Linearity and Detection Limits

Examples of Spectra

FYI: All spectra were obtained using a concentric glass nebulizer with no problems around salting out or plugging.

The following example is for an application where a submitter has been obtaining minor levels (0.1 to 1.0 %) of Cr in an alloy containing roughly equal amounts of Fe and Ni. The laboratory where this alloy is analyzed uses a procedure where 0.2 grams of the sample is dissolved in 5 mL of a 1:1 HNO₃ / HCl mixture and diluted to 1000 mL with DI water. The analyst is informed that a limit of detection (LOD = 3SD₀) of 1 ppm Cr based upon the original sample and the ability to quantify the Cr to within ±10 % relative at the 10 ppm level is an absolute minimum requirement.

The submitter then asks the analyst the usual question, “I need the results tomorrow – can you do it?” The analyst does a quick calculation and determines that using the most sensitive Cr line and the current procedure, the lowest possible detection limit is 4 ppm and a more realistic estimation would be ~ 4 times the IDL or ~ 16 ppm. The analyst then pulls up the following spectra, instrument detection limits, and linear regression data which were obtained on their radial view instrument about four years ago when installed using pure single element solutions as described above.

The 205.552 nm Cr line was found to be the most sensitive of the 16 Cr lines originally characterized with an IDL of 4.0 ppm = [ (0.0008 µg/mL Cr IDL) x 1000 ] / 0.2 based upon original sample size and dilution as described above. However, the spectrum of a 0.1 ppm Cr standard shows significant interference from both Ni and Fe at a concentration of 100 ppm making the line useless at low ppm Cr levels (see Figures 7.1 and 7.2).

Figure 7.1:
Spectra of pure 100 ppm Fe and Ni solutions, 0.1 ppm Cr
and a water blank at the 205.552 nm Cr wavelength



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Figure 7.2:
IDL, BEC and regression data for the 205.552 nm Cr line



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The analyst then begins the relatively simple process of identifying a Cr line with the most sensitivity that is spectrally clean. Figures 7.3 and 7.4 show the line identified using the same scan data shown for the 205 Cr line. The 267.716 nm Cr line looks clean at the current dilution factors and has an IDL of 0.0016 µg/mL Cr which increases the detection limit to somewhere between 8 to 32 ppm.

Figure 7.3:
Spectra of pure 100 ppm Fe and Ni solutions, 0.1 ppm Cr
and a water blank at the 267.716 nm Cr wavelength



Click to enlarge

Figure 7.4:
IDL, BEC and regression data for the 267.716 nm Cr line



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The good news is that the 267.716 line looks spectrally clean and the possibility of increasing the sample size while lowering the final volume by a factor of 100 is possible (i.e., 2 grams sample up to 100 mL using 20 mL of 1:1 HCl/ HNO₃). The concentrations of the Fe and Ni in the final solution would be ~ 10,000 µg/mL each. This capability was confirmed when 40,000 µg/mL solutions of both Fe and Ni were scanned as shown in Figure 7.5. These spectral data indicate a realistic detection of << 1 ppm Cr.

Figure 7.5:
Spectra of pure 40,000 ppm Fe and Ni solutions, 0.1 ppm Cr
and a water blank at the 267.716 nm Cr wavelength



Click to enlarge

Figure 7.6:
Simulated spectrum of a solution produced from 2 grams 100 mL solution of a 50/50 wt. % Ni/Fe alloy containing 1.25 ppm Cr at the 267.716 nm Cr wavelength



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The spectra in Figure 5 were used to artificially produce Figure 6 which approximates signals that would be measured for a Fe/Ni alloy where 2 grams to 100 mL dilution were made on a sample containing 1.25 ppm Cr. The entire investigation was performed using spectra that had been stored on computer (i.e., the analyst can literally provide an answer as to project feasibility while speaking on the phone with the client).

The above process is not intended to take the place of method validation, but rather to arm the analyst with sufficient data to make intelligent choices during the initial stages of method development.

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