3.4.1. Determination Method and Traceability
ICP-OES is an instrument used to determine the chemical composition of a substance based on the spectrum of atomic emission [
20]. In China, the standard solution of Cu (GBW08615) has a Cu element concentration of 1000 μg/mL and an expanded uncertainty of 1 μg/mL (
k = 2). The traceability of Cu contents of AlCu films is ensured using preparation, measurement methods, and measuring instruments that meet the requirements of metrological characteristics. First, a series of standard solutions with different Cu concentrations were prepared using GBW08615. ICP-OES was then used to measure standard solutions and a standard curve was obtained. The atomic emission spectrums of three AlCu films separated from the stainless steel sheets were obtained using ICP-OES and the Cu contents were calculated according to the standard curve.
Figure 6 illustrates the traceability of the three Cu content reference materials used in AlCu films.
The weights of three AlCu films were, respectively, weighed using a 1/100,000 electronic balance. Their weights were 18.98 mg, 26.37 mg, and 31.00 mg, respectively. The AlCu films were then dissolved in hydrochloric and nitric acids and the beaker containing the solution was heated on a heating table to expel the nitrogen oxide gas. After the AlCu films were completely dissolved, the AlCu solution samples with initial Cu contents of 2.5% and 14.5% were diluted with deionized water to 500 mL in two volumetric flasks, and the AlCu solution sample with an initial Cu content of 49.5% was diluted with deionized water to 1000 mL in a volumetric flask. The diluted solutions were shaken to be measured. GBW08615 was used to prepare eight Cu standard solution samples with different concentrations; then, ICP-OES was used to test the eight solution samples, and thus the standard curve was obtained. ICP-OES was subsequently used to measure the Cu contents of the three AlCu solution samples and the measurement was repeated six times for each AlCu solution sample.
The ICP-OES measurement parameters of the Cu concentration standard solutions and that of three AlCu solutions are the same. The three AlCu solutions were measured in eight independent laboratories. The measurement results are shown in
Table 1,
Table 2 and
Table 3.
3.4.2. Uncertainty Evaluation of Cu Content Determination
where
wCu is the Cu content of the AlCu film,
C is the Cu concentration of the AlCu solution sample,
V is the volume of the AlCu solution sample after dilution, and
m is the mass of the AlCu film.
- b.
The main sources of uncertainties
(1) The uncertainty induced by the electronic balance (um)
The uncertainty of measuring the mass of AlCu film using a 1/100,000 electronic balance is derived from the indicating error and the maximum allowable deviation. The resolution of the 1/100,000 electronic balance is 0.01 mg and its half-width resolution is 0.005 mg. According to the uniform distribution calculation, the standard uncertainty introduced by the indicating error is
um−1 = 0.005/
mg. The calibration certificate of the electronic balance shows that it has a maximum allowable deviation of 0.05 mg. According to the uniform distribution calculation, the standard uncertainty introduced by the maximum allowable deviation is
um−2 = 0.05/
mg. Two uncertainty components are independent and unrelated. The standard uncertainty induced by the electronic balance is:
(2) The uncertainty induced by the dilution of the AlCu solution sample (uV-sample)
The calibration certificate of the volumetric flasks shows that the maximum allowable deviation of a 500 mL volumetric flask is ±0.25 mL, and the maximum allowable deviation of a 1000 mL volumetric flask is ±0.40 mL. According to the uniform distribution calculation, the standard uncertainties introduced by the dilution volume are uV − vf = 0.25/ mL and 40/mL for 500 mL and 1000 mL, respectively.
The volumetric flasks were calibrated at 20 °C, and the temperature variations within the laboratories were ±2 °C. The volume expansion of the liquid is significantly greater than the volume expansion of the volumetric flasks; therefore, only the volume change in the solution needs to be considered. The volume expansion coefficient of water is 2.1 × 10−4/°C; therefore, the volume change in a 500 mL aqueous solution is ±(500 × 2 × 2.1 × 10−4) mL = ±0.21 mL and the volume change in a 1000 mL aqueous solution is ±(1000 × 2 × 2.1 × 10−4) mL = ±0.42 mL. Assuming a uniform distribution of temperature change, the standard uncertainties introduced by the volume changes in aqueous solutions are uV-water = 0.21/mL and 0.42/mL for 500 mL and 1000 mL, respectively.
The uncertainty induced by the dilution of the AlCu solution sample is calculated by:
(3) The uncertainty induced by the calibration process of ICP-OES using GBW08615 (uCRM-cal)
The uncertainty introduced by the calibration process of ICP-OES using GBW08615 consists of the dilution of GBW08615 (uCRM-dilution) and the fitting of the standard curve (ucurve). Furthermore, the uncertainty introduced by the dilution of GBW08615 mainly consists of CRM, pipette, and the dilution volume of CRM.
GBW08615 has a Cu element concentration of 1000 μg/mL and an expanded uncertainty of 1 μg/mL (k = 2). The standard uncertainty introduced by GBW08615 is uCRM = (0.5 μg/mL)/(1000 μg/mL) = 0.05%.
The GBW08615 standard solutions of 0 mL, 0.02 mL, 0.05 mL, 0.10 mL, 0.20 mL, and 0.50 mL were, respectively, transferred to six 100 mL volumetric flasks using a 1 mL pipette. Subsequently, the GBW08615 standard solutions of 1 mL and 2 mL were, respectively, transferred to two 100 mL volumetric flasks using a 5 mL pipette. According to the verification certificate, the expanding uncertainty of both 1 mL and 5 mL pipettes is 0.01 mL (k = 2). Therefore, the standard uncertainties introduced by the 1 mL and 5 mL pipettes are upipette = 0.005/1 and 0.005/5, respectively. We take the larger value upipette = 0.005/1.
The sources of volume uncertainty of GBW08615, which is diluted in a 100 mL volumetric flask, include volumetric error, volumetric repeatability, and laboratory temperature fluctuation. Since method repeatability will be included in subsequent calculations, including the repeatability of 100 mL volume determination, it will not be considered here. The verification certificate shows that the maximum allowable error of a 100 mL volumetric flask is ±0.1 mL; therefore, the uncertainty introduced by the constant volume of a 100 mL volumetric flask is uV-CRM-error = 0.1/100 = 0.1%.
The 100 mL volumetric flasks were calibrated at 20 °C and the temperature variations within the laboratories were ±2 °C. The volume expansion coefficient of water is 2.1 × 10
−4/°C, and the volume change in a 100 mL solution is ±(100 × 2 × 2.1 × 10
−4) mL = ±0.042 mL. The volume uncertainty of a 100 mL water solution introduced by the temperature variation is
uV-CRM-water = 0.042/100 = 0.042%. Therefore, the standard uncertainty (
uV-CRM) introduced by the process of GBW08615 diluted in 100 mL water is calculated by
The standard uncertainty introduced by the dilution of GBW08615 is calculated by
According to GB/T 38145-2019 [
21], a series of Cu element standard solutions with different concentrations were prepared and measured. The measured spectral intensity and concentration were fitted to obtain the linear regression equation of
Y =
bX +
a and the linear correlation coefficient
R2 was calculated. The standard uncertainty (
ucurve) introduced by the standard curve is calculated by
In the equations,
ucurve is the uncertainty introduced by the standard curve,
SR is the standard deviation of the residual of the standard curve,
p is the number of repeated measurements of the AlCu solution sample,
n is the total number of measurements of the Cu standard solution,
C0 is the measured Cu concentration of the AlCu solution sample,
Ci is the Cu concentration of the Cu standard solution (i.e.,
Xi),
is the average of the Cu standard solution, and
Yi is the spectral intensity of the Cu standard solution. Based on the measured Cu concentration and spectral intensity of the Cu standard solutions, the uncertainties induced by the standard curves for AlCu solution measurement obtained in eight laboratories are shown in
Table 4.
The uncertainty (
uCRM-cal) induced by the calibration of ICP-OES using GBW08615 is given by
(4) The uncertainty (ur) induced by the measurement repeatability of Cu content in AlCu solutions
For the three AlCu solution samples, the measurements were independently repeated six times. The Cu element content and corresponding standard deviation results were obtained, as shown in
Table 5,
Table 6 and
Table 7. The standard deviation represents the uncertainty (
ur) introduced by the measurement repeatability of the Cu contents in the AlCu solutions.