with the GIXRD (classic theta-2theta instrument) without the cradle of Eulero , it's possible , to control the penetration depth by the incident angle in a solid sample. what is the equation for the depth?
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).
Check the attenuation coefficient for XRD Measurements.. It depends on the configuration of the XRD Measurements, the density of the material and the type of tube you are using (Fe, Cu, Cr).,
NIST has a good resource here for finding the attenuation coefficients for different x-ray energies. You'll then want to use Beer-Lambert's law or something similar. The mean free path (λ) is where intensity drops to 1/e of the original value, it's reasonable to assume an analysis depth of 3λ.
You can get the equation for the depth in the paper" By vineyard, 1982:
Grazing incidence diffraction and distorsed wave approximation for the study of surface, Physical review (B), 26, p4146-4158:
D = λ./ 2
I recommend you to review the Parratt formalism (Phys. Rew. 95 (1954) 799-804 or direct applications of GIXRD (Penetration Depth vs. Incidence Angle) in Advanced Photon Source (1997) 1-7 by Sergey Stepanov. If you want more detail of the X-Ray interaction in the GIXRD modality, please consult chapter 5 (55-68 pgs.) of the PHD thesis “Nanoestructuracion superficial de la aleacion Fe22%wtCr5%wtAl y la caracterizacion fractal de su textura morfologica” by Jesus Israel Guzman Castañeda, Escuela Superior de Fisica y Matematicas del Instituto Politecnico Nacional (2013).
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).
When X-rays penetrate solid material, the beam intensity is absorbed by the solid and reduced following the equation for exponential absorption:
I=I0EXP(-WML).
where I0 is the initial intensity w is the weight fraction of the materials involved, M is the linear absorption coefficient and L is the distance that the X-ray beam travels. Since an X-ray
beam is absorbed and reduced exponentially with distance.
Please find enclosed a paper that can help you.
Dear
can you help me and calculate the penetration depth for incident angle of 3 and 5
for Ti
and also these angles for TiN in GIXRD method?
Thanks
if you have the software High score plus , there is a tool to calculate this parameter.
but It requires the density of your materials.
Thanks Mr. Vincenzo Riva
I don not have the software High score pluse, may you calculate for me?
the density of Ti is 4.506 g/cm³
and the density of TiN is 5.4 g/cm³
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