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Thermomechanical properties of rare-earth-doped AlN for laser gain media: The role of grain boundaries and grain size
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ScienceDirect Acta Materialia 86 (2015) 148–156 www.elsevier.com/locate/actamat
Thermomechanical properties of rare-earth-doped AlN for laser gain media: The role of grain boundaries and grain size ⇑
A.T. Wieg,a Y. Kodera,a Z. Wang,a,b C. Damesb and J.E. Garaya, a
Department of Mechanical Engineering and Materials Science & Engineering Program, University of California, Riverside, CA, USA b Department of Mechanical Engineering, University of California, Berkeley, CA, USA Received 13 May 2014; revised 18 October 2014; accepted 30 November 2014
Abstract—The low thermal conductivity and poor fracture toughness of traditional laser gain media (rare-earth-doped single crystals) limits the overall power deliverable from a laser system. We present an investigation of the thermomechanical properties of a promising laser gain candidate, Tbdoped aluminum nitride (Tb:AlN). We pay special attention to the effect of the average grain size and the dopant segregation at the grain boundaries on the relevant properties: Vickers hardness, fracture toughness and thermal conductivity. We find that all properties are affected by grain boundaries and/or dopant segregation. However, the thermal conductivity is significantly more affected than the mechanical properties and therefore dominates the thermal shock figure of merit, Rs. We obtained a thermal shock figure of merit in Tb:AlN more than 60 times that of the state-of-the-art laser gain material Nd:YAG. Ó 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Transparent ceramics; Spark plasma sintering (SPS); Current-activated pressure-assisted densification (CAPAD); Thermal conductivity; Indent fracture toughness
1. Introduction Thermal management continues to be a significant problem in the design of high-performance, high-energy lasers. For instance, thermal gradients in laser gain materials can lead to performance issues such as thermal lensing and ultimately irreparable failure through thermal shock. A gain material with high thermal conductivity will be able to dissipate more heat, reducing thermal gradients and thus producing more laser power for a given pumping–cooling scheme. Similarly, materials with high fracture toughness can tolerate higher thermal stresses before failure. Thus, the important design criterion for maximizing laser energy is dependent on both mechanical and thermal properties of the gain material, with a thermal shock resistance figure of merit given by [1]: kð1 mÞ rF ð1Þ aE where rF is the fracture stress, k is the thermal conductivity, E is Young’s modulus, a is the coefficient of thermal expansion and m is Poisson’s ratio. Traditionally, laser gain materials like Nd:YAG have been single crystals with relatively low thermal conductivity Rs ¼
⇑ Corresponding author. Tel.: +1 9518272449; e-mail: jegaray@engr. ucr.edu
and low toughness. Polycrystalline ceramics are often tougher than single crystals, but can suffer from inferior optical properties (because of scattering at pores and grain boundaries). This optical property challenge has been alleviated by the advent of advanced processing procedures. For example, Ikesue and others [2,3] have shown that slope efficiencies of polycrystalline ceramics are on a par with single crystals. Recently, current-activated pressure-assisted densification (CAPAD) has been receiving considerable attention for processing optical ceramics [4–9]. A clear advantage of CAPAD is that fast processing kinetics can create metastable phases that are not possible with singlecrystal growing techniques or pressureless sintering. We recently demonstrated over-equilibrium doping of active rare-earth (RE) elements, leading to luminescence in the AlN [10] and Al2O3 [11] systems. Since the thermal conductivity and fracture toughness of these ceramics are inherently higher than the state-of-the-art laser gain material Nd:YAG, metastable RE:Al2O3 and RE:AlN hold significant promise for next-generation high-energy lasers. As alluded to above, extended defects like grain boundaries can dominate the optical, thermal and mechanical properties of ceramics. The effects of grain boundary phases in AlN with RE additions have been reported [12,13], but in these cases the goal was to make tough, highly thermally conductive AlN ceramics, not photoluminescent, light-transmitting ceramics. Thus high concentrations (5 wt.%) of RE oxides were added. Very little
http://dx.doi.org/10.1016/j.actamat.2014.11.045 1359-6462/Ó 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
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attention has been given to microstructural features that influence the thermomechanical performance of polycrystalline ceramics for optical applications. Here we present a study on the influence of grain boundaries on the mechanical and thermal properties of translucent, photoluminescent rare-earth-doped aluminum nitride (RE:AlN). The ceramics were CAPAD processed under various conditions and with varying Tb dopant concentrations such that they had different grain sizes (and thus different concentration of grain boundaries) and different degrees of dopant segregation at the grain boundaries. The relevant properties examined are hardness, fracture toughness, thermal conductivity and the thermal shock resistance figure of merit. We find that all properties are affected by grain boundaries and/or dopant segregation. However, the thermal conductivity is significantly more affected than the mechanical properties, and therefore dominates the thermal shock performance. The thermal conductivity is strongly impacted by grain boundary scattering (made stronger by dopant segregation) at all temperatures, with Umklapp scattering also important at higher temperatures.
2. Experimental procedure 2.1. Powder processing All samples discussed in this paper were processed from commercially available aluminum nitride (97% purity as AlN, 1–2 lm particle size, Tokuyama Co., Japan) and rare earth powders (99.9% purity (REO) 40 mesh Tb powder, Alfa Aesar, USA) using CAPAD. The samples discussed in this paper were made from powders in three different conditions: as-received powders, low-energy ball-milled (LEBM) powders and powders milled with high-energy planetary ball milling (HEBM). Tb dopants were added either as pure Tb metal or as TbN (nitride synthesis described below). The dopant powders were mixed with AlN using either LEBM or HEBM. For HEBM, powders were planetary ball milled under argon using a Fritsch Pulverisette 7 premium line. The high-energy milling parameters were a ball:powder mass ratio of 10:1, at 450 rpm for 3 h. Either pure Tb or TbN was used as the dopant source. In order to synthesize TbN, Tb powder was nitrided in a tube furnace at 600 °C for 6 h under flowing nitrogen. The Tb was loaded into the furnace tube under an argon atmosphere and sealed before transfer to the furnace, initiating nitrogen flow and subsequent heating. The dopant concentrations, dopant source and ball milling method are available in Table 1. 2.2. CAPAD processing For consolidation using CAPAD, powders were loaded into a graphite die and plunger set under an argon atmosphere in an inert atmosphere glovebox. The die and plunger assembly was then loaded into our custom-built CAPAD apparatus. Once the sample was in the CAPAD, a mechanical vacuum was applied before processing took place. Densification was conducted using 105 MPa of applied pressure and a heating rate of approximately 500 °C min1. The maximum hold temperature was 1700 °C, and the processing times were less than 15 min.
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3. Characterization and property measurement 3.1. Microstructural characterization The relative density of the samples was measured using the Archimedes method. The microstructure of the samples was characterized using a Philips FEG30 scanning electron microscope (SEM) with both secondary (SE) and backscatter electron (BSE) detectors, for topography and phase distribution, respectively. Samples were also characterized for phase using a BrukerD8 Advance X-ray diffractometer with Cu Ka radiation. Samples were characterized for grain size by measuring individual grains on SEM micrographs using ImageJ. The results reported are averages of at least 100 grain measurements. 3.2. Measurement of hardness and fracture toughness via Vickers indentation AlN and Tb:AlN samples to be tested by Vickers indentation were wet polished with successively finer grits of diamond abrasive wheels followed by alumina paste on felt wheels to 0.5 lm abrasive particle size. Vickers indentations were made on a Wilson Tukon 2100 using an F = 10 kgF indentation force. Under these indentation conditions, uniform easily measureable indents and cracks were produced. In addition, we measured two commercially available materials, laser-quality single-crystal Nd:YAG (1.1% Nd) and undoped, polycrystalline AlN (Coorstek AlN 170). The indents used for hardness and fracture toughness measurements on Nd:YAG were made using F = 0.25 kgF indentation force since they shatter using an F = 10 kgF indentation force. An example of the indents produced from Vickers indentation of our Tb:AlN samples can be seen in Fig. 1. A micrograph of an indent on Nd:YAG is included for comparison. The indent diagonals and crack lengths were measured using an optical microscope, and the Vickers hardness was then calculated using the relation:
HV ¼
ðF Þ 2 sinð136 =2Þ ð2aÞ2
1:8544F ð2aÞ2
ð2Þ
where F is the applied load in kgf and 2a is the average length of the diagonal in mm. The mode 1 fracture toughness, KIC, was calculated using the indentation procedure described above and the Niihara relation as described in Ref. [14], with data measured using the indentation procedure described as follows: 12 3 l 1 2 3 5 5 2 K IC ¼ 0:035a E HV /5 ð3Þ a where a is the half diagonal, l is the crack length and / is the constraint factor. / = 3 [14] and E = 308 GPa [19] were used. The values of KIC and HV listed in Table 1 were calculated from averages of at least 10 Vickers indents. 3.3. Thermal conductivity measurement Due to the significant influence of thermal conductivity on the power limits of laser host materials (Eq. (1)), it is important to understand the influence of microstructure (both grain size and grain boundary cleanliness) and dopant concentration on the thermal conductivity of RE-doped AlN. A standard 3x method [15] was used to measure the
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Table 1. Summary of measured characteristics and properties for five AlN samples CAPAD processed using different doping and ball milling conditions. Sample
Processing parameters (at.%/dopant source/ milling energy)
Grain size (lm)
Vickers hardness, kgf HV ðmm 2Þ
Fracture toughness, 1 KIC ðMPa m2 Þ
Thermal conductivity, W k @ 310 K ðmK Þ
Thermal shock parameter, Rs ðWm Þ
1 2 3 4 5
None 0.25Tb(H) 0.25TbN(H) 0.5TbN(H) 0.5TbN(L)
2.6 4.2 4.7 4.3 3.3
1154 1136 1045 1150 1180
5.03 (1.5) 4.35 (1.1) 4.82 (0.7) 4.35 (0.35) 4.2 (0.25)
60 77 91 94 75
36000 (11000) 39000 (9800) 52000 (7500) 48000 (3800) 38000 (2200)
(52) (49) (91) (31) (44)
The values in parentheses are the standard deviations of the measurements in the same units as the measurements. Samples are grouped by dopant concentration. In the processing parameters, H refers to HEBM and L to LEBM.
3.4. Thermal shock figure of merit As mentioned above, the tolerance of a material to thermal gradients can be described by the parameter Rs, as given by Eq. (1). The fracture stress was not measured in this study; instead, we used the measured indent KIC values and the following equation in order to approximate the fracture stress: rf ¼
K IC 1
ðpcÞ2
ð4Þ
where c is the maximum flaw size. We used a conservative value of c = 20 lm (4 times the average grain size) for the maximum flaw size. These approximate fracture stresses along with measured thermal conductivity, k (at 310 K), were used to calculate the thermal shock figure of merits using Eq. (1). In the calculation, we used a = 2.7 106 K1, E = 308 GPa and m = 0.22 [19]. The following values were used for the comparison Nd:YAG sample a = 7.9 106 K1, E = 280 GPa and m = 0.25 [20].
4. Results and discussion Fig. 1. Examples of indents and the corresponding cracks that resulted from Vickers indentation in the various samples reported here. The crosshairs from the filar eyepiece on the microscope are also visible in some cases. (a) Single-crystal Nd:YAG with indentation force F = 0.25 kgF, showing distinct cracks. (b) Tb:AlN with indentation force F = 0.25 kgF, showing very minor cracks. (c) Tb:AlN with indentation force F = 10 kgF.
thermal conductivity of these samples. A narrow gold line was deposited on the well-polished surface of each sample using standard microfabrication techniques. Each heater line was 10 lm wide, 250 nm thick (including a thin chromium adhesion layer) and patterned in a four-point probe configuration with 1 mm between the inner voltage probes. There was no need for a dielectric insulation layer between the heater line and the substrate because AlN itself is an electrical insulator, as further confirmed by probing with a multimeter on each sample. The thermal wavelengths used are at least 40 lm, ensuring that this measurement yields an effective average thermal conductivity over many grains. Measurements were conducted in a high-vacuum cryostat over a temperature range from 80 to 310 K (up to 475 K for two samples).
4.1. Microstructural characterization The percent theoretical density of all the samples in this study as measured by the Archimedes method was 99+%. Fig. 2 shows X-ray diffraction patterns of various samples in the study. It is important to note that, despite the dopant additions, all of the X-ray diffractometry (XRD) peaks correspond to AlN, indicating that no X-ray-detectable phases are formed when adding Tb or TbN at this level (at most 0.5 at.%). This is in contrast to previous results, where significantly higher concentrations (5 wt.%) of RE additions to AlN led to the formation of RE–Al–O ternary phases [12]. Fig. 3 shows representative micrographs of CAPADconsolidated samples, taken with an SE detector in the top row and with a BSE detector in the bottom row. SEM characterization reveals that the grains of all samples are approximately equiaxed. A comparison between the four different samples in Fig. 3 clearly illustrates the influence of both milling energy and dopant type selection (Tb or TbN) on the microstructure of the consolidated samples. Sample 2 (Fig. 3a and b) was doped with 0.25 at.% Tb and milled with high-energy planetary ball milling. It can be seen that a small amount of dopant has segregated to the
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Fig. 2. XRD patterns for the five samples discussed. All of the peaks correspond to hexagonal AlN and are marked with a red dot. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 3. BSE and SE micrographs showing the influence of dopant source selection and milling on the microstructure of consolidated samples. Sample 2 (high-energy planetary ball milled, 0.25 at.% Tb) shows a small amount of dopant segregation. In sample 3 (planetary ball milled, 0.25 at.% Tb as TbN), almost no dopant segregation is visible. In sample 4 (planetary ball milled 0.5 at.% Tb as TbN), there is very little dopant segregation at the grain boundaries. Sample 5 (low-energy ball milled, 0.5 at.% Tb as TbN) has significant amounts of dopant segregated at the grain boundaries.
grain boundaries. Sample 3 (Fig. 3c and d) received the same concentration of Tb and the same milling conditions, the only difference being that the dopant source in sample 3 was TbN rather than Tb. The micrographs reveal that using TbN instead of Tb as the dopant source causes significantly less segregation at the grain boundaries. This is explained by AlN and TbN having the same metal-to-nitrogen stoichiometry. The Al atoms that are displaced when Tb is doped onto Al lattice sites can combine with N to form more AlN. In the pure Tb metal case, the displaced Al atoms presumably have to segregate to grain boundaries. Having observed the influence of dopant source on the segregation of dopants to the grain boundary, we can compare the influence of milling on segregation. Samples 4 and 5 were both doped with 0.5 at.% Tb as TbN. Sample 4
(Fig. 3e and f) was milled with high-energy planetary ball milling, while sample 5 (Fig. 3g and h) was milled with low-energy ball milling. The influence of milling energy is very clearly evident in the significantly greater dopant segregation observed in sample 5, i.e. high-energy milling causes less segregation. 4.2. Mechanical properties Table 1 lists the samples tested, dopants and concentrations, and a summary of the properties observed for AlN and Tb:AlN samples. The results reveal that, despite significant differences in grain size and dopant segregation, the hardness and indent fracture toughness values are actually quite similar. As discussed in detail below, we believe that grain boundaries and segregation do not significantly alter
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the crack propagation or plastic flow of the samples, implying that grain boundaries have similar mechanical properties whether or not they have significant dopant segregation. Fig. 4 shows Vickers hardness (HV) (Fig. 4a) plotted vs. grain size. The hardness values range from 1045 to 1180 kgF mm2. Overall there is a 12% difference in hardness between the sample with the highest hardness (sample 5) and the lowest (sample 3). It should be noted that the hardness does not follow a Hall–Petch (d1/2) trend. Four of the samples (1, 2, 4 and 5) have virtually identical hardness (only 3% difference) despite nearly a doubling in grain size. The degree of dopant segregation also does not play a significant role. For example, samples 4 and 5 have drastically different dopant segregation (see Fig. 3), yet the change in hardness is only minimal. Thus there is no significant effect of grain size and/or dopant segregation on hardness. The single-crystal Nd:YAG and polycrystalline commercial AlN we measured for comparison had respective hardnesses of 1745 and 1152 kgF mm2. The results show that our samples are similar to the commercial. Fig. 5 shows the indent fracture toughness, KIC, vs. grain size. Similar to hardness, the changes are not large (ranging from 4.2 to 5.0 MPam0.5); there is only a 16% change for KIC. The undoped AlN (sample 1) has the smallest grain size and the highest fracture toughness. The doped samples appear to have an opposite trend, i.e. the KIC increases with increasing grain size. However, as mentioned previously, the changes are minor. The commercial Nd:YAG we measured for comparison had an indent fracture toughness of 1.35 MPam0.5. This value is similar to the previously reported indent fracture toughness measurement on YAG single crystals of 1.48 MPam0.5 [20]. The measured value for commercial AlN was 4.45 MPam0.5, which falls in the range of our samples, indicating that the AlN and Tb:AlN measured in our samples are similar to high-quality commercial AlN. We believe that the similar fracture toughnesses observed in all samples despite the large difference in grain sizes and grain boundary segregation is due to similar crack propagation. Evidence of similar crack patterns is provided in Fig. 6, which shows both SE and BSE scanning electron micrographs of two Tb:AlN samples processed under dif-
Fig. 4. Vickers hardness values vs. grain size for AlN and Tb:AlN samples.
Fig. 5. Indent fracture toughness values vs. grain size for AlN and Tb:AlN samples.
Fig. 6. SEM micrographs of cracks resulting from microindentation in samples with very different amounts of dopant segregation (sample 4, a and b) and sample 5 (c and d). Grain boundaries have been highlighted in yellow to help better visualize the mixed inter/intra-granular crack path. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
ferent conditions. Fig. 6a and b are sample 4 and Fig. 6c and d are sample 5. In both samples we observe inter-granular as well as intra-granular fracture, i.e. it can be seen that the crack passes through several grains and also follows grain boundaries in some places. This can be clearly observed in both samples; however, because of the greater dopant segregation in Fig. 6c and d, the grain boundaries are more evident. Selected grain boundaries are outlined in yellow to make them more visible. Crack propagation is related to the work needed to create new free surfaces. If a crack is propagating through a completely isotropic medium, the crack will propagate as a straight line, since there are no microstructural features to divert it. AlN has a hexagonal structure that could lead to crack deflection in a randomly oriented ceramic, since fracture energies are expected to be different along different crystallographic directions. The anisotropic nature of crack
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propagation could be compounded by anisotropic residual stresses in hexagonal AlN. In addition, dopant segregation at grain boundaries could divert the crack. Crack deflection usually increases the fracture toughness, since there is an overall larger surface area created. In other words, the higher the ratio of the surface area created by a tortuous crack to a straight crack (Ator/Ao), the higher the fracture toughness. If we assume that the crack widths, w (the penetration depth perpendicular to the crack propagation direction), are the same for the various samples, then a measure of crack tortuosity can be given by the ratio of the total crack path length, ltot, to the crack path length of an undeflected crack (nominal crack length), L. Fig. 7 is a schematic showing the relationships between the deflection angles, h, the crack path segments, l, the total crack path length, ltot, and the nominal crack length, L. The area ratio and length ratios can be related to path lengths and average deflection angle, h, as follows: Ator wltot ltot 1 ¼ ¼ Ao wL h=2 ltot sinh=2 sin
ð5Þ
In order to compare the geometry of the crack paths quantitatively, we examined sections of indentationinduced cracks. We chose samples with large differences in dopant segregation for examination. For each sample, the crack segments, lengths and deflection angles were measured. The total crack path length is given by the sum of all crack segments, measured as: n X ltot ¼ li ð6Þ i¼1
where n is the number of segments. The average crack segment length is given by: Pn l ¼ i¼1 li ð7Þ n Similarly, the average deflection angle is given by: Pm hi h ¼ i¼1 ð8Þ m where m is the number of angles measured. Finally, the ratio of the total crack length to the crack path length of an undeflected crack (ltot/L) can be compared. These results are summarized in Table 2. The average path segment length l varies between the samples from 2.5 to 3.4 lm. However, despite the large differences in dopant segregation, the average path length to crack length ratios (ltot/L) are very similar for the three types of samples. Moreover, the average deflection angles measured are almost identical and very close to 120°. These measurements confirm that the crack tortuosity is very similar in all three samples, indicating that dopant segregation at grain boundaries in Tb:AlN does not affect crack prop-
Fig. 7. Schematic of crack tortuosity measurement methodology.
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h ¼ 120 in agation. It is interesting to note that, using Eq. (5), one gets 1.15, which is remarkably close to the measured values of (ltot/L), which range from 1.09 to 1.12. As mentioned above, toughness is expected to be related to crack tortuosity and, since the (ltot/L) ratio is a measure of crack tortuosity, it is not surprising that the samples have similar fracture toughnesses. Thus, we conclude that, despite notable differences in dopant segregation, the samples have similar fracture toughness because the cracks have similar tortuosity. 4.3. Thermal conductivity The measured thermal conductivities k of all five samples are given in Fig. 8. The data transition from increasing to decreasing k(T) trends, with the peaks occurring in the range from 160 to 250 K. The thermal conductivity results reveal a much stronger dependence on sample microstructures than the mechanical properties – there is a 56% difference between samples at 310 K and an almost 100% change at peak. As discussed below, the data can be explained by considering grain boundary scattering as well as segregation at grain boundaries. These measurements are all much lower than what is expected for pure, single-crystal AlN, which, according to Slack et al. [16], decreases monotonically from around 9000 W m1 K1 at 80 K to 135 W m1 K1 at 500 K (assuming a 5.4 mm sample diameter). The basic trends of Fig. 8 are consistent with strong thermal conductivity reduction by grain boundary scattering of phonons, which in the low-temperature limit usually corresponds to k(T) power laws ranging from T2 to T3 [17], becoming constant at high T. The importance of grain boundary scattering in these samples is reinforced by Fig. 9, which shows that the thermal conductivity generally increases with the average grain size, although there is also substantial scatter among the different samples. In addition, the decreasing k(T) trend at higher T is a well-known signature of Umklapp scattering, and impurity scattering may also play a role near the peak. It is noteworthy that the observed reductions in thermal conductivity in Figs. 8 and 9 are much stronger than those predicted by Slack et al. [16] for a 1 lm grain boundary scattering length and allowing for oxygen impurities (4.2 1019 cm3, or 0.04 at.%). Those calculations found the micron-grained sample to be virtually indistinguishable from the equivalent bulk sample above 200 K (at which point k = 540 W m1 K1), with both decreasing to around 125 W m1 K1 at 500 K. At lower temperatures the calculation for the 1 lm polycrystal diverges from the bulk sample, with the former exhibiting a peak of around 730 W m1 K1 at 120 K. Thus, simple grain boundary scattering as considered in Ref. [16] cannot explain our measurements, since the present samples have larger grains (2–5 lm, as compared to 1 lm) yet much lower thermal conductivities, by factors ranging from 2 to more than 10. Our samples may also be expected to experience stronger impurity scattering than considered in Ref. [16] due to the larger dopant concentrations (0.25–0.5 at.% Tb), but no amount of impurity (Rayleigh) scattering can explain the limiting trends of Fig. 8 at both low and high T. Instead, to understand these measurements, it is essential to recognize that dopant segregation at the grain boundaries dramatically increases the strength of grain boundary scattering for a fixed grain size. A similar effect
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Table 2. Summary of crack tortuosity measurements for three samples. Sample Average deflection angle, h (degrees) 1 4 5
119.5 (20.2) 123.9 (20.1) 118.0 (20.5)
Average segment length, l (lm)
ltot/L
3.42 (1.2) 3.96 (2.5) 2.52 (0.8)
1.12 (0.04) 1.09 (0.05) 1.11 (0.08)
Measurements were made according to Eqs. (6–8) and Fig. 7. The values in parentheses are the standard deviations of the measurements in the same units as the measurements.
Fig. 8. Temperature-dependent thermal conductivity of AlN and Tb:AlN samples.
dopant concentration of 0.25 at.% Tb. However, the micrographs in Fig. 3 show that sample 2 has more dopant segregation at the grain boundaries, and thus is expected to have lower thermal conductivity, consistent with the measurements in Fig. 8. Overall, the thermal conductivity of these samples is best understood as being in a mixed regime, with strong grain boundary scattering (as modified by dopant segregation) at all temperatures and Umklapp scattering also being important at higher temperatures. 4.4. Thermal shock figure of merit
Fig. 9. Measured thermal conductivity as a function of grain size, for two selected temperatures. Lines are straight-line fits passing through the origin, which is the limiting behavior expected if grain boundary scattering dominates.
has been reported by Watari et al. [18]. For example, samples 2 and 3 have similar grain sizes and the same nominal
Thermal shock is an important cause of failure in ceramics since they are typically used in high-temperature applications. Thus the causes of thermal shock, as well as methods to evaluate thermal shock performance, have been well studied [21,22]. One common test condition is based on quenching samples from elevated temperature in water or oil. Alternatively, the samples can be cooled by impinging a fluid jet onto a sample at elevated temperature. These tests rely on the accurate measurement of a thermal gradient and thus are reliable for large samples. The opticalquality ceramics produced in this study are considerably smaller than those typically used for structural applications, making accurate measurement of thermal gradients significantly more challenging. Considering the challenges, we use the thermal shock figure of merit Rs described in Eq. (1) to compare our samples. This figure of merit can be thought of as describing the
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ability of a material to tolerate thermal loading while maintaining a thermal gradient smaller than that required to induce fracture. This parameter has been plotted against grain size in Fig. 10 for each sample tested. Since the indent fracture toughness, KIC, is relatively constant across the samples examined in this study but thermal conductivity varies significantly, we find that the changes in Rs are dominated by the thermal conductivity and show a strong grain size dependence. In addition, our figure of merit allows us to compare the thermal loading tolerance of different laser host materials. Nd:YAG has been reported to have an Rs value of 790 W m1 [1]. The figure of merit calculated in this work using the same procedure as Tb:AlN for Nd:YAG has a value of Rs = 812 W m1, which is very close to previously report value. Fig. 11 compares the Rs value obtained in this work with that of a well-known laser host material. In contrast, the highest calculated Rs from the measurements conducted on Tb:AlN was 52,000 W m1. This high tolerance to thermal shock should allow much more aggressive pumping of an AlN host without damaging the material.
5. Summary We used CAPAD to produce Tb:AlN ceramics with varying grain sizes and dopant segregations. All samples had similar hardness (within 12%) and fracture toughness (within 16%) regardless of grain size and dopant segregation. We attribute the similar toughness results to similar crack morphology (i.e. tortuosity). Measurements revealed that thermal conductivity had a much stronger dependence on sample microstructures than did the mechanical properties – a 56% difference between samples at 310 K and an almost 100% change at peak. The thermal conductivity at room temperature and above is limited by grain boundary scattering (made stronger by dopant segregation) and Umklapp scattering. We used the fracture toughness and thermal conductivity results to calculate thermal shock resistance figures of merit for the samples. The highest value for Tb:AlN was 52,000 W m1, which is 64 times that of the state-of-the-
Fig. 10. Thermal shock figure of merit as a function of grain size. Values of k measured at 310 K were used.
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Fig. 11. Comparison of thermal shock figure of merit (Rs) values calculated from measurements for single-crystal Nd:YAG and Tb:AlN (sample 4).
art laser gain material Nd:YAG. This high figure of merit shows that RE:AlN can potentially be pumped much more aggressively, leading to a dramatic increase in the energy output of a laser based on RE:AlN ceramics. Acknowledgements We gratefully acknowledge the funding of this work by a multidisciplinary research initiative (MRI) from the High Energy Lasers – Joint Technology Office (HEL-JTO) administered by the Army Research Office.
References [1] W. Koechner, Solid-State Laser Engineering, Springer, New York, 2006. [2] A. Ikesue, Y.L. Aung, Nat. Photonics 2 (2008) 721. [3] A. Ikesue, Y.L. Aung, T. Taira, T. Kamimura, K. Yoshida, G.L. Messing, Annu. Rev. Mater. Res. 36 (2006) 397. [4] Y. Kodera, C.L. Hardin, J.E. Garay, Scr. Mater. 69 (2013) 149. [5] L. An, A. Ito, T. Goto, J. Eur. Ceram. Soc. 31 (2011) 1597. [6] H. Zhang, B. Kim, K. Morita, H. Yoshida, K. Hiraga, Y. Sakka, J. Eur. Ceram. Soc. 94 (2011) 3206. [7] J.R. Morales, N. Amos, S. Khizroev, J.E. Garay, J. Appl. Phys. 109 (2011) 093110. [8] E.H. Penilla, Y. Kodera, J.E. Garay, Mater. Sci. Eng. B 177 (2012) 1172. [9] G.R. Castillo-Vega, E.H. Penilla, S. Camacho-Lo´pez, G. Aguilar, J.E. Garay, Opt. Mater. Express 2 (2012) 1416. [10] A.T. Wieg, Y. Kodera, Z. Wang, T. Imai, C. Dames, J.E. Garay, Appl. Phys. Lett. 101 (2012) 111903. [11] E.H. Penilla, Y. Kodera, J.E. Garay, Adv. Funct. Mater. 23 (2013) 6036. [12] R. Terao, J. Tatami, T. Meguro, K. Komeya, J. Eur. Ceram. Soc. 22 (2002) 1051. [13] Y.D. Yu, A.M. Hundere, R. Hoier, R.E. Dunin-Borkowski, M.A. Einarsrud, J. Eur. Ceram. Soc. 22 (2002) 247. [14] K. Niihara, R. Morena, D.P.H. Hasselman, J. Mater. Sci. Lett. 1 (1982) 13. [15] D.G. Cahill, Rev. Sci. Instrum. 61 (1990) 802. [16] G.A. Slack, R.A. Tanzilli, R.O. Pohl, J.W. Vandersande, J. Phys. Chem. Solids 48 (1987) 641.
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[17] Z. Wang, J.E. Alaniz, W. Jang, J.E. Garay, C. Dames, Nano Lett. 11 (2011) 2206. [18] K. Watari, H. Nakano, K. Urabe, K. Ishizaki, S. Cao, K. Mori, J. Mater. Res. 17 (2002) 2940. [19] D. Gerlich, S.L. Dole, G.A. Slack, J. Phys. Chem. Solids 47 (1986) 437.
[20] L. Mezeix, D.J. Green, Int. J. Appl. Ceram. Technol. 3 (2006) 166. [21] D.P.H. Hasselman, J. Am. Ceram. Soc. 52 (1969) 600. [22] K.T. Faber, M.D. Huang, A.G. Evans, J. Am. Ceram. Soc. 64 (1969) 296.
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Thermomechanical properties of rare-earth-doped AlN for laser gain media: The role of grain boundaries and grain size ⇑
A.T. Wieg,a Y. Kodera,a Z. Wang,a,b C. Damesb and J.E. Garaya, a
Department of Mechanical Engineering and Materials Science & Engineering Program, University of California, Riverside, CA, USA b Department of Mechanical Engineering, University of California, Berkeley, CA, USA Received 13 May 2014; revised 18 October 2014; accepted 30 November 2014
Abstract—The low thermal conductivity and poor fracture toughness of traditional laser gain media (rare-earth-doped single crystals) limits the overall power deliverable from a laser system. We present an investigation of the thermomechanical properties of a promising laser gain candidate, Tbdoped aluminum nitride (Tb:AlN). We pay special attention to the effect of the average grain size and the dopant segregation at the grain boundaries on the relevant properties: Vickers hardness, fracture toughness and thermal conductivity. We find that all properties are affected by grain boundaries and/or dopant segregation. However, the thermal conductivity is significantly more affected than the mechanical properties and therefore dominates the thermal shock figure of merit, Rs. We obtained a thermal shock figure of merit in Tb:AlN more than 60 times that of the state-of-the-art laser gain material Nd:YAG. Ó 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Transparent ceramics; Spark plasma sintering (SPS); Current-activated pressure-assisted densification (CAPAD); Thermal conductivity; Indent fracture toughness
1. Introduction Thermal management continues to be a significant problem in the design of high-performance, high-energy lasers. For instance, thermal gradients in laser gain materials can lead to performance issues such as thermal lensing and ultimately irreparable failure through thermal shock. A gain material with high thermal conductivity will be able to dissipate more heat, reducing thermal gradients and thus producing more laser power for a given pumping–cooling scheme. Similarly, materials with high fracture toughness can tolerate higher thermal stresses before failure. Thus, the important design criterion for maximizing laser energy is dependent on both mechanical and thermal properties of the gain material, with a thermal shock resistance figure of merit given by [1]: kð1 mÞ rF ð1Þ aE where rF is the fracture stress, k is the thermal conductivity, E is Young’s modulus, a is the coefficient of thermal expansion and m is Poisson’s ratio. Traditionally, laser gain materials like Nd:YAG have been single crystals with relatively low thermal conductivity Rs ¼
⇑ Corresponding author. Tel.: +1 9518272449; e-mail: jegaray@engr. ucr.edu
and low toughness. Polycrystalline ceramics are often tougher than single crystals, but can suffer from inferior optical properties (because of scattering at pores and grain boundaries). This optical property challenge has been alleviated by the advent of advanced processing procedures. For example, Ikesue and others [2,3] have shown that slope efficiencies of polycrystalline ceramics are on a par with single crystals. Recently, current-activated pressure-assisted densification (CAPAD) has been receiving considerable attention for processing optical ceramics [4–9]. A clear advantage of CAPAD is that fast processing kinetics can create metastable phases that are not possible with singlecrystal growing techniques or pressureless sintering. We recently demonstrated over-equilibrium doping of active rare-earth (RE) elements, leading to luminescence in the AlN [10] and Al2O3 [11] systems. Since the thermal conductivity and fracture toughness of these ceramics are inherently higher than the state-of-the-art laser gain material Nd:YAG, metastable RE:Al2O3 and RE:AlN hold significant promise for next-generation high-energy lasers. As alluded to above, extended defects like grain boundaries can dominate the optical, thermal and mechanical properties of ceramics. The effects of grain boundary phases in AlN with RE additions have been reported [12,13], but in these cases the goal was to make tough, highly thermally conductive AlN ceramics, not photoluminescent, light-transmitting ceramics. Thus high concentrations (5 wt.%) of RE oxides were added. Very little
http://dx.doi.org/10.1016/j.actamat.2014.11.045 1359-6462/Ó 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
A.T. Wieg et al. / Acta Materialia 86 (2015) 148–156
attention has been given to microstructural features that influence the thermomechanical performance of polycrystalline ceramics for optical applications. Here we present a study on the influence of grain boundaries on the mechanical and thermal properties of translucent, photoluminescent rare-earth-doped aluminum nitride (RE:AlN). The ceramics were CAPAD processed under various conditions and with varying Tb dopant concentrations such that they had different grain sizes (and thus different concentration of grain boundaries) and different degrees of dopant segregation at the grain boundaries. The relevant properties examined are hardness, fracture toughness, thermal conductivity and the thermal shock resistance figure of merit. We find that all properties are affected by grain boundaries and/or dopant segregation. However, the thermal conductivity is significantly more affected than the mechanical properties, and therefore dominates the thermal shock performance. The thermal conductivity is strongly impacted by grain boundary scattering (made stronger by dopant segregation) at all temperatures, with Umklapp scattering also important at higher temperatures.
2. Experimental procedure 2.1. Powder processing All samples discussed in this paper were processed from commercially available aluminum nitride (97% purity as AlN, 1–2 lm particle size, Tokuyama Co., Japan) and rare earth powders (99.9% purity (REO) 40 mesh Tb powder, Alfa Aesar, USA) using CAPAD. The samples discussed in this paper were made from powders in three different conditions: as-received powders, low-energy ball-milled (LEBM) powders and powders milled with high-energy planetary ball milling (HEBM). Tb dopants were added either as pure Tb metal or as TbN (nitride synthesis described below). The dopant powders were mixed with AlN using either LEBM or HEBM. For HEBM, powders were planetary ball milled under argon using a Fritsch Pulverisette 7 premium line. The high-energy milling parameters were a ball:powder mass ratio of 10:1, at 450 rpm for 3 h. Either pure Tb or TbN was used as the dopant source. In order to synthesize TbN, Tb powder was nitrided in a tube furnace at 600 °C for 6 h under flowing nitrogen. The Tb was loaded into the furnace tube under an argon atmosphere and sealed before transfer to the furnace, initiating nitrogen flow and subsequent heating. The dopant concentrations, dopant source and ball milling method are available in Table 1. 2.2. CAPAD processing For consolidation using CAPAD, powders were loaded into a graphite die and plunger set under an argon atmosphere in an inert atmosphere glovebox. The die and plunger assembly was then loaded into our custom-built CAPAD apparatus. Once the sample was in the CAPAD, a mechanical vacuum was applied before processing took place. Densification was conducted using 105 MPa of applied pressure and a heating rate of approximately 500 °C min1. The maximum hold temperature was 1700 °C, and the processing times were less than 15 min.
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3. Characterization and property measurement 3.1. Microstructural characterization The relative density of the samples was measured using the Archimedes method. The microstructure of the samples was characterized using a Philips FEG30 scanning electron microscope (SEM) with both secondary (SE) and backscatter electron (BSE) detectors, for topography and phase distribution, respectively. Samples were also characterized for phase using a BrukerD8 Advance X-ray diffractometer with Cu Ka radiation. Samples were characterized for grain size by measuring individual grains on SEM micrographs using ImageJ. The results reported are averages of at least 100 grain measurements. 3.2. Measurement of hardness and fracture toughness via Vickers indentation AlN and Tb:AlN samples to be tested by Vickers indentation were wet polished with successively finer grits of diamond abrasive wheels followed by alumina paste on felt wheels to 0.5 lm abrasive particle size. Vickers indentations were made on a Wilson Tukon 2100 using an F = 10 kgF indentation force. Under these indentation conditions, uniform easily measureable indents and cracks were produced. In addition, we measured two commercially available materials, laser-quality single-crystal Nd:YAG (1.1% Nd) and undoped, polycrystalline AlN (Coorstek AlN 170). The indents used for hardness and fracture toughness measurements on Nd:YAG were made using F = 0.25 kgF indentation force since they shatter using an F = 10 kgF indentation force. An example of the indents produced from Vickers indentation of our Tb:AlN samples can be seen in Fig. 1. A micrograph of an indent on Nd:YAG is included for comparison. The indent diagonals and crack lengths were measured using an optical microscope, and the Vickers hardness was then calculated using the relation:
HV ¼
ðF Þ 2 sinð136 =2Þ ð2aÞ2
1:8544F ð2aÞ2
ð2Þ
where F is the applied load in kgf and 2a is the average length of the diagonal in mm. The mode 1 fracture toughness, KIC, was calculated using the indentation procedure described above and the Niihara relation as described in Ref. [14], with data measured using the indentation procedure described as follows: 12 3 l 1 2 3 5 5 2 K IC ¼ 0:035a E HV /5 ð3Þ a where a is the half diagonal, l is the crack length and / is the constraint factor. / = 3 [14] and E = 308 GPa [19] were used. The values of KIC and HV listed in Table 1 were calculated from averages of at least 10 Vickers indents. 3.3. Thermal conductivity measurement Due to the significant influence of thermal conductivity on the power limits of laser host materials (Eq. (1)), it is important to understand the influence of microstructure (both grain size and grain boundary cleanliness) and dopant concentration on the thermal conductivity of RE-doped AlN. A standard 3x method [15] was used to measure the
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Table 1. Summary of measured characteristics and properties for five AlN samples CAPAD processed using different doping and ball milling conditions. Sample
Processing parameters (at.%/dopant source/ milling energy)
Grain size (lm)
Vickers hardness, kgf HV ðmm 2Þ
Fracture toughness, 1 KIC ðMPa m2 Þ
Thermal conductivity, W k @ 310 K ðmK Þ
Thermal shock parameter, Rs ðWm Þ
1 2 3 4 5
None 0.25Tb(H) 0.25TbN(H) 0.5TbN(H) 0.5TbN(L)
2.6 4.2 4.7 4.3 3.3
1154 1136 1045 1150 1180
5.03 (1.5) 4.35 (1.1) 4.82 (0.7) 4.35 (0.35) 4.2 (0.25)
60 77 91 94 75
36000 (11000) 39000 (9800) 52000 (7500) 48000 (3800) 38000 (2200)
(52) (49) (91) (31) (44)
The values in parentheses are the standard deviations of the measurements in the same units as the measurements. Samples are grouped by dopant concentration. In the processing parameters, H refers to HEBM and L to LEBM.
3.4. Thermal shock figure of merit As mentioned above, the tolerance of a material to thermal gradients can be described by the parameter Rs, as given by Eq. (1). The fracture stress was not measured in this study; instead, we used the measured indent KIC values and the following equation in order to approximate the fracture stress: rf ¼
K IC 1
ðpcÞ2
ð4Þ
where c is the maximum flaw size. We used a conservative value of c = 20 lm (4 times the average grain size) for the maximum flaw size. These approximate fracture stresses along with measured thermal conductivity, k (at 310 K), were used to calculate the thermal shock figure of merits using Eq. (1). In the calculation, we used a = 2.7 106 K1, E = 308 GPa and m = 0.22 [19]. The following values were used for the comparison Nd:YAG sample a = 7.9 106 K1, E = 280 GPa and m = 0.25 [20].
4. Results and discussion Fig. 1. Examples of indents and the corresponding cracks that resulted from Vickers indentation in the various samples reported here. The crosshairs from the filar eyepiece on the microscope are also visible in some cases. (a) Single-crystal Nd:YAG with indentation force F = 0.25 kgF, showing distinct cracks. (b) Tb:AlN with indentation force F = 0.25 kgF, showing very minor cracks. (c) Tb:AlN with indentation force F = 10 kgF.
thermal conductivity of these samples. A narrow gold line was deposited on the well-polished surface of each sample using standard microfabrication techniques. Each heater line was 10 lm wide, 250 nm thick (including a thin chromium adhesion layer) and patterned in a four-point probe configuration with 1 mm between the inner voltage probes. There was no need for a dielectric insulation layer between the heater line and the substrate because AlN itself is an electrical insulator, as further confirmed by probing with a multimeter on each sample. The thermal wavelengths used are at least 40 lm, ensuring that this measurement yields an effective average thermal conductivity over many grains. Measurements were conducted in a high-vacuum cryostat over a temperature range from 80 to 310 K (up to 475 K for two samples).
4.1. Microstructural characterization The percent theoretical density of all the samples in this study as measured by the Archimedes method was 99+%. Fig. 2 shows X-ray diffraction patterns of various samples in the study. It is important to note that, despite the dopant additions, all of the X-ray diffractometry (XRD) peaks correspond to AlN, indicating that no X-ray-detectable phases are formed when adding Tb or TbN at this level (at most 0.5 at.%). This is in contrast to previous results, where significantly higher concentrations (5 wt.%) of RE additions to AlN led to the formation of RE–Al–O ternary phases [12]. Fig. 3 shows representative micrographs of CAPADconsolidated samples, taken with an SE detector in the top row and with a BSE detector in the bottom row. SEM characterization reveals that the grains of all samples are approximately equiaxed. A comparison between the four different samples in Fig. 3 clearly illustrates the influence of both milling energy and dopant type selection (Tb or TbN) on the microstructure of the consolidated samples. Sample 2 (Fig. 3a and b) was doped with 0.25 at.% Tb and milled with high-energy planetary ball milling. It can be seen that a small amount of dopant has segregated to the
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Fig. 2. XRD patterns for the five samples discussed. All of the peaks correspond to hexagonal AlN and are marked with a red dot. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 3. BSE and SE micrographs showing the influence of dopant source selection and milling on the microstructure of consolidated samples. Sample 2 (high-energy planetary ball milled, 0.25 at.% Tb) shows a small amount of dopant segregation. In sample 3 (planetary ball milled, 0.25 at.% Tb as TbN), almost no dopant segregation is visible. In sample 4 (planetary ball milled 0.5 at.% Tb as TbN), there is very little dopant segregation at the grain boundaries. Sample 5 (low-energy ball milled, 0.5 at.% Tb as TbN) has significant amounts of dopant segregated at the grain boundaries.
grain boundaries. Sample 3 (Fig. 3c and d) received the same concentration of Tb and the same milling conditions, the only difference being that the dopant source in sample 3 was TbN rather than Tb. The micrographs reveal that using TbN instead of Tb as the dopant source causes significantly less segregation at the grain boundaries. This is explained by AlN and TbN having the same metal-to-nitrogen stoichiometry. The Al atoms that are displaced when Tb is doped onto Al lattice sites can combine with N to form more AlN. In the pure Tb metal case, the displaced Al atoms presumably have to segregate to grain boundaries. Having observed the influence of dopant source on the segregation of dopants to the grain boundary, we can compare the influence of milling on segregation. Samples 4 and 5 were both doped with 0.5 at.% Tb as TbN. Sample 4
(Fig. 3e and f) was milled with high-energy planetary ball milling, while sample 5 (Fig. 3g and h) was milled with low-energy ball milling. The influence of milling energy is very clearly evident in the significantly greater dopant segregation observed in sample 5, i.e. high-energy milling causes less segregation. 4.2. Mechanical properties Table 1 lists the samples tested, dopants and concentrations, and a summary of the properties observed for AlN and Tb:AlN samples. The results reveal that, despite significant differences in grain size and dopant segregation, the hardness and indent fracture toughness values are actually quite similar. As discussed in detail below, we believe that grain boundaries and segregation do not significantly alter
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the crack propagation or plastic flow of the samples, implying that grain boundaries have similar mechanical properties whether or not they have significant dopant segregation. Fig. 4 shows Vickers hardness (HV) (Fig. 4a) plotted vs. grain size. The hardness values range from 1045 to 1180 kgF mm2. Overall there is a 12% difference in hardness between the sample with the highest hardness (sample 5) and the lowest (sample 3). It should be noted that the hardness does not follow a Hall–Petch (d1/2) trend. Four of the samples (1, 2, 4 and 5) have virtually identical hardness (only 3% difference) despite nearly a doubling in grain size. The degree of dopant segregation also does not play a significant role. For example, samples 4 and 5 have drastically different dopant segregation (see Fig. 3), yet the change in hardness is only minimal. Thus there is no significant effect of grain size and/or dopant segregation on hardness. The single-crystal Nd:YAG and polycrystalline commercial AlN we measured for comparison had respective hardnesses of 1745 and 1152 kgF mm2. The results show that our samples are similar to the commercial. Fig. 5 shows the indent fracture toughness, KIC, vs. grain size. Similar to hardness, the changes are not large (ranging from 4.2 to 5.0 MPam0.5); there is only a 16% change for KIC. The undoped AlN (sample 1) has the smallest grain size and the highest fracture toughness. The doped samples appear to have an opposite trend, i.e. the KIC increases with increasing grain size. However, as mentioned previously, the changes are minor. The commercial Nd:YAG we measured for comparison had an indent fracture toughness of 1.35 MPam0.5. This value is similar to the previously reported indent fracture toughness measurement on YAG single crystals of 1.48 MPam0.5 [20]. The measured value for commercial AlN was 4.45 MPam0.5, which falls in the range of our samples, indicating that the AlN and Tb:AlN measured in our samples are similar to high-quality commercial AlN. We believe that the similar fracture toughnesses observed in all samples despite the large difference in grain sizes and grain boundary segregation is due to similar crack propagation. Evidence of similar crack patterns is provided in Fig. 6, which shows both SE and BSE scanning electron micrographs of two Tb:AlN samples processed under dif-
Fig. 4. Vickers hardness values vs. grain size for AlN and Tb:AlN samples.
Fig. 5. Indent fracture toughness values vs. grain size for AlN and Tb:AlN samples.
Fig. 6. SEM micrographs of cracks resulting from microindentation in samples with very different amounts of dopant segregation (sample 4, a and b) and sample 5 (c and d). Grain boundaries have been highlighted in yellow to help better visualize the mixed inter/intra-granular crack path. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
ferent conditions. Fig. 6a and b are sample 4 and Fig. 6c and d are sample 5. In both samples we observe inter-granular as well as intra-granular fracture, i.e. it can be seen that the crack passes through several grains and also follows grain boundaries in some places. This can be clearly observed in both samples; however, because of the greater dopant segregation in Fig. 6c and d, the grain boundaries are more evident. Selected grain boundaries are outlined in yellow to make them more visible. Crack propagation is related to the work needed to create new free surfaces. If a crack is propagating through a completely isotropic medium, the crack will propagate as a straight line, since there are no microstructural features to divert it. AlN has a hexagonal structure that could lead to crack deflection in a randomly oriented ceramic, since fracture energies are expected to be different along different crystallographic directions. The anisotropic nature of crack
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propagation could be compounded by anisotropic residual stresses in hexagonal AlN. In addition, dopant segregation at grain boundaries could divert the crack. Crack deflection usually increases the fracture toughness, since there is an overall larger surface area created. In other words, the higher the ratio of the surface area created by a tortuous crack to a straight crack (Ator/Ao), the higher the fracture toughness. If we assume that the crack widths, w (the penetration depth perpendicular to the crack propagation direction), are the same for the various samples, then a measure of crack tortuosity can be given by the ratio of the total crack path length, ltot, to the crack path length of an undeflected crack (nominal crack length), L. Fig. 7 is a schematic showing the relationships between the deflection angles, h, the crack path segments, l, the total crack path length, ltot, and the nominal crack length, L. The area ratio and length ratios can be related to path lengths and average deflection angle, h, as follows: Ator wltot ltot 1 ¼ ¼ Ao wL h=2 ltot sinh=2 sin
ð5Þ
In order to compare the geometry of the crack paths quantitatively, we examined sections of indentationinduced cracks. We chose samples with large differences in dopant segregation for examination. For each sample, the crack segments, lengths and deflection angles were measured. The total crack path length is given by the sum of all crack segments, measured as: n X ltot ¼ li ð6Þ i¼1
where n is the number of segments. The average crack segment length is given by: Pn l ¼ i¼1 li ð7Þ n Similarly, the average deflection angle is given by: Pm hi h ¼ i¼1 ð8Þ m where m is the number of angles measured. Finally, the ratio of the total crack length to the crack path length of an undeflected crack (ltot/L) can be compared. These results are summarized in Table 2. The average path segment length l varies between the samples from 2.5 to 3.4 lm. However, despite the large differences in dopant segregation, the average path length to crack length ratios (ltot/L) are very similar for the three types of samples. Moreover, the average deflection angles measured are almost identical and very close to 120°. These measurements confirm that the crack tortuosity is very similar in all three samples, indicating that dopant segregation at grain boundaries in Tb:AlN does not affect crack prop-
Fig. 7. Schematic of crack tortuosity measurement methodology.
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h ¼ 120 in agation. It is interesting to note that, using Eq. (5), one gets 1.15, which is remarkably close to the measured values of (ltot/L), which range from 1.09 to 1.12. As mentioned above, toughness is expected to be related to crack tortuosity and, since the (ltot/L) ratio is a measure of crack tortuosity, it is not surprising that the samples have similar fracture toughnesses. Thus, we conclude that, despite notable differences in dopant segregation, the samples have similar fracture toughness because the cracks have similar tortuosity. 4.3. Thermal conductivity The measured thermal conductivities k of all five samples are given in Fig. 8. The data transition from increasing to decreasing k(T) trends, with the peaks occurring in the range from 160 to 250 K. The thermal conductivity results reveal a much stronger dependence on sample microstructures than the mechanical properties – there is a 56% difference between samples at 310 K and an almost 100% change at peak. As discussed below, the data can be explained by considering grain boundary scattering as well as segregation at grain boundaries. These measurements are all much lower than what is expected for pure, single-crystal AlN, which, according to Slack et al. [16], decreases monotonically from around 9000 W m1 K1 at 80 K to 135 W m1 K1 at 500 K (assuming a 5.4 mm sample diameter). The basic trends of Fig. 8 are consistent with strong thermal conductivity reduction by grain boundary scattering of phonons, which in the low-temperature limit usually corresponds to k(T) power laws ranging from T2 to T3 [17], becoming constant at high T. The importance of grain boundary scattering in these samples is reinforced by Fig. 9, which shows that the thermal conductivity generally increases with the average grain size, although there is also substantial scatter among the different samples. In addition, the decreasing k(T) trend at higher T is a well-known signature of Umklapp scattering, and impurity scattering may also play a role near the peak. It is noteworthy that the observed reductions in thermal conductivity in Figs. 8 and 9 are much stronger than those predicted by Slack et al. [16] for a 1 lm grain boundary scattering length and allowing for oxygen impurities (4.2 1019 cm3, or 0.04 at.%). Those calculations found the micron-grained sample to be virtually indistinguishable from the equivalent bulk sample above 200 K (at which point k = 540 W m1 K1), with both decreasing to around 125 W m1 K1 at 500 K. At lower temperatures the calculation for the 1 lm polycrystal diverges from the bulk sample, with the former exhibiting a peak of around 730 W m1 K1 at 120 K. Thus, simple grain boundary scattering as considered in Ref. [16] cannot explain our measurements, since the present samples have larger grains (2–5 lm, as compared to 1 lm) yet much lower thermal conductivities, by factors ranging from 2 to more than 10. Our samples may also be expected to experience stronger impurity scattering than considered in Ref. [16] due to the larger dopant concentrations (0.25–0.5 at.% Tb), but no amount of impurity (Rayleigh) scattering can explain the limiting trends of Fig. 8 at both low and high T. Instead, to understand these measurements, it is essential to recognize that dopant segregation at the grain boundaries dramatically increases the strength of grain boundary scattering for a fixed grain size. A similar effect
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Table 2. Summary of crack tortuosity measurements for three samples. Sample Average deflection angle, h (degrees) 1 4 5
119.5 (20.2) 123.9 (20.1) 118.0 (20.5)
Average segment length, l (lm)
ltot/L
3.42 (1.2) 3.96 (2.5) 2.52 (0.8)
1.12 (0.04) 1.09 (0.05) 1.11 (0.08)
Measurements were made according to Eqs. (6–8) and Fig. 7. The values in parentheses are the standard deviations of the measurements in the same units as the measurements.
Fig. 8. Temperature-dependent thermal conductivity of AlN and Tb:AlN samples.
dopant concentration of 0.25 at.% Tb. However, the micrographs in Fig. 3 show that sample 2 has more dopant segregation at the grain boundaries, and thus is expected to have lower thermal conductivity, consistent with the measurements in Fig. 8. Overall, the thermal conductivity of these samples is best understood as being in a mixed regime, with strong grain boundary scattering (as modified by dopant segregation) at all temperatures and Umklapp scattering also being important at higher temperatures. 4.4. Thermal shock figure of merit
Fig. 9. Measured thermal conductivity as a function of grain size, for two selected temperatures. Lines are straight-line fits passing through the origin, which is the limiting behavior expected if grain boundary scattering dominates.
has been reported by Watari et al. [18]. For example, samples 2 and 3 have similar grain sizes and the same nominal
Thermal shock is an important cause of failure in ceramics since they are typically used in high-temperature applications. Thus the causes of thermal shock, as well as methods to evaluate thermal shock performance, have been well studied [21,22]. One common test condition is based on quenching samples from elevated temperature in water or oil. Alternatively, the samples can be cooled by impinging a fluid jet onto a sample at elevated temperature. These tests rely on the accurate measurement of a thermal gradient and thus are reliable for large samples. The opticalquality ceramics produced in this study are considerably smaller than those typically used for structural applications, making accurate measurement of thermal gradients significantly more challenging. Considering the challenges, we use the thermal shock figure of merit Rs described in Eq. (1) to compare our samples. This figure of merit can be thought of as describing the
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ability of a material to tolerate thermal loading while maintaining a thermal gradient smaller than that required to induce fracture. This parameter has been plotted against grain size in Fig. 10 for each sample tested. Since the indent fracture toughness, KIC, is relatively constant across the samples examined in this study but thermal conductivity varies significantly, we find that the changes in Rs are dominated by the thermal conductivity and show a strong grain size dependence. In addition, our figure of merit allows us to compare the thermal loading tolerance of different laser host materials. Nd:YAG has been reported to have an Rs value of 790 W m1 [1]. The figure of merit calculated in this work using the same procedure as Tb:AlN for Nd:YAG has a value of Rs = 812 W m1, which is very close to previously report value. Fig. 11 compares the Rs value obtained in this work with that of a well-known laser host material. In contrast, the highest calculated Rs from the measurements conducted on Tb:AlN was 52,000 W m1. This high tolerance to thermal shock should allow much more aggressive pumping of an AlN host without damaging the material.
5. Summary We used CAPAD to produce Tb:AlN ceramics with varying grain sizes and dopant segregations. All samples had similar hardness (within 12%) and fracture toughness (within 16%) regardless of grain size and dopant segregation. We attribute the similar toughness results to similar crack morphology (i.e. tortuosity). Measurements revealed that thermal conductivity had a much stronger dependence on sample microstructures than did the mechanical properties – a 56% difference between samples at 310 K and an almost 100% change at peak. The thermal conductivity at room temperature and above is limited by grain boundary scattering (made stronger by dopant segregation) and Umklapp scattering. We used the fracture toughness and thermal conductivity results to calculate thermal shock resistance figures of merit for the samples. The highest value for Tb:AlN was 52,000 W m1, which is 64 times that of the state-of-the-
Fig. 10. Thermal shock figure of merit as a function of grain size. Values of k measured at 310 K were used.
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Fig. 11. Comparison of thermal shock figure of merit (Rs) values calculated from measurements for single-crystal Nd:YAG and Tb:AlN (sample 4).
art laser gain material Nd:YAG. This high figure of merit shows that RE:AlN can potentially be pumped much more aggressively, leading to a dramatic increase in the energy output of a laser based on RE:AlN ceramics. Acknowledgements We gratefully acknowledge the funding of this work by a multidisciplinary research initiative (MRI) from the High Energy Lasers – Joint Technology Office (HEL-JTO) administered by the Army Research Office.
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