-
____________________________________________________________________University
of Alabama in Huntsville Department of Chemical and Materials
Engineering
Thermophysical Property Measurements and their Application to
Materials Processing
Materials Science Seminar UAH 2012
R. Michael BanishDepartment of Chemical and Materials
Engineering
University of Alabama in HuntsvilleHuntsville, Alabama 35899
[email protected]
Financial Support by NASA and the State of Alabama is gratefully
acknowledged
-
____________________________________________________________________University
of Alabama in Huntsville Department of Chemical and Materials
Engineering
● Introduction- Mass Diffusivity: O~10-5 [cm2/sec]- Thermal
Diffusivity: O~10-1 [cm2/sec]
● Experimental Configurations● Mathematical Models- long thin
cylinder- central region heating- edge heating with no internal
generation- edge heating with internal heat generation
● Experimental Results
● Lead free alloys
-
____________________________________________________________________University
of Alabama in Huntsville Department of Chemical and Materials
Engineering
● Self-diffusivity of Mercury – Experimental Data
CC
CC
C
C
C
J
J
J
J
J
J
JJ
P
PPP
PP
P
PPP
AAA
AAA
A
GG
G
G
G
G
G
G
G
Hoffman(1952)
Meyer (1961)Nachtrieb, Petit (1956)
A Brown, Tuck (1964)Broome, Walls (1968)
logD = (1.854) logT – (9.349)
D = 8.5 10-5 exp –10051.99 T
D = 1.1 10-4 exp –11501.99 T
D = 1.26 10-4 exp –11601.99 T
PJ
C
1
5
1.8 2.3 2.8 3.3 3.8Inverse Temperature [103/K]
4
3
2
-
____________________________________________________________________University
of Alabama in Huntsville Department of Chemical and Materials
Engineering
● Terrestrial Determinations of Thermal Conductivity
PbHg
Ga
Temperature [K]
0.1
0.2
1.0
Sn
235 800 505 1300
303 600 600 1000
Ther
mal
Con
duct
ivity
[W/c
m K
]
-
____________________________________________________________________University
of Alabama in Huntsville Department of Chemical and Materials
Engineering
● Thermal Conductivity of Mercury- terrestrial and
low-gravity
(Nakamura, Hibiya, Yamamoto, and Yokota, 1991)
8.0
Temperature [ K]300 350 400
7.5
8.5
9.0
9.5
7.0
6.5
6.0
Low-g
Ther
mal
Con
duct
ivity
[w/m
k]
-
____________________________________________________________________University
of Alabama in Huntsville Department of Chemical and Materials
Engineering
● Thermal Diffusivity Temperature Dependence- Wiedemann Franz
Relation
SnHg
Ga
300 400 500 600 700 800
3.0
2.8
2.6
2.4
2.2
2.0
Temperature [K]
I ± 10%
Wakeham and Hix
-
____________________________________________________________________University
of Alabama in Huntsville Department of Chemical and Materials
Engineering
● Measurement Methodologies- Mass Diffusivity – long, thin
cylinder
0 z1 z2 L z
Time
n2(t)
Diffusion SampleRadioactiveTracer
RadiationShield
n1(t)
-
____________________________________________________________________University
of Alabama in Huntsville Department of Chemical and Materials
Engineering
● Measurement Methodologies con’t- long, thin cylinder con’t
n1(t)
n2(t)
Time
D
Codastefano, Russo and Zanza,Rev. Sci. Instr. 48 (1977) 1650
Z1 = L/6 and Z2 = 5L/6
ln[n1(t) - n2(t)] = const - (/L)2Dt
-
____________________________________________________________________University
of Alabama in Huntsville Department of Chemical and Materials
Engineering
● Measurement Methodologies- Disk with central region
heating
R
0.546
r0 = µ1/µ2
1
T(r1)T(r2)T(r3)
0.851 0.5430.236
Heated Region
-
____________________________________________________________________University
of Alabama in Huntsville Department of Chemical and Materials
Engineering
● Measurement Methodologies- Disk with central region
heating
8506.0a3r
5426.0a2r
2364.0a1r
t2a
21)ijln()ijTln(
→
• fine grained graphite• boron nitride
- sensitivity analysis
-
____________________________________________________________________University
of Alabama in Huntsville Department of Chemical and Materials
Engineering
Thermal Diffusivity Measurement MethodologyCylindrical Sample
with Edge Heating
2
2
1 1 . T T T
r r r t
● Initial Conditions- cylinder at initial T0- constant heat flux
Q”- flux applied 0 < t < te
● Transient form of Heat Equation
● Boundary conditionT(r,0) = T0 at r = R
''T- 1 r
e
k Q h t t
-
____________________________________________________________________University
of Alabama in Huntsville Department of Chemical and Materials
Engineering
Mathematical Model – edge heating con’t
2 21 12 2
110 0
21 0 1
2 " 1
e
jit t
R Rij
rrJ JR RQ RT e e
k J
212ln ln ij ijT tR
212
110 0
21 0 1
2 " 1
e
jit
Rij
rrJ JR RQ R e
k J
Note: ln(T) could be nondimensionalized by dividing by
2Q”R/k
-
____________________________________________________________________University
of Alabama in Huntsville Department of Chemical and Materials
Engineering
● Experimental Setup
-
____________________________________________________________________University
of Alabama in Huntsville Department of Chemical and Materials
Engineering
● Experimental Results – 303 Stainless Steel
3.4
3.6
3.8
4.0
4.2
310 350 390 430 470 510 550 590Temperature [K]
-
____________________________________________________________________University
of Alabama in Huntsville Department of Chemical and Materials
Engineering
● Thermal Diffusivity Determinations with Internal Heat
Generation- Cement Pastes (I-V)
-
____________________________________________________________________University
of Alabama in Huntsville Department of Chemical and Materials
Engineering
Mathematical Model – edge heating – internal heat generation
con’t
2 21 12 2
2211
0 1 0 1- -
22 1 0 1
22
0 0--3 3
1 1 1
e 1
24
e
jit t
R R
i je ji
i i j jtt
rrJ JR Re
JR TT Tt rr
J r J rR R e eR J R
21
22 11 2 3 4
ttR
i jT T C C e C C e
● Similar simplifications and linearization as before
-
____________________________________________________________________University
of Alabama in Huntsville Department of Chemical and Materials
Engineering
● Insensitivity to Deviations from 1D transport- numerical
modeling
x [mm]
0
3
5
7
30
25
L
0 3
wy [mm]
5L/6
L/6
x
01
(b)
D0/2
y [mm]0 0.5
0.1 0.3
D0/10
D0/10
D0
D0
D0
1
2
3
(a) (c)
-
____________________________________________________________________University
of Alabama in Huntsville Department of Chemical and Materials
Engineering
● Summary
→ Methodology is insensitivity to a wide range of perturbations
and initial conditions restrictions that are necessary for other
measurement methodologies.
-
____________________________________________________________________University
of Alabama in Huntsville Department of Chemical and Materials
Engineering
● Thermal Diffusivity Determinations in Lead-free solders
-
____________________________________________________________________University
of Alabama in Huntsville Department of Chemical and Materials
Engineering
● Thermal Diffusivity – Lead-free alloys- Cu6Sn5
-
____________________________________________________________________University
of Alabama in Huntsville Department of Chemical and Materials
Engineering
● Thermal Diffusivity – Lead-free alloys- Ag3Sn
-
____________________________________________________________________University
of Alabama in Huntsville Department of Chemical and Materials
Engineering
● Thermal Diffusivity – Lead-free alloys- SAC387
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
9 9.5 10 10.5 11 11.5 12 12.5 13
ln∆T
ij
time(s)
T22-T0
T32-T0
T22-T12
T21-T0
T31-T0
T21-T11
T31-T11
-
____________________________________________________________________University
of Alabama in Huntsville Department of Chemical and Materials
Engineering
● Thermal Diffusivity – Lead-free alloys- SAC387
-
____________________________________________________________________University
of Alabama in Huntsville Department of Chemical and Materials
Engineering
● Thermal Diffusivity – Lead-free alloys- Numerical Modeling-
Aspect ratio and orientation of second phases- Lattice mismatch
between host lattice and the
second phases.
→ Numerical modeling results showed that the driving parameter
was the lattice mismatch, and resulting thermal diffusivity
mismatch, between the host lattice and the second phases.
● Effect of gold addition on the MP of three SAC alloys.
● Distribution of gold in solidified SAC alloys - Nextek.
-
____________________________________________________________________University
of Alabama in Huntsville Department of Chemical and Materials
Engineering
Current Research Interest - Funding
• STTR awarded - Contract Negotiations
• Start of consulting agreement with outside company
–thermophysical property measurements high temperature melts –
pushing to go through UAH and hire a MS student.
• NASA continues to talk about needing diffusion measurements –
both for theoretical model development and current Material Science
Experiment support.
• Proposal on Mechanical Behavior of Lead Free Alloys
-
____________________________________________________________________University
of Alabama in Huntsville Department of Chemical and Materials
Engineering
● Diffusion in Liquids“If the reader has by now concluded that
little is known about the
prediction of dense gas and liquid diffusivities, he is correct.
There is an urgent need for experimental measurements, both for
their own value and for development of future theories.”
Bird, Stewart and LightfootTransport Phenomena, p. 515
“Equation [72] will predict the self-diffusion coefficient of
several liquid metals to better than an order of magnitude, though
good agreement is not obtained.”
Edwards, Hucke and MartinDiffusion in Binary Liquid Metal
SystemsMetallurgical Reviews (1968)
Thank you for your attention!
-
____________________________________________________________________University
of Alabama in Huntsville Department of Chemical and Materials
Engineering
● Estimation of Convective Contamination due to Temperature
Nonuniformities
Height/Radius [cm]
2 5
0.4 26 10200.6 17 8300.9 12 450
Convective Velocities [cm/sec]
H15gTLT
3RW
Garandet, et al, Phys Fluids 9 (1997) 510.
Water: = 0.008 cm2/sec, = 0.004 K-1
T = 1K/cm, LT= r3 – r1, terrestrial gravity
-
____________________________________________________________________University
of Alabama in Huntsville Department of Chemical and Materials
Engineering
x
y
a Pump beam
2b
Probe beam
● Effect of (Thermal) Diffusivity where you don’t expect it
→ Vapor Concentration Measurement in a Crystal Growth
Ampoule
-
____________________________________________________________________University
of Alabama in Huntsville Department of Chemical and Materials
Engineering
● Schematic Experimental Setup
PositionDetector
He-Ne
A
PM
Boxcar
Recorder
Argon
-
____________________________________________________________________University
of Alabama in Huntsville Department of Chemical and Materials
Engineering
● Experimental ResultsThermal Diffusivity (of nitrogen) was the
“adjustable” parameter
Chopping Frequency [hertz]2 12 22 32 42 52
30
24
18
12
6
0
B
0.025
0.05
0.10
0.175
-
____________________________________________________________________University
of Alabama in Huntsville Department of Chemical and Materials
Engineering
● Mass Diffusivity Experiments –low gravity
-
____________________________________________________________________University
of Alabama in Huntsville Department of Chemical and Materials
Engineering
● Mass Diffusivity Experiments –low gravity
D(190) = (2.08 ± 0.13) 10-5 cm2/s
D(24) =(2.09 ± 0.13) 10-5 cm2/s
190 keV
24 keV
Isolated mode
D(190) = (2.09 ± 0.13) 10-5 cm2/s
D(24) =(1.98 ± 0.13) 10-5 cm2/s
6.0
6.5
7.0
8.5
500 1000Time [min]
7.5
8.0
15001000 1500Time [min]
0
2
4
6
8
0 1000 2000 3000 4000
190 keV
24 keV
6.0
6.5
7.0
8.5
7.5
8.0
5000
Indium/Indium-114m
LMD-MIM-Mir Measurements
Latched mode0
2
4
6
8
0 1000 2000 3000 4000 5000
10
500
186.5 ± 0.6 °C 185 ± 0.4 °C
1.3 mCi 1.45 mCi
-
____________________________________________________________________University
of Alabama in Huntsville Department of Chemical and Materials
Engineering
● Insensitivity to Deviations from 1D transport- experimental
setup
Barrier Void
BN ampoule
BN plunger
Initial tracerlocation
Diffusion sample
BN plug
Sealed silicacartridge
Normal
Approximatecollimator locations
-
____________________________________________________________________University
of Alabama in Huntsville Department of Chemical and Materials
Engineering
● D(T) Predictions and Elements used for Confirmation
Aexp(-Q/RT)
AT2
AT
AT3/2
AT1/2
AT exp(-Q/RT)
AT-5/2 exp(-Q/RT)
AT1/2 exp(-Q/RT)
[AR2T(V-V0)]/[2VV0]
In, Sn, Hg, Ag, Na
In, Sn, Hg, Na, Ga
In, Sn, Ag, Hg, Na, Tl, Zn
In (at lower T's), Hg, Na
In, Sn, Hg
In, Sn, Hg, Ag, Na, Pb, Zn, Tl, K, Li
Sn, Hg, Pb, Cd
In, Sn, Hg, Na, Ag, Pb, Ga
solutes only