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The electrical resistance and enthalpy of industrial alloys based on nickel and copper
EISYIER
Journal of Non-Crystalline
Solids 205-207 (1996) 678-682
The electrical resistance and enthalpy of industrial alloys based on nickel and copper V.N. Korobenko, A.I. Savvatimski * High Energy
Density
Research
Center
(HEDRCI,
United instihtte IVTAN, Russian Academy Moscow, Russia
of Sciences, Izhorskaya,
13/19,
1274i2
Abstract The electrical resistance and enthalpy of industrially important nickel- and copper-based alloys were measured, from room temperatures into the liquid state using fast (50 ps> pulse-heating. The electrical resistance at the melting point and enthalpies of fusion are close to equilibrium data. However, the phase transition in solid nichrome under fast heating is
displaced to higher temperatures. The electrical resistanceof liquid brassdecreaseswith increasing mole fractions of Zn; this causes ‘zinc pulsation’
during melting of brasses in channel furnaces.
1. Introduction
The method of fast heating by a unitary impulse of electrical current is used widely to study the physical properties of metals [l]. Recently, this method has been applied to alloys. The problem of applying fast heating to metallic alloys with complicated structures is that sufficient diffusion time is needed to ensure conformity of the properties to those in the equilibrium phase diagram of the alloy. 2. Experiment
We investigated samples of alloys prepared as wires of diameter 0.05 to 0.15 mm, which were heated by a unitary impulse of current from a condenser battery. In addition to the sample in the electrical circuit, a ballast resistance was also in-
* Corresponding author. Tel.: +7-095 362 5773; fax: +I-095 485 7990. 0022-3093/96/$15.00 PII SOO22-3093(96)00383-3
eluded. This method provided a relatively constant current in the electrical circuit during the heating and melting of the samples. In this way it was possible to avoid significant changes of current during heating (except for the initial moment), and this method permitted more precise measurements. The period of the pulse heating was typically 50-100 ks. This duration is longer than those used for electrical explosion [l] but permits more precise measurements. Fig. 1 shows values of the resistivity of nickel and its alloys as a function of enthalpy 121. The melting region was determined by the presence of a plateau on the radiance curve. The compositions of the alloys are identified by the labels which give the weight
percent of the components.
Fig. 2 and Fig. 3 give the resistivity data for brasses Cu,,Zn,, Cu6sZnS2, Cu6,Zn,, and for bronzes [3]. The expansion of the alloys during heating was not taken into consideration. Therefore the resistivity data in Figs. 1-3 are based on sample sizes at room temperature.
Copyright 0 1996 Elsevier Science B.V. All rights reserved.
V.N. Korobenko,
A.I. Suvvatimski/
Journal
of Non-Crystalline
For Ni we obtained a heat of melting of 292 J g- ‘. The recommended data E6Jgive a value of 298 J g-‘. For the resistivity at the melting point in the solid state, our result is 59 p,fi cm and the literature value is 59.6 [7]. For Cu we obtained a heat of melting of 207 J g-l; the recommended value is 205 J g-l [S]. For the resistivity at the melting point in the solid state, our result is 10.2 pfi cm - practically the same as the recommended value in the literature. The formal systematic error estimation is + 3% (resistance) and + 5% (enthalpy) for our fast heating experiments in the best cases, when the start and finish of the melting could be clearly seen.
p",10-6R
Solids 205-207
(1996)
678-682
679
'm
I
Cr20Ni80
5
A--
* NiMdAlPSil /-CNiW
3. Discussion 3. I. Nichrome
The top curve in Fig. 1 displays the data for nichrome. This alloy, according to the literature, contains only a y-phase. Prior. to the melting region, the change in slope ,of the resistance curve arises from the solid state phase transition. The same curve (only up to the melting point) is shown in Fig. 4 and marked by number 3. In spite of the fact that in all three works (Refs. [4,5] and this experiment) the same nichrome was used, differences (10%) for initial resistivities between Refs. 141 and [5] were seen. Perhaps this was due to differences in thermal and mechanical treatment of the specimens used.
Table 1 Comparison
of data from
the present
work
and element
content
Initial resistivity (r~.fi cm) Enthalpy (J g-l> (800°C) Enthalpy at melting point (J g - ’ ), solid state (Smell = 1400°C)
From steady-state measurements 141 a solid state phase transition (at the peak of the resistance, marked with number 1 in Fig. 4) has been reported at 500°C.
and from Refs. [4,5] for nichrome Ref. E5]
Marks
Fig. 1. Electrical resistivity for nickel and its alloys plotted against enthalpy (H - Hsg3). Solid lines: pulse measurements; circles on the vertical axis: our steady-state measurements for room temperature. Arrows with C: Curie points. The arrows mark the melting region; left-hand arrow: the start of melting; right-hand arrow: the finish of melting.
chrome1 Cr-20% Ni-80%
‘A’
110.79 431 840 estimation over extrapolation of the heat capacity from 1200 to 1400°C [5]
Present data
Ref. [4]
nichrome ‘0’ Cr = 20-23% Si = 0.4-1.58 impurities = 2.6% remainder-Ni 101 425 (estimated) 864
Cr-18% Ni-82%
101 -
680
V.N. Korobenko,
A.I. Savvatimski/
Journal
of Non-Crystalline
At the heating rates of 600 K s-* used in Ref. [5], this phase transition was observed at 697°C with H = 363 J gg ’ . These authors f5] attributed this transition to the ordering reaction in the solid state. In Fig. 4 the effect of the heating rate on the phasetransition is shown. Notable effects occur even for low rates 151.Our experiments are faster, with heating rates of about lo6 K s-i (number 3 curve in Fig. 4). Under these conditions, the resistancepeak of the phasetransition in nichrome is associatedwith H = 7 15 J g- ‘, and T N 1190°C). This temperature is nearly 2 times greater than that reported in Ref.
0
Solids 205-207
(1996) 678482
[5]. The enthalpy of nichrome in the solid phaseat the melting point was found to be 864 J g-r. Data for nichrome are presentedin Table 1. The present work demonstrates that fast pulse heating can causelow-temperature statesto move to higher temperatures, However, data obtained under fast heating methods should be checked versus equilibrium data. Sometimesthis comparisonis impossible for refractory metals. For example, under stationary conditions [9] the resistivity of liquid chromium was measuredto be 150 IJJJ cm; chromium is the main component of the nichromes. However fast
250 H-
Fig..2. Electrical resistivity for brasses plotted against enthalpy (H - H&.
%gs,
kJm
Notations as in Fig. 1.
681
V.N. Korobenko, A.I. Savvatimski/ Journal of Non-Crystalline Solids 205-207 (1996) 678-682
pulse heating measurementsassumesthe availability of rolled metal - wire or foil - that were not at our disposal. In Ref. [lo] the melting of nickel and its alloy Inconel 625 was investigated under different speeds of pulse heating (microsecondsand milliseconds). It was observed that the electrical resistance of the solid state alloy near the melting region (for fast heating) is lessthan it is for slower heating.
95 0
200
400
600
800
1000
1 1200
i
1400
r/,00
3.2. Brasses
Fig. 4. Electrical nichrome (1) stationary’measurements s-l (our measurements).
and bronzes
In Fig. 2 we see that for brasses,with increasing Zn content in the alloy, the liquid phaseresistivity at the melting point increases. At the same time the nature of resistivity in liquid state changes - the resistivity increasein the liquid state is replaced by a decrease.
8 Fig. 3. Electrical resistivity for bronzes (17 - H&. Notations as in Fig. 1.
plotted
against
enthalpy
resistivity for different rates of heating: [4]; (2) 600 K s-l [5]; (3) 3 X lo6 K
For any method of heating (pulsed, or under heating by alternating current of 50-60 Hz in channel furnaces of metallurgical plants), non-uniform heating results. The parts of the liquid alloys with a lower resistanceare heatedmore becauseof a greater allocation of capacity. This effect can be the causeof the known phenomenonof ‘zinc pulsation’ in channel furnaces. For Zn contents less than 20%, brasses have no any such effect even for temperaturesllOO1200°C [ 111.(The resistanceof liquid zinc decreases with increasing temperature [ 121.) It is suggestedin the literature [ll] that the main reason for ‘zinc pulsation’ is the boiling of Zn, resulting in temporary breakage of the current and a shock phenomenon dangerous for the furnace. We note that, with an increasing content of Zn in brass, the temperature of the liquids CT,,,) drops. For brass Cu63Zn37, r,, = 91O”C, which is somewhat less than the boiling temperature of zinc (916°C). For brass Cu,,Zn,, Tli, = 870°C. Thus, for industrial melting of brasses in electrical furnaces, the excessof pouring temperature of the liquid alloy above the boiling temperature of Zn becomesa less probable explanation. On the other hand, with increasingzinc concentration in brass, non-uniformities of heating become more probable causes, connected with the falling resistanceof liquid alloy, and resulting in the growth of the temperature in those parts in which the resistance drops. This non-uniform .rise in temperature can result in the boiling of the liquid phase of the alloy in separateparts of the conducting channel.
682
V.N. Korobenko,
Table 2 Comparison Alloys,
A.I. Sauuatitnski/.Journal
of data from the present work
marks and element
content
ofNon-Crystallize
Solids 205-207
(1996)
678-682
and Ref. 1131 Initial
resistivity
ol,fl
cm)
Resistivity
in the liquid
state (p,fi
cm)
Literature
6.26 5.9
38.4 (for T,,,, = 1211 K> 54.5 (for T = 1373 K)
present work [131
10.5 9.45
39.0 (for Smelt = 1228 K) 45.2 (for T= 1373 K)
present work
CuSiaMn CDA 655 (high silicon bronze)
31 25.7
60 (for r,,,, = 1298 K) 63.2 (for T = 1373 K)
present work [I31
S%.jCuPox CDA 524 (Sn = 10%)
16.7 16.0
41 (for Tmelt = 1270 K) 44.5 (for T = 1373 K)
present work
cu6Szn32
CDA 260 (Zn = 30%)
Cu,, Be, CDA
172 (Be = 1.85%)
The enthalpies and resistances for brasses Cu,,Zn,, and Cub,Zn,,, as well as for bronze CuSn,Zn,, at their melting points, are within 2% of known equilibrium data. A lot of experimental data are presentedin Ref. [13] on the resistivities of the liquid alloys of copper. In this work stationary conditions of heating were used, and the liquid alloys were held inside molybdenum tubes. The comparative data for some similar alloys from Ref. [13] and for our measurementsare in Table 2. Our data (Table 2) relate to the liquid phaseat the melting point (the equilibrium temperaturesof melting T, are shown). The data of Ref. [13] are measured for liquid state, above the melting point, for T=‘1373 K. We investigated copper (with initial resistivity 1.76 p,fi cm), whose resistivity at T, in the liquid state is 19.9 p,sZ cm; our estimation for the expansion gives 21.3 I.~fi cm at T, = 1336 K. In Ref. [13] for oxygen-free pure copper (the initial resistivity was 1.78 l.& cm), the resistivity at 1373 K is 21.8 pA cm. The results with these alloys are mixed. Taking into acco.untthe differences of resistivities resulting from additional impurities, the uncertainties due to possible dissolving of MO tubes in the liquid alloys [13], and that our data were estimated sometimes
[131
1131
taking account of expansion, the agreementis reasonably good.
References [l]
[2] [3]
[4] [5] [6] [7] [8] [9] [lo]
[ll] [12] [13]
S.V. Lebedev and AI. Savvatimski, in: Thermal Physics Reviews, Section B, Vol. 5, ed. A.E. Sheindlin and V.E. Fortov (Harwood Academic, Yverdon, 1993) p. 3. V.N. Korobenko and AI. Savvatimski, Teplofiz. Vis. Temp. 28 (1990) 914. N.A. Kanaev, S.V. Lebedev, AI. Savvatimski, N.V. Stepanova and B.A. Fotchenkov, Izv. Akad. Nauk USSR Met. N3 (1989) 48. H. Thomas, 2. Phys. 129 (1951) 219. K.D. Maglic, A.S. Dobrosavljevic and N.L. Perovic, High Temp.-High Press. 24 (1992) 165. P.D. Desai, Int. I. Thermophys. 8 (1987) 763. A. Cezairliyan and A.P. Miller, Int. J. Thermophys. 4 (1983) 389. A.K. Chaudhuri, D.W. Bonell, L.A. Ford and J.L. Margrave, High Temp. Sci. 6 (1970) 203. J.B. Van Zytveld, J. Non-Cryst. Solids 61&62 (1984) 1085. E. Kaschnitz, J.L. McClure and A. Cezairliyan, paper presented at the 12th Symp. on Thermophysical Properties, Boulder, CO, June 1994, submitted to Int. J. Thermophys. S.A. Farbman and IF. Kolobnev, Induction Furnaces for Melting of Metals and Alloys (Metallurgiya, Moscow, 1968). H.J. Guntherodt, E. Hauser, H.U. Kunzi, R. Evans, .I. Evers and E. Kaldis, .I. Phys. F6 (1976) 1513. R.P. Tye and R.W. Hayden, High Temp.-High Press. 11 (1979) 597.
Journal of Non-Crystalline
Solids 205-207 (1996) 678-682
The electrical resistance and enthalpy of industrial alloys based on nickel and copper V.N. Korobenko, A.I. Savvatimski * High Energy
Density
Research
Center
(HEDRCI,
United instihtte IVTAN, Russian Academy Moscow, Russia
of Sciences, Izhorskaya,
13/19,
1274i2
Abstract The electrical resistance and enthalpy of industrially important nickel- and copper-based alloys were measured, from room temperatures into the liquid state using fast (50 ps> pulse-heating. The electrical resistance at the melting point and enthalpies of fusion are close to equilibrium data. However, the phase transition in solid nichrome under fast heating is
displaced to higher temperatures. The electrical resistanceof liquid brassdecreaseswith increasing mole fractions of Zn; this causes ‘zinc pulsation’
during melting of brasses in channel furnaces.
1. Introduction
The method of fast heating by a unitary impulse of electrical current is used widely to study the physical properties of metals [l]. Recently, this method has been applied to alloys. The problem of applying fast heating to metallic alloys with complicated structures is that sufficient diffusion time is needed to ensure conformity of the properties to those in the equilibrium phase diagram of the alloy. 2. Experiment
We investigated samples of alloys prepared as wires of diameter 0.05 to 0.15 mm, which were heated by a unitary impulse of current from a condenser battery. In addition to the sample in the electrical circuit, a ballast resistance was also in-
* Corresponding author. Tel.: +7-095 362 5773; fax: +I-095 485 7990. 0022-3093/96/$15.00 PII SOO22-3093(96)00383-3
eluded. This method provided a relatively constant current in the electrical circuit during the heating and melting of the samples. In this way it was possible to avoid significant changes of current during heating (except for the initial moment), and this method permitted more precise measurements. The period of the pulse heating was typically 50-100 ks. This duration is longer than those used for electrical explosion [l] but permits more precise measurements. Fig. 1 shows values of the resistivity of nickel and its alloys as a function of enthalpy 121. The melting region was determined by the presence of a plateau on the radiance curve. The compositions of the alloys are identified by the labels which give the weight
percent of the components.
Fig. 2 and Fig. 3 give the resistivity data for brasses Cu,,Zn,, Cu6sZnS2, Cu6,Zn,, and for bronzes [3]. The expansion of the alloys during heating was not taken into consideration. Therefore the resistivity data in Figs. 1-3 are based on sample sizes at room temperature.
Copyright 0 1996 Elsevier Science B.V. All rights reserved.
V.N. Korobenko,
A.I. Suvvatimski/
Journal
of Non-Crystalline
For Ni we obtained a heat of melting of 292 J g- ‘. The recommended data E6Jgive a value of 298 J g-‘. For the resistivity at the melting point in the solid state, our result is 59 p,fi cm and the literature value is 59.6 [7]. For Cu we obtained a heat of melting of 207 J g-l; the recommended value is 205 J g-l [S]. For the resistivity at the melting point in the solid state, our result is 10.2 pfi cm - practically the same as the recommended value in the literature. The formal systematic error estimation is + 3% (resistance) and + 5% (enthalpy) for our fast heating experiments in the best cases, when the start and finish of the melting could be clearly seen.
p",10-6R
Solids 205-207
(1996)
678-682
679
'm
I
Cr20Ni80
5
A--
* NiMdAlPSil /-CNiW
3. Discussion 3. I. Nichrome
The top curve in Fig. 1 displays the data for nichrome. This alloy, according to the literature, contains only a y-phase. Prior. to the melting region, the change in slope ,of the resistance curve arises from the solid state phase transition. The same curve (only up to the melting point) is shown in Fig. 4 and marked by number 3. In spite of the fact that in all three works (Refs. [4,5] and this experiment) the same nichrome was used, differences (10%) for initial resistivities between Refs. 141 and [5] were seen. Perhaps this was due to differences in thermal and mechanical treatment of the specimens used.
Table 1 Comparison
of data from
the present
work
and element
content
Initial resistivity (r~.fi cm) Enthalpy (J g-l> (800°C) Enthalpy at melting point (J g - ’ ), solid state (Smell = 1400°C)
From steady-state measurements 141 a solid state phase transition (at the peak of the resistance, marked with number 1 in Fig. 4) has been reported at 500°C.
and from Refs. [4,5] for nichrome Ref. E5]
Marks
Fig. 1. Electrical resistivity for nickel and its alloys plotted against enthalpy (H - Hsg3). Solid lines: pulse measurements; circles on the vertical axis: our steady-state measurements for room temperature. Arrows with C: Curie points. The arrows mark the melting region; left-hand arrow: the start of melting; right-hand arrow: the finish of melting.
chrome1 Cr-20% Ni-80%
‘A’
110.79 431 840 estimation over extrapolation of the heat capacity from 1200 to 1400°C [5]
Present data
Ref. [4]
nichrome ‘0’ Cr = 20-23% Si = 0.4-1.58 impurities = 2.6% remainder-Ni 101 425 (estimated) 864
Cr-18% Ni-82%
101 -
680
V.N. Korobenko,
A.I. Savvatimski/
Journal
of Non-Crystalline
At the heating rates of 600 K s-* used in Ref. [5], this phase transition was observed at 697°C with H = 363 J gg ’ . These authors f5] attributed this transition to the ordering reaction in the solid state. In Fig. 4 the effect of the heating rate on the phasetransition is shown. Notable effects occur even for low rates 151.Our experiments are faster, with heating rates of about lo6 K s-i (number 3 curve in Fig. 4). Under these conditions, the resistancepeak of the phasetransition in nichrome is associatedwith H = 7 15 J g- ‘, and T N 1190°C). This temperature is nearly 2 times greater than that reported in Ref.
0
Solids 205-207
(1996) 678482
[5]. The enthalpy of nichrome in the solid phaseat the melting point was found to be 864 J g-r. Data for nichrome are presentedin Table 1. The present work demonstrates that fast pulse heating can causelow-temperature statesto move to higher temperatures, However, data obtained under fast heating methods should be checked versus equilibrium data. Sometimesthis comparisonis impossible for refractory metals. For example, under stationary conditions [9] the resistivity of liquid chromium was measuredto be 150 IJJJ cm; chromium is the main component of the nichromes. However fast
250 H-
Fig..2. Electrical resistivity for brasses plotted against enthalpy (H - H&.
%gs,
kJm
Notations as in Fig. 1.
681
V.N. Korobenko, A.I. Savvatimski/ Journal of Non-Crystalline Solids 205-207 (1996) 678-682
pulse heating measurementsassumesthe availability of rolled metal - wire or foil - that were not at our disposal. In Ref. [lo] the melting of nickel and its alloy Inconel 625 was investigated under different speeds of pulse heating (microsecondsand milliseconds). It was observed that the electrical resistance of the solid state alloy near the melting region (for fast heating) is lessthan it is for slower heating.
95 0
200
400
600
800
1000
1 1200
i
1400
r/,00
3.2. Brasses
Fig. 4. Electrical nichrome (1) stationary’measurements s-l (our measurements).
and bronzes
In Fig. 2 we see that for brasses,with increasing Zn content in the alloy, the liquid phaseresistivity at the melting point increases. At the same time the nature of resistivity in liquid state changes - the resistivity increasein the liquid state is replaced by a decrease.
8 Fig. 3. Electrical resistivity for bronzes (17 - H&. Notations as in Fig. 1.
plotted
against
enthalpy
resistivity for different rates of heating: [4]; (2) 600 K s-l [5]; (3) 3 X lo6 K
For any method of heating (pulsed, or under heating by alternating current of 50-60 Hz in channel furnaces of metallurgical plants), non-uniform heating results. The parts of the liquid alloys with a lower resistanceare heatedmore becauseof a greater allocation of capacity. This effect can be the causeof the known phenomenonof ‘zinc pulsation’ in channel furnaces. For Zn contents less than 20%, brasses have no any such effect even for temperaturesllOO1200°C [ 111.(The resistanceof liquid zinc decreases with increasing temperature [ 121.) It is suggestedin the literature [ll] that the main reason for ‘zinc pulsation’ is the boiling of Zn, resulting in temporary breakage of the current and a shock phenomenon dangerous for the furnace. We note that, with an increasing content of Zn in brass, the temperature of the liquids CT,,,) drops. For brass Cu63Zn37, r,, = 91O”C, which is somewhat less than the boiling temperature of zinc (916°C). For brass Cu,,Zn,, Tli, = 870°C. Thus, for industrial melting of brasses in electrical furnaces, the excessof pouring temperature of the liquid alloy above the boiling temperature of Zn becomesa less probable explanation. On the other hand, with increasingzinc concentration in brass, non-uniformities of heating become more probable causes, connected with the falling resistanceof liquid alloy, and resulting in the growth of the temperature in those parts in which the resistance drops. This non-uniform .rise in temperature can result in the boiling of the liquid phase of the alloy in separateparts of the conducting channel.
682
V.N. Korobenko,
Table 2 Comparison Alloys,
A.I. Sauuatitnski/.Journal
of data from the present work
marks and element
content
ofNon-Crystallize
Solids 205-207
(1996)
678-682
and Ref. 1131 Initial
resistivity
ol,fl
cm)
Resistivity
in the liquid
state (p,fi
cm)
Literature
6.26 5.9
38.4 (for T,,,, = 1211 K> 54.5 (for T = 1373 K)
present work [131
10.5 9.45
39.0 (for Smelt = 1228 K) 45.2 (for T= 1373 K)
present work
CuSiaMn CDA 655 (high silicon bronze)
31 25.7
60 (for r,,,, = 1298 K) 63.2 (for T = 1373 K)
present work [I31
S%.jCuPox CDA 524 (Sn = 10%)
16.7 16.0
41 (for Tmelt = 1270 K) 44.5 (for T = 1373 K)
present work
cu6Szn32
CDA 260 (Zn = 30%)
Cu,, Be, CDA
172 (Be = 1.85%)
The enthalpies and resistances for brasses Cu,,Zn,, and Cub,Zn,,, as well as for bronze CuSn,Zn,, at their melting points, are within 2% of known equilibrium data. A lot of experimental data are presentedin Ref. [13] on the resistivities of the liquid alloys of copper. In this work stationary conditions of heating were used, and the liquid alloys were held inside molybdenum tubes. The comparative data for some similar alloys from Ref. [13] and for our measurementsare in Table 2. Our data (Table 2) relate to the liquid phaseat the melting point (the equilibrium temperaturesof melting T, are shown). The data of Ref. [13] are measured for liquid state, above the melting point, for T=‘1373 K. We investigated copper (with initial resistivity 1.76 p,fi cm), whose resistivity at T, in the liquid state is 19.9 p,sZ cm; our estimation for the expansion gives 21.3 I.~fi cm at T, = 1336 K. In Ref. [13] for oxygen-free pure copper (the initial resistivity was 1.78 l.& cm), the resistivity at 1373 K is 21.8 pA cm. The results with these alloys are mixed. Taking into acco.untthe differences of resistivities resulting from additional impurities, the uncertainties due to possible dissolving of MO tubes in the liquid alloys [13], and that our data were estimated sometimes
[131
1131
taking account of expansion, the agreementis reasonably good.
References [l]
[2] [3]
[4] [5] [6] [7] [8] [9] [lo]
[ll] [12] [13]
S.V. Lebedev and AI. Savvatimski, in: Thermal Physics Reviews, Section B, Vol. 5, ed. A.E. Sheindlin and V.E. Fortov (Harwood Academic, Yverdon, 1993) p. 3. V.N. Korobenko and AI. Savvatimski, Teplofiz. Vis. Temp. 28 (1990) 914. N.A. Kanaev, S.V. Lebedev, AI. Savvatimski, N.V. Stepanova and B.A. Fotchenkov, Izv. Akad. Nauk USSR Met. N3 (1989) 48. H. Thomas, 2. Phys. 129 (1951) 219. K.D. Maglic, A.S. Dobrosavljevic and N.L. Perovic, High Temp.-High Press. 24 (1992) 165. P.D. Desai, Int. I. Thermophys. 8 (1987) 763. A. Cezairliyan and A.P. Miller, Int. J. Thermophys. 4 (1983) 389. A.K. Chaudhuri, D.W. Bonell, L.A. Ford and J.L. Margrave, High Temp. Sci. 6 (1970) 203. J.B. Van Zytveld, J. Non-Cryst. Solids 61&62 (1984) 1085. E. Kaschnitz, J.L. McClure and A. Cezairliyan, paper presented at the 12th Symp. on Thermophysical Properties, Boulder, CO, June 1994, submitted to Int. J. Thermophys. S.A. Farbman and IF. Kolobnev, Induction Furnaces for Melting of Metals and Alloys (Metallurgiya, Moscow, 1968). H.J. Guntherodt, E. Hauser, H.U. Kunzi, R. Evans, .I. Evers and E. Kaldis, .I. Phys. F6 (1976) 1513. R.P. Tye and R.W. Hayden, High Temp.-High Press. 11 (1979) 597.