Can FGR and the fine structure constant explain high intensity in dark field?

In summary, you irradiated a sample that has an absorbance β with light of a wavelenght λ1. β (which is a function of the wavelength) just tells you how much light gets reflected/scattered. Absorbance is wavelength dependent.
  • #1
Talker1500
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Let's say I irradiate a sample that has an absorbance β with light of a wavelenght λ1. Is there a way to relate the initial λ1 and the diffracted/scattered λ2 using β?
 
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  • #2
Most materials will have λ2=λ1.
β (which is a function of the wavelength) just tells you how much light gets reflected/scattered.
 
  • #3
Absorbance is wavelength dependent

You can find the absorbance as a function of wavelength for many materials in palik's handbook of optical propeties. Most materials have peak absorbance where there is resonance between the energy levels of the various energy carriers and the incident photon energy (wavelength)
 
  • #4
mcodesmart said:
You can find the absorbance as a function of wavelength for many materials in palik's handbook of optical propeties. Most materials have peak absorbance where there is resonance between the energy levels of the various energy carriers and the incident photon energy (wavelength)

My sample has parabolic bands instead of quadratic, they touch inside the Brillouin zone, so I'm not sure as to how to find the reason of the ressonance with this kind of e-band.
 
  • #5
What kind of sample do you have?

Parabolic band and quadratic band are the same thing.

There are different band corresponding to the different levels and it is the transition between these levels that I was talking about. You can have two different types of transitions, interband and intraband.

Interband transition is the transition between the conduction and valence bands (electrons and holes)

Intraband transitions are the transitions between the quantized levels within the conduction or valence band.
 
  • #6
My sample is silicene-based, with dispersion relation E= hvk.
 
  • #7
I am not familiar with this material. Is it similar to graphene dispersion relation, where you have a discontinuity at k=0 (or infinite effective mass).

To know the absorption, you must do the following. Using Fermigolden rule. calculate the transition rate for an electron from one band to another due to the absorption of the photon. This is done as follows. You have to find the matrix element, <i|H'|f>, where, H' is the perturbing potential and in this case can be treated as a dipole moment caused by a classical electromagnetic wave, i.e H' = eEr*exp(ik*r). The initial and final states of the electrons are given by plane waves modulated by block functions. Finally, you need the density of states g(E). This is where your dispersion relation comes into play. In the case of silicene, assuming that it is similar to graphene, i would assume a 2D density of states.
 
  • #8
There's literature about the use of FGR to calculate the absorption in graphene, it yields the result A= Nπα, N is the number of layers (in my case, I use single layer silicene, or single layer graphene in the case you are proposing), and α is the fine structure constant. So for N=1, A= πα.

But this doesn't help me understand this high intensity I'm seeing in dark field, i cannot relate the two facts
 

1. What is absorbance?

Absorbance is a measure of how much light is absorbed by a substance. It is often used to quantify the concentration of a substance in a solution.

2. How is absorbance measured?

Absorbance is measured using a spectrophotometer, which measures the amount of light that passes through a sample at a specific wavelength. The higher the absorbance value, the more light is being absorbed by the sample.

3. What is the relationship between absorbance and concentration?

The relationship between absorbance and concentration is linear, meaning that as the concentration of a substance increases, the absorbance also increases. This relationship is described by the Beer-Lambert law: A = εcl, where A is the absorbance, ε is the molar absorptivity coefficient, c is the concentration, and l is the path length of the sample.

4. How does wavelength affect absorbance?

The absorbance of a substance is dependent on the wavelength of light used. Each substance has a unique absorbance spectrum, meaning that it absorbs different wavelengths of light to varying degrees. This can be used to identify and quantify substances in a sample.

5. What is the difference between absorbance and transmittance?

Absorbance and transmittance are two ways of measuring the amount of light that passes through a sample. Absorbance is the amount of light that is absorbed by the sample, while transmittance is the amount of light that is transmitted through the sample. They are inversely related, meaning that as absorbance increases, transmittance decreases.

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