I have XRD data of ZnFe2O4 nanoparticles. I want to calculate the porosity of sample. I wanna use the equation P = 1 - (X-Ray density / Bulk density) such as represented in many papers. I am still confuse because in some papers are explained the way to determine the bulk density of nanoparticle by using Archimedes method. Thank you.
Carefully pack a known mass of nanoparticles inside a narrow glass tube and measure the volume. Bulk density= m/v
If you need the true density (which you don't need!), you should use a Pycnometer with Heluim gas!
Dear Dr. I Putu Tedy Indrayana
My Greeting
X-ray density ρ(x) of the sample can be estimated by using the following relation that suggested by Smith and Wijn: ρ(x) = n.M/(N.a^3 )
where M is the molecular weight, N is Avogadro’s number (NA = 6.022×10^23) and (a) is the lattice constant. and n is the number of the lattice points per unit cell according to the lattice structure of your samples
Have a nice time
Please read also
Schaaf, P., Senger, B. & Reiss, H. Defining physical clusters in nucleation theory from the N-particle distribution function. J. Phys. Chem. B. 101, 8740–8747 (1997).
(1) The porosity is defined as 1 - bulk density/x-ray density, not as defined in your original question.
(2) The bulk density can be calculated from (mass/volume) by carefully weighing a regular and simple-shaped sample (such as cylindrical) and measuring its volume precisely by a vernier. However, the accuracy of this technique depends on the regularity of the shape of the sample, the smoothness of the surfaces, and the precision on the measuring instruments.
(3) Therefore, using a density meter is more accurate since the density of a sample of rough surfaces, with any shape, can be determined accurately.
(4) An alternative to the helium Pycnometer mentioned in the answers of some colleagues, a simple density meter composed of a balance with a density kit can be used, which allows measuring the mass (m) of the sample in air (or ideally in vacuum), and the apparent mass (m*) when it is immersed in a standard liquid.with known density (d0). The volume of the sample is (m/d), which is equal to the volume of the displaced liquid (m-m*)/d0. and therefore, the density (d) of your sample is given by:
d = d0[m/(m-m*)]
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Thank you for your answer. That are great and very useful for me.
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