Optická emisní spektroskopie atomů Diagnostické metody 1 Zdeněk Navrátil Ústav fyziky a technologií plazmatu Přírodovědecká fakulta Masarykovy univerzity, Brno OES Outline O OES Q CR modelling CR modelling Instrumentation • typically grating spectrometer of Czerny-Turner mounting equipped with CCD/ICCD detector • typical spectral range 190-1100 nm • sensitivity of detectors (silicon CCD, photocathode of PMT), grating efficiency 9 resolution: number of illuminated grating grooves, slit width, pixel size R = A/AA = mN DIFRACTION &RATIN< OES CR modelling Sensitivities PMC-150: Cathode Quantum Efficiency 100 0,1 f \ y —ii 3 - 1 -ii --21 —04 --2C 0 0 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 XI nm 9 grating efficacy, fibre efficacy, windows 200 300 400 500 600 700 800 900 1000 1100 1200 Wavelength (nm) Technique overview - how we measure • collecting the light emitted by plasma (optical emission spectroscopy, OES): • non-intrusive • sensing the light at the plasma boundary • optical probes • sending the light through the plasma (optical absorption spectroscopy): • based on Lambert-Beer law • can disturb the plasma, two ports • white light, hollow cathode lamps, lasers • collecting the light emitted and reabsorbed by the plasma (self-absorption methods of OES) OES CR modelling Technique overview - how we measure • collecting the light emitted by plasma (optical emission spectroscopy, OES): • non-intrusive • sensing the light at the plasma boundary —> self-absorption can play a role • optical probes • sending the light through the plasma (optical absorption spectroscopy): • based on Lambert-Beer law • can disturb the plasma, two ports • white light, hollow cathode lamps, lasers • collecting the light emitted and reabsorbed by the plasma (self-absorption methods of OES) Technique overview - what we look at • line positions = wavelengths: electric, magnetic fields, atom velocities (Stark, Zeeman, Doppler effect) • lineshapes and linewidths: electron density, gas pressure, density, temperatures (Stark, van der Waals, resonance, Doppler line broadening) • line intensities:... all Technique overview - what we look at • line positions = wavelengths: electric, magnetic fields, atom velocities (Stark, Zeeman, Doppler effect) • lineshapes and linewidths: electron density, gas pressure, density, temperatures (Stark, van der Waals, resonance, Doppler line broadening) • line intensities:... all • relative - instrument spectral sensitivity is taken into account, no absolute intensity calibration is performed output: relative populations of excited states, excitation temperatures etc. • absolute - access to absolute densities of excited states, electron density etc. Absolute intensity measurement • radiant flux/zarivy tok - energy emitted/incident on surface per unit time ♦=£, w a, • irradiance - flux density (per unit surface) = — =--. Wm 2 (2) dS dtdS' V ; • specified during calibratrion of calibrated light sources (spectral irradiance) • optical fibre is not a detector of irradiance (acceptance angle) • radiometric irradiance probes, cosine correction diffusers, integrating spheres,... Absolute intensity measurement 2 radiance (zář) - radiant flux per unit perpendicular surface and unit solid angle L = d20 á3ď dScosfldft dtdScosfldft Wm 2sr 1 (3) radiance x irradiance / = J L(0) cosOdQ ft For constant L (Lambert) radiators / = 7iL. for description of radiating solid surfaces (4) Absolute intensity measurement 3 • emission coefficient - radiant power emited by unit volume into unit solid angle d3 1.6 • 1012/7;(AE)3 (cm"3) - electron temperature from Boltzmann plot • non-LTE plasma - corona equilibrium, excitation saturation phase,... - low electron density plasma - use of Boltzmann-plot leads to erroneous electron temperature - CR modelling non-Maxwellian EDF - inelastic collisions, beam electrons, non-local EDF Col I isiona l-rad iative modelling coupled DE for densities of excited states drij dt drij ~dt c,r population and depopulation processes are very fast d tij ( d tij dt dt = 0 c,r not valid for ground-state atoms, ions, metastables, high pressure 0,0 2,0x10"' 4,0x10"' gas ^ 1,0x10^ 2,0x10* 3,0x10* Level balance dn0 dt dnion dt + V(^O^O) = -ScrA7eA70 + acrA7eA7 ion + V("ion^ion) = +5crA7eA70 - CCcrnQn ion classification of models (plasma state) 9 ionizing plasma SCYneno — ocCYneriion > 0 • plasma conducting current, ionizing waves o recombining plasma ScrA7e^o — ^cr^e^ion < 0 © afterglows, outer regions of flames • equilibrium plasma ScrA7e^o — ^cr^e^ion = 0 (ioniozation-recombination equilibrium) t i t i t i ion i V(n. w. ) ion ion/ ionizing plasma t I A A A \ V(n w. ) v ' ion ion' ion~^ — recombining plasma t t t t \ equilibrium plasma ion i Excitation phases: corona phase population by electron impact excitation, radiative deexcitation j>i j Excitation phases: excitation saturation phase population and depopulation by electron impact £ kjfnQnj + (a/A7eA7ion) = £ kfnQn-, + S/nen/ 1 V t ; t l if i \ .♦' / Y V • saturation of the excited state densities with increased nQ • no Saha equilibrium, S-,n; ^> OLjnlon OE< CR modelling Excitation phases: excitation saturation phase 2 • stepwise excitation —>• ladder-like excitation flow • coefficients of upward processes are larger (closer upper levels, higher statistical weights of upper levels) /c/_l,/nen/_i - /c/V_iA7eA7/ = /c/7/+iA7eA7/ /c/+i}/A7eA7/+i + S/A7eA7/ ion 1-1 Excitation phases: partial local thermodynamic equilibrium • 2 equilibria: excited state x ion state, neighbouring excited states • ionization ~ recombination ^> excitation flow /C/_i}/nen/_i - /C/,/-lA7eA7/ = /c/V+lA7eA7/ /c/+i}/A7eA7/+i S/A7eA7; + a/A7eA7i > r > k. Role of dominant electron collisions 1Q16 m-3 IT 10l 10 11 12 13 tV 14 nP =10 16 m 10 s 10* ■J-1-1_I I 10 11 12 13 ěV 14 _inl8 ™-3 He =10 m 101 .2- 10' 10* -I-1--1_t I 10 11 12 13 eV 14 A7P =1020 rrT3 70« 3 101 10' 10*- J_[_I_I_ 10 11 12 13 eV 14 -ep _m22 He =10 m Boltzmann n Saha n deviation from B & S n B _ S _ nogi/goe Ei/kTe nQnion^(h2/27imekTef/2eE'on,i/^ eesion rfnf + rj-n? Excitation phases argon van der Sijde B 1984. Beitr. Plasmaphys. 24 447 OES Collisional-radiative mode cross sections EDF Ť rate coefficients for electron excitation 7e, ne E/N, oj/N CR modelling line broadening I Einstein coefficients escape factors system of rate equations I emission spectrum rate coefficients Electron distribution function • Maxwellian EDF o solution of Boltzmann kinetic equation • normalization of the EDF f* oo / f(e)e1/2de = 1 (12) Jo • mean electron energy /-•oo ;e) = / f(e)eV2de, (13) rate coefficients k, /qnv of electron collision with cross section o and of inverse process k= J— [ o(e)fo(£)£d£ V m& Jo »00 kwv = \l — — I O(£)f0(£-£ij)£d£ mQ gi JSjj OE< CR modelling Approaches of OES data processing line ratio methods • selection of convenient line pair (sensitivity, model simplicity, ease of measurement) • no control of model validity ,,many line fitting"methods Line ratio method - ideal case Electron energy (eV) Electron temperature and EDF measurement by OES+CR Boffard J B et al 2012 J. Phys. D: Appl. Phys. 45 045201 Zhu X-M et al 2012 Plasma Sources Sei. Technol. 21 024003 Electric field measurement in air E/N [yd] wavelength (nm) R(E/N) F/VS(0,0) SPS(0,0) Kozlov and Wagner 2001 J. Phys. D: Appl. Phys. 34 3164 Bilek et al 2018 Plasma Sources Sei. Technol. 27 085012