Initial Sintering Mechanism of Mesocarbon Microbeads

1. Initial Sintering Mechanism of
Mesocarbon Microbeads
Christopher W. Norfolk
Alexander S. Mukasyan, Daniel E. E. Hayes,
Paul J. McGinn, and Arvind Varma
Sintering ‘03
July 25th, 2003

2. Motivation

3. Structure
5 µm

4. Morphology
2 µm
10 µm

5. Morphology
Sintering Sintering
Necks Necks
10 µm 1 µm 2 µm

6. Final Density Characteristics
1.7
1.9
1.6
Curve 1
1.5
3
Final Density ρf, g/cm
Density Ratio ρf/ρo
1.8
1.4
1.7 1.3
Curve 2
1.2
1.6
1.1
1.5 1.0
1.15 1.20 1.25 1.30 1.35 1.40 1.45
3
Initial Density ρo, g/cm

7. Shrinkage Dynamics
0.12 Experimental Curve
Least Squares Polynomial Fit
0.10
Dimensionless Shrinkage, λ
0.08
0.06
0.04
0.02
0.00
-0.02
400 600 800 1000 1200 1400 1600 1800
Temperature, K

8. Shrinkage Rate
3.00 I II III IV V VI
4
Shrinkage Rate, dλ/dT, X10
2.00
1.00
0.00
-1.00
T1 T2 T3 T4 T5
400 600 800 1000 1200 1400
Temperature, K

9. Activation Energy Analysis
∆L  x 
n
2
 x Bt
λ= = 
  = m
r r r Lo  2r 
−Q
B = B oT e
a RT x T = To + β t
d (ln λ ) 2(a + 1) 2Q 1
= + ⋅
d (lnT ) n Rn T

10. Activation Energy Analysis
140
VI V IV 3
120 Curve 2
2
100
dλ/dT, X10
d lnλ/d lnT
80
1
60
4
0
40
Curve 1
20
-1
0
8 10 12 14 16
4
1/T, X10

11. Summary
!Is an activation energy approaching
zero a reasonable result for a densifying
sintering mechanism?

12. Evolution of ρpyc
2.0
2.0
3 3
Pycnometric density ρ , g/cm
1.9
1.9
stage 2
stage 3
pyc pyc
1.8
1.8
1.7
1.7
1.6
1.6
stage 1
1.5
1.5
1.4
1.4
400
400 600
600 800
800 1000
1000 1200
1200 1400
1400 1600
1600 1800
1800
Temperature, K

13. Relative Density Results
pyc 1.00
0.95
Final relative density, ρf /ρf
0.90
0.85
0.80
0.80 0.85 0.90 0.95 1.00
pyc
Initial relative density, ρo/ρo

14. A Simple Example
ρoth=3Mo/4πro3
ro rf
Heat
Lo Lf
Treatment
ro rf
ρo=Mo/2πro3
ρoth=3Mo/4πro3 ρo=Mo/2πro3 ρfth=3Mf/4πrf3 ρf=Mf/2πrf3
ρf/ρo= ρfth/ρoth=(Mf/Mo)(ro/rf)3

15. Thermogravimetric Analysis
100
0.0
Mass Percent Remaining, W
98
-0.5
96
dW/dT, X 10
94 -1.0
92
-1.5
2
90
-2.0
88
86 -2.5
200 400 600 800 1000 1200 1400 1600 1800
Temperature, K

16. Thermogravimetric Analysis
6 0
-2
Mass #16 (Ion Current X 10 )
11
5
-4
dW/dT X 10
4
-6
3
2
-8
2
-10
1 -12
200 400 600 800 1000 1200 1400 1600 1800
Temperature, K

17. Thermogravimetric Analysis
3 0.0
-0.5
2
dW/dT X 10
4
dλ/dT X 10
-1.0
1
-1.5
2
0
-2.0
-1
-2.5
200 400 600 800 1000 1200 1400 1600 1800
Temperature, K

18. Titanium Carbide
6
4
Shrinkage, Adjusted for Mass, λ
Dimensionless Shrinkage, λ
2
50 wt %
0
-2
23 vol %
-4
-6
Increasing TiC
-8
-10 Content
-12
-14
200 400 600 800 1000 1200 1400 1600
1600 1800
1800
Temperature, K

19. Heating Schedule
1100 2
0.01
1000
900
0
0.00
Dimensionless Shrinkage, λ
Shrinkage Rate, dλ/dt
800
Temperature, K
-0.01
700
-2
600
-0.02
500
-4
-0.03
400
300
-0.04
200 -6
0 200 400 600 800 1000 1200
Time, min

20. Heating Schedule
1800 2
0.01
1600
0
0.00
Dimensionless Shrinkage, λ
1400
-2
Shrinkage Rate, dλ/dt
Temperature, K
1200
-0.01
-4
1000
-6
-0.02
800
-8
600
-0.03
400 -10
-0.04
200 -12
0 500 1000 1500 2000
Time, min

21. Conclusions
! The main role of the β-resin is to maintain
particle cohesion
! Sample shrinkage due primarily to increasing
theoretical density, caused by crystallographic
transformation
! Sample porosity remains largely unaffected
by the sintering process