Download Raman_Intensities

Raman Spectroscopy
Spectrum is defined by:
1. position of the peaks
2. 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.
Laser parallel to c
Laser parallel to a,
polarized parallel to c at angle = 0
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.
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.
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.
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
Topaz, Al2SiO4F2, orthorhombic
Let’s 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
b
c
Red = short
Green = long
Blue = medium x 2
Laser along a-axis,
0 = b-axis, 90 = c-axis
b
Red = short
a
Green = long
Blue = medium x 2
Laser along c-axis,
0 = a-axis, 90 = b -axis
c
Red = short
a
Green = long
Blue = medium x 2
Laser along b-axis,
0 = c-axis, 90 = a-axis
In general, tetrahedral groups produce strong peaks, while octahedral
groups do not.
Question, why is this so?