DC Atmospheric Nitrogen Discharge: Dye Fluorescence

I have been keeping these photo for some time now waiting for the completion of discharge spectra thermal analysis. Since I have been taking forever to do so thanks to the complexity of molecular spectrum; these two photos has been a constant annoyance on my desktop - a reminder of an incomplete work. I have finally decided to release it with some brief information. 

Figure 1: Homemade halogen lightbulb transformer driven flyback DC high-voltage source energizing a multimeter probe. UV emission from corona discharge excites blue fluorescence on paper.

The photo above shows a metallic multimeter probe I've energized with positively rectified high-voltage from a vintage flyback transformer driven by a 12 V halogen lamp high-frequency digital "transformer". Under such high electrical tension, the vertex of the sharp tip have the highest charge density with electric field strength significantly stronger than the dielectric breakdown value of air ~3 million V/m [1, 2]. This causes the tip to glow purple from corona discharge followed by simultaneous release of ozone gas (distinctive musty smell) from the breakdown of oxygen molecules.

Right below the metal tip is a piece of paper acting as electric ground, attracting the positive ions spraying out from the metal tip subsequently causing the paper to glow blue from fluorescence (paper fluoresce because "optical brighteners" has been added). This whole set up was taken with an exposure time of 0.5 second to reveal the corona discharge. The multimeter probe was illuminated briefly by a white L.E.D to cast a shadow, indicating the tip is at a distance away from the paper. 

Figure 2: Vibration energy level of  nitrogen molecule [3]. Major emission lines indicated by red arrow. 

Unfortunately before I am able to measure the output voltage accurately, my last attempt to generate high voltage with similar set-up has resulted permanent damage in the secondary winding of the flyback transformer. My guess is that it has an open-circuit potential around + 20 kV estimated simply based on sharp tipped spark gap distance of 25 mm. The damage was most likely contributed by high current draw (far exceeding 1 mA) without a current-limiting resistor in series with the load (I hooked it up directly to a glow discharge tube) causing a meltdown somewhere within its fine wire coils. 

The lesson: use a ballast resistor for any sort of load.

Figure 3: Emission spectrum of corona discharge. More than 90% light emitted are UVA radiation.

Figure above is the actual dark compensated, 3-second exposure spectrum of the corona discharge taken with OceanOptics USB4000 spectrometer. Even at 3 second exposure (instrumental limit) the data still appears noisy. It was definitely weak light to be picked up by the human eye but the spectrum certainly features at least four peaks within 300 to 400 nm falling under A-subtype UV radiation (keep in mind that ultraviolet light is invisible). 

The four relatively bright emission have wavelengths slightly shorter than peak emission from violet L.E.D but they are less harmful to the eyes compared to emissions from germicidal lamp. All four spectral lines correspond to the second positive system N₂ C → B (vibration bands) of atmospheric nitrogen molecules. More specifically for 337 nm line (important because it will be featured in TEA superluminal sources), the vibration level responsible for the transition is N₂ (C³Π⁺u, v'=0) → (B³Π⁺g, v"=0) of the second positive system [4].

Figure 4a (top): Two glass vials on paper holding water suspension of highlighter pigments, left and right are blue and yellow respectively. Figure 4b (bottom): Long exposure photography shows yellow highlighter dye fluoresce while blue dye remains dark. Notice the blue fluorescence of paper under UVA irradiation.

Now, without anymore further discussions available, I bring up an experiment from the past dealing with fluorescence of highlighter pigments. Earlier, I have tested the dyes and found out the blue highlighter dye does not fluoresce under violet L.E.D. I thought probably light with wavelength shorter than 390 nm might do the work, so I tested the blue dye with UVA emissions of a corona discharge. Not surprisingly, the blue still shows negative response.

REFERENCE

[1] Tipler, Paul A., "College Physics", Worth, 1987, pp.467

[2] Rigden, John S., "Macmillan Encyclopedia of Physics", Simon and Schuster, 1996, pp.353

[3] F. Arqueros, F. Blanco, F. Rosado, "Analysis of the Fluorescence Emission of Atmospheric Nitrogen by Electron Excitation and its Application to Fluorescence Telescopes", New J. Phys., 2009, pp.11

[4] H. Khatun, A.K. Sharma, P.K. Barhai, "Experimental Study of Low-Pressure Nitrogen Dielectric Barrier Discharge", Braz. J. Phys., Vol.40, No. 4, 2010, pp.450 

Crude Plasma Diagnostics for UVC Germicidal Lamp

* This article is closely associated with a previous entry. The author assumes reader understand basic definition of physical plasma as the fourth state of matter.

Figure 1: Applying magnetic field towards the plasma causes its shape to distort due to Lorentz force acting on moving charged particles.

It was a while ago I took a spectrum of the UVC germicidal lamp without its waterproof quartz glass. Its discrete sharp peaks can be described by hallmark of the old quantum theory - light emitted due to electronic transitions between discrete energy levels within the gaseous atoms contained inside the tube. Within the past hundred years, physicists has worked out many useful formulae to relate measurable parameters of a gas discharge spectra such as intensity and its associated wavelength with physical mechanisms that is happening inside the tube at the atomic level. Here, I have worked out some crude but important characterization of the plasma when the UVC germicidal lamp is energized.

Figure 2: Spectrum of UVC germicidal lamp with tagged wavelengths for 17 strong peaks 

After plotting the numerical data into a spectrum (above), I have listed down the wavelength and intensity for 27 individual peaks which I had identified its origin thanks to NIST online database. Interestingly, the peaks was the "fingerprint" of not one but two different chemical elements (as low pressure gas) inside the tube. As mentioned in previous post, the beautiful cyan glow and strong UVC emission at 253.7 nm are the principal character of electrically excited low pressure mercury-vapour, hence finding peaks corresponding to mercury atoms is not surprising. The second interesting element was argon which I presume it was the "filler" noble gas when they used to purge the tube before vacuuming down and filling it up with a small quantity of mercury vapour. All the peaks are of neutral, i.e. Hg (I) and Ar (I) atoms.

Out of 27 peaks, 10 belongs to Hg (I) transitions while the rest are Ar (I). Finding the peaks was easy with common graphing tool (I used Origin 7.0). To make further analysis clear, I shall begin by separating this study into a few components:

1. Calculation of Electron Temperature via Boltzmann Plot

2. Voigt Profile Fitting of Spectral Peak to Determine Broadening Mechanism

3. Estimation of Plasma (absolute) Temperature

4. Comparing Peak Intensity Ratio for Self-Absorption Mechanism

5. Conclusion on Plasma Diagnostics With Respect To Electrical Characteristics

ELECTRON TEMPERATURE AND BOLTZMANN PLOT

You can think of plasma as a "hot soup" of randomly colliding electrons and ions. The electron temperature of plasma allows us to gauge the "hotness" or more specifically the statistical kinetic energy of electrons bumping randomly to each other. Because electrons are so much lighter compared to ions, they transfer energy in different rates when they collide with ions than itself. As such, for the value of electron temperature to stay valid, it is important that the plasma have reached a state where all its particles, i.e. electrons, atoms and ions has reached a common temperature known as Local Thermal Equilibrium (LTE). Otherwise, this physical quantity is known as "excitation temperature".

This temperature can be calculated through the famous Boltzmann plot. In essence, it assumes two emission energy levels of the same atomic population, Ei and Ek are in thermal equilibrium at temperature T, given by:

Equation 1

where N1 and N2 denotes number density and g1 and g2 are the statistical weights respectively. The total number density (I skipped a few algebraic derivation steps) can be simplified to:

Equation 2

At LTE, the intensity for each spectral peak is given by:

 Equation 3

where Aji is the Einstein coefficient for upper transition probability. Rearranging equation 3 by taking natural logarithm on both sides for linearising the expression (y = mx+c) we arrive at:

Equation 4

where the gradient, (-1/kT) tells the electron temperature T, of the plasma. This is the Boltzmann plot where the x and y parameter of this linear expression can be obtained both experimentally (intensities and wavelengths) and from NIST standards (energy levels, Einstein coefficients and statistical weights). 

One interesting outcome for plotting this is that from the data points is that we can determine if the spectrum is "optically thin" through the degree of linearity, i.e. the points coincide a straight line. Optically thick spectra is typically associated with dense plasma where some part of its light has been re-absorbed into the plasma itself, rendering the spectra unreliable for temperature analysis. From tedious work finding all the parameters for Boltzmann plot, I managed to do it for both mercury and argon:

Figure 3: Boltzmann plot for argon lines (top) and mercury lines (bottom). While the data is chaotic for argon's case, data for mercury seems to exhibit linearity where the expected gradient enables calculation of the electron temperature. 

Even though argon has 17 emission lines, it is immediately obvious that the Boltzmann plot for argon lines yields chaotic results for a linear fit. Fortunately, there seems to be a linear relationship for mercury lines and I have used a linear fitting software which gave me a gradient of -1.43 with error of 0.35. This yields electron temperature at (0.699 ± 0.37) eV that is 8112 K for people not in plasma physics and 8384.7 degrees Celsius for non-physicists. The temperature is in the order of magnitude similar to discharge lamps reported in various literature elsewhere. 

PEAK PROFILE FOR BROADENING MECHANISM

The spectrum for plasma (refer to figure 2) contains discrete sharp peaks which I have briefly mentioned as the result of electronic transitions within trillions of atoms of the gas contained in the germicidal lamp. Following the quantum theory, ideally for each electronic transition, the atom emits one particle of light, the photon, with a fixed wavelength and should result an infinitely thin line. However, experiments should find that no matter how "pure" a plasma is, we will always see the peak profile having a broadened "waist", like a mountain. So what was broadening it? 

Broadly, there are three primary mechanisms causing this effect here listed with decreasing significance:

1. Doppler effect coming from light emitted from moving particles within the plasma which reveal itself as spectral line with a Gaussian profile.

2. Stark effect coming from energy levels (especially those close to the continuum) of an atom being "disturbed" by electric fields of nearby moving ions and/or externally applied E-field, this effect reveal itself in spectral line of Lorenzian profile. 

3. Intrinsic property of quantum mechanics itself. i.e. the Heisenberg Uncertainty Principle, which states that any electrically excited atoms having a finite lifetime will have slight indeterminate energy level, causing the light emitted from atoms having so slightly a shorter or longer wavelengths with one another. An effect I believe too insignificant to observe based on the resolution of our experiment set-up.

For simplicity sake, I have chosen the brightest peak of the spectrum, i.e. the line at 253.7 nm for profile analysis. As we magnify the wavelength scale, we will see the "line-like spike" resolve into a "mountain". There are a few types of fitting available to extract information regarding its shape. For further analysis, I used a combination of both Gaussian and Lorenzian profile fitting - the Voigt profile. 

Figure 4: Voigt profile fitting for the brightest spectral peak at 253.7 nm. Red line indicates the fitting.

Using a Voigt fitting, Origin 7 provides me two w parameters for defining the typology of the "mountain" shape. A ratio of wG and wL (0.00381/1.91006) gives us 0.002 which is significantly less than 0.5 - the threshold for Lorenzian profile, so Gaussian it is.      

Figure 5: First order derivative of fitted Voigt profile. The peaks enables calculation of FWHM value.

Identifying the peak having a Gaussian profile has an advantage. Other than confirming the dominant broadening mechanism as the result of Doppler effect, a simple equation based on Maxwellian distribution can be used to estimate the absolute temperature of the plasma by knowing the profile's full wave half maximum (FWHM) value. We will discuss that in the next sub-chapter but for the moment, I have worked out the FWHM via first order derivative of said Voigt profile. 

The positive and negative peaks of Voigt derivative correspond to the half-width value Δλ1/2, where |254.28 - 252.51| = 1.77 nm.   

ESTIMATION OF PLASMA TEMPERATURE 

As mentioned before, to characterize a plasma which composed of different types of particles, have to account two different temperatures. While we have characterized the electron temperature with Boltzmann plot, there is another class of particles - ions, which are heavier and moves slower relative to electrons and their temperature can be related to the absolute temperature of the plasma based on FWHM for Doppler broadening given by:

Δλ1/2 = 2λ SQRT (2kT ln 2 / mc^2)

Equation 5

where λ is the peak wavelength, m is the atomic mass and c is the speed of light. T is the absolute temperature where by rearranging the equation, I have calculated it to be 1.84E10 degree Kelvin. Which is rather nonsensical. For comparable results with our previously obtained electron temperature (plasma temperature should be slightly "less hotter" than electron temperature but LTE demands them to be as close as possible) the FWHM value should be in the order of 0.001 nm, which is far beyond the resolving capabilities of my spectrometer set-up. 

I would argue such absurdities are due to equation 5, which depends heavily on the FWHM value which was limited experimentally by my spectrometer slit width, not until we analyze FWHM for each 27 peaks using precision spectrometer (which is quite a lot of work), I cannot be convinced that the absolute temperature falls in that order of magnitude. Naturally, because the plasma temperature differs so greatly with the electron temperature, I cannot conclude the plasma is even in LTE. 

PEAK INTENSITY RATIO FOR SELF-ABSORPTION MECHANISM

There is however another way to determine the "usability" of the spectrum by finding its optical "thickness" with experimental intensity ratio between two emission lines that has the same upper energy level, described by:

Equation 6

we can eliminate the exponential term since E2 = E1, and therefore leads to: 

Equation 7

where the left hand side (L.H.S) can be obtained via experiment intensity and right hand side (R.H.S) through NIST standards. With that, I have came to using three Hg (I) lines of 404.11 nm, 435.34 nm and 545.94 nm having identical upper energy level at 62350.325 cm^-1 corresponding to electron shell 3s at 5d(10)6s7s configuration, calculated their LHS and RHS values to be 2.57 against 1.43 and 3.57 against 2.46. Both differ by at least 1.1 suggesting optically thick plasma. This can be interpreted as self-absorption of photons by the atoms inside the plasma and the rate of absorption differs between different spectral lines depending on factors like energy level lifetime and charge densities etc.

CONCLUSION

To be honest, eventually diagnosing the plasma as optically thick was rather disappointing considering the amount of work spent on gathering spectral data from NIST and the associated analysis. Nonetheless we learned that the plasma confined within the germicidal lamp's quartz tube contains argon. Even though no conclusion can be drawn on the state of LTE for the plasma, the electron "excitation" temperature was found to be in the order of magnitude expected for a discharge lamp, that is at around 8000 K based on Boltzmann plot. The plasma temperature was found to be in the order of 10,000,000,000 K is unrealistic, but it was due to experimental limitation vis-a-vis the design of the spectrometer (thus limiting the FWHM resolution). It could also be due to some other broadening mechanisms which I have overlooked. 

On optical thickness, I am tempted to suggest the difference between LHS and RHS terms from equation 7 arise from self-absorption are due to the electrical characteristics of the plasma. The germicidal lamp is most probably energized by alternating voltages which cause the particles in the plasma to "move" differently when it is energized by static DC sources. To understand these character of a plasma in detail, I recommend further work on a system that enables me to fix the state of vacuum and gas inside a chamber where we can manipulating the electrical properties of plasma to study its spectral changes although such work will be painstakingly time consuming. 

REFERENCES
[1] N.M. Shaikh, B. Rashid, S. Hafeez, Y Jamil and M.A. Baig, "Measuremement of Electron Density and Temperature of Laser Induced Zinc Plasma", 2006, J. Phys D: Appl. Phys., pp.1384
[2] C. Aragon, J.A. Aguilera, "Characterization of Laser Induced Plasmas by Optical Emission Spectroscopy: A Review of Experiments and Methods", 2008, Spectrochimica Acta B, pp.893
[3] A.D.Giacomo, V.A.Shakhatov, O.De Pascale, "Optical Emission Spectroscopy and Modeling of Plasma Produced by Laser Ablation of Titanium Oxides", 2001, Spectrochimica Acta B, pp.753

Uranium Glass: Radioactivity and Fluorescence

With the availability of two Geiger counters purchased from GQ-electronics, I have been looking for radioactive sources to "play" with. Other than the Am-241 alpha source I've extracted from smoke detectors, I came to know some vintage household products are actually doped with radioactive materials for aesthetic or practical reasons. One particularly curious example is the uranium glass.

Uranium glass are essentially glass that contains small amount of uranium (typically within a few percent) in the form of oxide uranate, U(VI) state within its amorphous glassy matrix. Long before the discovery of radioactivity, it was found that the mineral contained within blackish yellow ore of uranium - pitchblende, when added to clear transparent glass melt will solidify to a yellowish green tint. These coloured glass were priced for their aesthetic appeal and up to a certain period in our history it was even used as tableware and household decorative exhibits until the realization of its potential health hazards or more likely political influence on the control of uranium related compounds that brings production to halt.

Today, uranium doped glass are still sold worldwide but in much smaller sizes such as beads or cubes for scientific novelties. Despite the possible health hazards (even though they are in minute concentration within the glass), I went to look for such material in Malacca city - a place famous for its cuisine, art and antiques.

 Vintage handmade uranium glass bowl fluoresce bright green under shortwave ultraviolet light

Scouring the old rustic stores, it took a tour of more than ten different antique shops for me to finally come by a sample (image above) that is not too physically large and of course affordable under my budget. It was that unmistakable yellow-green colour, nicely handcrafted and from its construction, must have been blown with old techniques because there are air bubbles still trapped within the glass. I recognized the glass through its bright green fluorescence induced by a cheap violet LED lamp. The shop keeper charged me MYR 80 after a casual bargain, little did he knew about the true value of these radioactive glassware. When I got home, I carefully washed it and prepared it for radiation detection. 

Fluorescence in uranium doped glass are excited by ultraviolet radiation. Because a sheet of glass blocks completely the shortwave UV, the side of the bowl facing the glass did not glow in green. Note that visible light from the mercury lamp still passes through the glass (cyan reflection on the uranium glass bowl).

As mentioned, I have two Geiger counters. The detecting elements are different for both tubes because one of it has a small active diameter of only 6.4 mm with alpha-sensitive mica window, the other tube has a longer length and slightly higher volume for cross section (I did not measure it) but the tube was encased entirely with glass, so it is only sensitive to beta and gamma radiation. I was thrilled when the glass GM tube detects some low level radiation but I was frustrated with the lack of sensitivity when I used the GM tube with relatively small alpha-sensitive mica window because I expected the radiation emitted from such sources primarily consist of alpha particles (just like the Am-241 source). 

The lack of radioactivity when detected using the small CBON 6107/BS-212 GM tube can be attributed to the relatively dilute amount of uranium added to the glass thus result in a very weak radioactive source. The glass GM tube picks up more counts than background for three reasons: 

1. It has higher volume compared to CBON 6107/BS-212 GM tube, thus higher probability for detecting any non-alpha ionizing particles zipping through the tube. This increases the sensitivity towards relatively weak sources like our uranium glass bowl. 

2. The first radioactive element from the decay series of Uranium-238 (most abundant isotope of uranium) is Thorium-234 and Protactinium-234. Subsequent decay mode in Thorium-234 emits mostly beta negative particles with energy 0.273 MeV; and Protactinium for the probability of 99.84 % emission of beta negative particles at 2.271 MeV coupled with 0.16 % gamma (0.074 MeV) emission due to isomeric transition. 

3. Further radioactive decay products of U-238 other than the fore-mentioned Th-234 and Pa-234 even though very very small, but there is a probability of its existence within the glass matrix (vintage product), emitting beta and gamma ray particles. 

In any case, someone worked out the decay equilibrium for one mole of U-238. Because the half-life of uranium is so unbelievably long, within our lifetimes only 3 of the first decay products were taken into account. Thus, for one mole of U-238 (either pure sample or embedded within a compound like our case) one alpha, two beta and one gamma ray particles are emitted 3,000,000 times per second. This explains why my beta + gamma detecting GM tube picks up higher counts than the CBON 6107/BS-212 GM tube. The weak activity also provide a hint on how much uranium atoms were present in the bowl itself. 

Ortec systems: GM tube assembly and the uranium glass sample

Next, being unsatisfied with the performance of my GM tubes, I brought the bowl down to our radiation lab where it has GM tube with substantially larger surface area of about 35.6 mm and 19.8 mm effective length and diameter respectively. It was a Saint-Gobain N204/BNC GM tube driven by Ortec systems with alpha enabled mica window. I literally stick the mica end of the tube to the surface of the bowl and did a 4 minute integration time exposure to measure counts (figure above). Later I repeated the measurement using calibrated attenuators of different densities.

Detecting radiation through a sheet of aluminium attenuator.

Figure above shows the actual set up with an aluminium sheet attenuator. As expected, when aluminium was introduced, the counts did not drop drastically as exhibited by Am-241 alpha sources but decreases in an exponential profile in increasing attenuation density indicating radiation interaction with matter but during the process loses significant amount of energy per particle.

For this case since primary radiation are beta particles, its interaction with attenuators are mostly contributed by ionization and especially bremsstrahlung. Such interactions dictates the maximum length where the particle will be completely stopped; and it is proportional to the attenuators' density. For beta particle with kinetic energy higher than 0.6 MeV, empirical evidence has found the range of the particles given by: 

Range [kg/m^2] = (5.42 * E) - 1.33 , where E is the kinetic energy in MeV

This gives the maximum range of our beta particles from the uranium glass stopped at 109,700 mg/cm^2. Which is pretty thick! Nevertheless, even though thick shielding are technically required to block those particles emanating from the glass bowl but because the number of particles originating from it is so small, such precautionary steps becomes unnecessary.