Laser-Induced Breakdown Spectroscopy Fundamentals and Applications
This book is a comprehensive source of the fundamentals, process parameters, instrumental components and applications of laser-induced breakdown spectroscopy (LIBS). The effect of multiple pulses on material ablation, plasma dynamics and plasma emission i
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The annex starts with a section giving an estimate of the necessary energy to displace the ambient gas atmosphere caused by the expansion of the laser-induced plasma. The following sections list the abbreviations and symbols used in this book. The most relevant Stark data for the spectroscopic determination of the electron density of LIBS plasmas are compiled in Sect. A.4. Lists of wavelengths and elements are provided in Sect. A.5. Finally, Sect. A.6 describes a method to select spectral lines for Boltzmann plots.
A.1 Displacement of Ambient Atmosphere As shown in Sect. 8.1 and Table 8.2 more than 97% of the ambient atmosphere particles are displaced by the expanding laser-induced plasma. A result which is consistent with the simulations presented in Sect. 10.3, Fig. 10.5. In the following the energy necessary for the displacement of the ambient atmosphere will be estimated. The irradiated laser beam evaporates target material. The particles flowing off collide with particles of the ambient atmosphere. By these collisions, the ambient atmosphere is partially displaced. A part of the ambient gas particles diffuses into the material vapor (cf. Table 8.2, Fig. 10.5). For simplicity, it is assumed that the ambient atmosphere is displaced completely by the expanding material vapor. In case of a complete displacement, the material vapor and plasma has to do work, which will be calculated taking the following assumptions (a) spherical expansion, (b) the ambient gas is collected at the front of the expanding plasma. The latter is a simplification and yields an upper estimate for the displacement energy (a more realistic description would have to consider the flow of ambient gas induced by the expanding vapor). Then the expanding plasma has to provide the energy given by: Z R Z R d Ed D .ma rP / dr F dr D (A.1) 0 0 dt R. Noll, Laser-Induced Breakdown Spectroscopy, DOI 10.1007/978-3-642-20668-9, © Springer-Verlag Berlin Heidelberg 2012
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with Ed displacement energy, R radius of the expanding plasma, ma accumulated mass of ambient gas, rP velocity of the accumulated ambient gas at the expanding plasma front. For the accumulated mass of the ambient gas and a half sphere holds: ma .t/ D a
2 r.t/3 ; 3
(A.2)
where a is the density of the ambient gas. Insertion of relation (A.2) into (A.1) leads to: 2a Ed D 3
ZR
3 r rR C 3r 2 rP 2 dr:
(A.3)
0
The second integrand can be transformed as follows: Z
Z 3r 2 rP 2 dr D
Z rP 2 dr 3 D rP 2 r 3
Z r 3 drP 2 D rP 2 r 3 2
r 3 rR dr
(A.4)
which yields for (A.3): 2a Ed D 3
Z r rP 3 2
ˇˇR ˇ r rR dr ˇ ˇ 3
(A.5)
0
The kinetic energy of the accumulated gas at the front of the material vapor is given by: Ekin D
1 2a 3 P 2 R R : 2 3
(A.6)
Relations (A.5) and (A.6) show that for negligible acceleration of the front of the expanding material vapor, i.e., the second term in (A.5) can be neglected, the displacement work is just twice as much as the kinetic energy of the accumulated gas. This case is equivalent to a completely inelastic col
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