3.2.1 Structural analysis
The crystalline structures of samples are determined by using the x-ray diffraction (XRD) (Bruker D8 advance, as shown in Fig. 3.5) with Cu Kα1 radiation (λ = 1.56056 ˚A). To get the data efficiently, the detector of XRD is set for high speed and high sensitivity with a PSD detector of which resolution is about 0.03 ◦. The operating voltage is 40 kV and the operating current is 40 mA. The scanning range (2θ) is from 20◦ to 80 ◦ with a scanning rate of 1.5 ◦/min (scanning increment is 0.01◦; scanning speed is 0.4 s/step).
XRD patterns vary with different materials, just like our fingerprints. Therefore, they are used for determining the structures of materials. The operating principle of XRD is based on Bragg law, which will be described as following.
Assuming that the incident radiation is reflected specularly from parallel planes of atom in a crystal, the diffraction beams are found when the reflections interfere construc-tively. For the occurrence of constructive inference, two conditions have to be satisfied:
one is the same phase of the reflections from the successive planes, and the other is that the path difference is an integral number n of wavelength λ, so that
2d sin θ = nλ, (3.1)
This is the Bragg law, which can be satisfied only for wavelength λ ≤ 2d, where θ is measured as the angle from the plane, and d the spacing of successive plane [55]. The constraints on observing diffraction patterns are not only the requirements for Bragg’s law but also those for extinction conditions. For unit cells containing more than one atom,
the symmetry of the atoms determine the specific positions of diffraction peaks, called extinction conditions. Therefore, when a monochromatic light is incident in a crystal, the diffraction peaks can only be found at several specific incident angles which is determined by the shape and the volume of the unit cell as well as the symmetry. In addition, the different crossection for scattering x-ray at different atomic site lead to different intensity of diffraction peaks. Hence, even for the materials with single structure, the intensity distributions at different angles are different from each other. In conclusion, two factors provided in XRD, the positions of diffraction peaks and the intensities of diffraction peaks, reveal different information. The former one tells us the structure and the volume of a unit cell. On the other hand, the later one prevails the types of atoms and the positions of atoms.
Scanning electron microscopy (SEM) micrograph is taken with a filed emission scan-ning electron microscope (FESEM) (JSM-6700F, as shown in Fig. 3.6). SEM is a type of electron microscope capable of producing high-resolution images of a sample surface.
Due to the manner in which the image is created, SEM images have a characteristic of three-dimensional image and are useful for judging the surface structure of the sample.
The range of accelerating voltages and magnifications of our SEM images are 5 ∼ 10 kV and 3,000 ∼ 10,000 times, respectively.
In a typical SEM, the most common imaging mode monitors low energy (<50 eV) sec-ondary electrons. Due to their low energy, these electrons originate from a few nanometers depth from a surface. The electrons are detected by a scintillator-photomultiplier device and can be viewed and saved as a digital image. This process relies on a raster-scanned primary beam. The brightness of the signal depends on the number of secondary electrons reaching the detector. If the beam enters the samples perpendicular to the surface, then
the activated region is uniform about the axis of the beam and a certain number of elec-trons “escape” from within the sample. As the angle of incidence increases, the “escape”
distance of one side of the beam decreases, and more secondary electrons are emitted.
Thus steep surfaces and edges tend to be brighter than the flat surfaces, which results in images with a well-defined, three-dimensional appearance. Using this technique, resolu-tions less than 1 nm are possible. The spatial resolution of the SEM depends on the size of the electron spot which in turn depends on the magnetic electron-optical system which produces the scanning beam. The resolution is also limited by the size of the interaction volume, or the extent to which the material interacts with the electron beam. The spot size and the interaction volume are both very large compared to the distances between atoms, such that the resolution of the SEM is not high enough to image down to the atomic scale. However, the SEM has compensating advantages including the ability to image a comparatively large area of the specimen; the ability to image bulk material, and the variety of analytical modes available for measuring the composition and the nature of the specimen. Depending on the instrument, the resolution can fall somewhere between 1 and 20 nm.
3.2.2 Magnetic properties
Magnetic measurements are carried out with the superconducting quantum interference device (SQUID, MPMS-XL7, Quantum Design, as shown in Fig. 3.7) and physical prop-erty measurement system (PPMS, Quantum Design Model 6000, as shown in Fig. 3.8).
Several specifications of SQUID and PPMS are: the maximum of applied magnetic field is ± 7.0 T, the measuring temperature range is 2 ∼ 400 K, and the sensitivity is 10−8 emu. In this work, the magnetization are measured at 10 K and 300 K in field ±50 and
±20 kOe, respectively.
SQUID is a very sensitive magnetometers based on superconducting loops containing Josephson junctions. A Josephson junction is a weak link between two individual su-perconductors separated by a insulator, as shown in Fig. 3.9. According to Quantum mechanism, if the potential barrier between two separated superconductors is finite, the cooper pairs can go through the barrier, resulting in a tunneling current. The effects of pair tunneling include [55] (1) dc Josephson effect: a dc current flows through the junction without electric or magnetic field; (2) ac Josephson effect: a dc voltage applied through the junction causes a rf current oscillation through the junction. Moreover, applying both a rf voltage and a dc current simultaneously cause a dc current through the junction; and (3) macroscopic long-range quantum interference: a dc magnetic applied in the supercon-ducting circuit containing two junctions results in the maximum of current intensity with an interference effect as a function of magnetic field, as shown in Fig. 3.10. This effect can be utilized in a sensitive magnetometer, as shown in Fig. 3.11.
3.2.3 Dielectric properties
Dielectric properties are measured by LCR-Meter (Agilent 4294A) with a homemade probe, as shown in Fig. 3.12. In the beginning, the samples are coated with a layer of silver about 30-nm thick on the top and bottom surfaces by a manual high resolution sputter.
The conditions for coating silver on surfaces are as following: pressure = 4 × 10−2 mbar, operating voltage = 2 kV, current = 20 mA, time = 7 min. The as-prepared samples agglutinate with copper leads by silver paint. Finally, pellets are fixed on the home-made probe. The measured frequency range is from 40 Hz to 1 MHz and the oscillation level is 0.5 V.
The impedance measurement methods of 4294 a is “auto balancing bridge method”
[54]. The auto balancing bridge balances the range resistor current with the device under test (DUT) current to maintain a zero potential at the low terminal. Figure 3.13 shows a simplified block diagram of the bridge section. The detector D detects potential at the low terminal and controls both magnitude and phase of the OSC2 output, so that the detected potential becomes zero. The actual balancing operation is shown in Fig. 3.14. When the bridge is “unbalanced”, the null detector detects an error current and the phase detectors, at the next stage, separate it into 0◦ and 90◦ vector components. The output signals of the phase detectors go through loop filters (integrators) and are applied to the modulator to drive the 0◦ and 90◦ component signals. The resultant signal is amplified and fed back through range resistor Rr to cancel the current through the DUT, therefore no error current flows into the null detector. This balancing operation is performed automatically over the full frequency range of 40 Hz to 110 MHz. The section responses for the data analysis in 4294 is the vector ratio detector section. The vector ratio detector measures two vector voltages across the DUT (Edut) and range resistor Rr (Err) series circuit (as shown in Fig. 3.15). Since the range resistor value is known, measuring two voltages will give the impedance vector Zx of the DUT by Zx = Rr × (Edut/Err). Selector S1 selects either the Edut or Err signal so that these signals alternately flow identical paths to eliminate tracking errors between the two signals. Each vector voltage is measured using an A to D converter and separated into its 0X and 90X components by digital processing.
We figure out the capacitance of DUT by Cp mode (R parallel to C) because of the rather high resistance of DUT.