Analytical and Bioanalytical Chemistry

, Volume 385, Issue 2, pp 234–239

Systematic line selection for online coating thickness measurements of galvanised sheet steel using LIBS

Authors

    • Fraunhofer-Institut für Lasertechnik (ILT)
  • Stefan Hölters
    • Fraunhofer-Institut für Lasertechnik (ILT)
  • Volker Sturm
    • Fraunhofer-Institut für Lasertechnik (ILT)
  • Reinhard Noll
    • Fraunhofer-Institut für Lasertechnik (ILT)
Special Issue Paper

DOI: 10.1007/s00216-006-0348-y

Cite this article as:
Balzer, H., Hölters, S., Sturm, V. et al. Anal Bioanal Chem (2006) 385: 234. doi:10.1007/s00216-006-0348-y

Abstract

LIBS can be used as an online method of characterizing galvanized coatings on sheet steel moving through a production line. The traversing sheet steel is irradiated with a series of single laser bursts, each at a different position on the sheet steel. An ablation depth in the same range as the coating thickness (about 10 μm) is achieved by using a Nd:YAG laser at 1064 nm in collinear double-pulse mode. The coating thickness is determined from the ratio of the intensities of an iron line and a zinc line measured at a burst energy high enough to penetrate the coating with a single burst. Experiments at different burst energies were carried out to optimize the thickness resolution, and a method of systematically selecting iron and zinc lines was deduced, which is based on multivariate data analysis (MVDA) of the intensity ratios calculated for a set of 6 zinc lines and 21 iron lines. A temperature correction was applied, because the parameters of the plasma change with burst energy, and the influence of this on the thickness resolution is discussed. The ambient atmosphere present (air, Ar, N2) as well as self-absorption of spectral lines both have an influence on the thickness resolution. At optimum conditions, a thickness measurement accuracy of better than 150 nm was obtained for a set of electrolytic galvanized sheet steels with coating thicknesses in the range 4.1–11.2 μm.

Keywords

Laser-induced breakdown spectroscopyCoating thickness measurementGalvanized coatingZnOnline analysisMultivariate data analysis

Introduction

The composition and thickness of the coating must be monitored during the galvanized sheet steel production process. The quality criteria for later processing steps require that there is a constant coating thickness over the complete length of a coil.

X-ray fluorescence (XRF) is a state-of-the-art method for performing coating thickness analysis in galvanizing plants [1]. In this technique, the X-ray line arising from iron in the substrate is measured. This emission is partially absorbed by the zinc coating, to an extent that depends on the coating thickness. The thickness resolution achievable is in the range 150–400 nm. However, this method is less sensitive to light metals alloyed in the coating, like Al and Mg.

In a previous study we developed an online LIBS-based method that can be used to characterize the coatings—a method that is also sensitive to light elements—and used it to measure coating thicknesses and to monitor the Al depth profiles of hot-dip galvanised coatings [2]. A series of single laser bursts irradiated the sheet steel, each pulse irradiating a different (laterally displaced) position (here the term “burst” denotes a group of laser pulses generated during a single flash-lamp discharge). Depth information is obtained by tuning the ablation depth, which in turn is achieved by varying the burst energy and, unlike in the conventional method, by applying several laser pulses to the same sample position [413]. An ablation depth in the same range as the coating thickness (about 10 μm) per burst was achieved using collinear double pulses. Using this approach, it is possible to determine the coating thickness using the ratio of the intensities of an iron line and a zinc line (IFe/IZn) measured at a fixed burst energy EB high enough to penetrate the coating, see Fig. 1. A thickness resolution of about ∼400 nm was achieved recently for a set of reference samples with different coating thicknesses in the range 3.2–11.2 μm [2].
https://static-content.springer.com/image/art%3A10.1007%2Fs00216-006-0348-y/MediaObjects/216_2006_348_Fig1_HTML.gif
Fig. 1

Experimental procedure used to measure the coating thickness on moving sheet steel. The burst energy chosen is high enough to penetrate the coating with a single burst. The spectral line intensities of iron from the substrate and zinc from the coating are measured. The ratio of line intensities IFe/IZn is a measure of the coating thickness, and decreases with increasing coating thickness for constant burst energy

In this study, the aim is to further enhance the thickness resolution through multivariate data analysis [1417], plasma temperature correction [18, 19] and appropriate selection of the ambient atmosphere [2022].

In order to find the optimum experimental conditions and the most sensitive IFe/IZn ratio, 21 iron lines and 6 zinc lines were selected in the spectral range of 300–500 nm, and all possible IFe/IZn ratios were analysed in relation to thickness resolution via multivariate data analysis software and by applying a temperature correction.

Experimental

In the LIBS experiments a flash-lamp-pumped Q-switched Nd:YAG-laser (HY1200, GSI Lumonics, Novi, MI, USA) operating at 1064 nm and modified to emit up to six pulses at a repetition rate of 10 Hz (>2 μs interpulse separation) was used. The widths of the individual laser pulses in the burst were ∼15 to 20 ns, depending on the number of pulses in the burst. In our experiments the laser was operated in double-pulse mode (interpulse separation of Δt1=4 μs, energy ratio E1 :E2=1:1, burst energy EB=E1+E2=0.5–2.6 mJ) in order to achieve an ablation depth where a single burst exceeds the coating thickness (4.1–11.2 μm).

Figure 2 shows the experimental set-up. The laser light is guided via a dichroic mirror (high reflectivity for 1064 nm, transparent for the plasma light) and is focused by an achromatic lens L1 (f=60 mm) onto the surface of the sheet steel, where a small amount of the sample is evaporated and a plasma is generated. Ar and N2 gas flows are directed at an angle of 45° onto the sample surface via a gas nozzle mounted 12 mm from the sample. The estimated gas flows are ~170 l/min for Ar and ~215 l/min for N2. Experiments in air were performed at normal pressure without a gas flow. The plasma light is collected and collimated with the same lens (L1), it passes the dichroic mirror and is reimaged by a quartz lens (f=100 mm) onto the core of the optical fibre connected to an Echelle spectrometer (Model ESA 3000 from LLA, Berlin, Germany), in order to detect the plasma emission. The detector consists of a MCP image intensifier with a broadband S20 photocathode coupled to a Kodak KAF 1001 CCD chip (1024×1024 pixels). The spectrometer offers a broad spectral detection range (200–780 nm) with high spectral resolution (5–20 pm). In this study, a smaller spectral range of 300–500 nm was measured in order to obtain a measuring frequency of 1 Hz instead of ∼0.3 Hz for the complete spectral range. The time delays used for the signal integration were tdelay=1.0 μs in air and N2, and tdelay=1.0 and 2.0 μs in Ar, and the integration window was set to tint=1 μs in all measurements. tdelay and tint were not optimised in this study. The burst energy is adjusted with an external Pockels cell. The burst energy can be attenuated by up to a factor of 10 using this cell. The burst energy was varied in the range 0.5–2.6 mJ. The laser parameters chosen allow us to penetrate all of the zinc coatings with a single laser burst, which is a prerequisite of the approach used here.
https://static-content.springer.com/image/art%3A10.1007%2Fs00216-006-0348-y/MediaObjects/216_2006_348_Fig2_HTML.gif
Fig. 2

Schematic view of the experimental set-up. ST, steel substrate; C, coating; P, laser-induced plasma plume; L1, focusing lens; L2, imaging lens; M, dichroic mirror; OF, fiber optics; EC, energy control; LH, laser head; LC, laser control; SP, Echelle spectrometer; GN, gas nozzle

In the experiments performed here, the different sheet steels were mounted on a xy-translation stage and were moved under the (static) optical set-up. For each detector setting and ambient atmosphere, the burst energy was varied from 0.5 mJ to 2.6 mJ in 22 equidistant steps, and 40 measurements were performed for each energy step. This was repeated for each different coating thickness, so 40 repetition measurements are available for each parameter set for each of the eight coating thicknesses, giving a set of 3 (air, N2, Ar) × 22 × 40 × 8 = 21120 spectra in total.

Evaluation method

In the first step, the integrated line intensities of 21 iron lines and 6 zinc lines were calculated by fitting Voigt profiles to each of the lines in each Echelle spectrum and then performing numerical integration. This procedure is performed by a software tool developed at Fraunhofer ILT. The lines, along with their atomic data, are listed in Table 1.
Table 1

List of iron and zinc lines studied, along with their atomic parameters, in the spectral range 300–500 nm

 

Element

λ [nm]

log(gf)

Eupper [eV]

kt (Te=8500 K) [10-30m3]

Group A: iron lines for temperature determination

 

Fe I

385.26

−1.24

5.39

0.08

 

Fe I

392.29

−1.65

3.21

0.61

 

Fe I

410.75

−0.73

5.85

0.12

 

Fe I

410.98

−0.91

5.86

0.08

 

Fe I

411.85

0.28

6.58

0.46

 

Fe I

428.24

−0.81

5.07

0.27

 

Fe I

436.98

−0.73

5.88

0.1

 

Fe I

441.51

−0.62

4.42

0.99

 

Fe I

449.46

−1.14

4.96

0.14

 

Fe I

452.86

−0.82

4.91

0.3

Group B: additional iron lines for coating thickness measurement

 

Fe I

355.85

−1.12

4.47

0.48

 

Fe I

382.78

0.06

4.80

3.81

 

Fe I

384.33

−0.14

6.27

5.3

 

Fe I

404.58

0.28

4.55

7.74

 

Fe I

407.17

−0.02

4.65

3.31

 

Fe I

420.20

−0.71

4.43

0.86

 

Fe I

430.79

−0.07

4.43

3.54

 

Fe I

432.58

−0.01

4.47

3.82

 

Fe I

438.35

0.20

4.31

7.52

 

Fe I

440.48

−0.14

4.37

3.13

 

Fe I

495.76

0.13

5.31

1.32

Group C: zinc lines

 

Zn I

328.23

−0.38

7.78

1.61

 

Zn I

330.26

−0.06

7.78

3.3

 

Zn I

334.50

0.25

7.78

6.36

 

Zn I

468.01

−0.82

6.65

1.17

 

Zn I

472.22

−0.34

6.65

3.45

 

Zn I

481.05

−0.14

6.65

5.32

The lines in group A with low self-absorption (kt<1×10−30 m3 at Te=8500 K) were used to determine the plasma temperatures. All of the combinations of iron lines from group A and group B with zinc lines from group C were used in the multivariate data analysis. The quantity kt is a measure of the optical depth [23]

Then the average values from the 40 repetitions for all possible IFe/IZn ratios (6×21=126) for the 22 burst energies and the 8 coating thicknesses are calculated. To determine the coating thickness, the IFe/IZn ratio at a fixed burst energy is plotted as a function of the coating thickness, and a fit curve is determined, see Fig. 3 and [2]. Figure 3 shows the IFe438/IZn472 ratios (as used in a previous study [2], referred to as the “standard ratio” in the following) as a function of the coating thickness for three different burst energies measured in air. The calibration curves differ from that shown in [2], since a different set of tdelay and tint values are used here (tdelay=1 μs, tint=1 μs in this work, while 2 μs and 10 μs were used in [2]). The RMSE (root mean square error) value of the fit is defined as follows:
$${\text{RMSE}} = 2 \cdot {\sqrt {\frac{{{\sum\limits_{i = 1}^N {{\left( {d^{i}_{{{\text{Zn,m}}}} - d^{i}_{{{\text{Zn,c}}{\text{.t}}{\text{.v}}{\text{.}}}} } \right)}^{2} } }}}{N}} }$$
(1)
where dZn,m is the thickness determined using the measured IFe/IZn ratio and the calibration function, dZn,c.t.v. is the conventional true value of the thickness (determined by GD-OES), N is the number of different coating thicknesses (eight in this case).
https://static-content.springer.com/image/art%3A10.1007%2Fs00216-006-0348-y/MediaObjects/216_2006_348_Fig3_HTML.gif
Fig. 3

IFe438/IZn472 ratio as a function of the coating thickness for different burst energies measured in air. The lines are parabola fits, which can be used as calibration curves

The RMSE value is a measure of the accuracy of the thickness determination related to a specific IFe/IZn ratio for a given parameter set (burst energy, delay time and ambient atmosphere).

The parameter combinations studied were: 22 burst energies, three ambient atmospheres with two delay times for Ar and one delay time for N2 and air, 126 IFe/IZn ratios with and without temperature correction. This yields a total number of 22176 calibration curves to process. This large number of calibration curves was split into eight groups; two for each ambient atmosphere (with and without temperature correction), except for Ar, which had two delay times and therefore resulted in four groups. Each group comprises 2772 different IFe/IZn ratios (126 line ratios × 22 burst energies), which were processed by commercial software for multivariate data analysis (Unscrambler 9.2 from CAMO Technologies, Woodbridge, NJ, USA), see Table 2. Unscrambler calculates a linear model for predicting coating thickness from all of the IFe/IZn ratios using the partial least squares (PLS) method, and returns the regression coefficient for each of the IFe/IZn ratios for the 22 different burst energies. In the next step, all 2772 regression coefficients are sorted in a ascending order, and an algorithm is used to find the IFe/IZn ratio with the highest regression coefficients for five neighbouring energy steps. Thus, IFe/IZn ratios with higher regression coefficients at only one burst energy are neglected. In the final step, the model is recalculated using the IFe/IZn ratio with highest regression coefficients over five neighbouring energies, and the root mean square errors (RMSE) are calculated.
Table 2

Comparison of the accuracies obtained with the standard IFe438/IZn472 ratio and the best IFe/IZn ratio determined by MVDA

Ambient atmosphere

Delay time tdelay [μs]

Temperature correction

Intensity ratio IFe/IZn

RMSE [μm]

EB range [mJ]

IFe438/IZn472

     

Air

1

no

438.35/472.22

0.51

0.7–1.1

Air

1

yes

438.35/472.22

0.50

0.6–1.0

Ar

1

no

438.35/472.22

0.41

0.5–0.9

Ar

1

yes

438.35/472.22

0.41

0.5–0.9

Ar

2

no

438.35/472.22

0.30

0.6–1.0

Ar

2

yes

438.35/472.22

0.36

0.6–1.0

N2

1

no

438.35/472.22

0.61

1.0–1.4

N2

1

yes

438.35/472.22

0.80

1.2–1.6

IFe/IZn-ratios with the highest accuracy

     

Air

1

no

440.48/468.01

0.37

0.5–0.9

Air

1

yes

410.75/468.01

0.37

1.5–1.9

Ar

1

no

428.24/468.01

0.19

2.2–2.6

Ar

1

yes

411.85/472.22

0.32

0.5–0.9

Ar

2

no

410.98/328.23

0.14

1.5–1.9

Ar

2

yes

411.85/328.23

0.20

1.2–1.6

N2

1

no

495.76/334.50

0.27

2.2–2.6

N2

1

yes

382.78/481.05

0.68

1.3–1.7

The highest accuracy is obtained in an Ar atmosphere for tdelay=2 μs without temperature correction using the ratio IFe410.9/IZn328

A problem arises because the upper levels of an iron line and a zinc line are different. Then the corresponding IFe/IZn ratio is a function of the ratio of the number of iron atoms NFe and zinc atoms NZn in the ablated crater volume and the temperature, since the line intensity of species i depends on the temperature assuming negligible optical depth:
$$I_{i} \propto N_{i} {\left( {\frac{{g_{{\text{m}}} f_{{{\text{mn}}}} }}{{\lambda ^{3} \cdot Z{\left( T \right)}}}} \right)} \cdot \exp {\left( { - \frac{{E_{{{\text{upper}}}} }}{{K_{{\text{B}}} T_{{\text{e}}} }}} \right)}$$
(2)
where Ni is the number of atoms of species i, gm is the degeneracy of the lower level, fmn is the oscillator strength, λ is the transition wavelength, Z(T) is the partition function, Eupper is the energy of the upper energy level, kB is the Boltzmann constant, and Te is the electron temperature.
To account for this effect, and also to compensate for temperature fluctuations arising from fluctuations in the laser power or different sample surface absorptivities, a temperature correction was applied to the IFe/IZn ratios, as follows:
$$\frac{{I_{{{\text{Fe}}}} {\left( {T_{{\text{e}}} } \right)}}}{{I_{{{\text{Zn}}}} {\left( {T_{{\text{e}}} } \right)}}} \cdot \frac{{Z_{{{\text{Fe}}}} {\left( {T_{{\text{e}}} } \right)}}}{{Z_{{{\text{Zn}}}} {\left( {T_{{\text{e}}} } \right)}}} \cdot \frac{{\exp {\left( {\frac{{E_{{{\text{upper,Fe}}}} }}{{K_{{\text{B}}} T_{{\text{e}}} }}} \right)}}}{{\exp {\left( {\frac{{E_{{{\text{upper,Zn}}}} }}{{K_{{\text{B}}} T_{{\text{e}}} }}} \right)}}} \propto \frac{{N_{{{\text{Fe}}}} }}{{N_{{{\text{Zn}}}} }} \cdot $$
(3)

For each spectrum, Te was determined by a Boltzmann plot using iron lines with low self-absorption, i.e. kt<1.5×10−30 m3 (at Te=8500 K), see Table 1, group A. Te is determined separately for each spectrum, yielding values in the range of 6,000–9,000 K for the various parameter settings.

Samples

A set of reference samples of electrolytic galvanized sheet steel with well-defined coating thicknesses, provided by ThyssenKrupp Steel AG (TKS, Dortmund, Germany), were used for the experiments. The set consisted of sheet steel plates with different coating thicknesses, ranging from 3.1 to 11.2 μm. In this study experiments were carried out on samples with coating thicknesses of 4.1–11.2 μm.

Results and discussion

Figure 4 shows the line intensity ratio IFe438/IZn472 as a function of the burst energy for the coating thicknesses 4.1, 8.2 and 11.2 μm. This ratio was used in a previous study to determine the coating thickness, and a thickness resolution of 400 nm was estimated [2].
https://static-content.springer.com/image/art%3A10.1007%2Fs00216-006-0348-y/MediaObjects/216_2006_348_Fig4_HTML.gif
Fig. 4a–b

IFe438/IZn472 ratio as a function of the burst energy for different coating thicknesses: a without temperature correction, b with temperature correction. In both cases the ratio is higher for thinner coatings and can be used as a measure of the coating thickness

The Zn line at 472.22 nm (3S13P1, Eexc=6.65 eV) and the Fe line at 438.35 nm (4F54F4, Eexc=4.31 eV) are both strong lines, and the difference between the upper energy levels (ΔE) is 2.34 eV. Figure 4a shows the ratio IFe438/IZn472 as a function of the burst energy without temperature correction. The decrease in IFe438/IZn472 with increasing burst energy for dZn=4.1 μm seems to conflict with the higher relative number of Fe atoms expected, but can be explained by the different temperature behavior of the population density of the excited states corresponding to the IFe438 and IZn472 lines, according to the Boltzmann law. At low burst energies, the amount of ablated material and hence the size of the plasma generated is smaller, and it cools down more rapidly. This means that, at a given delay time tdelay, the plasma temperature is lower for lower burst energies. As the excitation energy of the IFe438 line (Eexc=4.31 eV) is much lower than that for the IZn472 line (Eexc=6.65 eV), the relative number of Fe atoms excited to the upper state of the Fe438 transition is higher in cooler plasmas than in the hotter plasmas expected for higher burst energies. At small coating thicknesses, this effect is stronger than the increase due to the higher number of ablated Fe atoms. For the thicker coating (d=11.2 μm), the intensity ratio starts at almost zero and rises for higher burst energies. Figure 4b shows the same data after applying a temperature correction, as described above. In this case the IFe438/IZn472 values for all three coating thicknesses increase with burst energy, as expected. However, it is apparent from both figures that at any burst energy the IFe438/IZn472 ratio is higher for thinner coatings. So the IFe438/IZn472 ratio at a fixed burst energy can be used as a measure of the coating thickness; see Fig. 3. The ratios in Fig. 3 decrease for increasing coating thickness, and all three calibration curves can be used to determine coating thickness. The solid lines are parabola fits. Table 2 lists the IFe/IZn ratios. The lowest RMSE values determined for a specific parameter set by multivariate data analysis are also shown, together with the RMSE values for the standard IFe438/IZn472 ratio used in the earlier study [2].

In each case the RMSE value is given for the burst energy range leading to the lowest RMSE values. Table 2 shows the effects of the type of ambient atmosphere, the delay time used and temperature correction on the RMSE values of the standard IFe438/IZn472 ratio. For a delay time of 1 μs, and without temperature correction, the thickness resolution is best in Ar (0.41 μm) and worst in N2 (0.61 μm). Physically reasonable temperature correction does not enhance thickness resolution for an N2 ambient atmosphere—it makes it even worse. In an argon atmosphere, a delay time of 2 μs enhances the resolution from 0.41 μm to 0.3 μm. The smallest RMSE values for a specific parameter set are found for the IFe/IZn ratios listed in the second part of Table 2. For each of the parameter sets, another IFe/IZn ratio was actually optimal, but most of the lines are lines with low self-absorption (kt<1.5×10−30 m3, Te=8500 K), see Table 1. In Ar, these values are more than a factor of 2 smaller than the RMSE values of the IFe438/IZn472 ratios. Again, temperature correction does not improve the resolution. The best thickness resolution of 140 nm was achieved in Ar atmosphere for a delay time of 2 μs with the IFe410/IZn328 ratio. Figure 5 visualizes the increase in thickness resolution in comparison to the IFe438/IZn472 ratio used in the previous study [2]. The plot shows the difference between the thickness dZn,m determined with the calibration model and the measured IFe/IZn ratio and the conventional true coating thickness dZn,c.t.v. as a function of dZn,c.t.v.. The thickness resolution is further enhanced compared to our previous study: from 510 nm down to 140 nm (by more than a factor of 3).
https://static-content.springer.com/image/art%3A10.1007%2Fs00216-006-0348-y/MediaObjects/216_2006_348_Fig5_HTML.gif
Fig. 5

Comparison of the resolving power of the IFe438/IZn472 ratio in air [with tdelay=1 μs, tint=1 μs (standard conditions)] with the the ratio IFe410.9/IZn328 in Ar [with tdelay=2 μs, tint=1 μs (optimised conditions)]. The optimised conditions were found by multivariate data analysis. The plot shows the deviations in the thicknesses determined with the calibration functions and the measured IFe/IZn ratio as a function of the conventional true coating thickness determined by GD-OES and wet chemistry. The RMSE value at optimum conditions is 140 nm, compared to 510 nm for standard conditions

Applying the temperature correction did not appear to lead to any improvement in the thickness resolution. An explanation for this is that the plasma temperature also depends on the coating thickness. For a particular burst energy, the plasma temperature was found to be higher for thinner coatings (ΔTe∼500–1000 K higher for dZn=4.1 μm than for dZn=11.2 μm). So Te also contains depth information that is eliminated by the temperature correction. Since we use a calibration method, the IFe/IZn ratio does not need to reflect the true ratio of ablated Fe atoms to Zn atoms.

Conclusion

The results demonstrate the potential of LIBS for online high-precision coating thickness measurements of galvanized sheet steel. At optimized measurement conditions, a thickness resolution of ∼140 nm can be achieved, which is comparable to the resolution limit of online XRF gauges. Compared to a previous study, where the measurements were performed by evaluating the IFe438/IZn472 ratio in air, the thickness resolution is further enhanced by more than a factor of 3 using this method. A multivariate date analysis was applied in order to find the optimum burst energy range and the best IFe/IZn ratio out of the 2772 possible combinations. The increase in resolution achieved here is mainly because lines with low self-absorption are selected and an Ar flow is directed onto the sample surface.

Acknowledgements

The authors thank Dr. S. Janssen, ThyssenKrupp Stahl AG (TKS), Germany for providing the different sheet steel samples and for sample analysis. Financial support by the European Coal and Steel Community (ECSC) and the Fraunhofer Society is gratefully acknowledged.

Copyright information

© Springer-Verlag 2006