Torsion pendulum studies of 4He in nanopores

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Torsion pendulum studies of 4He in nanopores
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Thesis (Ph. D.)--University of Florida, 1995.
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Includes bibliographical references (leaves 146-149).
Statement of Responsibility:
by Satoru Miyamoto.
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Typescript.
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Vita.
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In title "Torsion...4He...", 4 is a superscript.

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Full Text












TORSION PENDULUM STUDIES OF "He IN NANOPORES


By
SATORU MIYAMOTO






















A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

1995


UNIVERSITY OF FLORIDA LIBRARIES
















ACKNOWLEDGEMENTS


The author would like to thank his adviser, Yasumasa Takano for his patience and

open-mindedness which have made the time he has spent working for him very enjoyable

and interesting.

Thanks also go to Professors G. Ihas, J. Graybeal, C. Hooper, and M. Muga for serv-

ing on the author's supervisory committee. In addition, the author wishes to express his

gratitude to Professors G. Ihas, S. Nagler and N. Sullivan for providing pieces of equip-

ment which were crucial to this work and to Professor M. Meisel for the ruthenium oxide

thermometers.

Thanks go to Bob Fowler and co-workers in the machine shop for providing a number

of finely machined pieces for this work. Thanks also go to G. Labbe and B. Lothrop for

technical support and supply of liquid helium. The author also wishes to express gratitude

to the staff of the electronics shop for their support.

Special thanks go to the graduate students of the low temperature group for their help.

The author would like to thank Ray Strubinger and Miho Shraishi for assistance in

preparing the dissertation.













TABLE OF CONTENTS




ACKNOWLEDGEMENTS ...................... ......... ii

LIST OF FIGURES .................. .................. vi

LIST OF TABLES ....... .. .............. ... ......... vii

ABSTRACT ........... ......... ....... ... .......... viii

1 INTRODUCTION ................. ................. 1

1.1 Superfluid "He ................................... 1
1.2 Kosterlitz-Thouless Theory for Two Dimensional Superfluidity ...... 6
1.3 Superfluidity of Thin 4He Films in Porous Vycor Glass ...... 17
1.4 4He Adsorbed in Zeolite .... ........................ 17
1.5 4He Adsorbed in Porous Silica with a 25 A Pore Diameter .......... 21

2 EXPERIMENTAL TECHNIQUES AND CRYOSTAT ............... .22

2.1 Torsion Pendulum ............................... 22
2.2 Thermometry ...... ...... ..................... 33
2.3 Four-Wire Resistance Bridge ................. ........ 35
2.4 Data Acquisition .......................... ..... .. 41
2.5 Cryostat ..... ... .. .. .. .. ..... .... .. ... .. 45
2.6 Sample Gas-Handling System .... .............. ........ 53

3 CHABAZITE DEHYDRATION TECHNIQUE ....... ........... 58

3.1 Chabazite ..... ..... ...... ..................... 59
3.2 Vacuum Dehydration of Chabazite and Nitrogen Adsorption Isotherm. .. 62
3.3 High Pressure Dehydration of Chabazite ............... ... 70

4 TORSION PENDULUM EXPERIMENT ON 4HE ADSORBED IN CHABAZITE 82

4.1 Sample Cell .................... ............... 82
4.2 Results and Analysis ............................... 84
4.3 Conclusions .................... ............... 84

5 TORSIONAL PENDULUM EXPERIMENT ON 4He ADSORBED IN 25 A DIAM-
ETER PORES OF SILICA ........ .. ... ................... 90








5.1 Sam ple Cells .................... ......... ...... .. 90
5.2 Results and Discussions ....... ................. ..... 92
5.3 Conclusions ........ ..... .. ................... 114

A HELIUM VAPOR PRESSURE THERMOMETER ..... .... .. 117


B TORSION PENDULUM EXPERIMENT USING CHABAZITE CRYSTAL C16 123

B.1 Results for the Torsion Pendulum Containing Chabazite ........... 123
B.2 Results for the Torsion Pendulum with an Empty Cell (A Control Experiment)133
B.3 Analysis and Conclusions ...... ......................... 136
B.4 Conclusions .................................... 144


REFERENCES ....................................... 146















LIST OF FIGURES


1.1 Andronikashvili's torsional pendulum . ... 2
1.2 Superfluid density ...... ... ... .. .......... ...... ... 4
1.3 Dispersion curve of superfluid ......................... 5
1.4 Two-dimensional superfluid density . . 8
1.5 Vortex placed in a uniform external flow . . ... 10
1.6 Solutions of the Kosterlitz-Thouless recursion equation. . 16
1.7 Superfluidity density of 4He films in porous Vycor glass . ... 18

2.1 Torsion pendulum ... ....... .... ... .. ... .. ..... 23
2.2 Schematic diagram of the feedback circuit . . ... 25
2.3 Construction of the electrodes ......... ... ............... 27
2.4 Circuit diagram of the phase shifter . . 29
2.5 Circuit diagram of the zero crossing detector . . 30
2.6 Calibration of the ruthenium oxide thermometer Bk5pl04 34
2.7 Calibration of the ruthenium oxide thermometer Bk6p93 . ... 36
2.8 Circuit diagram of the Anderson bridge . ...... 37
2.9 Equivalent circuit for the four-wire bridge . . ... 39
2.10 Phase shift caused by the ferrite core . . ... 42
2.11 Ratio of the error signal to the resistance difference . ... 44
2.12 Dilution refrigerator ............ ....... ............. 47
2.13 Thermal anchoring box for the coaxial cables . ... 54
2.14 Gas-handling system ................... ........ ... .. 55

3.1 Cage structure of chabazite ...... ....... ...... ....... 60
3.2 Framework structure of chabazite . ... ... 61
3.3 Adsorption isotherm of nitrogen at 77 K on chabazite . ... 63
3.4 Heating curves of vacuum dehydration . ..... 65
3.5 Home-made furnace and the power controller . ..... 68
3.6 Ramp circuit ................... ....... ........ 69
3.7 High pressure furnace using a MS-17 reactor . . 71
3.8 High pressure furnace made from a 1/2 inch stainless steel tube ... 75
3.9 Heating curves for chabazite dehydration runs C3 and C4 . 79

4.1 Torsion pendulum containing a chabazite crystal. . 83
4.2 Resonance curve of the torsional pendulum . ... 85
4.3 Temperature dependence of the resonant frequency . ... 86
4.4 Temperature dependence of the amplitude . ..... 87
4.5 4He-loading sensitivity ................... ........... 88








5.1 Adsorption isotherm ............ ................... 91
5.2 Torsional pendulum for the porous silica experiment . 93
5.3 Frequency curves for porous silica . ..... ....... 95
5.4 Amplitude for porous silica ........................... 96
5.5 1-X for various amounts of adsorbed 4He . ...... 97
5.6 Frequency shift for coverages from 6.75 mmol to 7.80 mmol ... 99
5.7 Frequency shift for 8.01 mmol to 8.20 mmol . . 100
5.8 Critical temperature ......................... ..... 102
5.9 Fitting parameter for aT2 + 3T dependence of the frequency data at low
temperatures ...................... ....... ....... 104
5.10 Phonon velocity ... .. .......... ................... 106
5.11 Superfluid density calculated by the theory of Kotsubo and Williams. 110
5.12 Superfluid density for various film thicknesses . ... 111
5.13 Fitting to the superfluid density at 7.60 mmol and 7.80 mmol ... 113
5.14 Core radius obtained by Cho and Kotsubo . . 115

A.1 Helium vapor pressure thermometer . ...... .. ...... 119
A.2 Capacitance of the vapor pressure thermometer as a function of pressure at
77 K ........................................ 120
A.3 Circuit diagram of the capacitance bridge for the vapor-pressure thermometer122

B.1 Frequency of the torsion pendulum containing chabazite crystal C16. .... 124
B.2 Frequency as a function of temperature for various amounts of 4He. .... 125
B.3 Amplitude of the torsional pendulum containing chabazite crystal ...... 126
B.4 History dependence of the frequency anomaly . ... 127
B.5 Size of the frequency anomaly for various amounts of He .. 129
B.6 Frequency for the amounts of 4He larger than 2.32 mmol. ... 130
B.7 Adsorption isotherm of 4He at 4.2 K on the chabazite crystal ... 132
B.8 Frequency of the torsional pendulum with an empty cell . ... 135
B.9 Frequency of the floppy mode of the torsional pendulum with an empty cell 137
B.10 Amount of liquid 4He escaping from the cell . ... 138
B.11 fo adT as a function of temperature for superfluid He . ... 140
B.12 Onset temperature of the frequency anomaly . ... 141
B.13 Size of the frequency anomaly for the floppy mode and the torsional mode 143
















LIST OF TABLES


Resonance frequency and Q factor . . .
Specification of ferrite cores .....................
Resistance value of thermometers . . .
Volume of each part of the refrigerator system . .
Calibration coefficients for the Paroscientific pressure transducer


. .. 32
.. .... 41
. 51
. ..... 52
. ..... 56


Summary of vacuum dehydration .................. ......... 66
Summary of run H .................. .............. 67
Summary of Supercritical Dehydration . ..... 72
Summary of high pressure dehydration in the 1/2 inch furnace 74
Summary of high-pressure dehydration in the 9/16 inch furnace ... 78

Results of nonlinear least square fitting . . 94
Coherence length obtained from superfluid density near T .. 101
Fitting parameters with the Kotsubo-Williams theory . ... 112















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy


TORSION PENDULUM STUDIES OF 4He IN NANOPORES


By


Satoru Miyamoto


December 1995



Chairman: Professor Yasumasa Takano
Major Department: Physics


In this dissertation, experimental results are presented on the torsion pendulum studies

of 4He adsorbed in chabazite, whose pore is 13 A in diameter, and in silica with 25 A diam-

eter pores. The objective of this work was to search for superfluidity in extremely confined

4He.

A novel technique for dehydrating chabazite crystals has been developed for this work.

As we found out, chabazite crystals of millimeter sizes cannot be dehydrated simply by

heating them in vacuum as commonly done for zeolite powders, since the heating results in

pulverization of the crystals. To dehydrate the crystals without damage, a high pressure

dehydration technique has been developed. In this method, chabazite crystals are heated

in a high pressure helium atmosphere at pressures over 10,000 psi in a furnace attached to

a sorption pump filled with activated charcoal. The pump removes water selectively under








high pressure. Using a crystal prepared with this method, the experiment down to 100

mK found no superfluidity in 4He adsorbed in chabazite crystal with the torsion pendulum

technique.

In porous silica, superfluid transition was observed with the transition temperature

ranging from 0.12 K to 0.82 K depending on the 4He coverage. Near the full pore coverage,

the temperature dependence of the superfluid density was found to arise entirely from the

phonon excitation, with no evidence for other mechanisms such as vortex-pair unbinding.

The superfluid density for lower 4He coverages are compared with the Kosterlitz-Thouless

theory adopted by Kotsubo and Williams for a small sphere. The fitting parameters ob-

tained from the comparison are examined to address the applicability of the Kosterlitz-

Thouless theory to 4He films in extreme confinement.














CHAPTER 1
INTRODUCTION


1.1 Superfluid He

4He is believed to remain liquid even at T = 0 due to the small mass and the weakness of

the attractive force between the atoms. Liquid 4He becomes a superfluid when it is cooled

to Tx = 2.17 K. Although the superfluid has been known for decades, the microscopic

mechanism responsible for the transition has not yet been fully understood.


Andronikashvili's experiment. In 1946, Andronikashvili [1] confirmed the validity of

the two-fluid model [2, 3, 4] in his experiment, which measured the temperature dependence

of the superfluid density of 4He using a torsional pendulum. This device consisted of a stack

of equally spaced aluminum disks, which were attached to a phosphor bronze wire and

immersed in liquid 4He as illustrated in Fig. 1.1. The gap between the disks were chosen

to be smaller than the viscous penetration depth /277n,/wp, of the normal component of

superfluid 4He, so that the normal component between the disks follows nearly completely

the motion of the disks. Here rn, and p, are the viscosity and the density of the normal

component. The resonance frequency w of the torsional oscillation of the pendulum is

a function of the rigidity of the wire and the total moment of inertia of the pendulum,

including the liquid which moves with the disks. Above TX, where 4He is a normal liquid,

the entire liquid between the disks moves with the pendulum. Below TA, the resonance

frequency increases as the superfluid component, which has no viscosity, decouples from





































Liquid He


Phosphor bronze wire


Aluminum disks


Figure 1.1. Andronikashvili's torsional pendulum [1].


I








the motion of the pendulum. The frequency change is proportional to the superfluid density

p, as will be discussed in Section 2.1. The temperature dependence of p, measured by this

method is shown in Fig. 1.2, in which p, has been normalized by the total density p of

liquid 4He.


Landau's theory. In 1941, Landau [2, 3] predicted that the dispersion curve of ele-

mentary excitations in superfluid 4He should be linear at low energies and deviate at higher

energies from the linear relation, becoming a parabola with a local minimum at a finite

energy A and momentum po. The excitations in the linear region are called phonons and

those in the parabolic region are called rotons. Figure 1.3 shows the dispersion curve mea-

sured by Henshaw and Woods [6] in 1961 using neutron scattering. Their experiment, as

well as those of others, agrees with Landau's prediction.

When the velocity of the superfluid relative to a wall exceeds the critical velocity, which

is determined as the slope of the line drawn from the origin to the tangent of the parabola

near its minimum, the flow can lose its kinetic energy through roton creation. The Landau

critical velocity for roton creation is 58 m/sec. Below the critical velocity, the flow does

not dissipate any energy. An ideal gas which consists of free particles has a dispersion

E = p2/2m. Since the critical velocity is zero in this case, macroscopic flow of the ideal

gas loses kinetic energy at any velocity. Therefore, the ideal gas cannot be a superfluid.

In Landau's picture, the dispersion curve with a non-zero slope at p = 0 is crucial for the

occurrence of superfluidity. Bose-Einstein condensation has no direct role in superfluidity,

according to Landau.










































Temperature (K)


Figure 1.2. Superfluid density and the normal-fluid density of superfluid 4He as a function
of temperature, after Tilley and Tilley [5].




















38-

36-

34- TEMPERATURE 1.12*K
NEUTRON WAVELENGTH 4.04 A
32

30-
FREE PARTICLE--

26-
w
1.. Z6 --

<3 24-
I
W 22-/ -



/


/



4-


a- N.V.P.

6-- -

4,

2 --

0 02 04 06 1.0 L2 1.4 L6 L8 2 2.2 2.4 26 28 30
MOMENTUM CHANGE 0 (A")



Figure 1.3. Dispersion curve of elementary excitations in superfluid 4He, after Henshaw
and Woods [6].








In Landau's theory, the normal fluid density below T\ is


1 dn
Pn = p2d (1.1)
P

where p is the momentum of each elementary excitation, either a phonon or a roton, and

n = n(e, T) is the number density at energy E. The number density of phonons follows

Bose-Einstein statistics. Boltzmann statistics is appropriate for the rotons because the

Boltzmann factor exp(-A/ksT) is more than 50 at temperatures below TA for the roton

energy A = 8.65 K.

nph = 9.60r hc ; (1.2)


S2po(pkBT)'/2exp(-A/ikBT)
ro (2r)3/23 (1.3)

where c is the phonon velocity. From Eqs. 1.2,1.3 and Eq. 1.1, one can obtain the tempera-

ture dependence of the normal fluid density Pn. At low temperatures Pn increases as ~ T4

due to the phonon excitation. At higher temperatures, the roton excitation contributes to

the p, as ~ T-1/2exp(-A/kBT). These expressions indicate that the phonon excitation

dominates at temperatures lower than 0.6 K. Above 1 K, the roton excitation becomes

dominant. In the critical region near Tx, where the fluctuations are essential, the picture

of elementary excitations is no longer valid.

1.2 Kosterlitz-Thouless Theory for Two Dimensional Superfluidity

Bishop [7] and Agnolet [8] have studied the superfluid transition of thin 4He films

adsorbed on Mylar sheets by using torsional pendulum techniques. Figure 1.4 shows the

temperature dependence of the superfluid density of 4He films ranging in thickness from








a submonolayer to a few atomic layers [8]. Here the period shift AP of the pendulum is

proportional to the superfluid density, ps.

The superfluid transition observed by these authors has been successfully explained by

the theory developed by Kosterlitz and Thouless [10]. There are many good reviews of the

Kosterlitz-Thouless theory, including one by Agnolet and Reppy [9, 11, 12].


Vortex in an external superflow. The order parameter of superfluid 4He is written as



(r) = mexp(i(r)), (1.4)


where p, is the superfluid density, 0 is a real function of position f, and m is the atomic

mass of 4He. Since the current density is j(r) = h/m(f*VO OV )*) and jf(r) = pv4,

the superfluid flow field is v'(r-) = (h/m)Vq, which states that the superfluid flow is the

gradient of the phase of the order parameter.

When there is a vortex in superfluid 4He without an external flow, the flow field around

the vortex is quantized according to



vs = n- x F (1.5)

= n--, (1.6)
mr


where n is an integer, and 0 is a unit vector for the 0 direction of the polar coordinates in

which i is the direction along the core of the vortex. The energy of the vortex is a sum of

the kinetic energy of the superflow around the vortex core and the core energy Ec. It can



































O 6-
0

















T(mK)










Figure 1.4. Period shift and Q-1 as functions of temperature for a 4He film on a Mylar
sheet after Agnolet [9]. The coverage is 34.03 /imol/m2.








be written as


Evortex = P p2dF+ Ec

= n2rK'olog(R/a) + E, (1.7)



where the energies are per length of the vortex, Ko = ps(h/m)2, a is the vortex core radius,

and R is the size of area on which the film is present.

When a singly-quantized vortex (n = 1) is placed in a uniform superflow as shown in

Fig. 1.5, the flow below the core is faster than the flow above it. Since the phase (ri of the

order parameter changes by 27r on going around the core of the vortex, the phase increases

by 2r along a path taken below the core and decreases by 27r for a path taken above the

core. When a vortex moves downward, the velocity of the uniform superflow decreases by

h/Lm, where L is the width of the external flow. This means that a free vortex receives

a force downward from the uniform flow and, as it moves, dissipates the kinetic energy of

the flow. The force on the vortex is essentially the same as the Magnus force on a rotating

cylinder placed in an air flow.

In bulk and thick films of 4He, where vortices have macroscopic lengths, the energy given

by Eq. 1.7 is much larger than the thermal energy kBT. In atomically thin films of 4He,

however, vortices are the essential elementary excitations that determine the normal-fluid

density p, near the transition temperature.


Vortex-vortex interaction. In order to understand how the thermally excited vortices

in two-dimensional 4He determine the superfluid density near the transition temperature

Tc, one needs to start with the interaction between two vortices. From here on, p, will be



















7r -7 V 0=


-27r -7r


Figure 1.5. Flow around a vortex in a uniform external flow with superimposed phase
contours after Langer and Reppy [12].








the areal superfluid density instead of a three-demensional one. When there are two singly-

quantized vortices with superflow in the opposite direction from each other in the absence

of an external flow, the flow fields add constructively in the region between the cores and

cancel each other in regions far from the cores. As a consequence, the total kinetic energy

can be reduced by bringing the two vortices closer. This means that there is an attractive

force between the two vortices of opposite signs. The energy of a vortex pair is [13]



Epair(r) = 27p, log(r/a) + 2E (1.8)


where r is the separation of the cores.

When the vortex pair is placed in a uniform external superflow, the pair feels a force

tending to increase the separation. This force is a function of the separation r of the pair.

A sufficiently large external flow can break apart a vortex pair. The energy of the vortex

pair is written as

E(r) = Epair PpairVs, (1.9)


where v, is the external flow velocity and Ppair is the moment of the pair [12, 13], which is



Ppair = Psat- (1.10)
m


The energy E(r) has a maximum at


1 .h
= I -- (1.11)
27r, m


Vortex pairs with separations less than re remain bound, whereas pairs with separations

larger than r, are pulled apart by the external flow.








Screening effect of vortex pairs. At low temperatures, there are few vortices thermally

excited in the 4He film. The vortices form pairs because of the attractive forces between two

vortices with opposite superflow fluids around them. Therefore, the macroscopic superflow

does not decay as long as the flow velocity is not large enough to break vortex pairs. At high

temperatures where the number of vortices is large, the interaction between two vortices

forming a pair becomes influenced by the superflow field of other pairs. A vortex pair placed

between two vortices which are forming a larger pair increases the separation in response

to the flow field of the larger pair. This costs energy for the larger pair, resulting in the

reduction of the attractive force between the two vortices. This screening effect increases

as the density of the vortex pairs increases with temperature.

The situation described above is analogous to a dielectric in an electric field. In fact,

the problem of many vortex pairs in a uniform superflow can be exactly mapped to that of

positive and negative charges in an electric field. In this description, the screening effect

can be approximated by introducing a dielectric constant e(r), which represents the effect

of many nested pairs of vortices located between the two vortices forming a pair we are

considering. The dielectric constant E(r) can be written using the polarization a(r) of a

vortex pair with separation r as



(r) = 1 + 4rX(r)

= 1 + 47r dr'a(r')n(r'), (1.12)
JTo








where n(r') is the two-dementional density of vortex pairs with separation r' and ro is

The polarization is given by


nh 9 < rcos 0 >
a(r) = 0 < c(1.13)
m Ovs v'=o


The average is taken over the annulus r < r' < r + dr. The result is


rr2K0
a(r) = 2k (1.14)
2kBT


where Ko = p,(h/m)2. The density of vortex pairs can also be obtained by summing the

Boltzmann factor exp(-Eeff/kBT) over the annuls r < r' < r + dr divided by rI;



n(r) = 24 exp T (1.15)


where Eeff is the energy of a vortex pair in a dielectric medium


r dr'
Eeff(r) = 27rKo o (1.16)


As can be seen in these equations, these quantities have to be determined in a self-consistent

fashion.

In order to make the calculation simple, it is useful to define a new length scale I

log(r/ro) and dimensionless functions



y(1) = y( ) exp (2E (1.17)
ro 2k-T









K-(1) = E(r)kBTKo1.


Here yo = exp(-Ec/kBT). Using these definitions, one can rewrite Eq. 1.12 as


K-1(1) = kBTKo' + 47r3 dl'y2(') .
Jo1


(1.19)


Inserting Eq. 1.16 into Eq. 1.17 one obtains


y(l) = o exp (21 r 1 K(l')dl .


(1.20)


Differentiating Eqs. 1.19 and 1.20 with respect to I leads to


dK-'
dl = 4rr3y2(1)
dl

dl- = y rK()).


(1.21)


(1.22)


According to Eqs. 1.19 and 1.20, the initial conditions for Eqs. 1.22 are K-1(0) = kBTKo1

and y(0) = yo Combining Eqs. 1.22 one obtains


dK-1
dy


47r3y
2 rK(1)


Integrating this equation leads to


2K-1' +log(K- )=C()
22y2 +log C(T),
r 7r


(1.23)


(1.24)


(1.18)








where the constant of integration C(T) is determined by the initial conditions at 1 = 0 to

be

C(T) = 2r2y0 kTKo- + log (B (1.25)


Eliminating y2(1) from Eqs. 1.24 into yields


dK-1 K-1
-- = 4K-1 2r log + 27rC(T). (1.26)
dl r


A group of solutions for this differential equation are plotted in Fig. 1.6. The figure can

be divided into three regions according to the temperature. In region C above Tc, each line

representing a solution at a given temperature initially falls as I increases but starts to rise

for larger 1, without hitting the horizontal axis. Since I represents the separation of the

vortex pair and a larger y(l) means a higher density of vortex pairs, the solutions above

Tc can be interpreted as unbound states of vortex pairs. As K-1 diverges, the dielectric

constant e diverges, also indicating free vortex states. On the other hand, in region A for

T < Tc, the lines intercept the horizontal axis on which y = 0. All pairs are considered to

be in bound states. It is important to note that solution B for T = Tc also intercepts the

horizontal axis at finite 1. This means that there is a finite p, at T = Tc unlike in bulk

superfluid 4He or in films of superfluid 4He that are not atomically thin. Since y diverges

to infinity above Tc, p, becomes zero. This indicates that there is a discontinuity in p, at

Tc. Nelson and Kosterlitz [14] have shown that p,/T in the limit of T -- Tc from below is

a universal constant which does not depend on the thickness of the film:


2m2ks
lim p,/T = p,(T)/Tc 2m(1.27)
T-TCrh2 (1.
















0.06

0.05 C

0.04 -

S0.03 -
J, A \ I

0.02 \

001 1= 0 = 3.5


0.00
0.0 0.5 1.0 1.5 2.0 2.5
K-'(1)





Figure 1.6. Solutions of the Kosterlitz-Thouless recursion equation after Agnolet [9]. The
trajectories are classified into three groups according to the temperature. Line A represents
solutions whose temperature is below T.. These solutions intercept the horizontal axis with
finite 1. Line B is the solution for T = Tc and crosses the horizontal axis with finite I. Lines
C represent solutions for temperatures above T,. These solutions never cross the horizontal
axis. The dotted line shows values of y and K-1 at I = 0. The dashed line shows values of
y and K-1 for I = 3.5.








1.3 Superfluidity of Thin 4He Films in Porous Vvcor Glass

There have been a series of studies on the superfluidity of thin 4He films adsorbed in

porous Vycor glass [7, 12, 15, 16], whose pores are 70 10 A in diameter and randomly

connected to each other. Figure 1.7 shows the superfluid density p, measured by the torsion

pendulum technique []. The period shift 6P of the pendulum is proportional to p,.

The temperature dependence of the superfluid density obeys a power law AP(T) =

Ao(1 T/T,)C with a critical exponent ( = 0.635 0.050, which is close to the bulk liquid

4He value. As the density of the film gets smaller, Tc decreases down to 3 mK. Reppy

and co-workers have argued that the result suggests a cross-over from a regime of three

dimensional superfluidity to a dilute ideal Bose gas-like behavior [15].

There is a different, but not necessarily orthogonal, interpretation of the results. Kot-

subo and Williams [17] and other authors [18, 19] have argued that superfluidity of a thin

4He film in the porous Vycor glass can be explained by vortex-pair unbinding. In this pic-

ture, the three-dimensionally interconnected pores modify the inter-vortex interaction from

the logarithmic potential for the two-dimensional film case [18] to a linear potential at a

distance larger than the pore diameter. For a distance shorter than the pore diameter, the

interaction remains logarithmic. Due to the three-dimensional connectivity of the pores,

however, the transition belongs to a three-dimensional universality class, which explains

the critical exponent close to the value for the bulk superfluid transition in 4He .

1.4 4He Adsorbed in Zeolite

Zeolite is a group of aluminosilicate minerals containing water. There are over 130

species of zeolite known to date, either natural or synthetic. The most unique feature of

zeolite is that the mineral contains microscopic pores incorporated into the crystal structure.

















150


(f

0
S

50 -.. .

50 e. eve *
.


**



0) 0.8 .0 1*o .2 1.4

S T( K)







Figure 1.7. Superfluid density of He films in porous Vycor glass after Bishop








The diameter of these pores is typically less than 15 A, which is only five times larger than

the size of the 4He atom and is too small to accommodate vortices whose core diameters

are 25 12 A.

Recently, Shirahama et al. [20] have studied the superfluidity of thin 4He films in porous

glass with pore sizes ranging from 50 A to 1 psm in diameter. From the relationship between

Tc and the pore diameter, they found that the vortex core size to be ao = 25 12 A, which

is an order of magnitude larger than the vortex core of 2.6 A for bulk liquid 4He. If any

superfluid transition were to be seen in a He film in zeolite, one can expect the transition

to be of a novel type not associated with the unbinding of vortex pairs.

Another important characteristic of zeolite is that the surface potential of the pores

are periodic, since they are part of the crystal structure. This is in strong contrast to

porous glass which is a heterogeneous substrate with a random surface potential. In the

experiments of thin 4He films in porous glass, a localized layer corresponding to ~ 1.7 atomic

layer over the surface has always been observed. Only the 4He atoms above this localized

layer have been observed to become superfluid. Some workers have argued that because

of strong but short-range attractive force from the substrate, the layer that sits directly

on the substrate is compressed into a solid [7, 16]. However, this does not necessarily

mean that a subatomic layer should be localized, since the 4He atoms in this situation

should be able to move along the surface unless the surface potential contains deep wells.

Another argument is that 4He atoms are localized due to the random surface potential in

analogy to the localization of electrons in a random potential [21, 22]. If this is the case, a

submonolayer of 4He may exhibit superfluidity in zeolite, whose pores present a periodic

surface potential.








Some zeolite species have three-dimensionally connected pores, which provide 4He atoms

with a circular path of a diameter less than 15 A. In such a geometry, a vortex may exist

whose core is a part of the substrate rather than normal fluid to save the core energy. It is

interesting to speculate how a lattice of such vortices, which assume the periodicity of the

zeolite framework, may lead to novel effects on the superfluidity.

These are our motivations in studying 4He in zeolite. Chapter 3 of this dissertation

gives a detailed description of chabazite, a particular type of zeolite we have chosen as our

substrate. Following the discussion of dehydration technique for chabazite, Chapter 4 and

Appendix B discuss the experimental results.


Previous study on helium in zeolite. Wada and Kato [23] have studied heat capacities

and isosteric heat of sorption of 4He and 3He in Y zeolite (LTA). They have reported that

the atoms are localized near the cations in the pores, when the amount of helium is small. As

the amount of helium increases, 4He atoms form a solid-like layer in the pores. Eventually

4He starts to behave like either a gas or a liquid depending on the density of 4He atoms

over the first atomic layer. When 4He nearly fills up the pores, the heat capacity becomes

small again and this has been interpreted as an indication of a solid-like state. Wada and

Kato have observed a hump in the heat capacity of adsorbed 3He at a temperature below

1 K and they have interpreted it to be due to the Fermi degeneracy of 3He atoms. Despite

these pieces of evidence for 4He being a fluid for some film coverages, there has been no sign

of superfluidity in their results. However, looking for an anomaly in the heat capacity is a

notoriously difficult way to discover superfluidity in thin films of 4He in porous geometries.

Prior to this dissertation, no search for superfluid transition in 4He absorbed in zeolite has








been made with a torsional-pendulum technique, except for one negative study [] which

used powders of Y zeolite.

1.5 4He Adsorbed in Porous Silica with a 25 A Pore Diameter

Porous glass has been a very popular substrate in which to study the superfluidity of

4He films in confinement. As has been discussed in section 1.3, vortex-pair dissociation

may be responsible for the superfluid onset as in the case of the flat 4He film. Studies by

Shirahama et al. [20], mentioned in that section, have been our motivation to investigate

superfluidity in 4He films confined in pores whose size is close to the vortex core diameter.

Naively, if vortices are responsible for a superfluid transition and their pore diameter is

as large as claimed, then the transition temperature can be much enhanced in such pores,

since the two vortices forming a pair can hardly accommodate any other vortices between

them to screen the intra-pair interaction.

We have chosen porous silica with a nominal pore diameter of 25 A as a substrate. Unlike

zeolite pores, the pores have a random surface potential and are randomly connected with

each other. These features are similar to those of porous Vycor glass.















CHAPTER 2
EXPERIMENTAL TECHNIQUES AND CRYOSTAT


2.1 Torsion Pendulum

Use of a torsion pendulum in studies of superfluids dates back to Andronikashvili [1],

as discussed in Section 1.1. A modern version of this device has been developed by Reppy

and co-workers [16, 24], who made it a powerful tool to study superfluid 4He in confined

geometries and superfluid 3He. The torsion pendulums built for the experiments of this

dissertation are based on their design.


Principles. Each torsion pendulum consists of a sample cell, which contains a zeolite

crystal or a porous silica, and a torsion rod through which 4He is introduced to the cell

as shown in Fig. 2.1. When 4He in the cell becomes superfluid, the torsional oscillation of

the cell decouples from the superfluid component which has no viscosity. This decoupling

increases the resonance frequency of the oscillation.

The resonance frequency fo is given by



0 = (2.1)



where K is the spring constant of the torsion rod, and I is the moment of inertia of the

cell including that of the 4He. A small decrease 61 in the moment of inertia due to the



























Brass fin


Brass cell



Be-Cu torsion rod-


Stycast 2850 insulation


Stycast 2850 seal


SGas fill line


Figure 2.1. Torsion pendulum.








decoupling of the superfluid component produces a frequency increase



2f fo 2 (2.2)
2r I 2 r + T 2I -2 '


which is directly proportional to the superfluid density.


Detection of the pendulum oscillation. Figure 2.2 is a schematic presentation of the

feedback circuit that drives the torsion pendulum and detects the resonance frequency and

the amplitude of the oscillation. The pendulum is driven by the electrostatic force between

the drive electrode and the fin attached to the bottom of the sample cell. Another stationary

electrode facing the fin from the opposite side is employed to detect the oscillation. The fin

is dc biased from 100 to 200 volts for two purposes: (i) to cause the pendulum to oscillate at

the drive frequency instead of the first harmonic, and (ii) to make the oscillation produce.

a current signal. The detected signal is fed back to the drive electrode to maintain the

oscillation. Using a low loss material such as a Be-Cu alloy for the torsion rod, one can

achieve a Q factor close to 106. The very high Q factor is essential to good frequency

stability and the detection of small dissipation in 4He .

The bias line is connected to the fin by a thin copper wire (40 AWG). A regular 60/40

soft solder was used to attach the wire to the fin. The soldering was done with care to

avoid cold soldering, which not only increases the risk of an open circuit upon cooling but

also lowers the Q factor. Care was also taken to avoid prolonged heating which results

in a failure of the Stycast 2850FT epoxy that bonds the fin to the sample cell. The

wire was cut to a length so that it hung somewhat loosely. Problems such as parasitic

resonance modes associated with an oscillation of the biasing wire have not been observed

in this arrangement. The 0.1 AF Mylar capacitor between the bias and the cryostat ground


















100 -200 V
70k ,, I


Drive electrode


Figure 2.2. Schematic diagram of the torsional pendulum and the feed back circuit.








provides a path for the signal current. The capacitor is located on the base of the vibration

isolator which houses the torsion pendulum. A 70 kQ carbon resistor was placed outside the

cryostat in series with the high-voltage source (Bertan 205A-01R [25]) to protect against

short circuit to ground and to block the signal current.

Figure 2.3 shows the construction of the electrodes, one for driving the pendulum and

the other for sensing the torsional oscillation. Each electrode is a 1/16 inch diameter brass

button 0.3 inch in length, glued into a brass case with Stycast 2850FT epoxy. The gap

between the electrode and the fin was adjusted manually with a finger or a pushing screw.

In order to make the gap as small as possible to obtain a sufficient capacitance, the following

method suggested by Nobuo Wada was used. A sinusoidal signal is first fed to the biasing

line from which the capacitor and the resistor have been removed. The electrode is then

moved in and out while monitoring the signal picked up by the electrode on an oscilloscope.

In this way, a typical gap width of 50 ~ 100 Mm has been achieved, corresponding to a

capacitance of ~2 pF.


Feedback circuit. The home-made coaxial cable for the sensing electrode has a sep-

arate thermal anchor and shield from other cables in the cryostat in order to eliminate

electronic noise from the thermometer leads and the cable for the driving electrode. It has

a separate BNC connector port on the top of the cryostat for the same reason. The room-

temperature coaxial cable that connects the PAR 181 current-sensitive preamplifier [26]

to the port is made as short as possible to minimize the microphonic noise and the cable

capacitance which cuts down the signal. The gain of the preamplifier is set at 109 V/A, for

which the input impedance is 10 kQ at frequencies less than 100 kHz. Since the capacitance

of the entire sensing line is Cine ~ 220 pF as measured at the top of the cryostat, with a




















Connector

/- Brass casing


----- Brass button


Copper wire


Figure 2.3. Schematics for the sensing and driving electrodes.








corresponding impedance of 145 kf for a typical signal frequency of 5 kHz, only about 6%

of the signal current is lost through the line capacitance.

The output of the preamplifier goes to a PAR 124A lock-in amplifier [26]. The output of

the signal-monitor port of the lock-in amplifier is fed to a home-made phase shifter through

a Stanford Research SR560 low-noise preamplifier, which is needed to provide the zero

crossing detector (ZCD) with a sufficient level of signal to overcome the noise.

The circuit diagram of the phase shifter is shown in Fig. 2.4. This circuit has been

adapted from Horowitz and Hill [27] and consists of two stages. The first stage is a phase

splitter which creates a buffered signal and its inverse from the input signal. The CA3026

differential amplifier 1 used for this stage consists of two matched transistors fabricated on

a single monolithic substrate to reduce the temperature drift. The second stage combines

the two signals through a capacitor and a ten-turn potentiometer. The amount of phase

shift can be varied from nearly zero (R < 1/wC) to nearly 1800 (R > 1/wC) by adjusting

the potentiometer. The amplitude of the output is constant throughout the entire range of

the phase. Since the output signal is biased to 11.8 V, a blocking capacitor and a resistor

are needed at the output. This RC circuit gives an additional phase shift which should be

compensated by the phase shifter.

The signal from the phase shifter is fed to the ZCD, which is shown in Fig. 2.5. The

output of the ZCD is connected to the reference input of the lock-in amplifier, in which a

phase-locked oscillator creates a sinusoidal signal at the frequency of the reference signal.

This sinusoidal signal, after an internal ZCD, is available at the calibrator output, which is

directly fed the driving electrode. The output level was set at 0.2 to 50 mV,., depending

on the dissipation in 4He.

'Manufactured by RCA.











+12 V


Input


-12 V


SOutput


Inverted Vo --


Figure 2.4. Circuit diagram of the phase shifter.



















0.022 jAF


0.022 pF
iI


-12 V


Figure 2.5. Circuit diagram of the zero crossing detector.








Construction of the torsional pendulum. The Be-Cu torsion rod (see Fig. 2.1) was

heat treated in vacuum at 3200C for 3 hours for hardening. The sample cell was made

of brass. Using light materials like magnesium alloy [9] gives a large relative change in

the moment of inertia when 4He becomes superfluid, leading to a larger frequency increase

according to Eq. 2.2. However, we could not purchase such an alloy from the manufacturers

in a quantity we could afford.

For chabazite experiments discussed in Chapter 4 and Appendix B, a separate torsion

pendulum with a separate cell was made for each crystal, since the crystals differed in size.

The crystal was glued in the cell with black Stycast 2850FT, which was applied either on a

spot or on a line which stretched parallel to the axis of the cell. The reason for not applying

Stycast over the entire circumference of the inner wall of the cell was to prevent the thermal

contraction of Stycast from damaging the zeolite. Gluing of the crystal was done in a glove

bag filled with dry nitrogen gas to prevent adsorption of moisture by the crystal. The

torsion pendulum for the porous silica experiment, which is discussed in Chapter 5, was

built with a similar procedure except that the silica was coated with Stycast 1266 before

being glued in the cell. A detailed description of the construction is given in Chapter 5.

The cell was attached to the torsion rod with Stycast 2850FT in the glove bag. The

same epoxy was used to attach the fin to the bottom of the cell. To achieve electrical

insulation for the fin it was sufficient to place the fin on a thin layer of the epoxy rubbed

on the cell surface without using a spacer. This was done in situ on the cryostat. Two

dummy electrodes machined to the shape of the actual electrodes were placed against the

fin to keep it in the correct alignment with respect to the electrodes while the epoxy cured

at room temperature.


U J>









Temperature (K) Q factor Resonance frequency (Hz)
300 20,000 4794.841
77 68,000 4970.480
4.2 285,000 4992.779

Table 2.1. Changes in the resonance frequency and the Q factor of the torsional pendulum
observed during a cooldown from room temperature to 4.2 K. The sample cell, 0.2" in di-
ameter and 0.2" in height, was made of brass and contained chabazite crystal C16 discussed
in Appendix B.

Frequency and amplitude of the pendulum oscillation. The frequency of the torsion

oscillation can be estimated by using Eq. 2.1. The spring constant of the torsion rod is

K = rG(a4 b4)/32L, where G is the shear modulus of the rod (5.3 x 1011 dyne/cm2 for

Be-Cu), a is the outer diameter of the rod, b is the diameter of the hole, and L is the length

of the rod. The estimate of the resonance frequency does not give very accurate values due

to machining errors and the uncertainty in the contribution of the epoxy to the moment of

inertia. Table 2.1 shows an example of how the frequency and the Q factor change as the

pendulum is cooled from room temperature to 4.2 K. The changes are primarily due to the

stiffening of the torsion rod as the temperature is lowered. Discussions on other resonance

modes and variations of torsional-pendulum design can be found in the textbook written

by the Cornell low temperature group [24].

The amplitude of the oscillation can be obtained from the signal amplitude as follows.

The signal current I is the time derivative dQ/dt of the electric charge on the sensing

electrode. This charge is Q = CV, where C is the capacitance between the electrode and

the fin and V is the bias voltage applied to the fin. Therefore, the signal current is



I=VC= -VC-, (2.3)
d








where the approximation C oc 1/d has been used since the gap d between the electrode and

the fin is much smaller than the size of the electrode. Letting d = do 6ejwt (do > 6) and

I = jIoej'3 leads to the signal amplitude



Io = VWCo (2.4)



to first order in 6/do; i.e.,

6 = do 0 (2.5)
VwC

is the amplitude of oscillation. Typical values for the parameters are Io = 10-11 ampere,

do = 100 pm, C = 2 pF, the bias voltage V = 200 volt, and a resonance frequency of 5 kHz

for the pendulum, which yields a 6 of 0.8 A near the center of the electrode. The velocity

near the edge of the cell is twice the velocity of the fin near the center of the electrode, i.e.

Vedge = 2w6sinwt. The maximum velocity Vedge = 2w6 is about 5 pm/sec, which is well

below the critical velocity of 6 mm/sec for bulk superfluid 4He of measured by Craig and

Pellam [28].

2.2 Thermometry

The temperature of the experiment was measured with a ruthenium oxide resistance

thermometer, Bk5pl04, which was provided by Mark Meisel [29]. The resistor chip is

0.05 x 0.05 inch2 in size and is glued on a 1/16 inch thick copper plate with GE 7031

varnish. Copper leads are attached to the chip with silver epoxy. The chip and part

of the leads are covered with Stycast 2850FT for mechanical strength. Figure 2.6 shows

the calibration of a resistor from the same batch. Thermometer Bk5pl04 had not been

calibrated.



























I I I I I I I I


0
0
0
0
0
0
0
0
0


0
0
0
0




a00


) 100 1000

Temperature (mK)


Figure 2.6. Calibration provided by M. Meisel for the ruthenium oxide thermometer

Bk5pl04, which is representative of the batch from which our thermometer has come.


C3


I I I I


I I


.. .. .I I r -


"


I I I I I i I


, I








I have built the Anderson bridge described in Section 2.3 to measure the resistance of

the thermometer using a four-lead method. However, two of the four leads lost contact

in the first experiment which used a torsional pendulum containing a chabazite crystal as

described in Appendix B, forcing us to use a two-lead configuration. In order to keep consis-

tency in the thermometry between this cooldown and the succeeding ones, we chose to use

the two-lead configuration until the thermometer was calibrated later in this configuration.

Another ruthenium oxide thermometer, Bk6p93, which was loaned to us by Mark Meisel,

was installed on the cryostat before the next cooldown to calibrate the first thermometer.

The resistance of this thermometer was measured by the dc method in a four-lead configu-

ration. A Keithley 224 current generator was used to provide the 5 nA excitation current

for this thermometer, and a Keithley 182 digital voltmeter was used to read the voltage

across the thermometer. The current polarity was reversed for every reading to eliminate

the effect of the thermal emf, which was about 1 pV. Figure 2.7 shows the calibration for

Bk6p93.

2.3 Four-Wire Resistance Bridge

The circuit diagram of the home-made Anderson bridge [24, 31] is shown in Fig. 2.8.

Toroidal transformers T1 and T2 are placed in separate magnetic shields made of iron. The

excitation taken from the reference output of the Stanford Research SR530 lock-in amplifier

is fed to transformer T1, which has two secondaries. One of the secondaries is connected

to the op amp OPA-111BM (Burr-Brown) which gives a constant current I = V/R, to the

resistance thermometer R. Here V is the voltage across the secondary, and R, is the value of

the reference resistor. Non-inductive resistors [30] are used for references in order to avoid

off-phase components. The other secondary of the transformer is connected to the ratio






















SI I I 1111 1Irr --- ---~-~


0
0

0
0
0
0
O


0
0
0
0
0
O


I I I i i i i|


100


Temperature (mK)


Figure 2.7. Calibration for the ruthenium oxide thermometer Bk6p93. The data were
provided by Mark Meisel.


100


C:


0%~00


o 0


I I


1000


" I


' I


t


- -





































T2Rx
10K -I Ratio Transformer
JOP27
2K












Figure 2.8. Circuit diagram of the Anderson bridge. The reference resistors are Caddock
TN137 except for the 100 ft which is a MK132 [30]. Both types are non-inductive resistors
with 1% tolerance.








transformer, whose output is aV when the ratio setting is a, since the quadrature voltage

added by transformer T2 is small in comparison with V. When the bridge is balanced,

the output of the ratio transformer and the voltage across the thermometer are the same.

Therefore, the condition for the balance is


R
a= (2.6)
R,


The bridge has been used mostly off balance to run the experiments under computer

control. One can obtain the thermometer resistance from the error signal knowing the

setting of the ratio transformer. In order to understand how far the bridge can be used

off balance, let us consider the equivalent circuit shown in Fig. 2.9. The secondary of the

transformer T2 for the quadrature has been ignored in this circuit because the resistance

change in the thermometer affects only the in-phase component of the bridge. Again the

current supplied by the constant current source is I. The current through the primary

of the signal transformer for the lock-in amplifier is I', and the current through the ratio

transformer is I". The voltage across the ratio transformer is



V = jwL(I" + al'), (2.7)



where L is the total inductance of the ratio transformer. The voltage across the primary

inductance Ls of the signal transformer is


jwLsI' = R(I I') jwaL(I' + I").


(2.8)




































S2






























Figure 2.9. Equivalent circuit for the four-wire bridge.


_7 ;.,;--








Eliminating I" from Eqs. 2.7 and 2.8 leads to


RI (1 a)V
R + jw[Ls + a(1 a)L]


If Ro is the thermometer resistance for which the bridge has been balanced, then aV = Rol.

When the resistance increases to R = Ro + r by a small amount r, the error current I' is


rI
I' = (2.10)
Ro + r + jw[Ls + a(l a)L]


By expanding the real and imaginary parts of this equation separately in terms of r, one

obtains



A Ro [1 +( 2 ) r -] jw[L,+a(1-a)L 1- 2r + (2.11)


where

A = R2 + w2(Ls + a(l a)L)2. (2.12)


Since Ro/A is smaller than 1/Ro, both the real and imaginary components of the error

signal are proportional to r in so far as the resistance change r is a small fraction of the

resistance Ro for which the bridge has been balanced.

The second toroidal transformer T2, which supplies the quadrature signal to the ratio

transformer balances the off-phase component due to the cable capacitance. In order to

produce the 900 phase shift, a simple differentiation circuit is used. However, the differen-

tiator becomes unstable at high frequencies, because the total gain increases with frequency

as RCw and the op amps have internal phase shifts. It oscillated at 21.5 MHz, which was









Core FT-23-J
O.D. (inch) 0.23
I.D. (inch) 0.12
Height (inch) 0.06
Permeability 850


Table 2.2. Specification of ferrite cores. The data are from Iron-Powder and Ferrite Coil
Forms published by Amidon [32].

killed by inserting an extra resistor and capacitor. The phase-shifter looks like an integrator

at high frequencies because of these additions.

We have found that the ferrite core of T2 adds an unwanted phase shift to the quadra-

ture. Figure 2.10 shows the phase shift as a function of frequency. The phase shift is

probably caused by loss in the core which depends on the material and geometry of the

core. The core used for the transformer T2 is Amidon FT-23-J [32]. The specifications for

material J are given in Table 2.2. The windings are 70 turns for the primary and 11 turns

for the secondary. The inductance of the primary and secondary are 4.8 mH and 0.12 mH,

respectively.

2.4 Data Acquisition

Two computer programs were written in Quick BASIC [33] to take data. Program

TORCONT.BAS takes data at high temperatures where the frequency does not change

very much. This program takes data on the fly, without using active temperature control.

The rate of temperature change is controlled manually by partially closing a valve on

the still pumping line of the dilution refrigerator and increasing the heater levels on the

experimental stage and mixing chamber. The gate time of the frequency counter (see

Fig. 2.2) is set at 2 minutes by the program. The error signal from the Stanford Research




















I I I I IlII I I I 1111


I 1111 1 11.. I1IY v -


3 100

Freq


1000

uency


10000

(Hz)


Figure 2.10. Phase shift caused by the ferrite cores as a function of frequency.


100


80 -


0

C
C-
n
ot


60 h


40 -


201-


100000


I11 1


I


0


. QI I


S .... I








SR530 lock-in amplifier of the Anderson bridge is converted to a resistance by the program.

The conversion of resistance to temperature is done after the experiment.

The second program TORAUTO.BAS takes data with temperature regulation using

an ATC temperature controller manufactured by S.H.E. Since the Anderson bridge does

not automatically balance itself, the internal offset of the lock-in amplifier is used to offset

the error signal by an amount appropriate for the target resistance value. In order to get

the correct offset value, the error signal for various ratio transformer settings has been

measured at several temperatures by holding the mixing-chamber temperature constant.

Figure 2.11 shows the ratio of the resistance difference to the voltage output of the lock-in

amplifier as a function of the thermometer resistance. The ratio is a linear function of the

resistance except in the lowest resistance region.

After it sets the offset for a new temperature, the program waits for the temperature to

stabilize by monitoring the error signal. When the error signal indicates the resistance to

be within 0.01% of the target value for four consecutive readings which are a few seconds

apart, the program opens the gate of the frequency counter for 2 minutes. The temperature

remains stable within 3 mK around 1 K during the data taking. While the gate is open, the

amplitude of the torsion pendulum signal and the error signal of the Anderson bridge are

read continuously by a Keithley 199 System DMM scanner. Both quantities are averaged

by the computer and written to data files.

When thermometer Bk6p93 was installed before the second cooldown to calibrate Bk5pl04,

the two programs were modified to read the resistance of this thermometer before and after

each frequency count.

TORAUTO.BAS was later modified and renamed as TORSION3.BAS for the torsional

pendulum experiment using porous silica discussed in Chapter 5. The modified program




















60 -


0
o



< 40 o
No
< 40- o






cn 20-
0

L
LLJ



&1 0 2000 3000
Balance (c)




Figure 2.11. Ratio of the error signal to the resistance difference as a function of the
thermometer resistance. The sensitivity of the lock-in amplifier was 20 mV. The oscillator
was set at 10 Hz and 0.1 V.


I i








records the readings of the torsion pendulum amplitude and the Anderson-bridge error

signal in separate files for later analysis in addition to the averaged amplitude and the

thermometer resistance. It also takes three frequency readings at each temperature to check

the frequency stability. This program controls the heater on the mixing chamber as well as

the heater on the experimental stage to eliminate a possible temperature gradient between

the two stages. Since the ruthenium oxide thermometer Bk6p93 is located closer to the

mixing chamber than Bk5pl04, the temperature gradient may result in lower temperature

readings for Bk6p93.

The program was later modified again to use Bk6p93 for temperature regulation when

one of the leads for Bk5pl04 became grounded during the experiment. The modified pro-

gram calculates the appropriate heater output by simulating a PID temperature controller

and sets the heater level through a D-to-A converter. The temperature of the experimental

stage was regulated to within 3 mK by this method.

2.5 Crvostat

The cryostat, except for the dilution unit and part of the gas handling system, was

purchased from BTi when they quit the dilution refrigerator business.


Vibration isolation. The vibration isolation of the cryostat is provided by two com-

ponents. One is the concrete wall in which the plumbing from the gas handling system to

the cryostat is embedded. The top of the wall is filled with dry sand to completely cover

the plumbing. This wall helps to reduce the vibrations which originate from the mechan-

ical pumps located in the crawl space under the laboratory. The other component of the

vibration isolation is the floating table. The aluminum table is attached to three PVC

sewage tubes, 16 inches in diameter and 5 feet 8 inchs in height, filled with concrete. Each








of these columns sits on an air spring which is placed in the aluminum base of the column.

However, we have found that the bottoms of the columns started to slide sideways when

the air spring was inflated to ~100 psi. Because of this problem the air springs have never

been used in the actual experiments.

It is quite likely that the top of the columns are not flat. Since the aluminum table is

bolted onto each column with a rubber sheet between them, the bottoms of the columns

can slide. If this is the case, a possible solution is to grind flat the top surface of each

column and to insert a thick metal plate under each rubber sheet so that the top surfaces

of the plates are level and parallel to the table. It is also possible to guard the bottom of

the columns with small air springs.

The vibrations generated by the mechanical pumps are also intercepted by sand boxes

before they reach the gas handling system. These are wooden boxes 30 cm x 30 cm x 30

cm in size, each with a hole on the bottom for the plumbing. The gap between the hole

and the plumbing is sealed with silicon caulking to avoid direct contact. As is well known,

the sand should be kept dry to be effective.


Dilution unit. There are many good reviews on dilution refrigerators [24]. Figure 2.12

shows a schematic diagram of the dilution unit used in the experiments of this dissertation.

The still is made of copper and has a volume of 62.5 cm3. The return line capillary is

coiled inside the still to cool the liquefied 3He to the still temperature. The first still that I

constructed started to leak one week after the first cooldown of the refrigerator. The leak

was found at the soft solder joint between the base plate of the still and the body. Soft solder

had been used so that the joint could be undone later in case of a problem. However, it

seemed that the solder was not strong enough to withstand the stress of differential thermal













Condensor -


Flow impeadance-







Heat exchanger -





Thermometer
Bk6p93


-Still










Mixing

Heater


chamber


- Experimental


Thermometer
Bk5p104


stage


pendulum


Figure 2.12. Schematic of the homemade dilution refrigerator.








contraction. Resoldering did not solve the problem. A new still with the same design was

assembled with silver solder but also leaked at the same joint. Grinding away the leaky

part and filling it with soft solder did not eliminate the leak. After spending many days

trying to fix the leak, it was finally decided that the problem with the still design was the

bulkiness of the body, which had 0.3 inch thick walls and weighed about 620 g. Following

this diagnosis, yet another still with a smaller mass was built. In the new design, the wall

thickness was reduced to 0.2 inch and all the edges were milled down as much as possible,

reducing the mass to 480 g, whereas the inner volume was reduced by only 5%. In order to

make stronger solder joints, the edges of the indentation on the base plate have been raised

by 1/16 inch, 1/32 inch wide. The new still has worked well without a leak.

The heat exchanger is a continuous type of the tube-in-tube design using stainless steel

tubes of two different diameters. It consists of three segments connected in series by two

copper blocks and silver soldered together. The copper blocks are to provide convenient

thermal anchoring for leads and cables. Each segment is manufactured in the following

sequence. First a 0.03 inch diameter capillary is formed into a coil by wrapping it around a

1/16 inch tube. After inserting the coiled capillary into a 3/16 inch tube, the latter is filled

with water and plugged on both ends with Apiezon Q [341. Finally, the entire assembly,

which is about 45 inches long, is dipped into liquid nitrogen to freeze the water and is

bent into a 2.3 inch diameter coil with a pitch of about 0.3 inch by wrapping it around a 2

inch copper tube.2 The frozen water in the tube prevents the cross section from collapsing

during the bending. During the assembly of these segments into a single unit, it was difficult

2This freezing technique was also tried on the capillary to prevent flattening during the coiling, but it
was abandoned after one try. The problem was that the ice started to melt immediately during the handling
of the capillary.








to keep the stainless-steel tubes away from the direct flame of the torch during the silver

soldering. Because of several leaks, I had to discard one of the coils and make a new one.

The flow impedance between the still and the 3He condenser was made by inserting

a 0.0089 inch diameter Cu-Ni wire into a 4.7 inch piece of Cu-Ni capillary with a 0.01

inch inner diameter and by stretching the capillary from both ends with pliers until the

desired impedance value of 1.1x 1012 cm-3 was obtained. The impedance was measured by

immersing one end of the capillary in methanol and connecting the other end to a nitrogen

gas cylinder. By collecting the nitrogen bubbles in a graduated glass tube, the flow rate

was determined. The impedance Z was obtained from the flow rate 1V2 (cm3/sec) by using

the relation

Z = 2 (P2 P2 ), (2.13)


where P1 is the applied pressure of nitrogen and P2 is the atmospheric pressure. The

kinematic viscosity 17 of nitrogen gas at room temperature is 18.9 pPa-sec.

The upper part of the mixing chamber is made of OFHC copper for good thermal con-

duction. The part has sixteen 0.95 cm diameter holes packed with 700 A silver powder [35],

which was provided by Dwight Adams. The powder has been heated in vacuum at 3000C for

30 minutes to increase the grain size. The surface of the holes had been electroplated with

silver prior to the packing to improve the adhesion of the powder to the copper. A hole of

0.64 cm diameter was drilled in the center of each powder-packed hole. The bottom of the

mixing chamber is made of brass.

The Vespel SP22 [36] insulators are used on the supports between the mixing chamber

and the still3. Each insulator's outer diameter is 1 cm, the inner diameter is 0.43 cm, and

3Vespel SP22 is a ployimid resin containing 40% by weight of graphite.








the height is 1.27 cm. Two insulators are used on each support on the mixing chamber side.

Heat leak through the Vespel insulators can be estimated by considering a one dimensional

heat conduction problem. The heat flow Q through a material with a uniform cross section

A follows the equation



S= -A(T)d, (2.14)


where K is the thermal conductivity and dT/dz is the temperature gradient. The thermal

conductivity of Vespel SP22 is K = kT2, with k = 17 pW/cm/K [37]. Since Q is constant

over the length of the rod, integrating Eq. 2.14 leads to


Ak
Q = 3 Ti), (2.15)


where L is the length of the rod. The high temperature end TH is at about 0.6 K, a typical

temperature of the still, and the low temperature end TL is 80 mK. From Eq. 2.15, the

heat leak through one Vespel insulator is estimated to be Q=0.62 /W. Since there are six

of them, the total heat leak into the mixing chamber through the Vespel is 3.7 /W.


Thermometers. The operation of the dilution refrigerator was monitored with six

carbon resistance thermometers and one ruthenium oxide thermometer Bk7p27, which were

read by the LR110 resistance bridge [38] through a home-made connector box. The location

and typical resistance value of each resistor is summarized in Table 2.3.

The lowest temperature achieved with this refrigerator is 78 mK, according to the

thermometer Bk7p21 attached to the mixing chamber. This is disappointing, since a good

dilution refrigerator can reach 20 mK with a continuous heat exchanger alone. The reason









Thermometer Location R3oo (Q) R77 (Q) R4.2 (R)

1KH Cold plate 145.8 163.4 1024.7
1KL Cold plate 105.1 107.1 117.1
Still Still 146.0 149.0 142.5
HE Heat exchanger 146.6 146.0 118.5
MCout Outside mixing chamber 138.1 140.4 119.9
MCin Inside mixing chamber 123.1 119.0 64.3
Bk7p21 Outside mixing chamber



Table 2.3. Resistance values of the thermometers at room temperature, nitrogen tempera-
ture, and helium temperature. The resistors except 1KH and Bk7p21 are Matsushita 47 n.
1KH is Allen Bradley 100 f. The ruthenium oxide thermometer Bk7p21 was provided by
Mark Meisel. Each resistor except MCin and Bk7p21 have been ground on two sides with
sand paper and attached to a 1/16 inch thick copper plate with GE 7031 varnish. A 0.004
inch thick Mylar sheet has been placed between the resistor and copper plate for electrical
insulation.

for the high base temperature is not understood at the moment. Suspecting that 3He does

not liquefy completely at the condenser attached to the cold plate, I have installed an extra

3He condenser in series to the existing one. This has not improved the performance of the

refrigerator.


Volume of each part of the crvostat. The volume of each part of the cryostat and the

estimated amount of helium gas are listed in Table 2.4 for the diagnostic purposes of future

users.


Coaxial cables and the thermal anchors. Home-made coaxial cables are used for the

vapor-pressure thermometer, torsion pendulum, and ruthenium oxide thermometer Bk5pl04

placed on the experimental stage. The capacitance of each coax cable is 34 pF/m. The

outer conductor of each cable is a Cu-Ni tube with a 0.037 inch o.d. and 0.027 inch i.d.

The insulator of the inner conductor is provided by a TFE tube pulled off from hook-up










Still
M.C. (inside the sponge)
M.C. (outside the sponge)
H.E. out
H.E in
3He filter 1K
3He filter 4K
Leybold exhaust filter
ED500 mechanical pump
ED500 exhaust filter
Cold trap
Cold trap tube
Return line
Return line to cryostat
Total


Volume (cc)
62.5
9.12
30.62
43.45
0.9
3.1
16.5
1,700
2,000
200
851
56.9
210.2
3.86


Table 2.4. Volume of each part of the refrigerator and gas handling system. 'dil.' indicates
the dilute 3He phase, for which 6.4'conc.' indicates the 3He rich phase. The amounts of
3He and 4He are in liter of gas at STP.


wire (Alpha 30 AWG, Cat. No. 2841/1 WHT ) following a recipe of Olivier Avenel. The

inner conductor of each coaxial cable that runs from the top of the cryostat to the top of

the vacuum can is a 0.003 inch diameter Advance wire with 46.1 0/ft resistance.4 The

resistance of the inner conductor is about 200 fl for each cable. Each cable below the top

of the vacuum can uses superconducting wire for the inner conductor.5

Male MALCO connectors (Part No. 142-0002-0001) were used on both ends of each

cable. I first made the mistake of using liquid soldering fluxes such as Superior No. 50

and No. 30 to solder the connector to the inner conductor. Although these are not highly

corrosive fluxes, they are slightly conductive. I was surprised to find voltages from to 60 to

'Advance wire is too soft to put through the TFE tube. Karma wire of the same diameter was put
through the tube first as a guide. Advance wire was glued to the end of the Karma wire and was pulled
through.
SMono filament NbTi with a Cu-Ni matrix, with a 0.0042 inch diameter from Supercon [391.


4He (liter)
40.38

17.81
28.07


Condition
dil.
conc.
dil.+ conc.
dil.
cone.
cone.
gas at 4 K
gas
gas
gas
gas at 77 K
gas
gas
gas


3He (liter)
0.289
5.47
1.86+1.16
2.01
0.54
1.86
0.38
0.57
0.67
0.067
1.00
0.2
0.07
0.09
16.2


82.3








100 mV between the inner and outer conductor.6. This emf was eliminated by switching to

a rosin flux. Always use a rosin flux for electrical joints!

Nine home-made thermal anchors are attached to the top of the vacuum can, the cold

plate, and the mixing chamber, in order to reduce the heat leak along the coaxial cables

from room temperature without exposing the inner conductor of the cables. Figure 2.13

illustrates the interior of the anchor, which consists of a body, a cover, a Kapton sheet

with strips of copper conductors, and four or five female MALCO connectors (Part No.

141-0002-0002) on each side. The copper conductors have been made by the standard

etching procedure for a copper-plated Kapton sheet. The sheet has been glued with GE

7031 varnish onto the bottom of the box with the copper strips facing down, with a 0.004

inch thick Mylar film for electrical insulation. Each thermal anchor adds 1.8 ft to each

cable.

2.6 Sample Gas-Handling System

Figure 2.14 shows the schematic of the gas handling system used to introduce 4He gas

into the sample cell and vapor-pressure thermometer. The reference volume is 2.920.01

cm3, which has been calibrated against a 29.01 cm3 standard volume. All tubes on the

gas handling system stainless steel with a 1/16 inch in o.d. and 0.03 inch in i.d. from

HIP [40]. A Paroscientific model 223AT pressure transducer [44], whose pressure range is

from 0 to 158 kPa, is used to measure the amount of gas introduced into the sample cell

and to calibrate the vapor-pressure thermometers. The transducer gives two frequencies,

which are measured with a two-channel frequency counter and converted to a pressure P

in psia according to the formula given in Table 2.5 as provided by the manufacturer.

6Same effect has been seen with other liquid soldering fluxes such as Superior No.72 and La-Co Brite
soft solder flux.





















































Figure 2.13. Interior of the thermal anchoring box for the coaxial cables.






















gas


amorC UCi Auxiliary port
volume


yostat


S( ) Pumping port
Gas inlet



Cold trap
Paroscientific 223AT
pressure transducer





Figure 2.14. Gas-handling system. All connections are made of stainless steel tubes 1/16
inch o.d. and 0.03 inch i.d. The valves, the connectors, and tubes are from High Pressure
Equipment Company [40].





















T T2
P = C(1 1)[1 D( )]
C = C +C2U+ C3U2
D = D1+ D2U
To = T + T2U+ T3U2
U = t- Uo


(2.16)


Coefficient


Value


C1 123.2387 psia
C2 11.37897 psia/lisec
C3 150.0802 psia/jusec2
Di 0.0446672
D2 0.0000000
Ti 25.05889 usec
T2 0.6601851
T3 18.75280 /Jsec-1


Table 2.5. Formulae and coefficients of calibration for the Paroscientific 233AT pressure
transducer (S/N 35884) [41]. The data are from the Paroscientific calibration sheet. The
calibration accuracy is 0.015 % over the entire pressure range. rt is the temperature period
and r is the pressure period in psec.





57


The reproducibility of the pressure transducer is better than 8 Pa according to the

manufacture. However, the long term stability is limited by the 2C fluctuation of the

room temperature. This is not a problem for measuring the amount of gas for the torsion

pendulum, a task which takes less than 15 minutes. However, when the gas-handling

system is used for the adsorption isotherm, which is discussed in Section 3.2, a drift has

been observed due to changes in room temperature.















CHAPTER 3
CHABAZITE DEHYDRATION TECHNIQUE


This chapter describes the techniques developed to dehydrate the chabazite crystals used

in the torsional-pendulum experiments discussed in Chapter 4 and in Appendix B. There

are about 200 species of synthetic zeolites and 42 known species of natural zeolites [42].

Chabazite has been chosen from this zoo of zeolites as a substrate for 4He in our experiments

for two reasons. First, large crystals of chabazite up to about 1 cm in size are relatively

easy to obtain, unlike all synthetic zeolites which are typically 10 pm or less in size, and

many other natural zeolites are rare. In torsion pendulum experiments, a large crystal of

at least a few millimeters in size is necessary to get reasonable sensitivity for the superfluid

density of adsorbed 4He. If a cell is packed with zeolite powder instead of a large crystal,

most of the adsorbed helium will move with the motion of the grains, resulting in very

poor sensitivity. Second, chabazite is very stable at temperatures up to about 8000C [43],

unlike some zeolite species such as yugawaralite, which changes its crystal structures upon

dehydration. Chabazite can be dehydrated without any irreversible deformation of the

crystal.

To my knowledge, all dehydration techniques developed for zeolite prior to this disser-

tation involved either heating the crystals in vacuum or in air, or, in a few cases, prolonged

evacuation at room temperature. Small synthetic crystals such as ZSM5 [44, 45] or zeolite

Y, which are typically 10 pm or less in size, maintain structural integrity during heating,

but it was not at all clear when we started this work whether crystals of millimeter sizes








could stand such processes. To our surprise, we found that chabazite crystals are pulverized

even by heating to a temperature too low for dehydration. The high-pressure dehydration

technique we have developed to solve this problem is unique and will certainly find an

application in the manufacturing of molecular-sieve filters. The technique will probably be

useful also for removing solvents from other porous media for which supercritical drying is

inapplicable. For these reasons, descriptions given in this chapter are detailed, perhaps too

detailed for a thesis in low temperature physics, to benefit those who may want to further

refine the technique with applications in mind.

3.1 Chabazite

Chemical composition and structure of chabazite. The unit cell composition [42] of

idealized chabazite is Ca2[(A102)4(SiO2)s]. 13H20. In reality, the chemical composition of

chabazite can vary depending on the locality. The crystal is rhombohedral [46, 47] and

each unit cell contains a cage shown in Fig. 3.1. Each cage is connected to six neighboring

cages as shown in Fig. 3.2, each through an aperture made of a single 8-membered ring of

eight Si and Al atoms bonded by oxygen atoms.

The aperture is 3.1 x 4.4 A 2 in size and allows the passage of 4He atoms whose diameters

are 3 A. The top and the bottom of the cage have double 6-membered rings made of eight

Si and four Al atoms bonded by oxygen atoms. The aperture size of the double 6-ring is

2.6 A, which is smaller than 4He. The height of the cage is 10 A and the width is 6.7 A.

Each cage can accommodate about fourteen 4He atoms. There are two Ca2+ ions per cage

with three types of sites at which the ions are located [47]. Site I is at the center of the

double 6-membered rings, invisible to 4He adsorbed in the cage. Site II is on the exterior

of the double 6-membered rings. Site III is near a 4-membered ring which connects the

















































Figure 3.1. Cage structure of chabazite after Barrer [48]. Oxygen atoms are located between
Si and Al atoms, which occupy the apexes. I, II, and III indicate Ca2+ ion sites.


















































Figure 3.2. Framework structure of chabazite after Ruthven [49]. A Si or Al atom is located
at each apex, and an oxygen atom is located in the middle of each line.








double 6-membered rings to a single 8-membered ring. There are one site I, two sites II,

and twelve sites III in each cage. The occupancy rate of Ca2+ ions is 0.6 for site I, 0.35 for

site II, and .0625 for site III [47]. The cages are filled with water molecules which are part

of the crystal structure and need to be removed before introducing 4He .

3.2 Vacuum Dehydration of Chabazite and Nitrogen Adsorption Isotherm.

The first approach we took was to simply heat the chabazite crystals in vacuum, as

is most commonly done to dehydrate zeolite. This was done in a Thermolyne 21100 tube

furnace and a home-made furnace. The latter consisted of a 2" diameter Pyrex tube on

which a 10 ft length of nichrome wire with a 1.07 Q/ft resistance was wound. Glass wool

and glass tape were wrapped around the tube for thermal insulation, with a window about

1 cm in size to provide a view of the samples during heating. The samples were placed

in a Pyrex cell. The temperature of each furnace was measured by a copper-constantan

thermocouple placed in the tube. Each furnace was connected to a diffusion pump which

maintained a pressure of about 10-s Torr during the heating.


Nitrogen adsorption isotherm. A method often used to determine the amount of water

removed from zeolite is simply weighing the crystals before and after dehydration. However,

the chabazite crystals broke during heating into small pieces, some of which tended to

stick on the wall of the Pyrex cell. This made accurate weighing of the crystals difficult

after dehydration. Furthermore, weighing dehydrated crystals required a balance in a dry,

protected atmosphere, which is a non-trivial measurement.

As a better alternative, the adsorption isotherm of nitrogen gas was measured at 77 K.

The gas handling system used for the measurement was the same one used to introduce

the sample 4He gas to the cryostat described in Chapter 2 (See Fig. 2.14). Figure 3.3


Vff

















0.15


, 0. 10
O



C-
E



0.05






0.00
0


600


500

O
-(5

400 E
E

300 0.

c-
200
0C

100


I I I 0I I I0 60I
10 20 30 40 50 60


Pressure


(kPa)


Figure 3.3. Adsorption isotherm of nitrogen at 77 K on chabazite
at 320C. The dashed line is a fit to the Langmuir model.


dehydrated in vacuum








shows an example of a nitrogen adsorption isotherm, taken from run A listed in Table 3.1.

The isotherm appears to be type I according to Brunauer's classification [50] as commonly

found for zeolite, indicating that the pore size is not much larger than the molecular size

of the adsorbate. The figure also shows P/n as a function of pressure P, where n is the

adsorbed amount of nitrogen gas. The linear relationship between P/n and P indicates

good agreement with the Langmuir model [51],



P 1 P
n + -, (3.1)
n bn, n,

where b is an adsorption constant and n, is the amount of nitrogen gas at saturation.

Fitting the data to this equation gives 0.113 mmol for n, and (1.9 0.6) x 10-3 Pa-' for

b. The full-pore amount of nitrogen obtained from n, is 7.05 mmol per 1 g of the original

chabazite crystal before dehydration, corresponding to 7.3 nitrogen molecules per cage.

This corresponds to 88reported by [42].


Results of vacuum dehydration. Table 3.1 is a summary of the results of vacuum

dehydration. Figure 3.4 shows the heating curves. Runs A through G were done in the

Thermolyne furnace. The results show that a significant amount of water starts to come

out from chabazite at a temperature between 2200C and 2300C, and the crystal can be

completely dehydrated at 3000C in a very short time. Chabazite was pulverized in all

these runs regardless of whether or not water was removed except for run B in which the

maximum temperature was only 500C.

In particular, chabazite was pulverized even at 800C, a temperature far too low for

dehydration. It is clear that the pulverization of chabazite is not associated with the

removal of water. Although what breaks the crystals is unclear, at least one can exclude

















300


C)
O

200


0 / .e E
6D
OE
4 F
1) G

E 100 -AI
() O +K





0 10 20 30 40 50 60 70 80

Time (hours)


Figure 3.4. Heating curves for vacuum dehydration. The temperature in runs C through G
is the reading on the panel of the Thermolyne furnace. The temperature in the other runs
is that of a copper-constantan thermocouple inside the Pyrex glass furnace. The heater
was turned off at the end of each curve.









Run T (OC) Hours Void (%) Appearance Note
A 300 0.25 100 Powder Thermolyne set to LO
B 50 1.0 0 No change With Variac
C 80 8.5 0 Powder With Variac
D 150 0 1 Powder Slow heating. With Variac
E 210 2 15 Powder With Variac
F 200 70 1 Powder With Variac
G 220 18 Powder Slow cooling. With Variac
H 224 12 Powder Home-made oven with window
With ramp circuit
I 230 12 0.6 Powder Slow heating and cooling
With ramp circuit
J 319 0 Powder Power failure
With ramp circuit
K 227 21 Powder With ramp circuit


Table 3.1. Summary of vacuum dehydration. A Thermolyne furnace has been used for runs
A through G. A homemade furnace has been used for runs H through K. The amount of
nitrogen absorbed at 77 K is expressed as a percentage of the full-pore adsorption per unit
mass of the sample dehydrated in run A.

the possibility of framework deformation due to dehydration. One possible explanation is

the large thermal expansion of water in comparison with that of the framework1.

Only run G, in which cooling was slow, showed any promise. The crystal in this run

became completely white as in all other runs except run B, but was less fragile than the

other crystals which either turned into white powder during heating or crumbled during

handling with a pair of tweezers. On the other hand, the heating rate of 0.20C/min used

in run D did not prevent pulverization, although the final temperature of 1500C was too

low for dehydration. The observation that the pulverization occurs even when dehydration

does not take place and that the cooling rate made some difference in the strength of the

samples motivated us to study when the pulverization starts and how it progresses.

'The coefficient of the linear thermal expansion for chabazite is 2.3 x 10~6 K-1 near 300 K [42]. For
water, the coefficient is 303 x 10-8 K-I [52].









Time
(hours)
0.0
0.4
0.6

1.2

2.1

14.0

15.0

16.1

18.2
21.9
24.6
37.75


Description

No change
No change
Half of crystal white

Remaining half has a few cracks

No change

No change

Whole crystal is getting whiter

Same as above

Same as above
Same as above
Same as above
Completely white


Temperature
(C)
27
199
215

222

224

220

214

210

200
173
145
27


Table 3.2. Summary of run H. The size of the chabazite crystal was about 1 x 2 x 2 mm3.
The pressure inside the furnace was maintained at less than 4 x 10-s torr. The temperature
was measured by a copper-constantan thermocouple inside the furnace.

In order to observe the crystals during heating, a home-made furnace with a window in

the thermal insulation was built as described at the beginning of this section. The heating

and cooling rates of the furnace were controlled by the arrangement shown in Fig. 3.5. The

ramp circuit controls the combination of a Douglas Randall RDA input module and a R10

proportional controller [53] which regulates the power into the Variac. The setting of the

Variac determines the maximum voltage across the 10.3 1f heater. Figure 3.6 shows the

ramp circuit, which is a simple integrator using an operational amplifier. The ramp rate is

set by the variable resistor.

Table 3.2 shows the observations made in run H, in which the temperature was raised

at a rate of 8*C/min. The crystal showed little change until the furnace reached the


Note

Start heating








Start cooldown























To vacuum
pump


Pyrex tube
5 cm dia.
78 cm long


I 120 V AC

p RDA ROA
uuit input module proportional
controller




Fuse
10 A










Figure 3.5. Home-made furnace and the power controller. Glass tape and glass wool were
wrapped over the heater for thermal insulation. A see-through window was made by cutting
a 1 cm x 1 cm hole in the glass insulation.





















+5

Discharge

IOOK 2.7pFx7


-5 200 Ramp switch


100K ----OUT


200 LF355J
2.2M



+50
NC 0
-50
Preset switch










Figure 3.6. Ramp circuit for the furnace-heater controller. Seven 2.7 pF capacitors were
used in parallel for the integrator.








final temperature of 224C but started to turn white 10 minutes later. One half of the

crystal became white first, the other half turning white subsequently at a slower rate. This

observation suggests that pulverization occurs at different rates depending on individual

crystals or on parts of a crystal. Another important observation in this run was that there

was little change in the crystal for the first 20 minutes of heating, although the temperature

had reached about 2000C by the end of this period. The pulverization occurred primarily

after the furnace reached the highest temperature of 224*C and continued to progress while

the furnace cooled toward room temperature. In fact, much shorter heating as in run C

produced a badly pulverized crystal, implying that the pulverization continues even near

room temperature once the crystal has been heated. In run J, power failure terminated the

heating immediately after the temperature reached 3190C Even after the furnace reached

room temperature, the pulverization of the chabazite crystal progressed for at least 12

hours.

3.3 High Pressure Dehydration of Chabazite

Dehydration in an MS-17 reactor. In the manufacturing process of aerogel, the sol-

vent needs to be removed from the silica solution. If the gel is heated in vacuum for drying,

the silica framework collapses due to the surface tension of water. The common method to

avoid this is to heat the silica solution under high pressure so that water vaporizes above

the critical point [54], where the surface tension of water vanishes.

To see if this method can be applied to the dehydration of large chabazite crystals, a

high pressure furnace was built as shown in Fig. 3.7. The MS-17 high pressure reactor [40],

in which the chabazite crystals are placed, is connected through a stainless steel tube with

a 1/16 inch o.d. to a dip stick filled with activated charcoal, a nitrogen gas cylinder, and



















Pressure gauge-


To cylinder


To dip stick


Vent


MS-17 reactor

Pyrex tube
)5 cm dia.
78 cm long


S120 V AC
R1OA
RDA R-OA
SRDAproportional
it -input module ontroller
controller



Fuse
10 A










Figure 3.7. High pressure furnace using a MS-17 reactor. The reactor was inserted in the
Pyrex glass tube removed from the home-made furnace for vacuum dehydration.









Run T (C) P (psi) Description Note
H1 500 6500 Powder Nitrogen atmosphere
H2 400 7200 White and Intact Water atmosphere
pumped to vacuum
H3 240 7100 Surface clouded Leak. Heating halted
otherwise no change
H4 320 6000 White Glass cell also white
H5 200 5200 No change Nitrogen atmosphere
H6 250 900 No change Nitrogen atmosphere


Table 3.3. Summary of supercritical dehydration. The furnace is a HIP reactor (model
MS-17) pressurized by a charcoal-filled dip stick.

a pressure gauge. The entire reactor is inserted into the Pyrex glass tube scavenged from

the home-made vacuum furnace, including the heater. Nitrogen gas is introduced from the

cylinder at about 2,000 psi to the dip stick immersed in liquid nitrogen. Warming the dip

stick back to room temperature raises the gas pressure in the reactor to about 4,000 psi. By

repeating the process, a pressure of over 10,000 psi is achieved. The rated pressure of the

reactor and the stainless-steel tubing is 15,000 psi. However, the actual working pressure

turned out to be less than 10,000 psi because the pressure seals of the reactor are heated

in this arrangement.

The ramp circuit and the power control unit were the same as in the vacuum dehydration

experiment. Heating of the entire reactor oxidized the threads of the pressure seals. To

prevent the oxidation, the threads were coated with Fel-Pro C5-A [55] as recommended by

the reactor manufacturer. The oily component of this lubricant burned when heated and

left a nasty residue, which needed to be cleaned off the inner surface of the Pyrex tube and

the threads of the pressure seals after each run.

A total of six heating runs were made using this furnace: two in nitrogen atmosphere

and four in water vapor, as shown in Table 3.3. In run Hi, the chabazite crystal was heated








in a 6,500 psi nitrogen atmosphere to 5000C, at which time the furnace was pumped to

vacuum. This combination of pressure and temperature was chosen so that the water in

chabazite would be in the supercritical region of the phase diagram. This procedure yielded

88% of the void volume of the fully dehydrated sample, but the crystal was damaged as

the in heating in vacuum. Obviously, either supercritical dehydration does not work for

chabazite or the critical point for the zeolitic water is higher in pressure or in temperature

than the parameters we have chosen.

Run H5 was made in a 5,200 psi nitrogen atmosphere with a final temperature of 2000C.

Unlike in run H1, the furnace was never pumped. As expected, there was no measurable

void volume in the crystal, whereas the appearance of the crystal remained unchanged.

This showed that a high pressure atmosphere prevents pulverization of the crystal. Clearly,

the water needed to be removed from chabazite selectively by a sorption pump without

releasing the pressure in the furnace. Unfortunately, the end cap of the MS-17 reactor

accommodated only a 1/16 inch outer-diameter tubing, which added an unacceptably large

impedance to the sorption pump. In order to remove this limitation, a new home-made

furnace was built as described in the next section.

Runs H2 through H4 were made in water vapor on a hypothesis that high-pressure water

vapor in the reactor reduces the internal stress caused by the thermal expansion of water in

the chabazite framework by lowering the chemical potential difference of water between the

inside and outside of the framework. In run 2, the water vapor in the furnace was released

to the atmosphere after the furnace reached 5000C and was then pumped to vacuum. In

this run, the sample crystal became completely white but remained in one piece.

In run H3, the heating was halted due to an accidental failure of the pressure seal. The

highest temperature in this run was 2400C. The water was not removed from the furnace









Run T (C) P (psi) Void (%) Description Note
H7 245 1290 0
H8 300 1120 0.1
H9 320 1340 75.5 Three pressure leaks
H10 320 1200 1.5
H11 370 1000 34


Table 3.4. Summary of high pressure dehydration. The furnace was made from a 1/2 inch
o.d. stainless steel tube and was directly attached to a sorption pump.

until it cooled to room temperature. The crystal showed little change except for some

cloudiness on the surface, suggesting that the pulverization of the chabazite crystal can be

avoided even at temperatures high enough to pulverize the zeolite crystal in vacuum.

In run H4, the crystal was heated to 320C. The only differences from run H2 were a

lower ramping rate which required four days for the temperature to reach the final value,

as opposed to three days for run H2, and the maximum temperature which was lower by

about 80*C. The chabazite crystal and the Pyrex glass cell that held the crystal turned

completely white. It appears that water at high temperature and high pressure reacts with

chabazite and Pyrex.


Dehydration in the 1/2 inch stainless steel tube furnace. This home-made furnace con-

sisted of a stainless steel tube 1/2 inch in o.d., 0.035 inch in wall thickness, and 16 inch in

length with a sorption pump as illustrated in Fig. 3.8. A sorption pump filled with acti-

vated charcoal was connected to the furnace via a short length of a 1/4 inch o.d. tubing.

When immersed in liquid nitrogen, the pump removes water selectively from the high pres-

sure helium atmosphere. The same dip stick that had been used in the previous furnace

was used to pressurize the furnace with helium. Although the pressure rating of the tube

























(Only for 1/2 Stainless steel tube)


1/2 Stainless steel tube Sorption pump
or
9/16 Stainless steel tube


To cylinder


vent


interface


Fuse
10 A


- Liquid nitrogen
dewar
120 V AC


Figure 3.8. High pressure furnace made from a 1/2 inch stainless steel tube. The furnace is
connected to a sorption pump filled with activated charcoal for selective removal of water.








was 3,000 psi, the Stycast 2560 feedthrough for the thermocouple wires limited the actual

working pressure to less than 1,300 psi.

A total of five runs were made in this furnace as given in Table 3.4. All of them used

a helium atmosphere, since only a gas which does not liquefy at 77 K is compatible with

the liquid-nitrogen-cooled sorption pump. The helium pressure ranged from 1,000 psi to

1,340 psi, and the maximum temperature ranged from 245C to 370C. The crystals were

wrapped in a thin sheet of stainless steel to keep them from moving in the furnace. During

run H9, the pressure dropped three times nearly all the way to atmospheric pressure, and

the sample was found to be completely pulverized. Therefore, the result of this run should

be discarded. The pressure failure occurred at the valve located right above the sorption

pump, when the nitrogen dewar was topped off. Evidently, the rubber o-ring in the valve

froze out and ceased to seal the valve shaft properly when the liquid nitrogen level was too

close to the valve.

The results of these runs show clearly that a higher temperature is required to dehydrate

chabazite in helium gas at an elevated pressure than is needed in vacuum. (See Table 3.4.)

Even at 370C, a substantial amount of water remained in chabazite after one week. The

crystal was not pulverized at least up to this temperature, although it did turn white,

suggesting microscopic damage. At 320C, where only 1.5% of water could be removed in

10 days, the sample remained mostly transparent with little change. The results strongly

suggest that a temperature higher than 370C is required to completely dehydrate chabazite

in high-pressure helium gas and that pressures much higher than 1,000 psi may prevent

chabazite from turning white.








Dehydration in the 9/16 inch stainless steel tube furnace. Another furnace was made

from a 9/16 inch outer-diameter stainless steel tube purchased from HIP with an inner

diameter of 3/16 inch and a rated pressure of 60,000 psi, as opposed to 3,000 psi for the

1/2 inch o.d. tubing. The configuration of the furnace was similar to that of the 1/2 inch

o.d. furnace. The working pressure was limited to the rated pressure of 15,000 psi for the

1/16 inch o.d. tubing which connected the furnace to the dip stick. No thermocouple was

placed inside the furnace to get rid of a feedthrough, which was the weak spot in the 1/2

inch o.d. furnace. 10 ft of a 1.07 O/ft heater wire was wound over a glass sleeve which

covered the tube. A chromel-alumel thermocouple insulated with a small diameter glass

sleeve was placed underneath the larger glass sleeping.

Table 3.5 shows the results of dehydration runs done in this furnace. Runs Cl, C2, C4,

and C5 yielded no significant void volume. The surfaces of the crystals became lusterless

and white after the heating. The sample of run C5 was reheated in vacuum in order to

remove all remaining water. However, very little increase in the void volume was observed

in the nitrogen adsorption isotherm at 77 K, suggesting that the crystal had permanently

lost the pores. The result is surprising, since chabazite heated up to 800C in air can be

rehydrated at room temperature [43]. However, Aoki [56J has reported that chabazite in the

presence of water under a pressure up to 1 kbar transforms into other types of zeolite such

as wairakite and gonnardite around 250C depending on the heating conditions. In high

pressure helium gas whose density is not much lower than that of liquid helium, zeolitic

water which dissociates from the chabazite framework cannot move out of the crystal as

quickly as in vacuum heating. It is possible that prolonged contact with zeolitic water

under high pressure caused some transformation of chabazite into a structure with smaller

pores or without pores.



















Run T (C) P (psi) Time (hours) Void (%) Note
C1 600 8200 144 2.7 pressure failure
C2 580 9600 167 3.5 White. Shiny
C3 640 14000 133 49 Heating with a step
C4 600 15100 155 0 White. Fragile
C5 740 15700 150 0.2 Three steps
C6 660 12800 65 33 Pressure failure
C7 390 12800 brief 8 Three steps
C8 650 15600 120 20 Three steps
C9 560 12000 48 39 Active temperature control
One step here after


400 12800
320 12700
360 13000
320 13000
400 13800
360 13800
370 13600

370 13600
380 13850
390 13800
390 12450
390 12450
390 13800


Sample for Torsional
pendulum experiment
Heater rewound


Table 3.5. Summary of high-pressure dehydration of chabazite in the 9/16 inch diameter
stainless steel furnace.


C10
C11
C12
C13
C14
C15
C16

C17
C18
C19
C20
C21
C22
















800


0 100 200
Time (hours)


Figure 3.9. Heating curves for chabazite dehydration runs C3 and C4.








Run C3 yielded a significant void volume of 49% in contrast to runs C1, C2, C4, and

C5. The only important difference between run C3 and the other four runs is the heating

rate. Fig. 3.9 shows the heating curve for C3 and C4. In run C3, the temperature was

raised continuously from room temperature to the final value, whereas run C4 employed an

intermediate step in which the temperature was kept at 140C for 12 hours. It is not clear

whether this step enhances the dehydration by lowering the average rate of temperature

change or it is necessary to have a period of constant temperature before reaching the

final temperature. In order to explore further, heating with three steps was tried in runs

C6, C8, and C9, which yielded significant void volumes, although they were not as large

as obtained in run C3. Surprisingly, post-baking of samples of runs C6 and C9 produced

either no change or only a small increase in the void volume, revealing that the up to 67%

of the pores had been permanently lost. The loss was nearly less for the crystal dehydrated

at the lower temperature of 560C, indicating that an even lower final temperature needed

to be used. Heating with one step had produced a larger void volume than those with three

steps.

Lower final temperatures of 320C through 400C and one step during the ramp-up

of temperature were used in all runs after C9. All of them except runs C13 and C19

yielded larger void volumes than any previous runs, with the void volumes showing no

clear correlation with the final temperature. The results of the post-baking showed that

the permanent loss of pore volume can be minimized, in the best case only 8% of the total

pore volume as in run C12. The optimum temperature appears to be around 360*C. Run

C16 at this temperature yielded 85% of the total void volume, which is the highest of all

the runs.








After run C16, the heater wire on the furnace was rewound. This evidently caused the

actual temperature of the furnace to be somewhat lower than before for a given thermo-

couple reading. Run C17 indicates the result of dehydration after the rewinding at the

same nominal temperature as in C16. This result shows that the temperature was up to

30C lower around 360C. The optimum final temperature after rewinding the heater was

found to be 390"C.

The final runs are C18 and C19, in each of which a large crystal roughly 5 mm in size

were heated together with several small crystals ranging from 1 to 2 mm in size. For each

run, the nitrogen adsorption isotherms were measured separately for the large crystal and

the small crystals, yielding about a 10% larger void volume for the large crystal. Postbaking

of the small crystals revealed that 6 12% of water remained in the pores after the high-

pressure dehydration and 20 25% of the pore volume had been permanently lost. The

high-pressure dehydration either works less effectively for small crystals or causes larger

loss of pores in small crystals. At the present, it is unclear what causes this difference. At

any rate, the two large crystals prepared in these runs were considered satisfactory for the

torsional-pendulum experiments described in Chapter 4 and Appendix B, since the 75 -

77% for the fraction of open pores were certainly above the percolation limit. We leave it

up to material scientists and engineering chemists to perfect the technique of high-pressure

dehydration developed in this dissertation work.















CHAPTER 4
TORSION PENDULUM EXPERIMENT ON 4HE ADSORBED IN CHABAZITE


4.1 Sample Cell

A schematic representation of the torsion pendulum containing a dehydrated chabazite

crystal is given in Fig. 4.1. The crystal used in the experiment described in this chapter was

C22, whose preparation has been described in the previous chapter. Another pendulum

was constructed with crystal C16 prior to this experiment. However, it was realized at the

end of the experiment that the crystal adsorbed essentially no 4He introduced to the sample

cell. That experiment is discussed in Appendix B together with a control experiment using

a pendulum containing no chabazite crystal.

The crystal was 5 x 5 x 5 mm3 in size and weighed 87.6 mg before dehydration. The

void volume of the crystal after dehydration was estimated to correspond to 0.467 mmol

of nitrogen according to the nitrogen isotherm of smaller crystals dehydrated in the same

batch. The void volume of the sample crystals was not measured, since nitrogen-adsorption

isotherm measurement sometimes damages the crystal according to our experience. The

void volume corresponds to 77% of that of a fully dehydrated crystal. The estimated

amount of 4He that completely fill the pores is 0.75 mmol, based on the ratio of about 2.7

between the volumes of a nitrogen molecule and a helium atom.

The crystal was glued in place with Stycast 2850FT in a dry nitrogen atmosphere. The

moment of inertia of the pendulum was calculated to be I = 2.77 x 10-2 g-cm2 including

























Brass cell-



Be-Cu torsion rod


Chabazite crystal

Stycast 2850 seal


Figure 4.1. Torsion pendulum containing a dehydrated chabazite crystal.








the chabazite crystal. The quality factor Q was about 530,000 at 1 K as can be seen from

the resonance curve shown in Fig. 4.2.

4.2 Results and Analysis

Figures 4.3 and 4.4 show the resonance frequency and the amplitude of the torsion

pendulum for several amounts of 4He adsorbed in the chabazite crystal. There is no obvious

feature within the frequency curves indicating that a superfluid transition was detected

within the resolution of the experiment. The smooth increase in frequency with temperature

observed for amounts of 4He corresponding to 80% or more of the full pore volume was

due to evaporation of 4He from the chabazite. The null result of the experiment places

an upper limit for the possible superfluid density. The loading sensitivity of the pendulum

depended slightly on the amount of 4He, but the highest value was -0.25 mmol/Hz as

seen from Fig. 4.5, which shows the resonance frequency as a function of the amount of

4He at 150 mK, near the lowest temperature of the experiment. The standard deviation of

the frequency was typically 3.3 x 10-s Hz at a fixed temperature. Therefore, the smallest

amount of superfluid component that can be detected in our experiment was 8.2 nmol,

corresponding to 7.8 ppm of adsorbed 4He at full pore. Within this resolution, we have

observed no superfluidity in 4He adsorbed in chabazite.

4.3 Conclusions

We can hypothesize as to why we have not observed superfluidity. One obvious but

uninteresting possibility is that the pore size of the chabazite is too small for 4He to

become superfluid. In other substrates such as porous Vycor glass, the first 1.3 to 1.5

atomic layers of 4He do not show superfluidity [7]. The chabazite cavity is merely 9

A in the cross-sectional direction. In such a small space, only a few 4He atoms can be





















SI I I


0

0

0 0o

0


00000


00oo000 0000


S00 I


4647.75


I I I I I I I I I


4647.80


Frequency (Hz)


Figure 4.2. Resonance curve of the torsional pendulum containing a chabazite crystal, taken
near 1 K before introducing 4He into the cell. The Q factor is 530,000.


0.06








<0.04



C1)

D

0.

E 0.02


4647.85


- --


























N
-I


I I I I
4640 0.5 1.0 1.5 2.0

Temperature (K)


Figure 4.3. Resonance frequency of the torsional pendulum as a function of temperature
for various amounts of 4He absorbed in chabazite.






















0.838 mmol
o o0MOaIW 0OO 0 0 0 00 0


d 3(hgOmWC0 00ooooo000000COd O 0


0.748 mmol
0


0.654 mmol


"' --


aO 000





i lI i I


0.560 mmol
S00 0 0 0 0


0.467 mmol
0 0 0 0000


0.373 mmol
000 0 00 0 0


d.0 0.5 1.0 1.5 2.0

Temperature (K)




Figure 4.4. Amplitude of the torsional pendulum as a function of temperature for various
amounts of 4He absorbed in chabazite.


50 -


OM 0 P 0


40 I-


30 -


E


TD
-i

EC
E
Q:


20 -


_






















I


0
0

0


0o


0
0


0.6


amount


0.8

(mmol)


Figure 4.5. "He-loading sensitivity of the torsional pendulum
C22 at 150 mK.


containing chabazite crystal


4646



N
I

S4644
O
C

CD
04642
Q)
L 4642


46480
0d.


0


Adsorbed











accommodated on top of the first layer. If the 4He film in chabazite has a localized layer

as thick as in porous Vycor glass, this layer alone will fill up the pores, leaving no room

for a superfluid layer. The objective of this experiment was to see if 'He under such an

extreme confinement can still become a superfluid due to the periodic surface potential of

the chabazite pores. This evidently does not occur in chabazite. However, chabazite being

a natural mineral, it is possible that the sample crystal contained a large number of lattice

defects which blocked the superflow. It is also possible that the cations in the chabazite

cavities are located at random sites and destroy the periodicity of the surface potential.

For these reasons, it would be interesting to revisit 4He in zeolite in the future when an

ingenious chemist succeeds in growing a large synthetic crystal of zeolite either containing

no aluminum, hence, no cation, or with cations located only inside the lattice framework.

Another possibility is that the crystal contained microscopic cracks, although the crystal

remained macroscopically intact after dehydration. A sufficient number of cracks which

block the flow paths of superfluid can reduce the fraction of superfluid component that

decouples from the torsional pendulum.













CHAPTER 5
TORSIONAL PENDULUM EXPERIMENT ON 4He ADSORBED IN 25 A DIAMETER
PORES OF SILICA


This chapter describes the torsion pendulum experiment on 4He adsorbed in porous silica

whose nominal pore diameter is 25 A. The pore size is the smallest in which the superfluid

transition of 4He has been studied to date. Prior to this study, the superfluid transition

has been observed in the full pore case of a custom-made Vycor glass of similar pore size,

but little other than the transition temperature of Tc = 0.8 K can be extracted from the

data [57].

5.1 Sample Cells

The porous silica was obtained from Geltech [58] and was cylindrical, 0.388 inch in

diameter and 0.200 inch in height, weighing 0.42 g. According to the manufacturer, the

specific void volume is 0.4 cm3/g, which is equal to 43% porosity on the basis of the density

of silica, 2.15 g/cm3 [59].

Modeling the pores to be uniform cylinders 25 A in diameter leads to an estimate for

the surface area of 260 m2. Only four atomic layers of 4He can be adsorbed on the surface

because of the smallness of the pore diameter. The 4He capacities of the first layer and the

second layer are taken to be 4.30 mmol and 2.18 mmol, respectively, from the densities of

4He in porous Vycor glass given by Brewer et al. [60]: 18.3 /mol/m2 for the first layer

and 13.8 pmol/m2 for the second layer. The densities of the higher layers are assumed to

be that of bulk liquid 4He, 36.3 mmol/cm3 [60]. These estimates lead to 7.73 mmol for the

amount of 4He needed to completely fill the pores.






















0

0O
0O
)O
)O

)

)


20 40


Pressure


100


(kPa)


Figure 5.1. Adsorption isotherm of 4He at 4.2 K.


O
E
E


120