IEC 61788-17:2013

IEC 61788-17 ®
Edition 1.0 2013-01
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Superconductivity –
Part 17: Electronic characteristic measurements – Local critical current density
and its distribution in large-area superconducting films

Supraconductivité –
Partie 17: Mesures de caractéristiques électroniques – Densité de courant
critique local et sa distribution dans les films supraconducteurs de grande
surface
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IEC 61788-17 ®
Edition 1.0 2013-01
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Superconductivity –
Part 17: Electronic characteristic measurements – Local critical current density

and its distribution in large-area superconducting films

Supraconductivité –
Partie 17: Mesures de caractéristiques électroniques – Densité de courant

critique local et sa distribution dans les films supraconducteurs de grande

surface
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
PRICE CODE
INTERNATIONALE
CODE PRIX X
ICS 17.220.20; 29.050 ISBN 978-2-83220-583-9

– 2 – 61788-17 © IEC:2013
CONTENTS
FOREWORD . 4
INTRODUCTION . 6
1 Scope . 8
2 Normative reference . 8
3 Terms and definitions . 8
4 Requirements . 9
5 Apparatus . 9
5.1 Measurement equipment . 9
5.2 Components for inductive measurements . 10
5.2.1 Coils . 10
5.2.2 Spacer film . 11
5.2.3 Mechanism for the set-up of the coil . 11
5.2.4 Calibration wafer . 11
6 Measurement procedure . 12
6.1 General . 12
6.2 Determination of the experimental coil coefficient . 12
6.2.1 Calculation of the theoretical coil coefficient k . 12
6.2.2 Transport measurements of bridges in the calibration wafer . 13
6.2.3 U measurements of the calibration wafer . 13
6.2.4 Calculation of the E-J characteristics from frequency-dependent I
th
data . 13
6.2.5 Determination of the k’ from J and J values for an appropriate E . 14
ct c0
6.3 Measurement of J in sample films . 15
c
6.4 Measurement of J with only one frequency . 15
c
6.5 Examples of the theoretical and experimental coil coefficients . 16
7 Uncertainty in the test method . 17
7.1 Major sources of systematic effects that affect the U measurement . 17
7.2 Effect of deviation from the prescribed value in the coil-to-film distance . 18
7.3 Uncertainty of the experimental coil coefficient and the obtained J . 18
c
7.4 Effects of the film edge . 19
7.5 Specimen protection . 19
8 Test report . 19
8.1 Identification of test specimen . 19
8.2 Report of J values . 19
c
8.3 Report of test conditions . 19
Annex A (informative) Additional information relating to Clauses 1 to 8 . 20
Annex B (informative) Optional measurement systems . 26
Annex C (informative) Uncertainty considerations . 32
Annex D (informative) Evaluation of the uncertainty . 37
Bibliography . 43

Figure 1 – Diagram for an electric circuit used for inductive J measurement of HTS
c
films . 10
Figure 2 – Illustration showing techniques to press the sample coil to HTS films . 11
Figure 3 – Example of a calibration wafer used to determine the coil coefficient . 12

61788-17 © IEC:2013 – 3 –
Figure 4 – Illustration for the sample coil and the magnetic field during measurement . 13
Figure 5 – E-J characteristics measured by a transport method and the U inductive
method . 14
Figure 6 –Example of the normalized third-harmonic voltages (U /fI ) measured with
3 0
various frequencies . 15
Figure 7 – Illustration for coils 1 and 3 in Table 1 . 16
Figure 8 – The coil-factor function F(r) = 2H /I calculated for the three coils . 17
0 0
Figure 9 – The coil-to-film distance Z dependence of the theoretical coil coefficient k . 18
Figure A.1 – Illustration for the sample coil and the magnetic field during measurement . 22
Figure A.2 – (a) U and (b) U /I plotted against I in a YBCO thin film measured in
3 3 0 0
applied DC magnetic fields, and the scaling observed when normalized by I (insets) . 23
th
Figure B.1 – Schematic diagram for the variable-RL-cancel circuit . 27
Figure B.2 – Diagram for an electrical circuit used for the 2-coil method . 27
Figure B.3 – Harmonic noises arising from the power source . 28
Figure B.4 – Noise reduction using a cancel coil with a superconducting film . 28
Figure B.5 – Normalized harmonic noises (U /fI ) arising from the power source . 29
3 0
Figure B.6 – Normalized noise voltages after the reduction using a cancel coil with a
superconducting film . 29
Figure B.7 – Normalized noise voltages after the reduction using a cancel coil without
a superconducting film . 30
Figure B.8 – Normalized noise voltages with the 2-coil system shown in Figure B.2 . 30
Figure D.1 – Effect of the coil position against a superconducting thin film on the
measured J values . 41
c
Table 1 – Specifications and coil coefficients of typical sample coils . 16
Table C.1 – Output signals from two nominally identical extensometers . 33
Table C.2 – Mean values of two output signals . 33
Table C.3 – Experimental standard deviations of two output signals . 33
Table C.4 – Standard uncertainties of two output signals . 34
Table C.5 – Coefficient of variations of two output signals . 34
Table D.1 – Uncertainty budget table for the experimental coil coefficient k’ . 37
Table D.2 – Examples of repeated measurements of J and n-values . 40
c
– 4 – 61788-17 © IEC:2013
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
SUPERCONDUCTIVITY –
Part 17: Electronic characteristic measurements –
Local critical current density and its distribution
in large-area superconducting films

FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
all national electrotechnical committees (IEC National Committees). The object of IEC is to promote
international co-operation on all questions concerning standardization in the electrical and electronic fields. To
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agreement between the two organizations.
2) The formal decisions or agreements of IEC on technical matters express, as nearly as possible, an international
consensus of opinion on the relevant subjects since each technical committee has representation from all
interested IEC National Committees.
3) IEC Publications have the form of recommendations for international use and are accepted by IEC National
Committees in that sense. While all reasonable efforts are made to ensure that the technical content of IEC
Publications is accurate, IEC cannot be held responsible for the way in which they are used or for any
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4) In order to promote international uniformity, IEC National Committees undertake to apply IEC Publications
transparently to the maximum extent possible in their national and regional publications. Any divergence
between any IEC Publication and the corresponding national or regional publication shall be clearly indicated in
the latter.
5) IEC itself does not provide any attestation of conformity. Independent certification bodies provide conformity
assessment services and, in some areas, access to IEC marks of conformity. IEC is not responsible for any
services carried out by independent certification bodies.
6) All users should ensure that they have the latest edition of this publication.
7) No liability shall attach to IEC or its directors, employees, servants or agents including individual experts and
members of its technical committees and IEC National Committees for any personal injury, property damage or
other damage of any nature whatsoever, whether direct or indirect, or for costs (including legal fees) and
expenses arising out of the publication, use of, or reliance upon, this IEC Publication or any other IEC
Publications.
8) Attention is drawn to the Normative references cited in this publication. Use of the referenced publications is
indispensable for the correct application of this publication.
International Standard IEC 61788-17 has been prepared by IEC technical committee 90:
Superconductivity.
The text of this standard is based on the following documents:
FDIS Report on voting
90/310/FDIS 90/319/RVD
Full information on the voting for the approval of this standard can be found in the report on
voting indicated in the above table.
This publication has been drafted in accordance with the ISO/IEC Directives, Part 2.
A list of all the parts of the IEC 61788 series, published under the general title
Superconductivity, can be found on the IEC website.

61788-17 © IEC:2013 – 5 –
The committee has decided that the contents of this publication will remain unchanged until
the stability date indicated on the IEC web site under "http://webstore.iec.ch" in the data
related to the specific publication. At this date, the publication will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
IMPORTANT – The 'colour inside' logo on the cover page of this publication indicates
that it contains colours which are considered to be useful for the correct
understanding of its contents. Users should therefore print this document using a
colour printer.
– 6 – 61788-17 © IEC:2013
INTRODUCTION
Over twenty years after their discovery in 1986, high-temperature superconductors are now
finding their way into products and technologies that will revolutionize information
transmission, transportation, and energy. Among them, high-temperature superconducting
(HTS) microwave filters, which exploit the extremely low surface resistance of
superconductors, have already been commercialized. They have two major advantages over
conventional non-superconducting filters, namely: low insertion loss (low noise characteristics)
and high frequency selectivity (sharp cut) [1] . These advantages enable a reduced number of
base stations, improved speech quality, more efficient use of frequency bandwidths, and
reduced unnecessary radio wave noise.
Large-area superconducting thin films have been developed for use in microwave devices [2].
They are also used for emerging superconducting power devices, such as, resistive-type
superconducting fault-current limiters (SFCLs) [3–5], superconducting fault detectors used for
superconductor-triggered fault current limiters [6, 7] and persistent-current switches used for
persistent-current HTS magnets [8, 9]. The critical current density J is one of the key
c
parameters that describe the quality of large-area HTS films. Nondestructive, AC inductive
methods are widely used to measure J and its distribution for large-area HTS films [10–13],
c
among which the method utilizing third-harmonic voltages U cos(3ωt+θ) is the most popular
[10, 11], where ω, t and θ denote the angular frequency, time, and initial phase, respectively.
However, these conventional methods are not accurate because they have not considered the
electric-field E criterion of the J measurement [14, 15] and sometimes use an inappropriate
c
criterion to determine the threshold current I from which J is calculated [16]. A conventional
th c
method can obtain J values that differ from the accurate values by 10 % to 20 % [15]. It is
c
thus necessary to establish standard test methods to precisely measure the local critical
current density and its distribution, to which all involved in the HTS filter industry can refer for
quality control of the HTS films. Background knowledge on the inductive J measurements of
c
HTS thin films is summarized in Annex A.
In these inductive methods, AC magnetic fields are generated with AC currents I cosωt in a
small coil mounted just above the film, and J is calculated from the threshold coil current I ,
c th
at which full penetration of the magnetic field to the film is achieved [17]. For the inductive
method using third-harmonic voltages U , U is measured as a function of I , and the I is
3 3 0 th
determined as the coil current I at which U starts to emerge. The induced electric fields E in
0 3
the superconducting film at I = I , which are proportional to the frequency f of the AC current,
0 th
can be estimated by a simple Bean model [14]. A standard method has been proposed to
precisely measure J with an electric-field criterion by detecting U and obtaining the n-value
c 3
(index of the power-law E-J characteristics) by measuring I precisely at various frequencies
th
[14, 15, 18, 19]. This method not only obtains precise J values, but also facilitates the
c
detection of degraded parts in inhomogeneous specimens, because the decline of n-value is
more remarkable than the decrease of J in such parts [15]. It is noted that this standard
c
method is excellent for assessing homogeneity in large-area HTS films, although the relevant
parameter for designing microwave devices is not J , but the surface resistance. For
c
application of large-area superconducting thin films to SFCLs, knowledge on J distribution is
c
vital, because J distribution significantly affects quench distribution in SFCLs during faults.
c
The International Electrotechnical Commission (IEC) draws attention to the fact that it is
claimed that compliance with this document may involve the use of a patent concerning the
determination of the E-J characteristics by inductive J measurements as a function of
c
frequency, given in the Introduction, Clause 1, Clause 4 and 5.1.
IEC takes no position concerning the evidence, validity and scope of this patent right.
The holder of this patent right has assured the IEC that he is willing to negotiate licenses free
of charge with applicants throughout the world. In this respect, the statement of the holder of
this patent right is registered with the IEC. Information may be obtained from:
___________
Numbers in square brackets refer to the Bibliography.

61788-17 © IEC:2013 – 7 –
Name of holder of patent right:
National Institute of Advanced Industrial Science and Technology
Address:
Intellectual Property Planning Office, Intellectual Property Department
1-1-1, Umezono, Tsukuba, Ibaraki Prefecture, Japan
Attention is drawn to the possibility that some of the elements of this document may be
subject to patent rights other than those identified above. IEC shall not be held responsible for
identifying any or all such patent rights.
ISO (www.iso.org/patents) and IEC (http://patents.iec.ch) maintain on-line data bases of
patents relevant to their standards. Users are encouraged to consult the data bases for the
most up to date information concerning patents.

– 8 – 61788-17 © IEC:2013
SUPERCONDUCTIVITY –
Part 17: Electronic characteristic measurements –
Local critical current density and its distribution
in large-area superconducting films

1 Scope
This part of IEC 61788 describes the measurements of the local critical current density (J )
c
and its distribution in large-area high-temperature superconducting (HTS) films by an
inductive method using third-harmonic voltages. The most important consideration for precise
measurements is to determine J at liquid nitrogen temperatures by an electric-field criterion
c
and obtain current-voltage characteristics from its frequency dependence. Although it is
in applied DC magnetic fields [20, 21] , the scope of this standard is
possible to measure J
c
limited to the measurement without DC magnetic fields.
This technique intrinsically measures the critical sheet current that is the product of J and the
c
film thickness d. The range and measurement resolution for J d of HTS films are as follows:
c
– J d: from 200 A/m to 32 kA/m (based on results, not limitation);
c
– Measurement resolution: 100 A/m (based on results, not limitation).
2 Normative reference
The following documents, in whole or in part, are normatively referenced in this document and
are indispensable for its application. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any
amendments) applies.
IEC 60050 (all parts), International Electrotechnical Vocabulary (available at
)
3 Terms and definitions
For the purposes of this document, the definitions given in IEC 60050-815:2000, some of
which are repeated here for convenience, apply.
3.1
critical current
I
c
maximum direct current that can be regarded as flowing without resistance
Note 1 to entry: I is a function of magnetic field strength and temperature.
c
[SOURCE: IEC 60050-815:2000, 815-03-01]
___________
Numbers in square brackets refer to the Bibliography.

61788-17 © IEC:2013 – 9 –
3.2
critical current criterion
I criterion
c
criterion to determine the critical current, I , based on the electric field strength, E or the
c
resistivity, ρ
-13
Note 1 to entry: E = 10 µV/m or E = 100 µV/m is often used as electric field criterion, and ρ = 10 Ω · m or
-14
ρ = 10 Ω · m is often used as resistivity criterion. (“E = 10 V/m or E = 100 V/m” in the current edition is mistaken
and is scheduled to be corrected in the second edition).
[SOURCE: IEC 60050-815:2000, 815-03-02]
3.3
critical current density
J
c
the electric current density at the critical current using either the cross-section of the whole
conductor (overall) or of the non-stabilizer part of the conductor if there is a stabilizer
Note 1 to entry: The overall current density is called in English, engineering current density (symbol: J ).
e
[SOURCE: IEC 60050-815:2000, 815-03-03]
3.4
transport critical current density
J
ct
critical current density obtained by a resistivity or a voltage measurement
[SOURCE: IEC 60050-815:2000, 815-03-04]
3.5
n-value (of a superconductor)
exponent obtained in a specific range of electric field strength or resistivity when the
n
voltage/current U (l) curve is approximated by the equation U ∝ I
[SOURCE: IEC 60050-815:2000, 815-03-10]
4 Requirements
The critical current density J is one of the most fundamental parameters that describe the
c
quality of large-area HTS films. In this standard, J and its distribution are measured non-
c
destructively via an inductive method by detecting third-harmonic voltages U cos(3ωt+θ). A
small coil, which is used both to generate AC magnetic fields and detect third-harmonic
voltages, is mounted just above the HTS film and used to scan the measuring area. To
measure J precisely with an electric-field criterion, the threshold coil currents I , at which U
c th 3
starts to emerge, are measured repeatedly at different frequencies and the E-J characteristics
are determined from their frequency dependencies.
The target relative combined standard uncertainty of the method used to determine the
absolute value of J is less than 10 %. However, the target uncertainty is less than 5 % for the
c
purpose of evaluating the homogeneity of J distribution in large-area superconducting thin
c
films.
5 Apparatus
5.1 Measurement equipment
Figure 1 shows a schematic diagram of a typical electric circuit used for the third-harmonic
voltage measurements. This circuit is comprised of a signal generator, power amplifier, digital
multimeter (DMM) to measure the coil current, band-ejection filter to reduce the fundamental

– 10 – 61788-17 © IEC:2013
wave signals and lock-in amplifier to measure the third-harmonic signals. It involves the
single-coil approach in which the coil is used to generate an AC magnetic field and detect the
inductive voltage. This method can also be applied to double-sided superconducting thin films
without hindrance. In the methods proposed here, however, there is an additional system to
reduce harmonic noise voltages generated from the signal generator and the power amplifier
[14]. In an example of Figure 1, a cancel coil of specification being the same as the sample
coil is used for canceling. The sample coil is mounted just above the superconducting film,
and a superconducting film with a J d sufficiently larger than that of the sample film is placed
c
below the cancel coil to adjust its inductance to that of the sample coil. Both coils and
superconducting films are immersed in liquid nitrogen (a broken line in Figure 1). Other
optional measurement systems are described in Annex B.
NOTE In this circuit coil currents of about 0,1 A (rms) and power source voltages of > 6 V (rms) are needed to
measure the superconducting film of J d ≈ 10 kA/m while using coil 1 or 2 of Table 1 (6.5). A power amplifier, such
c
as NF: HSA4011, is necessary to supply such large currents and voltages.

IEC  013/13
Figure 1 – Diagram for an electric circuit used
for inductive J measurement of HTS films
c
5.2 Components for inductive measurements
5.2.1 Coils
Currently available large-area HTS films are deposited on areas as large as about 25 cm in
diameter, while about 5 cm diameter films are commercially used to prepare microwave filters
[22]. Larger YBa Cu O (YBCO) films, about 10 cm diameter films and 2,7 cm × 20 cm films,
2 3 7
were used to fabricate fault current limiter modules [3–5]. For the J measurements of such
c
films, the appropriate outer diameter of the sample coils ranges from 2 mm to 5 mm. The
requirement for the sample coil is to generate as high a magnetic field as possible at the
upper surface of the superconducting film, for which flat coil geometry is suitable. Typical
specifications are as follows:
a) Inner winding diameter D : 0,9 mm, outer diameter D : 4,2 mm, height h: 1,0 mm,
1 2
400 turns of a 50 µm diameter copper wire;
b) D : 0,8 mm, D : 2,2 mm, h: 1,0 mm, 200 turns of a 50 µm diameter copper wire.
1 2
61788-17 © IEC:2013 – 11 –
5.2.2 Spacer film
Typically, a polyimide film with a thickness of 50 µm to 125 µm is used to protect the HTS
films. The coil has generally some protection layer below the coil winding, which also
insulates the thin film from Joule heat in the coil. The typical thickness is 100 µm to 150 µm,
and the coil-to-film distance Z is kept to be 200 µm.
5.2.3 Mechanism for the set-up of the coil
To maintain a prescribed value for the spacing Z between the bottom of the coil winding and
the film surface, the sample coil should be pressed to the film with sufficient pressure,
typically exceeding about 0,2 MPa [18]. Techniques to achieve this are to use a weight or
spring, as shown in Figure 2. The system schematically shown in the left figure is used to
scan wide area of the film. Before the U measurement the coil is initially moved up to some
distance, moved laterally to the target position, and then moved down and pressed to the film.
An appropriate pressure should be determined so that too high pressure does not damage the
bobbin, coil, HTS thin film or the substrate. It is reported that the YBCO deposited on
biaxially-textured pure Ni substrate was degraded by transverse compressive stress of about
20 MPa [23].
IEC  014/13
Figure 2 – Illustration showing techniques to press the sample coil to HTS films
5.2.4 Calibration wafer
A calibration wafer is used to determine the experimental coil coefficient k’ described in the
next section. It is made by using a homogeneous large-area (typically about 5 cm diameter)
YBCO thin film. It consists of bridges for transport measurement and an inductive
measurement area (Figure 3). Typical dimensions of the transport bridges are 20 µm to 70 µm
wide and 1 mm to 2 mm long, which were prepared either by UV photolithography technique
or by laser etching [24].
– 12 – 61788-17 © IEC:2013
IEC  015/13
Figure 3 – Example of a calibration wafer used to determine the coil coefficient
6 Measurement procedure
6.1 General
The procedures used to determine the experimental coil coefficient k’ and measure the J of
c
the films under test are described as follows, with the meaning of k’ expressed in A.5.
6.2 Determination of the experimental coil coefficient
6.2.1 Calculation of the theoretical coil coefficient k
Calculate the theoretical coil coefficient k = J d/I from
c th
k = F , (1)
m
where F is the maximum of F(r) that is a function of r, the distance from the central axis of
m
the coil (Figure 4). The coil-factor function F(r) = –2H (r, t)/I cosωt = 2H /I is obtained by
r 0 0 0
R 2π Z
N 2 2 r ′zcosθ
′
F(r ) = dr dθ dz , (2)
∫ ∫ ∫
2 2 2 3 / 2
2π S R 0 Z
′ ′
1 1 (z + r + r − 2rr cosθ )
where N is the number of windings, S = (R – R )h is the cross-sectional area, R = D /2 is
2 1 1 1
the inner radius, R = D /2 is the outer radius of the coil, Z is the coil-to-film distance, and Z
2 2 1 2
= Z + h [17]. The derivation of the Equation (2) is described in A.3.
61788-17 © IEC:2013 – 13 –
IEC  016/13
Figure 4 – Illustration for the sample coil and the magnetic field during measurement
6.2.2 Transport measurements of bridges in the calibration wafer
a) Measure the E-J characteristics of the transport bridges of the calibration wafer by a four-
probe method, and obtain the power-law E-J characteristics,
n
E = A × J . (3)
t 0t
b) Repeat the measurement for at least three different bridges. Three sets of data (n = 20,5
to 23,8) measured for three bridges are shown in the upper (high-E) part of Figure 5.
6.2.3 U measurements of the calibration wafer
a) Measure U in the inductive measurement area of the calibration wafer as a function of
using a
the coil current with three or four frequencies, and obtain the experimental I
th
constant-inductance criterion; namely, U /fI = 2πL . The criterion L should be as small
3 0 c c
as possible within the range with sufficiently large S/N ratios, in order to use the simple
Equation (4) for the electric-field calculation (7.1 c) and D.2). An example of the
measurement is shown in Figure 6 with 2πL = 2 µΩ•sec.
c
b) Repeat the measurement for at least three different points of the film.
6.2.4 Calculation of the E-J characteristics from frequency-dependent I data
th
(= kI /d) and the average E induced in the superconducting film at the full
a) Calculate J
c0 th
penetration threshold by
E ≈ 2,04µ fd J = 2,04µ kfdI , (4)
avg 0 c 0 th
from the obtained I at each frequency using the theoretical coefficient k calculated in
th
6.2.1. The derivation of Equation (4) is described in A.4.
b) Obtain the E-J characteristics
n
E = A × J (5)
i 0i
from the relation between E and J , and plot them in the same figure where the
avg c0
transport E-J characteristics data were plotted. Broken lines in Figure 5 show three sets of

– 14 – 61788-17 © IEC:2013
data measured at different points of the film. Transport data and U inductive data do not
yet match at this stage.
6.2.5 Determination of the k’ from J and J values for an appropriate E
ct c0
a) Choose an appropriate electric field that is within (or near to) both the transport
E-J curves and the inductive E-J curves, such as 200 µV/m in Figure 5.
b) At this electric field, calculate both the transport critical current densities J and the
ct
inductive J values from Equations (3) and (5) respectively.
c0
c) Determine the experimental coil coefficient k’ by k’ = (J /J )k, where J and J indicate
ct c0 ct c0
the average values of obtained J and J values, respectively. If the J (= k’I /d) values
ct c0 c th
are plotted against E = 2,04µ kfdI , the E-J characteristics from the U measurement
avg 0 th 3
match the transport data well (Figure 5).
-1
YBCO/CeO /Al O , 300 nm
2 2 3
(CalbWF5A3 & TH052Au)
-2
77,3 K, 0 T
transport
-3
"CalbWF5A3"
"TH052Au"
20 kHz
-4
5 kHz
U inductive
-5 3
1 kHz
"CalbWF5A3"
0,2 kHz
-6
E-J obtained using k' E-J obtained using k
10 10 10
2 10 3 10 4 10
J (A/m )
IEC  017/13
Figure 5 – E-J characteristics measured by a transport method and the U
inductive method
E (V/m)
61788-17 © IEC:2013 – 15 –
IEC  018/13
Figure 6 –Example of the normalized third-harmonic
voltages (U /fI ) measured with various frequencies
3 0
6.3 Measurement of J in sample films
c
a) Measure U with two, three or four frequencies in sample films, and obtain I with the
3 th
same criterion L as used in 6.2.3.
c
b) Use the obtained experimental coil coefficient k’ to calculate J (= k’I /d) at each
c th
frequency, and obtain the relation between J and E (= 2,04µ kfdI , using k because of
c avg 0 th
the underestimation as mentioned in 7.1 c). An example of the E-J characteristics is also
shown in Figure 5) measured for a sample film (TH052Au, solid symbols) with
n-values (36,0 and 40,4) exceeding those of the calibration wafer (n = 28,0 to 28,6).
c) From the obtained E-J characteristics, calculate the J value with an appropriate electric-
c
field criterion, such as E = 100 µV/m.
c
d) Measurement with three or four frequencies is beneficial to check the validity of the
measurement and sample by checking the power-law E-J characteristics. Measurement
with two frequencies can be used for routine samples in the interests of time.
6.4 Measurement of J with only one frequency
c
As mentioned in Clause 1 and Clause 3, J is a function of electric field, and it is
c
recommended to determine it with a constant electric-field criterion using a multi-frequency
approach through procedures described in 6.2 and 6.3. However, one frequency
measurement is sometimes desired for simplicity and inexpensiveness. In this case, the J
c
values are determined with variable electric-field criteria through the following procedures.
a) Calculate the theoretical coil coefficient k by Equation (1) in 6.2.1.
b) Obtain the E-J characteristics of the transport bridges of the calibration wafer (Equation
(3)) through the procedures of 6.2.2.
c) Measure U in the inductive measurement area of the calibration wafer as a function of the
coil current with one frequency, and obtain the experimental I using a constant-
th
inductance criterion; namely, U /fI = 2πL . The criterion L should be as small as possible
3 0 c c
within the range with sufficiently large S/N ratios, in order to use the simple Equation (4) in
6.2.4 for the electric-field calculation. Calculate J (= kI /d) and the average E induced in
c0 th
the superconducting film at the full penetration threshold by Equation (4). Repeat the

– 16 – 61788-17 © IEC:2013
measurement for at least three different points of the film, and obtain average J and
c0
E .
avg-U3
d) Using the transport E-J characteristics of Equation (3), calculate J for the average
ct
obtained in c).
E
avg-U3
e) Determine the experimental coil coefficient k’ by k’ = (J /J )k.
ct c0
with the same frequency in sample films, and obtain I with the same
f) Measure U
3 th
criterion L as used in c). Calculate J (= k’I /d) using the obtained experimental coil
c c th
coefficient k’. Calculate also E with Equation (4), and this value should be accompanied
avg
by each J value.
c
6.5 Examples of the theoretical and experimental coil coefficients
Some examples of the theoretical and experimental coil coefficients (k and k’) for typical
sample coils are shown in Table 1 with the specifications and recommended criteria for the I
th
determination, 2πL = U /fI . Note that the k’ depends on the criterion L . Coil 1 is wound with
c 3 0 c
a 50 µm diameter, self-bonding polyurethane enameled round copper winding wire, and
coils 2 and 3 are wound with a 50 µm diameter, polyurethane enameled round copper winding
wire. Measured resistances at 77,3 K and calculated self-inductances when a
superconducting film is placed below the coil are also shown. The coil-to-film distance Z is
fixed at 0,2 mm. The images of coils 1 and 3 are shown in Figure 7, and the coil-factor
functions F(r) for the three coils show that the peak magnetic field occurs near the mean coil
radius (Figure 8).
Table 1 – Specifications and coil coefficients of typical sample coils
D D h Turns k k’ U /fI R L
1 2 3 0
mm mm mm 1/mm 1/mm µΩ•sec Ω mH
1 0,9 4,2 1,0 400 106,6 82,2 2 4,1 0,165
2 1,0 3,6 1,0 400 117,4 89,1 2 3,4 0,163
3 0,8 2,2 1,0 200 63,2 47,0 0,6 1,6 0,028

IEC  019/13
Figure 7 – Illustration for coils 1 and 3 in Table 1

61788-17 © IEC:2013 – 17 –
IEC  020/13
Figure 8 – The coil-factor function F(r) = 2H /I calculated for the three coils
0 0
7 Uncertainty in the test method
7.1 Major sources of systematic effects that affect the U measurement
The most significant systematic effect on the U measurement is due to the deviation of the
coil-to-film distance Z from the prescribed value. Because the measured value J d in this
1 c
technique is directly proportional to the magnetic field at the upper surface of the
superconducting film, the deviation of the spacing Z directly affects the measurement. The
key origins of the uncertainty are listed bellow (a)–c)). Note that the general concept of the
“uncertainty” is summarized in Annex C.
a) Inadequate pressing of the coil to the film
As the measurement is performed in liquid nitrogen, the polyimide film placed above the
HTS thin film becomes brittle and liquid nitrogen may enter the space between the
polyimide and HTS films. Thus, sufficient pressure is necessary to keep the polyimide film
flat and avoid the deviation of Z . An experiment has shown that the required pressure is
about 0,2 MPa [18]. Here it is to be noted that thermal contraction of polyimide films at the
liquid nitrogen temperature is less than 0,002 × (300 – 77) ≈ 0,45 %, which leads to
negligible values of 0,2 µm to 0,6 µm compared with the total coil-to-film distance (about
200 µm) [25].
b) Ice layer formed between the coil and polyimide film
The liquid nitrogen inevitably contains powder-like ice. If the sample coil is moved to scan
the large-area HTS film area for an extended period, an ice layer is often formed between
the polyimide film and the sample coil, which increases the coil-to-film distance Z from
the prescribed value. As shown later in 7.2, this effect reduces coil coefficients (k and k’),
and the use of uncorrected k’ results in an overestimate in J . Special care should be
c
taken to keep the measurement environment as dry as possible. If the measurement
system is set in an open (ambient) environment,
...