Material Breakdown Due to Electron Beam

ajhunte
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The problem asks me to determine the rate of breakdown due to firing 120 kev Electrons at Titanium of arbitrary thickness. I could solve this problem if I knew The average energy deposited per electron, or the Energy efficiency of the entire beam through the titanium.

Given:
Electron Flux (Current)=8.75e16 Electrons per second
Energy of Electrons= 120 keV per Electron
Density of Titanium= 4.506 g per cm^3
Thickness of Titanium= .0254 cm
Surface area of Titanium= 100 cm^2

Is there a formula that accurately describes the attenuation coefficient of electrons (or beta particles) based on the Z (# of protons) of the absorber. I am interested in the average energy deposited per electron or average energy deposited per second.
 
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To solve this, I first used the units to work out that a= m* a/m, i.e. t=z/λ. This would allow you to determine the time duration within an interval section by section and then add this to the previous ones to obtain the age of the respective layer. However, this would require a constant thickness per year for each interval. However, since this is most likely not the case, my next consideration was that the age must be the integral of a 1/λ(z) function, which I cannot model.
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