Application of Glow Discharge Mass Spectrometry for the Monitoring of Dopant Distribution in Optical Crystals Grown by TSSG Method

Direct analysis of matrix and admixture elements in non-conducting crystals is a relevant analytical task in terms of quality assurance of optical materials. The current study aimed to develop a method capable to assess the inhomogeneity of optical crystals with sufficient sensitivity. K1−xRbxTiOPO4 (x = 0.002 and 0.05) and KGd1−yNdy(WO4)2 (y = 0.05) were grown using the top-seeded solution growth method (TSSG). The samples were analyzed by microsecond direct current pulsed glow discharge time-of-flight mass spectrometry (μs-PDC TOF GDMS). The data were compared with the results obtained by scanning electron microscope-energy dispersive X-ray spectroscopy (SEM EDX) and spectrophotometry and validated by the analysis of certified reference material. Sample glow discharge sputtering and analysis were optimized and implemented in real samples. Sample coating with a silver layer and sample pressing in the metallic matrix were proposed to ensure effective sputtering for K1−xRbxTiOPO4 and KGd1−yNdy(WO4)2, respectively. Using the designed method, the inhomogeneity of the dopant’s distribution was demonstrated along the growth axis and in the case of K1−xRbxTiOPO4, also in the growth sectors of different faces. The designed method is applicable for the direct analysis of optical crystal and may be implemented in quality assurance in the manufacturing of optical materials.


Introduction
Optical single crystals are widely used in laser optics as laser generators, frequency multiplier, electro-optical shutters, etc. [1]. In the growing of optical single crystals, there are different effects causing inhomogeneous distribution of matrix elements, admixtures, and dopants in the crystal volume [2][3][4]. In particular, this is the case for crystals originating from the top-seeded solution growth method (TSSG) [2]. In the current study, we considered two types of TSSG-grown crystals: K 1−x Rb x TiOPO 4 and KGd 1−y Nd y (WO 4 ) 2 [5][6][7]. By varying the growth conditions and chemical composition of the initial growth charge by introducing the dopants, materials with the required properties can be obtained [8,9]. KGd 1−y Nd y (WO 4 ) 2 crystals are widely used as solid-state laser sources [10][11][12]. They are used for the generation and amplification of pulsed near-infrared range lasers. These crystals have effective The stoichiometry monitoring was developed based on microsecond pulsed glow discharge time-of-flight mass spectrometry (µs-PDC TOF GDMS) using a time-of-flight mass spectrometer Lumas-30 (Lumex, St. Petersburg, Russia) with a pulsed direct current glow discharge (DC GD) ionization source. The construction and technical characteristics of the instrument were described previously [26,31]. Special features of ionization processes and ion extraction in the µs-PDC TOF GDMS system are described in ref. [32]. In brief, the sample is gradually sputtered and ionized by argon plasma, and the ion components are detected by the time-of-flight mass spectrometer. A repelling pulse following the sputtering/ionizing discharge pulse channels the ions into the mass analyzer; the repelling pulse is synchronized with the discharge pulse and initiates after a delay-a repelling pulse delay. The combined hollow cathode (CHC) was used in this study. The discharge cell consisted of a hollow metallic cylinder (auxiliary cathode) with a diameter of 6 mm and the sample under study attached to it. In the current study, auxiliary cathodes made of high purity tantalum (99.99%) and aluminum (99.999%) were considered. A mixture of high purity argon (99.9999%) with 0.3% addition of hydrogen (LindeGaz Rus, St. Petersburg, Russia) was used as the discharge gas. Quantification data were calculated from six replicate measurements (n = 6) and are presented as mean ± confidence interval (n = 6, P = 0.95)

Samples
The crystals under study were grown at the Research and Technological Institute of Optical Materials All-Russia Scientific Center "S.I. Vavilov State Optical Institute", using the TSSG method. In total, three crystals were tested: K 1−x Rb x TiOPO 4 with x = 0.002 and 0.05, and KGd 1−y Nd y (WO 4 ) 2 with y = 0.05 in the growth charge.
The K 1−x Rb x TiOPO 4 crystals were grown from a phosphate melt solution. The procedure applied was as follows: the chemicals of 99.9% purity K 2 CO 3 , Rb 2 CO 3, KH 2 PO 4 , and TiO 2 (≥99%; Sigma Aldrich, Merck KGaA, Darmstadt, Germany) were loaded into a platinum crucible and fused at 980 • C. During the crystal growth, the temperature of the melt solution decreased about 50-70 • C, whilst the growth rate was maintained at ca. 0-3 mm/day.
To grow KGd 1−y Nd y (WO 4 ) 2 crystals, the growth charge was prepared by mixing Gd 2 O 3 , Nd 2 O 3 , WO 3 , and K 2 CO 3 (≥99%, Sigma-Aldrich, Merck KGaA, Darmstadt, Germany) in the required proportions in a platinum crucible followed by consequent calcination. The equilibrium temperature (980-1020 • C) was achieved under constant stirring in 40% melt solution of KGd(Nd)(WO 4 ) 2 and K 2 W 2 O 7 . The temperature decrease rate was 1 to 5 • C per day. The total growth procedure took up to one month.

Sample Preparation
The parts of the crystals proximal to the initial crystal seeding are further referred to as the "top"; the opposite part of the crystal is referred to as the "bottom". To study the elemental composition in the crystal faces and along different crystallographic axes, corresponding plates of 2 mm thickness were cut. K 0.998 Rb 0.002 TiOPO 4 cutting is shown in Figure 1a. Diffraction shadow images of the samples, obtained using a DRSh-250 setup equipped with a mercury-arc lamp (S.I. Vavilov State Optical Institute, Saint-Petersburg, Russia), are presented in Figure 1b,c. The crystal was investigated along the growth axis on the plate N0 (shadow image is shown in Figure 1b) and on the growth sector of crystal faces ( Figure 1c). For the K 0.95 Rb 0.05 TiOPO 4 crystal, growth faces (201) and (100) along the growth axis as well as the fragments from the top and bottom were investigated. The plate of KGd 1−y Nd y (WO 4 ) 2 crystal was cut along the growth axis; additionally, the plates perpendicular to the growth axis were cut from the top and the bottom parts. The samples were polished with diamond pastes of different grain sizes. For the µs-PDC TOF GDMS analysis, the sections of 10-20 mm were used.

Calibration
A panel of powdered calibration specimens with the close matrix to the samples under study was used. For K 1−x Rb x TiOPO 4 , calibration specimens were prepared by mixing K 2 CO 3 , Rb 2 CO 3 , KH 2 PO 4 , and TiO 2 (≥99%, Sigma-Aldrich, Merck KGaA, Darmstadt, Germany) with consequent fusion at 660 • C for 24 h. The polycrystalline charges with the matching matrix to K 1−x Rb x TiOPO 4 were obtained (x in the range of 0.025-0.25). The composition of the calibration specimens is presented in Supplementary Table S1.
In the case of KGd 1−y Nd y (WO 4 ) 2 , to calibrate for Nd (range 0.1-3 at% in the powder) and Gd (4-14 at% in the powder) the following chemicals were used: KCl (99.5%), WO 3 (99.5%), Al powder (99.9%), Nd 2 O 3 (99.9%), all purchased from Merck KGaA, Darmstadt, Germany. All required materials were thoroughly ground in an agate mortar for at least 30 min and then pressed into tablets (diameter 10 mm, thickness 2 mm) with the use of a manual hydraulic press PRG-400 (Rost, Moscow, Russia). The level of grinding and homogenization was controlled using a scanning electron microscope Zeiss Merlin (Carl Zeiss AG, Oberkochen, Germany). The composition of the calibration specimens is presented in Supplementary Table S2.
The parts of the crystals proximal to the initial crystal seeding are further referred to as the "top"; the opposite part of the crystal is referred to as the "bottom". To study the elemental composition in the crystal faces and along different crystallographic axes, corresponding plates of 2 mm thickness were cut. K0.998Rb0.002TiOPO4 cutting is shown in Figure 1a. Diffraction shadow images of the samples, obtained using a DRSh-250 setup equipped with a mercury-arc lamp (S.I. Vavilov State Optical Institute, Saint-Petersburg, Russia), are presented in Figure 1b,c. The crystal was investigated along the growth axis on the plate N0 (shadow image is shown in Figure 1b) and on the growth sector of crystal faces ( Figure 1c). For the K0.95Rb0.05TiOPO4 crystal, growth faces (201) and (100) along the growth axis as well as the fragments from the top and bottom were investigated. The plate of KGd1−yNdy(WO4)2 crystal was cut along the growth axis; additionally, the plates perpendicular to the growth axis were cut from the top and the bottom parts. The samples were polished with diamond pastes of different grain sizes. For the µs-PDC TOF GDMS analysis, the sections of 10-20 mm were used.

Characterisation by Other Techniques and Reference Material Analysis
The quantification of trivalent Nd in KGd 1−y Nd y (WO 4 ) 2 was performed using a spectrophotometer UV-3600 (Shimadzu Europa GmbH, Duisburg, Germany). A wavelength of 584 nm was used for the measurement. Spectrophotometry data were calculated from six replicate measurements (n = 6) and are presented as mean ± confidence interval (n = 6, P = 0.95).
For the colorless K 1−x Rb x TiOPO 4 crystal elemental characterization, a scanning electronic microscope Hitachi S-3400N (Hitachi, Tokyo, Japan), equipped with energy dispersive spectrometer X-Max 20 from Oxford Instruments (Abingdon, UK) with a Si detector was used. The spectrum was acquired for 30 s under an accelerating voltage of 20 kV and probe current of 1.8 nA. The beam current was optimized using metallic titanium every 30 min. The MAC (Micro-Analysis Consultants Ltd.) reference materials were used for standardization: Nd REE Glass and Gd REE glass for Nd and Gd, respectively; potassium chloride (99.9%) for K; and anhydrous rubidium nitrate (99.99%), purchased from Novosibirsk Rare Metals Plant Russia, for Rb. For the calibration, a spectrum of the standard was acquired for 120 s in the same conditions (20 kV, 1.8 nA). Matrix effects were automatically corrected via TrueQ procedure (based on the XPP algorithm) using Oxford Aztec Energy software. The estimation of the limit of quantification (LoQ) was performed based on the measurement of pure (non-doped) KTP crystal. The LoQ value was calculated as the 10-fold value of the standard deviation obtained for 10 replicate measurements (n = 10). SEM-EDX quantification data were calculated from 10 replicate measurements (n = 10) and are presented as mean ± confidence interval (n = 10, P = 0.95) To validate the µs-PDC TOF GDMS method, in respect of the determination of Rb/K wt% ratio, a geological state certified reference material SGD-1A Essexitic Gabbro (A.P. Vinogradov Institute of Geochemistry SB RAS, Irkutsk, Russia) was used. This reference material contains Rb = 0.0073 ± 0.0004 wt%, K= 2.46 ± 0.04 wt%, and Ti = 1.03 ± 0.02 wt%.

Electrictrical Conductivity Measurements
The conductivity of the crystals was studied by electrochemical impedance spectroscopy over 1 МHz to 0.01 Hz frequency range. For this purpose, an Autolab PGSTAT302 potentiostat/galvanostat (Metrohm AG, Herisau, Switzerland) with a quartz cell maintained in nitrogen atmosphere was used (procedure as described in ref. [33]).

Method Development
Direct sputtering of K 1−x Rb x TiOPO 4 and KGd 1−y Nd y (WO 4 ) 2 crystals resulted in extremely low intensities in the mass spectrum. Thus, the previously employed approach with silver surface coating was used [34]. For K 1−x Rb x TiOPO 4 , effective sample sputtering was ensured with silver coating after 10-15 min from the initiation of the discharge. An example of a mass spectrum is shown in Figure 2a. However, for KGd 1−y Nd y (WO 4 ) 2 , the silver coating was found to be ineffective, since a low sputtering rate of the bulk of the crystal was still observed. Consequently, an alternative sample preparation protocol was implemented. A small piece of a KGd 1−y Nd y (WO 4 ) 2 crystal (20-30 mg) was pressed into high purity aluminum to form a tablet (2 mm thick, 10 mm diameter). An aluminum auxiliary cathode was used in order to minimize the number of additional components in the mass spectrum. This protocol ensured effective sputtering of KGd 1−y Nd y (WO 4 ) 2 with increased sensitivity of ca. 2 orders of magnitude compared with unprepared crystal. Figure 2b demonstrates a sample mass spectrum of KGd 1−y Nd y (WO 4 ) 2 .

Method Development
Direct sputtering of K1−xRbxTiOPO4 and KGd1−yNdy(WO4)2 crystals resulted in extremely low intensities in the mass spectrum. Thus, the previously employed approach with silver surface coating was used [34]. For K1−xRbxTiOPO4, effective sample sputtering was ensured with silver coating after 10-15 min from the initiation of the discharge. An example of a mass spectrum is shown in Figure 2a. However, for KGd1−yNdy(WO4)2, the silver coating was found to be ineffective, since a low sputtering rate of the bulk of the crystal was still observed. Consequently, an alternative sample preparation protocol was implemented. A small piece of a KGd1−yNdy(WO4)2 crystal (20-30 mg) was pressed into high purity aluminum to form a tablet (2 mm thick, 10 mm diameter). An aluminum auxiliary cathode was used in order to minimize the number of additional components in the mass spectrum. This protocol ensured effective sputtering of KGd1−yNdy(WO4)2 with increased sensitivity of ca. 2 orders of magnitude compared with unprepared crystal. Figure 2b demonstrates a sample mass spectrum of KGd1−yNdy(WO4)2.
The next stage of the study involved the optimization of the discharge parameters, analogously to our previous publications [26,35]. The optimal parameters for K1−xRbxTiOPO4 crystals were as follows: repelling pulse delay 4 µs, discharge duration 3 µs, discharge voltage 1300 V, and cell pressure 37 Pa. For KGd1−yNdy(WO4)2 specimens, the parameters were as follows: repelling pulse delay 200 µs, discharge duration 4 µs, discharge voltage 1300 V, and cell pressure 40 Pa.  Both mass spectra were acquired using optimal parameters. The next stage of the study involved the optimization of the discharge parameters, analogously to our previous publications [26,35]. The optimal parameters for K 1−x Rb x TiOPO 4 crystals were as follows: repelling pulse delay 4 µs, discharge duration 3 µs, discharge voltage 1300 V, and cell pressure 37 Pa. For KGd 1−y Nd y (WO 4 ) 2 specimens, the parameters were as follows: repelling pulse delay 200 µs, discharge duration 4 µs, discharge voltage 1300 V, and cell pressure 40 Pa.
The following linear calibration curves for K, Rb, Nd, and Gd were obtained (Figure 3).

KGd0.95Nd0.05(WO4)2 Crystals
We studied the distributions of Nd and Gd along the crystals' growth axis using µs-PDC TOF GDMS ( Table 1). The concentrations at the top and bottom of the crystals were validated using a standard spectrophotometric assay, routinely used for the quality assurance of these crystals by the manufacturer. Importantly, both techniques provided an acceptable agreement within the experimental uncertainty. SEM EDX could not be used for validation due to the low levels of Nd in the specimens. As can be seen from Table 1, there was an increase in Nd concentration in the crystal in the growth process.
According to the literature, the distribution coefficients depend on the concentration of the doping component, unstable within the bulk of the crystal, and usually vary in the range from 0.6 to 1 [2,11,36]. In our case, the distribution coefficient was found to be 0.67 at the top and 0.93 at the bottom of the crystal. This demonstrates the necessity to monitor the dopant after the crystal growth to ensure the quality. Table 1. Atomic fraction ratios of Nd/Gd along the crystallographic growth axis from the crystal's top (seeding side -1) to its bottom (opposite side -5).  Table S1. Nd and Gd were calibrated using the specimens presented in supplementary

KGd 0.95 Nd 0.05 (WO 4 ) 2 Crystals
We studied the distributions of Nd and Gd along the crystals' growth axis using µs-PDC TOF GDMS ( Table 1). The concentrations at the top and bottom of the crystals were validated using a standard spectrophotometric assay, routinely used for the quality assurance of these crystals by the manufacturer. Importantly, both techniques provided an acceptable agreement within the experimental uncertainty. SEM EDX could not be used for validation due to the low levels of Nd in the specimens. As can be seen from Table 1, there was an increase in Nd concentration in the crystal in the growth process. Table 1. Atomic fraction ratios of Nd/Gd along the crystallographic growth axis from the crystal's top (seeding side-1) to its bottom (opposite side-5). According to the literature, the distribution coefficients depend on the concentration of the doping component, unstable within the bulk of the crystal, and usually vary in the range from 0.6 to 1 [2,11,36]. In our case, the distribution coefficient was found to be 0.67 at the top and 0.93 at the bottom of the crystal. This demonstrates the necessity to monitor the dopant after the crystal growth to ensure the quality.

K 1−x Rb x TiOPO 4 Crystals
The plates of K 1−x Rb x TiOPO 4 (x = 0.002 and 0.05) crystals were studied. SEM EDX was used for data comparison. The limits of quantification (LoQ) of SEM EDX were insufficient to quantify Rb in the K 0.998 Rb 0.002 TiOPO 4 crystal but were applicable for the Rb-enriched K 0.95 Rb 0.05 TiOPO 4 sample. For the latter, the results of µs-PDC TOF GDMS and SEM EDX were in adequate agreement, given the uncertainty of the measurements. The data on the inhomogeneous distribution of the dopant (Rb) was also corroborated by the resistance measurements (Table 2), which also demonstrated variability along the growth axis. The inhomogeneity of the chemical composition was observed both along the growth axis and for different growth sectors of crystal faces. We tested the distribution of the dopant along different crystallographic axes, observing much higher homogeneity compared with the growth axis. The average distribution coefficients were found to be 0.70 and 0.63 for K 0.998 Rb 0.002 TiOPO 4 and K 0.95 Rb 0.05 TiOPO 4 , respectively. The inhomogeneity observed is related to the gradual decrease of the temperature and the enrichment of the melt solution with the dopant during the growth process. Table 2. Atomic fraction ratios of Rb/K in K 1−x Rb x TiOPO 4 crystals (x = 0.002 and 0.05), determined by scanning electron microscope-energy dispersive X-ray spectroscopy (SEM EDX) and microsecond direct current pulsed glow discharge time-of-flight mass spectrometry (µs-PDC TOF GDMS) along the crystallographic growth axis from the crystal's top (seeding side-1) to its bottom (opposite side-5 and 3 for K 0.998 Rb 0.002 TiOPO 4 and K 0.95 Rb 0.05 TiOPO 4 , respectively). Sample N0 was used for measurements of Rb distribution along the growth axis [001] for the K 0.998 Rb 0.002 TiOPO 4 crystal.

Crystal Formula
Section of the Crystal  (201) and (100). SEM EDX was again used for data comparison. In these plates, the material was supposed to be growing simultaneously, so the dopant's concentration may be evaluated in two growth sectors. Considerable differences in elemental composition (  [37]. On the face {201}, there are nearly no such dislocation centers; the face {201} was previously shown to grow through the edge mechanism [37].

Rb/K Atomic Fraction
For the validation of the method, geological state reference material SGD-1A Essexitic Gabbro (A.P. Vinogradov Institute of Geochemistry SB RAS, Irkutsk, Russia) containing Rb = 0.0073 ± 0.0004 wt% and K = 2.46 ± 0.04 wt.% was analyzed. The following concentrations were obtained using the developed method: 0.0076 ± 0.0009 and 2.43 ± 0.15 wt.% (n = 6, P = 0.95) for Rb and K, respectively. Like for the real KTP samples, titanium was used for normalization (Ti content in SGD-1A is 1.03 ± 0.02 wt%). The comparison with the certified value demonstrated reliable agreement (α < 0.05). Table 3. Atomic fraction ratios of Rb/K in K 1−x Rb x TiOPO 4 crystals (x = 0.002 and 0.05), determined by scanning electron microscope-energy dispersive X-ray spectroscopy (SEM EDX) and microsecond direct current pulsed glow discharge time-of-flight mass spectrometry (µs-PDC TOF GDMS) in different sector growth faces. For details on crystal cutting, please refer to Figure 1.

Conclusions
In the current study, a direct method of dopant distribution analysis in optical single crystals was developed based on time-of-flight mass spectrometry with pulsed glow discharge. The applicability of the method was demonstrated while determining matrix and dopant components in two types of optical crystals, K 1−x Rb x TiOPO 4 and KGd 1−y Nd y (WO 4 ) 2 . For KGd 0.95 Nd 0.05 (WO 4 ) 2 , we were able to validate the method using spectrophotometry based on Nd 3+ absorption. For non-absorbing K 1−x Rb x TiOPO 4 , we could not validate the low concentration level due to insufficient sensitivity of the reference technique, since the designed method showed higher sensitivity than the reference techniques; however, the higher concentration range was compared and showed good agreement between the techniques. For both crystal types, considerable inhomogeneity in the dopant's distribution was observed along the growth axis, whereas for K 1−x Rb x TiOPO 4 , the difference was observed also in the growth sectors. Thus, µs-PDC TOF GDMS was demonstrated to be an effective and sensitive tool for the monitoring of the composition of optical single crystals.
Supplementary Materials: The following are available online at http://www.mdpi.com/2073-4352/10/6/458/s1, Table S1: Composition of the specimens used for calibrating of µs-PDC TOF GDMS system for analysis of K 1−x Rb x TiOPO 4 crystals. The preparation of the specimens is described in the main text in brief; Table S2: Composition of the specimens used for calibrating of µs-PDC TOF GDMS system for analysis of KGd 1−y Nd y (WO 4 ) 2 crystals. The preparation of the specimens is described in the main text in brief.