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Properties of hot expanded liquid aluminum
Journal of Non-Crystalline Solids 61 & 62 (1984) 59-64 North-Holland, Amsterdam
59
PROPERTIES OF HOT EXPANDED LIQUID ALUMINUM* G. Roger GATHERS and Marvin Ross U n i v e r s i t y of C a l i f o r n i a , Lawrence Livermore National Laboratory, Livermore, C a l i f o r n i a 94550 Measurements of temperature, volume, enthalpy, and e l e c t r i c a l r e s i s t i v i t y have been made on aluminum expanded i s o b a r i c a l l y by 50% in volume to temperatures of about 4000 K. These measurements are compared with the p r e d i c t i o n s of l i q u i d metal pseudopotential theory. I . BACKGROUND In the isobaric expansion experiment (IEX) I, c y l i n d r i c a l wire samples approximately 1 mm in diameter are r a p i d l y heated by the discharge of a capacitor bank through them in a time of 12-50 ~s.
The sample is subjected
to a predetermined ambient pressure of a few tenths of gigapascals by argon gas in a pressure c e l l .
The volume of the c e l l is large enough so t h a t
changes in pressure produced by gas displacement from sample expansion are negligible.
In a d d i t i o n , the r a t e of expansion is slow enough to allow sound
waves to communicate pressure changes throughout the c e l l in a time i n t e r v a l that is short compared with the measurement times of the experiment.
As a
r e s u l t , the pressure in the c e l l is r e l a t i v e l y constant and uniform.
The
c o m p r e s s i b i l i t y of the metal samples is s u f f i c i e n t l y are not s e n s i t i v e to the c e l l pressure.
small t h a t the r e s u l t s
The most important purpose of the
high pressure gas is to allow large expansion of the metal w i t h o u t large d i s t o r t i o n s in sample geometry.
The density of argon gas increases r a p i d l y with
pressure, and is 1.28 g/cm3 at a pressure of 0.24 GPa. Taylor i n s t a b i l i t y at the metal surface is thus s u b s t a n t i a l l y reduced.
In addition the amount of
expansion before the b o i l i n g l i n e of the metal is reached is increased.
The
i n e r t gas also prevents chemical i n t e r a c t i o n with the hot surface. Optical diagnostics are performed through sapphire windows as shown in Fig. I.
In one l i n e of sight (LOS) continuous back l i g h t i n g is provided by a CW
argon-ion l a s e r .
The shadow of the sample is directed to a s l i t
oriented
perpendicular to the wire sample a x i s , and an e l e c t r o n i c streak camera is used to record shadow width at the s l i t
as a function of time.
I f the sample is
*Work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract #W-7405-Eng-48. 0022-3093/84/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
G.R. Gathers, M. Ross / Properties o f hot expanded liquid aluminum
60
.
~
.- i
Pressure vessel
1.--~"
"-... • .%."
s"' F
•
,>C
Optics~.
' I BB l - ' l > (
~_11
-
/ I BB" I( ( ~
/I •
If ~"~Jl
| ~ m i~,,,,~,,,,.. ~11 I
"'~ am I
Pyrometer
r,wr-jJ
window
=~/
"~;'~ \~,\ F Fiber
pyrometerj,~,.....~--
[
"" I B I
image
- -
I m
"'"
~I E-I',~/'~ ~Sample
Sample
v
FIGURE 1 Schematic r e p r e s e n t a t i o n of o p t i c a l diagnostics f o r the isobaric expansion experiment. clamped at each end to prevent a x i a l motion then the s p e c i f i c volume of the sample varies as the square of the shadow width.
The streak is started s h o r t -
l y before the sample expansion begins in order to c a l i b r a t e the m a g n i f i c a t i o n of the system. A second LOS is used to determine the degree of sample d i s t o r t i o n in the measurement.
A Q-switched ruby laser is used as a back l i g h t i n g source to
take an o v e r a l l snapshot p i c t u r e of the sample at a l a t e time. show s i g n i f i c a n t d i s t o r t i o n are discarded.
Shots which
A f a s t three channel o p t i c a l
pyrometer is used to determine the surface temperature of the sample as a function of time. The sample heating current is measured using a wide band current t r a n s former.
Voltage probes are arranged to contact the sample surface at a known
distance of separation and the voltage d i f f e r e n c e between probes is recorded. Inductive voltage c o r r e c t i o n s are determined by d i f f e r e n t i a t i n g
the recorded
current pulse and using a sample s e l f inductance t h a t r e s u l t s in a r e s i s t i v e voltage which increases smoothly from zero at the s t a r t of the pulse. The i n t e g r a l of the product of current and r e s i s t i v e voltage gives the enthalpy input to the sample.
Since a l l v a r i a b l e s are measured simultaneously,
time can be eliminated as a common parameter.
The enthalpy is determined
G.R. Gathers, M. Ross /Properties of hot expanded liquid aluminum continuously as a function of temperature, giving s p e c i f i c heat data.
61
Since
current, sample diameter and r e s i s t i v e voltage are measured, one can determine the e l e c t r i c a l r e s i s t i v i t y ,
properly corrected f o r thermal expansion, as a
function of e i t h e r s p e c i f i c volume, enthalpy or temperature.
Since the pres-
sure is known, the volume data can be combined with e i t h e r the enthalpy or the temperature to produce an isobar of the equation of state. 2. MEASUREMENTS IEX measurements have been made on aluminum.
Since i t is such a good
conductor a sample diameter of 0.69 mm was chosen in order to reach melting in the desired time with the a v a i l a b l e capacitor bank.
Sudden rapid acceleration
in sample growth rate with a corresponding rapid r i s e in apparent e l e c t r i c a l r e s i s t i v i t y was observed, and determined the upper bounds of the data.
Figure
2 shows the pressure-volume plane with the track of these measurements, made at a pressure of 0.3 GPa. The dotted curve ends at the onset of the sudden
0.6
, I , I Young & Alder (1971)~._ Melting f
' I ...... ~--C.P. ~
c.P.
0,4 ~L
~o
0.2 //~//~-Kolgatin Jd
I
& Khachatur'yants (1982) I
I
2
3
L
I
4
v/v o
FIGURE 2 Pressure vs volume plane for aluminum. The c r i t i c a l points and b o i l i n g curves of Young and Alder and of Kolgatin and Khachatur'yants are shown along with the melting t r a n s i t i o n . The IEX track ends at the onset of sudden rapid growth in sample diameter and r e s i s t i v i t y .
G.R. Gathers, M. Ross / Properties o f hot expanded liquid aluminum
62
rapid growth.
Young and Alder 2 used a hard sphere van der Waals model to
predict a c r i t i c a l pressure of 0.546 GPa and a c r i t i c a l volume of 3.91 x 10-5 m3 mol- l corresponding to Vc/V0 = 3.93 where v0 is the specific volume at room temperature and atmospheric pressure. figure.
Their boiling line is shown in the
Kolgatin and Khachatur'yants 3 made a f i t to the c r i t i c a l data in
the review by Fortov, et al 4 and other standard thermophysicaI data to give an interpolation equation of state.
Their boiling line is also shown.
It
appears unlikely that the i n s t a b i l i t y is caused by the onset of boiling.
The
behavior is rather l i k e that described by Lebedev5 and the current densities of these measurements are in the range he discusses. The r e l a t i v e l y low mass density of the metal also contributed noticeably to hydromagnetic i n s t a b i l i t y .
The magnetic pressure evidently caused axial move-
ment of metal producing a bulge at the t i p of one sample clamping jaw.
As a
result the f u l l radial expansion was not achieved and the volumes are quite substantially less than those expected from the l i t e r a t u r e .
The e l e c t r i c a l
r e s i s t i v i t i e s near the beginning of the liquid range where this problem was not significant are in good agreement with the l i t e r a t u r e .
The pyrometer
measurements gave results in excellent agreement with extrapolation of the 1973 Hultgren 6 tables, and extend the data to 4000 K.
The f u l l details of
the measurementsw i l l appear in Int. J. of Thermophysics, along with data for copper. 3. DISCUSSION Aluminum is considered to be a simple, n e a r l y f r e e e l e c t r o n metal which provides a useful t e s t f o r theory.
The thermophysical properties of l i q u i d
aluminum near normal d e n s i t y have been c a l c u l a t e d using l i q u i d metal pseudopotential theory. 7
In the present c a l c u l a t i o n s we used a Harrison pseudo-
p o t e n t i a l 8 with a modified Geldart-Vosko d i e l e c t r i c constant, 9 ' I 0 and a set of parameters f i t t e d parameter.
to reproduce the s o l i d isotherm and the GrUneisen
The thermodynamic properties were calculated by minimizing the
Helmholtz free energy with respect to the hard sphere packing f r a c t i o n and taking the appropriate d e r i v a t i v e s of the free energy to obtain pressure and energy.
In these c a l c u l a t i o n s we used a s o f t sphere r a t h e r than a hard sphere II reference entropy. The r e s i s t i v i t y was c a l c u l a t e d by the method of Ashcroft and Lekner. 12 The predicted expansions (Fig. 3) and e l e c t r i c a l r e s i s t i v i t i e s reasonably good agreement with the measurements.
(Fig. 4) are in
These r e s u l t s suggest t h a t
l i q u i d metal pseudopotentials may be useful f o r metals expanded to 50% of t h e i r solid density.
G.R, Gathers, M. Ross / Properties of hot expanded liquid aluminum
63
16
15
14
O
E v
12
11-
10
0
1
i
I
1
1000
2000
3000
4000
T(K) FIGURE 3 Thermal expansion of aluminum. The e r r o r bars correspond to + 6%.
0.8
I
I
[
I
I
/
0.6 •
A~
.'~
t
i
E 0.4--
0.2--
0 10
I
L
[
[
I
11
12
13
14
15
16
v(cm3.mo1-1 ) FIGURE 4 Electrical r e s i s t i v i t y of aluminum. The error bars correspond to + 6%.
64
G.R. Gathers, M. Ross /Properties of hot expanded liquid aluminum
REFERENCES I) G. R. Gathers, J. W. Shaner, R. L. Brier, Rev. Sci. Instrum. 47 (1976) 471 2)
D . A . Young, B. J. Alder, Phys. Rev. A3 (1971) 364.
3)
S. N. Kolgatin, A. V. Khachatur'yants, High Temp. (USSR) 20 (1982) 380.
4)
V. E. Fortov, A. N. Dremin, A. A. Leont'ev, High Temp. (USSR) 13 (1975) 984.
5)
S. V. Lebedev, High Temp. (USSR) 17 (1980) 222.
6)
R. Hultgren, P. D. Desai, D. T. Hawkins, M. Gleiser, K. K. Kelley, D. D. Wagman, Selected Values of the Thermodynamic Properties of the Elements (American Society for Metals, Metals Park, Ohio, 1973).
7)
H. D. Jones, Phys. Rev. A8 (1973) 3215.
8)
W. A. Harrison, Pseudopotentials in the Theory of Metals (Benjamin, New York, 1966).
9)
D. J. W. Geldart and S. H. Vosko, Can. J. Phys. 44 (1966) 2137.
I0) D. J. W. Geldart and S. H. Vosko, Can. J. Phys. 45 (1967) 2229(E). I I ) M. Ross, H. E. DeWitt, and W. B. Hubbard, Phys. Rev. A24 (1981) 1016. 12) N. W. Ashcroft and J. Lekner, Phys. Rev. 145 (1966) 83.
59
PROPERTIES OF HOT EXPANDED LIQUID ALUMINUM* G. Roger GATHERS and Marvin Ross U n i v e r s i t y of C a l i f o r n i a , Lawrence Livermore National Laboratory, Livermore, C a l i f o r n i a 94550 Measurements of temperature, volume, enthalpy, and e l e c t r i c a l r e s i s t i v i t y have been made on aluminum expanded i s o b a r i c a l l y by 50% in volume to temperatures of about 4000 K. These measurements are compared with the p r e d i c t i o n s of l i q u i d metal pseudopotential theory. I . BACKGROUND In the isobaric expansion experiment (IEX) I, c y l i n d r i c a l wire samples approximately 1 mm in diameter are r a p i d l y heated by the discharge of a capacitor bank through them in a time of 12-50 ~s.
The sample is subjected
to a predetermined ambient pressure of a few tenths of gigapascals by argon gas in a pressure c e l l .
The volume of the c e l l is large enough so t h a t
changes in pressure produced by gas displacement from sample expansion are negligible.
In a d d i t i o n , the r a t e of expansion is slow enough to allow sound
waves to communicate pressure changes throughout the c e l l in a time i n t e r v a l that is short compared with the measurement times of the experiment.
As a
r e s u l t , the pressure in the c e l l is r e l a t i v e l y constant and uniform.
The
c o m p r e s s i b i l i t y of the metal samples is s u f f i c i e n t l y are not s e n s i t i v e to the c e l l pressure.
small t h a t the r e s u l t s
The most important purpose of the
high pressure gas is to allow large expansion of the metal w i t h o u t large d i s t o r t i o n s in sample geometry.
The density of argon gas increases r a p i d l y with
pressure, and is 1.28 g/cm3 at a pressure of 0.24 GPa. Taylor i n s t a b i l i t y at the metal surface is thus s u b s t a n t i a l l y reduced.
In addition the amount of
expansion before the b o i l i n g l i n e of the metal is reached is increased.
The
i n e r t gas also prevents chemical i n t e r a c t i o n with the hot surface. Optical diagnostics are performed through sapphire windows as shown in Fig. I.
In one l i n e of sight (LOS) continuous back l i g h t i n g is provided by a CW
argon-ion l a s e r .
The shadow of the sample is directed to a s l i t
oriented
perpendicular to the wire sample a x i s , and an e l e c t r o n i c streak camera is used to record shadow width at the s l i t
as a function of time.
I f the sample is
*Work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract #W-7405-Eng-48. 0022-3093/84/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
G.R. Gathers, M. Ross / Properties o f hot expanded liquid aluminum
60
.
~
.- i
Pressure vessel
1.--~"
"-... • .%."
s"' F
•
,>C
Optics~.
' I BB l - ' l > (
~_11
-
/ I BB" I( ( ~
/I •
If ~"~Jl
| ~ m i~,,,,~,,,,.. ~11 I
"'~ am I
Pyrometer
r,wr-jJ
window
=~/
"~;'~ \~,\ F Fiber
pyrometerj,~,.....~--
[
"" I B I
image
- -
I m
"'"
~I E-I',~/'~ ~Sample
Sample
v
FIGURE 1 Schematic r e p r e s e n t a t i o n of o p t i c a l diagnostics f o r the isobaric expansion experiment. clamped at each end to prevent a x i a l motion then the s p e c i f i c volume of the sample varies as the square of the shadow width.
The streak is started s h o r t -
l y before the sample expansion begins in order to c a l i b r a t e the m a g n i f i c a t i o n of the system. A second LOS is used to determine the degree of sample d i s t o r t i o n in the measurement.
A Q-switched ruby laser is used as a back l i g h t i n g source to
take an o v e r a l l snapshot p i c t u r e of the sample at a l a t e time. show s i g n i f i c a n t d i s t o r t i o n are discarded.
Shots which
A f a s t three channel o p t i c a l
pyrometer is used to determine the surface temperature of the sample as a function of time. The sample heating current is measured using a wide band current t r a n s former.
Voltage probes are arranged to contact the sample surface at a known
distance of separation and the voltage d i f f e r e n c e between probes is recorded. Inductive voltage c o r r e c t i o n s are determined by d i f f e r e n t i a t i n g
the recorded
current pulse and using a sample s e l f inductance t h a t r e s u l t s in a r e s i s t i v e voltage which increases smoothly from zero at the s t a r t of the pulse. The i n t e g r a l of the product of current and r e s i s t i v e voltage gives the enthalpy input to the sample.
Since a l l v a r i a b l e s are measured simultaneously,
time can be eliminated as a common parameter.
The enthalpy is determined
G.R. Gathers, M. Ross /Properties of hot expanded liquid aluminum continuously as a function of temperature, giving s p e c i f i c heat data.
61
Since
current, sample diameter and r e s i s t i v e voltage are measured, one can determine the e l e c t r i c a l r e s i s t i v i t y ,
properly corrected f o r thermal expansion, as a
function of e i t h e r s p e c i f i c volume, enthalpy or temperature.
Since the pres-
sure is known, the volume data can be combined with e i t h e r the enthalpy or the temperature to produce an isobar of the equation of state. 2. MEASUREMENTS IEX measurements have been made on aluminum.
Since i t is such a good
conductor a sample diameter of 0.69 mm was chosen in order to reach melting in the desired time with the a v a i l a b l e capacitor bank.
Sudden rapid acceleration
in sample growth rate with a corresponding rapid r i s e in apparent e l e c t r i c a l r e s i s t i v i t y was observed, and determined the upper bounds of the data.
Figure
2 shows the pressure-volume plane with the track of these measurements, made at a pressure of 0.3 GPa. The dotted curve ends at the onset of the sudden
0.6
, I , I Young & Alder (1971)~._ Melting f
' I ...... ~--C.P. ~
c.P.
0,4 ~L
~o
0.2 //~//~-Kolgatin Jd
I
& Khachatur'yants (1982) I
I
2
3
L
I
4
v/v o
FIGURE 2 Pressure vs volume plane for aluminum. The c r i t i c a l points and b o i l i n g curves of Young and Alder and of Kolgatin and Khachatur'yants are shown along with the melting t r a n s i t i o n . The IEX track ends at the onset of sudden rapid growth in sample diameter and r e s i s t i v i t y .
G.R. Gathers, M. Ross / Properties o f hot expanded liquid aluminum
62
rapid growth.
Young and Alder 2 used a hard sphere van der Waals model to
predict a c r i t i c a l pressure of 0.546 GPa and a c r i t i c a l volume of 3.91 x 10-5 m3 mol- l corresponding to Vc/V0 = 3.93 where v0 is the specific volume at room temperature and atmospheric pressure. figure.
Their boiling line is shown in the
Kolgatin and Khachatur'yants 3 made a f i t to the c r i t i c a l data in
the review by Fortov, et al 4 and other standard thermophysicaI data to give an interpolation equation of state.
Their boiling line is also shown.
It
appears unlikely that the i n s t a b i l i t y is caused by the onset of boiling.
The
behavior is rather l i k e that described by Lebedev5 and the current densities of these measurements are in the range he discusses. The r e l a t i v e l y low mass density of the metal also contributed noticeably to hydromagnetic i n s t a b i l i t y .
The magnetic pressure evidently caused axial move-
ment of metal producing a bulge at the t i p of one sample clamping jaw.
As a
result the f u l l radial expansion was not achieved and the volumes are quite substantially less than those expected from the l i t e r a t u r e .
The e l e c t r i c a l
r e s i s t i v i t i e s near the beginning of the liquid range where this problem was not significant are in good agreement with the l i t e r a t u r e .
The pyrometer
measurements gave results in excellent agreement with extrapolation of the 1973 Hultgren 6 tables, and extend the data to 4000 K.
The f u l l details of
the measurementsw i l l appear in Int. J. of Thermophysics, along with data for copper. 3. DISCUSSION Aluminum is considered to be a simple, n e a r l y f r e e e l e c t r o n metal which provides a useful t e s t f o r theory.
The thermophysical properties of l i q u i d
aluminum near normal d e n s i t y have been c a l c u l a t e d using l i q u i d metal pseudopotential theory. 7
In the present c a l c u l a t i o n s we used a Harrison pseudo-
p o t e n t i a l 8 with a modified Geldart-Vosko d i e l e c t r i c constant, 9 ' I 0 and a set of parameters f i t t e d parameter.
to reproduce the s o l i d isotherm and the GrUneisen
The thermodynamic properties were calculated by minimizing the
Helmholtz free energy with respect to the hard sphere packing f r a c t i o n and taking the appropriate d e r i v a t i v e s of the free energy to obtain pressure and energy.
In these c a l c u l a t i o n s we used a s o f t sphere r a t h e r than a hard sphere II reference entropy. The r e s i s t i v i t y was c a l c u l a t e d by the method of Ashcroft and Lekner. 12 The predicted expansions (Fig. 3) and e l e c t r i c a l r e s i s t i v i t i e s reasonably good agreement with the measurements.
(Fig. 4) are in
These r e s u l t s suggest t h a t
l i q u i d metal pseudopotentials may be useful f o r metals expanded to 50% of t h e i r solid density.
G.R, Gathers, M. Ross / Properties of hot expanded liquid aluminum
63
16
15
14
O
E v
12
11-
10
0
1
i
I
1
1000
2000
3000
4000
T(K) FIGURE 3 Thermal expansion of aluminum. The e r r o r bars correspond to + 6%.
0.8
I
I
[
I
I
/
0.6 •
A~
.'~
t
i
E 0.4--
0.2--
0 10
I
L
[
[
I
11
12
13
14
15
16
v(cm3.mo1-1 ) FIGURE 4 Electrical r e s i s t i v i t y of aluminum. The error bars correspond to + 6%.
64
G.R. Gathers, M. Ross /Properties of hot expanded liquid aluminum
REFERENCES I) G. R. Gathers, J. W. Shaner, R. L. Brier, Rev. Sci. Instrum. 47 (1976) 471 2)
D . A . Young, B. J. Alder, Phys. Rev. A3 (1971) 364.
3)
S. N. Kolgatin, A. V. Khachatur'yants, High Temp. (USSR) 20 (1982) 380.
4)
V. E. Fortov, A. N. Dremin, A. A. Leont'ev, High Temp. (USSR) 13 (1975) 984.
5)
S. V. Lebedev, High Temp. (USSR) 17 (1980) 222.
6)
R. Hultgren, P. D. Desai, D. T. Hawkins, M. Gleiser, K. K. Kelley, D. D. Wagman, Selected Values of the Thermodynamic Properties of the Elements (American Society for Metals, Metals Park, Ohio, 1973).
7)
H. D. Jones, Phys. Rev. A8 (1973) 3215.
8)
W. A. Harrison, Pseudopotentials in the Theory of Metals (Benjamin, New York, 1966).
9)
D. J. W. Geldart and S. H. Vosko, Can. J. Phys. 44 (1966) 2137.
I0) D. J. W. Geldart and S. H. Vosko, Can. J. Phys. 45 (1967) 2229(E). I I ) M. Ross, H. E. DeWitt, and W. B. Hubbard, Phys. Rev. A24 (1981) 1016. 12) N. W. Ashcroft and J. Lekner, Phys. Rev. 145 (1966) 83.