Iron nanoparticles by inert gas condensation
Xing, Lijuan
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Xing, L. (2018). Iron nanoparticles by inert gas condensation: Structure and magnetic characterization. University of Groningen.
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Chapter 2
Nanoparticle Synthesis and Characterization
T
his Chapter describes the techniques utilized for the
production of nanoparticles, and the subsequent experimental
methods employed for sample characterization and data analysis.
A nanoparticle deposition source, which combined high pressure
magnetron sputtering and gas condensation, was used to produce
nanoparticles. Transmission Electron Microscope (TEM) and
Scanning Probe Microscope (SPM) were used to determine the
nanoparticle morphology, structure, and their magnetic
properties.
2.1 Gas-Phase Synthesis of Nanoparticles
Gas-phase synthesis has been extensively explored as a versatile technique to produce a wide variety of nanostructured materials. This bottom-up method puts individual atoms or molecules together to form the desired nanoparticles. Compared to top-down processing that breaks down the bulk material into nanometer-sized particles, bottom-up techniques provide remarkably better control in size and shape of the resultant nano-structure1.
2.1.1 History
Inert-gas condensation derives from studies in the 1930s when Pfund et al. reported nucleation and growth of clusters in a noble-gas atmosphere and managed to produce nanoparticles via the referred inert-gas evaporation method. This technique affords more options of target materials. The subsequent study by Granqvist and Buhrman6 proposed modified experimental technique. Various metals were evaporated from a temperature-stabilized source, instead of a resistant filament, into a low pressure inert gas atmosphere to produce ultrafine particles with a well-controlled size and size distribution. Parameters such as evaporation rate, type of gas, and gas pressure were defined as factors that influence the particle size. However, the real breakthrough with respect to the development of this technique came about in 1981 when Gleiter referred to the products as “microcrystalline materials” or “interfacial materials”. It was suggested that ultrafine particles were produced by in-situ consolidation with a large proportion of atoms located in the grain boundaries3. Modifications and improvements have been made to the initial
experimental setup ever since to make inert-gas condensation nowadays a versatile technique to synthesize a large variety of nanostructured materials.
2.1.2 Inert-Gas Condensation (IGC)
Synthesis of nanostructured materials by inert-gas condensation involves two steps: evaporation of target materials, and controlled condensation. In general, the main apparatus consists of an ultrahigh-vacuum (UHV) system together with one or more vapor sources, and a cluster collection part. The generated metal vapor is confined by the local inert gas pressure and cooled by repetitive collision with the carrier gas. Supersaturation is consequently achieved, in which state nucleation occurs resulting in the formation of nanoparticles.
2.1.2.1 Cluster sources
In general, nanoparticles originate from a vapor source inside a vacuum chamber containing inert gas. The adopted vapor source evolved from a resistive filament in the earliest stage to a temperature-stabilized oven in 19762 to maintain
a constant evaporation rate and consequently a well-controlled particle size. Since then various techniques were developed and modified to produce clusters, including thermal evaporation, sputtering, and laser ablation. Fundamental choices have to be made when designing an experimental system, depending on the type of desired clusters, the size and species, the temperature requirement, and whether they should be ionized4.
Thermal evaporation using oven sources provides a simple and reliable manner to produce nanoparticles with a wide size range; nevertheless, this method is not applicable to substances with high cohesive energies that require high temperature for the evaporation. Moreover, a large quantity of starting materials as well as the reactivity of metal vapors with ovens needs to be taken into account in the experimental setup. Laser evaporation technique focuses a high-energy pulsed laser on target materials to generate clusters5. The high temperature caused by the
highly efficient vaporization overcomes the limitation of thermal evaporation, but a suitable laser can be quite expensive. Magnetron sputtering was first combined with inert gas condensation by Haberland et al.6, and the sputtering source can be
applied to not only metals but insulators (with radiofrequency sputtering). Despite of the different vapor source, the subsequent condensation, including cluster nucleation and growth, follows the same principle.
2.1.2.2 Achieving supersaturation
Generally speaking, the high pressure of inert gas in the aggregation volume contributes to the supersaturation of the metal vapor. This local confinement decreases the diffusion rate of the evaporated atoms away from the source region by frequent collisions between inert gas atoms and metal atoms. The collisions, additionally, result in energy loss and consequently the cooling of metal atoms, further shortening the mean free path. Based on Granqvist and Buhrman’s work, heavier gas atoms are more effective in limiting the mean free path.
2.1.2.3 Nucleation
Nucleation from a continuous vapor phase can occur heterogeneously or homogeneously. Heterogeneous nucleation occurs with foreign nuclei or dust particles being present in the vapor phase. However, homogeneous nucleation takes
place without any foreign particles, under which condition the metal vapor condenses to form embryonic droplets or nuclei. During gas phase synthesis of nanoparticles, homogeneous nucleation occurs when a sufficiently high supersaturation is achieved. Classical nucleation theory is based on the assumption that the formed embryonic clusters can be described as spherical liquid drops with the bulk liquid density inside and the vapor density outside. The cluster free energy, relative to the vapor phase, consists of two parts: a positive contribution from the surface free energy, and a negative contribution from the bulk free energy difference between the metal vapor and the liquid. The surface free energy originates from the reversible work required for the development of the interface between the liquid drop and the vapor atmosphere. The interface energy needed to generate a cluster containing n atoms or molecules can be described by7
n 4
3v 4
23n23A
(2.1)
where represents the surface energy per unite area, A(n) is the total surface area, and v gives the atomic volume in the bulk liquid. The contribution resulting from the bulk free energy difference produced during the transfer of the n molecules from vapor to cluster is given by7:
lv
nnkBTln
P Pe
(2.2) where l and v represent the chemical potentials per molecule in the bulk liquid and vapor state, respectively, kBis the Boltzmann constant, T is the temperature, and P Pe shows the supersaturation ratio with P the vapor pressure and Pe theequilibrium or saturation vapor pressure. The aforementioned two contributions make up the reversible free energy (work) needed to form a cluster consisting of n atoms or molecules, which is given by7:
n
v
n nkBT
P Pe
W 4 3 4 23 23 ln (2.3)
During the inert-gas condensation, it is thermodynamically stable to form solid state materials, i.e. nanoparticles in this case, relative to sustaining vapor phase. While the positive contribution from the surface free energy results in a barrier in the
nucleation. Equation (2.3) describes the competition of the surface free energy and the bulk free energy, which determines cluster stability or cluster concentration. The smallest stable cluster that can form with a free energy that decreases beyond this size (and increases up to this size) is determined by the condition W n0, giving the critical cluster size
n
*
andr
*
as follows:3 2 3 )) ln( ( 3 32 * v kBT P Pe n (2.4) r*2v
kTln
PPe
(2.5) Therefore, the barrier height W(n*) is determined by substitutingn
*
into equation (2.3), giving 3 2 2 )) ln( ( 3 16 *) (n v kBT P Pe W (2.6)A high supersaturation results in a decrease in the critical nucleus size as well as the barrier height, allowing more clusters to grow into stable droplets. However, for extremely high supersaturation, the steady-state nucleation theory is no longer applicable as the critical cluster size may reduce down to a few atoms, which is unreasonable to be regarded as a macroscopic entity with macroscopic properties, as for example, surface tension and density7.
2.1.2.4 Cluster growth
Once nucleation occurs, condensation of the vapor-phase atoms on the nuclei contribute to the growth of the clusters to some extent, which, on the other hand, depletes the partial pressure of the metal vapor and quenches further nucleus formation. However, cluster growth is predominantly attained by coalescence when clusters collide in high enough temperature, lose their kinetic energy, and form a larger cluster. Once the clusters are cooled down to a level that cannot affords the proceeding of coalescence, coagulation predominates the growth of clusters forming loose agglomerates with open structures. The growth time is determined by the efficiency of the cooling effect. In case of short growth time or low particle density, cluster agglomerations are small. Granqvist and Burhman8 reported that
the final particles size is principally an integration of several coalescence processes, leading to a log-normal size distribution.
2.1.3 Inert Gas Condensation with Magnetron Cluster Source
The instrument employed to deposit Fe nanoparticles (NPs) is a home-modified Nanosys50 from Mantis Deposition Ltd. (http://www.mantisdeposition.com) which is a combination of magnetron sputtering and gas condensation. Magnetron sputtering is applied as the vapor source. Figure 2.1 gives the system setup (Figure 2.1(a) and (b)), and details of nanoparticle sources (Figure 1(c)) consisting of two chambers: the aggregation chamber where nucleation and cluster growth take place, and the main chamber where produced nanoparticles are collected (as shown in Figure 2.1(a)). Two Leybold turbo molecular pumps with a capacity of 300 lt/s are employed to evacuate the system, and a Varian LTH 10 scroll vacuum pump is used to back the evacuation. The vacuum in the main and aggregation chamber can reach 1×10-8 mbar and 1×10-6 mbar, respectively. The pressure sensors in the two
chambers give pressure readings on the Mantis controller (shown in Figure 2.1(b)). The settings can be adjusted and monitored by the controller.
The sputtering process starts with the introduction of gas flow into the system where inert gas is generally used due to the minimal interference with the target material. The potential difference, caused by the applied voltage, accelerate electrons away from the target that acts as the cathode (with the magnetron cover acting as the anode), and the collisions between these electrons and inert gas atoms, normally Ar, result in the ionization of the sputtering gas forming excited species. The ionized Ar atoms (Ar+) are accelerated by the potential difference and
subsequently impact on the target breaking off particles (atoms, dimers etc.) which together compose the desired target material vapor. The release of secondary electrons are expected to occur accompanying the sputtering of the target, which are repelled away from the target and feed the ionization process further. The magnetron positioned under the target can enhance the efficiency of the ionization as the helical path that free electrons follow in the magnetic field results in a longer effective path length and therefore more chances of collisions with the sputtering gas atoms.
The material vapor is then swept by the gas flow to the aggregation volume just above the plasma where the vapor is confined by the local inert gas pressure and achieves supersaturation. The high pressure in the aggregation chamber can reduce the sputtering rate because collisions with inert gas atoms drain the energy
of the ions so that fewer of them keep sufficient threshold energy for the subsequent sputtering. However, in most cases there is an adequately broad pressure range in which a decent balance can be achieved between achieving supersaturation and maintaining an acceptable sputtering rate.
Figure 2.1 The nanoparticle deposition system (a), and the associated controller (b). Details
A magnetron sputtering system, as is schematically illustrated in Figure 2.1 (c), consists of the following main components: a magnetron head, a double gas inlet system, water cooling system for both magnetron head and aggregation chamber wall. A target material disk (2 inches in diameter) is placed on the magnetron, and an anode is then mounted on top connected to a TDK-Lambda Genesys Gen 600-1.3 programmable DC power supply with a range up to 600 V and 1.3 A. An adaptable DC voltage is applied between the target (cathode) and the anode, and the discharge power can be tuned by a built-in voltage and current limiter.
Once supersaturation is achieved, nucleation and cluster growth take place to produce nanoparticles with desired particle size. The produced nanoparticles are then carried by the gas flow to the main chamber because of the pressure difference between the two chambers, and then land on collecting substrates. The deposition rate can be monitored by a home-built quartz crystal microbalance (QCM) that is located slightly off-center of the conical cluster beam.
2.2 Transmission Electron Microscopy
Transmission Electron Microscopy (TEM) is a powerful technique that makes use of a high energy electron beam with high energy (200 keV), instead of optical light, to achieve high spatial resolution characterization of morphology, crystallography, and chemical structure depending on the operation mode. The high energy electron beam create very short electron wave (of a few pm, 2.5 pm in case of 200 keV) allowing sub-nanometer scale structure to be resolved with magnetic lenses9, and
atomic resolution can be readily obtained according to the Rayleigh criterion. In this case the highest obtainable resolution is directly proportional to the wavelength of the adopted radiation. However, in practice the resolution is not diffraction limited, but is limited by spherical aberration. However, in this case still a resolution of a few Angstrom is readily achieved. Besides its capability of high resolution imaging, interactions between the electron beam and the specimen result in characteristic processes that can be exploited in spectroscopies such as energy dispersive x-ray spectroscopy (EDX/EDS), and electron energy loss spectroscopy (EELS).
2.2.1 Beam Interactions with Specimen
The incident electron beam is transmitted through an ultrathin specimen, and various signals can be generated from the interactions between the highly energetic
electron beam with the ultrathin specimen, as shown in Figure 2.2, among which the elastically scattered electrons are basically responsible for the possibility to perform TEM imaging. The formation of elastically scattered electrons can be attributed to the interaction between the incident electron beam with the nuclei of the atoms in the sample. The scattering results in a relatively large deviation in the path of the electrons, but the velocity (
v
) and wavelength (
) exhibit no variation with little or no energy loss. The elastic scattering for non-crystalline materials depends principally on the mass-thickness of the sample, with more electrons scattered for samples with large mass-thickness. For crystalline materials, the scattering mainly results from Bragg diffraction, depending on the crystal structure and the relative orientation with respect to the incident beam. These elastically scattered electrons are focused by electromagnetic lenses to form images in the electron microscope. Interactions of the beam with orbital electrons generate inelastically scattered electrons, with a slight deviation in the path (104 radians),which are characterized by a loss of energy. The inelastic scattering of the electrons is generally accompanies by specimen damage. However, for TEM samples with a thickness smaller than 100 nm, as is normally the case, most of the highly accelerated electrons transmit through the specimen with inelastically scattered ones being a minor fraction.
Figure 2.2 Signals generated when a high‐energy electron beam interacts with a thin
specimen. The directions shown for each signal do not always present the physical direction of the signal, but indicate, in a relative manner, where the signal is strongest or where it is detected10.
2.2.2 Basic Operation Modes
The interactions between the incident electron beam and the specimen form the image that is subsequently magnified and focused on an imaging device (e.g. a photographic film, a fluorescent screen) or detected by a CCD camera, as schematically illustrated in Figure 2.3 (a). Different operating modes can be realized by lens strength variation or lens deactivation. The ray diagram of imaging and diffraction mode is shown in Figure 2.3 (b).
Figure 2.3 schematic Diagram of (a) a transmission electron microscope, and (b) imaging
and diffraction modes in TEM10,11.
2.2.2.1 Bright field imaging
In imaging mode, an objective aperture is inserted in the back-focal plane of the objective lens, as illustrated in Figure 2.3 (b) right. For bright field imaging, a small objective aperture is used with the central beam selected and the rest signal blocked. The selected signal is subsequently magnified and projected by intermediate and projector lenses to obtain the sample image. The image can be
assumed to be a simple two dimensional projection of the sample down the optic axis indicating the mass thickness distribution.
2.2.2.2 Diffraction
Diffraction contrast can be produced when the incident beam interacts with a crystalline sample, resulting in Bragg scattering that disperses electrons into discrete locations (diffraction spots). In diffraction mode, a selected area aperture is placed in the back-focal plane to define the specimen area to be projected on the screen.
Selected area electron diffraction (SAED), as a diffraction technique, is a powerful tool for crystal structure and orientation determination, as well as lattice defects identification. As can be noticed in the schematic of diffraction mode (Figure 2.3(b) left), a selected area aperture is inserted into the beam path, located below the sample holder and allowing selection of the area from which the diffraction pattern is recorded. The high-energy electron beam, typically with an energy of 100-400 keV, passes through the ultrathin sample and exhibits a wave-like behavior. As the spacing between atoms in a solid is around a hundred times larger than the wavelength of the high-energy electrons (a few thousands of a nanometer), atoms act as a diffraction grating resulting in the diffraction of electrons. Consequently, part of the electrons are scattered to particular angles that are determined by the crystal structure of the solid material, while the remaining part pass through the specimen without deflection. The resulted discrete diffraction spots are collected on the screen with each spot corresponding to a satisfied diffraction condition of the crystal structure. Individual spots will be obtained from a single crystal, whereas ring patterns form for polycrystalline materials or assemblies of randomly oriented single crystals.
2.2.3 Electron Energy Loss Spectroscopy (EELS)
The interactions between electrons and matter generate both elastically and inelastically scattered electrons. The elastically scattered ones contribute to imaging and diffraction patterns as mentioned above. Inelastically scattered electrons exhibit a characteristic energy loss, which highly depends on the atomic species present in the material. In this respect, a typical EEL spectrum is shown in Figure 2.4, which shows three regions, i.e. zero-loss peak (ZLP), Low-loss region, and core-loss region. ZLP represents the elastically scattered electrons with zero or negligible energy loss. The low-loss region covers the range 0-50 eV in the spectrum. It indicates the energy loss in the excitation of the valence electrons
within the specimen, and the broad peak is the representation of the resonant oscillations of the valence electrons (i.e. plasmons). The core-loss region gives the inner-core electronic structure of the atoms that are present in the sample. The energy loss of the core shell ionized edges determines the presence of certain atomic species in the sample, while the fine structures relates to the specific chemical environment, e.g. show variations for different valence states of atoms and different types of bonding between atoms.
Figure 2.4 A typical energy loss spectrum: (a) low‐loss region, and (b) core‐loss region,
showing ionization edges12.
2.3 Scanning Probe Microscopy
In 1981, G. Binnig et al. observed vacuum tunneling of electrons between a sharp tungsten tip and a platinum sample, which inspired the development of scanning tunneling microscope (STM). The first practice of this novel technique was reported in 1982 when G. Binnig et al.13 used vacuum tunneling to obtain
three-dimensional surface topographic images with an atomic-scale resolution. STM determines the surface topography by using the dependence of the tunneling current on the tip-sample separation, and it allows the imaging of atomic structures in real space, making the structures at the atomic level directly ‘visible’. Furthermore, the sharp tip provides the possibility to detect physical properties of materials on a small scale. However, besides vacuum tunneling of electrons, new means had been explored by which local properties of matter could be probed, triggering the invention of a whole class of techniques referred to as scanning probe microscopes (SPMs).
Among the various techniques, atomic force microscope (AFM) was developed in 1986 to image topographical structures of both conducting and insulating surfaces with atomic-scale resolution14. The introduction of AFM
overcomes the limit of STM that is only applicable to conductors or semiconductors. In AFM, sample surface is scanned by a tip, which is mounted to a cantilever spring. With the tip approaching the sample surface, AFM images are obtained by measurement of the forces between the atoms on the sample and the atoms on the tip. The following exploitation of SPMs was motivated by making use of almost every kind of interactions between the tip and sample of which one can think, to characterize topographical structures as well as physical properties.
In general terms, SPMs describe the family of instruments that were developed to characterize surfaces of materials by employing a sharp probe scanning over the surface with a very small tip-sample separation. AFM, together with its “daughter” techniques such as magnetic force and Kelvin probe microscopy (MFM-KPFM), has evolved to a crucial widely used SPM techniques.
2.3.1 Atomic Force Microscopy
AFM employs a cantilever with a sharp tip to provide the means for sensing the forces exerted on the tip by the sample surface atoms, and the cantilever is, in any case, a critical component. To detect the small interatomic forces, the cantilever should be insensitive to external disturbance from the surroundings, such as building vibrations (near 100 Hz). Therefore, cantilevers with high resonance frequency, greater than 2 kHz, should be employed to minimize the extraneous vibrational noise. Since the imaging forces in AFM are typically in the range of 10 -12-10-7 N, the spring constant of the cantilever should be less than 0.01 N/m so that
a deflection greater than 1 Å can be produced for a force of 10-12 N contributing to
the high sensitivity of this technique.
The schematic of AFM operation is demonstrated in Figure 2.5. A cantilever is fixed to the modulation piezo, and the sample is attached to a three-dimensional piezoelectric drive, i.e. the x, y, a scanner. The tip mounted at the end of the cantilever is brought in close proximity to the sample surface to sense the tip-sample interaction forces. A focused laser beam reflects off the back side of the deflected cantilever, and the displacement of the cantilever when scanning the sample surface is amplified in the movement of the reflected laser beam. The beam is subsequently collected by a position sensitive detector consisting of four closely spaced photodiodes. The amplified signal resulted from the angular displacement (including both normal bending and torsion) of the cantilever gives more light in
one photodiode than the others, producing an output signal that is proportional to the cantilever deflection. The differential signal is converted to voltage and provides feedback signal to maintain the force acting on the stylus at a constant level.
Figure 2.5 schematic of AFM operation15
2.3.1.1 Imaging modes
The commonly used imaging modes can be divided into two distinct operations: static and dynamic AFM. In static mode, the surface topography is mapped by scanning with a deflection of the tip in z direction and a constant tip-sample force/separation. The cantilever deflection is monitored during the scanning, and any variation is followed by a vertical movement of the tip to maintain a preset deflection value. According to Hooke’s law, the displacement of the cantilever is proportional to the applied force. So, in other words, the feedback loop maintains a constant force between the tip and sample, and the position of the cantilever is changed in such a way that the cantilever bending produces a constant force. The changes in z-direction required to maintain a constant tip-sample force/separation give the topographic information of the sample surface. Static mode operated with a close proximity to the sample surface and a repulsive tip-sample interaction is referred to as contact mode in which condition the last atoms of the tip-apex are
directly contacted to the sample surface. However, during scanning, the sample experiences compressive forces attributed to tip-sample interaction, as well as shear forces owing to the lateral movement with respect to the tip, both of which can substantially results in the deterioration of the tip and the sample. Besides, the stick-slip motion of the tip caused by capillary condensation and the lateral forces, combined with the degradation of the tip shape due to the tip-sample interaction, lead to a relatively poor resolution of the resulting imaging.
Dynamic AFM is operated with an oscillating cantilever, and the tip-sample separation is normally in the range where it shows a repulsive interaction. This non-contact mode provides a reliable method to image soft materials that would be damaged by the direct contact with the probe. In dynamic mode, the cantilever oscillates near its resonance frequency driven by a piezoelectric actuator. As the tip approaches the sample surface, the oscillation state of the cantilever, including the amplitude, the resonance frequency as well as the phase shift, is changed by the tip-sample interaction with respect to the driving signal. Any of the three type of changes can be detected to track the topography of surfaces and simultaneously provide the feedback signal to maintain a constant distance between the tip and sample and therefore a constant force. Two dynamic modes are mainly used for the scanning of the surface topography, i.e. amplitude modulation (AM) AFM and frequency modulation (FM) AFM, with different feedback signals. In dynamic mode, a tip-sample separation of about 5-15 nm is maintained, where the topographic information derives from the van der Waals forces between the tip and sample.
In view of the drawbacks of the aforementioned modes, amplitude modulation AFM was later developed to be used with a closer tip-sample distance involving repulsive interactions, which is referred to as “Tapping mode”16. This mode makes
it possible to achieve high resolution imaging without inducing destructive frictional forces. The cantilever oscillates near its resonance frequency with an amplitude typically in the range 20-100 nm. A certain distance between the tip and sample surface is maintained to establish an intermittent contact, where the probe strike the sample surface at the lowest position of each oscillation. However, for a large range of cantilever positions in z direction, the energy associated with the vibration can sufficiently overcome the stickiness of the surface, which is attributed to the large oscillation amplitude in tapping mode. The perturbation of the cantilever oscillation amplitude, resulted from the intermittent contact with the sample surface, is detected by the feedback system. The deviated amplitude can subsequently be used as a setpoint which is maintained constant by a height modulation throughout the lateral scanning, generating a topographic image.
Tapping mode AFM provides topographic imaging with high resolution due to its minimized sample deformation attributed to the reduced contact force per strike as well as the essentially eliminated lateral shear force.
2.3.1.2 Fundamentals of force microscopy
The basic concept of non-contact force microscopy is to raise the cantilever probe to a certain height away from the sample surface and to measure the long-range interactions exerted on the cantilever. The tip scans across the surface in a raster pattern, allowing the collection of special variations of the probe-sample interaction by detecting the change of the cantilever oscillation. The resonance frequency of the cantilever describes the characteristic part of the dynamic properties of the probe, which is be given by
m
c
f
0
(2.7) where c is the cantilever spring constant and m is the effective mass. In general, the sinusoidal oscillation of the cantilever is actuated by bimorph piezoelectric modulation with a frequency and an amplitude A0, and the tip likewise vibratessinusoidally with a distinct amplitude A and a phase shift Δφ with respect to the drive signal from the piezoelectric actuator. With a large enough bandwidth, the motion of the tip is monitored by the deflection sensor of the force microscope, which is preferentially an optical sensor. The output motion from the deflection sensor can be described by20
d
d
A
f
ft
f
t
d
f
t
d
cos
Q
0 0 0 2 0 0 2 2
(2.8)where d0 represents the tip-sample separation with zero oscillation amplitude (i.e.
the user-defined lift height) and d(t) the instantaneous distance. Besides the intrinsic properties of the cantilever itself, the equation also includes the exoteric influences by introducing a quality factor Q that is determined by the damping factor :
2 0 m Q (2.9)with describing the environmental medium, including a liquid, ambient surrounding, or ultrahigh vacuum (intrinsic dissipation). With the usual building-up, a steady-state solution for the forced oscillator can be derived from Equation 2.8, giving
t d A
ft
d 0 cos (2.10)
The tip vibrates with an amplitude, distinct from the excitation signal, given by
2
2 2 2 0 2 2 0 0 4 f f f f A A (2.11)The phase shift between this actual vibration and the drive signal is described by
2 0 2 2 arctan f f f (2.12)
The above-mentioned formulas are obtained assuming that a large enough tip-sample distance (d0) is adopted, so that a sufficiently small amplitude A is
describing the free cantilever oscillation with the absence of any tip-sample interactions. Once a force F is introduced with a decreased distance d0, the
cantilever vibration will be influenced by the tip-sample interactions and modifications have to be made to the left side of Equation 2.8 by introducing a term
F/m. Besides static interactions, dynamic forces have to be taken into account to
include all the interactions when measuring the magnetic forces of the form
t d d F F , . (2.13)
Supposing that the reduced tip-sample distance is till much larger than the driving amplitude (d0 ≫A0), only the vertical component, i.e. the z derivative, of the force
be modified to describe the cantilever behavior with the influence of the tip-sample interactions: z F c cF (2.14)
This modification results in an effectively softer cantilever under an attractive tip-sample interaction (∂F/∂z>0), and an effectively stiffer cantilever in the case of a repulsive interaction (∂F/∂z<0). Therefore, the resonance frequency of the cantilever in Equation 2.7 will also be modified as
z F c f f 0 1 1 (2.15)
Assuming that ∂F/∂z ≪ c, the variation of the cantilever resonance frequency can be described as z F c f 2 1 (2.16)
The change in the resonance frequency will lead to, as indicated in Equation 2.11 and 2.9, a variation in the oscillation amplitude of the probe A, and the phase shift
Δφ. Both the amplitude and phase shift, A and Δφ can be measured by the force
microscope to map the lateral variation of the vertical force gradient ∂F/∂z. The most commonly used mode is referred to as slope detection where the cantilever oscillation is driven at a frequency slightly off its resonance, and the resulting phase and amplitude shift are collected to map the force gradient. Moreover, frequency modulation (FM) can be alternatively used with a high Q cantilever oscillating at its resonance frequency. As the cantilever scans across the sample surface, variations in the z derivative of the force result in the changes of the oscillation frequency. The frequency variations can be detected by an FM demodulator that compensates the differences using positive feedback to maintain the oscillation at the resonance frequency as well as a constant amplitude. The precise measurements of the oscillator frequency can be attained by various methods including digital frequency counters and phase-locked loops.
2.3.2 Magnetic Force Microscopy
AFM technique is based on the interaction between the tip and the sample surface. However, different forces dominate in this interaction with distance dependency owing to different intermolecular, surface, and macroscopic effects. With increasing tip-sample distance these forces, i.e. quantum mechanical forces, capillary forces, van der Waals forces, as well as electric and magnetic forces, have a different actuating range as shown in Figure 2.6. Therefore, these forces can in principle be measured based on the idea of measuring forces by AFM, with a tip-sample separation where they play a dominant role in the interaction.
Figure 2.6 Different forces acting on the AFM tip and the distance range where each of
these force dominates the force signal17.
The 1980’s witnessed the first application of force microscopy for magnetic imaging, when a magnetic version of force microscopy was proposed to map magnetic field patterns and to resolve magnetic domain structures15,16. In 1987, Martin and Wickramasinghe18 reported a new method for imaging magnetic field
with 1000 Å resolution. A magnetized probe is used in the experimental setup to detect, instead of interatomic forces, magnetic interactions between the tip and the sample surface. As the tip scans in a raster pattern at a constant height above the sample surface, the magnetic field gradient is mapped as a variation of the force exerted on the tip. Two modes are examined. In the first mode for the imaging of dynamic magnetic fields, the tip is raised at a constant height over the sample surface while the magnetic field is dynamically modulated at a specific frequency. The force exerted on the cantilever in the aforementioned magnetic field gives rise to the vibration of the cantilever at the same frequency which is then detected by optical interferometry. In the second mode for static field pattern imaging, the
cantilever oscillates at its resonance frequency modulated by a pulsed exciter current, and the vibration is detected to map the magnetic field. Saenz et al.18
presented a similar experimental setup in the same year. The magnetic microscopy is based on the previously developed AFM. A single-domain magnetic tip scans over the magnetic sample with a large enough gap between the both, say ≈ 10 Å, where the interatomic force can be neglected. The normal component of the tip-sample force, i.e. magnetic interaction, can be detected to give corresponding domain configurations on the submicrometer scale. After these developments, MFM started to become a widely used technique in magnetic materials studies.
2.3.2.1 Hover Mode Scanning Method
The “Hover Mode Scanning Method”21,22, also referred to as “Two-Pass
Technique”, is mostly used nowadays to minimize the interference of the surface topography features on the imaging of the magnetic force gradient distribution. In this method, the magnetic tip performs twice scanning on the same line of the sample, with the first scan to collect the topographical information and the second to detect the magnetic signal, as schematically shown in Figure 2.4.
The first pass in this mode scans in AFM tapping mode. The intermittent contact between the tip and sample surface allows the long range van der Waals forces to dominate the detected force signal so that the topographical image can be produced, giving a height profile. In the subsequent second pass, the cantilever is raised to a user-defined height (eg. 50-60 nm) where another scanning is made following exactly the topographic contour collected in the first pass. Long-range interactions, such as magnetic forces, are predominant in this lift mode, thus allowing the collection of the magnetic signals. As can be noticed in Figure 2.7, the height profile from the tapping mode helps to maintain a constant tip-sample separation under which condition the cantilever is only affected by the long-range forces.
Figure 2.7 Schematic of the “Two‐Pass Technique” for MFM imaging. (1) The tip scans the
sample surface in tapping mode to detect the topographical contour in the first pass. (2) The cantilever is subsequently lifted to the required height away from the surface. The second scanning follows the height profile obtained from the former pass. (3) The constant tip‐sample separation ensures the reliability of the collected long‐range magnetic interactions. In both passes, the force signals are detected by the reflection of a laser beam off the back of the cantilever and into a photodiode where cantilever deflection variations are recorded. 23
We show in Figure 2.8 an AFM topographical image from tapping mode scanning and the corresponding magnetic phase image in lift mode of a standard magnetic sample (a metal evaporated tape). The bright contrasts indicate repulsive interactions, while the dark contrasts reveal attractive forces.
Figure 2.8 AFM and MFM imaging of a magnetic metal evaporated tape. (a) First pass:
surface topographical imaging in tapping mode. (b) Second pass: lift scanning follows the topographical contour to detect magnetic phase contrast image. The image size is 2.5 × 5 µm.
2.3.2.2 Magnetic Probe and Point Dipole Approximation
The force-detecting spring in the force microscope consists of a micro cantilever beam clamped at one end, and a probe tip mounted at the other end. The increasing demand for large quantities of reproducibly manufactured cantilevers integrated with sharp tips motivated the evolution of the production method, from original electrochemically etched metal wires to micro-fabrication techniques based on the machining of Si-related materials20. The sensing of magnetic forces
requires ferromagnetic probes that can detect the near-surface stray field originated from the sample. Commercially, the magnetic sensitivity of the cantilever is achieved using a thin magnetic coating by thermal evaporation or sputter deposition. The magnetic coating is normally with a thickness of 50-100 nm. The fabrication and structure of magnetic probes is schematically illustrated in Figure 2.9.
Figure 2.9 Schematic for the fabrication of amagnetic probe20. (a) A standard cantilever with integrated pyramidal tip. (b) Tip‐apex. (c) Tip and cantilever are completely coated with a deposited magnetic film to acquire magnetic sensitivity.
For the work described in this thesis, MESP-V2 magnetic probes produced by Bruker are used to detect the magnetic interactions between the tip and the isolated nanoparticles. The geometry and specifications are summarized in Figure 2.10. The hard Cobalt-Chromium coating is tailored for high magnetic sensitivity. The nominal tip radius is ~35 nm for high lateral resolution of MFM imaging. The probe has a nominal coercivity of 400 Oe, and a magnetic moment of 1-13 emu.
Figure 2.10 A MESP‐V2 magnetic probe consisting of a cantilever and a pyramidal tip
mounted at its end. The tip parameters shown on the right are provided by Bruker.
Harmann24 proposed in 1989 a criterion for the point dipole approximation of
MFM probes. It was realized that the complicated convolution of the sample microfield with the tip magnetization resulted in difficulties concerning the analysis of the MFM images. The magnetic field originating from the sample interacts with the whole magnetically active tip volume, instead of exclusively the surface point where the microscope tip is actually located. Therefore, the interpretation of the locally detected magnetic signals should take this factor into consideration, which remains a principal problem in the studies by MFM. In order to simplify the data analysis, the point dipole approximation of the magnetically active tip area is proposed, and with this assumption, the MFM tip can be regarded as dipole probing
the magnetic stray field of the sample. The validity of this approximation was discussed and checked for various field models, giving the criterion24
tan
2
1
1
1
1
4
1
10
3
2 2 2 2 2
z y xl
with
x ,,y z(2.14)
so that in the Taylor expansion of the tip magnetization one can keep only the volume term (zero order term while the second order term is given by Equation (2.14)) 24. As electrochemically etched metal wires or foils were used then, the
obtained tip was approximated as a symmetrical cone described by its length
l
and aperture angle θ. ξ denotes the coordinates x, y, z ( ξ = x, y, z ), and ζξx, ζξy, ζξzrepresents the characteristic decay length constrained by24
2 2 1 1 ( ) H r H r
(2.15)
where ξ and η represent independently the coordinates x, y, z. Hξ ) denotes the local microfield component in ξ direction (i.e. x, y or z direction) originating from the measured sample. If the criterion in Equation (2.14) is experimentally satisfied, the point dipole approximation of the magnetic tip facilitates the MFM image interpretation, which subsequently provides the possibility for detailed and quantitative analysis and simulation of magnetic structures in micro- and nano- scale24–27.
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