Structural characterization of materials
I. Optical spectroscopy of inorganic solids and liquids
A. The electromagnetic spectrum and optical spectroscopy
1. Characteristics parameters of electromagnetic energy
- The relations describing the electromagnetic waves are the following:
𝑐 ℎ𝑐
𝜈 = 𝜆 = 𝑐𝜈 ′ 𝐸 = ℎ𝜈 = = ℎ𝑐𝜈′
𝜆
where 𝜈 ′ is the wave number (𝑐𝑚−1 )
- It’s important to make the distinction between a radiative power and the intensity. The
radiative power = energy emitted per time unit and the intensity = power emitted by a
source per solid angle unit in one direction.
- The optical domain range is 200-3000 nm.
2. Processes contributing to the attenuation of the transmitted beam
- 3 processes are involved: absorption, reflection, scattering.
- In optical spectroscopy we speak about absorption, luminescence, reflection and Raman
scattering. For all of those, we will analyse the frequency/intensity of emerging beams as
function of the frequency/intensity of the incident beams.
- The information we can get from the optical spectroscopy are:
• The electronic structure of absorbing/emitting centres
• Their lattice (= réseau, maille) locations
• Their environment
3. Interaction between radiation and matter: three possible approximations
- The classical approximation:
• E-m radiation = classical e-m wave
• Solid = continuous medium
• Interaction = classical oscillator
The semi-classical approximation:
• Solid = quantum response
• Propagation radiation = classically
The quantum approximation:
• Radiation and solid = quantum
1
, 4. Absorption
- If the scattering is negligible, we can consider the Beer-Lambert’s law:
𝐼 = 𝐼0 𝑒 −𝛼𝑥 where 𝛼 is the absorption coefficient
- We speak about band of absorption and the broadening of these bands depends on the
Heisenberg’s uncertainty principle:
1
∆𝜈∆𝑡 ≥ 2𝜋 where ∆𝜈 = frequency width at 50% of the peak max and ∆𝑡= life-time
of the excited state
We can have a homogeneous broadening (= one peak) if all absorbing atoms are identical
and an inhomogeneous broadening (= convolution of different peaks) if different absorbing
centres have different resonant frequencies.
5. The measurement of absorption spectra: the spectrophotometer
- The incident beam is send to a monochromator which select a specific band of
wavelength. The monochromator send it to the sample and the result is detected. This is
done for each band of wavelength we have in the incident beam.
- The following parameters can be obtained by using the spectrophotometer:
• Optical density (OD)
𝐼
𝑂𝐷 = log ( 𝐼0 ) where 𝐼0 = incident intensity
• Absorbance (A)
𝐼
𝐴 = 1−𝐼
0
• Transmittance (T)
𝐼
𝑇=𝐼
0
- For sample with high 𝛼 (𝐼 would be too hard to detect), we can use the reflectivity(R)
𝐼𝑅
𝑅=
𝐼𝑂
Two modes exist to obtain the reflectivity spectrum:
• Direct reflectivity = projection in one direction and detection of the reflected beam in
the same direction → polished sample.
• Diffuse reflectivity = projection in one direction and detection of the reflected beam
in all directions → rough sample.
6. Luminescence
- Appears when we have emission of light from a system that is excited. We distinguish
two kind of spectra:
• Emission spectra = we send a fixed excitation wavelength and we measure the
emission intensity at different wavelengths.
• Excitation spectra = we impose a fixed emission wavelength and the excitation
wavelength is scanned in a certain spectra range.
2
I. Optical spectroscopy of inorganic solids and liquids
A. The electromagnetic spectrum and optical spectroscopy
1. Characteristics parameters of electromagnetic energy
- The relations describing the electromagnetic waves are the following:
𝑐 ℎ𝑐
𝜈 = 𝜆 = 𝑐𝜈 ′ 𝐸 = ℎ𝜈 = = ℎ𝑐𝜈′
𝜆
where 𝜈 ′ is the wave number (𝑐𝑚−1 )
- It’s important to make the distinction between a radiative power and the intensity. The
radiative power = energy emitted per time unit and the intensity = power emitted by a
source per solid angle unit in one direction.
- The optical domain range is 200-3000 nm.
2. Processes contributing to the attenuation of the transmitted beam
- 3 processes are involved: absorption, reflection, scattering.
- In optical spectroscopy we speak about absorption, luminescence, reflection and Raman
scattering. For all of those, we will analyse the frequency/intensity of emerging beams as
function of the frequency/intensity of the incident beams.
- The information we can get from the optical spectroscopy are:
• The electronic structure of absorbing/emitting centres
• Their lattice (= réseau, maille) locations
• Their environment
3. Interaction between radiation and matter: three possible approximations
- The classical approximation:
• E-m radiation = classical e-m wave
• Solid = continuous medium
• Interaction = classical oscillator
The semi-classical approximation:
• Solid = quantum response
• Propagation radiation = classically
The quantum approximation:
• Radiation and solid = quantum
1
, 4. Absorption
- If the scattering is negligible, we can consider the Beer-Lambert’s law:
𝐼 = 𝐼0 𝑒 −𝛼𝑥 where 𝛼 is the absorption coefficient
- We speak about band of absorption and the broadening of these bands depends on the
Heisenberg’s uncertainty principle:
1
∆𝜈∆𝑡 ≥ 2𝜋 where ∆𝜈 = frequency width at 50% of the peak max and ∆𝑡= life-time
of the excited state
We can have a homogeneous broadening (= one peak) if all absorbing atoms are identical
and an inhomogeneous broadening (= convolution of different peaks) if different absorbing
centres have different resonant frequencies.
5. The measurement of absorption spectra: the spectrophotometer
- The incident beam is send to a monochromator which select a specific band of
wavelength. The monochromator send it to the sample and the result is detected. This is
done for each band of wavelength we have in the incident beam.
- The following parameters can be obtained by using the spectrophotometer:
• Optical density (OD)
𝐼
𝑂𝐷 = log ( 𝐼0 ) where 𝐼0 = incident intensity
• Absorbance (A)
𝐼
𝐴 = 1−𝐼
0
• Transmittance (T)
𝐼
𝑇=𝐼
0
- For sample with high 𝛼 (𝐼 would be too hard to detect), we can use the reflectivity(R)
𝐼𝑅
𝑅=
𝐼𝑂
Two modes exist to obtain the reflectivity spectrum:
• Direct reflectivity = projection in one direction and detection of the reflected beam in
the same direction → polished sample.
• Diffuse reflectivity = projection in one direction and detection of the reflected beam
in all directions → rough sample.
6. Luminescence
- Appears when we have emission of light from a system that is excited. We distinguish
two kind of spectra:
• Emission spectra = we send a fixed excitation wavelength and we measure the
emission intensity at different wavelengths.
• Excitation spectra = we impose a fixed emission wavelength and the excitation
wavelength is scanned in a certain spectra range.
2
