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EVIDENCE OF SUPERCONDUCTIVITY IN THE MAGNETIC PROPERTIES OF SPECIALLY PREPARED PALLADIUM HYDRIDE AND DEUTERIDE
SAMPLES (Pd/PdO:HX AND Pd/PdO:DX)
Carlos Henry Castaño Giraldo, M. S.
Department of Nuclear, Plasma and Radiological Engineering
University of Illinois at Urbana-Champaign, 2002
George H. Miley, Adviser
Electrochemically cycled specially prepared palladium samples (Pd/PdO loaded
and deloaded with hydrogen and deuterium) have been studied with thermal
desorption and SQUID magnetic measurements. The cycling of the samples
produced a high concentration of dislocations, which trapped hydrogen and
deuterium. An activation energy of 0.91 eV is estimated for the deuterium
trapped in the dislocations. DC magnetic measurements as well as AC
susceptibility suggest the presence of weakly diamagnetic state (which suggest
possible traces of superconductivity) in Pd samples enriched with hydrogen and
deuterium. Some samples showed signatures of antiferromagnetism for
temperatures below 100 K and low magnetic fields. The material exhibits
ferroelasticity that is ascribed to the presence of domains similarly to some high
temperature superconductor ceramics. There is a transition to weak
diamagnetism at about 50 K in some of our samples for fields lower than 1 Oe.
Imaginary susceptibility shows the presence of a transition, possibly a new phase
that is ascribed to a diamagnetic nano-composite phase. Further research is
recommended to understand this new phase and its properties.
iii
Dedicated to my beloved mother and my dear family
without whom I would be a very different person for worst.
Thanks be to God for my wonderful family and friends.
iv
Acknowledgements
First and foremost I want to acknowledge Dr. Andrei Lipson, for his extensive
help and guidance when preparing this thesis. The original idea of the present
work belongs solely to him. Throughout the process of analysis and learning he
has been an invaluable help, guide, and a good friend. Thanks to my advisor
Professor George H. Miley for his initial invitation to study at the University of
Illinois, and for his continued support all these years, without him my graduate
education would not be a reality. Thanks to Professor Alexey Bezryadin by the
economical support of the research this thesis is based on, for letting me use his
data and accepting to be the reader of the thesis. I would like to acknowledge all
the people that help me throughout the process of writing and presenting this
work. To the Head of the Department, Prof. Jim Stubbins, for encouraging me to
finish in this timely fashion, to Becky Meline, Mya Clemens, Idelle Dollison,
Gaylon Reeves, Dee Staley, Kathy Ward, Jef Cornell, and Joshi Shrestha for
their help and support in personal, academic, and departmental issues. Thanks
to Tony Banks for his help on the use of the SQUID equipment and other
resources of the Materials Research Laboratory. I also want to acknowledge
innumerable people that I don’t mention individually, the staff members of
storerooms, machine shops, and other support facilities on campus whose
services I have used extensively. Thanks to all of them. Last but not least, thanks
to my family who have always been my main and daily moral support from the
distance, to my sister Vilma M. Ramirez-Castaño, my mother Ofelia M. Giraldo,
and my father Hernando J. Castaño. My extended family is too big to mention
individually, but they all fit in my heart, thanks to all.
v
Table of Contents
List of Figures .....................................................................................................viii
List of Tables ....................................................................................................... xi
List of Symbols.....................................................................................................xii
List of Abbreviations and Definition of Terms......................................................xiv
CHAPTER 1. INTRODUCTION ............................................................................1
CHAPTER 2. FUNDAMENTALS OF MAGNETIC MEASUREMENTS..................3
2.1. Description of the MPMS ...............................................................................3
2.2. Magnetic Units Used......................................................................................7
2.3. Magnetic Behavior of Materials......................................................................8
2.3.1. Magnetic Domains ...............................................................................8
2.3.2. Paramagnetism....................................................................................9
2.3.3. Ferromagnetism...................................................................................9
2.3.4. Ferrimagnetism..................................................................................11
2.3.5. Antiferromagnetism............................................................................11
2.3.6. Diamagnetism and Superconductivity................................................12
2.3.7. M(T) and χ(T) Curves for Simple Magnetic Behaviors .......................14
CHAPTER 3. THEORETICAL BACKGROUND ..................................................15
3.1. Initial Ideas...................................................................................................15
3.2. Hypothesis of Work......................................................................................17
CHAPTER 4. DESCRIPTION OF THE EXPERIMENTS.....................................19
4.1. The Samples................................................................................................19
4.1.1. Description of the Samples ................................................................19
4.1.2. Production of Dislocations in the Samples.........................................19
4.1.3. On the Naming of the Samples and Experiments ..............................22
4.2. Type of Experiments ....................................................................................23
4.2.1. DC Magnetometry..............................................................................24
4.2.2. Hysteresis Loops ...............................................................................24
vi
4.2.3. AC Magnetometry..............................................................................25
4.3. Experimental Results ...................................................................................26
4.3.1. Pd/PdO:Hx and Pd/PdO:Dx Samples ................................................27
4.3.1.1. M(T) and χ(T) Diamagnetic Transition ............................................27
4.3.1.2. M(T) Presence of a Small Diamagnetic Signal ...............................28
4.3.1.3. M(H) Hysteresis Loops ...................................................................29
4.3.1.4. Anti-Ferromagnetic Behavior ..........................................................33
4.3.1.5. AC Susceptibility Measurements. ...................................................34
CHAPTER 5. INTERPRETATION OF RESULTS ...............................................36
5.1. Activation Energy of the Pd/PdO:Dx System ...............................................36
5.2. Analysis of Pd/PdO:Hx and Pd/PdO:Dx Data ..............................................40
5.2.1. M(T) and χ(T) Diamagnetic Transition ...............................................40
5.2.2. Diamagnetic Signal from Subtracted M(T) Graphs ............................41
5.2.3. M(H) Hysteresis Loops ......................................................................43
5.2.4. Anti-Ferromagnetic Behavior .............................................................45
5.2.5. AC Susceptibility Measurements .......................................................49
CHAPTER 6. CONCLUSIONS............................................................................50
CHAPTER 7. RECOMMENDATIONS FOR FUTURE WORK ............................52
List of References...............................................................................................54
Appendix 1. Table of Conversion of Magnetic Units ...........................................57
Vita......................................................................................................................58
vii
List of Figures
Figure 2.1. MPMS Main Components. Taken from [9]. ........................................4
Figure 2.2. Graph of the superconducting coils and SQUID response (DC
runs). Compare to figure 2.3. ................................................................................5
Figure 2.3. Typical signal from the MPMS device, in this case the signal
shows a positive magnetic moment (paramagnetic-like). The two red lines
are the data and the blue is the best fit for the signal............................................6
Figure 2.4. (a) M(H) curve showing magnetic hysteresis taken from [11]. (b) Schematic representation of the structure of a ferromagnetic material. ..............10
Figure 2.5. Schematic representation of the structure of a ferrite that
exhibits ferrimagnetism. ......................................................................................11
Figure 2.6. Summary of the basic magnetic behavior of materials. Figure
taken from [13]. In this graph σs is the magnetization (M)...................................13
Figure 3.1. Temperature dependence of the resistivity (ρ) with I=1A. 1.
Original (pure) Pd. 2. PdH0.72 3. PdHx (low loading hydride). Taken from [7],
the units should read μΩ/cm. ..............................................................................16
Figure 4.1. Change of the initial electrolysis voltage with cycle number on
Pd/PdO:Dx..........................................................................................................22
Figure 4.2. Pd/PdO:Hx samples showing paramagnetic behavior at 5 Oe,
and diamagnetic behavior at 0.4 and 0.5 Oe. Two intermediate field values
are shown to illustrate the transition. See table 1 for description of the
samples. .............................................................................................................27
Figure 4.3. Difference in M(T) behavior for Pd/PdO:Hx. 801fg sample. H is
1 Oe for the blue points and 5 Oe for the pink points..........................................28
Figure 4.4. Difference in M(T) paramagnetic behavior between test (717fg
blue points) and reference (714bgr pink points) samples at 1 Oe.......................29
Figure 4.5. Typical M(H) Hysteresis loop for Pd/PdO:Hx sample (717fg),
T=50K. ................................................................................................................30
Figure 4.6. M(H) Hysteresis loop for Pd/PdO:Hx sample (717fg), T=298K. .......30
viii
Figure 4.7. Difference in M(H) behavior for Pd/PdO:Dx between test (621fg
pink) and reference (620bgr blue) samples at 2K. Compare to figure 4.4...........31
Figure 4.8. M(H) signal subtraction of foreground (627fg pink) and
background (626bgr blue) signals for Pd/PdO:Dx samples. ...............................32
Figure 4.9. Peculiarity of the subtracted signal of figure 4.8. Notice the
magnitude of the field..........................................................................................33
Figure 4.10. Moment of Pd/PdO:Hx sample (801fg) cooled in the presence
of a 1 Oe magnetic field exhibits a Curie-Weiss paramagnetic behavior
(pink points) as opposed to 1 Oe heating at 1 Oe after ZFC (blue points). .........34
Figure 4.11. Real susceptibility (χ’) for Pd/PdO:Hx sample (722fg). H=10
Oe, h=2 Oe. ω=1 kHz..........................................................................................35
Figure 4.12. Imaginary susceptibility (χ’’) for Pd/PdO:Hx sample (722fg).
H=10 Oe, h=2 Oe. ω=1 kHz. ...............................................................................35
Figure 5.1. Thermal desorption spectrum of deuterium from Pd/PdO:Dx,
partial pressure is in arbitrary units. ....................................................................36
Figure 5.2. Predicted peak position with activation energy for Do=1.4x10-3
cm2/s. ..................................................................................................................38
Figure 5.3. Predicted peak position with pre-exponential factor Uo=0.91 eV......39
Figure 5.4. Attempt to fit the 5 Oe data from figure 4.2 to a Curie-Weiss
model using the least square method implemented in the program
Tablecurve™ [34]................................................................................................42
Figure 5.5. Magnetic susceptibility vs. Temperature for PdHx (•) and PdDx
(+). In this picture taken from [33] x is called c (for concentration). This
measurements were performed at H=8000 Oe...................................................44
Figure 5.6. Fitting of Curie-Weiss paramagnetism model to the 1 Oe
cooling data of figure 4.10...................................................................................46
Figure 5.7. Fitting of the data of figure 4.10 (1 Oe cooling below 80 K), to
Curie-Weiss paramagnetism model. ...................................................................47
Figure 5.8. Pd/PdO:Dx sample cooled in the presence of a 1 Oe magnetic
field exhibits a Curie-Weiss paramagnetic behavior (pink), as opposed to 1
Oe heating after ZFC (blue). Compare to figure 4.10..........................................47
ix
Figure 5.9. Fitting of Curie-Weiss paramagnetism model to the 1 Oe
cooling data of figure 5.8.....................................................................................48
Figure 5.10. Fitting of the data of figure 5.8 (1 Oe cooling below 80 K), to
Curie-Weiss paramagnetism model. ...................................................................48
x
List of Tables
Table 1. Description of some of the samples used in this study. ........................23
xi
List of Symbols
A amperes.
B Flux density, or magnetic induction. Net local field inside a sample measured in
Gauss (G).
CH Hydrogen concentration.
Do Pre-exponential factor in the diffusivity, constant.
D(T) Diffusivity of hydrogen (or deuterium) in palladium.
FC Field Cooling (Cooling in the presence of a magnetic field).
H Applied magnetic field by the external magnet, this quantity is measured in
Oersteds (Oe). Sometimes referred as field strength, field intensity, or
magnetizing force.
Habs Hydrogen absorbed. This means inside the metal.
HAC, h driving field in the measurements of AC magnetic susceptibility.
Hads Hydrogen adsorbed, that is sitting in the surface.
k Boltzmann constant. 8.61 x 10-5 eV/K.
m meter.
M Magnetization, flux density, or intensity of magnetization, can be defined as
the pole strength per unit area of cross section, or more simply is the field that
changes the local field from H to B. The units are ergs/Oersted.cm3, but are often
written simply as emu/cm3.
μ Permeability = B/H (dimensionless).
nd Dislocation density [cm-2].
P Pressure.
PdDx Non stoichiometric Palladium Deuteride with loading ration of x deuterium
atoms per Pd atom (usually x<1).
PdHx Non stoichiometric Palladium Hydride with loading ration of x hydrogen
atoms per Pd atom (usually x<1).
ρ Resistivity, the ability of a material to resist electrical conduction (Ω.m).
℘m=9.27x10-24 A.m2. Bohr magneton.
xii
ppm Parts Per Million.
SI International System of Units.
T temperature (K).
TEM Transmission Electron Microscopy.
Uo Activation energy for atom diffusion.
χ Magnetic susceptibility = M/H (dimensionless but usually given in emu/cm3,
emu/g, emu/mole).
χac differential or AC susceptibility.
ZFC Zero Field Cooling. Cooling of the sample in the presence of a zero field
applied (H=0 Oe).
xiii
List of Abbreviations and Definition of Terms
Curie Temperature: Temperature above which there are not long-range
ordering magnetic properties in solids. The coupling of magnetic moments is
suppressed due to thermal vibration. All materials above their Curie temperature
behave like paramagnets.
Cycle Number: In this work, refers to one electrochemical loading of our sample
with hydrogen or deuterium, and its corresponding deloading as described in
section 4.1.2.
Differential or AC Susceptibility (χac): The same concept as susceptibility (χ) ,
but while χ is defined independent of field in general (presume is linear), χac is
defined at a point of the magnetization curve (χac=dM/dH) (see section 4.2.3 for a
formal definition).
Josephson Junction: Junction of two superconductor materials in which two
electrons forming a pair tunnel together as a pair, in such a way that they
maintain their momentum pairing after they cross the gap. This phenomenon
takes place when there is no difference in voltage between the superconductors,
so that a current may flow through the junction without an accompanying voltage
drop (sometimes this is called a tunneling supercurrent). For details see [1], [2],
and [3].
Kondo Effect: The screening of a free spin by conduction electrons at low
temperatures. The resultant strong scattering of electrons at the Fermi energy
leads to an increase in the resistance of a material with the decrease of
temperature (usually T<10K) [4].
xiv
xv
MPMS: Magnetic Property Measurement System. Device for magnetic
measurements manufactured by Quantum Design (http://www.qdusa.com),
available in MRL, Room 328.
MRL: Frederick Seitz Materials Research Laboratory (MRL). National Research
Facility located at the University of Illinois at Urbana-Champaign 104 S. Goodwin
Ave.,Urbana, IL 61801. (http://www.mrl.uiuc.edu).
Spin Glass: Magnetic state characteristic of certain dilute magnetic alloys (such
as CuMn or AuFe at 0.1-10 atom %) in which the local moments are frozen
(magnetic ordering) into particular, but random directions. Such alloys don’t
exhibit a long range ordering (magnetic domains) however. A paramagnetic to
spin-glass boundary in the susceptibility curve exhibits a characteristic “cusp” at
low fields (see [2]).
SQUID: Superconducting Quantum Interference Device (for details see [3]).
Susceptibility (χ): Differential increase in magnetization with field (χ=M/H).
Susceptibility is a very valuable diagnostic property for understanding magnetic
materials. See figure 2.6.
Ultra Low Field: Feature in the MPMS, that allows to work with very low fields
(<0.001 Oe) by cycling to demagnetize the shields and quenching the
superconductor magnets at the starting of the experiment. The usual value for
“zero” magnetic field corresponds approximately to –0.2 Oe when this feature is
not used, due to trapped magnetic fields in the shield (see figure 1, part 8). This
value is relatively stable and can be considered an offset of the equipment when
the ultra low field option is not used.
CHAPTER 1. INTRODUCTION
There has been a great deal of interest in the study of superconductivity of metal
hydrides since the discovery (in the 70’s) that PdH and Th4H15 are
superconductors at relatively high temperatures (Tc is 10.7 K for PdD). The initial
experiments were designed to demonstrate that metallic hydrogen was being
formed inside the metal lattice. This hypothesis however, was disproved and so
new theories emerged that pointed to electron-phonon coupling and electron
donations between the hydrogen and the metal [5]. Then, it was realized that one
of the biggest advantages using hydrides for the study of superconductivity
arises from the fact that the composition of a hydride is often non-stoichiometric
allowing for a wide range of compositions. This continuous composition variation
permits tests of theories behind superconductivity with relative ease, since the
electron density of states can be modified easily just changing the composition of
hydrogen in the hydride.
The present work was devised to study the behavior of Pd when modified by the
loading and deloading of hydrogen and deuterium. This loading and deloading
process is known to generate stresses and dislocations in the metal. Dislocations
by themselves are well known to modify the magnetic behavior of materials [6].
The original studies in the PdHx system tried to achieve as high a loading as
possible. In fact, x~1 was achieved using ion accelerators and stabilizing the
hydride cryogenically. These conditions were selected because of the
assumption that metallic hydrogen was formed and played a central role in the
presence of superconductivity. Metallic hydrogen is a high atomic density
condensed phase of hydrogen that exhibits metallic properties.
The main difference in this study is that our remnant hydrogen is very small
(x~10-4 is estimated in [7] and a similar value can be calculated from [8]) inside a
palladium matrix with high density of dislocations left after the process of loading
1
and deloading of hydrogen. It is very important to realize that the small amounts
of hydrogen play a central role since they, when trapped in the dislocation cores,
could form metallic or quasi-metallic hydrogen. This thought provoking idea was
first introduced by Prof. A. Lipson in [7], where it was shown that the
dehydrogenated PdHx exhibited up to 12% lower resistance that the virgin Pd
samples. Careful transport experiments then hinted that weak superconductivity
was present. To further spark our interest, it came to our attention recently that
the hydrogen atoms in dislocation cores, as measured by Prof. B. Heuser in
reference [8] might be at a higher density than that required for the presence of
metallic hydrogen. Even though some preliminary data are presented here, an
extended study would be required to prove or disprove the hypothesis that small
inclusions of metallic or quasi-metallic hydrogen are present in dislocation sites in
Pd.
We will start by defining our unit of measurements (cgs) and describing our
experimental equipment, followed by a description of samples and experiments.
Our approach is to present a variety of experimental evidence and then show
that the pieces of evidence are consistent with the presence of a weak
superconducting phase in our samples. The ultimate objective of this work in to
spark further interest that will allows us to do a systematic study of this
interesting and potentially groundbreaking subject. As such and because of
limitations in the author’s own understanding of the subject the results are not
exhaustively analyzed. There is more than can be said about the experimental
results, in this work we focus on what can support our hypothesis of work and will
allows us present a coherent picture to suggest a more in depth study.
2
CHAPTER 2. FUNDAMENTALS OF MAGNETIC MEASUREMENTS
2.1. Description of the MPMS
All the magnetic measurements where performed in the Magnetic Property
Measurement System (MPMS) manufactured by Quantum Design.
(http://www.qdusa.com) located on MRL room 328. This instrument is a SQUID
magnetometer of 1 Tesla maximum magnetic field. Figure 1 shows the main
components of the system, for further details see [9] and [10]. A SQUID device
consists of a closed superconducting loop including (one or two) Josephson
junctions in the loop’s current path (for a detailed description of a Josephson
junction see [1], or [3]). Because of the extreme non-linear behavior of the
Josephson junction SQUID devices can resolve changes in external magnetic
fields of about 10-15 Tesla while operating in fields as large as 7 Tesla. This
capabilities make SQUID devices the most sensitive available for the
measurement of magnetic fields [9].
The sample needs to be mounted inside a gel capsule, which is then fit inside a
drinking straw and inserted coaxially in the superconducting detection coils (for a
step-by-step description of the process, see [10]). Measurements are performed
indirectly by moving the sample through the superconducting detection coils (See
figure 2.2). As the sample moves there is a change in the flux within the detection
coil, which changes the current in the superconducting circuit. During the
measurement the sample is stopped at a number of positions. At each stop
several readings of the SQUID voltage are collected and averaged, improving the
signal to noise ratio. Notice that since the whole circuit is a superconductor the
current does not decay. The current induced in the detection coil correspond to
the movement of a point-source magnetic dipole through a second-order
gradiometer detection coil. This ideal signal is illustrated in figure 2.2.
3
Figure 2.1. MPMS Main Components. Taken from [9].
1. Sample rod. 2. Sample rotator. 3. Sample transport. 4. Probe assembly. 5.
Helium Level Sensor. 6. Superconducting solenoid. 7. Flow impedance. 8.
SQUID capsule. 9. Superconducting pick-up coil (see figure 2.2). 10. Dewar
cabinet. 11. Dewar. 12. Printer. 13. Power supply. 14. Temperature controller.
15. Cabinet. 16. Power distribution unit. 17. MPMS controller. 18. Computer. 19.
Monitor.
4
Figure 2.2. Graph of the superconducting coils and SQUID response (DC runs).
Compare to figure 2.3.
Once a signal like that shown in figure 2.3 is obtained, it is fit with the theoretical
signal of a dipole moving through a second-order gradiometer. This fit is done
automatically (even though it could be done manually also) by the package
MPMS Multivu Application. (Proprietary software, Revision 1.53. Build 056,
Copyright 1998-2001). One example of this can be seen as the blue line in figure
2.3. Notice that the standard deviation value is not calculated (error due to fitting
unknown), this however is not a problem for our interpretations. This MPMS
system allows measurements in the range from 2 to 350 K with accuracy ±0.01K,
using both DC and AC susceptibility measurements. Each parameter can be
varied independently (H, T, frequency of AC signal, etc), and data acquisition can
be automated (programming of experimental sequences). For more complete
and better details of how each component of the MPMS system works, see the
5
review [9] ([9] is a booklet that can be order free of charge from Quantum
Design).
Figure 2.3. Typical signal from the MPMS device, in this case the signal shows a
positive magnetic moment (paramagnetic-like). The two red lines are the data
and the blue is the best fit for the signal.
6
2.2. Magnetic Units Used
Due to the fact that this thesis is mainly an experimental effort and that the
experimental instruments used in the project uses the CGS units for magnetic
quantities, it is convenient to report our data in the CGS system of units.
Otherwise there would be a great deal of effort involved in changing the unit
system for every piece of data given by the MPMS system and its associated
software to the SI units. Thus the CGS units that are being used are defined here
along with the conversion factors that can be used to convert quantities of
interest to the International System of Units, SI (see appendix 1).
In CGS units, the B, M, and H fields are related through the equation,
MHB π4+=
Here B represents a net local field, H is the field applied to the sample with the
help of an external magnet, and M is the field that changes H to B. MPMS
reports values of magnetic moment in emu (the SI equivalent is A.m2).
Magnetization M is magnetic moment divided by mass, volume, or amount of
substance, e.g. emu/cm3. It can also be reported in units of G (1 emu/cm3 = 4π
G). B units are gauss, G (SI unit: 1 Tesla = 10000 G). H units are Oersteds, Oe
(SI unit A/m). Oersteds and Gauss have the same dimensions. Susceptibility is
given by χ=M/H. Notice χ should be dimensionless but is commonly reported as
emu/g, emu/cm3 or emu/(cm3 Oe). Finally the permeability is μ=B/H is
dimensionless. In appendix 1, a table of conversion factors for magnetic units is
presented as reference material.
7
2.3. Magnetic Behavior of Materials
In the next sections some typical magnetic behaviors of materials will be
described. This will help with the classification, explanation, and differentiation of
our experimental results. The fact that each electron has a “magnetic
momentum” (spin) allows materials to exhibit magnetic properties. The magnetic
moment of each electron is ℘m=9.27x10-24 A.m2. This is called a Bohr magneton.
Usually electrons tend to pair with spin “up” and “down” in ways that make the
global magnetic moment greatly or totally suppressed.
2.3.1. Magnetic Domains
Magnetic domains are regions with in crystals in which all the unit cells have a
common magnetic orientation. The way electrons pair and arrange in a particular
substance determines its magnetic behavior. There are some elements like Mn,
Fe, Co, Ni, that have some unpaired electrons in their structure. Some but not all
of them exhibit obvious magnetic properties. The reason lies in the fact that
within each material dipoles tend to align in such a way as to close the magnetic
lines inside the material. This gives rise to the formation of magnetic domains.
Notice that the boundaries of these magnetic domains can move easily in perfect
crystal materials. However these domain boundaries can be immobilized by
structures in the material like dislocations or grain boundaries. This impairment in
the mobility of domain boundaries is called “pinning”. And has important
consequences in the behavior of materials. Usually magnetic domains appear in
ferromagnetic materials.
8
2.3.2. Paramagnetism
Paramagnetism is the tendency of elementary atomic dipoles to align with an
applied magnetic field. This happens more readily in materials that don’t form
domains. If there are not domains, the elementary dipoles formed by atoms and
ions are randomly oriented in such a way that they cancel exactly each other in
the absence of a magnetic field. Therefore when applying a magnetic field the
dipoles tends to align with the field and there is an increase in flux density (M)
that is relatively low and linear. All materials exhibit paramagnetism above certain
temperature called Curie Temperature. The reason is that at some point the
thermal agitation in a material destroys the magnetic domains in a material.
Paramagnetic materials exhibit positive susceptibility. There are different origins
for paramagnetic behavior. Different types of paramagnetism can be
differentiated from the magnitude of χ and its temperature dependence. Curie
paramagnetism exhibits a linear 1/χ vs. T curve. Curie-Weiss paramagnetism is
different from curie paramagnetism in that besides the interaction of the dipoles
with the magnetic field, there is also an interaction between the magnetic
moments of the atoms. Pauli paramagnetism is a case present in metals due to
the conductions electrons being aligned with the applied field. Van Vleck
paramagnetism is associated with thermal excitation of low-lying states. For
further details about these various cases see [3].
2.3.3. Ferromagnetism
This is the strongest type of magnetism found in materials. The key features of
the M(H) curve is that the curve is non-linear and non-reversible as can be seen
in figure 2.4, it shows magnetic hysteresis or ferroelasticity.
9
Notice from the figure that after applying a magnetic field to the sample, and
returning to zero field, the magnetization of the sample don’t return to zero, but
retains a remnant magnetization (Mr). To return the magnetization to zero, it is
necessary to apply a magnetic field in the opposite direction of value Hc, called
the coercive field. Materials with high Mr values are called hard magnets, and
materials with low Mr values are called soft magnets. The reason for the
alignment of all the atoms in a domain in a parallel direction has to do with the
energy bands in a metal. Each energy level contains two electrons of opposite
magnetic spins, but the valence bands are not filled (as in all metals). When an
external field is applied, the energies of one spin direction are reduced, while the
other is increased. Some spins then realign into lower energy states such that
the Fermi energies are equalized. Some of these electrons remain aligned in the
new position even after the magnetic field is removed [12].
Figure 2.4. (a) M(H) curve showing magnetic hysteresis taken from [11]. (b) Schematic representation of the structure of a ferromagnetic material.
10
2.3.4. Ferrimagnetism
Some ceramics possess an atomic structure in which two atoms with different
atomic moment are opposed to each other. The fact that the moments are
different causes the compound to exhibit a net magnetization. The oldest known
magnetic material, magnetite (lodestone) has Fe+2 and Fe+3 ions equally divided
in the structure therefore generating a net magnetization. This case can be
thought as similar to that shown in figure 2.5, where the incomplete cancellation
of antiferromagnetic arranged spins gives rise to a net magnetic moment.
Figure 2.5. Schematic representation of the structure of a ferrite that exhibits
ferrimagnetism.
2.3.5. Antiferromagnetism
Antiferromagnetic materials provide a case that is similar in principle to
ferrimagnetism. But in this case the magnetic moment of the atoms opposed to
each other are equal so apparently the material is non-magnetic, even though
the atoms composing the material can have strong magnetic moments
individually. Ferromagnetism, ferrimagnetism, and antiferromagnetism are
related phenomena that appear due to the locking of individual magnetic atoms
at specific positions. Thermal vibrations can unlock the atom positions and
11
destroy these behaviors. The temperature at which this happens is called Néel
Temperature.
Notice that antiferromagnetic and paramagnetic materials would exhibit similar
magnetic behavior at a single point, as do ferromagnetic and ferrimagnetic
materials. To differentiate the different types of magnetism, magnetic
measurements must be made over a temperature range (M(T) curves).
2.3.6. Diamagnetism and Superconductivity
Diamagnetism is present in all substances but usually is a very weak effect as
compared to other magnetic phenomena. Hence other effects usually mask it.
Diamagnetism arises from electrons that are free to move (in non-magnetic
atoms) and react to the application of an external magnetic field by gyrating in
such a way that they produce a magnetic field opposed to the original one,
effectively reducing the flux density (M) inside the material. Substances that
exhibit diamagnetic behavior are repelled when brought near the pole of a strong
magnet (hence the name). The M(H) plot of a diamagnet is linear and reversible
but has a negative slope. That is, they have negative susceptibility, χ. There are
few applications for diamagnets since they are usually very weak. There is
however an exceptional case that occurs when a material becomes a
superconductor. In this case the material exhibits the strongest possible case of
diamagnetism, χ=-1/4π in cgs units (which is an enormous value when compared
to normal diamagnetic substances). Due to diamagnetism the flux density inside
a superconductor drops to zero, and it is said that superconductors reject
magnetic fields. In practice that means that superconductors are repelled by
magnetic fields, and this effect could have interesting applications (e.g. maglev
trains). For a superconductor state to exist, the materials must be bellow a
particular temperature and magnetic field, called the Critical Temperature (Tc)
12
and the Critical Field (Hc), respectively. Above these two conditions
superconductivity is destroyed and the material becomes a normal material
again.
Figure 2.6. Summary of the basic magnetic behavior of materials. Figure taken
from [13]. In this graph σs is the magnetization (M).
13
2.3.7. M(T) and χ(T) Curves for Simple Magnetic Behaviors
The five kinds of magnetism then can be divided into two broad categories: First,
diamagnetism, and ideal (Curie) paramagnetism, in which no cooperative
behavior of individual magnetic moments occur. Second, Non-ideal
paramagnetism, ferromagnetism, antiferromagnetism, and ferrimagnetism which
are all examples where cooperative phenomena occurs between the magnetic
moments of the atoms in the material. The behavior of a given material can be
deducted from the M(T) and χ(T) curves. For the simplest cases, this can be
nicely summarized in figure 2.6. Of course these are ideal cases, and many
materials don’t exhibit any of these effects. In this work, our material is at least a
compound of Pd and H. Furthermore if our ideas are correct this material is a
composite of a quite exotic phase (quasi-metallic hydrogen) embedded in a
palladium matrix. We don’t expect our samples to exactly follow any of the
behaviors shown in figure 2.6. Nevertheless this figure will serve as a guide to
understand the results obtained.
14
CHAPTER 3. THEORETICAL BACKGROUND
3.1. Initial Ideas
It is known that perfect Pd-metal does not exhibit superconductivity above
3.0mK, However Pd metal in which defects have been introduced by alpha
bombardment at low temperature shows superconductor behavior with Tc~3.2 K
[14]. On the other hand when hydrogen is introduced in palladium to form PdHx
for x~1 (using implantation of accelerated ions at cryogenic temperatures), the
critical temperature increases to about 8.8K. PdDx behaves similarly with
Tc~10.7K [5]. When the superconductivity of PdHx was discovered originally in
1972, it was thought to be due to the presence of metallic hydrogen inside the
palladium metal, since the density of hydrogen in highly loaded PdHx is higher
than that of the solid hydrogen. Further studies seem to have disproved that
original assumption; nevertheless the reason for the superconductivity in PdHx is
not clear. The presence of gases (including hydrogen) tends to decrease the Tc
in all transition metals, except for Th and Pd. There are some theories that claim
that additional electron-phonon couplings are responsible for the increase in Tc,
but there is not a definitive theory behind this unexpected phenomenon [5].
A. Lipson, et al. presented preliminary evidence of the presence of a weak
superconductor phase in PdHx and Pd/PdO:Hx, during transport measurements
in [7]. In figure 3.1 we can see the temperature dependence with resistivity, when
measured with a current of 1 A. At room temperature the resistivity of PdHx is
12% lower than the resistivity of the Pd pure metal. For further explanation of the
features of the curves refer to the original paper [7]. This resistivity decrease is
unexpected in the sense that hydrogen penetration on Pd is known to increase
the electrical resistance (not to reduce it). Other authors that have observed the
effect try to account for it by an unexplained re-crystallization process
15
accelerated by H-induced vacancy formation [15]. For present purposes, note
that the resistivity of palladium drops by 12% at T=300K, for a pressure of
71Kbar [7].
Figure 3.1. Temperature dependence of the resistivity (ρ) with I=1A. 1. Original
(pure) Pd. 2. PdH0.72 3. PdHx (low loading hydride). Taken from [7], the units
should read μΩ/cm.
With this background information in mind, we recently learned about a recent
study of PdDx in deformed single crystal palladium using Small Angle Neutron
Scattering (SANS), that reports the trap efficiency for deuterium in palladium is
16
between 2.1 and 5.1 deuterons per Å of dislocation [8] and [16]. It is somewhat
surprising that the linear density (number of hydrogen atoms per unit of length of
dislocation) of hydrogen atoms inside dislocations in Pd might be as high as 5 H
atoms/Å. These values could imply that the surface energy density is equivalent
to very high pressures in the dislocation cores of palladium as hinted in [7].
Notice we are not talking here of a bulk phase but of a “nano-composite”. That is,
fibers (dislocation cores) of a possibly superconductor phase embedded in the
matrix of a common material (Pd). Dislocation cores are one-dimensional nano-
structures (comparable in size to carbon nanotubes), the cores of edge
dislocations is where the highest pressure in the lattice is attained. Our proposed
material is composed of a matrix of ordinary metal with wires-like structures of
metallic or quasi-metallic hydrogen. From these basic ideas we will go on to
define the hypothesis behind the present research.
3.2. Hypothesis of Work
Earlier this year a study, using high vacuum thermal desorption coupled with a
quadrupole mass spectrometer analyzer, was performed during the desorption of
deuterium from Pd/PdO:Dx samples [17]. Figure 5.1 shows temperature vs.
partial pressure of deuterium desorbed in arbitrary units. From this picture we
can see that the temperature of desorption of the residual hydrogen in the
sample peaks at 441.5 oC (714.5 K). It was realized for Professor A. Lipson [17]
that if hydrogen only leaves at these high temperatures, the activation energy of
the diffusion process should be relatively high (See section 5.1). Because of this,
hydrogen has to be located at the core of edge dislocations.
Recently it was shown using SANS that dislocations in cold worked and cycled
Pd samples can contain relatively high amounts of hydrogen (deuterium) [8], [16].
For a dislocation density in Pd, nd~2-4x1011 cm-2, up to 5 hydrogen atoms per Å
17
of dislocation line were detected. The value of x in PdDx for this experiment was
3x10-3 (calculated from [8]). This value is of the same order of magnitude as our
samples (similar process in samples). Now, consistent with the high activation
energy observed, we assume that this condensed phase is located inside the
dislocation core in Pd, which is within one Burger’s vector from the dislocation
line (The Burger's vector of a dislocation is the net number of extra rows and
columns, combined into a vector). The Burgers vector in Pd is 2.75 Å, the
maximum hydrogen concentration that could be achieved is about CH~0.7 H
mol/cm3 of Pd host lattice. If this estimated value is correct at least at some
points, the pressure inside the dislocation core holding hydrogen would be
enough to produce metallic hydrogen. The criterion for hydrogen metallization is
fulfilled at CH~0.6 mol/cm3. As we can see from the previous disquisition, we
think of the possibility of partial hydrogen metallization for some of the hydrogen
trapped in our samples. Even if hydrogen doesn’t become metallic the
concentration of hydrogen is anomalously high. Reference [8] found that the
volume of the trapped hydrogen around the dislocations is at least 4 times lower
than previously believed. The properties of such a compound are unknown. It is
possible that such a compound is close in properties to metallic hydrogen due to
anomalously high concentration of bound hydrogen atoms.
In accordance with existing predictions, metallic hydrogen could demonstrate
superconductivity at temperatures as high as 400 or 600K (see [18] and [19]). So
in this experimental work we decided to investigate the magnetic properties of Pd
with small hydrogen inclusions (x~10-4), expecting to obtain some proof of high
temperature superconductivity in the weakly bound system of “quasi-metallic
hydrogen” nanophase localized in the dislocations in the Pd matrix.
18
CHAPTER 4. DESCRIPTION OF THE EXPERIMENTS
4.1. The Samples
4.1.1. Description of the Samples
Samples consisted of palladium foils with thickness 12.5μm from NIALCO Japan
(99.995%). Pd samples were previously oxidized using the butane torch to
produce a layer of PdO on top of the Pd. This PdO layer was found to be about
30nm using SIMS in another study [20]. The objective of this oxide layer is to
increase the mobility of the hydrogen atoms.
4.1.2. Production of Dislocations in the Samples
In order to produce Pd samples with small hydrogen inclusions, the Pd/PdO foils
where loaded with hydrogen (or deuterium) and deloaded by anodic polarization
in a LiSO4 solution several times. The current densities were between 1 and 5
mA/cm2 (geometrical area). It is well known that loading of hydrogen in palladium
and the subsequent formation of hydride causes a lattice volume increase of
~20%, introducing a large strain on the palladium metal that creates a high
density of dislocations. We were interested in making reproducible runs, so a
simple way of characterizing how much strain was induced in the sample in a
controlled way was to control the number of loading cycles for a given sample.
Each loading deloading cycle of hydrogen in the palladium metal was uniformly
done according to the following procedure. First, a solution 1M of LiSO4 was
prepared using deionized water, and Lithium Sulfate, 99,99+ % [21] for the
19
hydrogen experiments (using D2O [22] and Lithium Sulfate, 99,99+ % for the
deuterium experiments). Once prepared, the solution was pre-electrolyzed for 24
hours using a high area platinum anode and a platinum cathode. The purpose of
the pre-electrolysis is to reduce the concentration of impurities in the electrolyte
like iron, or other ferromagnetic materials by several orders of magnitude to sub-
ppm concentrations [23], [24].
The Pd was then polarized cathodically in this solution and the voltage was
monitored carefully. At the point the hydride PdHx reaches the composition x~0.7
there is a sudden voltage (galvanostatic control) change that is accompanied by
strong gas evolution from the surface. This sudden voltage change is due to the
change of the reactions happening in the surface. The reactions change from:
OHMHmetalineMOH ads 23 )( +→++ −+ Followed by
absads MHMH → Absorption of H
To
OHMHmetalineMOH ads 23 )( +→++ −+ Followed by
22 HMMHMH adsads +→+ Tafel reaction
The first set of two reactions are responsible for loading the metal. When the
metal comes close to saturation (x~0.7) the reactions change to the second set
[25]. The metal is indicated in the reaction equations to emphasize that these
reactions will not take place without the presence of a metal and the adequate
electrons at the right levels (Hydrogen Evolution Reaction).
Since we are not interested in overloading, at the moment the set of reactions
changes, the current polarity is reversed to start extracting the hydrogen from the
hydride phase, in a way inverse of the first set of reactions. Since the reaction is
reversed and the current constant, about the same time is taken to deload the
sample as is required to load. By the time the hydrogen inside the metal is almost
20
completely drained, there is also a strong voltage change, due to the beginning
of the following (simplified global) reaction: −+ ++→ eOHOOH 22213 322 Oxygen Evolution Reaction.
The reason of choosing these points to start and stop the processes is the
simplicity for reproducing the same points at different currents and with different
size samples, which eliminates the need for complicated diagnostics to estimate
similar treated (stressed) material.
How much “change” (dislocations, strain, etc) is being done to the material with
each consecutive cycle is difficult to determine. A quantitative measurement
would require destructive tests like Transmission Electron Microscopy (TEM). For
practical purposes in the scope of this work, we use the absolute value of the
potential at the beginning of the cycles as an indication of the change in our
samples. In figure 4.1 the change in this potential is plotted against the number of
cycles. Notice that in this case (using deuterium), about 4 cycles are sufficient to
produce most of the change in the sample. A similar experiment conducted for
hydrogen, showed that about 12 to 13 cycles were needed to reach a plateau.
This difference in the number of cycles required is ascribed to the different sizes
of the hydrogen and deuterium atoms.
After the desired number of cycles, the sample was annealed in an argon
atmosphere at 300 oC for 2 hours. This helps to guarantee that only tightly
bounded hydrogen will remain in the sample. It was shown by thermal desorption
mass spectrometry (figure 5.1) that the tightly bounded hydrogen leaves the
sample at temperatures around 450 oC. For this reason, blank samples
(background) were prepared by annealing at 600 oC, which guarantees that there
is no hydrogen trapped inside the metal (even at dislocations).
21
0
0.1
0.2
0.3
0.4
0.5
0.6
1 2 3 4 5 6 7 8 9Cycle Number
Vol
tage
Cha
nge,
Loa
ding
[V]
Figure 4.1. Change of the initial electrolysis voltage with cycle number on
Pd/PdO:Dx
Typical samples had weights ranging from 23 to 40 mg. Once these samples
were prepared (cycled and annealed), they were bent in a small cylindrical shape
and mounted with cotton in a small gelatin capsule. In preparation for magnetic
measurements in the SQUID.
4.1.3. On the Naming of the Samples and Experiments
All the present study’s magnetic data was gathered during June 14 and August
11 of 2002. The samples used were given mnemotechnic names according to
the dates the experiments on the SQUID were performed and if they were
hydride samples (fg= foreground, meaning samples with hydrogen or deuterium)
or blanks (bgr= background). So, for example, the blank sample run on June 15
has a codename: “615bgr” (June is month 6). All samples indicated in the figures
22
in this thesis will follow this simple nomenclature. When the M(T) signals of
samples with different masses were compared, the signal were normalized by
mass (M signals are directly proportional to their mass). Sometimes a single
sample has several names because it was used several times. This redundancy
shouldn’t lead to any confusion since every data file contains the sequence tag,
the sample tag, and the file tag as identifiers. The sequence tag contains the
step-by-step experimental procedure; the sample tag labels the name of the
sample and is made to coincide to the file name, which is always related to the
date.
Table 1. Description of some of the samples used in this study.
Name Mass [mg] Sample Preprocessing*
616fg, 621fg 23.2 Pd/PdO:Dx 9C* + A**
619bgr, 620bgr, 626bgr,
714bgr, 731bgr
23.3 Pd/PdO:Hx 10C + A(V)***
627fg 23.2 Pd/PdO:Dx 5x(1C+A)
711fg, 713fg, 722fg 23.4 Pd/PdO:Hx 3C + A + 3C + A + 4C + A
717fg 33.9 Pd/PdO:Hx 6C + A
726fg 30.3 Pd/PdO:Dx 2C + A + 2C + A + 3C
801fg 23.6 Pd/PdO:Hx 3C + A + 3C + A + 4C + A
*1C is one loading-deloading cycle. **A is one annealing process using argon at 300 oC. ***A(V) is one annealing process using vacuum at 600 oC.
4.2. Type of Experiments
Since the MPMS system is a very versatile instrument for magnetic
characterization, there were a variety of experiments performed in the samples to
23
explore different aspects of the magnetic behavior. We will describe the different
experimental sequences and explain its intended purpose below, before
describing the experimental results in next section.
4.2.1. DC Magnetometry
DC magnetic measurements determine the equilibrium value of the
magnetization (M) in a sample. The sample is magnetized by a constant
magnetic field and the magnetic moment in the sample is measured at a fixed
temperature. Different temperature scans were performed and the magnetization
was measured at different values of temperature, thus obtaining a M(T) curve for
a fixed H. At its simplest, such a curve will quickly disclose if a material is
paramagnetic or diamagnetic (much more information can be gathered from the
curve by the trained eye).
4.2.2. Hysteresis Loops
The second type of experiment is also DC magnetometry, but this time
temperature is kept constant while the applied magnetic field H is varied. Starting
from an Ultra Low Field (<1 Oe), any hysteresis can be observed as we increase
and reduce H to positive and negative values. This experiment shows an M(H)
curve that can exhibit hysteresis like that shown in Figure 2.4 for a ferromagnetic
material, from these curves paramagnetic and diamagnetic materials can
differentiated as well as ferroelasticity (hysteresis).
24
4.2.3. AC Magnetometry
In AC magnetic measurements, a small AC drive magnetic field is superimposed
on the DC field, causing a time-dependent moment in the sample. This measures
the differential or AC susceptibility (χac=dM/dH). The AC susceptibility has a real
and an imaginary part. The imaginary part is related to the energy losses in the
sample, and can provide information on structural details of the sample,
resonance phenomena, electrical conductivity due to increased currents, energy
exchange between magnetic spins (in the lattice of paramagnetic materials), as
well as relaxation processes such as flux profiles and flux creep in
superconductors [26].
The field of the time-dependent moment induces a current in the pickup coils,
allowing measurement without sample motion (see figure 2.2). The detection
circuit of the MPMS system is then configured to detect only a narrow frequency
band at the same frequency of the drive frequency. A more complete explanation
of this type of measurement can be found in [27].
For our purposes the main feature of this kind of measurement is its higher
sensitive to the small volume of hydride phase present. The reason is that the
actual quantity being detected is:
( )tSinHdHdMM ACAC ... ω⎟
⎠⎞
⎜⎝⎛=
Where HAC is the driving field (h in figures 4.11 and 4.12), and ω is the frequency
of the AC signal. Notice the AC measurement is sensitive to the slope of M(H)
and not to the absolute value. Therefore small magnetic shifts can be detected
even when the absolute value of the magnetic moment is large. Effectively, AC
magnetometry largely ignores the signal of the main phase (palladium), showing
more clearly the signal for the hydride phase of interest. Consequently the noise
to signal ratio is greatly enhanced [27].
25
4.3. Experimental Results
As an introduction to the result graphs, we need to mention that the software
(MPMS MultiVu Application) provided with the SQUID system does the fitting of
the second-order gradiometer signal automatically (as seen in figure 2.3).
Unfortunately this version of the software doesn’t provide an estimate of the error
associated with the fitting. Our graphs will not include error bars for this reason.
For some particular cases we estimated our error from the values obtained with a
magnetometer for low fields. We determined that if there is not an “Ultra Low
Field” calibration, the SQUID presents an error of about –0.2 G. The lack of
absolute numbers at higher fields is not impairment for this work, since we are
looking for the behavior of our sample from the graph trends. The trend of a set
of points is not likely to be greatly affected for statistical fluctuations. Some of our
lower field graphs look “noisy”, but the trend is nevertheless clear and easy to
identify.
Our samples are 99.995% purity Pd (50 ppm). Therefore the error due to
ferromagnetic impurities should be less than 5% at 1000 Oe [32]. The subtraction
of the background signal from similar samples we believe eliminates this problem
altogether. The presence of an oxide layer on the surface of the material should
not produce significantly differences in the behavior because the amount is too
small to produce a magnetic signal big enough (thickness 30nm).
26
4.3.1. Pd/PdO:Hx and Pd/PdO:Dx Samples
4.3.1.1. M(T) and χ(T) Diamagnetic Transition
As we mention in section 2.3.6 negative values of susceptibility (χ) mean
diamagnetic behavior. Pure palladium and palladium hydride exhibits a
paramagnetic behavior (see figure 5.5). In figure 4.2 we can see how at fields
above 5 Oe there is a paramagnetic behavior for palladium at all temperatures
(T>2K). Notice however how the behavior of the sample veers towards
diamagnetism as fields get lower (1.5 and 1 Oe). The sample even exhibits
overall diamagnetism at the lowest fields (0.4 and 0.5 Oe).
DC Susceptibility of Pd/PdO:Hx
-6.E-05
-4.E-05
-2.E-05
0.E+00
2.E-05
4.E-05
6.E-05
8.E-05
1.E-04
0 50 100 150 200 250 300Temperature [K]
χ711 fg @ 0.5 Oe713fg @ 0.4 Oe717fg @ 1.0 Oe717fg @ 1.5 Oe717fg @ 5.0 Oe
emu/g
Figure 4.2. Pd/PdO:Hx samples showing paramagnetic behavior at 5 Oe, and
diamagnetic behavior at 0.4 and 0.5 Oe. Two intermediate field values are shown
to illustrate the transition. See table 1 for description of the samples.
Not all of our samples exhibited a diamagnetic transition, but we observed at
least transitions like that shown in figure 4.3 in all samples, in which we can see
27
the markedly different behavior of the magnetization of our samples with the
applied field. At 5 Oe the material had a paramagnetic behavior and at 1 Oe the
paramagnetism is greatly suppressed.
M(T) of Pd/PdO:Hx 801fg
0.0E+00
5.0E-07
1.0E-06
1.5E-06
2.0E-06
2.5E-06
3.0E-06
0 50 100 150 200 250 300 350Temperature [K]
Mom
ent [
emu]
M(T) @ 1.0 OeM(T) @ 5.0 Oe
Figure 4.3. Difference in M(T) behavior for Pd/PdO:Hx. 801fg sample. H is 1 Oe
for the blue points and 5 Oe for the pink points.
4.3.1.2. M(T) Presence of a Small Diamagnetic Signal
In figure 4.4 we can see a detail typical of all our samples that is not apparent in
figure 4.3. When comparing test (Pd/PdO:Hx) and reference (Pd/PdO) samples
both exhibit paramagnetic behavior, but if we subtract the curves (normalized by
weight), test samples always exhibited a strongly reduced paramagnetism. At
about 50K the signals get very close and blend.
28
M(T) Pd/PdO:Hx 717fg and 714bgr @ 1 oe
-3.E-06
-2.E-06
-2.E-06
-1.E-06
-5.E-07
0.E+00
5.E-07
1.E-06
2.E-06
0 20 40 60 8Temperature [K]
Mom
ent [
emu]
0
717fg714bgr717fg-714bgr
Figure 4.4. Difference (yellow) in M(T) paramagnetic behavior between test
(717fg blue points) and reference (714bgr pink points) samples at 1 Oe.
4.3.1.3. M(H) Hysteresis Loops
When we performed our M(H) hysteresis loops experiments, the virgin part of the
hysteresis curve always showed a lower slope (χ) at low fields (H<10 Oe) than
the rest of the loop (H>10 Oe), A typical example is shown in figure 4.5. This
effect was present at temperatures, 2, 5, 10, 50 and, 100 K, but was not present
for T=298K (see figure 4.6).
29
M(H) Pd/PdO: Hx 717fg. @ 50 K
-2.E-05
-2.E-05
-1.E-05
-5.E-06
0.E+00
5.E-06
1.E-05
2.E-05
2.E-05
-20 -10 0 10 20Field [Oe]
Mom
ent [
emu]
Figure 4.5. Typical M(H) Hysteresis loop for Pd/PdO:Hx sample (717fg), T=50K.
M(H) Pd/PdO: Hx 717fg. @ 298 K
-4.E-06
-3.E-06
-2.E-06
-1.E-06
0.E+00
1.E-06
2.E-06
3.E-06
4.E-06
-20 -10 0 10 20Field [Oe]
Mom
ent [
emu]
Figure 4.6. M(H) Hysteresis loop for Pd/PdO:Hx sample (717fg), T=298K.
30
We decided then to compare, as before, the behavior of foreground and
background samples, and the presence of the diamagnetic signal could also be
seen (as in M(T) experiments). Figure 4.7 shows a typical example in which the
susceptibility of the foreground sample signal is lower than that of the
background sample, consistent with our previous observations in the M(T)
experiments (see figure 4.4).
M(H) Pd/PdO:Dx 621fg and 620 bgr @ 2K
-5.E-05-4.E-05-3.E-05-2.E-05-1.E-050.E+001.E-052.E-053.E-054.E-055.E-05
-20 -15 -10 -5 0 5 10 15 20Field [Oe]
Mom
ent [
emu]
620bgr621fg621fg-620bgr
Figure 4.7. Difference (yellow) in M(H) behavior for Pd/PdO:Dx between test
s we mentioned earlier, not all of our samples exhibited the same kind of
(621fg pink) and reference (620bgr blue) samples at 2K. Compare to figure 4.4.
A
behavior. In figure 4.8 the paramagnetic signals of a foreground and background
samples can be seen. It is apparent that the Pd/PdO:Hx sample exhibits a
diminished paramagnetism. When the signal of the Pd/PdO blank is subtracted,
we can see there is a weakly diamagnetic behavior present. The details can be
seen better in figure 4.9, where the subtracted signal is shown alone. It was
unexpected that the diamagnetic signal would persist at this relatively high
temperature (100K) and at fields as high as 400 Oe. This behavior was not
31
common to all of our samples; Thus it was decided that an in depth study of this
behavior was a suitable goal for future research (high temperature
superconductivity?).
M(H) Pd/PdO:Dx 627fg and 626bgr @ 100 K
-1.E-04
-8.E-05
-6.E-05
-4.E-05
-2.E-05
0.E+00
2.E-05
4.E-05
6.E-05
8.E-05
1.E-04
-600 -400 -200 0 200 400 600Field [Oe]
Mom
ent [
emu]
626bgr627fg627fg-626bgr
Figure 4.8. M(H) signal subtraction (yellow) of foreground (627fg pink) and
background (626bgr blue) signals for Pd/PdO:Dx samples.
32
M(H) Pd/PdO:Dx 627fg and 626bgr @ 100 K
-6.E-06
-4.E-06
-2.E-06
0.E+00
2.E-06
4.E-06
6.E-06
-1000 -500 0 500 1000Field [Oe]
Mom
ent [
emu]
627fg-626bgr
Figure 4.9. Peculiarity of the subtracted signal of figure 4.8. Notice the
magnitude of the field.
4.3.1.4. Anti-Ferromagnetic Behavior
An antiferromagnetic material is a material that has the moments of its atoms
fixed but opposing each other, causing the material to exhibit a paramagnetic
signal even though there is internal long range ordering. When our samples were
cooled with small fields applied, a behavior close to Curie-Weiss paramagnetism
was present. See figure 4.10. In this experiment there was a zero field cooling
(ZFC, not shown) followed by a M(T) experiment at 1 Oe. During the M(T)
experiment the temperature was raised from 2K to 350K (blue points). The
sample at this low field exhibits the already explained and observed tendency to
diamagnetism. Then the temperature change was reversed, that is, the
temperature was decreased from 350K to 2K still at 1 Oe (pink points). This
second curve is referred as FC M(T) at 1 Oe (), and behaves differently from the
original M(T) with ZFC. The sample behaves like a paramagnet all the way down
to 2K.
33
M(T) Pd/PdO:Hx 801fg @ 1 Oe
0.0E+005.0E-07
1.0E-061.5E-062.0E-06
2.5E-063.0E-06
3.5E-064.0E-06
0 50 100 150 200 250 300Temperature [K]
Mom
ent [
emu]
M(T) HeatingM(T) Cooling
Figure 4.10. Moment of Pd/PdO:Hx sample (801fg) cooled in the presence of a 1
Oe magnetic field exhibits a Curie-Weiss paramagnetic behavior (pink points) as
opposed to 1 Oe heating at 1 Oe after ZFC (blue points).
4.3.1.5. AC Susceptibility Measurements.
To further verify the presence of a transition in our material, AC-magnetometry
experiments where performed. As was explained before, AC-magnetometry has
the advantage that it allows to us to see changes in small phases (see section
4.2.3). A typical result from this experiment can be seen in figure 4.11 and 4.12.
The real susceptibility shows the normal value of susceptibility. Unfortunately the
signal for these conditions is relatively noisy, so to see better the trend we
applied a simple averaging filter. We can see the general behavior similar to our
previous samples even with a small diamagnetic transition. The imaginary
susceptibility (figure 4.12) shows clearly a gradual phase transition because the
properties of dissipation of energy in the sample are changing substantially.
34
AC Susceptibility Pd/PdO:Hx. 722fg H = 10 oe, h = 2 oe @ 1000Hz.
-5.0E-06
-3.0E-06
-1.0E-06
1.0E-06
3.0E-06
5.0E-06
7.0E-06
9.0E-06
1.1E-05
1.3E-05
1.5E-05
0 50 100 150 200Temperature [K]
Rea
l Sus
cept
ibili
ty [e
mu/
g]X'X' Filtered
Figure 4.11. Real susceptibility (χ’) for Pd/PdO:Hx sample (722fg). H=10 Oe,
h=2 Oe. ω=1 kHz.
AC Susceptibility Pd/PdO:Hx. 722fg H = 10 oe, h = 2 oe @ 1000Hz.
0.0E+002.0E-054.0E-056.0E-058.0E-051.0E-041.2E-041.4E-041.6E-041.8E-042.0E-04
0 50 100 150 200Temperature [K]
Imag
inar
y S
usce
ptib
ility
[em
u/g]
Figure 4.12. Imaginary susceptibility (χ’’) for Pd/PdO:Hx sample (722fg). H=10
Oe, h=2 Oe. ω=1 kHz.
35
CHAPTER 5. INTERPRETATION OF RESULTS
5.1. Activation Energy of the Pd/PdO:Dx System
The thermal spectrum for deuterium desorption can be seen in figure 5.1. The
partial pressure is in arbitrary units, the desorption pressure peaks at 441.5 °C.
The experiment was ended at 578 °C. If the process controlling the desorption of
the deuterium is diffusion then the problem can be solved exactly using the 1D
diffusion equation:
⎟⎠⎞
⎜⎝⎛
∂∂
∂∂
=∂∂
xCtxD
ttC ),(
Thermal Desorption Spectrum of Deuterium from Pd/PdO:Dx
100 200 300 400 500 600Temperature [Celsius]
Arb
itrar
y U
nits
Figure 5.1. Thermal desorption spectrum of deuterium from Pd/PdO:Dx, partial
pressure is in arbitrary units.
36
D(x,t) is the diffusivity of deuterium in palladium, and in general is:
kTUooeDTD /)( −=
The pre-exponential factor Do for deuterium in palladium is 1.4x10-3 cm2/s.(taken
from fig 12.16 of [28]). k is the Boltzmann constant. And Uo is the activation
energy that we are interested in. The thermal conductivity of palladium is high so
we can assume the temperature is uniform across the sample during the
desorption process. The experiment is done ramping the temperature at a
uniform rate (a-1=10K/min) from 23 to about 578 °C, so we can relate
temperature (T) and time (t).
baTt +=
The diffusion equation is then:
2
2
)(1xCTD
TC
a ∂∂
=∂∂
Where time was left out in favor of temperature. Our geometry is a thin foil of
metal of 12.5 μm, so our boundary and initial conditions are.
oo CTxCCITmxCTxCsCB
=====
),(..0),5.12(0),0('. μ
Here Co is the initial concentration of deuterium in the sample (10-4 H/Pd). We
can use separation of variables, with C(x,T)=X(x).Y(T). The solution is:
⎥⎥⎦
⎤
⎢⎢⎣
⎡= ∫
−kTU
kTU
woo
o
oo
dwwe
kUDa
ExpCTY/
/2
2
1)(λ
λ is the separation constant, To=296 K is the initial temperature. The solution for
the spatial part is:
)()()( 32 xCosCxSinCxX λλ +=
Using the B.C.’s, C3=0, and the eigenvalues are λn=nπ/L, so:
⎟⎠⎞
⎜⎝⎛= ∑
∞
= LxnSinCxX
nn
π1
2)(
37
Combining, C1 and C2n, and using the orthogonality of the sine function, the final
solution is:
⎟⎠⎞
⎜⎝⎛
⎥⎥⎦
⎤
⎢⎢⎣
⎡
⎟⎠⎞
⎜⎝⎛
⎟⎠⎞
⎜⎝⎛
= ∫∑∫
∫ −∞
= Lxndw
we
kLnUaDExp
dxL
xn
dxL
xn
CTxCkTU
kTU
woo
nL
L
o
o
oo
πππ
π
sinsin
sin),(
/
/22
22
1
0
2
0
Figure 5.2. Predicted peak position with activation energy for Do=1.4x10-3 cm2/s.
Since we are assuming that the release of hydrogen from the surface is due to
diffusion, using symmetry:
0)(2T)0,Jo(x =∂∂
−== xxCTD
We care only about the magnitude of Jo, the final expression to evaluate is:
38
[ ]
⎥⎥⎦
⎤
⎢⎢⎣
⎡
⎟⎠⎞
⎜⎝⎛
⎟⎠⎞
⎜⎝⎛
×
−=
∫∑∫
∫ −∞
=
kTU
kTU
woo
nL
L
oooo
o
oo
dwwe
kLnUaDExp
dxL
xn
dxL
xn
n
LkTUExpCDTJ
/
/22
22
1
0
2
0
sin
sin
/2)(
ππ
π
π
Figure 5.3. Predicted peak position with pre-exponential factor Uo=0.91 eV.
Evaluating the first 5 terms of this function in MathematicaTM [29], for different
values of Uo, we find than the activation energy should be 0.91 eV for our peak to
be at 441.5 °C (as experimentally measured in figure 5.1). In figure 5.2 we can
see the effect of changing the value of the activation energy. It is also well known
that the diffusion of deuterium changes due to the presence of dislocations and
damages in the metal [30]. This means that the pre-exponential factor Do in our
samples (electrochemically cycled) might be bigger than the accepted value used
39
before. Figure 5.3 shows the effect of Do in our equation. Comparing figures 5.2
and 5.3 we can see that the effect of Do is smaller than that of Uo. So our
estimated activation energy value of 0.91eV, is good even if Do is slightly
affected. In any case, an increase in the value of the pre-exponential factor just
would make the estimated activation energy value (Uo) even higher. On the other
hand, this value for our activation energy (0.91 eV) is comparable with other
values found in the literature for residual hydrogen trapped in metals [31], where
it was also find that for solid samples the desorption is not strongly dependent on
boundary conditions or recombination-limited surface kinetics.
5.2. Analysis of Pd/PdO:Hx and Pd/PdO:Dx Data
5.2.1. M(T) and χ(T) Diamagnetic Transition
From figure 4.2 a clear diamagnetic transition at low temperatures and low fields
is observed. Of course there is not enough data to assign a sharp value to the
superconducting transition Field Hc. Nevertheless it is clear that the critical field
for this experiment was less than 5 Oe. The transition temperature might be as
high as 70K. Again it is hard to say an exact value because our system is not an
ideal superconductor. In fact there might not be a Tc at all, because the
inhomogeneity of the distribution of the hydrogen in the material can produce
different phases with different behaviors. In the simplest case, the metallic-like
hydrogen region could be a small superconducting phase in a much bigger
paramagnetic phase.
Still in figure 4.2, the sample clearly exhibits paramagnetic behavior above 5 Oe.
If we try to fit the data using Curie-Weiss law
40
oTC χχ +Θ−
=
We find that the data doesn’t fit the model very well, as seen in figure 5.4. This is
not unexpected since our sample is not a perfect paramagnetic material. As a
comparison for this imperfect Curie-Weiss behavior, the M(T) behavior figure 5.5
(Taken from [33]) exhibits the magnetic susceptibility of PdHx and PdDx vs.
temperature. Notice how this graph shows a paramagnetic trend but does not
correspond with any of the simple magnetic behaviors mentioned previously.
This graph is included to see the actual behavior of the hydrogenated palladium
system (accepted), notice also that the figure is taken at 8000 Oe. The small
critical magnetic field shown by our system might be a good reason why nobody
had detected this behavior before, since scientists tends to work at relatively high
fields. For example, even 20 Oe is considered a small field when compared to
the Hc of the superconducting elements (see table 4.1 of [1]), and for
ferromagnets 20 Oe is very small. As a matter of fact, when the author was being
trained in the use of the SQUID facilities the centering of magnetic samples were
routinely performed at 100 Oe and more.
5.2.2. Diamagnetic Signal from Subtracted M(T) Graphs
All of our samples when heated (from 2K) in low magnetic fields (0.3-5.0 Oe)
show a lower susceptibility than blank Pd/PdO samples. Now it is well know that
except for Ti and Cr, hydrogenation of transition metals produces a decrease in
susceptibility [28], but this happens for high loading hydrides where it is assumed
that hydrogen donates its electron to the lattice producing a decline in the density
of states. In the present work, we have PdHx for x~10-4. At this level hydrogen is
an impurity and the change in susceptibility can’t be explained by donation of
electrons from hydrogen (too few to modify the dipoles). Similarly, we estimate
that the dislocations and general structure in our reference samples and test
41
(foreground) samples are similar, because the temperature and time of annealing
was not extended enough to produce recrystallization.
Figure 5.4. Attempt to fit the 5 Oe data from figure 4.2 to a Curie-Weiss model
using the least square method implemented in the program Tablecurve™ [34].
If the foreground and background signals are subtracted as shown in figure 4.4, a
signal is obtained that could be explained assuming the presence of a small
diamagnetic phase (assuming simple magnetic interactions). The other possible
explanation would be an anomalously high reduction in the paramagnetic signal
of palladium. But, it is known that the introduction of defects in palladium reduces
its susceptibility only by about 8% as measured in [6]. For our earlier discussion
(chapter 3) and because of the presence of diamagnetism in M(T) and AC
susceptibility measurements, we favor the hypothesis of a superconductor
nanophase formed in our samples. Some of the samples didn’t exhibit a
diamagnetic transition. All of them nevertheless showed lower paramagnetism
42
when compared to background (blank) samples. One typical case can be seen in
figure 4.4. This difference in magnetic behavior between both samples can again
be explained by a minute superconducting phase. A first order estimate
illustrates this. A superconductor has the highest possible diamagnetic signal
(χ=-1/4π emu/cm3). The mass of the sample in figure 4.4 is 33.9 mg, and using
the density of Pd. From the highest diamagnetic signal (at 2K in figure 4.4), the
amount of superconducting phase don’t need to be bigger than 1/100 of the
sample volume. This simple assumption must be questioned because we don’t
observe an ideal superconductor behavior. Thus we might have a weak
superconductor phase with a much smaller volume that modifies the properties of
the surrounding matrix (maybe as small as x, that is ~10-4).
5.2.3. M(H) Hysteresis Loops
Notice we don’t observe any signal with a negative slope (diamagnetism). The
reason is thought to be the relatively large fields (20 Oe) used, and the fact that
palladium (the matrix and main component) is paramagnetic. If we look to figure
4.5 alone by itself, we might think that our material is ferromagnetic since it looks
similar to figure 2.4. In section 5.2.4 is shown however that our material exhibits
antiferromagnetism below 80K, in fact what figure 4.5 is showing is ferroelasticity
due to the switching of domains. Ferroelasticity is present in ferromagnets and
also in some high temperature superconducting ceramics even below Tc [35].
Since we don’t have ferromagnetism in our samples (low ferromagnetic impurity
level, antiferromagnetic signal) this behavior might be linked to the presence of
domains in the structure of our material. The domains in our sample have
disappeared at 298 K (figure 4.6), which is the normal behavior expected with
increasing temperature [35].
43
Figure 5.5. Magnetic susceptibility vs. Temperature for PdHx (•) and PdDx (+).
In this picture taken from [33] x is called c (for concentration). This
measurements were performed at H=8000 Oe.
It is important to mention that not all of our samples exhibited the same behavior,
sometimes to our puzzlement, similarly prepared samples didn’t performed
consistently in the DC-magnetization experiments. We ascribed this behavior to
the lack of control loading and the dislocations produced in the samples (We
annealed our samples as mention in section 4.1 in an effort to uniformize the
samples).
44
We found some of our experiment hard to reproduce; a good example is seen in
figure 4.8 and 4.9. The data are very suggestive, with the diamagnetic signal
being destroyed at about 400 Oe. We could imply from this experiment that some
high temperature superconductivity was present, both T and H are relatively high
values.
5.2.4. Anti-Ferromagnetic Behavior
As we have seen in previous sections, the samples don’t exhibit a perfect Curie-
Weiss behavior. Nor should they do this since these samples are not perfect
paramagnetic materials. Surprisingly, when fitting the parameters of the Curie-
Weiss law (similarly as before) for the paramagnetic signal of our samples
undergoing FC (data from figure 4.10), the fitting shown in figure 5.6 was
obtained. Curie-Weiss paramagnetic behavior seems to be a good description for
our sample (we’ll make a better one yet). Notice the difference with figure 5.4. It
is interesting to see that this behavior was present for our hydrogen as well as
deuterium experiments. A similar experiment for Pd/PdO:Dx can be seen in
figure 5.8. And the corresponding fitting can be seen in figure 5.9, with similar
results. Notice the values for Θ (‘b’), are negative in both cases. Θ<0 in the Curie
Weiss model may indicate the presence of an antiferromagnetic transition at
T=|Θ|. We don’t expect our samples to show a perfect transition, but we consider
the value of Θ<0 significant.
So to make sure we don’t have an artifact, we fitted the data of figure 4.10 again,
using this time the value of χo (‘a’) obtained from the fitting of figure 5.6. This time
we fit to a straight line (1/(χ-χo) vs. T). The result can be seen in figure 5.7. As we
can see Curie-Weiss behavior is a good approximation for our data below 80 K.
After about 80 K some different behavior starts. We don’t try to fit the second part
45
of the data (T>80 K). For 2 <T< 80 K the linear fitting of the equation can be seen
in the figure 5.7. In this representation C-W equation is:
CCT
o
Θ−=
− χχ1
Therefore, C=1.14x10-3, and Θ=-4.36. The value of R2 indicates a good fitting.
Repeating the above process for Pd/PdO:Dx we find a good fitting below around
80 K also. This fitting can be seen in figure 5.10. In this case Θ=-15.79 with a
good fitting also. This negative value of Θ might indicate the presence of
antiferromagnetism, which can be linked to superconductivity; in fact some
authors suggest that at least for some materials, the antiferromagnetic state and
the superconductivity have a common mechanism [36].
Figure 5.6. Fitting of Curie-Weiss paramagnetism model to the 1 Oe cooling data
of figure 4.10.
46
1/(χ−χο) vs. Temperature
y = 874.52x + 3813.9R2 = 0.9652
0.0E+00
5.0E+04
1.0E+05
1.5E+05
2.0E+05
2.5E+05
3.0E+05
3.5E+05
0 50 100 150 200 250 300 350Temperature [K]
1/( χ−χο)
Figure 5.7. Fitting of the data of figure 4.10 (1 Oe cooling below 80 K), to Curie-
Weiss paramagnetism model.
M(T) Pd/PdO:Dx 726fg @ 1.0 Oe
0.E+001.E-062.E-063.E-064.E-065.E-066.E-067.E-068.E-069.E-06
0 50 100 150 200Temperature [K]
Mom
ent [
emu]
HeatingCooling
Figure 5.8. Pd/PdO:Dx sample cooled in the presence of a 1 Oe magnetic field
exhibits a Curie-Weiss paramagnetic behavior (pink), as opposed to 1 Oe
heating after ZFC (blue). Compare to figure 4.10.
47
Figure 5.9. Fitting of Curie-Weiss paramagnetism model to the 1 Oe cooling data
of figure 5.8.
1/(χ−χο) vs. Temperature
y = 197.46x + 3118.2R2 = 0.97260.E+00
1.E+042.E+043.E+044.E+045.E+046.E+047.E+048.E+049.E+04
0 50 100 150 200Temperature [K]
1/( χ−χο)
Figure 5.10. Fitting of the data of figure 5.8 (1 Oe cooling below 80 K), to Curie-
Weiss paramagnetism model.
48
5.2.5. AC Susceptibility Measurements
As mentioned before the AC magnetometry has the advantage of detecting small
changes regardless of the total size of the signal. In the case of real susceptibility
(figure 4.11) the advantage is not apparent because both the total signal and any
diamagnetic signal in the sample are comparable in magnitude and small; notice
however that we observe a transition to negative real susceptibility. We don’t
know exactly the mass of our phase; therefore the susceptibility is reported per
gram of the sample. It is interesting nevertheless to see that the behavior of our
sample is consistent and confirms our previous DC measurements. The
imaginary part of our sample is much less noisy. The sample shows what might
be a gradual phase change between about 20 and 100 K. The dissipation of
energy in the sample changes by about an order of magnitude. Changes in
energy dissipation accompany many transitions (superconductivity among them),
because of the interplay between long range ordering and other dynamic
phenomena in the material (e.g. [37]). This phase transition is yet another
indication of the magnetic ordering of our system below 100 K.
49
CHAPTER 6. CONCLUSIONS
The activation energy for the trapped deuterium in the sample is estimated to be
about 0.91 eV, assuming diffusion as the controlling desorption mechanism for
our samples. This value is about 4 times the normal value, but is comparable to
other studies of trapped hydrogen [31]. This high value hints that the trapping of
hydrogen occurs at the cores of edge dislocations in the palladium.
Pd/PdO:Hx samples, for x~10-4 exhibit a net diamagnetic transition at about 50K
and low magnetic fields (H<1 Oe). We propose that this transition could be
explained by the presence of a small amount of a weak superconductor
nanophase. Above 5 Oe, the same system exhibits a non-ideal paramagnetic
behavior (see figure 4.2).
Pd/PdO:Hx and Pd/PdO:Dx exhibit a reduced magnetization when compared to
Pd/PdO blank samples in M(T) and M(H) curves obtained by DC Magnetization
measurements. This reduction is too big to be explained by the introduction of
defects in the sample alone [6], and could be explained by the presence of a
weak superconducting phase.
The presence of Curie-Weiss paramagnetic behavior when the samples are
cooled in the presence of a small field is interpreted as evidence of the presence
of an antiferromagnetic behavior below 70 K. Antiferromagnetism is an example
of long range ordering in magnetic systems. Some authors hint that
antiferromagnetism and superconductivity in some systems arise from a common
mechanism.
The presence of ferroelasticity (domain switching) in our samples that are not
ferromagnets, may hint some long-range order similar to some high temperature
superconductor ceramics [35].
50
AC susceptibility measurements are consistent and confirm DC measurements.
The imaginary part of the susceptibility shows clearly a strong change in energy
dissipation in our samples below 100 K. We assume this transition to be linked
the presence of a new superconducting phase.
Some of our samples exhibited diamagnetic signals at temperatures and fields as
high as 100K and 400 Oe. We consider this a good indication that with the proper
choice of materials and conditions a potentially useful engineering material could
be produced, and further research is highly recommended (see next section).
51
CHAPTER 7. RECOMMENDATIONS FOR FUTURE WORK
Monetary as well as time constrains limited the scope of our research to be a
preliminary study of the properties of this material. The interesting properties
discovered as discussed in the previous sections compel us to recommend
further research, to this end a formal proposal is being prepared. The planned
experiments for this new research could address some of the following topics:
• From the different behavior of similarly prepared Pd/PdO samples (section
5.2.3), is clear than a better characterization of the samples is required, so a
characterization to the sub-ppm level in all our samples is required.
• Precise measurement of the loading ratio x in our M:Hx and M:Dx material,
using Thermal Desorption calibrated with TiH2 standard samples is required.
• Characterization of our samples using transmission electron microscopy (TEM)
is needed to unveil the structure of the dislocations in this material.
• The production of a sample with high density of dislocations might allow us to
compare with the results obtained with our electrochemically-generated sample.
Past studies have compared the difference of dislocation generated when using
different techniques to introduce dislocations in a sample [16]. In a more
complete study we need to try different techniques for generating dislocations in
Pd, like ion bombardment, gas loading, plastic deformation, etc.
• Our suggestion that the observed behavior corresponds to a phase of nano-
dimensions could be extended to use other nano-systems. For example single
and multi-wall carbon nanotubes can be loaded with hydrogen [38] and their
properties studied in an effort to model a similar, easier to control nano-system.
There is not guarantee that this approach might work, but notice that the density
52
of hydride “nano-phase” could be much more concentrated in this case. There
would be only hydrogen trapped in the nanotube, that we hypothesize is
somewhat similar to hydrogen trapped in the cores of dislocations. The matrix of
the palladium would not be present, only the hydride itself. Hence, even if the
effects were weaker or different, this experiment would be a valuable addition for
comparative purposes.
• To summarize, we suggest a systematic study of the conditions and materials
required to increase the effect in our samples, so that stronger signal can be
obtained. We also suggest trying newer materials in an effort to better
understand the observed phenomena.
53
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56
APPENDIX 1. TABLE OF CONVERSION OF MAGNETIC UNITS
Extracted from [2].
Quantity Symbol Gaussian Unit Conversion Factor*
SI or MKS Unit
Magnetic Flux
Density, Magnetic
Induction
B Gauss (G) 10-4 Tesla (T), Wb/m2
Magnetic Flux Φ Maxwell (Mx),
G.cm2
10-8 Weber (Wb),
volt.sec(V.s)
Magnetic Field,
Magnetization
H Oersted (Oe) 103/4π A/m
Magnetization
(volume)
M emu/cm3 103 A/m
Magnetization
(volume)
M G 103/4π A/m
Mass
Magnetization σ, M emu/g 1
4π x 10-7
A.m2/kg
Wb.m/kg
Magnetic Moment M emu, erg/G 10-3 A.m2, (J/T)
Volume
Susceptibility χ dimensionless,
emu/cm3 4π
(4π)2 x 10-7
Dimensionless,
H/m, Wb/(A.m)
Mass Susceptibility χ cm3/g, emu/g 4π x 10-3
(4π)2 x 10-10
m3/kg, H.m2/kg
Molar Susceptibility χ cm3/mol, emu/mol 4π x 10-6
(4π)2 x 10-13
m3/mol, H.m2/mol
Permeability μ dimensionless 4π x 10-7 H/m, Wb/(A.m)
*Multiply the quantity in Gaussian units to convert to SI (e.g. 1G x 10-4T = 10-4 T).
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58
VITA
Carlos Henry Castaño Giraldo was born in 1973 to Hernando de Jesus Castaño
and Ofelia Margarita Giraldo, in the city of Rionegro, state of Antioquia in
Colombia, South America. Antioquia is the home state of one of the proudest
peoples of Colombia. Known themselves as Antioqueños or “Paisas”. Carlos
stayed at his hometown until he received the title of Electronic and Electric
Technician from the Industrial Technical Institute “Santiago de Arma” of Rionegro
in December 1989. Then he moved to Medellín the capital city of Antioquia,
where he studied Chemical Engineering at the Universidad Nacional de
Colombia, Sede Medellín. At the National University Carlos with some of his
fellow students formed the group for the study of astronomy “Astronal” where he
had his first research experiences studying the total solar eclipse of 1991 in
Colombia. The next year Astronal created an astronomy introductory course for
the Undergraduate College. In this course Carlos Henry had the opportunity of
teaching classes at college level to freshman students for several years. Carlos
graduated from the university as a chemical engineer with a minor in
electrochemistry in May 1998. On January 1999, Carlos came to the United
Stated and studied in the Norwalk Community Technical College (NCTC), in
Norwalk, CT. There while living at his sister’s house, he pursued his formal
English education working at the same time as a Math, Physics, Chemistry, and
Spanish tutor in the Tutoring Center of the NCTC. Finally on January 2000,
Carlos came to the University of Illinois at Urbana-Champaign under the advisory
and support of Prof. George H. Miley and started his MS education. During his
graduate years he was supported by multiple research assistantships provided
by Prof. Miley, by several teaching assistantships provided by the Department of
Nuclear, Plasma, and Radiological Engineering, and by one research
assistantship provided by Prof. Alexey Berzyadin, from which this work is
derived. Carlos is a student member of the Electrochemical Society, the
American Physical Society, and the Neutron Scattering Society of America.
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