with the GIXRD (classic theta-2theta instruments) without the cradle of Eulero, it's possibile to control the penetration depth by the incident angle in solid samples. What is the equation for the depth?
Hi
Applying Beer-Lambarts law i.e., Ix = I0 exp(-[mu/rh]o. rho. x), and apply simple take-off andle correction you can calculate the thickness x of your sample.
ok, but I want to calculate The depth of diffraction in a solid sample. The thickness of the sample is needed to calculate?
How can I calculate I0?
Hi,
if you're talking about XRay Diffraction in reflexion, for the "x " instead of the thinckness of the sample you use the lenght of the path traveled by the X-Ray inside the material (geometrically related to the depth of diffraction).
Then you have to fix a value Ix/I0 (for example 0.9) to calculate that x. From x you deduce the "depth of diffraction", which will be in this case the thickness of material contributing to 90% (=Ix/I0) of the diffracted intensity.
You can not calculate the thickness corresponding to 100% of the diffracted intensity: it is infinite (because of Beer Lamber Law exponential decrease..)
Penetration depth is calculated from the mass absorption coefficient and the "density". The density value ρ is expressed as a combination of the specific gravity of the material and the packing density.
First the path length L is calculated:
IL = I0 × exp -(μ/ρ)ρL
Next the penetration depth (τ) :
τ = 0.5 L×sin(θ)
This is the thickness of the sample contributing 99% of the diffracted intensity for a given incident angle θ.
If u use HSP, there's a MAC calculator where u can calculate the penetration depth. All u need is the wavelength, chemical formulas, weight fraction of each, estimated packing density and angle of incident (w).
I think the above given answers are at least not fully related to the question. The main point is that the penetration depth decreases substantially when working in the vicinity of the critical angle of total reflection, or even below - check the fundamental paper of Parratt, where the required formulas are provided ( L. G. Parratt, Phys. Rev. 95 (1954) 359Article Surface Studies of Solids by Total Reflection of X-Rays
)You may analytically calculate the penetration depth if you have the index of refraction of your sample. Good luck, Dirk
- Badges
- Science method
- Similar topics
- Methodology
- Crystallography
- X-ray Diffraction