Analytical and Bioanalytical Chemistry

, Volume 385, Issue 2, pp 316–325

Comparison of detection limits, for two metallic matrices, of laser-induced breakdown spectroscopy in the single and double-pulse configurations

Authors

  • Marwa A. Ismail
    • National Institute of Laser Enhanced Sciences (NILES)Cairo University
  • Gabriele Cristoforetti
    • Applied Laser Spectroscopy LaboratoryInstitute for Chemical-Physical Processes of CNR
  • Stefano Legnaioli
    • Applied Laser Spectroscopy LaboratoryInstitute for Chemical-Physical Processes of CNR
  • Lorenzo Pardini
    • Applied Laser Spectroscopy LaboratoryInstitute for Chemical-Physical Processes of CNR
  • Vincenzo Palleschi
    • Applied Laser Spectroscopy LaboratoryInstitute for Chemical-Physical Processes of CNR
  • Azenio Salvetti
    • Applied Laser Spectroscopy LaboratoryInstitute for Chemical-Physical Processes of CNR
    • Applied Laser Spectroscopy LaboratoryInstitute for Chemical-Physical Processes of CNR
  • Mohamed A. Harith
    • National Institute of Laser Enhanced Sciences (NILES)Cairo University
Special Issue Paper

DOI: 10.1007/s00216-006-0363-z

Cite this article as:
Ismail, M.A., Cristoforetti, G., Legnaioli, S. et al. Anal Bioanal Chem (2006) 385: 316. doi:10.1007/s00216-006-0363-z

Abstract

Limits of detection have been studied for several elements in aluminium and steel alloys, at atmospheric pressure in air, by use of the single and collinear double-pulse configurations of laser-induced breakdown spectroscopy. For this purpose, calibration plots were constructed for Mg, Al, Si, Ti, Cr, Mn, Fe, Ni, and Cu using a set of certified aluminium alloy samples and a set of certified steel samples. The investigation included optimization of the experimental conditions to furnish the best signal-to-noise ratio. Inter-pulse delay, gate width, and acquisition delay were studied. The detection limits for the elements of interest were calculated under the optimum conditions for the double-pulse configuration and compared with those obtained under the optimum conditions for single-pulse configuration. Significantly improved detection limits were achieved, for all the elements investigated, and in both aluminium and steel, by use of the double-pulse configuration. The experimental findings are discussed in terms of the measured plasma conditions (particle and electron density, and temperature).

Keywords

Laser-induced breakdown spectroscopyDouble-pulseAESUV–visibleMetals/Heavy Metals

Introduction

Detection limits in laser-induced breakdown spectroscopy (LIBS) are typically poorer than those obtained by other elemental analysis techniques [1] and the LIBS signal for a specific element, even for fixed experimental conditions, may depend on the general composition of the sample investigated [2]. In a previous investigation based on single-pulse LIBS, large differences were observed between detection limits for Mg, Mn, and Cu, depending on the kind of the alloy (aluminium or steel) [3]. In this work we have extended the investigation to the double-pulse LIBS configuration, to check whether detection limits can be improved by use of this configuration rather than single-pulse.

The analytical benefits of using double-pulse irradiation in LIBS have been reported elsewhere [4, 5]. Since then, many efforts have been devoted to characterization of the mechanisms of the observed signal enhancement. Different double-pulse approaches have been proposed, ranging from collinear [513] to orthogonal geometry [4, 1419], from infrared [46, 816] to visible and ultraviolet laser wavelengths [7, 17], and from nanosecond [418] to femtosecond pulse duration [19, 20]. In these different modes, a large variety of results has been obtained. Intensity enhancements (compared with delivery of the same total energy in single-pulse mode) reported in the literature range from a factor of two [5, 13] to a factor of 30–40 [7, 1416]. The relative standard deviation of the signal has been found to be improved by use of the double-pulse configuration [5, 6]. Comparison of plasma temperature and electron density measured in the double and single-pulse configurations has provided different results which depend on the measurement conditions [5, 6, 8, 11, 16, 18]. The change in mass ablation has also been evaluated by several groups [5, 7, 8, 14, 21].

As far as we are aware, claims of signal enhancement have usually been based on comparison of the line intensity measured after single and double-pulse irradiation, under the same conditions of acquisition gate delay and width. It has, however, been demonstrated that time and space evolution of the plasma plume produced by double-pulse irradiation are very different from those in the single-pulse configuration [5, 8, 11, 13]. Acquisition of double-pulse spectra under conditions optimized for single-pulse spectra may therefore lead to underestimation of the potential of the double-pulse configuration. Equally, comparison of single and double-pulse spectra obtained under conditions optimized for the double-pulse configuration may lead to overestimation of the benefits achievable [13].

For these reasons a systematic investigation has been devised to determine the dependence of the signal-to-noise ratio (SNR) on acquisition conditions in single and double-pulse configurations. Measurements on certified samples were then performed under the conditions found to provide the best analytical performance in both single and double-pulse configurations. Finally, the results are discussed in terms of the measured plasma conditions.

Experimental

Instrumentation

The Modì instrument, a mobile LIBS system developed in the Applied Laser Spectroscopy Laboratory, Pisa, Italy, was used to perform the measurements. The schematic arrangement of the equipment is depicted in Fig. 1. The instrument integrates a dual-pulse Nd:YAG laser, operating at the fundamental wavelength, in which a single flash lamp simultaneously pumps two active rods. The laser can emit two collinear pulses of variable energy between 20 and 120 mJ per pulse at a maximum repetition rate of 10 Hz and with an inter-pulse delay which can be set from 0 to 60 μs. The pulse width is 12–13 ns for both channels, irrespective of the applied inter-pulse delay, at least in the range explored in this work (0 to 5 μs). A 100 mm-focal length lens was used to focus the beam on the sample surface. A translation stage enabled fine positioning of the sample relative to the focus of the lens, and a video camera provided a magnified image of the irradiated area. With the objective of achieving the best possible reproducibility, the lens-to-sample distance was tuned to approximately 95 mm [22]. The spatially integrated LIBS signal was collected through an optical fiber (3 cm distance, 45°-tilted relative to the plane of the sample surface, N.A.=0.22) and sent to a compact echelle spectrometer coupled to an intensified CCD camera for spectral acquisition. The Δλ/λ spectral resolution, constant over the available spectral range of 2000–9000 Å, was approximately 1/5000. The ICCD adjustable settings include the integration time width and the delay of the acquisition relative to the laser pulses. The LIBS spectra, after acquisition and storage, were analyzed by use of proprietary software (LIBS++).
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Fig. 1

Schematic diagram of the experimental arrangement used for measurement

For these measurements the pulse energy was set to 30 mJ per pulse with 1 Hz repetition rate. The pulse stability at the chosen energy level was approximately 5%, after discarding the first five shots of the sequence, used for preparation and not for analytical purposes. As a consequence of the loose focusing, irradiance on the sample was approximately 3 GW cm−2.

Samples and procedures

A set of aluminium alloy certified samples and a set of steel alloy certified samples were used to construct calibration plots for Mg, Al, Si, Ti, Cr, Mn, Fe, Ni, and Cu. Tables 1 and 2 list the certified concentrations of the elements under investigation in the sets of aluminium and steel samples, respectively.
Table 1

Certified mass concentration (%) of the elements under investigation in the aluminium samples used during this work

Element

Sample

A

B

C

D

E

F

Mg

0.1

0.31

0.329

0.05

0.016

Al

92.85

97.775

86.98

84.42

87.17

98.979

Ti

0.031

0.025

0.108

0.114

0.1575

Cr

0.022

0.01

0.032

0.039

Mn

0.37

1.46

0.8

0.19

0.331

0.025

Fe

0.58

0.2

0.5

0.9

0.47

0.58

Ni

0.0205

0.05

0.21

0.356

0.0572

Cu

5.05

0.05

9.45

2.93

0.0256

0.017

The aluminium concentration is also provided for reference

Table 2

Certified mass concentration (%) of the elements under investigation in the steel samples used during this work

Element

Sample

P

Q

R

S

T

Al

0.2

0.17

0.05

0.01

0.04

Si

1

0.8

0.17

0.29

0.01

Ti

0.34

0.11

0.04

0.01

0.01

Cr

1.3

3

0.19

1.2

0.01

Mn

1.5

0.4

1.2

0.44

0.14

Fe

92.636

92.44

93.247

95.723

99.67

Ni

1.1

0.1

3.4

1.5

0.02

Cu

0.39

0.11

0.47

0.15

0.02

The iron concentration is also provided for reference

Before the calibration measurements, an investigation was performed to find the experimental conditions leading to the best SNR (on average over the different lines of interest, as explained below) for both the single and double-pulse configurations. Certified aluminium sample D and certified steel sample R were used in this preliminary investigation. Samples with rather high analyte concentrations were chosen to this purpose to enable measurement of a detectable signal even in the single-pulse configuration with the expected less favorable timing settings (short gate, long delay). Usually a more complete and reliable procedure may be envisaged for choice of the optimum experimental conditions [23]. The acquisition gate width and delay were varied among the values 100, 500, 1000, and 5000 ns and 500, 1000, 2000, 3000, and 5000 ns, respectively; the inter-pulse separation was varied among the values 0 (single-pulse), 1000, 2000, 3000, and 5000 ns. Each spectrum was obtained by accumulation of ten shots (or bursts) after five cleaning shots on a fresh area of the surface. Because of the availability of a broad-band spectrum, as provided by the echelle-CCD detection equipment, several spectral lines from the elements of interest were considered for evaluation of the SNR under the conditions investigated. For each element, lines were chosen for which spectral interference from other alloy components was minimal; the lines investigated for the aluminium and steel samples are listed in Table 3; spectroscopic data were extracted from NIST database [24]. The lines used to evaluate the detection limits were then chosen from among those listed in Table 3, on the basis of their signal-to-noise ratio. In general, lines among the most intense for each element were chosen, to guarantee satisfactory detection limits, disregarding possible non-linearity of the calibration curves at high concentrations.
Table 3

Wavelength and spectral characteristics of the lines investigated in this study for both aluminium and steel alloys

Wavelength (Å)

Element

Ionization

Ej (eV)

Ei (eV)

gj

gi

Aij(108 s−1)

Al alloy

Steel alloy

2524.11

Si

I

0.010

4.920

3

1

1.818

 

X

2599.40

Fe

II

0.000

4.768

10

10

2.2

X

 

2852.13

Mg

I

0.000

4.346

1

3

4.95

X

 

2881.58

Si

I

0.781

5.082

5

3

1.894

 

X

2933.06

Mn

II

1.174

5.400

5

3

2

X

 

2949.20

Mn

II

1.174

5.377

5

7

1.9

X

X

3088.02

Ti

II

0.049

4.062

10

8

1.25

 

X

3247.54

Cu

I

0.000

3.817

2

4

1.37

X

X

3341.88

Ti

I

0.000

3.709

5

7

0.65

 

X

3349.41

Ti

II

0.049

3.749

10

12

1.33

X

X

3414.76

Ni

I

0.025

3.655

7

9

0.55

X

X

3515.05

Ni

I

0.109

3.635

5

7

0.42

 

X

3719.93

Fe

I

0.000

3.332

9

11

0.162

X

 

3961.52

Al

I

0.014

3.143

4

2

0.98

 

X

4030.76

Mn

I

0.000

3.075

6

8

0.174

X

X

4254.33

Cr

I

0.000

2.913

7

9

0.315

X

X

4823.52

Mn

I

2.319

4.889

10

8

0.499

 

X

To calculate the signal-to-noise ratio, the peak intensity was determined for each line in Table 3 after a best fitting procedure to separate the contributions from the continuum and from possible overlapping lines. The analytical function used for fitting was a Voigt function. The noise was determined as the standard deviation of the continuum baseline calculated for a spectral interval contiguous with the line and free from discrete emissions.

For the aluminium alloy the best SNR values were always obtained at the longest gate of 5000 ns. This evidence enables the gate width to be omitted as a variable setting; the dependence of the signal-to-noise ratio on the two remaining settings (acquisition delay and inter-pulse delay) can then be easily displayed as a 2D graph. For ease of representation, the results obtained from all the lines have been merged in two maps showing the average trend of the signal-to-noise ratio for neutral and ionized lines (Fig. 2a,b respectively). Because the SNR values of the different lines spanned different ranges (for example 2–37 for Cr 4254.33, 12–195 for Mn 2949.20), the two-dimensional maps corresponding to the different lines were previously normalized and then summed; specifically, the average SNR value for each map was set to unity and all the values of the SNR for the same line were rescaled accordingly. The final signal-to-noise ratio values shown in Fig. 2 should therefore be regarded as being given in arbitrary units.
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Fig. 2

Two-dimensional maps showing the dependence of the signal-to-noise ratio on inter-pulse delay (x-axis) and acquisition delay (y-axis), obtained by averaging the results corresponding to the neutral (a) and ionized (b) lines investigated for the aluminium-based alloy. The acquisition gate was fixed at 5000 ns. The average signal-to-noise values were normalized to unity

From these two maps it is evident that the signal-to-noise ratio is greatly improved by use of double-pulse rather than single-pulse irradiation of the same total energy (inter-pulse delay=0 in Fig. 2). Moreover, whereas neutral lines seem to benefit from long acquisition delays, for any value of the inter-pulse separation, for intermediate values of the acquisition delay ionic lines have the best signal-to-noise ratio.

On the basis of the results shown in Fig. 2a,b the conditions listed in Table 4 were chosen for subsequent measurements on the set of aluminium samples. Analysis of the steel spectra, not shown here, led to similar results (Table 4).
Table 4

Summary of the irradiation and acquisition settings chosen for measurement after optimization of the SNR

Alloy

Irradiation

Emitting species

Optimum inter-pulse delay (μs)

Optimum acquisition delay (ns)

Optimum gate width (ns)

Aluminium

Single

Neutral

 

5000

5000

Ionic

 

3000

5000

Double

Neutral

2

5000

5000

Ionic

1

2000

5000

Steel

Single

Neutral

 

5000

5000

Ionic

 

3000

5000

Double

Neutral

2

5000

5000

Ionic

3

2000

1000

Results

Measurements on the certified samples were performed in accordance with the procedure already followed for optimization. Each spectrum was acquired by irradiating a new area and accumulating ten laser shots (or burst) after five cleaning shots. Five spectra were acquired for each combination of settings listed in Table 4, to evaluate the reproducibility of the measurement. The intensity of the spectral lines chosen for the construction of the calibration plots was evaluated by means of best fitting using a Voigt function. Detection limits were calculated according to the 3s IUPAC criterion:
$$LOD = 3\frac{{s_{B} }} {S}$$
(1)
where sB is the standard deviation of the continuum background (called “noise”, above) and S is the slope of the calibration plot at the lowest measured concentration.
General enhancement of the signal intensity was observed in double-pulse spectra compared with single-pulse spectra obtained at the same total energy. This resulted in steeper slopes of the calibration plots, as shown in the example in Fig. 3.
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Fig. 3

Calibration plots obtained for manganese in steel, using the line Mn I at 4823 Å. Error bars represent the standard deviation of the intensity from five replicate measurements

Although noise was no lower in double-pulse spectra (rather, it increased slightly compared with single-pulse spectra), the balance between strong line enhancement and the weakly increased noise resulted in general improvement of the detection limits by approximately one order of magnitude in double-pulse experiments for the elements contained in the aluminium alloys (Table 5). The double-pulse configuration also resulted in improved LOD in analysis of the steel alloys, although the magnitude of the improvement was less than for aluminium.
Table 5

Comparison of limits of detection obtained in the single and double-pulse configurations for aluminium and steel alloys

Element

Wavelength (Å)

Single-pulse

Double-pulse

Aluminium alloys

Mg

2852.13

30 ppm

4 ppm

Ti

3349.41

100 ppm

10 ppm

Cr

4254.33

100 ppm

10 ppm

Mn

2949.20

0.1%

90 ppm

Fe

3719.93

400 ppm

50 ppm

Ni

3414.76

600 ppm

100 ppm

Cu

3247.54

150 ppm

80 ppm

Steel alloys

Al

3961.52

30 ppm

20 ppm

Si

2881.58

100 ppm

40 ppm

Ti

3088.02

50 ppm

25 ppm

Cr

4254.33

70 ppm

50 ppm

Mn

4823.52

300 ppm

120 ppm

Ni

3414.76

100 ppm

40 ppm

Cu

3247.54

25 ppm

5 ppm

It should be borne in mind, however, that the results obtained here are specific to the experimental equipment and conditions adopted during our measurements. LOD better than those in Table 5 have previously been obtained by other groups working with multiple pulses and different experimental setups (for example: measurements performed in argon buffer gas, with a Paschen–Runge spectrometer and with pulse energies of the order of 200 mJ) [25, 26]. The main objective of this work, however, was not achievement of the best possible LOD but evaluation of the effect of delayed-pulse irradiation at the same total energy value.

Under our conditions, double-pulse seems to be more efficient at improving detection limits for aluminium alloys than for steel. On the basis of the definition of detection limit given in Eq. 1, we can try to find the source of the different improvement. One possible explanation can be identified in the large number of weak lines emitted by the major element (iron) in the steel matrix—in double-pulse spectra, especially, the crowding of these lines may be responsible for overestimation of the noise and, therefore, of the detection limits.

If, on the other hand, we compare the line-intensity enhancements (and thus the slope increase) obtained by use of double-pulse irradiation for the two matrices, we obtain a factor of 4–5 for steel and a factor of 20–40 for aluminium. Therefore, not only possible overestimation of the noise, as mentioned above, but also less effective enhancement of the signal itself seem to contribute to the reduced improvement of the detection limits for steel compared with aluminium alloys.

Close inspection of the results listed in Table 5 reveals that for several elements (Cr, Cu, Ni) the same emission lines gave the best LOD for both matrices whereas for other elements different lines were chosen for the different matrices (Mn 2949.20, Ti 3349.41 for aluminium; Mn 4823.52, Ti 3088.02 for steel). If the most important criteria (lack of interference, high relative intensity) are fulfilled by several lines of the same element, the choice between neutral or ionized lines may still be open to the analyst. The dependence of the choice on the experimental conditions is discussed in the next section.

Discussion

To explain the results described in the previous section, we started with analysis of the spectra collected during the optimization step. In particular, the plasma temperature and electron density were calculated from these spectra. The electron density was evaluated from the Stark broadening of the Hα line at 6562.85 Å [27], after subtraction of the instrumental broadening. Even if not included in the alloy components, hydrogen is present in the LIBS plasma produced in air, because of the natural humidity. The electron temperature was calculated, assuming LTE (see below), using the Saha–Boltzmann plot method [28]. For the aluminium alloy the Saha–Boltzmann plot was constructed using several optically thin aluminium emission lines: Al I at 3050.07, 3054.68, 3057.14, 3064.29, 3066.14 Å; Al II at 3586.56, 4663.15 Å. For steel, the following non-resonant lines from iron were used: Fe II at 2598.37, 2611.87, 2613.82, 2739.55 Å, Fe I at 3815.84, 3820.42, 4071.73, 4260.47, 4325.76, 4404.75, 4918.99, 4920.50, 5383.37 Å. Relevant spectroscopic data were obtained from NIST database [24]. Line intensities were corrected for the combined spectral efficiency of the collection–detection system.

The resulting plasma temperature and electron density calculated from the spectra of aluminium alloy D are shown in Fig. 4a,b respectively. The data shown in this figure correspond to spectra acquired with an integration gate of 500 ns.
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Fig. 4

Two-dimensional maps of the dependence of plasma temperature (a) and electron density (b) on inter-pulse delay (x-axis) and acquisition delay (y-axis) for aluminium alloy sample D

Inspection of Fig. 4 reveals that double-pulse irradiation leads to quite different plasma conditions than single-pulse irradiation. The plasma temperature is similar at the beginning (taking into consideration uncertainty of approximately 3%) then decreases less rapidly. The electron density, in contrast, is lower in double-pulse spectra at the beginning but subsequent evolution leads to values equal to those of the single-pulse spectra. Uncertainty in the electron density may be evaluated as being approximately 10%. Similar behavior was observed for steel sample R (Fig. 5). The differences between the properties of single and double-pulse plasmas for a given delay time are in agreement with those observed in previous studies [5, 10] that investigated multiple pulse irradiation of steel samples. The main differences between Figs. 4 (aluminium alloy) and 5 (steel alloy) are the lower values of both temperature and electron density for the latter.
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Fig. 5

Two-dimensional maps of the dependence of plasma temperature (a) and electron density (b) on inter-pulse delay (x-axis) and acquisition delay (y-axis) for steel alloy R

Fulfillment of the necessary criterion for validity of the assumption of the LTE condition [29]:
$$n_{e} \geq 1.4 \cdot 10^{{14}} T^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \Delta E^{3} $$
(2)
(where ΔE, in eV, is the highest energy transition for which the condition holds, T, in eV, is the plasma temperature, and ne, in cm−3, is the electron density) was checked a posteriori on the basis of the measured values of temperature and electronic density as reported in the maps. The threshold value for electron density was found to be 1016 cm−3, therefore the LTE can be regarded as a reasonable approximation under our conditions.
For a given temperature, T, and electron density, ne, the intensity of a spectral line of known spectral properties, under optically thin conditions, may be expressed as [30]:
$$\overline{I} ^{z}_{{ij}} {\left( {T,n_{e} } \right)} = F^{{\det }} n^{z} {\left( {T,n_{e} } \right)}A_{{ij}} \frac{{g_{i} e^{{{ - E_{i} } \mathord{\left/ {\vphantom {{ - E_{i} } {k_{B} T}}} \right. \kern-\nulldelimiterspace} {k_{B} T}}} }}{{U^{z} {\left( T \right)}}}$$
(3)
where \(\overline{I} ^{z}_{{ij}} \) is the measured intensity of the line (counts), nz is the number density of the species of ionization state z in the plasma (cm−3), gi and Ei are, respectively, the statistical weight and excitation energy of the upper level of the transition, Aij (s−1) is the transition probability, kB is the Boltzmann constant, Uz(T) is the internal partition function of the species at temperature T and Fdet is an experimental factor taking into account the detection efficiency and the geometry of the collection.
The number density of the species considered (neutral or singly ionized, in a typical LIBS plasma) depends on the total particle number density of the plasma and on the concentration of the corresponding element. In addition to this dependence, the number density of a species depends, in turn, on the temperature and electron density according to the equilibrium condition [29]:
$$n_{e} \frac{{n^{{II}} }}{{n^{I} }} = \frac{{{\left( {2\pi m_{e} k_{B} T} \right)}^{{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2}} }}{{h^{3} }}\frac{{2U^{{II}} {\left( T \right)}}}{{U^{I} {\left( T \right)}}}e^{{ - \frac{{E_{{ion}} }}{{k_{B} T}}}} $$
(4)
where superscripts refer to the ionization state (I neutral, II ionized), me is the electron mass, h is the Planck constant and Eion is the first ionization potential of the element under investigation.
This discussion reveals clearly that choice of the optimum line of a given element to be used for construction of the calibration plot, under the constraints already stated, strongly depends on the temperature and electron density of the laser-induced plasma under the conditions of the measurement. In fact, assuming optically thin conditions, the ratio of the intensity of a neutral line to that of an ionic line for a given element is given by:
$$\frac{{I^{I}_{{ij}} {\left( {T,n_{e} } \right)}}}{{I^{{II}}_{{ij}} {\left( {T,n_{e} } \right)}}} = \frac{{n^{I} {\left( {T,n_{e} } \right)}A^{I}_{{ij}} \frac{{g^{I}_{{_{i} }} e^{{{ - E^{I} _{i} } \mathord{\left/ {\vphantom {{ - E^{I} _{i} } {k_{B} T}}} \right. \kern-\nulldelimiterspace} {k_{B} T}}} }}{{U^{I} {\left( T \right)}}}}}{{n^{{II}} {\left( {T,n_{e} } \right)}A^{{II}}_{{ij}} \frac{{g^{{II}}_{{_{i} }} e^{{{ - E^{{II}} _{i} } \mathord{\left/ {\vphantom {{ - E^{{II}} _{i} } {k_{B} T}}} \right. \kern-\nulldelimiterspace} {k_{B} T}}} }}{{U^{{II}} {\left( T \right)}}}}}$$
(5)
where \(I^{z}_{{ij}} \) is the number of photons emitted per unit volume and the other symbols have the same meaning as defined above. Substituting the ratio nI/nII from Eq. 4 we obtain:
$$\frac{{I^{I}_{{ij}} {\left( {T,n_{e} } \right)}}}{{I^{{II}}_{{ij}} {\left( {T,n_{e} } \right)}}} = \frac{{n_{e} }}{2}\frac{{A^{I}_{{ij}} g^{I}_{{_{i} }} }}{{A^{{II}}_{{ij}} g^{{II}}_{{_{i} }} }}\frac{{h^{3} }}{{{\left( {2\pi m_{e} k_{B} T} \right)}^{{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2}} }}e^{{{ - {\left( {E^{I} _{i} - E^{{II}} _{i} - E_{{ion}} } \right)}} \mathord{\left/ {\vphantom {{ - {\left( {E^{I} _{i} - E^{{II}} _{i} - E_{{ion}} } \right)}} {k_{B} T}}} \right. \kern-\nulldelimiterspace} {k_{B} T}}} $$
(6)
where the dependence of the intensity ratio on ne and T is made explicit. It is worth mentioning that Eq. 6 is valid irrespective of the matrix, because the dependence of the intensity on the sample matrix is included in the dependence on the temperature and electron density. It should be noted, however, that Eq. 6 applies to the ratio of intensities emitted by the plasma source; the actual ratio found by direct measurement can be different, because of the wavelength-dependence of the spectral response of the collection/detection systems.
To evaluate the variability of the intensity ratio expected under a range of different experimental conditions, we calculated, by use of Eq. 6, the ratio of intensity of the Mn I line at 4030 Å to that of the Mn II line at 2949 Å on a grid of temperature and electron density values representing the range of conditions found during the optimization procedure for both aluminium and steel. The results are shown in Fig. 6.
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Fig. 6

Ratio of the predicted intensity of the neutral 4030 Mn line to that of the ionized 2949 Mn line under different conditions of temperature and electron density representative of LIBS spectra obtained under our experimental conditions

It may be noticed that the expected intensity ratio of the two lines spans five orders of magnitude under the experimental conditions found during our optimization procedure. In particular, under the experimental conditions chosen as the working point for the calibration plots for aluminium, the neutral line intensity is comparable with that of the ionic line (expected ratio values are 1.7 under the conditions optimized for neutral lines and 0.5 under the conditions optimized for ionic lines). For steel, however, because of the slightly lower temperature and electron density conditions at the chosen working point, the equilibrium is displaced toward the neutral species. Expected ratio values are 16 under the conditions optimized for neutral lines and 2.3 under those optimized for ionic lines. It is, therefore, easy to recognize that for the steel matrix the best LOD for Mn may be obtained by using a neutral line whereas for the aluminium matrix the same is true for an ionic line, as reported in Table 5.

The expression for line intensity (Eq. 3) may also be useful in investigation of the causes of the different enhancements obtained by using the double-pulse configuration for aluminium and steel. Eq. 3 enables calculation of the dependence on temperature and electron density of the expected relative intensity values for a specific spectral line, assuming constant total plasma density and volume and element concentration (i.e. \(F^{{\det }} \cdot n^{{plasma}}\kern-3\cdot c^{{element}} = const.\)). The latter hypothesis corresponds to the assumption of stoichiometric ablation and homogeneous distribution of the elements inside the plasma, which are the basis of the measurement method itself. The former hypothesis of constant plasma density and volume is formulated per absurdum, and its validity will be checked after comparison of predictions with experimental results. Thus, the map of expected relative intensity was calculated, under the temperature and electron density conditions shown in Fig. 4 for aluminium alloy D, for the neutral Mn 4030 line (Fig. 7a) and the ionized Mn 2949 line (Fig. 8a). The results of the prediction were then compared with the maps of experimentally measured intensity, shown in Figs. 7b and 8b, respectively.
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Fig. 7

Two-dimensional maps of predicted (a) and experimental (b) intensity of the line Mn 4030, for the aluminium matrix, showing the dependence on the inter-pulse delay (x-axis) and the acquisition delay (y-axis) investigated during the optimization

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Fig. 8

Two-dimensional maps of predicted (a) and experimental (b) intensity of the line Mn 2949, for the aluminium matrix, showing the dependence on the inter-pulse delay (x-axis) and the acquisition delay (y-axis) investigated during the optimization

It is evident from Figs. 7 and 8 that the predicted and experimental behavior are different and that both change from the neutral line to the ionized line. This latter difference is mainly because of changes of the relative abundances of the neutral and ionized species, which is very sensitive to the actual combination of temperature and electron density in the plasma, as discussed above.

The difference between prediction and observation, on the other hand, suggests that the assumption of constant plasma density and volume for both single and double-pulse plasmas and for the different time settings is incorrect. As already mentioned, for double-pulse irradiation increases of the emitting volume of a factor of three have been reported [10, 11]. On the other hand, the collection optics enabled spatial integration of the signal emitted from a volume of more than 100 mm3, enough to gather the emission from the whole double-pulse plasma. The difference between prediction and observation can, then, be explained by changes in the plasma density and emitting volume, i.e. in the total number of emitting particles which is proportional in turn to the ablated mass. These changes are not surprising if we take into account the larger mass ablated in the double-pulse configuration compared with single-pulse mode [5, 7, 8, 14, 21]. By dividing the experimental intensity values by the corresponding values calculated by use of Eq. 3 we can obtain an estimate of the relative number of emitting particles (scaled by an unknown experimental factor) under the different conditions investigated. The enhancement of ablation in the double-pulse configuration compared with the single-pulse configuration can then be found by normalization of the result to the value obtained for single-pulse irradiation with the same delay time. These calculations were performed for the Mn 4030 and 2949 lines from the aluminium and steel samples.

Despite the large uncertainty affecting this kind of calculation (mainly because of errors arising from temperature and electron density in the predicted intensity and from the oversimplified assumption of plasma homogeneity), the mass ablation enhancements estimated from the neutral and ionic Mn lines were in substantial agreement for both aluminium and steel matrices. An average enhancement of six was obtained from the two lines obtained in aluminium. The value calculated for steel, averaged on the neutral and ionized lines, was 3.

Thus use of the double-pulse configuration with the aluminium matrix led to a larger increase of ablation than when used with steel (a factor of two, approximately), in agreement with the greater enhancement of the limits of detection observed for use of the double-pulse configuration with aluminium alloys than with steel alloys. Because the effectiveness of double-pulse irradiation in increasing mass ablation is a result of reduction of the plasma shielding effect [12, 21], it could be hypothesized on the basis of these experimental findings (compare Figs. 4 and 5) that reduction of plasma shielding was lower for steel because plasma shielding itself was lower for this matrix. More experimental work is required to prove the validity of this hypothesis, however.

Conclusions

LIBS in the single and double-pulse configurations has been used to determine detection limits for several elements in aluminium and steel alloys. The measurement conditions were chosen after optimization of the signal-to-noise ratio for the lines of interest.

General enhancement of the signal intensity was observed for double-pulse spectra compared with single-pulse spectra obtained with the same total laser energy. Significant and appreciable improvement of the limits of detection was achieved in the double-pulse experiments. The extent of the improvement was larger for aluminium alloys than for steel. These differences for aluminium and steel alloys may be explained in terms of greater enhancement of the ablated mass in the double-pulse configuration compared with the single-pulse configuration.

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© Springer-Verlag 2006