1. Introduction

1.1 Background

Nd doped YAG [Nd:YAG or (Y_1-xNd_x)₃Al₅O₁₂] is a well-known laser gain medium with an output mainly at 1.064 µm due to ⁴F_3/2 to ⁴I_11/2 transition [1,2]. It has diverse laser applications including materials processing (drilling and laser marking), electronic applications (resistor trimming and memory repairing medical applications), and military uses [2]. Nd:YAG single crystals are typically grown from the melt at 2200 K [1] using the CZ method by crystal pulling in the <111 > direction. Multiple rods or slabs are harvested from the CZ crystal [3]. Nd substitutes for Y in the cubic lattice of YAG with the fraction of Nd substitution for Y sites ranging from 0.10-1.5%. Throughout this paper, the terms Nd%, Nd at%, and Nd concentration refers to the fraction of Nd substituted for Y, that is $\frac{{Nd\; at\%}}{{Y\; at\%}}{\ast }100{\%}$.

In CZ growth of YAG, Nd has an equilibrium segregation coefficient of 0.18, and follows Scheil’s equation regardless of the pull or rotation rate, leading to relative Nd enrichment in the melt during growth; the Nd segregation coefficient changes slightly with rotation and pull rate [1,4]. This undesirable segregation leads to Nd variation along the grown boule, which imposes a limitation on the length of the Nd:YAG rods or slabs that can be extracted with uniform Nd concentration, and thus limits the laser power obtainable. This segregation further necessitates a much higher Nd concentration (∼4-5x higher) in the melt to obtain the desired average Nd concentration in the crystal, leading to increase in the raw material cost of Nd and the inevitable wastage of material not incorporated into the crystal. Higher Nd in the melt increases Nd clustering in the crystal, leading to cracking or stresses that impede laser performance [3,5–8]. Homogeneous Nd along the vertical axis and reduced Nd in the melt could allow for higher doping, longer and cost-effective rods for higher power lasers. Currently, Nd:YAG single crystals are grown with Nd concentration up to ∼2% by CZ [9], ∼3% by Temperature Gradient Technique (TGT) [10], and ∼4% by flux methods [11].

The previously mentioned issues are not intrinsic to Nd:YAG, but are commonly seen with all dopants in YAG and other crystal hosts grown by CZ. The objective of this work was to bypass the segregation in doped CZ crystals by modifying the convective flow in the melt during growth by the Accelerated Crucible Rotation Technique (ACRT). This paper provides the first successful attempt to significantly modify the dopant incorporation in CZ grown YAG. The metric of success for this study was to grow a single crystal of Nd:YAG using ACRT in CZ, to modify the Nd% concentration and change it by changing the ACRT parameters, and to obtain Nd% over 1.5% without cracks in the crystal.

1.2 ACRT theory and modeling

ACRT was initially proposed by Scheel for flux growth of high temperature solutions [12,13]. This technique allowed for a homogenized solution, improving nucleation and growth control, allowing for faster solution flow rates, reducing the thickness of the solute boundary layer, and leading to faster stable growth rates [12]. This technique was utilized in other crystal growth techniques such as Bridgman; it has been mainly used for II-VI and III-V compounds to improve growth rate and reduce radial and vertical segregation [14–16]. ACRT has been successfully applied for growth of Si [17], CdHgTe [14], CdZnTe [18], Rb₂MnCl₄ [19], YIG [20], InSb [21], and ZnTe [20]. Oxygen uniformity was improved in CZ growth of Si using ACRT [22]. Various models have been proposed to explain the effect of ACRT [15,16,23–26].

Typical parameters of an ACRT cycle include acceleration and deceleration rates, maximum rotation rate, hold time at maximum rotation rate, and hold time at minimum rotation rate. System parameters, such as the melt’s viscosity, density, crystal diameter, and length of the melt column, interact with the ACRT profile. The mathematical treatment of the fluid flow under ACRT is detailed and discussed in the literature [27,28], but a brief summary is presented below.

Three main flows occur during ACRT: spiral shear, Ekman flow, and transient Couette flow [27]. A spiral shearing force, operational in the bulk of the melt, causes two-dimensional flow during spin-up and spin-down cycles, and is useful in bulk melt mixing and homogenization of solute. Acceleration of the crucible causes shearing in the melt about the rotation axis, and results in spiral arms in the melt. The concentration differences in the spiral arms are neutralized via diffusion, with time scales estimated at a fraction of a second [27]. Ekman layer flow is the most dominant flow during the spin-up cycle, where the liquid near the solid-melt boundary is pushed away due to centrifugal forces, essential for radial mixing of the melt [27]. Ekman flow alters the thickness of the solute concentration layer ahead of the growth interface, which has significant effect on the solute segregation behavior [27]. The bulk of the vertical fluid mixing is achieved during spin-down by the formation of Couette flows [27]. During spin-down, the layer of fluid adjacent to the wall of the crucible decelerates faster than the fluid at the center, so the central fluid is pushed outward due to inertia.

Optimization of a rotation profile to establish stable flow patterns is essential for achieving improved mixing of the melt. These flows drive the liquid away from the equilibrium fluid flow state where the natural convection flows are dominant at slow rotations, and that alters the conditions at the solid/liquid interface, allowing for modification of dopant incorpration into the crystal. Theory serves as a starting point; however it is not presently complete, and experimental optimization is necessary.

In the current case, ACRT rotation parameters are designed based on the spin-up time criterion given by Horowitz et al. [29]. The spin-up time suggested by Horowitz et al. for acceleration from rest is [29]:

2. Experimental

2.1 Growth

The CZ growth furnace, as used previously [30,31], utilizes a rotating crucible rather than a rotating seed arm. Crystal mass is monitored to determine growth rate and power used. Crystal diameter is dynamically controlled based on growth rate by altering melt temperature. Experimentally, the only change implemented from the typical CZ growth is the rotation of the crucible. Four different rotation profiles are employed to study the effect of different rotation parameters on the crystal homogeneity, as shown in Fig. 1. Two profiles, RN1 and RN3, satisfy the criterion suggested by Horowitz et al., while RN0 and RN2 do not.

 

Fig. 1. ACRT profiles used and their parameters. *The spin-up time suggested is calculated based on the equation by Horowitz [29].

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Four ACRT CZ growths of Nd:YAG are accomplished and the details are summarized in Table 1. Batches are made by mixing yttria (99.999%), alumina (99.997%), and neodymium oxide (99.99%). In growths B1-1%RN0 and B2-1%RN0, Nd(OH)₃ is used instead of Nd₂O₃. Charge is mixed via ball milling for 18 hours using alumina balls (99.8%). After mixing, the charge is pressed at ∼140 MPa using an isostatic press and then calcined at 1400-1600°C for 15 hours in air.

Table 1. Growth parameters used.

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The charges are then melted in an iridium crucible (70 mm outer diameter, 70 mm height, 2.5 mm thick), which is heated inductively using an RF coil operating at 25 kHz. The growth environment is high purity N₂ mixed with 0.01% to 0.25% O₂ by volume. An undoped YAG seed, <111 > orientation and 6 mm diameter, is used in all growths. Before seeding, the melt is initially mixed using ACRT RN0 (except in C-0.7%RN3 where RN3 was used for premixing) for 3 to 4 hours followed by constant rotation of 5-6 rpm for the initial part of the growth, followed by ACRT for the rest of the growth. The ACRT profiles and other parameters are summarized in Table 1 and Fig. 1.

2.2 Nd% determination: FLTM, XRD, absorption

Nd% concentration in A-1%VR, B1-1%RN0, and B2-1%RN0 were measured using Fluorescence Lifetime Measurements (FLTM) at II-VI Optical Systems (Port Richey, FL) along the vertical axis of the ingot. The crystal surface was ground before measurement, as a non-reflective flat surface is needed for the FLTM. The relative accuracy for FLTM is 0.01% along the crystal boule, according to II-VI Optical Systems (Port Richey, FL), commercial suppliers of Nd:YAG CZ crystals. FLTM theory and method has been discussed in literature such as in [9,32].

Circular cross-sections, 2-3 mm thick, were cut at various positions along the vertical axis of the ingots then powdered using a tungsten carbide mill for X-ray diffraction (XRD). Samples were analyzed using a X’Pert Pro MPD (PANalytical B.V., the Netherlands) with a Cu tube between 30° and 125° 2θ. The lattice parameter was calculated and related to the Nd concentration using standards with known Nd concentration, as described in the Appendix. Cross-sections allowed for averaging the Nd% over the diameter. Standards were <111 > grown crystals: two samples from undoped YAG crystal grown by CZ in a similar system [30]; undoped YAG crystal from United Crystals Inc (NY, USA); and four Nd:YAG laser rods from II-VI Optical Systems (Port Richey, FL, formerly VLOC when rods were obtained) with average Nd concentrations 0.4%, 0.63%, 0.77% and 1.02%.

Windows were cut from ACRT grown CZ ingots and polished with Al₂O₃ slurry down to 0.3 µm media. Finished samples were ∼0.8-2.9 mm thickness. A Varian Cary 5 UV-VIS-NIR (Agilent, USA) was used to measure % transmission 200-3000 nm with 0.5 nm interval, 0.2 s integration time, and 1.0 nm spectral bandwidth. Results are shown in Appendix.

3. Results and discussion

3.1 Crystal quality

All ingots are <111 > single crystals, as typical for industry and in literature. B2-1%RN0 and C-0.7%RN3 formed cracks upon cooling and separating the crystal from the melt. This is possibly due to large vertical thermal gradient during growth as the insulation design and the position of the crucible with respect to the melt was modified. Figure 2 shows images of the cross-section of the crystal under cross-polarizers. As expected from Nd:YAG, crystals change color under optical excitation, as in Fig  2(b). All ingots show some faceting on the outer surfaces, being most prominent in A-1%VR, as seen in Fig. 2(a), and C-0.7%RN3, as seen in Fig. 2(d). Due to the relatively fast pull rate, some crystals show some possible bubble trapping and voids.

 

Fig. 2. Photographs of four of the grown Nd:YAG ingots, polished cross-sections, and polished cross-sections under cross-polarizers. (a) A-1%VR, (b) B1-1%RN0, (c) B2-1%RN0, and (d) C-0.7%RN0. (e) Ce:YAG grown using conventional CZ under cross-polarizers, showing the typical stresses and core breakdown in YAG; Ce added nominally in the charge was 1%.

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Single crystal YAG grown by conventional CZ is characterized by an effect known as “core breakdown,” in which high stresses accumulate around the center of the crystal and typically lead to fracture that starts around the core, reducing the usable crystal volume as in Fig. 2(e) [6,33]; the stressed regions around the core breakdown area are not usable for laser gain-media, as can be observed using visible light with cross-polarizers [6,33,34].

Polished ACRT samples observed under cross-polarizers show some stresses, but notably none show the usual signs of core break down. C-0.7%RN3, as in Fig. 2(d), does not show any stress-induced birefringence under cross-polarizers; the other crystals show some stress-induced birefringence, but the distribution is not typical of the core break-down stresses. Typical stresses and core break-down are shown in Ce:YAG samples grown by conventional CZ for a comparison, as in Fig. 2(e). The reason for absence of core breakdown is not yet clear, but previous work showed an increased density of Nd³⁺ clusters in the core regions when imaged using high-resolution transmission electron microscopy; others have suggested core breakdown is caused by the facets having different lattice constant and crystal orientation [6–8,35]. The effect of seed rotation rate on the stress and core breakdown have been studied in the literature as in [36]; however, to remove the core breakdown, rotations of 60-100 rpm on 10-20 mm diameter crystals are needed; these rates may not be realistic in large diameter crystals grown industrially.

Further, the angle of the heel (last part of crystal to grow) for ACRT grown crystals is very shallow and close to flat, indicating a nearly flat crystal-melt interface during the ACRT growth, as can be seen in Fig. 2(b,d) for B1-1%RN0 and C-0.7%RN3, respectively. However, when the crystals are pulled during constant rotation or no rotation, the heel shows an interface convex towards the melt, as can be seen in Fig. 2(a,c) for A-1%VR and B2-1%RN0, respectively. The optical absorption spectra which shows the optical quality is included in the Appendix.

3.2 General effects of ACRT on Nd%

The segregation in conventional CZ grown crystals under equilibrium conditions is characterized by a segregation coefficient (k_c), which can be used to estimate the distribution of the dopant along the crystal growth axis using Scheil’s equation [37]:

For ACRT grown Nd:YAG presented in this paper, the Nd% concentration and its distribution cannot be characterized by Scheil’s equation, the equilibrium phase diagram, or what is achieved by conventional CZ growth of Nd:YAG. The first observed difference when using ACRT is that the Nd% can be made higher, close to, or lower than the initial Nd concentration in the melt (c₀) as can be seen in A-1%VR (VR stands for Variable Rotation profile), as illustrated in Fig. 3. This crystal was doped with 1.0% Nd and was grown using four different sequentially changed rotation profiles. The Nd% is significantly higher than predicted by Scheil’s equation; the average measured Nd% also significantly exceeds the initial concentration in the melt; it is important to note that only about 30-40% of the melt is grown. The Nd% in A-1%VR can be seen to vary depending on the rotation profile used; this result, at the very least, demonstrates the ability to control the Nd% using ACRT. These results also demonstrates the ability to dope CZ grown Nd:YAG with over 3% Nd without cracks forming in the ingot. As stated before, Nd:YAG has been limited to Nd%∼2% using conventional CZ growth methods [9].

 

Fig. 3. Nd% concentration variation along the crystal length in A-1%VR measured via FLTM and calculated via Scheil’s equation; also included is the variation of the ingot diameter. The Nd% in the initial batch is 1.03%, and the average Nd% in the crystal is 1.98% (8.55% of Nd would be required to be added in the melt to achieve 1.98% Nd concentration using the conventional CZ method). The error bar on the FLTM measurement is smaller than the size of the used symbol.

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In A-1%VR growth, the Nd% concentration is shown to vary between each segment, caused by the use of multiple rotation profiles in one growth; however, the variation of Nd% does not show a power law pattern as would be achieved by the conventional CZ method, as shown in Fig. 3. Further, an average Nd concentration of 1.98% is seen (excluding the cone part) in this crystal. In order to achieve a similar average Nd concentration in the crystal using the conventional CZ method, the melt requires a much higher initial concentration of ∼8.55% Nd.

Further, as shown in Fig. 3, the diameter of the crystal is varied to study the possible effect of the crystal diameter (the area of the crystal-melt interface) on the resulting Nd% concentration. There is no clear dependence of the Nd% on the area of crystal-melt interface. The reason for the observed variation in the Nd% within an ACRT profile is possibly due to the ground flat for FLTM being kept parallel to the growth axis, which resulted in the radial distance, between the outer diameter of the crystal before the ground flat and the point being measured by FLTM, to vary depending on the vertical axis; due to the observed radial variation, as discussed later, the ground flat would lead to reading points along the radius and thus showing fluctuation of the Nd% measured.

3.3 Nd% average dependence on ACRT profile and initial Nd% concentration (c₀)

B1-1%RN0 and B2-1%RN0 are grown using profile RN0, which shows the highest observed Nd% concentration in the crystal A-1%VR. These two growths (B-1 and B-2), which have the same rotation profile and initial Nd% in the melt, demonstrate the reproducibility of the ACRT method in producing Nd:YAG crystals. Figure 4 shows the FLTM and XRD results for B1-1%RN0 and B2-1%RN0 crystals. In these growths, the Nd% is higher than predicted by Scheil’s equation and achieved by conventional methods. The same phenomenon, higher concentration than predicted by Scheil’s equation, can be seen also with C-0.7%RN3, in Fig. 5, which is grown using the RN3 rotation profile; this growth shows the closest Nd% to that added in the melt, and the lowest variation of Nd% among the four ACRT rotation profiles used in A-1%VR. Finally, it can be seen that none of the measured Nd% variations follow the power-law relation achieved by conventional CZ and predicted by Scheil.

 

Fig. 4. Nd% concentration variation along the crystal length in (a) B1-1%RN0, (b) B2-1%RN0 measured via FLTM and XRD, and calculated via Scheil’s equation. Note: the initial charge amount, and the ingot diameter and length in (a) and (b) are different. The error bar on the FLTM measurement is smaller than the size of the used symbol. For explanation of labels S1 through S4 ssee section 3.7 and Fig. 6.

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Fig. 5. Nd% concentration variation along the crystal length in C-0.7%RN3 measured via XRD, and calculated via Scheil’s equation.

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Due to the low concentration of Nd% in C-0.7%RN3, FLTM cannot be used to measure it, but instead XRD is used. Figure 4 and Table 2 show good agreement in the absolute Nd% concentration and its variation, as obtained from the XRD and FLTM results in B1-1%RN0 and B2-1%RN0; thus the XRD results should be a good measure of the Nd% in C-0.7%RN3.

Table 2. Summary of Nd parameters for the grown crystals.

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The exact mechanisms, leading to the difference in the Nd% between the crystals presented here and those grown by the conventional CZ method, remain unknown due to the complexity of the fluid flows induced by the continuous change in the rotation rate. However, a simple description for the possible cause can be inferred by considering the assumptions made in the derivation of Scheil’s equation. Scheil’s equation assumes no diffusion in the solidified crystal and homogeneous melt. The first condition is unaffected by the ACRT. Thus, it is possible that ACRT rotation, instead of leading to a perfectly mixed melt, rather affects the Nd% concentration at the solid-liquid interface (either increasing or decreasing it depending on the rotation profile and the initial Nd% in the melt). This can be seen by the change in the shape of the solid-liquid interface that ACRT causes in the crystals presented here (the interface is flatter when ACRT is used). It is also possible that the flow of the solute atom (the Nd%) toward the interface is controlled by the ACRT-enhanced fluid flows.

The difference in Nd% profiles for RN0 and RN3 grown crystals may be due to the difference in spin-up time used. RN3 uses a lower acceleration rate (longer spin-up and spin-down times) than RN0, allowing more time for the center of the melt to overcome inertia; as mentioned, Horowitz et al. [19,29] showed that longer spin-up times and higher rotation rates yield better crystals.

3.4 Initial Nd% in melt and its variation along the growth axis

As summarized in Table 2, much higher Nd% would be needed in the melt to obtain the same average Nd% along the ingot using conventional CZ method compared to what is obtained in the ACRT growths presented here, as in Fig. 4 and Fig. 5. Additionally, the variation along the crystals shown here is close to or less than typically achieved by conventional CZ methods; this variation is approximated by the max/min Nd% ratio along the crystal. The variation of Nd% is compared to the average and variation of Nd% calculated using Scheil’s equation; these are the conditions for the initial Nd in the batch which would be required to yield similar averages to those measured via FLTM or XRD on ACRT crystals, assuming equilibrium conditions and conventional CZ growth; this is the grey curve in Fig. 3, Fig. 4, and Fig. 5.

3.5 Implication on the lack of effect of crystal diameter

B1-1%RN0 and B2-1%RN0 show the same Nd% average concentration and variation, with different crystal diameters: B1-1%RN0 is 19-24 mm diameter, whereas B2-1%RN0 is 29.8 mm diameter. These diameters yield different surface areas on crystal-melt interface. Thus, the ACRT process and profile has a more dominant effect on Nd distribution than crystal diameter.

3.6 Nd% concentration using constant rotation following pre-mixing with ACRT

As shown in Table 1, there was a pre-mixing step with ACRT RN0 in all the growths (besides C-0.7%RN3 in which RN3 was used to pre-mix) for 3-4 hours followed by a growth using 5-6 rpm for 25-45 mm of growth before the start of the growth using ACRT; that is, there was a pre-mixing step with ACRT, then growth with constant rotation (i.e., conventional CZ growth), then growth using ACRT. In general, there is a high Nd% in the part of the crystal grown using constant rotation in most of the crystals grown here, as can be seen in Fig. 4 and Fig. 5. This indicates that there is a lasting effect of pre-mixing using ACRT, even during later growth under constant rotation. Most theories explaining the change of equilibrium segregation coefficient are based on phenomena that occur at the growth interface (i.e., diffusion boundary layer thickness). It is indeed a surprising result that there is a “memory” retained in the melt from a pre-mix segment; at this point it is not clear what causes this, but any melt structures or complexes that are present can be altered with stirring.

3.7 Nd% radial variation

Radial variation of Nd% was evaluated on select cross-sections by FLTM, demonstrating peculiar variation, as in Fig. 6, that is not typical for Nd:YAG grown by conventional CZ. In conventional CZ, the Nd:YAG crystal has an interface convex towards the melt, and the radial variation follows a convex towards the melt pattern where the center has a lower Nd% than the edges. What is observed here, in S1, S2, and S4, is that the Nd% has two local minima in the Nd%, surrounding a local maximum close to the radial section; the average Nd%, as shown in the legend of Fig. 6, is close to that estimated by FLTM on the edge, as well as that obtained by XRD on the cross-sections as shown in Fig. 4. S3 is different from S1, S2, and S4, in that it was cut from a section grown using constant rotation following ACRT pre-mixing, whereas the others were cut from sections grown by ACRT RN0 profile; thus, it can be seen although the pre-mixing led to an increase in the average Nd% in S3, the radial variation followed the convex towards the melt interface expected from constant rotation signifying the effect of rotation during the growth, and providing a better insight on the effect of premixing before the growth. Typical radial Nd% variation follows a shapes similar to that of sample S4 in Fig. 6(b), with radial gradients of less than 0.03 at% not including the core area (the variation is up to 20% higher within the core area than the rest of the crystal) [40].

 

Fig. 6. Shows the radial variation of Nd% measured by FLTM in (a) B1-1%RN0 and (b) B2-1%RN0; the legend shows the sample name, the distance from the top of the ingot, and the average Nd% along the radial cross-section. The fit is to guide the eye. The dashed line marks the center of the radial cross-section.

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4. Conclusion

This paper demonstrates the first successful implementation of ACRT in single crystal growth of Nd:YAG. ACRT is used to understand and control the doping concentration of Nd along the vertical growth axis of YAG, which can be greater or less than the initial concentration in the melt, depending on the ACRT rotation parameters used. This does not follow what is predicted by Scheil’s equation, as described by the equilibrium phase diagram, or achieved experimentally with conventional CZ methods, most likely because the ACRT results in non-equilibrium segregation, and non-equilibrium convection flows seen under stationary conditions. This demonstrates the ability to optimize the Nd% in the melt regardless of the Nd% added initially. The experiments show that the stirring effect of ACRT is the most dominant one and is independent of crystal diameter, at least for the diameters explored here.

Also reported here for the first time is the effect of ACRT pre-mixing on the Nd% in crystal grown with constant rotation. In other words, subsequent constant rotation during growth may not easily change the effect of previous ACRT rotation on the melt composition. The study shows radial variation different from conventional CZ, regardless of whether ACRT or constant rotation follows ACRT premixing. This radial segregation may also explain some of the measured variation along the growth axis. This study also demonstrates the ability to achieve high Nd% concentration (>3% Nd) in the crystal without fracturing or having a core breakdown, at least for the diameters considered here.

Similar crystal systems typically grown by CZ can likely be grown by ACRT to achieve comparable results. However, there are no models known to the authors to predict the optimum ACRT profile parameters needed, and ACRT has rarely been attempted as part of CZ growth in general. Thus, there is more work needed to successfully grow homogeneously doped Nd:YAG with Nd% close to that of the melt and to improve the quality of the crystals obtained.

Appendix

X-ray diffraction

Each XRD measurement was repeated 5 times, and the analysis was performed on summed scans. Summed scans were fit using HighScore Plus Software (PANalytical B.V., the Netherlands) using profile fit with Pseudo Voigt peaks with split width and shape asymmetry. The Weighted R Profile is generally <4 with a Goodness-of-Fit generally <3. The lattice parameters were calculated using the so-called “Accurate Method” as in [6,41]. Of the fitted XRD spectra, 26 K_α1 diffraction peaks between 2θ 50° and 125° were using in the determination of the lattice parameter using the accurate method by plotting the lattice constant calculated from each peak using Bragg’s law as a function of its cos²(θ°)/sin(θ°). The plot was linearly fit, and the y-intercept was used as the lattice parameter of the sample.

In order to relate the lattice parameter to Nd concentration, standard samples with known Nd concentration were also powdered and measured with XRD using the same method as for the other samples. The standard samples measured were: two samples from an undoped YAG crystal grown by the same method as described in a similar system in a previous publication [30]; undoped YAG crystal from United Crystals Inc (NY, USA); and four Nd:YAG laser rods from II-VI Optical Systems (Port Richey, FL, formerly VLOC when the crystal rods were obtained) with average Nd concentration of samples 0.4%, 0.63%, 0.77% and 1.02%. A calibration curve of the known Nd concentration as a function of the lattice parameter was constructed. A linear line was fit with an R²=0.956, and the linear fit was used to determine the Nd concentration for the grown Nd:YAG crystals.

Fig. 7(a) shows an example of an XRD spectrum obtained for the grown Nd:YAG crystals. Figure 7(b) shows the calibration curve that was constructed using YAG and Nd:YAG with known Nd concentrations and used to correlate Nd concentration to the measured lattice parameter.

 

Fig. 7. (a) Example of XRD measured on an Nd:YAG sample from B1-1%RN0, and (b) calibration curve of the lattice parameter as a function of Nd% concentration of three YAG crystals and four Nd:YAG crystals with known Nd concentration.

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Absorption

Fig. 8 shows the absorption spectra of samples cut from different parts of B1-1%RN0, B2-1%RN0, and C-0.7%RN3, corrected for Fresnel reflections. The absorption confirms the XRD and FLTM results, as it shows a similar trend in variation between crystals and within the same crystal as the Nd% measured by XRD and FLTM. However, sample surface flatness and polish and any bubbles and inclusions can cause variations in the transmission (and resulting calculation of absorption), therefore absorption alone cannot be used as a measure of the Nd% concentration and its variation.

 

Fig. 8. UV-VIS absorption of polished Nd:YAG samples; the spectra are offset.

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Funding

Washington State University, Center for Materials Research.

Acknowledgments

The authors would like to thank Bruce Glick, Michael Brennan, and Binh Vu from II-VI Optical Systems, Inc (Port Richey, FL) for the FLTM measurements. This paper is dedicated to Prof. Kelvin Lynn, who passed away suddenly during the review and publication of this manuscript. We will all miss him dearly.

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