_{1}

^{*}

In the present work, we have studied the temporal evolution of aluminum alloy plasma produced by the fundamental (1064 nm) of a Q-switched Nd:YAG laser by placing the target material in air at atmospheric pressure. The four Al I-neutral lines at 308.21, 309.27, 394.40 and 369.15 nm as well as Al II-ionic lines at 281.61, 385.64 and 466.30 nm are used for the determination of the electron temperature
T_{e} using Saha-Boltzmann plot method. The neutral aluminum lines were found to suffer from optical thickness which manifested itself on the form of scattered points around the Saha-Boltzmann line. The isolated optically thin hydrogen H
_{α}-line at 656.27 nm appeared in the spectra under the same experimental conditions was used to correct the Al I-lines which contained some optical thickness. The measurements were repeated at different delay times ranging from 1 to 5 μs. The comparison between the deduced electron temperatures from aluminum neutral lines before correction against the effect self-absorption to that after correction revealed a precise value in temperature. The results sure that, in case of the presence of self-absorption effect the temperature varies from (1.4067 - 1.2548 eV) as the delay time is varied from 0 to 5 μs. Whereas, in the case of repairing against the effect, it varies from (1.2826 - 0.8961 eV) for the same delay time variation.

The laser induced breakdown spectroscopy (LIBS) is a useful technique for elemental analysis of the materials in the form of solids, liquids and gases. It has a variety of applications like material analysis, environmental monitoring, determination of soil contamination, and biomedical studies, etc. [_{α}-line by focusing a 6 ns Nd:YAG laser pulse at 1064 nm on different solid targets material including aluminum target.

In this paper, we report the spectroscopic studies of the plasma generated at the surface of alumina (Al) by the fundamental (1064 nm) of a Q-switched Nd:YAG laser. We have studied the transitions at 256.87, 257.59, 265.32, 266.12, and 394.51 nm, and the resonance line at 396.26 nm of neutral aluminum. These transitions have been used to study the temporal behavior by estimating the plasma temperature T_{e} and the electron number density N_{e}.

The experimental setup is shown in

collected by a quarts fiber optics (25 µm diameter) positioned at a distance of 12.5 mm and normal to the direction of the laser beam. The optical fiber was connected with Echelle type spectrograph (type catalina, model SE 200) with resolving power of 2400 and equipped with a time gated ICCD Camera (1064 × 1064 pix with 13 µm × 13 µm pixel size at a binning mode of 1 × 1 (type Andor, model iStar DH 737-18F). The wavelength scale was calibrated using a low pressure Hg-lamp (type Ocean optics). The instrumental bandwidth was measured from the FWHM of the Hg lines and was found to be 0.12 ± 0.02 nm. The experimental setup was absolutely calibrated using a deuterium tungsten halogen lamp (type Ocean optics, model DH 2000 Cal.). The gain of the camera was kept at constant level of 200. The gate time was adjusted at a gate time of 2 µs while we have scanned the different delay times from 1 to 5 µs to measure the temporal variation of the plasma parameters at different delay times after the laser pulse.

In the first set of this experimental work, we have recorded the plasma emission generated by the fundamental (1064 nm) of a Nd:YAG laser. The laser was focused by a quarts lens with a focal length of 10 cm. Aluminum plasma was recorded at different delay times ranging from 1 to 5 µs along the direction of the propagation of the plasma. _{e}) and the electron temperature (T_{e}) respectively, and are listed with related details [

During the evaluation of laser induced plasma (LIP), excitation and ionization of the evaporated material occur. It is important to determine the thermodynamic parameters of LIP such as the electron number density and the

Element | Wavelength λ (nm) | Transition Probability A (sec-1) | Statistical Weight | Excitation energy (eV) | Stark broadening Parameter (nm)/Nr |
---|---|---|---|---|---|

Al I | 308.21 | 6.30e7 | 4 | 4.021 | 1.55/1e17 |

Al I | 309.27 | 7.40e7 | 5 | 4.022 | 0.005833/1e16 |

Al I | 394.40 | 4.93e7 | 2 | 3.143 | 0.001650/1e16 |

Al I | 396.15 | 4.93e7 | 2 | 3.143 | 0.001615/1e16 |

Al II | 288.61 | 3.83e8 | 1 | 11. 82 | 0 .00212/1e16 |

Al II | 358.64 | 2.35e8 | 9 | 15.30 | 0.040/1e17 |

Al II | 466.30 | 5.30e7 | 3 | 13.25 | 0.00603/1e16 |

electron temperature. One of the most reliable techniques to determine the electron number density is from the measured Stark broadened line profile of an isolated line of either neutral atom or single charge ion. The electron number density (N_{e}), related to the full width at half of maximum (FWHM) of the Stark broadening lines given by the following relation [

where, _{e} is the electron number density and N_{D} is the number of particles in the Debye sphere. The first term in Equation (1) refers to the broadening due to the electron contribution while, the second term is attributed to the ion broadening. Since the contribution of the ionic broadening is normally very small, therefore, it can be neglected. The electron number densities have been determined from the line profiles of the isolated aluminum neutral lines using Equation (1) by neglecting the contribution of the ion impact broadening and Doppler broadening to become in a new Equation:

where, Δλ is the Lorentzian FWHM of the line, and is the Stark broadening parameter, which can be found in [_{r} is the reference electron density which equal to 10^{16} (cm^{−3}) for neutral atoms and 10^{17} (cm^{−3}) for singly charged ions [

In the special case of the hydrogen H_{α}-line, the electron density can be related to the Lorentzian half width at the half of the maximum Δλ_{1/2} through the relation [

where, Δλ_{s} is the intrinsic full width at half of maximum (FWHM) of the spectral line in Angstrom, and α_{1/2} is the half width of the reduced Stark profiles in Angstrom. Precise values of α_{1/2} for the Balmer series can be found in [_{α}-line indicates the existence of self-absorption while, the aluminum ionic lines exhibits a good agreement with H_{α}-line reminiscent of free from self-absorption as shown in

The process of re-absorption of the plasma to the light photons in their path to outside the plasma active volume

T_{d} = 1 µs T_{d} = 2 µs T_{d} = 3 µs

is called the self-absorption. It is well known that this process affecting the spectral line shape i.e. the line intensity decreases and its full width at half maximum (FWHM) increases [

where, k(λ_{o})l is the optical depth of the plasma at the line center. Similarly, they suggested that the same amount (SA) can be expressed on the form of relative spectral line widths of Lorentzian components of the same line in a two different situations of self-absorbed line given by [

where, α = 0.56, Δλ_{o} is the intrinsic FWHM of the Lorentzian component of the spectral line if the line is optically thin and Δλ is the distorted Lorentizian of the same line which resulted from the effect of the self-absorp- tion. The Equation (5) can be modified to expressed in terms of the ratio of two electron density values as [

where, n_{e} (line) is the electron density of the line which suffering from self-absorption effect and n_{e}(H_{α}) is the electron density of H_{α}-line free from self-absorption. Hence, we utilized Equation (6) in order to calculate the amount of absorption (SA), and then used Equation (4) to get the corrected value of the spectral line intensity I_{o}(λ_{o}). The self-absorption coefficients were calculated using Equation (6) to the four resonance aluminum lines (Al I) at 308.21, 309.27, 394.40 and 396.15 nm.

The excitation temperature (T) of a given species is in general retrieved using the well known Boltzmann plot method [_{ji} (of a transition from an upper level j to a lower level i) is thus related to the energy of the upper level E_{j} by the relation:

where, λ is the wavelength of the transition, A_{ji} and g_{j} are the transition probability and the statistical weight of the upper level, k and h are the Boltzmann and Plank constants, c is the velocity of the light, N and U(T) are the number density and the partition function of the considered species, respectively. This relation leads to a linear plot against E_{j} if several transitions of the same species are considered. The temperature of this species can thus be deduced from the slope of such a plot. In order to increase the accuracy of the calculation, the range of E_{j} should be as large as possible. For this reason, a more precise method consists of representing the emissions from the different ionized states of the same element in the same plot. This method, called the Saha-Boltzmann plot allows a significant extension of the range of E_{j} and therefore an increase in the accuracy of the temperature determination [

where the superscript z represents the type of species (z = 0 for neutral atom, z = 1 for single ionized specie, etc). This relation is similar to Equation (7) as mentioned. However for ionized species (z ≥ 1) the quantities marked with the superscript ^{*} must be replaced by the following expressions (only z = 1 is considered in our work for simplicity):

Obviously for z = 0, Equation (8) become identical to Equation (7). In Equation (9), m refers to the mass of electron. In Equation (10), E_{ion} and

The use of the emission spectroscopy for the determination of the plasma temperature and the electron number density requires optically thin plasma spectral lines. The self-absorption depends on the oscillator strength, level energies degeneracy, broadening parameters and also on the plasma parameters. The condition that the atomic states should be populated and depopulated predominantly by electron collisions, rather than by radiation, requires an electron density which is sufficient to ensure the high collision rate. The corresponding lower limit of the electron density is given by McWhirter criterion, which is the necessary (but not sufficient condition) for attaining the minimum number density to check the validity of LTE [

where, ΔE_{ji} is the largest energy transition for which the condition holds and T_{e} is the plasma temperature in electron volts [^{17}, which higher than required number density to satisfy the LTE condition. In this condition, the collisionally contribution dominates the radiative contribution in the plasma. The electron densities determined in our experiment within the range to satisfy the LTE condition.

Before correction against (SA) After correction against (SA)

The LIBS method has been successfully applied as an analytical technique for the analysis of aluminum plasma using the fundamental (1064 nm) Nd:YAG laser. The optical emission spectrum of the aluminum plasma reveals transitions of neutral and singly ionized spectral lines. The effects of the self-absorption on Al lines at 308.21, 309.27, 394.40 and 396.15 nm were quantified utilizing simple formulas based on the measurement of the ratio of the apparent electron density from the lines of interest to that derived from the optically thin H_{α}-line. The spectral line intensities were then corrected. In the comparative study of the effect self-absorption, we have observed enhanced temperatures in the case of correction against self-absorption as compare to that before correction. The results show that the atomic aluminum lines (Al I) appeared in LIBS spectrum are good candidate for measuring the temperature of the plasma in LIBS experiments, especially after correction against self-absorption effect.

The author is thankful to laboratory of lasers and new materials (LINM) in Cairo University in Egypt for the encouragement in terms of provision of time and moral support to carryout research work. Beside, express his gratitude to the valuable discussions with Prof. Th. M. El Sherbini, Prof. S. H. Allam and Dr. A. M. El Sherbini.