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

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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

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Signal to Noise

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

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Sources of Noise

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

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Source of Noise

• Instrumental Noise
• Thermal noise
• Shot noise
• Flicker
• Environmental noise
• Thermal noise
• Thermal agitation of electrons in electronics
• Boltzmanns equation

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Instrument Noise

• Based on Boltzmann
• R is resistance
• k is Boltzmanns constant
• 1.38E-23 J/K
• T in K
• f is frequency bandwith (1/3risetime)
• Relates to response time in instrument
• Shot Noise
• Electrons crossing a junction
• pn junction, anode and cathode
• Random events
• e 1.6e-19 C

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Instrument Noise

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

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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

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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

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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

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Software Methods

• Ensemble Average
• Average of spectra
• Average can also be sum of collected spectra
• Boxcar average
• Average of points in a spectra

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Software Methods
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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

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Chap. 6 Introduction to Spectrometric Methods

• Electromagnetic radiation
• Interaction with matter
• Quantum mechanical properties
• Electromagnetic radiation
• orthogonal in phase oscillations

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Wave Parameters

• Amplitude and wavelength

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Electromagnetic Spectrum
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Methods
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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

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• 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.

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Energy from X-ray

• From Cu
• 13.6(292)11.4 keV
• Based on Bohr atom
• Family of lines due to different levels
• Determination of elements

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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

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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

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X ray lines
Lines with continuum function of voltage Mo
BCC from bremstrallung
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Bremsstrahlung
EqVeVE(photon)12400/V Ang Duane-hunt law
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Use x-ray to examine crystals

• Model atoms as mirrors
• Use classical optics
• Utilize interference
• Constructive and destructive

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X-ray diffraction

• Emission spectrum from x-ray generator
• Composite of 2 spectra
• Characteristic spectra
• Continuous spectra
• Calculate lines by Mosleys Law

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Braggs Law
Specifics conditions for interference Set of
reflections identifies structure
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XRD

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

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Data analysis
Normalize data to 1st sin2theta Clear
fractions Speculate on hkl Know wavelength from
source, solve for a
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Laue Technique
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Spot pattern

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

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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

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Atomic Spectra

• Quantum numbers
• n1,2,3,4
• raon2/Z for gases with 1 electron
• Energy
• E-(mee4/8eo2h2)Z2/n2
• For ground state H
• E2.18E-18 J/atomk
• Can determine J/mole 1312 kJ/mole
• Energy goes as k/n2
• System converges to limit

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Energy

• ninfinity, rinfinity , E0, unbound e-
• Ionization energy
• k is ionization energy
• Velocity
• vnh/2pmer
• Ionization energy
• Minimum energy required to remove electron from
  atom in gas phase
• Multiple ionization energies

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Balmer states

• Gas H in tube
• Four lines in visible region
• Fit lines
• 1/l(1/22-1/n2)R, R1.1E-7 m-1
• 1/ln (wavenumber)
• E1/2mev2eV (VVolts)
• At 1 V 1.6E-19 J eV
• K13.6 eV

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Matter energy interaction

• Eincident1/2mv2qV
• Escattered
• DE Eincident-Escattered
• DEkZ2(1/n2final-1/n2in)hnhc/l
• De-excitation of electron results in photon
  emission
• Corresponds to line emission

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Shell model and multielectrons

• Particle interaction
• Particle hits electron, electron has scatted
  kinetic energy
• EincEbindingEelectron scattered
• For ground state Ebinding is ionization energy
• Einc 0.5mv2
• DEtrans-kZ2D(1/n2)
• For photon Ehc/l

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Rydberg
k/hc1.1e-7 m-1 R (Rydberg constant) Visible
light 400-700 nm (1.8 to 3.1 eV) Quantum
numbers n1,2,3,4 l0 to n-1 ml -l Spin-1/2
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Bohr Atom

• Net force on the electron is zero
• 0FdynamicFcoulombic
• 1/2mev2/rq1q2/4peor2
• Force is 1/r2
• Energy 1/r
• 1/2mev2/r-Ze2/4peor2
• Z is charge on nucleus
• Quantize energy through angular momentum
• mvrnh/2p, n1,2,3.
• Can solve for r, E, v

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Bohr radius

• R(eoh2/pmee2)(n2/Z)
• Radius is quantized and goes at n2
• R0.529 Å for Z1, n1
• Ao (Bohr radius)

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Photoelectric effect