IEC 61788-4:2011

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

IEC 61788-4:2011 covers a test method for the determination of the residual resistance ratio (RRR) of composite superconductors comprised of Nb-Ti filaments and Cu, Cu-Ni or Cu/Cu-Ni matrix. This method is intended for use with superconductors that have a monolithic structure with rectangular or round cross-section, RRR less than 350, and cross-sectional area less than 3 mm2. All measurements are done without an applied magnetic field. The method described in the body of this standard is the "reference" method and optional acquisition methods are outlined in Clause A.3. This third edition constitutes a technical revision which adds two new annexes: "Uncertainty considerations" (Annex B) and "Uncertainty evaluation in test method of RRR for NbTi" (Annex C). Copper is used as a matrix material in multifilamentary 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 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.

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

La CEI 61788-4:2011 spécifie une méthode d'essai pour la détermination du rapport de résistance résiduelle (RRR) de supraconducteurs composites constitués de filaments de Nb-Ti et d'une matrice de Cu, Cu-Ni ou Cu/Cu-Ni. Cette méthode est destinée à être utilisée avec des supraconducteurs présentant une structure monolithique avec une section rectangulaire ou circulaire, un rapport RRR inférieur à 350 et une surface de section inférieure à 3 mm2. Toutes les mesures sont effectuées sans appliquer de champ magnétique. La méthode décrite dans le corps de texte de la présente norme est la méthode de "référence" et des méthodes d'acquisition facultatives sont présentées à l'Article A.3. Cette troisième édition constitue une révision technique qui ajoute deux nouvelles annexes: "Considérations relatives à l'incertitude" (Annexe B) et "Evaluation de l'incertitude de la méthode d'essai de RRR (rapport de résistance résiduelle) de NbTi" (Annexe C). Le cuivre est utilisé comme matériau de matrice dans les supraconducteurs multifilamentaires et fonctionne comme une dérivation électrique lorsque la supraconductivité est interrompue. Il contribue également à la reprise de la supraconductivité en dirigeant la chaleur générée dans le supraconducteur vers le fluide de refroidissement environnant. La résistivité à la température cryogénique du cuivre est une grandeur importante qui influe sur la stabilité du supraconducteur. Le rapport de résistance résiduelle est défini comme le rapport entre la résistance du supraconducteur à température ambiante et celle immédiatement supérieure à la transition supraconductrice.

General Information

• Status: Published
• Publication Date: 10-Jul-2011
• 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: DELPUB - Deleted Publication
• Start Date: 19-Jan-2016
• Completion Date: 26-Oct-2025

Relations

• Revised: IEC 61788-4:2016 - Superconductivity - Residual resistance ratio measurement - Residual resistance ratio of Nb-Ti and Nb₃Sn composite superconductors
• Effective Date: 05-Sep-2023
• Revises: IEC 61788-4:2007 - Superconductivity - Part 4: Residual resistance ratio measurement - Residual resistance ratio of Nb-Ti composite superconductors
• Effective Date: 05-Sep-2023

Standards Content (Sample)

IEC 61788-4 ®
Edition 3.0 2011-07
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Superconductivity –
Part 4: Residual resistance ratio measurement – Residual resistance ratio of
Nb-Ti composite superconductors

Supraconductivité –
Partie 4: Mesure du rapport de résistance résiduelle – Rapport de résistance
résiduelle des supraconducteurs composites de Nb-Ti

All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by
any means, electronic or mechanical, including photocopying and microfilm, without permission in writing from either IEC or
IEC's member National Committee in the country of the requester.
If you have any questions about IEC copyright or have an enquiry about obtaining additional rights to this publication,
please contact the address below or your local IEC member National Committee for further information.

Droits de reproduction réservés. Sauf indication contraire, aucune partie de cette publication ne peut être reproduite
ni utilisée sous quelque forme que ce soit et par aucun procédé, électronique ou mécanique, y compris la photocopie
et les microfilms, sans l'accord écrit de la CEI ou du Comité national de la CEI du pays du demandeur.
Si vous avez des questions sur le copyright de la CEI ou si vous désirez obtenir des droits supplémentaires sur cette
publication, utilisez les coordonnées ci-après ou contactez le Comité national de la CEI de votre pays de résidence.

IEC Central Office
3, rue de Varembé
CH-1211 Geneva 20
Switzerland
Email: [e-mail]
Web: www.iec.ch
About the IEC
The International Electrotechnical Commission (IEC) is the leading global organization that prepares and publishes
International Standards for all electrical, electronic and related technologies.

About IEC publications
The technical content of IEC publications is kept under constant review by the IEC. Please make sure that you have the
latest edition, a corrigenda or an amendment might have been published.
 Catalogue of IEC publications: www.iec.ch/searchpub
The IEC on-line Catalogue enables you to search by a variety of criteria (reference number, text, technical committee,…).
It also gives information on projects, withdrawn and replaced publications.
 IEC Just Published: www.iec.ch/online_news/justpub
Stay up to date on all new IEC publications. Just Published details twice a month all new publications released. Available
on-line and also by email.
 Electropedia: www.electropedia.org
The world's leading online dictionary of electronic and electrical terms containing more than 20 000 terms and definitions
in English and French, with equivalent terms in additional languages. Also known as the International Electrotechnical
Vocabulary online.
 Customer Service Centre: www.iec.ch/webstore/custserv
If you wish to give us your feedback on this publication or need further assistance, please visit the Customer Service
Centre FAQ or contact us:
Email: [e-mail]
Tel.: [phone]
Fax: [phone]
A propos de la CEI
La Commission Electrotechnique Internationale (CEI) est la première organisation mondiale qui élabore et publie des
normes internationales pour tout ce qui a trait à l'électricité, à l'électronique et aux technologies apparentées.

A propos des publications CEI
Le contenu technique des publications de la CEI est constamment revu. Veuillez vous assurer que vous possédez
l’édition la plus récente, un corrigendum ou amendement peut avoir été publié.
 Catalogue des publications de la CEI: www.iec.ch/searchpub/cur_fut-f.htm
Le Catalogue en-ligne de la CEI vous permet d’effectuer des recherches en utilisant différents critères (numéro de référence,
texte, comité d’études,…). Il donne aussi des informations sur les projets et les publications retirées ou remplacées.
 Just Published CEI: www.iec.ch/online_news/justpub
Restez informé sur les nouvelles publications de la CEI. Just Published détaille deux fois par mois les nouvelles
publications parues. Disponible en-ligne et aussi par email.
 Electropedia: www.electropedia.org
Le premier dictionnaire en ligne au monde de termes électroniques et électriques. Il contient plus de 20 000 termes et
définitions en anglais et en français, ainsi que les termes équivalents dans les langues additionnelles. Egalement appelé
Vocabulaire Electrotechnique International en ligne.
 Service Clients: www.iec.ch/webstore/custserv/custserv_entry-f.htm
Si vous désirez nous donner des commentaires sur cette publication ou si vous avez des questions, visitez le FAQ du
Service clients ou contactez-nous:
Email: [e-mail]
Tél.: [phone]
Fax: [phone]
IEC 61788-4 ®
Edition 3.0 2011-07
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Superconductivity –
Part 4: Residual resistance ratio measurement – Residual resistance ratio of
Nb-Ti composite superconductors

Supraconductivité –
Partie 4: Mesure du rapport de résistance résiduelle – Rapport de résistance
résiduelle des supraconducteurs composites de Nb-Ti

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
PRICE CODE
INTERNATIONALE
CODE PRIX U
ICS 17.220.20; 29.050 ISBN 978-2-88912-554-8

– 2 – 61788-4  IEC:2011
CONTENTS
FOREWORD . 4
INTRODUCTION . 6
1 Scope . 7
2 Normative references . 7
3 Terms and definitions . 7
4 Requirements . 8
5 Apparatus . 8
5.1 Material of measuring mandrel or of measuring base plate . 8
5.2 Diameter of the measuring mandrel and length of the measuring base plate . 8
5.3 Cryostat for the resistance, R , measurement . 9
6 Specimen preparation. 9
7 Data acquisition and analysis . 9
7.1 Resistance (R ) at room temperature . 9
7.2 Resistance (R *) just above the superconducting transition . 9
7.3 Correction on measured R * for bending strain . 11
7.4 Residual resistance ratio (RRR) . 12
8 Uncertainty and stability of the test method . 12
8.1 Temperature . 12
8.2 Voltage measurement. 12
8.3 Current . 12
8.4 Dimension . 12
9 Test report. 13
9.1 RRR value . 13
9.2 Specimen . 13
9.3 Test conditions . 13
Annex A (informative) Additional information relating to the measurement of RRR . 15
Annex B (informative) Uncertainty considerations . 21
Annex C (informative) Uncertainty evaluation in test method of RRR for Nb-Ti . 25

Figure 1 – Relationship between temperature and resistance. emperature T * is that at
c
the intersection point . 8
Figure 2 – Voltage (U) versus temperature (T) curves and definitions of each voltage . 10
Figure A.1 – Definition of voltages . 16
Figure A.2 – Bending strain dependency of RRR for pure Cu matrix of Nb-Ti composite
superconductors (comparison between measured values and calculated values) . 18
Figure A.3 – Bending strain dependency of RRR for round Cu wires . 18
Figure A.4 – Bending strain dependency of normalized RRR for round Cu wires . 19
Figure A.5 – Bending strain dependency of RRR for rectangular Cu wires . 19
Figure A.6 – Bending strain dependency of normalized RRR for rectangular Cu wires . 20
Figure C.1 – Distribution of observed RRR of Cu/Nb-Ti composite superconductor . 28

Table B.1 – Output signals from two nominally identical extensometers . 22
Table B.2 – Mean values of two output signals . 22

61788-4  IEC:2011 – 3 –
Table B.3 – Experimental standard deviations of two output signals. 22
Table B.4 – Standard uncertainties of two output signals . 22
Table B.5 – Coefficient of variations of two output signals. 23
Table C.1 – Uncertainty of each measurement . 27

– 4 – 61788-4  IEC:2011
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
SUPERCONDUCTIVITY –
Part 4: Residual resistance ratio measurement –
Residual resistance ratio of Nb-Ti 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, Publicly Available Specifications (PAS) and Guides (hereafter referred to as “IEC
Publication(s)”). Their preparation is entrusted to technical committees; any IEC National Committee interested
in the subject dealt with may participate in this preparatory work. International, governmental and non-
governmental organizations liaising with the IEC also participate in this preparation. IEC collaborates closely
with the International Organization for 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
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
misinterpretation by any end user.
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.
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 third edition cancels and replaces the second edition published in 2007. It constitutes a
technical revision. The main revisions are the addition of two new annexes, "Uncertainty
considerations" (Annex B) and "Uncertainty evaluation in test method of RRR for NbTi"
(Annex C).
61788-4  IEC:2011 – 5 –
The text of this standard is based on the following documents:
FDIS Report on voting
90/263/FDIS 90/275/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 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 – 61788-4  IEC:2011
INTRODUCTION
Copper is used as a matrix material in multifilamentary 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 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.
In this International Standard, the test method of residual resistance ratio of Nb-Ti composite
superconductors is described. The curve method is employed for the measurement of the
resistance just above the superconducting transition. Other methods are described in
Clause A.3.
61788-4  IEC:2011 – 7 –
SUPERCONDUCTIVITY –
Part 4: Residual resistance ratio measurement –
Residual resistance ratio of Nb-Ti composite superconductors

1 Scope
This part of IEC 61788 covers a test method for the determination of the residual resistance
ratio (RRR) of composite superconductors comprised of Nb-Ti filaments and Cu, Cu-Ni or
Cu/Cu-Ni matrix. This method is intended for use with superconductors that have a monolithic
structure with rectangular or round cross-section, RRR less than 350, and cross-sectional
area less than 3 mm . All measurements are done without an applied magnetic field.
The method described in the body of this standard is the “reference” method and optional
acquisition methods are outlined in Clause A.3.
2 Normative references
The following referenced document is indispensable for the application 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
3 Terms and definitions
For the purpose of this document, the terms and definitions given in IEC 60050-815 and the
following apply.
3.1
residual resistance ratio
RRR
the ratio of resistance at room temperature to the resistance just above the superconducting
transition
NOTE In this standard for Nb-Ti composite superconductors, the room temperature is defined as 293 K (20 °C),
and the residual resistance ratio is obtained in Equation (1) below, where the resistance (R ) at 293 K is divided by
the resistance (R ) just above the superconducting transition.
R
RRR= (1)
R
Figure 1 shows schematically a resistance versus temperature curve acquired on a specimen while measuring the
cryogenic resistance. Draw a line in Figure 1 where the resistance sharply increases (a), and draw also a line in
Figure 1 where the temperature increases but the resistance remains almost the same (b). The value of resistance
at the intersection of these two lines at T=T *, A, is defined as resistance (R ) just above the superconducting
c
transition.
– 8 – 61788-4  IEC:2011
Temperature T * is that at the intersection point.
c
Figure 1 – Relationship between temperature and resistance
4 Requirements
The resistance measurement both at room and cryogenic temperatures shall be performed
with the four-terminal technique.
The target relative combined standard uncertainty of this method is defined as an expanded
uncertainty (k = 2) not to exceed 5 % based on the coefficient of variation (COV) of 2,5 % in
the intercomparison test (see Clause C.2).
The maximum bending strain, induced during mounting the specimen, shall not exceed 2 %.
5 Apparatus
5.1 Material of measuring mandrel or of measuring base plate
Material of the measuring mandrel for a coiled specimen or of the measuring base plate for a
straight 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 measuring mandrel and length of the measuring base plate
Diameter of the measuring mandrel shall be large enough to keep bending strain of the
specimen less than or equal to 2 %.
The measuring base plate shall be at least 30 mm long in one dimension.

61788-4  IEC:2011 – 9 –
5.3 Cryostat for the resistance, R , measurement
The cryostat shall include a specimen support structure and a liquid helium reservoir for the
resistance, R , measurement. The specimen support structure shall allow the specimen,
which is mounted on a measurement mandrel or a measurement base plate, to be lowered
and raised into, and 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, and shall be 30 mm or longer. The distance
between two voltage taps (L) shall be 25 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 shall be taken during instrumentation
and installation of the specimen on the measurement mandrel or on the measurement base
plate so that no excessive force, which may cause undesired bending strain or tensile strain,
shall be applied to the specimen.
The specimen shall be instrumented with current contacts near each end of the specimen and
a pair of voltage contacts over a central portion of the specimen. The specimen shall be
mounted on a measurement mandrel or on a measurement base plate for these measure-
ments. Both resistance measurements, R and R , shall be made on the same specimen and
1 2
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 ≤ T ≤ 308. 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 A/mm based on the total wire cross-
sectional area, and the resulting voltage (U (V)), I and T shall be recorded. Equation (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 equation (3) for a wire with Cu matrix. The value of
R shall be set equal to R , without any temperature correction, for wires that do not contain
1 m
a pure Cu component.
U
R = (2)
m
I
R
m
R = (3)
[1 + 0,00393× (T – 293)]
m
7.2 Resistance (R *) just above the superconducting transition
Under a strained condition of the specimen, the measured cryogenic resistance, R *, is not a
correct value for R . The corresponding correction of the strain effect will be described in 7.3.
7.2.1 The specimen, which is still mounted as it was for the room temperature measurement,
shall be placed in the cryostat for electrical measurement specified under 5.3. Alternate
cryostats that employ a heating element to sweep the specimen temperature are described in
Clause A.2.
– 10 – 61788-4  IEC:2011
7.2.2 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.
7.2.3 During the acquisition phases of the low-temperature R * measurements, a specimen
current (I ) shall be applied so that the current density is in the range of 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.

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 is not
0rev
20+ 20–
shown coincident with U . Voltages U * and U * with asterisk are those at the intersection points.
0– 2+ 2–
Figure 2 – Voltage (U) versus temperature (T) curves and definitions of each voltage
7.2.4 When the specimen is in superconducting state and 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
condition shall be met for a valid measurement:
U − U
0+ 0 rev
< 1 % (4)
U
where U is the average voltage for the specimen in the normal state at cryogenic
temperature, which is defined at 7.2.10.
7.2.5 The specimen shall be gradually warmed so that it changes to the normal state
completely. When the cryostat for the resistance measurement specified under 5.3 is used,

61788-4  IEC:2011 – 11 –
this can be achieved simply by raising the specimen to an appropriate position above the
liquid helium level.
7.2.6 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.
7.2.7 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. Then, the
specimen current shall be decreased to zero and the corresponding voltage, U , shall be
20+
recorded at a temperature below 15 K.
7.2.8 The specimen shall then be slowly lowered into the liquid helium bath and cooled to
the same temperature, within ±1 K, where the initial voltage signal U was recorded. A
0+
specimen current, 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
0–
temperature. The procedural steps 7.2.5 to 7.2.7 shall be repeated to record the voltage
versus temperature curve with this negative current. In addition, the recording of U shall be
20–
made at the same temperature, within ±1 K, where U was recorded.
20+
7.2.9 Each of the two voltage versus temperature curves shall be analyzed 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 with temperature. U * and U * in Figure 2 shall be determined at
2+ 2–
the intersection of these two lines for the positive and negative polarity curves respectively.
7.2.10 The corrected voltages, U and U , shall be calculated using the following
2+ 2–
equations, U = U *– U and U = U *– U . The average voltage, U ,shall be defined

2+ 2+ 0+ 2– 2– 0– 2
as
| U − U |
2+ 2
−
U =   (5)
7.2.11 A valid R * measurement requires that the shift of thermoelectric voltage be within
acceptable limits during the measurements of the U and U . Thus, the following condition
2+ 2–
shall be met for a valid measurement,
|∆ −∆ |
+ −
< 3% (6)
U
where ∆ and ∆ are defined as ∆ = U – U and ∆ = U – U . If the R * measurement
+ – + 20+ 0+ – 20– 0– 2
does not meet the validity requirements in 7.2.4 and this subclause, then improvement steps
either in hardware or experimental operation shall be taken to meet these requirements
before results are reported.
*) just above the
7.2.12 Equation (7) shall be used to calculate the measured resistance (R
superconducting transition.
U
*
R =  (7)
I
7.3 Correction on measured R * for bending strain
If there is no pure Cu component in the superconductor, then R shall be set equal to R *.
2 2
– 12 – 61788-4  IEC:2011
For a specimen with a pure Cu component, the bending strain shall be defined by
ε = 100 × (h/r) (%), where h is a half of the specimen thickness and r is the bending radius. If
b
the bending strain is less than 0,3 %, then no correction is necessary, and R shall be set
equal to R *.
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
∆ρ is defined below and S and L are defined in 8.4. The increase in the resistivity of
where
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 equation (9) shall be carried out assuming that the equivalent tensile strain
ε is (1/2) ε and (4/3π) ε for rectangular and round wires, respectively. The bending strain
b b
dependency of residual resistance ratio for pure copper is described in A.1.
7.4 Residual resistance ratio (RRR)
The RRR shall be calculated using Equation (1).
8 Uncertainty and stability of the test method
8.1 Temperature
The room temperature shall be determined with a standard uncertainty not to exceed 0,6 K,
while holding the specimen, which is mounted on the measuring mandrel or on the measuring
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 to exceed 0,5 %.
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 standard uncertainty not to exceed
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 to exceed 0,3 %, shall be used.”
The fluctuation of d.c. specimen test current, provided by a d.c. 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 to exceed 5 %.
In the case of the wire with pure Cu matrix, the cross-sectional area of Cu matrix (S ) shall
Cu
be determined using a nominal value of copper to non-copper ratio and nominal dimensions of
the specimen.
61788-4  IEC:2011 – 13 –
9 Test report
9.1 RRR value
The obtained RRR value shall be reported as
RRR(1±U ) (n = ∙∙∙ ), (10)
re
where U = 2u (k = 2) is the expanded relative uncertainty with u denoting the uncertainty, k
re r r
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 the estimation of the standard deviation. If n is not
sufficiently large, a square distribution shall be assumed. In case of n = 1 the analytic method
–2
described in Annex C shall be used with b/R = 1,46 × 10 estimated from the
intercomparison test.
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
f) diameter of the filaments
g) Cu to Nb-Ti ratio, Cu-Ni to Nb-Ti ratio, or Cu, Cu-Ni to Nb-Ti ratio, or volume ratio among
Cu-Ni, Cu, and Nb-Ti.
h) cross-sectional area of the Cu matrix (S )
Cu
9.3 Test conditions
9.3.1 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 the current contacts
d) transport currents (I and I )
1 2
e) current densities (I and I divided by the total wire cross-sectional area)
1 2
f) voltages (U , U , U , U *, U , U , U *, U and U )
1 0+ 0rev 2+ 20+ 0– 2– 20– 2
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 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
– 14 – 61788-4  IEC:2011
9.3.3 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

61788-4  IEC:2011 – 15 –
Annex A
(informative)
Additional information relating to the measurement
of RRR (residual resistance ratio)

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 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 measuring mandrel or the measuring 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 measuring mandrel or in the measuring base plate after taking the specimen out of the
liquid helium bath in the cryostat.
b) Adiabatic 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 will be cooled to a temperature
of 5 K or lower. 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
measuring mandrel or the measuring base plate to the liquid helium bath allows the
specimen to be cooled to a temperature of 5 K or lower. The specimen can be
heated above the superconducting transition by a heater located in the measuring
mandrel or the measuring base plate under quasi-adiabatic condition.
c) Refrigerator method
In this method, an electromechanical apparatus (a refrigerator) is used to cool the
specimen, which is mounted to a measuring mandrel or a measuring base plate, to a
temperature of 5 K or lower. The specimen can be heated above the superconducting
transition by a heater or by controlling the refrigerator power.
*
A.3 Alternative R measurement method
*
The following methods can optionally be used for acquisition of R .
– 16 – 61788-4  IEC:2011
a) Modified reference method
This is a simplified method with acquisition of only one voltage-temperature curve. 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 current is then changed back to the initial
0+ 0rev
direction. After the transition to the normal state, the voltage is measured as U′ in a
2+
plateau region of the curve within about 4 K above the 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 from
2–
U
∗
R = (A.1)
I
with
U ' –U '
2+ 2–
U = (A.2)
This approximately compensates the effect of thermoelectric voltage. The following
conditions should be fulfilled for the assurance that the influence of the interfering voltage
and the thermoelectric voltage shift on R2* measurement is not appreciably large:
U – U
0+ 0rev
< 1 %
U
U" – U"
2+ 2–
< 3 %
U
where U" and U" are defined by U" = |U' – U | and U" = |U' – U |,
2+ 2– 2+ 2+ 20 2– 2– 20
respectively.
Figure A.1 – Definition of voltages
b) Fixed temperature method
*
In this method R is directly determined at a fixed temperature in a plateau region within
about 4 K above the transition, 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. Also

61788-4  IEC:2011 – 17 –
the U and U , which are defined in the body of the text, should be recorded as the zero
0+ 0–
voltage level in the fixed method. In order to eliminate the influence of thermoelectric
voltage, two voltage signals of the specimen, say U and U , should be acquired nearly
2+ 2–
simultaneously by reversal of the test current. For the fixed method the effect of
*
thermoelectric voltage on determination of cryogenic resistance can well be eliminated.
R
c) 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 current on and off cycles are used to correct for off-set
voltages in order that the measurements can be made during one cycle of changing the
specimen temperature. This method is useful when the transition to the normal state is not
too fast. The effect of thermoelectric voltage should also be checked.
d) Other simplified methods with periodic checks
Simplified methods without temperature measurement might also be accepted, if an
operator with sufficient experience performs the measurement using a given apparatus
and if the following condition is satisfied. If a simplified laboratory practice can be shown,
through periodic checks, to achieve the same result as the method in this standard, within
its stated uncertainty, then the simplified practice can be used in place of this reference
method. These periodic checks could be accomplished by doing one of the following:
1) an interlaboratory comparison where one laboratory uses the reference method and
another laboratory uses their simplified method;
2) a single laboratory comparison where one laboratory "checks" their simplified method
against the reference method;
3) periodic measurement of a small set of reference samples with well-known RRR
values using the simplified method.
A.4 Bending strain dependency of RRR
In general, the resistivity (ρ) of a pure metal such as copper at a very-low temperature
increases as its applied strain increases. In general, a lower ρ wire has a larger percentage
change in ρ than a higher ρ wire. There is almost no effect of strain on the room temperature
resistivity of a metal. This means that the change in RRR with strain is more significant for a
1)
material whose RRR is high. According to the result of the intercomparison tests [1] , the
dependency on bending strain was low for a specimen of low RRR. Bending strain is applied
when the specimen is mounted on the measuring mandrel. Since the bending strain is
inversely proportional to a radius of bent curvature, the smaller the diameter of the measuring
mandrel is, the larger the bending strain being applied to the specimen is.
The increase in resistivity, ∆ρ, at 4 K as a function of cold working ratio, CW [%], for pure
copper is shown in Chapter 8 of reference [2]. Since the value of CW is approximately equal
to the value of tensile strain, ε, when ε is small, the result is expressed as in Equation (9).
The dependency of the copper resistivity increase on bending strain can be obtained by
replacing the bending strain by an equivalent tensile strain.
Figure A.2 shows the relationship between RRR and bending strain for Nb-Ti composite
superconductors with pure Cu matrix, obtained from the measured values of the
intercomparison test performed in 1993 and 1994. The lines in the figure are the relationships
calculated according to Equation (9) for each specimen. The measured values basically agree
with the calculated values, and high RRR materials are sensitive to bending strain. Using
equation (9), Figure A.3 shows the dependency of round Cu wires where RRR with zero strain
varies from 50 to 350. Figure A.4 shows bending strain dependency of RRR normalized by the
value at zero strain. A similar dependency of rectangular Cu wires is shown in Figures A.5
___________
1)
The figures in square brackets refer to the reference documents at the end of this annex.

– 18 – 61788-4  IEC:2011
and A.6. For copper with RRR of 350, which is the highest limit of RRR in this standard, the
RRR decreases by 10 % for a bending strain of 2 %, with respect to the zero strain value.

Figure A.2 – Bending strain dependency of RRR for pure Cu matrix of Nb-Ti composite
superconductors (comparison between measured values and calculated values)

Figure A.3 – Bending strain dependency of RRR for round Cu wires

61788-4  IEC:2011 – 19 –
Figure A.4 – Bending strain dependency of normalized RRR for round Cu wires

Figure A.5 – Bending strain dependency of RRR for rectangular Cu wires

– 20 – 61788-4  IEC:2011
Figure A.6 – Bending strain dependency of normalized RRR for rectangular Cu wires
To evaluate a high-RRR material, it is therefore desirable to use a straight base plate or a
mandrel with a large coil diameter so that the evaluation can be performed with the least
possible bending strain being applied. In addition to this, special care should be taken with
the specimen so that there is no significant strain applied to it during handling.
A.5 Procedure of correction of bending strain effect
This clause describes the procedure of correction of bending strain effect on the resistance at
low temperature given in 7.3. For a specimen of thickness 2h mounted on a mandrel of radius
r, the bending strain is given by
ε = 100 × (h/r) %. (A.3)
b
Then, the equivalent tensile strain is
ε = (1/2)ε (A.4)
b
for a rectangular wire and
ε = [4/(3π)]ε (A.5)
b
for a round wire. The increase in the resistivity of pure copper at 4,2 K is calculated by
substituting this ε value into equation (9). Then, the corrected resistance at low temperature is
calculated using equation (8).
A.6 Reference documents of Annex A
[1] MURASE S., SAITOH T., MATSUSHITA T., OSAMURA K. Proc. of ICEC16/ICMC,
Kitakyushu, May 1996, p. 1795.
[2] SIMON N.J., DREXLER E.S., REED R.P. Properties of Copper and Copper Alloys at
Cryogenic Temperatures. NIST Monograph, 1992, 177.

61788-4  IEC:2011 – 21
...