourelov, Y. Aman, K. Berovski, P. Nédélec, N. Charvin, V. Garnier, and E. Djurado, “Structure characterization of spark plasma sintered alumina by positron annihilation lifetime spectroscopy,” Phys. Status Solidi A 208(4), 795–802 (2011).
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K. P. Muthe, K. Sudarshan, P. K. Pujari, M. S. Kulkarni, N. S. Rawat, B. C. Bhatt, and S. K. Gupta, “Positron annihilation and thermoluminescence studies of thermally induced defects in α-Al2O3 single crystals,” J. Phys. D: Appl. Phys. 42(10), 105405 (2009).
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E. Hirose, D. Bajuk, G. Billingsley, T. Kajita, B. Kestner, N. Mio, M. Ohashi, B. Reichman, H. Yamamoto, and L. Zhang, “Sapphire mirror for the KAGRA gravitational wave detector,” Phys. Rev. D: Part., Fields, Gravitation, Cosmol. 89(6), 062003 (2014).
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T. Blue, F. Goldner, F. Poc, J. Greene, and R. Fielder, “Testing of Sapphire Optical Fiber and Sensors in Intense Radiation Fields, when Subjected to Very High Temperatures Proposal,” NEUP Final Rep., 2012.

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G. Molnár, M. Benabdesselam, J. Borossay, D. Lapraz, P. Iacconi, V. S Kortov, and A. I Surdo, “Photoluminescence and thermoluminescence of titanium ions in sapphire crystals,” Radiat. Meas. 33(5), 663–667 (2001).
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J. Carrasco, J. R. B. Gomes, and F. Illas, “Theoretical study of bulk and surface oxygen and aluminum vacancies in α-Al2O3,” Phys. Rev. B: Condens. Matter Mater. Phys. 69(6), 064116 (2004).
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N. Djourelov, Y. Aman, K. Berovski, P. Nédélec, N. Charvin, V. Garnier, and E. Djurado, “Structure characterization of spark plasma sintered alumina by positron annihilation lifetime spectroscopy,” Phys. Status Solidi A 208(4), 795–802 (2011).
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W. J. Chung, B. J. Park, H. S. Seo, J. T. Ahn, M. H. Lee, and Y. G. Choi, “Effects of the weak absorption tail on the transmission loss of Ge-Sb-Se optical fibers,” J. Am. Ceram. Soc. 88(5), 1205–1208 (2005).
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N. Djourelov, Y. Aman, K. Berovski, P. Nédélec, N. Charvin, V. Garnier, and E. Djurado, “Structure characterization of spark plasma sintered alumina by positron annihilation lifetime spectroscopy,” Phys. Status Solidi A 208(4), 795–802 (2011).
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Djurado, E.

N. Djourelov, Y. Aman, K. Berovski, P. Nédélec, N. Charvin, V. Garnier, and E. Djurado, “Structure characterization of spark plasma sintered alumina by positron annihilation lifetime spectroscopy,” Phys. Status Solidi A 208(4), 795–802 (2011).
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T. Blue, F. Goldner, F. Poc, J. Greene, and R. Fielder, “Testing of Sapphire Optical Fiber and Sensors in Intense Radiation Fields, when Subjected to Very High Temperatures Proposal,” NEUP Final Rep., 2012.

Flaminio, R.

M. Marchiò, M. Leonardi, M. Bazzan, and R. Flaminio, “3D characterization of low optical absorption structures in large crystalline sapphire substrates for gravitational wave detectors,” Sci. Rep. 11(1), 2654 (2021).
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Gæuriot, D.

G. Moya, J. Kansy, A. Si Ahmed, J. Liebault, F. Moya, and D. Gæuriot, “Positron lifetime measurements in sintered alumina,” Phys. Status Solidi A 198(1), 215–223 (2003).
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Garnier, V.

N. Djourelov, Y. Aman, K. Berovski, P. Nédélec, N. Charvin, V. Garnier, and E. Djurado, “Structure characterization of spark plasma sintered alumina by positron annihilation lifetime spectroscopy,” Phys. Status Solidi A 208(4), 795–802 (2011).
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Goldner, F.

T. Blue, F. Goldner, F. Poc, J. Greene, and R. Fielder, “Testing of Sapphire Optical Fiber and Sensors in Intense Radiation Fields, when Subjected to Very High Temperatures Proposal,” NEUP Final Rep., 2012.

Gomes, J. R. B.

J. Carrasco, J. R. B. Gomes, and F. Illas, “Theoretical study of bulk and surface oxygen and aluminum vacancies in α-Al2O3,” Phys. Rev. B: Condens. Matter Mater. Phys. 69(6), 064116 (2004).
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C. Hidalgo, G. González-Doncel, S. Linderoth, and J. San Juan, “Structure of dislocations in Al and Fe as studied by positron-annihilation spectroscopy,” Phys. Rev. B 45(13), 7017–7021 (1992).
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T. Blue, F. Goldner, F. Poc, J. Greene, and R. Fielder, “Testing of Sapphire Optical Fiber and Sensors in Intense Radiation Fields, when Subjected to Very High Temperatures Proposal,” NEUP Final Rep., 2012.

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K. P. D. Lagerlo and R. W. Grimes, “The Defect Chemistry of Sapphire (a-Al2O3),” Acta Mater. 46(16), 5689–5700 (1998).
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J. C. Han, H. L. Zhang, M. F. Zhang, B. Y. Wang, Z. X. Li, C. H. Xu, and H. X. Guo, “Neutron irradiation and post annealing effect on sapphire by positron annihilation,” Appl. Radiat. Isot. 68(9), 1699–1702 (2010).
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K. P. Muthe, K. Sudarshan, P. K. Pujari, M. S. Kulkarni, N. S. Rawat, B. C. Bhatt, and S. K. Gupta, “Positron annihilation and thermoluminescence studies of thermally induced defects in α-Al2O3 single crystals,” J. Phys. D: Appl. Phys. 42(10), 105405 (2009).
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J. C. Han, H. L. Zhang, M. F. Zhang, B. Y. Wang, Z. X. Li, C. H. Xu, and H. X. Guo, “Neutron irradiation and post annealing effect on sapphire by positron annihilation,” Appl. Radiat. Isot. 68(9), 1699–1702 (2010).
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C. Hidalgo, G. González-Doncel, S. Linderoth, and J. San Juan, “Structure of dislocations in Al and Fe as studied by positron-annihilation spectroscopy,” Phys. Rev. B 45(13), 7017–7021 (1992).
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E. Hirose, D. Bajuk, G. Billingsley, T. Kajita, B. Kestner, N. Mio, M. Ohashi, B. Reichman, H. Yamamoto, and L. Zhang, “Sapphire mirror for the KAGRA gravitational wave detector,” Phys. Rev. D: Part., Fields, Gravitation, Cosmol. 89(6), 062003 (2014).
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Hoggatt, C.

C. H. Qiu, C. Hoggatt, W. Melton, M. W. Leksono, and J. I. Pankove, “Study of defect states in GaN films by photoconductivity measurement Study of defect states in GaN films by photoconductivity measurement,” Appl. Phys. Lett. 66(20), 2712–2714 (1995).
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Holmberg, G. E.

K. H. Lee, G. E. Holmberg, and J. H. Crawford, “Optical and ESR studies of hole centers in γ-irradiated Al2O3,” Phys. Status Solidi 39(2), 669–674 (1977).
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M. Hornak, “Energetics, Kinetics, and Optical Absorption of Point Defects in Sapphire,” The Ohio State University, 2016.

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X. Hu, T. Koyanagi, Y. Katoh, and B. D. Wirth, “Positron annihilation spectroscopy investigation of vacancy defects in neutron-irradiated 3C-SiC,” Phys. Rev. B 95(10), 104103 (2017).
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J. Xu, B. Somieski, L. Hulett, B. Pint, P. Tortorelli, R. Suzuki, and T. Ohdaira, “Microdefects in Al2O3 films and interfaces revealed by positron lifetime spectroscopy,” Appl. Phys. Lett. 71(21), 3165–3167 (1997).
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Iacconi, P.

G. Molnár, M. Benabdesselam, J. Borossay, D. Lapraz, P. Iacconi, V. S Kortov, and A. I Surdo, “Photoluminescence and thermoluminescence of titanium ions in sapphire crystals,” Radiat. Meas. 33(5), 663–667 (2001).
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Ikuhara, Y.

T. Saito, T. Hirayama, T. Yamamoto, and Y. Ikuhara, “Lattice strain and dislocations in polished surfaces on sapphire,” J. Am. Ceram. Soc. 88(8), 2277–2285 (2005).
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Illas, F.

J. Carrasco, J. R. B. Gomes, and F. Illas, “Theoretical study of bulk and surface oxygen and aluminum vacancies in α-Al2O3,” Phys. Rev. B: Condens. Matter Mater. Phys. 69(6), 064116 (2004).
[Crossref]

Innocenzi, M. E.

M. E. Innocenzi, R. T. Swimm, M. Bass, R. H. French, A. B. Villaverde, and M. R. Kokta, “Room-temperature optical absorption in undoped α-Al2O 3,” J. Appl. Phys. 67(12), 7542–7546 (1990).
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Kajita, T.

E. Hirose, D. Bajuk, G. Billingsley, T. Kajita, B. Kestner, N. Mio, M. Ohashi, B. Reichman, H. Yamamoto, and L. Zhang, “Sapphire mirror for the KAGRA gravitational wave detector,” Phys. Rev. D: Part., Fields, Gravitation, Cosmol. 89(6), 062003 (2014).
[Crossref]

Kansy, J.

G. Moya, J. Kansy, A. Si Ahmed, J. Liebault, F. Moya, and D. Gæuriot, “Positron lifetime measurements in sintered alumina,” Phys. Status Solidi A 198(1), 215–223 (2003).
[Crossref]

Katoh, Y.

X. Hu, T. Koyanagi, Y. Katoh, and B. D. Wirth, “Positron annihilation spectroscopy investigation of vacancy defects in neutron-irradiated 3C-SiC,” Phys. Rev. B 95(10), 104103 (2017).
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Kestner, B.

E. Hirose, D. Bajuk, G. Billingsley, T. Kajita, B. Kestner, N. Mio, M. Ohashi, B. Reichman, H. Yamamoto, and L. Zhang, “Sapphire mirror for the KAGRA gravitational wave detector,” Phys. Rev. D: Part., Fields, Gravitation, Cosmol. 89(6), 062003 (2014).
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Kokta, M. R.

M. E. Innocenzi, R. T. Swimm, M. Bass, R. H. French, A. B. Villaverde, and M. R. Kokta, “Room-temperature optical absorption in undoped α-Al2O 3,” J. Appl. Phys. 67(12), 7542–7546 (1990).
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Kortov, V. S

G. Molnár, M. Benabdesselam, J. Borossay, D. Lapraz, P. Iacconi, V. S Kortov, and A. I Surdo, “Photoluminescence and thermoluminescence of titanium ions in sapphire crystals,” Radiat. Meas. 33(5), 663–667 (2001).
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Koyanagi, T.

X. Hu, T. Koyanagi, Y. Katoh, and B. D. Wirth, “Positron annihilation spectroscopy investigation of vacancy defects in neutron-irradiated 3C-SiC,” Phys. Rev. B 95(10), 104103 (2017).
[Crossref]

Kulkarni, M. S.

K. P. Muthe, K. Sudarshan, P. K. Pujari, M. S. Kulkarni, N. S. Rawat, B. C. Bhatt, and S. K. Gupta, “Positron annihilation and thermoluminescence studies of thermally induced defects in α-Al2O3 single crystals,” J. Phys. D: Appl. Phys. 42(10), 105405 (2009).
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S. E. Kulkova, L. Y. Zagorskaya, and I. R. Shein, “Electronic structure of α-Al 2O 3 in the bulk and on the surface,” Russ. Phys. J. 48(11), 1127–1133 (2005).
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K. P. D. Lagerlo and R. W. Grimes, “The Defect Chemistry of Sapphire (a-Al2O3),” Acta Mater. 46(16), 5689–5700 (1998).
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Lapraz, D.

G. Molnár, M. Benabdesselam, J. Borossay, D. Lapraz, P. Iacconi, V. S Kortov, and A. I Surdo, “Photoluminescence and thermoluminescence of titanium ions in sapphire crystals,” Radiat. Meas. 33(5), 663–667 (2001).
[Crossref]

Lee, K. H.

K. H. Lee, G. E. Holmberg, and J. H. Crawford, “Optical and ESR studies of hole centers in γ-irradiated Al2O3,” Phys. Status Solidi 39(2), 669–674 (1977).
[Crossref]

Lee, M. H.

W. J. Chung, B. J. Park, H. S. Seo, J. T. Ahn, M. H. Lee, and Y. G. Choi, “Effects of the weak absorption tail on the transmission loss of Ge-Sb-Se optical fibers,” J. Am. Ceram. Soc. 88(5), 1205–1208 (2005).
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Leksono, M. W.

C. H. Qiu, C. Hoggatt, W. Melton, M. W. Leksono, and J. I. Pankove, “Study of defect states in GaN films by photoconductivity measurement Study of defect states in GaN films by photoconductivity measurement,” Appl. Phys. Lett. 66(20), 2712–2714 (1995).
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Leonardi, M.

M. Marchiò, M. Leonardi, M. Bazzan, and R. Flaminio, “3D characterization of low optical absorption structures in large crystalline sapphire substrates for gravitational wave detectors,” Sci. Rep. 11(1), 2654 (2021).
[Crossref]

Li, Z. X.

J. C. Han, H. L. Zhang, M. F. Zhang, B. Y. Wang, Z. X. Li, C. H. Xu, and H. X. Guo, “Neutron irradiation and post annealing effect on sapphire by positron annihilation,” Appl. Radiat. Isot. 68(9), 1699–1702 (2010).
[Crossref]

Liebault, J.

G. Moya, J. Kansy, A. Si Ahmed, J. Liebault, F. Moya, and D. Gæuriot, “Positron lifetime measurements in sintered alumina,” Phys. Status Solidi A 198(1), 215–223 (2003).
[Crossref]

Linderoth, S.

C. Hidalgo, G. González-Doncel, S. Linderoth, and J. San Juan, “Structure of dislocations in Al and Fe as studied by positron-annihilation spectroscopy,” Phys. Rev. B 45(13), 7017–7021 (1992).
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G. Zhang, Y. Lu, and X. Wang, “Hydrogen interactions with intrinsic point defects in hydrogen permeation barrier of α-Al2O3: A first-principles study,” Phys. Chem. Chem. Phys. 16(33), 17523–17530 (2014).
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Lytvynov, L. A.

E. R. Dobrovinskaya, L. A. Lytvynov, and V. Pishchik, Sapphire: Material, Manufacturing, Applications. 2009.

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J. Ma, M. E. Thomas, P. McGuiggan, and J. Spicer, “Weak absorption and scattering losses from the visible to the near infrared in single-crystal sapphire materials,” Opt. Eng. 59(8), 087101 (2020).
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J. Ma, M. B. Airola, M. E. Thomas, and J. Spicer, “Measurements of weak scattering and absorption in spinel and sapphire from the near infrared to the visible,” Proc. SPIE 10985, 1098502 (2019).
[Crossref]

Marchiò, M.

M. Marchiò, M. Leonardi, M. Bazzan, and R. Flaminio, “3D characterization of low optical absorption structures in large crystalline sapphire substrates for gravitational wave detectors,” Sci. Rep. 11(1), 2654 (2021).
[Crossref]

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J. Ma, M. E. Thomas, P. McGuiggan, and J. Spicer, “Weak absorption and scattering losses from the visible to the near infrared in single-crystal sapphire materials,” Opt. Eng. 59(8), 087101 (2020).
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C. H. Qiu, C. Hoggatt, W. Melton, M. W. Leksono, and J. I. Pankove, “Study of defect states in GaN films by photoconductivity measurement Study of defect states in GaN films by photoconductivity measurement,” Appl. Phys. Lett. 66(20), 2712–2714 (1995).
[Crossref]

Mio, N.

E. Hirose, D. Bajuk, G. Billingsley, T. Kajita, B. Kestner, N. Mio, M. Ohashi, B. Reichman, H. Yamamoto, and L. Zhang, “Sapphire mirror for the KAGRA gravitational wave detector,” Phys. Rev. D: Part., Fields, Gravitation, Cosmol. 89(6), 062003 (2014).
[Crossref]

Molnár, G.

G. Molnár, M. Benabdesselam, J. Borossay, D. Lapraz, P. Iacconi, V. S Kortov, and A. I Surdo, “Photoluminescence and thermoluminescence of titanium ions in sapphire crystals,” Radiat. Meas. 33(5), 663–667 (2001).
[Crossref]

Monakhov, E. V.

V. Quemener, L. Vines, E. V. Monakhov, and B. G. Svensson, “Electronic properties of vacancy related defects in ZnO induced by mechanical polishing,” Appl. Phys. Lett. 99(11), 112112 (2011).
[Crossref]

Moya, F.

G. Moya, J. Kansy, A. Si Ahmed, J. Liebault, F. Moya, and D. Gæuriot, “Positron lifetime measurements in sintered alumina,” Phys. Status Solidi A 198(1), 215–223 (2003).
[Crossref]

Moya, G.

G. Moya, J. Kansy, A. Si Ahmed, J. Liebault, F. Moya, and D. Gæuriot, “Positron lifetime measurements in sintered alumina,” Phys. Status Solidi A 198(1), 215–223 (2003).
[Crossref]

Muthe, K. P.

K. P. Muthe, K. Sudarshan, P. K. Pujari, M. S. Kulkarni, N. S. Rawat, B. C. Bhatt, and S. K. Gupta, “Positron annihilation and thermoluminescence studies of thermally induced defects in α-Al2O3 single crystals,” J. Phys. D: Appl. Phys. 42(10), 105405 (2009).
[Crossref]

Nédélec, P.

N. Djourelov, Y. Aman, K. Berovski, P. Nédélec, N. Charvin, V. Garnier, and E. Djurado, “Structure characterization of spark plasma sintered alumina by positron annihilation lifetime spectroscopy,” Phys. Status Solidi A 208(4), 795–802 (2011).
[Crossref]

Ohashi, M.

E. Hirose, D. Bajuk, G. Billingsley, T. Kajita, B. Kestner, N. Mio, M. Ohashi, B. Reichman, H. Yamamoto, and L. Zhang, “Sapphire mirror for the KAGRA gravitational wave detector,” Phys. Rev. D: Part., Fields, Gravitation, Cosmol. 89(6), 062003 (2014).
[Crossref]

Ohdaira, T.

J. Xu, B. Somieski, L. Hulett, B. Pint, P. Tortorelli, R. Suzuki, and T. Ohdaira, “Microdefects in Al2O3 films and interfaces revealed by positron lifetime spectroscopy,” Appl. Phys. Lett. 71(21), 3165–3167 (1997).
[Crossref]

Pankove, J. I.

C. H. Qiu, C. Hoggatt, W. Melton, M. W. Leksono, and J. I. Pankove, “Study of defect states in GaN films by photoconductivity measurement Study of defect states in GaN films by photoconductivity measurement,” Appl. Phys. Lett. 66(20), 2712–2714 (1995).
[Crossref]

Park, B. J.

W. J. Chung, B. J. Park, H. S. Seo, J. T. Ahn, M. H. Lee, and Y. G. Choi, “Effects of the weak absorption tail on the transmission loss of Ge-Sb-Se optical fibers,” J. Am. Ceram. Soc. 88(5), 1205–1208 (2005).
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B. S. Patel and Z. H. Zaidi, “The suitability of sapphire for laser windows,” Meas. Sci. Technol. 10(3), 146–151 (1999).
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P. Pellegrino, “Trace chemical vapor detection by photothermal interferometry,” Proc. SPIE4205, 2001.

Pint, B.

J. Xu, B. Somieski, L. Hulett, B. Pint, P. Tortorelli, R. Suzuki, and T. Ohdaira, “Microdefects in Al2O3 films and interfaces revealed by positron lifetime spectroscopy,” Appl. Phys. Lett. 71(21), 3165–3167 (1997).
[Crossref]

Pishchik, V.

E. R. Dobrovinskaya, L. A. Lytvynov, and V. Pishchik, Sapphire: Material, Manufacturing, Applications. 2009.

Poc, F.

T. Blue, F. Goldner, F. Poc, J. Greene, and R. Fielder, “Testing of Sapphire Optical Fiber and Sensors in Intense Radiation Fields, when Subjected to Very High Temperatures Proposal,” NEUP Final Rep., 2012.

Pujari, P. K.

K. P. Muthe, K. Sudarshan, P. K. Pujari, M. S. Kulkarni, N. S. Rawat, B. C. Bhatt, and S. K. Gupta, “Positron annihilation and thermoluminescence studies of thermally induced defects in α-Al2O3 single crystals,” J. Phys. D: Appl. Phys. 42(10), 105405 (2009).
[Crossref]

Qiu, C. H.

C. H. Qiu, C. Hoggatt, W. Melton, M. W. Leksono, and J. I. Pankove, “Study of defect states in GaN films by photoconductivity measurement Study of defect states in GaN films by photoconductivity measurement,” Appl. Phys. Lett. 66(20), 2712–2714 (1995).
[Crossref]

Quemener, V.

V. Quemener, L. Vines, E. V. Monakhov, and B. G. Svensson, “Electronic properties of vacancy related defects in ZnO induced by mechanical polishing,” Appl. Phys. Lett. 99(11), 112112 (2011).
[Crossref]

Rawat, N. S.

K. P. Muthe, K. Sudarshan, P. K. Pujari, M. S. Kulkarni, N. S. Rawat, B. C. Bhatt, and S. K. Gupta, “Positron annihilation and thermoluminescence studies of thermally induced defects in α-Al2O3 single crystals,” J. Phys. D: Appl. Phys. 42(10), 105405 (2009).
[Crossref]

Reichman, B.

E. Hirose, D. Bajuk, G. Billingsley, T. Kajita, B. Kestner, N. Mio, M. Ohashi, B. Reichman, H. Yamamoto, and L. Zhang, “Sapphire mirror for the KAGRA gravitational wave detector,” Phys. Rev. D: Part., Fields, Gravitation, Cosmol. 89(6), 062003 (2014).
[Crossref]

Saito, T.

T. Saito, T. Hirayama, T. Yamamoto, and Y. Ikuhara, “Lattice strain and dislocations in polished surfaces on sapphire,” J. Am. Ceram. Soc. 88(8), 2277–2285 (2005).
[Crossref]

San Juan, J.

C. Hidalgo, G. González-Doncel, S. Linderoth, and J. San Juan, “Structure of dislocations in Al and Fe as studied by positron-annihilation spectroscopy,” Phys. Rev. B 45(13), 7017–7021 (1992).
[Crossref]

Schaefer, H. E.

H. E. Schaefer and M. Forster, “As-grown metal oxides and electron-irradiated Al2O3 studied by positron lifetime measurements,” Mater. Sci. Eng., A 109, 161–167 (1989).
[Crossref]

Selim, F. A.

F. A. Selim, M. H. Weber, D. Solodovnikov, and K. G. Lynn, “Nature of native defects in ZnO,” Phys. Rev. Lett. 99(8), 085502 (2007).
[Crossref]

Seo, H. S.

W. J. Chung, B. J. Park, H. S. Seo, J. T. Ahn, M. H. Lee, and Y. G. Choi, “Effects of the weak absorption tail on the transmission loss of Ge-Sb-Se optical fibers,” J. Am. Ceram. Soc. 88(5), 1205–1208 (2005).
[Crossref]

Shein, I. R.

S. E. Kulkova, L. Y. Zagorskaya, and I. R. Shein, “Electronic structure of α-Al 2O 3 in the bulk and on the surface,” Russ. Phys. J. 48(11), 1127–1133 (2005).
[Crossref]

Shi, Y.

X. Xiang, G. Zhang, X. Wang, T. Tang, and Y. Shi, “A new perspective on the process of intrinsic point defects in α-Al2O3,” Phys. Chem. Chem. Phys. 17(43), 29134–29141 (2015).
[Crossref]

Si Ahmed, A.

G. Moya, J. Kansy, A. Si Ahmed, J. Liebault, F. Moya, and D. Gæuriot, “Positron lifetime measurements in sintered alumina,” Phys. Status Solidi A 198(1), 215–223 (2003).
[Crossref]

Singh, B. N.

M. Eldrup and B. N. Singh, “Studies of defects and defect agglomerates by positron annihilation spectroscopy,” J. Nucl. Mater. 251, 132–138 (1997).
[Crossref]

Solodovnikov, D.

F. A. Selim, M. H. Weber, D. Solodovnikov, and K. G. Lynn, “Nature of native defects in ZnO,” Phys. Rev. Lett. 99(8), 085502 (2007).
[Crossref]

Somieski, B.

J. Xu, B. Somieski, L. Hulett, B. Pint, P. Tortorelli, R. Suzuki, and T. Ohdaira, “Microdefects in Al2O3 films and interfaces revealed by positron lifetime spectroscopy,” Appl. Phys. Lett. 71(21), 3165–3167 (1997).
[Crossref]

Spicer, J.

J. Ma, M. E. Thomas, P. McGuiggan, and J. Spicer, “Weak absorption and scattering losses from the visible to the near infrared in single-crystal sapphire materials,” Opt. Eng. 59(8), 087101 (2020).
[Crossref]

J. Ma, M. B. Airola, M. E. Thomas, and J. Spicer, “Measurements of weak scattering and absorption in spinel and sapphire from the near infrared to the visible,” Proc. SPIE 10985, 1098502 (2019).
[Crossref]

Stapelbroek, M.

B. D. Evans and M. Stapelbroek, “Optical properties of the F+ center in crystalline Al2O3,” Phys. Rev. B 18(12), 7089–7098 (1978).
[Crossref]

Sudarshan, K.

K. P. Muthe, K. Sudarshan, P. K. Pujari, M. S. Kulkarni, N. S. Rawat, B. C. Bhatt, and S. K. Gupta, “Positron annihilation and thermoluminescence studies of thermally induced defects in α-Al2O3 single crystals,” J. Phys. D: Appl. Phys. 42(10), 105405 (2009).
[Crossref]

Surdo, A. I

G. Molnár, M. Benabdesselam, J. Borossay, D. Lapraz, P. Iacconi, V. S Kortov, and A. I Surdo, “Photoluminescence and thermoluminescence of titanium ions in sapphire crystals,” Radiat. Meas. 33(5), 663–667 (2001).
[Crossref]

Suzuki, R.

J. Xu, B. Somieski, L. Hulett, B. Pint, P. Tortorelli, R. Suzuki, and T. Ohdaira, “Microdefects in Al2O3 films and interfaces revealed by positron lifetime spectroscopy,” Appl. Phys. Lett. 71(21), 3165–3167 (1997).
[Crossref]

Svensson, B. G.

V. Quemener, L. Vines, E. V. Monakhov, and B. G. Svensson, “Electronic properties of vacancy related defects in ZnO induced by mechanical polishing,” Appl. Phys. Lett. 99(11), 112112 (2011).
[Crossref]

Swimm, R. T.

M. E. Innocenzi, R. T. Swimm, M. Bass, R. H. French, A. B. Villaverde, and M. R. Kokta, “Room-temperature optical absorption in undoped α-Al2O 3,” J. Appl. Phys. 67(12), 7542–7546 (1990).
[Crossref]

Tang, T.

X. Xiang, G. Zhang, X. Wang, T. Tang, and Y. Shi, “A new perspective on the process of intrinsic point defects in α-Al2O3,” Phys. Chem. Chem. Phys. 17(43), 29134–29141 (2015).
[Crossref]

Tauc, J.

D. L. Wood and J. Tauc, “Weak absorption tails in amorphous semiconductors,” Phys. Rev. B 5(8), 3144–3151 (1972).
[Crossref]

Thomas, M. E.

J. Ma, M. E. Thomas, P. McGuiggan, and J. Spicer, “Weak absorption and scattering losses from the visible to the near infrared in single-crystal sapphire materials,” Opt. Eng. 59(8), 087101 (2020).
[Crossref]

J. Ma, M. B. Airola, M. E. Thomas, and J. Spicer, “Measurements of weak scattering and absorption in spinel and sapphire from the near infrared to the visible,” Proc. SPIE 10985, 1098502 (2019).
[Crossref]

M. E. Thomas, “Low-level background absorption in durable window materials,” Proc. SPIE 10179, 101790B (2017).
[Crossref]

Tortorelli, P.

J. Xu, B. Somieski, L. Hulett, B. Pint, P. Tortorelli, R. Suzuki, and T. Ohdaira, “Microdefects in Al2O3 films and interfaces revealed by positron lifetime spectroscopy,” Appl. Phys. Lett. 71(21), 3165–3167 (1997).
[Crossref]

Villaverde, A. B.

M. E. Innocenzi, R. T. Swimm, M. Bass, R. H. French, A. B. Villaverde, and M. R. Kokta, “Room-temperature optical absorption in undoped α-Al2O 3,” J. Appl. Phys. 67(12), 7542–7546 (1990).
[Crossref]

Vines, L.

V. Quemener, L. Vines, E. V. Monakhov, and B. G. Svensson, “Electronic properties of vacancy related defects in ZnO induced by mechanical polishing,” Appl. Phys. Lett. 99(11), 112112 (2011).
[Crossref]

Wang, B. Y.

J. C. Han, H. L. Zhang, M. F. Zhang, B. Y. Wang, Z. X. Li, C. H. Xu, and H. X. Guo, “Neutron irradiation and post annealing effect on sapphire by positron annihilation,” Appl. Radiat. Isot. 68(9), 1699–1702 (2010).
[Crossref]

Wang, X.

X. Xiang, G. Zhang, X. Wang, T. Tang, and Y. Shi, “A new perspective on the process of intrinsic point defects in α-Al2O3,” Phys. Chem. Chem. Phys. 17(43), 29134–29141 (2015).
[Crossref]

G. Zhang, Y. Lu, and X. Wang, “Hydrogen interactions with intrinsic point defects in hydrogen permeation barrier of α-Al2O3: A first-principles study,” Phys. Chem. Chem. Phys. 16(33), 17523–17530 (2014).
[Crossref]

Weber, M. H.

F. A. Selim, M. H. Weber, D. Solodovnikov, and K. G. Lynn, “Nature of native defects in ZnO,” Phys. Rev. Lett. 99(8), 085502 (2007).
[Crossref]

Wirth, B. D.

X. Hu, T. Koyanagi, Y. Katoh, and B. D. Wirth, “Positron annihilation spectroscopy investigation of vacancy defects in neutron-irradiated 3C-SiC,” Phys. Rev. B 95(10), 104103 (2017).
[Crossref]

Wood, D. L.

D. L. Wood and J. Tauc, “Weak absorption tails in amorphous semiconductors,” Phys. Rev. B 5(8), 3144–3151 (1972).
[Crossref]

Xiang, X.

X. Xiang, G. Zhang, X. Wang, T. Tang, and Y. Shi, “A new perspective on the process of intrinsic point defects in α-Al2O3,” Phys. Chem. Chem. Phys. 17(43), 29134–29141 (2015).
[Crossref]

Xu, C. H.

J. C. Han, H. L. Zhang, M. F. Zhang, B. Y. Wang, Z. X. Li, C. H. Xu, and H. X. Guo, “Neutron irradiation and post annealing effect on sapphire by positron annihilation,” Appl. Radiat. Isot. 68(9), 1699–1702 (2010).
[Crossref]

Xu, J.

J. Xu, B. Somieski, L. Hulett, B. Pint, P. Tortorelli, R. Suzuki, and T. Ohdaira, “Microdefects in Al2O3 films and interfaces revealed by positron lifetime spectroscopy,” Appl. Phys. Lett. 71(21), 3165–3167 (1997).
[Crossref]

Yamamoto, H.

E. Hirose, D. Bajuk, G. Billingsley, T. Kajita, B. Kestner, N. Mio, M. Ohashi, B. Reichman, H. Yamamoto, and L. Zhang, “Sapphire mirror for the KAGRA gravitational wave detector,” Phys. Rev. D: Part., Fields, Gravitation, Cosmol. 89(6), 062003 (2014).
[Crossref]

Yamamoto, T.

T. Saito, T. Hirayama, T. Yamamoto, and Y. Ikuhara, “Lattice strain and dislocations in polished surfaces on sapphire,” J. Am. Ceram. Soc. 88(8), 2277–2285 (2005).
[Crossref]

Zagorskaya, L. Y.

S. E. Kulkova, L. Y. Zagorskaya, and I. R. Shein, “Electronic structure of α-Al 2O 3 in the bulk and on the surface,” Russ. Phys. J. 48(11), 1127–1133 (2005).
[Crossref]

Zaidi, Z. H.

B. S. Patel and Z. H. Zaidi, “The suitability of sapphire for laser windows,” Meas. Sci. Technol. 10(3), 146–151 (1999).
[Crossref]

Zhang, G.

X. Xiang, G. Zhang, X. Wang, T. Tang, and Y. Shi, “A new perspective on the process of intrinsic point defects in α-Al2O3,” Phys. Chem. Chem. Phys. 17(43), 29134–29141 (2015).
[Crossref]

G. Zhang, Y. Lu, and X. Wang, “Hydrogen interactions with intrinsic point defects in hydrogen permeation barrier of α-Al2O3: A first-principles study,” Phys. Chem. Chem. Phys. 16(33), 17523–17530 (2014).
[Crossref]

Zhang, H. L.

J. C. Han, H. L. Zhang, M. F. Zhang, B. Y. Wang, Z. X. Li, C. H. Xu, and H. X. Guo, “Neutron irradiation and post annealing effect on sapphire by positron annihilation,” Appl. Radiat. Isot. 68(9), 1699–1702 (2010).
[Crossref]

Zhang, L.

E. Hirose, D. Bajuk, G. Billingsley, T. Kajita, B. Kestner, N. Mio, M. Ohashi, B. Reichman, H. Yamamoto, and L. Zhang, “Sapphire mirror for the KAGRA gravitational wave detector,” Phys. Rev. D: Part., Fields, Gravitation, Cosmol. 89(6), 062003 (2014).
[Crossref]

Zhang, M. F.

J. C. Han, H. L. Zhang, M. F. Zhang, B. Y. Wang, Z. X. Li, C. H. Xu, and H. X. Guo, “Neutron irradiation and post annealing effect on sapphire by positron annihilation,” Appl. Radiat. Isot. 68(9), 1699–1702 (2010).
[Crossref]

Acta Mater. (1)

K. P. D. Lagerlo and R. W. Grimes, “The Defect Chemistry of Sapphire (a-Al2O3),” Acta Mater. 46(16), 5689–5700 (1998).
[Crossref]

Appl. Phys. Lett. (3)

J. Xu, B. Somieski, L. Hulett, B. Pint, P. Tortorelli, R. Suzuki, and T. Ohdaira, “Microdefects in Al2O3 films and interfaces revealed by positron lifetime spectroscopy,” Appl. Phys. Lett. 71(21), 3165–3167 (1997).
[Crossref]

V. Quemener, L. Vines, E. V. Monakhov, and B. G. Svensson, “Electronic properties of vacancy related defects in ZnO induced by mechanical polishing,” Appl. Phys. Lett. 99(11), 112112 (2011).
[Crossref]

C. H. Qiu, C. Hoggatt, W. Melton, M. W. Leksono, and J. I. Pankove, “Study of defect states in GaN films by photoconductivity measurement Study of defect states in GaN films by photoconductivity measurement,” Appl. Phys. Lett. 66(20), 2712–2714 (1995).
[Crossref]

Appl. Radiat. Isot. (1)

J. C. Han, H. L. Zhang, M. F. Zhang, B. Y. Wang, Z. X. Li, C. H. Xu, and H. X. Guo, “Neutron irradiation and post annealing effect on sapphire by positron annihilation,” Appl. Radiat. Isot. 68(9), 1699–1702 (2010).
[Crossref]

J. Am. Ceram. Soc. (2)

W. J. Chung, B. J. Park, H. S. Seo, J. T. Ahn, M. H. Lee, and Y. G. Choi, “Effects of the weak absorption tail on the transmission loss of Ge-Sb-Se optical fibers,” J. Am. Ceram. Soc. 88(5), 1205–1208 (2005).
[Crossref]

T. Saito, T. Hirayama, T. Yamamoto, and Y. Ikuhara, “Lattice strain and dislocations in polished surfaces on sapphire,” J. Am. Ceram. Soc. 88(8), 2277–2285 (2005).
[Crossref]

J. Appl. Phys. (2)

M. E. Innocenzi, R. T. Swimm, M. Bass, R. H. French, A. B. Villaverde, and M. R. Kokta, “Room-temperature optical absorption in undoped α-Al2O 3,” J. Appl. Phys. 67(12), 7542–7546 (1990).
[Crossref]

B. D. Evans, “Optical transmission in undoped crystalline α-Al2O 3 grown by several techniques,” J. Appl. Phys. 70(7), 3995–3997 (1991).
[Crossref]

J. Nucl. Mater. (1)

M. Eldrup and B. N. Singh, “Studies of defects and defect agglomerates by positron annihilation spectroscopy,” J. Nucl. Mater. 251, 132–138 (1997).
[Crossref]

J. Phys. D: Appl. Phys. (1)

K. P. Muthe, K. Sudarshan, P. K. Pujari, M. S. Kulkarni, N. S. Rawat, B. C. Bhatt, and S. K. Gupta, “Positron annihilation and thermoluminescence studies of thermally induced defects in α-Al2O3 single crystals,” J. Phys. D: Appl. Phys. 42(10), 105405 (2009).
[Crossref]

Mater. Sci. Eng., A (1)

H. E. Schaefer and M. Forster, “As-grown metal oxides and electron-irradiated Al2O3 studied by positron lifetime measurements,” Mater. Sci. Eng., A 109, 161–167 (1989).
[Crossref]

Mater. Sci. Forum (1)

G. Dlubek, “Positron Studies of Decomposition Phenomena in Al Alloys,” Mater. Sci. Forum 13-14, 11–32 (1987).
[Crossref]

Meas. Sci. Technol. (1)

B. S. Patel and Z. H. Zaidi, “The suitability of sapphire for laser windows,” Meas. Sci. Technol. 10(3), 146–151 (1999).
[Crossref]

Opt. Eng. (1)

J. Ma, M. E. Thomas, P. McGuiggan, and J. Spicer, “Weak absorption and scattering losses from the visible to the near infrared in single-crystal sapphire materials,” Opt. Eng. 59(8), 087101 (2020).
[Crossref]

Phys. Chem. Chem. Phys. (2)

X. Xiang, G. Zhang, X. Wang, T. Tang, and Y. Shi, “A new perspective on the process of intrinsic point defects in α-Al2O3,” Phys. Chem. Chem. Phys. 17(43), 29134–29141 (2015).
[Crossref]

G. Zhang, Y. Lu, and X. Wang, “Hydrogen interactions with intrinsic point defects in hydrogen permeation barrier of α-Al2O3: A first-principles study,” Phys. Chem. Chem. Phys. 16(33), 17523–17530 (2014).
[Crossref]

Phys. Rev. B (4)

B. D. Evans and M. Stapelbroek, “Optical properties of the F+ center in crystalline Al2O3,” Phys. Rev. B 18(12), 7089–7098 (1978).
[Crossref]

X. Hu, T. Koyanagi, Y. Katoh, and B. D. Wirth, “Positron annihilation spectroscopy investigation of vacancy defects in neutron-irradiated 3C-SiC,” Phys. Rev. B 95(10), 104103 (2017).
[Crossref]

D. L. Wood and J. Tauc, “Weak absorption tails in amorphous semiconductors,” Phys. Rev. B 5(8), 3144–3151 (1972).
[Crossref]

C. Hidalgo, G. González-Doncel, S. Linderoth, and J. San Juan, “Structure of dislocations in Al and Fe as studied by positron-annihilation spectroscopy,” Phys. Rev. B 45(13), 7017–7021 (1992).
[Crossref]

Phys. Rev. B: Condens. Matter Mater. Phys. (1)

J. Carrasco, J. R. B. Gomes, and F. Illas, “Theoretical study of bulk and surface oxygen and aluminum vacancies in α-Al2O3,” Phys. Rev. B: Condens. Matter Mater. Phys. 69(6), 064116 (2004).
[Crossref]

Phys. Rev. D: Part., Fields, Gravitation, Cosmol. (1)

E. Hirose, D. Bajuk, G. Billingsley, T. Kajita, B. Kestner, N. Mio, M. Ohashi, B. Reichman, H. Yamamoto, and L. Zhang, “Sapphire mirror for the KAGRA gravitational wave detector,” Phys. Rev. D: Part., Fields, Gravitation, Cosmol. 89(6), 062003 (2014).
[Crossref]

Phys. Rev. Lett. (1)

F. A. Selim, M. H. Weber, D. Solodovnikov, and K. G. Lynn, “Nature of native defects in ZnO,” Phys. Rev. Lett. 99(8), 085502 (2007).
[Crossref]

Phys. Status Solidi (1)

K. H. Lee, G. E. Holmberg, and J. H. Crawford, “Optical and ESR studies of hole centers in γ-irradiated Al2O3,” Phys. Status Solidi 39(2), 669–674 (1977).
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Phys. Status Solidi A (2)

N. Djourelov, Y. Aman, K. Berovski, P. Nédélec, N. Charvin, V. Garnier, and E. Djurado, “Structure characterization of spark plasma sintered alumina by positron annihilation lifetime spectroscopy,” Phys. Status Solidi A 208(4), 795–802 (2011).
[Crossref]

G. Moya, J. Kansy, A. Si Ahmed, J. Liebault, F. Moya, and D. Gæuriot, “Positron lifetime measurements in sintered alumina,” Phys. Status Solidi A 198(1), 215–223 (2003).
[Crossref]

Proc. SPIE (2)

M. E. Thomas, “Low-level background absorption in durable window materials,” Proc. SPIE 10179, 101790B (2017).
[Crossref]

J. Ma, M. B. Airola, M. E. Thomas, and J. Spicer, “Measurements of weak scattering and absorption in spinel and sapphire from the near infrared to the visible,” Proc. SPIE 10985, 1098502 (2019).
[Crossref]

Radiat. Meas. (1)

G. Molnár, M. Benabdesselam, J. Borossay, D. Lapraz, P. Iacconi, V. S Kortov, and A. I Surdo, “Photoluminescence and thermoluminescence of titanium ions in sapphire crystals,” Radiat. Meas. 33(5), 663–667 (2001).
[Crossref]

Russ. Phys. J. (1)

S. E. Kulkova, L. Y. Zagorskaya, and I. R. Shein, “Electronic structure of α-Al 2O 3 in the bulk and on the surface,” Russ. Phys. J. 48(11), 1127–1133 (2005).
[Crossref]

Sci. Rep. (1)

M. Marchiò, M. Leonardi, M. Bazzan, and R. Flaminio, “3D characterization of low optical absorption structures in large crystalline sapphire substrates for gravitational wave detectors,” Sci. Rep. 11(1), 2654 (2021).
[Crossref]

Solid State Commun. (1)

R. T. Cox, “Electron spin resonance studies of holes trapped at Mg2+, Li+ and cation vacancies in Al2O3,” Solid State Commun. 9(22), 1989–1992 (1971).
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D. L. Dexter, “Theory of the Optical Properties of Imperfections in Nonmetals,” Solid State Phys. 6, 353–411 (1958).
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Other (4)

P. Pellegrino, “Trace chemical vapor detection by photothermal interferometry,” Proc. SPIE4205, 2001.

T. Blue, F. Goldner, F. Poc, J. Greene, and R. Fielder, “Testing of Sapphire Optical Fiber and Sensors in Intense Radiation Fields, when Subjected to Very High Temperatures Proposal,” NEUP Final Rep., 2012.

E. R. Dobrovinskaya, L. A. Lytvynov, and V. Pishchik, Sapphire: Material, Manufacturing, Applications. 2009.

M. Hornak, “Energetics, Kinetics, and Optical Absorption of Point Defects in Sapphire,” The Ohio State University, 2016.

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Figures (3)

Fig. 1.
Fig. 1. Bulk absorption in sapphire Samples A, B, and C as a function of wavelength (blue, orange, and yellow broken lines respectively). Absorption bands are labeled with associated vacancy defects.
Fig. 2.
Fig. 2. Positron lifetime spectra for single crystal sapphire samples used in this study. Data points indicate measured counts while the solid curves represent fits to the data using a two-component lifetime model (a) Sample A, (b) Sample B, (c) Sample C.
Fig. 3.
Fig. 3. A Bar plot shows the total surface absorbance of each sample at each wavelength. The defect associated mean lifetime as a product of ${\mathrm{\tau }_2}\textrm{\; and\; \; }{\textrm{I}_2}$ is labeled for each sample.

Tables (4)

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Table 1. Concentrations of Anionic Vacancy Defects in Sapphire

Tables Icon

Table 2. Optical absorption coefficients obtained from PCI measurements

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Table 3. PALS analysis results of the studied samples

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Table 4. Estimated Vacancy Defect Concentrations in Sapphire

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

[ V O ] = [ F ] + [ F + ] = ( 1.86 α 206 + 0.292 α 225 + 0.167 α 255 ) × 10 16
κ = I 2 I 1 ( τ B 1 τ 2 1 )
κ = μ C
κ = μ V Al C V Al + μ V Al C V Al + μ V Al 2 C V Al 2 .

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