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NBSIR 75-79 o

Microsecond-Resolution Pulse

Calorimetry for Semiconducting

Materials at High Temperatures

(A Feasibility Study)

A. Cezairliyan and C. W. Beckett

Physical Chemistry Division

Institute for Materials Research

National Bureau of Standards

Washington, D. C. 20234

October 1 975

Report for Contract No. 31-109-38-3174

May 1975 - June 1975

Prepared for Argonne National Laboratory

QC~ gonne, Illinois 60439

NBSIR 75-793

MICROSECOND-RESOLUTION PULSE

CALORIMETRY FOR SEMICONDUCTING

MATERIALS AT HIGH TEMPERATURES

(A FEASIBILITY STUDY)

A. Cezairliyan and C. W. Beckett

Physical Chemistry Division

Institute for Materials Research

National Bureau of Standards

Washington, D. C. 20234

October 1 975

Report for Contract No. 31-109-38-3174

May 1975 - June 1975

Prepared for Argonne National Laboratory

Argonne, Illinois 60439

U.S. DEPARTMENT OF COMMERCE, Rogers C.B. Morton, Secretary

James A. Baker, III, Under Secretary

Dr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Acting Director

Contents

Page

1. Introduction 1

2. Description of the Method 2

3. General Design Considerations 6

3.1. Electrical Circuit Equations 6

3.2. Consideration of Various Phenomena 9

3.2.1. Specimen stability-gravitational .... 9

3.2.2. Internal magnetic forces 9

3.2.3. External magnetic forces 10

3.2.4. Skin Effect 11

3.2.5. Temperature distribution in the

specimen 12

3.2.6. Evaporation 13

3.2.7. Electrical breakdown in gases 14

3.2.8. Ionization 15

3.2.9. Thermionic emission 16

3.2.10. Other phenomena 16

4. Measurement of Experimental Quantities 18

4.1. Power Measurements 18

4.2. Temperature Measurements 22

4.3. Other Measurements and Diagnostic Techniques . . 25

4.4. Recording of Experimental Quantities 27

5. Special Considerations in Relation to U0

2

29

5.1. Heating of U0

2

29

5.2. Various Phenomena Related to IK^ 32

5.3. Measurements on 37

6. Summary and Conclusions 41

7. References 45

Abstract

A feasibility study is conducted for the applicability of microsecond-resolution pulse heating techniques to the measurement of

selected thermodynamic properties of semiconducting substances at

high temperatures. The method of pulse heating of the specimen

using capacitor discharge techniques is described and general design

considerations, including electrical circuitry and various physical,

electrical and chemical phenomena, are presented. Measurements of

experimental quantities, such as current, voltage, temperature and

pressure are described. The special problems in relation to measurements of heat capacity and vapor pressure of uranium dioxide in the

temperature range 2000 to 6000 K are discussed. It is concluded that

the capacitor discharge circuitry and the measurement of the experimental quantities, although difficult, are not likely to present

major problems. However, problems are likely to stem from the low

electrical conductivity of the specimen. The experimental chamber must

withstand high pressures, high voltages, with optical windows and

possibly a furnace. The nature of the problems are discussed and the

performance of some preliminary experiments are suggested.

1. Introduction

Experimental investigations reported during the last two decades

in connection with exploding wires [1] and recently more quantitative

measurements on good conductors [2-7] have suggested the potential of

rapid (submillisecond) heating techniques as means of measuring selected

thermodynamic and transport properties of solid and liquid substances

at high temperatures (above 3000 K) , where conventional techniques

become difficult or impossible to use. The efforts reported in the

literature were mostly exploratory and preliminary in nature and

were in connection with measurements on metallic materials or substances which are electrically good conductors at room temperature.

This report summarizes the results of a feasibility study for the

development of a transient (microsecond resolution) system for the measurements of selected thermodynamic and transport properties of solid

and liquid semiconducting substances (with special emphasis on VO^)

in the temperature range 2000 to 6000 K.

The report is arranged to include: (a) the general description

of the transient method, (b) general design considerations to include

various physical, electrical, mechanical and chemical phenomena

associated with transient experiments, (c) measurement of experimental

quantities, such as current, voltage, temperature, pressure in

transient experiments and performance of diagnostic measurements,

(d) special considerations in relation to VO^ specimens, and (e) summary

and conclusions.

1
2 . Description of the Method

The method is based on resistive self-heating of the specimen by the

passage of high currents through it and measuring the pertinent quantities

with appropriate time resolution. In general, the required quantities

are: current through the specimen, potential difference across the

specimen, and specimen temperature. Depending on the nature of the

experiment, additional quantities (electrical and thermal, such as

pressure) may be required.

Basically, the measurement system consists of an electrical powerpulsing circuit and associated high-speed measuring circuits. The

pulsing circuit includes the specimen in series with an electric

pulse power source (such as a capacitor bank), an adjustable resistance,

a standard resistance and a fast-acting switch. The specimen is

contained in a controlled-environment chamber. The high-speed measuring

circuits include detectors and recording system.

Some of the electrical power pulsing circuits and the instrumentation

required in a thermodynamic measurement system may be similar to those

used in exploding conductor or similar research. A variety of such

capacitive energy storage and discharge systems were developed in the

1950s and 1960s for various applications. Their capacity ranged from

joules to megajoules, and their discharge duration ranged from nanoseconds to milliseconds. In recent years, only minor changes have taken

place in such systems.

2
As of the present time, capacitive storage and discharge systems

have been developed for reliable and almost routine operation at voltages

as high as 30 kV. In spite of the difficulties that are encountered

above this voltage, a few systems have been developed and have been

operated at several hundred kilovolts.

TIMERS a

PULSE GEN.

CURRENT

MEAS.

CXKKIMCNT

TRIGGER

ADJ. RES.

STAND. RES.

VOLTAGE

MEAS.

±jOTHER

TEMP. MEAS.

' SPECIMEN —J CHAMBER

SWITCH rrn

TTTT

TRIGGER

CIRCUIT

CHARGING

CIRCUIT

SAMPLE A — D MEMORY

TELETYPE- COMPUTER a HOLD

AMPLIFIERS CONVERTERS WRITER

Figure 1. Functional diagram of a capacitor discharge system for

thermodynamic measurements.

A functional diagram of a typical system that may be used for

thermodynamic measurements is shown in Figure 1. The pulse-power

source is a capacitor bank. The charging circuit includes a conventional high voltage d.c. supply (usually with 1 to 100 mA current

3
rating), an electrostatic voltmeter, and a high-voltage switch for

disconnecting the supply from the main circuit prior to the discharge.

The capacitors used in such systems are designed to have very low

inductance (1 to 100 nH) . The majority of the capacitors used and

reported in the literature fall in the 1 to 15 yF range with voltage

ratings from 5 to 30 kV. Energy stored in a capacitor is expressed

2 as U = CE /2, where C is capacitance, and E is the voltage. Since

energy depends on the square of the voltage, higher energy discharges

are achieved more efficiently by increasing the charging voltage.

Because of their high current capacity and simplicity, spark

gaps are frequently used as switching devices in capacitor discharge

systems. A variety of types are reported in the literature. The type

most commonly used for voltages up to 50 kV consists of two highcurrent electrodes separated by a gap (air or other gas) . Closing

of the switch is achieved by a triggering circuit which ionizes the

gas in the gap. As a result of ionization, resistance of the gap

decreases to a negligible level, thereby causing initiation of the

discharge. Several techniques may be used to ionize the gas. The

most commonly used method is to supply a relatively low energy but

high voltage pulse to a trigger electrode located near or coaxial with

one of the main electrodes. The resultant spark between the trigger

and one of the main electrodes is sufficient to ionize the gas.

Another method is to expose the gas to the radiation from a pulsed

laser. Above 40 kV, the switching of high currents becomes more

A
difficult. It has been found that gas-type spark gaps are not reliable

due to their sensitivity to gas composition (primarily to moisture content). Vacuum type switches, composed of two electrodes placed in a

vacuum container, have shown higher reliability. In this case, switching

is achieved by supplying a low-energy, high-voltage pulse to one of the

electrodes in such a way that the net potential difference between the

two electrodes exceeds the natural breakdown voltage.

Standard resistances, which in discharge work are sometimes referred

to as "shunts", have a special coaxial configuration to reduce undesirable effects of high electromagnetic fields. Details regarding design

and operation of current and voltage measuring devices as well as

temperature measuring equipment are given in Section 4.

Depending on the experimental procedure and requirements, the

specimens initially may be in the form of a wire, rod, tube or a

composite made of a tube filled in the middle with the specimen in

solid or liquid form.

Recording of experimental quantities are generally made with

oscilloscopes. However, recent advances in the electronics field

permit the development of systems for digital recording of quantities

with microsecond resolution and with full-scale resolution of

approximately 0.1 percent.

5
3. General Design Considerations

3.1. Electrical Circuit Equations

The capacitor discharge system described in the previous section

and shown schematically in Figure 1 can be represented electrically as

a series RLC circuit. Dynamic characteristics of such a circuit may

be represented by the following equation:

dt

where, i is current, t is time, and R, L, C are resistance, inductance,

and capacitance of the entire circuit, respectively. The solution of

Equation (1) is given in Table 1 for three different cases. The results

are also represented graphically in Figure 2.

It should be considered that in the solutions of Equation (1), the

quantities R, L, and C are considered to be constant. In an actual

capacitor discharge experiment this assumption is reasonably satisfied

for L and C. However, R varies as a function of time because of the

change in specimen resistance during heating. The degree of departure

of actual results from those given in Table 1 depends on the relative

magnitude of the change in specimen resistance with respect to the

resistance of the entire circuit.

Critical damping is the most desirable case to have in a discharge

experiment. However, because of various conflicting design and operational

parameters in an actual system, this is very difficult to achieve. In
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TIME

Figure 2. Typical discharge characteristics of a capacitor system.

(1) overdamped, (2) underdamped, (3) critically damped.

with the circuit oscillating at a natural angular frequency w (defined

in Table 1). In some experiments, the oscillating discharge through

the specimen is avoided by switching a low resistance unit parallel to

the specimen at the end of the first cycle or part of the first cycle.

This scheme requires greater amount of stored energy since some of the

energy, which normally would be imparted to the specimen, bypasses the

specimen.

8^
3.2. Consideration of Various Phenomena

The successful design and operation of high-speed measurement

systems and the meaningful interpretation of the data depend on detailed

consideration of various thermal electrical, magnetic and other related

phenomena. In the following paragraphs some of the important items

are discussed.

3.2.1. Specimen Stability-Gravitational

A distinct advantage of the rapid pulse heating experiments is that

the specimen does not need to have a container. However, one must be

sure that the specimen remains in its original position and geometry

during the entire experiment (which may be several hundred microseconds)

.

Ultimately the gravitational forces will cause the specimen to collapse.

2

A simple computation using the relation £ = oi.t /2 (where £ is the distance,

t the time and a is the acceleration due to gravity) gives an estimate

of the movement of the specimen due to gravity. The results indicate

a movement of about 0.5 mm in 10 ms and 0.005 mm in 1 ms. Since the

experiment will be completed in less than 1 ms, the gravitational

force will have almost no effect on the measurements.

3.2.2. Internal Magnetic Forces

High currents through a conductor create magnetic forces which act

toward the center of the conductor. The effect of these forces is

especially critical for tubular conductors, for conductors with axially

asymmetric geometries, and for liquid conductors.

9
Magnetic force on a cylindrical conductor is

F - *2§^ (2)

where i is the current (A) , a is the radius (cm) of the conductor,

L the length (cm) of the conductor, and F is the force (uN)"^. The

corresponding magnetic pressure (Pa) is given by

P - ^4 (3)

3ira

3.2.3. External Magnetic Forces

The force between two current carrying conductors is expressed by

F - -f£- (4)

where, y is permeability (in vacuum, y = 1) , i^ and are the currents

(A) in the two conductors, L is the length (cm) of the conductor, r is

the separation (cm) of the conductors and F is the force (yN).

According to the above equation, force per unit length (cm) between two

conductors carrying the same current placed in vacuum becomes:

F i

2 - = -— (5) L 5 r

K J

1

1 yN = 0.1 dyne

2 -2

1 Pa = 1 N-m

10
It may be seen that forces resulting from currents in conductors are

proportional to the square of the current. For rapid pulse experiments,

4 6

where high currents (of the order of 10 to 10 A) are involved,

consideration of these forces become very important for the mechanical

stability of the overall system as well as of the specimen.

3.2.4. Skin Effect

The skin effect, which is caused by changing currents in a circuit,

alters the resistance of the specimen or other elements in the circuit

and creates temperature nonuniformities in the specimen.

For a cylindrical conductor the skin effect is a function of the

following parameter:

where, ot is the radius of the conductor (cm), f the frequency of

current (Hz), p is the electrical resistivity of the conductor (fi»cm),

and y is the permeability of the conductor (for non-magnetic materials

y = 1) . It may be noted that for a given geometry and frequency, the

skin effect is greater for a good conductor than for a poor conductor.

In general, the contribution of the skin effect in a specimen is

expressed in terms of the ratio of its electrical resistance at the

frequency in question to that under d.c. conditions. Results on the

resistance ratio in terms of the parameter x in Equation (6) are given

in the literature [8], The contribution of the skin effect may be

neglected for experimental conditions which yield a value of x less

than 0.5 (this corresponds to a value of 0.03 percent for the resistance

ratio)

.

(6)

11
3.2.5. Temperature Distribution In the Specimen

Heat transfer by conduction and convection are relatively slow

processes in comparison with submillisecond heating. Thus, they do not

affect the temperature distribution in the specimen provided that the

specimen is at a uniform temperature just before the start of pulse

heating. Heat transfer by radiation may be considerable at high

temperatures (above 3000 K) , especially for thin wires and strips.

However, for a specimen having a diameter of the order of a few

millimeters radiation heat loss (up to 6000 K) in submillisecond regimes

may not be significant (less than 1 percent). However, even though

the energy loss may be insignificant, the radiation heat transfer

creates a radial temperature gradient in the specimen which may create

nonuniform! ties in the electric current density in the specimen.

The major source of temperature nonuniformities in the specimen

during rapid pulse heating is likely to be the hot spots or zones

that result from material inhomo gene i ties or geometrical nonuniformities

in the specimen. Their effect becomes particularly pronounced and

amplified in a specimen which has a positive coefficient for its

electrical conductivity.

If the specimen geometry is not properly selected, skin effect

may also be a serious source of temperature gradients.

12
3.2.6. Evaporation

In general, the rate of evaporation from surfaces into vacuum at

high temperatures may be expressed as

m(T) = Ae"

E/kT

(7)

where, T is temperature, A is a constant for a given surface, E is

the energy of evaporation, and k is the Boltzmann constant. Evaporation

from solids and liquids at high temperatures increases very rapidly

with temperature and becomes an important phenomena to be considered

in the design and operation of measurement systems. The above

equation does not apply in cases where the specimen vapor pressure is

high (causing multiple collisions among the molecules) or where an

inert gas is used in the experiment chamber. In such cases, the

evaporation mechanism is complex and it is difficult to estimate

the amount of specimen evaporation.

Evaporation from the specimen affects the measurement mainly in

two ways: first, by contributing to the energy loss from the specimen,

and second, by disturbing the medium between the specimen and the

optical instruments, such as pyrometers, cameras, etc. The effect of

evaporation may be reduced by confining the specimen in a transparent

solid or liquid media or in a pressurized gas. Confinements in

solid or liquid media creates other problems that stem from chemical

reactions and heat conduction. In most cases, the use of an inert

gas under pressure may be the optimum choice. The high pressure gas

13
will reduce the evaporation and will confine the vapor to a thin

boundary layer. The thickness of the boundary layer is governed by

the diffusion of specimen vapor in the surrounding gas and it is proportional to the square root of the product of the diffusion coeffieient

and the time (experiment duration)

.

3.2.7. Electrical Breakdown in Gases

As it was discussed earlier, in order to suppress evaporation at

high temperatures, the specimen may be placed in a gaseous environment.

The high voltage holding characteristics of a gas is generally

expressed by the Paschen's Law, which states that the breakdown voltage

is a function of the product of the gas density (w) and the separation

between the electrodes (d) , that is E = f(ajd). Thus, for a given geometrical

configuration, breakdown voltage increases with increasing gas density.

This implies that breakdown voltage increases with increasing gas

pressure and decreases with increasing temperature. Using the perfect

gas law, it may be seen that the conditions of the gas (from electrical

breakdown standpoint) at 1500 K and at 0.5 MPa (^5 atm. ) pressure^"

is about the same as that at room temperature and 0.1 MPa (^1 atm.).

0.1 MPa = 1 bar ^ 1 atm.

14
Experimental studies, as summarized in [9], have shown that the

breakdown voltage in air at 0.1 MPa (^1 atm.) over a 5 mm gap is about

17 kV. When pressure is increased to 1 MPa (^10 atm.) , the breakdown

voltage is about 150 kV. Further increase of pressure to 4 MPa (^40 atm.)

causes the breakdown voltage to increase to about 330 kV.

The above are for conditions where the gas is electrically neutral

before the breakdown. Under the conditions where there are free

electrons present in the medium and the gas is partially ionized the

situation is completely different, that is, the breakdown voltage is

very low.

3.2.8. Ioni zation

The energy necessary for ionization may be given to an atom by an

electron impact, the impact of a positive ion, by the absorption of

radiant energy, or the gas may become so hot as to ionize the atoms

thermally by the collisions of neutral atoms. These processes may

occur either singly or in combination. It is generally believed that

in gas discharges the predominant mechanism of ionization is by electron

collisions. The ionization potential of gases is an important parameter

to consider in the selection of the proper environment for the specimen.

For the inert gases, the ionization potential decreases with increasing

atomic number. Helium has the highest ionization potential (24.6 ev) ;

the values are 21.6 ev for neon and 15.8 ev for argon.

15
3.2.9. Thermionic Emission

Thermionic emission from the specimen may have several undesirable

effects. It may alter the conditions of the gas, thereby causing a

parallel path for the electrical current and generation of random discharges. It may alter the true voltage across the potential probes,

causing measurement errors. In addition, energy loss from the specimen

by thermionic emission may become appreciable at high temperatures.

Thermionic emission in vacuum may be expressed as

e<fr

i = AT

2 e kT

(8)

where, T is the specimen temperature, e the electronic charge, k the

Boltzmann constant, <f> the work function, and A is a parameter different

for different materials. For metallic surfaces A is approximately

—2 —2 —8

60 A* cm »K and for oxides it may be in the range 1 x 10 to 10.

The quantity <f> may be in the range 2 to 5 V both for metals and oxides.

3.2.10. Other Phenomena

Thermal Expansion: A material expands (due to thermal effects)

approximately with the speed of sound in that material. In order to

avoid complications (practical and theoretical) , it is advisable to

limit the heating rate of the specimen to a value that allows the free

expansion of the specimen at any time during the rapid heating period.

The speed of sound in most solid materials is of the order of a few

millimeters per microsecond.

16
Thermoelectric Effects: The Thomson effect is probably the most

significant thermoelectric effect in rapid heating experiments. Its

contribution (absorption or evolution of heat) occurs only at the

extreme ends of the specimen (near the clamps) where sharp temperature

gradients exist.

17
4 . Measurement of Experimental Quantities

4.1. Power Measurements

The most frequently needed quantities in thermodynamic experiments

are power absorbed by the specimen and specimen temperature. Absorbed

power is determined from measurements of imparted power and power losses.

In experiments in which the specimen is heated resistively, imparted

power may be obtained from measurements of current through the specimen

and voltage across the specimen. In capacitor discharge experiments,

the only significant power loss from the specimen Is that due to thermal

radiation. In most cases, this loss comprises less than one percent

of imparted power. Therefore, a correction based on an estimated

emittance value is generally considered to be satisfactory.

Accurate measurement of current and voltage in capacitor discharge

experiments is a difficult task. This difficulty stems primarily from

the high degree of interaction (due to electromagnetic fields) between

the signal carrying circuits and the main discharge circuit. Since

the effect of this interaction is proportional to the quantity di/dt

(where i is current and t is time) , increasing difficulties with increasing

discharge speeds are encountered.

The state of the art of current measurement techniques is more

advanced than that for voltage. The coaxial shunt, shown schematically

in Figure 3, has the feature of eliminating, to a large extent, the effect

of induced voltages in the signal carrying circuit. This is accomplished

by having the resistance element in tubular form and by placing one of the

18
voltage probes along the axis of the tube. Because of radial symmetry,

the net electromagnetic force and the net induced voltage in the probe

are therefore zero. Inaccuracy in current measurements with this scheme

is estimated to be approximately 1-2 percent. Due to the skin effect

in the resistance element, this inaccuracy may increase at very high

oscillatory discharge frequencies (above 1 MHz)

.

TO

SPECIMEN

TUBULAR STAND. RES. L

POTENTIAL

LEADS

RETURN

Figure 3. Schematic diagram of a tubular standard resistance used

in capacitor discharge experiments.

Several methods have been used to measure voltage across the

specimen during a discharge experiment. However, as of now, no practical

and accurate technique has been developed. The most frequently used

technique is based on measurements with a voltage divider. The divider

ratio is dependent upon the voltage across the specimen and the input

voltage rating of the recording instrument. Such a measurement scheme

is subject to errors due to induced voltages in the measuring circuit.

19
The attempts that have been made to eliminate this error or to reduce

it to a negligible level may be classified in two categories: (a) by

extensive shielding of all the measuring circuits, and (b) by compensating for all the induced voltages. The first method is not satisfactory

because there are always portions of the circuit (those near the

specimen) that cannot be properly shielded. The second method, in

principle, is more promising. Several different types of compensation

(mathematical and physical) may be used. Mathematical compensation is

based on recording the gross voltage signal (sum of true and induced

components) in addition to current through the specimen, and adjusting

the voltage data (with the use of a computer) after the experiment to

bring it in phase with the current. The final voltage obtained by this

approach represents the true resistive component across the specimen.

The same result may be accomplished by physical compensation using an

adjustable coil placed in series with the voltage divider circuit.

The function of the coil is to cancel erroneous voltage during the discharge by generating an induced voltage equal in magnitude but opposite

in sign to that induced in the measurement circuit and the specimen.

Equality between the erroneous induced voltage and the generated compensating voltage may be established by rotating the coil (by trial and

error) until voltage and current traces are in phase with each other.

A schematic diagram of a voltage measuring circuit based on a physical

compensation technique is shown in Figure 4. An additional improvement

20
COMPENSATING COIL

DIVIDER I

SPECIMEN

G

DIVIDER 2

AAWv A/VV-1

Figure 4. Electrical circuit of a voltage measuring technique

utilizing two dividers and a compensating coil

incorporated in the circuit is the use of two voltage dividers. The

signals corresponding to voltages e^ and e^ are applied differentially

to an oscilloscope. The true voltage across the specimen is proportional

to the quantity (e^ - e^) . The advantage of the two-voltage-divider

system is that it allows measurement of specimen voltage even though

both terminals of the specimen may be at a high potential with respect

to ground. This provides flexibility (in the grounding procedure) in

the design of the main discharge circuit. Inaccuracy in voltage

measurements with proper compensation techniques is estimated to be

approximately three percent.

21
In recent years, techniques based on electro-optical and magnetooptical effects for the measurement of pulse voltages and currents

have been explored. The scheme that utilizes the optical attenuation

in a Kerr cell due to high voltages across the two electrodes shows

great promise for accurate measurement of pulse high voltages.

4.2. Temperature Measurements

There are no commercial instruments or established techniques for

accurate high temperature measurements with microsecond resolution.

Several attempts have been made for such measurements in connection

with research on shock waves, exploding wires, and pulsed plasmas.

They are generally based on photoelectric or photographic detection of

the specimen radiance. Conversion of the radiance to temperature is

accomplished by calibrating the detector with reference radiances

before and/or after the transient experiments.

The fact that calibration and transient experiment are not

made simultaneously may introduce uncertainties. For example, in the

case of photomultiplier tube detectors, fatigue, instability, or the

effect of high magnetic fields during a discharge may invalidate the

calibration. In the case of photographic films,| variations in emulsion

and development may introduce similar uncertainties. To avoid these

difficulties it is necessary to develop systems in which the detector

is calibrated during the transient experiment. In photoelectric

systems this may be accomplished using a high-speed chopper which allows

the alternate exposure of the detector to radiation from the unknown

22
and from a reference. In photographic systems, no chopping is

necessary and it suffices to photograph simultaneously one or more

reference radiances in addition to the unknown on the same film during

the transient experiment.

Another alternative that avoids the use of chopping schemes, is

the development of photoelectric or similar detectors which are very

stable and whose behavior is invariant under transient electromagnetic

fields. Recent developments in the area of solid-state detectors show

considerable promise. Their submicrosecond response characteristics

are attractive and their stability and reproducibility under relatively

slow experiments (millisecond resolution) have been satisfactory.

However, no careful study has yet been made regarding their stability

and behavior under intense short radiation pulses and strong electromagnetic fields. Most solid-state detectors developed so far have a

maximum response in the near infrared and infrared regions. In

some cases, the response curve does not show a sharp decrease toward

the visible region and extends to about 400 nra. These characteristics

are sufficient to satisfy some of the requirements of a microsecond

resolution temperature measurement system. However, as it was mentioned

above, their behavior under intense short radiation pulses and under

high electromagnetic fields needs to be studied.

Consideration of the photon energy requirements for the satisfactory

operation of a detector suggests that solid-state detectors can be

used for temperature measurements (with microsecond resolution) above

23
about 2500 K. By optimizing the effective wavelength, the exposure

times can be further reduced. Also, selection of the bandwidth of

radiation impinging on the detector contributes to the satisfactory

response of the detector. The bandwidth of the filters used for this

purpose may be in the range 10 to 50 nm.

Temperature measurements based on radiance measurements at one

wavelength are possible for cases where the specimen approximates

blackbody conditions or the normal spectral emittance of the specimen

at the effective wavelength of the instrument is known. If these

conditions are not met, the alternative may be to perform radiance

measurements simultaneously at two wavelengths. This provides one to

obtain the specimen's true temperature under the assumption that the

ratio of specimen emittance at the selected wavelengths is independent

of temperature. This approach seems to have promise in measuring

the temperature of rapidly heating solids and especially liquids at

temperatures above 2500 K in microsecond-resolution experiments.

However, it has the disadvantage of being insensitive compared to a

monochromatic pyrometer, and it is subject to a systematic error if

the ratio of emittances at the selected wavelengths varies with

temperature.

24
4.3. Other Measurements and Diagnostic Techniques

In addition to the measurement of imparted power to the specimen

and specimen temperature, time-resolved measurements of other quantities

may be required during a pulse heating experiment. For example, the

pressure, shape, expansion, and density of the specimen may be needed.

Transient pressure measurement techniques have been developed

primarily in connection with shock tube research. In general, they

utilize transducers whose operation is based on piezoelectric or

piezoresistive effects.

For the measurement of quantities related to specimen geometry,

high-speed photography and flash x-ray techniques may be employed.

However, in some cases considerable discrepancies have been observed

between the results obtained simultaneously by the two methods.

In general, results from x-ray data are considered to be more reliable

in measurements related to the diameter of an expanding specimen.

It is important to have diagnostic techniques to ascertain the

specimen behavior in submillisecond-duration experiments as well as

the electrical and optical conditions in the experiment chamber.

High-speed photography is used for both diagnostic and measurement

purposes. Improvements in films and optical components, including

utilization of electro-optical devices and pulsed lasers, have enhanced

the contribution of high-speed photography to capacitor discharge

experiments.

25
Techniques for modulating optical radiation play an important role

in high-speed experiments not only in connection with temperature

measurements but also in other optical studies as in high-speed photography, spectroscopy, and interferometry . They may be divided into

two general classes: (a) mechanical modulation, and (b) electrooptical or magneto-optical modulation. Most commonly used mechanical

modulators are disc-shaped choppers , and turbine mounted mirrors; they

4 7 may be used for modulating light to 10 and 10 Hz, respectively. For

9 higher frequencies (up to 10 Hz) electro-optical modulators (Kerr cell,

etc.) may be used. However, as of the present time, very little

accurate work has been done to assess the operational characteristics

of electro-optical modulators, such as transmission stability, and

behavior under varying internal and external parameters.

Generation of short-duration light pulses, which may be needed in

certain high-speed experiments, may be accomplished either by modulating

a steady light source or by having a pulsed light technique. The latter

has the advantage of delivering higher intensities. Flash lamps were

used in the past for this purpose. However, advances in pulsed lasers

have overshadowed all other pulsed light sources. They are capable

of providing intense monochromatic light, and their pulse duration

may be made as short as a few picoseconds.

26
4.4 . Recording of Experimental Quantities

The ultimate utility of a measurement system lies in the proper

recording of the experimental quantities. One of the major reasons

for the delay in the development of high-speed thermodynamic and

related measurement techniques has been the difficulties encountered

in accurate recording of the signals.

The first truly high-speed recording of quantities was realized

with the development of modern oscilloscopic techniques. Because of

the very fast response characteristics (as low as nanoseconds),

oscilloscopes were used for a wide range of experimental conditions,

requiring from millisecond to nanosecond resolution. However, they

have limitations which stem primarily from their relatively poor

recording accuracy. In general, under optimum conditions oscilloscopic

recording inaccuracy can hardly be less than one to two percent of full

scale. In special cases where pulses to be recorded are of rectangular

or trapezoidal shape, accuracy may be improved by suppressing the major

portion of the pulse and recording only the remainder of the signal.

Since oscilloscopic recording (on film) is in analog form, additional

effort is required to reduce the information to numeric (digital)

form using micrometer microscopes or similar reading instruments.

Advances in the electronics and computer fields during the last

decade have made the development of accurate high-speed digital

recording systems a possibility. Such systems generally consist of a

multiplexer, an analog-to-digital converter, a memory, pertinent

27
interfacing equipment, and an output device (such as a magnetic tape

deck, a teletypewriter, or a computer). For systems where recording

resolution must be less than a few microseconds, the multiplexer is

omitted and separate analog- to-digital converters in conjunction with

sample-and-hold amplifiers are used for each channel (experimental

quantity) .

With the presently available electronic components and technology

it is possible to build a digital data acquisition system capable of

digitizing and recording simultaneously a set of several experimental

quantities about every 0.5 ys with a full-scale signal resolution of

about 0.1 percent under optimum conditions.

28
The presentation and discussion of various phenomena and experimental conditions in the previous sections were based on the fact that

the specimen was a good electrical conductor, meaning that it could

have been resistively heated from room temperature up to the desired

high temperature by discharging a capacitor bank through it.

Almost all oxides are either nonconductors or poor conductors

at room temperature. However in a number of cases, their electrical

conduction properties increase rapidly with increasing temperature.

Uranium dioxide exhibits such a behavior. In this section, techniques

for performing transient measurements on UC^ and the problems

associated with such methods are discussed.

5.1. Heating of UO

^

Electrical conductivity is the most important property In considering the resistive self-heating of the specimen. The electrical

conductivity of uranium dioxide depends strongly on its composition,

namely on the oxygen to uranium ratio. The available literature on

electrical conductivity of uranium dioxide is not conclusive, but it

is sufficient to give a general idea as to the magnitude and the range

of values. For the stoichiometric composition, the electrical conductivity at room temperature is of the order of 10 ^ Q, ^'cm \ and

-3 -1 -1

increases to about 10 ft »cm for oxygen to uranium ratio of

2.001 [10]. The data reported in the literature for the oxygen

deficient cases are very few. The available results indicate that at

29
room temperature electrical conductivity is of the order of 10

ft "''•cm 1

for the case where the oxygen to uranium ratio is 1.990 [11],

It seems that as the temperature is increased the differences in

electrical conductivity due to differences in composition are reduced.

For discussion and general estimative purposes, one may consider the

values 1 ft" 1

. cm"

1

at 1500 K and 50 ft" 1. cm"

1

at 3000 K [12].

From the above figures, it may be seen that UO^ becomes a fairly

good conductor at temperatures above 1500 K. Therefore, one may consider a two-stage heating procedure, in which the specimen is heated

slowly up to about 1500 K and above that temperature it is heated

rapidly.

The first-stage slow heating may be accomplished either by resistive

self-heating or by external heating using a laser or a conventional

furnace arrangement. The slow resistive self-heating method may not

be desirable because it causes the establishment of axial and radial

temperature gradients in the specimen. For similar reasons, laser

heating is not suitable. Problems with electrical interference may

preclude the use of direct or indirect RF heating. It seems that a

conventional tubular furnace arrangement may be the best solution to

heat the specimen to about 1500 K.

Once the specimen is at a constant temperature at about 1500 K, the

second-stage rapid heating up to about 6000 K may be accomplished by

discharging a capacitor bank through the specimen, as was described in

the earlier sections of this report. The melting point of UO is
about 3130 K, thus the rapid heating will cover part of the solid

phase as well as the liquid phase.

Uniformity in specimen temperature distribution at the end of the

first-stage heating is a very important consideration. If temperature

gradients or other nonuniformities exist in the specimen before the

second-stage heating starts, these nonuniformities are likely to

be amplified and cause specimen failure during the rapid heating

period. | A specimen, 5 mm in diameter and 15 mm in length, has an

electrical resistance of about 7.6 0, at 1500 K (based on a conductivity

value of 1 0. ^cm ) . Considering the values of 1 uH for the inductance

and 100 uF for the capacitance of a typical discharge circuit, it may

be seen from the relation in Table 1 that the discharge will correspond

to the "overdamped" case, and the current waveform will resemble the one

shown in insert 1 of Figure 2. The waveform of current and voltage

may change as the resistance of the sample decreases from 7.6 fi at

1500 K to about 0.15 Q at 3000 K.

Energy required to heat the UO^ specimen from 1500 to 6000 K is

estimated based on the enthalpy data given in the literature [13] for

temperatures up to the melting point, the heat of fusion also given in

the literature [14], and assumed constant heat capacity of liquid UO

equal in value to that of solid U0

2

near the melting point. The results

yield a value of about 800 kJ*mol A specimen 5 mm in diameter

and 15 mm in length weighs about 3.12 g (0.0115 mol) . Thus, energy required

to heat the U0

2 specimen from 1500 to 6000 K is about 9 kJ.

31
A capacitor bank (eight capacitors, 20 kV, 15 uF each) capable of

storing 24 kJ should be sufficient to provide the required energy. This

allows for a 60 percent energy loss in the switch and other parts of

the circuit during the discharge.

The dimensions of the specimen given above are an upper limit.

A shorter specimen may be needed in order to increase the electric

field and the heating rate. In other cases, a smaller diameter may

be required in order to reduce the energy requirements because part of

the energy may be dissipated either in a series resistance or in a

current shunt (crowbar switch).

5.2. Various Phenomena Related to UO^

In Section 3.2 of this report, various phenomena that had to be

considered in the design and operation of high-speed measurement systems

were discussed on a general basis. In the present section, the contribution of these phenomena in the specific case of XJO^ as the specimen

are summarized. For the descriptions of the phenomena, for the pertinent

equations, and for relevant discussions one may refer to Section 3.2.

In the rest of this section, duration of the experiments is considered

to be in the range 10 to 1000 us. The various phenomena are evaluated

to correspond to the most unfavorable case.

Specimen Stability-Gravitational : Movement of the specimen due to

gravitational forces is estimated to be less than 0.01 mm in 1000 us.

32
Internal Magnetic Forces ; Internal magnetic forces create pressures

that act toward the axis of the specimen. This discourages the use of

tubular specimens; however, specimens in the form of rods should not

be significantly affected by these pressures.

External Magnetic Forces : The mechanical stability of the specimen

will depend to a very large extent on the balance of external magnetic

forces. To achieve this, a high degree of axial symmetry is required

between the specimen and the external current paths. An accurate coaxial

configuration between the specimen and the current return path will

minimize the effect. An eccentricity of 1 mm between the specimen

axis and that of the current return cylinder is likely to produce

magnetic forces sufficient to move the specimen several millimeters

in 1000 us. Since, the alignment accuracy can be better than 1 mm,

the contribution of this effect can be made small. However,

experimental studies of pulse discharges In metals have shown that the

specimen becomes unstable in times much less than 1000 us. From

the results of such studies, the time available for the measurements

in the liquid phase is likely to be in the range 10 to 20 us. This

corresponds to an average heating rate in the range 150 to 300 K»us

'

for heating the specimen from 3000 to 6000 K. An electrical field

in the range 5 to 10 kV»cm ^ will be required for these high heating

rates.

33
Skin Effect ; Considering that the specimen diameter is 5 mm and

that the experiment duration is 10 us, the skin effect is estimated to

be less than 0.03 percent at 3000 K; this value indicates the ratio of

the electrical resistance at the frequency in question to that under

d.c. conditions. At lower temperatures, the effect is even less, since

the electrical conductivity is less. No data on electrical conductivity

of liquid UO^ were found in the literature, thus it was not possible

to estimate the skin effect at temperatures above the melting point.

However, it may be said that, in order for the skin effect to be 1

percent at 6000 K it is necessary for the electrical conductivity at

6000 K to be 5000 times that of at 3000 K; which is a very

large factor for changes in electrical conductivity in liquids.

Temperature Distribution in the Specimen : In submillisecond duration

experiments heat transfer by conduction is very small, thus they do

not affect the temperature distribution in the specimen. Radiation

heat transfer may become appreciable at high temperatures. Considering

a specimen 5 mm in diameter which is heated from room temperature

to 6000 K in 1000 ys, heat loss by thermal radiation is less than

0.5 percent of the total power input to the specimen. The above

computation is based on a hemispherical total emittance of unity, which

means that in the real case heat loss is even less. By introducing

a correction term based on an assumed emittance, it is possible to reduce

the uncertainty in the measured property (heat capacity) due to the heat

loss correction to about 0.1 percent or less. As it was mentioned

34
earlier, the major source of temperature nonuniformlties in the specimen

is likely to be the hot channels or zones that result from material

inhomogeneities or geometrical nonuniformities . These are likely to be

pronounced in the case of IK^ specimens in contrast to metallic

specimens. A major contributing factor to this is the positive coefficient of the electrical conductivity of IK^. This means that as a

hot zone is developed in the specimen the likely trend will be the

amplification of this zone in terms of temperature with increasing

time (as long as electrical current flows through the specimen)

causing nonuniform heating similar to that causes breakdown of

dielectric materials in high electrical fields. Thus, it is of

utmost importance to have specimens with compositional homogeneity and

geometrical uniformity.

Evaporation ; The vapor pressure of UC^ is about 5 kPa (^.05 atm.

)

at 3000 K, and based on an extrapolation of the low temperature data it

is estimated to be of the order of 10 MPa (^100 atm.) at 6000 K [13],

Because of the high vapor pressure, it will be necessary to perform the

experiments with the specimen in a pressurized environment. An inext

gas, such as argon or helium, may be used. Based on the assumption

that the ambient pressure must be at least about 15 times the vapor

pressure of the specimen at any given temperature, it may be possible

to conduct experiments at about 0.1 MPa (^1 atm.) pressure near the

melting point of However, the pressure may have to be increased

with increasing temperature: 5 MPa (%50 atm.) at 4000 K, 50 MPa

35
(^500 atm.) at 5000 K and 150 MP a (^1500 atm.) at 6000 K. External

pressure will reduce the evaporation and thus will confine the vapor to

a thin boundary layer. Under these conditions, it is likely that

the boundary layer will be transparent enough not to interfere with

the optical temperature measurements. Under the above conditions,

heat loss due to evaporation will be negligibly small, less than 1

-2

J»cm . The evaporative cooling effect on the specimen surface may

be of the order of a few degrees.

Ionization, Thermionic Emission and Electrical Breakdown ; Since

the effects of these are interrelated they are discussed together.

Electrical breakdown in gases may be of the order of 20 to 30 kV«cm ^

at normal temperature and pressure. Since breakdown voltage

increases with gas pressure, voltage breakdown may not be a serious

consideration by itself provided that there is no gas ionization or

thermionic emission. If the UO^ specimen has to be preheated to about

1500 K before pulsing it to higher temperatures, the preheating

may present a serious problem if gas ionization or thermionic emission

gives an electrical conductivity in the gas sufficient to cause

shunting of an appreciable current around the specimen. Experimental

work in connection with exploding conductor research and thermal

measurements on metallic specimens has not indicated any electrical

breakdown in gases surrounding the specimen up to about 8000 K

when the gas pressure is high. However, because of lack of data on

U0„ at temperatures above its melting point, it is not possible to

36
predict the effect of thermionic emission and other related effects on

voltage breakdown in the gas surrounding the specimen. Pulse heating

of UC>2 will require much higher electric fields than that required

for metals because of the high electrical resistivity of UO^ relative

to that of metals.

5.3. Measurements on UC^

Measurements of the electrical quantities (current through the

specimen and potential across the specimen) are, to a large extent,

independent of the specimen material. The measurement techniques were

summarized in Section 4.1. From the accuracy point of view, it is

desirable to have the separation between the potential probes as large

as possible, however, considerations due to resistance, energy and

pressure are likely to restrict the length of the UC^ specimens to

1 to 2 cm. It is estimated that current can be measured with an

inaccuracy of about 2 percent and potential across the specimen with an

inaccuracy of about 3 percent. This means that the inaccuracy of power

measurements is likely to be within 5 percent if gas conduction is

small.

Measurements of the specimen temperature depend extensively on

the specimen and its reaction with its environment. Some of the

problems that arise from this were discussed in Section 5.2 for UO^.

From instrumentation point of view, studies have demonstrated the

feasibility of constructing a pyrometer capable of performing temperature

37
measurements in the range 2500 to 6000 K once or twice every microsecond.

The pyrometer will have two independent optical channels in order to

perform radiance measurements at two wavelengths. This scheme will

yield the specimen temperature from the measurements of two radiance

temperatures at the two wavelengths. Based on the detector (solidstate) characteristics, it seems that it is advantageous to select

the wavelengths from the range 500 to 1000 nm. The effective bandwidth of the interference filters may be in the range 10 to 40 nm.

The inaccuracy in temperature measurements contributed by the

pyrometer operation alone is estimated to be about 1 percent. About

the same level of uncertainty is likely to be introduced in the

interpretation of measured temperatures up to about 4000 K increasing

to twice that at 6000 K. Thus, it may be possible to measure

specimen temperature with an inaccuracy of about 2 percent in the

range 2500 to 4000 K increasing to about 3 percent at 6000 K.

Techniques for recording experimental quantities were discussed

in Section 4.4. It may be summarized by saying that it is within the

state-of-the-art to construct a high-speed digital data acquisition

system capable of digitally recording a set of several quantities

simultaneously every 0.5 us with a full-scale signal resolution of

about 0.1 percent under optimum conditions, but may be considerably

worse when large nonlinear variations in the signals occur.

38
It is of importance to consider protecting the measuring and

recording instruments from high electro-magnetic fields resulting

from the capacitor discharges. Proper shielding will reduce the interference of the fields on the measuring instruments and the signals.

From the measurements of current, voltage and temperature as a

function of time during the rapid heating period it is possible to

determine heat capacity as a function of temperature using the equation:

n 3t

where, e and i are voltage and current respectively, n is the amount

of specimen, dT/dt is the heating rate, and q is the rate of total energy

loss from the specimen. The quantity q is usually small (not more

than a few percent of imparted power) in submillisecond experiments

and depending on its magnitude, either it may be neglected or accounted

for by estimating the pertinent parameters. As a by-product of

these experiments it is possible to obtain the electrical resistivity

of the specimen.

It may be much more difficult to determine experimentally the

vapor pressure of UO^ up to 6000 K. Because of the high vapor

pressure at temperatures above 3000 K, the Langmuir method and the

atomic (molecular) absorption technique cannot be used. One possible

approach may be based on conducting a series of experiments with the

specimen in an inert gas environment at different static pressures.

39
The observation (by optical and/or electrical means) of the start of

boiling and its correlation with temperature may yield vapor pressure.

In the case of UC^ this corresponds to static pressures in the approximate

range 0.01 to 10 MPa (M3.1 to 100 atm.) to cover the range from the

melting point to 6000 K. Superheating of the liquid may occur before

the boiling becomes detectable. Optical absorption by the vapor also

may prevent measurement of radiation from the liquid surface and

therefore may prevent the measurement of specimen temperature. The

performance of preliminary experiments is essential in order to

assess the applicability of this technique to vapor pressure measurements of U0o .

40
6 . Summary and Conclusions

The design of a system for thermal measurements in submillisecond

duration experiments at high temperatures (2000 to 6000 K) on semiconducting materials is subject to considerations of various phenomena

characteristic of high voltage-high current discharges, high temperatures, and short experimental and measurement times. Item-by-item

consideration of the various phenomena does indicate the presence of

some surmountable problems. However, because of conflicting requirements, their combination may present some serious difficulties.

For the convenience of discussions, the measurement system may be

divided into three parts: (a) the discharge and associated control

equipment, (b) the specimen and the experiment chamber, and (c) the

measuring and recording equipment.

The electrical circuitry for the high-voltage capacitor discharge

system does not present any serious problems since it is likely that

a 20 kV capacitor bank will be sufficient for this purpose and the

techniques for constructing and operating such a circuit are available.

The experiment chamber including the specimen does present some

serious problems that stem from the combination of high voltages, high

pressures, and high temperatures. The high vapor pressure of UO^

at high temperatures necessitates the pressurization of the chamber

to reduce evaporation. Such high pressures restrict the size of the

working volume which, in turn, may create problems in relation to

preheating the specimen. The high voltages required for pulse heating

Al
the specimen may cause additional complications from electrical

insulation point of view. However, systems have been constructed and

operated under high pressure-high voltage conditions for rapid pulse

heating (microsecond resolution) of good conductors (at room temperature) to temperatures over 6000 K. Preheating of UO^ specimens

to about 1500 K has been performed in experiments in which slow

pulse heating (millisecond resolution) was used to heat the specimens

up to about 3000 K. Faster heating requires higher voltages. Nevertheless, in spite of all the difficulties, it may be possible to construct an experiment chamber for performing rapid pulse heating

experiments at high temperatures. Because of the high positive

coefficient of the electrical conductivity of UO^, compositional

inhomogeneties of geometrical nonuniformities are likely to create

large temperature gradients and thermal breakdown in the specimen.

However, by careful preparation of the specimens their effect may be

minimized.

The measuring equipment and the techniques which include current,

voltage, pressure, temperature, and other optical measurements with

microsecond resolution are only partially developed. Temperature

measurement is the most difficult one. Based on the available information, it seems likely that a pyrometer with microsecond resolution

can be constructed for radiance temperature measurements at two wavelengths. Recording of experimental quantities can be made using

oscilloscope-camera combinations, or for somewhat better accuracy and

42
convenience, digital recording techniques can be utilized. It is

within the state-of-the-art to construct a digital data acquisition

system for recording several quantities every 0.5 us with a fullscale signal resolution in the range 0.1 to 0.5 percent. It is

estimated that electrical power measurements can be made with an

Inaccuracy of about 5 percent and temperature measurements with an

inaccuracy of 2 to 3 percent. The resultant measurements are likely to

yield heat capacity with an inaccuracy of about 7 percent at 3000 K

increasing to about 10 percent at 6000 K. The inaccuracy of vapor

pressure measurements is likely to be considerably higher, however,

no specific estimation is possible at this time.

Based on the discussions in this report, it may be concluded that

the capacitor discharge circuitry and the measurement of the experimental

quantities, although difficult, are not likely to present major problems. The major experimental problems will primarily stem from the

experiment chamber and the specimen. The combined contributions

of some of the problems are difficult to estimate and therefore, some

preliminary experiments need to be performed to assess the applicability

of the submillisecond-duration heating techniques to measurements on

U02# The preliminary experiments should yield information on:

(a) the mechanical stability of the specimen (in the solid and

especially in the liquid phase) under high electromagnetic fields;

i (b) specimen integrity under rapid heating conditions which

includes the effects of thermal breakdown, thermal shock, disintegration that may result from rapid discharges through the specimen;
(c) level of evaporation and its effect on optical and electrical

measurements;

(d) the effect of specimen preheating furnace on gas ionization

and high voltage breakdown.

If a method can be found to heat the specimen to and through the

melting phase change at moderate pressures, then it may be possible

to increase the pressure sufficiently to achieve satisfactory results

in the liquid range up to 6000 K.

Positive results from the above preliminary experiments in conjunction with the development of electrical pulse power and temperature

measuring equipment will suggest the feasibility of conducting thermodynamic measurements on IK^ up to 6000 K utilizing submillisecondduration resistive self-heating techniques.

44
7. References

Chase, W. G. and Moore, H. K. , eds., "Exploding Wires", Plenum,

New York, Vol. I (1959), Vol. II (1962), Vol. Ill (1964),

Vol. IV (1968).

Lebedev, S. V., "The possibility of using the electrical explosion

of wires for investigation of metals at high temperatures", High

Temperature, 6_, 150 (1958).

Dikhter, I. Ya. and Lebedev, S. V., "Measurement of the specific

heat and the heat of fusion of tungsten at high temperatures by

the wire explosion technique", High Temp. -High Pres., 2^,

55 (1970).

Henry, K. W. , "A technique for measuring equilibrium thermodynamic

states of liquid metals at high temperatures and pressures",

Rev. Sci. Instr., 4j3, 1777 (1972).

Martynyuk, M. M. and Karimkhodzhaev, I., "Estimation of critical

temperatures of metals by the exploding wire method", Russ. J.

Phys. Chem. , 48, 722 (1974).

Gathers, G. R. , Shaner, J. W. , and Young, D. A., "Experimental

very high temperature liquid uranium equation of state", Lawrence

Livermore Laboratory Preprint 75668 (1974).

Martynyuk, M. M., Karimkhodzhaev, I., and Tsapkov, V. I.,

"Resistance and enthalpy of refractory exploding wires",

Sov. Phys. Tech. Phys., 19, 1458 (1975).

45
[8] Grover, F. W. , "Inductance Calculations", Van Nostrand, New York,

1946, p. 266.

[9] Cobine, J. D. , "Gaseous Conductors", McGraw-Hill, New York, 1941.

[10] Thermodynamic and Transport Properties of Uranium Dioxide and

Related Phases, Int. Atomic Energy Agency, Vienna, 1965.

[11] Iida, S. , "Electrical Properties of Non-Stoichiometric Uranium

Dioxide", Jap. J. Appl. Phys., 4_, 833 (1965).

[12] Bates, J. L., Hinman, C. A., and Kawada, T., "Electrical

Conductivity of Uranium Dioxide", J. Am. Cer. Soc, 50, 652 (1967).

[13] Chasanov, M. G., Leibowitz, L., and Gabelnick, S. D., "High

Temperature Properties of Fast Reactor Materials", J. Nuc. Mat.,

49, 129 (1973-1974).

[14] Hein, R. A., Flagella, P. N., and Conway, J. B., "High-Temperature

Enthalpy and Heat of Fusion of UO " , J. Am. Ceram. Soc, 51 ,

291 (1968).

USCOMM-NBS-DC 46
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U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLK ATI ON OR REPORT NO. 75-793

2. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Microsecond-Resolution Pulse Calorimetry for Semiconducting

Materials at High Temperatures (A Feasibility Study)

5. Publication Date

6. Performing Organization Code

7. AUTHOR(S)

A. Cezairliyan and C. W. Beckett

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project /Task /Work Unit No. 316141C

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Argonne National Laboratory

Argonne, IL

13. Type of Report & Period Covered

Interim

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

A feasibility study is conducted for the applicability of microsecond-resolution pulse

heating techniques to the measurement of selected thermodynamic properties of semiconducting substances at high temperatures. The method of pulse heating of the specimei}i

using capacitor discharges is described and general design considerations, including

electrical circuitry and various physical, electrical and chemical phenomena, are presented. Measurements of experimental quantities, such as current, voltage,

temperature and pressure are described. The special problems in relation to measurements of heat capacity and vapor pressure of uranium dioxide in the

temperature range 2000 to 6000 K are discussed. It is concluded that the capacitor

discharge circuitry and the measurement of the experimental quantities, although

difficult, are not likely to present major problems. However, problems are likely

to stem from the experiment chamber and the specimen. The nature of these problems

are discussed, and the performance of some preliminary experiments are suggested.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons) Capacitor discharges; heat capacity; high-speed measurements;

high temperature; thermodynamics; uranium dioxide.

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