Ultra-Fast Laser Fabrication of Alumina Micro-Sample Array and High-Throughput Characterization of Microstructure and Hardness

: In the light of recent advances in material informatics, there is a great demand for high-throughput approaches of sample fabrication and property characterization. Currently, no high-throughput approach has been demonstrated for the fast sampling of the microstructure and the correlated properties. In this paper, we demonstrate the ultra-fast fabrication of an alumina sample array and the high-throughput hardness characterization of these sample units. The alumina sample array was fabricated using picosecond (PS) laser micromachining and CO 2 laser sintering within a short time (i.e., less than a few minutes). After laser sintering, the hardness of these sample units was characterized using micro-indentation, and the microstructure was observed using scanning electron microscopy (SEM). In each sample unit, the microstructure was uniform for the entire top surface and within about 20 µ m depth from the top surface. The relative density (RD) and corresponding micro-hardness of the sample units was found to continuously vary over a wide range from 89% RD with 600 kgf/mm 2 hardness to 99% RD with 1609 kgf/mm 2 hardness. For these laser-sintered samples, the correlation of hardness and relative density of the alumina matched well with the literature reports on sintered alumina obtained using conventional low-throughput furnace sintering experiments.


Introduction
The correlation between microstructure and properties of ceramics has been studied for years. This is because the microstructure has a strong and deterministic effect on certain material properties [1][2][3]. For example, the grain size distribution strongly affects the conductivity of ceramic electrolyte [4][5][6] and the hardness of ceramics [7,8]. The porosity is an important factor that affects the elastic properties and hardness of ceramics [9,10] and the catalytical performance and conductivity of ceramic electrodes [11,12].
Recently, machine learning (ML)-guided materials design and prediction has attracted great attention [13][14][15][16][17][18][19][20][21][22]. For example, in our previous study, we demonstrate an ML algorithm that can predict alumina's microstructure based on the input of processing parameters [23]. One of the greatest challenges in the ML-guided materials design and prediction is the lack of consistent material's databases that contain a large quantity of data for ML training. Normally, ceramic samples are sintered in a furnace under a predetermined thermal cycle. The complete heat treatment, including heating up, isothermal soaking, and cooling down, takes several hours. Typically, each heat treatment cycle results in one unique data point in terms of the microstructure. If we want to explore a wide range of microstructures and the resultant properties, conventional furnace heat treatment is inefficient.
To effectively establish a material's database, high-throughput sample fabrication and characterization are desired. Many previous high-throughput ceramic sample fabrication methods have been demonstrated based on the combinatorial methods [24][25][26][27]. In these studies, the focus was to vary the compositions, not the microstructures, of the samples in a sample array. The sample array was typically sintered in a furnace that would take many hours. Typically, these high-throughput studies are focused on the materials whose properties are sensitive to the compositions, e.g., piezoelectric ceramics [24,25].
A high-throughput method that focuses on fast sampling in the space of microstructure has not yet been demonstrated. In our previous study, we reported the ultra-fast, selective laser sintering of alumina [28]. Due to the Gaussian distribution of the laser beam intensity, the laser-sintered alumina had a highly heterogeneous microstructure depending on the position of alumina relative to the laser beam [28]. At the center of the laser beam track, the material was sintered to a high density, and away from the center, the alumina was sintered to a relatively low density. Using this important observation of Ref. [28], in this paper, we demonstrate an experimental approach that fabricates an alumina sample array with a broad range of microstructures through picosecond (PS) laser micromachining and CO 2 laser sintering. With this approach, hundreds of samples can be quickly heat treated (i.e., within about one minute). After laser sintering, the hardness and microstructure of each sample unit were characterized using micro-indentation and scanning electron microscopy (SEM). We can effectively establish a database of a wide range of microstructures from 80 samples and their corresponding hardness. Due to the strong correlation between the hardness and the relative density of alumina [29,30], we characterized the relative densities of the laser-sintered alumina, based on the SEM micrographs. The correlation between the hardness and relative density agrees well with the literature. This validates our high-throughput approach of establishing the database of hardness and microstructure for laser-sintered alumina.

Green Alumina Paste Casting
Alumina paste was prepared by mixing 79.75 wt.% Al 2 O 3 powder (Almatis A152SG, d 50 = 1.2 µm, Purity: 99.8%, with 0.07% MgO as the sintering aid, the rest of the impurities are: 0.04% SiO 2 , 0.06% Na 2 O, 0.02% Fe 2 O 3 , and 0.05% CaO) with 0.1 wt.% dispersant (Darvan 821A) and 20.0 wt.% DI water. The suspension was ball milled for 48 h, and 0.15 wt.% binder (hydroxypropyl) methyl cellulose (HPMC) was added slowly. Finally, the mixture was mechanically blended in vacuum for 1 h to obtain the alumina paste. The alumina paste was deposited on a silica substrate with~500 µm thickness, using a doctor blade. The deposited alumina paste was dried at room temperature in air for 24 h to create the green tape.

High-Throughput Ceramic Sample Fabrication
A Picosecond Laser (APL-4000-1064, wavelength 1064 nm, Attodyne, Inc., Toronto, ON, Canada) was used to micromachine the green alumina deposition into square arrays with each unit of 400 µm × 400 µm size, shown in Figure 1. The repetition rate was set to 10 kHz, the energy per pulse was 20 µJ, and the scanning speed was 5 mm/s. The PS laser setup was the same as the setup in our previous paper [31]. In order to cut through the alumina green tape, the PS laser scanning was repeated five times. The laser micro-cutting penetrated the entire depth of alumina pastes, such that the alumina sample units were not touching each other. This micro-machined green alumna sample array was scanned using a CO 2 laser (Firestar v20, wavelength 10.6 µm, SYNRAD, Inc., Mukilteo, WA, USA), with a cylindrical lens (focal length = 1 inch, diameter 19.05 mm, Laser Mechanisms, Inc., Novi, MA, USA). The cylindrical lens resulted in a line-shaped laser beam, such that the width of the laser beam (~8 mm long) covered the entire area of the sample array when the laser scanned along the sample length of the array. The laser power was 64.5 W, and the laser scanning rate was 0.1 mm/s. These parameters are the same as those used in Ref. [28], where they are presented in detail. These parameters were shown to result in desired sintering behavior for alumina. Using this method, about one hundred alumina samples were sintered in one experiment with laser scanning. The low magnification SEM of the sample array is shown in Figure 2.
The absorptivity of alumina for the PS laser at a wavelength of 1064 nm is 3%, and for the CO 2 laser at a wavelength of 10.6 µm, it is 96% [32]. Although, alumina has low absorptivity for the PS laser, the micromachining of alumina paste using the PS laser can be well controlled, as discussed in our previous paper [31]. This is probably because the alumina paste was not sintered and was only powder compact when PS laser micromachining was conducted. Due to the good absorptivity at the CO 2 laser wavelength, the alumina was sintered quite effectively

Hardness and Microstructure Characterization
The microstructure was characterized using the SEM (Hitachi S4800, Hitachi, Ltd., Tokyo, Japan and Hitachi S6600, Hitachi, Ltd., Tokyo, Japan). The microhardness of laser-sintered alumina arrays was characterized using a microhardness tester (MHT-210 micro hardness tester, LECO Corporation, St. Joseph, MI, USA). Vickers indentation was introduced on the sample surface, and its size was measured on SEM-generated micrographs. A typical micro-indentation is shown in Figure 3.  According to the definition of hardness and geometry of Vickers indentation, the Vickers hardness can be calculated as [33]: where HV is Vickers hardness in kgf/mm 2 [34], F is the applied force in kgf, A is the surface area of the resulting indentation in square millimeters, and d is the average length of the diagonal left by the indenter in millimeters. The applied force and loading time were set as 500 gf for 30 s. Three indentation measurements were carried out for each sample unit. The hardness value of a sample unit was the average of the three measurements. Normally these three measurements were very close to each other (within 5% error). For rare cases, there was a failed indentation on one sample unit. For example, there was a crack in the indent and the measurement was not accurate. Then, the reported hardness for that sample unit was calculated based on the two successful measurements.
The detailed procedure of analyzing SEM micrographs to obtain the relative density of laser-sintered alumina is presented in our previous work [28]. Briefly, to calculate the relative density of each laser-sintered alumina sample, the pore area in the SEM image of the given microstructure was darkened and then analyzed using image processing software (ImageJ from NIH [35]). The SEM-based relative density was then calibrated with the Archimedes density on furnace-sintered alumina samples.

Microstructure Uniformity of Micro-Sample Units
After laser sintering, different microstructures were obtained for different sample units in the array. As shown in Figure 4, high and low relative densities were observed for different units. We examined different locations within sample units from the top-view, and found that within one sample unit, the microstructure is always uniform, in terms of grain size and relative density. As shown in Figure 4, we randomly picked three different locations in a sample unit and observed with high-magnification SEM. Typically, one location was in the center of the sample unit (e.g., Figure 4(a2,b2)) and the other two were close to the different sides of the unit (e.g., Figure 4(a1,a3,b1,b3)). For all the sample units we observed, no matter the relative density low or high, all these three locations had similar grain morphologies, grain sizes, and porosities. In summary, the surface microstructure of laser-sintered alumina sample units was different between units but the same within the unit.
The microstructure uniformity along the depth direction was also examined. We observed the cross-section view of the sample units, as shown in Figure 5. The microstructure of the sample units was not homogeneous along the Z-direction. This is typical for the laser sintering of alumina since most of the laser power was absorbed on the top surface, leading to a temperature gradient along the Z-direction (thickness). Compared to the bottom part of the alumina sample unit, the top surface part had a larger grain size and a higher relative density.
However, we examined the cross-sections of the sample units and found that within at least 20 µm from the top surface, the microstructure was uniform, as shown in similar relative density according to the Figure 5a,b. Considering the geometry of Vickers indenter, the depth of indentation, t, can be calculated as [36]: where d is the average length of the diagonal left by the indenter and θ is the included angle between plane faces of the indenter tip. Here, 136 • was used for Vickers indenter. Using the typical Vickers indentation diameter from Figure 3 (around 35 µm) and using Equation (2), the typical indentation depth is calculated to be~5 µm), which is much smaller than 20 µm (the estimated depth of uniform microstructure). Although the overall cross-section had a nonuniform microstructure, the top zone, probed by the Vickers indenter, had a uniform microstructure that ensures that each hardness measurement is on samples with uniform microstructures.

Distributions of Microhardness and the Corresponding Microstructure
The micro-indentation can be carried out for all the sample units. Since each sample unit is about 400 µm × 400 µm, and the size of the indent is about 40 µm along the diagonal direction, we took three independent indents on each sample unit. Then, the sizes of the indents of all the sample units were characterized under SEM.
As shown in Figure 6, along the laser scanning direction, we expect the microstructure, and the corresponding microhardness of the sample units are close, because these samples were irradiated under the similar laser power intensity. We group the sample units along the laser scanning direction as one series of samples. Each series contains nine individual units. As shown in Figure 6b, statistically the hardness varied between series. For example, Series 8 and 9 had an average hardness above 1200 kgf/mm 2 , while Series 2 and 6 had an average hardness below 900 kgf/mm 2 .
The laser power and scanning speed were kept constant during sintering. Under ideal conditions, the constant processing parameters would imply that the hardness of sample units in each of these series would be constant. However, as can be seen from Figure 6b, this is not the case. We believe that this is due to the inherent fluctuation of laser power and the difference between the boundary conditions of each sample unit. This is the reason that we need to correlate the hardness with microstructure, and not the locations of the sample in this study. This has been done in the following sections.

Quantitative Characterization of Relative Density from SEM Micrographs
The hardness of sintered alumina is strongly influenced by the microstructure features, such grain size and especially relative density [7,8,29,30]. Studies show that higher relative density corresponds to higher hardness [29,30]. The challenge to quantitatively characterize the relative density of laser-sintered alumina is that each sample unit is very small (i.e.,~400 µm × 400 µm), and the microstructural uniform region is limited to a depth of~20 µm from the top surface. Therefore, we cannot use the Archimedes method to measure the relative density. To quantitatively characterize the relative density from SEM micrographs, we developed a benchmarking method [28]. In this method, the pore areal fraction of the SEM from laser-sintered alumina is compared with that from the furnace-sintered alumina. When the two fractions match, we consider the laser-sintered alumina to have the same relative density as furnace-sintered alumina. The relative density of furnace-sintered alumina can be characterized using Archimedes' method. For example, as shown in Figure 7, the laser-sintered alumina has the same relative density as furnace-sintered alumina (relative density = 98%). Ideally, a polished surface should be used to characterize the microstructure features. However, the homogeneous layer of the laser-sintered layer was very thin (~20 µm). This part of the sample would be very easily ground off during polishing.

High-Throughput Database of Hardness and Corresponding Microstructure
We rearranged the samples' indices based on their hardness from low to high. Then, all the hardness results above 600 kgf/mm 2 can be rearranged from the lowest to the largest, as shown in Figure 8. The hardness of the microsamples continuously varied from 600 to 1609 kgf/mm 2 . A wide range of hardness values were represented in these sample units. Correspondingly, these samples also demonstrated continuously varying, vastly different microstructures. The relative densities of the micro sample units continuously varied from 88% to~100%. The correlation between the hardness and relative density of high-throughput samples is shown in Figure 9. Hardness increased monotonically with the increase in the relative density. The data points also agree well with the literature [29,30]. Since calculating relative density from SEM micrographs is time consuming, we did not plot all the relative densities from the sample array in Figure 9. In the future, ML algorithms will be developed to predict the microstructure from the hardness values, similar to our previous work [23]. Since the hardness measurement is much faster than microstructural characterization, we can conveniently predict the material's microstructure based on the hardness measurement. The hardness-relative density correlation, shown in Figure 9, was not solely caused by the relative density, but a combined effect of relative density and grain size. However, the relative density is the dominant factor for the density range investigated in this paper. In the literature, grain size has also been shown to be an important microstructural variable that controls the hardness, especially for the fully dense alumina. For example, a previous study found that submicrometer alumina had much higher hardness than the micrometer grainsized alumina, when the density was about the same (99.2 ± 0.4%) [37]. In general, the smaller grain size correlates to the higher hardness for sintered alumina. In laser-sintered alumina, there is a direct correlation between the grain size and density, as reported in our previous study [28]. A larger relative density corresponds to larger grain sizes. If the grain size were the dominate factor, we would have observed lower hardness for a higher relative density.

Conclusions
In this paper, we reported a novel approach for high-throughput alumina sample fabrication and characterization. Using PS laser prior micromachining and CO 2 laser sintering, an alumina sample array was obtained that contained~80 small sample units of 400 µm × 400 µm size. The laser fabrication was very fast (e.g., <1 min) compared to the conventional furnace sintering (e.g., hours to days). Due to the heterogenous temperature distribution during laser sintering, the microstructure and hardness of the sample units varied greatly. For each individual sample unit, the microstructure was uniform over the entire top surface and within about 20 µm depth from the top surface. Three micro-indentation measurements were carried out for each sample unit. The hardness of the sample units continuously varied from 600 to 1609 kgf/mm 2 , with a relative density ranging from 88% to nearly 100%. The hardness of each units showed a strong correlation with their relative density. This microstructure-hardness correlation matches the literature reports quite well. The database of the microstructure and hardness of laser-sintered alumina can be efficiently established through this high-throughput laser sintering approach.