ROMANIAN JOURNAL OF PHYSICS

CORRELATION ANALYSIS OF THE POLARIZATION DEGREE FOR THE GAS MIXTURE H2-Kr C. GAVRILA1, I. GRUIA2*, A.E. SANDU1 1

Department of Thermal-Hydraulic Systems and Atmosphere Protection, Technical University of Civil Engineering Bucharest 66, Pache Protopopescu Blvd., sector 2, 021414, Romania E-mail: [email protected] 2 University of Bucharest, Faculty of Physics, 405 Atomistilor, POB MG-11, RO-077125, 78 Bucharest – Magurele, Romania *Corresponding author: [email protected]; [email protected] Received May 20, 2015 Correlation Analysis it is used to study the intensity of the link between the variables. In this study it has been analysed the correlation of the Polarization Degree (PD), for the mixture of gases H2-Kr, (νH2/νNe = 27/38), using the intensities of the chromatic lines (λ1 = 758,7 nm, λ2 = 760 nm and λ3 = 811 nm), measuring at different values of the discharge current, I[mA] at the frequency of 25kHz for different values of the pressure (p1 = 27,5 torr, p2 = 42 torr, p3 = 65 torr and p4 = 80 torr). Key words: Polarization Degree, correlation analysis, gas mixture H2-Kr.

1. INTRODUCTION

The krypton emission spectrum can be reduced to three dominant spectral lines if small quantity of hydrogen is added to the dielectric barrier discharge krypton plasma. These lines have the following wavelengths: – λ1 = 758,7 nm [1], – λ2 = 760 nm, – λ3 = 811 nm. The reduction of the noble gas spectrum, in this case the krypton gas, to these three dominant lines appeared in the frame of the monochromatization effect of visible light in electronegative-electropositive gas mixtures plasma, known as M-effect. Although totally different from the point of view of the reaction mechanisms acting inside of the two types of plasma and of the corresponding experimental conditions [2, 3], such an effect on the emission spectrum of the basic plasmagen gas can be also noticed when adding a small quantity of hydrogen in nitrogen plasma. As presented in several researches [4–9], the M-effect has, as the main reaction mechanism, the resonant three-body polar reaction between electropositive and electronegative ions with the important contribution of the electronegative gas metastable atoms, standing as the third partner in the colliding reaction. Rom. Journ. Phys., Vol. 61, Nos. 3–4, P. 638–647, Bucharest, 2016

2

Correlation analysis of the polarization degree for the gas mixture H2-Kr

639

The general form of this reaction is the following:

 

*

A  B  Bmet  A*  B groundstate  Bmet  E,

E  0 ,

(1)

where the used notations are: A – is the symbol of the atoms of electropositive gases of the mixture, B – is the symbol of the atoms of electronegative gases of the mixture,

A – is the symbol for the positive ion,

B  – is the symbol of the negative ion,

B met – is the symbol for the metastable negative atom,

Bmet * – is the symbol of the excited electronegative atom standing in a upper state energy that the one of the metastable level, A* – is the electropositive atom in an excited state, E – is the reaction energy defect. The probability of a three-body resonant reaction is, theoretically, quite small. Still, the gas mixture used in discharge presents some specific features which increase this probability, such as: co-existence of negative and positive ions, moderate to high total gas pressures and the existence of the metastable electronegative atoms in convenient energy state. The negative and positive ions ensure a high probability of collisions because of the attraction Colombian forces which appear between opposite sign particles. The high total gas pressure provides a higher probability of the threebody interaction. The metastable-state atoms are long-lifetime species, so that their participation in the three-body reaction is favoured.

By the radiative de-excitation process of the A* atoms is emitted a quasimonochromatic light when the collision reaction (1) is accomplished, which obviously means a reaction probability equal to one. This takes place when the energy defect of reaction (1) has the (ideal) value of E  0eV . The energy difference between the participating particles before their interaction and after it provides the energy defect. The participating particles are: – –

the positively ionized and excited neutral atoms, A and A* respectively, and

 *

the metastable-state atoms B met and B met . The negative ions are considered to negative energy values in the calculations. It can be concluded that the result of the energy balance of the reaction (1) is the calculated energy defect.

 *

Those combinations of A* and B met leading to an energy defect close to 0eV generate the appearance of the M-effect. In fact, the values of E varying

640

C. Gavrila, I. Gruia, A.E. Sandu

3

between –1eV and +1eV are considered to be a valid condition for the generation of the M-effect. Table 1 presents the corresponding calculations of energy defect for (Kr+H2) gas mixture [10]. Table 1 Calculation of ΔE defect energy for (Kr + H2) gas mixture

A [eV]

B [eV]

14 14 14

0.75 0.75 0.75

B met [eV] 10.2 10.2 10.2

A* [eV] 11.44 11.55 11.67

B [eV] 0 0 0

Bmet * [eV] 12.09 12.09 12.09

E



[eV]

[nm]

− 0.08 − 0.19 − 0.31

811 760.15 758.74

As it can be observed, in the particular case of the krypton-hydrogen mixture, the most possible appearance of the M-effect is represented by the 811nm spectral line, but there are also other spectral lines for which is accomplished the energetic condition of a very small calculated energy defect (such as 760.15 nm and 758.74 nm spectral lines). 2. EXPERIMENTAL SET-UP

Figure 1 shows the experimental arrangement used in the investigation of the result of this paper.

Fig. 1 – Experimental arrangement used in the investigation dependence of polarization degree on the discharge electrical current intensity (λ = 758,7 nm).

4


641

The discharge, realized in a quartz tube, allows the UV radiation to pass. The characteristics of the tube are: – it has an inner diameter of 16 mm; – it has an outer diameter of 20 mm; – the tube is set between two wolfram-thorium cylinder electrodes of 12 mm diameter, both identical. The distance between the electrodes is of 6 mm. The reflection mirror in front of the discharge tube has the role of minimizing the loss of the emitted radiation. After draining the discharge device to a pressure of 1,33ˑ10–4 mbar, various gas mixtures with spectral purity are introduced. The experiment uses a RF electrical power supply with the following attributes: – filling factor: approximately 10–20%; – maximum output of the electrical tension: 2 kV; – maximal intensity of the electrical current: 150 mA; – two optional frequencies: 25 kHz and 50 kHz. After the emitted radiation passed through a polarization filter and a focusing lens system, we used an Optical Analyzer Multichannel (OMA) to record the optical emission spectra of the plasma discharges. The OMA is characterized as follows: – spectral range: 220÷900 nm; – integration time: 0,5 s; – spectral resolution: 1,5 nm. We used computers in order to process the obtained data. 3. METHODOLOGY

In a strictly way, the correlation is a measure of the intensity of the link between the variables [11–12]. The correlation can be expressed by: covariance, Pearson correlation coefficient, the Pearson correlation ratio, nonparametric correlation coefficients. 3.1. PEARSON CORRELATION COEFFICIENT

The correlation coefficient [13–15], which describes the link between two variables, is different. One of the most used correlation coefficients is the Pearson correlation coefficient (be noted rxy or r ), which is a parametric coefficient; the complete name of this coefficient is “Pearson product moment correlation coefficient”. The values of the Pearson correlation coefficient may vary between +1 and –1. A value close to +1 indicate a powerful positive correlation, a value close to –1 indicate a powerful negative correlation, and a value close to 0 indicate that between these variables there is no correlation. The Pearson correlation coefficient can be calculated with next formula:

642

C. Gavrila, I. Gruia, A.E. Sandu _ _ 1   ( xi  x )  ( yi  y ) n i rxy  sx  s y

5

(2)

where: n – the sample size formed by pair measurements (x, y); xi – the individual measures of the variable x; yi – the individual measures of the variable y; _

x – the arithmetic media of the x variables; _

y – the arithmetic media of the y variables; sx – standard deviation for the x values; sy – standard deviation for the y values.

The numerator from the equation (2) it is called covariance (denoted by sxy) or variability couple.

sxy 

_ _ 1   ( xi  x )  ( yi  y ). n i

(3)

The covariance is a measure of the degree in which variation of the variable suits the variation of the other variable. The correlation coefficient is the ratio between covariance and the total variability (the product of the two standard deviations). If covariance is equal to total variability, then the correlation coefficient is equal to unit (r = 1). If the covariance is much smaller than the variability, then r approaches to zero. Testing the significance of coefficients rxy it is very important especially when working with relatively small samples and it is possible to obtain a coefficient different from zero by random choosing of a total uncorrelated data. The signification of these coefficients can be tested on a sample of any dimension (but over 10 pairs of values) by using t distribution (Student): t r

n2 1 r2

(4)

where: n – the sample size formed by pair measurements (x, y) and r – the correlation coefficient. When is testing the signification of the correlation coefficient, it can be used a one-tailed distribution t or two-tailed distribution. So we will have the next assumptions:

6


643

Table 2 The signification of the correlation coefficient Hypothesis H0 H1

two-tailed ρ=0 ρ≠0

one-tailed ρ=0 ρ > 0 or ρ < 0

In both cases it is testing the null hypothesis, H0, this means to verify if the population correlation it is zero (as noted, assumptions stated above using parameter ρ, representing population correlation). When we expecting that the relationship between the two variables to be going in one particular direction, we will use one-tailed distribution for finding out if ρ is positive or negative. In these cases, the signification level from the table t, must be half of that used in two-tailed distribution. If we are not sure of the direction of relationship between the two variables, it will be using two-tailed test. 4. RESULTS AND DISCUSSIONS

The measurements of the polarization degree were performed in HydrogenKripton gas mixtures (νH2/νKr = 27/38) for the dominant spectral lines with λ = 758.7nm, λ = 760nm and λ = 811nm at four values of total pressures namely 27.5 torr, 42 torr, 65 torr and 80 torr, respectively. Each set of measurements was done for one frequency, at 25 kHz. The experimental data are presented in Tables 3. Table 3 Polarization Degree for different λ and p Polarization Degree for λ = 758.7nm Current i [mA] p=27.5 p=42 p=65 p=80 torr torr torr torr

Polarization Degree for λ = 760nm

Polarization Degree for λ = 811nm

p=27.5 torr

p=42 torr

p=65 torr

p=80 p=27.5 torr torr

p=42 torr

p=65 torr

p=80 torr

6

0.18

0.30

0.21

0.27

0.22

0.25

0.21

0.25

0.22

0.33

0.28

0.26

8

0.22

0.25

0.20

0.27

0.19

0.25

0.20

0.24

0.27

0.25

0.28

0.25

10

0.22

0.26

0.21

0.27

0.25

0.25

0.21

0.27

0.23

0.30

0.31

0.27

12

0.23

0.22

0.23

0.26

0.20

0.22

0.23

0.24

0.19

0.28

0.33

0.29

14

0.26

0.26

0.19

0.19

0.28

0.26

0.19

0.26

0.27

0.26

0.27

0.31

16

0.25

0.22

0.23

0.25

0.24

0.21

0.21

0.29

0.28

0.24

0.32

0.32

18

0.25

0.23

0.23

0.20

0.24

0.22

0.21

0.18

0.30

0.22

0.31

0.27

20

0.16

0.16

0.23

0.26

0.12

0.21

0.24

0.25

0.23

0.25

0.35

0.31

Based on the values indicated in the table were realized the graphs which are presenting the dependence of the polarization degree of the dominant spectral lines

644


7

with λ = 758.7 nm, λ = 760 nm and λ = 811 nm on the discharge electrical current intensity (Figs. 2–4).

Fig. 2 – The dependence of polarization degree on the discharge electrical current intensity (λ = 758,7 nm).

Fig. 3 – The dependence of polarization degree on the discharge electrical current intensity (λ = 760 nm).

Fig. 4 – The dependence of polarization degree on the discharge electrical current intensity (λ = 811 nm).

8


645

Figures 2÷4 show an interesting periodic dependence of the polarization degree on the electric current intensity. For achieve the correlation analysis was used the IBM-SPSS Trial program, version 22.0.0 [16], considering the data from the table 3 and also the following notations: wli _ pj, i  1  3, j  1  4 – The Polarization Degree of the spectral line i four value of total pressure j. The Correlations table is a matrix of correlation coefficient. Values are distributed symmetrically on both sides of the diagonal coefficients equal to 1, which corresponding to the correlation of each variable to itself. On both sides of the diagonal of the table are represented the values of the Pearson correlation coefficients between the variables, taken two by two, and the values of the signification limit (Sig. (2-tailed)). From the table we will observe that there are powerful positive correlations (the values are mark with blue), but there are also significant negative correlations (the values are mark with red). We will also observe that, for powerful correlated variables the signification limit, Sig., is smaller than 0,01. Table 4 Correlations of the Polarization Degree

wl1 Correlation _p1 Sig. wl1 Correlation _p2 Sig. wl1 Correlation _p3 Sig. wl1 Correlation _p4 Sig. wl2 Correlation _p1 Sig. wl2 Correlation _p2 Sig. wl2 Correlation _p3 Sig wl2 Correlation _p4 Sig. wl3 Correlation _p1 Sig. wl3 Correlation _p2 Sig. wl3 Correlation _p3 Sig. wl3 Correlation _p4 Sig.

wl1_ wl1_ p1 p2 1 ,299 ,472 ,299 1 ,472 -,173 -,557 ,683 ,151 -,601 -,048 ,115 ,911 ,826* ,665 ,012 ,072 ,143 ,796* ,735 ,018 -,631 -,76* ,094 ,027 -,026 ,042 ,952 ,922 ,609 ,063 ,109 ,882 -,388 ,568 ,342 ,142 -,386 -,86** ,345 ,005 ,151 -,607 ,722 ,111

wl1_ wl1_ p3 p4 -,173 -,601 ,683 ,115 -,557 -,048 ,151 ,911 1 ,119 ,779 ,119 1 ,779 -,388 -,578 ,342 ,134 -,91** -,079 ,002 ,852 ,706 ,476 ,050 ,234 -,210 ,362 ,618 ,379 -,105 -,648 ,805 ,082 -,287 ,481 ,490 ,227 ,801* ,283 ,017 ,497 ,331 -,295 ,423 ,478

wl2_ wl2_ p1 p2 ,826* ,143 ,012 ,735 ,665 ,796* ,072 ,018 -,388 -,91** ,342 ,002 -,578 -,079 ,134 ,852 1 ,505 ,202 ,505 1 ,202 -,857** -,72* ,007 ,043 ,094 ,066 ,825 ,877 ,473 -,023 ,236 ,957 ,052 ,527 ,902 ,179 -,640 -,85** ,087 ,007 -,055 -,570 ,897 ,140

*. Correlation is significant at the 0.05 level (2-tailed). **. Correlation is significant at the 0.01 level (2-tailed).

wl2_ p3 -,631 ,094 -,76* ,027 ,706 ,050 ,476 ,234 -,857** ,007 -,72* ,043 1

wl2_ p4 -,026 ,952 ,042 ,922 -,210 ,618 ,362 ,379 ,094 ,825 ,066 ,877 -,137 ,746 -,137 1 ,746 -,559 -,251 ,150 ,550 -,078 ,383 ,854 ,349 ,899** -,016 ,002 ,970 ,234 ,458 ,578 ,254

wl3_ p1 ,609 ,109 ,063 ,882 -,105 ,805 -,648 ,082 ,473 ,236 -,023 ,957 -,559 ,150 -,251 ,550 1 -,73* ,038 -,316 ,446 ,038 ,929

wl3_ p2 -,388 ,342 ,568 ,142 -,287 ,490 ,481 ,227 ,052 ,902 ,527 ,179 -,078 ,854 ,383 ,349 -,73* ,038 1

wl3_ p3 -,386 ,345 -,86** ,005 ,801* ,017 ,283 ,497 -,640 ,087 -,85** ,007 ,899** ,002 -,016 ,970 -,316 ,446 -,281 ,499 -,281 1 ,499 -,324 ,462 ,434 ,249

wl3_ p4 ,151 ,722 -,607 ,111 ,331 ,423 -,295 ,478 -,055 ,897 -,570 ,140 ,234 ,578 ,458 ,254 ,038 ,929 -,324 ,434 ,462 ,249 1

646


9

If we analyse the data from the table above, we will observe that, the variables: wl1_p1 and wl2_p1, wl1_p3 and wl3_p3, wl2_p3 and wl3_p3 are significant positive correlated, which means that, the polarization degree in Hydrogen-Kripton gas mixtures (νH2/νKr = 27/38) for the three spectral lines, at of total pressure p = 65 torr, have the same behaviour (the graphics have the same shapes, Fig. 5). The variables: wl1_p2 and wl3_p3, wl1_p3 and wl2_p2, wl2_p1 and wl2_p3, wl2_p1 and wl3_p3, are significant negative correlated (when the value of a variable increase then the other variable decreases, Fig. 6). It can be also observe that there is no significant correlations for PD corresponding to pressure p4 = 80torr for the three wavelengths.

Fig. 5 – Polarization Degree for λ and p = 65 torr.

Fig. 6 – Polarization Degree for λ = 758.7 nm, p = 42 torr and λ = 811 nm, p = 65 torr.

5. CONCLUSIONS

The aim of this study was to analysed the correlation of the Polarization Degree for the mixture of gases H2-Kr, (νH2/νNe = 27/38), using the intensities of the chromatic lines (λ1 = 758,7 nm, λ2 = 760 nm and λ3 = 811 nm), measuring at different values of the discharge current, I[mA] at the frequency of 25kHz for

10


647

different values of the pressure (p1 = 27,5 torr, p2 = 42 torr, p3 = 65 torr and p4 = 80 torr). The correlation analysis of the Polarization Degree for the mixture of gases H2-Kr (νH2/νNe = 27/38), indicates that, there is no need to consider λ = 760 nm (it has the same behaviour as λ = 758,7 nm) and p = 80 torr (it is irrelevant). The maximum of the monochromatization-effect is reached for λ = 811 nm, and p = 65 torr, Fig. 5. This conclusion confirms the results of the calculation of the reaction energy defect presented in Table 1 from which it can be observed that the energy defect for the 811 nm krypton spectral line is almost zero (0.08 eV) which means a very high emission probability of this line in the frame of M-effect. REFERENCES 1. 2.

3. 4.

5. 6. 7.

8.

9. 10. 11. 12. 13. 14. 15. 16.

M. K. Mishra, A. Phukan, Effect of additional cathode potential on diffused plasma parameters in presence of anode potential, Rom. Journ. Phys., 58 (1–2), 159–170, 2013. A. Surmeian, C. Diplasu, C. Atanasiu, M. Ganciu, Monitoring the evolution of the 3P2 Neon metastable level density in temporal afterglow plasma by absorption spectroscopy using a pulsed hollow cathode spectral source, Rom. Jour. Phys., 59 (5–6), 570–581, 2014. C. Gavrila, I. Gruia, Analysis of polarization degree of monochromatic line in H2-Ne gas mixture, Journal of Optoelectronics and Advanced Materials, 16 (11–12), 1374–1381, 2014. C. Gavrila, I. Gruia, Analysis of variance (ANOVA) of polarization degree of chromatic lines in H2-Kr gas mixture, Optoelectronics and Advanced Materials-Rapid Communications, 8 (11–12), 1250–1255, 2014. L.C. Ciobotaru, G. Musa, Monochromatization effect kinetic model for Penning gas mixtures emission mechanisms, Turkish Journal of Physics, 36 (1), 77, 2012. L.C. Ciobotaru, Plasma physics monochromatisation effect – AC/DC discharges comparative behavior, Romanian Reports in Physics, 62 (1), 134–141, 2010. L.C. Ciobotaru, Optoelectronics and Advanced Materials, Rapid Communications, Comparative Investigation of Monochromatization Light Effect at Molecular/Atomic Level in Electronegative-Electropositive Gas Mixtures Plasma, 6 (5–6), 668–672, 2012. L.C. Ciobotaru, Considerations on the Penning reactions role for the monochromatisation effect in noble gases-hydrogen mixtures, Optoelectronics and Advanced Materials, Rapid Communications, 5 (3–4), 327–329, 2011. L. Gales, R. Anghel, M. I. Gruia, V. Lungu, V. Negoita, I. Gruia, Rom. Journ. Phys., 60 (3–4), 521–527, 2015. C. C. Surdu-Bob, G. Musa, The kinetics of monochromatization of plasma light emission, J. Phys. D: Appl. Phys., 41, 172004 (2008). T. Le Chap, Introductory Biostatistics, New York: Wiley, 2003. Jaba E., Grama A., Statistical analysis with SPSS on Windows, Bucharest, Ed. Polirom, 2004. C. Gavrila, F. Ardelean, A. Coman, E. Burchiu, Statistical Analysis for Prognosis of a Photochemical Smog Episode, Mathematical Modelling in Civil Engineering, nr. 2, 25–29, 2013. C. Gavrila, N. Teodorescu, I. Gruia, Bayesian Modelling to the Water Loss Management Decisions, Journal of Water Science and Technology: Water Supply, 13(4), 883–888, 2013. C. Gavrila, R. Frunzulica, R. Patrascu, Bayesian networks for prognosing and managing the properly use of thermostatic, U.P.B. Sci. Bull., Series A, 76(1), 3–16, 2014. www14.software.ibm.com/download/data/web/en_US/trialprograms/W110742E06714B29.html.