Laser is acronym for light
amplification by stimulated
emission of radiation
• Most lasers are made of some material such as a crystal of ruby or a
gas that is enclosed in a glass tube, like argon.
• Suppose an atom was in an excited state. I.e. an electron was in a
higher energy orbit. If a photon of light, that has the same energy as
the difference between the excited state and the ground state, passes
by the atom then it might cause the excited electron to drop to its
ground state and emit another photon of the same wavelength. This is
the stimulated emissions part of the definition.
• Furthermore, the second photon is exactly in phase with the first
photon. When many photons are in phase, we say that the light is
coherent.
• Suppose that the ruby crystal or the gas
is constantly being excited. Then if a
first photon is created, and this would
happen spontaneously, then it will
create a second one that is coherent.
• As the photons travel along the tube or crystal, they create more photons, all of
which are coherent. Therefore, by constructive interference the light quickly
becomes bright. The crystal or the gas is constantly being excited so after the
photon is emitted, the atoms quickly get re-excited.
• The excited atoms are enclosed with mirrors at both ends. This way the photons hit
the mirror and are bounced back to pass through the material repeatedly. Only the
photons that are travelling precisely along the axis of the tube will remain, as the
others will bounce right out of the sides of the tube. Thus a beam of very bright,
coherent light is created that is aligned precisely through a cascading effect. The
photons will bounce back and forth millions of times.
• The mirrors are not perfect. They let out about 5% of the light. The light that
escapes forms the laser beam.
Two common lasers used for
Raman spectroscopy are:
1) Gas laser (eg. Argon, above)
2) Solid state laser (Nd:YVO4 left)
Sample
Holographic notch filter, to
remove laser line
Examples of Raman Instruments
Spectrum is defined by:
1) x-axis = position of peaks
2) y-axis = intensity of peaks
x-axis represents an energy shift
 = c/, where  = frequency, c = speed of light,  = wavelength
Raman shift = ύ = /c = 1/  (cm-1)
But E = h  = hc/  = hcύ, and since hc is a constant, then Raman shift is
proportional to change in energy
Origin of the Energy shift
•Consider the harmonic oscillator, with restoring force proportional to displacement:
F = -kx, F = force, k = force constant, x = displacement
•Then
x(t) = Asin(2t + ), A is amplitude, t = time,  = phase shift
•Solve for F = ma = -kx to obtain
 = 1/2 sqrt(k/m), ie. Frequency depends on mass and strength of bonds
•Energy is then E = h (n+1/2), where n = vibrational quantum number
Vibrational modes for BF3
Weak bonds
Heavy elements
Strong bonds
Light elements
Raman Frequency vs. M-O Bond Length
1700
NO3
1600
CO3
Raman Frequency (cm-1)
1500
IIIBO3
IVBO4
1400
SO4
PO4
1300
SiO4
1200
BeO4
CrO4
1100
AsO4
VO4
1000
MoO4
WO4
900
800
700
600
1.2
1.3
1.4
1.5
1.6
Bond Length (Å)
1.7
1.8
1.9
How do you compute the positions of the peaks?
•Lattice dynamics
•F = -kx
•E = ½ mv2 = kinetic energy
•  ½ xt D x, where D = dynamical matrix
•Eigenvalues provide frequencies, eigenvectors provide normal modes,
some can be the same as others, known as degenerate modes
How many peaks are there?
•In general, there are 3n-5 modes, where n = number of atoms in unit
cell, and the 5 represents translation and rotation of unit cell
•Bilboa crystallographic server, http://www.cryst.ehu.es/
•Using crystal structure information, you can determine the number of
peaks
How does chemistry affect the positions?
•C = XP,
where C = matrix of chemistry
X = transformation matrix
P = peak position matrix
•Then
CPt = XPPt
X = CPt(PPt)-1
•50 garnets, X3Y2(SiO4)3,
•16 elements, average error is 0.02
atoms per chemical formula
Raman spectra of garnets
Effect of pressure
pyroxene
Effects of temperature
Soft modes
Artifacts that should be removed from a spectrum
1. Cosmic rays
2. Notch filter effects