Application of Master Sintering
Curve Theory To Predict And Control
Nano-Crystalline Ceramic Sintering
Kevin G. Ewsuk, Christopher B. DiAntonio,
Donald T. Ellerby, and Denise N. Bencoe
Sandia National Laboratories
Albuquerque, NM 87185-1340
Sintering 2003
3rd Intl Conf on the Science, Technology, & Applications of Sintering
September 14-17, 2003
University Park, PA
Sandia National Laboratories is a multi-program laboratory operated
by Sandia Corporation, a Lockheed Martin Company for the US
Department of Energy under contract No. DE-AC04-94AL8500
A Science-Based Approach Can Be
Used To Improve Process Control
The Problem:
Processing defects impact manufacturing cost, and
component performance and reliability
Science-Based Processing
Technical Solution:
Form -> Sinter
Apply fundamental scientific
understanding to design
reproducible processes to
manufacture high performance
and reliability ceramics
• characterization
• predictive modeling
Form -> Sinter -> Grind ($$’s)
Traditional Processing
Characterization & Modeling
Are Advancing Sintering Science
Bilayer Sintering Experiment
Bilayer Sintering Simulation
Relative Density
0.893
0.910
0.926
Modeling
• Master Sintering Curve Theory
• 3D FE Modeling
• Microstructure Modeling
Free sintering of zinc oxide with different green densities.
Shrinkage
0.25
0.2
0.2
ZnO
57% Green Density
Sintering
47% Green Density
rgreen= 47%
Validation Sintering Model Validation
0.15
rgreen= 57%
0.1
0.1
L
8.049 mm
0.05
0.00
500
500
-0.05
600
600
700
700
800
800
900
900
Temperature (C)
Temperature
(°C)
1000
1000
Characterization
• Shrinkage (non-contact video)
• Shape Deformation (in-situ)
• Constitutive behavior
• Pore Characteristics (NMRI)
Hu
1.323 mm
L
Hl
Hu
W
Hl
1.308 mm
W
4.790 mm
Experiment
Model
∆
6.7 mm
6.431
4.0%
1.001
2.15 mm
1.2%
1.123
3.89
3.888
0.1%
Densification Can Be Predicted
And Controlled With The MSC
Density (%)
95
1100 1200 1300 1400 1500
Master Sintering Curve
Density vs. θ(t,T(t))
85
95
75
85
65
75
AKP53 Alumina
Q = 566 kJ/mole
55
Q
1
∫0 T exp(− RT )dt = θ(t,T(t))
10
t
J. Am. Ceram. Soc., 79 [12] 3211-17 (1996)
10 -22
10 -20
θ (t,T(t))
10 -18
65
55
Density (%)
Temperature (°C)
The MSC Offers Processing,
Microstructure, & Property Control
Sintering Time
And Temperature
3.2
Q
k
1
exp(−
)dt
≡
ρ
≡
∫o T
RT
γΩDo
t
Average MSC
2.95 g/cc
2.8
5oC/min,
750oC
2.6
2.4
2.2
2.0
1.8
1E-20
Microstructure &
Materials Properties
3.14 g/cc
3.0
Density (g/cc)
(G( ρ ))n
∫ρ o 3ρΓ(ρ) dρ
ρ
2.45 g/cc
5oC/min,
5oC/min, 950oC
700oC
2.00 g/cc
1.90 g/cc
1E-19
5oC/min 800oC
DuPont 951 Green Tape™
1E-18
1E-17
Theta [log (sec/K)]
1E-16
Two Different ZnO Ceramic
Powders Were Examined
Nano-Crystalline ZnO
Micro-Crystalline ZnO
600 nm
600 nm
48 nm average particle size
30 m2/g specific surface area
790 nm average particle size
3.2 m2/g specific surface area
The ZnO Powders Were
Granulated, Pressed, And Sintered
Nano-Crystalline ZnO
Micro-Crystalline ZnO
Pan Granulated
Spray Granulated (CBM)
Ground and Sieved
Sieved
>45µm to <150 µm
3 Wt% 50:50 PVA:PEG
<150 µm
3 Wt% 50:50 PVA:PEG
Dry Pressed (6 x 6mm dia pellets) Dry Pressed (5 x 6 x 50 mm bars)
140 MPa uniaxial
210 MPa Isostatic
18 MPa uniaxial
210 MPa Isostatic
Binder Burned out
Binder Burned out
Sintered
Sintered (4 x 5 x 10 mm bars)
RT - 600°C in Air
5, 10, 20, or 30°C/min to 1550°C
Netzsch Dilatometer 402ED
RT - 600°C in Air
5, 10, 20, or 30°C/min to 1550°C
Netzsch Dilatometer 402
62% TD ZnO Powder Compacts
Sintered To Greater Than 91% TD
Nano-Crystalline ZnO
Micro-Crystalline ZnO
Compact Density (w/o binder)
Compact Density (w/o binder)
Sintered Density
Sintered Density
62.6 ± 0.0% TD
99.2 ± 0.2% TD
62.2 ± 0.0% TD
91.3 ± 0.3% TD
Sintered Density Was Determined
From Measured Linear Shrinkage
6.0
Density (g/cc)
dL
dρ
=
Ldt 3ρdt
Linear Shrinkage
0.98
0.92
0.86
500
700
30C/min
20C/min
10C/min
5.0
4.5
4.0
3.5
500
30°C/min
20°C/min
10°C/min
600
5.5
Nano-Crystalline ZnO
600
700
800
900
Temperature (°C)
800
900
Temperature (°C)
1000
1100
1000
1100
Nano-Crystalline ZnO Sinters
Faster Than Micro-Crystalline ZnO
Crystalline ZnO sintering
Temperature (°C)
5.5
600
700
800
900
1000
1100
30C/min
20C/min
10C/min
5.5
5.0
4.5
5.0
Nano
4.0
4.5
3.5
4.0
Micro
700
800
900
1000
Temperature (°C)
1100
3.5
1200
Density (g/cc)
Density (g/cc)
500
A Consistent Activation Energy (Q)
Was Determined For ZnO Sintering
Micro-Crystalline ZnO
*Nano-Crystalline ZnO
LN(dP/dT * Heating Rate * T
(Kelvin/min)
Q for Densification (65-90%TD)
268 ± 25 kJ/mole
5.5
5.0
Q for Densification (65-90%TD)
296 ± 21 kJ/mole
4.8 g/cc
y = -36855x + 38.8
4.9 g/cc
y = -31926x + 33.6
4.5
Q = slope * R
4.0
3.5
3.0
5.1 g/cc
y = -40266x + 38.5
2.5
0.00084
5.0 g/cc
y = -31995x + 32.7
0.00088
0.00092
0.00096
1/T (Kelvin-1)
Q = 276 ± 13 kJ/mole Gupta & Coble - J Am Ceram Soc 1968
A Master Sintering Curve Was
Constructed For Micro-Crystalline ZnO
Temperature (°C)
700
800
900
1000
1100
1200
5.0
4.5
4.0
3.5
20°C/min
10°C/min
Density (g/cc)
Density (g/cc)
5.5
30°C/min
Micro-Crystalline ZnO
5.5
5.0
Q = 296 kJ/mole
4.5
4.0
3.5
3.0
10 -18
10 -16
10 -14
Theta (t,T,(t))
10 -12
A Master Sintering Curve Was
Constructed For Nano-Crystalline ZnO
Temperature (°C)
5.5
5.0
600
700
800
900
1000
1100
30C/min
20C/min
10C/min
Nano-Crystalline ZnO
Q = 268 kJ/mole
5.3
4.5
Density (g/cc)
Density (g/cc)
500
4.9
4.0
4.5
3.5
4.1
3.7
1E-16
1E-15
1E-14
Theta (t,T(t))
1E-13
1E-12
Master Sintering Curve
Predictions Were Tested & Validated
Nano-Crystalline ZnO Sintering
5.5
30°C/min to 870°C
Density (g/cc)
5.1
4.7
20°C/min to 780°C
4.3
10°C/min to 713°C
3.9
5°C/min to 633°C
3.5
1E-16
1E-15
1E-14
Theta (t,T(t))
1E-13
1E-12
A Slower Heating Rate May
Alter Sintering And The MSC
Relative Density (%)
95
90
Alcoa A-16 Alumina
85
1 °C/min
80
75
10 - 40 °C/min
70
• A-16 Al2O3 Sshows
seviation from the
MSC at 1°C/min.
• Surface diffusion
results in coarsening
at the expense of
densification.
65
60
55
10-20 10-19 10-18 10-17 10-16 10-15 10-14
θ (t,T(t))
10-13
MSC Theory Was Applied
To Nano-Crystalline ZnO Sintering
Nano-Crystalline ZnO Sintering
48 nm average particle size
30 m2/g specific surface area
62.6% TD compacts sintered to 99.2% TD
Q = 268 ± 25 kJ/mole
A master sintering curve (MSC) was constructed
Density (g/cc)
5.5
5.1
30°C/min to 870°C
4.7
4.3
3.9
3.5
1E-16
10°C/min to 713°C
5°C/min to 633°C
1E-15 1E-14 1E-13
Theta (t,T(t))
1E-12