What exactly is the quantity you want to know? And what is the significance of "calculating"? (either determine from applying some theory or determine from experimental data ?)

If I understand you correctly you have "big polymer balls" in which you embed smaller Fe particles. Right?

You will know that the definition of magnetization is "magnetic moment per volume". Alternatively, you might want to make a statement on "magnetic moment per Fe atom" at saturation, if you only wish to characterize these particles and expect that there is little to no magnetization in the polymer. [Care is recommended though: the polymer will make a diamagnetic contribution to the measurements. It then depends on the volume ratio of the different substances, whether this is a noticeable fraction of what you measure.]

Will continue to reply later.

Dear Dr. Fauth,

I am grateful that you kindly responses as best as you can. I may need to know magnetic moment/Mole or magnetic moment/volume (or atom) of FeNP@polymer. However, the Shape of the ball is a complex structure with smaller balls. Can that be safe if I can simply assume the value by taking your suggested way? Otherwise, Any other parameters do I need to take it into account in this case?

Best Regards,

 1) Let us suppose for a moment you knew the average magnetic moment per atom (mat) in the Fe particles. [Average to make things more simple for now]

2) The total moment of one nanoparticle is then mNP = mat*nat*VNP   , where nat is the atomic density of Fe atoms in the particles and VNP is the nanoparticle volume.

3) Each polymer "meta-particle" contains some number of Fe nanoparticles, both, polymer and Fe particles shall follow some size distribution (which may or may not be mutually independent, depending on growth mechanism of the resulting composite).

4) Assuming that (i) the average atomic Fe moment does not depend on the particle size (although it may do so for more than one reason) and that (ii) the atomic density in the particles is the same in all particles and (iii) the polymer does not contribute at all, then the average magnetization is simply Mav=mat * nat * Sum(VNP) / (Sum(VNP) + Sum(Vpol))

5) Each of these assumptions would require verification/justification under the circumstances of your measurement.

6) In my opinion there is not so much use in this average number [except for specific purposes], since you create an explicitely magnetically inhomogeneous material - so what would this average number stand for which could not better be expresseed in other terms?!

7) What do you know about the constitution of the Nanoparticles? Metallic fraction?

8) Are all Fe atoms in the specimen present in the form of nanoparticles? I have seen examples where that was believed, while in reality there were also single atoms / ions present in high abundance (but not seen by any microscopy method). These then chimed in with a substantial paramagnetic contribution at very low temperature!

9) When the particles are surface oxidized, this will reduce the average saturation moment per Fe atom. Even if there was no oxidation at all, the surface-near magnetic moments may still be quite different from those further inside. To do things properly, you would have to do your best to quantify (a) the total composit volume of your specimens {could well be that this is already not an easy task}, (b) the volume fraction of Fe NP's in your material, (c) the diamagnetic response of the polymer material [e.g. from reference measurements without Fe included]. Then you can determine by experiment (within appropriate error margins) the atomic moment and go on.

10) Alternatively, if you just want the average magnetization at saturation of the Fe particles, then it suffices to divide the total moment (result of magnetometry experiment, which always measures the total moment of the specimen) by the total specimen volume (see above). Even then, you should not forget to properly correct for the contributions of sample holder, substrate, or whatever else is being measured in the magnetometer.

Thanks for your super-prompt and fine responses !

I will follow your kind suggestions until meet a reasonable answer.

Sincerely,