IEC 61788-4:2020

Superconductivity - Part 4: Residual resistance ratio measurement - Residual resistance ratio of Nb-Ti and Nb₃Sn composite superconductors

IEC 61788-4:2020 specifies a test method for the determination of the residual resistance ratio (RRR) of Nb-Ti and Nb3Sn composite superconductors with Cu, Cu-Ni, Cu/Cu-Ni and Al matrix in a strain-free condition and zero external magnetic field. This method is intended for use with superconductor specimens that have a monolithic structure with rectangular or round cross-section, RRR value less than 350, and cross-sectional area less than 3 mm2. In the case of Nb3Sn, the specimens have received a reaction heat-treatment. This fifth edition cancels and replaces the fourth edition published in 2016. This edition constitutes a technical revision. This edition includes the following significant technical changes with respect to the previous edition:
a) change in the suitable distance of voltage taps on the specimen for reliable measurement,
b) new report on the result of the round robin test of the residual resistance ratio of Nb3Sn superconductors that proves the validity of the measurement method in this standard,
c) revision of the confusing definitions of the copper ratio and copper fraction.

Supraconductivité - Partie 4: Mesurage du rapport de résistance résiduelle - Rapport de résistance résiduelle des composites supraconducteurs de Nb-Ti et de Nb₃Sn

IEC 61788-4:2020 spécifie une méthode d'essai pour la détermination du rapport de résistance résiduelle (RRR) des composites supraconducteurs de Nb-Ti et de Nb3Sn avec une matrice de Cu, Cu-Ni, Cu/Cu-Ni et Al dans une condition sans contrainte et dans un champ magnétique externe nul. Cette méthode est destinée à être utilisée avec des éprouvettes de supraconducteurs présentant une structure monolithique avec une section rectangulaire ou circulaire, un RRR de valeur inférieure à 350 et une surface de section inférieure à 3 mm2. Dans le cas de Nb3Sn, les éprouvettes ont subi un traitement thermique de réaction. Cette cinquième édition annule et remplace la quatrième édition parue en 2016. Cette édition constitue une révision technique. Cette édition inclut les modifications techniques majeures suivantes par rapport à l'édition précédente:
a) modification de la distance adéquate des prises de tension sur les éprouvettes pour un mesurage fiable,
b) nouveau rapport du résultat de l’essai interlaboratoire du rapport de résistance résiduelle des supraconducteurs Nb3Sn qui atteste de la validité de la méthode de mesure utilisée dans la présente norme,
c) révision des définitions prêtant à confusion concernant le rapport entre le cuivre et la fraction de cuivre.

General Information

• Status: Published
• Publication Date: 19-Mar-2020
• ICS: 17.220.20 - Measurement of electrical and magnetic quantities
• ICS: 29.050 - Superconductivity and conducting materials
• Technical Committee: TC 90 - Superconductivity
• Drafting Committee: WG 4 - TC 90/WG 4
• Current Stage: PPUB - Publication issued
• Start Date: 20-Mar-2020
• Completion Date: 20-Mar-2020

Relations

• Revises: IEC 61788-4:2016 - Superconductivity - Residual resistance ratio measurement - Residual resistance ratio of Nb-Ti and Nb₃Sn composite superconductors
• Effective Date: 05-Sep-2023

Overview

IEC 61788-4:2020 - Superconductivity Part 4 - specifies a standardized test method to determine the residual resistance ratio (RRR) of Nb‑Ti and Nb3Sn composite superconductors. This fifth edition (2020) replaces the 2016 edition and introduces technical revisions including updated guidance on voltage tap spacing, results from a round‑robin test validating the method for Nb3Sn, and clarified definitions for copper ratio / copper fraction. The procedure targets monolithic specimens (round or rectangular cross‑section), in a strain‑free condition and zero external magnetic field, for RRR < 350 and cross‑sectional area < 3 mm2. Nb3Sn specimens are tested after reaction heat‑treatment.

Key topics and technical requirements

• Measurement scope: RRR of Nb‑Ti and Nb3Sn composite superconductors with Cu, Cu‑Ni, Cu/Cu‑Ni or Al matrices.
• Principle: RRR is defined as the ratio of the resistance at room temperature to the resistance just above the superconducting transition; the standard uses a curve method for the cryogenic resistance measurement.
• Specimen constraints: Monolithic structure, rectangular or round cross‑section, cross‑section < 3 mm2, RRR < 350, strain‑free mounting, zero external magnetic field. Nb3Sn must be heat‑treated.
• Apparatus and setup: Mandrel or measurement base plate, cryostat for low‑temperature resistance measurement, voltage taps and lead arrangements - the edition revises suitable voltage‑tap distances for reliable readings.
• Data acquisition & analysis: Procedures for measuring resistance at room temperature and just above Tc, corrections for bending/strain effects (especially for Nb‑Ti), and calculation/reporting of RRR.
• Uncertainty & validation: Clauses and annexes cover uncertainty evaluation, stability of the test method, and results from an interlaboratory round‑robin validating the method for Nb3Sn.

Practical applications

• Quality control and batch acceptance testing for superconducting wire/tape manufacturers.
• Material qualification for high‑field magnet projects (MRI, fusion, particle accelerators).
• Cryogenic stability and AC‑loss assessment, because copper/aluminium matrix resistivity at low temperatures affects quench protection and thermal recovery.
• Research and development of composite superconductors where reliable RRR data are required for modeling and design.

Who should use this standard

• Superconductor manufacturers and testing laboratories
• Magnet designers, cryogenic engineers, and R&D teams working with Nb‑Ti and Nb3Sn conductors
• Quality assurance and compliance personnel in industries deploying superconducting systems

Related standards

• Other parts of the IEC 61788 series (Superconductivity) and documents published by IEC TC 90 covering test methods and terminology for superconducting materials and components.

Standards Content (Sample)

IEC 61788-4 ®
Edition 5.0 2020-03
REDLINE VERSION
INTERNATIONAL
STANDARD
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Superconductivity –
Part 4: Residual resistance ratio measurement – Residual resistance ratio of
Nb-Ti and Nb Sn composite superconductors
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IEC 61788-4 ®
Edition 5.0 2020-03
REDLINE VERSION
INTERNATIONAL
STANDARD
colour
inside
Superconductivity –
Part 4: Residual resistance ratio measurement – Residual resistance ratio of

Nb-Ti and Nb Sn composite superconductors

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
ICS 17.220.20; 29.050 ISBN 978-2-8322-8033-1

– 2 – IEC 61788-4:2020 RLV © IEC 2020
CONTENTS
FOREWORD . 4
INTRODUCTION . 2
1 Scope . 7
2 Normative references . 7
3 Terms and definitions . 7
4 Principle . 8
5 Apparatus . 8
5.1 Material of measurement mandrel or of measurement base plate . 8
5.2 Diameter of the measurement mandrel and length of the measurement base
plate . 9
5.3 Cryostat for the resistance ( ) measurement . 9
R
6 Specimen preparation . 9
7 Data acquisition and analysis . 9
7.1 Resistance ( R ) at room temperature . 9
*
7.2 Resistance ( R or R ) just above the superconducting transition . 10
2 2
7.2.1 Correction of strain effect . 10
7.2.2 Data acquisition of cryogenic resistance . 10
7.2.3 Optional acquisition methods . 12
*
7.3 Correction on measured R of Nb-Ti composite superconductor for bending
strain . 12
7.4 Residual resistance ratio (RRR) . 13
8 Uncertainty and stability of the test method . 13
8.1 Temperature . 13
8.2 Voltage . 13
8.3 Current . 13
8.4 Dimension . 13
9 Test report . 14
9.1 RRR value . 14
9.2 Specimen . 14
9.3 Test conditions . 15
9.3.1 Measurements of R and R . 15
1 2
9.3.2 Measurement of R . 15
9.3.3 Measurement of R . 15
Annex A (informative) Additional information relating to the measurement of RRR . 16
A.1 Recommendation on specimen mounting orientation . 16
A.2 Alternative methods for increasing temperature of specimen above
superconducting transition temperature . 16
*
A.3 Alternative measurement methods of R or R . 16
2 2
A.4 Bending strain dependency of RRR for Nb-Ti composite superconductor . 19
A.5 Procedure of correction of bending strain effect . 22
Annex B (informative) Uncertainty considerations . 24
B.1 Overview. 24
B.2 Definitions. 24

B.3 Consideration of the uncertainty concept . 24
B.4 Uncertainty evaluation example for IEC TC 90 standards . 26
Annex C (informative) Uncertainty evaluation in test method of RRR for Nb-Ti and
Nb Sn composite superconductors . 28
C.1 Evaluation of uncertainty . 28
C.2 Summary of round robin test of RRR of a Nb-Ti composite superconductor . 31
C.3 Reason for large COV value in the intercomparison test on Nb Sn composite
superconductor . 32
Bibliography . 34

Figure 1 – Relationship between temperature and resistance. 8
Figure 2 – Voltage versus temperature curves and definitions of each voltage . 11
Figure A.1 – Definition of voltages . 18
Figure A.2 – Bending strain dependency of RRR value for pure Cu matrix of Nb-Ti
composite superconductors (comparison between measured values and calculated
values) . 20
Figure A.3 – Bending strain dependency of RRR value for round Cu wires . 20
Figure A.4 – Bending strain dependency of normalized RRR value for round Cu wires . 21
Figure A.5 – Bending strain dependency of RRR value for rectangular Cu wires . 21
Figure A.6 – Bending strain dependency of normalized RRR value for rectangular Cu
wires . 22
Figure C.1 – Distribution of observed r of Cu/Nb-Ti composite superconductor . 32
RRR
Table A.1 – Minimum diameter of the measurement mandrel for round wires . 22
Table A.2 – Minimum diameter of the measurement mandrel for rectangular wires. 22
Table B.1 – Output signals from two nominally identical extensometers . 25
Table B.2 – Mean values of two output signals . 25
Table B.3 – Experimental standard deviations of two output signals . 25
Table B.4 – Standard uncertainties of two output signals . 26
Table B.5 – COV values of two output signals . 26
Table C.1 – Uncertainty of each measurement . 31
Table C.2 – Obtained values of R , R and r for three Nb Sn samples .
1 2 RRR 3
Table C.2 – Obtained values of RRR for six Nb Sn specimens . 33
Table C.3 – Average, standard deviation and coefficient of variation for six specimens . 33

– 4 – IEC 61788-4:2020 RLV © IEC 2020
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
SUPERCONDUCTIVITY –
Part 4: Residual resistance ratio measurement –
Residual resistance ratio of Nb-Ti and Nb Sn
composite superconductors
FOREWORD
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International Standard IEC 61788-4 has been prepared by IEC technical committee 90:
Superconductivity.
This fifth edition cancels and replaces the fourth edition published in 2016. This edition
constitutes a technical revision.
This edition includes the following significant technical changes with respect to the previous
edition:
a) change in the suitable distance of voltage taps on the specimen for reliable measurement,
b) new report on the result of the round robin test of the residual resistance ratio of Nb Sn
superconductors that proves the validity of the measurement method in this standard,
c) revision of the confusing definitions of the copper ratio and copper fraction.
The text of this standard is based on the following documents:
FDIS Report on voting
90/448/FDIS 90/451/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 parts of the IEC 61788 series, published under the general title Superconductivity,
can be found on the IEC website.
The committee has decided that the contents of this publication will remain unchanged until the
stability date indicated on the IEC website 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 – IEC 61788-4:2020 RLV © IEC 2020
INTRODUCTION
Copper, Cu/Cu-Ni or aluminium is used as matrix material in Nb-Ti Ni-Ti and Nb Sn composite
superconductors and works as an electrical shunt when the superconductivity is interrupted. It
also contributes to recovery of the superconductivity by conducting heat generated in the
superconductor to the surrounding coolant. The cryogenic-temperature resistivity of copper is
an important quantity, which influences the stability and AC losses of the superconductor. The
residual resistance ratio is defined as a ratio of the resistance of the superconductor at room
temperature to that just above the superconducting transition.
This document specifies the test method for residual resistance ratio of Nb-Ti and Nb Sn
composite superconductors. The curve method is employed for the measurement of the
resistance just above the superconducting transition. Other methods are described in
Clause A.3.
SUPERCONDUCTIVITY –
Part 4: Residual resistance ratio measurement –
Residual resistance ratio of Nb-Ti and Nb Sn
composite superconductors
1 Scope
This part of IEC 61788 specifies a test method for the determination of the residual resistance
ratio (RRR) of Nb-Ti and Nb Sn composite superconductors with Cu, Cu-Ni, Cu/Cu-Ni and Al
matrix in a strain-free condition and zero external magnetic field. This method is intended for
use with superconductor specimens that have a monolithic structure with rectangular or round
cross-section, RRR value less than 350, and cross-sectional area less than 3 mm . In the case
of Nb Sn, the specimens have received a reaction heat-treatment.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies.
For undated references, the latest edition of the referenced document (including any
amendments) applies.
IEC 60050-815, International Electrotechnical Vocabulary (IEV) – Part 815: Superconductivity
(available at: www.electropedia.org)
3 Terms and definitions
For the purposes of this document, the terms and definitions given in IEC 60050-815 and the
following apply.
ISO and IEC maintain terminological databases for use in standardization at the following
addresses:
• IEC Electropedia: available at http://www.electropedia.org/
• ISO Online browsing platform: available at http://www.iso.org/obp
3.1
residual resistance ratio
RRR
ratio of resistance at room temperature to the resistance just above the superconducting
transition
Note 1 to entry: This note applies to the French language only.
Note 2 to entry: In this document for Nb-Ti and Nb Sn composite superconductors, the room temperature is defined
as 293 K (20 °C), and the residual resistance ratio is obtained in Formula (1), where the resistance ( R ) at 293 K is
divided by the resistance ( R ) just above the superconducting transition.
R
r = (1)
RRR
R
– 8 – IEC 61788-4:2020 RLV © IEC 2020
Here r is a value of the residual resistance ratio, R is a value of the resistance measured in a strain-free
RRR
condition and zero external magnetic field.
Figure 1 shows schematically a resistance versus temperature curve acquired on a specimen while measuring the
cryogenic resistance.
The cryogenic resistance, R , is determined by the intersection, A, of two straight lines (a) and (b) at
temperature T* .
c
Figure 1 – Relationship between temperature and resistance
4 Principle
The resistance measurement both at room and cryogenic temperatures shall be performed with
the four-terminal technique. All measurements are done without an applied magnetic field.
The target relative combined standard uncertainty of this method is defined as an expanded
uncertainty ( k = 2 ) not to exceed 5 %.
The maximum bending strain induced during mounting and cooling the Nb-Ti specimen shall
not exceed 2 %. The measurement shall be conducted in a strain-free condition or in a condition
with allowable thermal strain for the Nb Sn specimen.
5 Apparatus
5.1 Material of measurement mandrel or of measurement base plate
Material of the measurement mandrel for a coiled Nb-Ti specimen or of the measurement base
plate for a straight Nb-Ti or Nb Sn specimen shall be copper, aluminium, silver, or the like
whose thermal conductivity is equal to or better than 100 W/(m·K) at liquid helium temperature
(4,2 K). The surface of the material shall be covered with an insulating layer (tape or a layer
made of polyethylene terephthalate, polyester, polytetrafluoroethylene, etc.) whose thickness
is 0,1 mm or less.
5.2 Diameter of the measurement mandrel and length of the measurement base plate
The diameter of the measurement mandrel shall be large enough to keep the bending strain of
the specimen less than or equal to 2 % for the Nb-Ti specimen. The Nb Sn specimen on a base
plate shall be measured in a strain-free condition or a condition with allowable thermal strain.
The measurement base plate shall be at least 30 mm long in one dimension.
5.3 Cryostat for the resistance ( R ) measurement
The cryostat shall include a specimen support structure and a liquid helium reservoir for
measurement of the resistance R . The specimen support structure shall allow the specimen,
which is mounted on a measurement mandrel or a measurement base plate, to be lowered into
and raised out of a liquid helium bath. In addition, the specimen support structure shall be made
so that a current can flow through the specimen and the resulting voltage generated along the
specimen can be measured.
6 Specimen preparation
The test specimen shall have no joints or splices with a length of 30 mm or longer. The specimen
shall be instrumented with current contacts near each of its ends and a pair of voltage contacts
over its central portion. The distance between two voltage taps ( L ) shall be 25 15 mm or longer.
A thermometer for measuring cryogenic temperature shall be attached near the specimen.
Some mechanical method shall be used to hold the specimen against the insulated layer of the
measurement mandrel or base plate. Special care should be taken during instrumentation and
installation of the specimen on the measurement mandrel or base plate so that no excessive
force, which may cause undesired bending strain or tensile strain, would be applied to the
specimen. Ideally, the Nb Sn specimen is intended to be as straight as possible; however, this
is not always the case, thus care should be taken to measure the specimen in its as received
condition.
The specimen shall be mounted on a measurement mandrel or on a measurement base plate
for these measurements. Both resistance measurements, R and R , shall be made on the
1 2
same specimen and the same mounting.
7 Data acquisition and analysis
7.1 Resistance ( R ) at room temperature
The mounted specimen shall be measured at room temperature ( T (K)), where T satisfies
m m
the following condition: 273 K ≤ T ≤ 308 K. A specimen current ( I (A)) shall be applied so that

m 1
2 2
the current density is in the range of 0,1 A/mm to 1 2 A/mm based on the total wire cross-
sectional area, and the resulting voltage ( U (V)), I and T shall be recorded. Formula (2)
1 1 m
below shall be used to calculate the resistance ( R ) at room temperature. The resistance ( R )
m 1
at 293 K (20 °C ) shall be calculated using Formula (3) for a wire with Cu matrix. For wires that
do not contain a pure Cu component, the value of R shall be set equal to R , without any
1 m
temperature correction.
U
R = (2)
m
I
– 10 – IEC 61788-4:2020 RLV © IEC 2020
R
m
R = (3)
1+ 0,00393 ×−T 293 
( )
m
 
*
7.2 Resistance ( R or R ) just above the superconducting transition
2 2
7.2.1 Correction of strain effect
*
Under a strained condition of the Nb-Ti specimen, the measured cryogenic resistance, , is
R
not a correct value for R . The corresponding correction of the strain effect is described in 7.3.
7.2.2 Data acquisition of cryogenic resistance
The specimen, which is still mounted as it was for the room temperature measurement, shall
be placed in the cryostat for electrical measurement specified in 5.3. Horizontal mounting of the
specimen is recommended in Clause A.1. Alternative cryostats that employ a heating element
to sweep the specimen temperature are described in Clause A.2. The specimen shall be slowly
lowered into the liquid helium bath and cooled to liquid helium temperature over a time period
of at least 5 min.
*
During the acquisition phases of the low-temperature R measurements, a specimen current
2 2
( I ) shall be applied so that the current density is in the range 0,1 A/mm to 10 A/mm based
on the total wire cross-sectional area, and the resulting voltage ( U (V)), I (A), and specimen
temperature ( T (K)) shall be recorded. In order to keep the ratio of signal to noise high enough,
the measurement shall be carried out under the condition that the absolute value of the resulting
voltage above the superconducting transition exceeds 10 μV. An illustration of the data to be
acquired and its analysis is shown in Figure 2.

NOTE Voltages with subscripts + and – are those obtained in the first and second measurements under positive
and negative currents, respectively, and U and U are those obtained at zero current. For clarity, U ,
20+ 20− 0rev
measured at zero current is not shown coincident with U . Straight line (a) is drawn in the transition region with a
0−
sharp increase in the voltage with temperature and straight line (b) is drawn in the region with a nearly constant
voltage.
Figure 2 – Voltage versus temperature curves
and definitions of each voltage
When the specimen is in the superconducting state and the test current ( I ) is applied, two
voltages shall be measured nearly simultaneously: U (the initial voltage recorded with a
0+
positive current polarity) and (the voltage recorded during a brief change in applied
U
0rev
*
current polarity). A valid measurement requires that excessive interfering voltages are not
R
present and that the specimen is initially in the superconducting state. Thus, the following
condition formulae shall be met for a valid measurement:
UU−
0+ 0rev
< 1 % (4)
U
where U 2 is the average voltage for the specimen in the normal state at cryogenic temperature,
which is defined by Formula (5).
The specimen shall be gradually warmed so that it changes to the normal state completely.
When the cryostat for the resistance measurement specified in 5.3 is used, this can be achieved
simply by raising the specimen to an appropriate position above the liquid helium level. The
specimen voltage versus temperature curve shall be acquired with the rate of temperature
increase maintained between 0,1 K/min and 10 K/min. The voltage versus temperature curve
shall continue to be recorded during the transition into the normal state, up to a temperature
Sn specimen.
somewhat less than 15 K for the Nb-Ti specimen and less than 25 K for the Nb
Then, the specimen current shall be decreased to zero and the corresponding voltage, U ,
20+
– 12 – IEC 61788-4:2020 RLV © IEC 2020
shall be recorded at a temperature below 15 K for the Nb-Ti specimen and below 25 K for the
Nb Sn specimen.
The specimen shall then be slowly lowered into the liquid helium bath and cooled to within ±1 K
from the temperature at which the initial voltage signal U was recorded. A specimen current,
0+
I , with the same magnitude but negative polarity (polarity opposite that used for the initial
curve) shall be applied and the voltage U shall be recorded at this temperature. The
0−
procedural steps shall be repeated to record the voltage versus temperature curve with this
negative current. In addition, when the measurement current, I , decreases to 0, the recording
of U shall be made at within ±1 K from the temperature at which U was recorded.
20− 20+
Each of the two voltage versus temperature curves shall be analysed by drawing a line (a)
through the data where the absolute value of voltage sharply increases with temperature
(see Figure 2) and drawing a second line (b) through the data above the transition where the
voltage is nearly constant for Nb-Ti or raised gradually and almost linearly for Nb Sn with
* *
temperature increase. U and U in Figure 2 shall be determined at the intersection of these
2+ 2−
two lines for the positive and negative polarity curves, respectively.
The corrected voltages, U and U , shall be calculated using the following equations:
2+ 2−
* *
and . The average voltage, U , shall be defined as
U UU− U UU− 2
2+ 2++0 2− 20− −
UU−
22+ −
U =
2 (5)
*
A valid R measurement requires that the shift of thermoelectric voltage be within acceptable
limits during the measurements of U and U . Thus, the following condition shall be met for
2+ 2−
a valid measurement:
||∆ −∆
+−
< 3 % (6)
U
*
where ∆ and ∆ are defined as ∆= UU− and ∆= UU− . If the
R
+ − + 20++0 − 20− 0− 2
measurement does not meet the validity requirements in 7.2.2, specifically either in Formula (4)
or (6), then improvement steps either in hardware or experimental operation shall be taken to
meet these requirements before results are reported.
*
Formula (7) shall be used to calculate the measured resistance ( R ) just above the
superconducting transition.
U
*
R = (7)
I
7.2.3 Optional acquisition methods
The method described in the body main clauses of this document is the “reference” method and
optional acquisition methods are outlined in Clause A.3.
*
7.3 Correction on measured of Nb-Ti composite superconductor for bending
R
strain
*
If there is no pure Cu component in the superconductor, then R shall be set equal to R .
2 2
= =
For a specimen with a pure Cu component, the bending strain shall be defined by ε = 100 ×
b
(h/r) (%), where h is a half of the specimen thickness for rectangular wires or a radius for round
wires and r is the bending radius. If the bending strain is less than 0,3 %, then no correction is
*
necessary, and R shall be set equal to R .
2 2
If neither of the above two situations applies, then the resistance R just above the
superconducting transition under the strain-free condition shall be estimated by
L
*
R R−∆ρ× (8)
S
Cu
where ∆ρ is defined below and S and L are defined in 8.4. The increase in the resistivity of
Cu
pure copper at 4,2 K due to tensile strain, ε (%), is expressed by
-12 -14 2
∆ρ (Ωm) = 6,24 × 10 ε − 5,11 × 10 ε ; ε ≤ 2 % (9)
The calculation of Formula (9) shall be carried out assuming that the equivalent tensile strain
ε is (1/2)ε and (4/3 π)ε for rectangular and round wires, respectively. The bending strain
b b
dependency of residual resistance ratio for pure copper is described in Clause A.4.
7.4 Residual resistance ratio (RRR)
The RRR value shall be calculated using Formula (1).
8 Uncertainty and stability of the test method
8.1 Temperature
The room temperature shall be determined with a standard uncertainty not exceeding 0,6 K,
while holding the specimen, which is mounted on the measurement mandrel or on the
measurement base plate, at room temperature.
8.2 Voltage measurement
For the resistance measurement, the voltage signal shall be measured with a relative standard
uncertainty not exceeding 0,3 %.
8.3 Current
When the current is directly applied to the specimen with a programmable DC current source,
the specimen test current shall be determined with a relative standard uncertainty not exceeding
0,3 %.
When the specimen test current is determined from a voltage-current characteristic of a
standard resistor by the four-terminal technique, the standard resistor, with a relative combined
standard uncertainty not exceeding 0,3 %, shall be used.
The fluctuation of DC specimen test current, provided by a DC power supply, shall be less than
0,5 % during every resistance measurement.
8.4 Dimension
The distance along the specimen between the two voltage taps (L) shall be determined with a
relative combined standard uncertainty not exceeding 5 %.
=
– 14 – IEC 61788-4:2020 RLV © IEC 2020
For correction of the bending strain effect in the case of the wire with pure Cu matrix, the cross-
sectional area of Cu matrix ( S ) shall be determined using a nominal value of copper to non-
Cu
copper ratio and nominal dimensions of the specimen. The wire diameter (d) and mandrel radius
( R ) shall be determined with relative standard uncertainty not exceeding 1 % and 3 %,
d
respectively.
9 Test report
9.1 RRR value
The obtained RRR value ( r ) shall be reported as
RRR
r 1 ±= Un   , (10)
( ) ( )
RRR re
where
U is the expanded relative uncertainty:
re
U 2 uk( 2)
re r
where
u denotes the relative combined standard uncertainty,
r
k is a coverage factor, and
n is the sampling number.
It is desired that n be larger than 4 so that the normal distribution can be assumed for observed
results to estimate the standard deviation. If n is not sufficiently large, a rectangular distribution
shall be assumed.
9.2 Specimen
The test report for the result of the measurements shall also include the following items, if
known:
a) manufacturer;
b) classification and/or symbol;
c) shape and area of the cross-section;
d) dimensions of the cross-sectional area;
e) number of filaments or subelements;
f) diameter of the filaments or subelements;
g) Cu to Nb-Ti volume ratio, Cu-Ni to Nb-Ti volume ratio, or Cu, Cu-Ni to Nb-Ti volume ratio,
or Al, Cu to Nb-Ti volume ratio or volume ratio among Cu-Ni, Cu, and Nb-Ti or among Al,
Cu, and Nb-Ti for Nb-Ti specimen;
g) for Nb-Ti specimen, the volume ratio of the following material to Nb-Ti:
Cu,
Cu-Ni,
Cu and Cu-Ni,
Al and Cu,
or the following volume ratio:
Cu-Ni: Cu: Nb-Ti,
==
Al: Cu: Nb-Ti;
h) Cu to non-Cu volume ratio for Nb Sn specimen;
i) cross-sectional area of the Cu matrix ( S ).
Cu
9.3 Test conditions
9.3.1 Measurements of R and R
1 2
The following test conditions shall be reported for the measurements of R and R :
1 2
a) total length of the specimen;
b) distance between the voltage measurement taps (L);
c) length of each current contact;
d) transport currents ( and );
I I
1 2
e) current densities ( I and I divided by the nominal total wire cross-sectional area);
1 2
* *
f) voltages ( U , U , U , U , U , U , U , U and U 2 );
1 0+ 0rev 2+ 20+ 0− 2− 20−
*
g) resistances ( R , R , R and R );
m 1 2 2
h) resistivities ( ρ R× S /L and ρ R× S /L );
( ) ( )
1 1 Cu 2 2 Cu
i) material, shape, and dimensions of the mandrel or the base plate;
j) installation method of the specimen in the mandrel or the base plate;
k) insulating material of the mandrel or the base plate.
9.3.2 Measurement of
R
The following test conditions shall be reported for the measurement of R :
a) temperature setting and holding method of the specimen;
b) T : Temperature for measurement of R .
m m
9.3.3 Measurement of R
The following test conditions shall be reported for the measurement of R :
a) rate of increasing temperature;
b) method of cooling down and heating up.
Additional information relating to the measurement of RRR is given in Annex A. Annex B
describes definitions and an example of uncertainty in measurement. Uncertainty evaluation in
the reference test method of RRR for composite superconductors is given in Annex C.

= =
– 16 – IEC 61788-4:2020 RLV © IEC 2020
Annex A
(informative)
Additional information relating to the measurement of RRR
A.1 Recommendation on specimen mounting orientation
When a specimen is in the form of straight wire, horizontal mounting of the wire on the base
plate is recommended since this mounting orientation can reduce possible thermal gradient
along the wire compared to the vertical mounting orientation. Here the horizontal mounting
orientation means that the wire axis is parallel to the surface of liquid helium.
A.2 Alternative methods for increasing temperature of specimen above
superconducting transition temperature
The following methods are also recommended for increasing temperature above the
superconducting transition of the specimen. The rate of increasing temperature of the whole
specimen within a range between 0,1 K/min and 10 K/min should be applied for these methods.
In order to dampen the rate of increasing temperature and to avoid a large temperature gradient,
special care should be taken in selecting heater power, heat capacity (the specimen with the
measurement mandrel or the measurement base plate) and the distance between the heater
and the specimen.
a) Heater method
The specimen can be heated above the superconducting transition by a heater installed in
the measurement mandrel or in the measurement base plate after taking the specimen out
of the liquid helium bath in the cryostat.
b) Adiabatic Controlled methods
1) Adiabatic method
In this method, the cryostat holds a chamber in which the specimen, a sample holder, a
heater and so on are contained. Before the chamber is immersed in the liquid helium
bath, air inside the chamber is pumped out and helium gas is filled. Then, the chamber
is immersed in the liquid helium bath and the specimen is cooled to a temperature of 5 K
or lower below the critical temperature. After the helium gas is pumped out, the specimen
can be heated above the superconducting transition by the heater under adiabatic
condition.
2) Quasi-adiabatic method
In this method, the cryostat holds the specimen a certain distance above the liquid
helium bath for the entire cryogenic measurement. A thermal anchor from the
measurement mandrel or the measurement base plate to the liquid helium bath allows
the specimen to be cooled to a temperature of 5 K or lower below the critical temperature.
The specimen can be heated above the superconducting transition by a heater located
in the measurement mandrel or the measurement base plate under quasi-adiabatic
condition.
3) Refrigerator method
In this method, an electromechanical apparatus (a refrigerator) is used to cool the
specimen, which is mounted on a measurement mandrel or a measurement base plate,
to a temperature of 6 K or lower below the critical temperature. The specimen can be
heated above the superconducting transition by a heater or by controlling the refrigerator
power.
*
A.3 Alternative measurement methods of R or R
2 2
*
The following methods can optionally be used for acquisition of R or R .
2 2
a) Modified reference method
This is a simplified method with acquisition of only one voltage-temperature curve and is
used only for Nb-Ti composite superconductors. The voltage of the specimen is measured
in the superconducting state under a desired direction of current ( I ) and then with current
in the opposite direction. These values are U and U as shown in Figure A.1. The
0+ 0rev
current is then changed back to the initial direction. After the transition to the normal state,
'
the voltage is measured as U in a plateau region of the curve within about 4 K above the
2+
transition. Then the voltage is read under a zero current ( U ). The current direction is then
'
reversed and the voltage is measured again ( U ). The cryogenic resistance is obtained
2−
from
U
*
R = (A.1)
I
with
' '
UU−
22+ −
U = (A.2)
This approximately compensates for the effect of thermoelectric voltage. The following
conditions should be fulfilled to ensure that the influence of the interfering voltage and the
*
thermoelectric voltage shift on measurement is not appreciably large:
R
UU−
0+ 0rev
< 1 % (A.3)
U
∆ −∆
22+−
< 3 % (A.4)
U
' '
where ∆ and ∆ are defined by ∆= UU− and ∆= UU− , respectively.
2+ 2− 2++2 20 2−−2 20
– 18 – IEC 61788-4:2020 RLV © IEC 2020

Figure A.1 – Definition of voltages
b) Measurement of voltage vs. time
Instead of measuring the voltage as a function of temperature, one can determine the
cryogenic resistance from a voltage-versus-time curve that is continuously recorded both
below and above the transition. Care should be taken not to re-cool the specimen without
*
re-starting the acquisition of voltage-versus-time. The characteristic voltages, such as U ,
2+
can be similarly obtained from the intersection of the two straight lines drawn on the region
of steepest slope during the transition and on the relatively flat region sufficiently above the
transition in the voltage-versus-time curve. The analysis afterward to determine the
cryogenic resistance is the same as in the reference method.
c) Fixed temperature method
*
In this method R or is directly determined at a fixed temperature in a plateau region
R
2 2
within about 4 K above the transition for Nb-Ti composite superconductors, and R is
directly determined at 20 K for Nb Sn composite superconductors, instead of using the
method described in 7.2. In this case it is desirable to check that the whole specimen is at
a uniform and fixed temperature. In the measurement of Nb Sn composite superconductor
the fixed temperature of 20 K should be determined with a combined standard uncertainty
not exceeding 0,6 K. The fixed temperature and the combined standard uncertainty should
be noted in the test report. Also the U and U , which are defined in 7.2.2, should be

0+ 0−
recorded as the zero voltage level in the fixed temperature method. In order to eliminate the
influence of thermoelectric voltage, two voltage signals of the specimen, say U and U ,
2+ 2−
should be acquired nearly simultaneously by reversal of the test current. For the fixed
temperature method the effect of thermoelectric voltage on determination of cryogenic
resistance can be eliminated.
d) Computer-based method
A computer can be used to control the current direction and warming of the specimen and
to measure the voltage-temperature curve. Changes in current direction by periodic current
reversals or periodic curren
...

IEC 61788-4 ®
Edition 5.0 2020-03
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Superconductivity –
Part 4: Residual resistance ratio measurement – Residual resistance ratio of
Nb‑Ti and Nb Sn composite superconductors
Supraconductivité –
Partie 4: Mesurage du rapport de résistance résiduelle – Rapport de résistance
résiduelle des composites supraconducteurs de Nb-Ti et de Nb Sn
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IEC 61788-4 ®
Edition 5.0 2020-03
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Superconductivity –
Part 4: Residual resistance ratio measurement – Residual resistance ratio of

Nb‑Ti and Nb Sn composite superconductors

Supraconductivité –
Partie 4: Mesurage du rapport de résistance résiduelle – Rapport de résistance

résiduelle des composites supraconducteurs de Nb-Ti et de Nb Sn
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
INTERNATIONALE
ICS 17.220.20; 29.050 ISBN 978-2-8322-7916-8

– 2 – IEC 61788-4:2020 © IEC 2020
CONTENTS
FOREWORD . 4
INTRODUCTION . 6
1 Scope . 7
2 Normative references . 7
3 Terms and definitions . 7
4 Principle . 8
5 Apparatus . 8
5.1 Material of measurement mandrel or of measurement base plate . 8
5.2 Diameter of the measurement mandrel and length of the measurement base
plate . 9
5.3 Cryostat for the resistance ( ) measurement . 9
R
6 Specimen preparation . 9
7 Data acquisition and analysis . 9
7.1 Resistance ( R ) at room temperature . 9
*
7.2 Resistance ( R or R ) just above the superconducting transition . 10
2 2
7.2.1 Correction of strain effect . 10
7.2.2 Data acquisition of cryogenic resistance . 10
7.2.3 Optional acquisition methods . 12
*
7.3 Correction on measured R of Nb-Ti composite superconductor for bending
strain . 12
7.4 Residual resistance ratio (RRR) . 12
8 Uncertainty and stability of the test method . 13
8.1 Temperature . 13
8.2 Voltage . 13
8.3 Current . 13
8.4 Dimension . 13
9 Test report . 13
9.1 RRR value . 13
9.2 Specimen . 14
9.3 Test conditions . 14
9.3.1 Measurements of R and R . 14
1 2
9.3.2 Measurement of R . 15
9.3.3 Measurement of R . 15
Annex A (informative) Additional information relating to the measurement of RRR . 16
A.1 Recommendation on specimen mounting orientation . 16
A.2 Alternative methods for increasing temperature of specimen above
superconducting transition temperature . 16
*
A.3 Alternative measurement methods of R or R . 16
2 2
A.4 Bending strain dependency of RRR for Nb-Ti composite superconductor . 19
A.5 Procedure of correction of bending strain effect . 22
Annex B (informative) Uncertainty considerations . 24
B.1 Overview. 24
B.2 Definitions. 24

B.3 Consideration of the uncertainty concept . 24
B.4 Uncertainty evaluation example for IEC TC 90 standards . 26
Annex C (informative) Uncertainty evaluation in test method of RRR for Nb-Ti and
Nb Sn composite superconductors . 28
C.1 Evaluation of uncertainty . 28
C.2 Summary of round robin test of RRR of a Nb-Ti composite superconductor . 31
C.3 Reason for large COV value in the intercomparison test on Nb Sn composite
superconductor . 32
Bibliography . 34

Figure 1 – Relationship between temperature and resistance. 8
Figure 2 – Voltage versus temperature curves and definitions of each voltage . 11
Figure A.1 – Definition of voltages . 18
Figure A.2 – Bending strain dependency of RRR value for pure Cu matrix of Nb-Ti
composite superconductors (comparison between measured values and calculated
values) . 20
Figure A.3 – Bending strain dependency of RRR value for round Cu wires . 20
Figure A.4 – Bending strain dependency of normalized RRR value for round Cu wires . 21
Figure A.5 – Bending strain dependency of RRR value for rectangular Cu wires . 21
Figure A.6 – Bending strain dependency of normalized RRR value for rectangular Cu
wires . 22
Figure C.1 – Distribution of observed r of Cu/Nb-Ti composite superconductor . 32
RRR
Table A.1 – Minimum diameter of the measurement mandrel for round wires . 22
Table A.2 – Minimum diameter of the measurement mandrel for rectangular wires. 22
Table B.1 – Output signals from two nominally identical extensometers . 25
Table B.2 – Mean values of two output signals . 25
Table B.3 – Experimental standard deviations of two output signals . 25
Table B.4 – Standard uncertainties of two output signals . 26
Table B.5 – COV values of two output signals . 26
Table C.1 – Uncertainty of each measurement . 31
Table C.2 – Obtained values of RRR for six Nb Sn specimens . 32
Table C.3 – Average, standard deviation and coefficient of variation for six specimens . 33

– 4 – IEC 61788-4:2020 © IEC 2020
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
SUPERCONDUCTIVITY –
Part 4: Residual resistance ratio measurement –
Residual resistance ratio of Nb-Ti and Nb Sn
composite superconductors
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 this end and
in addition to other activities, IEC publishes International Standards, Technical Specifications, Technical Reports,
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preparation is entrusted to technical committees; any IEC National Committee interested in the subject dealt with
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Standardization (ISO) in accordance with conditions determined by 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
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4) In order to promote international uniformity, IEC National Committees undertake to apply IEC Publications
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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.
9) Attention is drawn to the possibility that some of the elements of this IEC Publication may be the subject of patent
rights. IEC shall not be held responsible for identifying any or all such patent rights.
International Standard IEC 61788-4 has been prepared by IEC technical committee 90:
Superconductivity.
This fifth edition cancels and replaces the fourth edition published in 2016. This edition
constitutes a technical revision.
This edition includes the following significant technical changes with respect to the previous
edition:
a) change in the suitable distance of voltage taps on the specimen for reliable measurement,
Sn
b) new report on the result of the round robin test of the residual resistance ratio of Nb
superconductors that proves the validity of the measurement method in this standard,
c) revision of the confusing definitions of the copper ratio and copper fraction.

The text of this standard is based on the following documents:
FDIS Report on voting
90/448/FDIS 90/451/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 parts of the IEC 61788 series, published under the general title Superconductivity,
can be found on the IEC website.
The committee has decided that the contents of this publication will remain unchanged until the
stability date indicated on the IEC website 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 – IEC 61788-4:2020 © IEC 2020
INTRODUCTION
Copper, Cu/Cu-Ni or aluminium is used as matrix material in Ni-Ti and Nb Sn composite
superconductors and works as an electrical shunt when the superconductivity is interrupted. It
also contributes to recovery of the superconductivity by conducting heat generated in the
superconductor to the surrounding coolant. The cryogenic-temperature resistivity of copper is
an important quantity, which influences the stability and AC losses of the superconductor. The
residual resistance ratio is defined as a ratio of the resistance of the superconductor at room
temperature to that just above the superconducting transition.
This document specifies the test method for residual resistance ratio of Nb-Ti and Nb Sn
composite superconductors. The curve method is employed for the measurement of the
resistance just above the superconducting transition. Other methods are described in
Clause A.3.
SUPERCONDUCTIVITY –
Part 4: Residual resistance ratio measurement –
Residual resistance ratio of Nb-Ti and Nb Sn
composite superconductors
1 Scope
This part of IEC 61788 specifies a test method for the determination of the residual resistance
ratio (RRR) of Nb-Ti and Nb Sn composite superconductors with Cu, Cu-Ni, Cu/Cu-Ni and Al
matrix in a strain-free condition and zero external magnetic field. This method is intended for
use with superconductor specimens that have a monolithic structure with rectangular or round
cross-section, RRR value less than 350, and cross-sectional area less than 3 mm . In the case
of Nb Sn, the specimens have received a reaction heat-treatment.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies.
For undated references, the latest edition of the referenced document (including any
amendments) applies.
IEC 60050-815, International Electrotechnical Vocabulary (IEV) – Part 815: Superconductivity
(available at: www.electropedia.org)
3 Terms and definitions
For the purposes of this document, the terms and definitions given in IEC 60050-815 and the
following apply.
ISO and IEC maintain terminological databases for use in standardization at the following
addresses:
• IEC Electropedia: available at http://www.electropedia.org/
• ISO Online browsing platform: available at http://www.iso.org/obp
3.1
residual resistance ratio
RRR
ratio of resistance at room temperature to the resistance just above the superconducting
transition
Note 1 to entry: This note applies to the French language only.
Note 2 to entry: In this document for Nb-Ti and Nb Sn composite superconductors, the room temperature is defined
as 293 K (20 °C), and the residual resistance ratio is obtained in Formula (1), where the resistance ( R ) at 293 K is
divided by the resistance ( R ) just above the superconducting transition.
R
r = (1)
RRR
R
– 8 – IEC 61788-4:2020 © IEC 2020
Here r is a value of the residual resistance ratio, R is a value of the resistance measured in a strain-free
RRR
condition and zero external magnetic field.
Figure 1 shows schematically a resistance versus temperature curve acquired on a specimen while measuring the
cryogenic resistance.
The cryogenic resistance, R , is determined by the intersection, A, of two straight lines (a) and (b) at
temperature T* .
c
Figure 1 – Relationship between temperature and resistance
4 Principle
The resistance measurement both at room and cryogenic temperatures shall be performed with
the four-terminal technique. All measurements are done without an applied magnetic field.
The target relative combined standard uncertainty of this method is defined as an expanded
uncertainty ( k= 2 ) not to exceed 5 %.
The maximum bending strain induced during mounting and cooling the Nb-Ti specimen shall
not exceed 2 %. The measurement shall be conducted in a strain-free condition or in a condition
with allowable thermal strain for the Nb Sn specimen.
5 Apparatus
5.1 Material of measurement mandrel or of measurement base plate
Material of the measurement mandrel for a coiled Nb-Ti specimen or of the measurement base
plate for a straight Nb-Ti or Nb Sn specimen shall be copper, aluminium, silver, or the like
whose thermal conductivity is equal to or better than 100 W/(m·K) at liquid helium temperature
(4,2 K). The surface of the material shall be covered with an insulating layer (tape or a layer
made of polyethylene terephthalate, polyester, polytetrafluoroethylene, etc.) whose thickness
is 0,1 mm or less.
5.2 Diameter of the measurement mandrel and length of the measurement base plate
The diameter of the measurement mandrel shall be large enough to keep the bending strain of
the specimen less than or equal to 2 % for the Nb-Ti specimen. The Nb Sn specimen on a base
plate shall be measured in a strain-free condition or a condition with allowable thermal strain.
The measurement base plate shall be at least 30 mm long in one dimension.
5.3 Cryostat for the resistance ( R ) measurement
The cryostat shall include a specimen support structure and a liquid helium reservoir for
measurement of the resistance R . The specimen support structure shall allow the specimen,
which is mounted on a measurement mandrel or a measurement base plate, to be lowered into
and raised out of a liquid helium bath. In addition, the specimen support structure shall be made
so that a current can flow through the specimen and the resulting voltage generated along the
specimen can be measured.
6 Specimen preparation
The test specimen shall have no joints or splices with a length of 30 mm or longer. The specimen
shall be instrumented with current contacts near each of its ends and a pair of voltage contacts
over its central portion. The distance between two voltage taps ( L ) shall be 15 mm or longer.
A thermometer for measuring cryogenic temperature shall be attached near the specimen.
Some mechanical method shall be used to hold the specimen against the insulated layer of the
measurement mandrel or base plate. Special care should be taken during instrumentation and
installation of the specimen on the measurement mandrel or base plate so that no excessive
force, which may cause undesired bending strain or tensile strain, would be applied to the
specimen. Ideally, the Nb Sn specimen is intended to be as straight as possible; however, this
is not always the case, thus care should be taken to measure the specimen in its as received
condition.
The specimen shall be mounted on a measurement mandrel or on a measurement base plate
for these measurements. Both resistance measurements, R and R , shall be made on the
1 2
same specimen and the same mounting.
7 Data acquisition and analysis
7.1 Resistance ( R ) at room temperature
The mounted specimen shall be measured at room temperature ( T (K)), where T satisfies
m m
the following condition: 273 K ≤ T ≤ 308 K. A specimen current ( I (A)) shall be applied so that

m 1
2 2
the current density is in the range of 0,1 A/mm to 2 A/mm based on the total wire cross-
(V)), and shall be recorded. Formula (2)
sectional area, and the resulting voltage ( U I T
1 1 m
below shall be used to calculate the resistance ( R ) at room temperature. The resistance ( R )
m 1
at 293 K (20 °C ) shall be calculated using Formula (3) for a wire with Cu matrix. For wires that
do not contain a pure Cu component, the value of R shall be set equal to R , without any
1 m
temperature correction.
U
R = (2)
m
I
– 10 – IEC 61788-4:2020 © IEC 2020
R
m
R = (3)
1+ 0,00393×−T 293
( )
m
 
*
7.2 Resistance ( R or R ) just above the superconducting transition
2 2
7.2.1 Correction of strain effect
*
Under a strained condition of the Nb-Ti specimen, the measured cryogenic resistance, R , is
not a correct value for R . The corresponding correction of the strain effect is described in 7.3.
7.2.2 Data acquisition of cryogenic resistance
The specimen, which is still mounted as it was for the room temperature measurement, shall
be placed in the cryostat for electrical measurement specified in 5.3. Horizontal mounting of the
specimen is recommended in Clause A.1. Alternative cryostats that employ a heating element
to sweep the specimen temperature are described in Clause A.2. The specimen shall be slowly
lowered into the liquid helium bath and cooled to liquid helium temperature over a time period
of at least 5 min.
*
During the acquisition phases of the low-temperature R measurements, a specimen current
2 2
( I ) shall be applied so that the current density is in the range 0,1 A/mm to 10 A/mm based
on the total wire cross-sectional area, and the resulting voltage ( U (V)), I (A), and specimen
temperature ( T (K)) shall be recorded. In order to keep the ratio of signal to noise high enough,
the measurement shall be carried out under the condition that the absolute value of the resulting
voltage above the superconducting transition exceeds 10 μV. An illustration of the data to be
acquired and its analysis is shown in Figure 2.

NOTE Voltages with subscripts + and – are those obtained in the first and second measurements under positive
and negative currents, respectively, and U and U are those obtained at zero current. For clarity, U ,
20+ 20− 0rev
measured at zero current is not shown coincident with U . Straight line (a) is drawn in the transition region with a
0−
sharp increase in the voltage with temperature and straight line (b) is drawn in the region with a nearly constant
voltage.
Figure 2 – Voltage versus temperature curves
and definitions of each voltage
When the specimen is in the superconducting state and the test current ( I ) is applied, two
voltages shall be measured nearly simultaneously: U (the initial voltage recorded with a
0+
positive current polarity) and U (the voltage recorded during a brief change in applied
0rev
*
current polarity). A valid R measurement requires that excessive interfering voltages are not
present and that the specimen is initially in the superconducting state. Thus, the following
formulae shall be met for a valid measurement:
UU−
0+ 0rev
< 1 % (4)
U 2
where U is the average voltage for the specimen in the normal state at cryogenic temperature,
which is defined by Formula (5).
The specimen shall be gradually warmed so that it changes to the normal state completely.
When the cryostat for the resistance measurement specified in 5.3 is used, this can be achieved
simply by raising the specimen to an appropriate position above the liquid helium level. The
specimen voltage versus temperature curve shall be acquired with the rate of temperature
increase maintained between 0,1 K/min and 10 K/min. The voltage versus temperature curve
shall continue to be recorded during the transition into the normal state, up to a temperature
somewhat less than 15 K for the Nb-Ti specimen and less than 25 K for the Nb Sn specimen.
Then, the specimen current shall be decreased to zero and the corresponding voltage, U ,
20+
shall be recorded at a temperature below 15 K for the Nb-Ti specimen and below 25 K for the
Nb Sn specimen.
The specimen shall then be slowly lowered into the liquid helium bath and cooled to within ±1 K
from the temperature at which the initial voltage signal U was recorded. A specimen current,
0+
I , with the same magnitude but negative polarity (polarity opposite that used for the initial
curve) shall be applied and the voltage U shall be recorded at this temperature. The
0−
procedural steps shall be repeated to record the voltage versus temperature curve with this
negative current. In addition, when the measurement current, I , decreases to 0, the recording
of U shall be made at within ±1 K from the temperature at which U was recorded.
20− 20+
Each of the two voltage versus temperature curves shall be analysed by drawing a line (a)
through the data where the absolute value of voltage sharply increases with temperature
(see Figure 2) and drawing a second line (b) through the data above the transition where the
voltage is nearly constant for Nb-Ti or raised gradually and almost linearly for Nb Sn with
* *
temperature increase. U and U in Figure 2 shall be determined at the intersection of these
2+ 2−
two lines for the positive and negative polarity curves, respectively.
The corrected voltages, U and U , shall be calculated using the following equations:
2+ 2−
* *
U UU− and U UU− . The average voltage, U , shall be defined as
2+ 2++0 2− 20− −
UU−
22+ −
U 2= (5)
*
A valid R measurement requires that the shift of thermoelectric voltage be within acceptable
limits during the measurements of U and U . Thus, the following condition shall be met for
2+ 2−
a valid measurement:
= =
– 12 – IEC 61788-4:2020 © IEC 2020
||∆ −∆
+−
< 3 %
(6)
U
*
where ∆ and ∆ are defined as ∆= UU− and ∆= UU− . If the R
+ − + 20++0 − 20− 0− 2
measurement does not meet the validity requirements in 7.2.2, specifically either in Formula (4)
or (6), then improvement steps either in hardware or experimental operation shall be taken to
meet these requirements before results are reported.
*
Formula (7) shall be used to calculate the measured resistance ( R ) just above the
superconducting transition.
U 2
*
(7)
R =
I
7.2.3 Optional acquisition methods
The method described in the main clauses of this document is the “reference” method and
optional acquisition methods are outlined in Clause A.3.
*
7.3 Correction on measured R of Nb-Ti composite superconductor for bending
strain
*
If there is no pure Cu component in the superconductor, then R shall be set equal to R .
For a specimen with a pure Cu component, the bending strain shall be defined by ε = 100 ×
b
(h/r) (%), where h is a half of the specimen thickness for rectangular wires or a radius for round
wires and r is the bending radius. If the bending strain is less than 0,3 %, then no correction is
*
necessary, and R shall be set equal to R .
2 2
If neither of the above two situations applies, then the resistance R just above the
superconducting transition under the strain-free condition shall be estimated by
L
*
R R−∆ρ× (8)
S
Cu
where ∆ρ is defined below and S and L are defined in 8.4. The increase in the resistivity of
Cu
pure copper at 4,2 K due to tensile strain, ε (%), is expressed by
-12 -14 2
∆ρ (Ωm) = 6,24 × 10 ε − 5,11 × 10 ε ; ε ≤ 2 % (9)
The calculation of Formula (9) shall be carried out assuming that the equivalent tensile strain
ε is (1/2)ε and (4/3 π)ε for rectangular and round wires, respectively. The bending strain
b b
dependency of residual resistance ratio for pure copper is described in Clause A.4.
7.4 Residual resistance ratio (RRR)
The RRR value shall be calculated using Formula (1).
=
8 Uncertainty and stability of the test method
8.1 Temperature
The room temperature shall be determined with a standard uncertainty not exceeding 0,6 K,
while holding the specimen, which is mounted on the measurement mandrel or on the
measurement base plate, at room temperature.
8.2 Voltage
For the resistance measurement, the voltage signal shall be measured with a relative standard
uncertainty not exceeding 0,3 %.
8.3 Current
When the current is directly applied to the specimen with a programmable DC current source,
the specimen test current shall be determined with a relative standard uncertainty not exceeding
0,3 %.
When the specimen test current is determined from a voltage-current characteristic of a
standard resistor by the four-terminal technique, the standard resistor, with a relative combined
standard uncertainty not exceeding 0,3 %, shall be used.
The fluctuation of DC specimen test current, provided by a DC power supply, shall be less than
0,5 % during every resistance measurement.
8.4 Dimension
The distance along the specimen between the two voltage taps (L) shall be determined with a
relative combined standard uncertainty not exceeding 5 %.
For correction of the bending strain effect in the case of the wire with pure Cu matrix, the cross-
sectional area of Cu matrix ( S ) shall be determined using a nominal value of copper to non-
Cu
copper ratio and nominal dimensions of the specimen. The wire diameter (d) and mandrel radius
( R ) shall be determined with relative standard uncertainty not exceeding 1 % and 3 %,
d
respectively.
9 Test report
9.1 RRR value
The obtained RRR value ( r ) shall be reported as
RRR
r 1 ±= Un   , (10)
( ) ( )
RRR re
where
U is the expanded relative uncertainty:
re
U 2 uk( 2)
re r
where
u denotes the relative combined standard uncertainty,
r
k is a coverage factor, and
==
– 14 – IEC 61788-4:2020 © IEC 2020
n is the sampling number.
It is desired that n be larger than 4 so that the normal distribution can be assumed for observed
results to estimate the standard deviation. If n is not sufficiently large, a rectangular distribution
shall be assumed.
9.2 Specimen
The test report for the result of the measurements shall also include the following items, if
known:
a) manufacturer;
b) classification and/or symbol;
c) shape and area of the cross-section;
d) dimensions of the cross-sectional area;
e) number of filaments or subelements;
f) diameter of the filaments or subelements;
g) for Nb-Ti specimen, the volume ratio of the following material to Nb-Ti:
Cu,
Cu-Ni,
Cu and Cu-Ni,
Al and Cu,
or the following volume ratio:
Cu-Ni: Cu: Nb-Ti,
Al: Cu: Nb-Ti;
h) Cu to non-Cu volume ratio for Nb Sn specimen;
i) cross-sectional area of the Cu matrix ( S ).
Cu
9.3 Test conditions
9.3.1 Measurements of R and R
1 2
The following test conditions shall be reported for the measurements of R and R :
1 2
a) total length of the specimen;
b) distance between the voltage measurement taps (L);
c) length of each current contact;
d) transport currents ( I and I );
1 2
e) current densities ( I and I divided by the nominal total wire cross-sectional area);
1 2
* *
f) voltages ( U , U , U , U , U , U , U , U and U );
2+ 2−
1 0+ 0rev 20+ 0− 20−
*
g) resistances ( R , R , R and R );
m 1 2 2
h) resistivities (ρ R× S /L and ρ R× S /L );
( ) ( )
1 1 Cu 2 2 Cu
i) material, shape, and dimensions of the mandrel or the base plate;
j) installation method of the specimen in the mandrel or the base plate;
k) insulating material of the mandrel or the base plate.
= =
9.3.2 Measurement of R
The following test conditions shall be reported for the measurement of R :
a) temperature setting and holding method of the specimen;
b) T : Temperature for measurement of R .
m m
9.3.3 Measurement of
R
The following test conditions shall be reported for the measurement of R :
a) rate of increasing temperature;
b) method of cooling down and heating up.
Additional information relating to the measurement of RRR is given in Annex A. Annex B
describes definitions and an example of uncertainty in measurement. Uncertainty evaluation in
the reference test method of RRR for composite superconductors is given in Annex C.

– 16 – IEC 61788-4:2020 © IEC 2020
Annex A
(informative)
Additional information relating to the measurement of RRR
A.1 Recommendation on specimen mounting orientation
When a specimen is in the form of straight wire, horizontal mounting of the wire on the base
plate is recommended since this mounting orientation can reduce possible thermal gradient
along the wire compared to the vertical mounting orientation. Here the horizontal mounting
orientation means that the wire axis is parallel to the surface of liquid helium.
A.2 Alternative methods for increasing temperature of specimen above
superconducting transition temperature
The following methods are also recommended for increasing temperature above the
superconducting transition of the specimen. The rate of increasing temperature of the whole
specimen within a range between 0,1 K/min and 10 K/min should be applied for these methods.
In order to dampen the rate of increasing temperature and to avoid a large temperature gradient,
special care should be taken in selecting heater power, heat capacity (the specimen with the
measurement mandrel or the measurement base plate) and the distance between the heater
and the specimen.
a) Heater method
The specimen can be heated above the superconducting transition by a heater installed in
the measurement mandrel or in the measurement base plate after taking the specimen out
of the liquid helium bath in the cryostat.
b) Controlled methods
1) Adiabatic method
In this method, the cryostat holds a chamber in which the specimen, a sample holder, a
heater and so on are contained. Before the chamber is immersed in the liquid helium
bath, air inside the chamber is pumped out and helium gas is filled. Then, the chamber
is immersed in the liquid helium bath and the specimen is cooled to a temperature below
the critical temperature. After the helium gas is pumped out, the specimen can be heated
above the superconducting transition by the heater under adiabatic condition.
2) Quasi-adiabatic method
In this method, the cryostat holds the specimen a certain distance above the liquid
helium bath for the entire cryogenic measurement. A thermal anchor from the
measurement mandrel or the measurement base plate to the liquid helium bath allows
the specimen to be cooled to a temperature below the critical temperature. The specimen
can be heated above the superconducting transition by a heater located in the
measurement mandrel or the measurement base plate under quasi-adiabatic condition.
3) Refrigerator method
In this method, an electromechanical apparatus (a refrigerator) is used to cool the
specimen, which is mounted on a measurement mandrel or a measurement base plate,
to a temperature below the critical temperature. The specimen can be heated above the
superconducting transition by a heater or by controlling the refrigerator power.
*
A.3 Alternative measurement methods of R or R
2 2
*
The following methods can optionally be used for acquisition of R or R .
2 2
a) Modified reference method
This is a simplified method with acquisition of only one voltage-temperature curve and is
used only for Nb-Ti composite superconductors. The voltage of the specimen is measured
in the superconducting state under a desired direction of current ( I ) and then with current
in the opposite direction. These values are U and U as shown in Figure A.1. The
0+ 0rev
current is then changed back to the initial direction. After the transition to the normal state,
'
the voltage is measured as U in a plateau region of the curve within about 4 K above the
2+
transition. Then the voltage is read under a zero current ( U ). The current direction is then
'
reversed and the voltage is measured again ( U ). The cryogenic resistance is obtained
2−
from
U
*
R = (A.1)
I
with
' '
UU−
22+ −
U =
2 (A.2)
This approximately compensates for the effect of thermoelectric voltage. The following
conditions should be fulfilled to ensure that the influence of the interfering voltage and the
*
thermoelectric voltage shift on R measurement is not appreciably large:
UU−
0+ 0rev
< 1 % (A.3)
U
∆ −∆
22+−
< 3 % (A.4)
U
' '
where and are defined by ∆= UU− and ∆= UU− , respectively.
∆ ∆
2+ 2− 2++2 20 2−−2 20
– 18 – IEC 61788-4:2020 © IEC 2020

Figure A.1 – Definition of voltag
...