Converting between at% and wt%

From wt% to at%

First we must consider weight in terms of grams. To do this, consider a 100 grams sample of the alloy. For example, 100g of Fe-7wt%C contains 7g of Carbon and 93g of Iron.

Atomic weight of Fe is 56
Atomic weight of C is 12
Avogadro's Number is 6.022 x 10²³

Number of atoms in 7 grams of Carbon
= 7 x Avogadro's Constant / atomic weight of C
= 7 x 6.022 x 10²³ / 12
= 3.513 x 10²³

Similarly, number of atoms in 93 grams of Iron
= 93 x Avogadro's Constant / atomic weight of Fe
= 93 x 6.022 x 10²³ / 56
= 10.000 x 10²³

Therefore, at% of Carbon
= C atoms x 100% / (total of C + Fe atoms)
= 3.513 x 10²³x 100 / (3.513 + 10.000) x 10²³
= 26%

So, Fe-7wt%C is equivalent to Fe-26at%C

From at% to wt%

Cementite forms at Fe-25at%C. At what weight percent is this?

Consider a sample containing 100 atoms. For example, a sample of Fe-25at%C would contain 25 Carbon atoms and 75 Iron atoms.

Weight of 25 C atoms
= 25 x atomic weight of C / Avogadro's Constant
= 4.98 atomic mass units

Weight of 75 Fe atoms
= 75 x atomic weight of Fe / Avogadro's Constant
= 69.74 atomic mass units

Therefore, wt% of Carbon
= C weight x 100% / (total weight of C + Fe atoms)
= 4.98 x 100 / (4.98 + 69.74)
= 6.66%

So, 25at%C is equivalent to 6.66wt%C