A DSP-enhanced AC susceptometer for characterisation of high temperature superconductors.

An AC susceptometer was successfully used to characterize the intergranular critical flow of YBCO samples. The relative intergranular critical flow was successfully estimated by a critical state model based on Bean's model.

Introduction

This is due to the highly anisotropic nature of the material and the countless number of grain boundaries in the material lattice. The intergranular critical current was derived using the critical state model, a modified version of Bean's model, by measuring the material's AC susceptibility response to a magnetic field (< 20 mT) using a DSP-enhanced susceptometer.

Superconductivity

Historical Background

The discovery of a superconducting material, which can withstand high magnetic fields of the order of Tesla, is undeniably an important application milestone in the construction of superconducting magnets. In this regard, Bernd Matthias, a German physicist, discovered in the 1960s that the Niobiumtin compound can withstand a magnetic field as high as 9 Tesla before returning to its normal state.

Theories of Superconductivity in brief

Resistivity in Metallic Conductors
BCS Theory
The London Equations
The Coherence Length, ξ
Magnetic Gibbs Free Energy
The Ginzburg-Landau Theory in brief
TYPE-II Superconductors
Josephson Effects
Bean Model

Therefore, both the imperfection in the crystal and the elevated temperature (resulting in an increase in the kinetic energy of the atoms and electrons) contribute to the resistivity of the material. Due to the fact that the induced magnetic field is independent of the current density, the slope of the field is assumed to be constant.

Figure 2. 1 Resistivity versus temperature for a typical metal.

High Temperature Superconductors

General Description of High Temperature Superconductor
Yttrium Barium Copper Oxide Superconductor

Discovery and General Description of YBCO
Variation of YBCO Properties with Oxygen Stoichiometry

Superconductivity in YBCO

Charge Carriers in YBCO
Anisotropy
Magnetic Properties of YBCO and HTS in general
Critical Current of HTS (YBCO)

Polycrystalline Nature of HTS
Dislocations
The Cottrell Atmosphere

Elastic Approximation
Summary

It is actually the average of the penetration depth in the ab plane and the c axis. In granular superconductors, both the critical intergranular and intragranular currents contribute to the critical current density of the superconductors. The texturing process reduces the misorientation angle, leading to an increase in the value of the critical current density [38].

The main parameter for the formation of the Cottrell atmosphere is the interaction energy of the solute atoms in the stress field near a dislocation line.

Figure 3. 2 Critical temperature v/s year of discovery.

AC Susceptibility

Introduction

However, for highly accurate sensitivity measurements, the susceptometer must be calibrated and the demagnetizing factor must be taken into account, based on the shape of the sample. For correct measurements, the measured AC sensitivity values must therefore be corrected for demagnetization based on the shape of the sample. Correcting the demagnetization effect is capital as a sensitive parameter, such as the magnetic energy stored in the space occupied by a superconducting sample, must be calculated based on accurate measurements of complex AC sensitivity [56].

There are several ways to cool a superconductor in an oscillating magnetic field for AC susceptibility measurements.

Magnetic Susceptibility

If the sample is placed in an axial magnetic field, (field parallel to the axis of the sample), so that the magnetic field. Where, N is the total number of turns, B is the magnetic flux density in Tesla and A is the cross-sectional area of the solenoid (π. The superconducting sample is placed in one of the secondary coils as shown in Figure 4.1.

The total induced magnetic flux will be due to the two secondary coils placed in an oscillating magnetic field (given by Eq. 4.27) and the magnetization M due to the superconducting sample.

Superconducting Parameters Determined from AC Susceptibility

Energy Converted
Critical Temperature and AC Susceptibility
Critical Current Density and AC Susceptibility
Penetration Depth

The real and imaginary components of the AC susceptibility can be derived from the voltages shunted by the AC susceptometer. The physical interpretation of the imaginary susceptibility is the energy, , converted into heat energy after one cycle of the AC field [51] due to magnetic field penetrating the sample. Referring to Figure 4.2, the first peak comes in at The first peak is related to the magnetic flux just reaching the center of the sample.

Knowing the value of , the value of the critical intergranular current, , can be estimated from equation 4.42.

Figure 4. 2 Ideal graph of against for a superconducting specimen at a constant temperature below [60], [61]

AC Susceptometer Design

Introduction

AC Susceptometer’s System Requirements

The Proposed AC Susceptometer

Design of the Primary Coil
Design of the Secondary Coil

The design of the primary coil is done before other aspects of the AC sensitivity measuring device are considered. The AC current rating of the AWG 23 wire used for the primary coil is 729 mA (at room temperature and 53 KHz). The dimensions of the secondary coils were chosen so that they could be placed on the primary coil.

6 (a) 3D diagram for secondary coil used for bulk samples (b) Schematic representation of the secondary coil built for bulk sample characterization.

Figure 5. 1 Simplified diagram of the AC susceptometer system.

Testing and Validation of the Primary Coil and the Secondary Coil

The minimum average volume of the sample was estimated to be and the minimum rms current through the primary coil was 0.4 mA. In the area of the primary coil, it performed satisfactorily with no excessive Joule heating observed under cryogenic conditions. The primary coil would be placed in a nitrogen bath for AC sensitivity measurement to magnetic field.

Under cryogenic conditions, Joule heating would actually have little adverse effect on the functionality of the primary coil.

Figure 5. 7 Apparatus set up for testing and validating the primary and secondary coils

Material Selection

Therefore, the primary coil could produce a maximum field of 20 mT (from equation 5.2 it can be deduced that when, ) without damaging the coil. The primary coil can produce the specified range of magnetic field, while the secondary coil can satisfactorily detect the magnetic field produced inside the primary coil. The thermal conductivity of silicon and sapphire varies with temperature, and sapphire generally has a better thermal conductivity than silicon.

Aluminum is a non-magnetic material and has a thermal conductivity of the order of 103 W/mK at 77 K [63].

The Lock-in-Amplifier

The Mathematics and Theory behind the Function of the Lock-In Amplifier
Implementation and Testing of the Lock-in-Amplifier in DASYLab

Testing the Lock-in-Amplifier Filtration Ability
Testing the Lock-in-Amplifier’s Ability to Act as a Discriminating Voltmeter

The detection process involved the multiplication of the fundamental signal across the pickup coils and the reference voltage. If the temperature of the primary coil were to vary, the amplitude of the in-phase and out-of-phase components would vary due to a change in the impedance of the coil. The lock-in amplifier extracted the first harmonic of the square wave and the following was obtained:

The software-based lock-in amplifier was then used to measure the fundamental in-phase and out-of-phase components of the magnetic response of superconducting samples.

Figure 5. 10 Block diagram of lock-in amplifier implemented in DASYLab 10.

Summary

It can be concluded that the lock-in amplifier has been successfully implemented in DASYLab environment. The lock-in amplifier was able to act as a discriminating voltmeter and extract the in-phase and the out-of-phase components of a signal. Additionally, the software-based lock-in amplifier effectively extracted the fundamental component of a square wave signal consisting of odd harmonics.

So, software-based custom key booster can also be classified as a flexible solution.

Experimentation

YBCO Pellets

YBCO Pellets Fabrication
Cutting of Bulk YBa 2 Cu 3 O 7-x Specimens

The furnace was flushed for several minutes with Argon before being degassed in an oxygen atmosphere. The YBCO pellets were held at 450 0C for another eight hours still under an oxygen atmosphere. Pellets were carefully clamped using the integrated clamp provided on the cutting machine providing satisfactory mechanical support.

Additionally, minimum current resulted in minimal joule heating of the YBCO samples and the current leads.

Figure 6. 1 Tube furnace used for the sintering of YBCO pellets.

Hydrogen Doping

One way to determine the amount of hydrogen absorbed by a sample of YBCO is by X-ray diffraction. The amount of time the sample was exposed to hydrogen inside the cell, under the same conditions of pressure and temperature, was used as a parameter to determine the relative amount of hydrogen absorbed by the doped sample. Thus, the hydrogenation time was used as an indicator of the relative amount of hydrogen absorbed by a given doped sample.

The hydrogen absorbed by the YBCO sample was proportional to the total doping time (under the same conditions of pressure and temperature).

Figure 6. 4 Taylor-made vessel for hydrogenation of YBCO specimens. (i) hydrogen cell (ii) gas inlet (iii) specimen holder with heater

Resistance Measurements

Contacts
Resistive Testing

The indium lumps do not adhere effectively to the surfaces of YBCO samples and the copper wires. The sample was exposed to the hot air blown until the silver paste was completely solidified, bonding the steel wires with the YBCO. The mechanical adhesion between the silver paste, the YBCO surface and the steel wire was very good.

Silver bands were dyed and a few turns of silver yarn were carefully wrapped around the YBCO specimen and the yarn was covered with lumps of silver paste, as shown in Figure 6.9.

Figure 6. 6 Contact using indium and copper wire.

AC Susceptibility Measurements

Critical Temperature Measurements
AC Susceptibility Measurements as a Function of Applied Magnetic Field

The purpose of this setup was to measure the AC susceptibility response of the sample under test with respect to magnetic field generated at the primary coil. Thus, an alternative way was developed to measure magnetic field generated at the primary coil. The "empty" balanced secondary coil was used as a sensor to measure the magnetic field at the primary coil.

The magnetic field and relative AC sensitivity were recorded by a computer through the DASYLab interface.

Figure 6. 15 AC Susceptibility setup at constant temperature for characterisation

Results and Discussions

Grain Morphology

SEM Images of Bulk Samples

Optical and scanning electron microscopy were used to investigate the morphology of the YBCO specimens. Scanning electron microscopy (SEM) was very useful in characterizing the bulk samples and the images obtained are of a superior quality compared to those from optical microscopy. SEM was performed on a raw sample of the YBCO sample at different magnifications, as shown in Figure 7.1.

AC Susceptibility Results

Measurement
AC susceptibility as a Function of Magnetic Field

Therefore, the nature of grain boundary strength can be deduced from the value of the critical intergranular current density. Similarly, the value of is normalized to the maximum value of the imaginary sensitivity of AC. The curve for the superconducting specimen is obtained after subtracting the reference curve from the curve due to the magnetic response of the aluminum and the superconducting specimen.

According to the simply modified version of the Bean critical model (Equation 7.3), the intergranular critical flow remained unchanged because there is no right or left shift in the peaks of the curves.

Figure 7. 2 Graph of 𝝌 against temperature for bulk YBCO sample.

Conclusion and Further Work

Summary

To carry out the resistance experiment in determining the critical temperature, we achieved good contacts with silver paste and silver wire. AC sensitivity and resistance tests were not performed on the hydrogen-doped samples to determine the critical temperature due to equipment limitations and the unavailability of a cryostat (which broke). The relative intergranular critical currents for control and hydrogen-doped YBCO were successfully estimated from magnetic measurements using a simple critical state model, the Bean model.

This is due to the weakening of Josephson couplings between grains, which is in agreement with literature reviews.

Further Work

Masumura, "Superconductor superlattice model for small angle grain boundaries in Y-Ba-Cu-O", Physical Review B, vol. 52, s.16237, december 1995. Pashitskii, " Current Transport through low-angle korngrænser i høj- temperatur superledere”, Fysisk gennemgang B, bind 57, no. Dew-Hughes, "The Critical Current of the Superconductors: an Historical Review", Low Temperature Physics, vol.

A simple AC susceptometer mounted on a cryostat cold finger”, Journal of Magnets and Magnetic Materials, vol .226, pp.