Oxygen Intercalation in Electrochemically-doped
La2Cu0 4 +6
by
Pamela Lena Washington Blakeslee
B.A. Physics
University of Chicago 1990
Submitted to the Department of Physics
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
February 1997
@ Massachusetts Institute of Technology 1997. All rights reserved.
Author ....
Department of Physics
December 20, 1996
,
/
Certified by
Marc A. Kastner
Professor of Physics
Thesis Supervisor
Accepted by ................................
..
..
..
.......
George F. Koster
Chairman, Departmental Committee on Graduate Students
1iE I1
097
Oxygen Intercalation in Electrochemically-doped La 2Cu04S+
by
Pamela LenS Washington Blakeslee
Submitted to the Department of Physics
on December 20, 1996, in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy
Abstract
Electrochemically-oxidized ceramic and single crystal samples of La 2 CuO 4±s are described in this thesis. Measurements of the interstitial oxygen density, 6, and magnetization coupled with staging data from neutron scattering experiments provide information on the superconductivity and on the staging ordering observed for 6S 0.05
which is analogous to staging in graphite. We show that ceramic samples can be oxidized at constant voltage to reproducibly achieve a particular superconducting phase.
We also find that the rate of oxidation is 10 times slower than that of reduction in
single crystals. In addition, the diffusion coefficients in single crystals are found to be
several orders of magnitude larger than those measured for electrochemically-oxidized
thin films (- 103) or thermally oxidized single crystals (- 1010). This demonstrates
that oxidation is not simply a diffusion-limited process as previously assumed. Finally, neutron data on crystals in this study have added information to the La 2 CuO4 +s
phase diagram. Stage 6 has been confirmed to occur for 6 - 0.06, and stage 4 has
been found to occur near 6 - 0.1.
Thesis Supervisor: Marc A. Kastner
Title: Professor of Physics
Acknowledgments
I would like to thank my research advisor, Marc Kastner. He has been very willing to
take the time to talk to his students. While in his lab, I have learned the importance
of knowing how to work independently and to be assertive. I am especially grateful
for his very careful reading of my thesis, which has made it a much better document
than it would have otherwise been. I hope that I will remember the importance of
discarding ideas that don't fit in with the facts, no matter what I ultimately do in
life.
The other members of my thesis committee, Takashi Imai and Hale Bradt, were
very flexible about setting the defense date for which I am grateful.
I am also grateful to the students in the Kastner lab: David Abusch-Magder,
Danielle Kleinberg, Nicole Morgan, and David Goldhaber-Gordon. They are all very
smart and good-natured people, who have all helped me out from time to time and
also who made graduate school more pleasant. I am glad to have known past students
in Marc's group including Paul Belk, Nathan Belk, and Ady Levy. I also appreciated
conversations and helpful criticisms of thesis by Beth Parks and Fangcheng Chou. It
has been a privilege to get to know them; they are always willing to share their time
with others. Young Lee, Barry Wells, and Rebecca Christianson have also made life
in Building 13 a richer, more pleasant experience. Rich Perilli and Tim McClure were
both fun to talk to and extremely helpful when I found myself needing to use the
CMSE fabrication lab or crystal growth facility. The people in the CMSE office have
also always been very nice and friendly - Carol Breen, Karen Fosher, Susan Rosevear,
Ron Hasseltine, and Virginia Esau.
Other people I have met - Ruti Abusch-Magder, Sandra Brown, Marta Dark,
Gillian Reynolds - have also made life easier here. Having someone to talk to when
things are not going so well makes a world of difference. Peggy Berkovitz and Pat Solakoff in the Physics Office are always helpful and willing to listen. Peggy Berkovitz's
sweet disposition is uplifting. She really cares about people.
The friends my husband John and I made at Tech Catholic Community have been
great. It is truly a community. The time we've spent with Christy and Michael Klug,
Diane and Bill Daughton, Leigh and Abram Dancy, Aimee and Stefano Schiaffino,
Mary K and Michael Crescimanno and their kids was encouraging and plain fun.
I certainly would not be here without my family. My mother and father have
encouraged and supported me my whole life with their love and prayers. Although
my dad is no longer in this world, I constantly recall all the time he spent with me,
and it encourages me even now. I am thankful for my brother who is willing to listen
to me "babble" and pray for me. My grandparents, aunts, and uncles have also been
there whenever I needed them. My best friend from high school, Christine Schott,
is a wonderfully smart and caring person, and our conversations have cheered me up
more times than I can count.
I especially thankful for my husband John. He loves me and is always there for
me. I have shared and continue to share my faith with him as we now share a child.
He is a gift and a reminder to me that there is a Wonderful God, who loves each
one of us. Although I constantly fall short of the mark, it is my prayer that John
and I will always strive to do what is right is God's eyes. That is, to be joyful in
hope, patient in affliction, faithful in prayer, to work hard, and to love each other
unconditionally and others as well.
Contents
1 Introduction
1.1
2
Structure and Properties of undoped La 2 Cu04
...........
1.1.1
Crystal Structure .
1.1.2
Electronic Properties .
1.1.3
Magnetic Properties
.........
..........
1.2
Previous Work done on La 2CuO 4 +s ......
1.3
Motivation for this thesis .
...........
28
Experimental Details
28
2.1
Overview . . . . . .
2.2
Sample Preparation . . . . . . . ..
2.3
..........
2.2.1
Ceramics .
2.2.2
Single crystals ........
2.2.3
Growth Methods of single cr:ystals
........
Experimental Setup .
2.3.1
Ceramics .
2.3.2
Single Crystals
..........
.......
......
2.4
Electrochemistry Basics
2.5
Electrochemical Reactions .....
2.5.1
2.6
Undesired or Side Reactions
Other Considerations .
- -
2.6.1
A Definition of sample equilibrium
2.6.2
Usefulness of cyclic voltammetry
. .
.
. . . . .
28
3
2.6.3
Temperature dependence of the Nernst equation ........
2.6.4
Bulk Diffusion ...........................
Experimental Results on Polycrystalline La 2 Cu04+s
3.1
Overview .................................
3.2
Interpreting the time decay of current in electrolysis experiments .
3.3
Data on a single pellet at room temperature .
3.4
Data on multiple pellets at room temperature .
3.5
Comparison of single pellet electrolysis data to multiple sample mag-
...........
.............................
netization data
4
............
3.6
Reproducibility of jump in Tc from another set of pellets
3.7
Stability of 45K superconducting phase .
3.8
5C Electrolysis Data ..................
3.9
Calculation of Diffusion Coefficients .
......
...............
.........
Experimental Results on Single Crystal La 2 CuO 4 +5
92
4.1
Overview .
92
4.2
Electrolysis data
4.3
4.4
.....
. . .. . . .. . .
. ..
. .
. . . . . .
93
4.2.1
Subtraction of background currents . . . . . . . .
. . . . .
93
4.2.2
Diffusion into a finite cylinder . . . . . .
4.2.3
Table of crystal data ..........
4.2.4
Sample XE1 .
4.2.5
Sample XE2 ............
4.2.6
Sample XE3 ......
4.2.7
Sample XE4
4.2.8
Sample XE5 .
4.2.9
Summary of electrolysis data . . . . . . .
..
............
....
..
.......
.
Magnetization Data .
........
............
......
.
..
.
94
.. ... ... ....
95
.. .. .... ....
96
.. ..
. . . . .. .
97
. . . . . .. .
98
.
...
.........
. . . .. . 98
.. .
. . .
..........
.....
. . . .
.
. . . . .
99
. . .
99
. . . .
4.3.1
Magnetic susceptibility in the oxygen-pooir phase
. ......
4.3.2
Magnetic susceptibility in the oxygen-rich phase
......
Neutron scattering data
.
............
.
. .
. . . . .
. 125
125
.
126
. 140
4.5
5
Sum m ary ................
.
.. ...
.
. . . .
. 141
Conclusions
147
A Units for magnetic susceptibility and charge plus experiment-related
schematics
B Preliminary Transport Data
150 D
154
L
List of Figures
.
.........
..
. . . . .
.
16
. . .
. . . . .
.
18
. . . .
.
22
. . . . . .
25
. . . . .
30
....
. .. .... ..
31
1-1
La 2 Cu0 4 Crystal Structure
1-2
Crystal field splittings for Cu d-orbitals . . . .
1-3
Phase diagram for La 2 -SrCu4
. . . . . . .
..
1-4
Tentative phase diagram for La 2 CuO 4 +s . . .
. . . . .
2-1
Powder x-ray diffraction pattern for La 2 Cu04
. . . . . .
2-2
Sketch of 0.25 inch die used for La 2 CuO4 . . .
2-3
Electrolysis Cell Schematic . . . . . . . ....
2-4
. . . . .
. . . . . .
36
Chronoamperometry scan at 80C . . . . . . .
. . . .
. . . . . .
41
2-5
Cyclic Voltammetry scan at 80C . . . . . . . .
. . .
. . . . . .
43
2-6
Cyclic Voltammetry scan at 25C . . . . . . . .
. . . . . . .
46
2-7
Temperature dependence of the Open-Circuit Reference Voltage .
2-8
Model Diffusion into a finite cylinder with impermeable end faces
3-1
Chronoamperometry scans for selected pellets
3-2
Charge as a function of time for a pellet
3-3
to and p as a function of reference voltage for several pellets
3-4
Equilibrium charge values as a function of reference voltage on a single
. . .
.............
................
pellet ....................................
3-5
Charge as a function of reference voltage on various pellets ......
3-6
Transition temperature, Meissner effect, and shielding fraction data:batch
one .....................................
3-7
Magnetic Susceptibility data for selected pellets .
3-8
Magnetic and Oxidation Data on selected pellets .
...........
...........
3-9
Meissner effect and shielding fraction for some oxidized pellets . . ..
71
3-10 Susceptibility data taken at electrolysis at 360K . ...........
73
3-11 Transition temperature for some oxidized pellets . ...........
74
3-12 Charge as a function of reference voltage on various pellets .....
.
75
3-13 Magnetic Susceptibility Data on a pellet:time dependence ......
.
77
. .
79
3-14 Current and charge versus time for a pellet de-intercalated at 5C
3-15 Current and charge versus time for a pellet oxidized at 5C ......
80
3-16 Current versus time for a pellet oxidized at 5C on a log plot .....
81
3-17 Current versus time for a pellet oxidized at 5C on a log plot ....
3-18 Partial phase diagram for a pellet oxidized at 5C
.
82
84
. ..........
3-19 Extraction of diffusion coefficients for pellets oxidized at 0.265V and
0.30V
..................
................
87
3-20 Extraction of diffusion coefficients for pellets oxidized at 0.35Vand 0.40V 88
3-21 Extraction of diffusion coefficients for pellets oxidized at 0.45V and 0.50V 89
3-22 Extraction of diffusion coefficients for pellets oxidized at 0.55V and 0.60V 90
3-23 Diffusion coefficients versus reference voltage for pellets oxidized for
one day
.................
91
................
4-1
Chronoamperometry scan at 80C for XEI:OV
. ............
4-2
(Qo, - Q)/Qo vs. time at 80C for XE1:0V . ...............
103
4-3
Chronoamperometry scan at 80C for XE1:0.53V . ...........
104
4-4
(Q, - Q)/Qo vs. time at 80C for XE1:0.53V . .............
105
4-5
Chronoamperometry scan at 80C for XE2:0.1V
106
4-6
(Qo, - Q)/Qo vs. time at 80C for XE2:0.1V . ..............
107
4-7
Chronoamperometry scan at 80C for XE2:0.35V . ...........
108
4-8
(Q, - Q)/Qo vs. time at 80C for XE2:0.35V . .............
109
4-9
Chronoamperometry scan at 80C for XE2:0.53V . ...........
110
. ...........
4-10 (Q, - Q)/Qo vs. time at 80C for XE2:0.53V . ..........
4-11 Chronoamperometry scan at 40C for XE3:0.1V
102
. ...........
4-12 (Q, - Q)/Qo vs. time at 80C for XE3:0.1V . ..............
.
. 111
112
113
4-13 Chronoamperometry scan at 80C for XE3:0.45V . .
114
4-14 (Q, - Q)/Qo vs. time at 80C for XE3:0.45V . . . .
115
. .
116
4-16 (Q, - Q)/Qo vs. time at 80C for XE4:0.1V . . . . .
117
4-17 Chronoamperometry scan at 80C for XE4:0.45V . .
118
4-18 (Q, - Q)/Qo vs. time at 80C for XE4:0.45V . . . .
119
. .
120
4-20 (Q, - Q)/Qo vs. time at 80C for XE5:0.1V . . . . .
121
4-21 Chronoamperometry scan at 80C for XE5:0.40V . .
122
4-22 (Qo - Q)/Qo vs. time at 80C for XE5:0.40V . . . .
123
. . . . . . . . .
124
4-15 Chronoamperometry scan at 80C for XE4:0.1V
4-19 Chronoamperometry scan at 80C for XE5:0.1V
4-23 Summary: crystal electrolysis data
4-24 Oxygen-poor phase fraction from weak ferromagnetic moment
......
at 80C . ..................
Vrei
. .
......
127
4-25 Magnetization data for XE1:0.53V
. ..................
131
4-26 Magnetization data for XE1:0.53V
. ..................
132
4-27 Magnetization data for XE2:0.35V
. ..................
133
4-28 Magnetization data for XE2:0.53V
. ..................
134
4-29 Magnetization data for XE3:0.45V
. ..................
135
4-30 Magnetization data for XE4:0.1V . ..................
.
136
4-31 Magnetization data for XE4:0.45V
.
137
.
138
. . .
139
. .................
4-32 Magnetization data for XE5:0.1V . ..................
4-33 Magnetization data for XE5:0.40V
. ...............
4-34 Neutron scattering data for XE1:0.53V . ................
142
4-35 Neutron scattering data for XE3:0.45V . ................
143
4-36 Neutron scattering data for XE5:0.40V .
144
................
4-37 Tentative phase diagram for La 2 Cu04+s including values for 5
145
A-1 Magnetic susceptibility and charge per formula-unit for La2CuO4
151
A-2 Electronic Circuit used for Chronoamperometry Experiments . . .
152
A-3 Experimental setup used for transport measurements
153
. . . . . . .
B-1 Transport data for XE1:0.53V ...................
11
...
155
List of Tables
3.1
La 2 Cu04+ pellets: batch one ...................
...
65
3.2
La 2 Cu04i+pellets: batch two .....
.. .
69
4.1
La 2 Cu04+S
4.2
La 2 Cu0 4+s single crystals: neutron data ...............
..............
single crystals: electrolysis data. .
..........
. .
96
.
140
Chapter 1
Introduction
High-temperature superconductors have been a subject of great interest to the scientific community since their discovery in 1986 by Bednorz and Miiller [5].
Dur-
ing the early years of investigation, the rate at which reported values of the superconducting transition temperature, Tc, grew with time was fantastic. The ink
had scarcely dried on a journal article before a new higher T, was being reported.
HgBa2Cam-1CumO2m+2+s,until
recently, has had the highest known transition tem-
perature, which is 164K under pressure for m=3 [20]. This T,, however, has been
exceeded by (Sr_-xCaz)1_yCu0
2
with T, of about 170K [32]. Despite the fact that
higher transition temperatures are no longer being found every few months, interest
in this class of materials has continued unabated for the past ten years.
One reason for this is that the parent compounds, which are non-metallic, are also
very exciting to study. The magnetic and transport properties of these compounds in
their normal state continue to be carefully studied because understanding the normal
state may help us to understand the mechanism for high-T, superconductivity. While
Bardeen-Cooper-Schrieffer (BCS) theory [4] very successfully explains conventional
superconductivity as resulting from a phonon-mediated coupling of a pair of electrons, it is unlikely to apply to the high-T, superconductors because the transition
temperatures are much higher in the latter case. The two electrons are not bound
together strongly enough to be stable in the presence of thermally excited phonons
at higher temperatures.
Many theorists now believe that high-T, superconductivity is related to electronelectron correlations [17, 64, 52].
The copper oxides fall into a class of materials
known as highly correlated electron systems for which band theory does not work.
Fluctuations in the magnetic structure resulting from these correlations most likely
play a key role in the superconductivity.
The structure of these materials can become quite complicated as the number of
atoms per primitive cell increases, but they all have in common a lamellar structure
consisting of CuO2 planes. Moreover, many of the properties observed in high-T,
superconductors are highly two-dimensional. These include the conductivity and the
interesting magnetic correlations primarily occurring in these CuO2 planes. To a
large extent, the other atoms which make up a particular high-T, compound can be
regarded as necessary only for providing carriers to the planes and for maintaining
overall charge neutrality.
As one of the structurally simpler parent compounds of high-T, superconductors,
La 2 CuO04 has been extensively studied. The introduction of charge carriers, holes in
this case, into the CuO2 planes of this material makes it superconducting. In fact,
the doping of this very compound leads to La2_>BaCu04, which was the first high-
T, superconductor discovered by Bednorz and Miiller [5]. La2-_MCuO
4+S can be
doped by substitution (x) of M = Sr or Ba, or by intercalation (6) of interstitial
oxygen. It is the latter case which will be explored here.
There are some notable differences between intercalant doping and substitutional
doping. First, substitutional doping is done during the high-temperature synthesis
of the material whereas intercalant doping is done at temperatures well below the
melting point of the material. Second, interstitial oxygen atoms are mobile down to
about 150K [34, 51, 49, 12], in contrast to virtually immobile strontium or barium
dopants.
Oxygen intercalants are thus free to move into a lower energy configuration, including the macroscopic formation of oxygen-rich and oxygen-poor regions for certain
values of 6 [29, 47]. A study of this phase separation, in particular, and how the oxygen intercalants are arranged in La 2 Cu0 4 , in general, has been the subject of intense
investigation. This thesis is a report on the oxygen doping of both single crystals and
ceramics, prepared by electrochemical oxidation.
Chapter 1 discusses the previous work which has been done on La 2CuO4 +s and
the motivation for the present study. Chapter 2 outlines the preparation of the samples and provides some relevant background information. Chapters 3 and 4 describe
experimental results for ceramics and single crystals, respectively.
These include
electrochemical oxidation and magnetization data. It is important to mention that
there are significant differences between experiments involving ceramics and single
crystals. Chapter 5 concludes with a discussion of these results and their possible
interpretation.
1.1
Structure and Properties of undoped La 2 Cu04
1.1.1
Crystal Structure
Stoichiometric La 2 CuO4 has a tetragonal structure (I4/mmm) [22, 30] at temperatures above about 550 K. Below this temperature, the oxygen octahedra tilt slightly
(~
10) [23] along the diagonal of the tetragonal structure distorting it to give or-
thorhombic symmetry (Bmab). Figure 1-1 shows the tetragonal structure. The CuO6
cluster of atoms, which defines the octahedron, is also illustrated in the figure. The octahedron is composed of a central Cu atom surrounded by a "square" of four in-plane
oxygen atoms equidistant from the central copper atom. There are also additional
oxygen atoms above and below the copper atom. These are called the apical oxygens,
and they are farther away from the central Cu atom than the in-plane oxygens. The
structure of La 2 Cu0 4 can be thought of as an octahedron placed at each lattice point
of a body-centered tetragonal structure which contains two formula units. Note the
positions of the copper atoms in Figure 1-1. Another way to view the structure is
that there are alternating layers of a CuO 2 plane and of two atomic planes of La 2 02
in a rock salt structure.
The orthorhombic structure in La 2 Cu0 4 can be thought of as resulting from the
1
,A
z0"
D
(
4
)
()
)o
SLanthanum
.* O
©o
o
@
O
Oxygen
*
Copper
O
)
)
Cu-O octahedron
V/12
La Cu04
Figure 1-1: This is a sketch of the undoped crystal in its tetragonal structure. Other
high-T, compounds also have the Cu0 2 planar structure.
octahedra tilting along the diagonal connecting second-nearest neighbor copper atoms
in the CuO 2 plane. The structure in a given crystal is twinned [21] because the octahedra can tilt along either diagonal as a sample is cooled through the tetragonal-toorthorhombic structural transition. Because the orthorhombicity is small, the lattice
axes of this structure are generally referred to in tetragonal notation and describe
a unit cell containing two formula units as shown in Figure 1-1.
a is the in-plane
distance between nearest copper atoms and c is perpendicular to the plane. For the
orthorhombic structure, the in-plane axes (a,b) are rotated by 450 relative to the
tetragonal axes about the c axis so that the b axis points along the octahedral tilt
direction.
The c axis remains the same. The lengths of the lattice constants are
a = 5.356 A, b = 5.399 A, and c = 13.167
A [30].
1.1.2
Electronic Properties
Band theory calculations predict that La 2 Cu04 ought to be a metal. Such calculations are quite lengthy and involved. It is possible, however, to gain an intuitive
understanding of this problem. We know from experiment that conduction occurs
primarily in the CuO2 planes in this quasi two-dimensional system. Because of this,
we will assume that if we know whether or not the highest occupied energy band in
the plane is full or part-full, we have a good idea of whether or not La 2 Cu04 should
be a metal. Because the valence charges of La and O are 3+ and 2- respectively, one
concludes from the chemical formula that the valence of Cu must be 2+. Cu2 + has
an electronic configuration of 3d9 , a partially filled d-shell. The five atomic d-orbitals
are all degenerate. However, in the presence of the crystal field, the degeneracy is
broken as shown in Figure 1-2. The axes are chosen so that the origin is centered
on a copper atom and the x and y axes point to neighboring in-plane oxygen atoms,
while the z axis points to the apical oxygens. Considering the arrangement of oxygen around each copper, one expects that the d-orbital, d,2_Y2 , with lobes pointing
toward in-plane oxygen atoms is the highest in energy because it experiences a larger
Coulombic repulsion from its proximity to the oxygen 2p orbital. The orbital pointing toward the apical oxygen, d3z2_r2, should have the second highest energy. The
d-orbitals not directly pointing toward a neighboring oxygen have the lowest energies. The 3d9 configuration results in an unpaired electron in the dX2_,2 orbital and a
partially filled band, so La 2 Cu0
4
should be a metal. Detailed band calculations give
the same result. In fact, however, La 2 CuO04 is an insulator.
This is puzzling until one remembers that electron-electron correlations are assumed to be negligible in band theory. It is amazing that band theory works so well
for the majority of crystalline solids despite the fact that interactions of the electrons
are approximated by a mean field. This approach works primarily because the Pauli
exclusion principle indirectly accounts for a major aspect of electron correlations that two electrons cannot be in the same state at the same time.
In most crystalline solids this approach works well because the kinetic energy saved
Crystal field splitting of d-orbitals in cubic and tetragonal symmetries
2
x -y
tetragonal
shape of xv,xz,vz. and
2 2
y orbitals
shape of 32 - r2 orbital
Figure 1-2: The degeneracy of the copper d-orbitals is broken in an actual crystal.
The higher energy states are those which feel the greater Coulombic repulsion from
neighboring occupied orbitals.
by de-localized electronic states outweighs the energy cost of Coulombic repulsion. If
the atoms in a crystal, however, are relatively far apart, then the kinetic energy saved
by the de-localization of electrons is relatively small, and so the electronic distribution
is better described by a linear combination of the original atomic orbitals with the
electrons confined for the most part to a particular atomic site.
N.F. Mott [40]
describes this as the metal-to-insulator transition which occurs as the atoms making
up a crystal are moved apart.
When the electrons are strongly localized to sites in the crystal, electron-electron
interactions cannot be neglected. The effect of these correlations can be easily seen
in the magnetism. The possible electronic ground states of a two-electron system
such as the hydrogen molecule are an example of this. In the Heitler-London picture,
the electrons are confined, one to each hydrogen atom resulting in singlet and triplet
states. Because the singlet state has lower energy, the electron spins are anti-parallel
so that the exchange is antiferromagnetic. In contrast, molecular-orbital theory would
provide a better description if both electrons are distributed over both atoms, and
there are bonding and anti-bonding states, each of which can contain two electrons,
one with spin up and one with spin down.
In the two-electron case, the singlet state always has a lower energy than the
triplet spin state. This, however, is not generally true in the N-atom solid [3]. As a
"2-atom" solid, the hydrogen molecule remains useful in illustrating how electrostatic
forces determine most of the magnetism. In the singlet state, because the spatial
state is symmetric, both electrons have lower energies from their proximity to both
nuclei. The closer the nuclei are together the more favorable this situation is. In the
triplet state, while the electrons lose some of the nuclear attraction because of the
node in the wavefunction between the nuclei, they reduce their Coulombic repulsion
by being spatially separate. This type of competition occurs in strongly correlated
systems such as La 2 Cu0 4 and helps us to understand not only why band theory
is inadequate, but also why such a material would have strong antiferromagnetic
ordering.
Let us return to our original quandary: La 2 CuO4 is not a metal as band theory
predicts so electron-electron correlations have to be included in the Hamiltonian. It is
impossible to solve a Hamiltonian which includes the complete set of electron-electron
interactions. There are theories, however, which take into consideration some of the
correlations between electrons. Specifically, the Mott-Hubbard model [27] correctly
predicts an insulator.
In this model, one considers a hopping exchange energy, t,
associated with moving a charge carrier to a neighboring site and a double-occupation
energy, U, associated with two charge carriers on the same site. When U > t, the
electronic states are completely localized; when U <K t, the states are extended.
La 2 Cu0
4
falls in between these two limits with U > t. The quest to understand
these correlations is among the reasons high-T, materials like La 2 CuO 4 +s are still so
interesting to study.
1.1.3
Magnetic Properties
La 2 Cu04 is an example of a two-dimensional Heisenberg spin-1/2 antiferromagnet
with small corrections for weak out-of-plane coupling and anisotropy. The 2-D Heisenberg Hamiltonian is
H =
JSi Sj,
u.n.
(1.1)
where n.n. refers a sum over nearest-neighbor copper spins and J is the coupling
constant, about 130meV. La 2 Cu0 4 +s is not exactly a two-dimensional system. A
perfect two-dimensional system does not order for T > 0. However, because there
is some out-of-plane coupling and a small x-y anisotropy, the copper 1/2-spins order
antiferromagnetically below a Neel temperature TN of about 320K. For La 2 Cu0 4 ,
there is also a term in the Hamiltonian, the Dzyaloshinsky-Moriya interaction [15, 38],
which goes like D - Si x Sj.
This term is possible because of the orthorhombic
distortion in the planes, and it results in a slight canting of the copper spins out of
the Cu0 2 plane. The direction of the canting alternates from layer to layer so bulk
ferromagnetism is not observed.
In a sufficiently high magnetic field, however, the
spins flip so that all of the canting is in the same direction and a weak ferromagnetic
transition is observed. This also gives rise to a peak in the zero-field susceptibility.
The magnetism is strongly affected by doping. In strontium-doped samples, the
effect on the magnetism is dramatic (see Figure 1-3). The long range magnetic order is
destroyed for x > 0.02 [7]. Interstitial oxygen added to La 2 Cu04+5 reduces magnetic
order. The Neel peak, indicative of the antiferromagnetic phase, decreases in size and
moves to lower temperature - about 250K, which corresponds to 6 _ 0.01 [50, 46].
Neutron powder diffraction [47] and magnetization experiments have shown that a
miscibility gap develops for 0.01 < 6 < 0.06.
In this region, La 2 Cu04f+macro-
scopically phase separates into an oxygen-rich, metallic phase and an oxygen-poor,
insulating phase in which magnetic long-range order is preserved. A phase diagram
of La 2 -SrCuO04 which does not phase separate and for which homogeneous single
crystals can be grown over a large range of x is shown in Figure 1-3 for comparison.
1.2
Previous Work done on La 2CuO4+±
La 2 Cu04+± has a natural propensity to contain some oxygen in excess of stoichiometry, that is, 6 > 0. Crystals grown in air often have trace amounts of superconductivity. The link between excess or interstitial oxygen and superconductivity, however,
was not immediately recognized. It took some investigation to find that excess oxygen
provides the carriers for the superconductivity seen in La 2 Cu0 4 +s [22, 6]. (Excess
oxygen also affects the conductivity in substitutionally doped samples.)
Adding interstitial oxygen was first accomplished by annealing samples in oxygen.
Jorgensen et al. [29] discovered that samples annealed at high temperature under
high oxygen pressure phase separate into oxygen-rich and oxygen poor regions. This
technique, however, achieves only 6 _ 0.03.
temperature of TNy
The oxygen-poor phase has a Neel
250K, and the oxygen-rich phase has superconducting transition
temperature of about 32K.
Prior to the work of Grenier and Wattiaux, oxygen-doping of La2CuO4 was limited
to high-temperature and high-pressure annealing in oxygen. The difficulties of this
method include inhomogeneity of the oxygen in the samples and relatively low doping
levels when compared to strontium doping. Wattiaux and Grenier found that it is
T[K]
530
322
40
10
Figure 1-3: La 2 -_SrCu04phase diagram from J.P. Falck PhD thesis 1993
possible to oxygen-dope La 2 Cu0
4
to greater concentrations at room temperature
using a method of electrochemical oxidation [58].
This method produces samples
with greater oxygen concentrations and transition temperatures as high as
'
45K for
ceramic samples. It is also possible to oxidize samples chemically by placing them in
contact with a strong oxidizer such as KMn0 4 [54] although it is more difficult to
obtain uniformly doped samples with this method.
There have been numerous studies of the effect of doping on the properties of
La 2 CuO4 +S. These include magnetization [19], heat capacity [28], and nuclear mag-
netic resonance (NMR) [44, 26] experiments. Magnetization experiments on superconductors provide such information as the Meissner effect, shielding fraction, and
T,. They have been used to reveal more subtle effects such as the fact that slowly
cooling (- 0.15K/minute) a sample near 195 ± 10K results in a higher transition
temperature (AT
44K) than quickly cooling (- 50K/minute) through this tem-
perature range [48]. Heat capacity measurements have also provided information on
La 2 Cu04+s. For instance, three anomalous peaks in the the heat capacity, Cp(T),
indicate structural transitions in La 2 CuO4+S below room temperature [28] which appear to be the result of oxygen doping. These anomalies occur at 200K, 250 - 270K
and 290K. NMR and nuclear quadrupole resonance (NQR) data have provided additional information about the onset of phase separation [26] and over what range of
6 it occurs in the phase diagram. Dabrowski et al. [13] and other researchers [47, 48]
have also studied the occurrence of macroscopic phase separation.
In samples with the higher oxygen concentrations (6 >ý 0.03) made possible by electrochemical oxidation, magnetization data show the occurrence of superconducting
transition temperatures around 45K [25] when more oxygen is added, and 15K [18]
after annealing at ll0C in oxygen flow. These are in addition to the 32K transition
temperature. Additional structural information includes the measurement of the lattice constants for electrochemically doped La 2 CuO4+s using x-ray powder diffraction
at room temperature [24, 35]. Initially, as 6 increases, the in-place lattice constants,
(a,b), approach the same value indicating that the orthorhombic distortion is decreasing; meanwhile the out-of-plane lattice constant, c, steadily increases. If one
attributes the orthorhombic distortion to the lattice mismatch between the La 2 02
and the CuO 2 layers [9], then the excess oxygen alleviates this strain somewhat. This
trend is seen in various ceramics reported by Grenier et al. up to 6 - 0.05. Once
6 2 0.06, c becomes roughly independent of 6 while the a,b orthorhombicity once
again increases, possibly indicating increased strain in the crystal.
We have mentioned that La 2 Cu04+J macroscopically phase separates into oxygenrich and oxygen-poor regions [13] for 0.01 < 6 < 0.06. Why phase separation occurs
at all has been the subject of some debate. One possibility is that it may be electronically driven [16]. It is argued that because the oxygen atoms are fairly mobile, they
follow the charge carriers which phase separate to preserve antiferromagnetic order
in the carrier-free region and to lower the kinetic energy in the carrier-rich region. In
support of this view, Kim et al. [33] suggest, from photoinduced infrared absorption
measurements, that phase separation of the charge carriers occurs in the absence of
dopants such as interstitial oxygen.
Another possibility is that the phase separation is chemically driven. This view is
supported by evidence of oxygen staging which Wells et al. observed in neutron scattering experiments [60] on electrochemically oxidized samples. (Stage n refers to intercalants going into the host compound every n"th layer.) An ordered, staged compound
suggests that a structural or chemical transformation has occurred. If the oxygenrich phase of La 2 Cu0
4 +s
is a new staged compound analogous to staged graphite
intercalation compounds [14], the phase separation may be structurally or chemically
driven. What is known so far about how the staging fits into the La 2 Cu0
4 +5
phase
diagram is presented in Figure 1-4.
1.3
Motivation for this thesis
Although La 2 CuO 4 +s has been long studied, much of the phase diagram, especially
for 6 > 0.05, is still unknown. The staging observed by Wells has provided much of the
motivation for the results presented here. Neutron scattering experiments have shown
that phase separation occurs around 290K. The stage ordering is seen at slightly lower
La 2CuO 4+6 Phase Diagram
400
300
200
100
0
Oxygen Doping (8 and Staging #)
Figure 1-4: based on neutron scattering experiments by B.O. Wells, Y.S. Lee, and R.
Christianson
temperatures, and in-plane ordering of oxygen is observed near 200K [61] in heavily
oxidized samples. As indicated in Figure 1-4, the values of 6 for the staged phases
and the size of the miscibility gaps between them are unknown. The reason is that
measurements have not been made of 6 for the crystals used in neutron scattering experiments. Most measurements of 6 have used thermogravimetric analysis, in which
the change in mass of a sample is measured as interstitial oxygen is eliminated by
heating the sample in a gas flow. This is subject to uncertainties because molecules
such as water adsorbed on the sample surface are also released during the measurement. More importantly, it requires eliminating the oxygen from samples which, for
crystals, take months to oxidize. It is possible instead to use the current during
electrochemical oxidation to determine 6.
The experiments described in this thesis were designed to provide more information about the staging by measuring 6 for crystals and ceramics. These samples
are oxidized at constant chemical potential using a constant voltage electrochemistry
technique, which will be explained in the Chapter 2. This technique also allows us to
determine when equilibrium is reached.
Single phase, staged samples prepared at fixed chemical potential facilitate studying such sample properties as stage number and To, which can be explored as a
function of interstitial oxygen concentration, 6. In the long run, it is hoped that comparison of the results for La 2 Cu04+5 with those for La 2-,SrCu0
4
could provide
clues to the nature of high-T, superconductivity.
A number of discoveries are reported here. Samples such as those studied in this
thesis, single crystals in particular, had not been prepared previously with a concerted
effort to achieve homogeneous samples at carefully measured, higher values of 6. Although it has turned out that preparing homogeneous samples past the miscibility
gap is very difficult, the samples studied still provide more information about the
phase diagram. In addition, this work has revealed that the equilibration of samples
during electrochemical oxidation is not diffusion-limited as previously believed. Although the oxidation is painfully slow, it is orders of magnitude faster than predicted
from previous measurements of the diffusion coefficient. In addition to new results
for single crystals, we have discovered a transition as a function of chemical potential
between two phases in ceramics with different superconducting T,'s. Although much
remains to be done, this thesis shows how careful electrochemical measurements can
be used to map out the phase diagram and prepare samples with well-defined 6.
Chapter 2
Experimental Details
2.1
Overview
The techniques used to prepare and to study samples are outlined in this chapter.
These include some definitions and a discussion of the electrochemical techniques
used to oxidized the samples. Possible sources of noise in the experiments and bulk
diffusion of oxygen intercalants are also discussed.
2.2
Sample Preparation
Both single crystals and (polycrystalline) ceramic samples are used in these experiments. An explanation of how each type of sample is prepared follows.
2.2.1
Ceramics
All samples are prepared using ultra-high purity (99.999%) starting materials here
at MIT in the Center for Material Science and Engineering (CMSE) Crystal Growth
Central Facility. These ceramics are produced by a standard solid-state reaction of
La 2 03 and CuO powders. A stoichiometric mixture of La 2 03 and CuO powders is
ground with an alumina mortar and pestle. It is then annealed in either an alumina or
platinum crucible. The solid-state reactions are conducted below the melting point of
the materials involved so that there is very little contamination from the vessel. This
powder mixture is annealed at 850C, then re-ground and annealed at progressively
higher temperatures, first at 950C, then 1050C. The powder is sintered and re-ground
repeatedly until an x-ray powder diffraction pattern demonstrates that the powder
is completely reacted and single phase La2Ct0 4 . Figure 2-1 shows a typical x-ray
powder diffraction pattern for La 2 Cu0 4. Incidentally, there ought to be small changes
in the lattice constants as La 2 CuO4 is doped with oxygen. However, the resolution
of the scattering peaks that is possible with this diffractometer is insufficient at room
temperature to detect the small changes in the lattice constants due to oxygen doping.
The powder is then sifted through a 43 pm wire-mesh screen, and a small amount
of powder, typically 100 mg, is pressed into a pellet. A thin piece of platinum wire is
simultaneously pressed into the pellet to provide good electrical contact. The pellets
are all pressed using a 0.25 inch die at 1.5-2.0 metric tons in a Carver hydraulic press.
A sketch of this die is shown in Figure 2-2. The first few batches of pellets were
compressed further in an isostatic oil press under 35000 psi and then slowly brought
back to atmospheric pressure to prevent the pellets from cracking. Since many of
these early pellets tended to crack during handling, later batches of pellets have been
annealed at 900C in an oxygen flow for 6 hours after being pressed in a 0.25 inch
die. Both of these methods increase the grain size slightly, and thereby increase the
mechanical strength of the pellet. They result in approximately the same density
- 5.11 g/cm 3 , which is 72% of the crystalline density. Producing low-density pellets
is desirable because the electrochemical reaction proceeds more quickly for a porous
sample.
2.2.2
Single crystals
The crystals used for the experiments in this thesis are all grown by Fangcheng
Chou in the CMSE Crystal Growth Facility using the Traveling-Solvent-FloatingZone Method [1], Since this method uses no crucible, the crystals contain fewer contaminants than those grown by other methods, usually the top-seed method. Neutron
scattering experiments have already shown that phase separation is not reversible in
:PS
Z vjvi
1600
1200
800
400
-
LAli
n-I
20
Figure 2-1: An example of a powder x-ray diffraction pattern for La 2 CuO 4.
81
I
m.
I
powder goes inside to be pressed into a pellet
'--
1/4 inch diameter
Figure 2-2: A cross-section of the 0.25 inch die used to make La 2 Cu0 4 pellets is
shown. The Carver hydraulic press used with this die consists of two parallel metal
plates which exert pressure on the die from the top and bottom to the desired pressure.
The resulting 0.25 inch diameter pellet was typically a little under 1 mm thick and
100 mg.
crystals grown in platinum crucibles [59]. Crystal defects such as vacancies and impurities may contribute to this. Since the mobility of intercalants through the sample
is greatly affected by defects [53], only float zone crystals are used. Typical crystals
as grown have volumes of about 0.5 cm 3 . The methods used to grow single crystals
of La 2Cu0
4
are described in the following section.
Sample preparation begins with cutting 100 - 200mg size pieces from a large
single crystal. The (001) c-axis orientation of the cut pieces is determined using a
Laue camera. These samples are then polished perpendicular to this axis in a slurry
of alumina grit and lubricant on a lapping machine. Progressively finer and finer grit
is used to achieve a highly polished surface. A shiny crystal surface makes it easier
to detect cracks. If a crack is seen on the surface of a crystal and appears not to go
all the way through, then the cracked side is polished until no cracks are apparent on
the surface. This is done on both c-axis surfaces, that is, the surfaces parallel to the
Cu0 2 planes.
The reason for taking such pains to eliminated cracks was to facilitate transport
measurements later on. Preliminary electrolysis measurements showed that there was
enough strain in the crystals to cause or worsen cracks and small fissures. After the
polishing is completed, the crystals are etched in a solution of 1% bromine in methanol
for about fifteen minutes. This removes several microns from the crystal to insure
that the polish-damaged region has been removed.
2.2.3
Growth Methods of single crystals
It is helpful to become familiar with these two methods used to grow large single
crystals of La 2 CuO0
4 since growth methods can influence the quality of resulting
crystal. We will briefly discuss them.
2.2.3.1
Czochralski or Top-Seed Method
In order to grow a crystal by this method, a molten mixture (called the melt) of La 2 03
and CuO is prepared. The melting point of the stoichiometric mixture is too high for
crystal growth. Therefore, a flux is added to lower the melting point of the mixture
below that of the crystal. In this case, CuO is used as a flux; it has the added benefit
of not contaminating the final crystal. A molar ratio of La 2 03 to CuO is chosen
near 15:85. This optimizes the conditions for growth. This is near the eutectic [45]
(the lowest possible melting point) for the mixture. The powders are mixed together
and placed in a platinum crucible. The mixture is heated above its melting point.
A "seed", either another crystal or a platinum wire, is attached to a slowly rotating
rod. This seed is then lowered until it just touches the melt. If the temperature of
the melt and the seed are right, the seed will not dissolve into the melt. The melt is
then slowly cooled, typically 0.25C/hour, and the seed is slowly raised (0.1mm/hour)
out of the melt. With the seed as a guide, elements of the melt begin to slowly form
a new single crystal.
2.2.3.2
Traveling-Solvent-Floating-Zone
Method
The crystals used in the study are all grown by this method. This method produces
a crystal in much less time and with fewer contaminants than the top-seed method.
There is, however, more strain on the crystals during the growth process because
of a much steeper thermal gradient.
First, one prepares a powder made from a
stoichiometric mixture of La 2 03 and CuO as for a ceramic. This powder is pressed
into a rod about 0.25 inches in diameter and then sintered in a flow of oxygen. This
rod is referred to as the feed rod. A flux rod is also prepared from a powder mixture
which is 4:1 of CuO to La 2 03. Ideally, for a seed, one starts with a small cylindrical
piece of a previously grown float-zone crystal. Otherwise, a piece of feed rod is used;
in this case, there will be crystals of several different orientations growing together at
first.
An optical floating-zone furnace can heat a very small volume to high temperature
by focusing the output of high-powered lamps. The furnace used to grow the crystals
in these experiments was manufactured by Crystal Systems, Incorporated.
In this
furnace, there are upper and lower shafts that can be rotated around a common axis
and move vertically along that axis through the focal point of the mirrors.
Some flux is required at the end of the feed rod. The feed rod is mounted in the
lower shaft and the upper shaft is loaded with the flux rod. A little of the flux rod is
melted onto the feed rod. The amount of this flux greatly affects how the subsequent
crystal will grow. Too little flux means that the melting point will be too high and
crystal will be very hard or impossible to grow. Too much flux will cause the surface
tension to be insufficient to maintain a stable molten zone as the crystal grows.
Everything is now ready to begin growing a crystal. One mounts the seed in the
lower shaft and moves the feed rod up into the upper shaft. The rod is adjusted
so that it is as centered as possible. The shafts are rotated in opposite directions;
this reduces the effects of inhomogeneity somewhat. The rods are moved together to
the focal point of the lamps, with the seed just outside the hottest region. The flux
covered tip of of the feed rod is slowly melted and joined to the seed. An ideal molten
zone should be about as high as it is wide. Once the zone is stable, the feed rod is
slowly moved through the molten zone with the crystal forming in its wake.
2.3
2.3.1
Experimental Setup
Ceramics
The electrochemical measurements are performed in a cell consisting of three electrodes. These are the pellet, which is the sample electrode, a platinum wire serving
as the counter electrode, and a silver/silver chloride (Ag/AgC1) reference electrode.
The electrodes are placed in a slowly-stirred sodium hydroxide (NaOH) solution in
a teflon container. A sketch of this setup is shown in Figure 2-3. Most of the room
temperature measurements are done in a 1 M NaOH solution, while the 80C measurements are done in a 0.01 M NaOH solution. At the beginning of a run, the typical
open-circuit voltage of a fresh pellet is 0.26V relative to the reference electrode for
room temperature measurements.
All reference voltages, Vre,I are measured with respect to a Fisher Scientific HighTemperature Ag/AgCl Reference electrode. A voltage is applied between the counter
and sample electrodes so as to maintain a constant reference voltage. The polarity of
the voltage is such that the sample electrode is at a higher potential than the counter
electrode.
We monitor the current as a function of time using either an EG&G
Versastat potentiostat or a Keithley Instruments Digital Multimeter (Model 196 or
2000) in conjunction with a circuit for maintaining a constant voltage relative to a
Ag/AgCl electrode. A diagram of this electronic circuit is provided in Appendix A.
We have limited the reference voltage to less than 0.55V for most experiments because
at higher voltages the decomposition of hydroxyl ions into water and oxygen ('oxygen
evolution') becomes significant and dominates the current.
We will refer to three techniques of electrolysis measurement. The first is cyclic
voltammetry (CV). This is performed by sweeping the reference voltage through
a range of values returning to the starting value and simultaneously recording the
current as a function of reference voltage. This technique is analogous to the measurement of current-voltage characteristics for electronic devices. This can be used to
locate any peaks or plateaus in the current. For example, a peak in the so-called anodic current indicates a range a reference voltages over which an increase in oxidation
occurs. (So-called because anodic current refers to the flow of negative charge into
the sample.) The second is chronoamperometry (CA); the reference voltage is held
constant and the current is measured as a function of time. The third is chronopotentiometry (CP); the current is held constant while the reference voltage is recorded
as a function of time. Although these terms are not conventionally used in solid state
physics, we will use them here because they are ubiquitous in the electrochemistry
literature describing the techniques.
For magnetization measurements, a Quantum Design Superconducting Quantum
Interference Device (SQUID) magnetometer is used. The samples are cooled from
room temperature to 5K in approximately one-half hour prior to taking shielding
fraction and Meissner effect data. During the measurements, the samples are mounted
either in a transparent plastic drinking straw or in a quartz tube sealed at one end, as
recommended by Quantum Design. Before electrolysis, the low-field susceptibility of
the samples reveal a Neel peak near 250K unless stated otherwise. The Neel temper-
Reference Electrode(Ag/AgCl)
hed mechanically
Platii
counter eleti
PFA teflon vessel
0.01-1.0 M NaOH in water
Figure 2-3: A sketch of the cell in which samples are electrochemically oxidized. The
solution is stirred with a small teflon stir-bar in a 300ml PFA teflon jar. The cell is
heated on a hot plate for experiments performed above room temperature.
ature for undoped La2Cu0 4 is about 325K. Adding oxygen causes this temperature
to decline monotonically.
2.3.2
Single Crystals
The experimental setup is nearly identical to that used with the ceramics. The crystals
are wrapped in platinum gauze and then attached to a platinum wire for electrolysis.
The electrolysis was done exclusively at 80C to speed up the reaction. A 0.01 M
NaOH solution has also been used. This concentration was selected because it does
not significantly slow the reaction, but it does minimize corrosion and side reactions.
The cells were set up in PFA teflon jars on hot plates. Chronoamperometry runs were
performed at various voltages, ranging from Vref = 0.35V to Vef = 0.53V.
2.3.2.1
Sample preparation for transport measurement
A resistivity measurement has also been conducted on an electrochemically oxidized
crystal. These tentative results are discussed in Appendix B, so sample preparation
for this experiment is outlined here.
This crystal is first etched in a 1% solution of bromine in methanol for ten minutes
to clean the crystal surface. Indium metal is then scratched into the crystal surface in
a five-contact geometry required for the resistivity and Hall effect experiments. The
reason for using indium is that it is a soft metal with a conductive oxide. Using indium
usually avoids the problem of oxygen diffusing out of the crystal and reacting with
the contacts creating an insulating barrier. Stripes of silver paint are painted on top
of the indium about 1 mm wide for voltage contacts, and silver paint is also applied
to the two opposing side faces for the current contacts. The crystal is then mounted
on a TO-8 chip carrier with mylar tape and Devcon Duco cement. 5 mil gold wire
is then used to attach the sample contact pads to the posts on the chip carrier. The
resistivity measurements are performed in a Quantum Design Magnetometer with an
special insert wired for transport measurements. A sketch of the contact configuration
and of the experimental setup used to take the transport data is in Appendix A.
2.4
Electrochemistry Basics
Electrochemical reactions are a type of chemical reaction in which charged reactants
are driven in a particular direction by applying a voltage. At room temperature, many
reactions of this type are done in an aqueous solution. For precise measurements, three
electrodes are placed in a conductive (electrolytic) solution. The ions in the solution
are the charge carriers. At one electrode, called the working electrode, the desired
chemical reaction occurs. This electrode is either oxidized or reduced according to
R
0o + ne-. At the other electrode, the counter electrode, there is a reaction
involving the products of the reaction at the working electrode and ions of the solution.
The exact reaction depends on which species in the solution are involved.
Although it is not necessary to drive the reaction, a third electrode called the
reference electrode is also included. It does not participate in the reaction, but is used
to provide a reference voltage relative to the solution. In the case of the Ag/AgCl
electrode, the reaction is AgCl(s) + e- V Ag(s) + Cl-. The electrode is designed so
that this reaction is stable with time while also not affecting the cell reaction in any
way. The reference electrode is separated from the rest of the electrolytic cell by a
porous barrier such as a fritted disk which allows enough ion exchange at the barrier
for electrical contact but prohibits free mixing of the solutions. The characteristic
energy associated with the Ag/AgC1 reaction can then be compared to the changes
in energy at the sample electrode. A good reference must be stable over time and
have a weak temperature dependence to be effective. (This is partly why a sparingly
soluble salt like AgC1 is used; its concentration varies little with temperature [37].)
Reference electrodes can be calibrated, and usually, are to the Standard Hydrogen
Electrode (SHE), allowing the comparison of one electrochemical reaction to another.
SHE is an extremely stable and reproducible reference standard.
The voltage of
the Ag/AgC1 electrode relative to SHE is 222 mV. The reference voltage gives us a
measure of the chemical potential of the working electrode. This will be explained
later in the chapter.
2.5
Electrochemical Reactions
The following electrochemical reaction for a La 2 Cu0 4+Sworking electrode in an aqueous solution containing OH- is known with relative certainty [24]. The current, I,
results from the chemical reactions at the electrodes. At the sample electrode, one
has the half-reaction
La 2 CuO 4 + 260H- -- La 2 CuO 4+s + SH 2 0 + 26e-
(2.1)
and at the counter electrode, the half-reaction is
26H 2 0 + 26e- -- 260H- + 6H 2 .
(2.2)
Thus, the charge Q passing through the cell is 26e. Another possible reaction involves
the entire hydroxyl ion entering the sample and not the oxygen alone. The reaction
at the sample would then be La 2 Cu0 4 + 60H- -+ La 2 Cu0 4 (OH)s + 6e-.
An
OH- signal, however, has not been observed in NMR experiments [44, 25].
The
reaction 2.1 suggested by Grenier et al. is generally agreed upon as correct. We can
see that by measuring the current as a function of time, we can calculate the total
charge transferred to the sample, which given two electrons per oxygen gives 6. This
method of doping is valuable even if only for this information. With other methods
of doping, one must determine 6 either by iodometric titration [41], which measures
the hole concentration, or by thermal gravimetric analysis, which measures mass loss,
both of which can be hard to interpret and destroy the original sample. A drawback
of measuring 6 from the current is that if the electrochemical cells are contaminated,
then some of the measured current comes from an undesired side reaction.
2.5.1
Undesired or Side Reactions
In these experiments, side reactions have been observed to become important only
above room temperature. The first samples were oxidized in a pyrex flask using 1 M
NaOH solution. At room temperature, the current decreased with time approaching
zero. At 80C, the current was larger and did not decay to zero with time. The
solution, in fact, became somewhat opaque after about a week. The Ag/AgCl reference electrode also appeared corroded after a time. It has been important to reduce
these side reactions because electrolysis is a fairly slow doping method and some cells
need to be heated both to accelerate the reaction and to allow a comparison to room
temperature data.
Originally, a 1 M or 0.1 M NaOH solution was prepared from the laboratory
building's supply of de-ionized water and reagent grade NaOH, but it quickly became
clear that impurities in the water and in the sodium hydroxide contribute to a side
reaction current which grows over the time-scale of the experiment. An egregious
example of this is shown in Figure 2-4. Note how quickly the background current
comes up in this two-day run.
To combat the side reaction problem, electrolysis at 80C is done using higher
purity 99.996% NaOH at a lower concentration as well as higher purity de-ionized
("18 MQ") water rather than "house" de-ionized water. (This sodium hydroxide is
supplied by Aldrich Chemical Company.) A lower solute concentration is also used
because it means that there will be less corrosion and possibly fewer contaminants in
the cell. However, the solute concentration also needs to be high enough not to limit
the reaction rate. Possibly, an even lower solute concentration would have worked, but
because there was no longer any visible corrosion (clouding of the solution, etc.) in
the cell, a 0.01 M NaOH was used. Removing the glass thermometer further reduced
the side reaction current.
The test to eliminate side reactions involved cyclic voltammetry (CV) scans done
with platinum wires for both the working and counter electrodes. In Figure 2-5, the
current passing through a 0.1 M NaOH solution during the CV scan is fairly small,
about
1 yA,
up to Vref ~ 0.6 V. Previously, it had been on the order of 10 - 100 PA
due in large part to contaminants in the cell. Such CV measurements are not the
best for determining side reaction currents. We use them, instead, to determine if
the concentration of NaOH is adequate.
Above about 0.7V, there is a dramatic
change in slope and the current quickly increases by several orders of magnitude.
2.0
1.5
1.0
0.5
-
S---
0
-0.5
0.5
1.0
Time (105s)
1.5
2.0
Figure 2-4: This sample weighs 83mg. This 2-day scan was done at 80C and Ve, =
0.6V. Note that background current steadily rises.
This current is primarily from oxygen evolution. The current increases sufficiently
above 0.7V to show that a 0.1 M NaOH solution provides enough hydroxyl ions such
that the current is not limited by tge concentration.
Another goal is to minimize
oxygen evolution with respect to desired cell reaction so oxidation of the samples is
conducted at Vref
0.6 V.
CV scans vary the reference voltage relatively quickly. Therefore, some of the
current below
-
0.6 V may be transient. On the other hand, in a typical CA mea-
surement, a cell is allowed to run at constant voltage for days or weeks. At constant
voltage less than - 0.6 V, the typical current between two platinum wires in a cell is
on the order of 10 nA a few minutes into the run when the precautions just described
are taken. With a sample in place, the oxidization current is on the order of a 1 pA.
Under these conditions, the reaction at the La 2 Cu04+s
electrode will be the dominant
one since the current with only a platinum wire is small in comparison.
2.6
2.6.1
Other Considerations
A Definition of sample equilibrium
For pellets run at room temperature in 1 M NaOH, the typical current density
for these constant voltage measurements is 10- 4 A/cm 2 initially, but it falls off to
10-6A/cm 2 or below in about one day. The current decays more slowly for single crystals. Temperature affects the magnitude of the initial current; generally the higher
the intercalation temperature, the larger the current. The charge that flows through
the La 2 Cu0 4 sample is directly proportional to the oxygen concentration because the
current is the result of La 2 Cu0
4
reacting with the solution to form La 2 Cu04+± [58].
If one holds the sample at a particular voltage relative to the reference electrode
long enough, the current flowing into the pellet approaches zero. If the diffusion into
the bulk is not limited by cracks, grain boundaries, or other inhomogeneities, then
the system should reach an equilibrium state. When these conditions are met, the
reference voltage, V,,f, is related to the chemical potential of the pellet in a simple
Cyclic Voltammetry Scan
104
103
10 2
.4 I-%
IU
4
IU
10
--
-
-
I
I
I
0.25
0.50
0.75
1.00
1.25
Voltage relative to Ag/AgCI electrode (V)
Figure 2-5: This scan was done at 80C with a platinum wire replacing the sample.
Notice that the current is relatively small for Vref
0.7 V. The slope on this semi-log
plot changes dramatically around 0.7 V, and the current quickly increases by several
orders of magnitude. The concentration of the solution is 0.01 M 99.996% NaOH.
way [39]:
e=
-( - Pref)/q,
where Apis the chemical potential associated with the half-reaction 2.1 and
(2.3)
,fre is
that of the reference electrode. From Equation 2.1, we see that q = 2e. Thus, by
measuring the integrated charge, Q, that flows through the sample for each reference
voltage, we can determine the oxygen concentration (S) as a function of p - ptre•.
For a given temperature, these measurements correspond to a cut through the t - 6
diagram. Unfortunately, not all of the data are taken at equilibrium, which is difficult
to attain. Samples not meeting this ideal are still included because they provide useful
information.
2.6.2
Usefulness of cyclic voltammetry
A La 2 CuO 4 sample serves as the working electrode at which the desired reaction occurs. Following Wattiaux's effort, Grenier et al. through the use of cyclic voltammetry
were able to identify oxidation and reduction occurring on the electrode surface. A
CV scan done on one of the pellets is presented in Figure 2-6. The precise voltages at
which the peaks occur is highly dependent on the condition of the electrode surface.
This scan has the same features as the one presented by Grenier [24]. Note that there
is a reduction peak near 100 mV corresponding to oxygen more quickly leaving the
La 2 CuO04 surface. A second peak (or shelf superimposed on a slope of rising current)
is located near 1.0 V, which corresponds the oxidation of the electrode surface as the
oxygen atoms move in. The oxidation peak occurs as the reference voltage is ramped
up while the reduction peak takes place as the reference voltage is ramped down.
The current begins going up very steeply near 700 mV as oxygen evolution becomes
significant. It is necessary to go to a significantly lower voltage to reduce the sample surface than to oxidize it. This once again points to the fact that CV scans are
very surface-sensitive. The oxidation peak shown in Figure 2-6 can appear at a considerably higher voltage than that used in chronoamperometry runs to successfully
dope the sample bulk. CV scans are still valuable in these experiments because the
presence or absence of surface reactions indicates whether or not the equivalent bulk
reactions can occur.
2.6.3
Temperature dependence of the Nernst equation
The potential of the reference electrode relative the sample electrode depends on
temperature and species activity. At equilibrium, this potential, E, and the generic
half-reaction at the sample electrode, E vOi + ne- -+ E viRi, are related to each
other by the Nernst equation:
E = Eo -
RT
nF
vgi log ai
(2.4)
where F is Faraday's constant and a, is the activity of species i. The activity is a
measure of how much a particular ion interacts with other species in solution. E0
is the electrode potential relative to the Standard Hydrogen Electrode for which all
species are at unit activity (ai = 1). In this thesis, the term Vef is used instead of
E.
When no current flows to the counter electrode, the electrode potential at equilibrium equals the open-circuit potential, Voc. The Nernst equation 2.4 predicts Voc, c T.
It is important to take note of this when comparing measurements because the electrolysis is done at different temperatures. A T, achieved at a given voltage will not
be the same once the temperature is significantly changed. To determine how closely
Voc scales with temperature, an additional electrolysis cell is set up according to the
method previously described. The cell is stabilized at various temperatures in a water
bath and allowed to equilibrate at each temperature, and then Vo, is recorded. These
data are reported in Figure 2-7. The slope is 0.5 mV/C, which is quite modest, but
a meaningful comparison of reference voltages as a function of of temperature should
take into account the temperature at which the electrolysis is done.
We can make a simple calculation using the Nernst equation to estimate the effect
of temperature on the reference voltage, AVef, (or AE as used in electrochemistry
literature). We then can compare the result to the experimental data. The Nernst
r4 '""'
,-
A-~r
I UUU
I
I
I
I
I
I
750
500
a,
C-)
250
0
-LJU
I
0
0.5
1.0
1.5
Voltage relative to Ag/AgCI electrode (V)
Figure 2-6: This CV scan is done at room temperature with the sample in place.
Notice the oxidation (ef = 1.0V) and reduction (Vf = 0.1V) peaks. The solution
is 0.01M 99.996% NaOH.
0.30
Temperature Dependence of Vref
0.25
O
0.20
0
0
O
0
OO`
0
0
0.15
0.10
20
40
60
Temperature (K)
80
100
Figure 2-7: The data presented use a La 2 Cu0 4 +s pellet working electrode with no
voltage applied to the counter electrode. The Nernst equation predicts that this
relation should be linear. Data fit to V, = mT + b, where m = -0.499 mrnV/C and
b = 230 mV.
equation 2.4 calls for the activities of solutes. However, what one usually calculates are
concentrations of species in solution, not activities. It is known that for dilute, weakly
interacting solutions (which is the case here) a = mc, where a is the species activity,
- a constant, and c the species concentration in moles per liter [8]. Substituting this
into Equation 2.4, we have
i
n[O,]"
d
In[E = E' + RT
nF
HI[R]"i
[0] and [R] refer to the concentrations of the oxidized and reduced species, respectively. For dilute solutions,
mis close to
1 and so terms containing In Yare small and
assumed negligible. Recall that
EviO i + ne- -- EviRi
is the generic half-reaction at the working electrode and in this case, the half-reaction 2.1
at the sample electrode is
La 2 CuO 4 (s) + 2SOH- --+ La2CCuO 4+s(s) + SH 2 0 + 2e-.
We plug this into the Nernst equation getting
RT
2SF
[La 2CuO4][OH-]23
[La 2CuO 4+s]][H 20]
Once we use the fact that solids and solvents have unity concentration, the equation
simplifies to
E = Eo -
RT
In([OH-]2),
2F
which only depends on temperature and hydroxyl ion concentration. If we substitute in 0.01 moles/liter for the concentration, then the difference in potential for a
temperature change from T1 to T2 is predicted to be
AE = 3.96849- 10-4(VIK- 1 )AT,
(2.5)
where AE = E2 - El and AT = T2-
T1. The 0.4 mV/C we get from this simple
calculation is not too different from the measured slope, 0.5 mV/C, reported in Figure 2-7. This supports the use of this half-reaction and the Nernst equation which
seem reasonable and are consistent with experiment.
2.6.4
Bulk Diffusion
The electrochemical reaction takes place only at the surface. Although the focus of
electrochemistry is on surface reactions, the same techniques have been used to dope
the bulk of a sample, which is important for the present experiments. Because of this,
it is beneficial to briefly discuss how oxygen might diffuse into the sample bulk.
The oxygen interstitials have to diffuse through the crystal in order to achieve
uniform doping. The actual mechanisms for interstitials moving within a crystalline
solid are quite complicated. For the present, we mention a simple hopping model for
the conductance of interstitials (or charged defects) in a solid [39]. The conductance
generally occurs by hopping between equivalent vacant sites. The interstitials can
move through the solid due the presence of a potential gradient or a concentration
gradient. This type of diffusion by hopping is thermally activated, and its diffusion
coefficient can be described by D = Do exp(-ED/kT), where ED is the characteristic
energy to hop from site to site.
In principle, the current through the sample in an electrolytic can have a contribution from the applied potential gradient. In general, the current density, J, for one
dimension, can be written as
J = -qNu(la(/x) - qD(ON/&x)
(2.6)
where N is the density of interstitials, -a/oax is the electric field and ,p is the
mobility [39].
However, because the dielectric relaxation time inside the sample resulting from
the electronic conduction is very short, the concentration gradient more likely determines the current. Furthermore, if field-assisted diffusion is important, a, study on
the time-dependence of the magnetic susceptibility [12] suggests that it only becomes
important for the relatively shorter times and distances over which phase separation
occurs [57], not in bulk diffusion important for the present experiments.
Assuming that the diffusion is primarily due to the concentration gradient, then
Equation 2.6 simplifies to
J = -qD(ON/Ox).
(2.7)
Furthermore, from equation 2.7, we see that the current measured at the surface of
the electrode during an electrochemical reaction should be of the form
I = -nFAJ/q = nFAD(N/x)s,,urf ,
(2.8)
where n is the number of electrons exchanged in the electrochemical reaction, F is
Faraday's constant (9.6485 104 C mol-1), and A is the surface area of the electrode [8].
When Fick's second law of diffusion
oN/O = D( 2N/X 2 )
(2.9)
is solved for N(x, t) and substituted into equation 2.8, one has I(t).
It is useful to discuss solutions to Fick's second law for two electrode geometries
that may be helpful in interpreting the data discussed in Chapters 3 and 4.
2.6.4.1
Model diffusion into a semi-infinite slab
Consider diffusion into a semi-infinite slab with the following boundary conditions.
The concentration of interstitials, N, is constant in the solution and at the surface of
the electrode: N(x = 0) = No for x > 0. At t = 0, the concentration inside the slab
(x < 0) is zero. At sufficiently short times, this model should be valid for electrodes
of other geometries. We will do this calculation in one dimension, but it can later be
generalized to two or three dimensions.
We begin with the general solution to Fick's second law of diffusion. Following
the treatment given by Jost [31], we try separation of variables for Equation 2.9:
N(x, t) = X(x)T(t). Such a solution would be of the form
N(x, t) = X(x)T(t) = (X 1 cos((k)
-x-X 2 Sin(kx)) exp(-k 2 Dt)
(2.10)
where X 1 , X 2 , and k are constants. The time dependence is the same for two and
three dimensions. A solution for a particular set of boundary conditions would determine the constants and be made up of a series of terms with the form found in
Equation 2.10.
For an unbounded system like an infinite slab, all values of k are
allowed as long as k 2 > 0 so N(x,t) remains finite as t -- 0o.
Consequently, the
solution will be of a form that sums over all values of k. The term sin(kx) drops out
so that N(x = 0) z 0. If the amplitude function X(x) describes the concerntration of
interstitials at each point x, then we have the following integral.
N(x,t) =
0 cos(k(x -
-oo X(x')dx'
x'))exp(-k
2
Dt)dk
(2.11)
This integral requires that we write cos(x) = (exp(ix) +exp(-ix))/2 and complete
the squares in the exponent. After the integration over k, N(x, t) can be written as
follows
N(x, t)
1
)
2(rDt)1/2
X(x') exp
-
('2-
-)2
)
4Dt
oo
dx'
(2.12)
Suppose we apply the boundary conditions for diffusion into the semi-inýinite slab:
X(x) = No for x > 0 and X(x) = 0 for x < 0 at t=
variables
0, and also make a change of
(x'- x)/2(Dt)1 /2. Now we have
=
N(
/()
exp(-u 2 )du
1 2
The first segment of the integral from -oo
to zero is (w)1/2/2. A second
(2.13)
segment
from zero to x/2(Dt)1 / 2 is just the error function. Rewriting the last eqgation, we
have
N=
-
No (1 2
erf(
x
2 'Dt
)),
(2.14)
where we have used erf(z) = -erf(-z). When this concentration is used tU evaluate
Equation 2.8, it gives what is known as the Cottrell equation.
~
i
r\t
13~T
AL1/UVo
A(t)
1 2
(7t) /
(2.15)
This equation gives us a relation between the measurable quantities, I and t, during
electrochemical reaction. In principle, we can calculate the diffusion coeffic ient given
I(t).
We can see now how the solution to the diffusion equation can used I 0o provide
a description of diffusion even for other geometries at times short in com )arison to
the time to diffuse across a finite sample. The mean displacement of a diffusing
particle can be estimated from spread in the error function after time t, v hich is of
order - (2Dt) 1 / 2 . Sufficiently short times should satisfy the condition I >>
(2Dt)1/2
or t <K 12 /2D, where 1 is the length of the sample. For finite samples, r,estrictions
placed on the values of k in Equation 2.10 to satisfy boundary condition: i result in
only certain values of k appearing in the solution and a different functiona 1 form.
The current may be determined by the rate of chemical reaction at the surface as
well as the concentration gradient. If the chemical reaction at the sample e Lectrode is
the limiting factor, then the current decay will follow a functional form diff,ýrent from
that predicted by Equation 2.15. If the current is diffusion-limited, then t he current
follow a t - 1/ 2 decay at short times.
The applicability of this model is discussed in Chapter 3 for ceramic -lectrodes.
The ceramic electrode is relatively porous, so the surface area is difficult to determine
accurately and in fact be larger than expected as will be discussed.
2.6.4.2
Model diffusion into a finite cylinder
For single crystal electrodes, the simplifying approximation that the sampl Selectrode
can be treated as a finite cylinder with impermeable end faces is made in 'hapter 4.
Evidence supporting the validity of this approximation include the follow' ng. X-ray
powder diffraction measurements, which have shown that the c-axis elonisates with
increased oxygen doping [24], are consistent with oxygen diffusing in be tween the
Cu02 planes. It has also been proposed that that the oxygen atoms are diffusing primarily between the Cu0 2 layers in electrochemical oxidation [2]. In addition, a study
of thermal diffusion using
1O as tracer in a strontium-doped crystal demonstrated
that the in-plane diffusion coefficient is three orders of magnitude larger than that
for c-axis diffusion at 500C [43].
Taken together, these experiments suggest a strong anisotropy (at least three
orders of magnitude) in the diffusion coefficient. This anisotropy means that the inplane diffusion is dominant, and the effective surface area of the sample electrode is
the edge faces.
In this case, Fick's second law of diffusion is solved using cylindrical co rdinates.
Equation 2.9 takes on the following form:
N/at = D( 2 N/ar
2
+ (1/r)&N/ar)
(2.16)
Jost [31] solves Fick's laws of diffusion to derive a form for diffusion int( or out of
a finite cylinder with sealed end faces. This treatment of the single crystal diffusion,
although it is a simplified view, is still useful because diffusion of the oxyl)en atoms
is predominantly in between CuO 2 layers. Therefore, the c-axis faces are effectively
impermeable to diffusion, and we can neglect this dimension.
The solution, evaluated at the surface of the cylinder r = ro, to th( diffusion
equation for a finite cylinder turns out to be a sum of exponentials given I
N =
Y(No/_,2)
exGp
(y
(2.17)
V=1
where ro is the radius of the cylinder and (, are the roots of Jo(x) = 0, Lhe Bessel
function of zero order.
Each term in the solution gets successively smaller. At sufficiently long times (for
t > 0.35r), omitting the third and greater terms results in less than a L% error),
the first two terms of the series should be a good approximation. ThiV solution,
Equation 2.17, is plotted in Figure 2-8. At sufficiently short times, the s,)lution no
longer looks exponential, but roughly follows a 1-1/
the solution for the infinite slab geometry.
2
decay, which is expected from
0
1
-I0.-
0.01
C,
0
0.25
0.25
C
0.20
.0
Figure 2-8: The top figure is a plot of Equation 2.17. J, refers to the vt h zero of
the Bessel function of zero order. The first zero, J 1 , is 2.405. The solution f :llows an
exponential form except at very short times, where we see some deviation i idicating
a slower decay. In the bottom figure, the same points are plotted at very sh ort times
to see how well the follow a t - 1/ 2 decay. In this limit, the generated points ro longer
look exponential, but roughly follow a t - 1/ 2 dependence.
Chapter 3
Experimental Results on
Polycrystalline La 2 CuO4+6
3.1
Overview
This chapter details a series of electrolysis experiments conducted on poly ystalline
or ceramic samples. These samples are relatively porous so the electrocl
mical re-
action can proceed quickly in comparison to the same reaction in a sing
crystal.
The initial oxidizing reaction at the surface and the subsequent diffusion
f oxygen
into the bulk are investigated by chronoamperometry (CA) experiments. ( her sample properties are probed through magnetization experiments, which pro
le useful
information such as the superconducting transition temperature, the MeiP ler effect
and shielding fraction, and the Neel temperature.
3.2
Interpreting the time decay of current i electrolysis experiments
The time decay of the current is important in the CA runs because it ind ates how
quickly a sample approaches equilibrium. The definition of equilibrium i the electrochemical cell has been touched on in Chapter 2, and it is discussed fu her here.
As already mentioned, Equation 2.3 shows that V',f oc y at equilibrium. I om measurements for which the current approaches zero and the integrated charg( aturates
one can draw conclusions about the relationship between 6 and p.
However, the decay of the current can be very slow. In Figure 3-1, plots
f current
versus time are shown on a log-log plot for two samples. The current de ly is not
exponential; the data are plotted for one pellet held at
ef
= 0.50 V and an her held
at Vef = 0.45 V. Note that the current for the 0.50V pellet begins to follo
a power
law at t - 103 s, and the decay is well-described by t- 1.5 for at least two
:cades of
current. Even though the current drops below the noise level, about 10after two days, the decay is clearly faster than t- 1 indicating that the charge aturates
after several days, as will be discussed. For the second pellet, held at 0.45 V. he initial
current is much smaller and the decay is slower than for the first pellet. N( etheless,
- 1
5
. . The initial current is about five times smalle
and the
power law begins only after - 104 s. This difference may reflect sample
>)-sample
variations rather than an intrinsic dependence of the time scale on Vre
since we
find that many samples oxidized with 0.40V < Vref ~50.55V have about
he same
it still approaches
, t
superconducting transition temperature. The exponent of the power law i1 he same
within experimental error for both pellets.
The current decay can be described approximately by (1 + t/to)P. I is would
mean that for p = -1.5 the charge reaches 90% of its saturation value at
, 100to,
where to is approximately the time at which the current begins to follow
re power
law. For the Vrf = 0.50V experiment in Figure 3-1, to is approximately
S103 s.
The 90% saturation level requires - 3 days of which one day (81% saturati
level) is
shown in Figure 3-1. The charge as function of time is shown in Figure 3-2. lowever,
saturation for the second pellet would take - 10 times longer.
Figure 3-3 shows to and p for several pellets oxidized at room temperatu
. Except
for Vf = 0.30 V, p seems to be independent of reference voltage. p is ex acted by
least-squares linear fit to the log of the data. The pellets oxidized at 0 0 V and
0.35 V appeared to have just reached to near the end of the scan, so p is c bermined
over a smaller range of data (less than an order of magnitude) and is subje
to large
10- 3
10- 4
10- 5
10
1
Fi
te
)5
0.150
0.125
0.100
0.075
0.050
0.025
(
Fig
tha
75
uncertainties.
We set out to study oxygen content as a function of voltage with multi] e pellets,
each at a different voltage. Ideally, these samples should have been oxidiz,
for very
long times. However, because of the pressing need to begin oxidizing sing] crystals,
which take on the order of months, the pellets were oxidized for only one or wo days.
A single pellet was oxidized by varying the reference voltage up and dow in small
steps and waiting at each step until the charge saturated. The single Y let data
provide some clues into the & versus p phase diagram.
3.3
Data on a single pellet at room tempei iture
Because of the very long time scale over which the charge saturates and its : mple-tosample variation, Q(Vref) is measured by oxidizing a single pellet, altering V f in very
small steps and waiting until the current is less than the noise after each tep. For
most steps, this requires four to five days and results in an uncertainty of al ut 0.002
electrons per formula unit (e/f.u.). These units are explained in Appene KA. For
the experiments described in the later sections, multiple pellets and short( electrolysis times have been used. These measurements are consequently subject
) greater
uncertainties.
Figure 3-4 shows data for a single La 2 C uO 4 pellet stepped up and t en down
in reference voltage. The data are clearly hysteretic below 0.40V.
Ho, 2ver, the
hysteresis vanishes above 0.40V; only one set of data points is plotted in 1 is region
because the two sets overlap for each voltage within the noise. Note that tw plateaus
appear as the voltage is decreased: one for 0.375V < V < 0.475V, wAh Q2 =
0.127(2) e/f.u., and other for 0.300V < V < 0.330V, with Qi = 0.11, 2) e/f.u.
Below 0.30V, where the data are denoted by a different symbol, equilibriu
can not
be attained at each step in times of the order of a few days. (It should be - ted that
another single pellet after a long oxidation for 0.40 V E Vef < 0.50 V accu ulated a
charge of Q • 0.14 e/f.u. This effect may be due to initially charging ceram
samples
quickly using a big voltage step so that total charge overshoots the energeti Illy more
2.0
1.5
1.0
0.5
4
3
2
0
1
0
V
Figure 3-3: The current decay follows a power law: (1 +t/to)P. A distributior of p and
to for several pellets is shown. p < -1 means that the charge will eventually saturate
at an equilibrium value. The error in p is largest for 0.30 V and 0.35 V be( ause the
current decays very slowly and p is extracted from date varying less than c ne order
of magnitude.
favorable value for the given voltage range. Perhaps, it is indicative a thi
plateau
at a slightly higher charge. However, it is more likely that variability in
e charge
measured for the upper plateau is related to the charging of grain boundar
s present
in ceramics as will be discussed later.)
3.4
Data on multiple pellets at room tempe: ature
The plateaus in Figure 3-4 show that there are ranges of Vef, and there re y, for
which 6 is constant. This suggests that approximately stoichiometric comy unds are
formed for these values of 6. A number of pellets have been oxidized at diffei nt values
of Ve, I to determine the superconducting properties of these special compos. ons. For
each pellet the reference voltage is maintained in the electrochemical cell ft one day.
Figure 3-5 shows a comparison of the single-sample experiment and the -ultiplesample experiment.
While the sample-to-sample variations are quite cl .r in the
multiple-sample data, the latter accurately reflects the trends in Q(Vref)
d allows
us to make important qualitative comparisons to the single-sample experim it, which
is run closer to equilibrium.
A summary of the data taken on this set of pellets, which will be reft :ed to as
batch one, is shown in Table 3.1. These pellets were die-pressed at 1.5 n tric tons
with an approximately 2 cm long piece of 0.003 inch diameter platinum wire and then
placed in an isostatic oil press at 35000 lbs/in 2 . These pellets were electro' emically
oxidized at room temperature for one day. Susceptibility data are taken i a 10 Oe
field. The sample masses in parentheses are the masses for magnetic meas rements.
(The pellets are fragile and broke once removed from the cells). Some o the data
from the table are also plotted in Figure 3-6.
Some of the pellets broke prior to magnetization measurements so the rst mass
reported in Table 3.2 is the one measured prior to electrolysis, and the
cond, in
parentheses, is that for the largest piece used in the magnetic measurem its. The
charge, reported in units of electrons per formula unit (see Appendix A' is based
on the mass of the samples during electrolysis. The superconducting trans ion tem-
In
n
*1
U. I JU
0.125
g
0
0.100
E•-
0
0.075
/o
0.050
0.025
-
O
A
ni
0.25
0.30
0.35
).50
0.40
0.45
Voltage relative to Ag/AgCI electrode ( )
Figure 3-4: Measurement of charge as a function of reference voltage at roo temperature on a single pellet. The reference voltage is ramped up and down inc mentally
and allowed to equilibrate at each point. For the voltages indicated by amonds,
equilibrium could not be attained.
0.175
K
I
I
I
I
I
I
I
0 single sample
0.150
0
0.125
different samples
0
0
0
0.100
0.075
o
0.05 ;0
0.02 5
n
*
II
0.25 0.30 0.35 0.40 0.45 0.50 0.55 ).60
Voltage relative to Ag/AgCl electrode (V
Figure 3-5: Comparison of charge measured for the single sample with those
neasured
for multiple samples, which were run at room temperature for one day. T
he single
pellet data were taken incrementally, and plotted in Figure 3-4 for increasii
Lg V.
Table 3.1: La 2 Cu04+S pellets: batch one
Sample
Name
Mass
mg
y25a
y25b
26a
26b
y26a
y26b
27a
27b
88 (75)
80 (60)
50 (36)
59 (50)
63 (48)
77 (50)
101 (73)
155 (82)
4r x y
(zfc)
Vrj
V
0.265
0.30
0.35
0.40
0.45
0.50
0.55
0.60
7.4%
21.2%
30.0%
26.3%
20.7%
19.9%
47.7%
47ry
(fc)
4.1%
10.8%
17.7%
15.9%
12.1%
12.7%
31.1%
T,
K
Charge
e/f.u.
0
31
32 (45)
46
46
47
47
47
0.0007
0.035
0.087
0.120
0.105
0.108
0.102
0.472
perature is determined by the onset of the diamagnetic signal rather than its midpoint.
Figure 3-7 shows some examples of the data. Magnetic suscepti ility data
are given as the dimensionless volume susceptibility for zero-field cooled (zfc) and
field cooled (fc), respectively.
The susceptibility is reported as
4 7rx,
aking use
of the fact that the magnetic induction, B, of a perfect superconductor is zero, so
B = H + 47rM = 0 --+
= M/H = -1/4r.
Although these data were taken before the side reaction problem di cussed in
Chapter 2 had been recognized, the side reaction currents at room temper ture have
since been found to be quite small. For data taken at 80C, which will be discussed
later, the side reaction currents are important.
One indication of this i the cor-
rosion observed in electrolysis cells run at elevated temperature before t e NaOH
concentration was reduced.
The sample run at 0.30 V has a T, of 32K while samples run at Vef > 0.40 V
have a T, of 45K. This is very reproducible, as data for another set of p llets will
demonstrate shortly. The sample oxidized at 0.35V has a mixture of two T, 's - 32K
and 45K. As already shown in Figure 3-5, the charge measured for samples oxidized
in the range 0.40V < V,,f < 0.55V is very similar. This suggests that there is a
preferred 6 which corresponds to a single phase.
The sample run at 0.6 V has a
much larger charge. A non-negligible portion of it is due to oxygen evoluti n at the
electrodes:
20H- --+ H 2 0 + -02 + 2e-, which becomes significant at a out this
65
60
50
40
-
30
20
10
80
60
~
40
I
20
0
0
0.2
0.4
0.6
Voltage relative to Ag/AgCI electrode
0.8
(V)
Figure 3-6: Superconducting transition temperature and magnetic susc ýptibility
(10 Oe field) for samples run for 1 day. For the susceptibility, both field-co oled (fc)
and zero-field-cooled (zfc) data are shown. In the top panel, the two poin Ls shown
for Vref = 0.35 V indicate that both T, phases are present.
voltage. However, the Meissner effect and shielding fraction are much I ger than
those for the other samples. This indicates that more oxygen atoms have
ost likely
been incorporated in the sample. T, is plotted as a function of referen
voltage,
along with 4,Xy for the pellets in batch one in Figure 3-6.
In Figure 3-7, magnetic susceptibility measurements taken in a 10 C field are
shown. The data, which have not been corrected for de-magnetization, arm )resented
as a percentage of the volume expected for the shielding fraction or th
Meissner
effect in a perfect superconductor. The open circles represent the zero-f
d cooled
(zfc) or shielding fraction data, and the filled circles represent the field col ed (fc) or
Meissner effect data. The pellet charged at Vre = 0.30 V has a supercon
acting Tc
of 31(1)K, and 4rX is quite small in comparison to that for the pellets
larged at
higher values of V. The 0.35 V pellet contains a mixture of phases as dei )nstrated
by its two transitions - one at 31(1)K and the other at 45(1)K. The pellet
iarged at
0.45V shows only a trace of the 31(1)K transition showing that most of
e sample
has Tc = 45(1) K.
3.5
Comparison of single pellet electrolysi
data
to multiple sample magnetization date
Figure 3-8(b) shows T, as a function of V:,f; the charge from Figure 3-4, for
eV',
ecreasing
is reproduced in Figure 3-8(c) for comparison. All samples chargec it eVf >
0.35 V, in the higher plateau of Q(Vref), have Tc = 45(1)K, whereas
e sample
charged below 0.35V, in the lower plateau of Q(V), has Tc = 31(1)K. I Jeed, the
sample that displays both transitions is that charged at 0.35V, correspon
ng to the
junction of the two plateaus in Q(Vrf). The dependence of T, on Vef in Fi ire 3-8(c)
confirms the observation that compositions at well-defined 6 are formed
a each of
the two plateaus and demonstrates the these two compositions have diffel at T,'s.
Figure 3-8(a) shows that
4
wxrincreases
with Vrej up to 0.40 V. At h her Vef,
the fluctuations in 47rX follow the variations in Q seen in Figure 3-5, sugg ting that
0
-5
i-10
-15
S-20
-25
0
-5
•- -1o
-15
•
S-20
-25
0
-5
-10
-15
"J -20
-25
-30
Figure 3-7: Mi
field-cooled (fc)
Both
Table 3.2: La 2 Cu04+s pellets: batch two
Sample
Mass
Name
(mg)
C
42
70(46)
24D
23C
23D
23A
23B
67(52)
73(49)
77(34)
71(55)
76(56)
•'A/ A
C)1 / AC)\
42
A
24B
Electrolysis
To
Treatment
3V
(K)
298K
.3V 360K
.4V 298K
.4V 360K
.5V298K
.5V 360K
nT
81(48)
.6V
88(75)
.6V
•?bC•T7
298K
360K
31
33
46
41
47
41
AIf
4xy
4xy
(zfc)
21
6%
22.6%
33.3%
41.4%
37.3%
35.5%
A,•
46
43.0%
41
28.8%
Q
(fc)
C•(>-I
13
(e/f.u.)
1%
0
076
12.2%
19.9%
22.0%
23.1%
14.8%
0.097
0.11
0.31
0.14
0.47
Ct"
(\•( A•
AfIf-
27.4%
12.2%
0.845
2.15
the latter result from incomplete oxidation of the pellets. Q at 0.6V cot Id not be
measured because the decomposition of water into water and oxygen giv es a large
current. However, the large Meissner effect and shielding fraction sugges
that the
pellet is more fully oxidized at higher voltages.
3.6
Reproducibility of jump in T, from ar Lother
•eL,
-V 11C
t~l
t.11ii
In order to check that the jump in T, at 0.35 V is reproducible, another set f pellets,
which will be referred to as batch two, was oxidized. These samples wee held at
different voltages and temperatures for two davs in a 1 M NaOH solution.
based on these pellets are summarized in Table 3.2. Plots of 4 7r
he data
are dis )layed in
Figure 3-9. The values of Q for 360K oxidation are unreliable because of the side
reaction, which gives a large current at elevated temperature.
A few points may be recognized immediately from Table 3.2. As with b itch one,
after room temperature electrolysis the observed superconducting transitior temperature is about 32(1)K for V,,e
0.3V while for V,,f > 0.4 V, the transitior temper-
ature goes up to about 46(1)K. For electrolysis done at 80C and V,,f 2 0.4 V, the
superconducting transition is only about 41(1)K, about 5K lower than tha seen at
&N"
60
50 - (a)
40
30
20
10
0
50
AML
45
--
-
zfc
fc
0
0
r\
0
i
~
(b)
·
·
0
0
I
I
I
40
I--
35
30
-)
0.150
0.125 S(c)
0.100
0.075
0.050
0.025
n
'
_
·I
Oo
single sample
I
I
I
0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.
Voltage relative to Ag/AgCI electrode
v)
Figure 3-8: Panels (a) and (b) show the susceptibility and To, respectively fi multiple
samples after one day of electrolysis. Panel (c) shows the charge incor, rated at
equilibrium for a single pellet in comparison.
100
zfc
* fc
0
80
298K
60
40
20
·
100
I
I
360K
80
60
40
0
20
I
0
I
0.2
0.6
0.4
0.8
Voltage relative to Ag/AgCI electrod
1.0
(V)
Figure 3-9: Susceptibility as a function of Vref for pellets oxidized for 2 da at room
temperature and at 80C as shown. The zero-field-cooled (zfc) and field- ,oled (fc)
measurements are taken in a 10 Oe field.
room temperature for the same voltage. One might suspect that the 41K p hase is not
pure. However, although the transition is not sharp at 41K, the susceptib ility varies
smoothly without the discontinuity normally seen at 32K for a mixture c f 32K and
V
A5r LK ,
p
In
This
ases.
Figure
3-11,
illustrates
oxidized
1l
xampes
the
that
at
both
the
298K
ata
Tc's
jump
and
lI
f_r_
f1
o
or
for
batch
in
360K.
To
d
sampes
oxi
two
near
The
.. ..
ized
pellets
0.35
lower
V
To
at
80C
are
is
are
plotted
as
reproducible
of
~
41K
shown
a
and
for
in
seen
3-10.
n
fr
oxidat
ir
1)
-
gure
functi
is
360K
F
of
Key.
samples
on
is
seen
for all the pellets which were oxidized with Ve,f > 0.40 V.
Although there are fewer the pellets in batch two for a comparison, t he charge
observed at the different voltages is reproducible - around Q
-
0.13e/f u. above
= 0.4 V. Figure 3-12 shows that the charge is similar to that mea ;ured and
Vef
displayed for batch one pellets in Figure 3-5.
3.7
Stability of 45K superconducting phase
It has been suggested that the 45K transition temperature seen in cerami c samples
is unstable [18]. Another possibility is that because samples are not in e( uilibrium
to begin with, one has a mixture of phases and those resulting from high r oxygen
density disappear as the phases equilibrate. Perhaps, a sample prepared
t high 5
would produce a homogeneous, stable sample with T, near 45K.
This issue was examined by looking at how the transition temperature f sample
26B evolved over a period of time. This sample was oxidized for one day t
Vre
=
0.40V. Magnetic data for it are shown in Figure 3-13 over a period of 18 mo ths. This
sample has an initial T, of about 45K. After six months, the transition te perature
decreases to 42K with the same shielding fraction at 5K of about 30%, not orrecting
for demagnetization effects. After about 18 months, T, is still 42K but the shielding
fraction has dropped to 26%. These changes are small but still significant.
Because the sample was not initially oxidized for very long, it is likely that the
sample was not yet in equilibrium.
Feng et al. [18] reported that T, ha
mostly
been converted to the 32K phase in less time than spanned in Figure 3-1 . Thus,
72
0
-0.1
-0.2
-0.3
-0.4
-0.5
0
-0.1
-0.2
-0.3
-0.4
Figure 3-10:
at the refern
demonstrate
60
I
'
I
i
0
0
r
o 298K
* 360K
50
-o
0
40
30
20
0
0
0
0.2
0.4
0.6
Voltage relative to Ag/AgCI electrod
0.8
(V)
Figure 3-11: T, versus V,e, for pellets oxidized for 2 days at room tempe ture and
at 80C as shown. The susceptibility measurements used to determine Tc ai taken in
a 10 Oe field.
0.175
0.150
_
0
--
single sample
different samples:batch 2
0
0.125
0
0
0.100
0.075
0.050
0.025
0
I
I
I
I
I
I
0.25 0.30 0.35 0.40 0.45 0.50 0.55
Voltage relative to Ag/AgCI electrode (
60
)
Figure 3-12: Comparison of charge measured for the single sample data, for nc]reasing
'ic h were
Vre from Figure 3-4, with those measured for the pellets in batch two,
oxidized at room temperature for one day.
a stable 40 - 45K transition temperature may depend on the manner an,I duration
of oxidation. For instance, Feng et al. used constant current whereas we have used
constant voltage oxidation.
F,
t'
3.8
r
+ blI45Kr
This difference in techniques may play a i ole in the
h'
50 Electrolysis Data
We had expected that the electrochemical oxidation of La 2Cu0 4 would be thermally
activated. Since the reaction is already quite slow at room temperature, )ne would
normally rely on electrolysis at room temperature or above. However, th re is evidence of oxygen staging just below room temperature in single crystals of L 2 CuO4 +S
from neutron scattering experiments [60]. Staging refers the ordering of intercalants
in a solid; they do not go in homogeneously, but rather they follow a p riodic arrangement. A stage number of four, for example, refers to intercalants goin in every
fourth layer of the host material. Staging has been seen definitively in graphite [14]
and superlattice features reminiscent of staging have been seen in La 2 Ni
4+S
[56].
Like both of these compounds, La 2 CuO 4 has a planar structure which sho ld facilitate staging. Experimentally, the onset of staging for most single crystal amples is
just below room temperature.
In the hope that different staging levels would manifest themselves as mo e sharply
defined plateaus in equilibrium Q(Vref) data, electrolysis was begun on a pe let below
room temperature, at 5C. If the plateaus in the single pellet data taken at room
temperature (Figure 3-4) are due to oxygen staging, then they ought to bec me even
more pronounced at 5C.
An electrochemical cell containing a fresh pellet in 1 M NaOH solution is placed
in a 5C water bath. The same procedure is used for this pellet as for the sin le pellet
for which the plateaus are observed. With the reference voltage held cons ant, the
current is monitored as a function of time. Because of how the samples are repared,
there is a small amount of excess oxygen in the pellets corresponding to n initial
Neel temperature of about 250K. Because of this, the first CA run was used to
76
0
-10
-20
-30
0
-10
-20
-30
0
-10
-20
-30
-40
Figure 3-13: M
- ..
. . . ... ..
. ,oU
ivc3u111m
ztollulU
-Cne -cooieal ZIC) measurements for samples having undergone oxidation at room temperature
with Ve,S= .4 V
for 1 day. After initial oxidation (top panel), the pellet has a
T,
data in the lower two panels show how the susceptibility changes of 45 K. The
with t me. No
de-magnetization corrections are made.
---
l
de-intercalate oxygen from this sample to see how closely the amount of oxygen in
the sample corresponded to S
0.010(5) estimated from TN
250K [50. 46]. This
de-intercalation run is presented in Figure 3-14. The measured S of 0.003 is smaller
than expected but still reasonable given the uncertainty in Ty~(S'. More oxx gen would
have probably come out of the pellet for Vref < 0.15 V, as we find in de-intercalation
experiments for single crystals. (This is discussed in Chapter 4.)
After de-intercalation, oxidation of the pellet was begun.
We had
lanned to
wait for the charge to saturate at a given voltage before the voltage w s stepped
up to allow more oxygen to enter the sample. Figure 3-15 illustrates on of these
chronoamperometry scans for Vf = 0.45 V. Note the length of the scan - over 62
days! Clearly, it would take more than a year to complete a series of these scans for
an entire phase diagram like the one at room temperature in Figure 3-4. This became
apparent only after some of the data were already taken.
Current data are plotted on log-log plots for de-intercalation and int rcalation
at 5C in Figures 3-16 and 3-17. The de-intercalation data are very simi ar to the
intercalation results at room temperature results. The data follow a p wer law,
t - 1 .6, for times longer than 104 s. The time scales are surprisingly similar at room
temperature and 5C. In contrast, the intercalation data show that oxidation is much
slower at the lower temperature. We see in Figure 3-17 that the power law b gins near
106 s with
ef
= 0.45 V. Following the argument used with the room te perature
data, one reachs 90% charge saturation after waiting - 100t o , where to is th time for
which the power-law decay begins. This suggests that one must wait at least 00 times
longer than at room temperature - about three years! It appears that de-int rcalation
proceeds more quickly than intercalation. It is odd that there should be such a large
difference between the two if the current is diffusion-limited. This becomes (specially
clear in electrolysis experments on single crystals, which are reported and discussed
in the next chapter.
Near the end of most chronoamperometry runs (50+ days), the curre t hovers
around 4 - 10-8 A for several days. This is taken to be the baseline curre t. This
background is also about that same size as that seen in the single crystal exp riments.
78
5C de-intercalation
6
5
4
3
2
1
0.010
0.008
0.006
m 0.004
o 0.002
0(
Figure 3-14:
open-circuit
intercalated
over 4 days.
the sample.
5
Time decay of current and charge extracted from a 67 mg p( Ilet. The
voltage for an as-prepared pellet is 258 mV at 5C. The sam )le is deat a voltage slightly below this: 255 mV. The experiment last( d a little
Note that the current is positive corresponding to oxygen ior s leaving
5C intercalation
1.50
1.25
1.00
0.75
C-
I
0.50
0.25
0.05
0.04
0.03
C-)
0.02
0.01
Time (106 s)
Figure 3-1
the same ,
of an acci(
days.
ion of
ecause
ver 62
10 - 4
10- 5
*0
•
0
a) 10L.
C-)
10- 7
10- 8
1U
10 `
10 4
Time (s)
Figure 3-16
follow a poi
105
)6
10 -
4
U
c
5
10--6
I
9
10
C)
0 9
4 I
IU
m
4;
n-8
1
I
II
I
i
I
i
I
1V
10
4
105
Time (s)
106
10
Figure 3-17: Time decay of intercalation current at VreJ = 0.45V an, 5C. The
discontinuity in the data results from an accidental interruption of the e )eriment.
The power-law begins for t > 10%.
This background current is subtracted before integrating the measured cur mnt to get
the total charge. These data are presented in Figure 3-18. The data sh w that
reachs
-
0.1 e/f.u., about the same above V,ef
i> 0.45V
Q
at 5C as at 23C. Although
one cannot say that there are plateaus in the phase diagram at 5C, this ( periment
suggests that at least by lowering the temperature
-
20C, one would achie e approx-
imately the same 6 for the upper plateau as at room temperature, and th refore the
same phase is also likely.
3.9
Calculation of Diffusion Coefficients
Because the rates at which oxygen is incorporated into these samples are mportant
to consider during oxidation, it is worthwhile to examine the diffusion
)efficients
obtainable from the CA scans at room temperature.
We have fit the current at short times under the initial assumptiol that the
intercalation is diffusion-limited as described in Chapter 2. For the pell s run for
one day each, we plot I vs t - 1/ 2 in Figures 3-19 to 3-22. The time interva chosen to
analyze the data is between about 7 minutes and 45 minutes after oxidat n begins.
Reasonable fits can be obtained from a t- 1/ 2 dependence over this limite range of
times. It is a compromise that avoids the effects of polarization of the eleci olyte and
surface reaction at the shortest times and the more complicated behavio at longer
times. The figures show fits to the data to extract the diffusion coefficients The data
follow a line fairly well with the exception of the measurements at Vef = 0.45 V in
Figure 3-21, which give a poorer fit. (As a reminder, a negative current c :responds
to oxidation of the sample.)
Equation 2.15 predicts that the diffusion-limited current is I = nNFA D/rt)l/ 2
Here N is the density just inside the surface. Using the charge measui d for the
single pellet (6 - 0.06) to estimate the excess oxygen density just inside 1 .e surface
and assuming the grains are of theoretical crystalline density, we deter- ine N
1.04 - 10- 3 moles/cm 3 . If we use this value for N and the geometric surf :e area of
the pellets (- 0.5 cm 2 ), we find that D
'
10- 10 - 10- 11 cm 2 /s from fits to 1 e current
0.15
O
0.10
:3
ciC
0.05
L-)
CU)
O
0
n n05
O
o o0oCo
0.1
0
O
-V.V0
0.25 0.30 0.35 0.40 0.45
Voltage relative to Ag/AgCI electrode
0.50
NV)
Figure 3-18: Measurements of charge accumulated as a function of Vre, uring intercalation at 5C. This measurement is analogous to the single pellet exp riment at
room temperature. (Figure 3-4) This is the same 67mg sample for whic data are
shown in Figures 3-14 to 3-17. Each data point takes - 50 days.
data. This is a factor of 103 larger than coefficients found in the electrc chemically
oxidized thin films (D = 10-13 - 10- 14 cm 2 /s) [2].
The pellets are qu te porous,
about 72% of crystalline density; consequently the surface area, A, of the (lectrode is
under-estimated by the geometric area. If we assume that the full area of tt e - 43 um
grains is exposed to the electrolyte (10 - 15 cm 2 ), we find the diffusion
are virtually the same 10- 12
-
oefficients
10- 13 cm 2 /s, which shows that the cerami s data are
consistent with previous experiments [2, 24].
The quantity, AD
1/ 2
, determined from the fits to the data in Figures 3 19 to 3-22
is plotted as function of Vfe
in Figure 3-23. (The non-zero y-intercepts reflect the
fact that the current deviates from a t-1/2 decay at longer times.) If on excludes
the diffusion coefficients calculated for
relf
> 0.55 V as being too large due to oxygen
evolution, we notice that the diffusion coefficients are all similar in magni ude. The
value calculated for Vf = 0.40 V is larger; however we expect that the diffusion
coefficient is calculable only within a factor of ten by this method.
At sufficiently short times in comparison to the time for diffusion acros the sample, one expects to observe I oct-1/2 as discussed in Chapter 2. The shorte t possible
time scale one would obtain if the dominant length scale in the ceramic, were the
grain size,
s
43, m, is t <K (1.8
10-5cm 2 )/(5
10- 13 cm 2 /s)
, 107 s.
This as-
sumes that diffusion along the grain boundaries is rapid compared to diff sion into
the grains. In this case, the t- 1/2 decay should have been seen at least for t
106 s or
about one day. The data clearly do not follow t-1/2 for times even approac ing 107 s.
At the longest times, the exponential decay of the current predicted by the diffusion
equation is also not observed. In this chapter, in fact, we have shown that t e current
begins to follow a power law of - t- 15 after - 104 s. It is also striking th t the diffusion coefficients are very large compared with those measured for thermal diffusion
(D ~r10-'
- 10-21 cn 2 /s). We expect some anisotropy (Da,b/Dc , 103) [43], but
even with this taken into account diffusion proceeds too quickly at room te 1perature
to be simply due to the concentration gradient of excess oxygen entering th sample.
Perhaps, what is being measured is not diffusion into the individual g ains, but
rather diffusion into the sample along grain boundaries. As these boundarie become
85
saturated, a slower process dominates oxidation into the individual grz ,ins. This
demonstrates that something besides a diffusion-limited mechanism is invi )lved.
2.5
Vref= 0.265V
.
1.0
o
-0.5
- = 0 .0001307150t- 1/ 2 - 4.95934e-06
**·.
'4*,
~
.*
~
,z...*
·
4
Vref0. V
LO
• •
·
•
•
0
•
•
o°
•
•
()
lr-; ·
0V
=0
.0
--e =
I = 0.0006579330t- 1/ 2 - 1.35026e-06
n
II
I
I
0.020 0.025 0.030 0.035 0.040 0.04 5 0. 050
Time-1/2 (s-1/2)
Figure 3-19: Current versus t-1/ 2 during intercalation. The sample oxidized It 0.265V
weighs 88mg, and AD 1 / 2 - 1.1498e - 6. The other at 0.30V weighs 8 Img, and
AD
1/
2
= 5.7872e - 6.
C
n
U.U
I
'
*
I
4.5
4.0
3.5
3.0
2.5
Vref 0.35V
0.00053408* V1! 2 + 2.02192e-05
1
3.0
I
.*
2.5
2.0
C-) 1.5
1.0
0.5
V
=0.40V
-
= 0.00517478 - 1 2
t / + 1.83471e-05
I
=0.I40V
I
0n
0.020 0.025 0.030 0.035 0.040 0.04
Time-1/
2
0.050
(s-1/2)
Figure 3-20: Current versus t - 1 / 2 during intercalation. The sample oxidizei at 0.35V
weighs 50mg, and AD 1/ 2 = 4.6978e - 6. The other at 0.40V weighs 5 mg, and
AD 1/ 2 = 4.5517e - 5.
1.50
0 &
1.25
CD
a,
1.00
0.75
- 0.45 V
r.**
I = 0.00153398*t-1/
1.0
I
I
2
+ 6.43481e-05
I
0.8
0.6
C-
0.4
.:
I)
0.2
t)
V ref = 0.50V
I = 0.000892172*t - 1/ 2 + 3.5638e-05
I
I
I
I
I
0.020 0.025 0.030 0.035 0.040 0.04 5 0.050
Time-1/2 (s-1/2)
Figure 3-21: Current versus t - 1 / 2 during intercalation. The sample oxidized at 0.45V
weighs 63mg, and AD 1/2 = 1.3493e - 5. The other at 0.50V weighs 7
7' mg, and
AD 1 / 2 = 7.8475e - 6.
A
I
A
3
Co
r
-
II
Vref= 0.55 V
I = 0.00530026*t-1/
2
- 8.83199e-06
1
E
2
1
-I
0,
1
6
5
4
I
i
C
=
L2
2
V
1
ref 0.60V
I = 0.00789977* - 1/2 + 0.000103835
0
0.020 0.025 0.030 0.035 0.040 0.04 i 0.050
Time-1/
2
(s-1/2)
Figure 3-22: Current versus t - 1 / 2 during intercalation. The sample oxidize at 0.55V
weighs 101mg, and AD1 /2 = 4.6621e - 5. The other at 0.60V weighs E1 mg, and
AD 1 / 2 = 6.9486e - 5.
0.5
0.4
E
0.3
I
0.2
0.1
0
0.
Figure 3-23: The diffusion coefficients are similar in magnitude for pellets ox idized at
room temperature if the assumption that the surface area is about constant i: correct.
An estimate of A - 10 cm 2 implies that D _ 10-13 cm 2 /s typically. The geometric
surface area of the pellets is about 0.5 cm 2
5
Chapter 4
Experimental Results on Singl
Crystal La 2 CuO4+6
4.1
Overview
In this chapter, we discuss the results of electrochemical oxidation and r agnetization experiments, as well as some preliminary transport data, on single
ystals of
La 2 CuO4+s. Data from neutron scattering experiments at Brookhaven Nat >nal Lab-
oratory, which revealed staging in some of these crystals, are also includec
The time scale for oxidizing single crystals is much longer than for poly ystalline
samples. Each chronoamperometry measurement takes anywhere from thi by-five to
eighty-five days. These experiments provide information on the time deper ence and
the total charge entering the sample. Magnetization results provide inform tion such
as the Neel temperature, the size of the weak ferromagnetic moment of tE sample,
the superconducting transition temperature, and the Meissner effect an( shielding
fraction. Some preliminary transport data are also presented in Appendix 3 as they
may useful in designing future experiments.
4.2
Electrolysis data
After some comments on the background current and oxygen diffusion, Ci scans for
the single crystals are presented. This section includes a discussion of the IA scans
for all the crystals studied. The figures for this discussion have been pla ,d at the
end of the section. As a reminder to the reader, a negative current corrt ponds to
oxygen going into the crystal while a positive one means that oxygen is cc iing out.
The fluctuations in the current observed in most scans average to zero onc the data
is integrated to get the charge. Because of this, the time constants are
alculated
from the charge.
4.2.1
Subtraction of background currents
Over the course of these very long runs, the issue of extraneous current due ) side reactions becomes especially important. We rely on the integrated current to etermine
6, so over very long runs, the error introduced from a spurious current acc mulates.
At the beginning of a CA run, the current is measured to be on th order of
- 50 nA between two platinum wires. After a sample has been oxidized in t' I cell, the
side reaction current measured between two platinum wires appears to hav< ncreased
to values around 0.1 - 1 pA over the months it takes to oxidize a sam] e. After
removing the sample for about a day, the measured side reaction current be ween the
wires has dropped back to around 50 - 80 nA. This suggests that the sampl dissolves
slightly creating contaminants in the cell that plate out on the platinum
lectrodes
after a short time. There is also some " dust" that settles at the bottom
I
over time so some of the crystal may dissolve into the solution. Perhaps
lis is the
the cell
source of the ions plating out on the electrodes. This amount of "dust" mi t be very
small because no change in the mass of the sample electrode is detected
the end
of a run.
It also should be noted that a similar change in the current occurs wher he cell is
temporarily disconnected so that no current flows through the cell; there is
spike in
the current once the cell is reconnected, and it takes some time for the cur. nt to fall
back to its previous value. The initial current measured between platinum
ires then
probably reflects a transient effect from contaminants in the cell. If the sic
reaction
current is 50 - 80 nA, then a current of 10- A measured near the end of
run may
still correspond to slow, but significant macroscopic diffusion of oxygen.
It is unclear how to model an increase in the side reaction current ov, time for
subtraction from the data. One possibility is to assume that the backgrou
current
increases linearly with time. This would correspond to a - 0.008 e/f.u. decrease
in the calculated integrated charge over most scans. This may be an ove estimate
because the current spikes up to higher values after the cell is disconnec
d to put
in a platinum wire for measurement of the background current. For this I tson, the
simpler approach of subtracting a flat baseline is used instead. The current , btracted
from the data is the current measured between two platinum wires that
wve been
run in the cell for a while toward the end of a run.
4.2.2
Diffusion into a finite cylinder
Next we consider the diffusion model discussed in Chapter 2 in light of
ie single
crystal data. When the data are plotted on a semi-log plot, the the dat
follow a
single exponential for most of the measurement. Using the solution in Equ
ion 2.17,
we find that fits to the data with first term or first two terms make little ifference
in r and thus indicate that a single exponential term dominates as well.
The current decay is of the form, I(t) = Io exp -t /T. Thus, the charge
Qo(1
iould be
- exp-t/'), where Qo is the saturation charge er
ýring the
sample during the measurement. The data are plotted on semi-log plots
)f (Qo -
of the form Q(t) =
Q(t))/Qo versus time. This makes it easier to see exponential behavior ir he data.
In the case of a diffusion-limited current, the time constant is 7 =
To2/
.405)2 D.
The constant, 2.405, comes from substituting the the first zero of the Besse Function.
The single crystal samples were cut and polished with rectangular c xis faces
rather than circular. The aspect ratio is of order 1 for all the samples. The
.dius, ro,
for the equivalent cylinder is ro2 = (lw)/wr, where 1 and w are the length
id width
along sides of c-axis face of the crystal. It is used to calculate the diffusion c fficients.
While this method does not determine the diffusion coefficient exactly, it 1 ould give
D to the correct order of magnitude and allows to make some comparisol
between
crystals and to the ceramics. This, of course, assumes that diffusion is the [ominant
mechanism in the oxidation process.
4.2.3
Table of crystal data
As grown, the crystals contain excess oxygen. The amount corresponds t
in La 2 Cu04+a
,
which lowers the Neel temperature to
-
240K from 325K
-ý 0.01
or 6 , 0.
Crystal XE5 initially contains more oxygen than the other crystals beca se it was
annealed at 900C for 1 hour in oxygen flow and then slowly cooled bac to room
temperature over 12 hours before de-intercalation. The reason for this w;
to see if
cooling slowly through the tetragonal to orthorhombic transition might di inish the
number of defects (vacancies, etc.) and improve oxidation.
In order to make accurate measurements of S, we first remove this excess xygen by
setting the reference voltage to 0.1 V (except for XE1 which was de-intercal
ed at 0 V
as will be explained), which is less than the initial open-circuit voltage. V measure
the time decay of the current and integrate it to determine the charge
xtracted.
After this de-intercalation is complete, we apply a reference voltage in he range
0.35 V to 0.53V and measure the charge during intercalation. The time :onstants
are determined using the method described in Chapter 2 and in the previc s section.
The results of these experiments are given in Table 4.1.
= 0.35 V then
t 0.53 V,
so it appears twice in the table. All the samples were oxidized at 80 C,
xcept for
sample XE3, which was de-intercalated at 40 C initially to determine th
effect of
temperature on the electrolysis. About half as much oxygen came out
XE3 as
One of the crystals, XE2, was oxidized first at
ref
XE4 (both have the same mass) during the de-intercalation runs. Ibg re rs to the
background current that was subtracted from the intercalation data.
is is the
constant that was approached near the end of the run.
Because the charge is obtained by integrating the current, random fl :tuations
in the current over such long scans are averaged out over time, and sc ;he error
Table 4.1: La2Cu04+5 single crystals: electrolysis data
2
Qout
e/f.u.
Qin
e/f.u.
O-Q
e/f.u.
Ibg
Tout
Ti
ro
A
days
da s
cm
35 (6.7)
86 (3.9)
0.00813
0.0339
0.0334
0.0756
0.002
0.005
0
0
2.5
1.0
13
38
0.0232
0.0191
0.45V
0.45V
57 (6.7)
85 (3.9)
0.00765
0.0169
0.114
0.0631
0.01
0.001
8e-8
0
1.9
1.0
20
41
0.0191
0.0165
0.53V
0.53V
53
62 (6.8)
0.00663
0.405
0.127
0.03
0.01
le-7
5e-8
1.9
10
19
0.00836
0.0191
Sample
Mass
V,, f
Scan Length
Name
(mg)
V
days
XE2
XE5
62
31
0.35V
0.40V
XE3
XE4
53
53
XE2
XE1
36
51
2
introduced from them in the charge is small. The error in Q is assumed to be mostly
from background currents, which have a cumulative effect over the length o the scan.
Qin and Qout refer to negative charge flowing in and out the sample, re pectively.
Both of these charges are reported assuming Q = 0 at the beginning of th run. All
of the samples are cut all from the same float zone crystal except for XE1
hich was
cut from a different float zone crystal. It is worthwhile to once more not that the
lengths of each oxidation scan reported in Table 4.1 are substantially lo ger than
those measured for the ceramics discussed in Chapter 3.
4.2.4
Sample XE1
XE1 was the first of the five crystals oxidized. Before oxidation, the crysta1 was deintercalated as shown in Figure 4-1. The reference voltage was lowered over he course
of the measurement in an attempt to speed up the reaction. Note that i creasing
Vef above the open-circuit voltage causes intercalation and decreasing it c uses deintercalation. Vf = 0.18 V proved insufficient to de-intercalate the crystal. Note how
little oxygen leaves the sample for this voltage in Figure 4-1. In fact, it app ars that
after initially coming out, oxygen starts to enter the crystal again. For Vef
0.15 V,
there is little change in the slope of the charge versus time as the referenc voltage
is increased as shown in the lower panel of Figure 4-1. This suggests th t once a
threshold voltage is exceeded, the current is limited by the rate at which ox gen can
diffuse out of the sample. The charge eventually saturates near 0.007 e/f.u.
In Figure 4-2, on a semi-log plot we show the charge plotted as (Qo
96
Q)/Qo,
where Qo is the saturation value. This shows that the charge approximat ly follows
an exponential over two decades. This time constant is 1.9 days, but it is somewhat
smaller, 0.87 days, if determined from data at t > 4 - 10' s.
Figure 4-3 displays the CA scan for the intercalation of XE1 at Vref = 0.53 V.
This scan takes sixty-two days. During the last part of the scan, the curre it hovered
around 10- 7 A. Because of this, the sample was removed and replaced with
platinum
wire. The current was initially about the same value, but dropped to half this value
which is taken to be the background level. Because it seemed likely after i ompleting
the measurement that some of the current measured with the sample in place still
corresponded to continuing oxidation, this lower background current is ubtracted
from the oxidation current data, and then the current is integrated to get 1he charge.
The time constant calculated from the slope is 19 days as we show in Figur, 4-4. This
time constant for intercalation is about 8 times larger than that for de-int rcalation.
4.2.5
Sample XE2
XE2 exhibits behavior similar to XE1. The de-intercalation scan also onl took one
week, with a measured time constant of 2.5 days as shown in Figures 4-5 and 4-6.
The charge extracted during de-intercalation is near 0.008 e/f.u.
The CA scans for intercalation, done at Vref = 0.35 V (Figure 4-7), are more difficult to interpret. Because of computer and equipment problems, there are a few gaps
in the current data. The discontinuities at t
2.1 _ 106 s and t • 2.6 - 106 s occurred
when the sample was disconnected for several days in order to correct comp ter problems. This apparently made a difference in the total charge measured. After both
episodes, the slope of the current begins to decay back to its pre-interruption value
as shown in Figure 4-7.
If we eliminate the current spikes, the total charge extrapolates about 0. 16 e/f.u.
instead of 0.033 e/f.u. This oxygen concentration places the crystal near th$ oxygenpoor edge of the miscibility gap. The magnetization results are consistent with this
interpretation since no superconductivity was observed for this sample. In Figure 48, the charge is plotted on a semi-log plot using the extrapolated value of Qo "
97
0.016 e/f.u., for the total charge excluding the current spikes. The exponei ial decay
of the current yields a time constant of 13 days.
After this run and some magnetization experiments, XE2 was returi d to the
electrolysis cell and oxidized at V/ef = 0.53 V. The current was noisier,
nd there
were erratic peaks in the current plot as shown in the top panel of Figure 4-9. The
background current was also quite large; 10- A was subtracted from t,
current
data. The total charge is much larger than for other crystals and ceramics ifter this
subtraction. We have no explanation for this anomaly. The time constant neasured
for this run was 10 days. The data are displayed on a semi-log plot in Figi e 4-10.
4.2.6
Sample XE3
This sample was de-intercalated at 40C to determine the effect of temp, ature on
the electrolysis. The data are shown in Figure 4-11. The charge approa hes Q r0.00665e/f.u. at 40C. The upturn in the current and charge during the ast 105 s
occurs when the temperature is raised to 80C. As shown in Figure 4-12
the time
constant is small, which is consistent with the other de-intercalation runs,
.9 days.
This sample was oxidized at Vef = 0.45 V as shown in Figure 4-13. The apparent
background current of 8 - 10- A is subtracted from the current data. TI
amount
of charge, 0.114 e/f.u., clearly shows that this sample is near the oxygen-r h side of
the miscibility gap. The time constant determined in Figure 4-14 is 20 day
which is
much larger than the one measured during de-intercalation.
4.2.7
Sample XE4
This sample de-intercalated very quickly as shown in Figure 4-15. It only ook four
days to see the current decay to zero and the charge to saturate at about 0. 69 e/f.u.
The time constant for this decay is shown in Figure 4-16 is about a day. TI
incidentally, has the same mass and similar shape to crystal XE3, which
sample,
s a time
constant of 1.9 day.
Figure 4-17 shows the CA scan and charge during oxidation at 0.45 V. T
current
has quite a few erratic jumps at times during the run. These changes are
bill fairly
small and get averaged out in the charge plot in the bottom panel. The s- ke in the
current at t • 5 - 106 occurred when the sample was disconnected from
e cell to
check the background current with a platinum wire in place. The total ch
Ye places
this sample in the miscibility gap even after 85 days in the cell.
ovides a
This
significant contrast to sample XE3, which was oxidized at the same referer
e voltage
for 57 days, but accumulated twice as much charge. The time constant fo
KE4 was
very long - 41 days as shown in Figure 4-18.
4.2.8
Sample XE5
The final crystal also de-intercalated very quickly as shown in Figure 4-19.
e charge
saturated in about four days. More oxygen comes out of this crystal bece se it was
annealed in oxygen flow prior to the experiment. Figure 4-20 shows that t
s sample
has a time constant of 1 day as did XE4.
This sample was intercalated at 0.40 V for 86 days. This sample also
,s still in
the miscibility gap after this very long run with a charge of 0.0756 e/f.u. II
Figure 4-
21, the charge does appear to be approaching saturation. The time consta
Sfor this
sample is 38 days. See Figure 4-22.
4.2.9
Summary of electrolysis data
First, sing
crystals
show exponential decay of the current at long times for both intercalatic
and de-
intercalation. This is in marked contrast to the ceramic samples discussed
Chapter
3, for which the current follows a power-law at long times. Furthermore
the time
constants of these decays are remarkably reproducible. As shown in Tal
4.1, for
de-intercalation, the time constant is 1.8 ± 0.75 days and for intercalatio
the time
Several general observations should be made at this point.
constant is 27 ± 14 days.
This dramatic difference in time constants for intercalation and de-intei dlation is
very important. If the process were diffusion-limited for both oxidation and
,duction,
the time constants would be identical. It is still possible that the de-intei calation is
diffusion-limited, but it is clear from these results that intercalation cann( ,t be.
Assuming that de-intercalation is diffusion-limited, we have determine(
i;
.
uon
~,~i
Lct ;llLtl
,
, a~
d.
-
UtL• I
i. ,
,
,
t
t*,
-1f
,,;,,,,
11
1 e
n1 goI
- c-, h,,;
Rt5LbII.
sellllllll
. 4-
on
IT
l1lt. e
.L
resuIs
the diffuret
poIUot•
in Figure 4-23. The diffusion coefficient is independent of reference volt ge, as expected, and has the value 2.8 ± 1.1
.
10-8 cm 2 /s at 80C. We note that thi value for
the diffusion coefficient is much larger than that measured for either electro hemically
oxidized ceramics and thin films (D
thermally oxidized crystals (D
-
-
10-
13
cm 2 /s) or 018 tracer c-axis diffusion in
10-20 cm 2 /s) [43], about D
-
10-
is
cm /s for in-
plane diffusion.
One might argue that fissures in the crystals may make their effective dimensions
smaller than the external ones. However, past experience has been that s ch cracks
are several millimeters or more apart, which is comparable to the size of th samples.
The samples would have to be cracked at dimensions much, much smaller than this
to account for discrepancy in diffusion coefficients.
This examination of diffusion
coefficients continues to suggest that the current is not simply diffusion-li ited.
The long times necessary to intercalate crystals have made it impossible for us to
carry out the detailed measurement of 6 versus Vref that we did for a sin le pellet.
However, it is still helpful to make a comparison to the single pellet data r ported in
Chapter 3. Because both the electrolyte concentration and temperature have changed,
the reference voltage necessary to achieve the same charge has also shifted. rhe open
circuit voltage for the ceramics at room temperature in 1 M NAOH is - 0.2 ± 0.02 V
while it is - 0.33 ± 0.02 V at 80C in 0.01 M NaOH for the single crysta s. Based
on this difference, we have shifted the singe pellet data from Figure 3-4 ly 0.08 V
to facilitate a comparison to the crystal data shown in Figure 4-23. Altho gh there
is a great deal of sample-to-sample variation, the charge entering the singl crystals
increases with reference voltage as it did with single pellet. The dashed
orizontal
lines in the figure correspond to the upper (S ~ 0.55) and lower (S r 0.01 bounds
of the miscibility gap [47]. We have also eliminated the anomalously high value for
XE2 at 0.53V.
100
This comparison between the ceramics and single crystal data suggests t it Vrej
0.45 V should be sufficient to achieve a 40K superconducting phase in tl
crystals.
A 40K phase has only been seen in single crystals for Vejf > 0.53 V; this d crepancy
may be due to an error in shifting the reference voltage or rooted in intri ic differences between single crystal and polycrystal oxidation. That is, at grain 1 undaries
the ceramics may contain a higher density of oxygen than the overall ch
Ye would
indicate. We have found that 6 > 0.06e/f.u. corresponds to the 40-45K
upercon-
ducting phase in the ceramics, which has also been found by others [18].
lowever,
we have not seen this in the single crystals. In fact, later in the chapter,
estimate
that the 40K phase corresponds to at least Q > 0.1 e/f.u.
101
'w
1.0
0.8
0.6
0.4
0.2
0.008
? 0.006
- 0.002
0
Figure 4-1:
over the cou
value of the
XE1
1
0.1
0
0.01
0Q=0.00663 e/f.u.
7=1.91days 1.5 x 105 s<t<3 x 05 s
7=0.87days 4 x 105s<t<5.7 x 05s
0.001
Time (105s)
Figure 4-2:
for two dif
103
4
3
2
I
1
0.150
0.125
- 0.100
a
-
0.075
0.050
0.025
0
Figure 4-3:
background
charge. This
1
XE1 Vref
0.53V
ref-
0.1
0
I
0
0.01
Qo=0.127 e/f.u.
T=19days t<4x 106s
0.001
Time (106 s)
Figure 4-4:
3 on a sere
105
10.0
7.5
5.0
ci
C)
2.5
0
0.010
0.008
ci
0.006
, 0.004
'
0.002
Time (105s)
Figure 4-5:
This scan la
1
XE2 Vref 01 V
0.1
0
CY
I
0
Cy
0.01
Qo=0.00813e/f.u.
r=2.5days 1x 105 s<t<4x 105s
0.001
Time (105s)
Figure 4-6
Vf = 0.1
d
107
4
S3
23
I
1
0.04
= 0.03
0.02
c5 0.01
I
0
Figure 4-7:
This scan L
from equipi
0
XE2 Vref 0.35V
0
Cr
0.1
0
Q0=0.016 e/f.u.
r=13days t<1.5x 106s
0.01
0.5
1.C 1.5
2.0
2.5
0
Time (106 s)
Figure 4-8
dashed cui
le
109
5
4
3
·3-
S2
1
0.5
0.4
$
0.3
0.2
I
0.1
0
Figure 4-9:
after being z
This scan la
5
XE2 Vre =0.53V
1
0.1
0
0
0.01
0Q=0.405 e/f.u.
T=10.4days 1.5 x 106s <t<3.75 x 10
0.001
1.5
3.0
Time (106 s)
Figure 4-1'
time const
5
le
111
5
4
.
-
C)
3
2
1
0
0.010
0.008
> 0.006
S0.004
o 0.002
0
Figure 4-11
the last 10O
ref
XE3 Vref 0. 1V
1
I
0
0.1
C
I
0
C0
Q, =0.0066%
=1 .9 days 1 x 105s<t<5 x 105s
U
0.01
1
2
3
4
Time (105s)
5
Figure 4-12: Deviation of the intercalated charge from its asymptotic va e at 40C
and at Vref = 0.1V.
113
a)
L.
C-
0.150
-0.125
-
a,
0.100
aD
0.075
cY)
0.050
CD
J
0.025
0
Figure 4-13
A backgrou
days.
versus time at 80C and Vre
1
o0
XE3 Vfref- = 0.45V
0.1
CY
I
0.01
Q0= 0.114 e/f.u.
7=19.5days t<4x 106s
0.001
2
3
Time (106s)
Figure 4-1
and Vef =
C
115
XE4 Vreff0.1V
10.0
7.5
=3,
le
L
L
3
(3
5.0
2.5
0
0.025
0.020
>0.015
L 0.010
a 0.005
0
Time (105s)
Figure 4-15
lasts 4 days
XE4 Vref=O.1V
1
o0
0.1
0.01
Q
0 =0.01 69 e/f.u.
1.0Oday t<3x 105 s
0.001
1
2
Time (105s)
Figure 4-1'
0.1V.
117
3
I.
1.0
0.8
0.6
L
0.4
C.)
0.2
0.08
0.06
0.04
a
0.02
0
Figure 4-17
lasts 85 day
1
XE4 Vref
ref 0.45V
0.1
0
CY
I
0.01
Qo=0.0631 e/f.u.
T=41 days t<6x 106s
0.001
Time (106s)
Figure 4-1
0.45 V.
119
XE5 Vref=O.1V
10.0
7.5
5.0
a,
C-
2.5
0
0.05
0.04
a,
0.03
a,
0.02
C-)
0.01
0
Time (105s)
Figure 4-19:
lasts 4 days
XE5 Vref= O.1V
1
o0
0.1
I
cO
0.01
Qo
T
0.001
0.0339e/f.u.
5s
O.97da~yS t<3x 10
1
2
Time (105s)
Figure 4-2
0.1V.
121
3
1.0
0.8
0.6
a)
C-
0.4
0.2
0.08
a,
a)
0.06
0.04
4=
C~)
0.02
0
Figure 4-21
last 86 days
1
XE5 Vref
=0.40V
ref-
0.1
0
I
0.01
QO= 0.0756 e/f.u.
T=38 days t<4.25 x 106 s
0.001
Time (106s)
Figure 4-2
0.40V.
=
123
Crystal electrolysis data
·
·
·
·
E
Co
I
3
2
O0
1
0.10
0.08
Cr-
0.06
I
0
single pellet
S*
crystals
------_
o000
0
0 O0
-
·
0
C
0.04
0.02
n
_
·
·
0.30 0.35 0.40 0.45 0.50 0.5
Voltage relative to Ag/AgCI electrod
Figure 4-23: Upper panel: Diffusion coefficients calculated from the tim4
for the de-intercalation as described in the text. Lower panel: 6 from the
experiments plotted vs. Vref. The single pellet data from Figure 3-4 shif
by - 0.08 V also plotted to facilitate a comparison as explained in the tex
a general increase in 6 with increasing Vre,. The horizontal dashed lines ii
approximate upper (0.55) and lower (0.01) bounds of the miscibility gap.
124
0.60
(V)
:onstants
)xidation
,d in Vef
There is
licate the
4.3
Magnetization Data
Magnetization experiments were also performed on the crystals to meas re the superconducting transition temperature as well as to detect any remnant oxygen-poor,
antiferromagnetic phase. This information indicates how close these sam les are to
equilibrium and provides more clues to the details of the phase diagram. The magnetization of the samples after de-intercalation will be discussed first. They e hibit only
the oxygen-poor phase after de-intercalation. The superconductivity seen in most of
the samples after intercalation will be discussed after this. The data are ormalized
for the sample mass and plotted as the susceptibility (M/H) rather than s the moment (M). Because the fields are the same for the data being compared, it makes no
difference in the discussion. As with the electrolysis data, the figures will appear at
the end of the section after the discussion of the data.
4.3.1
Magnetic susceptibility in the oxygen-poor p ase
All the crystals were de-intercalated at 0.1 V except for XE1 which was de-in ercalated
at 0V as described in the electrolysis section. After de-intercalation, the
eel tem-
perature increases from 250K to - 310K, which corresponds to 6 decrea ing from
- 0.01 to - 0. The susceptibility (M/H) is measured for the samples in high and
low magnetic field parallel to the c-axis. In low field, the peak, which co responds
to the Neel temperature, appears as the copper spins order antiferroma netically.
(See, for example, Figures 4-27 and 4-30.) In a sufficiently high field, there is a weak
ferromagnetic transition for which all the copper spins cant out of the pla es in the
same direction. (Figures 4-27 and 4-30). There is a discontinuity in the sus
where the transition occurs (about 100K in 5 Tesla field).
ptibility
This phenom non has
been thoroughly studied [15, 55]. For the low and high magnetic field meas rements
performed to study the oxygen-poor phase, 1 Tesla and 5 Tesla are used, res ectively.
The sample is first cooled in the low field before taking the high-field da a. Then
in high field, the susceptibility is measured as the temperature is rampe
up and
then down. The hysteresis seen in the data (e.g. Figures 4-27, 4-30) is expec ed since
125
the weak ferromagnetic transition is first order. For sample XE4, the
steresis is
especially pronounced. Once the samples are de-oxygenated via the de-i tercalation
experiments, only the oxygen-poor phase is present. The absence of superc nductivity
and the higher Neel temperature support this view.
The size of the weak ferromagnetic moment (M) or susceptibility (M H) is proportional to the oxygen-poor phase, so the ratio of this moment after o idation to
its value before oxidation provides a measure of how much of the samp e remains
oxygen-poor after the intercalation experiment. For XE1 and XE2, th high-field
susceptibility was measured only after oxidation. After we normalize fo the sample mass, the high-field susceptibility data taken before oxidation consiste tly result
in about AX • 3.0 ± 0.3 cm 3 /mole for other samples so it is reasonable o use this
value for samples XE1 and XE2. The percentage of oxygen-poor phase is plotted in
Figure 4-24. It decreases as the samples are oxygenated at higher referenc voltages.
4.3.2
Magnetic susceptibility in the oxygen-rich ph se
After intercalation, the samples, except for XE2 after oxidation at Vref = 0. 5 V, have
an oxygen-rich phase that becomes superconducting upon cooling. The sup rconductivity is studied using a 5 Oe field. XE1, which was run at 0.53 V, is the o ly one to
have any of the 40K superconducting phase as shown in Figure 4-25. The fi ld-cooled
diamagnetic fraction is almost 100 times smaller than the zero-field-cooled data and
has a fraction of about 2%.
Other crystals have been found to have a relatively
very small Meissner fraction as well [36]. Another crystal, prepared and s udied by
Fangcheng Chou, also had a 40K transition temperature; this crystal was prepared
using the constant current technique (CP scan) using reference voltages a high as
0.6 V.
From the lower panel in Figure 4-25, we see that in spite of the high transition
temperature, 40K, and what appeared to be a saturated charge in the el ctrolysis
data, there is still some oxygen-poor phase with a Neel peak at 250 K f
crystal
XE1. The weak ferromagnetic moment suggests that the sample is 20% oxy en poor,
estimated by AMoxy/AMde-oxy = AXoxy/AXde-oxy
126
_
0.6/3 = 0.20 (since he same
100
0
()
O
50
0
O0 O
C
O
C
0
o
0.o
o
50
Figure 4-2,
moment. i
ic
e.
127
field H is used). Neutron scattering data indicate that the oxygen poor regicn accounts
for about 40% of the sample.
Because of the discrepancy between the magnetic and neutron data, th magnetic
data were repeated (six months later) as shown in Figure 4-26. The higl field susceptibility is shown in the lower panel. The sample was cooled about t ice (300K
to 100K in 2 hours) as slowly in zero field than previously. Perhaps, th relatively
large undoped region in the crystal hinders phase separation and the m gnetic ordering. We now make a new estimate from the weak ferromagnetic mo ent that
AMoxy/AMae-oxy
1/3 = 0.33, or 33% of the sample is oxygen poor. T is will be
discussed further in the neutron data section.
The superconducting transition for sample XE1 was also measured again Note the
upper panel. Because the data clearly demonstrate that there is a 32K c mponent,
the 40K phase is likely to be only near the surface as suspected. The bilk of the
sample probably becomes superconducting at 32K.
For XE2, the lower panel of Figure 4-27 shows the susceptibility after oxidation at
0.35 V. No superconductivity was observed, but the Neel peak shifted dowi to about
260K indicating that oxygen has gone in.
Recall that the charge added in this first intercalation was measured to be 0.33 e/f.u.
(See Table 4.1). This corresponds to 6S 0.016, which is within the misci ility gap,
and we would have expected to observe some superconducting phase. Th t we did
not confirms our assumption that spikes seen in Figure 4-7 do not corr spond to
intercalation.
Figure 4-28 shows data taken after continued oxidation of crystal XE , but at
a higher voltage, 0.53 V. Unlike XE1 which was oxidized at the same vol age, this
sample has no remnant oxygen-poor phase and the superconducting transiticn is quite
sharp at 32 K. The Meissner effect is about 60%, and the shielding fraction is 100%.
The measured charge for this sample is 0.405e/f.u., which corresponds to g
and is probably incorrect. It does, however, place the sample well past the
0.202
iscibility
gap, which is consistent with this magnetic data.
Sample XE3 was oxidized at 0.45 V. Figure 4-29 shows that this crystal as a very
128
sharp transition at 32 K. The Meissner effect and shielding fraction are 25% and 200%,
respectively. The charge measured entering this sample is 0.114e/f.u., w ich places
this crystal just to the oxygen-rich side of the miscibility gap with 6 • (.057e/f.u.
This sample also has no trace of a Neel peak and so no oxygen-poor phase separated
region.
This value of 6 is completely consistent with the upper bound ry of the
miscibility gap determined by Radaelli et al. for ceramics [47]. The abs nce of an
oxygen-poor phase determined from the weak ferromagnetic moment is also consistent
with neutron scattering data.
Data taken on crystal XE4 are displayed in Figure 4-30. The upper lot shows
a Neel peak of about 240 K before electrolysis. After de-intercalation at
.1 V, the
Neel peak shifts up to 312 K. The high field (5e4 Oe) weak ferromagnetic is clearly
first order. Also, the copper spins appear not completely relax into antiferr magnetic
ordering; AXde-oxy is smaller than expected for this sample given its high
eNel tem-
perature. When we calculate the antiferromagnetic moment, we get - 1/1.5 ' 67%.
After XE4 was oxidized at 0.45 V, it had a very sharp transition at 32 K as can be
seen in Figure 4-31. The field cooled data show a very small Meissner eff ct, about
0.15%. Unlike sample XE3, which was oxidized at the same voltage, there s a small
Neel peak at 250K. The measured charge, Q = 0.0631 e/f.u. or 65 0.03 5, places
this sample right in the middle of the miscibility gap. Because of this low r oxygen
content, the 32K phase may be mostly near the surface. The Meissner f action is
more than 800 times smaller than the shielding fraction.
Sample XE5 was annealed in oxygen at 900C and slowly cooled to roon temperature before beginning the electrolysis experiment. The reason for this a neal was
to see if it might reduce disorder in the crystal somewhat so the electrolysis would
produce a more uniformly doped crystal. This made no difference that could be detected. The data taken before electrolysis and after de-intercalation are shown in
Figure 4-32.
Oxidation was performed at Vrf = 0.40 V as shown in Figure 4-33. There is
a poorly defined superconducting transition at 32 K. The weak ferromagr etic mo-
ment indicates that - (3.6 - 1.4)/3 - 2.2/3 - 73% of the sample is oxy en poor.
129
This is consistent with the neutron data which show that the sample is ibout 75%
oxygen poor.
It is also consistent with the charge measured entering t e sample,
Q = 0.0756e/f.u., which places it in the miscibility gap. It is another r minder of
how long this oxidation process can be; the sample was run at 0.40 V for S0 days.
130
XE1
1.0
I
I
o zfc
0.5 * fc x10
0
I.
-
-0.5
-1.0
-1.5
I
-2.0
10
I
,
I
,
20
30
40
50
60
3.0
0o
2.5
E 2.0
E
1.5
o
H=5e40e
H= le40e
HI Cu0 2 pie les
00000 0
0 00"
@60
0ýO
1.0
o oO
0
0.5
0
I
I
I
100
I
I
200
300
Temperature (K)
400
Figure 4-25: Upper panel: Field-cooled and zero-field-cooled suscep bility at
H = 10 Oe. Lower panel: Susceptibility at H = 1 Tesla and 5 Tesla. ntercalation was done at 80C and V,,f = 0.53 V.
131
1.0
0.5
0
-0.5
S-1.0
-1.5
-2.0
-2.5
3.5
S3.0
05
E 2.5
E 2.0
1.5
1.0
<x 0.5
0
Figure 4-26: Upper panel: Field-cooled and zero-field-cooled susceptibility at
H = 5 Oe six months after oxidation. Note that there is now some 32 phase.
Lower panel: Susceptibility at H = 5 Tesla. Sample was cooled more slowl in comparison to the previous experiment (Figure 4-25). Intercalation was done at 80C and
Vref = 0.53 V.
132
XE2
2.0
H=2e40e
Vre f = 0.1 V
E 1.5
E
Sref~
00
1.0
0
o4
0
o
0.5
0
I
SI
I
*
100
I
*
E
-nn
II
I
HI CuO 2 plc nes
H=le40e
E
400
400
I
100 7nn
200
o H=5e40e
-5
o)
.
Vref=0.35V
0o0
0
0
Oo
4-
0e1l
O(SO
0 o
1
0
I
I
*
*
100
0.0.066
I
I
200
300
400
Temperature (K)
Figure 4-27: Upper panel: Susceptibility after de-intercalation using H =
2 Tesla.
Lower panel: Susceptibility at H = 1 Tesla and 5 Tesla. This sample sh
[owed no
superconductivity. Intercalation was done at 80C and Vrf = 0.35 V.
133
XE2 Vref
=0.53V
ref-
1.0
0.5
I
I
,
o zfc
* fc
0
iv-0
A0-@*
SA0
-1.0
-1.5
-2.0
SI
10
1.0
io
-3
0.8
.
I
30
40
I.
20
oHe40
o H=5e40e
* H=le40e
50
~co33D0
0
60
HI Cu0 2 pie ines
0.6
C)
E
1
00Go
d
o 0
( (0
0
0
0
3o 0
0.4
I
O
0.2
0
I
50
I
000 (0600t0((0o r4re
00
I
I
I
100 150 200 250
Temperature (K)
00
,
30 3 350
Figure 4-28: Upper panel: Field-cooled and zero-field-cooled susceptibilit'
7 using H
5 Oe. Lower panel: Susceptibility at H = 1 Tesla and 5 Tesla. Intercal Ation was
done at 80C and VAej = 0.53 V.
-
134
XE3 Vref= 0.45V
1
o zfC
0
* fc
0
-1
0o
-2
-3
10
1.50
o
1.25
E 1.00
E
C, 0.75
20
I
30
I
40
50
I
60
I
I
o H=5e40e
* H=le40e
Hi Cu0 2 pl nes
0o a
, , . . * * *0
e.S
v
' 0.50
%
f-r)00U
0,%
o OO*
0••OO
OO
<0.25
0
_r
I.
I
I
100
I
I
I.
.
I
I
200
300
Temperature (K)
I
400
Figure 4-29: Upper panel: Field-cooled and zero-field-cooled susceptibility
= 5 Oe. Lower panel: Susceptibility at H = 1 Tesla and 5 Tesla. Intercal; using H
Ltion was
done at 80C and V,,f = 0.45 V.
135
3.0
2.5
0
E
2.0
E
o 1.5
1.0
c
0.5
0
9
0
E
\6
E
CD
3
0(
Figure 4-30: Upper panel: Susceptibility at H = 2 Tesla of as-grown samp~1le. Lower
panel: Susceptibility at H = 1 Tesla and 5 Tesla. De-intercalation was do ie at 80C
and Ve,f = 0.1 V.
136
XE4 Vref
=0.45V
ref
1.0
o zfc
0.5 * fc x100
0
0
-0.5
-1.0
-1.5
-2.0
·
|
·
20
10
1L
•
•
•
•
30
40
60
50
HI Cu0 2 plc nes
a)
I
0
E
000
O O S ((((((((R[(L
0Cn r ****
@
_
~ooo~oco~I 2
)
*
@
0
0
* es
0
000
· ·
E
o H=5e40e
H=le40e
I
I
0
100
300
200
Temperature (K)
Figure 4-31: Upper panel: Field-cooled and zero-field-cooled susceptibilit
400
using H
= 5 Oe. Lower panel: Susceptibility at H = 1 Tesla and 5 Tesla. Intercal tion was
done at 80C and Vef = 0.45 V.
137
XE5
3.0
H= le40e
annealed in 02 flow at 900C for 2 hours
trace superconductivity
2.5
o
E 2.0
E 1.5
o
C
1.0
0
o 0
0 OO O0000c325
0
0.5
0
I
100
8
E
0,
6
0
4
E
000
·
·
200
300
·
·
o 5e40e
* 1e40e
HI Cu
400
O
2
plc nes
Vref=
0.1V
ref-
me
r)OOo4
o,
0 00Q
CD
I
0
100
200
300
Temperature (K)
400
Figure 4-32: Upper panel: Susceptibility at H = 1 Tesla of oxygen-anneale sample.
Lower panel: Susceptibility at H = 1 Tesla and 5 Tesla. De-intercalation vas done
at 80C and V,,f = 0.1 V.
138
1.0
XE5 Vref
0.40V
ref-
0.5
0
-0.5
-1.0
-1.5
-2.0
6
-5
o
E
I.
\4
0
b
3
2
~
Temperature (K
Figure 4-33: Upper panel: Field-cooled and zero-field-cooled susceptibilit) using H
= 5 Oe. Lower panel: Susceptibility at H = 1 Tesla and 5 Tesla. Intercal. tion was
done at 80C and Vre, = 0.40 V.
139
Table 4.2: La 2 Cu04+± single crystals: neutron data
4.4
Sample
Mass
Name
1
V ei
Stage
(mg)
V
number
XEI
XE3
51
53
0.53V
0.45V
4(6)
6
0.00332
0.00383
XE5
31
0.40V
0
0.0169
Sout
Sin
Oxygen-poor
T,
phase
K
0.0635
0.0570
40%
0%
40
32
0.0378
75%
32
Neutron scattering data
I have been very fortunate to have some of the crystals studied at Brook haven National Laboratory's High Flux Beam Reactor (HFBR) by Barry Wells,
oung Lee
and Rebecca Christianson. The crystals studied were XE1, XE3, and
E5. This
data allows us to look for any correlation between the electrolysis data, nagnetization data, and the staging or lack thereof as seen in neutron scattering ex eriments.
The estimates of the oxygen rich and poor phases are made by compari g the relative integrated peak intensities in the neutron data for the two phases ince they
are proportional to volume of the sample in those phases. There are also ,xtinction
effects in neutron scattering which may result from attenuation of the neu ron beam
within a crystal. Extinction disproportionately affects higher intensity pea ýs so that
the more intense peaks tend to be somewhat smaller than expected.
A summary of the neutron data is included in Table 4.2. Some neutron scattering
data are also shown in Figures 4-34, 4-35 and 4-36.
The charge for sample XE1 appeared to have saturated.
Neutron s attering,
however, showed that about 40% of the sample is oxygen poor in contrast to the 20%
value determined from magnetic measurements. The value from the neutron data may
be an over-estimate for the reasons just explained. The 20% figure from the weak
ferromagnetic moment may be an under-estimate as well. When the latter e periment
was repeated as described in the previous section, the weak ferromagneti moment
indicates that the sample is 33% oxygen poor.
In either case, this larg residual
oxygen-poor phase despite saturation of the charge could be explained by
140
a region
within the crystal, which is isolated and does not become fully oxidized. S me oxygen
is present in the oxygen poor phase; the Neel temperature drops to about 240K after
oxidation, which corresponds to S r 0.01. If we use an average antifer omagnetic
fraction of 35% (from the weak ferromagnetic transition: - 30% and ne tron data:
40%) and assume that all the oxygen goes into the oxygen rich part, exc pt enough
oxygen to give SAF M 0.01, we have 5 OR
r
0.0923 in the oxygen rich ph se. Since
stages 4 and 6 coexist in this sample, this suggests that S • 0.0923 lies i a second
miscibility gap. Recall the phase diagram in Figure 1-4. If the ratio of the s age 4 and
6 neutron scattering peak intensities (see lower plot in Figure 4-34) correspC nds to the
relative volume of each stage in the sample, then stage 6 corresponds to 6 - 0.06, and
stage 4 corresponds to S
-
0.105, just the oxygen rich side of this second niscibility
gap. (The ratio of stage 4 to stage 6, 2.45:1, has been corrected by the structure
factor .51 for stage 6 and .60 for stage 4 [36]. Without the correction, t e ratio is
2.13:1.)
Sample XE3 was homogeneous with only stage 6 present. This sample shows no
phase separation. A S of 0.057 measured from the charge is completely consi tent with
neutron data [60] and previous studies on ceramics [47]. XE3 was oxidized at 0.45 V,
which corresponds to a chemical potential on the oxygen-rich side of the
iscibility
gap.
The final crystal studied, XE5, gives the most puzzling result. It wa oxidized
at 0.40 V. This sample phase separated, but surprisingly showed no stag ng. The
oxygen-rich phase is expected to order as stage 6 below
-
270K. Since t e staging
peak was seen in crystals XE1 and XE3, which are comparable in size, it i unlikely
that this peak is hidden within the noise. However, it does have the smalle t oxygen
rich fraction of the three crystals - 25%.
4.5
Summary
The neutron and electrolysis data on crystal XE3 confirm that the oxygen-ri h edge of
the first miscibility gap is near S6~ 0.055 as previously reported in the cera ics [47].
141
450
300
0
150
0
5.
150
5
125
100
o
75
50
25
0
3.
Figure 4-34: The upper plot shows a scan along L near (0, 0, 6). The t o peaks
correspond to the oxygen rich and oxygen poor regions. The oxygen rich p ase has a
larger c-axis lattice constant and is smaller in L than the oxygen poor one. he lower
plot shows the staging peaks by scanning along L close to (0, 1, 4). The stag number
is given by n = A - 1 , where A is determined by by the peak positions (0, ,4 ± A).
Stages 4 and 6 are both present in this sample. These data were taken by B. Wells
and R. Christianson.
142
O
XE3
I
700
(006)
600
150K
500
400
300
200
100
0
5.95
5.97
200
'
V,
C-
·
I
·
I
I
o
00
0
0
0
0
0
00
5.99
·
·
S
00000
0
cP
6.01
·
1
6.03
·
·
6.05
_·
(014)
150
220K
V)
I
-
I
-
100
-)
50
0
0'
V
3.50
3.75
0
0
0
0(bNZ"(5
4.00
L (r.I.u.)
0
4.25
4.0 0
Figure 4-35: The upper plot shows only one peak. This means that the sample
is single phase, and thus there is no phase separation. The lower plot shows two
strong peaks which correspond to stage 6. These data were taken by Y.S. Le and R.
Christianson.
143
1000
800
-
600
o
400
200
0
5.
80
60
40
20
0
3.
Figure 4-03: i ne top plot snows tne two (u,u,,
) peaKS.
I 1is sample Is p ase sep-
arated, but from the relative size of the peaks, it is about
bottom plot is a close up view of where the staging peaks
peaks would appear around (0, 1,4.17) and (0, 1,3.83) and
this stage were present. These data were taken by Y.S. Lee
144
72% oxygen p
would appear.
should be easi
and R. Christi
or. The
Stage 6
y seen if
nson.
La2CuO 4+8 Phase Diagram
400
)
300
o 200
100
0
0
2
Figure 4-37: B
R. Christiansoi
ee, and
They also sugg
06, and
that stage 4 occurs for 6 - 0.1. These numbers can tentatively be added to the phase
diagram shown in Figure 1-4 reproduced in Figure 4-37.
The differences in the rates of oxygen intercalation and de-intercalation are quite
remarkable. There is no evidence that different oxygen species are involved in oxidation and reduction, yet the rates differ by a factor of 10. From our discu sion and
calculation of diffusion coefficients, we also know that the coefficients for ele trochemically oxidized samples are many orders of magnitude larger than those me sured for
thermally oxidized crystals [43].
Small fissures and structural defects can play a crucial role in the oxida ion rate.
It is clear that the oxidation process puts additional strain on the crystal tructure;
several of what were high-quality the crystals fell apart after oxidation. 0 e might
argue that small fissures in a crystal might provide additional surface are
145
so that
the reaction can proceed more speedily. While the crystals can have crac s in them,
these cracked regions are on the order of millimeters apart - insufficient to -hange the
magnitude of the diffusion coefficient calculated from the crystal data. Fu thermore,
there are as many cracks likely in the single crystals used in the 018 trac r thermal
diffusion experiments [43] (also grown in the CMSE Crystal Growth Fac lity) as in
these experiments.
One might also suspect that there are different strain energies in the rystal lattice, which account for the difference between the oxidation and reduction rates. For
instance, the time constants measured for reduction are always from an ini ially oxygen poor sample so there is little change in the c-axis lattice constant indic ting very
little structural strain. However, the time constant measured for interca lation at
Vref = 0.35V is much larger (13 days for oxidation versus - 1 day for eduction)
even though this sample (XE2) is still oxygen-poor (8 - 0.01) after oxida ion. (See
Figure 4-27). The true explanation must involve something besides a strain rgument.
Taken together, this suggests that a simply diffusion-limited process cannot explain the data.
The enhancement of the "diffusion" in these materials must be
achieved by some other mechanism.
146
Chapter 5
Conclusions
This thesis research has yielded a number of discoveries. First, we have s own that
for electrochemical oxidation of La 2 Cu04+s the voltage can, to some exte t, be used
to control 6. In particular, ceramic samples can be reproducibly oxidized y holding
the voltage constant and allowing the sample to come to equilibrium. (Figures 3-5
and 3-12). The reproducibility of 6 at fixed voltage is less in single cryst s (Figure
4-23) because there are regions within the crystal which refuse to be oxi ized even
when the oxidation current decays to zero.
Second, although the time scales for intercalation of ceramics and,
specially,
single crystals seem painfully long, they are actually orders of magnitude sh rter than
expected. Measurements of the time dependence at short times of electroly is on thin
films by other workers [2] give diffusion coefficients varying between 10 - 1 3
2 /s
Mm
and
10- 14 cm 2 /s. Measurements of self-diffusion of oxygen using 018 as a tracer ive much
smaller values of - 10-20 Cm2 /s. Even the largest of these predicts time co stants of
order 1010 s for oxygen diffusion through a sample of a few millimeters in siz . We find
that single crystals approach equilibrium in times of order - 106 s for oxi ation at
80C. Somewhat smaller, but similar times are found for ceramics at room te perature
when the power-law decay is taken into account.
This is only one piece of evidence that the electrochemical oxidation is not diffusionlimited. In addition, we observe that the exponential decay of the current is 10 times
faster for de-intercalation than for intercalation, whereas for diffusion the ti es would
147
be identical. Furthermore, the time constant for de-intercalation at 40C is the same
as at 80C, whereas Opila et al. [43] find that the diffusion coefficient i , as usual,
thermally activated with activation energy 0.83 eV. We have no model to xplain the
rapid equilibration of the oxidation and reduction reactions. However, it i clear that
the reaction is not diffusion-limited as previously believed.
Third, we have provided more information about the phase diagram of L
2 Cu04+s.
Before these experiments it was known that the miscibility gap between t e antiferromagnet and the stage 6 phase was between S6 0.01 and S - 0.055 [47]. We have
confirmed the latter point with crystal XE3, which has only stage 6 superlat ice peaks,
no antiferromagnetic phase (Figure 4-35) and a charge of 0.114e/f.u., cor esponding
to 6 - 0.057. In addition, we have found that the oxygenated portion of crystal
XE1 has 6 - 0.09 and contains both stage 6 and stage 4. Assuming that stages 6
and 4 occur in the same ratio as the relative intensities of their neutron scattering
peaks (Figure 4-34, lower panel), we find that stage 6 corresponds to 6 - 0.06 (see
Figure 4-37 and stage 4 corresponds to 6 - 0.1. The ratio of these values
6f, 0.6, is
close to the ratio of the two stages, 2/3. Based on data from crystal XE , we have
modified the phase diagram for La 2 Cu04+S to include the additional valu s of 6, as
shown in Figure 4-37.
A correlation between the staging peaks and and their respective oxygen concentrations (n
1
o( 6) has also been seen in the analogous La 2 NiO 4+S syst m, which
shows similar superlattice peaks corresponding to staging. Tranquada et a . [56], using neutron scattering, found staging in this system just as has been obse ved more
recently in La 2 Cu04+s [60]. They find 6 = 0.067 for n = 3 and 6 = 0.105 or n = 2,
for example. We note that the ratio of the two 6 values is also quite close t the ratio
of the staging numbers.
Last, we have shown that in electrochemically oxidized ceramics of L
two superconducting compounds are formed: one with T,
a
32K for V,,r
2
Cu0 4+s
< 0.35 V
and the other with T, - 45K for Vref > 0.35 V. The latter has a somewhat lower T,
when the oxidation is carried out at 80C instead of room temperature. A ver careful,
step-by-step de-intercalation experiment reveals two plateaus in the density of excess
148
oxygen as a function of the reference voltage. The step between these is at 0.35 V.
(See Figures 3-4 and 3-6). Although we see plateaus in the charge for ce amics, the
charge versus Vre, data for the single crystals (Figure 4-23) are inadequate to conclude
that similar plateaus exist for each staged phase. However, we make that
ssumption
in the phase diagram.
Unfortunately, the results on ceramics and single crystals seem contradi tory. The
single crystals appear to have T, -, 32K whether stage 6 or stage 4. Thi has been
well-documented by Wells et al. [60]. We would have expected to see p ateaus for
the ceramics with charges corresponding to 0.11 e/f.u. (6 r 0.057) and -
.165 e/f.u.
(6 r 0.0825), for stage 6 and stage 4, respectively, both with T, _ 32K. The lower
plateau is consistent with stage 6, but the upper is not consistent with st ge 4. The
voltages used to obtain at 32K phase and stage 4 in single crystals are c mparable
to those used for the single pellet, which give at - 45K phase and
Q=
0.125e/f.u.
It may be that the Tc ,, 45K phase arises from a higher oxygen content a ong grain
boundaries in the ceramics.
A phase with T, above 40K in single cry tals must
correspond to stages 2 and 3 [10]. However, the reason why the charge corr sponding
to stage 4 is not seen in the ceramics is unclear, but it may be that because the single
pellet data are taken at room temperature, charge corresponding the differ nt stages
are too close in energy to be resolved.
It is clear that the phase diagram associated with staging of La 2 CuO 4 s requires
measurements of 6. Previous attempts have been made to measure &by the mogravimetric analysis (TGA): measuring the weight loss while oxygen is removed by heating
the sample in an inert gas flow. In contrast to TGA, the electrochemical rethod allows one to make a variety of measurements after 6 is determined. Althoug we have
found that the long time scales and the presence of regions of the cryst Is, which
remain unoxidized, makes the process arduous, it appears that much of he phase
diagram could be determined using the approach in this thesis.
149
Appendix A
Units for magnetic susceptibility
and charge plus
experiment-related schematics
150
Molar Magnetic Susceptibilty
La2Cu04
Molecular weight = 405.3546
r,
Crystalline density - levit-7 1IJ~J/'~.,III
-
X = (Moment[emu] x Mol. Wgt.[g/mol])/(Field[Oe]
= [cm 3/mole]
[emu] = [Oe x cm3 ]
Charge per formula unit
No. of electrons
= (Total charge)/(electron charge)
= Q/
No. of formula units
= (Mass[g] x ),vogadro's number)/I Mol.
- Electrons/formula unit - e/f.u.
= Q/m * (4.2013 10 - 3 grams/Couloimb)
Figure A-i:
151
Wgt.
Circuit for Electrolysis Experiments
220pf
Ref. El
Coun er Electrode
Fix Re]
hiere.
Wor ing Electrode (sample)
7
-6V
V
Figure A-2:
152
Experimental Setup for transport measurements
RL
V 0
Sample
Sample
OO
O
O
lmm
VL
mm
.I-IIIIII
to PAR voltagle amplifier
Figure A-3:
153
Appendix B
Preliminary Transport Data
Transport experiments have been conducted on sample XE1. Although these measurements are inconclusive, they are presented here to provide guidance an information for future transport experiments on electrochemically oxidized sampl s.
In comparison to other data, the magnitude of the resistivity is reasonab e [11, 63].
The measurement was very noisy, and the contacts degraded quickly over time. This
noise was primarily from the poor quality of the contacts. An insulating oxi e formed
quickly at the crystal surface soon prohibiting any current from passing th ough the
sample.
One notable feature in Figure B-1 is that the resistivity drops sudde ly as the
temperature is decreased below 200K. From neutron scattering experi
ents, this
temperature corresponds closely to the in-plane ordering temperature of he interstitial oxygens [62]. As the temperature is decreased further, the resistivit goes up
before the sample becomes superconducting. This is characteristic of ligh ly doped
samples. It is probably an effect of a phase-separated, non-uniformly dop d sample
resulting in filamentary superconductivity. This measurement shows that the sample goes superconducting around 32K, so the 40K diamagnetic phase se n in the
magnetism is likely only near the surface of the crystal.
These data suggest that with better contacts, the correlations of quen hing the
sample to oxygen ordering and T, might be studied. For example, if th drop in
resistivity near 200 K is due to in-plane ordering, quenching the sample past this
154
8
6
E
0-C
E
0
lemperature
IK)
Figure B-1: Resistivity vs. temperature for oxidized sample using indium contacts.
Vref = 0.53V.
155
temperature and then warming the sample back up through the transition might
verify it.
Hall effect experiments, which would have provided the carrier density, were not
possible because the contacts were so poor. Gold paint in combination with pressure
contacts might improve the success of this experiment.
Because the ojidation of
single crystals takes so long and a homogeneous sample is not guaranteed, transport
measurements on ceramics might be worth a try. Hall effect measuremen s on other
high-To compounds suggest the Hall coefficient for ceramics varies only by 10% in
comparison to single crystals [42].
156
Bibliography
[1] T. Akashi, K. Matsui, T. Okada, and T. Mizutani. IEEE transactions on magnetics, MAG-5:289+, 1969. report on traveling float zone growth method.
[2] Frederic Arrouy, Jean-Pierre Locquet, Erica Williams, Erich Maichleq, Riidiger
Berger, Christopher Gerber, Christophe Monroux, Jean-Claude Gr nier, and
Alain Wattiaux. Growth, microstructure, and electrochemical oxidation of mbegrown c-axis La 2 Cu0 4 thin films. Physical Review B, 54:7512, 1996.
[3] Neil W. Ashcroft and N. David Mermin. Solid State Physics. W.B.( Saunders
Company, Philadephia, 1976.
[4] J. Bardeen, L.N. Cooper, and J.R. Schrieffer. Physical Review, 108:11 5, 1957.
[5] J. G. Bednorz and K. A. Muller. Zeitschrift fir Physik B, 64:319, 1986.
[6] J. R. Beille, C. Cabanel, B. Chevalier, G. Demazeau, F. Deslandes, J. E tourneau,
P. Lejay, C. Michel, J. Provost, B. Raveau, A. Sulpice, J. L. Tholence, and
R. Tournier. C. R. Academy of Sciences, 304:1097+, 1987.
[7] R.J. Birgeneau and G. Shirane. Neutron scattering studies of structural and
magnetic excitations in lamellar copper oxides. In Donald M. Ginsbe ig, editor,
Physical Properties of High Temperature Superconductors I, page 151. World
Scientific, Teaneck, New Jersey, 1989.
[8] Christopher M. A. Brett and Ana Maria Oliveira Brett. Electrochemistry Principles, Methods, and Applications. Oxford University Press, New York 1993.
157
[9] J.F. Bringley, S.S. Trail, and B.A. Scott. J. Sol. St. Chem., 86:310, 1990.
[10] Fangcheng Chou. private communication.
[11] F.C. Chou, J.H. Cho, and D.C. Johnston. Synthesis, characterization, and superconducting and magnetic properties of electrochemically oxidized La 2CuO04+
and La 2-,SrzCu0 4+S (0.01 < x < 0.33, 0.01 < & < 0.36). Physica 0, 197:303,
1992.
[12] F.C. Chou and D.C. Johnston. Phase separation and oxygen diffusion in electrochemically oxidized La 2 CuO 4 +s: A static magnetic susceptibility study. Physical
Review B, 54:572, July 1996.
[13] B. Dabrowski, J.D. Jorgensen, D.G. Hinks, S. Pei, D.R. Richards, H.B. Vanfleet,
and D.L. Decker. Physica C, 162-164:99, 1989.
[14] M.S. Dresselhaus and G. Dresselhaus. Intercalation compounds of graphite. Advances in Physics, 30(2):139, 1981.
[15] I.E. Dzyaloshinski. J. Phys. Chem. Solids, 4:241, 1958.
[16] V. J. Emery, S. A. Kivelson, and H. Q. Lin. Physical Review Letters, 64:475,
1990.
[17] V.J. Emery. Physical Review Letters, 58:3759, 1987.
[18] H.H. Feng, Z.G. Li, P.H. Hor, S. Bhavaraju, J.F. DiCarlo, and A.J. Jacobson.
Superconducting phases of La 2 CuO 4 +s prepared by electrochemical oxidation at
ambient temperature. Physical Review B, 51(22):16499, 1995.
[19] M.E. Filipkowski, J.I. Budnick, and Z. Tan. Physica C, 167:35, 1990.
[20] L. Gao, Y.Y. Xue, F. Chen, and Q. Xiong. Superconductivity up to 164K in
HgBa2Cami-Cu,0O 2m+2+ (m=l, 2, and 3).
Physical Review Letters, Rapid
Communications, 73(7):4260, 1994. report of 164K T, for HgBa2Ca 2Cu308+s.
158
[21] Urs Geiser, Mark A. Beno, Arthur J. Schultz, Han H. Wang, and Thomas J.
Allen.
Structural instability in single crystals of the high-T, superconductor
La2_-Sr'Cu0 4 . Physical Review B, 35:6721, 1987.
[22] B. Grande, H. Muller-Buschbaum, and M Schweizer. Z. Anorg. Alg. Chem.,
428:120, 1977.
[23] P. M. Grant, S. P. Parkin, V.Y. Lee, E. M. Engler, M. L. Ramirez, J. E. Vazquez,
G. Lim, R. D. Jacowitz, and R. L. Greene. Physical Review Letters, 58:2482+,
1987.
[24] J. C. Grenier, N. Lagueyte, A. Wattiaux, J. P. Doumerc, and P. Dordor.
Transport and magnetic properties of superconducting La 2 Cu0 4 +s phases (0 <
6 < 0.09) prepared by electrochemical oxidation. Physica C, Superconductivity,
202(2-4):209, November 1992.
[25] J.-C. Grenier, A. Wattiaux,
N. Lagueyte, J.
C. Park, E. Marquestaut,
J. Etourneau, and M. Pouchard. Physica C, Superconductivity, 173:139, 1991.
[26] P.C. Hammel, E.T. Ahrens, A.P. Reyes, J.D. Thompson, D.E. MaqLaughlin,
Z. Fisk, P.C. Canfield, and J.E. Schirber. Phase separation, structure, and superconductivity in oxygen-annealed La 2 Cu04+s. In E. Sigmund and K. A. Muller,
editors, Phase Separation in Cuprate Superconductors, Proceedings of the first
international workshop on Phase Separation in Cuprate Superconductors, page
139, Erice, Italy, 1992. World Scientific.
[27] J. Hubbard.
Proc. Roy. Soc., A281:401, 1965. report on Hubbard model to
explain localized electronic states.
[28] Mitsuru Itoh, Masaharu Oguni, Toru Kyomen, Hiroyasu Tamura, Jian Ding
Yu, Yoshitaka Yanagida, and Tetsuro Nakamura. Calorimetric and resistometric
studies of La 2 Cu04+S single crystals: Displasive character of phase tiansitions
in 190 - 310k. Solid State Communications, 90(12):787, 1994.
159
[29] J.D. Jorgensen, B. Dabrowski, S. Pei, D. G. Hinks, L. Soderholm, B. Morosin,
E. L. Venturini, and D. S. Ginley. Physical Review B, 38:11337, 1988.
[30] J.D. Jorgensen, H.B. Schuettler, D.G. Hinks, D.W. Capone, H. K. Zhang,
Lattice instability and high-T, superconductivity in
and M.B. Brodsky.
La2_-BaxCuO4 . Physical Review Letters, 58:1024, 1987.
[31] W. Jost. Diffusion in Solids, Liquids, Gases. Academic Press, Inc., New York,
New York, 1952.
[32] T Kawai et al.
High T, update, 6(19),
1996.
report of 17IK T, for
(Srl-xCax)l_,Cu02[33] Y.H. Kim, S.-W. Cheong, and Z. Fisk. Phase separation of charge carriers in
La 2 CuO 4. Physica C, 200:201-206, May 1992.
[34] R. K. Kremer. Zeitschrift fiir Physik, 86:319, 1992.
[35] N. Lagueyte,
A. Wattiaux, J.C. Park, J.-C. Grenier,
L. Fou nes,
and
M. Pouchard. J. Phys. III, 1:1755, 1991.
[36] Young S. Lee. private communication.
[37] Walter J. Moore.
Physical Chemistry. Prentice-Hall, Englewood Cliffs, N.J.,
third edition, 1962.
[38] T6ru Moriya. Anisotropic superexchange interaction and weak ferromnagnetism.
Physical Review, 120(1):91+, 1960.
[39] Stanley Roy Morrison. Electrochemistry at Semiconductor and Oxid zed Metal
Electrodes. Plenum Press, New York, 1980.
[40] Nevill Francis Mott. Proc. R. Soc. London A, 382:1, 1982.
[41] A.I. Nazzal, V.Y. Lee, E.M. Engler, R.D. Jacowitz, Y. Tokura, and J.B. Torrance.
New procedure for determination of [Cu - O]+P charge and oxygen content in
high T, oxides. Physica C, 153-155:1367, 1988.
160
[42] N.P. Ong. The hall effect and its relation to other transport phenomena in the
normal state of the high-temperature superconductors. In Donald M. Ginsberg,
editor, Physical Properties of High Temperature Superconductors II, page 459.
World Scientific, Teaneck, New Jersey, 1990.
[43] Elizabeth J. Opila, Harry L. Tuller, and Bernhardt J. Wuensch. Oxygen tracer
diffusion in La2-zSrCuO4 -_ single crystals. J. Am. Ceram. Soc., 76:0363, 1993.
[44] J.C. Park, P.V. Huong, M. Rey-Lafon, J-C. Grenier, A. Watt aux, and
M. Pouchard. Physica C, 177:487, 1991.
[45] P.J. Picone, H.P. Jenssen, and D.R. Gabbe. Phase diagram and single crystal
growth of pure and sr doped La 2 CuO 4. Journalof Crystal Growth, 91:463, 1988.
[46] N. W. Preyer, R. J. Birgeneau, C. Y. Chen, D. R. Gabbe, H.P. Jenssen, M. A.
Kastner, P. J. Picone, and Tineke Thio. Conductivity and hall coefficient in
La 2 CuO4+, near the insulator-metal transition. Physical Review B, 39(j6):11563,
June 1989.
[47] P.G. Radaelli, J.D. Jorgensen, and R. Kleb. Miscibility gap in electro hemically
oxygenated La 2 CuO4+s. Physical Review B, 49:6239, 1994.
[48] A.P. Reyes, P.C. Hammel, E.T. Ahrens, J.D. Thompson, P.C. Canfield, Z. Fisk,
and J.E. Schirber. Phase separation and superconductivity in La 2CuOI+s effects
of oxygen diffusion. J. Phys. Chem. Solids, 54(10):1393, 1993.
[49] J. Ryder, P. A. Midgley, R. Exley, R. J. Beynon, D. L. Yates, L. Af lfliz, and
J. A. Wilson. Physica C, 173:9, 1991.
[50] J. Saylor, L. Takacs, C. Hohenemser, J. I. Budnick, and B. Chamberlapd. Physical Review B, 40:6854, 1989.
[51] 0. F. Schirmer, G. Wubbeler, and T. Wahlbrivnk. In E. Sigmund aad K. A.
Muller, editors, Phase Separationin Cuprate Superconductors, Proceedi gs of the
161
second international workshop on Phase Separation in Cuprate Superconductors,
pages 133-141, Cottbus, Germany, September 1993. Springer-Verlag.
[52] J.R. Schrieffer, X.G. Wen, and S.C. Zhang. Physical Review B, 39:11663, 1989.
[53] Paul Shewmon. Diffusion in Solids. The Minerals, Metals, & Materi4ls Society,
Warrendale, Pennsylvania, second edition, 1989.
[54] E. Takayama-Muromachi,
T. Sasaki, and Y. Matsui.
Direct oxidation of
La 2 CuO04 in an aqueous solution of KMn0 4. Physica C, 207:97-101, 1993.
[55] Siok-Tien (Tineke) Thio. Antisymmetric Exchange and Its Influence on the Magnetic Structure and Conductivity of La 2 CuO4 . PhD thesis, Massachusetts Institute of Technology, 1988.
[56] J. M. Tranquada, Y. Kong, D. J. Buttrey, D. E. Rice, and V. Sachani. Physical
Review B, 50:6340, 1994.
[57] D. Vaknin, J.L. Zarestky, D.C. Johnston, J.E. Schirber, and Z. Fisk. Phase
separation to antiferromagnetic and superconducting domains in oxygen-rich
single-crystal La 2 CuO4+x: Magnetic and structural neutron diffraction studies.
Physical Review B, 49(13):9057, 1994.
[58] A. Wattiaux, J. Park, J.-C. Grenier, and M. Pouchard. C. R. Acad. Sci. Paris,
310(Serie II):1047, August 1990.
[59] B.O. Wells. private communication.
[60] B.O. Wells, R.J. Birgeneau, F.C. Chou, Y. Endoh, D.C. Johnston, M.A, Kastner,
Y.S. Lee, G. Shirane, J. M. Tranquada, and Y. Yamada. Intercalation and staging
behavior in super-oxygenated La 2 Cu04+S. Zeitschrift fiir Physik, 100:535-545,
July 1996.
[61] X. Xiong, P. Wochner, S.C. Moss, Y. Cao, K. Koga, and M. Fujita. Evidence of
in-plane superstructure formation in phase-separated and staged single crystal
La 2 Cu04+5 . Physical Review Letters, 76:2997, April 1996.
162
[62] X. Xiong, Q. Zhu, Z.G. Li, S.C. Moss, H.H. Feng, P.H. Hor, D.E. Cox,
S. Bhavaraju, and A.J. Jacobson. Synchrotron x-ray study of interstitial oxygen ordering in the superconducting phase of La2CuO4 +s. Journal of Materials
Research, 11:2121, 1996.
[63] Jian Ding Yu, Yoshiyuki Inaguma, Mitsuru Itoh, Masaharu Oguni, and T6ru
Kyomen. Effect of oxygen content on the anomalies at successive phase transitions of La 2 Cu04+5 single crystal below 320 k. Physical Review B, 54(10):7455,
1996.
[64] F.C. Zhang and T.M. Rice. Physical Review B, 57:3759, 1988.
163