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Melting temperature of lead and sodium at high pressures
I. Phys. Chem. Solids, 1976,VoL31,pp.795-797.PerganonPress.Printed inGreat Britain
MELTING TEMPERATURE OF LEAD AND SODIUM AT HIGH PRESSURESt PETERW. MIRWALDS and GEORGEC. KENNEDY
Institute of Geophysicsand PlanetaryPhysics,Universityof California,Los Angeles,CA90024,U.S.A. (Received 11November 1975;accepted3 December 1975)
Abstract-We have redeterminedthe melting temperatureof lead and sodiumas a function of pressure in a new pressure cell made up of low strength materials. Many of the anomalies reported in a prior determination of the melting curve of lead have largely disappeared. The slope of our new melting curve for lead is in close agreement with the slope computed from thermochemical data. One new curve for sodium differs only slightly from the prior published curves.
Data showing the effect of pressure on the melting temperature of lead and sodium have been published from this laboratory by Akella et al. [l] and by Luedemann and Kennedy[2]. Quite substantial friction corrections were made in both of these works. Recently we have developed a cell that shows exceedingly low friction and yields essentially the same melting temperatures in both compression and decompression runs. This has been described by Mirwald et al. [3]. We report here details of the melting curve of lead to 60 kbar. We have also redetermined the melting temperature of sodium at high pressures. Essentially identical results have been published by various investigators for the melting temperature of sodium below 12kbar. Therefore, for sodium, this investigation has been restricted to the range of 15-60 kbar. Our measurements were made in a typical end-loaded piston cylinder device of conventional design. Pressed rods and shells of sodium chloride were used as the insulating and the pressure transmitting medium in the lead experiments and rods and shells of silver chloride were used for the sodium runs. Our lead sample had a stated purity of 99.99% and the sodium sample had a purity of ca. 99.9%. This was taken from the same batch studied by Luedemann and Kennedy [2]. All samples were encapsulated in tantalum. Extensive precautions were taken to prevent the oxidation of the sodium sample. The specimen was encapsulated while submerged in alcohol under a nitrogen blanket. Chromelalumel thermocouples were used both for a temperature measurement and for the DTA signal. Our data on lead are summarized in Fig. 1. We also show here the prior published work. We show in Table 1 the melting temperatures of lead and sodium at various pressures. These temperatures have been plotted from the results of the second degree polynomial fit. The parametpublication No. 1480,Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90024,U.S.A. SPresent address: Institut fur Mineralogfe, Ruhr-Universitat, D-463 Bochum, West Germany.
700 -
600-
Y &$-"-
Fig. 1. Melting curves for lead.
Table1. Meltingdata of lead and sodium to 60 kbar PresSWe
Lead
Sodium
[%I 97.6
0
325.7
5
367.39
139*
10
405.33
167*
15
441.56
189.42
20
476.30
200.96
25
509.70
226.40
30
541.92
292.30
33
573.08
257.00
40
603.27
270.74
45
b3P.W
Z8J.W
50
661.07
295.48
55
688.83
307.67
60
715.90
318.X7
l
795
T,
from Luedemann and KennedyC21.
7%
P. W. MIRWALD and G. C.
ters of the polynomial fit are shown in Table 2. A%of the observed data points lie within 6” of the plotted melting curves whether taken on a compression or decompression cycle. The largest fraction of the data points he within 2’ of the plotted curves.
Table 3. Comparisonof initial slopes of melting for various
equation t = ffz+ [a&p - ~~)]‘“/a, %I
aI
%d.dW.
%!
Pb
-44.349
0.E38.10-4
-400
o.50°
NC3
-2.176
0.835.10-3
46
o.40°
Et
in
oc
P in Kbar]
Neither the lead nor the sodium melting curves were corrected for the effect of pressure on the emf of the thermocouples as the effect is small, little more than l”, at the low temperatures invoIved[15]. The accuracy of the the~~ouples is believed toady 2 2.0”. The lead data of Butzov et nt.141,Mellet[5], Kennedy and Newton [6] and Akella et al. [l] are all shown in Fig. 1. Our new data are in close agreement with the data of Millet [5] and are in greatest disagreement with the early data of Kennedy and Newton[6].
Pb from
studies
SGurce
'Jkbar
Present
a.20 7.23
Akella et al., 1972
Table2. Parametersof the meltingcurveof Pb and Na to 60kbar in data
KENNEDY
Millet
1969
7.30
Babb
1963 f121
7.73
Butuzov et al.,1956 [133
7.23
Johnston et al.,1911 1141
8.00
Themochenical
8.33
data
Akella et al. [l] noted in their study that lead exhibited a distinct deviation from the empirical linear relation between T, and AV~VO noted earlier by Kraut and Kennedy [ 113.This empirical relation has held for most other investigated metals. Our current data greatly reduces this deviation and up to 30 kbar we find no deviation from linearity. Above 30 kbar, however, some curvature toward the T, axis can indeed by noted. While systematic, this deviation from linearity is little more than the experimental unce~~nty. This departure from a straight line fit was interpreted by Akella et aI. [ l] in terms of the Lindemann law. We have re-calculated the melting temperature by means of a modified Lindemann relationship using the values y = 3 and b = 1.5 as suggested by Akella er al. [l] and we show in Table 4 compression, the melting temperature calculated from the Lindem~ relationship, and the melting temperature observed. The percentage of deviation between the observed temperature and the computed temperature is also shown. Table 4. C~c~lation of meIting terrace mod&d Linden TCPl
hWO
[OKI
T
of Iead by means of Law*
ohs
IoK1
iIT
WI
0.00
598.7
598.7
0
0.02
668.0
670.5
0.35
0.05
776.9
782.1
0.51
0.07
855
865.0
0.57
0.09
946
961.5
0.90
* Akella et al., 119721
yo
Fig. 2. The melting temperature of lead plotted vs temperature compassion of the solid.
=3;b=1.5
room
The initial slope of the melting curve of lead, evaluated from data points in our low pressure rauge between 0.5 and 5 kbar, give a result of 82”/kbar. This is in excellent agreement with the slope computed from the tbermochemical data: 8337kbar. The initial slope of the melting curve determined by prior investigators is shown in Table 3.
Ex~~mental determ~ations of the initial slope of the sodium melting curve by different investigators show close agreement, e.g. Bridgman[7]: 8.@/kbar. Ivanov et al.[lO] suggest a steeper trajectory of the melting boundary than ours and previous investigators. Our new sodium data are shown in Fig 3. Strangely, the closest agreement is the early data of Newton et al.[9]. In general we note that our current data he on the high temperature side of prior published work. This is probably
Melting temperature of lead and sodium at highpressures
797
Acknowledgements-We are grateful for Grant NSF DES7420742and our Grant from Lawrence Livermore Laboratory for partial financial support of these investigations.
80 40
0
I
I
IO
I
I
20
30
*
40
”
5
6
60
70
80
b
50
Pressure, kbar Fig. 3. Melting curves for sodium.
because the earlier data was obtained in cells that had a relativefy strong and in~ompressl~ie insulating bushing. Thus, a subst~ti~ly large fraction of the piston load was carried by the insulating and pressure transmitting bushing thus leading to a systematic over-estimate of pressure.
1. Akella J., Ganguly J., Grover R. and Kennedy G., J. Pkys. Ckem. Solids 34, 631 (1973). 2. Luedemann H. D. and Kennedv G. C., J. Geopkys. _ . Res. 73, 2795 (1968). 3. Mi~ald P. W., Getting I. C. and Kennedy G. C., L Geopky~. Res. 80, 1519(197.5). 4. Butuzov V. P.‘and~Go~kberg M. G., Zkur. Neorg. Skim. I, 1543(1956). 5. Millet L. E., Unpub, Thesis, Brigham Young University (1%9). 6. Kennedy G. C. and Newton R. C., Solids Under Pressure (Edited by W. Paul and D. Warshauer), p. 171.McGraw-Hill, New York (1%3). 7. Bridgman P. W., Pkys. Rev. fH(3), 153 (1914). 8. Ponvatowskii Y. G.. Fiz. Metal Met&wed 11. 146. (1962). 9. Newton R. C., Jayaraman, A. and Kennedy G. C., ph;s. Rkv. 126, 1363,(1962). 10. Ivanov V. A., Makarenko, I. N. and Stishov, S. M., JE’FP Letters 12,7 (1970). 11. Kraut E. A. and Ketmedy G, C., Pkys. Rev. Letters 16,608 ff966). 12. Babbs S. E. Jr., Reu. Mod. Pkys. 35,400 (1%3). 13. Butuzov V. P., Ponyatovskii E. G. and Sh~hovskoi G. P., Dok. o/red. nauk. SSSR 109,519 (1956). 14. Johnston J. and Adams L. H., Am. J. Sci. 31,501 (1911). 15. Getting I. C. and Kennedy G. C.,L Appl. Pkys. 41,4552(1970).
MELTING TEMPERATURE OF LEAD AND SODIUM AT HIGH PRESSURESt PETERW. MIRWALDS and GEORGEC. KENNEDY
Institute of Geophysicsand PlanetaryPhysics,Universityof California,Los Angeles,CA90024,U.S.A. (Received 11November 1975;accepted3 December 1975)
Abstract-We have redeterminedthe melting temperatureof lead and sodiumas a function of pressure in a new pressure cell made up of low strength materials. Many of the anomalies reported in a prior determination of the melting curve of lead have largely disappeared. The slope of our new melting curve for lead is in close agreement with the slope computed from thermochemical data. One new curve for sodium differs only slightly from the prior published curves.
Data showing the effect of pressure on the melting temperature of lead and sodium have been published from this laboratory by Akella et al. [l] and by Luedemann and Kennedy[2]. Quite substantial friction corrections were made in both of these works. Recently we have developed a cell that shows exceedingly low friction and yields essentially the same melting temperatures in both compression and decompression runs. This has been described by Mirwald et al. [3]. We report here details of the melting curve of lead to 60 kbar. We have also redetermined the melting temperature of sodium at high pressures. Essentially identical results have been published by various investigators for the melting temperature of sodium below 12kbar. Therefore, for sodium, this investigation has been restricted to the range of 15-60 kbar. Our measurements were made in a typical end-loaded piston cylinder device of conventional design. Pressed rods and shells of sodium chloride were used as the insulating and the pressure transmitting medium in the lead experiments and rods and shells of silver chloride were used for the sodium runs. Our lead sample had a stated purity of 99.99% and the sodium sample had a purity of ca. 99.9%. This was taken from the same batch studied by Luedemann and Kennedy [2]. All samples were encapsulated in tantalum. Extensive precautions were taken to prevent the oxidation of the sodium sample. The specimen was encapsulated while submerged in alcohol under a nitrogen blanket. Chromelalumel thermocouples were used both for a temperature measurement and for the DTA signal. Our data on lead are summarized in Fig. 1. We also show here the prior published work. We show in Table 1 the melting temperatures of lead and sodium at various pressures. These temperatures have been plotted from the results of the second degree polynomial fit. The parametpublication No. 1480,Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90024,U.S.A. SPresent address: Institut fur Mineralogfe, Ruhr-Universitat, D-463 Bochum, West Germany.
700 -
600-
Y &$-"-
Fig. 1. Melting curves for lead.
Table1. Meltingdata of lead and sodium to 60 kbar PresSWe
Lead
Sodium
[%I 97.6
0
325.7
5
367.39
139*
10
405.33
167*
15
441.56
189.42
20
476.30
200.96
25
509.70
226.40
30
541.92
292.30
33
573.08
257.00
40
603.27
270.74
45
b3P.W
Z8J.W
50
661.07
295.48
55
688.83
307.67
60
715.90
318.X7
l
795
T,
from Luedemann and KennedyC21.
7%
P. W. MIRWALD and G. C.
ters of the polynomial fit are shown in Table 2. A%of the observed data points lie within 6” of the plotted melting curves whether taken on a compression or decompression cycle. The largest fraction of the data points he within 2’ of the plotted curves.
Table 3. Comparisonof initial slopes of melting for various
equation t = ffz+ [a&p - ~~)]‘“/a, %I
aI
%d.dW.
%!
Pb
-44.349
0.E38.10-4
-400
o.50°
NC3
-2.176
0.835.10-3
46
o.40°
Et
in
oc
P in Kbar]
Neither the lead nor the sodium melting curves were corrected for the effect of pressure on the emf of the thermocouples as the effect is small, little more than l”, at the low temperatures invoIved[15]. The accuracy of the the~~ouples is believed toady 2 2.0”. The lead data of Butzov et nt.141,Mellet[5], Kennedy and Newton [6] and Akella et al. [l] are all shown in Fig. 1. Our new data are in close agreement with the data of Millet [5] and are in greatest disagreement with the early data of Kennedy and Newton[6].
Pb from
studies
SGurce
'Jkbar
Present
a.20 7.23
Akella et al., 1972
Table2. Parametersof the meltingcurveof Pb and Na to 60kbar in data
KENNEDY
Millet
1969
7.30
Babb
1963 f121
7.73
Butuzov et al.,1956 [133
7.23
Johnston et al.,1911 1141
8.00
Themochenical
8.33
data
Akella et al. [l] noted in their study that lead exhibited a distinct deviation from the empirical linear relation between T, and AV~VO noted earlier by Kraut and Kennedy [ 113.This empirical relation has held for most other investigated metals. Our current data greatly reduces this deviation and up to 30 kbar we find no deviation from linearity. Above 30 kbar, however, some curvature toward the T, axis can indeed by noted. While systematic, this deviation from linearity is little more than the experimental unce~~nty. This departure from a straight line fit was interpreted by Akella et aI. [ l] in terms of the Lindemann law. We have re-calculated the melting temperature by means of a modified Lindemann relationship using the values y = 3 and b = 1.5 as suggested by Akella er al. [l] and we show in Table 4 compression, the melting temperature calculated from the Lindem~ relationship, and the melting temperature observed. The percentage of deviation between the observed temperature and the computed temperature is also shown. Table 4. C~c~lation of meIting terrace mod&d Linden TCPl
hWO
[OKI
T
of Iead by means of Law*
ohs
IoK1
iIT
WI
0.00
598.7
598.7
0
0.02
668.0
670.5
0.35
0.05
776.9
782.1
0.51
0.07
855
865.0
0.57
0.09
946
961.5
0.90
* Akella et al., 119721
yo
Fig. 2. The melting temperature of lead plotted vs temperature compassion of the solid.
=3;b=1.5
room
The initial slope of the melting curve of lead, evaluated from data points in our low pressure rauge between 0.5 and 5 kbar, give a result of 82”/kbar. This is in excellent agreement with the slope computed from the tbermochemical data: 8337kbar. The initial slope of the melting curve determined by prior investigators is shown in Table 3.
Ex~~mental determ~ations of the initial slope of the sodium melting curve by different investigators show close agreement, e.g. Bridgman[7]: 8.@/kbar. Ivanov et al.[lO] suggest a steeper trajectory of the melting boundary than ours and previous investigators. Our new sodium data are shown in Fig 3. Strangely, the closest agreement is the early data of Newton et al.[9]. In general we note that our current data he on the high temperature side of prior published work. This is probably
Melting temperature of lead and sodium at highpressures
797
Acknowledgements-We are grateful for Grant NSF DES7420742and our Grant from Lawrence Livermore Laboratory for partial financial support of these investigations.
80 40
0
I
I
IO
I
I
20
30
*
40
”
5
6
60
70
80
b
50
Pressure, kbar Fig. 3. Melting curves for sodium.
because the earlier data was obtained in cells that had a relativefy strong and in~ompressl~ie insulating bushing. Thus, a subst~ti~ly large fraction of the piston load was carried by the insulating and pressure transmitting bushing thus leading to a systematic over-estimate of pressure.
1. Akella J., Ganguly J., Grover R. and Kennedy G., J. Pkys. Ckem. Solids 34, 631 (1973). 2. Luedemann H. D. and Kennedv G. C., J. Geopkys. _ . Res. 73, 2795 (1968). 3. Mi~ald P. W., Getting I. C. and Kennedy G. C., L Geopky~. Res. 80, 1519(197.5). 4. Butuzov V. P.‘and~Go~kberg M. G., Zkur. Neorg. Skim. I, 1543(1956). 5. Millet L. E., Unpub, Thesis, Brigham Young University (1%9). 6. Kennedy G. C. and Newton R. C., Solids Under Pressure (Edited by W. Paul and D. Warshauer), p. 171.McGraw-Hill, New York (1%3). 7. Bridgman P. W., Pkys. Rev. fH(3), 153 (1914). 8. Ponvatowskii Y. G.. Fiz. Metal Met&wed 11. 146. (1962). 9. Newton R. C., Jayaraman, A. and Kennedy G. C., ph;s. Rkv. 126, 1363,(1962). 10. Ivanov V. A., Makarenko, I. N. and Stishov, S. M., JE’FP Letters 12,7 (1970). 11. Kraut E. A. and Ketmedy G, C., Pkys. Rev. Letters 16,608 ff966). 12. Babbs S. E. Jr., Reu. Mod. Pkys. 35,400 (1%3). 13. Butuzov V. P., Ponyatovskii E. G. and Sh~hovskoi G. P., Dok. o/red. nauk. SSSR 109,519 (1956). 14. Johnston J. and Adams L. H., Am. J. Sci. 31,501 (1911). 15. Getting I. C. and Kennedy G. C.,L Appl. Pkys. 41,4552(1970).