Spectroscopy and Optical Diagnostics for Gases

290 Pages·2016·8.188 MB·English

by  Ronald K. Hanson, R. Mitchell Spearrin, Christopher S. Goldenstein (auth.)

Ronald K. Hanson
R. Mitchell Spearrin
Christopher S. Goldenstein
Spectroscopy and
Optical Diagnostics
for Gases
Spectroscopy and Optical Diagnostics
for Gases

Ronald K. Hanson • R. Mitchell Spearrin
Christopher S. Goldenstein
Spectroscopy and Optical
Diagnostics for Gases
123
RonaldK.Hanson
DepartmentofMechanicalEngineering
StanfordUniversity
Stanford,CA,USA
R.MitchellSpearrin
MechanicalandAerospaceEngineeringDepartment
UniversityofCalifornia,LosAngeles(UCLA)
LosAngeles,CA,USA
ChristopherS.Goldenstein
SchoolofMechanicalEngineering
PurdueUniversity
WestLafayette,IN,USA
ISBN978-3-319-23251-5 ISBN978-3-319-23252-2 (eBook)
DOI10.1007/978-3-319-23252-2
LibraryofCongressControlNumber:2015949092
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Preface
This text provides an introduction to the science that governs the interaction of
light and matter (in the gas phase). It provides readers with the basic knowledge
to exploit light-matter interactions to develop quantitative tools for gas analysis
(i.e. optical diagnostics) and understand and interpret the results of spectroscopic
measurements. The text is organized to cover three sub-topics of gas-phase spec-
troscopy: (1) spectral line positions, (2) spectral line strengths, and (3) spectral
lineshapesbywayofabsorption,emission,andscatteringinteractions.Greaterfocus
is dedicated to absorption and emission interactions. The latter part of the book
describesopticalmeasurementtechniquesandequipmentforpracticalapplications.
The text is written for graduate students, advanced undergraduate students, and
practitioners across a range of applied sciences including mechanical, aerospace,
andchemicalengineering.
The text grew out of a course, Introduction to Spectroscopy and Laser Diag-
nostics for Gases (ME364), first offered in 1977, in response to the growing use
of spectroscopic diagnostics in the research conducted by graduate students in
the High Temperature Gasdynamics Laboratory (HTGL) at Stanford. At the time,
the field of spectroscopy was undergoing a revolution owing to the development
and application of lasers, and many of the standard texts on laser physics and
spectroscopy dealt primarily with theory, e.g., quantum mechanics and optics,
ratherthanengineeringapplications.Therewasthusnosingletextbookthatseemed
suitableforstudents(orfortheprofessor!)withtraditionalmechanicalengineering
backgrounds, nor was there a suitable text that focused on applied measurements
in high temperature gases. As a result, I initially used various introductory texts,
writtenforundergraduatesandmaster’slevelstudentsinphysicsandchemistry,and
Isupplementedthesematerialswithmyownnotesfortopicsnottreatedinexisting
booksbutcriticaltothediagnosticsemployedintheHTGL.
Over time, my own notes became more complete, until finally in 2001 an
energeticstudent,MichaelWebber,helpedputthenotesintoelectronicformforuse
as a course reader at Stanford. The material continued undergoing expansion and
refinement until two recent doctoral students, Mitchell Spearrin and Christopher
Goldenstein, agreed to help convert my reader into a textbook. They are now my
co-authors,havingmadenewcontributionstothelatterhalfofthebook.
v
vi Preface
I am deeply indebted to the many graduate students who have passed through
theirdoctoralstudiesinmygroupatStanfordandcontributedinmanywaystothe
evolutionofthistext.Thoughtoomanytomentionallbyname,Imustacknowledge
onestudent,XingChao,whoheroicallyconvertedmynotesintopowerpointlectures
andcreatedmanyimprovedfiguresforthelectureslidesandthetext.
Finally,IwanttoacknowledgethepleasureIhaveenjoyedinworkingtodevelop
and apply laser-based spectroscopic diagnostics to engineering problems. It has
been a very rewarding experience, particularly in watching Stanford’s mechanical
engineeringgraduatesbecomeleadersinthefieldofappliedspectroscopy.
Stanford,CA,USA RonaldK.Hanson
June2015
Contents
Preface............................................................................. v
1 Introduction................................................................. 1
1.1 RoleofQuantumMechanics ........................................ 1
1.2 EmissionandAbsorptionSpectra ................................... 1
1.3 Planck’sLaw ......................................................... 3
1.4 Wavelength,Frequency,andOtherUnitsandConversions ........ 4
1.5 SpectralRegions...................................................... 5
1.6 BasicElementsofSpectroscopy..................................... 6
1.6.1 Positions,Strengths,andShapesofLines................. 6
1.7 TypicalAbsorptionSpectroscopySetup ............................ 6
1.8 Beer’sLawofAbsorption............................................ 7
1.9 SpectralAbsorptionCoefficient ..................................... 8
1.10 BoltzmannDistribution.............................................. 8
Reference..................................................................... 8
2 DiatomicMolecularSpectra............................................... 9
2.1 InteractionMechanismforEMRadiationwithMolecules......... 9
2.1.1 MicrowaveRegion:Rotation............................... 10
2.1.2 InfraredRegion:Vibration................................. 11
2.1.3 UltravioletandVisibleRegions:Electronic............... 11
2.1.4 SummaryofBackground................................... 11
2.2 RotationalSpectra:SimpleModel................................... 12
2.2.1 RigidRotor(RR) ........................................... 12
2.2.2 ClassicalMechanics........................................ 13
2.2.3 QuantumMechanics........................................ 13
2.2.4 RotationalEnergy .......................................... 14
2.2.5 AbsorptionSpectrum....................................... 15
2.2.6 UsefulnessofRotationalLineSpacing.................... 16
2.2.7 RotationalPartitionFunction .............................. 17
2.2.8 RotationalTemperature .................................... 17
2.2.9 IntensitiesofSpectralLines................................ 19
2.3 VibrationalSpectra:SimpleModel.................................. 19
2.3.1 SimpleHarmonicOscillator ............................... 19
2.3.2 ClassicalMechanics........................................ 19
vii
viii Contents
2.3.3 QuantumMechanics........................................ 21
2.3.4 VibrationalPartitionFunction ............................. 21
2.3.5 VibrationalTemperature.................................... 22
2.4 ImprovedModelsofRotationandVibration........................ 23
2.4.1 Non-rigidRotation ......................................... 23
2.4.2 AnharmonicOscillator ..................................... 24
2.4.3 TypicalCorrectionMagnitudes............................ 25
2.5 RovibrationalSpectra:SimpleModel............................... 27
2.5.1 Born–OppenheimerApproximation....................... 27
2.5.2 SpectralBranches........................................... 28
2.6 RovibrationalSpectra:ImprovedModel............................ 30
2.6.1 BreakdownofBorn–OppenheimerApproximation....... 30
2.6.2 SpectralBranches........................................... 31
2.6.3 RotationalConstant......................................... 32
2.6.4 Bandhead.................................................... 32
2.6.5 FindingKeyParameters:B ,˛ ,! ,x .................... 33
e e e e
2.6.6 EffectsofIsotopicSubstitution ............................ 35
2.6.7 HotBands................................................... 36
2.7 ElectronicSpectraofDiatomicMolecules.......................... 37
2.7.1 PotentialEnergyWells ..................................... 37
2.7.2 TypesofSpectra............................................ 39
2.7.3 RotationalAnalysis......................................... 40
2.7.4 VibrationalAnalysis........................................ 44
2.8 Summary.............................................................. 46
2.9 Exercises.............................................................. 48
References.................................................................... 49
3 BondDissociationEnergies................................................ 51
3.1 Birge–SponerMethod................................................ 51
3.2 ThermochemicalApproach.......................................... 53
3.3 Predissociation ....................................................... 53
3.3.1 HNO......................................................... 54
3.3.2 N2O.......................................................... 55
3.4 Exercises.............................................................. 56
Reference..................................................................... 57
4 PolyatomicMolecularSpectra ............................................ 59
4.1 RotationalSpectraofPolyatomicMolecules ....................... 59
4.1.1 LinearMolecules ........................................... 60
4.1.2 SymmetricTop.............................................. 61
4.1.3 SphericalTop ............................................... 64
4.1.4 AsymmetricRotor.......................................... 64
4.1.5 RotationalPartitionFunction .............................. 64
4.2 VibrationalBandsofPolyatomicMolecules........................ 66
4.2.1 NumberofVibrationalModes ............................. 66
4.2.2 ParallelandPerpendicularModes ......................... 66
Contents ix
4.2.3 TypesofBands ............................................. 69
4.2.4 RelativeStrengths .......................................... 70
4.2.5 VibrationalPartitionFunction ............................. 71
4.3 RovibrationalSpectraofPolyatomicMolecules.................... 71
4.3.1 LinearPolyatomicMolecules.............................. 71
4.3.2 SymmetricTopMolecules ................................. 73
4.4 Exercises.............................................................. 76
References.................................................................... 78
5 EffectsofNuclearSpin:RotationalPartitionFunction
andDegeneracies ........................................................... 79
5.1 Introduction........................................................... 79
5.2 NuclearSpinandSymmetry......................................... 80
5.3 CaseI:LinearMolecules ............................................ 82
5.3.1 Asymmetric(e.g.,COandN O)........................... 82
2
5.3.2 Symmetric(e.g.,O ,CO ,andC H )..................... 83
2 2 2 2
5.4 CaseII:NonlinearMolecules........................................ 87
5.4.1 AsymmetricRotor(e.g.,CHFClBrandN H )............ 87
2 4
5.4.2 SymmetricTop.............................................. 87
5.4.3 Others(e.g.,C H ;CH ;andP )........................... 90
6 6 4 4
5.5 Exercises.............................................................. 90
References.................................................................... 90
6 RayleighandRamanSpectra ............................................. 91
6.1 LightScattering ...................................................... 91
6.1.1 Cross-Sections.............................................. 92
6.2 QuantumModel...................................................... 95
6.3 ClassicalTheory...................................................... 95
6.4 RotationalRamanSpectra ........................................... 96
6.4.1 LinearMolecules ........................................... 96
6.4.2 SymmetricTopMolecules ................................. 98
6.5 VibrationalRamanSpectra .......................................... 99
6.5.1 Polarization ................................................. 100
6.5.2 SelectionRules ............................................. 101
6.5.3 Diatomics ................................................... 101
6.5.4 Temperature................................................. 102
6.5.5 TypicalRamanShift........................................ 103
6.6 SummaryofRayleighandRamanScattering....................... 103
6.7 Exercises.............................................................. 103
References.................................................................... 105
7 QuantitativeEmissionandAbsorption .................................. 107
7.1 SpectralAbsorptionCoefficient ..................................... 107
7.2 EquationofRadiativeTransfer:ClassicalApproach............... 109
7.2.1 Case1:EmissionExperiments.I0 D0/................... 110
(cid:2)
7.2.2 Case2:AbsorptionExperiments.I0 (cid:2)Ibb/.............. 111
(cid:2) (cid:2)