at%, wt%전환

1. wt% (Weight%)
C1 = (m1)/(m1+m2+m3) x 100
       C1 : 물질구성1의 중량%
       m1 : 물질구성1의 중량, m2 : 물질구성2의 중량, m3 : 물질구성3의 중량

2. at%(atom%)
C'1 = (N1)/(N1+N2+N3) x 100
      C'1 : 물질구성1의 원자%
      N1 : 물질구성 1의 몰수, N2 : 물질구성 2의 몰수, N3 : 물질구성 3의 몰수

3. wt% -> at% 전환
 [ (C1*A2)/{(C1*A2)+(C2*A1)} ] x 100 = C'1

 [ (C2*A1)/{(C1*A2)+(C2*A1)} ] x 100 = C'2       (∴C1+C2 = 100, C'1+C'2 = 100)

 

예1) 97wt%Fe와 3wt%C으로 이루어진 탄소강의 at%?(AFe원자량 : 56, AC원자량 : 12)

C'Fe = [ (CFe*AC) / {(CFe*Ac)+(Cc*AFe)} ] * 100

        = [ (97*12) / {(97*12)+(3*56)} ] * 100

        = 87.4

C'c  = 100-C'c

       = 100-87.4

        = 12.6

 

4. at% -> wt% 전환

[ (C'1*A1)/{(C'1*A1)+(C'2*A2)} ] x 100 = C1

[ (C'2*A2)/{(C'1*A1)+(C'2*A2)} ] x 100 = C2       (∴C1+C2 = 100, C'1+C'2 = 100)

 

CFe = [ (C'Fe*AFe) / {(C'Fe*AFe)+(C'c*Ac)} ] * 100

        = [ (87.4*56) / {(87.4*56)+(12.6*12)} ] * 100

        = 97

Cc = 100-CFe

     = 100-97

     = 3

 

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