Quantification of non-stoichiometry in YAG ceramics using laser-induced breakdown spectroscopy

: Strict control of composition is of paramount importance for the reproducible fabrication of advanced ceramics. In particular, the preparation of high-grade transparent ceramics of definite line-compounds requires that the ratio of major constitutive elements be quantified with a precision better than a fraction of a mole percent to prevent the precipitation of secondary phases and the scattering of light. Such a requirement poses difficult challenges to most analytical methods, especially when applied to nearly-stoichiometric insulating phases. In this work, we show that laser-induced breakdown spectroscopy (LIBS) is a well-suited technique for the assessment of non-stoichiometry in yttrium aluminum garnet (YAG) ceramics and that the aluminum to yttrium ratio can be determined with a resolution of 0.3 mol %, well within the phase boundaries of YAG.


Introduction
The ability to control materials composition is decisive in obtaining reliable characteristics and performance. In particular, non-stoichiometry has profound consequences on the physical properties of multinary crystalline materials, and has been, for this reason, a long-standing research topic in the fields of electron [1][2][3][4] and phonon transports [5][6][7][8][9], magnetism [5,10,11] and optics [12][13][14]. The example of transparent ceramic materials used as specialty optical components [12,13,[15][16][17][18][19] is no exception to this and color centers [20], charge carrier trapping sites [21] and light-scattering phases [22] induced by non-stoichiometry defects have largely been documented. Whether the result of imperfect powder preparation (e.g. slight weighing errors due to water absorption on high surface-area powders, inhomogeneous co-precipitation of precursors with distinct solubility constants, contamination by grinding media during blending), thermal decomposition during hightemperature sintering [23,24] or because of unbalanced condensation rates, as in the synthesis of chemically-vapor deposited (CVD'ed) ceramics [25], composition-control poses severe challenges to the consistent fabrication of ceramics with high optical quality. It has been shown, for example, that the solid-solution range for the Yttrium Aluminum Garnet (YAG, Y 3 Al 5 O 12 ) [26,27], a material widely used as laser gain medium [12,28], phosphor [29] and scintillator [20], lies within (5/3-0.03) <Al/Y< (5/3 + 0.008) [20,30]. From a quality assurance standpoint, as well as for defect-engineering purposes [20], such tight tolerances demand flexible analytical techniques capable of discerning the ratio of major elements with sufficient accuracy.
In the past, nonstoichiometry in YAG samples has been investigated by X-ray diffraction [27], THz spectroscopy [31], and optical spectroscopy [20,32]. However, the non-monotonic relationship between the Al/Y molar ratio and the instrumental response of the first two techniques and the specific methodoly of the latter limit their applicability for general quantitative assessments. In this letter, we report on the use of Laser-Induced Breakdown Spectroscopy (LIBS) for the quantification of non-stoichiometry in YAG ceramics. This optical emission spectroscopy technique consists in igniting a micro-plasma on the surface of a sample using a focused high-energy pulsed laser. At a given plasma temperature and electronic density, the atomic emission line intensities produced in the plasma are proportional to the number of species undergoing the corresponding transitions, therefore allowing for quantitative elemental analysis. The amount of material ablated in the process is typically in the pico-to nanogram range, and damage to the sample is minimal. The versatility, rapidity and limited sample preparation have all contributed to making LIBS a widely used quantification technique for trace, minor and major elements in a variety of matrices, including alloys, composites and ceramics [33][34][35][36][37][38][39][40][41]. Moreover, LIBS can be adapted to real-time in-situ analysis [42].

Experimental
To carry out this study, yttrium aluminum oxide ceramic samples of varied compositions near the garnet stoichiometry were prepared by solid-state reaction between alumina and yttria [43]. A 50 g powder mixture of 38 mol% α-Al 2 O 3 (Inframat) and 62 mol% Y 2 O 3 (Inframat) was ball-milled for 8 hours in the presence of ethanol and alumina balls as a grinding medium. Tetraethoxysilane (Sigma Aldrich) was added to the slurry at a concentration of 0.5 wt % as a sintering additive. After drying, 4 g aliquots of this mixture were blended with controlled quantities of Y 2 O 3 to prepare pellets of known composition. Fourteen such samples were prepared with Al/Y molar ratio ranging from 1.600 to 1.684, with step size no more than 0.007. The ratio of 1.667 corresponds to stoichiometric YAG. The degree of hydration of the raw powders and imprecision of the weighing scale (0.2 mg) both contributed to composition uncertainties. The weight loss of the raw powders after calcination at high temperature was determined and accounted for in the fabrication of the ceramic samples. The cumulated error amounted to 0.02% of the nominal compositions (i.e. an order of magnitude smaller than the composition increments between samples). The powder samples were then uniaxially pressed at 20 MPa into pellets and cold isostatically pressed at 200 MPa. After compaction, the pellets were vacuum-sintered in a tungsten-mesh furnace at 1750°C at a pressure of 10 −6 torr for 2 hours and hot-isostatically pressed at 1700°C at 200 MPa for 2 hours. The samples were subsequently annealed in air at 1400°C for 3 hours. To prevent secondary phase precipitation, cooling rates were maintained above 15°C per minute. Samples within 1.635<Al/Y<1.669 are transparent but translucent outside this composition range.
The spectral line intensities used for quantitative LIBS analysis are affected by several parameters, such as the laser focusing condition, the temporal and spatial stability of the laser pulse, the pulse energy and the plasma stability [44]. Our LIBS system controls these parameters and the detailed description can be found in [45]. The schematics of the apparatus is shown in Fig. 1. The laser ablation was carried out at the fourth harmonic of a Q-switched Nd:YAG laser (266 nm, 10 mJ, 5 ns, 10 Hz, Quantel). The laser pulse energy was optimized to produce a stable plasma and maximum ablation for increasing the signal-to-noise ratio and reducing the effect of possible sample heterogeneity. The laser energy is stabilized during the experiments using a combination of a power-meter and a computer controlled attenuator (ATT266 from Quantum Composers). The laser beam is expanded by lenses L1 and L2, with focal lengths of −50 and 100 mm, respectively (Fig. 1). It is then reflected off mirror M towards the converging lens L3 (focal length 75 mm). Lenses L1, L2 and L3 are made of fused silica and the dielectric mirror M has a high reflectance at 266 nm and a high transmittance for wavelengths above 300 nm. The beam is focused few hundreds of micrometers under the sample surface which is necessary to prevent air breakdown and produce a stable plasma [45]. The focus point of the laser can be adjusted in height by translating lens L1 horizontally with a motorized translation stage. The ability to control the distance between lens L3 and the sample surface is an important feature of the present system, which guarantees the production of identical fluences and plasma conditions from sample to sample. A laser pointer is directed towards the sample in an oblique fashion and the light reflected off the sample surface is focused by lens L4 onto the CCD camera C1. In the field of view of the camera, the barycenter of the laser spot is very sensitive to the vertical positioning of the sample surface and allows for locking the lens-to-sample distance with an accuracy better than 5 μm. This technique is detailed in [45]. The plasma light is collected by lens L5 of 5 cm focal length and fed into a Czerny-Turner spectrometer (1200 1/mm grating) via an optical fiber consisting of a bundle of 19 fibers of 200 µm core diameter each. The stability of the plasma is monitored by the CCD camera C2 (Thorlab) and the collection fiber is centered with respect to the plasma to account for the shot-to-shot fluctuation of plasma morphology. An intensified charge coupled device (ICCD) camera (Andor Technology) is used for recording the spectra. In this experiment, delay for the laser pulse and the duration of acquisition by the ICCD camera were set to 900 and 1000 ns, respectively.
Because the quantification of major elements by atomic spectroscopy techniques is hampered by self-absorption [46,47], the non-resonant lines of singly-ionized aluminum (281.61 nm) and yttrium (278.52 nm) were chosen for this analysis [48]. These lines are well isolated and do not suffer any spectral interference. The typical emission spectrum produced by an yttrium aluminum oxide sample, in the 274 to 290 nm spectral window, is shown in Fig. 2. For each sample, 100 spectra were averaged over a 10x10 spot grid to decrease the variance of the measurement and overcome a possible sample heterogeneity. Each individual spectrum was recorded with the accumulation of 10 laser shots at the same position. With this protocol, the duration of a measurement sequence of 100 spectra for a sample was less than 2 minutes. The center to center spacing between neighboring craters was 300 μm.  Figure 3 shows the correlation between the sample composition and the intensity ratio of the 281.61 nm aluminum and 278.52 nm yttrium lines. The calibration curve has three separate trends that correlate to the transparency of the samples. The relationship between the Al/Y intensity and molar ratios is monotonic irrespective of the visual appearance of the samples. The sensitivity of the calibration curve in group I, II and III is 4.31 ± 1.4, 1.53 ± 0.09 and 3.09 ± 0.78, respectively. This correlation is likely due to differences in laser-sample interaction brought about by light-scattering from secondary phases (Al 2 O 3 or YAlO 3 ) outside the garnet solid-solution (i.e. outside of group II). As discussed above, the small magnitude of the error bars on the composition axis does not show on the graph. The measured shot-to-shot fluctuations of the Al and Y lines over 1000 spectra is 1%. The propagation of this error into the Al/Y intensity ratio, r, and obtained from:

Results and discussion
where I Al and I Y designate the line intensities of both Al and Y species, leads to a 1% relative standard deviation on the Al/Y intensity ratio. This allows resolving a 0.3 mol% difference in the Al/Y molar ratio for group II samples. These calibration curves can be used for the precise determination of composition in yttrium aluminum oxide ceramics on either side of the garnet stoichiometric composition. Fig. 3. Variation of the 281.61 nm aluminum and 278.52 nm yttrium line intensity ratios with sample composition. The arrow points to the sample with the stoichiometric garnet phase composition (YAG). The 3 domains (labeled group I, II and III) correspond to the visible appearance of the samples: transparent for group II and translucent for groups I and III. The changes in slope seen in the calibration curves between these groups reflect differences in laser-sample interaction.

Conclusion
In summary, we carried out LIBS analysis on fourteen samples of yttrium aluminum oxide ceramics with Al/Y molar ratios near the garnet composition. The intensity ratio of nonresonant spectral lines of singly-ionized aluminum (281.61 nm) and yttrium (278.52 nm) showed a positive correlation with their molar ratios. The smallest difference in molar ratio currently resolved is 0.3 mol%. We believe that such performance will allow better composition control in the fabrication of advanced ceramics of definite line-compounds, including that of high-grade transparent ceramics.