Raman Spectroscopy

1
Raman Spectroscopy

• Spectrum is defined by
• position of the peaks
• Intensity of the peaks
• Peak positions are a function of the force
  constants, and are constant for a given
  material, even with variations in incident
  wavelength.
• Intensities, however, vary with incident
  wavelength, direction of polarization of the
  beam, and orientation of the crystal.

2
Laser parallel to c
Laser parallel to a, polarized
parallel to c at angle 0
3

• Intensities are difficult to compute
• Arm waving explanation, you can get Raman
  intensity if the vibration of the atoms causes a
  change in the polarization of the electron
  density at the macro scale. Of course every
  vibration of an atom causes a change in the
  polarization of the electron density at the
  atomic scale.
• Important case, if an atom is located on a point
  of inversion, then any vibration in one direction
  is associated with another vibration in the exact
  opposite, resulting in no change in macro scale
  polarization, and therefore, no peak intensity
  associated with the vibration of that atom.
• Consequences, rocksalt and ccp elements have no
  Raman spectra because every atom is on a center
  of inversion.
• Eg. Calcite, CaCO3. Ca is on a center of
  inversion, so Raman is only associated with CO3
  vibrational modes.

4
Calcite, peak at 280 cm-1, laser along a,
horizontal is // b, vertical is // c, rotate
crystal in 5 increments
Distance from center of plot is proportional to
intensity. Vibrational mode is rocking of planar
CO3 group about a axis.
5
Laser parallel to c

• In this case, there is no variation in intensity
  for any of the different vibrational mode as the
  polarization of the beam is varied.
• That is because we are shooting down an axis of
  4-fold symmetry, so the optical ellipsoid is
  circular. All properties of a crystal show no
  variation as a function of polarization when
  examined along the axes of 3-, 4-, or 6-fold
  symmetry.
• In particular, there is no change in the
  polarizability of the electron density in rutile
  when the beam is directed along the c-axis.

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Crystal structure of rutile, TiO2, looking along
the a axis. Note that maximum in 450 cm-1 peak is
when polarization direction is nearly parallel to
the TiO bond
7
Topaz, Al2SiO4F2, orthorhombic Lets examine the
Si-O bond stretching modes. There are 3
non-equivalent SiO bonds, R(SiO1) 1.636
Å R(SiO2) 1.648 Å R(SiO3) 1.640 Å twice
SiO3
SiO2
SiO1
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b
Red short Green long Blue medium x 2
c
Laser along a-axis, 0 b-axis, 90 c-axis
9
b
Red short Green long Blue medium x 2
a
Laser along c-axis, 0 a-axis, 90 b -axis
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c
Red short Green long Blue medium x 2
a
Laser along b-axis, 0 c-axis, 90 a-axis
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In general, tetrahedral groups produce strong
peaks, while octahedral groups do not. Question,
why is this so?