Nd:YAG ceramics for laser applications were elaborated with various residual porosities by reaction-sintering process. The porosity analysis with CLSM and SEM led to the determination of the pore volume fraction after sintering. This study revealed that the mean pore size of Nd:YAG ceramics was around 0.7 µm while the residual porosity was ranging between 10−1% and 10−4%. These pore contents affect the transparency and laser efficiency of ceramics. The analytical model based on the Mie light scattering fairly fits the experimental data. This demonstrates that the porosity in Nd:YAG ceramics should be lower than 10−4% to reach single-crystal laser efficiency.
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Nd:YAG (Neodymium-doped Yttrium Aluminum Garnet - NdxY3-xAl5O12) belongs to the family of attractive materials for applications in the field of high energy lasers. Low duration and low cost of manufacturing, absence of severe limitation in size and geometry make the Nd:YAG ceramics attractive with comparison to single crystals [1–3]. The ceramics are usually considered as polycrystalline materials resulting from the densification during heating of green compacts composed of micro-sized crystallized grains. Ikesue et al. [4,5] were the first to elaborate transparent Nd:YAG ceramics with required optical properties for laser applications by the vacuum-reaction sintering method. This technique consists of mixing the starting powders (Al2O3, Y2O3, Nd2O3) in stoechiometric proportions, forming and sintering them at high temperature (> 1700°C) under vacuum to produce the Nd:YAG phase. From literature [6,7], transparent and defects-free (i.e. without pores or secondary phases) ceramics appear difficult to manufacture. For Nd:YAG ceramics, transparency could be achieved by promoting the formation of a liquid phase during sintering thanks to silica additions [8,9].
For laser applications, defect-free ceramics are required to minimize light scattering due to residual pores or secondary phases. Actually, it appears that microstructural properties of Nd:YAG govern their optical properties [10,11]. Consequently, the aim of the present work is to establish correlations between porosity contents and optical properties of Nd:YAG ceramics in order to determine the porosity level leading to the Nd:YAG single-crystal laser efficiency. In particular, in a first step, Nd:YAG specimens have been prepared under different isothermal conditions of vacuum-reaction sintering and their porosity content has been accurately analyzed by using an experimental set up which couples Scanning Electron Microscopy (SEM) and Confocal Laser Scanning Microscopy (CLSM) . In a second step, optical properties of Nd:YAG ceramics (transmittance, attenuation coefficient) and laser-oscillation experiments have been investigated as a function of the pore features (size, volume fraction) obtained from the Mie light scattering theory.
2. Materials and method
Preparation of raw materials and sintering: The manufacturing process is similar to that reported by Rabinovitch et al. . Neodymium-doped Yttrium-Aluminum Garnet (Y3-xNdxAl5O12, Nd:YAG) transparent ceramics with Nd3+ concentrations of 2 at.% were synthesized by a solid-state reaction method using high purity powders. Submicron-sized α-Al2O3 (purity > 99.99%, Baïkowski, France) and Y2O3, Nd2O3 powders (purity > 99.99%, Alfa Aesar, Germany) were mixed together in stoechiometric proportions to form Y2.94Nd0.06Al5O12. Nanosized silica particles (purity > 99.8%, Alfa Aesar) was added at a content of 0.3 wt.% as sintering aid. After ball-milling in an aqueous solvent and drying, the powder was shaped under an uniaxial load of 200 MPa in a steel die to make pellets nominally 20 mm in diameter by 5 mm in thickness. Pellets were placed in an alumina crucible and then treated in air at 1000°C to remove organic residues. Finally, the bodies were sintered at 1750°C under vacuum (PT ≤ 10−2 Pa) to provide fully dense materials (relative density ρ > 99.9%). The dwell time at 1750°C was chosen between 1 and 10 hours to elaborate sintered bodies with different residual porosity contents. Finally, samples were annealed in air at 1250°C for 20 h in order to eliminate color centers mainly due to oxygen vacancies .
Microstructural characterizations: The microstructure (i.e. grain size, porosity) has been analyzed by using both Scanning Electron Microscopy (SEM, Philips XL30 and FEG-SEM, JEOL 7400) and confocal laser scanning microscopy (CLSM, LSM 510META, Zeiss, Germany) according to the method described in previous work . In fact, SEM observations have been performed on fracture surface of samples to measure the average pore size whereas CLSM scanned volumes (100 × 100 × 20 µm3) allowed to count pores for the same polished samples. The average pore size has been determined by considering the equivalent disc diameter of each inter- or intragranular pore. The measurement of the average pore size was done by using Scion Corporation Software (Scion Corporation, USA) from SEM micrographs. Finally, these coupled observations provide all the main characteristics of the residual porosity in each Nd:YAG specimen, such as the volume concentration and the size distribution of pores.
Optical properties: Before optical characterization, all specimens were polished on both surfaces in order to reach an average roughness inferior to 0.2 nm, flatness near to λ/10 and a parallelism of 10”. Transmittance of Nd:YAG specimens was measured over a 0.3-1.1 µm wavelength range thanks to an UV-Vis-NIR spectrophotometer (Cary 5000, Varian, USA). Further real in-line transmittance measurements (RIT) were performed at a wavelength of 633 nm with a dedicated device as shown in Fig. 1 . This device rests on the separation of a He-Ne laser beam of 1.5 mm in diameter into two beams of intensities I0 (intensity of incident light) and I (intensity of transmitted light through the sample) which values were measured with silicon photodiodes (Hamamatsu, Japan). Samples were placed on the laser beam path after the splitting mirror at a distance of 60 cm from a diaphragm (aperture of 5 mm). Such configuration allowed to measure the average RIT value over 3 measurements as a function of samples thickness x with an angular aperture of 0.5°.
Laser performance of specimens 13 mm in diameter and 2.5 mm thick was evaluated using a laser oscillation device pumped by a focalized beam of 808 nm laser diode stack with a 5 Hz repetition rate. It must be noticed that no sample cooling was used and no antireflection coating was applied on the sample surface. Therefore, sample surfaces were orientated at Brewster’s angle from the optical axis of the laser cavity (cavity length of 0.29 m). A 2 m radius of curvature reflection mirror (>99.8% reflection) and a half-mirror (70% reflection) were situated in parallel to each other on both sides of the specimen. Laser beam energy was measured by a joulemeter detector (ED200, Gentec, Canada). A 1.1 at.%-Nd:YAG single crystal (Czochralski grown, FEE, Germany) was used as the optical reference for all measurements.
3. Results and discussion
3.1. Microstructural properties of Nd:YAG ceramics
Whatever the sintering time at 1750°C, all the Nd:YAG specimens appeared to be transparent (Fig. 2 ). Indeed, no heterogeneity and high levels of transparency have been detected. Moreover, the transparency was clearly improved when sintering time was increased.
From TEM observations (Fig. 3 ), no secondary phase was detected at the grain boundary or inside grains. Only few pores have been detected through the microstructure of Nd:YAG with regards to the higher values (>99.9%) of the relative density obtained from the Archimedes method. This was confirmed by the SEM observations (Fig. 3). Indeed, only some small pores (diameter of 0.5 µm) were detected within the grains or at the grain boundaries.
We assumed that the total volume fraction of pores P could be calculated from Eq. (1) by assuming spherical pores:equivalent disc diameter of pores and N(Ф) the pore size distribution function. In order to determine P from Eq. (1), two complementary methods have been used. From previous work , it was shown that scanning electron microscopy and confocal laser scanning microscopy could respectively provide N(Ф) and Cn precisely in transparent Nd:YAG ceramics.
First, CLSM measurements have been achieved to determine the values of the pore volume density (Cn). 3-D micrographs obtained as a function of sintering time of Nd:YAG ceramics are reported in Fig. 4 . From these observations, pores appeared as luminous spots on a dark background thanks to laser beam reflection at the pore/Nd:YAG matrix interface. The analysis of CLSM micrographs made the pore density measurement possible for each Nd:YAG specimen. The corresponding values which are reported in Table 1 tend to decrease versus increasing sintering time. This phenomenon can be related to the grain boundary migration which can occur for the most severe thermal treatment (i.e. at temperatures higher than 1700°C). In fact, it is well known that the grain boundary moving is necessarily accompanied by both grain growth and pore coalescence .
In a second step, the treatment of SEM micrographs taken for different Nd:YAG samples was carried out to determine the pore size distribution function [N(Ф)]. Figure 5 gives several examples of pore size distributions obtained for Nd:YAG specimens sintered under vacuum during different isothermal conditions. From the observation of Fig. 5, it clearly appears that each size repartition can be correctly described from a log-normal law like:
From Eq. (2), the mean diameter of pores Фmoy can be calculated as follows:
Under these conditions, the value of the mean pore diameter (Фmoy) varied between 0.60 and 0.76 µm when the sintering time at 1750°C was equal to 2 h or 10 h, respectively. In terms of optical properties, such a small variation of the mean pore diameter was considered as negligible in comparison with the strong evolution of the volume density of pores . Consequently, Фmoy and σ were fixed to the average values (0.68 μm and 0.48 μm, respectively) to simplify further calculations. Table 1 provides the volume fraction of pores calculated according to Eq. (1) and by assuming Фmoy and σ equal to 680 nm and 480 nm, respectively. It can be noticed that the volume fraction of pores of Nd:YAG ceramics ranged from 0.0886% to 0.0018% while the sintering time at 1750°C varied between 1 h and 10 h, respectively. With regards to the strong effect of sintering conditions on the volume fraction of pores for Nd:YAG ceramics, further optical characterizations have been done and some attempts of correlations with microstructural properties for the same ceramics have been carried out.
3.2. Optical properties
Sintered samples showed a transmittance baseline higher than 60% in the extended visible wavelength range (300-1100 nm) (see Fig. 6 ). Moreover, the transmittance value increased continuously when the volume fraction of pores decreased. The values of the Nd:YAG ceramics transmittance have been compared to that of Nd:YAG single-crystals. From Fig. 6, it appears that the Nd3+ absorption peaks are the same between Nd:YAG ceramics and single crystals. According to the literature , the presence of color centers such as oxygen vacancies or impurities is usually correlated to the appearance of broad absorption peaks in the wavelength range 400-500 nm. Since no similar phenomenon has been observed from Fig. 6, the ceramics so-elaborated can be considered as free from color centers or impurities. As a result, optical losses should be only due to the presence of residual pores evidenced by microstructural characterizations (see paragraph 3.1).
Further transmittance measurements have been carried out by using the device shown in Fig. 1. These experiments have been performed as a function of sample thickness (2.5, 5 and 10 mm) by orientating successively the specimen in the tree different directions perpendicular to the faces of parallelepipeds presented in Fig. 2. This latter allows determining the Real In-line Transmittance (RIT) which obeys the Beer-Lambert law and depends on the sample thickness as follows:16] and from Eq. (5), T value for a YAG ceramic specimen appeared to be equal to 0.846 at a wavelength of 633 nm. Otherwise, the RIT values were reported in a logarithmic plot as a function of the volume fraction of pores of Nd:YAG ceramics (see Fig. 7 ). According to Eq. (4), the slopes of lines in Fig. 7 provide the attenuation coefficient values (see Table 2 ). From Table 2, it can be noticed that attenuation coefficient values obtained from RIT measurements were in accordance with those determined from optical spectroscopy in Fig. 6. The discrepancy between the different data does not exceed 10% by considering measure errors meaning the good reproducibility of such optical characterizations.
According to Tables 1 and 2, a good correlation exists between attenuation coefficients and residual porosities. In particular, the values of the attenuation coefficient ranged between 3.40 cm−1 and 0.27 cm−1 while the volume fraction of pores varied between 0.0886% and 0.0018%. Even if the residual porosity of Nd:YAG ceramics remained low, the attenuation coefficient value always exceeded 0.27 cm−1. It can be emphasized that this latter value is still much larger than that of single-crystal (i.e. 0.03 cm−1 ).
Figure 8 reveals the dependence of the residual porosity versus the laser output energy of Nd:YAG ceramics. From these results, laser slope efficiency was computed from the slope of lines and reported in Table 2. The laser efficiency of specimens increases when the volume fraction of pores decreases. For example, laser slope efficiency ranged between 1.6% and 34.1% while the volume fraction of pores varied between 0.0886% and 0.0018%. This result highlights the influence of residual porosity on lasing performance of transparent ceramics. Even if the volume fraction of pores remains small (0.0018%), the lasing performance of Nd:YAG ceramics was significantly lower than the single-crystal one.
These results reveal that Nd:YAG ceramics sintered for 10 h at 1750°C would present a laser energy higher than 100 mJ with a repetition rate of 5 Hz. This performance appears to be promising in comparison with those reported in the literature for similar ceramics [4,5]. Finally, under the hypothesis that the sintering time would be longer than 10 h (e.g. > 20 h), the optical quality of Nd:YAG ceramics and the laser slope efficiency could be significantly enhanced to reach the single crystal ones.
3.3. Modelling of pore-induced light scattering by Mie theory
To get the volume fraction of pores required to reach single-crystal lasing performances, further calculations were performed according to Mie light scattering theory. Koechner’s law  could be used in first approximation to compute the theoretical laser slope efficiency as a function of experimental set up parameters:Eq. (6) and the laser slope efficiency value obtained for a 1.1 at.% Nd:YAG single-crystal. In the present conditions, attenuation coefficient from the single-crystal was considered as negligible so αcavity = 1.33 cm−1. According to the Mie light scattering theory [18,19], the attenuation coefficient related to the sample could depend on both the volume fraction of pores and the pore size as follows:Eq. (6) and Eq. (7), the theoretical laser slope efficiency could be expressed as reported below:
According to Refs [18,19], K values could be computed by assuming randomly distributed pores in a Nd:YAG matrix with a refractive index n equal to 1.829. Considering a wavelength of 633 nm, Фmoy and σ equal to 0.68 μm and 0.48 μm, it became possible to evaluate the K coefficient as being close to 3.07. Consequently, Fig. 9 displays experimental values of laser slope efficiency (issued from data reported in Table 2) as a function of the Nd:YAG ceramic volume fraction of pores. The theoretical evolution of laser slope efficiency, computed according to Eq. (8), was also reported.
Figure 9 shows that the theoretical evolution was in a good agreement with the experimental data. As a result, Mie light scattering model should allow to extrapolate the laser slope efficiency values for very low volume fraction of pores in Nd:YAG ceramics. In particular, it clearly appeared that a volume fraction of pores lower than 10−4% must be reached to approach the single-crystal laser slope efficiency. Nevertheless, this latter value is often debated in literature. So far, Ikesue et al.  reported a value of about 0.015% whereas Kumar et al.  advocate that porosity level should be less than 10−4% to reach single-crystal laser properties. This disagreement highlights the crucial role of the experimental method used to characterize porosity. In fact, most of these authors have performed statistical analyses from SEM or TEM planar observations. Nevertheless, these investigations usually lead to significant errors because the analyzed volume is imprecisely known. Moreover, before TEM observations, the thin slice preparation by using ultramicrotomy could create artificial porosity such as micro-voids and/or modify the starting shape of pores. On the contrary, CLSM is a non-destructive technique which allows to determine the pore density in situ for a well known sample volume. Moreover, this technique permitted to analyze a sample volume (100 × 100 × 20 µm3) larger than that required for SEM or TEM observations, then leading to reduced errors.
4. Conclusion and perspectives
From porosity measurements by 3-dimensional confocal laser scanning microscopy and calculations achieved according to the Mie light scattering theory, it was shown that correlations between optical (transmittance, attenuation coefficient and laser efficiency) and microstructural properties in Nd:YAG ceramics could be established. So, the present work revealed that Nd:YAG ceramics should exhibit a porosity value lower than 10−4% to approach the Nd:YAG single-crystal laser efficiency.
Nevertheless, the comparison of this result with those reported in the literature clearly indicated that the porosity content of Nd:YAG ceramics should not be only considered but also the morphological features of pores (e.g. average size). So, this result clearly confirms that the microstructural characterization of Nd:YAG transparent ceramics consists in a critical point to interpret the optical properties of these ceramics. Therefore, the mean properties of pores (i.e. the pore size distribution) could be strongly dependent on the processing conditions (raw materials properties, shaping, thermal treatment) even if the optical properties remain similar. Consequently, further investigations could be dedicated in future to explore various manufacturing conditions (silica content, sintering temperature) and to reach different pore size distributions. Thanks to the present characterization method of porosity, it would be then possible to understand well the origin of residual porosity and second to enhance laser performances of Nd:YAG transparent ceramics.
The authors are grateful to Dr. Luc Nguyen (Cilas, Orleans, France) for laser measurements and to Dr. Claire Carrion (GEIST, Limoges, France) for Confocal Laser Scanning Microscopy characterizations.
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