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Engineering, Technology & Applied Science Research Vol. 9, No. 4, 2019, 4495-4499 4495  
  

www.etasr.com Chigvinadze et al.: Vibrating Reed Study of Superconducting Cuprates Fabricated by Superfast Melt … 

 

Vibrating Reed Study of Superconducting Cuprates 

Fabricated by Superfast Melt Quenching in a Solar 

Furnace 
 

J. Chigvinadze  

Department of Condensed Matter Physics, 
Andronikashvili Institute of Physics,  
Ivane Javakhishvili Tbilisi State 

University,Tbilisi, Georgia 
chigvinadze@yahoo.com 

V. Tavkhelidze 

Department of Condensed Matter Physics, 
Andronikashvili Institute of Physics,  
Ivane Javakhishvili Tbilisi State 

University,Tbilisi, Georgia 
tawge@yahoo.com 

G. I. Mamniashvili 

Department of Condensed Matter Physics, 
Andronikashvili Institute of Physics,  
Ivane Javakhishvili Tbilisi State 

University,Tbilisi, Georgia 
mgrigor@rocketmail.com 

G. Donadze 

Department of Condensed Matter Physics, 
Andronikashvili Institute of Physics,  

Ivane Javakhishvili Tbilisi State 

University,Tbilisi, Georgia 
donadze_g@yahoo.com 

J. V. Acrivos 

Department of Chemistry, 
San Jose State University,  

San Jose, USA 

jacrivos@earthlink.net 

D. Gulamova 

Institute of Materials Science SPA 
“Physics-Sun” of Academy of Science, 

Tashkent, Uzbekistan  

gulamova@uzsci.net 

 

 

Abstract—In this study, the potential possibilities of the precision 

of the vibrating reed method for the evaluation of the Тс of 

superconducting precursors in an HTSC Bi-Pb-Sr-Cu-O system 

were investigated. A special technology for obtaining these 

samples by using solar energy for melting and following superfast 

melt quenching was applied to increase their internal 

inhomogeneity, allowing to receive high-quality textural ceramic 
samples of Bi1,7Pb0,3Sr2Can-1CunOy (n=2-30) showing critical 

temperatures of superconducting precursor transitions above 

bulk Тс. To determine critical temperatures of superconducting 

precursors above bulk Тс for the first time, the original vibrating 

reed method of studying these multiphase samples in an applied 

magnetic field was used. It was shown that this method has 
sensitivity to superconducting diamagnetism making possible to 

reveal new superconducting precursor phases above bulk Tc. 

Keywords-HTSC; solar energy; superfast quenching; vibrating 

reed technique; ctitical temperature of superconducting transition; 

high-temperature superconducting phases; pinning  

I. INTRODUCTION  

After the discovery of high-temperature superconductors 
(HTSC) in 1986, great efforts were made to the further increase 
the critical temperature of superconducting transition Тс with 
aim to reach room temperatures. Such a discovery would cause 
the emergence of new HTSC materials with Тс higher than the 
ones of liquid nitrogen (~77K) and hydrogen (19К) (Tc in 
YBaCuO and MgB2, correspondingly) opening great 
possibilities for their applications in electronics and energetics. 
From this point of view, particular interest attracts the Bi-Pb-
Sr-Ca-Cu-O system, because it is characterized by high 
Тс=107К and the record high second critical magnetic field Нс2 

~150T. Our group has undertaken research on the possibility to 
increase the Тс of this system [1-5]. In [1-3, 5] the melt 
technology for obtaining Bi-Pb-Sr-Cu-O HTSC ceramics using 
solar energy for melting and subsequent superfast melt 
quenching for increasing of internal inhomogeneities was 
developed, allowing the receiving of homogeneous, high-
quality, textured ceramic samples with controllable 
microstructure and pinning centers. In [4], Hot Shock Wave 
Consolidation Technology was used to produce Bi-Pb-Sr-Ca-
Cu-O compositions with increased internal inhomogeneity and 
for studying their superconducting precursor phases by 
torsional magnetometry method. This time, for increasing 
internal inhomogeneity we used solar melting and following 
superfast quenching technology. 

Previous measurements of pinning and dissipation 
processes were carried out in the Andronikashvili Institute of 
Physics using an original vibrating torsion mechanical 
magnetometry method to study the torsion oscillations of 
samples in an applied magnetic field realized using an 
automated multipurpose device [6] and standard methods of 
magnetic and electric parameter measurements. It was showed 
that samples obtained using the suggested solar technology 
were multiphase containing phases with higher critical 
temperatures Тс reaching ~200К. But the concentration of new 
HTSC phases appeared to be so small that for more precision 
assessments it was necessary to find alternative and more 
sensitive methods. One of such methods could be the vibration 
reed (VR) method for the first time developed in works of our 
group and then independently [7]. As the frequency and 
dissipation of VR could be measured with high precision, the 
VR method exceeds in sensitivity a conventional ac-

Corresponding author: G. I. Mamniashvili



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susceptometer, and besides, it is contactless. Using the VR 
method one could study the elastic coupling between the 
Abrikosov vortex lattice and the crystal lattice even in micron 
sized grains inserted in the normal matrix. The field 
dependence measurements of VR resonance frequency and 
dissipation could be used for the precision investigation of the 
first critical magnetic field Нс1 temperature dependence without 
the introduction of free parameters, along with the energy 
distribution character caused by the motion of the Abrikosov 
vortex lattice. 

In [8], the example of successful application of the VR 
method for investigation of two-phase Bi-Ca-Sr-Cu-O 
superconducting ceramics and the precision assessment of their 
bulk critical temperatures Тс were presented. The VR method 
was used for the first time to determine critical temperatures of 
superconducting precursors above bulk Тс. So, the aim of the 
current work is to determine critical temperatures of 
superconducting precursors above bulk Тс. We used for the first 
time the original VR method to study these multiphase samples 
in an applied magnetic field. It was shown that this method has 
sensitivity to superconducting diamagnetism sufficient to 
reveal new superconducting precursor phases above bulk Tc. 

II. RESULTS AND DISCUSSION 

For the study of high-temperature superconductors, we used 
a setup consisting of a cryostat with a block-holder of the 
sample, placed in the gap of a permanent magnet, and an 
electronic part. The electronic part of the setup contains a 
mechanical spectrometer developed in the Andronikashvili 
Institute of Physics operating at a frequency of ~1kHz [9], and 
instruments for powering the permanent magnet and creating a 
weak (~0.5mT) alternating magnetic field on the sample. The 
high sensitivity of the equipment provides measurements of the 
natural frequency of the sample f with an accuracy of ~0.1%. 
Figure 1 shows actual devices/set up view and measuring cell 
photos. Figure 2 shows the principal electronic circuit of the 
installation. 

 

(a) 

 

(b) 

 
Fig. 1.  (a) Actual devices/set up photo, (b) measuring cell. 

 
Fig. 2.  Electronic block-diagram of the installation. 

The basis of the operation of a mechanical spectrometer is 
the electrostatic method of exciting bending oscillations of a 
sample having the shape of a rectangular plate. The electronic 
equipment of the spectrometer allows measurements in the 
mode of self-excitation of samples at their natural resonant 
frequency. The electrode, located in the immediate vicinity of 
the sample, makes up with the capacitance included in the 
oscillating circuit of the high-frequency generator, and serves 
simultaneously to excite and detect oscillations of the sample. 
Measurements of the resonance frequency fr of the oscillation 
of the sample allow the determination of the elastic modulus E 
according to: 

2r

d E
f k

L ρ
=     (1) 

where d is the thickness of the sample, L is the length of the 
oscillating plate, E is the modulus of elasticity, ρ is the density 
of the sample, and k is a constant coefficient. Figure 3 shows 
the block-holder of the superconducting sample. It is made of 
ultrapure copper and is placed in a low-temperature cryostat. 

 

 
Fig. 3.  Block-holder 

Block-holder provides oscillations of a superconducting 
sample in constant and alternating magnetic fields without 
affecting it by mechanical deformations. This is achieved by 
the fact that the metal substrate acts as a vibrator of a 
mechanical spectrometer, cut in the shape of E character, and 



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the superconducting sample is glued to the tip of its middle 
reed. As a substrate, high-purity niobium is specially selected. 
In the temperature range from nitrogen to 200K, which is of 
interest to us, there are no anomalies of the elastic modulus and 

a very low level of oscillation energy dissipation (∼5×10
-4
). 

Figure 4 shows a cryostat placed in the gap of a permanent 
magnet and operating in the temperature range from 80K to 
500K. In Figure 4: 1) The block-holder with the sample is 
rigidly fixed on the console of ultrapure copper. 2) The tank 
into which liquid nitrogen is poured is integrated with the 
console. 3) A furnace is wound in the lower part of the console. 
These allow to measure both the temperature spectra and the 
field dependences of the elastic modulus in the temperature 
range of 80-500K. 4) The poles of the permanent magnet are 
located on both sides of the cryostat and can be moved so that 
the direction of the constant field H relative to the sample plane 
can be changed at any angle. 

 

 
Fig. 4.  Cryostat 

To study the dynamics of the Abrikosov vortex, a lattice in 
HTSC is provided for the creation of a relatively weak exciting 
magnetic field, oscillating with a certain frequency. In order to 
create such a field, 5 especially wound Helmholtz coils are 
placed inside the cryostat, covering the block-holder. The 
location of the coils in the immediate vicinity of the sample 
allows the creation of a sufficiently strong alternating field on it 
by using a standard low-frequency generator. The alternating 
field h created by the Helmholtz coils can also be directed at 
different angles that were combined with application of solar 
energy and superfast quenching melt technology [1-5]. 
Amorphous precursors and their use make possible the 
manufacturing of high-density low porous texturized ceramics 
with given dimensions of grains. Starting mixtures of nominal 
composition were prepared from previously annealed Bi2О3, 
PbO, SrCO3, CaО, CuО high purity powders. The synthesis by 
solar melting and the following superfast quenching was 
realized using as a heating source the concentrated solar flux in 
a solar furnace. The phase composition of samples was 
determined by X-ray phase analysis. The form of 
superconducting samples used in the experiments was such that 

their size in the direction of the magnetic field was less than the 
depth of its penetration. In this case, the Abrikosov magnetic 
vortices (AV) penetrated the sample through in the direction of 
the magnetic field. 

The variation of the square of the resonant oscillation 
frequency (f

2
) of the sample can be considered in the 

framework of the so-called magnetomechanical approach [7] 
according to which, when the superconductor is displaced 
relative to the external magnetic field H, acts as a restoring 
mechanical force on each “pinned” magnetic vortex. As a 
result, the oscillation frequency of the entire sample changes by 

∆f(H), depending on the density of the fixed vortices, the 
moment of inertia of the superconductor and its volume. 
Measuring the dependence of the elastic modulus of the 
substrate-sample system (in units of f

2
) on the magnitude of the 

magnetic field gives information about the elastic interaction of 
the AV with the crystal lattice. This is a convenient method for 
determining the magnitude of the vortex pinning force, 
especially by measuring the Labusch parameter, which 
determines the slope of the pinning potential curve. In addition, 
the dependence f

2
(H) provides a simple and convenient method 

for determining the value of the lower critical magnetic field 
Нс1. Figure 5 shows the dependence of f

2
(H) of sample (2267), 

taken at T=88K, while its superconducting transition 
temperature is Тс=97К. 

 

 

Fig. 5.  Field dependence of the square of the natural frequency of the 
sample (2267) 

The anomaly f
2
(H) at 42mT shows the moment of the 

magnetic field vortex penetration into the sample, i.e. Нс1. An 
increase in f

2
 corresponds to an increase in the number of AVs 

with an increase in H. By the slope of this curve, one can judge 
the pinning force in this particular sample. One could also 
study the phase transitions in the Abrikosov vortex lattice. As 
an example, Figure 6 shows the field dependences of a single-
phase polycrystalline sample of ErBa2Cu3O7-δ prepared 
according to standard technology. According to the 
temperature dependence of the electrical resistance Ω (Figure 
6), the temperature and width of the superconducting transition 
were determined: Тс=91.2K and ∆Тс=0.8K respectively. The 
dependences of f

2
(H) were measured in the superconducting 

state of the sample at T=79K. Two different dependencies were 
taken. In the first case, the sample oscillated only in an external 
constant magnetic field, (curve □). In the second case, along 
with the constant magnetic field, from the very beginning the 



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sample was affected by a weak, h=0.5mT alternating magnetic 
field of low frequency (curve ■). On the first curve (□) of the 
dependence f

2
(H), at Н=173mT, there is a feature characteristic 

of order-disorder phase transformations. This feature indicates 
that when H=173mT and higher, AV exist in the sample in the 
form of ordered lattice. If during the taking of the field 
dependence a variable magnetic field h acts on the sample, then 
the feature on the f

2
(H) curve is not observed. This is due to the 

fact that the alternating magnetic field constantly shakes the 
vortices in the sample, preventing their ordering in the lattice. 
In this work, the temperature dependence of the square of the 
natural frequency f

2
(H) of an HTSC sample oscillating in a 

magnetic field is used to obtain information about the phase 
composition of high-temperature superconducting precursors 
above Тс. When a superconducting VR is subjected to applied 
fields and temperature variations, a step-like increase in the 

resonant frequency ∆f=f−fo compared to its normal state value 
fo is observed near or below the upper critical magnetic field 
Нс2(T), when flux lines are rigidly pinned to VR. This is due to 
the diamagnetic surface currents flowing in the superconductor 
and producing diamagnetic restoring force proportional to the 
MxH torque. This feature when applied above Tc completely 
removes normal-state contributions and thus allows tracing the 
diamagnetic signal above Tc with great precision. Prior to the 
measurements, the samples were cooled to a nitrogen 
temperature in an external magnetic field, after which the 
temperature dependences of f

2
 were taken during a slow, 

≈1K/min, heating. In order to separate the effects associated 
with the penetration of AV into the superconducting sample 
from the effects of the niobium substrate proper, we measured 
the temperature dependence of f

2
 of pure niobium. Figure 7 

shows the dependence of f
2
(T) of a niobium substrate without 

an HTSC sample taken in an 300mT external magnetic field. 

 
Fig. 6.  Field dependence of f

2
of oscillation of the sample ErBa2Cu3O7-δ: 

□ – h = 0, ■ - h = 0.5mT. T=79K 

It is seen that the f
2
(T) curve, in the temperature range from 

nitrogen to 170K, has a uniform slope and does not contain any 

features. Figure 8 shows the dependence of f
2
(T) of sample 

(2267) taken in an external magnetic field of 300mT. The curve 

contains a single feature at T=97K. Such features on the f
2
(T) 

dependence are typical for phase transition points, the 97K 
point is the sample transition temperature from normal to 
superconducting state. There are no other features on the curve, 
this means that the sample (2267) is monophase. Another 

picture is observed on the f
2
(T) curve of the sample (2-2-19-

20), shown in Figure 9. On dependencies taken at a magnetic 
field of 300mT during the heating process, 4 features were 
observed. This means that in the sample (2-2-19-20), along 
with the main superconducting phase and the transition 
temperature of 104K, there are inclusions of other 
superconducting phases with higher transition temperatures: 
118, 127 and 151K. 

 

Fig. 7.  Temperature dependence of f
2
of a niobium substrate in a magnetic 

field of 300mT. 

 
Fig. 8.  Temperature dependence f

2
 of oscillations of the monophase 

sample (2267) in a magnetic field of 300mT 

 
Fig. 9.  Temperature dependence of f

2
of the multiphase sample (2-2-19-20) 

in a magnetic field of 300mT 



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III. CONCLUSIONS 

We investigated the potential possibilities of the vibrating 
reed method for the evaluation of Тс of superconducting 
precursors in an HTSC Bi-Pb-Sr-Cu-O system. We applied a 
special technology for obtaining these samples using solar 
energy for their melting and subsequent uperfast melt 
quenching for increasing their internal inhomogeneity, 
allowing the receiving of high-quality textural ceramic samples 
of the Bi1,7Pb0,3Sr2Can-1CunOy (n=2-30) system showing critical 
temperatures of superconducting precursor transitions above 
bulk Тс. To determine the critical temperatures Tc of 
superconducting precursors above bulk Тс we used for the first 
time the original vibrating reed method to study this multiphase 
samples in an applied magnetic field. It was shown that this 
method has sensitivity to superconducting diamagnetism 
making possible to reveal new superconducting precursor 
phases above bulk Tc. 

ACKNOWLEDGMENT 

This work has been supported by the Shota Rustaveli 
National Science Foundation Grant STCU-2016-51 & STCU 
Grant N 6317. 

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