NBS

PUBUCATIONS

NBSIR 80-2082

NATL INST. OF STAND & TECH R.I.C.

A111D5 1S7TS^

I NBS: Materials Measurements

J. R. Manning

National Bureau of Standards

U.S. Department of Commerce

Washington, D.C. 20234

Phone: (301)921-3354

July 1980

Annual Report

For the Period 2 April 1979 - 1 April 1980

NASA Government Order H-27954B

Properties of Electronic Materials

U56

80-2082

1980

J.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

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NBSIR 80-2082

• •• NBS: MATERIALS MEASUREMENTS

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J. R. Manning

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National Bureau of Standards

U.S. Department of Commerce

Washington, D.C. 20234

Phone; (301)921-3354

July 1980

Annual Report

For the Period 2 April 1979 - 1 April 1980

NASA Government Order H-27954B

Properties of Electronic Materials

U.S. DEPARTMENT OF COMMERCE, Philip M. Klutznick, Secretary

Luther H. Hodges. Jr.. Deputy Secretary

Jordan J. Baruch. Assistant Secretary for Productivity. Technology, and Innovation

NATIONAL BUREAU OF STANDARDS. Ernest Ambler. Director
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TABLE OF CONTENTS

Page

Summary 1-2

Task 1 - SURFACE TENSIONS AND THEIR VARIATIONS WITH TEMPERATURE

AND IMPURITIES by

S. C. Hardy and J. Fine 3-36

Task 2 - SOLUTAL CONVECTION DURING DIRECTIONAL SOLIDIFICATION by

W. J. Boettinger, S. R. Coriell and F. S. Biancaniello

,

and M. R. Cordes 37-76

Task 3 - A THERMOCHEMICAL STUDY OF CORROSIVE REACTIONS IN OXIDE

MATERIALS by

H. S. Parker 77-87

Task 4 - THERMODYNAMIC PROPERTIES OF REFRACTORY MATERIALS AT

HIGH TEMPERATURES by

J. H. Colwell 88-113

i

National Bureau of Standards

Materials Measurements

Summary

This report describes NBS work for NASA in support of NASA's Materials

Processing in Space Program under NASA Government Order H-27954B (Properties

of Electronic Materials) covering the period April 2, 1979. to April 1, 1980.

The work emphasizes materials measurements and has two main thrusts:

1) Carrying out precision measurements in space and investigating the

feasibility of improved measurements when the space environment offers a

unique opportunity for performing such measurements. These measurements

would be useful for either space processing or processes on the ground.

2) Obtaining precision measurements on materials properties when these

properties are important to the design and interpretation of space processing

experiments. These measurements would be carried out either in apace or on

the ground.

This work has been carried out in four tasks. These tasks have, as two

of their focal points, the role of convection effects and the role of container

effects, both of which would differ in space-based experiments from those

found in ground-based experiments. The results obtained for each task are

given in detailed summaries in the body of the report. Briefly, in Task 1 -

Surface Tensions and Their Variations with Temperature and Impurities -

/ measurements in an Auger spectrometer of surface impurity concentrations on

liquid gallium showed that the principal impurities were oxygen and carbon.

The impurities showed a tendency to collect into plates or clumps. Heating

in hydrogen atmospheres and ion sputtering were both found to be effective

methods of removing impurities. When these methods of removing impurities

were applied, reproducible surface tension (y) values at room temperature

1
2

were found with y

- 710 mj/m . The surface tension decreased quadratically

2 with increasing temperature to y

- 690 mJ/m at 500 °C. In Task 2 - Solutal

Convection During Directional Solidification - in Pb-rich Pb-Sn off-eutectic

alloys, macro segregation caused by solutal convection was not reduced by

vertical or horizontal fields of O.IT, but downward solidification (liquid

below solid) virtually eliminated macro segregation in small ('^ 3 mm) diameter

samples. Calculations were made to predict the onset of convective and

interfacial instabilities during directional solidification of lead-tin

alloys including effects of variations in gravitational acceleration and

Prandtl number. Results obtained in calculations with a constant gravitational

acceleration of 10 ^ g^ show a noticeably larger stability range than those

—4 — 6

for 10 g^; at 10 g^ the instabilities will develop more slowly with time.

In Task 3 - A Thermochemical Study of Corrosive Reactions in Oxide Materials -

phase assemblages of selected compositions on the joins ^LPe^ ^Si^ 0^

-

SiO^ and KFe02 - Si02 were determined over a large range of oxygen partial

pressures and the temperature range 800 °C to 1400 °C. In melts containing

ferrous ions, excessive reaction with platinum containers occurred. In Task

4 - Thermodynamic Properties of Refractory Materials at High Temperatures -

use of pyroelectric detectors to determine the radiant heat loss from

spherical samples as cooling occurs in free-cooling experiments is being

investigated. The heat capacities and, under some conditions, the thermal

conductivities in leviatated high temperature materials can be derived from

simultaneous measurement of radiant heat loss and rate of temperature change.

Details of the thermal gradients to be expected in both metallic and nonmetallic samples have been examined. Limitations from sample vaporization

-4

will occur when the vapor pressure reaches the vicinity of 10 Pa (10 atm)

.

2
Task 1

Surface Tensions and Their Variations

with Temperature and Impurities

S. C. Hardy

Metallurgy Division

Center for Materials Science

and

J. Fine

Surface Science Division

Center for Thermodynamics and Molecular Science

Summary

The surface tension of gallium has been measured as a function of temperature in vacuum and hydrogen atmospheres using cups of quartz and graphite

to contain the sessile drops. The results are generally in good agreement

with two previous measurements and show that the surface tension decrease is

nearly quadratic in temperature. A non-linear least squares analysis gave

the following function as the best fit to the data:

Y

= 709.9 + .0016 (T-29.87) -.0000923 (T-29.37)^.

Measurements in vacuum using quartz cups, however, have revealed a complex

heating history dependence which we think is due to an oxide contamination of

the gallium by the quartz.

In related work the surfaces of liquid gallium sessile drops have been

studied in an Auger spectrometer to determine the concentration of impurities.

The gallium surface after formation of the drop was found to be covered with

a solid layer containing a high concentration of oxygen and carbon. Prolonged

heating to several hundred degrees effectively desorbed the oxygen but the

carbon was still present in the form of a precipitate. The conditions under

3
which these precipitates form is not understood. The surfaces were also

cleaned by sputtering with argon ions and complex flow phenomena observed.

The surface tension at the melting point of a drop with a sputtered clean

surface was in fair agreement with the results of the sessile drop measurements.

4
Introduction

Studies of liquid gallium surfaces have proceeded along two lines in

the past year. Extensive surface tension measurements have been made using

the apparatus and techniques described in last year’s report. In addition,

we have attempted to characterize the surface composition of liquid gallium

in an Auger spectrometer. These latter experiments have revealed complex

impurity phenomena which we do not fully understand.

The central problem in determining the surface tension of liquids is

to produce a clean surface. Segregation of impurities at the liquid-vapor

interface will drastically alter the surface tension as described by the

Gibb’s equation. This sensitivity to surface active impurities is probably

the basic cause for the wide discrepancies in reported surface tension

values. A related problem is that there is almost no independent characterization of the chemical composition at the interface with a surface tension

measurement. It is assumed that the procedures and materials used have

produced a clean surface, the cleanest surface being ascribed to the one

with the highest surface tension, i.e. , the one with the least surface

segregation. An independent characterization of the surface by some

direct technique would be extremely valuable in the interpretation of

surface tension measurements, particularly in cases where there is a wide

discrepancy in the results. The Auger work was undertaken primarily to

address this problem.

Oxygen is probably the most troublesome surface contaminant for most

metals; galliiam, which is chemically similar to aluminum, is particularly

subject to the formation of stable surface oxides. These may be either

5
Ga.^ or 0032©^^^^ . There are four additional modifications of the trioxide

which are formed only under unusual conditions. Several approaches are

available which one hopes might succeed in producing a gallium surface free

of oxide. Our samples are prepared in a syringe under, alcohol containing

V' X HCl which dissolves gallium oxides. The gallium is squeezed out into a

shallow cup to form the sessile drop under an atmosphere of flowing nitrogen

or helium. Although gross oxides are removed by the acid, a thin oxide

film undoubtedly remains after this procedure. Observations supporting

this will be discussed later in connection with the Auger work. Once the

sessile drop is formed in the vacuum system, it may be cleaned further by

heating. This desorbs weakly bound gases and, at around 500 ®C, decomposes

the trioxide to the suboxide according to the following reaction:

Ga^O^ + 4Ga ^ 3Ga20

The suboxide has a high vapor pressure and is deposited on the walls of the

vacuum system. This reaction, however, does not go to completion as shown

by x-ray diffraction measurements . Alternatively, the surface oxide can

be reduced by heating in hydrogen by the following reactions:

Ga202 + 2H2 ^ Ga20 + 2H

2

O

Ga20 + H

2 ^ 2Ga + H2

O

We have used both of these approaches in attempts to produce clean surfaces.

A third possibility for cleaning the surface is ionic sputtering. We will

discuss this technique in connection with our Auger work. This alternative

is very attractive because it can be carried out at low temperatures, thus

minimizing the diffusion of gases and other impurities from the cup into

6
the gallium and any reaction of the gallium with the cup or residual gases.

A detailed discussion of the apparatus and techniques used in this

[ 2 ] work is contained in last year's report . Rather than repeat this, we

will simply note that the galliimi drops are contained in cups of various

materials in an ion pumped vacuum system capable of reaching the 10

torr range. The optics and film used in the measurements have a resolution

which permits the surface tension to be measured over the profile of the

drop with a precision of about 0.5% using the Bashforth and Adams technique.

This was verified last year with a computer program which fitted the entire

measured profile to calculated solutions of the Young-Laplace equation.

Thus we have some confidence in the measurements themselves. Additional

experimental details will be given when necessary with the presentation of

the data.

Surface Tension Measurements

The initial surface tension measurements used quartz cups to contain

the sessile drops. Fig. 1 reproduces data shown in last year’s report.

Although the surface tension appears to decrease linearly with temperature

above 120 ®C, there is a maximum in the curve at that temperature. This

kind of behavior is usually interpreted as evidence of impurity segregation

which builds up at low temperatures because desorption is too slow to keep

the surface clean. This seemed to be a reasonable explanation because

hours were required to cool the drop to this temperature range after the

initial high temperature bake, a time sufficient to adsorb many monolayers

of gas from the residual atmosphere of the vacuum system which was at a

_ - 8

pressure of 10 torr.

7
Analysis of subsequent measurements proved this adsorption explanation

to be wrong in that the impurity did not originate in the residual gases in

the vacuum system. When the drop was heated for twenty hours at 570 °C and

then cooled, the data shown as open circles were obtained. The lengthy heat

treatment enhanced the low temperature depression of the surface tension and

moved the maximum in the data to a higher temperature. An additional twenty

hour heat treatment lowered the surface tension even more dramatically as

shown by the open boxes. The vacuum level during these measurements was

—8

about 10 torr. In subsequent experiments on other drops the entire vacuum

system was baked and the pressure was in the mid 10 torr range. Measurements at this lower pressure confirmed the behavior shown in Fig. 1,

suggesting the residual gases were not the adsorbed species.

This observation that the temperature and heating time control the

behavior at lower temperatures indicates a contamination of the sample by the

crucible at high temperatures. Although gallium is known to attack quartz at

[3] temperatures over 1000 °C , it was thought to be non-reactive at the

maximum temperatures used in our experiments. It is possible, however, that

the contamination does not come about from gallium dissolving the crucible

but rather from gases or other components of the crucible diffusing into the

gallium. Alternatively, the silica glass tube forming the vacuum jacket

could release gases during bakeout which react at the gallium surface. A

likely candidate for this would be water which is the primary constitutent

[4] desorbed from quartz at 600 °C . Thus a possible reaction taking place

might be the following:

8
2Ga + H

2

O ^ Ga^O + H

2

Another possibility for contamination exists, however. Silicon contamination

of gallium in quartz containers has been studied in connection with the growth

[41 of GaAs^

Support for the oxide contamination hypothesis is shown in Fig. 2. This

sample was loaded into the cup as a solid under high vacuum conditions in an

attempt to avoid adsorbed gases at the quartz-gallium interface. The gallium

was frozen under alcohol in the form of a cylindrical ingot with a thin

rhenium wire along the axis. The rhenium wire was attached to iron slugs

which could be moved magnetically through the silica wall of the vacuum

system. With this solid loading technique, the cup could be baked at high

temperature and the gallium loaded into it without breaking vacuum and back

filling with an inert gas, a procedure which undoubtedly results in some

oxygen and water adsorption on the quartz cup. When this procedure was

followed and the gallium subsequently heated to 760 °C for twenty-four hours,

the surface tension varied with temperature as shown by the solid points in

Figure 2; a very strong surface tension depression at low temperatures with a

maximum at about 300 °C. This behavior resembles that shown in Fig. 1.

Hydrogen gas was then admitted to the tube through a liquid nitrogen cooled

trap to about atmospheric pressure. When the gallium was heated to 550 °C for

30 minutes, the surface tension at low temperatures increased dramatically and

effectively removed the maximum in the curve. These data are shown as open

circles in Fig. 2 and suggest that an oxide at the surface is being reduced by

heating in hydrogen, the second cleaning procedure mentioned in the Introduction.

9
The surface oxides in this experiment may not have been identical to

those formed with the drop of Fig. 1 because of the different procedures

used to form the sessile drop. There was probably a heavy oxide layer

present when the gallium was loaded as a solid because the ingot was

exposed to air during transfer to the vacuum system. Larger surface

tension depressions were found at low temperature in this case than when

the liquid loading procedure was used. This high concentration of oxide

may have led to silicon contamination of the gallium by dissolving the

quartz during the extensive high temperature bake.

A third experiment was performed in the quartz cup. Prior to forming

the sessile drop the system was evacuated and the cup and adjacent tube

baked at 900 ®C for eighteen hours in an attempt to thoroughly eliminate

water. The gallium was then added to the cup as a liquid and the system

_8 evacuated to the 10 torr range. After heating the gallium to about

100 °C to desorb weakly bound gases, hydrogen was admitted to the tube

through a copper coil immersed in liquid N

2

* Heating to progressively

higher temperatures for periods of about 30 minutes and then cooling to the

melting point and measuring the surface tension established that significant

cleaning of the surface occurred at temperatures as low as 316 ®C. After

30 minutes at 460 °C, the low temperature depression of the surface tension

was found below 50 °C and was so slight it could not positively be separated

2

from measurement imprecision, i.e. , it was about 7 mJ/m , which is 1% of

the surface tension. The gallium was then heated to 550 °C for fifteen

minutes and photographed. The surface tension was measured after equilibration

10
at a number of lower temperatures. These data are shown as filled circles

in Fig. 3. We also show as filled squares the results obtained after

heating to 600 °C for eighteen hours. This hotter and longer heat treatment

seems to have raised the surface tension at the melting point, but the

2

change is only 2 mj/m , well within the normal measurement imprecision. The

general agreement of the two sets of data is good. '

We see, therefore, that prolonged heating in hydrogen with the

quartz cup seems to have little effect on the surface tension at lower

temperatures in contrast to the behavior in the vacuum experiments typified

in Fig. 1. Moreover, the surface tension now varies monotonically with

temperature; there is no identifiable relative maximum in the data. The

temperature variation, however, does not seem to be linear. The departure

from linearity could be caused by impurities in the hydrogen gas being

adsorbed at low temperatures. An increase in surface tension of 1% to about

2

718 mJ/m at the melting point would effectively linearize the data.

After the measurements described above, the system was evacuated. When

—8

the pressure had dropped to the high 10 torr range, the gallium was heated

for about 15 hours at 550 °C. A subsequent measurement of surface tension

as a function of temperature produced the data plotted as open triangles in

Fig. 3. The surface tension has been reduced significantly, but the

variation with temperature is still monotonic. This is quite different from

the results cited earlier and illustrated in Fig. 1. It is not clear

whether the change has been brought about by the extended high temperature

treatment prior to forming the drop or by initially heating in hydrogen

rather than vacuum. The results using quartz cups seem to be very

dependent on the history of the sample; i.e., the atmosphere and previous

11
heat treatment. Although the results in hydrogen are encouraging, the

depression of surface tension with heating in vacuum indicates a container

reaction which raises questions about the sample purity in all of the

experiments. Presumably the contaminant is ..an oxide which is reduced by

the hydrogen, but there may be an associated silicon contaminant also

playing a role.

The ambiguous results with quartz led us to try a number of other cup

materials. Sessile drop experiments were pexformed in cups of alumina,

boron nitride, and two types of graphite. Jor the most part these materials

were inferior to the quartz. Cups of high purity, pyrolitic graphite,

however, gave more reproducible and consistent results than the other

materials. A series of measurements were made under a variety of conditions

in one of these graphite cups in an attempt to see if the surface tension

changed systematically with heat treatment and atmosphere. To eliminate

considerations of changing drop sizes and cup orientations or uncontrollable

differences in the -gallium introduced during preparation, all of the data

we will show have been taken with the same drop. These results, however,

are reproducible from drop to drop.

After the drop was formed using the liquid loading technique, the

system pressure quickly reached the low 10 ^ torr region. The drop was

heated overnight to about 85 ®C to desorb weakly attached gases. The

2

surface tension was under 600 mJ/m at this temperature afterwards indicating no significant cleaning of the surface had occurred. The temperature

was then raised to 185 °C for two hours, the pressure in the system being

about 10 ^ torr. When the drop was cooled to the melting point, the surface

12
2

tension was measured , to be 696 mJ/m indicating a substantial cleaning of

the surface had been achieved. Subsequent heating for short periods to

progressively higher temperatures slightly increased the melting point

surface tension. Fig. 4 shows that the temperature variation of the

surface tension after heating to 465 °C is approximately linear with no

evidence of a maximum. The vacuum level during these measurements was

—8

about 2 X 10 torr. Subsequently the drop was heated to 565 °C for

eighteen hours with the results shown in Fig. 5. These results do not

differ significantly from those shown in Fig. 4. The important fact is

that the measured surface tension has not been changed with a prolonged

high temperature bake, in contrast to the results with quartz cups in

similar vacuums.

After these measurements hydrogen was admitted to the vacuum system in

the normal manner and the temperature was raised briefly to 550 °C. This

produced no significant changes from the data of Fig. 5. An overnight

heating to 600 °C produced the results shown in Fig. 6. Again, there does

not seem to be any significant change from the results in vacuum shown in

Fig. 5.

A direct comparison of the data obtained after prolonged high temperature

heating with graphite cups in vacuum and hydrogen and with quartz cups in

hydrogen is made in Fig. 7. We have simply plotted the data shown in Figs.

3, 5, and 6 on one graph; no adjustment or normalization has been used. As

is evident, the measurements are in agreement and suggest that the surface

tension of gallium does not vary linearly with temperature. A least squares

non-linear fit to an equation of the form

13
Y = a - b (T-29.87) - c (T-29.87)^

gave final parameter estimates of

a = 709.92 (.57)

b = -.160275 X lO"^ (.5311 x lO"^)

c = .923122 X lO""^ (.9474 x 10“^)

where the numbers in parentheses are the approximate standard deviations. For

b the standard deviation is larger than the estimate of the parameter indicating

that this coefficient is negligible. Thus, the dependence is essentially

quadratic

.

The general agreement of the vacuum and hydrogen measurements in graphite

with the hydrogen measurements in quartz reinforces our feeling that gallium

picks up an oxide impurity when it is heated to high temperature in quartz.

This oxide presumably is effectively reduced in hydrogen but in vacuum it

segregates at the surface and depresses the surface tension at low temperatures.

A superposition of Fig. 1 on Fig. 7, however, reveals an additional complication.

Although the high temperature data of Figs. 1 and 7 superpose nicely, at and

below 200 °C, the surface tension in the quartz cup in vacuum rises above the

data of Fig. 7. The maximum of Fig. 1 which occurs at about 150 °C is about 6

2 mj/m higher than the curve of Fig. 7. This is not a large discrepancy but a

reexamination of the original data indicates that it is real. It may result

from the fact that gallium oxides seem to form in patches rather than in a

uniform surface layer. Thus, it is possible that the surface is no longer

strictly described by the Young-Laplace equation and the Bashforth and Adams

analysis is invalid.

14
Auger Spectrometer Experiments

As mentioned previously, the lack of any independent characterization of

the surface is a serious problem in surface tension measurements. A number of

modern surface analysis techniques are available which. might fill this need,

but they have been applied infrequently to liquids. The high vapor pressure

of most liquids, of course, reduces the range of materials which can be studied.

Nevertheless, the complementary use of these techniques with surface tension

measurements seems feasible for some liquids and such studies are being

attempted by several groups.

Liquid gallium is compatible with high vacuum instruments because of its

low vapor pressure and melting point. It melts near 30 “C and the vapor

—6

pressure is about 10 torr at 700 °C so that a large temperature range is

usable. We have been studying liquid and solid gallium in an Auger spectrometer.

Our specimens are in the form of sessile drops and are contained in cups of

graphite or rhenium which can be heated to over 500 °C and cooled to low

temperatures. The drops are formed using the liquid loading technique described

previously. The geometry of the spectrometer is not ideal for these measurements

because the drops must be positioned well off the axis of the bell jar in

order to be within working range of the horizontal cylindrical mirror analyzer.

This makes simultaneous Auger analysis of the surface and photography of the

drop profile impossible. Furthermore, the cup cannot be precisely aligned

with the horizontal. Thus surface tension measurements in the present spectrometer are less accurate than those we have been discussing.

Although the surface of the drop during Auger analysis is difficult to

observe visually, a video image can be obtained by a technique similar to that

15
used in scanning electron microscopy (SEM) . A primary electron beam is

rastered over the surface of the specimen and the local change in secondary

electron emission is used to intensity modulate a video monitor in synchronization

with the two-dimensional position of the electron beam. This imaging mechanism

reveals surface features which are difficult to see optically. Although the

video images do not have high contrast or resolution, they provide valuable

information about the surface. Furthermore, the video imaging permits the

sample orientation to be adjusted so that selected regions may be analysed

with the Auger spectrometer. The instrument is equipped with an ion gun and

a gas handling system so that the sample surface can be sputtered. In

addition, a quadrupole mass spectrometer permits residual gas analysis. The

pumping is provided by liquid nitrogen cooled sorption pumps and ion pumps

so that the system is oil free.

After forming the sessile drop in the cup and evacuating the system to

-9

the low 10 torr region, an Auger spectrum of the surface has intense

oxygen and carbon lines as seen in Fig. 8. Although the video image of the

drop is uniform and featureless as would be expected of a liquid, the

surface is actually solid. If the electron gun is left on for a number of

hours, a dark rectangular spot develops where the beam has been rastered

over the surface which persists unchanged and stationary after the beam is

turned off. The amplitude of the Auger lines vary differently over this

dark region, oxygen decreasing and carbon increasing as the beam is moved

from the center of the raster area to an unbombarded area. This does not

necessarily mean that the concentration of these constitutents is varying in

the same way because the Auger line intensities of different elements are

interrelated.

16
The loading technique, therefore, produces a sessile drop with a solid

oxide surface layer containing significant concentrations of carbon. Our

experience with the surface tension measurements suggested this layer might

be decomposed and desorbed by heating to a moderate temperature. The effect

of heat treatment on the gallium surface was examined by heating the drop

briefly to progressively higher temperatures, then cooling and taking Auger

spectra. After heating to 250 °C for five minutes, the oxygen line was

halved and the carbon line was also reduced somewhat. However, the surface

was no longer uniform and featureless. A "white" streak (as seen on the

video picture) developed which gave Auger lines for oxygen and carbon at

least twice the amplitude of the adjacent, featureless surface. Thus it

appears that the thermal decomposition and desorption of the surface layer

is not uniform, or that segregation and growth may occur during the heating

and cooling procedure. The surface of the drop after heating is, of course,

no longer solid and flows can develop. As the drop cools a phenomena is

seen which we do not yet fully understand. The drop surface is initially

featureless after heating to 400 °C. On cooling to about 120 °C, however,

small black spots appear near the apex of the drop and move down the side

collecting into a broad band on the surface above the cup edge. An Auger

spectrum of the deposit shows carbon but no noxygen. This process was

observed in both rhenium and graphite cups. The Auger spectra of areas of

the surface without precipitates have oxygen and carbon lines which have

diminished to the point at which they are indistinguishable from the noise.

Concurrently the gallium lines become more intense.

17
Other experiments have shown that heating to 200 °C for several hours

produces a surface which is clean except for the precipitates described

above. The surface of the precipitates remains clean for long periods; no

oxygen or carbon was detected after twenty-four hours at a pressure of 6 x

—8

10 torr. Exposure to the residual atmosphere for a number of days produced

a significant carbon line and a somewhat smaller oxygen line. This is to be

expected because CO is an important residual gas in the vacuum system

presumably because of the hot filaments in the ionization gauge.

In addition to carbon and oxygen the measurements in the vitreous

graphite cup found some precipitates with a high sulfur content. An Auger

analysis of the cup wall also found some sulfur. We suspect that the

sulfur was introduced in a grinding procedure used on the cup during modification. A more stringent cup cleaning procedure eliminated or greatly

reduced sulfur indications in later experiments. Several precipitates on

one drop gave strong lead lines.

Another surface cleaning procedure we have tried is ionic sputtering.

Within ten seconds of the initiation of sputtering with 2.5 keV argon ions,

the uniform, solid surface film breaks up into large islands which move and

rotate about the bombardment area. These islands shrink in the ion beam and

eventually, when the surface is sufficiently clean, fluid flow develops

which brings small islands from the rest of the drop to the site of sputtering.

When the ion beam is turned off, the motion of the islands abruptly halts.

With continued sputtering, the niomber and size of the islands decreases.

Eventually the flow slows and stops with a few residual islands resting near

the cup edge below the ion beam impact area. An Auger spectrum of the surface

18
after sputtering for several hours is shown in Fig. 9. This is identical

to the result found after thenaal cleaning and shows no carbon or oxygen.

The same spectrum is obtained if the gallium is frozen and sputtered further.

Although there are other explanations for the processes seen on the

surface during sputtering, the generation of fluid flow by surface tension

gradients comes immediately to mind. In this model the sputtering produces

and maintains a clean area of high surface tension. If adjacent areas have

a lower surface tension because of adsorption, a high surface tension

gradient will exist about the periphery of the sputtering site. The

tangential shear stress generated on the liquid surface by the gradient

will set up a fluid flow on the surface which will be directed from the

area of low surface tension into the area of high surface tension, i.e.,

into the sputtering site. Presumably this becomes a convection node with

the surface flow entering the drop volume at that point. If the sputtering

is interrupted, the surface quickly equilibrates and the flow stops. As

the surface becomes cleaner, the gradient is reduced and the fluid flow

disappears.

A surface cleaned by sputtering will apparently stay clean for days

with no change in the Auger spectrxim or any additional island formation.

If, however, the gallium is heated briefly, on cooling a precipitation

process occurs which is similar to the one described previously. Small

dark islands appear and descend from the apex of the drop piling up in a

belt of precipitates at the base. An Auger spectrum of these precipitates

again shows a strong carbon line and no oxygen. Most of these precipitates

disappear under ion sputtering within a minute which indicates they are

19
very thin. Repeated sputtering and heating seems to reduce their numbers,

but it is not clear that they can be totally eliminated in this way.

Our understanding of these sputtering and precipitation phenomena is

limited with major questions to resolve about the origin and evolution of

carbon in the gallium. It does not seem likely that the carbon concentration

can be only that originally adsorbed on the surface, probably as CO^- We

suspect a continuing source of contamination which is logically the graphite

cup. Occasionally large and thick carbon islands have been seen which we

feel must have originated in the cup. Thus it is possible that the cup

surface is flaking off under repeated heating and cooling cycles. It does

seem that there was significantly less carbon with rhenium cups. However,

this work is very limited because the gallium drops tend to run out of

rhenium cups probably because of good wetting. Some carbon is certainly

due to long exposures to the residual gases in the vacuum system because it

is uniformly present on the surface and not associated with a precipitate,

at least before heating. It is possible that the sputtering does not

effectively remove carbon from the system but just disperses it into the

vo ..ame as very fine particles so that it is not seen. Heating then could

lead to agglomeration and reappearance at the surface because of buoyancy

and fluid flow.

As mentioned earlier we cannot make accurate surface tension measurements on the sessile drops in the Auger spectrometer because of geometric

and alignment problems. We have, however, measured the surface tension of

a drop which was sputtered for several hours and whose Auger spectrum

indicated a clean surface. In order to make the measurement, the drop was

repositioned in the Auger spectrometer after sputtering and analysis so

20
that its profile could be photographed in parallel light. The surface

2

tension was about 700 mj/m . Recognizing that this may be inaccurate, it

seems unlikely that the error could be more than a few percent. It seems

2

beyond possibility that the surface tension could be as high as 800 mJ/m ,

[ 2 ] the anomously high values found previously in two instances . A new

spectrometer is being assembled which will permit accurate surface tension

measurements and simultaneous Auger spectral analysis. We believe that it

will permit a resolution to this discrepancy in previous measurements.

Discussion

The experiments with gallium in the Auger spectrometer have shown the

primary surface impurities to be oxygen and carbon. A relatively low

temperature heating in vacuum can clean the surface of oxygen but the carbon

is either not effectively desorbed or is being resupplied, possibly from the

crucible. The carbon after heating is contained in thin plates which

collect on the drop surface near the cup edge. Thus the surface of the

drop, although clean for the most part, will have regions in which it is not

liquid. The entire drop shape in this case is not described precisely by

the Young-Laplace equation. Because the precipitates collect at the base,

however, the resultant distortion of the drop near the apex may be small.

Thus the surface tension values calculated by the Bashforth and Adams

technique above the drop maximum may not be seriously affected. Assuming

such a precipitation phenomenon is also occurring in our sessile drop

experiments, the fact that very nearly the same surface tension is calculated at various points on the drop in this region suggests the profile

is not severely perturbed. We do not know, of course, that precipitation

21
is occurring in the sessile drop experiments. The cups are different forms

of graphite from different sources in the two experiments; the Auger cup is

"vitreous” graphite and the sessile drop cup is high purity pyrolitic

graphite. Sessile drop measurements in a companion vitreous graphite cup

indicated some surface tension depression at low temperatures, but it is

difficult to compare the results because of variations in procedure in the

two groups of measurements. The approximate agreement at the melting point

of the surface tension values shown in Fig. 7 with that measured for a drop

that was sputtered clean in the Auger spectrometer is additional evidence

that the precipitates, if present, are not having much effect on the drop

shape.

The sessile drop surface tension measurements and the measurements and

observations in the Auger spectrometer demonstrate a strong sensitivity on

cup material and heating history. Certainly quartz cups used at high

temperatures in vacuum result in contamination of the gallium with what

seems to be an oxide because of the ease with which it is reduced in

hydrogen. The gallium may also be contaminated with silicon which has

little effect on surface tension values presumably because of low concentration or no tendency for surface segregation.

The surface contamination by the residual gases in the vacuum system

is much less significant than that originating in the cup. We have found

in the sessile drop experiments that surface tension values at the melting

—8 —7

point decline very slowly at vacuum levels of 10 to 10 torr. This is

also true in the hydrogen atmospheres. The Auger measurements support this

observation.

22
The general agreement of the surface tension values measured in

graphite cups in vacuum and hydrogen with the values found in quartz cups in

hydrogen is shown in Fig. 7. Although this is strong evidence the gallium

surfaces are in a similar state for these three groups of measurements, it

does not prove the surfaces are clean. The very limited measurements of

surface tension on the one drop in the Auger spectrometer, however, gave

surface tensions at the melting point which are only about 1% lower than

those shown in Fig. 7. Given the probable error in these measurements,

this is good agreement and suggests that the data of Fig. 7 are typical of a

clean surface.

There are, however, unanswered questions and unresolved contradictions

in the surface tension measurements. Fig. 1 is data taken in a quartz cup

which shows a low temperature surface tension depression which we have

interpreted as arising from surface segregation of an oxide contaminant. A

comparison of this data with the compilation of data from "clean” surfaces

in Fig. 7 shows a very good agreement at higher temperatures. However,

between 250 °C and the melting point, the surface tensions in the oxide

contaminated gallium of Fig. 1 rise above that for the clean gallium by as

2 much as 6 mj/m at the maximum. We, therefore, have a contradiction; if

surface segregation is producing the maximum in Fig. 1 by depressing the

surface tension at low temperatures, how can the surface tension of the

contaminated surface be higher than that of a clean surface? A possible

resolution would be that an impurity is also active in the data of Fig. 7

and the curvature evident at low temperatures is due to adsorption. This

impurity would necessarily be independent of cup material and atmosphere.

Another hypothesis is that the impurities in the "contaminated" gallium

23
are confined to patches so that the drop shape is not being described by

the Young-Laplace equation. We have no evidence supporting either of

these speculations.

As mentioned in last year's report, there have been three previous

measurements of the surface tension of gallium as a function of temperature.

The functions suggested by the authors to describe their data are as

follows:

= 708 - .0031(1-29.87) - .000067(1-29.87)^^^^

Yjj = 706.7 - .000647(1-29.87) - .0000965(1-29.87)^^^^

Yjjj = 718.0 - .101(1-29.87)

The non-linear least squares analysis of the data shown in Fig. 7 mentioned

previously gave the relationship

Y =709.9 + .0016(1-29.87) - .0000923(1-29.87)^.

Note that our results and those described by the first two relations above

2 differ at the melting point by no more than 3.2 mj/m . Since small systematic

errors must exist in all work, it is interesting to compare the various

measurements by making them all coincide at one temperature. We do this

in Fig. 10 where we have translated Yj and y^-j to agree with Fig. 7 at the

melting point. Our data is then seen to lie between the two curves over

the entire temperature range. The differences in the data adjusted in

this way is hardly more than the precision with which the measurements

were made in- our work except possibly at the high temperature end of the

curve.

We also show the linear relationship (unadjusted). These

measurements clearly disagree with the other data shown in Fig. 11. The

24
linearity of the surface tension values as a function of temperature in

this work was cited as evidence that the gallium was cleaner than that

used in the measurements showning non-linear behavior. However, at

temperatures above 125 °C, the surface tension values in the linear data

are lower than the non-linear data. At 360 °C, the highest temperature

2

used, they find a surface tension value about 15 mj/m lower than the

other results in Fig. 11. Thus it is hard to argue that the linear data

represents a cleaner surface. This is the same problem discussed previously

with respect to our own Fata and we cannot rationalize the contradiction.

We note, however, that the gallium preparation used in this work involved

heating to 1000 °C in a quartz ampoule. We suspect their gallium may have

been contaminated with silicon. We do not know how this would have affected

their surface tension values.

25
1 .

References

I. A. Sheka, I. S. Chans and T. T. Mityureav, The Chemistry of Gallium ,

Elsevier Publishing Co., New York, 1966.

2. S. C. Hardy and S. R. Coriell, Properties of Electronic Materials ,

NBSIR 79-1767, 1 (1979)

.

3. A. P. Thompson, Rare Metals Handbook, Second Edition, Edited by

Clifford A. Hampel (Chapman & Hall Ltd., London, 1958) p. 178.

4. L. Ekstrom and L. R. Weisberg, J. Electro Chem. Soc. 109 , 321 (1962).

5. 0. A. Timof eevicheva and P. P. Pugachevich, Dokl. A. Kad. Nan K. SSR,

134 , 840 (1960).

6. V. I. Nizhenko, L. P. Sklyarenko and B. N. Evemenko, Ukrain. Khin.

Zhur. 550 (1965).

7. k. k. Karashaev, S. N. Zadumkin and A. I. Kukhno, Russ. J. of Phys.

Chem. 329 (1967).

26
720

710

700

690

680

670

O

O

QUARTZ CUP

P« 10"® torr

- o A

A

A

o

o

o

o

o

o

100 300 500 700

TEMPERATURE (®C)

. 1. The surface tension of gallium as a function of temperature (quartz

cup; sample heated in vacuum).

27
720

710

700

690

680

670

QUARTZ CUP • 10'®torr

O HYDROGEN

O

O

2.

100 300 500 700

TEMPERATURE (®C)

The surface tension of gallium as a function of temperature (quartz

cup; sample heated initially in vacuum, then in hydrogen).

28
720

710

700

690

680

670

QUARTZ CUP

{

HYDROGEN

O 10"® torr

O O

O

O

#

O

100 300 500 700

TEMPERATURE («C)

-g. 3. The surface tension of gallium as a function of temperature (quartz

cup; sample heated initially in hydrogen, then in vacuum)

.

29
720

710

700

690

680

670

GRAPHITE CUP

10 ® torr

100 300 500 700

TEMPERATURE (®C)

Fig. 4. The surface tension of gallium as a function of temperature (graphite

cup; sample heated to 465 ®C for 30 min. in vacuum).

30
720

710

700

690

680

670

GRAPHITE CUP

lo"® torn

O

O

O

O

O

O

) 100 300 500 700

TEMPERATURE (®C)

ig . 5. The surface tension of gallium as a function of temperature (same

drop as Fig. 4; sample heated to 565 *C for 18 hours in vacuum).

31
720

710

700

690

680

670

GRAPHITE CUP

HYDROGEN

O

o

o

o

o

o

o

o

. -.tr • 100 300 500 700

TEMPERATURE (®C)

ig . 6. The surface tension of gallium as a function of temperature (same

drop as Fig. 4; heated to 600 *C for 18 hours in hydrogen).

32
SURFACE

TENSION

(mJ/m

M

720

710

700

690

680

670

^ - O ^

GRAPHITE CUP • HYDROGEN

O I0"8 torr

QUARTZ CUP

HYDROGEN

O

#

100 300 500 700

TEMPERATURE (®C)

Fig. 7. The surface tension of gallium as a function of temperature

(combination of Figs. 3, 5, and 6).

33
AUGER

SPECTRUM

OF

GALLIUM IIII

34

100

200

300

400 |

600

ENERGY

(eV)

Fig.

8.

The

Auger

electron

spectrum

of

an

uncleaned

Jic[uid

gallium

surface.
AUGER

SPECTRUM

OF

GALLIUM j1

35

100

200

300

400

500

600

ENERGY

(eV)

Fie

9.

The

Auger

electron

spectrum

ofa

liquid

gallium

surface

which

was

sputtered

with

2.5

keV

Argon

ions

for

several

hours.
720

710

700

690

680

670

100 300 500 700

TEMPERATURE (®C)

Fig. 10. Comparison of the surface tension of gallium as a function of

temperature found previously with this measurement.

36
Task 2

Solutal Convection During Directional Solidification

W. J. Boettinger, S. R. Coriell and F. S. Biancaniello

Metallurgy Division

Center for Materials Science

and

M. R. Cordes

Mathematical Analysis Division

Center for Applied Mathematics

Summary

The effect of solute gradient induced convection during vertical

solidification on the macrosegregation of Pb-rich Pb-Sn off-eutectic

alloys is determined experimentally as a function of composition and

growth rate. In many cases macrosegregation is sufficient to prevent the

plane front solidification of the alloy. The transition from dendritic to

composite structure is found to occur when the composition of the solid is

close enough to the eutectic composition to satisfy a stability criterion

based on G /V (liquid temperature gradient/growth rate). A vertical or

J_i horizontal magnetic field of O.IT (1 kilogauss) does not reduce macrosegregation, but downward solidification (liquid below solid) virtually

eliminates macrosegregation in small ('^^3 mm) diameter samples.

Additional calculations of the onset of convective and interfacial

instabilities during the directional solidification of lead-tin alloys have

been carried out with particular emphasis on constant gravitational

— 6 2 accelerations of 980 (10 ) cm/s .

37
A. SOLUTAL CONVECTION INDUCED MACROSEGREGATION AND THE DENDRITIC TO

COMPOSITE TRANSITION IN OFF-EUTECTIC ALLOYS

Introduction

The ability to solidify two-phase aligned structures from a wide range

of compositions near a eutectic composition has importance in the full

utilization of this class of composite materials. The early work of Mollard

& Flemings claimed that the range of compositions for which plane front

composite growth was possible was restricted not only by constitutional

supercooling requirements but also by the requirement that convection be

avoided. In fact, their experimental work using vertical upward solidification

was limited to the Sn-rich side of the Pb-Sn eutectic where the fluid

density, influenced by temperature and composition, always decreases with

distance from the interface (height). On the Pb-rich side of the eutectic,

the concentration gradient in the liquid can cause the density to increase

with distance near the interface and possibly cause convection (here termed

[2 3] solutal convection). Subsequently, it was argued ’ that as long as a

stagnant boundary layer exists whose thickness is large compared to the

eutectic spacing, plane front growth of the composite should be possible in

the presence of convection. This was in fact verified by experiments ^

which demonstrated the growth of Pb-rich Pb-Sn composites. However, Verhoeven,

Kingery and Hofer^ subsequently showed that significant macrosegregation

(10 w/o) down the length of solidified samples occurs in samples only 1 w/o

on the Pb-rich side of the Pb-Sn eutectic, and attributed this macro segregation

to solutal convection.

The purpose of this research is to describe the microstructure and

macro segregation produced during upward solidification of off-eutectic

alloys 2-5 w/o from the eutectic composition when the liquid density near

38
the interface increases with distance from the interface and to determine if

a magnetic field or solidification downward can eliminate solutal convection

and hence macro segregation.

Experimental Procedures

Alloys were prepared from 99.99% pure Sn and Pb in evacuated and sealed

borosilicate crucibles. The directional solidification furnace is constructed

of non-magnetic materials and has a bifilar wound cylindrical resistance

heating element with upper and lower sections and a circulating water cooled

chill zone. A 3 mm I.D. silica tube containing the desired alloy is pulled

down through the chill, sealed by 0-rings, at constant velocity to accomplish

directional solidification. The cooling water comes directly in contact

with the silica tube. Using two separate A. C. proportional temperature

controllers for the furnace, and water cooled by a heat exchanger, temperatures

are constant to 0.1 °C over an hour and 1 °C over several days. The vertical

drive is powered by a synchronous motor with a multi-speed gear box. Speeds

from 0.5 ym/s to 0.5 mm/ s are possible. The tube is attached to the pull

shaft using a device which permits the sample to be suddenly pulled down

about 3 cm to quench the liquid-solid interface.

The value of the liquid temperature gradient measured for several

typical experiments with 0.25 mm diameter sheathed thermocouples was 360 +

10 K/cm. This value was assumed for all other experiments. The furnace is

I designed so that a permanent magnet with a pole diameter of 8 cm and a pole

separation of 11 cm could be slid around the furnace to apply a O.lT (1

kilogauss) horizontal magnetic field. Alternately, an 11 cm diameter solenoid

could be placed over the furnace-chill to apply up to O.lT vertical magnetic

39
field. Additionally the furnace could be inverted for solidification downward.

In this case a fibrous ceramic plug was used to maintain a small upward

pressure on the inverted melt to prevent separation of the liquid from the

freezing solid.

A specific directional solidification experiment was conducted in the

following manner. A tube filled with the desired alloy was inserted through

the chill, with the alloy completely in the chill section. The tube was

evacuated and the furnace temperature was equilibrated. The sample was then

driven quickly into the furnace melting about 12 cm of alloy. The tube was

backfilled with argon and temperatures were allowed to stabilize for about 1

minute. Excessive holding times at this stage are undesirable because a

layer of Pb-rich solid solution will slowly solidify and disrupt the uniformity

of the initial liquid composition. The tube was then pulled at the desired

rate until about 6 cm had solidified. The remainder of the sample was then

quenched, delineating the liquid-solid interface in the microstructure. The

silica was removed with HF acid and the specimens were mounted in a coolsetting epoxy for characterization.

Samples were routinely examined in a longitudinal section (parallel to

the solidification direction) using standard metallographic techniques. For

each experiment the shape of the liquid-solid interface was examined to be

certain that heat flow was unidirectional. In the present experiments, the

macroscopic liquid-solid interface of two-phase composite growth, when

achieved, was convex towards the liquid by only 10-20 ym across a 3 mm

diameter sample.

Measurement of macro segregation (average composition of the two-phase

solid) along the length of solidified samples was performed using two methods.

40
x-ray fluorescence and a titration method. The former method, which was

described previously

,

uses incident monochromatic (22.1 keV) x-rays

collimated to 1/2 mm x 1/2 mm. The use of x-rays permits deeper penetration

into the samples and hence better averaging over the two-phase structure

than does the use of electron probe methods. This data was used to nondestruct ively evaluate the extent of macro segregation and to indicate those

rsi

samples for which the titration method would be used. The titration method^

was performed on approximately 2 mm discs cut transverse to the growth

direction. Accuracy of the titration method is approximately + 0.25 w/o Pb.

Experimental Results

Results on the microstructure and macro segregation of Pb-rich offeutectic alloys solidified upward with and without magnetic field and

downward are presented here and will be discussed in the next section.

Directional solidification experiments were conducted vertically upward

(liquid above the solid) on the Pb-rich side of the eutectic. In all cases,

solidification begins with the dendritic growth of the Pb-rich phase even

when the ratio of the temperature gradient G in the liquid to the growth

1j velocity V substantially exceeds the requirement of constitutional supercooling for the bulk composition of the alloy. The volume fraction of

dendrites decreases slowly as a function of distance as shown, for example,

in Fig. 1, until the structure is a two-phase composite. The region of

t dendritic growth in most instances is very long compared to D/V (where D is

the liquid interdiffusion coefficient) and does not correspond to an initial

transient of the type described by Mbllard and Flemings

This long

region of dendritic growth will be shown to be a manifestation of the

macro segregation which occurs in these alloys due to solutal convection.

41
Table I is a summary of these experiments showing the original composition

(C ), growth rate (V), G /V, D/V, the initial length of the liquid alloy

(L) , the length of the dendritic zone (Z^) , and the average solid compositions

at three positions in the solidified samples: C (0.0), C (0.1) and C ^ at

s s s 0.0, 0.1 fraction solidified and at the transition from dendritic to composite

structure, respectively. Fraction solidified, f^, is the ratio of distance

solidified to the initial length of molten alloy. Other experiments conducted

with an imposed magnetic field and with solidification downward are included

in Table 1.

Fig. 2 shows the measured composition as a function of fraction solidified

for five 43.0 w/o Pb alloys solidified at 0.5 ym/s. [The eutectic composition,

is 38.1 w/o Pb.] Two samples were solidified upward without magnetic field

with initial melt lengths of 5.2 cm and 11.8 cm respectively. The initial

solid composition is very high in Pb content 72 w/o Pb (the boundary of

the two phase field occurs at 81 w/o Pb) , and falls to the vicinity of the

eutectic composition as solidification proceeds. The fractions solidified

f^^, at which the dendritic structure disappears in the two samples are

essentially identical. Beyond this position the samples continue to solidify

nondendr itically as a two phase composite with changing composition until at

a f^ 0.22 the rate of change of composition with distance decreases

sharply. Because of the excellent agreement of the macro segregation of

these two samples as well as the dendrite disappearance position, it is

apparent that fraction solidified is the proper variable to describe changes

in composition. This strongly suggests that the dendritic zone is not

caused by an initial transient but by macrosegregation. Henceforth, we will

use fraction solidified as the length parameter to describe macrosegregation.

"E’

42
Also shovTii in Fig. 2 are two samples solidified upward with imposed

horizontal and vertical magnetic fields of O.lT (1 kilogauss) . The macrosegregation and position of dendrite disappearance for these experiments are

similar to the samples solidified without magnetic field. The final sample

shown in Fig. 2 was solidified vertically downward (liquid below solid).

Here a significant reduction in the macro segregation was observed. Except

for an initial transient (length 2 D/V) the composition is relatively

constant. [The slight decrease in composition is caused by thermal diffusion.]

Furthermore, the structure is completely two phase composite. There is no

initial region of dendritic growth.

The effect of a faster interface velocity (2.6 ym/ s) on macro segreg,at ion

for 43.0 w/o Pb alloys is shown in Fig. 3. Samples solidified upward with

or without a magnetic field show an initial Pb content of 52 w/o and

freeze dendritically up to fraction solid of about 0.25. Their macrosegregation profiles are slightly different at large f but certainly

s macrosegregation is quite evident in both. On the contrary the sample shown

in Fig. 3 which was solidified vertically downward shows very little macrosegregation and is two phase composite over most of its length. As shown in

Table I, the dendritic region in this sample has not been completely

eliminated by inverted solidification as did occur at 0.5 ym/s. This is

probably due to the closeness of the value of G /V compared to the critical

value for plane front growth. (See discussion below and Fig. 7)

With an initial composition closer to the eutectic composition (40.7

w/o Pb) macrosegregation during upward solidification is reduced compared

to 43.0 w/o Pb alloys but is still significant as shown in Fig. 4. The

43
sample solidified dendrit ically to a fraction solid of 0.06. On the

contrary, the sample solidified downward has a reduced level of macrosegregation and is two-phase composite over its entire length.

Of all the Pb-rich samples solidified upward only one was composite

over its entire length (with the exception of a 1 mm initial transient) .

The composition of this sample was close to the eutectic composition and it

was solidified relatively rapidly (40.7 w/o Pb, 5.1 ym/s) . The macrosegregation data for this sample is shown in Fig. 5.

Discussion of Results

Upward Solidification - No Field

The extensive macro segregation shown in Figs. 1 through 5 occurs only

for alloys on the Pb-rich side of the eutectic when freezing vertically

upward. Experiments on the Sn-rich side of the eutectic under conditions

identical to those used in the Pb-rich experiments exhibit only a relatively

small amount of macrosegregation which can be quantitatively accounted for

by thermal diffusion alone. An example of measured macro segregation on the

Sn-rich side is shown in Fig. 6. The data agrees with previous work of

[ 9 ] Verhoeven, Warner & Gibson , and can be fit using their equation (17) with

—8 2 a thermal diffusion coefficient, D, of 2.1x10 cm /(s*K), a diffusion co-

-5 2 efficient of 0.6x10 cm / s and no mixing near the liquid-solid interface (6

large). This absence of significant macrosegregation on the Sn-rich side in

experiments conducted under conditions identical to those on the Pb-rich

side is strong evidence that solutal convection (and not thermal convection

caused by radial temperature gradients) is the cause of the extensive

macrosegregation on the Pb-rich side of the eutectic.

44
It is useful to describe a qualitative model for the macro segregation

and resultant changes in microstructure for Pb-rich alloys. Solutal

convection is sufficiently vigorous to disrupt the normal diffusion controlled (Sn-rich) solute field near the liquid-solid interface regardless of

whether it is planar or dendritic. This solute is transported by the

convection to the bulk liquid far from the interface which is almost always

[9] well mixed* by the radial temperature gradients which exist there

Hence the bulk liquid, which initially was of composition on the Pb-rich

side of the eutectic, gradually becomes more Sn-rich. This causes a slow

change in the solid to compositions which are also more Sn-rich as solidification proceeds. The transition from dendritic to composite structure

appears to occur when the solid composition is close enough to the eutectic

composition that plane front composite growth becomes stable as documented

below. After plane front solidification is established, macrosegregation

continues until the bulk liquid composition approaches the eutectic

composition. Because the average composition in the liquid at the interface

must be very close to the eutectic composition for two-phase plane front

growth, the average composition gradient in the liquid vanishes when the

bulk liquid composition reaches the eutectic composition. At this point

solutal convection presumably ceases. This situation is reflected by the

sharp break at f^ 0.22 of the macro segregation curve in Fig. 2. The fact

that the solid composition at this point is 44 w/o Pb and not equal to the

* In the present experiments the composition of the liquid, determined

after quenching, was constant to within + 0.25 w/o Pb. The large

sample size 2 mm) used for chemical analysis prevents detection of

the solute boundary layer.

45
r 61 liquid composition (38.1 w/o Pb) is caused by a thermal diffusion effect^ . From Eq. (15) of Ref. 9, the average composition gradient vanishes when

the average solid composition, C^, is C^(1+D"G^/V) , which for this alloy

and these growth conditions is 43.9 w/o Pb. Macrosegregation after

this point is greatly reduced and is caused only by thermal diffusion.

A quantitative description of the location of dendrite disappearance is

possible. Fig. 7 is a plot of G^/V vs. the composition of the solid at the

position where the structure changed from dendritic to composite. It

resembles the expected form of the relation between G /V vs. composition for

J-i the stability of plane front solidification, i. e. , it falls slightly below

the requirement of the simple constitutional supercooling criterion

G,/V = - m(C -C J/D

L E s where m = 3.2 K/(w/o) and is the liquidus slope of the Pb-ricL phase. It

[ 2 ] also agrees with the data of Davis & Fryzuk on zone melted of f-eutectics

where macrosegregation is avoided by the fact that solid of constant composition is fed into the melted zone. Hence the transition from dendritic

to composite structure occurs when macrosegregation has caused the composition

of the solid to change to a level which satisfies a stability criterion for

plane front growth of a composite.

Quantitative description of the observed macro segregat ion is more

difficult. Verhoeven et al. ^

, using a thermotransport-corrected BurtonPrim-Slichter type (stagnant film) analysis of plane front composite

growth, have formulated an expression to predict macro segregat ion. The 40.7

w/o Pb sample run at 5.1 ym/s is dendritic for an extremely short distance

(long compared to D/V) and hence this analysis is applicable. The previously given value of the thermal diffusion coefficient D^, and a value of

46
90 ym for 6 (the thickness of the umnlxed zone near the interface) gave the

best fit to the measured data in close agreement with 6 values of Verhoeven

[9] et al. . This calculated curve of the macro segregation is shown superimposed on the data of Fig. 5. In this experiment, it was determined

experimentally that the liquid composition remained on the Pb-rich side of

the experiment up to the quench point and solutal convection probably existed

throughout this experiment. The calculated value of the bulk liquid composition

using this value for 6 also agreed to within 0.25 w/o with the measured

composition of the quenched liquid. The success of this approach during

composite growth is somewhat suprising given the fact that the driving force

for solutal convection only exists in the diffusion boundary layer. On the

contrary, samples Wj.th long regions of dendritic growth cannot be fit with

this equation. In the data shown in Fig. 3 a substantial number of data

points exist in the dendritic zone of the sample and a marked change in

slope occurs as tne volume fraction of dendrii'es decreases. Clearly the

existence of the dendritic interface influences both the driving force for

solutal convection and the geometry for the flow. Fluid flow during

dendritic solidif icat ion^^^^ is known to require a different approach to

macro segregation than a stagnant film approach. Quantitative description of

the macro segregation curves during dendritic growth is a topic for future

research.

It is significant to note several aspects of solutal convection observed

in this research. Fig. 8 shows an optical micrograph of a quenched liquid

solid interface of a 43.0 w/o Pb alloy freezing at 2.6 ym/s. The sample was

quenched at f^ = 0.1, so solutal convection was present at the time of

47
quenching. The Pb deudrites are uniformly spaced across the sample and the

eutectic interface appears quite flat. It seems unclear that a single (or

double) convection cell would lead to such a microstructure.

Additional insight into the nature of solutal convection is seen in

Fig. 2, where the sharp break in the data at f^ 0.22 marks the transition

from macro segregation caused by solutal convection to macro segregation

caused by thermal diffusion. This sharp transition from regimes of convection to no convection may be an indication of the extremely low concentration

differences (i.e., deviation from eutectic composition) necessary for the

onset of convection. Low concentrations for the onset of solutal convection

[ 12 ] during single phase solidification have been predicted theoretically

For example, for vertical solidification of single phase Pb containing Sn,

at an interface velocity of 1 ym/ s and a temperature gradient of 200 K/cm,

-4

solutal convection will occur at all compositions above 3x10 w/o Sn.

Another suprising feature of solutal convection is the failure of the

small (3 mm) diameter container to suppress convection. The results of

[ 12 ] Coriell et al. indicate that a solute Rayleigh number based on a length

of D/V is significant for the prediction of the onset of solutal convection

during solidification. The fact that D/V is smaller than the radius of the

tubes used in this study may explain this observation.

The presence of growth rate fluctuations has been observed in some

cases in the present study. However, as can be seen for example in Fig. 1,

many samples have been obtained which contain no fluctuations. Hence, it is

our belief that these fluctuations are caused by artifacts, such as for

[13] example, by nonsteady thermal contractions . Solutal convection seems to

48
be sufficiently steady so as to not cause growth rate fluctuations.

Upward Solidification - Magnetic Field

Static magnetic fields have long been known to influence the flow of

electrically conducting liquids^^^^. Chandrasekhar calculated the

influence of a vertical magnetic field on suppression of thermal convection

in an infinite horizontal layer of fluid heated from below. Other theoretical work has been performed for different geometries. Experiments on

r 1 b 1 liquid mercury^ ^ confirmed the inhibition of thermal convection by a

vertical magnetic field. During solidification, liquid temperature

fluctuations and associated growth rate fluctuations and solute banding

caused by time-dependent convection during the horizontal growth of crystals

were eliminated by imposition of a vertical magnetic f ield

However, time independent laminar flow may still have been present. Because

of this previous work, attempts were made in the present study to suppress

solutal convection and the concomitant macrosegration by the imposition of

a static magnetic field.

For most experiments a vertical field of O.lT (1 kilogauss) was used

[15] based on the following analysis from Chandrasekhar . The fluid elements

are subject to the Lorentz force which is proportional to curl H x H, where

H is the magnetic field in the fluid. Clearly, if H is constant the Lorentz

force vanishes, and the magnetic field does not affect the fluid motion.

Even though the applied magnetic field is constant, the magnetic field in

the fluid is not in general constant. In fact, a constant H will satisfy

the basic partial differential equation for H if and only if curl (u x H)

vanishes, where u is the fluid velocity. Clearly if u is parallel to H,

49
then u X H vanishes, and the magnetic field has no effect on the fluid

motion, i.e., if the fluid motion does not cross the magnetic field, there

is no effect. More generally, however, a constant H is possible if and only

if (H*V)u = 0 for an incompressible fluid, which reduces to (3u/3x^ = 0

for a magnetic field only in the x^ direction. Thus, a constant magnetic field

and a vanishing Lorentz force will occur if the fluid velocity is independent

of the coordinate x^ in the direction of the magnetic field. Such a case

occurs for flow between two infinite horizontal plates heated from below

where the critical Rayleigh number is unaffected by a horizontal magnetic

f ield.

Experimental results shown in Figs. 2-3, show little or no effect of a

O.IT (1 kilogauss) magnetic field on reducing the macrosegregation produced

by solutal convection. As was described above, the solutal convection

y present in these experiments is sufficiently steady that growth rate

fluctuations do not occur. Hence the nature of the convection present in

these experiments is quite different from that observed by Utech & Flemings

during horizontal solidification. Recent theoretical work may explain the

[ 12 ] ineffectiveness of a magnetic field on damping solutal convection . For

example, for vertical solidification of single phase Pb containing Sn, at an

interface velocity of 1 ym/s, a temperature gradient of 200 K/cm and a

imposed vertical magnetic field of IT (10 kilogauss), solutal convection

_3 will occur at all compositions above 3 x 10 w/o Sn.

Downward Solidification

As shown by the data in Figs. 2-4, solidification of Pb-rich offeutectic alloys downward greatly reduces macro segregation. In fact the

50
remaining macro segregation in these experiments can be quantitatively

accounted for by thermal diffusion. In this geometry the Sn-rich solute

layer near the interface is above the Pb-rich liquid away from the interface

and for the conditions used in these experiments, creates a stable density

gradient near the interface even though the temperature gradient is destabilizing.

Outside the solute diffusion layer the density gradient is destabilizing.

At first glance the reason for the reduction of macrosegregation during

downward solidification appears obvious. Solutal convection is eliminated

because of the stable density gradient near the interface and hence diffusion

controlled solidification is not interrupted. However, the large vertical

temperature gradient present during these experiments would tend to promote

extensive thermal convection farther from the interface. The results indicate,

however, that such flow if it exists, is sufficiently distant from the

diffusion boundary layer as to be ineffective in causing significant macrosegregation.

A second rationale could be that the small tube diameter (3 mm) is

effective in greatly reducting the thermal convection far from the interface.

One can calculate a thermal Rayleigh nvimber R = agG r^/v< for this geometry,

L

where a is the expansion coefficient, g the acceleration of gravity, the

j-i temperature gradient in the liquid, r the tube radius, v the kinematic

[ 12 ] viscosity and k the thermal diffusivity. For typical parameters of the present

Oi experiments R = 65, which is very close to typical critical Rayleigh numbers

for closed containers as summarized by Verhoeven

For larger tubes

thermal convection away from the interface may become more effective in

causing macro segregation and hence it is anticipated that suppression of

51
macro segregation by solidification downward may be very sensitive to tube

diameters. This effect was not, however, investigated in the present study.

Conclusions

1. Solute gradient induced convection can cause extensive macrosegregation in off-eutectic alloys.

2. Macro segregation is frequently sufficiently large to prevent plane

front solidification of the alloy.

3. The transition from dendritic to composite structure occurs when

the composition of the solid is close enough to the eutectic

composition to satisfy a stability criterion based on G^/Y.

4. Horizontal or vertical magnetic fields of O.lT (1 kilogauss) do

not prevent macro segregation of off-eutectic alloys caused by

solutal convection.

5. For small diameter samples, inverted solidification eliminates

macro segregation caused by solutal convection.

52
B. CALCULATION OF CONDITIONS FOR THE ONSET OF SOLUTAL CONVECTION

Introduction

During the vertical directional solidification of a binary alloy at

constant velocity V, the steady state concentration field is exponential

in form, i.e., c = c^+(c^/k) (1-k) exp (-Vz/D) , where c is the concentration

of solute in the liquid at a distance z from the solid- liquid interface,

the distribution coefficient k is the ratio of the solute concentration

in the solid at the solid-liquid interface to the solute concentration in

the liquid at the solid-liquid interface, c^ is the solute concentration

as z and D is the liquid diffusion coefficient. The temperature

field is also exponential but with decay length k/V, where k is the thermal

diffusivity of the liquid. In general, k >> D so that the temperature

gradient G in the liquid is essentially constant in the region in which

Lj the concentration gradient is significant. It is well known that as the

concentration is increased for fixed V and G the planar solid- liquid

Lj interface becomes morphologically unstable. The constitutional supercooling

principle predicts instability when mG > G > where m is the slope of the

C 1j liquidus line and G^ = (c^V/Dk) (k-1) is the concentration gradient at the

planar solid-liquid interface. In addition to morphological instability,

there is the possibility of a convective instability. For solidification

vertically upwards (positive z-direction) the thermal gradient alone

results in a negative density gradient (stabilizing) while the solute

gradient alone can cause a negative (stabilizing) or positive (destabilizing)

density gradient depending on the density variation with solute concentration

and the distribution coefficient. When the solute gradient gives rises

to a positive density gradient, e.g., a solute which is rejected at the

solid-liquid interface and which is lighter than the solvent, a convective

53
instability will occur if the solute concentration is sufficiently large

that the destabilizing solute field overcomes the stabilizing influences of

the thermal field and viscous effects. Thus, for fixed values of velocity V

and temperature gradient G , as the solute concentration increases, one

1j expects an instability to occur, i.e., for sufficiently small solute

concentrations, the planar interface is stable and the horizontal components

of the fluid flow velocity vanish (a vertical flow due to the volume change

on solidification is always present), but for solute concentrations above

some critical value the interface and the fluid flow field are unstable.

[12 21 22 ] In our previous publications *

’

, a linear stability analysis and

numerical algorithms have been described which allow the calculation of the

critical concentration for the onset of convective and morphological instabilities during the directional solidification of binary alloys. In

addition, a number of results were obtained for the specific case of the

solidification of lead containing tin. In this report we combine the

previous results and new results with particular emphasis on small constant

gravitational accelerations.

Results and Discussion

We recall that the dependence of the perturbed temperature, concentration, fluid velocity, and interface shape on the horizontal coordinates

X and y and the time t is of the form exp [at + i(oj x+oo y) ] , where co and cd ^ X y-^ X y are spatial frequencies. If the real part, a^, of the time constant a is

positive for any values of and the system is unstable. If < 0

for all values of w and o) , the system is stable. We refer to instabilities

X y

^

54
corresponding to large values of o) (small wavelengths, X = 2tt/oj) as

morphological instabilities and to instabilities corresponding to small

values of co (large wavelengths) as convective instabilities.

The basic results for the critical concentration c** above which • GO instability occurs as a function of growth velocity are shown in Fig. 9,

We have previously discussed the curves corresponding to gravitational

2 -4 -6

accelerations of g^ = 980 cm/s and 10 g^. For g

= 10 g^, the convective instability occurs at a lower concentration than the morphological

instability only if V < 1.3 ym/s. The concentration above which the

2 2 ^

interface is unstable as a function of the spatial frequency w = (w^+oj^) ^

of the perturbation is shown in Figs. 10 and 11 for V = 1.2 and 1.3 ym/s,

respectively. The critical concentration c** corresponds to the minimum

value of the concentration as a function of w. The solid curves on the

right of Figs. 10 and 11 correspond to morphological instability while the

solid curves on the left correspond to convective instability. Along the

curves the real part of a vanishes; along the solid curves a vanishes

while along the dashed curve, which connects the convective and morphological

branches, the imaginary part of a is non-zero. The value of is

shown in the insets in Figs. 10 and 11 and attains a maximum value of less

-4 -1

than 2.0(10 )s . For V = 1.2 ym/s, the minimum value of c^ is 4.61 wt.

% at 0) = 1.35 cm ^ or a wavelength A = 4.7 cm. There is a relative minimum

on the morphological branch at w = 204 cm ^ with c^ = 6.47 wt. % (not

shown in the figure). For V = 1.3 ym/s, the minimum value of c^ is 5.98

wt. % at 0) = 210 cm ^ (not shown in the figure) and a relative minimum

with c = 7.15 wt. % at w = 1.4 cm 00

55
In our previous publications, it was shown that the critical concentrations for convective instability could be correlated in terms of the

Rayleigh number and the solute Rayleigh number based on the length

(D/V) , i.e.

,

R" = -gaG (D/V)^/vk

XJ S' = -ga^G^(D/V)^/vD = (ga^/vDk) (1-k) (D/V)

where a is the thermal coefficient of expansion, v is the kinematic

viscosity and is the solutal coefficient ,of expansion. To fit our

previous results we used an expression of the form

^5

S" + a^(R') = (1)

or in dimensional form

c^ = a^V^/g + a^(V^/g)(gG^/V^) (2)

where the a^ are constants independent of G^^, c^, V and g. The a^ were

determined by minimizing the differences between the numerical values of

c^ and the values obtained from the above expression. Using the previously

determined values of the a., we calculate critical concentrations of

X

0.32, 2.48, 4.27, and 5.42 wt. % for V = 0.5, 1.0, 1.2, and 1.3 ym/s,

_ g respectively, for g = 10 g^; these are in reasonable agreement with the

numerically calculated values of 0.31, 2.39, 4.61, and 7.15 wt. % for V =

0.5, 1.0, 1.2, and 1.3 ym/s.

In our previous calculations for g = g^, we obtained oscillatory instabilities with ^ 0.1 s

^ or a period of the order of 60 s. For

“*6 "A "“X A g = 10

gg ,

'Vi 10 s or a period of the order of 6(10 )s. This

suggests that the fluid motions are very slow at reduced gravity levels.

56
To further verify this, we carried out a few calculations with ^ 0.

_6 For V = 1.2 pm/s and g = 10 ^ concentration of 7.68 wt. % is required

-4 -1

for = 10 s on the convective branch. Thus, although > 0 for

c^ > 4.61 wt. % for V = 1.2 ym/s, the amplitude of the convective in4

stability for c^ = 7.68 wt. % increases very slowly, requiring 10 s to

increase by a factor of e. In contrast, the morphological instabilities

are only slightly affected by reduced gravity. For example, for V = 1.2

-1 -4

ym/s and o) = 205 cm , the concentrations corresponding to = 0, 10 , —2 “X “6

and 10 s are 6.47, 6.50 and 11.0 wt. %, respectively, for g = 10 g^

-4 -2 -1

whereas for g = g^, = 0, 10 and 10 s correspond to concentrations

of 6.47, 6.49 and 11.2 wt. %, respectively. We emphasize that these

calculations for g = 10 ^ g^ assume that g is constant, and since the

convective instabilities develop very slowly, it seems unlikely that this

is a valid assumption for space experiments.

Liquid metals have low Prandtl numbers, e.g., the Prandtl number

Pr = v/k = 0.0225 for lead. In contrast, a large class of liquids have

much larger Prandtl numbers, e.g., Pr ^ 10 for water. In order to study

the effect of Prandtl number, we have carried out some calculations using

the properties of lead-tin alloys except that the thermal conductivities

and thermal dif fusivities of both liquid and solid were 100 times lower

than the actual conductivities and dif fusivities. Thus, the Prandtl nximber

for this hypothetical alloy is 2.25; for fixed G and V the thermal Rayleigh

Lj number is also increased by a factor of 100. The tin concentrations at the

onset of convective instability as a function of growth velocity for G =

Lj 200 K/cm for lead-tin alloys (Pr = 0.0225) and the hypothetical alloy

57
(Pr = 2.25) are shown in Fig. 12. At low velocities the critical concentrations are a factor of 50 greater for the liquid with reduced thermal

properties than for the lead alloy. At higher velocities, the two curves

approach each other and the thermal properties have little effect on the

critical concentration. This behavior can he understood qualitatively

from eq. (1) through the effect of the reduced thermal properties on the

Rayleigh number; in general, however, we expect the a^ to depend on the

Prandtl number.

A few additional calculations of the effect of magnetic fields and

thermal gradients were carried out. These tpgether with previous results

are presented in Figs. 13 and 14. For discussion of these results, see the

previous publications.

The present linear stability analysis and numerical algorithm allows

the determination of the onset of convective and morphological instability

during directional solidification. We plan additional calculations for

conditions and materials relevant to experimental investigations. For a

particular double diffusive system with linear temperature and solute

[231 gradients, Baines and Gill ' have shown that the spatial frequency 03,

corresponding to the most unstable mode, increases very rapidly as the

concentration exceeds the critical concentration for the onset of instability. Calculations of a as a function of to for fixed concentration

will allow us to determine whether similar behavior occurs during

directional solidification. Mathematical analysis and algorithm development

for fluid flow occurring in the non-linear regime (after the onset of

instability), with particular emphasis on solute distribution, will be

initiated in the near future.

58
Ac knowledgment s

We acknowledge the substantial contributions of Prof. Robert F. Sekerka

of Carnegie-Mellon University and Consultant to the National Bureau of

Standards to the theoretical part of this research along with the support

and suggestions of John R. Carruthers. We would also like to thank

Charles H. Brady for the metallography of these alloys and Barry I. Diamondstone

for the wet chemical analysis.

59
References

1. F. R. Mollard and M. C. Flemings, Trans. AIME, 1967, Vol. 239, p. 1534.

2. K. G. Davis and P. Fryzuk, Can. Met. Quart., 1971, Vol. 10, p. 273.

3. J. D. Verhoeven and R. H. Homer, Met. Trans., 1970, Vol. 1, p. 3437.

4. J. D. Holder and B. F. Oliver, Met. Trans., 1974, Vol. 5, p. 2423.

5. L. Vandenbulcke, R. J. Herbin and G. Vuillard, J. Cryst. Growth,

1976, Vol. 36, p. 53.

6. J. D. Verhoeven, K. Kingery and R. Hofer, Met. Trans., 1975, Vol.

6B, p. 647.

7. W. J. Boettinger, H. E. Burdette and M. Kuriyama, Advances in X-ray

Analysis, 1980, Vol. 23, p. 209.

8. M. J. Tschetter and R. Z. Bachman, Talanta, 1974, Vol. 21, p. 106.

9. J. D. Verhoeven, J. C. Warner and E. D. Gibson, Met. Trans., 1972,

Vol. 3, p. 1437.

10. J. A. Burton, R. C. Prim, and W. P. Slichter, J. Chem. Phys. 1953,

Vol. 21, p. 1987.

11. M. C. Flemings and R. Mehrabian, Solid if icat ion , ASM, 1969, p. 311.

12. S. R. Coriell, M. R. Cordes, W. J. Boettinger and R. F. Sekerka,

J. Cryst. Growth, 1980, Vol. 49, p. 13.

13. J. D. Verhoeven and E. D. Gibson, J. Cryst. Growth, 1971, Vol. 10,

p. 235.

14. J. Hartmann and F. Lazarus, Kgl. Danske Videnskab. Selskab, Met.-Fys.

Medd., 1937, Vol. 15, Nos. 6 & 7.

15. S. Chandrasekhar, Hydrodynamic Stability , Oxford Univ. Press, London,

1961 p. 146.

16. B. Lehnert and N. C. Little, Tellus, 1957, Vol. 9, p. 97.

60
17. H. P. Utech and M. C. Flemings, J. Appl. Phys., 1966, Vol. 37,

p. 2021.

18. H. P. Utech and M. C. Flemings in Crystal Growth , edited by H. S. Peiser,

Pergamon Press, New York, 1967, p. 651.

19. M. C. Flemings, Solidification Processing , McGraw-Hill, New York,

1974, p. 227.

20. J. D. Verhoeven, Trans. Met. Soc. AIME, 1968, Vol. 242, p. 1940.

21. W. J. Boettinger, S. R. Coriell, F. S. Biancaniello and M. K. Cnrdes

in NBS: Properties of Electronic Materials, edited by J . R. Manning

and R. L. Parker, (NBSIR 78-1483, National Bureau of Standards,

Washington, D.C.) p. 15.

22. W. J. Boettinger, S. R. Coriell, F. S. Biancaniello and M. R. Cordes

in NBS: Properties of Electronic Materials, edited by J. R. Manning,

(NBSIR 79-1767, National Bureau of Standards, Washington, D.C.) p. 25.

23. P. G. Baines and A. E. Gill, J. Fluid Mech., 1969, Vol. 37, p. 289.

61
Table

I.

Summary

of

Experiments

4-1 0)e CCJ ccJ 43 o T3 t5 cO 43 cO T3 ccJ o

(U o

1-J CN iH CM CO

O C33 43 D s 1—1

rH CN CO

OO

M-l

Q • • • • O

O • • • • O o N o o o o <? o o o o 'w'

Q

B v£)

m o^ 45 1 1 -d- CO 00

N1 o • • • • O • • • • • O • o o tH c' o CO CO o o c? o

43

Ph 00 LO vO CN o I—1

rH •<r D s • • • • j j • • • j • u O 00 o 00 rH 1 1 45 Mf 03 CO 43 m 45

43 lO o O lO o LO o LO • • • • • • • • • o iH tH CM m u~> 45 r-i O 4) CM CN O vO vO 4> 45 LO LO <d* m *' o

43O LD CO o LO

/—S

P4 • • • • • o CN CS 03 00 45 r-*. CN CN CO CO O 45 45 LO LO LO lO 'd- CD U IS

ci

d CN CM CN CN CN 1 CO CO CO LO

•H

Pn S • (N 00 fO CN

O o <oi o CO CO 45

hJ CJ • • • • • • • • • • • • rH 45 LO <f o 00 CN LO 00

tH rH rH rH rH

Cs| CM CN CN CM to CN CN CM lO LO r-H > B 1 1 rH rH o o o o o o o a • • • • • • • • • • • • Q 'w' o o O o o o o o o o o o

\01 CN O

B

iHu CN CM CN CN CM 00 00 00

X • > CO r-- CN rH rH rH CN CN o

1-4

/-N

CD 'b

m

m

mm CO 45 45 45 CO CO rH > • • • • • • • • • • • • 3- o o o o o rH CN CN CN rH rH LO

/—S

43

P4 o o o o o o o o o r--

O

O cn CO CO* CO CO CO CO CO CO o o cd

u

Vw'

'4* OJ xiH

62

Upward,

O.IT

Vertical

Magnetic

Field

Upward,

O.IT

Horizontal

Magnetic

Field
Fig. 1. Longitudinal section of directionally solidified sample

showing the change in volume fraction of Pb dendrites (dark) as a function of distance (fraction solidified) . Solidification

proceeded from bottom to top. At the extreme top there are

no dendrites. Solidification velocity is 1.3 ym/ s - original

composition is 40.7 w/o Pb.

63
FRACTION SOLIDIFIED

Fig. 2. Average solid composition versus fraction solidified for

43.0 w/o Pb alloys solidified at 0.5 ym/s showing extensive

macrosegregation during upward solidification, negligible

effect of magnetic field and large effect of inverted solidification on reduction of macro segregation.

64
lOd

d

tod

CVJ d

o

u

9

_i

o

CO

o

<

tr

(

65

Fig.

3.

Average

solid

composition

versus

fraction

solidified

for

43.0

w/o

Pb

alloys

solidified

at

2.6

ym/s.

Inverted

solid

fication

greatly

reduces

the

macrosegregation.

The

symbol

DD

respresents

the

positions

of

transition

from

dendritic
(qd%) NOiiisodi/\ioo anos

66

Fig.

4.

Average

solid

composition

versus

fraction

solidified

for

40.7

w/o

Pb

alloys

solidified

at

1.3

pm/s.
67

Fig.

5.

Macro

segregation

data

for

a

40.7

w/o

Pb

alloy

solidified

upward

at

5.1

ym/s.

The

curve

is

the

best

fit

of

the

data

using

only

6

as

a

parameter

in

equation

(17)

of

Ref.

(9).
SOLID

COMPOSITION

(%

Pb)

Fig. 6. Average solid composition versus fraction solidified for a 35 w/o Pb alloy at 0.5 pm/s. For this alloy on the Sn-rich

side of the eutectic, solutal convection is absent and the

relatively small amount of macro segregation is caused by

thermal diffusion.

68
1 oK

c/) o

CL

UJOz<

or<

UJ

QQ.

S2Q

LlJ H

orQz

UJo<9o

CO

u.ozoH

COo

0-o

CJ

69

Fig.

7.A

plot

of

G^/V

versus

solid

composition

at

the

position

of

dendrite

disappearance

for

all

of

the

samples.

The

data

follows

the

general

trend

of

plane

front

interface

stability

for

off-eutectic

alloys.
bOa

‘H3

Xl0) o

pj

OJ

P!cr

cuo

cfl M

(U

4-1 •St3 •H

r—I 0w1 TJ

•H

P)

cr' *HI—I

MHOdo

•HUO

(Uw

w

cn(Ud

4-1 rt rH • m cuo

<u nj rd m

4-1 P40) dd

•HdJd

4-1 'H

bO QJ d M O 'H

i-J TP)dd '

00

bO

•H

70

unirorm

dxstr

ibutxon

or

Pb

dendrxtes

as

well

as

of

the

interdendrltic

eutectic

liquid-solid

int
**

Fig. 9. The critical concentration c** of tin above which instability

occurs as a function of the velocity V of directional solidification of lead-tin alloys for a temperature gradient in

the liquid of 200 K/cm. The solid curves represent gravitational accelerations of g = 980 cm/s ,10 g , and 10 g . The upper line with negative slope represents the onset of

morphological instabilities; the nearly parallel dashed-dot

line labeled (3p/3z) = 0 represents the neutral density

criterion. The dotted extension of the curve labeled g^ 6 corresponds to oscillatory instabilities.

71
0/M

Fig. 10. The concentration at the Onset of instability during directional solidification at V = 1.2 ym/ s of a dilute alloy of tin

in lead as a function of the spatial frequency o) of a sinusoidal

perturbation; the temperature gradient G in the liquid is 2g0

K/cm^and the constant gravitational acceleration is 980 (10 ) cm/ s . The solid curves mark the onset of non-oscillatory

instabilities (a.=0); whereas the dashed curves mark the onset

of oscillatory instabilities (the value of a. is given in the

inset)

.

72
CcD

w/o

Fig. 11. The concentration at the onset of instability during directional solidification at V = 1.3 ym/ s of a dilute alloy of tin

in lead as a function of the spatial frequency w of a sinusoidal

perturbation; the temperature gradient in the liquid is 2g0

K/cm^and the constant gravitational acceleration is 980 (10 ) cm/ s . The solid curves mark the onset of non-oscillatory

instabilities (a.=0); whereas the dashed curves mark the onset

of oscillatory instabilities (the value of a. is given in the

inset)

73
TIN

CONCENTRATION

w/o

Fig. 12. The critical concentration of tin above which instability occurs as a function of the velocity of directional solidification for a temperature gradient in the liquid of 200 K/cm.

The curve with Prandtl number Pr = 0.0225 corresponds to a lead-tin alloy whereas the other curve corresponds to calculations

for a hypothetical lead-tin alloy with thermal properties

reduced by a factor of 100, i. e. , Pr = 2.25.

74
TIN

CONCENTRATION

w/o

TEMPERATURE GRADIENT K/cm

Fig. 13. The critical concentration of tin in lead above which instability occurs as a function of the temperature gradient in

the liquid for solidification velocities of 1.0 and 20.0 ym/s.

75
TIN

CONCENTRATION

w/o

MAGNETIC FIELD T

Fig. 14. The critical concentration of tin in lead above which instability occurs as a function of the strength of a vertical

magnetic field for solidification velocities of 1.0, 5.0, and

20.0 ym/ s and a temperature gradient of 200 K/cm.

76
Task 3

A Thermochemlcal Study of Corrosive Reactions in Oxide Materials

H. S. Parker

Ceramics , Glass and Solid State Science Division

Center for Materials Science

Summary

Phase assemblages of selected compositions on the joins

K[Fe ^Si ^]02“Si02 and KFe02“Si02 have been determined after heat

treatment at oxygen partial pressures of 10 ^ and 10 atm and

temperatures in the 800®-1400°C range. Excessive reaction between

platinum containers and melts containing some ferrous iron was noted.

A comparison of conventional and containerless techniques for phase

equilibrium studies is presented.

77
Introduction

The objectives of this task are to investigate the nature, extent

and limitations on experimental studies imposed by sample-container

reaction at high temperature and to evaluate containerless techniques

for melt and solid state investigations. Alkali and transition elements

are among the most reactive and are of great technological importance

because of their application in the fields of MHD, fuel cells,

catalysts and solid state electronic and ionic conductors. Reaction

with the container can severely compromise the bulk composition of the

sample and adversely affect the electrical and chemical properties.

This, together with the inability in general to electromagnetically

levitate ceramic materials, makes low gravity experiments attractive

for containerless study of such materials.

The general approach is to select a system of current technological

importance and investigate: a) the maximum temperature limits for the

container material and characterize the reaction products, b) determine

the equilibrium phase assemblages in selected portions of the systems

within the limitations imposed by a) , and c) in collaboration with MSFC

provide specimens for levitation experiments at MSFC and characterize

and correlate results of levitation experiments with container experiments

to evaluate problems associated with low gravity experiments.

The system being Investigated is the K20-iron oxide-Si02 system.

This system is of major interest to the magnetohydrodynamics (MHD)

effort, where these oxides are present as components of seed and coal slag.

78
The first portion of this system investigated during the course of this

project was compositions on the KFe02~”Fe202" binary. Due to the high

temperatures involved (T > 1500® C) platinum was chosen as the container

material. As a result of this study, it was reported [1] that, contrary

to the expected result, platinum was a suitable container at temperatures

as high as 1600®C, provided most of the Fe was kept in the 3+ state.

Also, the existence of a B"' -alumina structure type phase was reported.

As an extension of this study, selected compositions in the K

2

Oiron oxide-Si02 system have been examined at lower partial pressures of

oxygen, where divalent iron is present.

Experimental Procedures

The preparation of compositions for study and characterization methods

following heat treatment has been described [1,2]. The same methods were

utilized for this portion of the study, except that all calcinations and

heat treatments were performed in controlled partial pressures of oxygen.

In order to provide atmosphere control during heat treatment of

specimens, a gas blending and purifying train was assembled. Mass flowmeters were used to establish desired mixing ratios of inert gas (argon)

,

95N

2

/ 5H

2

, N

2

and 0^, The inert gas was further purified by passing

over hot titanium sponge at approximately 800®C when desired. The actual

oxygen partial pressure in the furnace atmosphere was continuously

monitored using a stabilized zirconia oxygen sensor. The furnace chambers

consisted of impermeable high purity aliomina tubes provided with suitable

metal end fittings for gas flow and temperature measurement, with silicone

rubber gaskets.

79
Because of the lower temperatures involved, the choice of container

materials included iron, gold and platinum. The use of iron as a container material must be limited, however, to oxygen pressures determined

-12 -17

by the Fe-FeO equilibrium, of the order of 10 to 10 atm at the

temperatures involved in this study. Gold containers were utilized

for heatings at higher oxygen pressures and temperatures up to the

1000“-1050°C range. For heatings above this temperature, platinum

containers were used.

Experimental Results

The compositions, temperatures and oxygen partial pressures investigated are shown in Table 1. Selected initial compositions on two joins

were examined, the K(Fe ^Si K20-*'Fe0"-Si02 system

and the analogous KFe02~Si02 join in the K20-Fe202~Si02 system. Thus,

all final compositions fall between these bounding planes in the system

K-Fe-Si-0. The compositions in the K(Fe ^Si ^)02~Si02 join are an

extension to lower silica content of the region studied earlier by

Roedder [3]. The KFe02~Si02 join has been studied in air by McDaniel [4].

When heated at temperatures of 800*C and oxygen partial pressures

of 10 ^ atm, all compositions on the K[Fe ^Si 2]02-Si02 join yielded a

phase similar in structure to the high temperature orthorhombic form of

KFeSlO^ previously reported [4,5], In air, this orthorhombic KFeSiO^

transforms reversibly to a low temperature hexagonal form at about 945**C.

Apparently, the reduced oxygen pressure during these experiments Increases

the stability region of the orthorhombic structure. Reheating in air at

80
Table

1.

Compositions

Investigated

in

the

System

K-O-Iron

Oxide-SiO

>4- O rH +

•H CO P

sr CP >vr 3 Nd“ U St 3

o O <U o o O •H o O 1—

•H •H •H 00 •H •H •H •H

OO C/3 S CO 3 CO a CO CO a

0) (U CU X 3 O 3 3 •H U <U (p 43 3

w *H 43 P

43 O 3

o u 0 O •% O 43 o U 3

•H •H o •H 3 •H P •H •fH 3

.P 43 43 3 P ,£ 43 43 S S Vi 0 a a o 0 g (X o o o O •H o O o

43 43 43 43 U 43 O 43 43 +

VI Vi P Vi 3 P P P P > o o VI o O. 3 o o O

43 43 o 43 3 3. 43 P 43 43 O *H

VI P P P 3 P P CTO

3 Vl VI * Vi 00 P U rH P P 3 3

o o <u o 3 o iH O O Pn Ph 3 CM •H 3 a 3

rH o o •H O o •3 Vi o •H P o O O

3 •P p rH *H P 3 3 p 3 3 P P P O

a iH C/3 U P P •H

0) Vi VI CO Vi 3 O p 3 3 P P P 4i

Pi CO cO P + CO VI 3 3 3 3 3 3 3 a

j—i tH CO 1—CV Vi tH 3 P fH rH rH O

•H •H p>^ (U •H P •H 43 P •H •H •H 43 6 (U 6 <u Vi CO 0 CU cp (0 a 3 3. 3 a 3 a a P

•H Vi •H Vi O CO •H Vi O •H P •H P •H •H O

CO 3 to ;3 43 CO 3 •<t (0 3 # St 3 3 3 3 43

4J P >> (X P P O P *0 O P P

0) Cj 0) tJ r—i CU O ctS *H 3 O 3 •H 3 o 3 3 P

00 3 m 3 VI cu CO 3 3 CO 3 3 P CO 3 3 3 O 3 O

(0 Vi . cO Vi o ^ CO VI 43 3 3 P rH 3 3 P 3 CO 3

43 -M 43 P O *H 43 p 3 |4 43 P 3 43 P 43 3 43 O

P. (0 (X CO ev rH CX CO Vi S 3. 3 a (X 3 a, p

so SO rH SO SO so SO so so

CNJ a 1 1 1 1 P 1 1 1 1 1 o p 0 0 0 0 •H 0 0 0 0 0

3 rH rH rH rH 3 1—

rH iH rH rH

3

P St IS. CO CM 0 CM 0 CM

•H 4: CN CM CM CO CJS CO CM IS St St H rH

3 |a 0 0 0 0 0 0 0 0 0 CO 0 0 0 0 0 0 0 rH 0 0 0 CO 3 0 CO 00 IS. 00 00 00 CJS 00 00 0

H rH

CM CM 0 0

•H •H CM CM

13 CO CO CM 0 0

O 0 m 0 •H •H •H CM CM •H CO CO P • • •• CO CO CO

•H CM CM • • • • • • 3 0 0 CM CM CM o 0 0 0

P. m m CM a

• • in m m 0

o •H •H • • • •H o CO CO •H •H •H CO 10 m CO CO CO CO

rH • • m m m • • 3 3 3 • • 0 CM

•H (P (P 3 3 3 0 P (P (h P^ 3

lH txi pH a 0 m Ui Ui M 00 CM in St

81
'3- CO

CO(1)

ui "ao

rC

CO

(U

OS

cd 43a

<u

ti 143UO

43

4Jo o

•HsO

43O

43UUO

cn OCM

0) o

(3d o

•H C M -H o Pi 4J 4J PI 4-1 CP DO O CO + T3 • cO 43 >v Pi Pi + (U CO (U Pi X •M Pi cO cO CO cn 00 tH •H (U

0) Pi

O iH r—1

(U CO

O S3 cO CO CO 43 O •H •H CO 43 CM •H CU cO O a a CO a 0) -d S3 S3 43 O O (3 •H •H 43 [p| S3 S3 •H CP

4-t Pi P CO CO CP c3 •H CO 3 0t 3 + Pi T3 Pi

>-i Pi

O CD (U (U (U

O 00 CU CU

O

cO CO

q CO CO CO 4<Jq CM Pi

G VH

rH IH i2 CO CO CO •H

M o O (U •H

•H •H a tH 43 43 iH

G •H •H CJ S3 6 B d 00 (X FX. 1 d CO d tH O

t-f •H vO o (U CO •H

CO CD + 4-1 0k 'O' •*

O 0k 0k •H (xt CJ PJ 'O G -d cI T3 O CM d Pi CO

(U (U (U (1) 0) 1-i (U -H •H (U (U CU 4.4 CU S3

CO CD

O 4J CO PJ CO PI CO CO 4-1 4-1 CP

G Pi •H

CO co cn 1—1

CU iH (U tH (U (U tH I—i

<U CU

g

43 43 (U (U Pi (U [X1 CU PE4 Ftj (U (U 43 tH 5c Co (X O. Fl, B 0- a ! a S 2 a a 4-1 CO X

•H > S3 (U > •H O

*d Pi S3

CO •H

O

00 •H

d S3 PJ 4J o •H S3 CJ 43 G CU cO •H tH Pi 3 VO iH vO vO vO vO VO O CO cd ipi 1 1 1 1 1 1 1 O PJ > CH O o 'o o o O o o tH C! •H •H tH I—1 T—1 iH iH tH tH tH 1 O T3 O O 4-1 CO >k

CO >v CO

Pi S3 I—tPi

OO S3 1 C4-I •H O X

PI o CM o CM n O CM O CJ •H 00 Pi MT CM CM '0- >o- 0 CO S3 CU O O •H TJ

CP S3 a •H

O o cO CP •d CJ PJ

S3 S3 t3

CO

O • O o 0) O iH CD

CO S3 •H TO

CUd

G 3

•H

O

O 43

»H CD

CO CO U -H

O cn

m

m o O COOO 43

G

O

O CO iH CM

m

O CO

O vO COO •H 00 o O CM CO OO o 00 PI •H PJ tH iH tH tH tH PJ PJ COaO

CO S3 pJ CJ G <U •H CO • O a S3 o S3 •H PJ •H Pi O

PJ CO

O •H •H (U 0k •H PJ

CO Pi vO a co O PJ 1 u

CM CM CP o S3 •H CM o o a PJ tH O «H O •H •H o cO •H

•H Vi CO o 0) II T3 PJ CO CM CO 43 CU S3 • • • • • • tH CM CO (U CM CM CM I—1 O O cO T> o o O <J PJ SP PQ •H

(U (U (U

c0|

82
800°C of a sample of 2K(Fe _S1 c)0_:Si0_ previously heated at 800°C in

P = 10 ^ atm (Table 1) resulted in oxidation and formation of the

expected hexagonal, low temperature structure of KFeSiO^. Heating at

lower partial pressures of oxygen, 10 atm, showed decomposition of

the orthorhombic structure, with the appearance of free Si02 in the

x-ray diffraction pattern.

Compositions on the KFe02~Si02 join, prepared by calcining in air

to yield trivalent iron, showed generally similar results to those

initially containing divalent iron in that phases having structures

similar to hexagonal and orthorhombic KFeSiO^ were observed after heating

at reduced oxygen pressures. The initial composition 4KFe02:3Si02

is known [4,5] to have a tetragonal structure in air, at temperatures

above 850°C, however, apparently not stable at partial oxygen pressures

“6

of 10 atm. Melting points of compositions on this join are lowered

100°-150°C by heating at the oxygen pressures shown in Table 1 as

compared to the same compositions heated in air [4,5],

The use of gold containers for low temperature experiments was

generally satisfactory. In cases where melting occurred, minor goldsample reaction was evident. For temperatures above the gold limit

where platinum was used, reaction between the molten specimen and

platinum was pronounced. Attempts to prepare homogenous glasses for

equilibrium recrystallization experiments at oxygen partial pressures

“8

of 10 atm and temperatures in the 1200°-1400°C range were unsuccessful.

Three compositions were tried: KFe'^^SiO, , 2K[Fe'*’^Si c]0„:Si0_ and

83
+2

5K[Fe p-Sl c]0 :SiO_. Reaction between the platinum containers and

the molten specimens was observed in all three compositions. Considerable embrittlement of the platinum due to iron pickup was evident.

In the case of the 1400°C heating, traces of the melt were observed

on the outside of the container suggesting diffusion through the

container wall.

Conclusion and Discussion

Phase assemblages of selected compositions on the joins K[Fe ^Si^]02~Si02

and KFe02~Si02 have been determined after heat treatment of specimens

at oxygen partial pressures of 10 ^ and 10 atm. The use of gold as a

container appears to be suitable for lower temperatures where no liquid

is present. Attempts at higher temperatures to prepare homogenous glasses

for equilibrium recrystallization experiments were unsuccessful due to

excessive reaction between the platinum container and ferrous iron in the

melt at these oxygen pressures.

Discussions with Dr. Oran of MSFC have shown that it is not feasible

to acoustically levitate in a 1-g environment and simultaneously heat

specimens of these materials to the required temperatures, either for

preparation of homogenous glasses or for melting point studies. An

alternate technique is the use of aerodynamic jet levitation and it is

suggested that this possibility be explored further.

A comparison of experimental conditions and requirements for conventional and containerless phase equilibria studies as well as

anticipated problem areas are given in Tables 2 and 3.

84
Table 2. Comparison of Experimental Conditions for Phase Equilibria

Studies

CONVENTIONAL CONTAINERLESS

Specimen Pre-reacted, powder, packed

into tube, tube sealed.

Mass 'MD.l to 0.3 g

Maximum Heat- No restrictions, plunge

Ing Rate into hot furnace

Temperature

A. Measurement Thermocouple or optical

pyrometry ±1® to ±5®C

B. Control ±2® to ±5®C

C. Time at

Temperature

1. Subsolidus

Experiments hrs to days

2. Solidus Minutes to 1-2 hrs after

and isothermal equilibrium

Liquidus

Determination

Pre-reacted powder, formed

into sphere or right

cylinder. Mass '^^O.l to

0.3 g

Limted only by thermal

stress resistance of

specimen

Two color pyrometry or non-contacting method

Better than ±25®C at

final temperature

Not feasible at present

Minutes to 1 hr after

isothermal equilibrium

Cooling Rate Quench into water As rapidly aj possible

Characterization In all cases, specimens are examined post- test

and Evaluation by optical and scanning electron microscopy

and X- ray diffraction to determine phase

assemblage, partial or complete melting.

Where appropriate, chemical analyses of

specimens are performed.

85
Table 3. Some Problem Areas Associated with Containerless Experiments.

1) Heating technique for 1300® - 1800°C range

1) radiant wall furance

2) laser

3) arc-image furnace

2) Temperature measurement and control

1) two-color pyrometer

2) other non-contacting method

3) Thermal gradients in specimen must be as small as possible

4) Changes in bulk composition of specimen must be measured or estimated from vapor pressure measurements

5) Density of specimen will change with sintering and melting

during experiment

6) Electrical conductivity will vary with both temperature and

composition

In the case of low gravity experiments, electromagnetic positioning

is an alternate technique applicable to a more limited class of oxide

materials. As part of an investigation in the area of refractory oxides

having good electronic conductivity, a group of NBS investigators has

recently reported [6] conductivities as high as 1 ohm ^cm ^ in the 100®-

250®C range in calcium-doped yttrium chromites. Melting points are in

excess of 1750®C, making the choice of container material severely limited

for high temperature property measurements. The conductivities appear to

be large enough to make electromagnetic positioning feasible.

86
References

1. J. R, Manning, NBS: Properties of Electronic Materials, NBSIR

19-nei

,

pp. 82-95, June 1979.

2. J. R. Manning and R. L. Parker, NBS: Properties of Electronic

Materials, NBSIR 78-1483, pp. 84-100, June 1978.

3. E. Roedder, Am. J. Sci. (Bowen Volvime) , pp. 435-456 (1952).

4. C. L. McDaniel, unpublished work.

5. R. S. Roth, Advances in Chemistry Series "Solid State Chemistry

A Contemporary Overview", to be published.

6. T. Negas, W. R, Hosier and L. P. Domingues, Proc. Saint-Vincent

Conf. on Energy and Ceramics, Faenza, Italy, May 1979.

87
Task 4

Thermodynamic Properties of Refractory Materials

at High Temperatures

Jack H. Colwell

Chemical Thermodynamics Division

Center for Thermodynamics and Molecular Science

Summary

The current status of the program to obtain high temperature (1500-4000 K)

heat capacities of materials while they are levitated in a space environment

is presented. The heat capacities are to be derived from the simultaneous

measurement of the radiant heat loss and the rate of temperature change of

spherical samples as they cool freely. Details of the thermal gradients to

be expected in both metallic and nonmetallic samples have been examined. In

metallic samples the gradients, in general, will be tolerably small and cause

little difficulty. In nonmetallic samples the gradients will be large but

by making measurements on samples of different size, it should be possible to

get moderately precise values of both the heat capacity and the thermal

conductivity. The upper temperature limit of the experiments will be determined

by sample vaporization and will occur when the vapor pressure reaches the

-4

vicinity of 10 Pa (10 atm) . The program for a ground-based simulation of

the free-cooling experiment is discussed.

88
Introduction

The purpose of this research is to measure the heat capacities of

refractory materials at high temperatures, 1500-4000 K, by using the lowgravity environment of space to maintain the samples without physical

contact. The samples will be spherical, fabricated in that form as solids

and maintained in that form as liquids by their surface tension. They will

be heated to a high temperature and then allowed to freely cool by radiation

in a cold-walled vacuum chamber.

As the sample cools its temperature will be determined by radiation

pyrometry and the total radiative heat loss will be determined simultaneously

using a wide-band pyroelectric detector. The ratio of the heat loss to the

rate of change of temperature will be a measure of the heat capacity.

To give an indication of the nature of the experiment, two pertinent

quantities are presented in Fig. 1. The rate of cooling of a sphere by

radiation is obtained, assuming no thermal gradients, by equating the rate

of heat loss

dH = -47TR^£aT^dt (1)

with the thermal capacity

dH = (4/3)T7R^cpdT (2)

which yields

dT/.-’t = -3eaT^/(cpR) . (3)

e is the total hemispherical emissivlty, O the Stef an-Boltzmann Constant,

c the specific heat and p the density. In Fig. 1 the rate of cooling as a

function of temperature is shown for a sphere of radius R = 0.5 cm with

values of e and pc typical of refractory metals. For the region of interest

the rate varies quite widely, from 20 K/s to nearly 1000 K/s. Since it is

89
reasonable to consider measurements on samples as small as 1 ram radius, the

inverse dependence on the radius, Eq. (3), would lead to cooling rates as

high as 5000 K/ s . The detectors will be operating at frequencies of about

1 kHz, so the temperature will not be changing appreciably during the

sampling period even for the highest cooling rate. Depending on sample

size, the free-cooling period will last between about 5 and 30 seconds for

coolings to 2000 K and considerably longer for coolings extending below

that temperature.

The total power radiated by the sample, as shown in Fig. 1, gets quite

large at the highest temperatures and will, of course, be even larger foi'

larger samples or ones with higher emissivities . At these levels, the

heating of specimens to the desired temperature will become a major problem.

For metals, inductive heating will be the principal source, but to reach

the highest temperatures it may have to be supplemented with a radiative

source. Nonmetals will almost certainly require supplementary heating.

The large amount of power being radiated by the sample, however, will

simplify considerably the determination of that power at a distance. As a

result, there should be no problem with signal level except possibly for

the pyroelectric detectors with very small samples at the lowest temperatures.

We foresee no insurmountable obstacle to the free-cooling experiments

from the physical measurement aspect, that is, the radiation pyrometry

measurement or the measurement of total radiant power with pyroelectric

detectors. Some of the problems in making these measurements have been

pointed out in an earlier report and are further discussed in this

report. The real limitation to the free-cooling experiments arise from the

experimental approach. Because of the rapid cooling of the samples, temperature

gradients will exist in the samples and for those of low thermal conductivity

90
will be quite large. At some point these will make it impossible to extract

meaningful data from the measurements. We have spent considerable effort

in the determination of the temperature gradients likely to be encountered

in the experiments and what information can be extracted. The vaporization

and/or decomposition of the sample will determine the maximum temperatures

which can be reached in these experiments. Both of these limitations on

the applicability of the experiments will be discussed as well as the

current plans for future development.

Temperature Gradients

The thermal gradients within a sphere, freely cooling by radiation,

are given by the Fourier equation

8^T . 1 ^ ^ 1 ir ...

„ 2 r 8r a 8t

dr

with the thermal diffusivity a = , ) /pc, X being the thermal conductivity and

pc the density times the specific heat, i.e., the heat capacity per unit

volume. Solutions to Eq. (4) must satisfy the boundary condition

3T 4

Xtt- = £oT at r = R, (5) dr

where X 3T/3r is the heat conducted to the surface of the sphere which must

equal the heat radiated from the surface given by the Stef an-Boltzmann

4 4 relation eaT . The T term in the boundary condition, Eq. (5), makes the

equation nonlinear and it cannot be solved analytically. Solutions to this

[2 3] problem have been obtained by other workers ’ using the numerical method

of finite differences, but their results are not available to us in a

usable form. We are fortunate in having two generalized programs in the

NBS computer library for the numerical solutions of nonlinear partial

91
differential equations. The programs are MOLID (method of lines, one

dimension)^ and PDECOL (partial differential equations, collocation over

piecewise polynominals) . The MOLID program can be used to produce

tabulated temperature values at various radii for a given set of times. We

have used this program in generating the data discussed below. The program

can be made very general in allowing for various initial temperature gradients

and for different temperature dependences of the physical parameters, c,

p, e, and X. The results are somewhat awkward to use in that one cannot

conveniently generate data for different input parameters at the same

temperatures. The PDECOL program produces a polynomial solution which may

be better suited for this purpose but it has not been run to date.

To describe and understand the temperature gradients in free-cooling

spheres it has been extremely useful to define what we term the "limiting

parabolic temperature distribution." Once a cooling sphere has this limiting

distribution, its form will be maintained for the rest of the cooling cycle.

To derive this limiting temperature distribution we assume first, that a gradient

exists and second, that the gradients do not change as the

sample cools. The second assumption is not strictly true, of course, and will be

modified subsequently. In Fig. 2 we define the quantities describing the

heat flow from a sphere; Q is the power radiating from the surface of

the sphere of radius R, and q is the heat flux across a surface within

the sphere at radius r. If all parts of the sphere are cooling at the same rate,

and assuming that c, £, and X are all independent or only weak functions of

T, then

, 3 3

4irr ^ r ^ q

3 Q = 3 Q.

4ttR R

( 6 )

This equation simply states that as the sphere cools, each volume element

92
gives up the same amount of heat and that all the heat must be conducted to

the surface at R. For q to be conducted across the surface at r, the

temperature gradient at r must be such that

q = -47Tr^A^. . (7)

Q is given by the Stefan-^ oltzman relation

Q

= 4'^R^eaT^^ (8)

where T indicates the surface temperature,

s

Substituting (7) and (8) into (6) we have

4

eaT

dT = - -^Q^ --rdr, (9)

and integration from r to R yields

eaT

T(r) - l3[l+-2XR ( 10 )

The temperature at the center of the sphere relative to that at the surface is

^ = [1 + ( 11 ) s

the temperature difference being

4

eGT R

AT = T(o) - T = ^

(12)

s LK

These equations are accurate when the temperature difference, AT, is only a few

percent of T^, but not for large values. Eq. (12) shows that the temperature

difference is diminishing as T^ drops whereas the initial assumption in Eq. (6)

was that the difference was constant. To be correct, the temperature at the center

of the sphere must drop more than the temperature at the surface. Therefore,

q in Eq. (6) must be proportionately larger toward the center of the sphere

by an amount which varies with r and T much as T(r)/T . We have found that

s modifying Eq. (6) so that

93
3

q = [T(r)/T —- Q = [1 +

® R

eaT

2AR

2 2 2

(R -r )]^

R

Q, (13)

solving for a new T(r)/T^ using Eqs. (7) and (8), and by iterating

repeatedly, one obtains

3

eaT

9 9 _i

T(r) = T^[l - -^(R -r )] (14)

which closely fits the computed results.

In Fig. 3 we compare the temperature distributions derived from the partial

differential equation (solid lines) with the predicted limiting parabolic

distributions (dashed lines). We have assumed an initial condition of uniform

temperature at 3000 K. The material parameters are A = 1.0W/cm*K,

3

pc = 3.0 J/K*cm , and E =0.3, values that correspond to tungsten and are

relatively typical of most refractory metals. When the sphere initially

starts to cool, the surface temperature drops rapidly until the temperature

distribution within the sphere becomes parabolic and then the entire sphere

commences to cool unifomly. This system reaches the limiting parabolic distribution

in slightly over 0.5 seconds and after the temperature has fallen only about 2 1/2%.

It is interesting to note that the limiting temperature distribution depends only

on the thermal conductivity and not on the heat capacity. Once the limiting

distribution is established, the heat capacity determines the rate of cooling only.

The solution of the partial differential equation is needed to describe how the

initial conditions die away and at what point the limiting parabolic behavior

is applicable.

Shown in Fig. 4 are results for spheres of three different radii for a

hypothetical nonmetal where the material parameters, X = 0.046 W/cm*K,

3

pc = 4.6 J/K*cm , and e =0.3, are similar to those of solid alumina. The

initial condition is again a uniform temperature of 3000 K and the material

parameters are considered to be independent of temperature. In the figure

94
the time variable is reduced by dividing by the radius of the spherical

specimen (see Eq. (3)) which permits a better comparison of the effect of

the radius. vJ e see that initially the surface temperature of the larger

samples falls more rapidly (on our reduced time scale) until the limiting

parabolic gradient is reached. The limiting distributions for the spheres are reached

when t/R is approximately 3, 6, and 12 s/cm for the 0.125, 0.25, and 0.5 cm

radii, respectively. At t/R = 20 the surface temperatures are nearly

identical and the proportionality of the temperature differences to the radii

is obvious. That the three surface temperatures are the same at this time

is only coincidental, for once the samples have achieved the limitng

parabolic distribution, the surface temperature of the smaller sphere is always

cooling faster (in t/R units) than the larger sphere. This is a consequence

of the initial rapid cooling of the surface of the larger sphere, so that

it was losing proportionately less heat during subsequent periods than the

smaller sphere. As a result, the average temperature of the larger sphere

will always be greater than that of the smaller sphere. At lower temperaures,

when the temperature gradients are small, the surface temperature of the

larger sphere will be higher than that of the smaller sphere.

The magnitude of the change in the apparent heat capacities caused by

the temperature gradients can be readily calculated when the gradients have

the limiting parabolic form. The observed temperature change during a

given time interval is that of the surface temperature, T^. The heat evolved

during that interval, however, will depend on the change in the average

temperature of the sample. The change in this average temperature,

T^^, on cooling will always be greater than the change in T^ because of the

diminishing gradient with diminishing temperature. As a result, the apparent

heat capacity, i.e., the observed energy radiated divided by the change in

T^, will always be greater than the actual heat capacity. The average

95
temperature for a sphere as determined by

T r 47tr^T(r)dr, (15)

(4/3),tr3 i

and using Eq. (14) for T(r) gives

3T

T = —5

1 i— tan"^ -R , (16)

bR^ b „K

a

where a = 1 - eaT \/(2A) and b = eaT ^/(2AR).^^^

s s

In Table 1, changes in are given for each of two different radii,

conductivities and surface temperatures. The results show that the increase

in the apparent heat capacity over the actual varies, as might be expected.

Table 1. Changes in T relative to changes in T for spheres of two av s different radii and two different thermal conductivities including

the percentage increase in the apparent heat capacity over the

actual heat capacity

R = 0.25 cm R = 0.5 cm A(W/K*cm) T^(K) AT

s Tav

ATav%AC Tav

AT

av

%AC

0.1 3000

2950 50

3071.24

3016.50 54.74 9.5

3147.58

3087.49 60.09 20.2

0.1 2500

2450 50

2533.87

2481.20 52.65 5.3 2569.09

2513.57 55.52 11.0

1.0 3000

2950 50

3006. 91

2956.46

50.45 0.9

3013.87

2962.96

50.91 1.8

1.0 2500

2450 50

2503. 33

2453.07 50.26 0.5

2506.67

2456.15 50.52 1.0

linearly with R, inversely with A, and as the temperature cubed. The increases

found for A = 0.1 W/K*cm are distressingly large for the conductivities of most

96
nonmetals will lie at or below this value. The conductivities of refractory

metals tend to lie between about 0.3 and 1.2 W/K*cm, so the increase in

apparent heat capacity will be sizable even for many metals.

Because the heat capacity increase is nearly an exact linear function

of the sample radius, it should be a relatively simple matter to correct

for the increase by measuring samples of different size. Indeed, when the

apparent heat capacity increase is large, it should be possible to determine

thermal conductivities from a set of precise data. This process could be

appreciably complicated by the temperature dependence of c, X, and

e; these quantities were taken as constants in the above analysis, but they

are usually relatively weak functions of T. This will work for solids but

may break down completely for liquids if there is any stirring of the

sample. If a sample is heated inductively, appreciable stirring action

will occur during the heating period which may take time to die away. If a

sample were radiantly heated in a low-gravity environment it may remain

quiescent, but this will have to be determined. It is our intention,

however, to use induction coils, operating at low power levels, to electromagnetically position the samples within the apparatus. This action alone

would probably add some stirring action to a liquid sample.

Sample Vaporization

In the high-temperature levitation calorimetry carried out by David

Bonnell with John Margrave, the upper temperature limit of the experiments

was determined by the vaporization of the refractory metal samples. In

their case, the samples were in an inert-gas atmosphere and the vaporizing

atoms condensing into a smoke which physically obscured the sample. This

occurred at vapor pressures of about 10 Pa, which, in general, corresponds

to temperatures about 200 K above the melting point of the metals.

97
The free-cooling experiments will be in a vacuum so there will not be

any smoke formation; sample vaporization, however, will still cause difficulties

and determine the high temperature limit for the experiments. Assuming the

evaporation coefficient for metals to be y = 1, the rate of evaporation at

-3 2 3 10 Pa will be about W = 10 g/cm *s. Using a sample density of p = 12.5 g/cm ,

the rate of sample loss will be W/p = 8 x 10 ^ cm/s. As a fraction of the

total sample, this will be F = W4ttR^/ (4/3ttR^P) = W/ (Rp) = 8 x 10 ^/R s

For R between 0.1 and 1 cm the loss will be less than 0.1%/s and can probably

be ignored. This vaporizing material will, however, be condensing on the

apparatus. Consider a detector or detector objective lense 10 cm from a

sample of R = 0.5 cm, the rate of deposition of the metal coating on these

objects will be about 2 nm/s. This may seem a small amount but considering

that an opaque metallic coating has a thickness of about 50 nm, indicates

that the detectors will have to be protected if exposed to samples vaporizing

at these rates for periods of a few seconds or more.

The heat loss from a sample will be significant at vapor pressures of

10 Pa. Using AH^ = 750 kJ/mol for the heat of vaporization of refractory

[81 3 metals,^ ^ and V = 10 cm /mol as the molar volume, the power of heat loss m

by vaporization at a vapor pressure

In Table 2, is compared with the

three different temperatures.

Table 2. Power of evaporative heat

with radiative power (e =

T(K) P^(W/cm^)

2000 27

3000 137

4000 435

of 10 Pa is P = WAH /(pV ) = 6 W/cm'

V V m

radiative power, P , for surfaces at

R

loss (vapor pressure = 10 Pa) compared

0.3) at various surface temperatures

P^(W/cm^) P /P„ X 100 (%) V K

22

4.4

1.4

98
It is apparent that with samples at temperatures where the vapor pressure

is 10 Pa, a significant correction will have to be made for sample vaporization, and for those sample materials reaching that pressure at low

temperatures, the correction will have to be of fairly high accuracy.

There are also potential problems from the sample vapor due to its

absorption spectrum. Nearly all materials will have absorption bands in

the region of interest, 0.3 ym to 15 ym for the total radiance measurement.

The atomic absorption lines of metal vapors will probably remain sharp up to

pressure of 10 Pa and block out very little of the total radiation. Above

that pressure, however, the lines will begin to broaden and an appreciable

amount of radiation from the sample would be blocked from the detector. For

the radiation pyrometry, which will use narrow bandwidths between 0.4 and

1 ym, care will have to be taken that absorption lines do not occur at the

wavelengths being used.

This discussion on vaporization has been restricted to metals because of

the availability of data and the generalizations that can be made. The same

type of problems and limitations will occur with nonmetallic samples and will

probably be much more involved and stringent. The evaporation coefficient will

most likely be less than 1 and vaporization can be accompanied by dissociation

of the molecular species so that quantities such as rates and heats of

vaporization are less well defined. Molecular species in the vapor will make

the absorption spectrum much more complex with numerous broad absorption bands.

Finally, if decomposition is occurring at the surface, the radiative properties

of the surface could be altered considerably and introduce errors in interpretation of the radiation measurements.

99
Total Radiance Measurement

The unique aspect of the free-cooling experiment and that with least

precedent, is the proposal to use pyroelectric detectors to measure the

total radiant heat loss from the sample. The detectors must be uniformly

black over the wavelength 0.4 to 14 ym which will include 99% of the radiation

from samples at tanperatures between 1500 and 4000 K. When the field of

view of the detector encompasses the entire sphere of the sample, the

signal will be proportional to the total hemispherical emittance, the

proportionality will be the area of the detector relative to the area of

the sphere whose radius is the distance from the detector to the center of

the sample.

A pyroelectric is a poled ferroelectric, which, when heated, changes

its spontaneous polarization. LiTaO^ detectors will be used because the

883 K Curie temperature of this material makes it well suited for a high

temperature apparatus and they are available in a wide range of products

from several manufacturers. A pyroelectric detector has electrodes on two

sides of a thin wafer of material forming a capacitor, a change in polarization

of the material can then be used to generate a current in an external

circuit. The current is proportional to the rate of change of temperature

so that radiation from a continuous source must be chopped to get useable

response. A black coating is applied to the front surface of the pyroelectric

to enhance the light absorption and the back surface is bonded to the

mounting which serves as a heat sink. Fig. 5 shows the thermal response of

an idealized pyroelectric detector. The diagram at the top of the figure

describes the model used; P is the power of the incident radiation, c is

the thermal capacity of the pyroelectric which is at temperature T, h is

the thermal conductance to the heat sink at T . The response of the model

100
is given by

P - h(T-T ) _h

P - h(T,-T ) " ^

1 o

which is plotted as curve A in Fig. 5 with P = 0 and the initial temperature,

T, > T and as curve B with P = P and T. = T . The thermal response of the detector

1 o X o

to chopped radiation is represented by the saw-toothed curve which rises from when

the radiation is turned on until reaching a steady state. At the steady

state, the temperature of the pyroelectric will be following the path

indicated by the arrows at the intersection of curves A and B in Fig. 5.

For this idealized example, che electrical response will be a square wave

when the chopping period is sufficiently small compared with the thermal

relaxation of the device, t = c/h. As the chopping period is made longer,

the curvature in the thermal response will become more evident and the

square wave will begin to droop.

The model for the thermal response is idealized in several ways.

Foremost is that the model implies that the pyroelectric is uniformly

heated whereas it actually responds to the thermal pulse as it propagates

through the material. Also, the black coating introduces a thermal lag

which together with electrical response of the circuit produce a sizable

rise-time for the device. Fig. 6 shows oscilloscope tracings of the response

of a pyroelectric detector at four different chopping frequencies. At 300

Hz the rise time of the response is very evident but part of this is due to

the transition period of the chopper. The constant voltage period is

somewhat less than a millisecond. At 150 Hz the voltage is essentially

constant for more than 1 1/2 ms. At 75 Hz the droop in the voltage signal

is evident and from the 15 Hz curve the thermal time constant for the

device of 15-20 ms can be deduced. It was intended that this particular

101
detector could be used at 300 Hz with the voltage sampled for 1 ms during

each half cycle. The 300 Hz curve in Fig. 6 shows that either the sampling

period or the chopping frequency will have to be reduced to get the full

signal

.

Gold black is used for the absorptive coating on the pyroelectric

detectors and numerous reflectance measurements have shown these coatings

to be uniformly black to between 98 and 100% for wavelengths from 0.3 to

10 ym. Beginning between 10 and 20 ym there is a drop-off to values as low

as 90% with the position of the drop-off varying from sample to sample. At

wavelengths above 10 y, however, we are concerned only with the long wavelength

tail at the lowest temperature so the errors introduced should be small.

Because of the smallness of the detectors and the degree of difficulty in

making accurate reflectance measurements, the blackness of individual

detectors cannot be determined directly and must be assumed to be similar

to the measured coatings.

The calibration of the pyroelectric detectors will present some difficulties. The response of the detectors are supposed to be linear over the

range of power to be covered by the experiments for samples of 0.1 to 1 cm

radius and temperatures from 1500 to 4000 K. The linearity and magnitude

can be established to a fair degree of precision using standard tungsten

filament lamps. There will be, however, uncertainties of several percent

arising from the transfer of the calibration as well as the original lamp

calibration itself.

Current Experimental Plan

Because of the untried nature of the pyroelectric detection system in

particular and the free-cooling experiment in general, we are proceeding

102
with a ground based simulation of the space experiment. The setup to be

used is shown in Fig. 7 where in place of the sample being levitated within

the apparatus, it is simply suspended from a wire of the same material.

Tungsten is the material of choice since with its high melting point,

3650 K, experiments could probably be run at temperatures up to 3500 K or,

as is more likely, up to the limit of the available power for induction

heating. The heat capacity and emittance are reasonably well known for

solid tungsten so that the observed results for the free-cooling of the

sample can be compared with calculated results. The correction for the

heat leak to the suspension wire will probably be relatively small and, in

any case, it can be minimized by electrically heating the wire. A hole

drilled in the sample can be used for blackbody temperature measurements so

that it will not be necessary to rely on any assuaptions about the surface

emittance in order to determine the sample temperature. The simulated

experiments will allow investigation of many of the problem areas such as

reflected light getting into the wide aperture of the pyroelectric detector

and light reflected from the coils back onto the sample.

A high-speed, 12 bit, digital voltmeter will be used to record the amplified

pyroelectric detector signals. The unit is controlled and the data logged

by a desk-top computer. Pyrometry will initially be carried out with an

existing millisecond pyrometer, but we are about to start designing a new

pyrometer which will be dedicated to the free-cooling experiments. The

pyrometer will be a two or three color instrument sampling at millisecond

intervals. Control and data logging will be handled by the same system

used for the pyroelectric detector.

103
Conclusions and Discussion

The upper temperature limit of the free-cooling experiments will be

limited by the vaporization of the sample. This will occur when the vapor

pressure of the material reaches the vicinity of 10 Pa.

For nonmetals there will be problems from numerous sources. The low

electrical conductivity may preclude inductive heating and limit the ability

to use radio frequency fields for positioning the samples. The transparency

of some nonmetallic materials will cause difficulties in temperature

determinations . Temperature gradients, determined by the thermal conductivity of the material, will limit the precision of the derived physical

quantities. For X < 0.01 W/K*cm, it may be difficult to extract any

meaningful results from the data. For 0.01 < X < 0.1 W/K*cm, it should be

possible to obtain both heat capacities and thermal conductivities of

moderate precision for solid samples. For X > 0.1 W/K*cm, relatively

precise heat capacities should be obtained together with a low precision

value of X, again for solid samples. Meaningful data on liquid samples

with X much below 1 W/K*cm could only be obtained in the limits of rapid

stirring or no stirring. It will probably not be possible to derive heats

of fusion from the cooling curves of poorly conducting materials.

With metals, vaporization of the sample appears to be the only impediment

to heat capacity measurements by the free-cooling technique. The high

thermal conductivity of the samples will keep the gradients small enough

that stirring within liquid samples will produce only a minor perturbation

on the measurements. It is unfortunate that with few exceptions (Hf, Zr,

and Pt), the vapor pressure of high-melting metals will limit the experiments

to temperatures just slightly above their melting points, because it would

be of great value to obtain the heat capacities of liquid metals over a

104
wide temperature range. The free-cooling experiments do, however, open a

new prospect; to measure the heat capacities of the liquid metals into the

[91 supercooled range. Containerless samples should, and have been observed

to, supercool to a considerable extent. The free-cooling experiment will

permit the heat capacity to be determined all the way to the point where

solidification commences and the sample recalesces. It will also be possible

to change the sample size and thus the rate of cooling, which may produce

variations in the extent of supercooling and even possibly the heat capacity.

The prospect of the supercooling experiments with metals makes the development

of the free-cooling technique worthwhile even if the determination of

nonmetal heat capacities were to turn out to be infeasible.

105
References

[ 1 ]

[ 2 ]

[3]

[4]

[ 5 ]

[ 6 ]

[7]

[ 8 ]

[9]

J. H. Colwell, NBSIR 79-1767, NBS; Properties of Electronic Ilaterials ,

J. R. Manning, Ed., p. 103.

D. L. Ayers, J. Heat Trans., Trans. ASME 92, 180 (1970).

G. Wouch, E. L. Gray, R. T. Frost, and A. E. Lord, Jr., High Temp.

Sci. W, 241 (1978).

J. M. Hyman, The NYU Report-Method of Lines Solution of Partial

Differential Equation, Oct. 1976, or contact James M. Hyman, Group

T-7, Mail Stop 233, Los Alamos Scientific Laboratory, Los Alamos, New

Mexico 87545.

N. K. Madsen and R. F. Sincovec, ACM-TOMS 326 (1979).

Using Eq. (10) as an approximation for T(r), a much simpler expression

is obtained for T : 3.V

David W. Bonnell, Ph.D. Thesis, Rice University, Houston, Texas (1972).

S. Dushman and L. R. Roller, Scientific Foundations of Vacuum Technology ,

2nd Edition, S. Dushman and J. M. Lafferty, Eds. (Wiley, N.Y., 1962),

Chap. 10; R. E. Honig, The Characterization of High-Temperature Vapors ,

John L. Margrave, Ed. (Wiley, N.Y., 1967), Appendix A.

D. W. Bonnell and W. J. Boettinger, private communications.

106
T(K)

Fig. 1. The rate of temperature change and total radiant power for a free-cooling 1 cm sphere of refractory material, e = 0.3,

pc = 3.0 J/K*cm^.

107
Q

Fig. 2. Diagram for the derivation of the limiting parabolic temperature

distribution.

108
Fig. 3. Temperature gradients in a sphere of 1 cm radius freely cooling by

radiation from an initial constant temperature of 3000 K. The

material parameters, £ = 0.3, pc = 3.0 J/K*cm^, and A = lW/K*cm

correspond closely to those of tungsten. The solid curves are solutions of the partial differential equation describing the system.

The dashed curves are the limiting parabolid temperature

distributions for the same surface temperatures.

109

Time

(s)
Fig. 4. Temperature gradients in freely cooling spheres of three different

radii of a hypothetical material with e = 0.3, pc = 4,6 J/K*cm^ and

A = 0. 046 /K’cm. The initial condition is a uniform temperature

of 3000 K. The dash-dot line at the bottom is a reference line to highlight the direct proportionality of the magnitude of the

gradients to the radii.

110

Time

(s)/R

(cm)
Ill

Fig.

5.

Thermal

behavior

of

an

idealized

pyroelectric

detector.
g. 6. Oscxllograph tracing of the output of a pyroelectric detector at four

different light chopping frequencies. i

7

112
Suspension

Wire

Spherical Specimen

with Blackbody Cavity

Induction

Heating Coils

Pyroelectric

Detector

Chopper

Pyrometer

Fig. 7. Diagram of simulated space free-cooling experiment.

113
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NBS-114A (REV. 0-78)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR 80-2082

2. Gov't Accession No. 3. ReciiJtent' $ AccossionNo.

, ^ ^

'Y;f;

4. TITLE AND SUBTITLE

NBS: Materials Measurements

5. Publication Date July 1980

6. Performing Organization Code

7. AUTHOR(S)

J. R. Manning

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, DC 20234

10. Project/Task/WorK Unit No.

11. Contract/Grant No. Government Order

H-27954B

12. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS fS«ree(, City, State, ZIP)

Materials Processing in Space Program

National Aeronautics and Space Administration

Washington, DC 20546

13. Type of Report & Period Covered Annual

Apr. 1979 - March 1980

l4. l^KMisoring Ag»tcy Code

15. SUPPLEMENTARY NOTES

1 1 Document describes a computer program; SF-185, FIPS Software Summary, is attached.

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.) The report describes NBS work for NASA in support of NASA's Materials Processing

in Space Program covering the period April 2, 1979 to April 1, 1980.

The results obtained are given in detailed summaries in the body of the report.

Briefly, in Task 1 - Surface Tensions and Their Variations with Temperature and Impurities - measurements in an Auger spectrometer of surface impurity concentrations on

liquid gallium showed that the principle impurities were oxygen and carbon. The

impurities showed a tendency to collect into plates or clumps. In Task 2 - Solutal

Convection During Directional Solidification - in Pb-rich Pb-Sn off-eutectic alloys,

macro segregation caused by solutal convection was not reduced by vertical or horizontal

fields of O.lT, but downward solidification (liquid below solid) virtually eliminated

macro segregation in small 3 mm) diameter samples. In Task 3 - A Thermochemical

Study of Corrosive Reactions in Oxide Materials - phase assemblages of selected com- positions on the joins K[FeQ

5

I ^2 ~ ^^*^9 KFeO^ - Si02 were determined over a large range of oxygen partial pressures and the temperature range 800 °C to 1400 °C.

In Task 4 - Thermodynamic Properties of Refractory Materials at High Temperatures - use of pyroelectric detectors to determine the radiant heat loss from spherical

samples as cooling occurs in free-cooling experiments is being investigated.

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)

Auger measurements on liquids; convectionj gallium; heat capacity; lead-tin alloys;

magnetic field effect; phase diagram; potassium-iron-silicon oxides; solidification;

surface tension; thermodynamic properties

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