NBSIR 77-1208

NBS Space Processing

Research

E. Passaglia, R. L. Parker

Institute for Materials Research

National Bureau of Standards

Washington, D. C. 20234

Phone: (301) 921-2822

February 1977

Annual Report

For the Period 1 January 1976 - 31 December 1976

NASA Government Order H-19333B

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

NBSIR 77-1208

NBS SPACE PROCESSING

RESEARCH

E. Passaglia, R. L. Parker

Institute for Materials Research

National Bureau of Standards

Washington, D. C. 20234

Phone: (301) 921-2822

February 1977

Annual Report

For the Period 1 January 1976 - 31 December 1976

NASA Government Order H-19333B

This report was prepared by the National Bureau of Standards

under Government Order H-19333B - NBS Space Processing Research,

for the Advanced Missions Program of the National Aeronautics

and Space Administration

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

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

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Acting Director

I TABLE OF CONTENTS

Page

Summary 1-2

i Task 1 - CRYSTAL PERFECTION IN CZOCHRALSKI GROWTH — NICKEL by

M. Kuriyama, W. J. Boettinger and H. E. Burdette 3-33

Task 2 - EVAPORATIVE PURIFICATION OF ULTRA-HIGH PURITY MATERIALS

Part A, by E. R. Plante 34-40

Part B, by W. J. Boettinger and F. S. Biancaniello 41-63

Task 3 - VAPOR TRANSPORT SYNTHESIS AND CRYSTAL GROWTH by

H. S. Parker 64-71

Task 4 - MELT SHAPE IN WEIGHTLESS CRYSTAL GROWTH by

S. R. Coriell, S. C. Hardy and M. R. Cordes 72-108

Task 5 - CONSULTING SUPPORT 109

Distribution List 110-111

i

1^

National Bureau of Standards

Space Processing Research

Summary

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

Processing Program covering the period January 1, 1976 - December 31, 1976.

The objectives of the NBS program are to perform ground-based studies

(and, where appropriate, space-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 four tasks in the

areas of crystal growth, purification and chemical processing. There is

an additional task on consulting support.

The results obtained for each task are given in detailed summaries

in the body of the report. Briefly, in Task 1 - Crystal Perfection in

Czochralski Growth - large nickel single crystals have been grown having

dislocation densities as low as 400 lines /cm 2 as assessed by x-ray

dynamical diffraction techniques. In Task 2 - Evaporative Purification of

Ultra-High Purity Materials - Part A - it was determined that the use

of sessile drops as a means of support for the study of molten alumina

places severe restrictions on the type and validity of the data that can

be obtained in view of temperature measurement and control problems encountered.

In Part B, rates of evaporative purification were determined for Nb-Mo

and for Mo-Zr alloys at elevated temperatures using R.F. levitation of

- 1“
molten drops. In Task 3 - Vapor Transport Synthesis and Crystal Growth -

the growth of 1.5 cm diameter crystals of mercurous chloride crystals by

a vapor Bridgman technique is described. In Task 4 - Melt Shape in Weightless

Crystal Growth, thermocapillary forces on air bubbles in a viscous oil

were measured, and the shape of axisymmetric liquid zones and their

stability with respect to perturbations has been investigated numerically.

- 2 -
Task 1

Crystal Perfection in Czochralski Growth—Nickel

M. Kuriyama, W. J. Boettinger and H. E. Burdette

Metallurgy Division

Institute for Materials Research

Summary

To study the relationship between crystal growth conditions and

resultant crystalline perfection, large nickel single crystals more than

12 cm long and 2 to 3 cm in diameter have been grown from the melt by

the Czochralski method. Unlike semiconducting materials, one cannot

easily thin metal crystals, without straining them, for the purpose of

applying ordinary Lang topography with yL^l where kinematical scattering

in imperfect crystals is a good approximation. This situation with

metal crystals necessitates the use of dynamical diffraction effects in

imperfect crystals to permit sample crystals to be thick enough to demonstrate their imperfections as in the bulk.

The crystal perfection of as-grown nickel single crystals has been

assessed by x-ray dynamical diffraction topography with an asymmetrical

(double) crystal topographic (ACT) camera. Transmission topographs

were obtained from crystals of thickness ranging from 0.37 mm (yL=18)

to 1.03 mm (yL=52) using {111}, (002) and (220) diffraction. The

crystals grown under favorable conditions have shown strong anomalous

transmission. The O-diffracted (transmitted) and the H-diffracted

(Bragg-diffracted) beams display almost identical disruption images of

crystal imperfections in the interior of the crystals. The types of

- 3-
imperfection and the degree of crystal perfection will be sorted by a

set of crystal growth parameters, such as seed orientation and rotation

rate. In addition to the images of crystal imperfections, there are

disruption images of 71° and 109° magnetic domain walls in the topographs .

In this work it has been found, as in previous works on copper,

that nickel single crystals can be produced with perfection far better

(-^400 dislocation lines/cm2

) than the common level by controlling practical process parameters, such as the rotations of the seed and the

melt, and the growth directions. However, more crucial factors influencing the ultimate level of crystal perfection are governed by^some

crystallographic effects closely related to the behavior of dislocations in grown crystals. Anisotropic and directional dependence of dislocation properties plays a significant role in improving the crystalline perfection above a certain level. Some factors which are required

to obtain dislocation-free crystals will be discussed based on the

present experimental results, along with some comments on crystal growth

experiments in space.

Introduction

X-ray double crystal diffraction topography has recently been

employed to establish the fact that crystal growth conditions play a

significant role in producing large copper single crystals of high

perfection from the melt by the Czochralski technique^ . In particular, several interesting crystallographic effects, such as seed

orientation and dislocation type, have been found to influence the

- 4

-
resultant crystalline perfection. However, these results alone are not

sufficient to draw the conclusion that the observed effects take place

in. most metal crystals. Nickel has a face-centered cubic crystal structure like copper, while material properties such as dislocation mobility,

stacking fault energy and dislocation velocities are considerably different from copper. We have thus extended our work to large nickel

single crystals grown from the melt by the Czochralski technique.

Nickel is ferromagnetic. Production of highly perfect nickel

single crystals certainly provides the opportunity to study magnetic

domain configurations in the interior of bulk nickel crystals by x-ray

dynamical diffraction topography. In the past most of the magnetic

domain observations in the interior of metal crystals were restricted

to iron crystals or iron-silicon crystals; thus this new opportunity

with nickel will be quite significant in understanding the behavior of

ferromagnetic domains and their walls In industrial applications of

soft magnetic materials where the minimization of electric energy loss

is an important problem.

When compared with iron, nickel has smaller saturation magnetization, larger magnetostriction and a substantially smaller magnetic

anisotropy energy. Nickel crystals thus deviate more significantly

from cubic symmetry than iron or iron-silicon crystals. The magnetic

domain walls would be broader since the wall thickness is inversely

proportional to the square root of the magnetic anisotropy energy

These different magnetic properties may display diffraction phenomena

in such a favorable way that one can approximate a real domain wall by

- 5 -
a simple mathematical model of crystal imperfections, to which a general

7-9

dynamical diffraction theory can be applied rather rigorously.

Experimental Procedures

At the current stage of crystal growth research, it is not only

inevitable, but desirable to characterize growth conditions by a set of

variables chosen from the simplest, most practical and controllable

process parameters available. These variables are indeed related in a

very complex manner to the independent physical and thermodynamic variables which truly describe a physical system consisting of a growing

crystal and the melt. In spite of this complexity, those chosen process

parameters can be considered as reasonable variables, only if they are

capable of describing results with sufficient reproducibility . For a

study of the relationship between crystal growth conditions and resultant crystalline perfection, the first task will therefore be to assess

the crystal perfection nondestructively and accumulate these data under

several fixed growth conditions for a check of reproducibility. In

this work, we choose as principal variables the angular velocities of

crucible and seed, bottlenecking, the pulling speed, diameter control

during growth, and the effect of seed orientation. There are, of

course, some other important variables such as temperature gradient

and deviation of the rotations from axial symmetry. However, we assume

in this work that they are fixed.

Large nickel single crystals were grown by the Czochralski technique from either polycrystalline or single crystal ([100], [110] and

[111] grown directions) seeds in an argon atmosphere. The procedures
of nickel single crystal growth and sample preparation for x-ray diffraction topography have been described in detail previously"^

Briefly, the melt and seed were rotated around a common axis in the same

direction independently with different rotational speeds; the relative

speed of rotation ranged from 0.1 to 4.0 rpm, as shown in Table I.

Nickel of 99.99% purity was used as the melt charge. Crystal boules

were initially narrowed down in one region, thus forming a "bottleneck."

The grown crystals were about 12 to 16 cm long with diameters between

2.0 and 3.0 cm and with a bottleneck diameter, whenever achieved, of

slightly less than 1 mm. The boules were oriented by the Laue method

and sliced into discs with an acid saw. The discs were polished on an

acid polishing wheel. The following chemical compositions were found

to be most effective for the strain-free cutting and polishing of

nickel samples: 45% nitric acid, 33% hydrochloric acid, 20% acetic

acid and 2% ethyl alcohol (in volume percent) . Among these, ethyl

alcohol plays an important role in maintaining the solution in a highly

volatile state. A freshly prepared solution should be used at all

times. For the cutting the crystal boule should be heated to about

90°C to keep the cutting time reasonable. The discs have (110) planes

as their parallel faces in this work.

X-ray diffraction topographs were taken in both the transmission

and the surface reflection geometry with an asymmetric (double) crystal

1 2 11 topographic (ACT) camera

*

’

. In the transmission geometry both the

O-diffracted (transmitted) beam and the H-diffracted (Bragg-diffracted)

beam are recorded simultaneously on the same nuclear plate. A high3 resolution double-crystal scanning diffractometer (SCAD) was used to

-7 -
obtain the profiles and widths of rocking curves at various locations in

the crystal. CuKai radiation was used throughout the present work. To

avoid damage to the crystals caused by conventional measuring techniques,

the thicknesses of the discs were determined by the anomalous transmission effect from the separation between the undiffracted and the trans3 4 mitted (O-dif f racted) beam in a manner described previously ’

. For the

crystals used in this work the product of the ordinary linear absorption

coefficient, y = 49.6 mm

-1

, and the thickness, L, ranges from 18 to 52.

Topographs were taken using symmetric (220) diffracting planes in the

surface reflection geometry and (111) and (111) planes in the transmission geometry. Occasionally, (220), (002) and other {111} planes were

used for transmission topographs; specific diffracting planes are listed

12 for individual samples in Table I. Ilford L-4 nuclear plates (50 ym

emulsion thickness) were used for all topographs.* The rocking curves

were obtained from these sample crystals with the SCAD for the 220

diffracted beam in the surface reflection geometry and mostly for the

111 beam in the transmission geometry, using silicon (220) in the surface reflection mode for the first crystal. These results are also

listed in Table I. The rocking curve width in transmission becomes

narrower for the same degree of perfection, when the crystal disc

becomes thicker. The values of yL for each sample are therefore

included in Table I.

* In the topographs black represents fewer photons except Figure 9

which is reversed.

- 8 -
Experimental Results

Figure 1 shows an example of crystal boules which demonstrate a

successful bottleneck of less than 1 mm and diameter control at will by

changing temperature in the melt. The lower part of the crystal boule

represents the shape when the diameter was controlled to be constant

during growth. Figure 2 shows a typical shape of crystal boules with a

spiral growth form. This shape is to be contrasted with the usual

cylindrical growth form shown in Fig. 1. The spiral growth form has

been reproduced repeatedly whenever the difference between the seed and

the crucible rotation speed. A, becomes less than 0.3 rpm with a pulling

speed of 1 mm*min-1

. It has also been observed that A has a lower

bound, perhaps MD.l rpm for this growth form. When the pulling speed

was reduced to 0.4 mm*min-1

, crystals grew in a regular cylindrical form

even with a small value of A . In Table I, crystal boules grown with a

spiral form are indicated by letter C. As shown later, the growth shape

does not seem to affect resultant crystal perfection as much as the

growth direction does.

The growth directions of the crystal boules grown with a polycrystalline seed were found to be very close to the [111] direction.

It has also been confirmed that boules grown from oriented crystal

seeds have the same crystallographic orientation as the seeds.

Figure 3 shows drastic changes in the gross aspects of crystal

perfection as the crystal growth conditions vary. Figure 3a shows that

the crystal was polycrystalline when a [110] oriented seed was used.

Figure 3b indicates that the crystal consists of several grains whose
misorientations are within 100 seconds of arc; this crystal was grown

from a [100] oriented seed. Figure 3c represents a typical surface

topograph from crystals grown from a polycrystalline seed or a [111]

oriented seed under poor diameter control; small angle grain boundaries

are visible. Figure 3d is an example of surface reflection topographs

obtained from crystals grown under satisfactory diameter control from

either a polycrystalline or a [111] oriented seed. For all of these

crystals the growth conditions characterized by the rotational speeds

and the pulling speed are almost identical. These crystals have a

successful bottleneck. As also seen in Table I, boules grown in either

[100] or [110] direction are not as perfect as those grown from a polycrystalline or [111] seed.

When the gross aspects of crystal perfection shown in surface

topographs surpass the level represented by Fig. 3b, crystals can display anomalous transmission. Figure 4 shows ACT transmission topographs

of the O-diffracted and the H-diffracted beams from crystal #194231

grown from a [100] seed without a bottleneck and without diameter control. They show a multigrain structure. When crystals were grown

under more favorable conditions from a polycrystalline or a [111] seed

with a successful bottleneck and good diameter control, their transmission topographs displayed a prominent anomalous transmission effect

with detailed dislocation arrangements. As shown in Fig. 5, an

arrangement of Lomer-Cottrell sessile dislocations has been confirmed

in several crystals grown under a condition similar to that for sample

#280232. This arrangement has been observed in copper single crystals

4 5 —

under certain growth conditions *

. Figure 6 shows ACT 111

- 10-
transmission topographs obtained from sample #363232, in which very

small angle grain boundaries, generally curved, are visible along with

isolated dislocations. Figure 7 shows ACT 111 transmission topographs

from sample #310232, in which no small angle boundaries exist and

isolated dislocation images are clearly visible. In both of these

figures, the regular straight-line images correspond to ferromagnetic

domain walls, as will be discussed in the next section.

1-3

As shown previously , spectroscopic data—namely, rocking curve

widths—alone supply adequate information regarding the degree of

crystal perfection in sample crystals. The value of each rocking curve

width was measured as the full width at half maximum (FWHM) of each

rocking curve or spectral profile. The crystals are considered to be

more perfect, the smaller the observed width for the same yL-value.

These results are listed in Table I. When crystal boules were grown

without a bottleneck and without diameter control, they were so imperfect that spectroscopic data could not be obtained. It has also been

found that sample crystals from the boules grown in [100] and [110]

directions display such a broad diffraction profile that they are much

less perfect than those grown from a polycrystalline or [111] seed. A

possible effect of the growth direction will be discussed later, in

particular concerning the [110] growth direction. By contrast, the

failure of diameter control does not affect the resultant perfection

as much as the other factors. However, the spectroscopic data suggest

that the rocking curve widths are usually smaller, indicating more

perfect crystals, if the diameter is controlled during the entire

period of growth.

- 11 -
Conclusion and Discussion

a) Crystal Imperfections—dislocations and micro-subgrain boundaries

Although the ultimate goal of this type of work is to find the best

growth condition for the production of crystals free of dislocations, it

is important to characterize the nature of dislocations and imperfections

in crystals grown under different conditions, particularly when the

crystals become nearly perfect. Figure 5 implies, as in the growth

4 5

process for copper, * that new dislocations are often created continuously during the growth, but they become immobile under particular

growth conditions. This mechanism results in a more perfect crystal

as a whole than under some other growth conditions.

It is known that the formation of grain boundaries is closely

related to dislocations in the crystal. Figure 8 shows very-smallangle subgrain boundaries revealed in a surface reflection topograph.

In contrast with ordinary subgrain boundaries, these should be called

microsubgrain boundaries in which two adjacent domains are mutually

tilted less than 500 seconds; of arc. This crystal was grown in an

unfavorable growth direction, [100]. By our standards, this crystal is

quite imperfect, although each subgrain displays anomalous transmission,

as shown in Fig. 4, indicating that this crystal is far more perfect

than ordinary crystals. This topograph indicates an important feature

in the relation between crystal perfection and growth conditions. In

this surface topograph, the boundaries are shown as a black or white

trace as a consequence of overlapping or separation of beams diffracted

from different subgrains. These traces give a value of approximately

270 seconds of arc for mutual tilt of subgrains. The rotation axis of

- 12 -
the subgrain is found to be the growth axis. It should be noted also,

in contrast with predictions of ordinary continuum crystal growth

theories, that these boundaries are not straight lines, although many

ate close to (111) directions. This phenomenon may account for the

reason why the growth directions other than [111] would not produce

perfect crystals. A further study on this aspect will be published

13 shortly elsewhere

When crystals are grown under favorable growth conditions, they

become highly perfect. Figure 9a and b demonstrate dislocation densities of about 400 lines/cm2 or less. It has so far been confirmed that,

whenever crystals were grown under the favorable conditions, dislocation

densities seldom exceed 2000 lines/cm2

. These results are quite remarkable, if one takes into account the fact that nickel is a metal and

these densities have been obtained in the as-grown state.

b) Ferromagnetic Domains and Their Walls

14 15

In the past, two attempts ’ were made to observe magnetic

domains in nickel crystals with x-ray diffraction topography, while

many extensive topographic studies'1' were carried out with Fe-Si and

iron crystals. The primary difficulty of x-ray topographic observation

of magnetic domains and domain walls in nickel crystals lies in the

required degree of crystal perfection. As demonstrated in the previous

section, it is now possible to achieve a sufficiently high level of

crystal perfection in large nickel crystals grown by the Czochralski

technique. There exist, in fact, extremely straight-line images along

with rather random arrangements of crystal imperfection images in the

transmission topographs as shown in Figs. 6 and 7. These straight-line

- 13-
images usually form regular rectangular arrangements, and they disappear

upon application of a magnetic field in one of easy magnetization directions (111) as shown previously^ ’ ^ . It may be helpful for the identification of images to correlate crystallographic directions with the

easy magnetization directions. The magnetization vectors in the sample

crystals probably are the directions of easy magnetization ([111] and

[111]) in the (110) plane which is parallel to the surfaces of all our

crystal discs. In such crystals, 71° and 109° domain walls intersect

the crystal surfaces in lines parallel to [001] and [110], respectively,

while 180° walls intersect the crystal in lines parallel to [111] and

[111] . An interesting topograph of oblique magnetic domain walls in

the interior of the crystal is shown in Fig. 10. The success of direct

observation of magnetic domain walls by x-ray topography is quite significant, since it will enable one to study the dynamic behavior of

ferromagnetic domain walls under a varying magnetic field and to understand the mechanism of micro-eddy currents, and in turn, electric

energy losses in industrial applications of soft magnetic materials.

However, the x-ray topography study of magnetic domain walls in nickel

crystals is beyond the scope of this report. Although detailed work on

26 29 this aspect has been published elsewhere, we will demonstrate a

basic mechanism of magnetization in B-H curves by x-ray topography

through Fig. 11a, b, c and d: (a) the initial domain structure; (b)

domain wall motion in a small field; (c) a change in domain arrangements and dominance of domains with particular magnetization directions

in an intermediate field; and (d) a single domain and saturation of

magnetization in a large field.

- 14 -
c) Concluding Remarks

Although the documentation of resultant crystal perfection with

varying growth conditions has not been completed at this state, it can

be concluded from the present results that in order to obtain highly

perfect nickel crystals, I) bottlenecking at the initial stage of crystal

growth ig necessary, II) satisfactory diameter control is desirable

during the entire period of growth, III) a polycrystalline or [111]

oriented seed is preferable, in contrast with the previous results of

2

copper single crystal growth, and IV) there is a general trend towards

a reproducible relationship between crystal perfection and growth conditions characterized by the practical process parameters describing the

rotations of a seed and the melt. It is also worth mentioning that,

when crystals are grown from a polycrystalline seed, the resultant

growth direction usually turns out to be very close to [111] . This may

explain why the results obtained from a polycrystalline seed are similar

to those from a [111] seed. It has also been observed that the resultant crystal perfection is usually high, when boules are grown at a

slower rate, say, .4 mm/min. This condition, however, creates some

technical difficulty in routinely obtaining a bottleneck and controlling

the diameter with our crystal growing apparatus.

As we have demonstrated, a proper choice of sets of process parameters is indeed require to improve crystal perfection to a certain

level, as is the case for the copper crystal growth. The critical

factor is, however, several crystallographic effects. For example,

crystals with a spiral growth form can easily reach a certain level

of perfection if the growth condition and the growth direction are

- 15 “
selected properly. The formations of Lomer-Cottrell dislocation locks

and of curved small-angle grain boundaries all indicate that the ultimate

level of crystal perfection is governed by some factors which diminish

the generation of dislocations and make dislocations immobile. Anisotropic properties of crystals definitely make one direction more preferable than others. Even though the difference may be very small, it is

significant for dislocations. An approach to the crystal growth mechanism through isotropic theories certainly is not adequate. It is

indispensable to obtain knowledge on the behavior of dislocations in

highly perfect crystals in order to accomplish the production of crystals

free of dislocations.

It is also important to be aware of the fact that an initial

crucial factor influencing the ultimate level of crystal perfection is

found in the bottlenecking effect, or rather the original perfection in

seed crystals. Purity of the melt should not be ignored; although we

have not studied the effect of purity in this work, previous experiences

with our metals have indicated that the purer the melt, the better the

resultant perfection.

In this work, we have found- that nickel single crystals like copper

can be produced with the perfection far better (^400 dislocation

lines/cm2

) than the existing level by controlling the practical process

parameters and growth directions. Although they are not dislocationfree, the level of perfection is quite remarkable as a metal, and

almost reaches the level which most semiconducting materials have so

far enjoyed. These nickel crystals certainly serve as a precusor of

commercial magnetic materials for the study of basic magnetic domain

- 16 -
properties under more idealized conditions.

Finally some comments will be made on crystal growth experiments

in space, from our knowledge of ground based experiments on copper and

nickel. Crystal growth experiments have no significant meaning, unless

a careful choice of growth conditions are made and perfect seed crystals

are used. Since most crystals can be made nearly perfect on earth if a

careful and systematic study is made on the growth conditions, the lack

of sensitive techniques for the characterization of crystal perfection

often causes an incapability of distinguishing subtle changes in

crystals grown in space from those grown on earth. It is imperative

to use a sensitive technique, such as asymmetric (double) crystal

topography (ACT) and scanning double crystal diffractometer (SCAD),

for reliable characterization of crystal imperfections in crystals grown

in space and/or on earth.

-17 -
References

1. M. Kuriyama, J. G. Early and H. E. Burdette, "Characterization of

Thermal Convection and Crystal Perfection in Metals Grown from the

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(1974) .

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-18 -
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- 19 -
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12. The trade name is included for completeness and does not represent

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- 20-
in Czochralski-Grown Nickel Single Crystals," J. Mater. Sci.,

in print (1977)

28. M. Kuriyama, W. J. Boettinger and H. E. Burdette, "Crystal Perfections and Magnetic Domain Walls in Thick Czochralski-Grown Nickel

Single Crystals" in Advances in X-Ray Analysis , Vol. 20 (1977).

29. W. J. Boettinger, H. E. Burdette, E. N. Farabaugh and M. Kuriyama,

"Some Topographic Observations of the Effects of Dynamical

Diffraction in Imperfect Metal Crystals," in Advances in X-Ray

Analysis , Vol. 20 (1977).

- 21 -
Crystal

Rotation

Speed

(RPM)

Pulling

ACT

Rocking

Curve

Width

(FWt»l)

- 22 -

Poor

diameter

control

C

=

Spiral

growth

*

=

[111]

seed

grown

from

original

pol;
Fig. 1 Photograph of a Ni single crystal grown

by the Czochralski technique with

bottleneck diameter roughly 1 mm.

23

MPSE

Fig. 2 Czochralski-grown Ni single crystal

boule #274200 with spiral growth

form. This shape is to be con- trasted with the usual cylindrical

growth form obtained by the

Czochralski technique. Note also

the small bottleneck which has been

obtained near the seed material.

- 24 -

c d

Fig. 3 ACT (220) surface reflection topographs of nickel crystals of

increasing perfection; a) grown with a [110] seed; b) grown

with a [100] seed, indicating misorientation of about 100

seconds of arc; c) grown with a [111] seed under poor diameter

control, indicating misorientation of about 20 seconds of arc;

d) grown with a [111] seed and good diameter control,

indicating absence of subgrain structure.

- 25 -
I

'
O 22

01 o O 1—

O P 22 1—

bO

a)

*S

p cd cd

0)

a

cd 42

p P 5-i P 2 O p *H o

42

cn •H P

42 T3 r| -H

CX 1 § & c

22

O

5-i 5-i 22

bO 05 bO (2 O 42 cd CX P i—1 o cd 4*5 p ^ N p a

42 05 05

a c o 22 5-i 0) •H (2 a 1—

03 cdp

03 i—i •H 6 0) o • B cd 4*5 42 P

03 0) CJ

O

(2 42 *H cd 5-i cd (2 P

5-i 22

p 2 P 05 cd 2 o P o a a B 42 O cd o p 5-i o 5-i i-i •H 0) CM p P Ds p '

p 05 H B 22 B H 22 cd 05 2 U 1 05 2 •H <5 O 42 03 22

bO

•H

P'h - 26-

- 27 -

#280232

showing

an

arrangement

of

Lomer-Cottrell

sessil

dislocations.

(a)

0-diffracted

beam;

(b)

H-diffracted

beam.

Pd

CDaP H ^ D T) p 14-1 p p

4-1 4-4

p P cd -h

p

do Pd Cd Cd -H p I a) P P o td -H o B p -H O p ^ id w p o po pd cd ^ P u a

Cd

p

O -H -P •»> O rH 4-) ft e p m a) p p -HP p 0) P Pd bd

bO 42 -H

p

O P P E ftp p (1) O dJ M 44 P

44 44 P O U <U I—

p P 1-4 O CO O P bO Cd P

•H 4-4 P -H

O

Cd 4-(

p -H

Cd "H -P 4-4 •H Pd t—I 4-4 P B I 1—I "H 6

COO

p J3p

p e o p c-s Cd bO M-4 P P P

4-1 ^ fo

O P p I—I p

CD

p rH

H • > 3

rH CM 0) bd >H CO tH P w CM • rid P

co

B

H 4-4

H md P CO

O

u co 0) •H 0) <H =s= P4 > P

Md

bO

•rH

pL) - 28 -

walls

X)

ai

4-1 u

rH l

n3 lm

4-t ip

CO -H to XI L I U ffi

4-4 c-' ° &

CO -C ••> CL B

03 cfl L CU bC X O

CL

X

O <13 P 4-1 u C Cfl O L

•H 4-1

CO <4-4 CO -H

•H

X

B l CO o c0) ^Li 0)

rH CM i—! co w Csi O H .—

U CO

r->.

bO

•H

U-< - 29- *

beam.

Isolated

dislocation

images

are

distinctly

visible

along

with

rectangular

formations

of

magnetic

domain

walls.

Fig. 8 ACT (220) surface reflection topograph of

nickel crystal showing subgrain boundaries

some of which are parallel to <111> directions.

The misor ientation of these subgrains is about

300 sec.

- 30-

02o 1—

0) cd -0 CJ 02 4-1 4-1 •H o O ^ 4-1 *H cd E 0 a CO e 0

CD bO P •H • i—

0 0 4J CO <r E

a) •H CO •

5-i CO CD o 0 0 0 1 1 0

14-1 0 i—

0

<4-4 03 0 cd •H O 4-J

X T3 0 CO 0 o '

<4-4 •h e u O 4-1 O a 0 0 'H 0 a 0 cd -0 O 0 0 a iH 0 0

cd CO *H bO

*H i—

0

bO 03 r\ E O 0 02 •H a 5 o a o O -H •H 0

4-1 r-H 4-1 ,0 0 0 4-1 •H 0 bO V i—H o 0 O 6

•H •H i—

E i—

0 5 0 0 • 0 O -H ro 4-1 CO H r0 03 0> 0 1—

6 0 • O rH 0 O o N cd 0 0 o •H 0 i—1 0T 1—

0

!-i 0 0 O 0

4-1 4-1 4-1 4-1 -0

H 0 0 0 0 H >, o >•» 0 E O 0 02 0 02 o < CJ 0 a H 03

bO

•H - 31 -

- 32 -

Fig.

10

ACT

(111)

transmission

topographs

of

crystal

#180231,

showing

oblique

magnetic

domain

walls,

(a)

0-diffracted

beam;

(b)

H-diffracted

beam.

Fig. 11 ACT (111) transmission topographs of crystal

// 363232 showing changes in the domain structure

as an external magnetic field is applied. (a)

the initial domain structure; (b) domain wall

motion in a small field; (c) a change in domain

arrangement and dominance of domains with

particular magnetization directions in an intermediate field; and (d) a single domain and

saturation of magnetization in a large field.

i

- 33-

Task 2

Evaporative Preparation of Ultrahigh Purity Materials

Part A: Mass Spectrometr ic Studies of Vaporization Processes

E. R. Plante

Inorganic Materials Division

Institute for Materials Research

Summary

Part A of task 2 has involved studies by mass spectrometry and

optical pyrometry of the apparent vapor pressure and temperature of

radiatively heated aluminium oxide supported as a sessile drop.

Previous studies have shown that an apparent increase in the vapor

pressure of a factor of 3 on melting is due to an actual increase in

the temperature of the molten Al^O^ to a temperature well above the

melting point. Although this effect had been observed prior to this

work, it had erroneously been attributed in the literature as being

due to a discontinuous increase in the vaporization coefficient at

the melting point.

9 Experiments were undertaken during this contract period in an

attempt to better control the temperature of the supported drop in

the vicinity of the melting point by using more nearly isothermal

furnaces. However , it did not prove possible to achieve stable sessile

drops of alumina under more isothermal conditions and it was concluded

that it would probably be more profitable to study the purification

and/or evaporation behavior of materials by more conventional techniques

such as the Knudsen effusion method. Future vaporization studies

associated with thermochemical studies of corrosive reactions in oxide

- 34 -
.
materials will be made using this method under a continuing NASA

contract. Problems related to temperature measurement of levitated

melts in tube furnaces for space experiments are briefly mentioned.

- 35-
Part A; Mass Spectrometric Studies of Vaporization Processes

Introduction

The objective of part A of task 2 has been to study the vaporization characteristics of non-conducting liquids under conditions

resembling those which might be encountered in high temperature

space processing. Although the major interest was initially on

purification processes, it became evident during the program that

problems involving temperature control and measurement of radiatively

heated non-conductors supported as sessile drops were of greater

importance to earth bound experiments and might be of considerable

importance to space processing experiments. These problems in temperature

control and measurement can become important in cases where a material

is heated in a non-uniform radiation field, the energy transfer is

largely by radiation, and where discontinuous changes in emissive

properties occur at a melting point. The principal effort during

the past year has involved attempts to better control these effects

in order to observe vaporization behavior of liquid A^O^ under

container free conditions.

Experimental Procedures

The experimental procedures and previous results have been reported

in detail (1,2). Briefly, commercially available A^O^ rods were

mounted in the sampling position of a modulated beam, mass spectrometric

system and observed by optical pyrometry and mass spectrometry when

the tip of the alumina rod was heated and became molten. Heating was

accomplished by radiation transfer between a resistively heated tungsten

furnace and the alumina rod. Since the mass spectrometer is highly

- 36-
evacuated with background pressure of the order of 1 x 10 ^ torr,

free vacuum evaporation conditions are achieved. Under these

conditions it was observed that when the 0^ sample melted an

increase in the apparent vapor pressure of approximately a factor

of 3 and a decrease in apparent temperature of several hundred

degrees took place. Although this phenomena had been observed and

described in the literature previously (3) , it had been attributed

to a discontinuous increase in the vaporization coefficient of

alumina at the melting point.

A second type of experiment in which A^O^ was melted in a shallow

container so that free evaporation conditions would be maintained but

a significant fraction of the energy transfer was by conduction, did

not show an increase in the pressure on melting although a decrease

in apparent temperature was observed. Since the vapor pressure is a

fundamental property of a material it was concluded that in the sessile

drop experiments an actual increase in the temperature or T-jump had

taken place when the sample melted. It was possible to account for

the general behavior observed in the sessile drop experiment by the

changes in the total and spectral emissivities of solid and molten

alumina and the conductivity loss of the alumina sample due to its

support, by balancing the radiation gains and losses at the melting

point when the alumina was solid and when it was molten. The apparent

decrease in temperature on melting can be accounted for by the decrease

in reflectivity of molten alumina as compared to solid alumina and the

non-ideal nature of the heater and sample arrangement which results

in the heater being much hotter than the sample.

- 37-
Experimental Results

Experimental work during the past year has been carried out with

two objectives in mind. First, the sessile drop arrangement was

considered desirable because it simulates a condition which can be

achieved in space research; namely, that there is no physical contact

between a heated sample and a container. It is recognized however that

interaction of the sample and its environment via gas-solid reactions

is possible. Secondly, it was considered worthwhile to attempt such

experiments under conditions in which more uniform heating was achieved.

In principle, the use of a more ideal furnace- sample arrangement

would; (a) decrease the magnitude of the temperature measurement error

caused by reflection or radiation from the sample surface, (b) decrease

the magnitude of the T-jump caused by an increase in the total emissivity

of the sample on melting and, (c) would lead to more accurate temperature

measurement both above and below the melting point. Balanced against

these objectives however is the requirement that the production of a

stable sessile drop requires the presence of a temperature gradient

at the droplet-solid interface. Thus, only an approach to ideal

isothermal conditions can be achieved. In addition, the sessile drop

owes its stability to the surface tension of the liquid and since the

surface tension usually decreases with increasing temperature, the

temperature range of a stable sessile drop will be limited.

Attempts at achieving these objectives were for the most part

negative. It appears that sessile drops of relatively pure

are quite fluid and difficult to support in vacuum. Relatively large

sessile drops of tantalum oxide-contaminated Al^O^ could be supported

- 38 -
but these were not considered worthy of further experimentation.

Other measurements were made using relatively open tungsten

heaters in which an attempt to reduce the magnitude of the T-jump

was made by using longer heaters which have the effect of reducing

thermal conductivity losses. The results of these experiments however

did not differ appreciably from those in which short conical heaters

were used to heat the sample. With the sample somewhat below the

melting point, an apparent temperature of 2030° C (uncorrected for

window, prism, and modulation disk) was observed while on melting

the apparent temperature would typically decrease to 1920°C. In

the molten state an image of the heater was apparent on the sample

surface and appeared as alternating light and dark regions on the

sample surface. This indicated that a molten alumina surface has

a high degree of specular reflection.

Conclusion and Discussion

The results of this part of task 2 suggests that the use of sessile

drop as a means of support for molten liquids places severe restrictions

on the type and validity of the data that can be obtained. The observations of T-jump, and pressure discontinuity are real observable

effects but they result from very strong interactions between the

experimental apparatus arid the sample. Thus, they are not properties

of the sample alone. The results of these experiments indicate that

it would be more profitable to study the purification and/or evaporation behavior of materials by more conventional techniques such as

the Knudsen effusion method and try to determine if important interaction

problems are encountered between the sample and its container. Studies

of this method are planned for a continuing NASA project.

- 39-
Some of the results of this work lead to questions concerning

whether or not similar temperature measurement problems or temperature

•discontinuity effects encountered in space experiments involving

levitated melts of materials heated in tube furnaces in cases where

energy transfer is mainly by radiation. The extent to which this

type of effect can occur depends among other things on the relative

sizes of the sample and furnace cavity as well as on the temperature

distribution of the furnace and the emissive properties of the sample.

This problem may become apparent if the temperature homogeneity of the

furnace is compromised in order to provide positioning devices and

observation ports. Because of the complexity of this problem it

will probably have to be dealt with on an ad hoc basis.

References

[1] Passaglia, E. , and Parker, R. L. , NBS Space Processing Research,

NBSIR 76-980, 25-39.

[2] Paule, R. C., Mass Spectrometric Studies of A1„0„ Vaporization

Processes, High Temp. Sci. , _8, 257 (1976).

[3] Burns, R. P., Jason, A. J. , and Xnghram, M. G., Discontinuity in

the Rate of Evaporation of Aluminum Oxide, J. Chem. Phys., 40 , 2739 (1964).

- 40-
Task 2

Evaporative Preparation of Ultra-High Purity Materials

Part B. Evaporative Purification of Refractory Metals

Using R.F. Levitation

W. J. Boettinger and F. S. Biancaniello

Metallurgy Division

Institute for Materials Research

Summary

To obtain quantitative data on the rate of purification of refractory alloy melts under well-characterized conditions, samples of Mo and

Nb have been R.F. levitation melted, held liquid for times up to 30 min.

and frozen in vacuum without a container. By initial and final chemical

analysis of selected impurities, rates of purification of the samples

are obtained and compared to calculations of such evaporations.

Advantages of R.F. levitation for this purpose are rapid heating to

and cooling from test temperature, excellent stirring in the liquid to

prevent transport limitation in the liquid, and an isothermal and simply

shaped evaporation surface.

In this work rates of purification are determined for Nb-2 w/o Mo

and Nb-5 w/o Mo at 2900K and for Mo-1 w/o Zr and Mo-5 w/o Zr at 3000K.

These rates of purification agree quite well with predictions of calculations based on Knudsen evaporation of a well-stirred isothermal

ideal binary solution of the two components.

Introduction

The continuing search for new materials with new or improved

properties requires simultaneous advances in techniques of material

- 41 -
preparation and processing. One such possible advance is the ability

present in microgravity to process substantial quantities of high temperature materials without a container in vacuum. Regardless of the particular material involved in such a process, the evaporation of volatile

constituents will have an important role.

This work has been performed to determine the ability of calculations to correctly predict the rate of purification of materials by the

evaporation of volatile impurities. In a previous report,'*' methods for

the calculation of the purification rate of materials where complex

interactions between vapor species are present have been formulated.

These calculations are necessary to handle, for example, the purification of CaO from AI2 O 3

. In order to provide an overall check of the

calculation under more simple conditions, however, the measurement of

purification rate of several simple binary liquid alloys has been

undertaken here. These measurements are made under the well-defined

experimental conditions available through the use of the technique of

R.F. levitation melting in vacuum. This report will conclude the work

on this subject and hence a brief summary of prior accomplishments will

be made.

Previously, the development of a R.F. levitation system was

2 3 described 5 which accomplished the melting, holding at test temperature

and solidification of small (3-4g) metal samples in vacuum without a

container in the temperature range of 2600-3100K. The routine accomplishment of solidification during levitation without the introduction

of a quenching gas is unique to this task. Also the ultra-purification

- 42-
3

of Fe from Mo has been accomplished . Samples initially containing

50 ppm Fe were purified to less than 50 ppb in approximately six seconds.

A

- major conclusion drawn here was that the transport of impurities to

the evaporation surface was very rapid and that the assumption of a

completely-stirred sample was accurate for R.F. levitated samples.

The work reported herein, consists of measurements of the purification rate of Mo and Nb with the intentionally added impurities of Zr

and Mo respectively at levels of 1 to 5 w/o. These impurities give

purification rates sufficiently slow to permit meaningful analysis of

data. The rather high levels of impurity were employed to permit

greater accuracy in the chemical analysis of samples. These results

are compared to calculated rates of purification which were developed

3 previously . For Nb-Mo alloys the calculation agrees with the experimentally determined values within the experimental error. For the

Mo-Zr alloys the agreement is good, but a slight discrepancy is attributed to possible deviation from ideal solution behavior.

Experimental Procedures

The R.F. levitation apparatus has been described in detail pre2 3 viously, * but a brief description will be given here. Samples (3-4g)

are placed in a R.F. coil consisting of two identical opposing conical

sections of three turns each with a base diameter of approximately

2 cm. After evacuation of the vacuum chamber to less than 7x10” 5 pa ,

the coil is energized causing the sample to be levitated and to be

quickly melted. The sample is then brought to the desired test temperature. After a predetermined time, the sample is frozen and cooled to

- 43-
about 200K below the solidus temperature while still levitated in

vacuum. The sample is then dropped into a copper dish. Temperatures

are measured using an automatic optical pyrometer which sights through

a moving window to prevent errors due to vapor condensation. Absorbtion

by the window and emissivity of the sample are accounted for by measuring the apparent melting temperature of pure Mo or Nb. Temperature

measurements are considered to be accurate to about 15K.

After cooling to room temperature , samples are removed from the

vacuum and cut and etched for chemical analysis. Half of the sample is

analyzed to minimize the effects of solute segregation which may occur

upon solidification. Samples were analyzed by the Analytical Chemistry

Division of NBS by Atomic Absorption Spectrometry or by Flame Emission

Spectrometry. (See Appendix.) For Nb-Mo and for Mo-Zr, values are

considered to be accurate to about 2% and 4% respectively of the values

stated.

Preparation of samples for levitation required considerable care.

Because fairly high impurity levels (1-5 w/o) were required to simplify

chemical analysis, impurities must be artificially introduced into metal

samples. Alloys have been prepared by powder metallurgy and by inert

gas arc-melting. In the former, samples were pressed from elemental

powders and sintered at 1700K in vacuum. Although this procedure

produces samples which can be levitation melted, the oxygen content of

these samples is quite high (0.5 w/o). Such high oxygen contents will

effect the evaporation rate of Zr and complicate the results of purification experiments. This necessitated the use of the alternative method

of sample preparation. Four alloy ingots of approximately 60g with

- 44 -
nominal composition Mo-1 w/o Zr, Mo-5 w/o Zr, Nb-2 w/o Mo and Nb-5 w/o

Mo were prepared by arc-melting on a cold copper hearth under gettered

argon. This produced Mo-Zr alloys with less than 100 ppm 0. Ingots

were remelted several times to maximize homogeneity. These ingots were

cut into approximately 4g samples for levitation. Several smaller

samples from different parts of each ingot were retained for chemical

analysis to represent the initial composition of the samples taken from

each ingot. The values obtained from these samples are given in Table I

along with the mean values. In addition to the alloy samples, pure Nb

and Mo samples were also levitated and held molten for various lengths

of time to determine the vapor pressure of the pure base metals. These

experiments were performed in an identical manner with the experiments

for the metal with alloying addition. The Mo and Mo-based samples were

purified at 3Q00K and the Nb and Nb-based samples were purified at

29Q0K. This represents about equal superheat for each. Although R.F.

levitation permits extremely rapid heating to and cooling from test

temperature, the sample is above 0 . 9T for about 1 minute longer than

m

it is at test temperature. The effective time of evaporation is then

slightly longer than the time at test temperature. However, the effect

of this is small compared with the scatter in the results.

Experimental Results

The results of experiments on pure Nb, Nb-2. 04 w/o Mo and Nb~5 . 02

w/o Mo are summarized in the first six columns of Table II. The last

three columns will be described later. The experimental results are

also shown in Figs. 1 and 2 where the composition as a function of time

- 45 -
TABLE

I

-

Initial

Composition

- 46-
TABLE

II

-

Summary

of

Experiments

on

Nb

and

Nb-Mo

Alloys

at

2900

K

inO /-n rH a X U

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•rH cd c

HH h cn cn c^n cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn

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Ps p p p P p p p p p p p p P P P p P p p p p» p^ p^ p' p'

rH

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i 00 -18-l Cn

1 m

H

00 CN

1

-12- -11- -d1 m

1

-16- -17- -13- <r

rH p.rH

ccHCNH o

H H

rH HCM -26-

-IT in

1 NO »HrH -TI

1 NO1 NO 12 11- 11 rH

rH ii- ii -II -IT TI ii -TI -IT m m m m m m m m m

ot.i n / 7 — ma nu n l..c CKT

- 47 -

0410

1437

0.133

3.56
at test temperature is plotted respectively for the 2.04 w/o Mo and the

5.02 w/o Mo series.

The results of experiments on pure Mo, Mo-0.99 w/o Zr and Mo-5.24

w/o Zr are summarized in Table III. The composition versus time is

plotted in Figs. 3 and 4 respectively for the 0*99 w/o Mo and 5.24 w/o

Zr series.

Conclusions and Discussion

This section will first review the calculation of purification rate

3 ) presented previously and using available thermochemical data, show the

relation between the experimental data and the calculated results. The

small discrepancy between the two will then be examined in detail and

information on the thermochemical data; specifically, the possible

deviation from ideality of dilute liquid Mo-Zr and Nb-Mo alloys will be

described

.

a) Purification Rate

In a previous report,'*' calculations for the purification of materials where complex interactions between species are present has been

performed. This computer program can be used (in a trivial fashion)

to predict the rate of evaporation into vacuum of a well-stirred

isothermal ideal binary solution of two metals. However, in this

simple case the rate can be obtained analytically.

Let n^(t) and ng(t) be the number of moles of A and B present in

the liquid at time t. Assuming Knudsen evaluation conditions apply,

the relevant equations describing the purification process are:

- 48 -
TABLE

IIISummary

of

Experiments

on

Mo

and

Mo-Zr

Alloys

at

3000 K

CM (Tv <3" 00 oo rH 00 CN CN CO rH o a 00 CO 00 rH CTv CN O CO CN rH X

•U£CM o vo

O (Tv CN rH vO 00 < CN CM rH CM rH CM CN rH r—

r—

rH

IT)< Cti

O0 <r CN oo rH CN o oo CO <3- o uo <r

00 00 rH <r U0 CN ON vO uo uo

un CN Mj* CO CTv uo oo o rH

OO

oo (Tv oo ON 00 CTv oo (Tv CTv (Tv ON ON On ON

uo vO U0 CO vO CO

O rH CO vO

O on <r o 00 rH CN CO CO rH

<3- CO uo <r UO uo <* UO o O o o o o o O O o o

<UU£

4-J

CTJ U /-n

(1> CO a. ^6

•H <U H H

on o o O rH CN oo oo cn on on o cm

cm ^ r-^ o <f co o O O rH o i-\ <t <t <t

un o

rH CM

r^. r>.

uM £o a

•H o £

*H

O

PnU

4-J rH 00 ON vO rH U0 ON CO U0 oo

*H 4-J 00 vO vO uo rH 00 00 vO VO CO U0

co CJ

O o o O CO CO CO CO CO CO o CO O o o o o o o o o o o

Cl.

p

a fa

O o o o o o o o o o o

/*“s

3-4 N

ao c

•H o U v-l rH H 4J ON ON ON ON <r

03 CO <J ON ON ON ON CN CN CN CM CN CN CN

*H

O 03 o o O o UN UN UN UN UN UN UN

4J D. ^ o O o o O o o O

O o o a fa c O o o o o O O o o o o o M QJ CO

CO£2'w' o vO rH oo no ON rH CN ON ON rH rH

rH co r-' vD

O 00 oo CM rH <3" o CM CM NT

O

o3 03 —•>

O 00 vO CO CO <3* uo »H UN i—

O CN

C 03 00 ON vO 00 <3- CN 00 CN CO CM r- r- r-

*H 2 ^ • • fa C-J CN CN CO CO CM CM CO CO co CM CN CN CM

rH O0 <3- CO LO CO 00 CN UN <r UN CO vO CN UN

03 CO 00 CN CO UN CM rH CN ON o <3" co •H CO ^ vO UN UN CN UN CO rH <3" CO UN CO CN <3*

4-J co oc CM CN CM ON CM CN CN CN CM CM CN CM CM 04 H 03 v~' • • • a 2 <3- <3- CO <r <3- <r <3“ MT <1 H"

(H

vO vO vO vO VO vO vO vO vO vO vO vO vO vO

r- r- r^. ON oo 1 CN vO CO 00 o oo rH CN CM ON

rH rH CM Ol rH CN rH *H CO CO CO CM CN CM CM CO CO CO CO CO co CO ok — J ZO/nI-°W— JZ %vH°W
dn

A

“A dt ( 1 )

^B n. + il, ^B dt

A B

”b , dnB

( 2 )

where k.

1

(27TRTm

i

)'i and

A

P. = vapor pressure of pure i at temperature T

nu = molecular weight of component i

A = area of sample available for evaporation

R = universal gas constant

T = absolute temperature.

The solution* when A is a constant is given by

(4)

( 3 )

where and are the initial number of moles of A and B respectively

and a = (PA

/p

fi ) *•

*Equation (3) is valid even if A is not constant and even if there are other components in the solution.
It should be noted here that if the solution is non-ideal, this

non-ideality can be treated for dilute solutions of component B and A by

replacing p^ by the Henry's Law constant for B in A. It is well

known that for dilute solutions which deviate from ideality, Henry's

4

Law is obeyed for the solute and Raoult's Law is obeyed for the solvent .

In this case, the solution to Eqns. 1 and 2 is still given by Eqns. 3

and 4 with k substituted for p . In the rest of this report, comH , B B

ponent A will be taken to be the solvent and component B, the solute,

for any given alloy.

The parameters needed for the calculations are p., p_(or k T , T

A B ri , B

and A. Having no information on k^ , p and p are obtained from the

n , B A B

JANAF Thermochemical Tables’*. For Mo-Zr at 3000K, p

= 1.002 x 10 ^ atm,

ii

pm = 1.556 x 10 4 atm. For Nb-Mo at 2900K, p. = 3.890 x 10~ 6 atm,

B

r A

p_ = 4.395 x 10 5 atm. The sample has been assumed to be spherical and

of constant area. Treatment of cases where the area changes significantly during purification can be treated using the original calculation

by Paule\ The densities of liquid Mo and liquid Nb are 9.34 and

7.83 g/cm2 respectively^. Using an average initial mass of 4.2136g

and 3.7612g for the Mo and Nb based alloys respectively, areas of

2.845 and 2.966 cm2 are obtained. Using the mean initial compositions

given in Table I, the composition-time profiles are calculated using

Eqns. 3 and 4. These calculated curves are shown in Figs. 1, 2, 3 and

4.

The agreement is considered quite good especially when the degree

of experimental scatter and the variability of thermochemical data are

considered (see, for example, values published in Hultgren et al.^).

- 51 -
The overall prediction of the calculations are also accurate enough for

the design of most refining operations. This is a major conclusion of

this work.

b) Solution Behavior

In order to more closely examine the small difference between the

calculated rates and the experimentally determined rates, the theory will

be used to analyze the experimental data to arrive at experimental values

of p and p (or k., ). In the last three columns of Tables II and III, A B H,B

values of a, p,r and p„ are calculated from the initial and final mass, A B

the initial and final composition, and the time for each experiment.

For the pure metals, p^ is calculated from the expression

. dn

; PA

= "k

A dT (5)

and, of course, p and a are meaningless. The mean and standard

D

deviation of these values are given in Table IV. These means also have

been used as parameters to calculate the curve of "best fit" for the

experimental data shown in Figs. 1 through 4 using Eqns. (3) and (4).

For the Nb and Nb-Mo samples,' the experimental values are the same

as the values obtained from JANAF within the limits of the experimental

scatter. This is, in essence, the reason for the previous claim of

good agreement. However, assuming that the JANAF value for pure Mo

is correct, there is a slight trend towards the experimental value of

Pg(or kjj g) being low. Hence one might conclude that

g ^ Pg f°r Mo

in Nb at 2900K, that k^

^ = 3.4 x 10-5

atm, and that the solution

exhibits slight negative deviation from ideality. This means in

- 52 -
TABLE

IV

-

Summary

of

Means

and

Standard

Deviations

of

P.,

P_

and

a

Obtained

from

Experiments

53
effect that the purification rate of Mo from Nb is slightly slower than

if the solution were ideal.

For the Mo and Mo-Zr alloys there is a small but statistically significant difference between the experimentally determined values of p^

and p and JANAF. Assuming the solution is dilute enough, deviations

D from ideality cannot explain the difference for component A. Hence,

for p one concludes that the value of the vapor pressure of pure Mo is

fi slightly high in JANAF. This may also account for the previous result

for Nb-Mo alloys rather than the slight negative deviation from ideal

solution behavior postulated. For p^(or k^ the experimental value is

higher than JANAF. Again assuming that JANAF value for pure Zr is

correct, there is a positive deviation from ideality; i.e.,

^ at

3000K for Zr in Mo is 2 x 10 -4

atm. This means in effect that the

purification rate of Zr from Mo is slightly faster than if the

solution were ideal.

There is, however, another interesting possibility for the slightly

enhanced rate of purification of Zr from Mo which has previously been

g described . The presence of 0 as ZrO£ in the alloy can have a considerable effect. If ZrC>2 is immiscible in the alloy, the effect is

negligible. However, if as little as 10 ppm 0 present as ZrO£ is

dissolved into the Mo-Zr liquid alloy, interactions of the type

originally treated by Paule under this contract, can easily account

for enhanced rates of apparent Zr loss of the magnitude observed here.

Complications of this sort are better studied using a detailed analysis

of vapor species present during evaporation than with the techniques

used in this work.

- 54 -
It should be noted that changes in purification rate caused by

deviations from ideality are usually only significant in marginal cases

where a^lO-1 or greater. When a^lO

~

3 enormous deviations from ideality

are required to effect the purification process significantly. In j,

marginal cases, however, extreme care must be taken with regard to

details like solution behavior and possible effects of other impurities.

- 55 -
References

1. Paule, R. C., NBSIR 73-402, 33 (1973).

2. Paule, R. C., Boettinger, W. J., Biancaniello , F. S., NBSIR 74-611,

24 (1974).

3. Paule, R. C., Boettinger, W. J., Biancaniello, F. S., NBSIR 76-980,

22 (1976).

4. Darken, L. S., Gurry, R. W. , Physical Chemistry of Metals , McGrawHill Book Co., New York (1953).

i 5. JANAF Thermochemical Tables , Dow Chemical Co., Midland, Mich. (1975).

6. Smithells, C. J. ed., Metals Reference Book , fifth edition,

Butterworth & Co., London (1976).

7. Hultgren, R. , Orr, R. L., Anderson, P. D., Kelley, K. K. , Selected

Values of Thermodynamic Properties of Metals and Alloys , John Wiley

& Sons, New York (1963).

8. Paule, R. C., Boettinger, W. J. , Evaporative Purification Processes ,

"Materials Processing in a Microgravity Environment" Conference

Lehigh University, Bethelehem, Pa., Oct. 15-17, 1975, (unpublished).

- 56 -
Appendix PP

- 57-
form NBf-343

(12-M)

U.S. DEPARTMENT OF COMMERCE

NATIONAL. BUREAU OF STANDARDS

WASHINGTON, D.C. 20234 September 8, 1976

REPORT OF ANALYSIS

To: W. Boettinger

Subject: Determination of Molybdenum in NiobiumMolybdenum Alloys.

Method: Atomic Absorption Spectrometry (AAS)

Procedure: Transfer test portion to Teflon beaker.

Add 10 ml of water and cover the beaker with Teflon

lid. Add 10 ml of HF and then slowly add 5 ml of

HN0 3 . After sample is dissolved, evaporate solution to approximately 5 ml and transfer to 100-ml

plastic volumetric flask. Determine molybdenum by

AAS using a nitrous oxide-acetylene flame. To prevent ionization, add 100 yg of K to standard and

unknowns. Check the recovery by the standard addition method.

___ 9 Analytical Spectrometry Section

Analytical Chemistry Division

cc: P.D.LaFleur

R.W. Burke

f.n

T. C. Rains, Chemist

- 58-
form NBS-348

(12-SS)

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

WASHINGTON. D.C. 20234 January 3, 1977

REPORT OF ANALYSIS

To: W. Boettinger

Subject: Determination of Zirconium in MolybdenumZirconium Alloys

Method: Flame Emission Spectrometry with Repetitive

Optical Scanning (FES)

Procedure: Transfer test portion to a Teflon beaker. Add

15 ml of HC1, 5 ml of HNO^, 2 ml of HF and digest on hot

plate until sample is dissolved. Transfer solution to

100 ml plastic volumetric flask and dilute to calibrated

volume. Since nitrate interferes in the atomic emission

of zirconium, transfer a 10 ml aliquot into a 50 ml beaker

and evaporate solution to dryness. Add 5 ml of HC1 and

repeat the evaporation. Add 5 ml of HC1 and warm to

dissolve the solids. Transfer the solution to a 10 ml

volumetric flask and dilute to calibrated volume with

10 M HC1. Then transfer an aliquot of the sample which

contains 20-40 yg Zr/ml to a volumetric flask. Add 1000

yg K/ml and dilute to calibrated volume. Determine the

zirconium concentration by FES using a nitrous oxideacetylene flame. To prevent ionization, add 1000 yg K/ml

to standard solutions. Also, add molybdenum to standard

solutions to match the matrices. Check the recovery by

the standard addition method.

T. C. Rains, Chemist

Analytical Spectrometry Section

Analytical Chemistry Division
'

-

'

.
0|fl % 1H9I3M

o

a>V)

- 60-

Fig.

1.

Plot

of

composition

versus

time

at

temperature

for

the

Nb-2.04

w/o

Mo

series.

The

solid

line

represents

the

best

fit

of

the

data

while

the

dashed

line

represents

the

calculated

values.

CM

in

)dt

co Jo

0J •H

CD

MCM

CMI CD O

yj * 2

CM

(0 CU CO c

•H o tH a

XJ o aj

''s.

X & CO

to CM X) o• a) to X1 4-1 rOz QJ

i-H a) •H

-3 ,3 u & P cd c 4-1 <44 cd XJ

a) QJ 3 X u u

cd

<4-1 (U O

cx0 4-1 a) •H u *4-1

4J 4-1 cd CO • aj CO

QJ

X QJ 0 3

•H 0) rH

4-1

X 3

4-1 >

CO3 CD X)

CO 4-1 QJ e 4-1 QJ 0) 3 > CO i—1 a) 3 C u O o di rH

•H QJ cd

4-1 *4 CJ •H

CO QJ QJ O a X

CU *H 4-1 0 iH O CO a X) 4-1 •H C

*4-1 r—

QJ o O CO CO QJ

4-1 >-l o aj P- iH X QJ

P-4H 14

CM o

GO

•H

o.

OW % 1H9I3M- 61 -

o(VI

00

(0

CVJ o

<u

(/> o °f

00

x

L±J mh

(0

CVJ

CVJ

q

CO CD

—

— o o d

JZ % 1H9I3M

>4

qj <u

co f2 •H

>4 r—

NJ TJ 0 oj 42 U co

cd a\ T3

CJs. (U O 42 1 -U o£ <U

QJ -H

42

4J £>

V-i CO o -u

<4-1 CO

QJ>4 QJ 3 42

44 4-1 CO

V4 <44 aj O a0 44

QJ •H

4-1 <44

44 44

cO CO • QJ CO

QJ 42 QJ a 3

QJ rH

+4 42 cd 44 >

CO3 CO T3

CO 44 QJ V4 12 44

OJ 0J cd > CO rH

QJ 3 c 14 o o CV tH

“H QJ cd 44 V4 o

•H

CO QJ QJ O a 42

o. •rH 44 a -h o CO o 03 44 •H 3

<44 i—OJ o O CO

CO QJ 44 V4 O OJ Cu

rH 42 0) P4 H >4

CO

00 •H

P<4

>de

Jo. • 62 -

3000

K

>de

CO

CM

O

CO

CO

CM

CM CO

if) q co

ro

CM

ro

oo

CM JZ % 1H9I3M

Jo.

-63-

TIME

x

SO" 2

(sec.)

Fig.

4.

Plot

of

composition

versus

time

at

temperature

for

the

Mo-5.24

w/o

Zr

series.

The

solid

line

represents

the

best

fit

of

the

data

while

the

dashed

line

represents

the

calculated

values.

Task 3

VAPOR TRANSPORT SYNTHESIS AND CRYSTAL GROWTH

H. S. Parker

Inorganic Materials Division

Institute for Materials Research

SUMMARY

Attempts to increase the size of mercurous chloride crystals

grown by evaporation-condensation in a static system are described.

Because of the simple experimental arrangement, the static technique

should be useful for growth of small crystals of this and similar

materials of suitable vapor pressure. The growth of large (1.5 cm

diameter) mercurous chloride crystals by a vapor Bridgman technique

is described. Spontaneous nucleation is a problem with both techniques

and the use of inert gas to help control the problem should be investigated further.

- 64-
,
Introduction

The major objective of this study has been the investigation of

advanced techniques for vapor transport crystal growth and definition

of the limitations imposed by convective effects in a temperature

gradient, for comparison with results of similar experiments in near

zero-gravity conditions . The theory and applications of the vapor

growth technique have been described by several authors [1,2,3].

Mass transport in the presence of a temperature gradient can be

achieved either by the addition of a suitable transporting agent,

generally a halide, or by a simple evaporation-condensation mechanism.

The presence of the transporting agent necessitates consideration of

the reversible reaction occurring at both source and growth end of

the transport tube, and separation of these effects from other growth

parameters is often difficult. In the case of an evaporation-condensation

process, independent control of the total pressure in the system is lost

because the vapor pressure of the material is fixed by the operating

temperature.

The work described in this report is a continuation of the study

of the growth of mercurous chloride by an evaporation-condensation

mechanism as described in the previous report [A]

Experimental Procedures

The ampoule loading procedure and growth furnaces have been described

previously [4,5]During this period, both static growth experiments

with no relative motion between transport tube and gradient and vapor

- 65-
Bridgman growth experiments with the tube either lowered or raised

through the temperature gradient were performed.

The modified transport tube [A], using an evacuated annular space

as thermal insulation at the growth end with a fused silica rod to

provide an axial heat flow path [Figure 1] , was used for the majority

of growth experiments. A few runs were made using growth tubes containing a small reentrant thermocouple well at each end in an attempt

to more closely monitor the actual temperature gradient within the tube

In order to examine the effect of an inert gas on nucleation and

growth rate, a series of runs were made with the transport tubes back

filled with argon at partial pressures calculated to be 0.1 to 0.5

atmospheres at the average growth temperature. The corresponding

mercurous chloride pressure is of the order of 0.9 to 1 atmosphere.

Experimental Results

In view of the success obtained with the modified transport tube

described previously [A], attempts were made to increase crystal size

in the static system. Runs were made under the same conditions

utilized previously, a source temperature of 355°C and a AT of 15°C

(Ap = 0.15 atm) over the last 6 cm of transport distance. The charged

tube was placed in the cold furnace and raised to temperature over a

6 hour period, maintaining the temperature gradient during heating.

Inside diameters of the tubes used in the growth region were 8, 10 and

12 mm. Transport times ranged from 16 to 26 hours. In no case was

the quality of the resulting boule comparable to that previously

- 66 -
obtained in a 6 mm growth tube. The deposit was coarsely polycrystalline

in every case and control of nucleation and interface stability remain

obvious problems. Figure 2 shows the development of a polycrystalline

deposit during initial stages of a run. In addition to the growing

deposit, many smaller crystals can be seen on the tapering walls of the

growth tube.

Five growth runs were made using the transport tubes with reentrant

thermocouple wells at the source and growth ends of the tube. The source

temperature was maintained at 390°C with the growth end 8-10°C cooler

(Ap ^0.2 atm). Excessive scatter in transport rates and polycrystalline

growth was observed.

Because of the limited success attained in increasing the size of

single crystals of mercurous chloride grown in a static system, it was

decided to utilize the vapor Bridgman technique. Previous work at

NBS [6] was done in a geometry favoring convection, but no attempts

were made to determine maximum growth rates or to estimate the magnitude

of the convective contribution to transport rates.

Using the vapor Bridgman technique, and the modified transport

tube, mercurous chloride crystals larger than 1.5 cm diameter were

grown. The crystal shown in Figure 3 was grown at a rate of 0.1 mm

per hour, with a furnace temperature of 380°C, corresponding to a

mercurous chloride pressure of about 0.9 atmospheres. Results obtained

both in a maximum convective configuration (tube raised through gradient)

and minimum convective configuration (tube lowered through gradient)

- 67 -
were comparable, using 1 cm I.D. growth tubes and growth rates of 0.1

to 0.15 mm per hour. The maximum rate consistent with reasonable

crystal quality for the condition of minimum convection is in the

range of 0.15 to 0.2 mm/hr. This rate is not significantly greater

than the rates observed in a maximum convection arrangement.

The results of vapor Bridgman growth runs made using argon backfill pressures in the range of 0.1 to 0.5 atmospheres at growth

temperatures of 380° - 385°C (mercurous chloride pressure 0.9 to 1

atmosphere) were inconclusive. Growth rates were varied from 0.1 to

0.3 mm/hr and no effect on nucleation or quality was observed.

Conclusion and Discussion

During the course of this project, the evaporation-condensation

crystal growth of mercurous chloride has been investigated using both

a static system and a vapor Bridgman technique. Crystals up to 0.6

cm x 1 cm of good quality have been produced by the static technique.

Attempts to produce large, bulk single crystals by this technique were

unsuccessful, due to spontaneous nucleation. Because of its simple

experimental arrangement, the static technique should be useful for

growth of this and similar materials of suitable vapor pressure within

the size limitations. The vapor Bridgman technique is much more successful for the growth of large single crystals by evaporation-condensation,

although growth rates of 0.1 mm/hr or less are necessary for high quality

specimens

.

- 68-
In the application of both techniques , spontaneous nucleation on

the walls of the growth chamber remains a problem and the investigation

of the effect of an inert gas on the growth process should be investigated

further

References

[1] a) H. Schafer, "Chemical Transport Reactions", Academic Press,

New York, 1964.

b) H. Schafer in "Preparative Methods in Solid State Chemistry",

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

[2] E. Kaldis, in "Crystal Growth, Theory and Techniques, Volume I",

C. H. L. Goodman, Ed., 49-191, Plenum Press, New York, 1974.

[3] M. M. Faktor and I. Garrett, "Growth of Crystals From the Vapor",

John Wiley and Sons, New York, 1974.

[4] E. Passaglia and R. L. Parker, "NBS Space Processing Research",

NBSIR 76-980, 120-130, February 1976.

[5] E. Passaglia and R. L. Parker, "NBS Space Processing Research",

NBSIR 74-611, 69-78, November 1974.

[6] R. A. Forman, W. S. Brower and H. S. Parker, "Mercurous Chloride

Polarizer Material", AFML-TR- 74-56 , April 1974.

- 69 -

>de

Jo.

o.

Figure 1. Modified growth tube. Annular space between growth tube

and outer tube evacuated for thermal insulation. Heat

flow path is 3 mm fused silica rod connecting tubes at

left end.

Figure 2. Polycrystalline deposit of mercurous chloride during initial

stages of growth run.

- 70 -

Figure 3

>de

Jo.

o.

•t

Single crystal of mercurous chloride grown by vapor

Bridgman technique.

- 71 -

Task 4

Melt Shape in Weightless Crystal Growth

S. R. Coriell, S. C. Hardy

Metallurgy Division

Institute for Materials Research

and

M. R. Cordes

Applied Mathematics Division

Institute for Basic Standards

Summary

We have made measurements of the motions of air bubbles in a

viscous silicone oil as determined by buoyancy and thermocapillary

forces. The oil is contained in a small cell across which a linear

temperature gradient is established. This temperature gradient causes

the surface tension to vary over the air-oil interface of a small bubble

at the center of the cell. As a consequence, Marangoni convection

develops in the oil and the bubble experiences a thermocapillary force.

We have measured the gradient required to generate a thermocapillary

force which just balances the buoyancy force and thus stabilizes the bubble.

A plot of this gradient as a function of bubble diameter is in excellent

agreement with the theoretical behavior predicted by solving the Navier-Stokes

equations in the creeping flow approximation. Measurements of bubble

velocity away from equilibrium are also in agreement with theory.

The shape of axisymmetric liquid zones and their stability with

respect to axisymmetric perturbations has been investigated numerically.

For growth of constant diameter crystals by the floating zone process,

the necessary boundary conditions are prescribed freezing radius R^,

- 72 -
I

-
melting radius and meniscus angle <J>^ at the freezing interface. For

these boundary conditions with R =R and fixed length L to radius ratio,

t m

the maximum value of the gravitational field for which such a liquid

zone exists is calculated. Under certain conditions, it is found that

there exist two different zone shapes which satisfy the boundary conditions.

- 73-
The processing of materials in space will involve free liquid

surfaces. These free surfaces may be intentional as in processes

analogous to floating zone or Czochralski or may develop unexpectedly

as bubbles form or the liquid separates from the container wall. If

surface tension gradients are established on these free surfaces,

Marangoni convection may develop and spread throughout the volume.

Recent calculations ^ ^ have indicated that such convection can be

quite vigorous even for small gradients in some situations. Thus

I an understanding of surface tension driven fluid flow is important to

the proper design and interpretation of space experiments and processes.

We have started experimental studies of Marangoni convection in the past

year and will report some measurements in part A of this report. An

understanding of the shape and stability of liquid zones is also essential

to the development of a microgravity materials processing technology.

We have continued our work in this area and part B of this report will

discuss some new results.

A. Marangoni Convection Studies

Introduction

We have initiated studies of Marangoni convection this past year

with measurements of the motion of air bubbles in a viscous silicone

- 74 -
oil in response to buoyancy and thermocapillary forces. This problem

was selected because its theoretical analysis is relatively simple

( 2 ) compared to other geometries and had already been developed. The

analysis considers a fluid sphere of radius R and density p' immersed

in a second fluid of density p. A temperature gradient G in the bulk

liquid results in a variation of tension over the interface. This surface

tension gradient produces a tangential sheer stress at the interface

which sets the fluid into motion both inside and outside the bubble

as illustrated in figure 1. Usually the variation of surface tension

with temperature, y'=dy/dT, is negative and the fluid flows from hot

to cold at the interface. As a result the bubble experiences a thermocapillary force opposite to the fluid flow, i.e. from cold to hot.

In the approximation of creeping flow the linearized Navier-Stokes

equations describe the fluid flow and the temperature fields reduce to

solutions of Laplace's equation. The appropriate boundary conditions

on the stress, temperature, and heat flux result in an expression for

the velocity of the bubble.

For air in silicone oil, p^<<p,y^<<y and k^«k where y and k are the

viscosity and thermal conductivities respectively and the prime denotes

the bubble fluid. In this case the expression for the bubble velocity

becomes __ _ pgR 2 _ 2. 2

( 1 )

where the first and second terms in the bracket give the effects of the

volume buoyancy and surface tension forces respectively. The coordinate

- 75-
system is chosen so that the positive direction is upward. Since y'<0,

there is a G

q

<0 at which the thermocapillary force and the buoyancy

force are in balance so that the bubble is motionless. In this case,

we have „ _

3Y

"* (2)

where D=2R. Thus a plot of G as a function of D is linear, passes

o through the origin and has slope dG0 = pg , assuming p and y' are constant.

dD 3y"

For values of G < G , the bubble will move downward; for G > G , the

o o bubble will move upward.

Experimental Apparatus and Procedures

The earlier paper (2) in which the above theory was developed also

presented the results of some measurements of G as a function of

o bubble diameter for silicone oils. The experimental results are so

scattered, however, that only general agreement with theory is indicated.

These experiments used uncontained oil zones held between the end pieces

of a micrometer by capillarity. The temperatures of the end pieces were

controlled with small heaters wound about copper blocks in contact with

the micrometer shafts; the temperatures were measured with thermometers

thrust into these blocks. The temperature measurement and control were,

consequently, not precise and the optical observations were affected by

the curved surface of the zone. In addition, the large uncontained

air-oil interface of the zone probably gave rise to a general Marangoni

convection which may have affected the motion of bubbles even near the

axis where observations were made.

- 76 -
To avoid these obvious experimental problems, we constructed the

simple device shown in Figure 2. The oil is contained in the small

rectangular cell (A) which has flat double glass windows in front and

back and insulated sides. The top (B) and bottom (C) surfaces of the

cell are brass plates which are soldered to tubes wound with small

nichrome heaters (D, E,). The top plate rests on narrow spacing strips

of plastic which give the cell a depth of about 0.3 cm. At this depth,

the fluid viscosities and negative gradients employed in these experiments

give calculated Raleigh numbers far below the value required for

convection due to density variations; no convection could be detected

from observations of small particles in the absence of a bubble.

Miniature thermocouples (F, G) pass through the plates and are cemented to

the top and bottom surfaces near their centers. The heaters are controlled

by variable transformers connected to a constant voltage source. The

thermocouples are read with a millivoltmeter whose output drives a strip

chart recorder. In operation, the cell temperatures after adjustment

of the heaters were constant to about 1°C for several hours. The top

heater was usually not used. Instead, the top temperature was held nearly

constant by blowing compressed air over the uninsulated brass tube.

The linearity of the temperature gradient in the cell was checked

by inserting a microthermocouple (.003" wire) through a small side tube

(H) thus permitting temperature measurements at three points. The results

are shown in figure 3 where the temperature differences given by the

three thermocouples are plotted as a function of their positions for

various gradients. These data show that the temperature distribution

- 77 -
in the cell was linear at gradients higher than any used in bubble motion

measurements

.

To avoid complications arising from possible interactions and

perturbations of the flow fields, measurements were made with only one

bubble in the cell. Single bubbles were inserted in the middle of the

cell through the side tube (H) using a microliter syringe. Figure 4

shows a bubble shortly after ejection from the syringe as it drifts

upward. The bubbles are observed and photographed through a microscope

) equipped with a micrometer eyepiece.

Experimental Results

In the introduction the motion of air bubbles in a viscous fluid

was treated as the result of buoyancy and thermocapillary forces. In our

experiments the behavior is more complicated than this model suggests

because the bubble radius is generally changing due to the temperature

dependent solubility of air in silicone oil. Since the temperature

varies with position in the cell, the solubility also varies. Although

the oil is initially undersaturated with air, when the temperature

gradient is established, the oil is supersaturated near the bottom where

it is hot while remaining undersaturated at the top. Thus an air bubble

at the top of the cell will shrink and at the bottom of the cell it

will grow. For a given gradient and air concentration there is only

one temperature i.e. one location in the cell at which a bubble can be

at equilibrium with the silicone oil.

The changes in bubble radius caused by the position dependent

solubility give rise to complicated bubble motions. For most experiments

- 78 -
the temperature gradient in the cell is fixed and the bubble when inserted

is usually sufficiently large for the buoyancy force to exceed the

thermocapillary force. Consequently the bubble will move upward and come

to rest against the top plate. It is now in the coolest area of the

cell and the oil is undersaturated with air; the bubble will be shrinking.

Eventually the radius will become sufficiently small for the thermocapillary

force to exceed the buoyancy force and the bubble will detach from the

top plate and move downward. It will continue to shrink as it decends

until it passes the solubility equilibrium point and moves into the

region of supersaturated oil where it will begin to grow. Usually the

radius will become large enough to make the buoyancy force dominant

before the bottom plate is reached and the bubble will reverse its motion

and ascend to the top of the cell. For the same air concentration and

a different gradient, the bubble may completely dissolve before passing

the position of solubility equilibrium on its first descent. Alternatively,

for a certain range of gradients, the bubble motion and diameter will

fluctuate with almost sinusoidal regularity. This oscillatory mode is

shown in figure 5 where bubble position Z and diameter D are plotted

as a function of time over one cycle.

One of the major goals of these experiments was to measure the

gradients required to make bubbles motionless. The size fluctuations

discussed above, although seeming to complicate the experiments, make

available a simple technique for these stabilizing gradient measurements

with the important feature that the cell gradient can remain constant

during the measurement. All that is necessary is to record the bubble

diameter when the motion reverses, either in rising or descending. At

- 79-
the direction reversal the velocity is zero and the buoyancy and

tbermocapillary forces are equal. The reversal point is easily determined

using the micrometer eyepiece and the bubble is photographed to measure

the diameter. Figure 6 shows the bubble diameter at reversal as a function

of temperature gradient. A line through the points passes through the

origin and has a slope which give y . 055 mJ . If a y' is calculated

deviation of + .002 mJ . This y' is about 10% lower than the .061 mJ

the observations of bubble diameter as a function of stabilizing gradient

are in agreement with theoretical predictions; the scattered results of

the earlier work were the result of the non ideal experimental conditions.

We have also made some measurements of bubble velocities in order

to compare with the theoretical predictions expressed in Equation (1).

This was undertaken because the viscosity dependence of the bubble

velocity drops out at v=0 thus reducing the problem to a special case.

The agreement between calculated and measured velocities was not good.

However, this is to be expected because the calculation of V requires

the subtraction of two terms which are nearly the same. A better way

to compare measurement and theory is to use the measured velocity

along with the gradient and bubble radius in equation 1 to calculate

a valve of y'

.

The calculation requires a determination of the temperature

of the bubble so that the proper value of the viscosity may be used.

This is easily determined from the known gradient and the position at

which the velocity is measured. The velocity is measured by determining

for each point using eq. 2, we find Y^Vg.053 mJ with a standard

value (probable error of 10%) found by direct measurement ( 2 ) Thus

- 80-
Z as a function of time and finding the slope at the desired point

to get v=dZ . Table 1 shows the results of such measurements with some

dt

isothermal bubble velocity data. The average calculated value of y' is

about .052 mJ , in good agreement with the results of the zero velocity

ra2K

measurements

.

Discussion

These observations of air bubble motion in response to buoyancy

and thermocapillary forces seem to be in excellent quantitative

agreement with the predictions of theory for the fluid flow velocities

used. Several incidental observations, however, are worth noting. It

was evident from early measurements not shown here that the behavior

of bubbles at and near the top and bottom plates was somewhat different

from the behavior in the center of the cell. The difference was evidenced

in slightly higher values of y' than those reported here. Some

deviation from center cell behavior was anticipated because of the obvious

disturbance to the fluid and temperature fields by the rigid surfaces.

In addition, some observations were made of bubble interactions. These

were appreciable in the case of two bubbles of greatly different size.

It appeared that the convection field of the larger bubble could

influence the motion of the smaller bubble at large distances i.e. several

large bubble diameters. This indicated that the flow velocities were

significant at some distance from the interface generating the convection.

Observations of the motion of small particles contained in the silicone

oil support this conclusion.

- 81 -
Part B - Shape and Stability of Liquid Zones

In connection with modelling the floating zone process we have

3 continued our studies of the shape and stability of liquid zones. In

addition, in collaboration with Dr. T. Surek of Mobil-Tyco Solar Energy

Corporation, we have developed a theory which predicts the time evolution

and stability of the dimensions of the solidifying crystal during the

floating zone process.

The shape and stability of liquid zones has been discussed extensively

in previous annual reports. In this report we will emphasize new

developments and results. We consider a liquid zone of length L between

two solids which are circular cylinders (plates) and are coaxial. The

radii of the upper and lower plates are and R, respectively. Defining

the usual cylindrical coordinate system (r, 0, z) with origin midway

between the two solids and coaxial with them, we study the effects of

a constant gravitational acceleration g along the negative z-axis and

of rotation with constant angular velocity ft about the z-axis. We

assume that the liquid-vapor interface is axisymmetric and denote the

shape by the function r = r (z). This assumption is consistent with

the direction of the gravitational field and the axis of rotation. We

assume that the wetting behavior of the liquid is such that r(-L/2)=R and

r(L/2)=R

u are appropriate boundary conditions. For a static (or uniformly

rotating) liquid, the liquid-vapor interface shape is given j by the Laplace

capillary equation, viz.,

y{r

~

1 (l+r 2 )~^ - r (l+r 2

)- ^2 }= -pgz+(pft2 r

2 /2)+P • (3)

z zz z where y is the liquid-vapor surface tension, p is the density difference

between liquid and vapor, p is a constant (Lagrange multiplier), and

- 82 -
the subscript z indicates differentiation with respect to z i.e., r^dr/dz.

3

In our previous annual report , results for the shape and stability

of liquid zones were presented based on numerical solutions of the Laplace

capillary equation and the associated Jacobi differential equation. The

numerical method failed whenever |r | became too large. To avoid this

difficulty, we have rewritten the equations in terms of arc length t.

Defining

r'= sin <}) (4)

z'= cos <p (5)

where the prime indicates differentiation with respect to t, i.e., z^=dz/dt.

The Laplace capillary equation is then

4>^=[cos (<j>) /r]+(pgz/y)- (pft 2 r

2 /2y)- (p/y) • (6)

The Jacobi equation is obtained from the Laplace capillary equation by

letting z -* z + 6 z, r -> r + 6 r, p

-* p

- (y/2). and <j> -* 4> + <$4>. Retaining

only linear terms in the variational quantitities 5r, 6z and 6<J>, we find

W"+(sin<}>/r) W'+W {<{>^ 2+cos 2 4>/r 2+(pg/y)sin4> + (pft 2 r/y)coscf)}=y/2y , (7)

where W^cos<f>Sr-sin(f) 5 z; this is the Jacobi equation. The stability criterion

is ^ t * > t (8) m

where the conjugate point t* is the first positive root of the equation

u(t*) C

C v r d t - v(t*) f u r d t = 0 (9)

Jo Jo

The origin of arc length has been chosen such that r(0)=R, z(0)=-L/2 and

r(tmum )=R , z(t )=L/2. The functions u(t) and v(t) are non-trivial solutions of the

homogeneous (y=0) and inhomogeneous (y^O) Jacobi equation which vanish at t—0.

The arc length formulation allows us to treat zones which are not

representable by a single valued function r (z), i.e., we can now consider

zone shapes such that there are two or more values of r for a given

value of z.

- 83-
The Laplace capillary equation is solved as an initial value

problem. At present the computer program can consider two types of

boundary conditions. For fixed L, p, y» g and ft, type I finds a solution

for specified values of R, and volume V, while type II obtains a

solution for specified values of R, R^ and ^s<j)(0)= arctan [r (z=-L/2)].

The program has been written so that it will be relatively easy to

incorporate other types of boundary conditions; only type I was available

in the previous computer program. For type I boundary conditions, the

solution is obtained by guessing values of <J>^, p, and t^ and iterating

to obtain values of d> , p and t which give the desired values r (t )=R , i m m u

5

z(t

m

)=L/2, and volume V. The iteration on t^ is not strictly necessary

but was introduced for programming convenience. For type II boundary

conditions, <f> . is specified so that the iteration is only on p and t^.

The iteration method is similar to that previously used. In testing

for stability of the solution only axisymmetric perturbations which

conserve the zone volume are considered. For zone shapes representable as

r(z), it has been shown that one need only consider axisymmetric

perturbations to determine stability. It is also known that under some

circumstances axisymmetric menisci become unstable with respect to

asymmetric perturbations. Thus, for zone shapes not representable by a

single valued function r(z), it will be necessary to consider stability

with respect to asymmetric perturbations. At present we have not attempted

this

.

Before discussing the numerical results, we will briefly describe

a theory of shape stability of the dimensions of the solidifying crystal

in the float zone process. For greater detail the reader is referred to

- 84 -
reference 7. We consider the following floating zone system; a

solid cylinder of radius is grown by melting a solid

cylinder S of radius R . The liquid zone of volume V is between

m m

the solids S_ and S , which are being moved at velocities v * and v *,

f m

b f m

respectively. At the - liquid interface solid is freezing at a rate

Vf, while at the - liquid interface solid is melting at a rate v .

The basic equations for the time evolution of the system are

L=(v - v *) - (v ( 10 ) f mm - v *),

t r

V=’,(f> s/pL>

(R

m

2v

m

‘ R

f

2v

f

)

R

f=vf

tan (<(» f ~ <J) o

)

4> f

=f (V, L, R

f

, R

m

)

(ID

( 12 )

(13)

The first equation expresses the change in zone length L as a function

of the pulling velocities v * and v * and the freezing and melting

m t velocities. The dot indicates differentiation with respect to time T.

The second equation represents the change in zone volume due to the

freezing and melting process; p and p T are solid and liquid densities,

respectively. The third equation describes the dependence of the change

in freezing radius on the meniscus angle <f>£ at the freezing interface.

For the floating zone geometry previously described with the lower

interface as the freezing interface, <j>^ is identical to <j)^, viz, <j)^=(})(0) =

arctan [r (z=-L/2)l. Results for the upper interface freezing can be

z obtained by changing the sign of the gravitational acceleration. The angle ^

is a property of the material and is the meniscus angle necessary for

constant radius growth, i.e., <J> o

=<J)£ for Rf=0. For silicon, recent

g measurements indicate that d> =11°. The final equation expresses <{> =4>. o t i as a function of the zone variables V, L, R-. and R ; the dependence on

t m

- 85 -
p, y, g and ft is not explicitly indicated. The functional relationship

is found by solving the Laplace capillary equation as previously described.

It should be pointed out that the Laplace capillary equation assumes a

static liquid (a uniformly rotating liquid can be taken into account) . In

the actual floating zone process there is certainly Marangoni convection

due to temperature gradients (and on earth gravity driven convection)

.

The effects of such convection on zone shape remains to be investigated.

We ^ have carried out a perturbation treatment to test the

stability of the steady state solution of the above equations. At

I

• • • steady state L = 0, V = 0, R^ = 0 and <})^ = cj)^. We denote small deviations

from steady state by the symbol A; e.g., <j>=

<J> o+A <j) , R^R^Q+ARg, etc.,

where a subscript 0 denotes the steady state value. Upon writing

the above equations in terms of the perturbed quantities and neglecting

any non-linear terms, we obtain a set of three linear inhomogeneous

equations for the quantities AV, ARg and A<f>g. An important assumption

in this procedure is that the freezing and melting velocities are

functions only of time and are not functions of the variables R,., R , L,

f m

V and (j)^. Thus we are neglecting thermal effects which would cause

v,. and v to depend on these variables; future work will consider the

f m

thermal fields.

The stability of the dimensions of the crystal is determined by

the solution of the homogeneous equations for AV, ARg and A<J)^; these

solutions are of the form exp (Ax). If the real part of A is negative,

the exponential decays with time and the steady state is stable. For the

real part of A positive, AV, ARg and AcJ) f increase exponentially with

time and the steady state is unstable. It can be shown that the

- 86-
necessary and sufficient conditions for stability of the dimensions

of the freezing crystal are

04»

o

/ 9 R

f

) < 0 and (&<j> /3V)> 0. (14)

For a stable system, it is convenient to write a=-o+i 3 where a and 6 are

frequencies of decay and oscillation, respectively. Explicit formulas

for a and 3 are a=-(v

fo /2) (3<|> o /3R

f

) (15)

3=v

f0

{2TTRf0 (P s /p L

) 0<J> o

/aV)-(9<J>o /3R

f

) 2 /4}.^ (16)

The derivatives (3t() o /9R^) and (dtp^/dV), which determine the time evolution

and stability of the dimensions of the resolidifying crystal can be

determined using the computer program previously described.

The liquid zone shape depends on five dimensionless parameters

R /R, V/itR2 L, L/R, e EpS] 2 R

3 /y and cEpgR2

/ [y (1+e ) ] . In the calculations

U K R

to be discussed we have taken ft=0 so that e =0 and c=pgR2 /y. In our

previous annual report we considered in detail the case R

u/R=l and V/ttR2 L=1.

Experimental results for water zones in air were presented. Additional

experiments on water zones in dibutyl phthalate, which is only slightly

soluble in water and is of slightly higher density, using both solid end

plates and open tubes, have further confirmed the theory. The comparison

of theoretical and experimental results is indicated in Fig. 7. The

surface tension of water-dibutyl phthalate was measured by the pendant

drop technique and the value of 22.8 m J/m2 was used in the comparison

of theory and experiment.

We have also carried out experiments to determine the maximum stable

length as a function of e for horizontal liquid zones. For this case,

there are no exact theoretical results, however, for small e, one can

- 87 -
obtain an approximate analytic result by expanding the appropriate Euler

and Jacobi equations in powers of e and retaining terms of order e

2

.

3 The basic result for small e is that the zone is stable when

L/R < 2tt (1 - (tte/2) 2 + } . (17)

In Figure 8 we show the experimentally measured L/R values as a function

of the Bond number for horizontal zones. The solid line in the figure is

the theoretical prediction just stated; the dashed curve is the result for

vertical zones shown in Figure 7. The horizontal zones are more stable

than the vertical zones for e less than approximately 0.5.

The present numerical calculations have chiefly been concerned

with the liquid zone shapes which permit constant diameter crystal growth,

i.e., the angle <p . is in the vicinity of zero. An approximate

9 calculation of zone stability for <j>_^=0 has been made by Heywang. We

will briefly outline this calculation. We take fi=0 (no rotation) and

consider the case R=R

u

« For large R (or large Bond number e) , we neglect

the term containing r~ 1 on the left hand side of eq (3). The Laplace

capillary equation can then be integrated and we obtain

r

n = h(n)/[l-h 2 (n)], (18)

where h (q) = (pg/2y) r) 2- (p /y)n and n=z+(L/2). Note that r^=0 and hence

<J)^=0 at the freezing interface n=0 as desired. Further integration yields

r(n)-R= \ (h (n)

/

[1—

h

2 (n) ])dn . (19)

-'o

This satisfies the boundary condition r(0)=R; the boundary condition

r(L)=R requires that

r

L

\ (h(n)/[i-h 2 (n) ]}dn=0, (20)

- 88 -
i.e. p is chosen such that the above equation holds. However if L is

sufficiently large that h

2 (L)=l, the denominator 1-h2 of the above

expressions vanish; note that this corresponds to an infinite value of

r^, i.e., <j>=± 90°. Heywang assumes that this corresponds to the

largest possible zone length, which we denote by L*. In order to

find L* we define A=(pg/y) ZL* and x=n/L*; eq (20) with

p=(pg/2)L* - y/L* becomes

C

\ (g(x) /[l-g 2 (x) ] }dx=0, (21)

J 0 where g(x)=(A 2 /2) (x) (x-1) + x. Heywang found that A=2.84 satisfied the

above equation; Green found A=2.62 and our own numerical evaluation

yields A=2.67. Thus the Heywang approximate calculation yields

L*=2.67 (A/pg) 2 for the largest possible zone length.

In table 2 for <j)^=0 at the lower interface, which is freezing,

we give results for maximum zone length based on numerical calculations

using the computer program previously described. These zones contain

liquid volumes V < tt R

2 L. The zone radius is R at z=-(L/2); the radius

decreases to a minimum and then increases reaching R at z=(L/2). For

a planar solid-liquid melting interface perpendicular to the zone (z)

axis it is impossible for the angle <J> to be greater than 90° since the

liquid-vapor interface would intersect the solid-liquid interface prior

to reaching the triple junction of liquid, vapor and solid at r (z=L/2)=R.

Such behavior is illustrated in fig. 9. Thus for (L*/R)=1.0, 0.5 and 0.25,

we have used as the criterion for maximum zone length, the value of e

at which <J> = 90° at z = L/2. For non-planar solid-liquid interfaces the

<f> = 90° criterion is not appropriate; depending on the shape of the

solid-liquid interface <{> could be greater or less than 90°. Our

- 89-
calculations indicate that zone shapes with tp > 90° can be stable with

respect to axisymmetric perturbations (stability with respect to asymmetric

perturbations remains to be investigated) . Note that the Heywang

7s approximation, which may be written (L*/R)e z = 2.67 is excellent for

large Bond numbers e.

For L*/R = 6.0, 4.0 and 2.0 in Table 2, the maximum zone length is

determined by a different mechanism, which will now be described. In

figure 10 we plot as a function of zone volume for all other variables

fixed for two different Bond numbers, e = 1.38 and 1.50. The interesting

and somewhat surprising feature of the V(c(k) curve is that a given

value of d) . can be obtained for two different volumes. For e = 1.38

l

and - 0.1° £ (p^ <_ 5.9°, there are two volumes which give the same <j> .

For <}>^ _> 5.9°, there is a unique volume, and a <|k <_ - 0.1° is not

possible for e = 1.38. For volumes less than those indicated in the figure the

liquid zone is unstable with respect to axisymmetric perturbations.

As e increases the V(<ft^) curve moves to the right as illustrated by the

e=l . 5 curve in fig. 10. For e>1.384 a value of c})^=0 is no longer possible.

Thus, as given in Table 2, for e>1.384 a liquid zone with L/R=2.0 and

<J> =0 does not exist. Recalling that one of the criteria for the stability

of steady state growth during the floating zone process was (3<j> o /3V)>0, it

is clear that in those cases for which two different volumes give the same

<J> o one volume corresponds to (3<() /3V) positive and the other volume to

(3<J> o /3V) negative. Obviously for constant diameter crystal growth it

is highly desirable to use the volume corresponding to (3<J> /3V) positive.

For e=1.25, figures 11 and 12 illustrate two liquid zones with different

volumes but both having <Jk=0.

- 90 -
Table 3 gives results for maximum zone length for <j>^=0 at the

upper interface which is freezing. The calculations are actually carried

out by taking <J>^=0 at z=(-L/2) and g negative. These zones contain

liquid volumes V>irR2 L; a zone shape is illustrated in figure 13. Note

that for this particular liquid zone, the magnitude of <p at the melting

interface exceeds 90° . This zone is not representable as a single

valued function r(z). For specified L/R, Table 3 gives the e value

at which the zones become unstable with respect to axisymmetric perturbations.

Since it is possible that zones not representable as r(z) first become

unstable with respect to asymmetric perturbations, we also give in Table 4,

the value of e, denoted by egg, at which | <f> | =90 ° at the melting interface,

i.e., for e>ego, the liquid zone is not representable as r(z). As can

be seen from Table 3, e is about 6% greater than ego* The Heywang

approximation (L*/R) e

z=2. 67 is very good at large Bond numbers.

In comparing Tables 2 a-: 3, it is clear that for large e, the

values of e for a given maximaun zone length differ only slightly; the

maximum zone length depends only weakly on whether the lower or upper

interface is freezing. However, for small e(L*/R”4.0 and 6.0) there

are order of magnitude differences between the e values for freezing at

the lower and upper interfaces. However, the zone volumes are very

different; for (L*/R)=6.0 with the lower interface freezing (Table 2)

V/ttR2 Le 0.97 while for the upper interface freezing (Table 3 ) V/ttR2 Lz5 . 5

.

The larger volume greatly increases the stability of the zone. Recall

that for e=0 and L/R=2ir, zones with V<ttR 2L are unstable.

- 91 -
TABLE 2

Maximum zone length L* as a function of Bond number e=pgR2 /y;

R

u

=R, ft=0, and cf>£=0. Lower interface is freezing.

L*/R e (L*/R)

6.0 4.6(10~ 5

) 0.041

4.0 5.24(10 2

) 0.915

2.0 1.384 2.35

1.0 7.223+ 2.69

0.5 28.98+ 2.69

0.25 115.3+ 2.68

+ Valued of (L*/R) based on <f>> 90° at melting interface.

TABLE 3

Maximum Zone Length L* as a function of Bond number e=pgR2 /y;

R

u

=R, fl=0 and cj> ^=0 „ Upper interface is freezing. ego corresponds

to the Bond number at which the meniscus is horizontal at the

melting interface.

L*/R e e 90 (L*/R)

e

6.0 .1121 .1046 2.01

4.0 .325 .307 2.28

2.0 1.631 1.543 2.55

1.0 7.135 ' 6.728 2.67

0.5 29.555 27.838 2.72

0.25 119.90 112.88 2.74

92 -
There are a number of areas for further investigation. The stability

of axisymmetric zones with respect to asymmetric perturbations, (e.g.,

perturbations which correspond to a translation of the zone) is unkown

when the zone shape cannot be described by a single-valued function r(z).

The maximum zone length when the meniscus angle <f> f at the freezing

interface is not zero has not yet been systematically studied. The

g value <j>f=ll° is appropriate for Si crystal growth . A more fundamental

and difficult problem is the evaluation of the effect of fluid flow and

electromagnetic fields on zone shape and stability. The present

calculations assume a static liquid. In actual floating zone systems

there will be Marangoni convection due to surface tension gradients and

convection due to gravitational forces. In the special case of a

uniformly rotating fluid, it is clear that zone shape and stability can

be completely modified. However, for the fluid flow present in the

floating zone process, the magnitude of the fluid flow effect on zone

shape and stability is not known.

We are indebted to H. W. McLaughlin, R. F. Sekerka and T. Surek

for helpful comments and discussion.

- 93-
References

1. Chang, C. E. , and Wilcox, W. R. , Proceedings of the "International

Colloquiem on Drops and Bubbles," 1974, pg. 194.

2. Young, N. 0., Goldstein, J. S., and Black, M. J., J. Fluid Mech. 6^, 350(1959).

3. Coriell, S. R. , Hardy, S. C., and Cordes, M. R., NBS Space Processing

Research (NBSIR 76-980) February 1976, p. 99

4. Bolza, 0., Lectures on the Calculus of Variations, Dover, New York,

1961.

5. Gillette, R. D. and Dyson, D. C., Chem. Eng. J. _3, 196(1972).

6. Michael, D. H. and Williams, P. G., Proc. R. Soc. London A 351 , 117(1976).

7. Surek, T. and Coriell, S. R. , J. Crystal Growth, to be published.

8. Surek, T. and Chalmers, B., J. Crystal Growth, ^9, 1(1975).

9. Heywang, W., Z. Naturforschg. 11a , 238(1956).

10.

Green, R. E., Jr., J. Appl. Phys. 35, 1297(1964).

- 94 -
Table

\ CM6

•ne

.051

.

050

.

052

.054

COo

• rH o X rH vO H" LO o CM

rH • o 00 LO LO rH o lO

c

d

u • • • • • • • u <D CM CM CO o i>- >

G

u

COo

rH

• X LO cn 00 CTi o LO CO

Lrt • O c- CO LO LO CT> cn

J=> U • • • • • • • O a> CM CM to LO LO LO to > (/} Gu

y

CO CO C^ 00 o c~ o rH rf CM o CT> CO

rH • • • • • • • Q£ X 00 CT> 00 *3- LO LO o

G rH u

H u CM CO LO •H- c- LO

0 CM CM LO to to CO

v /

G CO rH O'! to u • • • • CJ o o o to rH rH cr

i

u CTi o o CM

0 rH rH rH

- 95 -

Fig. 1 Fluid flow generated by thermocapillary forces about a sperical interface.

- 96 -

Fig. 2 Temperature gradient cell for studies of bubble motion.

- 97 - F*i

=

167

K/cm

- 98-

Fig.

3

Temperature

distribution

in

the

cell.
i
>d<

Jo

o.

xa — —

•t

Fig. 4 Bubble shortly after injection into the silicone oil.

-99-

0.3i

....

—

!

0.03

(ujo) a

Od — doo o

o

(ujo) z

o

Q)

</>

a>E

i-

- 100-

Fig.

5

Oscillations

of

bubble

diameter

and

position.

0.03

O

<0

O

OJ

O

00

o

o

CVJ o

o

o

o

o

(

uio

) J040UUDJQ 0|qqng

E

o\

c

CD

• mmm TJ

a

CD

- 101 -

Fig.

6

Bubble

diameter

at

which

the

velocity

vanishes

as

a

function

of

temperature

gradient.

(L/R)

Fig. 7 A comparison of numerical (solid line) and experimental

(points) results for the maximum stable zone length

(vertical zones) as a function of the Bond number

e=pgR2 /y.

- 102 -

Fig. 8 The circles represent experimental results for the

maximum stable zone length (horizontal zones) as a function of e. The solid line is an approximate

analytic result for small e for horizontal zones. The dashed line represents vertical zones.

- 103 -

2-

a) w o

*• cO O u-i

0) i-i

II 0 <U O 4J DSN 0

CJ *H

CO

>d<

Jo

o.

- 104 -

Fig.

9

Liquid

zone

for

R

/R

-

1.0,

L/R

1.0,

e

=

7.51,

and

<J>

=

0.

Note

that

such

impossible

if

the

upper

solid-liquid

Fig. 10 Liquid zone volume V (in units of R^) a function of

<j>£ (in degrees) for e = 1.38 and 1.50 with R^/R^. = L/Rf * 2.0 and e R

= 0. There may be zero or one or volumes which give a specified 4> ^

.

- 105-

1 . 0 , two jE

2-F

>dt

- 106 -

2-

Fig.

11

Liquid

zone

for

R^/R

=

1.0,

L/R

=2.0,

e

=

0,

e

=

1.25

and

<j)£

=

0.

Compare

this

zone

with

Fig.

12

which

also

has

these

values;

for

this

zone

V/R 3

=

2.9

while

the

ro

31

-107-

2-

12

Liquid

zone

for

R

/R

=

1.0,

L/R

-

2.0,

-

e

=

1.25

and

=

0.

Compare

with

Fig.

11.

o

II Pi

)de

Jo.

o.

3E

- 108 -

2-1

Fig.

13

Liquid

zone

for

R

/R

=

1.0,

L/R

-

1.0

Task 5

NBS personnel continue to consult extensively with NASA

Headquarters and NASA field offices as required. We have visited

Marshall SFC, Alabama on numerous occassions and have provided

advice on many aspects of the Space Processing Program, including

Shuttle Payloads. We continue our Space Processing Seminar at

NBS.

- 109 -
National Aeronautics and Space Administration

Washington, D. C. 20546

Mr. F. L. Williams Code ES 1 copy

Dr. J. ,H. Bredt Code ES 4 copies

National Aeronautics and Space Administration

Johnson Space Center

Houston, Texas 77058

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National Aeronautics and Space Administration

George C. Marshall Space Flight Center

Marshall Space Flight Center, Alabama 35812

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- 110-
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California Institute of Technology

4800 Oak Grove Drive

Pasadena, California 91103

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National Aeronautics and Space Administration

Langley Research Center

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Grumman Aerospace Corporation

Bethpage, New York 11714

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General Electric Company

Space Sciences Laboratory

P.0. Box 8555

Philadelphia, Pennsylvania 19101

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European Space Research Organization

114 Avenue Charles de Gaulle

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German Federal Republic

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1 copy

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- 111 -
'
NBS-1 14A (REV. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR RKPORT NO.

NBSIR 77-1208

2. Gov’t Accession

No.

3. Recipient’s Accession No.

4. TITLE AND SUBTITLE

NBS Space Processing Research

5. Publication Date January 1977

6. Performing Organization Code

7. AUTHOR(S)

E. Passaglia & R. L. Parker

8 . Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No.

11. Contract/Grant No.

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

NASA - Marshall SFC

Huntsville, Alabama

13. Type of Report & Period

Covered Annual Report

1/76-12/76

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

Annual Report

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

bibliography or literature survey, mention it here.)

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

Program covering the period January 1, 1976 - December 31, 1976.

The results obtained for each task are given in detailed summaries in the

body of the report. Briefly, in Task 1 - Crystal Perfection in Czochralski Growth - large nickel single crystals have been grown having dislocation densities as low

as U00 lines / cm^ as assessed by x-ray dynamical diffraction techniques. In Task 2

Evaporative Purification of Ultra-High Purity Materials - Part A - it was determined

that the use of sessile drops as a means of support for the study of molten alumina

places severe restrictions on the type and validity of the data that can be obtained

in view of temperature measurement and control problems encountered. In Part B,

rates of evaporative purification were determined for Nb-Mo and for Mo-Zr alloys at

elevated temperatures using R.F. levitation of molten drops. In Task 3 - Vapor

Transport Synthesis and Crystal Growth - the growth of 1.5 cm diameter crystals

of mercurous chloride crystals by a vapor Bridgman technique is described. In

Task k - Melt Shape in Weightless Crystal Growth, thermocapillary forces on air

bubbles in a viscous oil were measured, and the shape of axisymmetric liquid zones and their stability with respect to perturbations has been investigated numerically.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons

)

Convection; crystal growth; crystal perfection; microgravity; purification;

space processing.

19. SECURITY CLASS

(THIS REPORT)

21. NO. OF PAGES

Unclassified 114

UNCL ASSIFIED

20. SECURITY CLASS

(THIS PAGE)

22. Price

UNCLASSIFIED

$5.50

18. AVAILABILITY Unlimited

d For Official Distribution. Do Not Release to NTIS

Order F rom Sup. of Doc., U.S. Government Printing Office Washington, D.C. 20402, SD Cat. No. CH

[ X Order From National Technical Information Service (NTIS)

Springfield, Virginia 22151

USCOMM.DC 29042-P74
.

'

-