A STUDY OF VACANCIES EN TUNGSTEN
QUENCHED 2N SUPERFLUM HELIUM

Thesis for the Degree of Ph. D.

MECHiGAN STATE UfléVERSéTY

RONALD 503EPH GREPSHQ‘VER
1969

This is to certify that the
thesis entitled

A Study of Vacancies in Tungsten

Quenched in Superfluid Helium.

presented by

Ronald Joseph Gripshover

has been accepted towards fulfillment
of the requirements for

M degree in 5 {C

Betta“.

a Major professor

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ABSTRACT

A STUDY OF VACANCIES IN TUNGSTEN

QUE NCHED IN SUPERFLUID HELIUM

By

Ronald Joseph Gripshover

A system has been constructed which permits the refractory body-
centered-cubic metals to be annealed and quenched in the ultrapure
conditions which exist in and directly above superfluid helium. Studies
were made on vacancies quenched into fine tungsten wires and the subse-
quent annealing away of this quenched-in resistance. To determine the
effective vacancy formation energy, BF, tungsten specimens are quenched
from temperatures between 1500K and 3200K. The quenched-in resis—
tance varies somewhat from specimen to specimen, but the effective
formation energy obtained for the fast quench data is nearly the same for
all specimens and equal to 3. 1i 0.2ev. This data, together with Schultz's
data, establishes both the magnitude of the quenched-in resistance and the

effective formation energy for fast quenched tungsten.

Ronald Joseph Gripshover

By studying how the quenched-in resistance varies with quench speed,
itis shown that the equilibrium vacancy concentration is probably not being
retained even with the fast quench speeds. By extrapolating the data to
infinite quench speed we get an estimate of the equilibrium vacancy resis-
tance. The extrapolation leads to an estimate of Ef = 3. 5i 0.2 ev. The
extrapolated data is also used to test Flynn's theory of vacancy annealing
during the quench. The theory fits the infinite quench speed data, but there
is slightly too much scatter to state definitively that Flynn's theory is
applicable. This theory yields avalue of 1. 4i 0.2 ev for the vacancy motion
energy.

To study the annealing away of the quenched-in resistance, both iso-
chronal and isothermal anneals were performed. There is a single major
isochronal recovery stage in the range 800-1000K in quenched tungsten,
consistent with Stage IV recovery in radiation damage and cold work studies.
This single major recovery stage suggests that there is a single defect
present, presumably the vacancy. The isothermal recovery curve has an
"S" shape suggesting complex annealingprocesses. Isothermal anneals with
change-of—slope measurements yield an effective motion energy of 1. 5i 0.3 ev.
This estimate of the effective motion energy is in good agreement with the
estimate obtained from the Flynn theory analysis.

If we take our "best values" for the effective formation and motion
energies, we obtain a value of about 5 ev (3. 5ev + 1. 58V) for Q. This is
in reasonable agreement with the 5.2 ev estimate of Danneberg. The
maximum Q which would still be consistent with our data is Q N 6 ev.
However, our data do not appear to be consistent with either Q = 6.‘ ev,

or with Elin = 3. 3 ev obtained from recent radiation damage studies.

A STUDY OF VACANCIES IN TUNGSTEN

QUENC HED IN SUPERFLUID HELIUM

By

Ronald Joseph Gripshover

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOC TOR OF PHILOSOPHY

Department of Physics

1969

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ACKNOWLEDGMENTS

I would like to thank my advisor, Dr. Jack Bass, for his invaluable
guidance and assistance during the entire course of this work. I wish to
thank Mr. John Zetts for assisting in taking much of the data and for many
helpful discussions. I am indebted to Dr. J. M. Galligan for kindly supply-
ing us with a very pure 2. 0 mil tungsten specimen.

I would also like to acknowledge the financial support of the Atomic
Energy Commision.

Finally, Iwish to express my deepest appreciation to my wife, Sharon,
whose support and encouragement throughout this work have been invaluable.
I am also deeply indebted to her for performing much of the analysis and

preparation of this manuscript.

ii

TABLE OF CONTENTS

Page

LIST OF TABLES ............................ v
LIST OF FIGURES ........................... vi
I. INTRODUCTION ......................... 1
A. Imperfections in Metals ................ 1

B. Vacancy Formation Energy, E? ............ 1

C. Techniques for Measuring E2] ............. 2

D. Vacancy Motion Energy, Ean ............ . 4

E. Techniques for Measuring Em ............. 5

F. Previous Work on Tungsten ............... 6

G. Previous Work on Molybdenum ........... 10

H. Present Experiment ................. 11

II. QUENCHING TECHNIQUE ................... 14
A. Specimen Preparation ................ 14

B. Quenching Procedure ................. 16

1. Room ’Emperature Measurements ...... 16

2. Lighting Procedure .............. 17

3. Temperature Determination .......... 19

4. Quenching under the Superfluid ........ 20

5. Determination of Quenched—in Resistance. . .21

6. Advantages and Disadvantages ......... 21

III. APPARATUS ........................... 23
A. Specimen Holder .................... 23

B. Cryostat ........................ 25

C. Circuits ........................ 27

1. DC Circuits .................. 29

3. Measuring circuit ............ 29

b. Heating circuit .............. 31

0. Potential circuits .............. 34

2. AC Circuits .................. 38

a. Constant current source ......... 38

b. Amplifier ................. 42

0. AC to DC converter ........... 44

d. Readout devices ............. 47

e. Calibration and evaluation ........ 49

iii

IV. TUNGSTEN QUENCHING RESULTS .............. 51
A. Quench Speed Data .................. 51
B. Fast Quench Tungsten Data .............. 53
C. Dependence of Quenched—in Resistance on
Quench Speed ................... 58
D. Additional Tungsten Data ............... 64
E. Experimental Accuracy of the Quench Data ..... 67
F. Extrapolation ..................... 70
G. Flynn Theory Analysis ................ 73

V. ANNEALING OF DEFECTS QUENCHED INTO TUNGSTEN. . .77

A. Isochronal Anneals .................. .78
B. Isothermal Anneals .................. 85
1. Isothermal Anneal ............... 85

2. Isothermal Anneal with Change-of—
Slope Measurements ........... 87
VI. MOLYBDENU M DATA ...................... 92
VII. SUMMARY ............................ 94
LIST OF REFERENCES ......................... 97
APPENDD( A Significance of the Superfluid ............. 100
APPENDIX B Operational Amplifiers ................ 102

iv

LIST OF TABLES

Table Page
1 Summary of Past Work on Tungsten .......... . ............... 9
2 Summary of Past Work on Molybdenum ...................... 12

LIST OF FIGURES

Figure Page
1. Isochronal Recovery of Irradiated Tungsten .......... 8

2. Simplified Schematic of the capacitance Discharge Circuit . . . 18

3. Specimen Holder ......................... 24
4. Cryostat .............................. 26
5. Block Diagram of Circuits ..................... 28
6. Measuring Circuit ........................ .30
7. Heating Circuit .......................... 32.
8. Quench Speed Control Capacitors ................ .33
9. Capacitor Charging Circuit .................... .35
10. Potential Circuits ......................... 36
11. Block Diagram of the AC Circuits ................ 39
12. AC Constant Current Source ................... 40
13. AC Amplifier ........................... 43
14. Twin T Network .......................... 45
15. AC to DC Converter ....................... 46
16. Diode Output to Resistive and Capacitive Loads ......... 48
17. Quench Speed Graphs ...................... 52

18. Quench Speed versus Quench Temperature for Specimen C
(1.2 mil) ............................. 54

19. Quench Speed versus Quench Temperature for
Specimen A (1. 0 mil) ....................... 55

vi

Figure Page

20. Fast Quench Data for Specimen A (1. 0 mil) .......... 56
21. Fast Quench Data for Specimens A, B, C, and D ....... 59
22. Dependence of Quenched—in Resistance on

Quench Speed for Specimen C ................ .60
23. Dependence of Quenched-in Resistance on

Quench Speed for Specimen B .................. 62
24. Dependence of Quenched—in Resistance on

Quench Speed for Specimen A . ................. 63
25. Dependence of Quenched-in Resistance on Quench

Speed for Specimen A with Constant Subtracted ........ 65
26. Radiation Shield ......................... 69
27. Data Extrapolation for Specimen A ............... 71
28. Extrapolated Infinite Quench Speed Data ............ 72
29. 1/Tq q versus 1/TCl Plots for the Flynn Analysis ...... 75
30. Isochronal Anneals for Specimens Quenched

from 2800K to 3000K ...................... 79
31. Isochronal Anneals for Specimens Quenched from

Temperatures above 3200K ................... 81
32. Second Order Analysis of the Data from Figure 31 ....... 84
33. Isothermal Anneal ........................ 86

34. Isothermal Anneal with Change-of—Slope
Measurements .......................... 89

35. Isothermal Anneal with Change-of—Slope
Measurements .......................... 90

36. Preliminary Molybdenum Data ................. 93

vii

I. INTRODUCTION

A. Imperfections in Metals

 

Many important properties of metals are affected by imperfections in
the ideal lattice. A number of these properties are determined more by
the nature of the imperfections than by the nature of the host crystal.
Some well-known examples are: the electrical conductivity of semicon-
ductors, the low temperature resistivity of metals, atomic diffusion, the
mechanical and plastic properties of solids. To understand these properties,
one must understand the nature and properties of the imperfections involved.

The simplest imperfection is a missing atom, or lattice vacancy.
It is the imperfection which we wish to study. The study of the properties
of the single vacancy standardly focuses upon two quantities, the vacancy

formation energr E}: and the vacancy motion energy El’n'

B. Vacancy Formation Energy, E:
The fractional concentration of single vacancies nV(T) in a pure mater-
ial in thermal equilibrium at a temperature T and zero pressure can be

1_/

written in terms of the vacancy formation energy as

nvn‘) - exp<-Gl’(r)/k'r) - exp(s¥/k)- exp(-El’/kT> (1)
where T is the absolute temperature, k is Boltzman's constant, G}, is
the Gibbs free energy per vacancy, and S}, is the entropy increase per
vacancy. The pressure correction for metals at atmospheric pressure
is negligible. If the equilibrium vacancy concentration could be measured

1

as a function of T, the slope of a plot of ln(nv) versus 1/T would be -E¥/k
Typically, for pure metals, E¥~1 electron volt (ev) and the fractional
vacancy concentration at the melting point is less than 10-3. Hence, to
get an appreciable thermal equilibrium vacancy concentration, the metal must

be at a high temperature.

C. Techniques for Measuring};

 

In theory the vacancy concentration can be studied by measuring any
property of the material which is affected by the presence of vacancies,
such as electrical resistance, specific heat, hardness, length, etc. The
difficulty is that one must know to high accuracy how this property behaves
in the absence of vacancies. This problem was solved by Simmons and
Balluffig/ They showed that for a cubic crystal the vacancy concentration

could be written as

*

R.T. a‘R.T. ( )

where AL(T)/LR. T. is the fractional increase in the macroscopic length of

 

the specimen from room temperature to T and A a(T)/aR.T. is the fractional
increase in the microscopic lattice parameter. By taking this difference,
they showed that all effects not associated with the presence of vacancies are
removed. While this is a direct method for determining the vacancy con-
centration, it has limited accuracy and it is not easily extended to high
temperatures with presently available techniques. Also, since the vacancies

are studied at thermal equilibrium, this method gives no direct information

 

*Strictly speaking, the left hand side of this equation is nV -ni, where ni is
the fractional interstitial concentration. At high temperatures in the metals of
interest, ni is almost surely much less than nv, giving the above result.

about vacancy mobility. To date, this method has been most useful in
establishing the vacancy concentration at the melting point and the validity
of other techniques, such as quenching.

If a specimen is cooled sufficiently rapidly from a high temperature,
most of the vacancies present before the quench are trapped in the material,
allowing them to be studied at lower temperatures. Several methods can
be used to study vacancies at these temperatures: 1) vacancy clusters
canbe viewed by electron microscopyéJZ) individual vacancies, as well as
clusters, can be seen and counted with a field-ion microscopeé/3) length
change between the quenched and unquenched specimen can be measured;
4) changes in the heat output can be observed at temperatures where the
quenched-in resistance begins to anneal away; 5) resistivity increases can
be measured, usually, though not always, at liquid helium temperatures.
The last method is most commonly used because resistances canbe accurately
and precisely measured. Since it is used in this experiment, it will be
described in some detail.

To find the vacancy concentration as a function of temperature with this
method, the specimen is first carefully annealed to get a stable, vacancy—
free, base resistance. This resistance is measured at liquid helium tem-
peratures to keep the normal lattice resistance from masking the vacancy
contribution to the resistance. The specimen is then quenched from a lmown
temperature, and its resistance at helium temperature again measured.
The vacancy concentration is assumed to be proportional to the increase in
resistance. If equation (1) holds, a plot of the legarithm of the resistivity

increase against the inverse quench temperature will yield a straight line

whose slope is the formation energy divided by the Boltzmann constant.

In general, when quenching with a finite quench speed, one does not expect
to retain all the vacancies originally present in thermal equlibrium at the

quench temperature T The data obtained will therefore not be expected

q'
to reproduce equation (1) exactly. When dealing with quench data analyzed
in terms of equation (1) we will speak of an "effective formation energy",
to distinguish the experimentally determined numbers from the "correct"
formation energy.

The quenching technique has inherent in it several potential difficulties.
It assumes that the increase in the base resistance is due solely to quenched-
in vacancies, when, in fact, many things, such as changes in the internal
structure of the specimen (grain boundaries, etc. ), different impurity
contributions, strains in the specimen, etc. , could conceivably contribute
to such aresistance increase. Each vacancy is also assumed to contribute
the same amount to the resistivity increase. If there is vacancy-vacancy
or vacancy-impurity clustering, this may not be true. Also it is assumed
that all of the vacancies present at the quench temperature are quenched-
in. This again may not be correct, especially when the specimen is
quenched from very high temperatures. However if these difficulties are
kept in mind, quenching experiments can be of great value. From them
effective vacancy formation energies can be determined, and by measuring
how the quenched-in resistance varies as a function of quench speed, one

can obtain an estimate for the "correct" vacancy formation energy, as is

described in Section IV of this thesis.

D. Vacancy Motion Energy, EV,n
It is usually assumed that at constant temperature an excess vacancy

concentration will anneal down to the thermal equilibrium concentration

é/

according to the equation
-EVm/kT

33,, : -F(nv) e (3)

dt
where Elln is the vacancy motion energy, and F(nv) is a function of the
vacancy concentration whose form is determined by the details of the
annealing process. Ifsome function of nV is measured, such as the vacancy
resistivityf), it is assumed that

-E;',,/kT
11%: ’F(P) e (33)
d

This assumption introduces some problems; first, pmay not be proportional
to nv, and secondly, this equation assumes that the only mobile entity is the
single vacancy. In a real experiment, small vacancy clusters, vacancy-
impurity complexes, and other entities such as interstitials may also be
mobile, and by their motion to sinks or to large clusters contribute to a
change in resistivity. Therefore, when analyzing annealing data using
equation (3a) we will speak of an "effective motion energy" to distinguish
the experimentally determined quantity from the real motion energy of
single, free vacancies. IfF(nv) is proportionaltonv, the annealing process
is said to be a "first order process" or to involve "first order kinetics".
If F(nv) is proportional to (nv)2, the annealing process is said to involve
"second order kinetics". We shall return to this equation in the analysis

of the annealing data in Sections V and VI.

 

E. Techniques for Measuring E;

Efn can be estimated most directly by studying the annealing of vacancies

from a specimen. There are two annealing procedures generally used to

determine motion energies: isochronal annealing and isothermal annealing.
An isochronal anneal consists in heating the specimen for a fixed time at each
of a series of increasing temperatures until most of the quenched-in resistance
anneals out. This gives the recovery as a function of the annealing tem-
perature. An isothermal anneal consists in heating the specimen to a
fixed temperature to obtain the recovery as a function of the annealing
time. The detailed methods used for the calculation of El’n from annealing
data will be discussed in conjunction with the analysis of the annealing data
in Sections V and VI.

The quenching technique is the best method of producing vacancies in
a metal at low temperatures without producing large concentrations of
other defects. However, point defects (vacancies, interstitials, etc.) can
also be produced by radiation damage and cold working The difficulty with
producing vacancies in these ways is that they represent only a fraction of
the defects present, making it difficult to interpret the annealing data
satisfactorily.

The vacancy motion energy can also be estimated if the vacancy forma-
tion energy E; and the activation energy for self diffusion, Q, are known.
If diffusion takes place by means of single vacancies, which appears to be

§/
the case for many pure metals, it can be shown that Elln = Q - E¥

F. Previous Work on Tungsten

 

There is only one short paper in the literature which reports quantita-

7J
tive quenching results on tungsten. In 1964 Schultz published the results
of quenching a single 1. 2 mil tungsten wire using the superfluid technique.

He obtained an effective vacancy formation energy of 3. 3ev. By extrapolating

his data to the melting point and assuming that nV : 0. 02%;”, where ARq
is the resistance that would be quenched—in during a quench from the melting
point, he obtained a fractional vacancy concentration at the melting point of
1.1 x 10’.4

Vacancies and other defects in tungsten have been investigated by
several experimenters using techniques other than quenching. From
measurements of the high temperature specific heat, Kraftmakher and
Strelkov§/<)btained aformation energy of 3.14ev and a vacancy concentration
of 2. 7 percent at 3600 degrees Kelvin (3600K). In this technique, the low
temperature specific heat is linearly extrapolated to high temperatures and
any deviation of the data from the extrapolation is considered to be due to
vacancies. It is difficult to make this extrapolation accurately, and it is
not likely that all deviations from linearity are due solely to vacancies.
The formation energy they obtained is in reasonable agreement with that
obtained by Schultz, but their vacancy concentrations are two orders of
magnitude greater than Schultz's.

There have also been a number of radiation damage and cold work
experiments with tungsten. On the next page is shown-94. typical isochronal
recovery curve for radiation damaged tungsten. The fractional defect
concentration is plotted as a function of the annealing temperature. The

annealing stages have been labeled according to current practice. During

each stage a particular defect becomes mobile and anneals away.

a—I-ple I
LO~ l
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I

 

 

if

 

 

oloofififisbfismw

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D
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Figure 1: Isochronal Recovery of Irradiated Tungsten

Table 1 is a summary, in chronological order, of the previous work on
tungsten. The remaining comments in this section will be in reference to
this table. First note that there are no estimates for Ern’ or for the temper-
ature at which vacancies become mobile, obtained from annealing studies of
quenched tungsten. Since vacancies are the predominant defect in quenched
tungsten, one would expect that annealing studies of quenched tungsten would
yield the most reliable values for both the temperature at which vacancies
become mobile and Evm. Until the mid-sixties it was thought that vacancies
became mobile in Stage III but recent work, especially the field ion micro-
scopy work of Galligan, et. al., suggests that vacancies are not mobile
until Stage IV. Consequently, the estimates for Ei’n have recently been
increased from 1. 7 ev to about 3 ev, and the estimate of the temperature
at which vacancies become mobile has increased from the 600—700K range
to the 700-1000K range.

The experimental values for Q listed in Table 1 are not mutually con-

sistant. This rules out for the present any estimate of the vacancy motion

 

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10

energr from the relation, EX, = Q - E}, until the value of Q is more firmly
established for tungsten.

There have been only two theoretical papers published concerning the
vacancy formation and motion energies for the body-centered cubic (bcc)
transition metals. In 1963, Gregory published a short paper in which he
used "reasonable" values for the quantities in equations (1) and (3) to
conclude that "it may just be possible to quench in a measurable concen-
tration of lattice vacancies in bcc transition metalszg/ In 1968, from an

elastic theory of metals, Flynn calculated a vacancy motion energy of

2. 8 ev for tungsten.

G. Previous Work on Molybdenum

 

No systematic study of vacancies quenched into molybdenum has been
published. Meakin et.al.g_4_/quenched a molybdenum single crystal from
vacuum into molten indium. They then used electron transmission micro-
scopy to examine what they interpreted as vacancy loops. From the number
of loops they saw, they estimate a fractional vacancy concentration at the
melting point of 5 x 10—5, from which they deduced a formation energy of
2 .4 ev. Nihoulzjjperformed " preliminary quenching experiments" by
breaking the glass envelope of the specimen (immersed in water) when the
specimen reached the desired temperature. He used the results of these
experiments to strengthen his contention that vacancies do not become mobile
until Stage IV in molybdenum. Kraftmakher, again using specific heat
determinationsgfijobtained a formation energy of 2.24 ev and a vacancy
concentration at the melting point of 4. 3 percent. The formation energy

obtained by Kraftmakher is consistant with Meakin's, but the vacancy

concentration is higher by three orders of magnitude.

11

As with the tungsten, there have also been a number of radiation
damage and cold work studies of molybdenum. These results, a recent
calculation of El’n by Flynn, and measurements of Q for molybdenum,

are summarized in Table 2.

H. Present Experiment

 

Vacancies in the common face—centered cubic (fcc) metals, especially
2223/

gold, have been extensively studied. Most of the above techniques have
been applied to these metals. All of the quench techniques, as well as the
Simmons—Balluffi technique,yield values for the vacancy formation energy
which are mutually consist nt. These studies serve to validate the
quenching technique. The fee metals were studied first because they are
much easier to purify and to work with. They can be resistance heated in
air and quenched by plunging them into water or some other suitable liquid,
or by merely turning off the current and allowing them to cool in air.

This is not the case for bcc transition metals. Only recently have
these metals been purified sufficiently for meaiingful quenching experiments
tobeperformed on them. They also contaminate rapidly when heated in air,
making the usual quenching technique of heating in air and plunging into a
suitable liquid inapplicable. In 1963, atechnique was developed byRinderer
and SchultzZ—g/which permits these metals to be annealed and quenched in
the ultrapure conditions which exist in and directly above superfluid helium.
They showed that fine wires could be resistance heated and quenched in
the superfluid. This technique is used in the present experiment, which is

the beginning of a planned systematic study of vacancies quenched into the

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13

large part of the experiment consisted of the design, construction, and testing
of the apparatus to be used. In this thesis the apparatus and technique for
superfluid quenching are described in detail, and new experimental results
on quenched tungsten and molybdenum are presented.

To checkout our apparatus, we first performed fast quenches on tungsten
in an attempt to reproduce Schultz's data. We also studied how the quenched-
in resistance varied as a function of quench speed to investigate vacancy loss
during the quench, and to test Flynn's theory of vacancy annealing during
the quench.

We then performed isochronal anneals on quenched tungsten specimens
to see whether the quenched-in resistance recovered in a single annealing
stage. This data was analyzed using first and second order kinetics to
get an estimate of the effective motion energy for comparison with cold
work and radiation damage experiments. Isothermal anneals with change-
of—slope measurements were performed to get another, presumably more
reliable, estimate of the effective motion energy. Preliminary experiments

on vacancies quenched into molybdenum are also described.

II. QUENCH TECHNIQUE

A. Specimen Preparation

 

The tungsten specimens used for all of the quantitative data reported
here were obtained f1 om Westinghouse Electric Corporation. They were
fabricated from highest purity zone-refined single crystal tungsten rods
which had a guaranteed resistance ratio of at least 30, 000 and typically
60, 000. These rods were drawn to 2, 1. 5, 1.2, and 1.0 mil wires by
Westinghouse.

We first gave the as—received wires a short pre-anneal of ,1/2 to 1
minute at 950-1000K in a vacuum of 10"5 Torr or better, to remove the
"springiness" from them, making them easier to work with. The wires
were then mounted on holders described below. The specimen, which
was about 3 inches long with gauge length of about 1 inch, was supported
by 10 mil platinum current leads. The potential leads were of 1/2 mil
Westinghouse HRE Grade tungsten. For the earliest specimens, the
potential leads were merely spot-welded to the specimen. However, we
had trouble with these spot-welds breaking loose. To avoid this problem,
most of the later specimens for which data were obtained had the potential
leads tightly tied on with the knot spot—welded in place. Occasionally
these leads broke loose from the specimen, in which case they were spot-
welded back in place. For the later annealing studies we used 0. 3 mil
(General Electric #218 EES tungsten) potential leads, spot-welded on,

to minimize temperature variations along the specimen.

14

15

The resistance ratio of the wires at this time was about 10. The
earlier specimens were then annealed above the superfluid helium, within
a few centimeters of the surface. The specimens were resistance heated
to about 3000K for 5-15 minutes, then cooled in about 300 degree steps of
1—2 minutes each until the specimen temperature was down to about 800K,
after which it was quenched. The base resistance was then measured.
This procedure was repeated until the base remained constant to within
one per cent. The total time at 3000K was usually about 1/2 hour. After
this anneal the resistance ratio was in the range 600—650 for the 1. 0 mil
specimens and 700-7 50 for the 1.2 mil specimens. This annealing tech-
nique required several liters of helium per specimen, and constant attention
to keep the specimen within a few contimeters of the superfluid surface.

Several attempts were made to anneal specimens in a vacuum of
5 x 10-6 Torr instead of over the superfluid helium with resultingresis-
tance ratios anywhere between 50 and 550. After a short helium anneal
these ratios increased to the same range as those given above for the
helium anneals. The later tungsten specimens were given a wet hydrogen
anneal. The specimen was placed in a NRC evaporator, which was evac-
uated to about 10-6 Torr. Commercially pure hydrogen was then passed
over distilled water and allowed to bleed into the evaporator so as to main—
tain a pressure of 2 to 3 x 10-4 Torr. The specimen was then resistance
heated to 27 00—2800K for several hours, and cooled in 300 degree steps of
1-5 minutes each until the specimen was down to room temperature.
This procedure yielded resistance ratios in the range 400-650. Short
superfluid helium anneals (5 minutes at 3000K) increased this ratio to the

same range, or slightly higher (up to 850 for some 1.2 mil specimens),

16

than the helium anneals on the earlier specimens. Apparently the hydro-
gen combined with some of the impurities and formed volatile compounds
which were carried away with the hydrogen flow.

The molybdenum specimens were also obtained from Westinghouse.
They were fabricated from highest purity molybdenum and were drawn-to
1. 5 and 1. 1 mil wires. These wires were not given a pre-anneal. Short
anneals above the superfluid (6 minutes) resulted in a stable base resis-
tance, hence the molybdenum specimens were annealed only above the
superfluid. The details of the annealing of the molybdenum specimens

are described in the discussion of the molybdenum results.

B. Quenching Procedure

 

1. Room temmrature Mgasgzemgnts

Before each experiment (and several times during the experiment)
each specimen was placed in a draft-free plexiglass box where its room
temperature resistance was determined by passing a small known current
(typically one milliampere) through the specimen and measuring the voltage
drop across the gauge length. The resistance at 273K was then calculated

from the formula,

R : AR!!! ,
273 1 +C£AT

where R(T) is the resistance at room temperature, AT is the difference
between room temperature and 273K, and CC is the temperature coefficient
of resistivity taken as 4. 5 x 10"3(K)'-1 for timgsten. To cancel the effect
of the specimen geometry from the data, all measured resistances were

divided by R273.

17

2 1° ll' E l

The specimen was placed in the cryostat and lowered to within about
two inches of the surface of the superfluid helium. Since the specimen
was then approximately at liquid helium temperature, its resistance was
several hundred times lower than its room temperature resistance. Large
current was required to put enough energy into the low resistance specimen
to cause it to heat. However, as soon as the specimen started to heat
appreciably, its resistance increased very rapidly. The current then had
to be rapidly decreased, to keep the specimen from burning out.

To do this we discharged a capacitor through the specimen. Figure 2
is a simplified schematic of the circuit used. The power supply was
adjusted to pass a current through the specimen sufficient to keep it heated
once it was lit. Of course, this current was much too small to light the
cold specimen. The 120 microfarad capacitor which had been charged by
the charging circuit, was then discharged through the specimen by closing
81' This impulse current was made high enough to instantaneously heat
the specimen; the heating current already passing through the specimen then
kept it lit. The impulse current could be changed by varying either the
capacitance or the charging voltage across the capacitor. For this ex—
periment the 120 microfarad capacitor was charged to a voltage of 10 to
50 volts depending on the particular specimen. The diode was used to keep
the impulse from being shorted by the power supply. The power supply
must be a constant current source rather than a constant voltage source
because it must supply approximately the same current both when the spec—
imen is heated and when it is cold. The power supply we used was a

Kepco model KS-60, which could operate either in constant voltage or

18

 

 

 

 

 

 

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Figure 2: Simplified Schematic of the Capacitance Discharge Circuit

19

constant current mode. We adjusted the power supply so that it was in
constant current mode until the specimen lit, at which time it automatic-
ally shifted to constant voltage mode. This was done because the spec—
imen's temperature could be controlled more easily by controlling the
voltage across it rather than the current through it.

When a specimen was first lit, it usually had a "hot spot" 1/8 to 1/2
inch long, The voltage across the specimen then had to be slowly and care—
fully increased until the hot spot spread across the whole specimen. It
was much easier to light the specimen after it had once been uniformly
glowing above the superfluid. Presumably this was due either to a sur-
face effect or some local defect which annealed away during the first
superfluid anneal.

3. Temperature determination

After the specimen was uniformly glowing, it was heated to the de-

sired temperature by increasing the voltage across it. The temperature

was determined from the ratio R(T)/R where R(T) is the resistance

273’
at the temperature T and R273 is the resistance of the same specimen at
273K. The resistance ratio versus temperature data of the National
Bureau of Standards3—6/(NBS) was used to determine the temperature. *
When the temperature had to be known accurately, for example,
immediately before a quench, the direct current and voltage were deter-

mined with precision potentiometers. When the temperature of the spec-

imen had to be known only to a few per cent, as for anneals and for

 

37 .
*The data of Langmuir and Jones—(v/vhich Schultz used) do not agree with this
data. They differ by approximately 60 degrees in the range 2000 to 3200K.
We have adjusted Schultz's data to the NBS temperature scale for compar-
ison with our data. We have also changed Schultz's data from resistivity
to resistance using the formula:R(T)/R = (T)/ 7 , where P was
taken to be 5. OSSchm. 273 P ’02 3 273

20

attaining the approximate temperature before a quench, alternating current
(AC) circuits (described in Section III C. 2.) were used to find the resis-

tance ratio (hence temperature).

4, Quenching under the superfluid

The specimenis usuallylit and annealed about an inch above the super-
fluid. For a quench the lit specimen is lowered into the superfluid. If one
watches the specimen pass through the surface one sees essentially nothing
happen; as near as one can tell by eye the temperature of the specimen
doesn't change and the superfluid remains calm. As the specimen is lower—
ed through the surface, a thin gaseous layer of helium forms around the
wire to insulate it from the superfluid. The superfluid conducts the heat
away from the gaseous layer so well that no gas bubbles form around the
specimen. Also, when the specimen passes through the surface of the
superfluid the current changes only slightly, indicating that the energy
dissipated by the specimen is very nearly the same in the superfluid as
it is in the low pressure helium gas just above the surface. During a
typical experiment the pressure above the liquid helium is 1 to 5 Torr.
At these pressures the helium gas is a poor heat conductor, hence the
energy is dissipated almost entirely by radiation. This is confirmed by
the fact that nearly the same energy (within a few per cent) is dissipated
when the specimen is heated to a given temperature inavacuumof 1.0-6Torr,
as when it is heated to the same temperature in the superfluid. The fact
that the liquid helium is a superfluid is not critical;* only the low pressure

above the liquid helium is important to keep the heat loss by gaseous

 

*See Appendix Afor further discussion of the significance of the superfluid.

21

convection currents to a minimum. If the helium pressure rises above a
few centimeters of mercury, the temperature uniformity along the spec-
imen becomes variable and very poor.

After the specimen was immersed in the superfluid, and the quench
temperature determined, the specimen was quenched. For fast quenches,
the heating current was abruptly turned off. Slower quench speeds were
obtained by merely connectinga capacitor in parallel with the specimen and
allowing the capacitor to discharge through the specimen after the power
supply was disconnected. By varying the capacitance we could conveniently

vary the quench speed as needed.

After the specimen was annealed or quenched, its resistance was
measured at liquid helium temperature. The "measuring circuit" (de-
scribed below) was used to pass a known direct current (typically either
1 or 1/2 ampere) through the specimen while it was immersed in liquid
helium. This current was determined by measuring the voltage drop
across a 1 ohm standard resistor in series with the specimen. Both this
voltage and the voltage across the gauge length were measured with pre-
cision potentiometers. For both room temperature and base resistance
measurements, reversing procedures were used to cancel the effects of

any slowly varying thermal voltages.

Was
The superfluid helium quenching technique has several advantages
over conventional quenching techniques. 1) The specimen is in a pure

helium atmosphere at temperatures so low that all other gases are solid.

22

2) Since the specimen is quenched in situ, it is not strained or deformed
as in water quenches. 3) The specimen is quenched directly to liquid

helium temperatures so that the quenched—in resistance can be measured
immediately. 4) The quench speed can be conveniently varied by simply
allowing a capacitor to discharge through the specimen. The main dis-
advantage of the technique is that very fine wires or foils must be used
to keep the quench speed high and to keep the helium consumption low.
Another disadvantage is that thin specimens do not glow uniformly at tem-
peratures lower than about 1500K, limiting use of the technique to high

melting metals.

IH. APPARATUS

A. Specimen Holder

 

The specimen holder is drawn to scale in Figure 3. It consists of
an 1/8 inch thick teflon sheet to which a 20 mil tungsten or galvanized
steel sheet is attached. Teflon is used because it is an electrical insu-
lator and is easy to work with. The specimen is mounted on the metal
sheet so that expansion and contraction of the holder relative to the spec-
imen will be minimized when they are cycled between room temperature
and liquid helium temperature. After annealing, the specimens are quite
brittle, and differential contraction between the specimen and the holder
will break the specimen. The steel holders were much easier to make
than the tungsten holders, hence, steel was used after it was decided that
it worked as well as the tungsten. The large holes in the teflon reduce
the mass of teflon so that less helium is used in cooling the specimen
holder. The 10 mil platinum current leads are passed through a narrow
hole in a nylon screw and threaded teflon post as shown in the figure. A
nylon set screw holds the current lead in place. The specimen is
spot-welded to the 10 mil platinum current leads. The 0.5 mil or
0. 3 mil tungsten potential leads are spot-welded to the 10 mil platinum which
is fastened to the holder under a washer and screw as shown in the figure.
Platinum is used because it is a high melting metal which is easy to work

with and which spot-welds well to tungsten. Copper wire is spot-welded

23

24

teflon post

  
   

8" teflon sheet

10 mil current

lead ’fi

threaded
teflon post a .

10 mil Pt lead

20 mil tungsten sheet
V

set screw

1/2 mil tungsten
potential lead

specimen

Figure 3 Specimen Holder

25

to the current lead and connected to a plug. The four long teflon posts
are used to protect the specimen from hitting the sides of the dewar and to
keep the specimen holderfrom banging around in the dewar as the specimen

is raised and lowered.

B. Cryostat

 

Figure 4 shows the cryostat and associated equipment. The cryostat
is a standard double dewar with a 3-1/ 4 inch diameter helium dewar. The
outer dewar has two 1/2 inch wide viewing strips; the inner dewar has two
1-1/ 4 inch wide viewing strips. Above the dewar is a collar to which the
main helium pump and manometers are connected. The pump is a Stokes
Microvac model 212-H. With this pump we can obtain pressures of about
one Torr above the liquid helium. On top of the collar is a CVC type VCS
41B, four inch diameter clearance, gate valve.

Above the gate valve is the "annealing chamber", which served as an
airlockto get specimens in and out of the partially evacuated dewar. This
chamber was also going to be used to anneal specimens in vacuum or in a
gas, but the NRC evaporator became available and was used instead.

The specimen holder is supported by a 6 foot long, 1/ 2 inch diameter,
thin-walled German silver tube. Current leads consisting of a twisted pair
of #26 gauge insulated copper wire, and potential leads consisting of a twisted
pair of #30 gauge insulated copper wire were passed down the center of this
tube. To minimize thermal voltages in the circuit, the copper leads were
continuous from the plug which mated to that on the specimen holder to a
similar plug at room temperature. During measurements the lower plug
was submerged in liquid helium and the room temperature plug was shield-

ed from drafts by foam rubber. At the top of the tube the leads passed

26

\Kovar lead through
t—l/Z inch quicx connect

 

A/Annealing chamber
(water cooled)

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to vacuum L
pump

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valve

 

 

 

 

 

 

 

 

 

inlets to the
various annealing 3:1 11111151111
gases

to Hg and oil
manometers

 

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aeuum jacket

a

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. aeuum jacket

 

 

itspecimen

liquid helium bath
‘ all i

Figure 4 Cryostat

 

 

 

 

27

through Kovar "lead throughs" to which they were soldered to make
vacuum-tight connections. Near the bottom of the tube two smaller Kovar
"lead throughs" were used to get the leads out of the tube. Again the leads

were soldered to make vacuum-tight connections.

C. Circuits

 

Both alternating current (AC) and direct current (DC) circuits were
used in this experiment. A block diagram of these circuits is shown in
Figure 5. A and B are the current leads to the specimen; C and D are the
potential leads. The DC circuits consist of three parts: 1) the "measuring"
circuits, 2) the "heating" circuit, and 3) the DC potential circuits. The
"measuring" circuit is used to pass a known, constant current through the
specimen when its room temperature or helium temperature resistance is
being determined. The "heating" circuit is used to supply current to heat
the specimen to various temperatures. The DC potential circuits are used
to measure the voltage drop across standard resistors in series with the
specimen to determine the current in the heating and measuring circuits,
and to measure the voltage across the gauge length of the specimen. $1,
a double pole, double throw (DPDT) switch, is used to reverse the current
through the specimen when obtaining the specimen's helium temperature,
or room temperature resistance. 82, another DPDT switch, is used to
connect the specimen to either the heating or measuring circuits.

The AC circuits are connected to the specimen through small capacitors
(about 0. 01 microfarad); hence they have no measurable effect on the DC

circuits. Each of these curcuits will now be discussed in detail.

28

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29

1. DC circuits

 

a. Measuring circuit

Figure 6 is a schematic of the measuring circuit. For the earlier
experiments the power supply was a set of 6 volt storage batteries. Now
a Princeton Applied Research (PAR) model TC 602R power supply is used.
The output voltage of this power supply is more constant than the output of
the batteries.

Rv is a series of resistors and switches used to control the measuring
current. A detailed schematic of RV is shown at the bottom of Figure 6.
By appropriately varying the variable resistors and the switches, Rv is
nearly continuously variable between 1 ohm and 52,221 ohms. The 1 kilohm
and 50kilohm variable resistors are 10-turn helipots The fixed resistors
are used to protect the variable resistors when they are turned to low re-
sistance. With this system we can control a 1 ampere current to five
places.

The 1 ohm standard resistor is a Leeds and Northrup NationalBureau
of Standards type resistance standard #4020B. It is used to measure the
current when the specimen's liquid helium temperature resistance is being
determined.

The 100 ohm standard resistor is a Leeds and Northrup National
Bureau of Standards type resistance standard #4030B, It is used to measure
the low current usedin measuring the room temperature resistance. When-
ever currents above a few milliamperes were used, the 100 ohm standard
was shorted by S3 to avoid damaging it and to decrease the resistance of
the measuring circuits. The standard resistors are both four—terminal
resistors; the potential terminals are connected to the potential circuits as

indicated.

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Figure 6: Measuring Circuit

 

 

 

 

 

 

31
b. Heating circuit

Figure 7 is a schematic of the "heating" circuit. The power supply is
a Kepco model KS- 60M power supply which can operate either as a constant
voltage ora constant current source. For large currents (0.1- 10 amperes)
the 0.001 ohm shunt is used to determine the heating current. For the
lower currents, used in the tungsten annealing experiments, typically a
few hundredhs cf manpere, the 0. 02 ohm shunt is used. Both of these shunts
are four-terminal resistors with their potential terminals connected to the
potential circuits as indicated. They were both accurately calibrated
against the 1 ohm standard in the measuring circuit. Switch S4 is used to
disconnect the 0.02 ohm shunt and other components in this branch from
the circuits when the higher currents are used for other experiments; for
all the experiments reported here this switch was positioned as shown.
The 2 ampere fuse is used to protect the low current branch if S4 is in the
wrong position and high currents are used.

The 4 millihenry inductor and the 0.25 microfarad capacitor form a
parallel tuned circuit to keep the AC circuits from being shorted by the
quench speed capacitors and the power supply. The diode is used to keep
the current impulse used to light the specimen from discharging through
the power supply as discussed above. 85 can be used to short the diode;
for the present experiments it was always left open.

Switch 86 is used to disconnect the power supply and let the quench
speed capacitors discharge through the specimen as described earlier.
Figure 8 is a schematic drawing of the quench speed capacitors. With this
circuit, the capacitance can be varied from zero to 4100 microfarads in

twelve steps.

32

 

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Figure 9 is a schematic drawing of the capacitor charging circuit which
is used to light the specimen. T1 is an isolation transformer; T2 is an
autotransformer. The meter is calibrated to read the charging voltage
(0-100 volts), The 1 kilohm resistor limits the charging current. The 10
kilohm resistor is connected directly across the capacitor terminals to
insure that it discharges when the system is turned off. It also allows the
capacitor to discharge faster if the Variac output voltage is decreased
(i.e., it decreases the time constant RC of the 120 microfarad capacitor).

S is a single pole, single throw, spring loaded open switch used to dis—

7

charge the 120 microfarad capacitor through the specimen.

c. Potential circuits

Figure 10 is a diagram of the potential circuits. Switches S8 and S9
are double pole, twelve position switches made by Grayhill (number 44D30-
02-1-ADJ—N). These switches are connected in parallel so that either of
the potentiometers can be used to read the potential of interest.

PotentiometerA is a Honeywell model 2780 with a Leeds and Northrup
DC Null Detector (No. 9834). Potentiometer B is a Honeywell model 2779
microvolt potentiometer. A photocell galvanometer amplifier (type 5214/
9460) and a secondary galvanometer (type SR21/9461),made by Guildline
Instruments Limited, are used as a null detector for this potentiometer.
The reversing switch precedi ng the microvolt potentiometeris a Honeywell
model 3565 thermal-free reversing switch. It is used to reverse the poten—
tial when the current through the specimen is reversed during room tem-
perature and helium temperature resistance measurements.

The letters "a" through "h" correspond to the same letters on the

standard and shunt resistors in the measuring and heating circuit diagrams;

35

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"i" and " j" connect to the potential leads of the specimen. These account
for the first five positions of the switches. Position 6 reverses the poten-
tial leads to the potentiometers.

When the specimen is heated, the voltage across the gauge length is on
the order of ten volts. Since this is too large for the potentiometers to
measure, the voltage divider shown in the lower part of Figure 10 was
designed and built. Voltages as high as several hundred volts can be mea-
sured with this circuit and a potentiometer capable of reading 1. 5 volts.
For the present experiments switch 812 is always closed, shorting the
500 kilohm resistor and permitting a voltage ratio of ten to be used.

Before using the voltage divider circuit it must be calibrated. This is
done by first opening 810 to disconnect the specimen and closing $11 which
connects the mercury cell into the circuit. Potentiometer A is then switch-
ed to position 9 and the voltage measured. This voltage is then divided by
the desired ratio, potentiometer A is turned to position 7 and the 50 kilohm
helipot adjusted until the potentiometer measures the divided voltage. The
50 kilohm helipot is then looked into place, and the readings checked again.
511 is then opened and S10 closed. The specimen voltage divided by the
ratio is then measured by measuring the potential at position 7.

Potentiometer A is used to measure the voltage across: the 100 ohm
standard for room temperature resistance measurements; the 1 ohm
standard for helium temperature resistance measurements; and the gauge
length of the specimen when it is heated. Potentiometer B is used to
measure the voltage across the gauge length of the specimen for room and
helium temperature resistance measurements, and across the 0.02 ohm

or 0.001 ohm shunt resistor for high temperature resistance measurements.

38

2. AC circuits

 

Since the specimen's temperature is changed by varying the direct
current through it, the DC voltage across the gauge length of the specimen
is not directly proportional to its resistance. For fast quenches the current
is turned off, hence there is no DC signal across the gauge length during
the quench, making it impossible to determine the quench speed directly.
To avoid these difficulties a small, constant AC current of 5000 hertz (Hz)
is passed through the specimen continuously during the experiment. The
AC signal across the gauge length of the specimen is then directly propor-
tional to its resistance, regardless of the direct current flowing through
the specimen. This technique could also be applied to conventional quench—
ing experiments, and would be especially useful for "air" quenches when
the specimen is quenched by turning off the heating current. Figure 11 is
a block diagram of the AC circuit. It consists of four major sections: 1) a
source of constant AC current which is passed through the specimen in
parallel with the direct currents, 2) an AC amplifier, 3) an AC to DC
converter, and 4) read out devices. To assist the reader in understanding
these circuits, a brief description of operational amplifiers is given in

Appendix B.

a. Constant current source

The AC constant current source drives a constant alternating current
of several milliamperes through the specimen independent of the specimen's
resistance. A schematic diagram for this device is shown in Figure 12.
The generator "G" is a Hewlitt Packard model 202C Audio generator. The
operational amplifier is a Philbrick P65AU. It has an open 100p gain of

better than 20, 000 and a maximum output of 2. 2 milliamperes at 22 volts

39

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peak to peak. The diodes are Sylvania 485 silicon diodes; R2 is a ten-turn
helipot; T3 is a filament transformer (117v. to 24v. ).

R1 and R2 form a voltage divider which permits fine control of the
voltage em. Since point '8' is a virtual ground, the current input iin is
ei n/ 1000. As described in AppendixB this current flows through the

primary of the coupling transformer T regardless of the impedence seen

3
by the secondary as long as the operational amplifier is not overloaded (i.e.,
it is a constant current source). T3 is a step—down transformer usedto
match the impedence of the specimen to the operational amplifier. Since
there is a DC potential between the points A and B, whenever a DC current
is flowing through the specimen, a capacitor C1 is placed in series with
the secondary of the transformer to keep it from shorting the specimen.

However, during a quench this capacitor must discharge through the spec-
imen and T3. Hence, to get the fastest quenches and to minimize overload-
ing of the operational amplifier, Cl should be small. On the other hand, C1
shouldbe large enough to pass the AC with little impedence. This problem
is solved by using the series tuned circuit (tuned to the operating frequency)

consisting of C1 and L1 (assuming that T is a "perfect" transformer and

3
that the operational amplifier is "resistive").

The diodes are used to protect the operational amplifier. If the spec-
imen breaks or is disconnected, the operational amplifier will stillitry to
maintaina constant current. This would severely overload the operational
amplifierif it were not for the diodes which conduct when the voltage rises
above a few tenths of a volt. In normal operation the voltage across the

diodes is at most a few millivolts; with a forward bias this small, the

diodes have a very high impedence (essentially infinite).

42

B. Amplifier

 

Figure 13 shows a schematic diagram of the amplifying section of the
AC circuit. T 4 is a United Transformer Company No. H-20 transformer.
It must be capable of operating at 5000Hz, and the resistance in the windings
must be low since it is part of the input resistance of the operational
amplifier. Also, it must be well shielded since it passes small signals and
rather large stray fields are present. The capacitor C3 is used only as an
added safety to keep direct current out of the operational amplifier circuit.
R 4 is the input master for the operational amplifier. The operational
amplifier is a Philbrick P45AU. It has an open loop gain of 300, 000 and
a maximum output of 20 milliamperes at 20 volts peak to peak.

The transformer T4 enables one side of the signal to be grounded. As
above, capacitor C2 is needed to block the direct current from the amp—
lifier circuit. The AC signal is on the order of millivolts, whereas the DC
potential is around ten volts before a quench. At the time of a quench the
capacitor C2 must discharge through the diodes and transformer. Since the
diodes don't "turn on"until there is a few tenths of a volt across them, the
amplifieris overloaded with a pulse more than a hundred times larger than
the signal. For this reason C2 must be kept as small as possible so that
the pulse is over quickly, allowing the AC circuits to follow the resistance
of the specimen as it cools. Many attempts were made to keep most of
this pulse from the amplifier. The most successful was the series tuned

circuit consisting of C2 and L as shown. L2 blocks most of the pulse

2
from the transformer thereby forcing most of it to flow through the diode.
As in the constant current source the voltage across the diodes in normal

operation is only a few millivolts, leaving them with essentially infinite

impedence.

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To decrease noise and to help remove the spurious pulse discussed
above,afrequency-selective network was used for the feedback impedence.
As discussed in Appendix B' the gain of the operational amplifier is _I_tf_ . If.
Rf is small for all frequencies except a narrow band of frequenciesfmdnly
this narrow band will be amplified by the amplifier. A twin T network is
used for this purpose. It is called a twin T network because of the shape
of its schematic (see Figure 14). The resonant frequency is given by

w: 1/RC. The twin T network was made by carefully mountingprecision
components on a terminal strip. A 380 picofarad capacitor was used instead
of a 360 picofarad (2 x 180 picofarad) because a 360 picofarad capacitor
was not immediately available at the time. At the resonant frequency the

impedence of the twin T was about 10 megohms. This network determines

the operating frequency of the AC circuits.

c. AC to DC converter

The output of the amplifying circuit e 0 is a 5000Hz signal whose am-
plitude is proportional to the resistance of the specimen. The circuit shown
in Figure 15 is used to convert this signal to a DC signal which is directly
proportional to the amplitude of the AC signal. T 5 is a 6:1 step-up trans-
former, which steps up the output voltage to the diodes. Since the diodes
are not fully turned on below approximately 1/ 2 volt, non-linear response
results if the AC signal is not much larger than this. The typical output of
the operational amplifier is 10 volts peak to peak. With the 6-fold voltage
increase, the diodes typically rectify 60 volts peak to peak, and the non-
linearity in the first half volt is negligible. The 40 kilohm resistor is
placed before any capacitors so that the diodes see a resistive load. If

the filter capacitor were placed before the major resistance of the load,

45

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47

the diodes would be turned on only a short time with a small voltage drop
across them. See Figure 16 and accompanying discussion.

The capacitors C 4 and C 5 are used to smooth the rectified DC to pro-
vide nearly pure DC for the read out devices. Some care must be taken to
use low values for these capacitors for two reasons: 1) to measure the
quench speeds, the time constant should be less than a few milliseconds
and, 2) the overloading pulse through the amplifier at the beginning of the
quench shouldbe quickly discharged from the capacitors so that the circuits

can again indicate the specimen's resistance.

d. Readout devices

At this stage the signal is a DC voltage which is proportional to the
resistance of the specimen. To "read" this signal four devices (connected
as shown in Figure 11) are used, a DC meter, a digital voltmeter, a strip
chart recorder, and an oscilloscope.

The DC meter is a Weston model 271 which reads full scale at 50
microamperes. The meter shunt resistor RS is chosen to give full scale

deflection when e is nearly at the maximum output of the Operational am—

0
plifier.

The digital voltmeter (Data Technology Corporation model 323) was
acquired after most of the present experiments were finished. Its read—
ings are accurate to within :10. 01 per cent, much better than the DC meter.
After calibration the AC circuits give the resistance ratio in the region of
interest to within a few tenths of a per cent with the digital voltmeter; they
were accurate to only a few per cent with the DC meter. The DC meter is

now used only as a check on the output of the AC circuits.

The recorder is a Honeywell model 153X11V-X-28 strip chart recorder.

48

 

 

 

AC INPUT

 

 

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cycle for resistive loads

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CAPACITANCE LOAD

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short time and then at a much condUCl'A
smaller potential difference AV C "’0!” dISEharges

than for resistive leads. through lOad

Figure 16: Diode Output to Resistive and Capacitive Loads

49

A voltage divider must be used at the recorder input because the recorder
gives full scale deflection for 10 millivolts input. The recorder is used to
record resistance of the specimen as a function of time during a run. The
recorder chart then allows one to have for future reference a permanent
record of: the temperatures at which the specimen was annealed and for
how long it stayed there, the time the specimen was at the quench temper-
ature before a quench was made, and any unexpected changes in the resis-
tance of the specimen, e.g., when a specimen breaks or potential leads
come loose.

The scope is a Tektronix model 531. It is used with a scope camera
to provide pictures of the DC output as a function of time during a quench.
The scope is triggered by the DC voltage change at point B (Figure 5) when
the heating current is turned off. These pictures are then used to deter-
mine the quench speed. The AC circuits were operated at a frequency of
5000Hz so that the electronics will respond sufficiently rapidly to accurately

depict the cooling curve of the specimen during a quench.

e. Calibration and evaluation

The AC circuits must be calibrated each time a different specimen is
used. The calibration is done in the following manner: 1) the specimen is
heated to some intermediate temperature determined by eye; 2) the spec-
imen's resistance is measured with the DC circuits, and divided by its
room temperature resistance to give the resistance ratio; 3) the AC current
through the specimen is adjusted to make the digital voltmeter (or DC
meter) read this ratio. After this calibration, the digital voltmeter (or DC
meter) indicates the resistance ratio of the specimen to within a few tenths

of a (or a few) per cent. The AC circuits make it relatively easy to get

50

the specimen to any desired temperature by minimizing the number of hunt
and test operations necessary to obtain this temperature.

We intend ed to use this circuit in conjunction with other circuits to
allow us to program the power supply to give slower quenches of any de-
sired speed and shape. However, I found that slower quench speeds could
be obtained quite satisfactorily by merely connecting a capacitor in parallel
with the specimen and allowing the capacitor to discharge through the
specimen, as discussed above. If capacitance discharge technique is not
suitable for some future application, the programmed system could still

be tried.

IV. TUNGSTEN QUENCHING RESULTS

A. Qgench Speed Data

 

As stated in Section III C, the AC circuits are used in conjunction with
an oscilloscope and Polaroid camera to determine quench speeds. In
Figure 17 two of these pictures are drawn to scale. The vertical scale is
proportional to the resistance of the specimen; since the resistance of
tungsten is very nearly linear with temperature above room temperature,
this scale is essentially proportional to the temperature of the specimen.
The horizontal scale is proportional to time. A simplified fast quench
speed picture, taken during a quench from 2905K, is shown at the top of
the figure. The time scale is 20 milliseconds per division. The upper
horizontal line is obtained by triggering the scope while the specimen is
at the quench temperature; it marks this temperature on the vertical scale.
The lower line is obtained by triggering the scope after the quench; it gives
a base or zero temperature line. The curve between these lines gives the
temperature of the specimen as a function of time during the quench. The
quench speed is obtained by finding the slope of the first part of this curve
as indicated by the dashed line in the figure. The first part of the curve is
used because the vacancies are much more mobile at the higher temper-
atures, hence most of the vacancies lost during the quench are lost during
this time. The fast quench speed calculations are accurate to about 10 per

cent.

51

(arbITr-arg Scale)

SpeCImen Tamer-ature

52

 

 

 

 

 

l l 1 I l 1 I l l l

 

 

 

 

 

 

 

 

 

I L i i l i l l

 

 

50 mscyflmaon

F i g u r e 17: Quench Speed Graphs

53

A slower quench picture is shown at the bottom of the figure. This
picture was taken during a quench from 2580K with an 1800 microfarad
capacitor connected across the specimen to reduce the quench speed. The
time scale was changed to 50 milliseconds per division. In this picture,
the lines marked AC are equivalent to those in the upper picture. Here
the slope is much easier to obtain because the curve is nearly linear;
hence the slow quench speed determinations are accurate to a few per cent.
The oscilloscope we use has a dual trace. The lines in the picture marked
DC were obtained by using the second trace to monitor the DC voltage across
the specimen. This gives a permanent check on the value of the capacitor
used for a quench, since different capacitors discharge at different rates.
For fast quench speeds there is no DC curve, of course, only an upper DC
and lower DC line. These lines were left out of the upper picture.

Figure 18 illustrates how the quench speeds vary with quench temper-
ature for a 1.2 mil specimen. Notice that the fast quench points have con—
siderable scatter at high quench temperatures. This will be discussed later.

Figure 19 illustrates how the quench speeds vary with quench temper-
ature for a 1. 0 mil specimen. The fast quench speeds rapidly increase
with increasing quench temperature, while the slower quench speeds are
nearly independent of the quench temperature. Again most of the scatter
is in the faster quench speeds. The small numbers by some of the points

will be discussed later.

B. Fast Quench Tungsten Data

 

Figure 20 shows the fast quench speed data obtained for a 1. 0 mil

tungsten specimen. Here the quenched-in resistance is plotted on a

 

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Figure 20: Fast Quench Data for Specimen A (1. 0mil)

57

logarithmic scale as a function of the inverse quench temperature. As
stated above, the quenched-in resistance is divided by R273to cancel the
effect of the specimen geometry. From the equation for the equilibrium
vacancy concentration (equation 1, page 1), this data should fall on a straight

line with slope -E}'/ k if the quenched—in resistance is in fact proportional

to the equilibrium vacancy concentration. The circles are our data and

 

the solid line is a best fit line for Schultz's data (converted to AR/R27 3 and
to our temperature scale). The dashed line is Schultz's data without the
temperature correction.

Our data is in agreement with Schultz's data, except for the low quench
temperature points. It is possible that this discrepency arises from a
small quenched—in resistance, apparently independent of the quench tem-
perature, which should be subtracted from each of the data points to give
the vacancy contribution to the quenched-in resistance. This will be shown
and discussed in Figure 24. The correction does not affect the higher
points because it is only a small fraction of the quenched-in resistance
there.

The scatter at the low quench temperatures is due mostly to insta-
bility in the base resistance. At the higher quench temperatures, the
scatter is probably due to variations in the quench speed. The small
numbers by the high quench temperature points correspond to the numbers
in Figure 19, the quench speeds for this data. There is good correlation
between the quenched—in resistances and the quench speeds. When the
quenched—in resistance is less than average, so is the quench speed, and
vice versa. This correlation was found in all specimens. The originof

the quench speed scatter will be discussed in the next section.

58

Fast quench speed data obtained for two 1. 2 mil and two 1. 0 mil tung-
sten specimens are given in Figure 21. The solid circles are the data
shown in Figure 19. The slopes are nearly the same for each set of data,
so that they give nearly the same effective formation energy, EE’ 2 3120.2 ev.
However, the 1. 2 mil data lie systematically above the 1. 0 mil data. The
most likely explanation for this shift is a systematic change in the tem-
perature scales due to different resistance versus temperature curves
for different specimens. A short paper published in 1962 by Davis:,18_/
indicates that errors of several hundred degrees are possible for tungsten
wires which differ only in trace impurities. The data shifts more at lower
temperatures than at higher temperatures as one would expect from a
temperature shift. (Note in Figure 20 how Schultz's data changed for a
constant temperature shift). If the data for the open circles are system-
atically shifted to the left by 110 degrees and the data for the closed circles
shifted to the left by 70 degrees, they both coincide, to within the scatter
of the data, with the 1. 0 mil data.

Another possible, but less likely, explanation for the data shift is that
different impurities, grain size, etc, cause different vacancy sink den-
sities in different specimens. More or less vacancies would then be lost
to sinks during the quench. This would result in different quenched-in

resistances for different specimens.

C. Dependence of Quenched-in Resistance on @ench Speed
Figure 22 shows how the quenched—in resistance varies with quench
speed for a 1. 2 mil specimen (specimen C). The open circles and triangle

were taken during the first run with this specimen. For some reason they

 

59

 

 

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Figure 22: Dependence of Quenched—in Resistance on Quench Speed for

Specimen C.

61

are systematically higher than the data taken on subsequent runs, hence
they weren't considered when the fast quench speed line was drawn.

The circles are fast quench data with the quench speeds shown in
Figure 18. The data for the triangles were obtained by connecting a 900
microfarad capacitor across the specimen to lower the quench speed. The
other points were obtained by increasing the capacitance as shown, thereby
lowering the quench speed. The dashed line in this figure and the next will
be discussed in Section IV. F.

Figure 23 shows how the quenched-in resistance varies with quench
speed for a 1. 0 mil specimen (specimen B). These data show that the
quenched-in resistance is dramatically affected by the quench speed. In
later sections these data will be used to extrapolate to infinite quench
speeds, and are compared to the predictions of Flynn's theory of vacancy
annealing during a quench. Figure 24 shows similar data for another 1. 0
mil specimen (specimen A). The quench speeds for this data are given in
Figure 19. Data for a larger temperature range is shown here; the pre-
vious data all ended at an inverse quench temperature of 4.3 x 10.-4 This
data shows that the quenched-in resistance does not continue to decrease
with decreasing quench temperature as the vacancy concentration formula
would indicate. Apparently for this specimen there is a small, temperature
independent, contribution to the quenched-in resistance. We suspect that
it is due to some impurity, probably carbon, being quenched into the
lattice. The solubility of carbon in tungsten varies with temperature,

M
reaching a maximum at about 2700K. When the specimen is slowly

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63

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64

the tungsten lattice to various sinks. However, during a quench the carbon
is quenched into the lattice; it doesn't have time to leave the lattice before
the temperature is too low for the carbon to move. This additional carbon
in the lattice would increase the helium temperature resistance of the

specimen. This is the quenched—in resistance which we propose to sub—-
tract from the data for specimen A shown in Figures 20 and 21. We do not
have sufficient data to accurately determine the quenched-in resistance to
be subtracted from the other specimens in Figure 21, butafew low temper-
ature data points on each specimen indicate that the quenched—in resistance
is considerably lower than for specimenA at the lower temperatures. The
three high points in the lower right in Figure 24 are the first two points
of one run and the first point of another run, taken before the base resistance
had stabilized. This illustrates how critical the base resistance is for low
temperature quenches. Figure 25 shows the data of Figure 24 with this
constant quenched-in resistance subtracted from each data point. The
data now decrease nicely into the next decade. The dashed line will be

discussed in Section IV E.

D. Additional Tungsten Data

 

We have some fast quench data not shown in Figure 21. This data
falls into four categories. First, we have data from high purity tungsten
specimens which broke after a few quenches. This data is in general
agreement with the data in Figure 21. Secondly, we have data from 2.0
mil tungsten specimens obtained from the Mate rials Research Corporation.

This was their highest purity (99. 999 per cent) tungsten. However, even

 

 

 

 

 

 

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Specimen A with constant subtracted

66

after extended annealing directly above superfluid helium we could not get
the resistance ratio to rise above 400; with ratios of 250 more typical.
This data has more scatter than that given above. The low temperature
data was a factor of ten higher than that in Figure 21; while the high tem-
perature data was only a factor of three higher. Thirdly, data on some
Westinghouse HRE grade (lamp filament wire) tungsten were also obtained.
After long anneals above the superfluid we obtained ratios of about 200.
This data fell about a factor of two lower than the data in Figure 21, and
again had substantial scatter. Fourthly, we have data on a very pure 2. 0
mil tungsten specimen, kindly given to us by J .M.Galligan. This specimen
was fabricated by carefully etching a high purity single crystal rod down
to 2.0 mil diameter; it was not drawn. After being mounted on its holder,
this specimen had an initial resistance ratio of 2670. A short series of
anneals above the superfluid increased this ratio to over 5000. The data
obtained from the first run with this specimen were in excellent agreement
with the data from specimenA (1.0 mil). The data obtained from the second
run were shifted upward by about 50K, in better agreement with the 1. 2
mil data in Figure 21. The data from this very pure specimen confirms
both the magnitude and the temperature dependence of our other data, and
indicates that the shifts in the quenched-in resistance are present even in
the purest specimens. These additional sets of data suggest that for purity
less than that of our 600 ratio specimens, both the magnitude of the quenched-
in resistance and effective formation energy are dependent on the purity

of the specimen.

67

E. Experimental Accuracy of the Quench Data

The accuracy of the present quench data is limited by four factors:
1) uncertainties in temperature determination, already discussed on page
58; 2) carbon retained in solution as discussed on page 61; 3) changes in
the base resistance, and 4) variations in the quench speeds. All other
sources of error are insignificant compared to these four. Wehave
checked two other possible sources of scatter. We found no difference in
the quenched-in resistance for specimens annealed in hydrogen or helium
Also, there was no difference in the data when it was taken with ascending
quench temperatures as opposed to descendirg quench temperatures.

The accuracy with which the specimen's temperature can be determined
depends upon how accurately its room temperature and high temperature
resistance can be measured, how constant its average temperature remains
when it is hot, how uniform the temperature is along the specimen gauge
length, and finally, how well its resistance ratio at a given temperature T,
R(T)/R273, corresponds to the value on the NBS temperature scale used to
estimate its temperature. The specimen glows uniformly along the gauge
length as far as the eye can tell. The room temperature and high temper—
ature resistance can be measured with a precision of better than 0 .1 per
cent. Continuous readout on a digital voltmeter showed that short term
fluctuations were less than 0.1 per cent of the high temperature resistance,
and that long term variations occurred slowly enough so that they could be
followed on the potentiometers. Taken together these three factors lead to
an uncertainty in the specimen temperature of several degrees Kelvin.
Therefore, the systematic difference in quenched-in resistance observed

between 1. 0 and 1.2 mil diameter specimens must be ascribed to differences

68

in the temperature scales, or to differing sink densities as discussed on
page 58 .

For low temperature quenches the quenched—in resistances are only
a few per cent of the base resistance, hence, if the base resistance varies
by as little as one per cent, large errors are introduced. To minimize
this, the low temperature points were taken only after the base was sta-
bilized as much as possible. If one is very careful, it is possible to keep
the base fairly stable. For example, the base resistance changed only by
0.008 per cent during the measurements of the four lowest temperature.
points in Figure 24. These data were obtained after about fifty higher
temperature points. When the base did change during a set of quench points,
the base to which each quench point was referred was obtained by linearly
interpolating between the initial and final bases, assuming that the base
changed by the same amount for each quench.

After most of the data was taken, we formulated a possible explanation
for much of the quench speed scatter. As stated above, the specimen
cools primarily by radiation during the first part of the quench. For this
reason, the temperature of the surroundings seen by the specimen is
important. If the specimen were in a perfectly reflecting container, its
surroundings would appear to be the same temperature as the specimen
regardless of the temperature of the container walls; consequently, it
would not cool at all by radiation. The dewar used for this experiment
was nearly a "perfectly reflecting container"; it was silvered except for
two 1-1/4 inch slits, and of course, the top of the dewar. The rate at
which energy was radiated, therefore depended on the orientation of the

Specimen with respect to the slits in the dewar, and the depth of the spec-

69

imen in the dewar. When the specimen was perpendicular to the line of
sight as viewed through the slits, it would see more room temperature
than if it were rotated 90 degrees, in which case it would see mostly
its own temperature reflected from the silvered walls.

To test this idea a few quenches were tried with 1.2 mil specimens
in the two extreme orientations described above. The quench from the
first orientation gave a higher quench speed than the second orientation
(by about 10 per cent). To further test this idea, I built a "radiation
shield" out of sheet metal covered with black friction tape. It wentover

the specimen as shown below.
side view
specimen I/\radiation shield

holder
k/ C

Figure 26: Radiation Shield

 

specimen

Several quenches were tried with the radiation shield in place. The results
were inconclusive;a more detailed study will have to be made to determine

if the radiation shield gives faster, more reproducible, quench speeds.
With the radiation shield in place, the helium consumption was roughly
twice as high for a given temperature, indicating that more heat was being

absorbed in the helium rather than radiating out of the dewar.

70

F. Extrapolation

 

To estimate whether our fast quench speed was fast enough to quench
in most of the equilibrium vacancy concentration, we extrapolated our data
to infinite quench speed. For specimen A, quenched-in resistance values
taken from smooth curves drawn through the data of Figure 25 were
plotted on a logarithmic scale as a function of the inverse quench speed
for a series of quench temperatures. The results are shown in Fig-
ure 27. Each curve corresponds to a different inverse quench temper-
ature, as indicated. Each of the four quench speeds shown in Figure 25
contribute one of the four points for the constant quench temperature curves
in Figure 27. The slowest quench speed data in Figure 25 give the points
in the far right of Figure 27. These points are less critical than the others
for the extrapolation, hence the large scatter of these points in Figure 25
has no significant effect on this extrapolation. French curves are used to
carefully extrapolate these curves to zero inverse quench speed (infinite
quench speed).

If this extrapolationis assumed to be valid* the quenched-in resistance
corresponding to infinite quench speed can be read directly from this plot.
The data along the line marked specimen A in Figure 28 show these
quenched—in resistances plotted on a logarithmic scale as a function of
the inverse quench temperature (same plot as the previous data). This
data falls nicely on a straight line with an effective formation energy of
3. 52 0. 2ev. The error bars in Figure 28 represent the maximum possible
errors in the quench speed and the quenched-in resistance. These possible

errors introduce the :I: 0. 2 ev uncertainty.

 

*For a critical discussion of the validity of this technique see reference 43.

ail»

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71

 

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0

Figure 27: Data Extrapolation for Specimen A

JJLJI

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72

 

 

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Figure 28: Extrapolated Infinite Quench Speed Data

1

lllLll

l

L

11111

 

73

The dashedline in this figure is a best fit line to the fast quench speed data
for this specimen.

A similar analysis was also performed on specimen B (1. 0 mil) and on
specimen C (1. 2 mil). Both of these specimens give extrapolation curves
similar to these shown in Figure 27. The lines marked specimen B and
specimenC in Figure 28 are best fit lines to the infinite quench speeds for
those specimens. As in Figure 21, the 1.2 mil data lies above the 1.0 mil
data, but they both give an infinite quench speed effective formation energy
of 3. 5 ev. Again the re is an uncertainty of about :1: O. 2 ev associated with
possible errors in the quench speed and quenched—in resistance values.
We did not get enough low quench speed data on specimenD to perform this

analysis on it.

G. Flynn Theory Analysis

 

We have also attempted to compare our data with the predictions of
Flynn's theorygj of vacancy annealing during a quench. This theory
assumes that the concentration of single vacancies is changed during the
quench only by annihilation of vacancies at fixed sinks (eg. grain boundaries
and dislocations). For quenches in which the temperature decreases linearly
with time, the fraction of vacancies lost during a quench is shown to depend,

to good approximation, only on the product DqTq’Tq, where D is the vacancy

q
diffusion coefficient at the quench temperature Tq, and Tq is the quench
time. For the slower quench speeds the temperature of the specimen
decreases nearly linearly with time as shown in Section IV A. For the

fast quench speeds the temperature does not decrease linearly with

time; but in the high temperature region where one expects most of the

74

vacancies to be lost, a linear approximation is not too bad; this is in fact
the way the quench speeds were calculated.
For a given fractional vacancy loss during the quench, eg., 50 per

cent, the theory leads to the equation,

: Z
DqTqTq ’

where Z is a constant. Since Dq is proportional to exp (-E¥n/kT), the relation

V V
Doexp(—Em/kTq) = Z/Tq'rq

follows. To test this theory, 1n(1/Tq‘Tq)is plotted against l/T if the data

q,
is consistent with the theory, a straight line will result.

The data in Figures 22, 23, and 25 were used to test the theory. The
dashed lines in Figures 22, 23, and 25 are the infinite quench speed lines
obtained in Figure 29. Two separate tests of the theory were made. First,
the fast quench speed data were assumed to represent infinite quench speed
for the Flynn analysis. The upper half of Figure 29 shows plots of
ln(1/Tq‘1;l) versus 1/ Tq resulting from this assumption, for all three sets
of data. The error bars represent possible errors in the quench speed
determinations. These results have considerable scatter, but if a "best
fit" slope is determined, one obtains a' vacancy motion energy of 1.1 :h 0. 4ev

If the fast quench speed effective formation energy is added to this
vacancy motion energy, one obtains a value of 4. 4 ev for Q. This value is
considerably lower than the lowest Q listed in Table 1 (5. 2 ev).

The second test of Flynn's theory was made by using the extrapolated
data in Figure 28 as the infinite quench speed data. The lower half of

Figure 29 shows plots of 1n(1/Tq’7;1) versus l/T for this data, again for

q

 

 

 

 

 

  
 

 

 

 

 

_ l I I I l I T l 7 '
3: oSPEC. A 1
g: OSPECB :
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701

Figure 29: l/Tq'l'q versus l/Tq Plots for the Fjlynn Analysis

76

all three specimens. There are three additional points on this graph be-
cause the fast quench speed data is now included. These results fall
nearly on a straight line, allowing the slope to be determined more pre-
cisely than above. This data yields a vacancy motion energy of 1.4:!: O. 2ev.
If the effective formation and motion energies (3. 5i 0. 2 and 1. 4&0. 2ev)
used for this analysis are added together, a value of 4. 91-0. 4 ev results
for Q. This is consistant with the 5. 2 ev value in Table 1, but consider—
ably lower than the 5. 89 ev and 6. 6 ev values.

We conclude that our data appear tobe generally consistant with Flynn's
theory, but that scatter in the data, and the lack of a clearly established
value for Q make a positive conclusion unwarranted at this time. If our
upperlimit of E}, : 3.7 ev is used in the Flynn analysis, a vacancy motion
energy of 1.9:1: 0.6 ev results. Hence, if the Flynn theory is valid,

it wouldbe difficult to reconcile our data withavalue of Q much over 6.0 ev.

V. ANNEALING OF DEFECTS QUENCHED INTO TUNGSTEN

In addition to measurements of the quenched-in resistance, some
studies were also made of the annealing out of this resistance in order to
obtain information about the mobility of the quenched-in defects. For
these studies the specimen was first quenched in the superfluid as described
above, and the quenched—in resistance measured at the superfluid temper-
ature. The helium pump was then turned off and helium gas bled into the
dewar until the pressure was up to atmospheric pressure. This was done
because it was much easier to get the specimen in and out of the dewar at
atmospheric pressure, and because much less liquid helium was used when
the experiment was done at 4.2K. The helium temperature resistance was
then re-measured, with the specimen about an inch below the liquid sur-
face where the liquid should have been warmed to nearly 4.2K by the warm
helium gas bled in. This was done to obtain a 4.2K resistance reading,
because all of the annealing data was taken at this temperature. The change
in resistance between 1. 3 and 4. 2K was small, typically less than one per
cent of the quenched-in resistance. The specimen was then removed from
the cryostat and placed in the NRC evaporator, which was evacuated to less
than 2 x 10"5 Torr. In this vacuum the specimen was resistance-heated to

the annealing temperatures. After the specimen was heated to the annealing

temperature, its resistance (hence temperature) was held constant to with—

in a few tenths of a per cent.

77

r-i

 

78

A. Isochronal Anneals

 

We first performed isochronal anneals to find the temperature range
in which the quenched-in resistance anneals away. An isochronal anneal
consists in heating the specimen for a fixed time (eg. 5 minutes) at a series
of increasing temperatures until most of the quenched-in resistance anneals
away. Figure 30 shows data obtained from four isochronal anneals on two
different specimens quenched from temperatures in the 2800 to 3000K
range. Here the fraction of the quenched-in resistance remaining is plotted
as a function of the annealing temperature. The solid circles and squares
are data obtained from the first run on each specimen; the open circles
and squares are from the second run on each specimen. These data were
taken using five minute holding times. There are three regions in the
recovery: 1) the low temperature region; 2) the major recovery stage in
the vicinity of 950K, and 3) the high temperature region above the recovery
stage.

The resistance of the specimen always increased when it was cycled
from 4.2K to room temperature and back. However, the resistance usually
returned to the original quenched resistance after the specimens were
taken out of the cryostat and allowed to warm in the room. In all cases the
resistance went back to the original quenched resistance after the first
resistance-heated anneal (650-850). In addition, tests showed that for a
given specimen this increase in resistance upon cycling from 4.2K to room
temperature and back was very nearly the same whether the specimen had
been quenched or not. For these reasons, we do not believe that this
resistance increase is likely to be associated with vacancies. Rather, we

are inclined to attribute it to a surface impurity effect.

79

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80

The major recovery stage at about 950K, in which over half of the
quenched-in resistance anneals away, occurred in each run for each spec-
imen. The data indicated by the solid squares decreased until only a small
fraction of the original quenched—in resistance was left, as one would expect
when simple defects are annealing away. The data for the solid circles
behaved similarly, but terminated abruptly because the specimen broke.
The open circles and squares, the second run for both specimens (the solid
circle specimen was spot-welded together outside the new gauge length),
begin to increase after reaching a minimum of about 45 per cent. After
the resistance of these specimens increased, we tried some quenches from
2000K to 2500K. The quenched-in resistances were one hundred times
higher than the "normal" quenched—in resistances. This strongly suggests
an impurity problem. After a high temperature (above 2700K) quench or
anneal, further quenching gave "normal" quenched-in resistances, showing
that this anomaly can be removed.

Note that the quench temperatures are in the 2800 to 3000K range.
Since the solubility of carbon in tungsten reaches a maximum at about
2700170] quite near the quench temperature, we suspect these increases are
caused by carbon redistributing itselfin the lattice. To test this hypothesis
we performed two more isochronal anneals on a specimen which had been
quenched from over 3200K. At this temperature the carbon solubility
decreases by a factor of three from its value at 2800K.

The results are shown in Figure 31. The holding time was increased
to ten minutes so that the time taken to get to the annealing temperature
was a smaller fraction of the total annealing time, allowing more precise

data to be obtained. The solid circles represent the first run and the open

81

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82

circles the second run. In both runs the quenched-in resistance decreases
to a small fraction of the original quenched-in resistance. This time the
data are very reproducible from one run to the next. The recovery stage
is now centered about 850K, approximately 100 degrees lower than for the
specimens quenched from 2800 to 3000K.

We conclude that most of the resistance quenched into tungsten anneals
away in a single, Sharp recovery stage in the range of 800-1000K. This is
in agreement with Stage IV recovery in radiation damage studies which
Galligan et. fié—O/ showed to be due to vacancy migration.

We have analyzed the data of Figure 31“ using the chemical rate equation

18,20,45 /
frequently used in radiation damage studies. We do not propos e to
justify this analysis; it is used only to compare the motion energy obtained
from our data to those c 31 c ul ated from radiation damage studies. The

42/

chemical rate equation can be written as:
g? - -V exp(-E}’n/kT) (4)

where Pis the quenched-in resistivity, t is time, V is the frequency factor,
Xis the order of the reaction. This is the same as equation (3a) except
that F(o) is assumed to beVP? For an isochronal anneal, T is constant

during a given heat pulse allowing (4) to be integrated directly. Fora

first order process X: 1 and (4) integrates to

mpg/of) = VTexp(-E}’n/k'r). (5)

For a second order process, X : 2 and (4) integrates to

“'1 -".1 ’
pf - Pi : VTexp(-E¥n/kT). (6)

83

Here Pi is the vacancy resistivity at the beginning of the jth_ heating pulse
at temperature Tj , Pf is the vacancy resistivity at the end of this pulse;
’7' is the pulse time. If Pi is assumed to be proportional to ARi, the vacancy

resistance (1. e. , [Oi = KARi), then equations (5) and (6) can be written as

v
lnEéBJJ- VT exp[-Em] (7)
AR ' ‘ kT
v
(ARf)-1 - (ARi)—1 = KVTBXPE%¥1] 18)

AR-

AR

against .1— and the resulting plot examined for linearity. Similarly, to
T

test for a second order process, ln[(ARf)"1 - (ARi)-1] is plotted against

__1_ . We have performed both of these tests on the major recovery stage

T
in Figure 31 using the end of the major stage as the base. The first order

 

respectively. To test for a first order process, ln[ln is plotted

test gives linear results only over one decade for the temperature range
785K to 855K. If an effective motion energy is calculated, a value in the
range of 2. 2 ev results. The second order test shown in Figure 32 gives
nearly linear results in over three decades, covering the temperature
range 785K to 950K. This analysis gives an effective motion energy of
about 2. 5 ev. These effective motion energies lie about midway between
the estimates of 1. 7 ev and 3. 1 ev obtained from radiation damage and
cold work studies for Stage III and Stage IV respectively. As we will
discuss below, isothermal anneals after quenches from about 3200K yield
data which cannot be adequately described by equation (4). We therefore
tend to believe that this second order fit is at least partly accidental, and
that the effective motion energy obtained must be treated with extreme

caution.

84

 

 

 

  
 

 

 

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Figure 32: Second Order Analysis of the Data from Figure 31

85

The data are not consistent with the "first order" kinetics reported
by Galligan w for Stage IV recovery in radiation damaged tungsten.
Either the process by which vacancies are annihilated is different in
radiation damage (1 specimens than in quenched ones, or one of these
analyses obtain agreement with simple kinetics by accident. We believe
these data caution against oversimplifying the interpretation of isochronal
annealing data. To get a more direct estimate of the effective motion

energy, involving less initial assumptions, we performed isothermal

anneal s .

B. Isothermal Anneals

 

1) Isothermal anneal

 

For an isothermal anneal, the specimen is heated to a given temper-
ature and the recovery measured as a function of time. For these anneals,
the resistance of the specimen was measured, with a precision of a few
hundredths of a per cent, 5 to 8 times during a typical 10 minute anneal.
Using these measurements, the temperature was adjusted so that the positive
and negative deviations from the temperature of interest were balanced.
In this manner, the average temperatures from one 10 minute anneal to the
next were held constant to within about 1K.

The circles in Figure 33 represent an isothermal recovery curve for
specimen A annealed at 798K. The specimen was quenched from 3230K to
avoid the impurity problem encountered with the isochronal anneals after
lower quench temperatures. The X's are data from another 1. 0 mil spec-
imen which broke after the fourth data point was obtained. The most impor-

tant point to be made about these two curves is that they are not consistent

86

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87

with equation (4) for any value of x Z 0 . Equation (4) predicts that
the magnitude of the slope of the annealing data in Figure 33, should always
decrease with increasing time (because P decreases with annealing time),
i.e., a curve through the data should always be concave upward. However,
for short annealing times the data curve is definitely concave down, and
only later does the curve go through an inflection point and become concave
W

upward. Similar curves have been seen before, and categorized under

the name, "S" shaped curves. In general, sucha curve is taken as an indica-
tion that the annealing of the vacancies is a complex process, possibly
involving vacancy-vacancy clustering and time varying sink densities.
This "S" shaped curve was also observed in the isothermal anneals with
change-of—slope measurements discussed in the next section. Other than
this "S" shaped curve,the data decrease smoothly again consistent with the
existance of a single major recovery stage. We had some trouble with

temperature uniformity along specimen A during this anneal, hence no

quantitative results were obtained from this data.

gflsothermal anneals with change-of-slope measurements
From equation (3a), we see that if we could measure dP/dt at two

different temperatures T1 and T under conditions where F(P) is the

2’

same, we could obtain the energy of motion from the relation:

1 d .

EV = HEELg/fltgl (9)
m _1_ "1.)

T2 T1

Here 3% is the slope of the T1 isothermal curve at a time to; flz
(it t1
o

 

 

l
k

0
is the slope of the T2 isothermal curve at the same time to;

88

T1 is the first annealing temperature, and T2 is the second annealing tem-

perature. Equation (9) forms the basis for the so—called "change—of—slope"
_5_/
technique introduced by Bauerle and Koehler. In this technique, one begins

an isothermal anneal at the temperature T1 and obtains enough points to

accurately determine the slope of the recovery curve ~39 1. At time to,
to

the annealing temperature is then changed to T2 which changes the rate of

 

annealing. Enough points are taken at the new annealing temperature T2

to enable one to extrapolate the data back to the point to, and thereby, ob—

 

tain the slope £61 2. All of the quantities on the right side of equation (9) L
are now known allowing the effective motion energy to be obtained.

After the recovery curve is determined sufficiently to obtain its slope
at the second annealing temperature, the annealing temperature can again
be changed and the above process repeated to obtain another estimate of the
motion energy. This technique has the advantage that only equation (3a) is
assumed to hold. The additional restrictions required to obtain equation (4)
are not necessary for this analysis.

Figures 34 and 35 show the results of such measurements made on two
independent 1.0 mil specimens. These specimens had 0. 3 mil , potential
leads spot—welded on to minimize temperature non-uniformities; with these
leads, no temperature variation was visible along the gauge length when
the specimen was heated in vacuum until it barely glowed in a darkened
room. Both of these sets of data also have the "S" shape discussed in
connection with the isothermal anneals on page 87. The annealing temper—
atures and the effective motion energy calculated for each change-of—slope
point are marked in the figures. For these experiments to give meaning-

ful results, the data must have very little scatter, and the curve connecting

 

 

E3

02- —

0.1- specs (1.0 mil)

 

 

 

O_'—‘2'oJ 46' 5'51 8'6l 1501120
TIME (MlNUTES)—>

Figure 34: Isothermal Anneal with Change-of—Slope Measurements

 

O.l

 

SPEC H (1.01m)

 

 

 

O1

 

l l l l l l l
265—4—‘4'0 so ' 80 70750 120

TIME (M1NUTES)——-

Figure 35: Isothermal Anneal with Change—of-Slope Measurements

91

the data points must be carefully drawn so that the slopes can be accurately
determined. The curves shown in Figures 34 and 35 were drawn through
the data points with the aid of French curves. A mirror placed at the point
of interest was positioned to make the curve and its image appear continuous.
A line was drawn along the edge of the mirror giving the normal to the

curve at the change of slope point. The normal to this line then gave the
slope of the curve. In this manner, the slopes could be obtained accurately
to a few per cent, except possibly where there is extreme. curvature.

The data give an effective motion energy of 1. 5:1: 0. 3 ev. It should be
noted that the effective motion energies calculated here are from specimens
which were quenched from very high temperatures, and only the upper
two-thirds of the recovery curve was used.

The effective motion energy determined here is in good agreement
with the motion energy (1. 4i- 0. 2 ev) obtained above with the Flynn theory
analysis. However, these effective motion energies are much lower than
those obtained for Stage IV radiation damage studies (see Table 1). They
are even somewhat lower than the 1.7 ev motion energies obtained for
Stage III.

While the agreement on the vacancy motion energy between the Flynn
analysis and change-of—slope analysis is suggestive, we do not believe that

5411/

it shouldbe taken ho seriously yet. In several other metals effective

motion energies measured after high temperature quenches are found to be
substantially lower than the single vacancy migration energy, presumably
reflecting the effects of mobile vacancy-vacancy complexes. The "S" shaped
isothermal curve suggests complexities of this type are likely to be found in
the annealing of tungsten. It is likely that careful annealing studies from a
series of quench temperatures will be necessary to obtain a satisfactory

understanding of vacancy annealing in tungsten.

VI. MOLYBDE NUM

We have annealed and quenched molybdenum using the superfluid
technique. A 1. 5 mil specimen and a 1.1 mil specimen were annealed
for six minutes at about 2350K and cooled in steps, resulting in resistance
ratios of 524 and 750 respectively. Further annealing and quenching in-
creased these ratios to 620 and 870. Surprisingly, the thinner wire had
the larger resistance ratio.

Preliminary quench data for these specimens are shown in Figure 20.
The 1.5 mil data is three orders of magnitude higher than the 1.1 mil data.
Also the 1. 5 mil data is not very temperature-dependent; suggesting that
something besides vacancies are being quenched into this specimen. The
data for the 1. 1mil specimen appears more likely to be due to vacancies.
However, the effective formation energy is only about 1.1 ev, which is

w 2_6/
half of the value estimated by Meakin and Kraftmakher. These data are
very preliminary and are reported primarily to give an indication of the

difficulties which are likely tobe encountered in a systematic study of

vacancies quenched into molybdenum.

92

93

 

 

 

 

     
  

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Figure 36: Preliminary Molybdenum Data

VII. SUMMARY

We have described an apparatus and technique for superflu1d quenching,
and have used this system to study vacancies quenched into fine tungsten
wires. We have demonstrated that the quench speeds obtained are fast
enough to allow studies of the dependence of quenched-in resistance on
quench speed. We have found that the quenched-in resistance varies some-
what from specimen to specimen, but that the effective formation energy
determined for the fast quench data is nearly the same for all specimens
and equal to 3. 1:}: 0.2 ev. Both the magnitude of the data and the effective
formation energies are in satisfactory agreement with a similar study by
Schultz. By studying how the quenched-in resistance varies with quench
speed, we have shown that the equilibrium vacancy concentration is proba—
bly not being retained even with the fastest quench speeds. By extrapo—
lating our data to infinite quench speed we can get an estimate for the
vacancy formation energy, BF. This extrapolation leads to the value
BF: 3. 5:1: 0.2 ev. We have also used this extrapolated data to test Flynn's
theory of vacancy annealing during the quench. We find that the theory fits
the infinite quench speed data, butttwe believe our data has slightly too
much scatter to state definitively that Flynn's theory is applicable. As-
suming El.” : 3. 5 ev, this theory yields avalue of 1. 4:1: 0.2 ev for the vacancy
motion energy. If the maximum value of 3. 7 ev is used, a motion energy

of 1. 9i 0.6 ev results.

94

 

95

Isochronal and isothermal studies were made of the annealing away of
the quenched-in resistance. Isochronal anneals were performed on spec—
imens quenched from temperatures in the ranges 2800-3000K and above
3200K. There is a Single major lSOChI‘Ol‘lal recovery stage in the temper-
ature range 800—1000K, which is consistent with the Stage IV recovery in
radiation damage studies. This single recovery stage, in which most of
the quenched-in resistance anneals away, suggests that there is a Single
type of defect present, presumably the vacancy. The isothermal anneals
were made on specimens quenched from above 3200K. These recovery
curves have an "S" shape suggesting that the annealing process is complex
and does not obey a simple chemical rate equation. Change-of—slope mea-
surements yield effeCtive motion energies of 1. 5:1: 0.3 ev, in agreement
with the value obtained from the Flynn analysis. Although this agreement
is suggestive, it should be treated with caution. Previous experience
with effective motion energies measured after high temperature quenches
suggests that they are often somewhat lower than the single vacancy
motion energies.

If we take our "best values" for the vacancy formation and motion
energies, we obtain a value of about 5 ev for Q. This is consistent with the
lower value of Q reported in recent literature. The maximum value of Q
which would still be consistant with our data is Q 29 6 ev. However, our
data do not appear tobe consistent with either Q = 6. 9 ev,or with Bin: 3. 3 ev
obtained from recent radiation damage studies.

During the progress of this experiment, a number of interesting pro-
blems were uncovered which require further study. These problems will

merely be liSted here: 1) possible deviations from specimen to specimen

 

96

of the resistance versus temperature characteristics for tungsten; 2) resis-
tance increase when a tungsten specimen is cycled from 4. 2K to room
temperature and back; 3) increase in resistance during isochronal anneals
after quenches in the range of 2800 to 3000K; 4) possible complex annealing
processes suggested by the "S" shaped curve; 5) superfluid bubbling

phenomena; 6) problems involved in molybdenum quenching.

LIST OF RE FERE NCES

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Schultz, H. Z. Naturforschg. 143, 361 (1959)
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APPE NDICES

100

APPENDIX 'A

Significance of the Superfluid

The fact that superfluid is not essential for this experiment was dis-
covered accidentally during a test of the "radiation shield" described in
Section IV E. The specimen was at a high temperature (about 3000K) in
the superfluid; after 2 to 3 minutes the liquid around the specimen began
to bubble indicating that the liquid near the specimen was no longer super-
fluid even though the pressure was still in the 1-5 Torr range. Further
tests indicate that bubbles form around the specimen and float to the top
until the specimen is about 3/ 4 inch below the surface. If the specimen is
lowered further, bubbles seem to form along the specimen, but do not
leave it to rise to the surface. If the specimen is lowered still further
(below about 1-1/ 2 inch), these bubbles form only at the ends of the spec-
imen. They also appear to be smaller, and again do not float away from
the specimen. If the specimen is placed slightly below the depth where
the bubbles rise to the surface, there seems to be "pulsation", the bubbles
rise to the surface for a while, then stop and start again. The period of
these "pulsations" is of the order of a second.

During all of these tests, as nearly as one can tell by eye, neither the
average temperature nor the temperature uniformity of the specimen

changed significantly. This fact was verified by direct readout of the spec—

101

imen resistance on a digital voltmeter. This is direct proof that bubble
formation around the specimen does not burn it out, or ruin the experiment.
This implies that the superfluid is not necessary.

We believe that the superfluid around the specimen turns normal be-
cause the radiation shield restricts the flow of the superfluid. This
causes the superfluid to reach its critical velocity and turn normal when it
passes through the holes in the radiation shield. More study of this phe—

nomena is necessary before it can be adequately explained.

102

APPENDIX B

Operational Amplifiers

To assist the reader in understanding the AC circuits, a brief description
of operational amplifiers is given. The symbol for an operational amplifier
em :D— e.

The principal characteristics of a typical operational amplifier are high input
impedence, high gain (100, 000), and good frequency response. The ope rational
amplifier alone is no better thana conventional amplifier. The addition of the
negative-feedback path (control loop) makes the amplifier circuit stable and
suitable for accurate control. A simple operational feedback circuit is

shown below.

  

 

o
r _L 8°
The feedback impedence Rf ?connects the output of thEamplifier to the input.
The amplifier' 3 very high gain and phase reversal makes point 'S' (the summing
point)_a "virtual ground',’ i.e., it is ideally at ground potential but not
connected to the ground. Hence the input currrent iin is just ein/Rin.
Since the voltage at 'S' is zero we see that the output voltage is just 'Rfiin
Substituting for iin from above, gives the important result, 60 : -Rf/Rin) em.
That is, the output voltage is directly proportional to the input voltage with

the gain given by Rf/Rin Since these impedences can be made quite stable,

103

the gain of the operational amplifier can be made very constant. This is
important in the AC amplifier system described in Section III C 2).

For a constant current source, the load is put in the place of R f’ The
output voltage will then always adjust itself so that the current through the

load is ein/Rin as described above. This will remain true so long as the

operational amplifier is not overloaded.

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