When we radiate a solid film with gamma radiation, the film will experience a temperature rise. But we don't have access to the film to measure the change in temperature. How to calculate the change in temperature based on the radiation energy and exposure time?
Dear Hadi Alqahtani ,
One has to know how the gamma radiation interact with the material.
Conceptually every photon can make partly permeant change in the material. This part will produce no heat as it is converted to a potential energy.
The radiation can also interact with electrons where they will produce radiation and heat. Only the heat part will contribute to the warming of t he material.
It is only required to know the fraction of the energy converted to heat.
Assume this will be F.
Then the heat generated in the material can be expressed by:
H= F PHI gamma T
where PHI gamma is the gamma flux absorbed by the material.
T is the time of subjection.
By searchi8ng the internet you find F for specific material.
Best wishes
Dear Hadi Alqahtani ,
unfortunately there is no simple formular for the energy deposition of gammas or x-rays in films or even in thin films.
But for homogenous bulk material you can use the KERMA (kinetic energy released in material), which gives you the energy deposition in sample depths, where the incoming and outgoing amounts of scattered radiation are in balance.
The energy dose of a film on top of a substrate is inbetween about 50% and 100% of the bulk KERMA value, because about half of the incoming radiation is scattered out of the film, especially for high energetic radiation, such as gammas.
For getting more precise data you have to do Mont Carlo calculations/simulations on that topic.
For monochromatic radiation (as in your case) the KERMA is calculated via the energy fluence psi times the mass-energy-transfer coeffcient µtr/rho:
KERMA = psi * (µtr/rho,)
the energy fluence psi is given by your photon flux phi times the photon energy E.
So you will have:
KERMA = E * phi * (µtr/rho).
This expression will give you the amount of energy deposited per mass of the material. For converting into any temperature change you only need the heat capacity of your material. You will see that the temperature rise is very, very small.
The µtr/rho values of your material are found in:
https://physics.nist.gov/PhysRefData/XrayMassCoef/chap3.html
https://physics.nist.gov/PhysRefData/XrayMassCoef/tab3.html
https://physics.nist.gov/PhysRefData/XrayMassCoef/tab4.html
Here the mass energy transfer coefficient is named µen/rho.
Details about the KERMA you can find in:
Frank H. Attix; Introduction to radiological physics and radiation dosimetry; John Wiley & Sons.
I have copied the relevant page and will send it to you via RG messenger.
Good luck
Dear Jerhard,
Thank you so much for the helpfull answer and references. I very much appreciate it.
Best regards,
Hadi
Dear Hadi Alqahtani ,
an additional remark:
unfortunately the µen/rho values of the NIST tables are only presented for the elements and special compounds/molecules.
According to the first link given above the mass-energy attenuation values can be calculated via a weighted sum of the elemental components:
µen/rho=sum (wi*(µen/rho)i) of all components i.
wi is calculated via the atomic masses Ai and the molecular weight M:
M = sum(Ni*Ai) with Ni being the number of atoms of type i in the molelcule;
and wi= Ni*Ai/M.
Good luck
There are some software simulators that can be used for such tasks e.g. you may look https://europepmc.org/article/pmc/pmc6716400
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