Hi everyone,
I'm trying to calculate densities with MELTS. I'm wandering how densities of the bulk system given in melts.out are calculated, because if I calculate the weighted average of the components present I don't get the same result given in melts.out.
To calculate the average I use
m1/mtot*rho1+m2/mtot*rho2+....+mn/mtot*rhon
where mn and rhon are the masses and densities of the n-component given in melts.out (or in the .tbl files) and mtot is the total mass.
It seems that the calculated weight average densities are always higher (of about 0.1g/cm^3) than the default output densities.
Do you have any clues?
Thank you very much,
alberto
Hi Alberto,
The MELTS output is right. Your averaging formula is weighted incorrectly.
A universal rule for computing weighted averages of ratios is that each component must be weighted by its contribution to the DENOMINATOR, not the numerator. Consider in this case a simple example: you have 1 g of a material with a density of 1 g/cm^3 (and so 1 cm^3 of this material) plus 1 g of a material with a density of 0.5 g/cm^3 (and so 2 cm^3 of this material). Evidently, your formula will weight them equally (my mass) and give a bulk density of 0.75 g/cm^3. But also evidently, you have 2 g total and 3 cm^3 total, so the correct bulk density is 2/3 g/cm^3. Mass weighting gives a result that is too high (by about 0.1 g/cm^3)!
The correct formula is mtot/(sum[m_i/rho_i]).
-- P
Thank you very much! calculating the equivalent bulk volume do indeed solve my issue!