For the powder, there are different types of density, these include:

1- The apparent density: weight divided by the total volume occupied by the powder freely poured in a measuring cylinder.

2- Tamped or packed density: the weight divided by the total volume occupied by the powder poured in a measuring cylinder and tamped according to standard conditions (there is ASTM in this regard).

3- The true density: the weight divided by the true volume of the powder (the voids between the particles are NOT included), the true volume can be measured using the pycnometer.

Please note that in order to convert the (wt%) of the powder to (vol%) and vice versa, the true density must be used.

Good luck

Dear Thomas I mean for whole amount of nanoparticles if we assume the shape is spherical with average diameter 20 nm.

The density of the powder could be measured by gas pycnometry Which will give you the volume of the powder for which you know the mass. This would work for any powder even if it is not crystaline or poorly crystaline.

For the powder, there are different types of density, these include:

1- The apparent density: weight divided by the total volume occupied by the powder freely poured in a measuring cylinder.

2- Tamped or packed density: the weight divided by the total volume occupied by the powder poured in a measuring cylinder and tamped according to standard conditions (there is ASTM in this regard).

3- The true density: the weight divided by the true volume of the powder (the voids between the particles are NOT included), the true volume can be measured using the pycnometer.

Please note that in order to convert the (wt%) of the powder to (vol%) and vice versa, the true density must be used.

Good luck

Dear Dr. Imad, thanks for replaying but the intergranular spaces should be included for volume in order to measure the true density so why the voids are not included? could you more explain? thanks in advance