Chap. 5 (Signals and Noise), Chap. 6 (Spectroscopy introduction)

1. Chap. 5 (Signals and Noise), Chap. 6 (Spectroscopy introduction) • Signal to noise • Source of noise • Signal to noise enhancement • Signal has the information of the analyte • Noise is the extraneous information in the information due to electronics, spurious response, and random events • Signal to noise ratio • Noise is generally constant and independent of the signal • The impact of noise is greatest on the lowest signal • The ratio of signal to noise is useful in evaluating data

2. Signal to Noise • Value of the signal to noise can vary • Values less than 3 make it hard to detect signal

3. Sources of Noise • Chemical Noise • Uncontrollable variables affecting chemistry of system under investigation • Change in equilibria due to variations • Temperature • Pressure • Sample variation • Humidity

4. Source of Noise • Instrumental Noise • Thermal noise • Shot noise • Flicker • Environmental noise • Thermal noise • Thermal agitation of electrons in electronics • Boltzmann’s equation

5. Instrument Noise • Based on Boltzmann • R is resistance • k is Boltzmann’s constant • 1.38E-23 J/K • T in K • f is frequency bandwith (1/3*risetime) • Relates to response time in instrument • Shot Noise • Electrons crossing a junction • pn junction, anode and cathode • Random events • e = 1.6e-19 C

6. Instrument Noise • Flicker Noise • Inverse of signal frequency • Important below 100 Hz • Drift in instruments • Environmental Noise • Emanates from surroundings • Electromagnetic radiation

7. Signal to Noise Enhancement • Hardware and software methods • Hardware is based on instrument design • Filters, choppers, shields, detectors, modulators • Software allows data manipulation • Grounding and Shielding • Absorb electromagnetic radiation • Prevent transmission to the equipment • Protect circuit with conduction material and ground • Important for amplification

8. Hardware • Difference and Instrumentation Amplifiers • Subtraction of noise from a circuit • Controlled by a single resistor • Second stage subtracts noise • Used for low level signal • Analog filtering • Uses a filter circuit • Restricts frequency

9. Hardware • Modulation • Changes low frequency signal to higher frequency • Signal amplified, filter with a high pass filter, demodulation, low pass filter • Signal Chopping • Input signal converted to square wave by electronic or mechanical chopper • Square wave normalizes signal

10. Software Methods • Ensemble Average • Average of spectra • Average can also be sum of collected spectra • Boxcar average • Average of points in a spectra

11. Software Methods

12. Digital Filtering • Numerical methods • Fourier transform • Time collected data converted to frequency • NMR, IR • Least squares smoothing • Similar to boxcar • Uses polynomial for fit • Correlation

13. Chap. 6 Introduction to Spectrometric Methods • Electromagnetic radiation • Interaction with matter • Quantum mechanical properties • Electromagnetic radiation • orthogonal in phase oscillations

14. Wave Parameters • Amplitude and wavelength

15. Electromagnetic Spectrum

16. Methods

17. X-ray Structure • X-rays • 0.01 to 100 angtroms • 12 keV to 1 MeV • Ionizing radiation • Roentgen • Gas discharge tube • Detector with Ba/Pt CN • Scintillator

18. In November of 1895, Wilhelm Roentgen (1845 - 1923) was working in his laboratory using a Crookes tube (known in German as either a Hittorf valve or a Hittorf-Crookes tube) when he noticed that a sample of barium platinocyanide, which accidentally lay on the table, gave off a fluorescent glow. As the Crookes tube was covered at the time, Roentgen was puzzled as to the mechanism whereby the platinum compound was being stimulated to glow. After carrying out a series of exceptionally careful experiments, Roentgen realized that the Crookes tube was emitting a new kind of radiation which he described as "X-rays". In investigating the penetrating ability of these rays, Roentgen placed a photographic plate behind his wife's hand and recorded the first x-ray photo. In this figure, below, notice his wife's wedding rings that stand out as dark rings.

20. Energy from X-ray • From Cu • 13.6(29^2)=11.4 keV • Based on Bohr atom • Family of lines due to different levels • Determination of elements

22. Mosley • Measured 38 elements • Measured emission spectra and found pattern • Based on Z, not mass (Ar/K, Co/Ni, Te/I) • Place lanthanides on periodic table • 14 lanthanides • Up to U there are 92 elements

25. X-ray Structure • Review of cathode ray tube and nomenclature • Determination of elements from X-rays • Coolidge • 1913 • Vacuum tube • Reduction of collision with gas • Reduce glow • Heating Cathode • Water cooling • Shielding (Pb), Be windows

26. X ray lines Lines with continuum function of voltage Mo BCC from bremstrallung

27. Bremsstrahlung E=qV=eV=E(photon)=12400/V Ang Duane-hunt law

28. Use x-ray to examine crystals • Model atoms as mirrors • Use classical optics • Utilize interference • Constructive and destructive

29. X-ray diffraction • Emission spectrum from x-ray generator • Composite of 2 spectra • Characteristic spectra • Continuous spectra • Calculate lines by Mosley’s Law

30. Braggs Law Specifics conditions for interference Set of reflections identifies structure

31. XRD • Fixed wavelength, vary angle • Powder specimen • Grains act as single crystal • Plot I vs angle • At Bragg angle produce angle

32. Data analysis Normalize data to 1st sin^2theta Clear fractions Speculate on hkl Know wavelength from source, solve for a

33. Laue Technique

34. Spot pattern • For symmetry • 2, 3, 4 fold symmetry • May not work for thick specimen • Backscatter and transmission

35. Transmission of radiation • Polarization • Directional filtering of light • Light will be scattered by larger molecules • Radiation transfer to molecules • Absorption spectroscopy • Material consideration • Glass, quartz, plastic

36. Atomic Spectra • Quantum numbers • n=1,2,3,4 • r=aon2/Z for gases with 1 electron • Energy • E=-(mee4/8eo2h2)Z2/n2 • For ground state H • E=2.18E-18 J/atom=k • Can determine J/mole 1312 kJ/mole • Energy goes as –k/n2 • System converges to limit

37. Energy • n=infinity, r=infinity , E=0, unbound e- • Ionization energy • k is ionization energy • Velocity • v=nh/2pmer • Ionization energy • Minimum energy required to remove electron from atom in gas phase • Multiple ionization energies

38. Balmer states • Gas H in tube • Four lines in visible region • Fit lines • 1/l=(1/22-1/n2)R, R=1.1E-7 m-1 • 1/l=n (wavenumber) • E=1/2mev2=eV (V=Volts) • At 1 V = 1.6E-19 J =eV • K=13.6 eV

39. Matter energy interaction • Eincident=1/2mv2=qV • Escattered • DE =Eincident-Escattered • DE=kZ2(1/n2final-1/n2in)=hn=hc/l • De-excitation of electron results in photon emission • Corresponds to line emission

40. Shell model and multielectrons • Particle interaction • Particle hits electron, electron has scatted kinetic energy • Einc=Ebinding+Eelectron scattered • For ground state Ebindingis ionization energy • Einc= 0.5mv2 • DEtrans=-kZ2D(1/n2) • For photon E=hc/l

41. Rydberg k/hc=1.1e-7 m-1 = R (Rydberg constant) Visible light 400-700 nm (1.8 to 3.1 eV) Quantum numbers n=1,2,3,4 l=0 to n-1 ml= +-l Spin=+-1/2

42. Bohr Atom • Net force on the electron is zero • 0=Fdynamic+Fcoulombic • 1/2mev2/r+q1q2/4peor2 • Force is 1/r2 • Energy 1/r • 1/2mev2/r-Ze2/4peor2 • Z is charge on nucleus • Quantize energy through angular momentum • mvr=nh/2p, n=1,2,3…. • Can solve for r, E, v

43. Bohr radius • R=(eoh2/pmee2)(n2/Z) • Radius is quantized and goes at n2 • R=0.529 Å for Z=1, n=1 • Ao (Bohr radius)

44. Photoelectric effect