We have developed a simulation program that allows to calculate the plasma emission spectrum of a coal sample in a LIBS experiment. We used the acquired data to evaluate the effect of temporal integration on the accuracy of measured concentration obtained using the calibration free method

D.A. Redoglio

S. Musazzi

U. Perini

AIR Universita degli studi di Milano

EFFECT OF THE TEMPORAL INTEGRATION ON THE ACCURACY  
OF THE MEASURED CONCENTRATION IN LIBS MEASUREMENTS 
D. A. Redoglio1, S. Musazzi2, U. Perini2  
1 Università degli Studi di Milano, Dipartimento di Fisica, Via Celoria 16, 20133 Milano. Daniele.redoglio@unimi.it 
2 Ricerca sul Sistema Energetico – RSE SpA, via Rubattino 54, 20134 Milano. Sergio.musazzi@rse-web.it 
 We have developed a simulation program that allows to calculate the plasma emission spectrum of a coal sample in a LIBS experiment. We used the acquired data to evaluate the effect of temporal 
integration on the accuracy of measured concentration obtained using the calibration free method. 
Introduction 
The Laser Induced Breakdown Spectroscopy (LIBS) is a laser based analytical technique 
capable of providing both qualitative and quantitative chemical composition of gas, liquid 
and solid samples. The principle of operation relies on the generation of a breakdown 
plasma by means of high irradiance (>1010 W/cm2) laser pulses. Light contributions emitted 
by the plasma are collected and spectrally analyzed by a properly designed detection unit. 
To get quantitative measurements, this method usually requires the construction of 
empirical calibration curves, which in many cases (like e.g. in non-homogeneous materials) 
can hardly be derived. To cope with this problem we are evaluating the use of the so called 
calibration free method. With the present work we intend to estimate the dependence of 
the measured concentration on the measuring integration time.  
Calibration free method  
Using Local Thermal Equilibrium approximation, the intensity of 
a spectral line due to a transition between the atomic level k and 
i is given by the Eq. 1, where C is the concentration of the atomic 
species of interest, U(T) is its partition function at temperature T, 
Aki is the Einstein transition probability of k i transition, gk and 
Ek are respectively the statistical weight and the energy of the k-
th level, while Kb is the Boltzmann constant. As shown in Eq. 2, 
derived from Eq. 1, a linear relationship exists between the 
upper energy k  and the quantity ln 𝐼 𝐴𝑔 . By means of a linear 
fit it is possible to obtain both the temperature T and the 
quantity 𝛼𝐶𝑛 for every atomic species. The 𝛼 factor can thus be 
determined by normalizing to the unit the sum of the species 
concentration  𝐶𝑛 = 1𝑛 . In this way the relative concentration 
of the sample’s component can be derived 
Simulation program 
Utilizing data taken from the NIST database, we developed an algorithm that allows 
to calculate the emission spectrum generated by a sample of chosen composition. 
We also used the values of temperature and electron numerical density measured 
by Dong et al. (J. Anal. Act. Spectrom., 27, 2066, 2012)  to simulate the evolution of 
the spectra as a function of time. By summing up a number of these spectra it was 
possible to reproduce the effect of time integration. As shown in the figure, the 
ratio between line intensities of different elements changes as a function of the 
integration time, thus preventing a correct measure of the concentration. 
Results 
By means of the simulation program, we have calculated the LIBS spectra of samples with different 
elemental composition and for each one we have evaluated the elemental concentrations for different 
integration times. As an example we show the result relevant to a sample with the following 
composition: 90.5% of carbon, 5% silicon, 3% aluminum, 1% iron and 0.5% calcium. As it can be 
noticed, the calculated carbon concentration does not significantly change as a function of the 
integration time, while the concentration of the other elements vary up to 25% with respect to the 
input original concentration. We have also observed that the concentration of more abundant species 
changes more slowly than concentration of the less abundant ones and that concentration of elements 
with stronger emission lines usually changes faster than concentration of elements with lower intensity 
line. Furthermore, it seems that concentration changes faster in samples made by few elements. The 
only evident exception we have found so far is the case of samples with a high content of hydrogen. In 
fact, in spite of the fact hydrogen lines are weak, the measured hydrogen concentration can vary up to  
60% of the input value. The same anomalous behavior is observed for other elements of the sample. 
𝐼𝑘𝑖 = 𝛼𝐶
𝐴𝑘𝑖𝑔𝑘
𝑈 𝑇
𝑒
−
𝐸𝑘
𝑘𝐵𝑇 
𝑙𝑛
𝐼𝑘𝑖
𝐴𝑘𝑖𝑔𝑘
= −
1
𝑘𝐵𝑇
𝐸𝑘 + 𝑙𝑛
𝛼𝐶
𝑈 𝑇
 2  
1  
This work has been financed by the Research Fund for the Italian Electrical System under the Contract Agreement between 
RSE (formerly known as  ERSE) and the Ministry of  Economic Development - General Directorate for  Nuclear Energy, 
Renewable Energy and  Energy Efficiency    stipulated on  July 29, 2009 in compliance with the Decree of  March 19, 2009. 


Effect of the temporal integration on the accuracy of the measured concentration in LIBS measurements

https://air.unimi.it/retrieve/handle/2434/257261/354277/poster%20fotonica%202013%20ufficiale.pdf

Effect of the temporal integration on the accuracy of the measured concentration in LIBS measurements

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