4 Microanalysis of trace elements and defect centre characterisation
4.1 Electron probe microanalysis (EPMA)
Trace elements in quartz were determined by wavelength-dispersive Electron Probe Micro Analysis (EPMA) on the JEOL JXA 8900 operating at an accelerating potential of 15 keV, at a beam current of 120 nA on the Faraday cup, and with a beam diameter of 7 µm. Analyses were performed for Al, Ti, K, and Fe. Raw intensities converted into concentrations, making appropriate matrix corrections after the phi-rho-z method by Armstrong (1991).
Measurements were carried out as single point analysis, or as line scans, yielding distribution profiles. CL imaging was performed prior and after EPMA analysis. In this way the measurement points in relation to the CL textures can be exactly located.
Quartz contains trace elements of at such low concentrations that a quantification by EPMA poses a major difficulty. Therefore, particular attention had to be paid to a number of parameters: 1) long counting time, 2) high beam current, 3) precise background measurement, 4) high polishing quality of the sample surface, and 4) carbon coating with constant thickness.
The most decisive and often underestimated is the effect of the sample surface quality on the sensitivity of the measurement (Fig. 4.1). The increase of the Al background between measurement 39 and 48 during sample change is caused by sample surface contamination,
Fig. 4.1 Variation of brutto intensities of the Al and Ti background measurements (upper minus lower background) of three trace element profiles.
whereas the Ti background remains constant. This effect results in a decrease of the detection limit for Al from 27 ppm to 50 ppm. Finally, for high precision and sensitivity, the high beam current of 120 nA, the beam diameter of 7 µm, and the counting rate of 10 min per shot means 180 s per element were chosen.
The determination of element concentrations in analytical chemistry is based on repetitive measurements and on the application of statistical methods (e.g. Miller and Miller, 1988;
Miller, 1991). In EPMA, concentrations are calculated from the difference between the accumulated peak counts and the background (BG) at the position of the X-ray line maximum. For extremely low concentrations only qualitative analysis is possible. The concentration at the detection limit, CDL, as the lowest concentration of an analysed element that can be distinguished with reasonable confidence from zero concentration of the analysed element in a sample (blank). Ziebold (1967) suggested different definitions of the CDL, and also Miller (1991) emphasises that a single, “correct”, definition of the limit of detection, cannot be given and should be specified.
We used two definitions of the detection limit. The intensity (in counts) of the detection limit (I1DL) is given in equation (4.1) (e.g. Merlet and Bodinier, 1990):
150
I1DL = 3 σBG (4.1) where σBG = standard deviation of the background.
To reach a probability of 95% that a peak is present, the peak counts must exceed three times the standard deviation of the background, whereby the number of background measurements n must be =5. I1DL was calculated for each trace element profile on the base of 12 background measurements.
A second method for determining of the intensity of the detection limit (I2DL) is based on the level of significance applied to Student’s t-distribution and the standard deviation obtained from background measurements (Plesch, 1982):
I2DL = tz (P;f) sBG (4.2)
where sBG = standard deviation of the mean of the background; tz (P;f) = level of significance of the Student’s t-distribution for binomial limitation determined by the confidence level P and the degrees of freedom f = number of background measurements n – 2.
For each trace element profile both I1DL and I2DL were determined. For the latter a confidence level of 95% and 12 background measurements were used which result in the binomial level of significance tz (P;f) of 2.228 (Table 4.1). The application of the equation (4.2) in this case results in a lowering of IDL.
For the determination of the detection limit CDL the determination of the regression coefficients a and b are necessary, which represent the gradients of the regression line intensity vs. concentration of an element:
CDL = a + b IDL (4.3)
where a and b = the regression coefficients of the regression line intensity vs.
concentration.
The regression coefficients a and b were determined by equation (4.4) and (4.5):
? C ? I2 - ? C I ? I
a = ————————— (4.4) n ? I2 – (? I )2
n ? C I - ? I ? C
b = ———————— (4.5) n ? I2 – (? I )2
where I = intensity; C = concentration of measurements; n = number of measurements.
The regression lines of intensity vs. concentration for the elements Al, Ti, K, and Fe are illustrated in figure 4.2. The regression coefficients a and b were calculated from 273 measurements for each element. The coefficient a represents the concentration for zero counts and should be theoretically zero. But small systematic errors of the equipment result in a shift of the regression line (a ? 0) for Al at about 19 ppm. Consequently, the Al content calculated by the EPMA software is generally 19 ppm to high. For the other elements a is about zero.
The concentrations of the detection limit for Al, Ti, K and Fe calculated after the equations (4.2) and (4.3) are shown in figure 4.3 and listed in table 4.2.
Table 4.1 Level of significance of the Student’s t-distribution for binomial limitation (Plesch, 1982).
f tz (P;f)
P = 95% P = 99%
1 12.710 63.660
2 4.303 9.925
3 3.182 5.841
4 2.776 4.604
5 2.571 4.032
6 2.447 3.707
7 2.365 3.499
8 2.306 3.355
9 2.262 3.250
10 2.228 3.169
12 2.179 3.055
15 2.131 2.947
20 2.086 2.845
30 2.042 2.750
50 2.009 2.678
8 1.960 2.576
Fig. 4.2 Calculated regression coefficients a and b of regression lines of netto counts vs. element concentration.
Under ideal conditions a should be zero, but systematic errors of the equipment cause a shifting of the regression line for Al at about 19 ppm.
56Fe
Fig. 4.3 Detection limits of trace elements in quartz for EPMA. The detection limit C1DL bases on the calculated intensity I1DL after equation (4.1) and C2DL on the intensity I2DL
after equation (4.2). In the case of the EPMA the C2DL is ca. 25% lower than C1DL caused by the level of significance which is lower than three standard deviations.
0 2000 4000 6000 8000 10000
Al (netto cts)
0 200 400 600 800 1000 1200
Fe (netto cts)
Table 4.2 Detection limits CDL (ppm) of EPMA calculated after the equations (4.2) and (4.3) with a confidence level of 95%.
Profile number
n f Al Ti K Fe
1 12 10 41.8 10.9 9.1 9.1
2 12 10 27.9 11.2 5.5 11.2
3 12 10 51.3 7.3 13.0 14.5
4 12 10 66.4 13.0 5.7 7.4
5 12 10 32.2 6.8 5.6 8.0
6 12 10 32.1 12.1 5.7 12.7
7 12 10 28.6 9.5 5.4 7.7
8 12 10 27.2 6.5 6.4 6.4
9 12 10 26.0 5.9 5.8 8.6
10 12 10 23.6 6.2 6.7 8.1
11 12 10 50.2 9.7 3.6 6.6
12 12 10 25.2 6.7 8.3 9.1