Dear Saurabh Gupta ,

you know that the critical angle φc is related to the optical constant δ of the x-ray refractive index n ( n = 1 - δ - iβ ) via the following relation:

critical angle φc of total reflection: sin²(φc) = 2*δ or φc² ~ 2*δ

δ is related to the density ρ as well as to the atomic number Z and the atomic or molecular weight M by:

δ = 415,31*10-6/(E[keV])² * ρ[g/cm³] * Z/M[g]

(with ρ = density; M = atomic/molecular weight, Z = atomic number)

M is calculated as a weighted sum of the atomic masses according to the chemical formula;

Z is calculated via the weighted sum of the atomic numbers according to the chemical formula.

Knowing φc, E (x-ray photon energy in use), Z and M you are able to solve for the density ρ.

Please see for example page 8 of

Presentation Attenuation Length and Penetration Depth of X-rays

and the references therein.

Good luck

and best regards

G.M.

Sorry, Saurabh Gupta ,

I forgot to sketch the relation of the electron density (in number of mols of electrons per volume or number of electrons per volume) to the mass density ρ (in mass per volume).

a) Let us start with the electrons per mass:

For one mol of your material (here Al2O3 or SnO2) you have the molar mass M as the weighted sum of the atomic weights Ai, weighted according to the numbers given in the chemical formula.

For the amount Z of mols of electrons in that mol of material you have to take the weighted sum of the atomic numbers Zi, weighted by the numbers given in the chemical formula.

The 'electron mol number per mass' is now: Z/M (that expression already shows up in the answer above)

The absolute number of electrons per mass is Av *Z/A, with Av being the Avogadro number [= total number of electrons in one mol].

b) Now we change from mass to volume:

The 'electron mol density' [electrons per volume] is now given by the product:

'electron mol number per mass' * ρ; ρ [is a mass/volume];

thus we now get electron mol number/volume.

So we have: 'electron mol density' [in electron mols per volume] = Z/M * ρ (also showing up in the answer above)

or the electron density [in electrons per volume] = Av * Z/M * ρ

By the way; for low atomic number elements and molecules/compounds of them we have Z/M ~ 1/2. Hydrogen is an exception; here we have Z/M ~ 1

I hope that helps a bit...

Best regards

G.M.