____________________________________________________________________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

banishm@uah.edu

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