ZERO-DIMENSIONAL MAGNETITE A Dissertation Presented to The Academic Faculty by Melissa ...
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His kind words and encouragement from day one have provided the . Figure 3.20: Optical Spectra of One to 6.7 nm (Fe3O4)&...
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ZERO-DIMENSIONAL MAGNETITE
A Dissertation Presented to The Academic Faculty
by
Melissa Gayle Arredondo
In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in Chemistry
Georgia Institute of Technology December 2006
ZERO-DIMENSIONAL MAGNETITE
Approved by: Dr. Robert L. Whetten, Advisor School of Chemistry Georgia Institute of Technology
Dr. Mostafa A. El-Sayed School of Chemistry Georgia Institute of Technology
Dr. Lawrence A. Bottomley School of Chemistry Georgia Institute of Technology
Dr. C. David Sherrill School of Chemistry Georgia Institute of Technology
Dr. Uzi Landman School of Physics Georgia Institute of Technology
Dr. Walter A. de Heer School of Physics Georgia Institute of Technology Date Approved: November 15, 2006
Pick a flower on earth and you move the farthest star. -Paul Dirac
Dedicado a mis abuelos, a mis padres, y a mi amor Ryan C. Price !
The simple beauty of a quantum system lies in its potentiality. Reality is waiting to occur, waiting for the system to evolve.
1
I have been successful at Georgia Tech due to the generosity of many people. I would like to sincerely thank the members of my committee for their time and patience; I know it has been trying. Dr .Mostafa El-Sayed was my first chemistry professor at the college level, and even though there were over 400 students in that class he still found a way to interact with me, and I’ll never forget this fact. Dr. David Sherrill was a brand new professor when I started in his group and provided a great foundation for my graduate career. Dr. Uzi Landman has been a very charismatic professor and a great teacher. I learned more than just condensed matter physics from all his classes and I sincerely appreciate all of our conversations about science and life in general we had over the years. Dr. Walt de Heer was a great neighbor for several years and I can still think in rhythm to the sound of vacuum pumps. He also shared a certain philosophy about how to work with undergrads that I utilized for the rest of my time as a teaching assistant. Dr. Larry Bottomley is responsible for the trip from California out into foreign territory, The South. His kind words and encouragement from day one have provided the backbone for my entire time here. And finally, the advisor to the doctoral candidate, Dr. Robert L. Whetten, your unique way of seeing things has changed the way I view the world and science in general. Please continue to save the world, one PhD at a time! I would also like to thank the other people from the Tech community that have been instrumental to my work, including Dr. Angus Wilkinson, Dr. Les Gelbaum, Dr. Alexi Marchenkov, Dr. Rick Moore, Dr. Robert Braga, Dr. Cam Tyson, and finally Ty Fife.
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Ty was my first friend at Tech; she seemed to immediately recognize my fish-out-ofwater feelings and went about fixing this by showing me horses. By the way, the gardenia you gave me is thriving! I have made many friends here and they have all added immensely to my quality of life including Mr. Russell Dondero, Dr. Bryan Herger, Dr. Christy Vestal, Man Hann, and Dr. Ed Valeev. Dr. Mutasem Sinnokrot, you were my first real student friend at Tech. Thanks for all of those quantum nights at the Waffle House, I they have paid off! To current and past members of the Whetten research group, Dr. Rich Wyrwas and James Bradshaw; you guys made life in the lab unique and fun (an understatement), from chips and dip to conspiracy theories, I’m still waiting to build the TOFCatMS. Dr. Sidney Gordon has been a constant in our group for over 3 years and provides a unique prospective no matter what the topic. Thank you all! My journey to grad school began with a simple conversation with Dr. David Brown at Cal Poly. My professors at Cal Poly were always very supportive of my quirky ways, Dr, Michael Keith, Dr, Charles Millner, Dr.Chevy Goldstein and the fantastic physics department, Dr. Peter Siegel, Dr. Mary Mogge, Dr. John Mallinckrodt, Dr. Roger Morehouse and my friend Marie Ramos. Dr. Glenn Kageyama gave me my first research project through the MBRS program, and Dr. Pamela Sperry was extremely helpful. I had a great set of friends at Cal Poly including Lloyd and Susanne Schenck and Dave Metzger, more quantum nights at Borders and Round Table.
0 I never would have found the strength to throw my books, clothes and saddle into my little white truck and drive 3000 miles without the overwhelming support of my family and friends. My parents have always encouraged my scientific endeavors, whether it be
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listening to the lifecycle of the blue gill repeatedly or fossil hunting when it was freezing outside, and also not ever laughing at me for loving Star Trek. I thank you! Rick Fliederman, I never EVER could have left California without you. You were the final support I needed and I left you with my most precious possession and you saved him. Thank you! I have been extremely fortunate to have a complete life outside of science, and this second life has enabled me to sleep peacefully at night and have plenty of things to love, Sox, Cary, Darrien, Repeat and Julian. To my friends at Lancaster Oaks; Chuck and Danny Wharton, you have provided me with a second family since mine was so far away. The importance of a solid foundation is tantamount to success and I found that at your farm. Laura, sanity is a precious thing, and I would have lost mine along ago if not for you. You and your horses provided shelter from the storm. Well the clouds have lifted and we are on our way to the Olympics! Coleen, thanks for all of the great conversations and advice. Sunday night hot bran mashes for everyone! So after all of this, I had a great support network, lots of encouragement, lifelong friends and yet I could have achieved nothing without you Ryan. You are the center of my fractal, from that first night out at Taco Bell, thru two broken ankles 3 plates and 18 screws, two horses and now two dogs, we can finally begin our lives. It is definitely good to be a quantum system, superposition is the way to go!
1 0
vii
TABLE OF CONTENTS Page ACKNOWLEDGEMENTS
v
LIST OF TABLES
xi
LIST OF FIGURES
xii
LIST OF SYMBOLS AND ABBREVIATIONS
xv
SUMMARY
xvii
CHAPTER 1
2
Introduction To Quantum Magnetism
1
1.1 History
1
1.2 Atomic Origins of Magnetism
4
1.3 Magnetic Fundamentals
4
1.3.1 Variables
5
1.3.2 Order, Structure, and Exchange
6
1.3.2.1 Paramagnetism
9
1.3.2.2 Ferromagnetism
10
1.3.2.3 Antiferromagnetism and Ferrimagnetism
10
1.3.2.4 Superparamagnetism and Domain Walls
13
1.4 Magnetic Characterization
16
1.5 References
24
Nanostructured Magnetic Systems
26
2.1 Classifications
26
2.1.1 Quantum Dots
27
2.1.2 Single Molecule Magnets
29
2.1.2.1 Quantum Effects
33
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2.2 Spinel Ferrites
37
2.2.1 Metal Ions
38
2.2.2 Iron Oxide Systems
40
2.3 Nanoparticle Characterization
46
2.3.1 Transmission Electron Microscopy (TEM)
46
2.3.2 Powder X-Ray Diffraction (XRD)
46
2.3.3 Matrix Assisted Laser Desorption Ionization MS (MALDI-MS)
48
2.3.4 Optical Spectroscopy
49
2.3.5 Vibrational Spectroscopy
49
2.3.6 Elemental and Thermogravimetric Analysis
49
2.3.7 Proton Nuclear Magnetic Resonance
50
2.3.8 Superconducting Quantum Interference Device Magnetometry
50
2.4 References 3
51
Iron Oxide Nanoparticcles with Sub-2.0 Nanometer Cores
54
3.1 Methods to Produces Fe3O4 Nanoclusters
54
3.2 Experimental Parameters to Synthesize Sub-2.0 nm Fe3O4 Clusters
59
3.2.1 Reaction Results
62
3.3 Characterization of Sub-2.0 nm Fe3O4 Nanoclusters
67
3.3.1 Size Dependent Characterization
67
3.3.1.1 Large Angle X-Ray Diffraction (LAXRD)
71
3.3.1.2 MALDI-MS
78
3.3.1.3 Elemental and Thermogravimetric Analysis
81
3.3.2 Physical Properties of Sub-2.0 nm Magnetite MPCs
88
3.3.2.1 Optical Spectroscopy
88
3.3.2.2 Infrared Spectroscopy
96
3.3.2.3 Proton Nuclear Magnetic Resonance
99
ix
3.3 Magnetic Properties of Sub-2.0 nm Fe3O4 Nanoclusters 3.3.3.1 Magnetic Data for Sub-2.0 nm Fe3O4 Nanoclusters
103 106
3.4 Conclusions and Future Work
123
3.5 References
124
APPENDICES
129 A. Magnetic Units
129
B. Common Mathematical Descriptions of Magnetic Behavior
130
C. Photon Energy Expressed in Various Units
140
x
LIST OF TABLES Page Table 2.1: Tabulated Single Molecule Magnets
31
Table 2.2: Conductivites of Spinel Ferrites and Iron
43
Table 3.1: Reaction Parameters for (Fe3O4)x(carboxylate)y MPC Production..
64
Table 3.2: Approximate Solublities for the Fe3O4 MPCs after Reprecipitation
66
Table 3.3: TEM Lattice Spacings of Fe3O4 MPCs
70
Table 3.4: Lattice Constants for Some Iron Oxides
72
Table 3.5: X-ray Diffraction Peaks for Synthetic Iron Oxides
73
Table 3.6: Mass Spectral Assignment of (Fe3O4)x(hexanoate)y MPCs
80
Table 3.7: Elemental Analysis of 2.6 nm Core (Fe3O4)x(oleate)y MPCs
81
Table 3.8: Compositions for (Fe3O4)x(carboxylate)y MPCs Synthesized
88
Table 3.9: Number of Atoms in the Cores of the Smallest Magnetite MPCs
93
Table 3.10: Saturation Magnetization for Colloidal Magnetite MPCs
105
Table 3.11: Core Volumes of (Fe3O4)x(carboxylate)y MPCs
106
Table 3.12:TB and Keff for (Fe3O4)x(carboxylate)y MPCs
109
Table 3.13:Magnetic Anisotropies per Cluster and per Iron Atom for the MPCs
111
Table 3.14 Saturation Magnetizations of (Fe3O4)x(carboxylate)y MPCs
121
xi
LIST OF FIGURES Page Figure 1.1: Magnetic Dipoles and Monopoles.
3
Figure 1.2: Spin Alignments Within the Four Principal Types of Magnetism
8
Figure 1.3: Superexchange in a Ferrimagnetic Metal-Oxide Molecule
11
Figure 1.4: Magnetic Susceptibiilty as a Function of Temperature for Ferrimagnets
12
Figure 1.5: Diagrams of a Bloch wall and a Neel Wall.
13
Figure 1.6: Multi-domain and Single Domain Ferromagnets.
14
Figure 1.7: Magnetic Susceptibiilty for the Three Types of Magnetic Materials
17
Figure 1.8: Reciprocal of Magnetic Susceptibility vs. Temperature for the Types of Magnetic Materials
18
Figure 1.9: Reciprocal of Magnetic Susceptibility vs. Temperature for Antiferromagnetism
19
Figure 1.10: Magnetic Hysteresis Loop for a Mult-idomain Magnetic Material.
20
Figure 1.11: Particle Coercivity as a Function of Diameter.
22
Figure 2.1: Electronic Density of States in 3,2,1 and 0 Dimensional Systems.
28
Figure 2.2: Energy Level Diagram for a S=10 Ground State.
30
Figure 2.3: Single and Multi-domain Size Regimes
32
Figure 2.4: Quantum Tunneling of Magnetization Hysteresis Loops for a Single Molecule Magnet
36
Figure 2.5: Unit Cell of a Spinel Ferrite
38
Figure 2.6: Bethe-Slater curve for Mn, Cr, Fe, Co, and Ni.
39
Figure 2.7: Splitting of the Five d Orbitals by an Octahedral Field.
41
Figure 2.8: Different Possible Electronic Configurations of a Fe2+ Ion.
41
Figure 2.9: Schematic Representation of Iron Electronic Energy Levels in Fe3O4
42
Figure 2.10: Electron Transfer between Octahedral Sites in Fe3O4.
43
Figure 2.11: Distorted Cubic Phase of Fe3O4 below Tv from Cation Ordering
44
xii
Figure 2.12: Spins of Fe3O4 Result in a Magnetic Moment Near High Spin Fe2+
45
Figure 2.13: Bulk Magnetite Crystal Forms.
45
Figure 3.1: Stages of Nucleation and Growth of Monodisperse Nanoparticles.
56
Figure 3.2: Method for Obtaining Magnetite Monolayer Protected Clusters.
58
Figure 3.3: High Resolution Tunneling Electron Microscopy of 6 nm Fe3O4
58
Figure 3.4: Synthetic Scheme for 1.3 nm (Fe3O4)x(hexanoate)y Clusters.
61
Figure 3.5: Transmission Electron Micrographs of ~2.0 nm (Fe3O4)x(octanoate)y.
68
Figure 3.6: Transmission Electron Micrographs of ~1.0 nm (Fe3O4)x(propionate)y.
69
Figure 3.7: Selected Area Diffraction of (Fe3O4)x(octanoate)y.
70
Figure 3.8: Gaussian Peaks Fit to X-Ray Diffraction Data for ~6.7 nm Fe3O4.
72
Figure 3.9: X-Ray Diffraction Data for one to 6.7 nm (Fe3O4)x(carboxylate)y MPCs.
75
Figure 3.10: Increased Relative Intensity of 111 Diffraction Peak Below 2.0 nm
76
Figure 3.11: (Fe3O4)x(propionate)y Core Diameter as A Function of Synthesis Temperature
77
Figure 3.12: MALDI-MS of (Fe3O4)8(propionate)4 MPCs .
79
Figure 3.13: MALDI-MS of (Fe3O4)16(propionate)60 MPCs .
80
Figure 3.14: Thermogravimetric Analysis Plot of 2.6 nm Core (Fe3O4)x(oleate)y.
82
Figure 3.15: TGA Plot of 1.0 nm Core (Fe3O4)8(propionate)4.
84
Figure 3.16: TGA Plot of 1.3 nm Core (Fe3O4)16(hexanoate)59.
85
Figure 3.17: TGA Plot of 2.0 nm Core (Fe3O4)56(octanoate)71.
86
Figure 3.18: TGA Plot of 6.8 nm Core (Fe3O4)x(propionate)y.
87
Figure 3.19: Optical Absorbance Spectra of Maghemite and Magnetite.
90
Figure 3.20: Optical Spectra of One to 6.7 nm (Fe3O4)x(carboxylate)y MPCs.
91
Figure 3.21: NIR-Optical Region of One to Two nm (Fe3O4)x(carboxylate)y MPCs.
93
Figure 3.22: Differential Optical Spectra of (Fe3O4)x(carboxylate)y MPCs.
95
Figure 3.23: IR Spectra of ~11 nm (Fe3O4)x(oleate)y and Oleic Acid.
96
Figure 3.24: IR Spectra of One to Two nm (Fe3O4)x(carboxylate)y MPCs.
98
xiii
Figure 3.25:1H-NMR of One to 2.4 nm Core (Fe3O4)x(carboxylate)y.
101
Figure 3.26: Aliphatic Region of 1H-NMR Spectra.
102
Figure 3.27: Temperature Dependence of Zero Field Susceptibility of 2.0to 6.7 nm (Fe3O4)x(carboxylate)y MPCs. 107 Figure 3.28: Differential Susceptibility vs. Temperature for 2.0 to 6.7 nm (Fe3O4)x(carboxylate)y MPCs.
108
Figure 3.29: Field Dependent Magnetization of 6.8 nm Fe3O4 MPCs at 5 K.
113
Figure 3.30: Langevin Fit Failure for Non-Magnetically Saturated 2.0 nm Fe3O4.
114
Figure 3.31: Field Dependent Magnetization of 2.0 nm Fe3O4 (2, 5, 100, and 300 K) 115 Figure 3.32: Field Dependent Magnetization of 2.0 nm Fe3O4 at 5 K with Remnant Magnetization and Coercivity. 116 Figure 3.33: Field Dependent Magnetization of 1.3 nm Fe3O4 (5 and 100 K).
117
Figure 3.34: Field Dependent Magnetization of 1.0 nm Fe3O4 (2,5 and 100 K).
118
Figure 3.35: Size Dependence of Remnant Magnetization and Coercivity of Fe3O4 MPCs from 1.3 to 3.6 nm. 120 Figure 3.36: Saturation Magnetization in PB per Fe vs. (core radius)-1 at T= 5 K.
xiv
122
LIST OF SYMBOLS AND ABBREVIATIONS EA
elemental analysis
FTIR
Fourier Transform Infrared
FWHM
full width at half maximum
Hc
magnetic coercivity
1
H-NMR
(HR)TEM
proton nuclear magnetic resonance (high resolution) transmission electron microscopy
IVCT
intervalence charge transfer
kB
Boltzmann’s Constant
Keff
magnetic anisotropy
(LA)XRD
(large angle) x-ray diffraction
LMCT
ligand to metal charge transfer
MR
remnant magnetization
Ms
saturation magnetization
MS MALDI
mass spectrometry matrix-assisted laser desorption ionization
MPC(s)
monolayer protected cluster(s)
nm
nanometer
NP(s)
nanoparticle(s)
QTM
quantum tunneling of magnetization
SAED
selected area electron diffraction
SMM
single molecule magnet
SPM
superparamagnetic
SQUID
superconducting quantum interference device
TB
blocking temperature
TGA
thermogravimetric analysis
xv
LIST OF SYMBOLS AND ABBREVIATIONS (CONTINUED) F
magnetic susceptibility
PB
Bohr Magneton
xvi
SUMMARY
Low-dimensional magnetic systems are of interest due to several new effects and modifications that occur at sizes below the average domain grain boundary within the bulk material. Molecule-like magnetite (Fe3O4) nanoparticles, with sizes ranging from one to two nm were synthesized and characterized in order to investigate new properties arising from quantum size effects. These small systems will provide opportunities to investigate magnetism of zero-dimension systems. A zero-dimensional object is usually called a quantum dot or artificial atom because its electronic states are few and sharply separated in energy, resembling those within an atom. Since the surface to volume ratio is the highest for zero-dimensional systems, most of the changes to magnetic behavior will be observed in ultra-fine magnetic particles. Chemically functional magnetic nanoparticles, comprised of a Fe3O4 magnetite core encased in a thin aliphatic carboxylate, have been prepared by sequential high temperature decomposition of organometallic compounds in a coordinating solvent. In this work, aliphatic carboxylic acid chain length, reaction temperature and duration were varied to produce small core diameters. In order to correlate size effects with changes in particle formation, it is important to have a through understanding of the structural components. This includes studies of the core size, surface effects, decomposition, electronic properties and magnetic behavior. Quantum size effects were observed in the (Fe3O4)X(carboxylate)Y monolayer protected clusters (MPCs) when the average core diameter was 2.0 nm, evidenced by a blue shifted absorbance band maxima, suggesting the onset of quantum confinement. These (Fe3O4)X(carboxylate)Y MPCs also posses a complex interplay between surface and finite size effects, which govern the magnetic properties of these zero-dimensional systems. These MPCs are all superparamagnetic above their blocking temperatures with total magnetic anisotropy values greater than the bulk value due to an xvii
increase in surface and magnetocrystalline anisotropy. A non-linear decrease in saturation magnetization (MS) (ȝB per cluster) as a function of the reciprocal of core radius have been attributed to surface effects such as a magnetically inactive layer or an increase in spin disorder as core diameter decreases. The reduced core dimensions of these MPCs make them ideal candidates for further investigation of quantum magnetic systems. Chapter 1 provides a brief introduction to magnetic properties on the quantum scale and methods to examine those properties. Chapter 2 is an introduction to nanostructured magnetic systems including metals and oxides. Specific instrumentation and methodologies needed to provide insight about nanoparticles are discussed. Chapter 3 is an investigation of zero-dimensional magnetite monolayer protected clusters. The aim of this research is the preparation, isolation, and characterization of sub-colloidal (diameter 2.0 nm) magnetite (Fe3O4) nanocrystals. The synthetic procedures within are the first reports of 1.0 – 2.0 nm (Fe3O4)X(carboxylate)y materials, approaching the scale of single-molecule magnets.. Appendix A includes some of the common units and formulas used in magnetism while Appendix B summarizes the Langevin model of paramagnetism and how it relates to quantum effects, and Appendix C presents a table of values pertaining to photon energies in various units.
xviii
CHAPTER 1 INTRODUCTION TO QUANTUM MAGNETISM
The magnetic nature of matter has been an intriguing problem for millennia and a thorough understanding of it has yet to be achieved. While our knowledge of the basics of magnetism is well established, several interesting questions remain, ranging from the overall magnetic behavior of the universe down to the nature of fundamental particles. Low-dimensional magnetic systems are of interest due to the fact that as the grain or domain region decreases past the characteristic length scale associated with a specific property; several new effects and modifications can occur. Effective manipulation of these new properties requires a better understanding of the relationship between overall particle size and the arising effect. Magnetism emerges from interactions at the smallest measurable scales from the quantum regime, arising from electronic and nuclear interactions.
1.1 History Ancient Greek philosophers realized the value of the magnetic iron ore FeOFe2O3, and hypothesized on its origins. Throughout recorded history numerous references to the Loadstone occur worldwide, from the English Renaissance philosopher William Gilbert and his work De Magnete1 published in 1600 to the more modern approaches of Maxwell, Poisson and Faraday. 2 One thing is certain: many ideas built upon each other in order to mathematically describe magnetism. When the modern ideas of quantum mechanics were developed in the early twentieth century, physicists rapidly developed models for magnetism based on descriptions of systems that were not considered “bulk”. Effects of fields and their
1
sources became the area of interest. In 1907, Pierre Weiss assumed that interactions between magnetic molecules could be described by a molecular field3, however the exact origin of that field was undetermined at that time. Despite the centuries old determination that magnetic materials have dipoles, it was not until1931 that Paul Dirac proved mathematically the existence of a monopole, illustrated in Figure 1.1. He combined electricity and magnetism reminiscent of the work of the 18th century scholars, with magnetic materials consisting of combinations of north and south poles analogous to positive and negative electrical charges. The monopole would explain the quantization of the electric charge, which follows from the existence of at least one free magnetic charge.4 He established the essential relationship between the elementary electric charge e and the basic magnetic charge g
eg
n!c / 2
where n is an integer, n = 1,2,… The magnetic charge is g
gD
!c / 2 e
(1)
ng D ;
68.5e and is called the unit Dirac charge. The existence of even one
monopole in the universe would be enough to ensure the quantization of electricity. Unfortunately, to date, experimental evidence of the monopole has eluded high-energy physicists. The lack of symmetry between electric and magnetic fields is one of the most profound problems in modern physical research, and work continues on it to this day. Many examples can be found to illustrate the close link between the fundamental physics of magnetic phenomena and their technological applications. As material boundaries continue to diminish, the physics that occur at those reduced dimensions become increasingly important. One can only imagine what Dirac would have achieved with just a few of the tools available to the scientific communities of today.
2
(a)
(b)
(c)
Figure 1.1. (a) A small bar magnet5 has properties analogous to those of the electric dipole (two electric charges, one positive and one negative, separated by a small distance). It is now possible to imagine the magnetic dipole as consisting of two monopoles of opposite charge. (b) Origin of magnetic dipoles, the spin of the electron produces a magnetic field with a direction dependent on the quantum number ms. Electrons orbiting around the nucleus create a magnetic field around the atom. (c) Electric field configurations of point particles.6
3
1.2 Atomic Origins of Magnetism The magnetic behavior of materials can be traced to the structure of atoms. Many studies of magnetism have focused on atoms or ions of transition state metals such as iron, cobalt and nickel. In these instances, electron spins on atomic orbitals are the main contributors to magnetism. With these interactions in mind, traditional magnetism can be thought of as “atomic magnetism”. The motion of the electron about the nucleus produces a magnetic dipole moment, similar to the electric dipole that consists of two opposite charges separated by distance. Based on this assumption, it is feasible that a magnetic dipole could be thought of in terms of the Dirac monopole indicated in Figure 1.1. While magnetism is the result of moving charges, orbital and spin motion of electrons, nuclear effects also contribute. An example of nuclear effects is evident in solid He3, however they will not be considered in this work.
1.3 Magnetic Fundamentals Perhaps the most important contribution to the understanding of magnetism is that of James Maxwell. In his work, A Treatise on Electricity and Magnetism - 1873, a mathematical description of electromagnetic fields and their interactions with matter is described.7 The most useful formulation of Maxwell’s equations is the introduction of the vector potential A(r, t) in terms of the magnetic field H(r, t) and the magnetization M(r, t) as
uA
H 4SM
B
(2)
The vector B, flux density or magnetic induction, is defined as the curl of A, and is solenoid in nature. In cgs, the units of B, H, and M are essentially the same and equation (2) is more commonly viewed as
4
H 4ʌM
B
(3)
However the magnetic field vector H may be introduced by expressing the magnetic field in a vacuum as
Bo
ȝoH
(4)
with P o the permeability of vacuum. Again with the conversion of units
B
ȝ o H M
Bo P oM
(5)
is an important relationship used to describe the magnetic susceptibility F of a material,
F
Po MB
M
H
(6)
where magnetic susceptibility is the quantitative measure of the response of a material to an applied magnetic field. Magnetic interactions are typically characterized by their responses to variations in temperature and the applied magnetic field; therefore susceptibility is an important parameter to describe the general classes of magnetic interactions that arise due to order, structure and exchange. 1.3.1 Variables The cgs unit of the magnetic field H is the oersted; to convert to SI, 1 Oe= (103/4S) Am-1. The unit of the field B (3) is numerically and dimensionally the same, but it is a gauss (G). The related SI unit is 1 Tesla { 104 G. Weak fields have been traditionally expressed in G, while standard fields are usually in units of Tesla.
5
This section provided the basic equations used to describe the effects of an applied magnetic field, and they can be presented in either SI or CGS-emu. It is important to clearly distinguish which system is in use, otherwise parameters such as susceptibility data can be off for example, by a multiple of 4S. A more complete description of common units and equations used can be found in appendix A. 1.3.2
Order, Structure and Exchange In any magnetic material, unpaired electrons on atoms produce magnetic
moments. The alignment, or mis-alignment, of these moments determines the type of magnetic structure that the material will possess. The most important parameter for determining the magnetic structure is the exchange overlap integral of the electronic wavefunctions on neighboring atoms.8 This overlap depends on neighboring atomic distances, which are subject to size effects and or crystal lattice parameters. If the atoms are sufficiently near to each other then the potential to produce long range order exists. All materials are affected in some way by a magnetic field, and depending on this interaction they can be classified into one of several categories. Opinions vary on the methods for producing these classes, however all materials fit into one of three basic classifications, and subsets within. 1. Paramagnetism: interaction is weakly attractive toward a magnetic pole 2. Ferromagnetism: interaction is strongly attractive toward a magnetic pole. 3. Diamagnetism: interaction is weakly repulsive from a magnetic pole. These magnetic states are shown schematically in Figure 1.2.
6
All materials have some degree of diamagnetism, evident in the Hamiltonian (H) of an atom in a magnetic field that contains a paramagnetic term and a diamagnetic term. Appendix B provides a mathematical description for these terms. Diamagnetism occurs through a deformation of the electric charge distribution when a field is applied and it disappears when the field is removed. A diamagnetic material is further distinguished from all others due to the fact that its magnetic susceptibility (equation 6) is negative. This susceptibility is usually independent of both temperature and applied field strength for purely diamagnetic materials. Diamagnetic materials have characteristics that arise from a fundamental principle of electromagnetism called Lenz’s Law, which states that when a conducting loop is acted upon by an applied magnetic field a current is induced in the loop that counteracts the change in the field.9 The electron orbits are resistanceless, so the induced current remains after the field has been applied and is constant. This is also the case for superconductors, which are perfectly diamagnetic ( F = -1) and therefore also completely exclude an applied field.
7
Figure 1.2. The alignment of magnetic moments at absolute zero for the four principle types of magnetism. (a) Paramagnetism has no alignment of adjacent moments, (b) Ferromagnets show parallel alignment of moments. (c) Antiferromagnets exhibit antiparallel alignments. (d) Ferrimagnets consist of two magnetic spins of different strength.
8
1.3.2.1
Paramagnetism Paramagnetism occurs when the atomic, ionic, or molecular constituents
have a nonzero magnetic moment, allowing the applied field to align the moments and create a positive susceptibility. Each individual electron spin is independent from its neighbors. These spins, however, can be easily aligned by the applied magnetic field. Removal of the field will allow for an eventual relaxation of the aligned states back to the random distribution of the moments. Typical paramagnets contain at least one unpaired electron resulting in an unbalanced angular momentum, orbital or spin. Appendix B provides a further explanation. Another important feature of paramagnets arises from a temperature dependent behavior. The alignment of spins by an external magnetic field is impeded by random thermal interactions. Pierre Curie10 studied the thermal properties of magnetic materials, where he noted that the magnetic susceptibility (from equation 6) for a paramagnet is inversely dependent on temperature.
F
M H o0 H lim
C T
(7)
Curie’s constant C is characteristic of the atomic or molecular species, and temperature T starts at absolute zero. Equation 7 is known as the Curie Law. The Curie law is only valid when H
kT
is small. Field dependence for a paramagnet is described by the
Brillouin function without regard to the magnitude of H an explanation.
9
kT
. Appendix B again provides
1.3.2.2
Ferromagnetism
The appearance of spontaneous order at low temperatures is a fundamental phenomenon of condensed matter physics. Ferromagnets, antiferromagnets, liquid crystals and superconductors are all ordered phases. These ordered phases all share temperature dependence such that some relevant physical property will exhibit a difference above and below a critical temperature TC. For each phase one can define an order parameter which is zero for T > TC and non-zero for T < TC. This parameter can now be used to determine whether a system is ordered or not.11 Ferromagnets are characterized by the parallel alignment of adjacent magnetic spins resulting in a large magnetic moment. Ferromagnets are rare because alignment of adjacent magnetic spins can only occur if there is zero quantum mechanical overlap between the spin orbitals. Additionally, long range ordering that occurs with ferromagnets is a function of the domains that occur within a sample. Unlike paramagnets, ferromagnets exhibit a net magnetic moment in the absence of an applied magnetic field. The most common examples of ferromagnets include nickel, cobalt, iron and some of the rare earths (gadolinium, dysprosium).
1.3.2.3
Antiferromagnetism and Ferrimagnetism
In an antiferromagnet, exchange coupling exists between neighboring moments resulting in an antiparallel alignment and thus a material with no net magnetic moment. At absolute zero, antiferromagnets behave like diamagnets when subjected to an applied field. However, as the temperature increases, the antiparallel alignment of the magnetic spins becomes vulnerable to thermal fluctuations. The susceptibility F will increase until it reaches a temperature characteristic of the material where it will decline sharply. This abrupt change is indicative of a transformation from antiferromagnetism to
10
paramagnetism, and is known as the Néel temperature (TN). Below the Néel temperature, the system is ordered. Many antiferromagnetic materials are ionic compounds such as metallic oxides, chlorides and sulfides. The exchange interaction in antiferromagnetic ionic solids occurs indirectly through a mechanism called superexchange. This is dependent on the simultaneous covalent bonding of the metal cations with their nonmetallic anions. The nearest neighbors to the metallic ions, which contain the magnetic moments, are anions such as O2-, Cl-, and S2- that act as the bridges for the spin states, shown in Figure 1.3.
Figure 1.3. Superexchange with a metal-oxide molecule with the metal ions each with spin ½ and the ligand oxygen spin zero (but charge of –2e).2
Ferrimagnets similarly use the superexchange mechanism to link two sublattices to create an antiparallel alignment of moments. However, ferrimagnets differ from antiferromagnets because the ions on the sublattices are not equal and hence do not cancel. This difference in spin magnitude results in a net magnetic moment in the absence of an applied magnetic field. Above the Curie temperature, the spontaneous magnetization can be eliminated by thermal energy resulting in paramagnetism. Figure 1.4 depicts changes in magnetic susceptibility and magnetization as a function of temperature.
11
In addition to the basic classes of magnetism, many subsets exist. Ordering and exchange mechanisms, as well as dimensionality can produce subtle variations in magnetic behavior.
Figure 1.4. All magnetic materials behave as paramagnets at high temperatures because the great increase in thermal energy will overcome spin alignment.12 (a) The susceptibility F declines sharply as antiferromagnetism changes to a non-ordered paramagnetic state. The switch from paramagnetism to ferro as the temperature is decreased, (b) the susceptibility F at the Curie temperature and (c) magnetization M.
12
1.3.2.4
Superparamagnetism and Domain Walls
Ferromagnetic materials exhibit a long-range ordering phenomenon at the atomic level that causes the unpaired electron spins to line up parallel with each other in a region called a domain. In 1906 Weiss proposed that these domains would align such that the total magnetic moment of the material was minimized.3 The result is that within ferromagnet domains, the local magnetization for each domain reaches the saturation value. Between each domain is a boundary called the domain wall. These domain walls are classified by the angle of magnetization that will exist between them with the most common type of boundary being the Bloch wall. The Bloch wall consists of a 180° separation of the domain magnetization. The magnetization rotates in a plane parallel to the plane of the wall. The Néel wall consists of a 90° rotation perpendicular to the plane of the wall. Both types are shown in Figure 1.5.
Figure 1.5. (a) A Bloch wall, (b) A Néel wall.11
13
Figure 1.6. The random orientation of domains in a two dimensional ferromagnet is exhibited in (a), while (b) show the coherent orientation of spins in a single domain particle.
14
Energy is required to spatially orient spins within a magnetic domain with those in neighboring domains, however magnetocrystalline anisotropy interactions prevent removing or lowering domain walls by an external field. This results in a directional dependence of the measured susceptibility within the material. Crystalline anisotropy is intrinsic to the material, and the saturation value will differ for each crystalline direction. These directions are commonly referred to as the easy and hard axis. The physical origin of magnetocrystalline anisotropy is the result of electron spin coupling and the resulting magnetic moment in turn couples to the lattice. For a ferromagnet the magnetic domains preferentially lie along the easy axis. For a nanostructured magnetic system, a critical dimension exists at which it is so energetically unfavorable for domain walls to exist; therefore the system is a single domain. This reduction in particle size also allows for the magnetic anisotropy energy to be influenced by thermal energy, resulting in a superparamagnetic state. Magnetization reversal in a single domain particle can only occur via spin rotation, thus single domain particles generally have a higher coercivity value than multi-domain particles simply because it is much more difficult to rotate magnetization than it is to overcome a domain wall. Stoner and Wolfarth13 described a method for calculating the magnetization curve for a single domain particle with uniaxial anisotropy. The response of MS to an applied field is directly affected by the anisotropy (shape or crystalline) and for coherent rotation can be described by,
Ea
KV sin 2 T
(8)
where Ea is the anisotropic energy, K is the magnetic anisotropy for a particle and V is the particle volume. With decreasing particle size, KV decreases until the thermal energy kT can disrupt the total magnetic moment of the particle. The moment can then
15
freely respond to an applied field. This resembles the normal paramagnetic behavior, but has a large magnetic moment, hence the term superparamagnetism. Particles that exhibit superparamagnetic behavior have a large saturation magnetization but no remanence or coercivity. Hysteresis will appear and superparamagnetism disappears when particles of a certain size are cooled to a particular temperature or when the particle size at a constant temperature increases beyond a particular diameter. 1.4
Magnetic Characterization
The magnetic interactions described in the previous sections are quantified by measuring the magnetic response of the material to controlled changes in an applied magnetic field at a given temperature. Depending on how they respond, the specific magnetic properties and overall magnetic strength can be identified and quantified. As described previously, all magnetic materials can behave as paramagnets at high enough temperatures due simply to an overwhelming increase in the thermal energy that randomizes all spins. The critical temperature TC is the onset of magnetic ordering and is a function of the material. Temperatures above and below TC are of interest because magnetic behavior in these regions can change with particle size. The Curie law (equation 7) describes temperature dependence in paramagnetic materials. Magnetic susceptibility quantitatively measures the response of a material to an applied field. An example of typical plots for a paramagnet, ferromagnet and an antiferromagnet are illustrated in Figure 1.7. There does not appear to be much difference between the para and ferromagnets, however the antiferromagnet has an interesting feature. Applying a magnetic field to an antiferromagnet at temperatures below TN is more complicated than the case of a ferromagnet below TC due to the direction in which the magnetic field is applied. There is no longer an energetic
16
advantage for the moments to line up along the field because any energy saving on one sublattice will be cancelled by the energy cost for the other sublattice, if the magnetization on the two sublattices is equal and opposite.11 The formation of the peak is due to the direction of the field as either parallel or perpendicular to the magnetization of one of the sublattices. The shape of the peak maximum suggests dimensionality of the interactions, with one and two-dimensional antiferromagnets producing a rounded maximum and three-dimensional structures producing a sharper peak.
Figure 1.7. Magnetic susceptibility as a function of temperature for three types of magnetic materials.14
For a ferromagnetic material the temperature dependence deviates from the Curie law, and follows a slight modification known as the Curie-Weiss law
F
C T T
(9)
where ș is the Weiss constant. Figure 1.8 is a plot of inverse susceptibility versus temperature for the three types of materials previously discussed. An ideal paramagnet has a linear relationship that intersects zero as defined by the Curie law (equation 7).
17
The other types of materials exhibit cooperative magnetic effects. The ferro and antiferromagnetic materials exhibit opposite deviations.
Figure 1.8. Plot of inverse susceptibility as a function of temperature for three type of magnetic materials14.
At high enough temperatures all material behave linearly since thermal energy can overcome any magnetic interaction. Positive Weiss constants indicate ferromagnetic interactions at sufficiently low temperatures, but it can be negative for antiferromagnets. If C is constant (equation 9), as indicated in Figure 1.9, then the straight line intercept of the abscissa will occur at T= ș.
18
Figure 1.9. Plot of inverse susceptibility as a function of temperature for an antiferromagnetic material illustration the Curie-Weiss law, and negative value for the Weiss constant ș12.
Another feature that is commonly used to describe the multidomain properties of magnetic materials is how they respond in an applied field. Hysteresis arises from rearrangement of the domain walls either through displacement, pinning, nucleation or rotation.15 An ideal hysteresis (M versus H) loop for a multidomain material is depicted in Figure 1.10. The remnant magnetization (Mr) and the coercive field (HC) typically define the hysteresis of a material. The hysteresis or width of the loop results from wall pinning or nucleation or both. A direct measurement of these effects is HC, the reverse field necessary to reduce M to zero in the descending loop. Remnant magnetization (Mr) is obtained by applying and removing a large magnetic field and represents the ability of a multidomain material to exhibit spontaneous magnetism. The saturation magnetization is the maximum induced magnetic moment that can be obtained in a magnetic field (MS); beyond this field no further increase in magnetization occurs. The difference between
19
spontaneous magnetization and the saturation magnetization has to do with magnetic domains. Saturation magnetization (MS) is an intrinsic property, independent of particle size but dependent on temperature. At large size, particles have many domains, thus magnetic reversal is dominated by domain wall motion, which energetically is not too difficult, and therefore coercivity is low. When a particle continues to decrease in size the coercivity also continues to decrease until the single domain limit is achieved. The largest values for HC occur at the single domain size and then gradually decrease due to thermal activation over anisotropy barriers.9 At the superparamagnetic limit HC = 0, as viewed in Figure 1.11.
Figure 1.10. Hysteresis loop for a multidomain magnetic material. MS is the magnetic saturation limit, Mr is the remnant magnetization at H=0, HC is the coercivity.
20
Figure 1.11. Particle coercivity versus diameter size. DSP is the superparamagnetic size and DS is for a single domain particle.
As a ferromagnetic particle reaches the superparamagnetic limit, the direction of the magnetic moment becomes unstable and changes direction, influenced by time and temperature. The experimental criteria for superparamagnetism are:17-18 1. The magnetization curve does not show hysteresis 2. The magnetization does not saturate even at high applied fields 3. Irreversibility appears below the blocking temperature. The anisotropy energy KV (equation 8) can be represented as an energy barrier to the total spin reorientation as illustrated in Figure 1.12.
21
Figure 1.12. The energy density of a magnetic particle contains the term K sin2ș (equation 8). The energy will be at a minimum when ș = 0 or S .11 The probability for jumping this energy barrier is proportional to the Boltzman factor. Néel16 calculated the rate for the magnetic vector of a single domain to overcome the energy barrier. The relaxation time W of the moment on a particle is given by
W
W 0e
KV
kT
(10)
where W 0 is considered an attempt timescale of ~10-9 s. At high temperatures the moments on the particles are able to fluctuate quickly. The fluctuations will slow down as temperature decreases ( W increases). If W becomes much longer than the measuring time t used by a particular measuring instrument then the particle moments are considered blocked.
22
The blocking temperature TB is given by
TB
and if W ! Dt and D
KV
k b ln(Dt
W0
(11)
)
100 s then each magnetic particle will be locked into one of its
two minima11. The blocking temperature TB is the temperature at which the moments are able move over the barrier. Because of the logarithmic dependence on Dt
W 0 , any
D , W 0 or t can be changed by a few orders of magnitude with only a small change to TB. The most common time used is t =100 s and Néel’s W 0 = 10-9 s, resulting in an equation for the critical volume,
VSP
25k bT K
.
(12)
A particle with a volume smaller than equation 12 will behave superparamagnetically on a 100 s time scale.18 The previous sections are an attempt to outline physics describing nanoscale magnetic materials. It is no way a comprehensive review, however for the purpose of this work is sufficient. The basic ideas presented here are expanded in Chapter 2, specifically utilizing spinel ferrite nanoparticles as examples.
23
1.5 References [1]
W. Gilbert, De Magnete,(1600), translation, Gilbert Club, London (1900), rev.ed.
[2]
Daniel C. Mattis, The Theory of Magnetism Made Simple, World Scientific Publishing, (2006)
[3]
P.Weiss, J. de Phys. 6(4), 661 (1907)
[4]
P.A.M. Dirac, "Quantized singularities in the electromagnetic field" Proc. Royal Soc. London, A133, 60–72, (1931)
[5]
R. Nave, http://hyperphysics.phy-astr.gsu.edu/ May 10 (2006)
[6]
J.Song, J. Undergrad. Sci. 3: 47-55, (1996)
[7]
J.C. Maxwell, A Treatise on Electricity and Magnetism, (1873), Dover, New York (1953)
[8]
Bekir Aktas, Nanostructred Magnetic Materials and their Applications, Springer (2001)
[9]
C.M. Sorensen, Nanoscale Materials in Chemistry, Wiley and Sons Inc. (2001)
[10]
P.Curie, Ann.Chim.Phys. 5(7), 289 (1895)
[11]
S. Blundell, Magnetism in Condensed Matter, Oxford University Press,(2001)
[12]
Adapted from A.F. Orchard, Magnetochemistry,Oxford Universitry Press,(2003)
[13]
E.C. Stoner, E.P.Wohlfarth, Phil. Trans. Of the Royal Society A, 240, 599,(1948)
[14]
Adapted from J.Maurer, PhD Thesis, California Institute of Technology,(2003)
[15] D. Dunlop, O.Ozdemir, Rock Magnetism Fundamentals and Frontiers, Cambridge University Press, (1997)
24
[16]
L. Néel, Ann. Geophys (C.N.R.S), 5, 99, (1949)
[17] G. Kataby,Y. Koltypin, A. Ulman, I. Felner, A. Gedanken, “ Blocking Temperatures of Amorphous Iron Nanoparticles Coated by Various Surfactants,” Appl. Surface Science, 201, 191-195, (2002) [18] C.P. Bean, J.D. Livingston, “Superparamagnetism,”J. Appl. Phys., 30,1205, (1959) [19]
B.D. Cullity, Introduction to Magnetic Materials, Addison-Wesley,(1972)
[20] R.C. O’Handley, Modern Magnetic Materials: Principles and Applications, Wiley & Sons, New York, (2000) [21] C. Kittel, Introduction to Solid State Physics 8th ed. Wiley & Sons, (2004)
25
CHAPTER 2 NANOSTRUCTURED MAGNETIC SYSTEMS
Advances in several research areas have increased interest in nano-scale magnetism. Improved material syntheses at sizes below magnetic domain scales have opened the possibility for creating materials with new magnetic properties. Example systems include nanoclusters, quantum dots, superlattices, tunneling devices, and single-molecule magnets. Sample characterization technique advances now allow detailed exploration of structure-property relationships that might arise in nanostructured magnetic systems. This chapter entails the magnetic phenomena that may occur in zerodimensional magnetite, also known as quantum dots. 2.1 Classifications In 1959 physicist Richard P. Feynman1 gave his famous lecture about what could be construed as the future interaction of quantum physics and chemistry. He spoke eloquently about a new problem that occurs when matter is reduced to the smallest sizes, “Atoms on a small scale behave like nothing on a large scale, for they satisfy the laws of quantum mechanics”. It is this idea that is the basis for today’s interest in nanotechnology. The driving force is that for every change in composition or size at reduced dimensions, new physical and chemical properties can emerge. The terminology used to describe these new small systems, unfortunately tends to vary in the literature, resulting in confusion similar to that which occurs when units are given as a combination of SI and CGS. Kenneth J. Klabunde2 suggests some boundaries that will suffice for this work. Cluster: A collection of units (atoms or reactive molecules) of up to about 50 units. Colloid: A stable liquid phase containing particles in the 1-1000 nm. For the rest of this thesis, anything over 3 nm in diameter will be considered a colloid.
26
Nanoparticle,NP: A solid particle in the 1-1000 nm range that can be noncrystalline, an aggregate of crystallites, or a single crystal. Nanocrystal,NC: A solid particle that is a single crystal in the nanometer range. Quantum Dot: A particle that exhibits a size quantization effect in at least one dimension. Normally scaling is thought of as an isotropic scale reduction in three dimensions.3 Scaling can also be accomplished in one or two dimensions, for example scaling of a cube to a two-dimensional (2D) well or to a one-dimensional (1D) wire. Zerodimensional (0D) is a term used to describe an object limited in all three dimensions. A 2D film can behave as a quantum well for spin carriers. These spin carriers are reflected by the walls of the well and their wave functions interfere to form a standing wave with discrete energy levels.4 Figure 2.1 illustrates the changes in the density of states for these materials. 2.1.1 Quantum Dots A zero-dimensional object is usually called a quantum dot or artificial atom because its electronic states are few and sharply separated in energy, resembling the electronic states of an atom3. Since the surface to volume ratio is the highest for zerodimensional systems, significant changes to magnetic behavior should be observed in ultra-fine magnetic particles. The smallest magnetic particles are single-molecule magnets and clusters with finite numbers of units. Typical quantum dot behavior is reached only in the region of a few nanometers, with 5.0 nanometers being a general estimate for most materials.5 In the early 80’s, the realization of zero-dimensional quantum confinement was just beginning.6 Cadmium selenide with core sizes < 10 nm were found to exhibit new properties due to electron confinement. While semiconductor research has a long history, it was not until the early 90’s that magnetism in a purely artificial system was extensively studied.7
27
Figure 2.1. Electronic density of states for systems with 3,2,1 and 0 degrees of freedom for electron propagation. Systems with 2,1 and 0 degrees of freedom are generally referred to as quantum wells, wires and dots, respectively.
28
These magnetic quantum dots or molecular nanomagnets are comprised of large molecules that have a finite number of magnetic centers and possess magnetic properties intermediate between those of isolated paramagnets and bulk magnets. They show both magnetic hysteresis as a bulk magnet, yet are small enough to exhibit quantum effects8.
2.1.2 Single Molecule Magnets In the early 80’s while quantum size effects within II-VI semiconductors were being intensely studied, Lis reported a structure of a dodecanuclear manganese cluster with the formula [Mn12O12(CO2CH3)16· 4(H2O) · 2(HO2CCH3)], now known as Mn12Ac. 9 At the time of publication it was not known that the nature of the ground state was a high spin (S=10) system. It was not until 19937 that this molecule was reported to have a magnetization relaxation time following an exponential rate (equation 10) at low temperatures. This relaxation time is on the order of two months at 2K. Under these conditions a single molecule magnet (SMM) becomes like a tiny magnet due to its ability to retain magnetization for days after being magnetized by an applied field.10 These molecules possess magnetic hysteresis, the main condition for storing magnetic information. Based on this new knowledge of quantum effects, the field of single molecule magnets (SMM) expanded. In addition to Mn compounds, many other types of SMMs have been discovered. Table 2.1 shows some examples. In order for them to be effective information carriers, the ideal SMM would have a high spin (S) value and a large negative axial anisotropy (D). Figure 2.2 illustrates these properties for a Mn12 cluster with a S=10 ground state.
29
Figure 2.2. Energy level diagram for an S=10 ground state with a negative axial zerofield splitting, D, in the absence of an applied magnetic field. The spin reversal barrier is given by U = S2|D|=100|D|. For Mn12, D = -0.5 cm-1., resulting in a barrier of U = 50 cm-1.11
Reduced magnetization curves for this SMM deviated from the Brillioun function (Appendix B), suggesting that the S=10 ground state is subject to a substantial zero-field split, resulting in a splitting parameter of |D| = 0.5 cm-1. The negative axial zero-field splitting removes the degeneracy in the MS levels of the ground state, placing the higher magnitude levels lower in energy, as depicted in Figure 2.2. With the selection rule of ǻMS = ±1 for allowed transitions, this results in an energy barrier U separating the two lowest energy levels of MS = +10 and MS = -10. In general, for an integral spin state, the energy barrier will be U = S2|D|. A positive D value would result in the MS = 0 level having the lowest energy resulting in no energy cost for changing the direction of the spin. Table 2.1 presents some values for other SMMs.
30
Table 2.1. This is a table of just some of the new SMMs presented in Reference 11. The table by J.R. Long is an extensive list with many references and chemical information for each SMM presented. The value (D) here is the negative axial anisotropy, (Ueff) is the barrier to spin reversal. Chapter 1 equation 10 gives a further explanation of these values. In order for these SMMs to be capable of storing information one would like them to have a high spin value, and a large negative axial anisotropy.
W
W 0e
KV
kT
here KV
U eff
Spin S
D (cm-1)
Ueff (cm-1)
10
-0.19
15
3
-1.5
14
13/2
-0.33
10
33/2
-0.035
9.5
12
-0.047
7
12
-0.037
4.9
15/2
X
4.2
[Fe10Na2O6(OH)4(O2CPh)10(chp)6(H2O)2(O2CCH3)2]
11
X
3.7
[Ni4(OCH3)4(sal)4(HOCH3)4]
4
X
3.7
3
X
2.9
[Fe4(O CH3)6(dpm)6]
5
-0.2
2.4
[Fe2F9]3-
5
-0.15
1.5
Single Molecule Magnets (SMMs) [Fe8O2(OH)12(tacn)6]
8+
[V4O2(O2CCH3CH2)7(bpy)2]
1+
[((CH3)3tacn)6MnMo6(CN)18]
2+
[Fe19O6(OH)14(metheidi)10(H2O)12]
1+
[ [Ni12(chp)12(O2CCH3)12(H2O)6(THF)6] [Mn10O4(biphen)4Br12] [(tetren)6Ni6Cr(CN)6]
4-
9+
[ [Ni21(OH)10(cit)12(H2O)10]
16-
Abbreviations for ligands noted above, in order of appearance are: tacn = 1,4,7 triazacyclononane. bpy = 2,2’-bipyridine. methidi =N-(1hydroxynethyethyl)iminodiacetic acid. chp = 6-chloro-2-pyridonate. biphen = 2,2biphenoxide. tetren = tetraethylenepentamine. sal = salicylaldehyde. dpm = dipivaloylmethane
31
Magnetic anisotropy is vital within these clusters, stemming from anisotropy in the electronic structure of the individual metal centers, and it is a direct function of the spin-orbit coupling. Metal ions with orbital angular momentum and a strong tendency to undergo a Jahn-Teller distortion are particularly suitable for generating a large negative axial anisotropy.11 While Table 2.1 lists some SMMs containing Fe and Ni, Mn clusters with the S=10 ground state still have the largest reported barrier to spin reversal (Ueff§ 42 cm-1), resulting in the longest magnetization relaxation time at 2K. It is anticipated that substitutions in higher-spin metal clusters may lead to SMMs with the needed enhanced spin-reversal energy barrier at higher temperatures. The criteria for a useful SMM for device applications are a large spin in the ground state S, and a large magnetic anisotropy of the easy axis D, leading to an energy barrier U for reversing the direction of their magnetization. This slow magnetic relaxation is in many ways analogous to the behavior of a superparamagnetic nanoparticle below its blocking temperature. Quantum effects are readily studied within these materials at cryogenic temperatures.
Figure 2.3. Quantum effects are evident in materials that are single domain and usually 10 nm.
32
2.1.2.1 Quantum Effects In order to demonstrate quantum size effects, appropriate materials are needed with sizes from 1 to 10 nanometers as shown in Figure 2.3. It can be assumed that somewhere within this range quantum behavior will be observable and be substantially different from typical bulk properties. Changes in electronic, optical and magnetic properties arise from the confinement of electrons and Heisenberg’s uncertainty principle becomes a controlling factor. Nanoparticles in the limited range of 1- 10 nm possess very high surface to volume ratios due to fine grain size. These materials are characterized by a very high number of low coordination number atoms at edge and corner sites that can provide a large number of active sites influencing thermodynamic behavior.12 For example, the melting point of a solid is reached when the order of the lattice begins to diminish. If the number of surface atoms becomes equal to or exceeds the number of core atoms, rearrangement of the lattice structure will require less energy, reducing the melting temperature. Quantum size effects are also evident in the optical spectra of many metal clusters and semiconductor nanoparticles. In CdSe, for example at sizes 10 nm, it can be seen that the photo absorption and emission bands shift to shorter wavelengths (blue shift) region with decreasing core diameter.13 This effect within semiconductors can occur when an electron is moved from the valence band to the conduction band across the bandgap, leaving a positively charged hole. This electron-hole pair, known as an exciton contributes to the shift in three possible ways: first, the increase in exciton energy can be influenced by the electric field of the electron; second, the effect of filling the lowest vacant state of the conduction band with the electron requires higher energy;
33
and third, a decrease in the oscillator strength of the excitonic transition arising from the properties of trapped electrons and holes14. Due the nature of band structure, in which electrons move freely within a lattice, the band structure of the quantum dot itself will change with a decrease in particle size, allowing for discrete energy levels. Electron tunneling can occur if an external voltage enhances the Coulomb energy of the quantum dot. The result is the Coulomb staircase from repeated tunneling of single electrons15. Electron quantum confinement is the most important aspect of inorganic nanoparticles and this unique property is also important to magnetic quantum size effects as their magnetism arises from unpaired electrons. The novel electronic states within magnetic quantum dots will inevitably give rise to new magnetic properties. Two specific scenarios that can be envisioned are cases where the available energy bands within the material force normally unpaired electrons to pair (a size induced low-spin state) or new magnetic effects arising from the greatly increased ratio of surface to bulk states (surface mediated magnetic effects). As previously discussed in section 2.1.2, single molecule magnets posses a high ground state spin and a large magnetic anisotropy. The slow relaxation also leads to magnetic hysteresis at low temperatures, however the loops are substantially different from those of an ordered ferromagnet. Steps form in the hysteresis loops that are a direct result of a magnetic quantum size effect, analogous to the Coulomb blockade charging behavior in metallic quantum dots.16 SMMs exhibit superparamagnetic-like properties normally associated with larger single domain clusters. As a result below their blocking temperature (TB) they exhibit magnetization hysteresis, a classical macroscale magnetic property, as well as quantum tunneling of magnetization (QTM)17. Figure 2.4 shows the steps in the hysteresis loops for a Mn12Ac single crystal. The steps originate from a loss of spin polarization in the molecules due to tunneling of magnetization through the energy barrier (Ueff) rather than
34
simple thermal activation. This tunneling only occurs with the resonant alignment of two or more Ms levels, also shown in Figure 2.4. The rates of tunneling observed between various SMMs differ. The distinction is most noticeable at low temperatures where thermal energy can in no way assist the tunneling process.
35
Figure 2.4. QTM hysteresis loops at low temperatures for (Mn12-ac) SMM with S=10. Steps in the loops are indicative of pure QTM through the barrier U eff . Data adapted from Reference 18.
36
2.2 Spinel Ferrites Many groups of materials are thought to manifest interesting correlation effects, these include transition metal compounds, especially their oxides, transition metal clusters, rare earths and actinides, and some organic compounds.19 Spinel ferrites are metal oxides originally found in crystalline minerals which crystallize in the isometric system with an octahedral habit. The general formula is (X)(Y)2(O2-)4, with X representing cations occupying tetrahedral sites and Y cations occupying octahedral sites. Divalent, trivalent, and quadrivalent cations can occupy the X and Y sites, and they can include but are not limited to Mg, Zn, Fe, Mn, Al, Cr, Ti, and Si. The unit cell is large, containing eight formula units. The mineral protoype for which they are named is the normal spinel MgAl2O4, within which the oxygen anions are arranged in a cubic closepacked structure.
For inverse spinels, half the Y cations occupy the tetrahedral sites, and both X and Y cations occupy the octahedral sites. Magnetite (Fe3O4) is a prominet example with the general form Y(XY)O4. The ionic distribution in this type of structure may be represented by [MGFe1-G]X[M1-GFe1+G]YO4, where G is the inversion parameter and G=0 and 1 stand for the inverse and normal cases, respectively. Within the unit cell eight trivalent ions and eight divalent ions are in the octahedral positions, while the remaining trivalent ions are in the tetrahedral site. Figure 2.5 represents a normal spinel unit cell.
37
Figure 2.5. The unit cell of a spinel ferrite, for an inverse spinel ferrite X and Y cations would both occupy the octahedral postions.20
2.2.1 Metal Ions In Chapter 1.3.2.3 the exchange interaction in antiferromagnetic materials was briefly introduced in terms of spin relations between lattices. Exchange interactions along spin-orbit (L-S) couplings are the primary factors for determining the magnetic properties of a material. A two-electron system with two atoms can only have one of two spin configurations: parallel or antiparallel. If the atoms are sufficiently near, the electron wavefunctions overlap, and based on the Pauli, probability of overlap increases if spins are antiparallel, or decreases if the spins are parallel. This combined with coulombic interaction means the parallel and antiparallel spin configurations have different energies21. Heisenberg showed these effects combined to produce an exchange energy between neighboring spins given by
E ex
& & 2 J ex S i S j & &
(1)
with J ex the exchange integral and S i S j neighboring spins. If J ex is positive, the lower
38
energy configuration is that of parallel spins, while a negative value for J ex allows for the antiparallel configuration to prevail and hence an antiferromagnetic state. Transition metal ions in spinel ferrites can have unbalanced spins in the 3d shell. Slater found a correlation that exists between the ratio of the interatomic distance 2ra to the radius of the incompletely filled d shell rd of some of the transition metals and the sign of the exchange integral. The result is the Bethe-Slater curve, Figure 2.6.
Figure 2.6. The Bethe-Slater curve represents the variations of the exchange integral J ex with the interatomic spacing (ra) and radius of unfilled d shell (rd). The three types of known exchange energy consist of direct exchange, indirect exchange and superexchange. The Bethe-Slater curve correctly differentiates iron, cobalt and nickel as having a positive J ex and ferromagnetic behavior, while manganese and chromium are antiferromagnetic. The magnitude of J ex is in the order of Ni-Fe-Co, which parallels the order of their Curie temperatures. The main implication from this trend is that if the atomic spacings can somehow be controlled, magnetic exchange energy can be altered.
39
2.2.2 Iron Oxide Systems Magnetite is a Fd3m space group cubic material with an inverse spinel crystal structure and the formula (Fe2+Fe23+O4). Oxygen anions form a face-centered cubic lattice with Fe2+ and Fe3+ cations in interstitial sites22. Each unit cell, with a lattice constant (a) of 8.396 Å, consists of eight formula units based on 32 O2- ions, 16 total Fe3+ ions and 8 Fe2+ ions or (Fe3O4)8. Eight trivalent ions and eight divalent ions are in the octahedral positions, while the remaining trivalent ions are in the tetrahedral site. Even though magnetite or “Loadstone” has been studied for centuries it still has some remaining mysteries. What makes magnetite such a complicated material is the partial filling of the d-shells, and the types of exchange that can occur. Fe2+ is 3d6, and Fe3+ is 3d5 and are configurations of a partially filled d-shell. Isolated ions with partially filled 3d-shells have 5-fold degenerate orbitals (l =2, (2l+1)degenerate levels) in which up to 10 electrons can be placed.23 The filling of these levels follows Hund’s first rule: to minimize the Coulomb repulsion energy, the electrons form a state with the maximum possible spin. When a transition metal ion is in a crystal, the spherical symmetry of an isolated ion is reduced, and some of the orbital degeneracy is lifted. The resulting splitting of the fields is due to a crystal field (CF). For magnetite, the octahedral position is the most complicated due to the mixed-valency and is depicted in Figure 2.7.24 The electron configuration of the Fe ions within Fe3O4, which can be thought of as the X (tetrahedral site) [Fe3+ ( t2g3 eg2, S=5/2)] and the Y (octahedral site) [Fe2+ (t2g4 eg2, S=2)] and [Fe3+ ( t2g3 eg2, S=5/2)] are depicted in Figure 2.9. Within a d subshell the greatest loss of exchange energy is expected when the d5 configuration is forced to pair, Figure 2.8 shows the spin states for Fe2+.
40
Figure 2.7. Splitting of five d orbitals by an octahedral field. The condition represented by degenerate levels is a hypothetical spherical field. The terms D and q are quantities inherent in the formal mathematical derivation of the electrostatic model. They depend on the charge on the metal ion, the radial distribution of the valence d electrons, and the metal-ligand distance. The factor 10 in 10Dq arises specifically for single electron in an electrostatic potential of octahedral geometry.24
Figure 2.8. Different possible electronic configurations for a Fe2+ (d6) ion: (a) low-level spin state; (b) intermediate spin state; (c) high-spin state. Figure adapted from ref. 23.
41
Figure 2.9. Schematic representation of the electron energy levels of the Fe ions in Fe3O4. Adapted from Brus et.al. reference 25. The particular charge-transfer for Fe3O4 promotes a ferromagnetic coupling with the Y lattice that then facilitates the overall ferrimagnetic ordering. Thus magnetite is a spin-polarized metal.25
The dominant source of dipolar coupling in most transition metal compounds is superexchange, which is an indirect mechanism dependent on the simultaneous covalent bonding of metal ions with their bridging ligands. It leads most commonly to antiferromagnetic ordering. The particular charge-transfer for Fe3O4 promotes a ferromagnetic coupling with the Y lattice that then facilitates the overall ferrimagnetic ordering. The electron transfer of the lowest energy electron from the Fe2+ ion, see Figure 2.8 (c), must be that of the lone spin, thus preserving the stable parallel arrangement of the remaining five electrons, now S = 5/2. The Pauli principle controls the orientation of the neighboring Fe3+ ion such that they are also ordered parallel to the majority of spins in the Fe2+ ion. This mechanism is called double-exchange and is illustrated in Figure 2.10.
42
Figure 2.10. Electron transfer between the Y octahedral sites in Fe3O4. Figure adapted from reference 26. Another interesting property of Fe3O4 that makes it unique among spinel ferrites is also a function of the electron hopping mechanism (Fe2+
Fe3+). Fe3O4 is a semi-
metal, having an almost metallic condutivity at ordinary temperatures, ca. 2.5 x 104 (ȍ m)-1. The extra electron of the Fe2+ ion undergoing the charge transfer mechanism facilitates this property. Table 2.2 provides a comparison of the conductivities of other spinel ferrites.
Table 2.2. Values of conductivities at 298 K for some spinel ferrites and iron. Magnetite has a value closer that that of a pure metal than for the other spinel ferrites. Since most spinel ferrites are insulators, this is a unique property27. Spinel ferrites
Conductivity (ȍ m)-1
MnFe2O4
.01
Fe3O4
2.5 x 104
CoFe2O4
1 x 10-5
NiFe2O4
.1 to .01
Mg Fe2O4
1 x 10-5
Iron
1 x 107
43
Magnetite is a relatively good conductor at room temperature as indicated in Table 2.2, however when the temperature goes below 122K, a sharp drop in the conductivity occurs. This temperature known as the Verwey temperature28 (TV) is the limit for a metal-insulator transition that occurs in magnetite crystals. The cubic symmetry of the Fe3O4 lattice becomes distorted. Work on an explanation for this feature has been on going since Verwey’s original research29. Recent efforts have seemed to favor the distorted-cubic phase as the source of the transition30. Below the TV 122K, there is an ordered arrangement of Fe2+ and Fe3+ ions on the octahedral sublattice resulting in the distortion of the unit cell, Figure 2.11. Above TV electron hopping destroys the cation ordering. All {100} directions are then equivalent and the unit cell lattice is cubic. At the Verwey transition between these states, the increased electron mobility converts magnetite from an electrical insulator (with metallic tendencies) to a semiconductor.22 This conversion is not completely understood due the complications that occur when electron-electron interaction, electron-phonon interaction and electronic bandwidth all equally contribute.30
Figure 2.11 Distorted cubic phase below the TV, as the result of cation ordering. 31
Another property arising from the electron hopping mechanism is the net magnetic moment. At 0 K, the net magnetic moment per formula weight of Fe3O4 is 4.1
P B , which is close to the moment of high spin Fe2+ ( S= 2, P 44
4 P B ). This is expected
since Fe3+ ( S= 5/2, P
5P B ) occurs in equal numbers on both sublattices, as shown
in Figure 2.12
Figure 2.12. Spins of Fe3O4 result in a magnetic moment similar to high spin Fe2+.
Natural and synthetic magnetite in the bulk occurs most commonly as octahedral crystals bounded by {111} planes and as rhombo-dodecahedra. Twinning can occur on the {111} plane. There is currently no definitive shape information for single domain nanoparticles, other than the basic sphere. Figure 2.13 indicates crystal structures for bulk Fe3O4.
Figure 2.13. Bulk magnetite crystal forms: (a),(c) octahedron, (b) rhombodecahedron, (d) twinned.32
45
2.3 Nanoparticle Characterization A brief summary of the instrumental techniques used to characterize nanoparticles is now provided. Numerous techniques are used to fully study new systems of interest. Presentation and interpretation of data are the keys to success with each characterization method.
2.3.1 Transmission Electron Microscopy (TEM) Transmission electron microscopy (TEM) images help elucidate the individual shape and internal structure of nanoparticles. It is also used to determine the crystal structure through the use of electron diffraction in selected areas. TEM images were collected with a JEOL 4000EX high resolution electron microscope (HREM) operating at 400kV. The instrument is located in the Center for Nanostructure Characterization and Fabrication at Georgia Tech. Images were acquired at a magnification strength of 500,000, resulting in a scale factor of 1 mm in the image equaling 2.0 nm within the actual sample image. Dr. Yong Ding acquired and processed the images.
2.3.2 Powder X-Ray Diffraction (XRD) X-ray diffraction is a method used to characterize bulk materials and the crystalline phase of nanoparticles. Diffraction peaks can be compared to known spectrum peak positions through the JCPDS (Joint Committee on Powder Diffraction Standards) database33. All x-ray data in this work were collected on a Scintag Inc. X-GEN 4000 powder diffractometer. Each sample was prepared by dissolving dry powders into either toluene
46
or hexane. The solution was deposited on a Si111 (miscut 50) in 5 ȝL aliquots with airdrying between each aliquot to form a thin film. Large angle x-ray diffraction (LAXRD) (2ș = 10 - 90°; s = 1.1 – 10 nm-1) will allow comparison of bulk materials with nanoparticles. Small angle x-ray diffraction (SAXRD) (2ș = 0 - 10°; s = 0 – 1.13 nm-1) is used to determine if long range ordering is present between nanocrystalline cores. Average core diameter estimates are obtained as the reciprocal of the full peak width at half maximum (FWHM) for each peak present. To minimize any bias or human error, the diffraction patterns were fit with Gaussian functions using Microcal’s Origin software to obtain diffraction peak locations and their FWHM33. Most XRD data is composed of peaks at specific angles with varying intensity, and is plotted as 2ș versus intensity. Cores (grain) sizes are often estimated by the Scherrer formula,
B
0.9O t cos T
,
(2.1)
where B is the broadening of the x-ray diffraction peak measured at half max, O is the wavelength, t is the diameter of the particle and T is the diffraction angle34. The Scherrer formula is not really applicable to nanoclusters below five nanometers to due to peak broadening, thus Bragg diffraction is useful to estimate size35. Bragg’s law for diffraction physics can be applied by converting the 2ș values into simple scattering vector amplitudes by
s
2 sin T
O
47
,
(2.2)
where T
2T and O is the diffracted x-ray wavelength (0.15406 nm). Prior to Gaussian 2
fitting, the intensity data was multiplied through by s, in order to eliminate strong peak asymmetry at low angle values.36 The general output from Origin contains information about peak positions, integrated intensities ( area under the peak), maximum widths and heights. In order to determine lattice constants, peaks are assigned corresponding (h,k,l ) indices and s values equivalent to peak positions are plotted vs.
h 2 k 2 l 2 . The
lattice constant is then determined through
s
s 0 a 1 h 2 k 2 l 2
1/ 2
(2.3)
where s0 is a free parameter correcting for zero-angle offset and vertical sample displacement, and a is the lattice constant in nm. This method allows for the presentation of a series of diffraction peaks of similar widths that are wavelength independent. The crystalline diameter is given as the averaged reciprocal of the diffraction peak FWHM.16,35-37
2.3.3
Matrix Assisted Laser Desorption Ionization Mass Spectrometry (MALDIMS) MALDI-MS were collected at The Georgia Institute of Technology Bioanalytical
Mass Spectrometry Facility, with David Bostwick’s assistance.
48
2.3.4
Optical Spectroscopy Optical absorbance spectra were collected with a Perkin Elmer Lambda 19 UV-
Vis-IR spectrophotometer. The optical absorbance spectra were all collected in equal intervals of wavelength, with typical ranges from 1100 to 300 nm. For a more natural comparison to band structure or charging energies within the metallic cores the wavelengths were converted to energy. Since the conversion from wavelength to energy is reciprocal rather than linear (1 eV = 1239.84 O1 ), the data must be presented in a physically relevant manner.39 This requires the division of absorbance by energy squared (eV2) to preserve the area under the spectral curve as a function of energy.
2.3.5 Vibrational Spectroscopy Infrared spectra were collected with a Nicolet 520 FT-IR Spectrometer at the Georgia Institute of Technology. The spectra were collected from dry powders in reflectance mode on a diamond cell from 128 scans at 2.0 cm-1 resolution.
2.3.6
Elemental Analysis (EA) & Thermogravimetric Analysis (TGA) Two types of thermal analysis method were performed on the materials,
thermogravimetric analysis (TGA) and elemental analysis (EA). The TA Instruments TGA 2950 is located in the Georgia Institute of Technology Materials Science Department. The TGA data are presented as percent mass change versus temperature and time. They were collected from dried powders in a platinum pan from 30°C to 600°C at a rate of 10°C per minute and held at 600°C for 10 minutes to ensure complete organic volatile loss. Galbraith Laboratories performed EA on dried powder samples. The data are presented as elemental percent ratios.
49
2.3.7
Proton Nuclear Magnetic Resonance 1
H-NMR spectra were collected with a Bruker AMX-400 multiprobe nuclear
magnetic spectrometer by Dr. Les Gellbaum of the Georgia Institute of Technology NMR center. The samples were prepared as saturated solutions in d8-toluene. 2.3.8
SQUID Superconducting Quantum Interference Devices (SQUIDs) are the most
sophisticated instruments for measuring magnetic properties. Magnetization was measured by two different procedures: Zero-field-cooled (ZFC), the sample was ZFC to 2 K, a field was applied and magnetization was measured as a function of temperature, and Field-cooled (FC), the sample was field-cooled from above 100 K to 2 K and magnetization was measured. The temperature at which the two curves ZFC and FC is traditionally the blocking temperature TB. Hysteresis loops, in which the sample’s magnetization is measured as a function of the applied field were run at temperatures from 2 K to room temperature 300 K. The majority of magnetic data presented in this work was collected with a Quantum Design Magnetic Property Measurement System (MPMS)40 housed at the Molecular Materials Research Center at the Beckman Institute of the California Institute of Technology. The particular MPMS is a SQUID gradiometer that can measure moments of < ~ 1 cm3 samples at temperatures from 1.8 K to > 300 K while immersed in fields from < 0.2 mT to 5.5 T. Additional SQUID work was also done at Georgia Institute of Technology on a Quantum Design MPMS-5S SQUID with assistance from Dr. Christi Vestal and Mr. Man Hann.
50
2.4 REFERENCES
[1]
R.P. Feynman, There’s Plenty of Room at the Bottom, Cal Tech Archives (1959)
[2]
K.J.Klabunde, Nanoscale Materials in Chemistry, Wiley and Sons Inc. (2001)
[3] E.L. Wolf, Nanophysics and Nanotechnology, Wiley-VCH, (2004) [4]
B. Aktas, Nanostructred Magnetic Materials and Their Applications, Springer (2001)
[5]
G.Schmid, Nanoscale Materials in Chemistry, Wiley and Sons Inc. (2001)
[6]
A.I. Ekimov, A.A. Onoshchenko,” Quantum Size Effect in Three-Dimensional Microscopic Semiconductor Crystals,” J. Exp. And Theor. Phys. Letters, 34,6,346349, (1982)
[7]
R.Sessoli, D.Gatteschi, A.Caneschi, M.A. Novak, “Magnetic Bistability in a MetalIon Cluster,” Nature, 364,141-143, (1993)
[8]
D. Gatteschi, R.Sessoli, “ Molecular Nanomagnets: the First 10 Years,” J. Mag. And Mag. Mat., 272-276, 1030-36 (2004)
[9]
T. Lis, “ Preparation,Structure and Magnetic Properties of a Dodecanuclear Mixedvalence Manganese Carboxylate,” Acta Crystallogr. B36, 2042 (1980)
[10] D.Gatteschi, R.Sessoli, “Quantum Tunneling of Magnetization and Related Phenomena in Molecular Materials,” Angew. Chem. Int. Ed., 42,3 (2003) [11] J.R. Long, “Molecular Cluster Magnets,” The Chemistry of Nanostructed Materials, World Scientific Publishing (2003) [12] S.G. Louie, “ Nanoparticles Behaving Oddly,” Nature,384,612-13 (1996) [13] C.B. Murray, D.J. Norris, M.G.Bawendi,” Synthesis and Characterization of Nearly Monodisperse CdE (E= S, Se, Te) Semiconductor Nanocrystallites,” JACS,115,8706-15 (1993)
51
[14] Adapted from, www.uaf.edu/chem/467Sp05/lecture19.pdf, 8-20 (2006) [15] M.A. Kastner,”Artificial Atoms,” Physics Today,24-31 (1993) [16] G.Schaff, M. Shafigullin ,J.Khoury , I. Vezmar, R. Whetten ,W.Cullen, P.First, J.Phys. Chem B,101,7885 (1997) [17] M. Soler, W. Wernsdorfer, K. Folting, M.Pink, G. Christou,” Single-Molecule Magnets: A Large Mn30 Molecular Nanomagnet Exhibiting Quantum Tunneling of Magnetization,” JACS., 126, 2156-2165 (2004) [18] L.Thomas, F. Lionti, R.Ballou, D.Gatteschi, R.Sessoli, B.Barbara,” Macroscopic Quantum Tunneling of Magnetization in a Single Crystal of Nanomagnets,” Nature, 383,145-147 (1996) [19] P.Fazekas, ”Electron Correlation and Magnetism,” World Scientific (1999) [20] Adapted from, www.tf.unikiel.de/matwis/amat/def_en/kap_2/basics/b2_1_6.html, (2004) [21] C.M. Sorensen, Nanoscale Materials in Chemistry, Wiley and Sons Inc. (2001) [22] D.J. Dunlop, Ö.Özdemir, “Rock Magnetism Fundamentals and Frontiers,” Cambridge University Press (1997) [23] D.Khomskii,”Electronic Structure,Exchange and Magnetism in Oxides,” Spin Electronics, Springer (2001) [24] J.E.Huheey, E.A.Keiter, R.L. Keiter, “Inorganic Chemistry 4th Ed”. Harper Collins (1993) [25] J. Tang, M. Meyers, K. A. Bostwick, L. E. Brus,” Magnetite Fe3O4 Nanocrystals: Spectroscopic Observation of Aqueous Oxidation Kinetics,” J.Phys.Chem. B, 107, 7501-7506 (2003) [26] Adapted from A.F. Orchard, Magnetochemistry,Oxford Universitry Press,(2003) [27] CRC Handbook, 84th Edition (2003-2004)
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[28] E.J.W. Verwey, Nature, 144,327 (1939) [29] F.Walz.” The Verwey Transition- a Topical Review,” J. of Phys.: Cond. Matter, 14,R285-R340 (2002) [30] G.K. Rozenberg, M.P. Pasternak, W.M. Xu, Y. Ameil, M.Hanfland, M.Amboage, R.D. Taylor, R.Jeanloz, “ Origin of the Verwey Transition in Magnetite,” Phys. Rev. Lett., 96,045705 (2006) ; L.V. Gasparov, D.B. Tanner, D.B. Romero, H. Berger, G. Margaritondo, L. Forro, “ Infrared Studies of the Verwey Transition in Magnetite,” Phys. Rev. B, 62,12,7939-44 (2000) [31] Adapted from www.paleomag.net/members/rixiangzhu/research/Rockmagnetism.htm, Sept. (2006) [32] R.M. Cornell, U. Schwertmann,” The Iron Oxides : Structure, Properties,Reactions, Occurrence, and Uses,” Weinheim ; New York : VCH, (1996) [33] JCPDS International Center for Diffraction Data, Swarthmore,PA [34] R.C.Price, Ph.D. Dissertation, Georgia Institute of Technology (2006) [35] R. Jenkins, R. Snyder,” Introduction to X-Ray Powder Diffractometry,” New York, Wiley (1996) [36] R. Whetten , M. Shafigullin, J.Khoury , G.Schaff, , I. Vezmar, , M. Alvarez, A. Wilkinson, Acc. Chem. Res. 32,397 (1999) [37] M.Shafigullin, Ph.D. Dissertation, Georgia Institute of Technology (1999) [38] G.Schaff, M. Shafigullin ,J.Khoury , I. Vezmar, R. Whetten , J.Phys. Chem B,101,8785 (2001) [39] J.Khoury, Ph.D. Dissertation, University of California Los Angeles (1999) [40] M. McElfresh,” Fundamentals of Magnetism and Magnetic Measurements Featuring Quantum Design’s MPMS, Quantum Design (1991)
53
CHAPTER 3 IRON OXIDE NANOPARTICLES WITH SUB-2 NANOMETER CORES
Chemically functional magnetic nanoparticles, comprised of a Fe3O4 magnetite core encased in a thin aliphatic carboxylate, have been prepared by sequential high temperature decomposition of organometallic compounds in a coordinating solvent.1 In this work, aliphatic carboxylic acid chain length, reaction temperature and duration were varied to produce small core diameters. Octanoic, hexanoic and propionic acid were selected for this purpose, producing successively smaller cores of 2.0 nm, 1.3 nm and 1.0 nm, respectively. Currently these represent the smallest diameter magnetite clusters, approaching the scale of molecular magnets.
3.1 Methods to Produce Fe3O4 Nanoclusters Synthetic methods for producing homogenous nanoparticles are important for the determination of physical properties arising from size effects. Preparation of monodisperse materials enables systematic characterization of the structural, electronic, optical and magnetic properties as they evolve from molecular to bulk in the nanometer size range.2 Synthetic routes yielding monodisperse nanoparticles (NPs) are required to attempt understanding the unique properties inherent to a specific size regime. Potential applications utilizing these properties include magnetoelectronics3, high density memory devices4, qubits for quantum computing5, and medical applications.6 Many methods exist for the formation of NPs, however the majority of them produce polydisperse colloidal-sized NPs. These methods include sonochemical, solgel, hydrothermal aqueous coprecipitiation and chemical microemulsions.14
54
Each method produces colloids with suitable application specific properties. Efforts continue to find appropriate methods for specifically tailoring NP chemical and magnetic functionality. These efforts are a vital part of research for the development of more sophisticated materials. For the purpose of this work, only methods involving nucleation of metal-organic precursors will be discussed. In 1950 La Mer and Dinegar7 provided evidence for the growth of monodisperse colloids based on a temporally discrete nucleation event2, shown in Figure 3.1. Continued NP growth is on a much slower scale until saturation is achieved. If the precursors are introduced by rapid addition to the reaction vessel, the precursor concentration will be temporarily above that of the nucleation threshold. A short nucleation period will overcome the supersaturation. Control of the growth rate is the key to producing monodisperse NPs. A second growth phase called Ostwald ripening can occur, due to the high surface energy of the small NP precursors. This high surface energy allows dissolution of small clusters and addition of the dissolved material on to larger NPs. This process is also a function of reaction time and can allow for the controlled formation of larger NPs. Transition metal oxides can be synthesized by several of the methods previously mentioned, however the most effective method for achieving size selection is through a thermal decomposition reaction. Stable magnetic NPs protected by a layer of surfactant, also known as monolayer protected clusters (MPCs) are readily prepared by a high temperature reduction of a metal salt in the presence of a stabilizing agent forms.1,8-13 Metal halides or acetates are typically brought to a high temperature in a high-boiling inert solvent such as octylether or phenylether. Additional additives may include longchain alkylphosphines, alkylphospine oxides, alkylamines and long-chain carboxylic acids. Most of the NPs isolated are colloidal in nature with the additives molecule(s) stabilizing the surface. These stabilizing molecules are often dubbed “surfactants” in the
55
literature and their steric repulsion is hypothesized to prevent agglomeration arising from inter-particle magnetic ordering. Dynamic adsorption and desorption of surfactants on particle surfaces during the high temperature synthesis enables the reactive metal precursors to form final stable products.1 The final MPCs can be dispersed in several organic solvents or dried in a powder form.
Figure 3.1 An example of the stages of nucleation and growth of monodisperse nanoparticles based on the work of La Mer and Dinegar.7 This figure was adapted from reference 2.
56
Monodisperse nanoparticles are generally considered to be samples with standard deviations 5% for spherical particles.13 While much progress has been made for the production of MPCs in the 3-20 nm range, a consistent method for the production of (Fe3O4)X(carboxylate)Y with core diameters 2.0 nm has yet to be introduced. Sun et. al.1,8 presented a method based on the high temperature thermal decomposition of iron(III) acetylacetonate, Fe(acac)3 to produce monodisperse magnetite Fe3O4 with a narrow size distribution, ı 10% in the 3 to 20 nm range, Figure 3.2 and Figure 3.3. In this method, the reactants are mixed at room temperature and slowly heated to generate nuclei. The growth of nanoparticles can be stopped by rapidly decreasing the temperature. Particle size can be readily increased via Ostwald ripening at the elevated temperature. Strict temperature control and timing are essential to control particle size. Murray and co workers15 discussed the polyol process for generating hcp cobalt nanoparticles, in which a high boiling alcohol is used as both a reductant and a solvent for the metal salt precursor compound. The polyol solvent is preferably a viscous alcohol, such as a diol, triol, or tetraol, in order to minimize particle diffusion and inhibit particle growth. In a typical synthesis, 1,2-dodecanediol was added into a hydrated cobalt acetate solution dissolved in diphenyl ether containing oleic acid and trioctylphosphine at 250 °C. The nanoparticles were isolated by size selective precipitation, and the average core size was tuned by changing the relative concentration of precursor and stabilizer. For example, when a 1:1 molar ratio of cobalt acetate and oleic acid was used in the synthesis, 6–8 nm sized cobalt nanoparticles were produced, while increasing the concentration of stabilizing surfactants by a factor of two yielded smaller 3–6 nm nanoparticles. Particle size could also be varied by controlling the steric bulkiness of the phosphine stabilizers.
57
Figure 3.2 Method for obtaining magnetite & related ferrite monolayer protected clusters (MPCs) in robust molecule-like forms from Sun et. al.1,8
Figure 3.3 (A) High resolution TEM (HRTEM) image of a single 6 nm Fe3O4 nanoparticle1,8, crystal lattice fringes evident. (B) Selected area electron diffraction (SAED) for the 6.0 nm particle.
58
3.2 Experimental Parameters to Synthesize Sub-2nm Fe3O4 Nanoclusters
Monolayer protected magnetic nanoparticles, comprised of a Fe3O4 magnetite core encased in a thin organic shell, have been prepared by sequential high temperature decomposition of organometallic compounds in a coordinating solvent. The synthesis was performed with commercially available reagents. Diphenyl ether (99%), 1,2hexadecanediol (90%), oleylamine (70%), octanoic acid (99.5%), iron(III) acetylacetonate [Fe(acac)3], ethanol, hexane, and toluene were purchased from Aldrich. The Fe(acac)3 (5 mmol),1,2-hexadecanediol (25 mmol), diphenyl ether (50 mmol), oleylamine (15 mmol) and octanoic acid (15 mmol) were added to a three-neck round bottom flask with magnetic stir bar. All reactions were carried out in a 500 ml three-neck flask fitted with a reflux condenser. One port was used for introducing a continuous flow inert atmosphere at ~1.5 atm pressure, and the other port was used for monitoring the reaction temperature. Under argon or nitrogen, the mixture was heated at a rate of < 1o per minute. The initial reaction mixture was red-brown in coloration and proceeded to a black-brown color as the temperature was elevated. When a temperature of approximately 200 °C was obtained, the mixture was allowed to reflux for ½ hour. The reaction was then further heated to a temperature of 252 °C, held at that temperature for 30 minutes, then cooled to room temperature. The final product was a thick black slurry with a variable viscosity, depending on diphenyl ether loss during reflux. The ether had a tendency to solidify in the condenser if the circulating water was too cool, or azeotrope with volatile by-products if the condenser was too hot. Proceeding directly to reflux without holding the reaction at ~ 200 oC results in a wide size distribution of NPs.8 To investigate if any NPs nucleate during the homogenization phase, the
59
reaction was sampled after the first holding phase. No NPs were re-precipitated from this sample, indicating the occurrence of nucleation a higher temperature. The final slurry was transferred to an Erlenmeyer flask and re-precipitated from ethanol (100 ml) at least three times to remove excess diphenyl ether, or until supernate was no longer yellow. The remaining precipitate was dried via rotory evaporation and redispersed in hexane or toluene for further characterization. As dried powders the nanocrystals had colors ranging from black-purple to a reddish-brown, depicted in Figure 3.4.
60
Figure 3.4 Synthesis for 1.3 nm (Fe3O4)X(hexanoate)Y clusters. Clusters as a dry powder (lower left) and in toluene solution (lower right).
61
3.2.1 Reaction Results Several different sizes of MPCs were produced with mean core diameters 2.0 nm by using a variant of the polyol process in which a reaction mixture containing Fe(acac)3 and various short chain carboxylic acids ( 8 carbons) are heated. The influence of aliphatic carboxylic acid chain length with temperature and time on the magnetite core diameter formed will be evaluated. The coordinating solvent used was diphenyl ether, which has a boiling point of 259oC. Due to the enhancement of Ostwald ripening at elevated temperatures, it is important to not let the reaction temperature increase too much, therefore other ethers such as benzyl ether with a boiling point of 298oC were not considered. The ratio of solvent to metal salt was maintained at 10:1 for all reactions. It was also critical to heat the solution to ~200oC and hold for a length of time no longer than ½ hour. Holding the reaction at this temperature for 30 minutes homogenizes the reaction slurry and enables a uniform nucleation process. Further heating after homogenization to reflux temperature (a value that varied with carboxylic acid boiling point), while keeping all other parameters constant (amine and reducing agent concentration), allowed formation of different corediameter clusters. The reaction time at reflux was fixed at 30 minutes to prevent excessive Ostwald ripening. Once the reflux had proceeded for this duration, the reaction was allowed to cool to room temperature under the influence of an inert gas. The starting material iron(III) acetylacetonate Fe(acac)3 was reduced by the inclusion of a diol or polyalcohol. The use of a diol or polyalchol to reduce metal salts to metal particles is called the polyol process.16-19 The long-chain diol 1,2-hexadecanediol is used as a weak reductant for the Fe+3 of Fe(acac)3. Its net effect is reduction of 1/3 of the Fe+3 to Fe+2, generating Fe3O4 in the process. The ratio of Fe(acac)3 to diol was 1 equivalent to 5 to ensure partial reduction. The inclusion of a fatty acid and an amine are
62
necessary for the formation of MPCs.8 In previous thermal decomposition reactions oleic acid and oleylamine were the fatty acid and amine typically utilized. A protective organic shell around reactive transition metal cores is needed to provide chemical stability. Initially this method was applied to semiconductors20 and has now been extended to magnetic materials such at FePt, Co and Ni nanoparticles.12,16,21 It has been suggested that organic molecules act as tunable spacers preventing magnetic coupling between adjacent particles.12 With FePt nanoparticles as an example, 6.0 nm (FePt)X with a nearest neighbor spacing of ~ 4.0 nm was maintained by oleic acid and oleylamine capping groups. Room temperature ligand exchange of those linear long-chain capping groups for shorter RCOOH/RNH2 (R =C12 –C6 alkyl chains) allows the interparticle distance to be adjusted. Ligand exchange with hexanoic acid/hexylamine yielded 6 nm (FePt)X with spacing of ~1.0 nm.16 While adjusting NP spacing is important for magnetic properties, it is also relevant to note that core size might be affected by a change in length of surfactants by overall reduction of the nucleation temperature. By initially repeating the synthetic procedure of Sun et.al8, MPCs with an average core size of 2.4 nm were produced. Maintaining a ratio of 1:3:3 Fe(acac)3 to oleic acid/oleylamine with monitoring of the heating rate and final reaction temperature, MPC batches in that size range were produced. Increasing the passivant concentration by adjusting the ratio of Fe(acac)3 to oleic acid/oleylamine to 1:4:4 and 1:5:5 did not reduce the core size. It was postulated that a greater abundance of the capping agents would limit core growth. A ligand exchange procedure with sodium acetate and sodium benzoate (ethching) also failed to produce smaller core sizes. This was unfortunate in lieu of etching being successful for gold cluster compounds, reducing the core masses from 14 kDa to ~ 8 kDa.26
63
Switching to short chain carboxylic acids resulted in MPCs with smaller core diameters. Octanoic (C8H16O2), hexanoic (C6H12O2) and propionic (C3H6O2) acid were selected for this purpose, producing successively smaller cores, 2.0 nm, 1.3 nm and 1.0 nm respectively listed in Table 3.1. Currently, these represent the smallest diameter magnetite clusters, approaching the scale of molecular magnets. The lowered boiling point of the carboxylic acids with decreasing chain length directly correlates to the boiling point depression of (reflux temperature) the reaction slurry
Table 3.1 Reaction parameters for production of (Fe3O4)x(carboxylate)y MPCs. All reactions were done with the starting material to carboxylic acid ratio of 1:3.
Starting Carboxylic Material Acid
Formula
Carboxylic Acid Final Core Diameters BP Reaction Temp (nm)
C18H34O2
360oC
265oC
3.5 + 0.6 nm
Fe(acac)3 Octanoic
C8H16O2
237oC
252oC
2.0 + 0.1 nm
Fe(acac)3 Hexanoic
C6H12O2
204oC
200oC to 212oC
1.3 + 0.1 nm
Fe(acac)3 Propionic
C3H6O2
142oC
200oC
0.9 + 0.1 nm
Fe(acac)3
Oleic
The polyol process for the preparation of metallic powders by reduction of inorganic compounds in liquid polyols requires that the reduction proceed via a solution rather than in the solid state. Accordingly, the mechanism would have the polyol act as the solvent for the starting inorganic compound, followed by reduction of the dissolved species by the polyol, and then nucleation and growth of the metal particles from the solution.19 Passivation of the inorganic cores occurs during this process, and it is this step that is thought to control the shape of colloidal nanoparticles.9,12,19-25 Table 3.1 also shows the vital correlation between decreasing carboxylic acid and boiling point,
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decreasing reflux reaction temperature, and decreasing nanoparticle core growth. The synthesis of MPCs with the smallest core diameters has been repeated several times in order to further study the reaction parameters, however at this time the full reaction mechanism remains unknown. This synthesis could benefit from a full chemometric study in order to determine that exact controls needed to consistently produce MPCs with size-tailored properties. Another important step in isolating MPCs is the purification phase. Addition of a flocculant, such as cold ethanol, and subsequent rinse steps is required to remove excess starting materials and solvent. Excessive purification with a Soxhlet extractor however, resulted in oleate MPCs that were difficult to redisperse. The issue of particle dispersibility in various solvents is a major criterion for some of the desired applications of magnetic nanoparticles, such as ferrofluids and biomedical studies.27 Solubility is also important for understanding interparticle magnetic interactions, where it is important to obtain well-isolated particles. Magnetic nanoparticles coated with oleate are dispersible in nonpolar solvents such as hexane and toluene, as are octanoate, hexanoate and propionate NPs, albeit at varying concentrations. Their solubilities are listed in Table 3.2. To estimate the solubilities of the varying clusters, saturated 5 mL solutions of cleaned NPs were prepared, evidenced by precipitation in each vial. Each NP solution was injected through a 0.16 ȝm syringe filter and allowed to settle for 24 h to verify that no insoluble material remained. A one or two mL aliquot was drawn and dried in a tared flask to measure the solubility per mL of solvent. For the smallest NPs, the molecular weights for determining solubility are estimated from XRD core diameter (Chapter 3.3.1.1) and from mass spectrometry (Chapter 3.3.1.3), correlated by TGA (Chapter 3.3.1.4).
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Table 3.2. Approximate solubilities (ȝM) for the smallest (Fe3O4)x(carboxylate)y MPCs, after reprecipitation and drying. Uncertainty in diameters arise from variances in estimated XRD peak FWHM in each powder pattern. Core Diameter ~ Molecular. (nm) Weight.
g/L
~ Solubility (PM)
2145 g/mol
5.9
2800
(Fe3O4)X(hexanoate)Y 1.3 ± .1
10,499 g/mol
1.1
100
(Fe3O4)X(octanoate)Y
23,154 g/mol
3.1
130
MPCs
(Fe3O4)X(propionate)Y
1.0 ± .1
2.0 ± .1
The MPCs with cores ~ 1.3 nm have the lowest solubility detected and the quantity of soluble material has been observed to diminish upon successive reprecipitation from ethanol. (Fe3O4)x(oleate)y MPCs appeared insoluble in either hexane or toluene, with no detectable coloration to the eye after extensive cleaning. It is possible that at these small sizes, with shorter chain carboxylates on the surfaces, clumping of the nanoparticles is occurring upon drying to powder form after reprecipitation resulting in diminished solubilities. Magnetic interparticle interactions can also contribute to this agglomeration, further hampering re-dispersion in solvents. These issues will be discussed further when magnetic data is presented.
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3.3 Characterization of Sub- 2.0 nm Fe3O4 Nanoclusters
In order to correlate size effects with changes in particle formation, it is important to have a through understanding of the structural components. This includes studies of the core size, surface effects, decomposition, electronic properties and magnetic behavior. A variety of characterization techniques were utilized to understand these properties for 2.0 nm Fe3O4 nanoclusters. Information about the various instruments used and presentation of the data were provided in Chapter 2.
3.3.1 Size Dependent Characterization Mean core sizes for Fe3O4 MPCs were determined from high resolution transmission electron microscopy (HRTEM), powder x-ray diffraction (XRD), MALDI mass spectrometry (MS), elemental analysis (EA), and thermogravimetric analysis (TGA). TEM samples were prepared from dilute solutions of (Fe3O4)X(octanoate)Y MPCs and (Fe3O4)X(propionate)Y MPCs . Both types of nanoparticles were dissolved in hexane and dropped on to carbon–coated copper grids. Figure 3.5 is HRTEM micrographs of 2.0 nm (Fe3O4)X(octanoate)Y MPCs. The selected area electron diffraction (SAED) pattern is the same as figure 3.3. All TEM data were produced at a magnification ratio of 500,000, therefore 1.0 mm = 2.0 nm in the actual images. Figure 3.6 is a HRTEM image of 1.0 nm (Fe3O4)X(propionate)Y MPCs.
67
(a)
(b)
(c)
Figure 3.5 (a) Full TEM image at 500,000X of (Fe3O4)X(octanoate)Y MPCs. (b) Enlargement of (a)crystal lattice fringes are evident and size is ~2 nm. (c) SAED pattern is similar to figure 3.3, indicative of Fe3O4, reference 8. Figures have been subjected to contrast level adjustment in Photoshop.
68
(a)
(b)
Figure 3.6. (a) Full TEM image at 500,000X of (Fe3O4)X(propionate)Y MPCs. (b) Enlargement with minor contrast levels adjustment, MPCs are ~ 1.0 nm by XRD.
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Figures 3.5 and 3.6 show the similar diameters within each MPC sample, consistent with monodispersity. The images show clear lattice fringes across the nanoparticles indicating good crystallinity within the MPCs. The SAED pattern in Figure 3.5 is also an indicator of the crystalline lattice. This can be further verified by large angle x-ray diffraction (LAXRD).
Table 3.3 Measured lattice spacing, distance in (nm), from reference 8. Ring distance (nm)
1 2 3 4 5 6 0.486 0.298 0.254 0.212 0.173 0.163
Fe3O4
0.486 0.297 0.253
hkl
111
220
311
7 8 9 10 0.15 0.134 0.129 0.122
0.21 0.171 0.162 0.148 0.133 0.128 0.121 400
422
511
440
620
533
444
Figure 3.7 SAED data, the top image is the 2.0 nm (Fe3O4)X(octanoate)Y MPCs, and the bottom image is a 6.0 nm (Fe3O4)X(oleate)Y MPCs from Reference 8. Table 3.1 has the lattice parameters used to compare their 6.0 nm particle to bulk Fe3O4.
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3.3.1.1 Large Angle Diffraction (LAXRD) Large angle x-ray diffraction (LAXRD) (2ș = 10 - 90°; s = 1.1 – 9 nm-1) will allow for the comparison of bulk materials to nanoparticles. The (Fe3O4)x(carboxylate)y MPCs may be considered to be a less-ordered system, which can be neither completely crystalline nor completely amphorous.27 When crystals are very small ( 2 nm), it becomes very difficult to distinguish between truly amorphous solids and crystalline solids, even by advanced techniques such as XRD and TEM. Amorphous materials have some short-range ordering among atomic positions when length scales are 5 nm. 29 Large portions of the atoms are located at or near the surface of very small crystals; relaxation of the surface and interfacial effects can distort these atomic positions thereby decreasing structural order. The finite size of nanoparticles causes line broadening of diffraction peaks, resulting in the failure of the Scherrer equation to determine particle size. This is a known problem for x-ray diffraction of nanoparticles. 29-32 The Scherrer equation is based on the assumption of a perfect lattice limited in size. Nanoparticles with significantly reduced dimensions are often terminated by a variety of different hkl-planes, and have a large fraction of their atoms at the surface which often contain some degree of disorder. This finite size broadening will widen the reflections to cover several degrees of 2 T , thus the pattern will resemble that of an amorphous material. Chapter 2.2.3.2 covers this in more detail. The ability of Fe3O4 to oxidize to J-Fe2O3 and then to D-Fe2O3 must also be accounted for when examining XRD data. Table 3.4 provides a list of the lattice constants for several iron oxides.
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Table 3.4. Lattice constants in nm for some iron-oxides. Composition
Name
Type
Lattice Dimensions (nm) Unit Cell Z
Structure
Fe3O4
Magnetite Ferrimagnet
a=0.8396
8
Cubic
J Fe2O3
Maghemite Ferrimagnet
a=0.83474
8
Cubic
D Fe2O3
Hematite
Antiferromagnet
a=0.50356
6
FeO
Wustite
Antiferromagnet
a=0.4296
4
Rhombohedral Cubic
It is important to carefully determine the differences in phases between magnetite and maghemite as they have very similar lattice constants and positions in s space. Table 3.5 is a comprehensive listing of iron oxides and their relative positions in s space along with their miller indices (h k l). Figure 3.8 is an example of the guassian fit used to determine core diameter estimates. By using a fitting function with Microcal Origin, any bias due to human error is minimized.
Figure 3.8. Example of a guassian fit for LAXRD. The red dotted lines are the guassians fitted to data for larger ~6.7 nm Fe3O4-propionate MPCs.
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Table 3.5. X-ray diffraction for synthetic iron oxides.
2T 18.3 30.1 35.4 37.1 43.1 47.1 53.4 56.9 62.5 65.7 66.8 70.9 74 75 78.9 81.9 86.7 89.6
2T 24.2 33.2 35.6 39.3 40.9 43.5 49.5 54.1 56.2 57.5 57.6 62.5 64 66 69.6 72 72.3 75.2 75.5
Fe3O4 Synthetic Intensity s space s*I(s) hkl 100 2.06 206 111 295 3.37 994.15 220 999 3.95 3946.05 311 77 4.13 318.01 222 201 4.76 956.76 400 5 5.19 25.95 331 86 5.83 501.38 422 277 6.19 1714.63 333 365 6.74 2460.1 440 8 7.05 56.4 531 1 7.15 7.15 442 28 7.53 210.84 620 69 7.81 538.89 533 29 7.9 229.1 622 21 8.25 173.25 444 4 8.5 34 711 28 8.91 249.48 642 99 9.15 905.85 731 JCPDS - 82-1533
DFe2O3 Synthetic Intensity s space 312 2.72 999 3.71 709 3.97 19 4.37 188 4.54 18 4.81 327 5.44 387 5.9 4 6.11 24 6.24 80 6.25 244 6.73 239 6.88 2 7.07 23 7.41 80 7.63 19 7.66 2 7.92 49 7.94
2T 14.97 18.4 23.8 26.1 30.3 32.2 35.7 37.3 43.3 50.1 53.8 57.3 63 69.4 71.4 72.5 74.6 75.5 81.5 87.4 90.3
s*I(s) hkl 848.64 0 12 3706.29 104 2814.73 110 83.03 006 853.52 113 86.58 202 1778.88 0 24 2283.3 116 24.44 211 149.76 122 500 0 18 642.12 214 1644.32 300 14.14 125 170.43 208 610.4 1 0 10 145.54 119 15.84 217 389.06 220
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JFe2O3 Synthetic Intensity s space 5 1.69 4 2.08 5 2.68 5 2.93 35 3.39 2 3.60 100 3.98 3 4.15 16 4.79 2 5.50 10 5.87 24 6.22 34 6.78 1 7.39 3 7.58 1 7.68 5 7.87 2 7.95 1 8.47 2 8.97 7 9.20
s*I(s) 8.46 8.30 13.38 14.66 118.75 7.20 397.93 12.45 76.63 10.99 58.74 149.38 230.63 7.39 22.73 7.68 39.33 15.90 8.47 17.94 64.43
hkl 110 111 210 211 220 221 311 222 400 421 422 511 440 611 620 540 533 622 710 642 731
2T 77.8 78.8 79.5 80.6 80.7 83 84.5 85 88.6
JCPDS - 39-1346 Intensity s space s*I(s) 17 8.15 138.55 8 8.24 65.92 1 8.3 8.3 14 8.4 117.6 31 8.41 260.71 38 8.6 326.8 2 8.73 17.46 57 8.77 499.89 51 9.07 462.57 JCPDS - 79-1741
2T 36.1 41.9 60.7 72.7 76.5
FeO Synthetic Intensity s space s*I(s) hkl 668 4.02 2685.36 111 999 4.64 4635.36 200 458 6.56 3004.48 220 164 7.69 1261.16 311 112 8.037 900.144 222 JCPDS - 77-2355
hkl 036 223 131 312 128 0 2 10 0 0 12 134 226
LAXRD was used to determine the mean core dimensions of several (Fe3O4)x(carboxylate)y MPCs. Average core sizes were between 1.0 nm and 6.7 nm. As previously shown, the smallest particle sizes were confirmed with TEM as well as SAED patterns. At the bottom of Figure 3.9 are the miller indices and their peak intensities for bulk magnetite, further confirming the Fe3O4 core. Since the unit cell of Fe3O4 is facecentered cubic (FCC), only peaks from lattice planes that are all even or odd indices are expected. The diffraction pattern for the 2.6 nm (Fe3O4)X(oleate)Y MPCs prepared following the Sun8 et. al. procedure still have most of the features present in bulk magnetite. It is not until the mean core diameters are 2.0 nm that significant broadening appears due to the finite number of lattice planes. At these small sizes large portions of the atoms are located at or near the surface. Relaxation of the surface and interfacial effects can distort these atomic positions thus decreasing structural order, similar to the effect manifested at the Verwey transition. The LAXRD data presented in Figure 3.9 show an intensified (111) peak for nanoparticles 2.0 nm, suggesting the surface structure may differ from that of the bulk structure. The SAED data from the HRTEM also suggests enhanced intensity of the (111) peak for the 2.0 nm (Fe3O4)X(octanoate)Y cluster. Figure 3.10 shows the change in relative intensity for the (111) peak as a function of particle size. A noticeable shift of the peak position is also evident and may result from an overall lattice relaxation. This altered intensity of the (111) peak could also be related to the surfactant interaction with a greatly increased surface volume. Surface studies are needed to further examine this enhanced diffraction feature and analogous changes have been seen in other NPs such as gold.33 These LAXRD figures indicate that further size characterization needs to be completed to fully understand the structures in these size regimes. A next step might involve the theoretical calculation of diffraction patterns for a single unit cell of Fe3O4, similar in size to the 1.0 nm MPCs.
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Figure 3.9. LAXRD data for (Fe3O4)x(carboxylate)y MPCs. The miller indices and intensities for bulk Fe3O4 are provided at the bottom of the figure for comparison. Significant line broadening is apparent in clusters with average core diameters 2.0 nm.
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Figure 3.10. Change in the relative intensity of the (111) peak from LAXRD as a function of particle size. A noticeable shift in the peak position is evident for clusters smaller than 2.0 nm.
Differentiating between small Fe3O4 and J -Fe2O3 MPCs is further complicated by their similar lattice constants (.8396 and .8347 respectively), coupled with increased line broadening at these dimensions. A 2 nm Fe3O4 MPC however, is expected to have more surface Fe+2 cations, so some overlap with J -Fe2O3 features might be expected. Figure 3.11 is a three-dimensional plot of the growth of (Fe3O4)X(propionate)Y clusters as a function of reaction temperature. In addition to clearly illustrating the effect of temperature on particle growth, this figure also emphasizes the growth of pure Fe3O4 core clusters. While the smallest MPCs with the largest (111) peaks are difficult to separate from J -Fe2O3 peaks, it is clear that they resemble bulk Fe3O4 at diameters above 2.6 nm.
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Figure 3.11. A three-dimensional plot of the growth of (Fe3O4)X(propionate)Y clusters as a function of reaction temperature clearly illustrates the growth of particles as the reaction temperature increases. The purple and blue diffraction patterns are for MPCs that range in size from 1.0 ± .1 nm. The black pattern is for 6.7 nm MPCs that show all of the diffraction features of bulk magnetite.
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3.3.1.2 Matrix Assisted Laser Desorption Ionization Mass Spectrometry ( MALDI-MS)
MALDI-MS data were collected on the smallest (Fe3O4)X(propionate)Y MPCs and (Fe3O4)X(hexanoate)Y MPCs. Figure 3.12 shows the full range for the (Fe3O4)X(propionate)Y MPCs with a 25X inset featuring the fragmentation pattern of the parent mass at 1900 amu. The complex pattern along the x-axis clearly indicates the presence of molecules. Two dominant patterns arise for these small MPCs, a loss of Fe3O4-C at 244 amu and for a single Fe atom at 54-56 amu. The parent ion at 1900 amu can be attributed to (Fe3O4)8C4, with the larger of the two fragments 244 amu at 1657,1414,1169 and 921. The high energy (3.67 eV) of the ionization laser likely dissociates the ethyl chains from the carboxylate moiety, precluding observation of intact (Fe3O4)8(propionate)Y. The LAXRD data presented in section 3.3.1.1 also suggest a core diameter of ~ 1.0 nm and based on the bulk density for magnetite (5.195 g/cm3) are consistent with 8 units of Fe3O4 (1852 amu). Figure 3.13 shows the full mass range for the (Fe3O4)X(hexanoate)Y MPCs, while the inset shows a 5X enlargement of the fragmentation pattern. The peak spacing indicated that the masses where dianionic hence the 2*(M/Z), and the complex pattern is once more due to the presence of a molecular species. Two dominant patterns also arise for the (Fe3O4)X(hexanoate)Y MPCs. From the parent ion at 4411 amu, a loss of Fe3O4-C at 248 amu and Fe-hexanoate at 187 amu alternate throughout the fragmentation pattern. A loss of an Fe at 57 amu is also prevalent, however the mass losses appear 7 amu greater in this spectrum due to low resolution (adjacent averaging). The parent ion can be attributed to (Fe3O4)16C60. For these MPCs, the LAXRD data indicated a core diameter of ~1.3 nm, and when the bulk density of magnetite (5.195 g/cm3) is multiplied by the volume of 1.3 nm spherical shape diameter (also evident in the TEM), results in a (Fe3O4)16 with a core mass of 3705 amu.
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Figure 3.12. MALDI-MS for (Fe3O4)8(propionate)4 MPCs. The x-axis shows the full range, while the inset shows a 25X enlargement of the fragmentation region from 1300 amu to 2000 amu.
79
Figure 3.13. MALDI-MS for (Fe3O4)16(hexanoate)60 MPCs. The x-axis shows the full range, while the inset shows a 5X enlargement of the fragmentation range from 3000 amu to 4500 amu. Table 3.6.Peak assignments for high mass region for (Fe3O4)X(hexanoate)Y. Anion Theoretical Mass Peak Composition Mass
Anion Theoretical Mass Peak Composition Mass
4599
(Fe3O4)17C55
4597
3600
(Fe3O4)13C37
3602
4411
(Fe3O4)16C49
4411
3538
(Fe3O4)13C44
3538
4227
(Fe3O4)15C47
4225
3413
(Fe3O4)12C53
3415
4159
(Fe3O4)15C57
4158
3353
(Fe3O4)12C36
3354
3974
(Fe3O4)15C42
3978
3288
(Fe3O4)12C42
3283
3853
(Fe3O4)14C38
3850
3223
(Fe3O4)12C37
3223
3789
(Fe3O4)14C46
3794
3168
(Fe3O4)11C52
3171
3724
(Fe3O4)14C40
3722
3103
(Fe3O4)11C35
3107
3662
(Fe3O4)13C54
3659
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3.3.1.3 Elemental and Thermogravimetric Analysis
Atomic absorption elemental analysis (EA) was performed by Galbraith Laboratories on ~2.6 nm (Fe3O4)X(oleate)Y MPCs .The weight percentage for each element evaluated were: 50.01% Fe, 17.07% C, and 3.4% H. Table 3.7 presents the values from EA, with the assumption that 100 g of material was used. The amount of oxygen was an estimate, as the remainder of the mass not evaluated by EA. This value may be an overestimate, as atmospheric contaminants may be adsorbed on the surface as well.
Table 3.7. Percent weight of elements by (EA) in a ~2.6 nm (Fe3O4)X(oleate)Y MPC. By using the core diameter estimate from LAXRD data the number of atoms present can be calculated resulting in an estimate of the total molecular weight of a cluster.
Atomic mw. # of moles # of atoms
A
Element
wt. (g)
Fe
50.01
55.85
0.90
372.00
20774.60
C
17.07
12.01
1.42
590.39
7091.03
H
3.40
1.01
3.37
1401.26
1412.39
O
29.52
16.00
1.85
766.44
12262.87
Sum =
Total mw. (amu)
41540.9
(A) A multiplier of a constant to match XRD estimate.
If the final MPC has an estimated molecular weight of 41,541 amu, then the final cluster could have a formula of (Fe3O4)124(oleate)42-46, estimated from a spherical bulk core with a ~2.6 nm diameter. There is a slight discrepancy in the carbon/oxygen ratio that cannot be accounted for. Some possible reasons for this difference are, no error analysis was provided with the outside lab work, the nanoparticles had reduced solubility at the outside lab, or they were not as clean, i.e. completely free of solvent and/or by-products,
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as the EA analysis was performed on one of the earliest produced samples, before product purification was more thoroughly understood. In addition to EA, thermogravimetric analysis (TGA) was performed on the ~2.6 nm (Fe3O4)X(oleate)Y MPCs in order to estimate the core to shell mass ration. The sample was heated from room temperature to 600°C at a rate of 10°C per minute under a nitrogen purge. The sample was held at the final elevated temperature for 10 minutes to ensure complete removal of all volatile materials. Figure 3.14 is the TGA plot for the (Fe3O4)X(oleate)Y MPCs and shows a volatile mass loss of 27%.
Figure 3.14. Thermogravimetric (TGA) plot for ~2.6 nm (Fe3O4)X(oleate)Y MPCs. The black plot is for % volatile mass loss, the blue dotted line is temperature change per minute. The green dotted line is a guide to the y-axis value.
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The ~2.6 nm (Fe3O4)X(oleate)Y MPCs core mass estimate of ~ 41,550 amu with 46 passivation oleates massing 12,947amu would be expected to give a 24 % volatile mass loss. The experimental 27% loss of volatile from the total cluster mass is 3% larger than expected. This amount suggests remnant organic reactants or additional surface species present and may indicate the need for further purification. The ~2.6 nm (Fe3O4)X(oleate)Y MPC was the only sample evaluated by EA analysis. The goal was to relate LAXRD, EA and TGA data to correlate core diameter/mass for this cluster. The remaining smaller MPCs use MS in place of EA, offering a more direct view of the core composition. The addition of MS validates the final proposed core sizes from LAXRD for the two smallest cluters. A summary of cluster compositions is provided. Figure 3.15 is the TGA plot for the ~1.0 nm (Fe3O4)8(propionate)4 MPCs and indicates three distinct mass loss regions. Since the core diameter is 1.0 ± 0.1 nm with a parent mass of 1900 amu attributed to (Fe3O4)8C4, it is expected that for (Fe3O4)8(propionate)4 the mass would be ~ 2145 amu of which 1852 amu or 86.4% is Fe3O4 core. A theoretical mass loss of the volatile material was expected to be 13.3 %, agreeing well the experimental value of 13%. After the initial removal of surface carboxylates, the core rearranges to more thermodynamically stable forms via loss of formerly stabilized surface Fe3O4 units. The loss of these six Fe3O4 would theoretically account for a mass loss of 64.8%, very near the 66.0 % observed. The last mass loss, seen for all short chain passivated MPCs ( 8 carbons) is assigned as a loss of two FeO units, which would theoretically yield a 6.7% mass loss, once more near the 7.0% observed. The remaining mass would thus be Fe2O3, which is more thermodynamically stable than magnetite at elevated temperatures.34 The high surface /core ratio in these smallest MPCs effected the stability at elevated temperatures, the mass loss is consistent with a (Fe3O4)8(propionate)4 starting material decomposing to more thermodynamically stable FeO.
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Figure 3.15. Thermogravimetric (TGA) plot for the ~1.0 nm (Fe3O4)8(propionate)4 MPCs.
Figure 3.16 is the TGA plot for ~1.3 nm (Fe3O4)X(hexanoate)Y MPCs and indicates two distinct mass loss regions. From the LAXRD data and MS, a core size of 1.3 nm and 3705 amu is proposed with a composition of (Fe3O4)16(hexanoate)60 and a total cluster mass of 10499 amu. A theoretical TGA mass loss of 64.7% was expected and the first mass loss region was at 62.5%, resulting in an error of only 3.4%. Since this is the second smallest cluster studied, the larger surface/core ratio again produced a second mass loss region of ~ 13 FeO or another 9.5 %, therefore increasing the total mass loss to 72%. The remaining mass after thermal decomposition should have a mixed phase composition with a (Fe3O4)3(Fe2O3)13 stoichiometry.
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Figure 3.16. Thermogravimetric (TGA) plot for the ~1.3 nm (Fe3O4)X(hexanoate)Y MPCs. Figure 3.17 is the TGA plot for the ~ 2.0 nm (Fe3O4)X(octanoate)Y MPCs and shows two distinct mass loss regions. The LAXRD data and TEM indicate a core size of 2.0 nm which is equivalent to (Fe3O4)56(octanoate)y, with a core mass of 12,966 amu. The first mass loss region is attributed to the desorption of the organic volatiles on the cluster surface, in this case a 44% mass loss. If the 56% remaining mass is all core then the total surface/core mass would be ~23,154 amu. One octanoate has a mass of 143.2 amu, thus ~71 octanoates were removed from the surface. The second mass loss region of an additional 5% is attributed to the removal of 16 FeO from the surface volume, suggesting mixed-phase material with a stoichiometry of (Fe3O4)40( Fe2O3)16 remains after thermal decomposition of the MPCs.
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Figure 3.17. Thermogravimetric (TGA) plot for the ~2.0 nm (Fe3O4)X(octanoate)Y MPCs.
Finally, Figure 3.18 is the TGA for the bulk-like ~6.8 nm (Fe3O4)X(propionate)Y MPCs unexpectedly shows two mass loss regions, although the second is very subtle. From LAXRD data, the core has a ~6.8 nm diameter resulting in a core mass of 489,710 amu or (Fe3O4)2115. The TGA shows a final weight of 83% that is assumed to be mostly core mass, with a composition of (Fe3O4)1955(Fe2O3)160. Due to the size of these MPCs, the surface/core ratio is much lower than the others, therefore the less stable surface state was expected to contribute less to the net mass loss. With a 15% mass loss only attributed to the propionate chains a final cluster of (Fe3O4)2115(propionate)1183 is proposed with total mass of 576,176 amu.
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Figure 3.18. Thermogravimetric (TGA) plot for the ~6.8 nm (Fe3O4)X(propionate)Y MPCs. Table 3.8 provides a complete summary of the estimated compositions and masses for the (Fe3O4)X(carboxylate)Y MPCs from the size-dependent characterization techniques. The different techniques discussed so far represent a correlated set of parameters enabling a fairly accurate description for each (Fe3O4)X(carboxylate)Y MPC material. Surface/core interactions may be present, altering other properties of the MPCs. The next section will examine optical, vibrational and NMR effects present in sub2.0 nm MPCs, all of which may posses surface effects.
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Table 3.8. A complete set of values for synthesized (Fe3O4)X(carboxylate)Y MPCs MPCs
Diameter (nm)
Core Core Mass Composition (amu)
Estimated Compositions
~Total MPC Mass (amu)
Fe3O4 – propionate
1.0 ± .1
( Fe3O4)8
1,852
(Fe3O4)8(propionate)4
2,144
Fe3O4 – hexanoate
1.3 ± .1
( Fe3O4)16
3,705
(Fe3O4)16(hexanoate)59
10,499
Fe3O4 – octanoate
2.0 ± .1
( Fe3O4)56
12,966
(Fe3O4)56(octanoate)71
23,154
Fe3O4 – oleate
2.6 ± .1
( Fe3O4)124
28,710
(Fe3O4)124(oleate)46
41,550
Fe3O4 – propionate
6.8 ± .1
( Fe3O4)2115
490,000
(Fe3O4)2115(propionate)1183
576,000
3.3.2 Physical Properties of Sub-2.0 nm (Fe3O4)X(carboxylate)Y MPCs 3.3.2.1 Optical Spectroscopy As nanoparticles decrease in size changes in electronic, optical and magnetic properties arise from the confinement of electrons. Optical spectra often appear blue shifted or red shifted from the maxima observed for bulk structures. Bulk magnetite crystals appear black and absorb throughout the UV-vis-IR spectrum as a result of three types of electronic transitions: Fe+3 crystal or ligand field transitions, interactions between magnetically coupled Fe+3 ions and ligand metal charge transfer (LMCT) excitations from the oxygen (2p) non-bonding valence bands to the Fe (3d) ligand field orbitals. Occasionally charge transfer between Fe+2 and Fe+3 ions also occurs. These charge transfer transitions, either from Fe+3– O or from Fe+2–Fe+3 ions are responsible
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for the absorption of visible light. The absorption band for Fe+2–Fe+3 electron transfer in magnetite is centered in the near IR at ~1400 nm (.89 eV) and extends into the visible region.34 Magnetite (Fe3O4), maghemite (Fe2O3) and wüstite (FeO) are all semiconductors, with magnetite displaying almost metallic properties. For magnetite, the bandgap is small (0.1 eV) resulting in it having a near-metallic conductivity of 2.5 x 104 (ȍ m)-1 (Chapter 2 Table 2.2). Magnetite can be slightly metal deficient with vacancies on the octahedral sites, and therefore can be both an n and p type semiconductor. Electrical conductivity results from the motion of free charge carriers in a solid. These may be either electrons (in the empty conduction band) or holes (vacancies) in the full valence band. In edge sharing octahedral, the near vicinity of Fe+2 and Fe+3 ions allow for the easy migration of the holes resulting in the good conductivity. Conversely, maghemite (Fe2O3) has a band gap of 2.03 eV and is an n type semiconductor. Compared to magnetite; the large band gap of maghemite makes it more like an insulator. Wüstite (FeO) is also a semiconductor, but a p type semiconductor with a 2.3 eV band gap.34 Movement of oxygen nuclei around delocalized electrons, within magnetite gives it weak Marcus-type electron localization, resulting in a polaron. This localization results in an intervalence charge transfer (IVCT) absorption band in the IR at 0.6 eV. Brus et al. monitored this band as ~ 6.0 nm Fe3O4 was oxidized to Fe2O3.35 Figure 3.19 shows the optical spectra of magnetite and maghemite. Brus et al. monitored the conversion of magnetite to maghemite in an aqueous solution during oxidation and heating, via the loss of near-IR absorption. The absorption of Fe3O4 in the near-IR region decreased and eventually became flat upon conversion to Fe2O3. If oxygen was excluded from the Fe3O4 solution, then the absorbance during heating did not change. Throughout the synthetic procedures for the formation of the all (Fe3O4)X(carboxylate)Y MPCs in this
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work, atmospheric oxygen was excluded by continuous inert gas flow, thereby preventing uncontrolled oxidation. Figure 3.20 shows the UV-vis spectra for several sizes of (Fe3O4)X(carboxylate)Y MPCs. The spectra were normalized at 2.2 eV in order to compensate for the different concentrations (solubilities) within these solutions.
Figure 3.19. Optical absorbance of maghemite (top) and magnetite (bottom). Data for this plot was extracted with Data Thief from reference 35. The data was converted from absorbance/ wavelength (nm) to absorbance/eV2 vs. energy (eV). The complete loss of NIR absorption for maghemite is clearly evident.
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Figure 3.20. UV –vis spectra for (Fe3O4)X(carboxylate)Y MPCs, normalized at 2.2 eV. All MPCs show absorbance in the NIR range, indicating Fe3O4 is the dominant phase present.
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All of the MPCs clearly absorbed in the near-IR, indicating Fe3O4 within the clusters. Deviations from bulk magnetite did not appear until the core diameters were below two nanometers. Even at those reduced dimensions, enough Fe3O4 was present to dominate the spectra. When the MPCs have a core size below 2.0 nm, the absorbance band maxima is clearly blue shifted, suggesting the onset of quantum confinement. This feature is most noticeable in the ~ 1.0 nm cluster, as evidenced by a band centered of ~1.3 eV. This cluster has eight times fewer Fe3O4 units than the ~2.0 nm cluster, therefore the edge sharing octahedral Fe+2 and Fe+3 holes are easily confined resulting in the blue shift. Figure 3.21 shows the full optical absorbance spectra for the three smallest magnetite MPCs isolated. Table 3.9 shows the number of iron atoms in the core of the smallest MPCs. At diameters of ~1.0 and 1.3 nm, the Fe3O4 MPCs have similar number of core atoms to gold and cadmium quantum dots.20,31 These known quantum dots clearly illustrate the divergence of nanocrystalline properties from the bulk with decreasing core diameter. The optical spectra of nanometer gold indicate quantum size effects on the electronic structure by the emergence of discrete electronic energy level spacings.
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Figure 3.21. Expanded UV-vis spectra for the smallest MPCs. The blue shift of the absorbance band for charge transfer (0.89 eV) is evident for the two smallest clusters. The spectra are normalized at 2.2 eV for direct comparison.
Table 3.9. Number of iron atoms in cores of smallest magnetite MPCs.
Est. Compositions
Diameter (nm) # atoms # Fe
(Fe3O4)8(propionate)4
1.0 ± .1
56
24
(Fe3O4)16(hexanoate)59
1.3 ± .1
112
48
(Fe3O4)56(octanoate)71
2.0 ± .1
392
168
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Figure 3.22 presents the optical data from Figure 3.20 in differential form to better compare the varying optical spectra as a function of core diameter. The derivative plots are analogous to a partial density of states plot for the core electronic states. The differential plot is then a direct representation of the energy-level quantization (quantum size effects) of the unoccupied parts of the conduction band.33,36 Each minima (inflection point) indicates the energy onset for an electronic transition to a higher energy molecular orbital. Three distinct onsets are evident in the ~1.0 nm core (Fe3O4)8(propionate)4 MPC at 1.49,1.81 and 1.91 eV. These features are completely absent for 2.0 nm and larger core MPCs. Similar features may also be present in the ~1.3 nm MPCs, however its lower solubility (100 ȝM vs. 2700 ȝM) compared to the ~1.0 nm MPCs prevented collection of strongly absorbing solutions between 0.6 and 1.8 eV.
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Figure 3.22. Differential optical spectra of (Fe3O4)X(carboxylate)Y MPCs. Three minima for ~1.0 nm Fe3O4 – propionate clusters are indicated as the onsets of absorbance bands.
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3.3.2.2 Infrared Spectroscopy
The infrared spectrum for magnetite is very simple, with only two broad bands at 580 and 400 cm-1, corresponding to vibrations of Fe+3– O and Fe+2 – O bonds. Maghemite has many IR bands in the Fe-O region making IR spectroscopy useful for differentiating between the two phases. Roca et al. used IR to demonstrate covalent bonding of oleate to the Fe3O4 surface.37
Figure 3.23. IR spectra for ~11 nm Fe3O4 – Oleic Acid and pure oleic acid, adapted from Roca et al.37
Figure 3.23 illustrates the surface binding of oleic acid to magnetite in the 1700 to 1400 cm-1 region. The two absorption bands at 1625 and 1530 cm-1 arise from C-O stretching. The lowered frequency of these bands compared to the frequency of pure oleic acid at 1715 cm-1 indicates covalent binding to the surface, with no free oleic acid molecules detectable. Roca et al. also presented TGA data confirming loss of volatile oleate, further confirming the nature of the surfactant/core interaction.37
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Figure 3.24 is the IR spectra for the three smallest (Fe3O4)X(carboxylate)Y MPCs. The starting material Fe(III)(acac)3 is also presented in order to verify its absence in the product. All three spectra show the broad Fe-O bands characteristic of Fe3O4 and not Fe2O3. The C-O stretches are also illustrated in the 1700 to 1300 cm-1 range possibly indicating the nature of the surfactant/core bond. Unbound carboxylic acids have dimerically hydrogen bonded C = O stretches that are intense at 1715 cm-1 but are absent upon binding to the magnetite core. This is further evidenced by the absence of an –OH stretches or bends. Additionally a series of C-H stretches appear in the proper ranges of 2850 to 3000 cm-1. The set of IR spectra along with the TGA data presented earlier confirm the presence of covalently bonded carboxylic acids on the core surfaces.
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Figure 3.24. Infrared spectra of the smallest (Fe3O4)X(carboxylate)Y MPCs responsible for the various C-O absorbance modes are shown. No N-H stretches characteristic of oleylamine or carboxylic acid O-H stretches were observed in the MPCs.
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3.3.2.3 Proton Nuclear Magnetic Resonance (1H-NMR)
This is the first reported use of proton nuclear magnetic resonance (1H-NMR) applied to (Fe3O4)X(carboxylate)Y MPCs, with one to seven methylene units within the alkane backbone. Figure 3.25 are the 1H-NMR spectra for several MPCs as saturated solutions in deuterated toluene. It is interesting to note the solvent peaks at 2.05 ppm and near 7.8 ppm are very sharp for the smaller one and 1.3 nm MPCs. As the MPCs increase in size, the sharpness of these solvent peaks decreases somewhat at 2.0 nm and much line broadening occurs within the 2.4 nm core solution. This effect can not be attributed to concentration, as the 1.0 nm core solution has the highest concentration (~2.7 mM) and the two largest clusters are at lower concentrations (130 ȝM and 400 ȝM) Figure 3.26 is the 1H-NMR spectra featuring the methyl (.95 ppm) and methylene (1.4 ppm) features for each size MPC. The line broadening in 2.0 – 4.0 nm gold and metallic MPCs is known. As the core sizes increase above 2.0 nm, the cores may rotate slower allowing spectral features to broaden from a decrease in spin-spin relaxation (T2).33,38 Smaller clusters may rotate faster yielding peaks with less broadening. For magnetite clusters, the local magnetic field of the core can also exceed the 9.4 T applied field of the Bruker AMX-400, preventing detection of surface-bound aliphatic species. This may be responsible for the distinct solvent broadening and loss of aliphatic spectral features within the 2.6 nm core sample. The expected methyl/methylene/hydrogen ratios for the corresponding carboxylic acids are not observed in the MPC 1H-NMR spectra. The 1.3 nm and 2.0 nm core MPCs have decreased methylene proton signal intensity, while the largest no carboxylate protons at all. The methylene proton signal in the (Fe3O4)X(propionate)Y MPCs, is abnormally high, being three times larger than expected for free propionic acid.
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This NMR data further confirms the presence of carboxy chains on the core surfaces, and emphasizes that changes in proton signal occur as a function of core diameter, whether the changes are strictly related to core sizes or if magnetic interactions are contributing is not known at this time. The clusters with diameters at or below two nanometers posses considerably less magnetic behavior than the 2.6 nm MPC, which likely allows the detection of the aliphatic protons in these systems. Chapter 3.3.3 discusses the magnetic properties of these MPCs in detail.
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Figure 3.25. 1H-NMR spectra for several sizes of (Fe3O4)X(carboxylate)Y MPCs. The concentration of MPCs in the deuterated toluene solvent (from top to bottom) are ~2.7 mM, ~100ȝM, ~130 ȝM, and ~400 ȝM. The corresponding concentrations of iron within these solutions are indicated in each spectrum.
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Figure 3.26. 1H-NMR spectra for the methyl/methylene regions on the surfaces of (Fe3O4)X(carboxylate)Y MPCs.
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3.3.3 Magnetic Properties of Sub- 2.0 nm Fe3O4 Nanoclusters
One of the main features of nanoscale materials is the emergence of new macroscopic properties arising from their unique molecular structure. Significant research is currently devoted to tailoring nanomaterial structure and correlating it to macroscopic properties, such as giant magnetoresistance, magnetocaloric effect enhancements and quantum tunneling of magnetization.39 The new phenomena observed arise from interactions between intrinsic properties, finite size effects, and interparticle interactions. Finite-size effects are the most dominating factor on the magnetic behavior of individual nanoparticles as their size decreases.39 Superparamagnetism (SPM) is a much studied size effect simply because the particle anisotropy is generally proportional to its volume. The dependence of magnetic properties on a preferred direction is called magnetic anisotropy (Keff). As the particle volume decreases, the volume can be considered a zero-dimensional magnetic system, which strongly affects its magnetic behavior. The reduction in size also allows for the magnetic anisotropy energy to be influenced by thermal energy. Sub- 2.0 nm (Fe3O4)X(carboxylate)Y MPCs can be considered zero-dimensional systems analogous to quantum dots (Chapter 2.1.1). Some common problems that influence the magnetic response in SPM NPs are high saturation fields, high-field irreversibilities, extra anisotropy contributions and shifted hysteresis loops after field cooling (FC). These observed problems have been attributed to core/surface coupling in small magnetic nanoparticles.39 Magnetic characteristics of the NP surface differ from the core because of the unique atomic coordination and possible surface defects. While the core can posses a spin arrangement similar to its bulk counterpart, the surface layer may be much more disordered. There is no current analytical technique available to distinguish
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the core and surface states, preventing determination of the contribution of surface and core states to the observed magnetic behavior. Bulk magnetite is ferrimagnetic at room temperature with a Curie temperature (TC), of 850 K. The two different cation sites, tetrahedral (X) occupied by Fe+3 and octahedral (Y) occupied by both Fe+3 and Fe+2 form two interpenetrating magnetic sublattices (Chapter 2.2.2). Below TC, the spins on the X and Y sites are antiparallel, and the magnitudes of the two spins are unequal, causing ferrimagnetism. At the Verwey transition temperature (TV) of 120 K an ordered arrangement of Fe+3 and Fe+2 ions on the Y sites exists and inhibits electron delocalization.34 Bulk magnetite has cubic magnetic anisotropy, with the 111 and 100 directions being the easy and hard axis of magnetization, respectively. At room temperature, the first-order magnetocrystalline anisotropy has a negative value (K1 = -1.1 to -1.35 x 105 erg/cm3) and gradually increases at lower temperatures until becoming positive at TV with a resultant loss of crystal anisotropy. Bulk magnetite has a total magnetic anisotropy Keff of ~ 105 –106 erg/cm3 and a saturation magnetization value MS = 92-100 emu/g or 84.5 emu/g for commercially made magnetite fine powder.40,8 Magnetic properties of nanoscale materials follow known trends, but with slight variations in specific property values, dependent upon their synthetic methods. Particles produced by different synthetic procedures can exhibit different magnetic properties such as magnetic saturation, coercive field strengths and blocking temperatures. Some of these discrepancies might result from finite surface effects that can be modified depending on preparation, kinetic versus thermodynamic control effecting cation distribution, and possibly from annealing altering the cation distribution.39,41-42 Despite these factors, general trends can still be observed in magnetic behavior. These trends include a decrease in the blocking temperature (TB) as a function of NP size, a lowering
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remnant magnetization (Mr) and saturation magnetization (MS) as a function of size below TB, and increased coercivity (HC) at smaller NP core sizes (Chapter 1, Figure 1.10). Nanoscale magnetite particles exhibit a common trend of decreasing MS versus core size. Table 3.10 presents saturation magnetization values at room temperature for several different sized NPs. Differences in sample preparation account for the varying values, however the trend is evident. As the NP size decreases so does the MS value.
Table 3.10. Saturation magnetization (MS) values at 300 K as a function of magnetite nanoparticle core size (nm).
NP Diameter (nm) MS (emu/g) @ 300K Reference 4.3 31.8 43 5.8 ± 1.3 65 ± 3 37 6.7 ± 1.5 71 ± 2 37 8.9 49.6 44 10 60.1 44 10.7 54 43 16 83 8
Magnetic NPs also change their properties from ferromagnetic to superparamagnetic below a critical size. The critical size for magnetite particles is 13 – 15 nm.45 At these sizes surface effects have been invoked as a large source of magnetic anisotropy (Keff). By assuming a spherical core geometry for the NPs, a zero net contribution from surface anisotropy occurs.46 An additional trend for the NPs listed in Table 3.8 is decreased TB at smaller diameters. For example, the NP with a core diameter of 4.3 nm has TB ~ 45 K, while a 7.0 nm NP has TB ~ 105 K.47 The TB can be used to calculate the magnetic anisotropy constant Keff (Chapter 1.4 equation 12), to verify size effects and core/surface interactions on anisotropy constants.
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3.3.3.1 Magnetic Data for Sub-2.0 nm Fe3O4 Nanoclusters
Magnetic Data was collected on Quantum Design MPMS systems described in Chapter 2.3.8. Table 3.11 presents data on the average core volume for the (Fe3O4)X(carboxylate)Y MPCs.
Table 3.11. Core volume (nm3) for the (Fe3O4)X(carboxylate)Y MPCs.
Estimated Compositions
Core Mass (amu)
Diameter (nm)
~ % Fe Core Volume by weight (nm3) in cluster
(Fe3O4)8(propionate)4
1,621-1,852
1.0 ± .1
0.524
62.5
(Fe3O4)16(hexanoate)59
3,473-3,705
1.3 ± .1
1.15
25.5
(Fe3O4)56(octanoate)71
12,966
2.0 ± .1
4.19
40.5
(Fe3O4)124(oleate)46
28,710
2.6 ± .1
9.2
50
(Fe3O4)2115(propionate)1183
490,000
6.8 ± .1
164.6
61.5
The temperature-dependent dynamic susceptibility of magnetic NPs contains information on the potential energy barrier U (Chapter 2.1.2) that separates different minima in the energy diagram of the magnetic particle (Chapter 1, Figure 1.12). The energy barrier distribution of (Fe3O4)X(carboxylate)Y MPCs were calculated from zero field cooling-field cooling (ZFC/FC) measurements (Chapter 2.3.8).
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Figure 3.27. Temperature dependence of Zero field (ZFC) susceptibility for (Fe3O4)X(carboxylate)Y MPCs, under a magnetic field of 100 G. In Figure 3.27, ZFC curves show a displacement of TMAX from 125 to 14 K as the MPCs decrease in from 6.7 nm to 2.0 nm. The non-normalized plot illustrates broadening that can occur in the larger MPCs, and is related to the relaxation time distribution. In order to calculate the most accurate TB value, it is necessary to differentiate the susceptibilities and then plot against temperature, illustrated in Figure 3.28.
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Figure 3.28. Differential plot of susceptibility versus temperature for (Fe3O4)X(carboxylate)Y MPCs. The x-intercept of each plot indicates the TB
Figure 3.28 shows the differential plot of F vs. temperature used to determine blocking temperatures for several sizes of (Fe3O4)X(carboxylate)Y MPCs. The 1.3 and 1.0 nm were excluded as their TB was at or below the 5K temperature limit of the instrumentation. Microcal’s Origin software was used to obtain precise TB values. Temperature decay of remanence (TDR) measurements are more accurate for the calculation of TB values and should be considered for future work.48 Table 3.12 tabulates TB values for (Fe3O4)X(carboxylate)Y MPCs.
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Table 3.12 Blocking temperatures (TB) and effective anisotropy constants for several sizes of (Fe3O4)X(carboxylate)Y MPCs
Est. Compositions
Diameter (nm) Sample1 TB (K)
Sample 2 Theoretical
Keff**
TB (K)
erg/cm3
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