Spectral plasma diagnostics by molecular spectra and continuum Petr Vašina and Jan Janča Department of Physical Electronics, Masaryk University, Brno, Czech Republic I.Molecular spectra OH radical - influence of resolution measured spectrum simulated spectrum using LIFBASE 2.0.55 program molecular spectrum measured with sufficiently high resolution composes from many lines moderate or low resolution – spectral bands are observed – one band results from superposition of many individual lines – see N2 spectrum, next page decreasing resolution decreasing resolution Example of spectra – N2 second positive vibration bands measured spectrum hν Atomic spectroscopy • Energy levels are defined by the configuration of all electrons in the electron cloud of the atom • Change of the electrons configuration may give rise to the emission of a photon – “jump from higher energy level to the lower one” Molecular spectroscopy • Energy levels are defined by the configuration of all electrons in the electron cloud of the molecule • Change of the electrons configuration may give rise to the emission of a photon – “jump from higher energy level to the lower one” HOWEVER – simultaneously with the jump from the higher energy lever to the lower one, the molecule can change its state of vibration and rotation molecular spectra will be a little more complicated • same electronic transition • different vibrations at higher and upper electronic state • vibration bands 0-0 0-1 1-2 2-3 1-0 2-1 0-2 1-3 2-4 certain vibration band Example of spectra – N2 second positive vibration bands, rotation lines increasing resolution • a vibration band is composed by many rotation lines • characteristic structure of a molecule – its “fingerprint” emitting a photon molecule may change simultaneously • configuration of electron cloud (notation, selection rules) • vibration (energy, selection rules, population of states) • rotation (energy, selection rules, population of states) molecular plasma spectroscopy in UV-VIS region all three events take places simultaneously object of our study We will treat electronic states, rotations and vibration separately. For all practical cases it is very good approximation. The basic of such factorization is the Born-Oppenheimer approximation. E = Ee+Ev+Er iode two potential curves of I2 molecule picture taken 18.6.2007 from : http://itl.chem.ufl.edu/4411L_f00/i2_lif/i2_lif_il.html Classification of electronic states component of the orbital angular momentum along the internuclear axis designation multiplicity – 2S+1 components of the spin angular momentum along internuclear axis are symmetry properties of electronic wave function Te energy of the electronic state energy of vibrations and rotations must be added iode two potential curves of I2 molecule picture taken 18.6.2007 from : http://itl.chem.ufl.edu/4411L_f00/i2_lif/i2_lif_il.html Vibration of molecule, dissociation harmonic oscillator parabolic shape curve, no dissociation anharmonic oscillator non-parabolic shape curve non-equidistant differences between levels dissociation dissociation energy molecule dissociate to two atoms both in 2P3/2 ground state molecule dissociate to two atoms one in 2P3/2 state one in 2P1/2 Note that for simplicity potential curves do not show rotational levels Rotation of molecule rigid rotor m1 m2 r angular momentum moment of inertia iode two potential curves of I2 molecule picture taken 18.6.2007 from : http://itl.chem.ufl.edu/4411L_f00/i2_lif/i2_lif_il.html B depends on both - configuration of electron cloud Example: equilibrium position for lower state rl = 2.7 A rl2 = 7.3 A2 equilibrium position for upper state ru = 3.1 A ru2 = 9.6 A2 - vibration state of the molecule more vibrating molecule has higher r2 than less vibrating one Selection rules 0-0 1-2 2-3 1-0 2-1 0-2 1-3 2-4 0-1 N2 second positive system Origin of R,P,Q branches since measured spectral band corresponds to the transition, where the upper and lower electronic and vibration states of molecule are the same according to selection rules in the example case, since B’>B’’ P branch form the head of band R branch form the tail Intensity of rotation line intensity of a line in general number of particles at the given upper electronic level, at the given state of vibration and rotation at equilibrium characterized by temperature T one may write Einstein coefficient Hőnl-London factor factor representing importance of R,P,Q branches at a given band • depends on branch type (R,P,Q) • depends on J’ constant characterizing intensity of a certain band (same E’-E’’,v’-v’’) Finally, intensity of a rotation line at a given band is proportional to Since the rotation quanta are relatively small (~ 10-4 eV), translation and rotation thermalize almost immediately. Thus, temperature determined from rotational spectra (“rotation temperature”) is usually very close to the temperature of the neutral gas. higher temperature = molecule rotates more = shape of spectra changes the recommended normalization for HJ’J’’ g = 2S+1 for Σ - Σ transitions g =2(2S+1) for all other transitions Change of the band shape with temperature 300 K 1000 K 3000 K in order to estimate the rotation temperature – measured spectra are simulated • resolution, instrumental function, line broadening • temperature (distribution of rotation states) II. Continuum spectra up to now one has been entirely concerned with line radiation involving transitions between two bonded states (note that even molecular bands were composed by many lines) plasma with appreciable degree of ionization • radiative transition between bound and free states • radiation emitted or absorbed by the free electrons in the neighborhood of ion Eg Ee2 Ei Ee1 free electron bound electron • photoionization – absorption of photon • radiative recombination – emission of photon fb continuum will • be the most pronounced at lower wavelengths • have fingerprints of energy levels of concerned species • called braking radiation, deceleration radiation or bremsstrahlung bremsem – to brake strahlung – radiation ff continuum will • be pronounced at higher wavelengths v j Continuum spectra –fb continuum Eg Ee2 Ei Ee1 free electron bound electron • emissivity (power emitted by solid angle per Hz by unit volume) of bf continuum follows for H-like ions and all highly excited species • assumtion Maxwellian velocity distribution for the electrons edge structure “taping on lower and lower states” • there exist a region of frequencies (the transitions which involve the region of energy levels very close to ionization threshold), where the edge structure can be neglected. j • for plotting versus • gives a straight line with slope h/kT element C N O Ar Xe Vg [1015Hz] 0.843 0.950 1.007 0.690 0.49-0.80 • in the regions between the edges a plot of versus give a straight line, where T pertains to the Maxwellian velocity distribution of the electrons and not to any ratio of populations of excited states j Continuum spectra – fb + ff continuum Eg Ee2 Ei Ee1 free electron bound electron • emissivity of fb continuum in the wavelength where edge structure can be neglected • emissivity of ff continuum • combining these two types of emission, there is a region of frequencies where • equation does not depend on • LTE was not assumed, only Maxwellian distribution for electrons • knowing absolute value of emissivity (calibrated measurement ) and Te (from relative evolution of bf continuum) one can derive the product nine absolutely at low frequencies • ff continuum dominates • since absorption coefficient increases as 1/ plasma is getting optically thick whatever the particle density • al low frequency emission hit the blackbody curve and j ~ (Reyleigh-Jean aproximation) • moreover, at plasma frequency, the emission fall absurdly to zero j Conclusion • spectral plasma diagnostics • • • • • molecular spectra and continuum • • • • • • • efforts in interpretation are rewarded by manifold results • • there exist many good books about this subject where one can learn more • plasma monitoring • • • quantitative analyses • in situ • non-invasive • easy to perform • little hard to analyse • identification of species (impurities) • plasma stability • plasma parameters (ne, Te) • particle densities • plasma chemistry •A. Thorne, U. Liezén, S. Johansson : Spectrophysics, Principles and Applications, Springer, 1999 •J. M. Hollan : Modern Spectroscopy, John Wiley & Sons, 1996 •I. Kovacz : Rotation Structure in the Spectra of Diatomic Molecules, Adam Hilger Ltd., 1969 •A.A. Ovsyannikov, M.F. Zhukov : Plasma Diagnostics, Cambridge International Sci. Pub., 2000 •R.W.B. Pearse, A.G. Gaydon : Identification of Molecular Spectra, John Wiley & Sons, 1976 •G. Hertzberg : Molecular Spectra and Molecular Structure, New York, 1939 •A. Ricard : Reactive Plasmas, Societe Francaise du Vide, 1996 •W. Demtroder : Laser Spectroscopy, Springer, 1998 •M. Capitelli, C.M. Ferreira, B.F. Gordiets, A.I. Osipov: Plasma Kinetics in Atmospheric Gases, Springer, 2000 •V.P. Shevelko : Atoms and Their Spectroscopic Properties, Springer, 1997 •E. Oks : Plasma Spectroscopy, Springer, 1995