Calculation of the integrated diffusion coefficients

Calculation of the integrated diffusion coefficients

Calculation of the integrated diffusion coefficients
Let us calculate the integrated diffusion coefficients in the Co-Si system. Three
phases grow with very narrow homogeneity range. Very low dissolution of Si in Co is
found. So we need the thickness of the phases only to draw the composition profile,
since these phases grow with a fixed composition.
1100 OC for 100 hrs
Vm (m3/mole)
Co2Si
6.56 x 10-6
CoSi
6.6 x 10-6
CoSi2
7.75 x 10-6
2t = 2 x 100 x 60 x 60 s
= 7.2 x 105 s
Integrated diffusion coefficient of the Co2Si phase
Q
R
b
a
2
ab ∆xCo2 Si ∆xCo2 Si
~ Co2 Si
Dint =
+
a + b 2t
2t
= 1.77 x10 −14 m 2 / s

 VmCo2 Si
VmCo2 Si  
 b(0 ) + a CoSi Q + CoSi2 R  
Vm
 Vm




a+b




a = 1/3-0
b = 1-1/3
 1
Q = 1 − x321x10 −6
 2
 2
R = 1 − x6.8x10 −6
 3
Integrated diffusion coefficient of the CoSi phase
R
b
P
2
∆x
ab ∆xCoSi
~ CoSi
+ CoSi
Dint =
a + b 2t
2t
= 4.6x10 −14 m 2 / s
a
  VmCoSi   VmCoSi  
 b Co2 Si P  + a CoSi2 R  
  Vm

  Vm


a+b




a = 1/2-0
b = 1-1/2
1

P =  − 0 x131x10 −6
3 
 2
R = 1 − x 6.8x10 −6
 3
Integrated diffusion coefficient of the CoSi2 phase
b
Q
a
P
2
ab ∆xCoSi2 ∆xCoSi2
~ CoSi2
Dint =
+
a + b 2t
2t
= 7.7x10 −16 m 2 / s

  VmCoSi2
VmCoSi2 


(
)
b
P
Q
a
0
+
+
  Co2 Si

CoSi

V
V
m

  m



a+b




a = 2/3-0
b = 1-2/3
1

P =  − 0 x131x10 −6
3 
 1
Q = 1 − x321x10 −6
 2
Let us now consider another example where only one phase grows in the
interdiffusion zone. ThO2 particles indicate the location of the Kirkendall marker
plane.
At 1186 oC for 100 hrs
xK
Si
+
N Si = 1
b
CoSi2
N Si
= 2/3
N Si− = 0.52
a
R
Co0.48Si0.52
102.2 µm
(
S
Co1/3Si2/3
52.2 µm
)
2
2
ab ∆xCoSi2 ( 2 / 3 − 0.52)(1 − 2 / 3) 154.4x10 −6
~β
Dint =
=
= 3.35x10 −15 m 2 / s
a + b 2t
1 − 0.52
2 x100 x 60 × 60
VCo DSi
DSi*  N Si+ S − N Si− R   1x (1 − 2 / 3) x 52.2 − 0.52x (2 / 3 − 0.52)x102.2 
= * =
=
 = 1.337
+
−
(
)
VSi DCo DCo
−
N
S
+
N
R
−
0
x
(
1
−
2
/
3
)
x
52
.
2
+
0
.
48
x
2
/
3
−
0
.
52
x
102
.
2


Co
Co 
