NBSIR 73-402

NBS Materials Science and

IManufacturing in Space Research

E. Passaglia, R. L. Parker

Institute for Materials Research

Metallurgy Division

National Bureau of Standards

Washington, D. C. 20234

November 1973

Final Report

For the Period 1 November 1972 - 31 October 1973

Annual Report, NASA Contract W-13,475 No. 1

U. S. DEPARTMENT OF COMMERCE

IMATIOIMAL BUREAU OF STANDARDS

NBSIR 73-402

NBS MATERIALS SCIENCE AND

MANUFACTURING IN SPACE RESEARCH

E. Passaglia, R. L. Parker

Institute for Materials Research

Metallurgy Division

National Bureau of Standards

Washington, D. C. 20234

November 1973

Final Report For the Period

1 November 1972 - 31 October 1973

Annual Report, NASA Contract W-13,475 No. 1

This report was prepared by the National Bureau of Standards under

contract W-13,475 No. 1 - NBS Materials Science and Manufacturing

Space Research, for the Advanced Missions Program of The National

Aeronautics and Space Administration.

U. S. DEPARTMENT OF COMMERCE, Frederick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS, Richard W. Roberts, Director

Table of Contents

Page

Summary 1-2

Task 1 - EFFECTS OF CONVECTION ON CRYSTAL PERFECTION IN

CZOCHRALSKI CRYSTAL GROWTH by M. Kurlyama,

J. G. Early and H. E. Burdette 3-24

Task 2 - VAPOR TRANSPORT SYNTHESIS AND CRYSTAL GROWTH OF

OXIDES by H. S. Parker 25-32

Task 3 - PREPARATION OF ULTRAHIGH PURITY MATERIAL by

R. C. Paule 33-44

Task 4 - ROLE OF SURFACE TRACTION AND RELATED PHENOMENA IN

CHEMICAL PROCESSING IN SPACE by A. L. Dragoo 45-56

Task 5 - VACUUM EFFECTS IN THE PREPARATION OF COMPOSITE

MATERIALS by H. Yakowitz and D. E. Newbury 57-68

Appendix 69-88

Distribution List 89-90

i

National Bureau of Standards Materials Science

and

Manufacturing in Space Research

Summary

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

Materials Science and Manufacturing in Space (MS/MS) (now Space

Processing) program, covering the period November 1, 1972 to

October 31, 1973. The objectives of the NBS program are to perform

ground-based studies of those aspects of space that could possibly

provide a unique environment for making materials more perfect or

more pure. The approach taken deals primarily with experimental and

theoretical studies of the possible effects of the absence of gravitational forces on those materials preparation processes where the

presence of gravity may be important in reducing perfection or purity.

The materials preparation processes studied comprise 5 tasks in the

areas of crystal growth, purification and chemical processing, and the

preparation of composites.

The results obtained for each task are given in detailed summaries

in the body of the report. Briefly, in Task 1 - Effects of Convection

on Crystal Perfection in Czochralski Crystal Growth - an intensive

study has been performed, and optimum solidification parameters

determined for the production of highly perfect copper crystals by the

Czochralski growth process, using x-ray topographs and rocking curve

measurements of crystal perfection. In Task 2 - Vapor Transport

- 1 -
Synthesis and Crystal Growth of Oxides - the Zr02-Ta20^ mixed oxide

system was investigated in chemical vapor transport and met severe

problems in attack of quartz reaction tubes. In Task 3 - Preparation

of Ultrahigh Purity Materials - a calculational procedure involving

the use of complex chemical equilibrium was developed and showed

that extensive purification can be obtained in evaporative purification.

In Task 4 - Role of Surface Traction and Related Phenomena in Chemical

Processing in Space - the pattern of thermocapillary convection cells

in a liquid drop with an axially symmetric temperature field on the

surface was deduced. In Task 5 - Vacuum Effects in the Preparation of

Composite Materials - the scanning electron microscope was used to

study the effects of strain, surface coatings and specimen tilt in

electron channelling patterns.

While it would be premature to draw, at this stage, extensive

conclusions from these studies on space processing, it is clear

that the role of gravity in materials processing can have significant,

and possibly limiting, effects on purity and perfection of materials,

and that extensive experimental and theoretical investigations, in

ground-based environments, are important base-line information needed

for the efficient use of the space environment in materials processing.

- 2 -
Task 1

Effects of Convection on Crystal Perfection

in Czochralski Crystal Growth

M. Kuriyama, J. G. Early and H. E. Burdette

Metallurgy Division

Institute for Materials Research

Summary

In the absence of gravity, thermal convection, i.e., convection

induced by gravity acting on density differences in the melt, would

be expected to be negligible. Fluid flow in the melt, including

thermal convection, probably affects crystals grown from the melt.

At present, the relationship between crystal growth conditions, in

particular fluid flow conditions, and the degree of crystal perfection

has not been well established for metals. As a continuation and

expansion of our previous work (Government Order H-84832A, NASA), an

Intensive study has been performed and reported here on optimum solidification parameters for the production of highly perfect copper crystals

by Czochralski growth. In this research, the crystal perfection has

been assessed by non-destructive methods of x-ray diffraction, such as

Borrmann anomalous transmission and rocking curve measurements by double

crystal dif fractometry . The copper single crystals have been grown

under various growth conditions where the rotation of the seed and of

the melt and the diameter of the bottle-neck are chosen as variables.

X-ray topographs have been analysed along with the data obtained from

- 3 -
rocking curve measurements. Tables of growth conditions and quantitative

data of rocking curve widths are presented in this report with the x-ray

topographs. Optimum growth parameters resulting in highly perfect

crystals have been determined. Possible mechanisms for obtaining highly

perfect crystals have been discussed.

- 4 -
Introduction

Although for many years certain semiconducting materials, such as

Si and Ge have been grown from the melt phase, free of dislocations, it

has not generally been possible to grow sizable metal crystals free of

dislocations. The reasons for this are still not entirely clear. The

difficulty in growing highly perfect metal crystals may be attributed

to their low dislocation energy and high dislocation mobility, compared

with those factors for semiconducting crystals. Imperfections can be

produced by impurity particles present in the melt which may originate

in the container used to hold the melt.

In addition to these defect sources, one certainly cannot neglect

sources related to thermal conditions. Among them, the presence of

thermal convection and other fluid flow phenomena in the melt may affect

solidification processes resulting in the build-up of inhomogeneous

strain fields sufficiently large to cause dislocations to multiply.

Since thermal convection is induced predominantly by gravity acting on

density differences in the melt, it is usually impossible to control

completely fluid flow, especially convection, during crystal growth on

the earth's surface.

At the present time, the relationship between the crystal growth

conditions and the degree of crystal perfection has not been well

established for metals. As a continuation and an expansion of our

previous work, an intensive study has been performed and reported here

on optimum solidification parameters for the production of large, highly

perfect metal crystals by Czochralski growth. In this research as well

- 5 -
as In the previous study, a non-destructive assessment of the crystal

perfection of the grown crystals is indispensable. Further development

.has, therefore, been continued on high resolution X-ray diffraction

methods for the characterization of such crystals. Hereafter, our

previous work will be referred to as Report I .

In the present report, emphasis will be placed on studying the

resultant crystal perfection from the following aspects:

a. reproducibility of crystal perfection for given growth

conditions,

b. "bottle-necking" effects in the processes of crystal growth,

c. annealing effects after sample crystals are prepared in a

disc form.

In studying crystal perfection as a functional of fluid flow, it is

necessary first to establish the fact that there is, indeed, a relation

between the crystal perfection and the fluid flow conditions. In

Report I, we have discussed such a relation, based on our preliminary

experiments. However, it was not conclusive whether or not the variations of crystal perfection are caused by fluid flow conditions, per se,

or by other factors, such as the perfection of seed crystals, and the

procedures of handling grown crystals. In view of this, it is important

to check whether one can reproduce the same degree of crystal perfection

for a given fluid flow condition. This check cannot be done without

including aspects b and c, although analysing the results in aspect a

* Government Order H-84832A, National Aeronautics and Space

Administration; NBS Report 10873.

- 6 -
alone seems sufficient enough to define the optimum fluid flow conditions

in the melt for the present purpose.

Experimental Procedures

The details of the experimental procedures and the principles of

x-ray diffraction mechanisms which are required to perform the present

work have been described in Report I. In the present report, only

changes and improvements will be discussed, along with a brief description of the techniques we use.

The schematic diagram of the Czochralski pulling apparatus is shown

in Fig. 1, where the principle variables defining growth conditions are

denoted by x (pulling speed), y (seed rotation) and z (crucible rotation).

The pulling speed is generally between 0.013 cm/min. and 0.1 cm/min. The

speed does not cause as significant a change in diameter, except for

crystals having a very small bottle-neck diameter (~0.05 cm), as does

the temperature in the melt. When the crystal initially grows with a

very small bottle-neck diameter, the pulling speed affects the diameter

of the growing part significantly until the bottle-neck region completely

clears the top of the furnace.

Crystal boules were grown by narrowing the diameter at one region

of the boule and increasing the diameter for the rest of the boule till

the desired crystal diameter (1.5 cm ~ 3.0 cm) is reached. Narrowing

the crystal diameter (the bottle-neck) can be produced by increasing

the temperature of the melt. Two examples of crystal boules are shown

in Fig. 2. Because of extremely narrow bottle-necks, the removal of

- 7 -
crystal boules from the puller required the following procedures to be

adopted to prevent any flexing of the crystal in the neck region which

would induce strains and dislocations. When the boule has cooled to

room temperature, a mold is placed around the boule, but not touching it.

The mold is then filled with molten paraffin (at approximately 40°C)

.

When the wax has cooled, the crystal is released from the puller. The

wax supports the neck while the crystal is mounted on an acid saw.

At least three slices of sample crystals were cut from different

regions of each boule. One of the slices was annealed at 1000°C for

three days in a hydrogen (dew point = -90 °F) flow furnace. The thicknessi

of the slices were determined by use of the Borrmann (anomalous transmission) effect of x-ray diffraction. Fig. 3 illustrates schematically

the experimental arrangement and the derivation of the thickness equation

D = (Lq - Lg)/tan 9.

In the present work, the slit placed in the x-ray beam before the crystal

is 0.01 cm wide. A photograph of a nuclear plate used for the determination of thickness is shown in Fig. 4, where the (111) Bragg diffraction

was used with Cu Ka-j^ radiation.

For the characterization of the perfection of sample crystals, we

have used two different x-ray optical alignments, namely an asymmetrical

topographic camera and a high resolution double crystal spectrometer.

The former, which will be called ATC hereafter, was designed in order

to enable us to survey a large number of sample crystals effectively

in a shorter time period than that required for ordinary topography.

Although this was accomplished at the expense of high resolution, the
quality of topographs from the ATC remained just as good as in ordinary

x-ray topography. (It was one of the requirements for this design to

maintain such high quality in the topographs.)

In the ATC, the first crystal is a silicon crystal whose surface

makes an angle of 13.5° with the (111) diffracting plane. The incident

x-ray beam falls on the crystal surface almost parallel to it, and the

(111) diffracted beam appears with a size of 1.7 cm x 2.5 cm, being

sufficiently large enough to cover the entire area of sample crystals.

Care must be taken with the first crystal so that it would not superimpose its own surface structure on topographs of the structure of the

sample crystal. This requirement often induces an unavoidable lack of

ideal high resolution in the ATC. The schematic diagram of the ATC is

shown in Fig. 5. Topographs are taken from the sample crystal (Cu)

both in transmission geometry, where the (111) diffraction of copper is

used, and in reflection geometry, where the (220) diffraction is used.

To obtain diffraction rocking curves and high resolution topographs

at various locations on the sample crystals, the high resolution double

crystal spectrometer (hereafter called the spectrometer) has been used

with a scanning stage mounted on it. The schematic diagram of the

spectrometer is shown in Fig. 6, where the first crystal is only shown

in reflection geometry. A photograph of the spectrometer in operation

is shown in Fig. 7. A silicon crystal of disc shape whose surface is a

(110) crystallographic plane has been chosen as the first crystal to

obtain a well collimated monochromatic beam from the (220) Bragg diffraction both in reflection and transmission geometry. Between the x-ray

- 9 -
source of a point focus x-ray tube and the first crystal, a horizontal

slit of 6 mm and a vertical slit of 0.3 mm have been inserted. When the

first crystal is in reflection geometry, two vertical slits of 0.15 mm

and 0.10 mm, respectively, are placed a distance of 3 cm apart from each

other before the second crystal. When the first crystal is in transmission

geometry, no slits are inserted.

The quality of the beam was checked by measuring the rocking curves

of a dislocation free germanium crystal which was placed at the second

crystal position. The full width at half maximum (FWHM) of the rocking

curve from the (220) germanium diffraction was determined to be 12.8

seconds of arc in the Si (220) surface/Ge (220) surface mode and 15.5

seconds of arc in the Si (220) transmission/Ge (220) surface mode,

where Cu Ka radiation is used throughout.

Experimental Results

1. Fluid Flow Conditions

The fluid flow conditions in the melt during crystal growth are

classified into groups by different sets of values of the principle

variables, angular velocity of crucible and seed rotation, as listed

in Table I, By interchanging the values of y and z, we obtain A with

opposite signs. Based on the results in Report I and the results in

the present work, there appears to be no significant difference in the

resultant crystal perfection due to the difference in the sign of A.

Therefore, we do not discriminate fluid flow conditions from each other

when the sign of A is changed by exchanging the values of y and z.

- 10 -
In addition, we have introduced another parameter indicating the

diameter of the bottle-necks grown during the crystal growth process.

There are always at least two different bottle-neck diameters chosen

in each group; one is very narrow, usually less than 1 ram and the other

between 2 mm and 4 mm.

2. Spectroscopic Data

In Table II, we list the values of rocking curve widths (FWHM)

observed in both transmission and surface reflection geometry for all

the growth conditions, including annealing. The crystal is considered

to be more perfect, the smaller the observed width. The crystals are

ranked, as shown in the eighth and ninth columns, in increasing order

of their widths. The annealed crystals are ranked separately with

the letter A accompanied by their rank. The ranks based on the

transmission data should be judged along with the values of yL, because,

even with the same degree of perfection, thicker crystals show narrower

widths.

In most crystals, the perfection is not uniform throughout the

crystal. Rocking curves taken at different locations from the same

crystal are shown in Fig. 8, where the (220) diffraction is set in

reflection geometry. Other examples of local rocking curves are shown

in Fig. 9, where the (111) diffraction is set in transmission geometry

(yL ~ 25) . In this figure, the horizontal axis represents a decreasing

glancing angle to the right. The little humps on the right side of the

individual profiles correspond to the Bragg diffraction due to Cu

radiation. The separation of the a and a_ peaks in the Si (220) /Cu (111)

- 11 -
non-parallel (11) setting is -20.8 second of arc, which is given by the

difference between the separation of and due to Si (220) and that

due to the Cu (111) diffraction.

Typical rocking curve profiles are shown in Fig. 10 and 11 for

various crystals. In Fig. 10, the curves were obtained in both transmission and surface reflection geometry of the copper crystal with the

first crystal, Si (220), in transmission geometry. The horizontal axis

represents an increasing glancing angle to the right. The smaller peaks

correspond to the diffraction: the separation in the reflection

geometry is calculated to be +163.0 seconds of arc. Fig. 11 shows the

rocking curve profiles from a crystal of good quality (#037303) and a

typical rocking curve from a crystal of poor perfection (#035302) . The

latter crystal did not produce observable anomalous transmission.

3. X-Ray Topographs of the Grown Crystals

As mentioned previously, diffraction topographs were taken by two

different x-ray alignments, the ATC and the scanning spectrometer. The

topographs taken by the ATC usually gave the entire view of the sample

crystals, unless the crystal size was larger than the size of the x-ray

beam. Examples of the topographs are shown in Figs. 12a, b and 13a, b

in both the reflection and the transmission geometry from as grown

crystals. Since for lack of space we cannot show all the topographs

here, we shall describe the qualities of the crystals as-grown in

various growth conditions, based on their topographs.

* Many of the enlargements of the topographs are formed as composite

photographs as a result of limitations of the microscope used in the

enlargement technique.

- 12 -
The crystals grown in Growth Condition I with a narrow neck

generally produced surface topographs (obtained by a surface Bragg

diffraction) almost as good as those shown in Figs. 12a and 13a, but

with a continuous distribution of darkness (excess intensity) areas

which we call "strain contours". The transmission topographs (taken

in transmission geometry) indicated, however, much poorer quality in

those crystals, showing the anomalous transmission only in about 50%

of the total area.

In contrast, the crystals grown in Growth Condition I with a

wider neck showed much poorer quality in their surface topographs, in

which not only the strain contours, but many lines of imperfections

appeared. These crystals usually did not produce good transmission

topographs

The crystals grown in Growth Condition II were of a quality

similar to those grown in Growth Condition I with larger necks. The

surface topographs showed many strain contours and often the topograph images did not cover the entire exposed area of the crystals.

The transmission topographs were broken up into many areas, indicating

that the perfect crystal areas were very much limited within small

local regions. These results were consistent in this growth condition,

regardless of their bottle neck diameters.

The crystals grown in Growth Condition III with a narrow neck

generally displayed the best quality of perfection. Fig. 12a, b and

Fig. 13a, b are examples of the topographs from the crystals grown in

this condition. The surface topographs showed much fewer crater-type

- 13 -
images than those taken from the crystals grown under other growth

conditions. The number of visible dislocations in the surface topo2 graphs are found to range between 11 and 100 dislocations per cm for

the crystals as-grown in this condition. The transmission topographs,

however, reveal more imperfections in the interior of the crystals, as

shown in Fig. 12b and 13b. One of the common features in the transmission

topographs from these crystals is shown in Fig. 13b, although this

crystal happened to show this feature in a somewhat exaggerated fashion.

In this topograph, many lines runs normal to the <111> direction. The

Bragg diffraction in this case is (111). Also, additional lines,

though less visible, run normal to the <111> direction. In addition,

there appear black and white bands parallel to the <110> direction.

Those lines are caused by extended dislocations associated V7ith a

stacking fault, running almost parallel to the <101> direction. The

lines probably represent Lomer-Cottrell locking of the interacting

dislocations.

The crystals grown in this condition but v/ith a large neck diameter

generally produced topographs of almost the same quality of perfection

as the crystals grown in Growth Condition I with a large bottle-neck. The

transmission topographs consisted of several regions, indicating that

there were few highly perfect regions throughout the crystals.

The crystals grown in Group Condition IV could not be investigated

by x-ray topography, as they were not single crystals.

Under Growth Condition V, regardless of the bottle-neck diameter,

the crystals displayed typical mosaic structures, as shown in Fig. 14a.

No transmission topographs were produced.

- 14 -
Now we turn to the annealing effects. As Indicated in Table II, at

least one crystal from the boules in each growth condition was annealed.

As shown in Fig. 14b, the surface topograph from an annealed crystal of

Growth Condition V is just as bad as Fig. 14a, indicating that the

mosaic structure was not at all affected by annealing. The annealed

crystals of Growth Condition II showed polygonization, which usually

resulted in the formation of several subgrains.

All the topographs taken from the annealed crystals in Growth

Conditions I and III showed an equally high degree of perfection in

both surface and transmission geometry. The resultant degree of

perfection was almost independent of the bottle-neck diameters.

Examples of the surface and transmission topographs are shown in Fig. 15a,

b and Fig. 16a, b, respectively of Growth Condition I and Growth Condition

III. As seen in the transmission topographs, the Lomer-Cottrell locks of

dislocations disappeared and dislocations net works appeared rather

randomly

.

The number of dislocations counted on the surface topographs for

2 these annealed crystals was less than 23 dislocations per cm , the smallest

2 number observed was 7 disl./cm . The dislocation densities can be

obtained from the transmission topographs which show all the dislocations

in the interior of the crystals. In this case, the dislocation density is

equal to the number of dislocations multiplied by the length of each

dislocation divided by the volume where the dislocations are counted.

The average number of dislocations thus obtained was 15 dislocations per

2 2 cm . The smallest number was 12.8 dislocations per cm . In these

- 15 -
annealed crystals, there were always subgrain boundaries observed, which

were, of course, considered to be piled-up dislocations, but were not

included in the count of individual dislocations. These subgrain

boundaries would have eventually been driven out of the crystals, if we

had annealed the crystals for a longer period of time.

In Fig. 17a and b, we show the composite topographs taken from the

same crystal as in Fig. 15a and b by the scanning spectrometer. The

resolution is much higher in Fig. 17 than Fig. 15. The striation-like

background which is seen in Fig. 15 is not present in Fig. 17. This

background was caused by the image structure due to the asymmetrical

silicon crystal. In the transmission topograph of the scanning

spectrometer, the details of the dislocation networks are clearly

visible. A few examples of enlarged topographs taken by the spectrometer are shown in Fig. 18a, b and c, representing a highly perfect

region, an intermediate region and a highly dislocated region,

respectively.

Conclusion and Discussion

Before concluding this annual report, we would like to emphasize

one of our principles followed in conducting the present work. At

present, many people believe that growing perfect crystals is still an

art where personal skills play significant roles. Although we do not

object to this view, and often agree with this view based on our

experience, we have attempted to eliminate such an art from the present

work. This attitude probably resulted in producing crystals less

- 16 -
perfect than they could be. However, we see significance in establishing

reproducibility of the resultant crystal perfection as a functional of

growth conditions, rather than a functional of the ''art" part of crystal

growth technology. In the present work, we grew crystals as routinely

as possible, with the least effort of human control. Once the variables

were set, we did not attempt to modify these variables in response to

local perturbations which occurred from time to time during growth.

During the growth process, we were tempted more often than not to

correct the diameter by changing temperatures or to increase the pulling

or rotation speed when the melt surface started vibrating occassionally

.

However, we made none of these possible corrections.

In the present work, the spectroscopic data indicated that Growth

Condition III generally produced crystals of higher perfection, along

with crystals produced under Growth Condition I with narrow necks.

These results are in good agreement with the observations of the x-ray

topographs. The topographs obtained by the scanning spectrometer further

helped to distinguish the subtle differences in the resultant qualities

from conditions I and III. Those topographs indicated that Growth

Condition III with narrow bottle-necks usually produced crystals of

better quality than Condition I. The other growth conditions are

clearly inferior to Conditions I and III. It is, therefore, concluded

that Growth Condition III is most optimum for growing a single crystal

of high perfection, when the bottle-neck is made less than one

millimeter in diameter.

- 17 -
If one anneals as-grown crystals afterward, Growth Conditions I

and III with narrow bottle-necks result in almost the same degree of

crystal perfection. However, crystals grown in the other conditions

did not show much improvement in quality as a result of annealing. It

is, therefore, further concluded that annealing becomes most effective

only when the grown crystals are already highly perfect.

In the optimum growth condition, the density of dislocations can

2 be as low as 11 dislocations per cm for "as-grown" crystals, and as

2 low as 7 dislocations per cm for annealed crystals. The lowest

dislocation density measured from the transmission topographs was 12.8

2 dislocations/cm which is in good agreement with the dislocation

densities determined from surface topographs.

Apart from the growth conditions that we studied from the viewpoint of fluid flow, it may be worthwhile to mention that gravity can

be considered as a driving force to produce slip in the crystals during

their growth process, as indicated in the previous section. The

weight of the crystal may cause slip when the crystal is being pulled.

However, these dislocations interact with each other, forming LomerCottrell locks and becoming immobile. Then the resultant crystal

becomes highly perfect. This presumably takes place in Growth

Conditions I and III. If wide-spread slip occurs or if many dislocations form randomly, as in the case of the other growth conditions,

then the locking would not take place and the dislocations would still

be mobile and affect the subsequently grown part of the crystal,

resulting in a less perfect crystal. The lack of gravity in space

- 18 -
may favor the growing of perfect crystals from this point of view, which

may be entirely independent of fluid flow conditions.

Because of the lack of time, we could not investigate crystal

perfection in Growth Conditions III in more detail by the use of high

resolution scanning spectrometry. It is highly desirable to pursue

the study of this growth condition combined with "art" part of crystal

growth techniques and establish the correlation between the crystal

perfection and the fluid flow motion.

- 19 -
Table 1

Group

Number

Crucible

Rotation (Y)

Seed

Rotation (Z)

Difference

(A = Y - Z)

Crystal

boules*

I -5. A rpm -6.0 rpm +0.6 rpm 21,22,23,24,25,

' 29,35,36

II +6.0 rpm +10.0 rpm -4.0 rpm 10,13,16,26,27,

38,39

III -20.6 rpm -20.0 rpm -0 . 6 rpm 20,28,30,37

IV +30.0 rpm +20.0 rpm +10.0 rpm 31,32,33

V -6.6 rpm +6 . 0 rpm -12.6 rpm 14,15,34

1

Boule number 21, for example, stands for the first three digits 021

of the number of sample crystals.

- 20 -
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VVAA i } CO CO

Q

flo

x: -H

•U 4-1 S -H

M 1 1 M hH IH tH 1—iH 1—

1—4 1—

1—

^—t 1—

1—1—1—4 l> •~>

O 1—

1—

l-H 1—

1-4 HH hH

M

C 1—

1—

h-

M

M

M o o

t_5 - 21 -
Figure Captions

Figure 1 Schematic diagram of Czochralski crystal growing apparatus

A - seed crystal

B - bottle-neck region

C - solid/liquid interface region

D - melt

E - crucible

F - resistance heater

X - pulling speed and direction

Y - seed rotation speed and direction

Z - crucible rotation speed and direction

Figure 2 Photograph of crystal boules grown with different bottleneck diameters

a. bottle-neck diameter =4.7 mm crystal #020000

b. bottle-neck diameter = 0.675 mm crystal #024000

Figure 3 Schematic of experimental procedure used in the determination

of the crystal thickness

Figure 4 Photograph of nuclear plate used to dermine the thickness of

copper crystal #028301

Figure 5 Schematic diagram of the asymmetrical topographic camera illustrating both the surface reflection and transmission

mode

Figure 6 Schematic diagram of the high resolution double crystal

spectrometer with scanning capability illustration both

the surface reflection and transmission mode

Figure 7 Photograph of high resolution double crystal spectrometer

with scanning stage

A - x-ray tube

B - 1st crystal, silicon, shown in reflection geometry

C - slit system

D - 2nd crystal, copper sample crystal shown in transmission

geometry

E - nuclear plate

F - counter system

G - scanner stage

Not shown for clarity is adjustable slit system between D and E

which stops direct and transmitted x-ray beams from reaching

film.

- 22 -
Figure 8 Diffraction rocking curves taken in the surface reflection

geometry for copper crystal #028303 at three different

locations on the crystal

Figure 9 Diffraction rocking curves taken in the transmission

geometry for copper crystal //030303 at four different

locations on the crystal

Figure 10 Diffraction rocking curve taken in both the surface reflection and transmission geometry for copper crystal #026302

at one location. For this alignment, both the copper Ka^

and components are present with the smaller peak due to

the component.

Figure 11 Diffraction rocking curves taken from a typically good copper

crystal (#037303) in both surface reflection and transmission

geometry and a typically poor copper crystal (#035302) in

surface reflection.

Figure 12 ATC x-ray topographs of as-grown copper crystal #028303,

growth condition III

a. (220) surface reflection composite topograph

b, (111) transmission topograph

Figure 13 ATC x-ray topographs of as-grown copper crystal #037303,

growth condition III

a. (220) surface reflection composite topograph

b. (Ill) transmission topograph

Figure 14 ATC x-ray topographs of copper crystals grown under growth

condition V

a. (220) surface relfection composite topograph of as- grown copper crystal #034303

b. (220) surface reflection composite topograph of

annealed copper crystal #034301

Figure 15 ATC x-ray topographs of annealed copper crystal #025302,

growth condition I

a. (220) surface reflection composite topograph

b. (Ill) transmission composite topograph

- 23 -
Figure 16 ATC x-ray topographs of annealed copper crystal #030303, growth

condition III

a. (220) surface reflection composite topograph

b. (Ill) transmission composite topograph

Figure 17 Scanning spectrometer topograph of annealed copper crystal

#025302

a. (220) surface reflection composite topograph

b. (Ill) transmission composite topograph

Figure 18 Enlarged regions of scanner topographs

a. highly perfect region

b. intermediate region

c. highly dislocated region

- 24 -


Fig. 2

Fig. 3



ASYMMETRICAL TOPOGRAPHIC CAMERA

(ATC)

Fig. 5

SPECTROMETER

Fig. 6

Fig. 7

CO

o

o

o

llJ CO

E

E

+

o

CVJ

CVJ O

I- roO

o ro

LiJ GO

UJ

q:

LJO

£

(O

CVJ o

3

o

i

T

E

E

O _l

CD

UJQ

O

E

E

I

OO

lO

o

o

Q

aN003S d3cJ siNnoo

o

o

in

A1ISN31NI

Fig. 8

_J I : I o o o

o o o

lo Q lo

QNOOaS a3d SlNflOD A1ISN31NI

Fig. 9

o^ 6

o o

CVJ o

ro

(M

o

*

o

CDz

<

u

<X J--

3 u

t'* 1 CO T .. .. ..

-

V) .: S . ^ <

A1ISN31NI
\
950

Q

Z

o

LJ 800

cn

Cu. # 037303

SURFACE REFLECTION TRANSMISSION

(220) (Ml)

SECONDS

Ill Q.

CO

I-z

z>o

o

600

400

^ 200

z

LJ

J LJ J I—I L J I I I L

O

z

o

o

1500 en

111 Q.

CO

1000 ^

o

o

-1500 >

cn

111

800

O

LiJ in

CO

600

§ 400

>-^ 200

u

INCIDENT ANGLE

Cu. # 035302

SURFACE REFLECTION (220)

\^\0 SECONDS

I'll'' I I I I I I I L INCIDENT ANGLE

Fig. 11

Fig. 12a

<IIO>

<lll>

Fig. 12b

Fig. 13a
r I
Fig. 13b

Fig. 14a

I mm

<iTo> <ooi>

^^-^

<lll >

Fig. 14b

Fig. 15a

Fig. 15b

<V\o>

<iii>

Fig. 16a

<M0> <00l>

<lll>

Fig. 16b

<ooi> <,,o>

Fig. 17a



Fig. 18a

Fig. 18b

Fig. 18c

Task 2

Vapor Transport Synthesis and Crystal Growth of Oxides

H. S. Parker

Inorganic Materials Division

Institute for Materials Research

Summary

The primary objective of this task is the development of advanced

techniques for vapor transport synthesis and crystal growth in mixed

oxide systems. The Zr02-Ta20^ system was chosen for investigation not

only because it is a typical mixed oxide system but because successful

development could provide a new type of stabilized ZrO^.

The results of transport experiments using I^ + S2 and ZrCl^

for transport of ZrO^ in the 3-7 atmosphere range at average temperatures

of about 950-1100°C were largely negative. Simultaneous transport

experiments of Zr02 + '^^2^5 ^^^'^S ^^'-'-'-4 ^'^^ TaCl^ resulted in severe

attack of the quartz reaction tubes. Minor success was obtained in

simultaneous transport using ZrCl. + S„ as transport agents.

- 25 -
Introduction

The objectives of this study are the Investigation of advanced

techniques for vapor transport synthesis and crystal growth in binary

•and ternary oxide systems and definition of the limitations imposed

by convective effects on the process at high pressures and large

temperature gradients.

Crystal growth of binary and ternary chalcogenides by vapor

transport reactions has received considerable attention in the past

1 2

'

. Applications of the technique to the synthesis and growth of

oxide crystals have been confined to single oxides in most cases,

2 with the major exceptions being certain spinels and germanates .

3 4 5 Emmenegger ' and Emmenegger and Petermann have investigated

the transport and crystal growth of ternary metal oxides and transition

metal niobates and tantalates. More recently, Bowen and co-workers

have described the growth of transition metal oxide solid solutions.

The selection of ordered fluorite structure type phases in oxide

systems for initial investigation was motivated by scientific interest

in extension of the vapor transport growth technique and potential

technological application of materials possessing this structure. The

specific material for initial consideration is ZrO^ in combination

with either ^^^2^5 '''^ ^^2*^5* Zirconium dioxide is an important refractory

material because of its high melting point, chemical inertness and low

vapor pressure. In the pure form, Zr02 undergoes a reversible phase

transition from the monoclinic to tetragonal form at about 1000°C which

is accompanied by a disruptive volume change of nine percent. In order

- 26 -
to avoid this problem, ZvO^ is commonly stabilized in a cubic form by

the use of up to 15 percent of CaO, Y^O^ or MgO as an additive.

Work at NBS has indicated that an alternative method of stabilizing

ZrO^ is the formation of ordered fluorite structure type phases

7 8 9 (orthorhombic) ' ' . This structure is an anion excess type rather

than the oxygen (anion) deficient type obtained with CaO, Y^O^ or MgO

additives and should have greater stability. Melting points of suitable

compounds in the Zr02-Ta20^ systems are in excess of 2000°C, thus, a

more stable form of Zr02 would be of considerable importance. In

addition, little is known about the structure, physical and electrical

properties of these phases.

The high melting points present a problem in synthesis and growth

of single crystals suitable for characterization and investigation.

The largest crystals we have been able to obtain from flux or solid

9 state techniques are of the order of 0.5 mm in size . Vapor phase

transport techniques offer the potential for obtaining larger sized

crystals at temperatures well below the melting points.

The use of closed tube transport techniques for synthesis and

crystal growth, together with the criteria for selection of a suitable

transport reaction has been described by Schaf er"'"'

"'"^ and Laudise''"'''

.

Basically, an attempt is made to select a suitable transport agent such

that the desired phase is the only solid product at the working temperatures, the equilibrium position is not extreme (AG° 0) and, for

reasonable transport rates, the AH° value for the reaction should be

near zero.

- 27 -
The transport of Ta^O^ with halogens is well established

according to the reaction:

Ta^O^ + 3TaCl^ t STaOCl^

.at total pressures of 1 atmosphere at temperatures of 750° and 650°

x^7ith transport rates in excess of 10 mg/hr. However, only one report

of the closed tube transport of Zr02 was found in the literature.

2 Nitsche reports the use of + S2 as transporting agents and

temperatures of 1050° - 1000°C although no further experimental details

were given.

Exper imental

Transport studies were carried out in quartz tubes of 8 mm inside

diameter and about 15 cm total length. Prior to use, the tubes were

cleaned, evacuated and baked out at about 300°C at pressures of about

—6

1 X 10 Torr overnight prior to loading. A sorption rough pump and

ion diffusion pumping system was used to avoid contamination from oil

vapors.

Following bakeout, the tube was charged with an excess of high

purity oxide together with the calculated amount of transport agent.

The tube was then re-evacuated and sealed off at pressure of 5 x 10

^

Torr or less. The oxides used were nominally of 99.99% or higher purity.

In the case of simultaneous transport experiments, two different types

of charge were used. In one case, the ZrO^ and Ta20^ were added as

the unreacted oxides. The alternative method chosen was to first react

the two materials at 1500°C to yield a single phase product of the

desired composition and subsequently use this material as the charge.

- 28 -
The furnaces used were of the multlzone type, with Independent

control of each zone. By the use of suitable thermal baffles, two

isothermal regions (+10°C) of about 15 cm length could be established,

separated by a central region of about 1.5 cm over which the AT for

transport was established. Both vertical and horizontal configurations

were used. The transport tubes were placed in the furnace such that

the center of the tube coincided with the temperature gradient.

Total pressures for the various transport agents were calculated

on the basis of average tube temperature and assumed ideal behavior

of the gaseous species. Typical tube loadings were of the order of 4

3

to 7 mg per cm of tube volume for the pressure ranges chosen, about

3-7 atmospheres.

Results and Discussion

The results of the transport experiments are summarized in Table 1.

Because of the lack of information regarding the transport of ZrO^, the

major effort was devoted to attempting to establish suitable conditions

for the transport of reasonable amounts of ZrO^ alone. All attempts to

2 duplicate the reported transport using + were largely unsuccessful, up to the temperature and pressure limits of the quartz tubes. At

the highest temperatures and pressures, only milligrams amounts of

transport were achieved in reasonable times.

Attempts to use ZrCl^ as a transport agent yielded poor results

except at the limits of the quartz tube, although crystallinity of the

deposit was improved greatly. A more serious problem when transport of

- 29 -
ZrO^ + Ta^O^ was attempted was the severe attack on the quartz tube in

the presence of ZrCl^ and/or TaCl^. The amount of attack was directly

related to temperature. This resulted in a large percentage of tube

failures during a run. Optical and x-ray diffraction examination of

a typical run with ZrCl^ indicated the major reaction product to be low

cristobalite with no detectable ZrSiO^ present. Thus, it appears that

the devitrification of the fused quartz is enhanced by the presence of

ZrCl^ and/or ZrOCl2. This limitation on maximum working temperature,

together with the low transport rates observed, suggested that ZrCl^

with or without TaCl^ is not suitable for larger scale crystal growth

in a closed quartz tube system.

Attempts to modify the transport reaction by the addition of another

component to the system and thus reduce the temperature required as well

as increase transport rates are being investigated. Preliminary results

using ZrCl^ and sulfur at lower temperatures, 1070°-970°C, have yielded

milligrams of transported material with small, well-formed crystals.

However, the transport rate must be increased if sizeable amounts of

material are to be grown.

Conclusions and Future Work

The major problem is the matter of transport rate of Zr02. Future

work will concentrate on the use of more complex transport reactions to

produce a more favorable mass transport. The temperature and pressure

limitations imposed by the use of quartz as a closed reaction chamber

may necessitate the consideration of an open system of more refractory

material such as ^.120^ in order that temperatures be increased to

increase transport rates.

- 30 -
COX

LD

(/) -1^ 0 +J E (J u

r— I/) E fd (O (O

X

=3 o +-> +->

M

r ^ </) -M +-> -M -M -M 4-3 4—' LO

(U (/) i- ^ &- t- +-> • fO <d fd t- • Q Q Q 0 CO C 1 0 0

Q. to Q. Q. Q. O- >,V O) Q.

1/5 &- CO </) CO 10 s-^ > •p- > > CO CO

4-J

C E 0 fO fd fd •r—

C r—

<o (O rd "O M- M- **- CO ns to

s- s- s- s- s- S- t— (U 0 0 0

-M o +J +J 4-> +J r- E CU s- O) S- (U S- -P CO JD s- S- O CD 01 0 cn E 0 0 3 0 0 0.^ E E E sz E CO M- -M 0 +-> 0 +-> 0 E 0

CQ

CD

i~O)Q.X

s-o

Q.

COc

fds-O

>>

i~fd3

t>0

0)

sCO

CO

Q)

s- Q.

fd

+-> o

(Us- -M

fd

iO)Q.E

4->&.O 4-> Q. C

(/) CU E O)

fd <C E E E

+->

M

fd fd fd CO r>. E E

4-> +-> _r

fd fd E E E E E _E _ 1 E [„> 1 ^ 1 ^ LO fd fd (d fd fd fd fO 00 CO LO CO LD LO LO LO * * * * * * * - * - * i- >- >- >- >- >- _E -C -C^

C>U /—\^—

J /—\ /—\

CM CCS LA,/ 0 0 CO

•"^ p" CM '

V

V 0 0 0 0 0 0 0 0 0 0 0 0 CD LO 0 0 0 0 0 0 0 CM LO 0 0 0 0 0 0 0 LO

CT»1 1 ! 1 001 1 1 en1 cn1 a\1 0 0 0 0 0 0 0 0 0 0 LO 0 LO 0 0 0 LO LO 0 0 C\J CXI LO 0 0 0 0 r-

LO LO LO

C_> (0 fO fd C> 1— 1— I— U~) CM CM CM CM

1—1

*^ •v + + + + 0 0 0 0 0 s- s- s- i~ $- CM CM CM M M M M M M 1—1

1—1 1—1

S- in LO LO M 00 00 00 • • •

^1

LO LO LO

u0 CM Osi CSJ 0

fd CM

fd fd

S- 0 0 0 0 0 0 O) s- s- S- S- S- S- CM CM

+->

M

MM

MM 0 0 fd

CM OM

fd

CM oM

CO

0)

+-> MO

fd

CUs.

(U

&-

C3. - 31 -
References

1. H. Schafer, Chemical Transport Reactions, Academic Press,

New York 1964.

2. R. Nitsche, Crystal Growth, H.S. Peiser, Ed., 215-220, Pergamon

Press, London 1967.

3-.. F. Emmenegger, J. Crystal Growth _2, 109-110 (1968).

4. F. Emmenegger, J. Crystal Growth 2. A» 135-140 (1968).

5. F. Emmenegger and A. Petermann, J. Crystal Growth 2^, 33-39 (1968).

6. H.K. Bowen, W.D. Kingery, M. Kinoshita and C.A. Goodwin,

J. Crystal Growth 13, U, 402-405 (1972).

7. R.S. Roth and L.W. Coughanour, J. Res. Natl. Bur. Stds. 55,

209-213 (1955) R.P. 2621.

8. R.S. Roth, J.L. Waring, W.S. Brower and H.S. Parker, "Proceedings

of 5th Materials Research Symposium", R.S. Roth and S.J. Schneider, Jr.,

Eds., Natl. Bur. Stds., Special Publication 364, GPO Washington 1972.

9. Jean Galy and R.S. Roth, "The Crystal Structure of Nb Zr 0 ",

J. Solid State Chem. , 7^, 277-285 (1973).

10. H. Schafer, "Preparative Methods in Solid State Chemistry",

P. Hagenmuller, Ed., 251-277, Academic Press, New York 1972.

11. R.A. Laudise, "The Growth of Single Crystals", 225-256, Prentice-Hall,

Inc., New Jersey 1970.

- 32 -
Task 3

Preparation of Ultrahigh Purity Material

R. C. Paule

Inorganic Materials Division

Institute for Materials Research

Summary

A calculational procedure Involving the use of complex chemical

equilibria has been developed to describe the purification of refractory

materials in space. High temperature evaporative purification of

refractories is considered under vacuum conditions and under conditions

of very low oxidizing or reducing ambient pressures. The calculations

show that extensive purification can be obtained and that very low

oxidizing or reducing ambient pressures can be used to control the

rates of purification. This method could also be used to allow the

production of doped materials to pre-selected levels.

Consideration is given to the assumptions affecting the purfication

calculations, and an experimental program is being developed to check

the calculated results. This program involves mass spectrometric

measurements on a sessile drop of molten Al-0^.

- 33 -
Introduction

Hot containers used In the production and purification of refractory

materials are themselves a common source of contamination. Space with

Its zero gravity, high vacuum conditions offers an opportunity for

contalnerless purification of refractories. The heating and distilling

out of Impurities Is a natural means of purification. Evaporative

purification of refractories normally involves many complex equilibria

since numerous minor impurities are present and since the high temperatures Involved allow many "side" reactions. The general formalism for

the calculation of complex equilibria has been modified and adapted to

describe evaporative purification. Four classes of problems have been

investigated. The evaporating gases are described under conditions of

(1) constant pressure, (2) constant volume, (3) vacuum, and (4) vacuum

but with a low oxidizing or reducing ambient pressure. The latter two

conditions (3 and 4) are of particular Interest to this project since

they allow for greatest isolation of sample and least chance of container

contamination.

Calculations

There is much work in the literature dealing with the calculation of

complex equilibria^"'" Available calculations and computer programs,

however, do not deal with the problem at hand and would have required

extensive modifications. We, therefore, developed our own equations

and computer programs. Modifications and adaptations were made to

Kandiner and Brinkley ' s

^"'"^ general formalism for the calculation of

- 34 -
complex equilibria. Some basic changes were required to properly describe

evaporation into vacuum.

The general formalism for the calculations is not particularly

difficult, but the actual calculations do get involved and do require

the aid of a computer. The calculations, in general terms, can be

described as follows:

One needs to determine the number of moles of all chemical species

in a system during purification and to determine the distribution

of moles between the condensed phase and the evaporating (gas)

phase. For the sake of simplicity one wants to work with the

minimum information needed to fully describe the system. This is

equivalent to determining a set of independent chemical species.

All chemical species are thereby separated into two groups:

independent components and dependent constituents. The solution

to our problem then deals primarily with the determination of the

amount of each independent component. Independent mass balance

equations are written for each component. These equations do not

directly involve any dependent constituents, and the NewtonRaphson iteration method ^^'^^ is used to simultaneously solve the

mass balance equations.

The dependent constituents are determined from equilibrium

constant relationships which only involve the activities and

pressures of the independent components. Ideal solution properties

are used to describe the condensed phase activities and, for the

vacuum evaporation case, the Knudsen equation is used to describe

- 35 -
the pressures in terms of the number of moles. A series of

sequential solutions are obtained for fixed evaporation times

with the condensed phase results from each mathematical solution

being used as input feed data in the following problem. It is

thus possible to sequentially follow the evaporative purification

of a material.

The above general calculational approach is very general and allows for

relatively easy and direct modifications to describe a variety of

situations of practical interest. A manuscript describing the calculations and examples of their use has been written and NBS approved, and

will be submitted for publication. It is enclosed as an Appendix.

Results '

•

Our calculations show that good evaporative purification of

refractories in vacuum can be obtained, and that the introduction of

a low oxidizing or reducing ambient pressure can be used to control

rates of vaporization.

Table 1 shows the results for calculations of Al^O^ evaporative

purification in vacuum at 2400 K, where 10 ppm (mole basis) FeO and

Si02 impurities are initially present. Row 3 of the table shows that

the rate of ^^2^3 loss is very low, while rows 4 and 5 show that FeO

and Si02 are rapidly lost from the melt. The FeO and SiO^ concentrations

are approximately halved over a period of only 1.15 seconds. The

remaining 12 species in the table, under the heading "Moles of Species

Present", represent the moles of gases vaporized during each time

- 36 -
interval (0-0.005 seconds, 0.005-0.28 seconds, 0.28-0.46 seconds, etc.).

Finally the instantaneous pressures of all species are reported at the

bottom of the table. It is evident that the calculations yield

considerable information. The computer results, as indicated by this

table, are automatically obtained from the solution of each problem.

Calculations showing very high rates of purification (as above) may

not be completely accurate in describing the evaporative process. High

rates of purification can result in a depletion of impurities at the

surface and a concentration gradient can occur. The calculations assume

a completely mixed, homogeneous melt. Numerous processes, however, can

occur to minimize the concentration gradient. Task 4 (Role of Surface

Traction and Related Phenonema in Processing in Space) , being carried

out by A. L. Dragoo, is looking into some these processes. A general

view of the problem would seem to minimize concern regarding surface

depletion and concentration gradients since practical purification

times can be of the order of 10 minutes rather that the above 0-1.15

seconds. Mixing processes can occur during these longer time periods.

Further investigations into this possible problem area are still needed.

Purification rates can be slowed to allow better mixing, or to

better control the evaporation process. One should not overlook the

possibility of controlled low level doping of materials to pre-selected

levels. Slower purification of A1„0^ can be obtained by exposing the

melt to a low ambient oxygen pressure. Such a pressure can be kept low

enough to maintain vacuum (Knudsen) flow conditions and yet be high

enough to shift chemical equilibria and slow the varporization rates.

- 37 -
Table 1

Vacuum Evaporation of Al 0„ + 10 ppm FeO and SIO

Moles of Species Present

Temperature (K)

Cuml . Time (Sec) 0.005 .28

Liquids

A1„0„ 1. OOOOE+OO 1 OOOOF+00 \J\J\J\Ji-i i \J\J FeO 9. 98z1E-0d 9. 0607E-06

SiO„

z 9. 9667E-06 8. 3538E-06

Gases

0 - 1. 8199E-07 6. 2370E-06

'/ 6. 1007E-09 2. 0593E-07

Al 8. 9146E-08 3. 1734E-06

AlU ±

.

2000E-08 4. 2074E-07

AiU2 :

• D • 6628E-10 2. 3009E-08

A1„0

z 1. 8579E-09 6. 6641E-08

A1„0„

2 2 1. 0292E-11 3. 6359E-10

Fe 1. 7815E-08 5. 7128E-07

FeO 8. 2998E-11 2. 6215E-09

Si 2. 2587E-13 6. 7909E-12

SiO 3. 3262E-08 9. 8495E-07

SiO 2. 0138E-11 5. 8734E-10

Pressure of Species Present (Atm)

Gases

0 ; 3.5140E-06

°2 1.6659E-07

Al 2.2352E-06

AlO 3.7976E-07

AlO^ 2.4700E-08

Al^O 7.5013E-08

Al^O^ 4.6061E-10

Fe 6.4267E-07

FeO 3.3961E-09

Si 5.7788E-12

SiO 1.0661E-06

SiO^ 7.5356E-10

2400

.46 .81 1.15

1. OOOOE+OO 9. 9999E -01 9. 9999E -01

QO . 5012E -06 —i1

.

4yiOE -06 o

.

6129 E -06

7. 4416E--06 5. 9152E -06 4. 7170E -06

6. JlJ U X J_j 6. 0993E--06 5. 8593E -06

z

.

0833E -07 1

.

9652E--07 •1 1

.

8638E -07

3. 3121E--06 3. 2990E--06 3. 2725E--06

4. 3523E--07 4. 2682E--07 4. 1799E--07

2. 3590E--08 2. 2778E--08 2. 2022E--08

6. 9864E--08 7. 0130E--08 7. 0015E--08

3. 7780E--10 3. 7339E--10 3. 6802E--10

5. 5694E--0 7 4. 8504E--07 4. 2203E--07

2. 5330E--09 2. 1720E--09 1. 8657E--09

6. 3420E--12 5. 0603E--12 4. 0287E--12

9. 1167E--07 7. 1622E--07 5. 6293E--07

5. 3881E--10 4. 1677E--10 3. 2340E--10

3.4610E-06

1.6161E-07

2.2867E-06

3.8265E-07

2.4514E-08

7.7327E-08

4.6766E-10

5.9228E-07

3.0826E-09

4.9931E-12

9.0729E-07

6.3161E-10

3.4303E-06

1.5875E-07

2.3175E-06

3.8437E-07

2.4405E-08

7.8718E-08

4.7185E-10

5.6068E-07

2.8923E-09

4.5279E-12

8.1546E-07

5.6264E-10

3.3774E-06

1.5389E-07

2.3721E-06

3.8736E-07

2.4216E-08

8.1202E-08

4.7923E-10

5.0180E-07

2.5486E-09

3.7127E-12

6.5834E-07

4.4724E-10

3.3343E-06

1.5000E-07

2.4182E-06

3.8986E-07

2.4061E-08

8.3313E-08

4.8542E-10

4.4870E-07

2.2499E-09

3.0377E-12

5.3178E-07

3.5665E-10

- 38 -
Tables 2 and 3 list results for the evaporative purification of ^12^3

containing 10 ppm CaO. Table 2 is for the "pure" vacuum case and

Table 3 is for a "vacuum" containing 10 ^ atm oxygen. The higher

oxygen pressures shown in Table 3 result in equilibrium shifts away

from the reduced vapor species Ca(g) [Ca(g) + 0(g) CaO(l)] and this

causes slower rates of purification. Figure 1 shows the rate of CaO

removal both for the case of "self-developed" oxygen (Table 2) and for

the case of equal to 10 "'"^ atm (Table 3)

.

It is clear that many modifications in oxidizing or reducing

conditions can be used to achieve desired vaporization (purification)

goals

.

Some results from this Task and from Task 4 will be presented as

a talk at the 12th Aerospace Sciences Meeting of the AIAA to be held

January 30 - February 1, 1974 in Washington, D.C. This talk by

A. L. Dragoo and R. C. Paule is entitled "Production of Ultrapure

Materials: Containerless Evaporation and the Roles of Diffusion and

Maragoni Convection."

Discussion

In using the above calculated results one must ask: "How accurate

are the calculations?" One can partially answer this question by noting

that if the calculational assumptions are correct, then the calculations

should be accurate. It appears that we should be able to pick purification conditions of practical interest that will satisfy the assumptions.

In general, the method of evaporative purification should be feasible.

- 39 -
Table 2 Vacuum Evaporation of Al 0„ + 10 ppm CaO

Moles of Species Present

Temperature (K)

V^LlitlJ- • J- J^lllC. V'-' / 0. 005 ?0 00

Liquids

Al^O^ 1. OOOOE+00 9. 9975E -01

CaO 9. 9998E-06 9. 2986E -06

Gases ' i0 ,

' 1

.

6143E-07 6. 4560E--04

0

2 4. 8005E-09 1. 9197E--05

Ca 1. 8850E-10 7. 0120E--07

Al 1. 0670E-07 4. 2676E--04

AlO

' 1. 2741E-08 5. 0957E--05

A10„

I

'

- 6. 2753E-10 2. 5097E--06

Al 0 2. 3611E-09 9. 4435E--06

Al^O^ ' 1. 1602E-11 4. 6402E--08

Pressure of Species Present (Atm)

Gases

0 3. 1171E-06 3. 1170E--06

"2 1. 3109E-07 1. 3108E--07

Ca 5. 7606E-09 5. 3581E--09

Al 2. 6754E-06 2. 6756E--06

AlO 4. 0321E-07 4. 0322E--07

AlO

2 2. 3264E-08 2. 3264E--08

Al^O 9. 5332E-08 9. 5338E--08

Al^O^ 5. 1926E-10 5. 1927E--10

2400

9. 9950E -01 9. 9925E--01

8. 6465E -06 8. 0401E -06

6. 4548E--04 6. 4535E--04

1. 9193E--05 1. 9189E--05

6. 5210E--07 6. 0643E--07

4. 2671E--04 4. 2665E--04

-J • Kj y *-t y ill -05 0941 F--0 5 2. 5092E--06 2. 5088E--06

Qy • H H- Z. H- J_j -06 Q 441 "^F--06

4. 6396E--08 4. 6389E--08

3. 1169E--06 3. 1168E--06

1. 3107E--07 1. 3106E--07

4. 9838E--09 4. 6355E--09

2. 6757E--06 2. 6758E--06

4. 0323E--07 4. 0323E--07

2. 3263E--08 2. 3263E--08

9. 5343E--08 9. 5348E--08

5. 1929E--10 5. 1930E--10

- 40 -
Table 3

Evaporation of Al-0„ + 10 ppm CaO, Vacuum + 10 Atm Oxygen

Moles of Species Present

Temperature (K) 2400

Cuml. Time (Sec) 0.005 60.00 120.00 180.00

Liquids

Al^O^

2 3 1. OOOOE+00 9. 9984E--01 9. 9967E-01 9. 9951E-01

CaO 9. 9999E-06 9. 3413E--06 8. 7259E-06 8. 1511E-06

Gases

Ca 5. 8757E-11 6. 5868E--07 6. 1532E-07 5. 7482E-07

Al 1. 8569E-08 2. 2281E--04 2. 2278E-04 2. 2276E-04

AlO 7. 1134E-09 8. 5352E--05 8. 5343E-05 8. 5333E-05

AIO2 1. 1240E-09 1. 3486E--05 1. 3485E-05 1. 3483E-05

Al 0

2 2. 2941E-10 2. 7526E--06 2. 7523E-06 2. 7520E-06

AI2O2 3. 6165E-12 4. 3393E--08 4. 3388E-08 4. 3384E-08

Pressure of Species Present (Atm)

Gases

0 1. OOOOE-05 1. OOOOE--05 1. OOOOE-05 1. OOOOE-05

°2 1. 3491E-06 1. 3491E--06 1. 3491E-06 1. 3491E-06

Ca 1. 7956E-09 1. 6776E--09 1. 5674E-09 1. 4644E-09

Al 4. 6560E-07 4. 6560E--07 A fi560F-07 4. 6560E-07

AlO 2. 2512E-07 2. 2512E--07 2. 2512E-07 2. 2512E-07

AIO2 4. 1669E-08 4. 1669E--08 4. 1669E-08 4. 1669E-08

AI2O 9. 2626E-09 9. 2626E--09 9. 2626E-09 9. 2626E-09

Al^O^ 1. 6186E-10 1. 6186E--10 1. 6186E-10 1. 6186E-10

- 41 -
We must, however, still pick optimum conditions and be able to predict

the extent of purification.

Some questions that need to be considered in the evaluation of the

accuracy of the calculations are as follows:

Are there significant vapor species other than those used in the

calculations ?

Are the literature values of the thermodynamic equilibrium constants

correct?

Is ideal solution behavior observed? (Because of the low impurity

levels considered we would expect Henry's law to be obeyed, but

this does not Insure that the impurities will obey Raoult's law.)

Is there adequate mixing of the melt to avoid surface depletion and

concentration gradients?

Are the evaporation coefficients equal to unity or near unity?

We are now engaged in an experimental program to get an overall check on

these and other possible problem areas. We plan to directly observe

evaporative purification from Al^O^ samples and to be able to check the

calcuations. If necessary, correction factors could be developed to

describe any non-ideal behavior.

Current and Future Experiments

Our current work is in preparation for the experimental measurement

of impurity vaporization from kl^O^ using the TOF mass spectrometer.

Work is centered on improving usable M.S. sensitivity, and on improving

quantitative M.S. measurements. A molecular beam chopping system has

- 42 -
been built and a lock-in amplifier added to the system to allow modulated

beam detection of species coming from a sessile drop of molten Al^O^.

Lock-in detection will be particularly important for measuring evaporating

species such as 0^ and 0^ since these species are normally present in the

M.S. background. The modulated beam system is now operational.

A new calibrated He and Xe leak system has been installed in our M.S.

to improve reproducibility. Scales have been added to several instrument

potentiometers for better reproducibility. New, more linear electron

multiplier strips have been installed on the M.S.

A considerable effort has been devoted to minimizing the M.S.

background to increase the usable sensitivity. In addition to extensive

leak-checking, we have found it necessary to water cool the walls of the

furnace to avoid excessive outgassing. A new smaller water-cooled

furnace with a lower heat load is now being built and will replace our

current furnace for the heating of the

M.S. measurements will be made on evaporating molten to

determine any non-ideal behavior. This type of experiment should allow for

an overall check of the calculations and, if necessary, for the development

of correction factors. Other refractory materials may also be tested.

- 43 -
References

1. H.J. Kandlner and S.R. Brlnkley, Ind . Eng. Chem. , 42, 850 (1950).

2. W.B. White, S.M. Johnson and G.B. Dantzig, Chem. Phys . , 28, 751

(1958).

3. ^' S. Gordon and B.J. McBride, NASA, SP-273 (1971).

4. H.F. Feldmann, W.H. Simons and D. Bienstock, U. S. Bur. of Mines,

RI-7257 (1969).

5. F.J. Zeleznik and S. Gordon, Ind. Eng. Chem., 60, 27 (1968).

6. F. Van Zeggeren and S.H. Storey, The Computation of Chemical

Equilibria , Cambridge University Press, 1970.

7. M. Klein, Physical Chemistry , Vol. 1/ Thermodynamics , Chapter 7,

edited by Eyring, H.E., Jost, W. , and Henderson, D., Academic

Press, New York, 1971.

8. H. Margenau and G.M. Murphy, The Mathematics of Physics and

Chemistry, 2nd. ed., page 492, D. Van Nostrand Company, Princeton,

New Jersey, 1956.

9. F.E. Hildebrand, Advanced Calculus for Engineers , page 353,

Prentice-Hall, New York, 1949.

- 44 -
Figure 1 T 1—-""-^—

T 1 r

Task 4

Role of Surface Traction and Related Phenomena

in Chemical Processing in Space

A. L. Dragoo

Inorganic Materials Division

Institute for Materials Research

Summary

Theoretical analyses of processes occurring in levitated melts

during evaporative purification were carried out. The interactions

of non-uniform evaporation and of thermal and solutal capillary

convection were considered qualitatively. Studies were begun on pure

diffusion coupled with non-uniform evaporation. The pattern of thermocapillary convection cells in a drop with an axially symmetric temperature field on the surface was deduced by determining the zero-points in

the velocity field and the streamlines in the liquid drop. Initial

work on the derivation of a formula for the circulation time associated

with such cells is described.

- 45 -
Until May of this year, work on this project overlapped with an

earlier NASA project on the "Investigation of Convective Effects and

Crystal Growth" (Contract No. W-13475) . Since there was no clear

demarcation between the work on these two projects, all the work through

May was presented in a final report for the latter project. In this

report, I will describe two problems which have remained under investigation since then. I will summarize the results that were reported in May

and then I will focus on current work.

These two problems are:

1. thermal and solutal capillary convection and mass transfer with

non-uniform evaporation (Section 2.4 in the May report);

2. thermocapillary convection for a general steady-state temperature field on the surface of a drop (Section 2.5).

Thermal capillary, or thermocapillary, convection is convection driven by

a surface tension gradient which is generated by a gradient in the

superficial temperature. Solutal capillary convection is convection

caused by a superficial concentration gradient including a surface tension

gradient. Where the meaning is clear, the word "capillary" will be

dropped and only the terms "thermal convection" and "solutal convection"

will be used.

Both of these problems are important to the fluid dynamics of

levitated melts. Implicit in both is the assumption that any practical

heating configuration will produce a non-uniform heating of the surface

of the drop which can result in thermal convection and other effects.

- 46 -
The first problem appears when one attempts to describe the evaporative

purification of a melt in which convective-diffusion, non-uniform evaporation, thermal capillary convection and solutal capillary convection are

present. Qualitative aspects of all four of these phenomena are considered

here. Next, progress on a problem involving pure diffusion coupled with

non-uniform evaporation is described.

Work on the second problem extends results, given in the May report,

of an analysis of the components of the velocity field. The arrangement

of convection cells and the location of zero-points in the velocity field

for the general axially symmetric case are considered in this report.

Current work on a general expression for the circulation time is described.

1. Thermal and Solutal Convection; Diffusion with Non-uniform Evaporation

In the previous report, a simple convective-diffusion-evaporation

problem was solved in which the evaporation rate was assumed to be uniform

over the surface although the surface temperature was not uniform. The

non-uniform superficial temperature was assumed to operate only through

the thermocapillary effect. The convective-dif fusion equation was solved

by splitting the concentration into a spherically symmetric and an

angular dependent part. The former part was found to be expressible in

terms of a standard solution to the diffusion equation plus a perturbation

term. Furthermore, the rate of loss could be expressed in terms of a

standard diffusion result evaluated at the surface plus a perturbation

term similar to the above. A self-consistent method of solution was

outlined. This simplified solution had two weaknesses:

- 47 -
1. the non-isotropic thermal condition was assumed to influence

the surface tension but not the evaporation rate constant,

2. an attendent variation of concentration over the surface and

its influence on the surface tension was ignored.

a. Qualitative aspects of the more general problem

The more general problem is one in which convection is driven bysurface tension gradients arising both from thermal and solutal gradients

and in which diffusion is perturbed both by convection and by non-uniform

evaporation. Moreover, these various processes interact. For example,

diffusion will alter concentration gradients on the surface which were

produced by non-uniform evaporation. The change in these gradients will

modify the convection which will react back on both the diffusion and the

evaporation processes. A more general problem is which heat transfer is

coupled to the above processes was not considered; instead, steady-state

heat transfer was assumed to persist throughout.

To simplify the further discussion, the drop will be assumed to be

heated at one pole and to be cooled at the other. Evaporation will be

faster at the hotter pole, so that the concentrations of volatile

impurities will be lower there than at the colder pole. If normal thermal

convection is present, liquid adjacent to the surface will be pulled

toward the colder pole, liquid will descend in the colder hemisphere and

will rise in the hotter one. The impurity-rich liquid from the interior

will tend to replenish the depleted liquid near the hotter region of the

surface while surface currents will tend to smooth out concentration

differences between hotter and colder surface regions. The net effect of

non-uniform evaporation and normal thermal convection is toward

- 48 -
homogenizatlon of the surface concentration. Anomalous thermal capillary

convection, on the other hand, will tend to enhance the variation in

surface concentration brought about by evaporation.

If, in addition to thermal capillary convection, solutal capillary

convection is present, not only will interactions take place in terms of

concentration but they will also appear in the velocity. If normal

solutal convection is assumed to produce movement of surface liquid from

regions of high impurity concentration to regions of low concentration,

it will tend to oppose the flow due to thermal convection. As an

additional contrast to normal thermal convection, it most likely will

enhance the disparity in surface concentration because it will bring

impurity-rich liquid from the interior to the colder surface region

which already would be enriched with respect to the hotter surface by

evaporation. However, the resulting surface flow will tend to level

out the concentration disparity between the two regions, albeit not as

effectively as the transfer of material from the interior.

The expected consequences of the various processes are summarized

in Table I. Non-uniform evaporation is assumed to be present in processes

'4." through "9." as the means to the concentration gradients needed for

solutal convection although it is only cited explicitly in "1.". The

second column shows the direction of fluid flow at the surface for each

process both in terms of temperatures, e.g. hot -> cold, and in terms of

concentration, e.g., low -> high. The third column gives the departure

of surface concentration near the hotter pole from the average for the

total surface. The changes in concentration are those for the process,

per se , so that the net concentration is obtained by adding the effect

of evaporation if it is required to be present.

- 49 -
b. Pure diffusion coupled with non-uniform evaporation

Work was begun on the problem of diffusion with non-uniform

evaporation, the evaporation rate constant having the form

a = a + a T cos 9

0 1 1 Although the solution to the angular-dependent diffusion problem can be

performed easily—the form of the solution being suggested by the

analogous quantum mechanical problem of the wavefunctions for a threedimensional square well, the kinetic boundary condition

-DOc/9r) 1^ = ac|^

now introduces a major complication because its dependence on cos 9

couples successively higher order of the Legendre polynomials of the

concentration expression

2 c(r,9,t) = c - EEC e - ^^jil (k r) P (cosO) . O - 36 S 36 S X/ i=os

The functions and P^ are the £th order spherical Besset function and

the £th order Legendre polynomial, respectively. The index s runs over

values of the wavenumber k^^ satisfying the boundary conditions.

2. Thermocapillary Convection for a General Steady-State Temperature

Field on the Surface of a Drop

In the previous report, a mathematical analysis developed by Miller

and Scriven"*" for the oscillations of a fluid droplet immersed in a

second fluid was applied to the steady-state problem of surface tension

induced flow when an arbitrary superficial temperature field is present

on the drop. The temperature field was described by a series expansion

in spherical harmonics and the velocity components were found for an

- 50 -
arbitrary term in the temperature field, say Y^(9,(f)). To obtain a solution

it was necessary to introduce a function B(9,(f)) which described small

deformations of the surface of the drop. An expression was given for the

generalized characteristic speed

£(£+1)y_ T„

U =

0 T £m , £m 2y [(2£+1)(£+2)Yq + Y^RL^] ^

(the various coefficients are identified at the end of this report) . The

circulation time t for the second-order mode (£=2, m=0) was estimated and

compared with the first-order mode (£=1, m=0) . It was found that

t^/t^ - 20

when (3T/9R) was the same in both cases. This suggests that the

r—K , 0 —(J first-order mode could be considerably more Important than the secondorder mode in such processes as mass transfer.

Subsequent work has been carried out on

1. the identification of the zero-points of the flow rate v for

a "pure" axially symmetric mode, i.e., one corresponding to a

Y°(9,(})) term in the temperature expansion,

2. the development of a general solution for x for the axially

syimnetric case.

The rate of flow

V = [u/ + + u/]''\ (5)

where

- 51 -
u = Z u (i,m)

u = E u (Ji,m)

u = Z u (£,in)

(6a)

(6b)

(6c)

are the components of the velocity field. For the axially symmetric case,

= 0. The determination of the zero-points of v requires a detailed

knowledge of the temperature field at the surface of the drop.

For a pure axially symmetric mode resulting from a superficial

temperature field

T^(e) = T^QR^Y°(e,(|)) = T^QR^[(2£+l)/4Tr]^/^P^ (cosB) , (7)

the rate of flow in reduced form is

= ^^'^ {(1-r^)^ (P^)^ + [(£+l)-(S,+3) . (8)

1/2 where v^^ = v^/U^^ [(21+1) /^n] and r - r/R. It is obvious that = 0

~2

inside the drop where r = (l+l) / (1+3) and = 0. Since has I nodes,

there must be £ of these points. On the surface of the drop (i.e., r = 1)

,

v^ = 0 if P^

11= 0. P^ has l+l nodes, including one at each pole, so that

V = 0 at (l+l) points on the surface. In addition, if £ > 1, v = 0 when

9j ^

- 52 -
r = 0 which implies that flow occurs through the center of the drop only

if £ = 1. Finally, we must consider the possible occurrence of other

internal zero-points. That is, are there other points such that

(l-r2)^(P^)^ + [(1+1) - (il+3)r^]^(pp^ = 0 ?

The answer is no. Since each term is either positive or zero, and

~2 "2

since neither (1-r ) and [ (5,+l)-(Jl+3)r ] nor and P^ vanish at identical

values of r and cos 6, respectively, there are no other internal zeroes

for V.

Evaluation of the streamlines shows that each of the internal zeropoints serves as a focus for a set of streamlines. Thus, the £th-order

axial-symmetric mode will consist of i convection cells.

The circulation times x, which are given formally by

=(t)dL/V

and which are associated with each of the £ convection cells, can be

evaluated by requiring that the quantity of material circulating about

a zero-point in a time t equals the quantity of material in the volume

containing the streamlines about that zero-point. It is not apparent

from work performed to date that the circulation times associated with

the various convection cells are necessarily equal. An expression for

T , the circulation time associated with the "s" zero-point, has been

s obtained in terms of the angles 6,6', and 6', where P. (cos 6 ) = 0, ^ s s-1 s I s

^[ ^'

i) = PJ, (cos 6') = 0 and 6' . and 9

' are the nearest lower n b X X- S S —1 S

- 53 -
and upper bounds of 6^, respectively. This expression is very complicated

and it is hoped that the analyses of the roots of P and P', which are now

in progress, will help to simplify this expression, in addition to

establishing the relationship between all the t^s.

Sjnnbols Used in This Report

R radius of the drop

T temperature

c concentration

u^, Uq , u^ components of the velocity field

V rate of flow

R rate of evaporation

D diffusion coefficient

a evaporation coefficient

circulation time

Yq surface tension coefficient

Yrp thermal coefficient of the surface

tension, = (dy/dT)^

o

L thermal coefficient for the surface

deformation, = (3T/9R)^

Quantities associated with the (£,m)-mode, i.e., Y^(9,4))

u^(£,m), etc. components of the velocity field

U„ characteristic speed

£m

v„ rate of flow

Im

T„ thermal coefficient of the temperature

field expansion

- 54 -
References

C.A. Miller and L.E. Scriven, J. Fluid Mech. yZ, 417 (1968).

- 55 -
Table 1

Interaction of Evaporation, and Thermal and Solutal Convection

Process

1. Evaporation, 3a/8T>0

2. Normal thermal conv.

3 . Anomalous thermal

4. Normal solutal conv.

5. Anomalous solutal

6. "2." + "4."

7. "3." + "5."

8. "2." + "5."

9. "3." + "4."

Direction of

Convective Flow

at the Surface

hot cold

(low c -> high c)

cold hot

(high low)

high c low c (cold -> hot)

low -y high

(hot -> cold)

tend to cancel

tend to cancel

hot -> cold

cold -> hot

Departure of Concn,

at Hot Pole from

Average

Decrease

Increase

slight increase

slight increase

Increase

Increase

Increase

strong increase

slight increase

- 56 -
Task 5

Vacuum Effects in the Preparation of Composite Materials

H. Yakowitz and D. E. Newbury

Metallurgy Division

Institute for Materials Research

Summary

Useful composites usually have strong continuous bonds between matrix

and core. Improved bonding might be obtained by improving the final

vacuum under which the composite is prepared so as to remove most adsorbed

gases from the matrix-core interface. Good bonding can be expected when

strains between matrix and core are minimal and coherent. Hence, this

exploratory phase of the study was largely devoted to obtaining a means

to study the bond both microscopically and with regard to determining

strains at or near the bond. For this purpose, the scanning electron

microscope was chosen as the primary tool. A means to use electron

channelling patterns prepared in the scanning electron microscope to

obtain strain data was formulated. The effect of strain, surface coatings

and specimen tilt with respect to the primary electron beam was studied.

Divergent beam x-ray microdif fraction patterns were also prepared in the

scanning electron microscope as a means to obtain strain data at the

micrometer level of spatial resolution.

- 57 -
Introduction

Composite materials are well known entities. Such materials have

been used for a long time in an effort to obtain improved material

characteristics through combining disimilar constituents such as soft

matrices with very hard cores. One of the keys to preparing useful

composites is to obtain strong, continuous bonding between the matrix

and core. One of the ways improved bonding might be obtained would be

to improve the vacuum under which the final composite is prepared. In

this case, more adsorbed gases can be removed and better bonding is

possible.

The purpose of the work carried out in the first phase was to

explore whether or not bonding could be studied by means of electron

channelling patterns in the scanning electron microscope. In this first

phase, only conventional materials were used in order to establish

techniques. One of the main objectives was to correlate channelling

patterns with divergent beam (Kossel) x-ray patterns in order to obtain

quantitative stress-strain data from the channelling pattern. Such a

procedure would allow mapping of the strain field in the vicinity of

the matrix-core interface. The lower the strains, the better the bond.

Divergent Beam (Kossel) Microdif fraction

This method can provide quantitative information about the stressstrain configuration in a material. In particular, the Kossel internal

stress-strain analysis yields for the sampled volume:

(a) Average Cauchy strains

(b) Principal strains and their axes

- 58 -
(c) Principal stresses and their axes

(d) Maximum shear strain in any (hkl) plane

(e) Total stored elastic energy

(f) Shear stored elastic energy

However, the time and effort needed to obtain a sufficient amount

of data from a given material by the Kossel method is prohibitive"^.

Another problem is the large amount of data required to describe the

results of a single point using the Kossel internal stress-strain

analysis. More than one-hundred separate measurements are needed to

completely describe the point. Hence, using the Kossel method alone

represents a nearly impossible situation for carrying out a practical

task. Therefore, another means of determining quantitative stressstrain relationships at the micrometer level of spatial resolution was

sought for this task. The most appealing method is to use electron

channelling patterns prepared with the aid of the scanning electron

microscope. This is because the scanning electron microscope itself

provides an ideal means to locate and examine regions of interest on

the specimen, and electron channelling patterns can usually be obtained

rapidly from the region of interest.

Scanning Electron Microscopy

In the scanning electron microscope, an electron beam of 1 to 50KV,

o having a small diameter, ranging from lOOA to lym, is scanned in a square

raster on a specimen. The beam interacts with the specimen to produce

(<^50eV) , x-rays and visible light which can be monitored continuously by

- 59 -
appropriate detectors. The detector signal is used to control the

brightness of the flying spot of a cathode ray tube (CRT) which is

scanned in synchronism with the same raster as the specimen. A one-toone correspondence is made to exist between points on the specimen and

the image on the cathode ray tube. Thus, the micrograph is built up.

The scanning electron microscope is useful for surface analysis because

of (1) the high spatial resolution which can be achieved, (2) the large

depth of focus - about 100 times greater than an optical microscope, and

(3) the large variety of contrast mechanisms which result from beamspecimen interactions. For further details see Ref . [2].

Electron Channelling Patterns

i Electron channelling contrast arises because electrons can penetrate

crystals more easily along certain directions than others (Fig. 1) . When

the electrons are able to enter open passages (channels) in the crystal

lattices, they penetrate deeply, and few escape. By slightly altering

the angle the beam makes with the crystal, these channels become difficult

to enter, and the electrons interact with the specimen nearer the surface

so that more escape. An electron channelling pattern can be obtained by

rocking the beam through a range of angles in the form of a cone.

Electron channelling patterns are capable of providing information

about the orientation of the crystal as well as its perfection. To date,

almost the only quantitative use of electron channelling patterns has

been in orientation determination. This is because the relationships

by which the state of perfection can be determined contain factors such

3 as the so-called extinction length , which are not well known. For example,

4 Schulson has suggested the following:

- 60 -
2u3g = 2/(?g|||) (1)

where 2ca^ is the channeling pattern line width in radians

E is the extinction distance for the reflection excited

g

|g| is the reciprocal lattice vector translation.

Now |g[ is equivalent to 1/d where d is the interplanar spacing for a

plane of Miller indices (hkl) . It has been shown that if Ad/d can be

measured properly, then the entire stress-strain configuration for the

sampled crystal volume can be determined'^.

The use of a few Kossel patterns in order to provide a basis for

inferring the needed d values from channelling patterns may, therefore,

be attractive. In such a case, one would require a well annealed crystal

and the capability of simultaneously preparing the electron channelling

pattern and the Kossel pattern in the scanning electron microscope.

Accurate d values could be obtained from the Kossel pattern; the

corresponding channelling pattern line widths, 2co , can be measured.

Changes due to strains result in changes in 2w ; from these Ad values can

be obtained through simple manipulation of eqn. (1). Hence, Ad/d can be

determined from the channelling information. Hence, the factor (2/E ) in

g

Eqn. (1) could be determined empirically. Then, electron channelling

patterns could be used to provide the necessary Ad/d values for determining

the stress-strain configuration from the sampled volume.

One of the major thrusts of this exploratory project was to see if

such a correlation could be carried out. This necessitated devising a

means to simultaneously prepare electron channelling patterns and Kossel

- 61 -
patterns as well as a means to accurately observe and record electron

channelling line profiles in the scanning electron microscope. In

particular, we needed to know the effect of applied stresses on electron

channelling patterns. The response of electron channelling patterns to

experimental conditions such as specimen tilt had to be investigated as

well as effects of surface deposits on the pattern. The former is an

experimental response and the latter a material effect.

Investigation of Electron Channelling Line Profiles

A typical electron channelling pattern from a well-annealed single

crystal of aluminum is shown in Fig. (2) . There are crystallographic

bands and lines whose width and intensity depend upon the state of

perfection of the crystal and the basic crystal parameters such as the

lattice spacing. The sample was electropolished to remove any surface

damage after the crystal was held for fifteen hours at 610°C in a

purified argon atmosphere. The crystal was normal to the electron beam

which was accelerated through 30kV. Aluminum was chosen for study since

it is often used as the matrix in composite materials.

The line seen in Fig. (2) shows where the electron beam was made to

scan in a single line along the crystal. The profile produced by this

line is shown in Fig. (3). This profile was recorded on an oscilloscope

screen; the y-intensity is shown as a function of position. The profile

can be related to the lines and bands of Fig. (2) in a straightforward

manner; features responsible for intensity variations can be identified.

Next, the crystal was cold rolled 5% and electropolished again.

Fig. (4) shows the electron channelling pattern after rolling. Clearly,

the pattern is diffuse compared to Fig. (2). The corresponding profile

- 62 -
(Fig. 5) shows that virtually all details except the major (200) type band

have been eliminated. Material deformed up to 10% tensile strain has been

g successfully studied using electron channelling contrast .

The effect of surface layers was studied with a niobium single

crystal. Niobium can be used in directionally solidified composite

materials. The crystal was chemically polished in a mixture consisting

of 70% concentrated HNO^ and 30% concentrated HF. The electron channelling

pattern of the as-polished crystal is shown in Fig. (6); the <012> pole

is at the left of the pattern. The profile corresponding to the impressed

o line is shown in Fig. (7) . Next, a 200A layer of carbon was evaporated

onto the surface of the crystal. The thickness was determined with a

piezo-electric method said to be accurate to about +10%. The electron

channelling pattern is shown in Fig. (8) and the line profile in

Fig. (9). Noticeable changes in the profile have occurred. Increasing the

o carbon thickness to 450A resulted in further degradation of the pattern as

o shown in Figs. (10 and (11). A layer of amorphous carbon lOOOA in thickness

caused still more degradation but certainly an identifiable pattern

remained as seen in Figs. (12) and (13). The crystal was a deep purple

after this much carbon had been evaporated onto it.

These results were both surprising and extremely encouraging because

previously it was believed that only a few hundred angstroms carbon

deposit would wipe out the electron channelling pattern completely. The

fact that this is not the case means that perhaps composites consisting

of a metal matrix and non-metallic core can be studied by depositing

a few hundred angstrom layers of carbon onto the surface to make it

- 63 -
conducting. Perhaps totally non-metallic materials can be studied in

this way as well

.

As we shall see, a tightly bound oxide layer gives quite different

and less encouraging results. Oxidizing the niobium crystal in a

controlled fashion was somewhat difficult. We used a bath devised by

Picklesimer to anodize the niobium, with layer thickness determined by

o color. A layer about 750A thick as indicated by the gold color produced

was grown onto the surface. The clean crystal case is shown in Figs. (14)

and (15) while after anodizing, the corresponding results are shown in

Figs. (16) and (17). This oxide thickness virtually destroys the

o channelling pattern. Anodizing until a purple color developed (>1000A)

did destroy the pattern.

The effect of tilting the specimen on the properties of channelling

bands and lines was investigated next. This effect is important since

surfaces in a true composite will not necessarily be flat and perfectly

aligned over long distances. Hence, it will be necessary to separate

tilt effects from effects due to internal strains and/or surface layers.

For the tilt study, a silicon crystal was chosen; silicon is frequently

a component in composite materials.

The results are shown in Figs. (18) - (23). Tilting the crystal with

respect to the electron beam causes the contrast to undergo a change in

character. For example, the {440} type reflections change from close

black/white pairs at normal beam incidence to distinctly black or white

lines for tilted specimens, as indicated by the corresponding line traces.

- 64 -
Preparation of Kossel Patterns In the Scanning Electron Microscope

We were able to prepare both reflection and transmission Kossel

patterns in the scanning electron microscope. The reflection patterns

using a tilted specimen will almost certainly be the ones of most

interest in the study of composites; preparing thin (~50ym) sections of

composites will be difficult so that transmission work may not be feasible.

Hence, the tilted foil electron channelling study was essential in order

to establish a basis for attempting to correlate Kossel patterns and

electron channelling patterns prepared from composite materials.

Reflection patterns were prepared from an iron crystal; a typical

pattern is shown in Fig. (24). Here, the crystal was tilted about 60°.

The lines are sharp and have enough contrast to carry out meaningful

measurements. Tilted foil electron channelling patterns can be prepared

simultaneously using the NBS specimen current amplifier constructed for

the scanning electron microscope^.

Preliminary Study of Conventional Composite Materials

Two types of composite materials were obtained from Sandia and

the U.S. Army Research Center (Watertown, Mass.) respectively. The

Sandia material consisted of plasma sprayed aluminum onto boron-silicon

(borsic) fibers. The fibers were prepared using a thin tungsten wire

as a base. This material, imaged in the scanning electron microscope,

is shown in Fig. (25). First attempts to obtain electron channelling

patterns from this material failed. The probable causes for this

failure were the huge fabrication strains and the extremely fine

"grain-size" of the aluminum matrix, as indicated by conventional x-ray

- 65 -
diffraction techniques. The grains were probably smaller than the minimum

region from which we could obtain an electron channelling pattern, i.e.,

about ten micrometers.

The Army material consists of carbon fibers in a magnesium matrix.

Work will be underway on this material shortly. We also have some

directionally solidified eutectic material on hand for study.

Conclusions

(1) Line profiles from electron channelling patterns can be measured

with our apparatus so that the 2oo term in Eqn. (1) can be determined for

a variety of specimen conditions, i.e., strained, coated and tilted.

(2) Kossel patterns can be prepared from bulk specimens in the

scanning electron microscope with sufficient information to provide

satisfactory |g| data for Eqn. (1). Then the term (2/^ ) in Eqn. (1)

can be determined empirically for the specimen of interest. Hence,

electron channelling patterns can be used to study strains at the

micrometer level of spatial resolution.

(3) A reduction of 5% by rolling nearly destroys electron channelling

contrast. Hence, highly strained material cannot be investigated by means

of electron channelling contrast.

o (4) Surface layers of oxides and carbon on the order of lOOOA

destroy electron channelling contrast.

o (5) Layers of 200A affect the line profiles of electron channelling

patterns

.

- 66 -
(6) Electron channelling patterns change characteristically as the

specimen is tilted with respect to the electron beam; band contrast

decreases and line character changes.

This work virtually completes the preliminary exploratory phase of

the study. Next, strains in various materials will be investigated using

electron channelling patterns. Then strains at matrix-fiber interfaces

will be investigated.

- 67 -
References

1. H. Yakowitz, NBS Monograph 130 , 75p (1973).

2. C. Oatley, The Scanning Electron Microscope, Pt.I, The Instrument,

Cambridge University Press, Cambridge (1972),

3. P.B. Hirsch, et al. Electron Microscopy of Thin Crystals , Butterworths , London, p. 100-103.

4. E.M. Schulson, phys . stat. sol. (b) 46, 95 (1971).

5. T. Imura, S. Weissman and J.J. Slade,-Acta. Cryst. 8^, 786 (1962).

6. M.L. Picklesimer, The Microscope 15, 472 (1967).

7. H. Yakowitz, C.E. Fiori and D.E. Newbury, SEM/1973 () . Johari, ed.)

IITRI, Chicago, 111. (1973) p. 173.

8. D.C. Joy and D.E. Newbury, SEM/1971 (0. Johari, ed.) IITRI,

Chicago, 111. (1971) p. 113.

- 68 -
Fig. 1 Origin of electron

channelling patterns; electrons

penetrate the crystalline specimen

more deeply in certain directions

than in others.

Fig 4 Electron channelling pattern 5 ^tensity profile along line

of aluminum crystal rolled to 5% p^- (4)^ scale: 2 volts/cm.

reduction and then electropol ished. Compare with Fig (3) Line indicates profile trace

position.

Fig. 6 Electron channelling pattern

from chemically polished niobium

crystal. Line indicates profile

trace position.

Fig. 7 Intensity profile along line

in Fig. (6). Scale: 2 volts/cm.

Fig. 8 Electron channelling pattern

from niobium crystal after evaporation of 200a thick carbon layer onto

the surface. Line indicates profile

trace position.

Fig. 9 Intensity profile along line

in Fig. (8). Scale: 2 volts/cm.

Compare with Figs. (7), (11) and (13)

Fig. 10 Electron channelling

pattern from niobium crystal

after evaporation of 450A thick

carbon layer onto the surface. Line

indicates profile trace position.

Fig. 11 Intensity profile along

line in Fig. (10). Scale: 2 volts/cm

Compare with Figs. (7), (9) and (13).

Fig. 12 Electron channelling pattern

from niobium crystal after evaporation of 1000^ thick carbon layer

onto the surface. Line indicates profile trace position.

Fig. 13 Intensity profile along

line in Fig. (12). Scale: 2 volts/cm

Compare with Figs. (7), (9) and (11).

Fig. 14 Electron channelling pattern Fig. 15

of chemically polished niobium in Fig.

crystal. Line indicates profile

trace position.

Intensity profile along line

(14). Scale:2 volts/cm.

Fig. 15 Electron channelling pattern

of niobium crystal after anodic

oxidation yielding about 750A thick

layer as indicated by coloration.

Line indicates profile trace position.

Fig. 17 Intensity profile along line

in Fig. (16). Scale: 2 volts/cm.

Compare with Fig. (15)

.

Fig. 18 Electron channelling pattern Fig. 19 Intensity profile along

of silicon with crystal normal to line in Fig. (18). Scale: 2 volts/cm.

electron beam axis. Line indicates

profile trace position.

Fig. 20 Electron channelling pattern Fig. 21 Intensity profile along

of silicon with crystal tilted 17° line in Fig. (20). Scale: 2 volts/cm.

with respect to electron beam axis. Compare with Figs. (19) and (23).

Line indicates profile trace position.

Fig. 22 Electron channelling pattern

of silicon with crystal tilted 24.6°

with respect to electron beam axis.

Line indicates profile trace position.

Fig. 23 Intensity profile along

line in Fig. (22). Scale: 2 volts/

Compare with Figs. (19) and (21).

Fig. 24 Reflection Kossel pattern

of iron crystal. Lines (indicated

by arrows) include {220}, {211} and

{200} types.

Fig. 25 Scanning electron micrograph

of plasma sprayed aluminum matrix-borsic

fiber composite. The bright central

region of the borsic fiber is tungsten

wi re.
€
CALCULATION OF COMPLEX EQUILIBRIA INVOLVING VAPORIZATION INTO VACUUM

by

Robert C. Paule

ABSTRACT

A simplified, direct approach is presented to the description of

complex equilibria involving vaporization into vacuum. Emphasis is on

the basic problem solving process and on modification of existing

techniques. Sequential solutions are presented to problems involving

purification of a melt by vaporization into vacuum. The effects of

concentration of melt and oxygen partial pressures on vaporization

rates are demonstrated.

Key Words; AI2O2, chemical doping, complex equilibria, purification

(evaporative), vacuum vaporization.

- 69 -
INTRODUCTION

Complex condensed phase equilibria with accompanying vaporization

into vacuum is a problem that is frequently encountered by high temperature

scientists. The problem is generally solved only for cases involving

simple systems. We shall show that the general formalism for calculation

of complex equilibria can be adapted to this problem.

We will develop the case for vaporization into vacuum and will show

that the techniques are adequate for dealing with either equilibrium or

non-equilibrium vaporization. Examples will be given of problems involving

either vacuum evaporative purification or doping. Vaporization from

solutions will be discussed.

There have been a number of articles describing calculations of

complex equilibria^^"'^^. The calculations of complex equilibria have been

found to be widely useful and their development has closely followed the

development of the high-speed digital computer. Elaborate, extensively

documented computer programs have been developed for performing some of

the calculations^'^'^^ A number of modifications and approaches to the

f5-7) calculations have been reported^ '

.

- 70 -
ANALYTICAL APPROACH

The basic problem is to determine the number of moles of all species

present in a system, and to determine the distribution of these moles

between the various physical phases. For our general analytical approach

we want to work with the minimum information needed to fully determine the

physical and chemical system. This is equivalent to specifying a set of

independent physical properties and independent chemical species. In

simplest terms, our task is to solve one mass balance equation for each

independent chemical species. In this process we shall require that the eq

librium constant relationships between the independent and dependent chemic

species be maintained. This problem could also be cast in terms of

(2) the free energy^ . GENERAL CALCULATIONAL PROCEDURE

As an introduction to the calculational procedures, consider the

following simple equilibrium process in which we will allow any of the

chemical species to be in stoichiometric excess.

2400 K

Al203(l) , 2Al(g) + 3 0(g).

(For simplification of this presentation we will ignore other chemical

species that might be present. Our resultant "answers" are, of course,

affected by this approximation. In actual practice, one must consider

all species that are present.)

In our procedure we will first distribute all the gram-atoms of

the elements present in the system among the independent chemical species

and then follow, through the mass balance equations, the equilibration of

the system. To be specific, assume that we have a system containing

- 71 -
4 gram-atoms of Al and 3 gram-atoms of 0. We may assign these two

elements to an initial number of moles, q., of two independent chemical

species (components) which are involved in the above chemical reaction.

In this example, we have chosen AlgO^ and Al for our components.

gram-atoms Al = 4 = 2

q^^-j q + q^^-j

gram-atoms 0 = 3 = 3

q^^-j q

and

*^A1 0

~ ^ '"^^^ ^Al

~ ^ moles.

2 3

(The rules for the proper choice of components will be discussed below.)

The general equation for assigning the elements to the components is

# of components

where Qj^ is the number of gram-atoms of the kth element, and a^j^ is the

subscript occurring on the symbol of the kth element in the chemical

formula of the jth component. The q. may be thought of as the initial

J feed components to the system, before any equilibration occurs. (In

some problems the initial feed components q., are knov/n, in which case

one simply bypasses the above steps and starts at this point.)

For the vast majority of cases, the number of independent components

that need to be considered will be equal to the number of elements present.

- 72 -
In our example we have two elements, Al and 0, and therefore two

components. Exceptions to this general rule can occur when several

chemical species have the same stoichiometric ratio of elements. This

point will be further discussed in the Appendix.

The rules for choosing the components to describe the system are

that the species must be stoichiometrically independent {e.g., KCl and

KgCl^ cannot both be used), and all elements in the system must be

present within the group of components selected. Also, any chemical

species whose concentration is not expressible by an equilibrium constant

relationship, such as a pure solid phase, must be selected as a component.

With the components chosen and the q. assigned, we are now ready to

make a mass balance for each independent component. For our example,

let n^-j Q and n^^-j be the number of moles of the independent components

at equilibrium, and let n^ be the corresponding number of moles of oxygen

determined by the equilibrium constant for the reaction. Inspection of

the chemical equation shows that each mole of oxygen gas produced came

from the consumption of 1/3 mole of Al202(l) and resulted in the production

of 2/3 "extra" moles of Al(g).

Thus:

q^^^Q^

- 1/3 n^ = n^^^^^ (1)

^Al ^ 2/3 no = n^^ (2)

The general mass balance equations have been conveniently described by

Kandiner and Brinkley^^^ in the form:

- 73 -
where the j index refers to the independent components, the i index refers

to the dependent species, and v.. refers to the coefficient(s) of component

j in the i chemical reaction(s) written in the form:

1/3 ^203(1) - 2/3 Al(g) -_giaJ = 0.

Note that the products are transposed to the left side of the equation

and that the equation is expressed in terms of one mole of the dependent

(product) species. For the general case, one such chemical equation can

be written for each dependent species, and each of these equations must

be written so as to involve only one dependent species. The independent

components will, of course, be used repeatedly in these equations.

At this point, for the problem at hand, we have two mass balance

equations (1 & 2) representing the two independent components, n^^-j q

2 3

and n^^i . We have an additional dependent unknown, nQ, which can be

determined from the equilibrium constant relationship set up on the basis

of one mole of oxygen.

K

= _AJ y_ (3)

'^Al203

For a usual system of contained gases, the pressures can be related to moles

using Dalton's law

= JP (4)

where N is the total number of moles of gas and P the total pressure.

- 74 -
Therefore k = P) ij- P) (5)

p -5/3 -2/3

and

"O " %^ "a1

If we specify, in addition to the temperature, the total pressure or

alternately the total volume, then we have three equations (1, 2, 6)

and three unknowns (n^^^ 0 ' "a1 * "o^* problem is solvable.

2 3

Mathematical solutions to the problem,s are frequently obtained by using the

Newton-Raphson method^^^, as described below,

APPLICATION TO THE PROBLEM OF EVAPORATION INTO A VACUUM

The above general procedure can also be used to describe a completely

different situation, i.e., the case of evaporation into a vacuum. The

equil ibrium constant relationship [equation (3)] is still valid, but

equation (4) now needs to be replaced by the Knudsen equation:

n. 1/2

Pi = ^ (27rRTM.) (7)

where n^. moles of vapor with molecular weight M^ effuse from the condensed

phase surface of area A in time t. The analogs to equations (5 & 6) are

thus:

- 75 -
, 'AL 2/3 r

1/2

and Hq = K

(2TrRT ) At

1/2

-5/3

^(2.RTMo)

-1/3 -1/2 -2/3

^Al ^0 "Al

(8)

(9)

Again we have three equations (1, 2, 9) and the same three unknown, and

the problem is solvable.

If non-equilibrium congruent evaporation occurs, the situation is

described by introducing an evaporation coefficient, a, to the Knudsen

equation:

1/2

(10)

Note that the above use of an evaporation coefficient assumes the nonequilibrium is related to the evaporation step, and that chemical

equilibrium is maintained within the condensed phase.

For the case of evaporation from a solution containing several

condensed species, it is necessary to modify the condensed phase activity

term in the equilibrium constant equation. If we assume the solution to

be homogeneous and ideal, we can write the activity of any component to

be equal to the mole fraction of that component in the solution. As an

- 76 -
example, consider a case where our original Al202(l) contained Si02(l)

impurity, and as a result the vapor phase also contained Si(g). We now

have five chemical species, Al203(l), Al(g), Si02(l), 0(g), and Si(g),

with the first three being assigned as components. Following the previously

described rules and assuming the solution to be ideal, we can write chemical

equations for the two dependent species, 0(g) and Si(g), and can them write

the mass balance equation for the components.

The equilibrium constant relationship between the dependent species and

the components are as follows:

1/3 Al203(l) ^ 2/3 Al(g) + OM

Si02(l) + 4/3 Al(g) -> 2/3 Al203(l) + Si(q )

^Al203 - "O

^ 2/3 ng. = n^^^Q^

^Al ^ 2/3 no - 4/3 n3. = n^^

^Si02 "Si = "Si02

K

- 77 -
^h°3 " "S102

,4/3

"Si02

The above equations can be adapted to describe either evaporation into

a vacuum, or evaporation in a contained gas system. The resultant five

equations and five unknowns can then conveniently be solved by using

the Newton-Raphson method. The use of a computer in handling the

calculations Is desirable at this stage of complexity.

For all situations to be described we have j mass balance equations,

where j is the number of independent components, and i equilibrium constant

equations, where i is the number of dependent chemical species. Various

substitutions can be made for the pressures and condensed phase activities

in the equilibrium constant equations depending on the physical system.

The unknowns can then be determined since we have equal numbers of

equations and unknowns.

- 78 -
NEWTON- RAPHSON METHOD

For very simple gas systems, most high temperature scientists have

directly solved the equations for the unknowns. For more complex chemical

systems involving larger numbers of unknowns, direct solution is impractical

since the equilibrium constant equations are frequently non-linear. A

number of methods have been devised for the solution of these equations^^^

.

One convenient approach makes use of iterative approximations to linearize

the equations and solve for the unknowns.

The Newton-Raphson method^ ^ is frequently used for the linearization.

This iterative method involves an approximation consisting of truncating

(g)

a Taylor series expansion^ . For example, for two equations involving two

independent variables U and V we have:

F(U,V) = 0 G(U,V) = 0 (11,12)

t h

For the 1 approximation:

and

^< VV <f)

AU, . (f) ^^^^

.V, . . . . 03,

^("i -^i) ^"i ^(w) *

• • • (14)

Equations (11) and (12) can, for the simple A1203 example, represent mass balance equations (1) and (2) with the dependent variable, n^, being

- 79 -
replaced by using equilibrium relationship (6, 9, or 10). To describe

the simple AI2O2 vaporization into vacuum we use equations (1,2,9) to obtain

To simplify notation we define

' 1 f27rRT)^/2 -5/3 -1/3 -1/2

•^1 ^ ^

i\t Al "0

. nT^l/2 -5/3 -1/3 -1/2

and k2 = fK[^ ] M^l ^0

so that qAi203 ^ ^l^Al"^^^ - "AI2O3 = 0- ^^^"^

and q^^ +

'^2"Ai'^^^ "a1

= ^' ^^2")

Using initial estimates, n^-j q and n^-j -j, equations (13) and (14) are:

2 3)1

- 80 -
Equations (13*) and (14') are linear in An^^ q and An^-j

i and can

2 3 5

1

easily be solved to obtain better estimates for n^^-j q

and n^^i ^ *°

2 3)2

used in the next iteration of equations (13') and (14'). The iteration

process is repeated until acceptably constant n^-j q and n^-j are obtained.

2 3

The n^ is obtained from equation (9), i.e., from the relationship

involving the equilibrium constant and values for the independent species.

One advantage of this treatment is that it deals primarily with the

independent components and thus minimizes the number of unknov/ns that

need to be handled.

In using the iterative approach, it is sometimes found necessary to

limit the relative size of the corrections to avoid large overcorrections

which can even result in negative numbers of moles. Overcorrections can .'

occur since we have truncated the Taylor series expansion after the

first derivative.

COMPLEX PURIFICATION PROBLEM

Problems of practical interest frequently involve the description and

handling of complex situations. The use of computers allows the convenient

solution to these problems. As one example of a complex problem, consider

the situation where we have one mole of AI2O2 containing 10 ppm CaO (mole

basis) and wish to purify the ^"^r^-^ by evaporation by heating it in vacuum

at 2400 K. Such a process might be used either for purification or for

controlling the level of doping. Questions of interest are how much AI2O2

and CaO remain at given times and how fast does the purification proceed.

For this problem, there are three elements and three components. The

independent components were taken to be Al202(l), CaO(l), and 0(g), and

the dependent gaseous species considered were Al , AlO, AIO2J .AI2O,

A1202, O2, and Ca. For the sake of brevity we will only outline the

calculational procedure. We first set up the three mass balance equations

- 81 -
and the seven equilibrium constant relationships using JANAF data^ ' for

the equilibrium constants, and then use the Knudsen equation to relate

the pressures to moles. Unit evaporation coefficients v/ere assumed. The

evaporation area used in the Knudsen equation was calculated using a

molten drop of spherical geometry and the number of moles and density of

^^2*^3^^^' AlgO^vl) and CaO(l) were assumed to have ideal activites

and to be completely mixed in the melt. The initial time interval was

taken as 0.005 seconds, and an iterative (Newton-Raphson) solution was

obtained (see column one of the table). In this iteration procedure

the corrections were limited to be either equal to or one half the

estimated value. The pressures were calculated using equation (7),

and represent initial vaporization pressures. Sequential calculations

for vaporization were then made at subsequent twenty second intervals

with the Al202(l) and CaO(l) feed for each interval being obtained from

the previous intervals results. The moles of gas represent vaporization

during each time interval.

- 82 -
Moles of Species Present

Temp (K)

Cumulative Time

(Sec)

AI2O3

CaO

0

Al

AlO

AlOo

AI2O

A1202

Ca

0

1.0000x10 0

9.9998x10

-6

1.6143x10"'

4.8005x10

-9

1.0670x10

-7

1.2741x10

6.2753x10

-8

2400

-10

2.3611x10'

-9

1.1602x10

1.8850x10

•11

-10

20.00

9.9975x10"

9.2986x10"

6.4550x10"

1.9197x10"

4.2676x10

5.0957x10

2.5097x10

9.4435x10'

4.6402x10'

7.0120x10'

40.00

^ 9.9950x10"^

^ 8.6465x10"^

6.4548x10"^

1.9193x10"^

4.2671x10"^

5.0949x10"^

2.5092x10"^

9.4424x10'^

4.6396x10"^

6.5210x10"''

60.00

9.9925x10'

8.0401x10

-6

6.4535x10

-4

1.9189x10

-5

4.2665x10

5.0941x10

2.5088x10

9.4413x10

4.6389x10

6.0643x10

-4

-5

-6

-6

-8

-7

Pressures of Species Present in Atmospheres

A1203 0. 0. 0. 0.

CaO 0. 0. 0. 0.

0 3.1171x10"^ 3.1170x10"^ 3.1169x10"^ 3. 1168x10"^

O2 1.3109x10"'^ 1.3108x10"^ 1.3107x10"^ 1. 3106x10"''

Al 2.6754x10"^ 2.6756x10'^ 2.6757x10"^ 2 .6758x10"^

AlO 4.0321xl0"'^ 4.0322x10"^ 4.0323x10"'^ 4 .0323x10"^

AIO2 2.3264x10"^ 2.3264x10"^ 2.3263x10"^ 2 .3263x10"^

Al20 9.5332x10"^ 9.5338x10"^ 9.5343x10"^ 9 .5348x10"^

AI2O2 5.1926x10"^° 5.1927x10"^° 5.1929x10"^° 5 .1930x10"^°

Ca 5.760x10"^ 5.3581x10"^ 4.9838x10"^ 4. 6355x10-9

- 83 -
As vaporization proceeds, the concentration of CaO in the melt

decreases and this results in a lowering of the Ca vapor pressures. It

should be noted that for each time interval the moles (and mole fractions)

of the liquid components are treated as if they are constant throughout

that interval. Since allowance is not made for liquid concentration changes

within each time interval, it is necessary to choose time intervals small

enough such that the liquid concentration changes between intervals are

relatively small. The use of computer calculations minimizes the

inconvenience of using such sequential steps.

Step approximations, dependent upon time, are not encountered in

calculations for gas systems since these systems are functions

only of total volume or pressure. Gases associated with contained gas systems

are in constant equilibrium with the condensed phase, while gases

evaporating into vacuum can be in equilibrium with the condensed phase

only at the moment of evaporation.

In the above example the CaO vaporization rate may be too rapid if

one wishes to control the level of the CaO doping. The chemical

equilibria, however, can be shifted to inhibit the rates of vaporization

by use of a constant low oxygen pressure surrounding the melt. If one

-5

chooses the oxygen pressure to be 10 atm. v/e still maintain near

Knudsen flow conditions and can continue to calculate vaporization rates

using the Knudsen equation. For these calculations we can conveniently

-5

assign Al90-(1) and CaO(l) as components and use a P« of 10 atm. The

- 84 -
purification rates as indicated by the CaO(l) concentrations are shown

-5

in Figure 1, both for the case of Pq equal to 10 atm. and for the

case of self-developed oxygen (as tabulated above). It is seen that an

-5

oxygen pressure of 10 atm. significantly inhibits the rate of

vaporization.

It is clear that many modifications in oxidation or reduction

conditions can be used to achieve desired vaporization goals.

- 85 -

ACKNOWLEDGEMENT

The author would like to thank Dr. John B. Wachtman, Jr. for his

original suggestion and his aid in modifying vaporization equations to

describe evaporative purification from mixed melts. The author is also

indebted to Dr. Ernest R. PI ante for many helpful suggestions and for use

of a computer program from which our modified programs were v;ritten.

Financial support provided by NASA under contract W-13,475 #1, is gratefully

acknowledged.

REFERENCES

1. Kandiner, H. J., and Brinkley, S. R. , Ind. Eng. Chem. , 42, 850 (1950).

2. White, W. B., Johnson, S. M. , and Dantzig, G. B. , J. Chem. Phys., 2a,

751 (1958).

3. Gordon, S., and McBride, B. J., NASA, SP-273 (1971).

4. Feldmann, H. F. , Simons, W. H. , and Bienstock, D. , U. S. Bur. of

Mines, RI-7257 (1969).

5. Zeleznik, F. J., and Gordon, S., Ind. Eng. Chem., 60., 27 (1968).

6. Van Zeggeren, F. , and Storey, S. H., The Computation of Chemical

Equil ibria , Cambridge University Press, 1970.

7. Klein, M. , Physical Chemistry , Vol 1/Thermodynamics , Chapter 7,

edited by Eyring, H. E. , Jost, W. , and Henderson, D. , Academic

Press, New York, 1971.

8. Margenau, H., and Murphy, G. M. , The Mathematics of Physics and

Chemistry , 2nd ed., page 492, D. Van Nostrand Company, Princeton,

New Jersey, 1956.

9. Hildebrand, F. B. , Advanced Calculus for Engineers , page 353,

Prentice-Hall, New York, 1949.

10. JANAF Thermochemical Tables , Dow Chemical Co., Midland, Mich.,

loose-leaf, 1972.

- 87 -
APPENDIX

DETERMINATION OF THE NUMBER OF COMPONENTS

Kandiner and Brinkley^^^ have developed a convenient method for

determining the number of independent components. The method is based

on forming equations for the production of each chemical species from

the elements and then determining the number of independent equations

within the total system. Kandiner and Brinkley construct a table with

column headings determined by the elements present, and row headings

determined by the chemical species present. The table entries are the

numbers of atoms present in each chemical species. The number of

independent components is equal to the order of the largest non-zero

determinant that can be formed from the table, or the rank of the matrix.

For the simple AI2O2 system we have a matrix of rank two.

Al 0

Al203(l) 2 3

Al(g) 1 0

0(g) 0 1

If the chemical system contains only Al202(l) j Al202(gJ or

KCl{g) t K2Cl2(g) we would have matricies of rank one and therefore

only single components.

K CI

KCl(g) 1 1

K2Cl2(g) 2 2

88 -

= -3

Al 0

Al203(l) 2 3

Al203(g) 2 3
Distribution:

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- 90 -
FORM NBS-114A (1-71)

U.S. PF Pr. OF COMM. 1. IMIIU.IC A 1 ION 01< RI' l->OR r NO. 2. Gov't Acces.sion BIBLIOGRAPHIC DATA No. SHEET NRSTR 73-402

3. Rc( i jil em' -s Ariession No.

4. 11 11.1. AND ^HH 11 1 1 1:

NBS Materials Science and Manufacturing in Space Research

5. Publii ation D.ite November 1973

6. Performing Oganization Code

j 7. AUTHOR( .^)

j E. Passaglia and R. L. Parker

8. l-'erforming Organ ization NBSIR 73-402

9. PHRFORMING ORGANIZATION NAMi; AND ADDRHSS

NATIONAL BURKAU OI- STANDARDS

DHPARTMLNT 01- COMMI'RCII

WASHINGTON, D.C. 20234

10. Pro|ect/ l ask/ Work Unit No.

11. Contract/Grant No.

W-13,475 ill

12. Spon.soring Organization Name and Address

NASA

FOB 10

600 Independence Avenue S .W.

II Washington, D.C. 20546

13. Type of Report & Period Covered

Final

14. Sponsoring Agency Code

iflS. SUPPLKMENTARY NOTES

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

bibliography or literature survey, mention it here.)

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

IManuf acturing in Space (MS/MS) (now Space Processing) program, covering the period

jNovember 1, 1972 to October 31, 1973. The objectives of the NBS program are to perform

iground-based studies of those aspects of space that could possibly provide a unique

jenvironment for making materials more perfect or more pure. The approach taken deals

iprimarily with experimental and theoretical studies of the possible effects of the

iabsence of gravitational forces on those materials preparation processes where the

Ipresence of gravity may be important in reducing perfection or purity. The materials

preparation processes studied comprise 5 tasks in the areas of crystal growth,

ipurif ication and chemical processing, and the preparation of composites.

'• KEY WORDS (.Alphabetical order, separated by semicolons)

aterials processing; perfection; purity; space manufacturing; space processing;

ero-g.

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