Our strategy for obtaining gain in Nd:Al 2 O 3 is a twofold design of nano/microstructure that relies on (1) crystallite sizes below the wavelength of pump and emitted light and (2) a dopant distribution in the grain volumes with minimal segregation at the grain boundaries. Figure 1 summarizes our strategy. In anisotropic ceramics with large grains, light is scattered at grain interfaces since they represent discontinuities in refractive index (Fig. 1a). However, as grain size decreases, the scattering efficiency of uniaxial grains is significantly lower38, 39, 42. Thus, fine-grained ceramics can be highly transparent media with losses that are low enough to achieve optical gain (Fig. 1b).

Fig. 1: Length scale relationships important for achieving gain in anisotropic ceramics. a Light is scattered at grain interfaces in ceramics with large crystallites because randomly oriented grains represent discontinuities in refractive index. RE segregation (represented as a close-packed monolayer) at the grain boundary on a section of Al 2 O 3 (the blue atoms are Nd, those in white are O, and those in black are Al). b Scattering efficiency decreases significantly when pump (λ 1 ) and emitted light (λ 2 ) wavelengths are smaller than the grain size, permitting low optical losses. Small grains also permit spreading out of RE dopants at grain boundaries, increasing average interionic distance,\(\tilde l\) allowing for optical gain. c A close-packed arrangement of dopant l = 0 and one with realistic interionic distance for gain (l = 1 nm). d Calculation of grain size necessary to accommodate all the dopants for a given dopant arrangement and concentration on the grain boundary, d eff vs. grain size using Eq. 4 for two concentrations and arrangements shown in (c) Full size image

In addition to low losses, RE-dopant concentrations must be within a critical range—high enough to achieve a sufficient absorption cross-section and emission cross-section, yet low enough to prevent concentration quenching (energy relaxation through phonon rather than radiative photon processes), which occurs when ions are too closely spaced.

Traditional material processing can be employed in systems such as glasses and garnets where RE solubility is high. However, in low solubility media, agglomeration occurs at grain boundaries (as shown in Fig. 1a). In the isotropic laser ceramics that have been demonstrated, grain sizes are typically 10–20 μm14. In this large grain size case, there are relatively few grain boundary regions to accommodate the RE-dopant, and the average distance between RE ions decreases, resulting in luminescence quenching.

A key insight here is that the fine crystallite sizes that allow for high transparency in anisotropic polycrystalline materials can also play a crucial role in absorption/emission by providing a possibility for higher RE incorporation without luminescence quenching. By reducing grain size, grain boundary volume increases. When holding the global dopant concentration constant while decreasing grain size, RE dopants can ‘spread out’ along grain boundaries, increasing the average distance \(\tilde l\) between RE- ions (Fig. 1b). In other words, for very fine-grained materials, it should be possible to reach dopant concentrations sufficient to achieve gain even without solubility in the grain interior. The effective grain size d eff necessary to accommodate all the dopants on the grain boundaries rather than in the grain interiors depends on the arrangement of dopants on the boundary (function of \(\tilde l\)) and scales with d3/2 (see the Materials and methods for details).

To illustrate this scenario, we plot d eff as a function of grain size (Eq. 4) in Fig. 1d for various concentrations (at.% Nd) and dopant arrangements (Fig. 1c). The shaded regions in Fig. 1d are conditions in which it is possible to accommodate the global concentration of dopant atoms c without any solubility in the grain. In the non-shaded regions, d eff > d, meaning that it is not possible to accommodate all the dopant ions without solubility in the grains. In the limiting case example of a close-packed monolayer (\(\tilde l\) = 0) (Fig. 1c), it is possible to accommodate c = 0.25 at.% and c = 0.35 at.% of Nd on the grain boundary of a grain with d~250 nm. The close-packed monolayer case would likely not lead to gain because the distance between RE ions would result in luminescence quenching. Using a realistic value of \(\tilde l\)=1 nm, we see that grain sizes <25 nm are necessary to accommodate 0.35 at.% of Nd. The need for such small grain sizes is alleviated in our case because alumina does have solubility in the grain interiors which is likely higher near grain boundaries and can be increased under specific processing conditions as will be discussed below. It is interesting to discuss this level of dopant incorporation relative to Nd:YAG. The high Nd equilibrium solubility in YAG is due to the more open crystal structure leading to a lower cation density compared to that for alumina. Because the cation density is higher in Al 2 O 3 , the volume concentration, c vol , of Nd is significantly higher in Al 2 O 3 vs. YAG for a given at.% dopant. At c = 0.25 at.%, c vol = 1.18 × 1020 atoms/cm3 for Nd:Al 2 O 3 , compared to c vol = 9.26 × 1019 atoms/cm3 for Nd:YAG, which is an increase of ~26%. Ultimately, this indicates that a 0.25 at.% Nd:Al 2 O 3 ceramic will contain a suitable concentration of RE for lasing.

To obtain gain in an Nd:Al 2 O 3 bulk polycrystalline material, processing techniques that will produce fully dense ceramics with fine average grain size (AGS) and/or that offer processing “windows” with increased rare-earth solubility are needed. Fortunately, the Nd solubility can be increased using high heating and cooling rates (to be discussed below), easing the necessity for extremely fine grains. Using a solid-state powder processing route along with a one-step simultaneous reaction/densification approach with CAPAD, we can achieve an Nd concentration as high as 0.35 at.% (Nd:Al ratio).

At processing temperatures of 1200 °C (un-doped) and 1260 °C (Nd-doped), the samples have a fine AGS of ~250 nm, near the theoretical density, and are phase pure. As such, they possess long-range transparency (Fig. 2a) and when doped emit light at the characteristic Nd3+ wavelength of 1064 nm when pumped with 806 nm, which are prerequisites for gain. However, all samples processed at 1300 °C are diffuse and white due to an increased AGS to ~2.1 µm ± 0.25 µm for the un-doped α-Al 2 O 3 and 1.9 µm ± 0.22 µm and 1.87 µm ± 0.23 µm for 0.25 at.% and 0.35 at.% Nd:Al 2 O 3 , respectively. At these larger grain sizes, the scattering efficiency is significantly higher (Fig. 1a).

Fig. 2: Physical and microstructural characterization of Nd:Al 2 O 3 . a the effect of CAPAD temperature on the relative density of un-doped and samples doped with 0.25 and 0.35 at.% Nd. The inset is a picture demonstrating long range transparency. b XRD profiles of the starting Al 2 O 3 and Nd-doped Al 2 O 3 powders. For the 0.25 and 0.35at. % powders, there are peaks attributed to the Nd 2 O 3 dopant as indicated by arrows. c XRD profiles of Al 2 O 3 and Nd-doped ceramics. The un-optimized Nd-doped sample shows a clear secondary phase (indicated with an arrow). The optimized samples do not show signs of a secondary phase present. The inset on the right clearly shows a peak shift relative to an α-Al 2 O 3 standard (dashed line) for optimized Nd:Al 2 O 3 Full size image

The CAPAD processing parameters were varied to optimize the microstructure and properties of various concentrations of Nd:Al 2 O 3 (see the Materials and methods for details). Figure 2a shows the effect of CAPAD temperature on the relative density of un-doped samples and others doped with 0.25 and 0.35 at.% Nd. The results show a sigmoidal temperature dependence, where the density increases abruptly at a temperature referred to as the densification on-set temperature, T OD . There is a clear influence of Nd dopant on T OD . For the Nd-doped Al 2 O 3 samples, T OD is ~200 °C higher than in the un-doped case (a shift from ~900°C to ~1100°C). There is also a small effect between the two different Nd concentrations on T OD . The densities of the 0.25 at.% Nd samples are slightly higher than those for the 0.35 at.% Nd samples at most processing temperatures. Nd addition also affects the temperature required to obtain full density; relative densities > 99% are achieved in the un-doped Al 2 O 3 case at 1200 °C and ~1260 °C for the Nd:Al 2 O 3 samples.

We have previously observed reduced densification kinetics caused by RE addition in reaction/densification of ceramics19, 43. This is due primarily to the presence of the RE oxide dopant powder along the particle/grain boundaries when the two phases are still separate reactants. In our previous work on alumina with Tb as a dopant, the decrease in density was lower compared to the present case of Nd at similar global concentrations19. The difference in behavior between the Nd and Tb dopants can be attributed to the larger ionic radius of Nd3+ (0.983 Å) compared to Tb3+ (0.923 Å). A similar shift in the T OD with respect to RE ionic radius was reported for a Nd3+, Eu3+, and Er3+ doped Al 2 O 3 system (0.2 at.% RE to Al 2 O 3 ratio, ~0.04 at.% RE:Al) via free-sintering and hot-pressing by Drdlík et al.44. It is worth noting that in their work, the T OD was significantly higher (>1400 °C), and a lower ~98% relative density was achieved at processing temperatures >1500 °C. The higher processing temperatures resulted in larger AGS (>500 nm) which diminished the material transmission and dopant concentration.

Figure 2b shows X-ray diffraction (XRD) profiles of the Al 2 O 3 and Al 2 O 3 + Nd 2 O 3 powders after planetary ball milling (PBM) with varying Nd concentrations. These XRD spectra reveal a peak at 2θ = 30.72°, corresponding to the highest intensity peak for Nd 2 O 3 . Comparison of the XRD of the PBM starting powders to the α-Al 2 O 3 reference does not show discernible peak shifts irrespective of Nd concentration, suggesting that Nd3+ doping into the α-Al 2 O 3 matrix did not occur through mechanical alloying during PBM. This is expected considering the relatively low energy of the PBM conditions.

Figure 2c shows XRD spectra of fully dense polycrystals using optimized and non-optimized CAPAD conditions. The heating rates, processing temperatures, and hold times of the optimized and non-optimized cases were similar (HR = 300 °C min−1, T = 1260 °C, and HT = 5 min); the largest difference in each case was in the cooling rate, CR, which was significantly higher for the optimized case (Optimized CR = 300 °C min−1 and Non-optimized CR~42 °C min−1). The XRD spectra of the non-optimized sample reveal an unwanted secondary phase, Nd 4 Al 2 O 9 , (marked with an arrow). The highest intensity alumina peak is also at the same angle compared to the un-doped alumina ceramic, suggesting that Nd had not been adequately incorporated in the lattice.

By contrast, XRD of the ceramics processed using optimized CAPAD conditions reveal single phase α-Al 2 O 3 with no signal from the starting Nd 2 O 3 or from the ternary Nd 4 Al 2 O 9 and NdAlO 3 phases. This is in contrast to some previous reports that showed secondary phases in RE-doped α-Al 2 O 3 that have been produced at RE concentrations above the equilibrium solubility limit with other processing approaches45, 46. Moreover, the XRD spectra of the optimized Nd-doped samples reveal clear peak shifts to lower angles with increasing Nd concentration. The dashed line in the inset on the right is the location of highest intensity peak from the reference. This shift is evidence of stretching of the α-Al 2 O 3 lattice from the doping of Nd ions caused by CAPAD processing. The absence of the Nd 2 O 3 reactant and ternary phases strongly indicates a fundamental difference in the reaction kinetics associated with CAPAD processing in comparison to that for traditional processing approaches.

We attribute the ability to incorporate high concentrations of RE into Al 2 O 3 to the high heating and cooling rates we employed in CAPAD. The high heating rate ~300 °C min−1 allows us to reach the desired temperature quickly, minimizing unwanted grain growth19, 47 while achieving a near theoretical relative density, which are pre-requisites for high optical transparency in Al 2 O 3 . We previously observed an increase in reaction kinetics associated with high heating rates in the Ce:YAG system43. We found ~20-fold increases in reaction coefficients in comparison to reaction/densification in free-sintering using much slower heating rates. Since the largest difference between the optimized and un-optimized samples in this work was in the CR, we believe this parameter also plays a crucial role in RE incorporation. The Nd solubility increases at higher temperatures so that the high CR has the effect of “freezing in” Nd, thus minimizing segregation. There is a synergistic effect between fine AGS and RE incorporation during CAPAD. A more detailed investigation of the relationships between CR, microstructure, and optical properties is underway but is beyond the scope of this communication.

We used TEM to further confirm incorporation of Nd into the alumina matrix. A high-angle annular dark-field (HAADF) TEM micrograph and corresponding energy-dispersive X-ray spectroscopy (EDS) distribution maps of a 0.35 at.% Nd:Al 2 O 3 polycrystal (T = 1260°C, HT = 5 min, HR = 300 °Cmin−1, and CR = 300 °Cmin−1) are shown in Fig. 3a. The EDS maps reveal that a significant portion of the Nd dopant is found within the matrix and along some grain boundaries and triple points. The minimal segregation corroborates the XRD spectra in Fig. 2c, which shows a shift in the XRD peaks to lower 2θ angles and does not show the presence of unwanted secondary phases. This is in-line with observations by Rohrer, Harmer and co-workers 48, 49 showing differences in the local grain boundary structure in RE-doped α-Al 2 O 3 and an increasing concentration gradient from the grain interior towards the grain boundary.

Fig. 3: High-angle annular dark-field transmission (HAADF) TEM micrograph of 0.35 at.% Nd:Al 2 O 3 bulk ceramic (optimized sample) with corresponding energy-dispersive X-ray spectroscopy (EDS) elemental maps for Al, O, and Nd (L-Lines). The EDS maps reveal that a significant portion of the Nd dopant is found within the matrix. In addition, there is some Nd along some grain boundaries and triple points Full size image

The optical transparencies of the consolidated bulk Nd:Al 2 O 3 polycrystals are shown in Fig. 4a with the corresponding transmission spectra presented in Fig. 4b. The transmission values of our undoped alumina ceramics rival those previously reported for sinter-HIPed samples38 and high pressure CAPAD50. More importantly, the Nd-doped samples have similar transmissions. In the area of interest for lasing of Nd3+ media at ~1064 nm (4F 3/2 → 4I 11/2 transition), the transmission is ~75% for the Nd:Al 2 O 3 . We attribute this high transmission to the high density (>99%), fine AGS (~250 nm), low Nd segregation, and lack of secondary (undesired) phases in the Nd:Al 2 O 3 . It is important to note that this transmission is not corrected for refection losses. When corrected for reflection losses, the transmission at 1064 nm is ~90%, leading to a loss coefficient (absorption+scattering) of ~1.317 cm−1. For laser oscillation, a gain greater to this total loss is required for net positive gain. Our single-pass gain measurements presented below show that the optical quality of our ceramics is indeed suitable for lasing.