Reduction of molecular background emission and sample matrix management in a solution cathode glow discharge

Abstract

A device and method to reduce molecular background emission and to increase matrix management in solution cathode glow discharge (SCGD). A purging device for purging atmospheric gases from a solution cathode glow discharge (SCGD) apparatus, comprising a hollow body that encloses a plasma generated between a solid anode and a solution cathode, wherein the body comprises at least one opening for release of water vapor generated by the plasma. A method for reducing matrix interferences from a SCGD comprising introducing an internal standard into a sample to be analyzed, wherein the sample comprises at least one element of interest; determining a spatial emission profile of the internal standard; using linear correlation between the spatial emission profile of the internal standard and the element of interest to predict a crossover point; and using the crossover point of the element of interest to select a vertical acquisition height for SCGD analysis.

Claims

1. A self-purging device for purging atmospheric gases from a solution cathode glow discharge (SCGD) apparatus, comprising a hollow body that encloses a plasma generated between a solid anode and a water solution cathode, wherein the body comprises at least one opening extending across the entire region between the solid anode and the water solution cathode for release of water vapor generated by the plasma and for viewing the plasma across the entire region between the solid anode and the water solution cathode.

2. The device of claim 1, wherein the body comprises a cylinder.

3. The device of claim 1, wherein the body has a sealed top and an open bottom.

4. The device of claim 1, wherein the body has a sealed top and a sealed bottom.

5. The device of claim 1, wherein the opening comprises one or more slots in a wall of the body.

6. The device of claim 5, wherein the one or more slots are adapted to allow visual observation and detection of emitted light from the SCGD across the entire region between the solid anode and the water solution cathode.

7. The device of claim 2, wherein the body is a stainless steel tube.

8. The device of claim 4, wherein the sealed top comprises a plurality of pieces.

9. The device of claim 8, wherein the sealed top comprises an upper piece around the solid anode resting on a lower piece, the lower piece having a larger internal diameter than the upper piece, providing an annular gap between the internal diameter of the lower piece and the solid anode, wherein relative horizontal movement between the upper piece and the lower piece is provided.

10. A SCGD apparatus comprising the device of claim 6.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1A is a prior art SCGD without a purging device of the present disclosure.

(2) FIG. 1B is a SCGD without a purging device of the present disclosure.

(3) FIGS. 1C-1D depict an example of a solution cathode glow discharge with a purging device with a sealed top and open bottom.

(4) FIGS. 2A-2E depict an example of a solution cathode glow discharge with a purging device with a sealed top and bottom.

(5) FIGS. 3A-3B depict a comparison of the background emission spectra without (3A) and with (3B) atmospheric gas purging.

(6) FIG. 4A-4B depict a comparison of the background emission spectra without (4A) and with (4B) atmospheric gas purging.

(7) FIGS. 5A-5B depict a comparison of the background emission spectra without (5A) and with (5B) atmospheric gas purging.

(8) FIGS. 6A-6B depict a comparison of the background emission spectra without (6A) and with (6B) atmospheric gas purging.

(9) FIG. 7 depicts the 200 ppb Ca spatial emission profile with different sodium concentrations.

(10) FIG. 8 depicts the 200 ppm Ga spatial emission profile with different sodium concentrations.

(11) FIG. 9 depicts the 200 ppm Mg spatial emission profile with different sodium concentrations.

(12) FIG. 10 depicts the relative intensity from 200 ppm Ca (signal with Na matrix divided by the signal of a matrix-free standard).

(13) FIG. 11 depicts the relative intensity from 200 ppm Ga (signal with Na matrix divided by the signal of a matrix-free standard).

(14) FIG. 12 depicts relative intensity from 200 ppm Mg (signal with Na matrix divided by the signal of a matrix-free standard).

(15) FIG. 13 depicts the correlation of Ca to Ga crossover point for concentrations of Na ranging from 100 to 400 ppm.

(16) FIG. 14 depicts the correlation of Mg to Ga crossover point for concentrations of Na ranging from 100 to 400 ppm.

DETAILED DESCRIPTION

(17) In a first embodiment, referring to FIGS. 1C-1D, a purging device, shown in the form of a tube 130 having an open bottom 145 is provided for the SCGD emission cell 10. The tube 130 may be for example a stainless steel tube (O.D. 19 mm or 0.75). The tube 130 is sealed on the top 140 so that all the water vapor produced by the plasma must exit either through the bottom 150 or through an aperture, shown in the form of a small slot 160 facing the spectrometer (not shown). Slot 160 and the spectrometer entrance slit (not shown) are aligned. FIG. 1C shows the outside of the purging device around the SCGD; FIG. 1D shows a cross-section of the same. In an embodiment disclosed, the O.D. of the tube is 19 mm and the remainder of the figure is drawn approximately to scale. In FIG. 1D, the purging device has been rotated by 90 degrees with respect to the purging device in FIG. 1C, e.g. clockwise if viewed from above.

(18) In an embodiment disclosed, the tube 130 is electrically isolated from the anode and ground. In an embodiment disclosed, the tube 130 is brought to ground potential.

(19) A significant proportion of the water pumped to the SCGD is vaporized when it interacts with the high temperature plasma. When this water vapor is contained by the tube 130, it purges the plasma emission region 80 of atmospheric gases such as nitrogen, oxygen, and carbon dioxide. Background emission from atmospheric gases is thus eliminated or at least reduced from the spectra produced by the SCGD and the elimination or reduction of this background emission significantly improves the signal-to-noise ratio of this analytical technique.

(20) Additionally, the full viewing height between the tip 100 of the anode 30 and the flowing solution sample 60 (cathode) can now be used since the interfering molecular emission near the anode 30 has been eliminated. Taking advantage of the full viewing height of the plasma emission region 80 will allow for the effective management of matrix interferences per the method described below.

(21) In a second embodiment, referring to FIGS. 2A-2E, the tube 130 is sealed on the top 140 and the bottom 150 so that all the water vapor produced by the plasma must exit through a plurality of apertures, two slots 170 and 180 shown. The stainless steel tube has two slots to allow visual observation and detection of emitted light. In an embodiment disclosed, the O.D. of the tube is 1.75 and the remainder of the figure is drawn approximately to scale.

(22) The top 140 and the bottom 150 may be made from machinable non-porous ceramic (e.g. Macor), which is an electrical insulator. The top 140 may be made from a plurality of pieces (two shown). An upper piece 142 of the top 140 has a smaller internal diameter than the lower piece 144. The upper piece 142 fits snuggly around the anode 30 and rests atop the lower piece 144 (but is not affixed to the lower piece 144). The lower piece 144 has a larger internal diameter and provides a gap 146, e.g. an annular gap, between the internal diameter of the lower piece 144 and the anode 30 (see FIG. 2D). The gap 146 allows the anode 30 and associated anode assembly to be shifted horizontally to align the anode tip 100 with the capillary tube 50, while maintaining a seal between the upper piece 142 and the lower piece 144. The snug-fitting upper piece 142 rests on top of the lower piece 144 to prevent water vapor from escaping through the gap in the lower piece 144. In an embodiment disclosed, a floating seal is formed between the upper piece 142 and the lower piece 144, which allows relative horizontal movement between the upper piece 142 and the lower piece 144.

(23) A drain 190 (FIG. 2B) through the bottom 150 to allow the waste sample solution to drain from the plasma cell. A drain tube (not shown) is connected to the drain 190 that directs the waste sample solution to a waste reservoir (not shown). The bottom of the drain tube is submersed in waste sample solution in the waste reservoir. This forces all of the water vapor from the plasma-water interaction to exit through the slots 170 and 180.

(24) The slots 170 and 180 allow detection of emitted light and visual observation respectively. The tube 130 of the second embodiment (FIGS. 2A-2E) is also larger than the tube 130 of the first embodiment (FIGS. 1C-1D), for example with an O.D. of 1.75. The second embodiment provided complete purging of atmospheric gases as in the first embodiment.

(25) Slot 170 is narrower than slot 180. It is narrower to aid in blocking random droplets from the plasma impinging on an external optical window (not shown). The slot 170 and the slot 180 are offset by an angular offset (for example about 90 degrees as shown in FIG. 2A). Slot 170 and the spectrometer entrance slit (not shown) are aligned, and the slot 180 may be used for visual observation by an operator while the spectrometer is used to measure the emission spectra via the slot 170. The dimensions of the slots 170 and/or 180 are chosen so that they are small enough to effectively block atmospheric gases (e.g. nitrogen) from entering the plasma cell and large enough to minimize the effort required for optical alignment.

(26) In an embodiment disclosed, the tube 130 is electrically isolated from the anode and ground. The tube 130 may pick up a charge from the plasma, but this floating potential is assumed to be negligible. In an embodiment disclosed, the tube 130 is brought to ground potential. In an embodiment disclosed, a larger sized body for the purging device, e.g. larger diameter tube 130 is selected to reduce the risk of the plasma arcing to the tube 130 from the tip 100 of the anode 30 and to provide a larger volume of the plasma cell that reduces the risk of the sample boiling inside the cell.

(27) Adding the purging device, e.g. tube 130 may create a potential concern of trapping too much heat from the plasma that may lead to temperatures that exceed the boiling point of the waste sample solution. Violent boiling of the waste sample solution is not desired since it would contribute to plasma instability. Such boiling was not observed for the tube 130 having an open bottom 145 (first embodiment, FIGS. 1C-1D) nor for the tube 130 having a sealed bottom 150 (second embodiment, FIGS. 2A-2E), but the diameter (and thus internal volume and surface area) was increased for the second embodiment to reduce a concern for elevated temperatures that may lead to undesired boiling of the waste sample solution. With a higher volume inside the stainless steel tube 130 and a higher surface area of the tube 130 that assists cooling, elevated temperatures that lead to boiling of the waste solution have not been observed. In an embodiment disclosed, external cooling may be applied to the tube 130, for example by supplying an air flow 135 (see FIG. 2E) of a few litres per minute directed at the outside of the stainless steel tube 130 to remove some excess heat. A larger stainless steel tube 130 was also used in the second embodiment (FIGS. 2A-2E) to reduce or eliminate the likelihood of electrical arcing to the tube from the high voltage applied to the anode 30.

(28) While FIGS. 1C-1D and 2A-2E depict a generally uniform cylindrical/tubular purging device, the purging device may be configured in a different shape or manner or both. For example, in an embodiment disclosed, the purging device may be rectangular, cube shaped, etc. In an embodiment disclosed, the purging device is a hollow body that at least partially encloses the plasma cell, while providing controlled exit of water vapor from the plasma cell and permitting observation of the plasma emission region 80 by a spectrometer (not shown).

(29) As shown in the examples below, the inclusion of a purging device to a SCGD apparatus substantially eliminates the interfering molecular emission for the analysis of calcium and gallium. In addition, lower detection limits were achieved for a variety of elements commonly analyzed by SCGD, demonstrating an improved signal-to-noise ratio.

(30) The present disclosure also provides a unique method of reducing matrix interferences in SCGD analyses using the correlation between spatial emission profiles from one element to another.

(31) As described in Schwartz (2016), there exists a location in the vertical profile of the plasma where matrix interferences are substantially eliminated if emission is measured from that location (i.e. the crossover point). As shown in the present disclosure, the inventors have found that spatial analysis can be performed on one internal standard, spiked at a high concentration, and the appropriate crossover points of other elements can be determined by a correlation function (rather than performing spatial analysis of each element individually). By eliminating molecular background emission, the purging device of the present disclosure allows the use of crossover points to manage matrix interferences when analyte concentrations are very low. Theoretically any element can be used as an internal standard. In some embodiments, the internal standard is gallium.

Example 1

Purging Device

(32) Experiments were performed using a purging device with an O.D. of 19 mm and the open bottom tube design as illustrated in FIGS. 1C-1D. The background emission spectra and atomic emission for an unpurged and purged SCGD is shown in FIG. 3A and FIG. 3B, respectively, showing emission intensity 200 versus wavelength 210 in nm for the spectra 220. These spectra 220 originate from the same solution sample and were acquired with the same acquisition parameters. Identical acquisition parameters were used for both spectra including 80 mA current, 0.1 s integration, full vertical pixel usage (1-512), 30 micron spectrometer entrance slit, 1.0 mL/min sample flow rate, and 0.1M HNO.sub.3 spiked at 200 ppb with a 23 element standard solution (FIGS. 3A/3B and FIGS. 4A/4B). The sample solution contains 200 ppb of Ag, Al, B, Ba, Bi, Ca, Cd, Co, Cr, Cu, Fe, Ga, In, K, Li, Mg, Mn, Na, Ni, Pb, Sr, Tl, and Zn. Molecular background emission from NO, CO, (see e.g. FIG. 3A NO and CO (230)), OH (240), and N.sub.2 (250) is clearly visible. Narrow line-width atomic emission is easier to observe in the purged configuration between 200-250 nm and 365-500 nm. The purged configuration cannot remove the presence of OH bandhead emission seen between 255 and 355 nm. However, this OH emission can be managed with adequate optical resolution for the determination of Mg at 285.2 nm and Cu at 327.4 nm. Although not clearly visible in FIG. 3A, the N.sub.2 background emission extends all the way to 500 nm as seen in FIG. 4A (without purging) and FIG. 4B (with purging). With a 0.1 s integration time, the detection of Ca becomes observable in FIG. 3B (200 ppb Ca, 422.7 nm (260)). The spectra 220 also indicates H beta, 486.1 nm (270).

(33) The usefulness of purging atmospheric gases from the plasma region is dramatically illustrated in FIG. 5A/5B for the detection of calcium (Ca) and gallium (Ga) where a 5 s integration time is used. Identical sample and acquisition parameters are used for FIGS. 5A and 5B. Identical acquisition parameters were used for both spectra including 80 mA current, 5 s integration, full vertical pixel usage (1-512), 30 micron spectrometer entrance slit, 1.0 mL/min sample flow rate, and 0.1M HNO.sub.3 spiked at 200 ppb with a 23 element standard solution. In the unpurged configuration (FIG. 5A), the emission of calcium is superimposed on top of the emission of N.sub.2. Therefore, any fluctuation or noise in the N.sub.2 spectrum will be added to the noise for calcium and gallium and detecting Ca or Ga in the resulting spectra 220 is difficult if not impossible. The magnitude of the N.sub.2 interference for calcium and gallium is relatively small as observed in FIG. 3A and 200 ppb Ga, 417.3 nm (280) and 200 ppb Ca, 422.7 nm (290) are readily detectable in FIG. 5B. For other regions of the spectrum where interfering molecular emission is more pronounced, the improvement in the signal to noise ratio will be even greater than what is displayed in FIG. 5B.

(34) When using a two dimensional array detector, e.g. charged coupled device (CCD), it is possible to record an image of the plasma and obtain spatial information regarding plasma emission. This is illustrated in FIGS. 6A/6B where identical sample solution and acquisition parameters are used with an unpurged (FIG. 6A) and purged (FIG. 6B) configuration. Image analysis of the SCGD was performed as illustrated in Schwartz (2016). Identical acquisition parameters were used for both spectra including 80 mA current, 200 s integration, full vertical pixel usage (1-512), 30 micron spectrometer entrance slit, 1.0 mL/min sample flow rate, and 0.1M HNO.sub.3 spiked at 200 ppb with a 23 element standard solution. Vertical pixel number, spatial (pixels) (300) is plotted against wavelength and the vertical pixel number correlates to the location between the 3 mm electrode gap where emission occurs (e.g. the plasma emission region 80 between the outlet tip 90 of capillary tube 50 and tip 100 of anode 30, see FIG. 2C). The emission from calcium at 422.7 nm and gallium at 417.3 nm respectively is seen to be most prominent near the cathode but also to fill the 3 mm gap towards the anode. FIG. 6B is a spatial emission image analysis showing Ga emission at 417.3 nm and Ca emission at 422.7 nm. What is most observant from FIG. 6B is the complete absence of N.sub.2 molecular emission in the purged configuration in contrast to the molecular emission lines (dark features near the top of FIG. 6A, marked 250).

(35) Eliminating background emissions using the purging device of the present disclosure was found to substantially lower detection limits in multiple elements of interest to SCGD analyses as shown in Table 1. The detection limits were calculated as three times the standard deviation of the blank signal divided by the slope of the calibration curve (3.sub.blk/slope). The standard deviation of the blank signal was calculated based on 16 consecutive readings.

(36) TABLE-US-00001 TABLE 1 Element Detection Limit (ppb or ng/mL) Ni 0.6 Co 2 Zn 0.5 Ca 0.4 Mg 0.02 In 0.08 Ga 0.2 Tl 0.08 Al 7 Na 0.003

Example 2

Sample Matrix Management

(37) The following experimental conditions were used in this Example:

(38) TABLE-US-00002 SCGD current 80 mA Ballast resistor 25 k Slit width 30 m for Ca and Ga, and Mg Amplification setting high sensitivity, for Ca and Ga; high light for Mg Sample flow rate 1.0 mL/min Standard Concentrations 200 ppb for Mg, Ga, and Ca Matrix 0.1M HNO.sub.3, sodium ranging from 0 to 500 ppm Image Analysis 230 s integration for Ca and Ga, 60 s integra- tion for Mg Magnesium 285.2 nm (see FIGS. 9 and 12) Calcium 422.7 nm Gallium 417.3 nm Interference filter 320 nm filter used for Ca and Ga

(39) For the data shown in FIGS. 7-9, the background molecular emission from N.sub.2 was present and contributes to the observed noise.

(40) Spatial emission profiles for calcium, gallium, and magnesium with changing concentrations of sodium are shown in FIGS. 7-9. Background corrected emission intensity (310) is shown versus vertical pixel number (320) for changing concentrations of sodium, 0 ppm Na (330), 100 ppm Na (340), 200 ppm Na (350), 300 ppm Na (360), 400 ppm Na (370) and 500 ppm Na (380). As can be seen, the concentration of sodium has a significant impact on the spatial emission profiles. In all cases, the addition of sodium decreased the emission intensities observed lower in the plasma and increased the emission intensities higher in the plasma. Note that the position of the cathode is located near pixel 100 and the tip of the anode is located near pixel 350. The anode and cathode are separated by a distance of 3.0 mm and there is an internal magnification of 10% in the Horiba spectrometer. The individual pixel dimensions are 13.5 m.

(41) Using a similar analysis as Schwartz (2016), relative intensity was calculated by dividing the signal with matrix by the signal of a matrix free standard. Relative intensity profiles are shown in FIGS. 10 to 12. A 5-point moving average was used to smooth the data. Relative emission intensity (420) is shown versus vertical pixel number (430) for increasing concentrations of sodium, 0 ppm Na (440), 100 ppm Na (450), 200 ppm Na (460), 300 ppm Na (470), 400 ppm Na (480) and 500 ppm Na (490). Increasing concentrations of sodium as the matrix modifier influence the position of the crossover point for calcium, gallium, and magnesium.

(42) The correlation between the crossover points of gallium towards calcium and magnesium are shown in FIGS. 13 and 14. In FIG. 13, calcium crossover point (500) is shown versus gallium crossover point (510) for 100 ppm Na (520), 200 ppm Na (530), 300 ppm Na (540) and 400 ppm Na (550). A fit line (560) having a formula: y=1.3795x5.7134 has an R.sup.2=0.9962. In FIG. 14, magnesium crossover point (570) is shown versus gallium crossover point (580) for 100 ppm Na (590), 200 ppm Na (600), 300 ppm Na (610) and 400 ppm Na (620). A fit line (630) having a formula: y=0.8643x+100.72 has an R.sup.2=0.9805.

(43) This linear correlation will allow the spatial emission profile of an internal standard to predict the crossover points for multiple analytes. Since an internal standard can be introduced to the sample solution at a relatively high concentration, accurate spatial profiles Ca (390), Ga (400) and Mg (410) can be acquired with relatively short integration times. This provides a practical method of determining the vertical pixels to use for analyte analysis in a manner that is free from matrix interferences.

(44) The disclosed methods and apparatus are widely applicable to the detection and measurement of the elements described herein. One example is the measurement of elements of interest in water, for example Ca or Mg in water as a measure of water hardness, which may be important for industries such as for boiler feedwater. Higher hardness of boiler feedwater may lead to increased maintenance, operating costs or downtime, for example if the water hardness leads to scaling or plugging of boiler components such as boiler tubes. Because the sodium content of boiler feedwater varies, direct measurement of Ca or Mg or both may be challenging. The disclosed methods and apparatus provide matrix managementi.e. allows measurements that are substantially free from the variable matrix interference. Referring to FIGS. 13/14 (prepared from FIGS. 7-12), one can spike the sample of boiler feedwater with an internal standard, in this example Ga, in order to determine the vertical pixel height (location) at which to obtain SCGD spectra that are free of matrix interference. Gallium is rarely, if ever present in boiler feedwater, but this can be confirmed by laboratory testing and if any problem, another appropriate internal standard can be used instead. One can observe/measure a Ga crossover point and then use FIGS. 13-14 to provide the vertical pixels to use for analyte analysis for Ca (FIG. 13) and Mg (FIG. 14). For example, if a Ga crossover point of 125 pixels is observed/measure, then the correlation of FIG. 13 indicates that using a vertical height of about 165 pixels (167 pixels using the fit formula) for Ca should be relatively free from matrix interference. The Ga crossover point of 125 pixels could be re-used, i.e. for the Mg crossover point of FIG. 14, or a fresh/renewed reading for the Ga crossover point could be obtained. If the fresh/renewed Ga crossover point is at 150 pixels because of the variable matrix (in this example sodium concentration), then the correlation of FIG. 14 indicates that using a vertical height of about 230 pixels (230 using the fit formula) for Mg should be relatively free from matrix interferences.

(45) This disclosure provides methods, apparatus, and systems that are generally applicable to SCGD, including but not limited to be used for lab-based analysis, portable applications, on-line analysis, and any other mode of use where SCGD is involved.

(46) Aspects of the disclosed methods, apparatus, and systems may use software code and one or more computer processors to perform certain elements or features and/or provide output and/or results.

EMBODIMENTS

(47) Embodiments of the invention may include any combination of the features, methods, apparatus and systems shown herein, and in particular in the following numbered paragraphs. This is not to be considered a complete listing of all possible embodiments, as any number of variations can be envisioned from the description above.

(48) Embodiment 1. A purging device for purging atmospheric gases from a solution cathode glow discharge (SCGD) apparatus, comprising a hollow body that encloses a plasma generated between a solid anode and a solution cathode, wherein the body comprises at least one opening for release of water vapor generated by the plasma.

(49) Embodiment 2. The device of embodiment 1, wherein the body comprises a cylinder.

(50) Embodiment 3. The device of any of the above embodiments, wherein the body has a sealed top and an open bottom.

(51) Embodiment 4. The device of any of the above embodiments, wherein the body has a sealed top and a sealed bottom.

(52) Embodiment 5. The device of any of the above embodiments, wherein the opening comprises one or more slots in a wall of the body.

(53) Embodiment 6. The device of any of the above embodiments, wherein the one or more slots are adapted to allow visual observation and detection of emitted light from the SCGD.

(54) Embodiment 7. The device of any of the above embodiments, wherein the body is a stainless steel tube.

(55) Embodiment 8. The device of any of the above embodiments having a sealed top, wherein the sealed top comprises a plurality of pieces.

(56) Embodiment 9. The device of any of the above embodiments having a sealed top, wherein the sealed top comprises an upper piece and a lower piece, the lower piece having a larger internal diameter than the upper piece.

(57) Embodiment 10. A SCGD apparatus comprising a purging device of any of the above embodiments.

(58) Embodiment 11. A method for reducing matrix interferences from a SCGD comprising: A method for reducing matrix interference in a SCGD analysis of a sample to be analyzed, wherein the sample comprises at least one element of interest, the method comprising:

(59) a. determining a spatial emission profile of an internal standard;

(60) b. determining a spatial emission profile of the at least one element of interest;

(61) c. determining a linear correlation between the spatial emission profile of the internal standard and the spatial emission profile of the at least one element of interest;

(62) d. introducing the internal standard into the sample;

(63) e. using SCGD analysis of the sample, measure a crossover point of the internal standard; and

(64) f. selecting a vertical acquisition height for SCGD analysis of the sample for the at least one element of interest from the crossover point of the internal standard using the linear correlation.

(65) Embodiment 12. The method of embodiment 11, further comprising:

(66) g. obtaining a SCGD analysis of the sample, centered at about the vertical acquisition height; and

(67) h. measuring the emission intensity of the at least one element of interest to provide the SCGD analysis of the sample.

(68) Embodiment 13. The method of any of the above embodiments, wherein a. to c. are performed in advance, in a calibration portion of the method and d. to h. are performed subsequently, repeatedly, continuously or semi-continuously in a measurement portion of the method.

(69) Embodiment 14. The method of any of the above embodiments, wherein the sample comprises a variable matrix, wherein the spatial emission profile of the internal standard in a. and the spatial emission profile of the at least one element of interest in b. are determined for a plurality of conditions of the variable matrix, wherein the crossover point in e. is a matrix-free crossover point, independent of the variable matrix, and wherein the crossover point in f. is the matrix-free crossover point.

(70) Embodiment 15. The method of any of the above embodiments, wherein the variable matrix comprises variable sodium (Na) concentration.

(71) Embodiment 16. The method of any of the above embodiments, wherein the internal standard or the at least one element of interest or both comprise an alkali-metal cation.

(72) Embodiment 17. The method of any of the above embodiments, wherein the internal standard comprises Ga and is substantially free of Ca and Mg, and wherein the at least one element of interest comprises Ca or Mg or both.

(73) Embodiment 18. The method of any of the above embodiments, wherein the sample comprises boiler feedwater.

(74) Embodiment 19. The method of embodiment 18, further comprising determining a water hardness of the boiler feedwater from a concentration of Ca or Mg or both.

(75) Embodiment 20. The method of any of the above embodiments, further comprising providing a SCGD apparatus of any of the above embodiments, wherein the SCGD analysis is performed using the SCGD apparatus.

(76) The above-described embodiments are intended to be examples only. Alterations, modifications and variations can be effected to the particular embodiments by those of skill in the art. The scope of the claims should not be limited by the particular embodiments set forth herein, but should be construed in a manner consistent with the specification as a whole.