ABSTRACT

In this article we will present an attempt to measure the Stark broadening parameter of the Zn I-line at 636.23 nm utilizing the optical emission spectroscopy (OES) technique, taking into consideration the possibility of existence of self absorption. This method is standing on comparison of the Lorentzian FWHM and spectral line intensity of the unknown Stark broadening parameter line (Zn I-636.23 nm—in our case) to a well known Stark parameter line (e.g. Zn I-lines at 472.2, 481 and 468 nm) at a reference electron density of 2.7 × 10¹⁷ cm⁻³ and temperature of 1 eV. We have utilized the emission spectral data acquired from well diagnosed plasma produced by the interaction of Nd: YAG laser at wavelength of 1064 nm with ZnO nanomaterial target in open air. The results indicates that the Stark broadening of the Zn I-line at 636.23 nm is centered at 5.06 ± 0.03 Å with a 25% uncertainty at the given reference plasma parameters. The knowledge of the Stark broadening parameter of the 636.23 nm line may be important in the diagnostics of the laser plasma experiments especially in the absence of the H_α-line.

1. INTRODUCTION

The measurement or/and the calculation of the Stark broadening parameter of emission spectral lines is of prime importance in different fields e.g. plasma diagnostics, modeling and investigation of interstellar atmosphere [1,2].

Different plasma sources were employed e.g. the gasdriven shock tubes [3], wall-stabilized arcs [4-10], lowpressure pulsed arcs [11] and plasma jets [12]. In these investigations, temperature and electron density values were at the ranged of 0.85 - 2.2 eV and 10¹⁶ - 10¹⁷ cm⁻³, respectively.

The Stark profiles of atomic lines in plasma are produced under the action of the low-frequency fields of ions and/or under the action of high-frequency fields of electrons [13-15].

The contribution of the high frequency micro field electrons to line broadening was assumed as a collision broadening which is the most important effect of distant non-adiabatic encounters and was treated in terms of perturbation theory [14]. These moderated fields act not to split the upper emitting state, but it rather acts to broaden the emitted line. It was shown earlier that this effect leads to inhomogeneous broadening of spectral line i.e. the emitted line become of Lorentzian shape on contrast to other broadening mechanisms e.g. Doppler effect which leads to a homogeneous broadening [15].

In order to investigate the Stark broadening parameter of any spectral line, a source of light as well as a suitable analytical technique should be employed. One of the promising light sources is the plasma produced via laser interaction with matter in what is called LIBS (Laser Induced Breakdown Spectroscopy) or laser ablation.

Two measurable parameters are utilized to describe the thermodynamical state of the plasma; namely plasma electron density and temperature. Both quantities can be measured spectroscopically via a reliable optical technique called optical emission spectroscopy (OES). In this technique, one has to assume that the emitted light from the plasma is sufficiently influenced by the plasma parameters. In normal laboratory plasmas excited via laser ablation, the plasma is characterized by a density in the range around 10¹⁷ cm^–3 and temperatures of around 1 eV which indicate the existence of the plasma in local thermodynamical equilibrium (LTE) regime [16].

The emitted spectra from plasma contain a wealth of information that are stored in the emitted line shape as well as the continuum radiation often appeared under the emitted lines. The relative spectral radiance (in the units of counts per sec) of some emitted lines can be related to the plasma temperature while the Lorentzian full width of the line at half of the maximum spectral radiance (FWHM) is usually contains information about electron density and/or ion density [14-16].

In the measurements of the Stark broadening parameters, certain criteria should be fulfilled and are summarized as following [17]:

• The plasma source must be well diagnosed (i.e. is of well known electron density and temperature), homogeneous and appear quasistatic during the period of observation;

• The electron density and temperature should be measured independently of the investigated line;

• Other broadening mechanisms should be calculated and compared to the Lorentzian FWHM;

• The investigated spectral line should be optically thin.

However, the condition imposed on the optical depth of line raises the following question; what if the line is optically thick! In this article, we shall take the optical depth of the line into consideration.

The Zn I-lines are of interest and have been observed in many stellar plasma as well as the solar spectra [18]. The Stark broadening parameter of the Zn I-triplet lines at 468, 472.2, 481, 328.23, 330.23, and 334.5 nm can be found at different tables as measured and/or calculated according to different models and extensively collected and reviewed at references, see for example [17-19].

For unknown reason and after a careful revision of the different tables, the Stark broadening parameter of the Zn I-line at 636.23 nm was found not found either theoretically predicted or experimentally measured.

In this article we shall present a simple and straightforward method to measure experimentally the Stark broadening parameter of the Zn I-line at 636.23 nm. This is in order to use this line to measure the electron density of the plasma produced by laser interaction with a nano as well as bulk ZnO material whereas the H_α-line [20-22] may not any longer be appeared, especially in the interaction of laser with nanomaterials.

2. THEORETICAL BASIES

For a well resolved, optically thin spectral line, the spectral radiance over line labeled (k), centered at wavelength as a result of a transition from upper state of energy E_k, and having a statistical weight of g_k and a transition probability of A_m can be expressed as [16]:

(1)

Is the population density of the ground state per unit statistical weight (U₀ is the partition function of the ground state, h and c having their usual meaning, is plasma electron temperature. If this line is subjected to certain absorption, its spectral intensity should decreases to. The amount of decrease was quantified by the coefficient of self absorption [16]:

(2)

where is the optical depth of a homogeneous plasma slap [16]. Eq.2 indicates that varies from unity in case of pure optically thin line to the limit of zero in case of completely self absorbed line [22].

Not very recently, the author was suggested that the same physical quantity can be expressed in terms of the ratio of the Lorentzian full width at half of the maximum (FWHM) components of the same spectral line with and without absorption [22]:

(3)

is the plasma electron density as measured from the suspected line (labeled-k) and is the electron density as derived from the optically thin H_α- line (which should appeared in the same emission spectrum under the same experimental condition). Eq.3 also indicates that is in the range from zero in the case of completely absorbed line to unity in the case of perfectly optically thin line.

As an extension to the previous work, we shall define the ratio of the self absorption coefficients of two lines labeled (k & u), one at the transition wavelength (k) with known Stark broadening parameter and the other at wavelength labeled (u) with unknown Stark parameter as. Consequently, the term in Eq.3 would be canceled, and with the help of the expression plugged in Eq.3, the relative self absorption coefficients should read:

(4a)

After a rearrangement to Eq.4a we can get in terms of as;

(4b)

The ratio of the Lorentzian FWHM of both lines (labeled-u, k, respectively) can be measured experimentally with fair precision via fitting of the emitted spectral line profiles to the Voigt line shape [15,16, 22]. On the other hand, the ratio can be expressed, with the help of Eq.2 for the two lines k & u as:

(5a)

The term is the experimentally measured relative spectral radiance at the lines centers (in the units of counts/sec), while the term is the well known theoretical relative intensity of the two lines which can be expressed as:

(5b)

After combining Eqs.5a and b then substitute in Eq. 4b, the unknown Stark broadening parameter coefficient can be expressed as;

(6)

With the measurement of the relative Lorentzian FWHM of the two different lines together with their spectral intensities at the lines centers, one can evaluate the Stark broadening of the unknown line in terms of the well known parameter

and other known atomic quantities.

It is worth noting that the term is unity if both lines are originated from the same upper state, otherwise, it should be taken into consideration with a rough knowledge of

3. EXPERIMENTAL SETUP

In this article we shall utilize the data gained from the interaction of the high peak power Nd: YAG laser with nano and bulk targets in open air and was published earlier at Ref [21]. The experimental setup is shown in Figure 1 and described in details in a previous publication [21]. The irradiation system comprises an Nd: YAG laser able to deliver an energy of 650 mJ/pulse at the fundamental wavelength 1064 nm, at constant duration of 5 ns.

The detection system consists of an SE-200 echelle type spectrograph equipped with time gated Andor iStar^®-ICCD camera. The emitted light from plasma is spatially integrated and collected at the entrance hole of spectrograph via a 25 μm quartz fiber, positioned, with the help of precise xyz-translational stage holder, at 15 mm from the laser-plasma axis. In this article we have utilized the acquired data resulted from the plasma generated from the nano ZnO target only. The relative spectral response of the camera-MCP (Micro channel plate) and spectrograph including optical fiber over the entire wavelength window from 200 to 1000 nm was measured using a Deuterium-Halogen lamp (type, DH-2000-CAL). The processing of the experimental data was carried out using home-made routine built under the MATLAB7^® package [23].

4. RESULTS AND DISCUSSION

Before the application of Eq.6, one has to choose the

suitable experimental plasma condition i.e. the suitable delay and gate times at which the measured plasma electron density and temperature are close as much as possible, to the values of the plasma parameters at which the known Stark broadening parameters are given at the standard tables [17-19]. It is worth noting that, the data of the known given at references [17-19] were measured and/or calculated at two different reference electron density values namely; 4.5 × 10¹⁷ and 1 × 10¹⁷ cm^–3 at 1 eV, therefore, we have considered the average electron density (i.e. 2.7 × 10¹⁷ cm^–3 at 1 eV) as our reference plasma parameters with the corresponding values at each line are given at Table 1.

Fortunately, a fine inspection to the measurements made before to a plasma initiated via interaction of laser with nanomaterial ZnO target (published in reference [21]) shows that the suitable plasma experimental condition (electron density of 2.5 ± 0.2 × 10¹⁷ cm^–3 and temperature of 0.997 ± 0.1 eV) was only, at a delay time of 2 μs and gate time of 1 μs. This means that, we shall apply Eq.6 to the analyzed light emerged from a plasma having electron density of 2.7 × 10¹⁷ cm^–3 [21] (which will be taken as the reference density N_r) at the reference electron temperature of 1 eV. It is worth noting that, these values of the measured plasma parameters ensure the existence of our plasma in the LTE condition

Figure 2 shows the recorded emission spectrum from the Zn-I lines at delay time 2 μs and at a gate time of 1 μs. A relatively small continuum component appeared under the lines resulted from the free-free transitions of the fast