Iec 61788 4 2016

15 A.2 Alternative method for in re sin temp rature of sp cimen a ove s p rcon u tin tran ition temp rature.. 7.2.2 Data a quisition of cryoge ic re ista ce The sp cimen, whic is sti mou

Part ie 4: Mesurage du rapport de résist ance résiduel e – R apport de résist ance

résiduel e des composit es supraconduct eurs de Nb- Ti et de Nb

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Part ie 4: Mesurage du rapport de résist ance résiduel e – R apport de résist ance

résiduel e des composit es supraconduct eurs de Nb- Ti et de Nb

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FOREWORD 4

INTRODUCTION 6

1 Sco e 7

2 Normative ref eren es 7

3 Terms an def i ition 7

4 Prin iple 8

5 Ap aratu 8

5.1 Material of me s rement man rel or of me s rement b se plate 8

5.2 Diameter of the me s rement man rel an len th of the me s rement b se plate 8

5.3 Cryostat for the resistan e (R 2 ) me s rement 9

6 Sp cimen pre aration 9

7 Data ac uisition an analy is

9 7.1 Resistan e (R 1 at ro m temp rature 9

7.2 Resistan e (R 2 or * 2 R ) ju t a ove the s p rcon u tin tran ition 9

7.2.1 Cor ection of strain eff ect 9

7.2.2 Data ac uisition of cryogenic resistan e 10 7.2.3 Optional ac uisition method 12 7.3 Cor ection on me s red * 2 R of Nb-Ti comp site s p rcon u tor for b n in strain 12 7.4 Resid al resistan e ratio (RRR) 12 8 Un ertainty an sta i ty of the test method 12 8.1 Temp rature 12 8.2 Voltage me s rement 12 8.3 Cur ent 13 8.4 Dimen ion 13 9 Test re ort 13 9.1 RRR value 13 9.2 Sp cimen 13 9.3 Test con ition 14 9.3.1 Me s rements of R 1 an R 2 14 9.3.2 Me s rement of R 1 14 9.3.3 Me s rement of R 2 1

4 An ex A (informative) Ad itional information relatin to the me s rement of RRR 15 A.1 Recommen ation on sp cimen mou tin orientation 15 A.2 Alternative method for in re sin temp rature of sp cimen a ove s p rcon u tin tran ition temp rature 15 A.3 Alternative me s rement method of R 2 or * 2 R 15 A.4 Ben in strain de en en y of RRR f or Nb-Ti comp site s p rcon u tor 18 A.5 Proced re of cor ection of b n in strain ef fect 21

An ex B (informative) Un ertainty con ideration 2

B.1 Overview 2

B.2 Definition 2

B.3 Con ideration of the u certainty con e t 2

B.4 Un ertainty evaluation example for TC 9 stan ard 2

An ex C (inf ormative) Un ertainty evaluation in test method of RRR for Nb-Ti an Nb 3 Sn comp site s p rcon u tors 2

C.1 Evaluation of u certainty 2

C.2 Summary of rou d ro in test of RRR of a Nb-Ti comp site s p rcon u tor 3

C.3 Re son f or large COV value in the intercomp rison test on Nb 3 Sn comp site s p rcon u tor 31

Biblogra h 3

Fig re 1 – Relation hip b twe n temp rature an resistan e 8

Fig re 2 – Voltage vers s temp rature c rves an def i ition of e c voltage 10 Fig re A.1 – Definition of voltages 17 Fig re A.2 – Ben in strain de en en y of RRR value f or pure Cu matrix of Nb-Ti comp site s p rcon u tors (comp rison b twe n me s red values an calc lated values) 19 Fig re A.3 – Ben in strain de en en y of RRR value f or rou d Cu wires 19 Fig re A.4 – Ben in strain de en en y of normal zed RRR value for rou d Cu wires 2

Fig re A.5 – Ben in strain de en en y of RRR value f or rectan ular Cu wires 2

Fig re A.6 – Ben in strain de en en y of normal zed RRR value for rectan ular Cu wires 21

Fig re C.1 – Distribution of o served r R R of Cu/Nb-Ti comp site s p rcon u tor 31

Ta le A.1 – Minimum diameter of the me s rement man rel f or rou d wires 21

Ta le A.2 – Minimum diameter of the me s rement man rel f or rectan ular wires 21

Ta le B.1 – Output sig als f om two nominal y identical exten ometers 2

Ta le B.2 – Me n values of two output sig als 2

Ta le B.3 – Exp rimental stan ard deviation of two output sig als 2

Ta le B.4 – Stan ard u certainties of two output sig als 2

Ta le B.5 – COV values of two output sig als 2

Ta le C.1 – Un ertainty of e c me s rement 3

Ta le C.2 – Obtained values of R 1 , R 2 an r R R f or thre Nb 3 Sn samples 31

INTERNATIONAL ELECTROTECHNICAL COMMISSION

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International Stan ard IEC 617 8-4 has b en pre ared by IEC tec nical commit e 9 :

Sup rcon u tivity

This fourth edition can els an re laces the third edition publ s ed in 2 1 This edition

con titutes a tec nical revision

This edition in lu es the fol owin sig if i ant tec nical c an es with resp ct to the previou

The text of this standard is b sed on the fol owin doc ments:

Ful inf ormation on the votin for the a proval of this stan ard can b foun in the re ort on

votin in icated in the a ove ta le

This publ cation has b en draf ted in ac ordan e with the ISO/IEC Directives, Part 2

A l st of al p rts of the IEC 617 8 series, publ s ed u der the general title Su erc nd uctivity,

can b f ou d on the IEC we site

The commit e has decided that the contents of this publ cation wi remain u c an ed u ti

the sta i ty date in icated on the IEC we site u der "ht p:/webstore.iec.c " in the data

related to the sp cif i publ cation At this date, the publ cation wi b

• reconfirmed,

• with rawn,

• re laced by a revised edition, or

• amen ed

IMPORTANT – The 'colour inside' logo on the cov r pa e of this publ c tion in ic te

that it contains colours whic are considere to be us f ul f or the cor e t

understa din of its conte ts Us rs s ould th ref ore print this doc me t using a

colour printer

Co p r, Cu/Cu-Ni or aluminium is u ed as matrix material in Nb-Ti an Nb

3

Sn comp site

s p rcon u tors an work as an electrical s u t when the s p rcon u tivity is inter upted It

also contributes to recovery of the s p rcon u tivity by con u tin he t generated in the

s p rcon u tor to the s r ou din co lant The cryogenic-temp rature resistivity of co p r is

an imp rtant q antity, whic influen es the sta i ty an AC los es of the s p rcon u tor The

resid al resistan e ratio is defined as a ratio of the resistan e of the s p rcon u tor at ro m

temp rature to that ju t a ove the s p rcon u tin tran ition

This p rt of IEC 617 8 sp cifies the test method f or resid al resistan e ratio of Nb-Ti an

Nb

3

Sn comp site s p rcon u tors The c rve method is employed for the me s rement of

the resistan e ju t a ove the s p rcon u tin tran ition Other method are des rib d in A.3

Sn comp site s p rcon u tors with Cu, Cu-Ni, Cu/Cu-Ni an Al

matrix This method is inten ed f or u e with s p rcon u tor sp cimen that have a monol thic

stru ture with rectan ular or rou d cros -section, RRR value les than 3 0, an cros

-sectional are les than 3 mm

The f ol owin doc ments, in whole or in p rt, are normatively ref eren ed in this doc ment an

are in isp n a le f or its a pl cation For dated ref eren es, only the edition cited a ples For

u dated referen es, the latest edition of the referen ed doc ment (in lu in an

amen ments) a pl es

IEC 6 0 0-815, I ntern tion l El ectrote h ic l Vo a ulary – Part 815: Su erc nduct ivity

(avai a le at: www.electro edia.org)

Note 1 to e try: This n te a ple to th Fre c la g a e o ly

Note 2 to e try: In this p rt of IEC 617 8 for Nb-Ti a d Nb Sn c mp site s p rc n u tors, th ro m temp rature

is d fin d a 2 3 K (2 °C), a d th re id al re ista c ratio is o tain d in Formula ( ), wh re th re ista c (R

1)

at 2 3 K is divid d b th re ista c (R

2) ju t a o e th s p rc n u tin tra sitio

21

R R

RR

c n itio a d z ro e tern l ma n tic field

Fig re 1 s ows s h matic ly a re ista c v rs s temp rature c rv a q ire o a s e ime whie me s rin th

cry g nic re ista c

Th cry g nic re ista c , R

2, is d termin d b th inters ctio , A, of two straig t ln s (a) a d (b) at

The resistan e me s rement b th at ro m an cryogenic temp ratures s al b p r ormed

with the f our terminal tec niq e Al me s rements are done without an a pl ed mag etic field

The target relative combined stan ard u certainty of this method is def i ed as an exp n ed

u certainty (k = 2) not to ex e d 5 %

The maximum b n in strain in u ed d rin mou tin an co l n the Nb-Ti sp cimen s al

not ex e d 2 % The me s rement s al b con u ted in a strain-f re con ition or in a

con ition with al owa le thermal strain for the Nb

3

Sn sp cimen

5 Apparatus

5.1 Material of me s reme t ma drel or of me s reme t ba e plate

Material of the me s rement man rel for a coied Nb-Ti sp cimen or of the me s rement

b se plate for a straig t Nb-Ti or Nb

3

Sn sp cimen s al b co p r, aluminium, si ver, or the

l ke whose thermal con u tivity is eq al to or b t er than 10 W/ m·K) at l q id helum

temp rature (4,2 K) The s race of the material s al b covered with an in ulatin layer

( a e or a layer made of p lyeth lene tere hthalate, p lyester, p lytetraf l oro thylene, etc.)

whose thic nes is 0,1 mm or les

5.2 Diameter of the me s reme t ma drel a d le gth of the me s reme t ba e plate

The diameter of the me s rement man rel s al b large enou h to ke p the b n in strain of

5.3 Cryostat for the re ista c (R

2) me s reme t

The cryostat s al in lu e a sp cimen s p ort stru ture an a l q id hel um reservoir for

me s rement of the resistan e R

2 The sp cimen s p ort stru ture s al al ow the sp cimen,

whic is mou ted on a me s rement man rel or a me s rement b se plate, to b lowered

into an raised out of a l q id helum b th In ad ition, the sp cimen s p ort stru ture s al b

made so that a c r ent can f low throu h the sp cimen an the res ltin voltage generated

alon the sp cimen can b me s red

6 Specimen preparation

The test sp cimen s al have no joints or spl ces with a len th of 3 mm or lon er The

sp cimen s al b in trumented with c r ent contacts ne r e c of its en s an a p ir of

voltage contacts over its central p rtion The distan e b twe n two voltage ta s (L) s al b

2 mm or lon er A thermometer f or me s rin cryogenic temp rature s al b at ac ed ne r

the sp cimen

Some mec anical method s al b u ed to hold the sp cimen again t the in ulated layer of

the me s rement man rel or b se plate Sp cial care s ould b taken d rin in trumentation

an in tal ation of the sp cimen on the me s rement man rel or b se plate so that no

ex es ive f orce, whic may cau e u desired b n in strain or ten i e strain, would b a pled

to the sp cimen Ide l y, it is inten ed that the Nb

3

Sn sp cimen b as straig t as p s ible;

however, this is not alway the case, th s care s ould b taken to me s re the sp cimen in

its as received con ition

The sp cimen s al b mou ted on a me s rement man rel or on a me s rement b se plate

for these me s rements Both resistan e me s rements, R

1

2, s al b made on the

same sp cimen an the same mou tin

7 Data acquisition and analysis

1) at room temperature

The mou ted sp cimen s al b me s red at ro m temp rature (T

m(K) , where T

msatis es

the f ol owin con ition: 2 3 K ≤ T

m

≤ 3 8 K A sp cimen c r ent (I

1(A) s al b a pl ed so

that the c r ent den ity is in the ran e of 0,1 A/mm

2

to 1 A/mm

2

b sed on the total wire cros

-sectional are , an the res ltin voltage (U

1(V) , I

7.2.2 Data a quisition of cryoge ic re ista ce

The sp cimen, whic is sti mou ted as it was for the room temp rature me s rement, s al

b placed in the cryostat f or electrical me s rement sp cified in 5.3 Horizontal mou tin of

the sp cimen is recommen ed in A.1 Alternate cryostats that employ a he tin element to

swe p the sp cimen temp rature are des rib d in A.2 The sp cimen s al b slowly lowered

into the lq id hel um b th an co led to l q id hel um temp rature over a time p riod of at

on the total wire cros -sectional are , an the res ltin voltage (U (V) , I (A), an sp cimen

temp rature (T (K) s al b recorded In order to ke p the ratio of sig al to noise hig enou h,

the me s rement s al b car ied out u der the con ition that the a solute value of the

res ltin voltage ab ve the s p rcon u tin tran ition ex e d 10 µV An i u tration of the

data to b ac uired an its analy is is s own in Fig re 2

NOT Volta e with s b cripts + a d – are th s o tain d in th f irst a d s c n me s reme ts u d r p sitiv

a d n g tiv c re ts, re p ctiv ly, a d U

2 +

a d U

2 –are th s o tain d at z ro c re t For clarity, U

0rev

me s re at z ro c r e t is n t s own c in id nt with U

0 Straig t ln (a) is drawn in th tra sitio re io with a

s arp in re s in th v lta e with temp rature a d straig t ln (b) is drawn in th re io with a n arly c n ta t

v lta e

Figure 2 – Volta e v rs s temperature c rv s

a d def initions of e c volta e

When the sp cimen is in the s p rcon u tin state an the test c r ent (I ) is a pl ed, two

voltages s al b me s red ne rly simultane u ly: U

0( he initial voltage recorded with a

p sitive c r ent p larity) an U

0re( he voltage recorded d rin a brief c an e in a pled

c r ent p larity) A val d

*

2

R me s rement req ires that ex es ive inter erin voltages are not

present an that the sp cimen is initial y in the s p rcon u tin state Th s, the f ol owin

con ition s al b met for a val d me s rement:

U is the average voltage for the sp cimen in the normal state at cryogenic

temp rature, whic is def i ed by Formula (5)

The sp cimen s al b grad al y warmed so that it c an es to the normal state completely

When the cryostat f or the resistan e me s rement sp cif ied in 5.3 is u ed, this can b

ac ieved simply by raisin the sp cimen to an a pro riate p sition a ove the l q id hel um

level The sp cimen voltage vers s temp rature c rve s al b ac uired with the rate of

temp rature in re se maintained b twe n 0,1 K/min an 10 K/min The voltage vers s

temp rature c rve s al contin e to b recorded d rin the tran ition into the normal state, up

to a temp rature somewhat les than 15 K f or the Nb-Ti sp cimen an les than 2 K for the

c r ent, I , with the same mag itu e but negative p larity (p larity o p site that u ed for the

initial c rve) s al be a pl ed an the voltage U

0–

s al b recorded at this temp rature The

proced ral ste s s al b re e ted to record the voltage vers s temp rature c rve with this

negative c r ent In ad ition, when the me s rement c r ent, I , decre ses to 0, the

recordin of U

2 –

s al b made at within ±1 K f rom the temp rature at whic U

2 +was

recorded

Eac of the two voltage vers s temp rature c rves s al b analy ed by drawin a l ne (a)

throu h the data where the a solute value of voltage s arply in re ses with temp rature (se

Fig re 2) an drawin a secon l ne (b) throu h the data a ove the tran ition where the

voltage is ne rly con tant for Nb-Ti or raised grad al y an almost lne rly for Nb

*

2U

in Fig re 2 s al b determined at the intersection of

these two lnes f or the p sitive an negative p larity c rves, resp ctively

The cor ected voltages, U

+

= U

2 +– U

0–

If the

*

2R

me s rement

do s not me t the valdity req irements in 7.2.2, sp cifical y either in F rmula (4) or (6), then

improvement ste s either in hardware or exp rimental o eration s al b taken to me t these

req irements b f ore res lts are re orted

Formula (7) s al b u ed to calc late the me s red resistan e (

R

I

7.2.3 Optional a quisition methods

The method des rib d in the b dy of this p rt of IEC 617 8 is the “referen e” method an

Sρ

(8)

where ∆ρ is defined b low an S

u

an L are defined in 8.4 The in re se in the resistivity of

pure co p r at 4,2 K d e to ten i e strain, ε (%), is expres ed by

The calc lation of Formula (9) s al b car ied out as umin that the eq ivalent ten i e strain

ε is (1/2)ε an (4/3 π)ε f or rectan ular an rou d wires, resp ctively The b n in strain

de en en y of resid al resistan e ratio for pure co p r is des rib d in A.4

7.4 Re idual re ista c ratio (RRR)

The RRR value s al b calc lated u in Formula (1)

8 Uncertainty and stabi ity of the test method

8.1 Temperature

The ro m temp rature s al b determined with a stan ard u certainty not ex e din 0,6 K,

whi e holdin the sp cimen, whic is mou ted on the me s rement man rel or on the

me s rement b se plate, at ro m temp rature

8.2 Volta e me s reme t

For the resistan e me s rement, the voltage sig al s al b me s red with a relative

8.3 Cur e t

When the c r ent is directly a pled to the sp cimen with a programma le DC c r ent source,

the sp cimen test c r ent s al b determined with a relative stan ard u certainty not

ex e din 0,3 %

When the sp cimen test c r ent is determined f rom a voltage-c r ent c aracteristic of a

stan ard resistor by the four terminal tec niq e, the stan ard resistor, with a relative

combined stan ard u certainty not ex e din 0,3 %, s al b u ed

The flu tuation of DC sp cimen test c r ent, provided by a DC p wer s p ly, s al b les

than 0,5 % d rin every resistan e me s rement

8.4 Dime sion

The distan e alon the sp cimen between the two voltage ta s (L) s al b determined with a

relative combined stan ard u certainty not ex e din 5 %

For cor ection of the b n in strain eff ect in the case of the wire with pure Cu matrix, the

cros -sectional are of Cu matrix (S

u) s al b determined u in a nominal value of co p r to

non-co p r ratio an nominal dimen ion of the sp cimen The wire diameter (d ) an man rel

radiu (R

d) s al b determined with relative stan ard u certainty not ex e din 1 % an 3 %,

It is desired that n b larger than 4 so that the normal distribution can b as umed f or

o served res lts to estimate the stan ard deviation If n is not s f ficiently large, a rectan ular

b) Clas ification an /or s mb l;

c) Shap an are of the cros -section;

d) Dimen ion of the cros -sectional are ;

e) Numb r of f ilaments or s b lements;

f ) Diameter of the fi aments or s b lements;

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 amon Cu-Ni, Cu, an Nb-Ti or amon Al,

Cu, an Nb-Ti for Nb-Ti sp cimen;

0, U

0re,

*

2

2 +, U

0–,

*

2

2 –an

2

U );

g) Resistan es (R , R

1,

*

2

2);

i) Material, s a e, an dimen ion of the man rel or the b se plate;

j) In tal ation method of the sp cimen in the man rel or the b se plate;

k) In ulatin material of the man rel or the b se plate

9.3.2 Me s reme t of R

1

The f ol owin test con ition s al b re orted for the me s rement of R

1:

a) Temp rature set in an holdin method of the sp cimen;

m: Temp rature for me s rement of R

m

9.3.3 Me s reme t of R

2

The f ol owin test con ition s al b re orted for the me s rement of R

2:

a) Rate of in re sin temp rature;

b) Method of co l n down an he tin up

Ad itional information relatin to the me s rement of RRR is given in An ex A An ex B

des rib s def i ition an an example of u certainty in me s rement Un ertainty evaluation

in the referen e test method of RRR for comp site s p rcon u tors is given in An ex C

Annex A

(inf or mative)

Additional inf ormation relating to the measurement of RRR

A 1 Recommendation on specimen mounting orientation

When a sp cimen is in the f orm of straig t wire, horizontal mou tin of the wire on the b se

plate is recommen ed sin e this mou tin orientation can red ce p s ible thermal gradient

alon the wire comp red to the vertical mou tin orientation Here the horizontal mou tin

orientation me n that the wire axis is p ral el to the s rf ace of lq id hel um

A 2 A lternative methods f or incre sing temperature of specimen above

superconducting transition temperature

The fol owin method are also recommen ed for in re sin temp rature a ove the

s p rcon u tin tran ition of the sp cimen The rate of in re sin temp rature of the whole

sp cimen within a ran e b twe n 0,1 K/min an 10 K/min s ould b a pl ed f or these

method In order to damp n the rate of in re sin temp rature an to avoid a large

temp rature gradient, sp cial care s ould b taken in selectin he ter p wer, he t ca acity

( he sp cimen with the me s rement man rel or the me s rement b se plate) an the

distan e b twe n the he ter an the sp cimen

a) He ter method

The sp cimen can b he ted a ove the s p rcon u tin tran ition by a he ter in tal ed in

the me s rement man rel or in the me s rement b se plate after takin the sp cimen out

of the l q id hel um b th in the cryostat

b) Adia atic method

1) Adia atic method

In this method, the cryostat hold a c amb r in whic the sp cimen, a sample holder,

a he ter an so on are contained Bef ore the c amb r is immersed in the l q id hel um

b th, air in ide the c amb r is pump d out an helum gas is fi ed Then, the c amb r

is immersed in the lq id hel um b th an the sp cimen is co led to a temp rature of

5 K or lower After the helum gas is pump d out, the sp cimen can b he ted ab ve

the s p rcon u tin tran ition by the he ter u der adia atic con ition

2) Quasi-adia atic method

In this method, the cryostat hold the sp cimen a certain distan e a ove the l q id

hel um b th for the entire cryogenic me s rement A thermal an hor f rom the

me s rement man rel or the me s rement b se plate to the lq id helum b th al ows

the sp cimen to b co led to a temp rature of 5 K or lower The sp cimen can b

he ted a ove the s p rcon u tin tran ition by a he ter located in the me s rement

man rel or the me s rement b se plate u der q asi-adia atic con ition

c) Ref rigerator method

In this method, an electromec anical a p ratu (a ref igerator) is u ed to co l the

sp cimen, whic is mou ted on a me s rement man rel or a me s rement b se plate, to

a temp rature of 6 K or lower The sp cimen can b he ted a ove the s p rcon u tin

tran ition by a he ter or by control n the ref igerator p wer

A 3 A lternative measureme t methods of R

2

or

*

2R

The f ol owin method can o tional y b u ed for ac uisition of R

a) Modif ied ref eren e method

This is a simpl fied method with ac uisition of only one voltage-temp rature c rve an is

u ed only for Nb-Ti comp site s p rcon u tors The voltage of the sp cimen is me s red

in the s p rcon u tin state u der a desired direction of c r ent (I ) an then with c r ent

in the o p site direction These values are U

0

0re

as s own in Fig re A.1 The

c r ent is then c an ed b c to the initial direction Af ter the tran ition to the normal state,

the voltage is me s red as

'

2

U in a plate u region of the c rve within a out 4 K a ove

the tran ition Then the voltage is re d u der a zero c r ent (U

2) The c r ent direction is

then reversed an the voltage is me s red again (

This a proximately comp n ates for the eff ect of thermo lectric voltage The fol owin

con ition s ould be f ulfi ed to en ure that the influen e of the interf erin voltage an the

thermo lectric voltage s ift on

2

22

22

an

2'

22

Figure A.1 – Def inition of volta e

b) Fixed temp rature method

is directly determined at a fixed temp rature in a plate u region

within a out 4 K a ove the tran ition f or Nb-Ti comp site s p rcon u tors, an R

2

is

directly determined at 2 K for Nb

3

Sn comp site s p rcon u tors, in te d of u in the

method des rib d in 7.2 In this case it is desira le to c ec that the whole sp cimen is at

a u iform an fixed temp rature In the me s rement of Nb

3

Sn comp site s p rcon u tor

the f i ed temp rature of 2 K s ould b determined with a combined stan ard u certainty

not ex eedin 0,6 K The fixed temp rature an the combined stan ard u certainty s ould

b noted in the test re ort Also the U

0

0–, whic are defined in 7.2.2, s ould b

recorded as the zero voltage level in the fixed method In order to el minate the in uen e

of thermo lectric voltage, two voltage sig als of the sp cimen, say U

2

2–

, s ould b

ac uired ne rly simultane u ly by reversal of the test c r ent For the fixed method the

eff ect of thermo lectric voltage on determination of cryogenic resistan e can b el minated

c) Computer b sed method

A computer can b u ed to control the c r ent direction an warmin of the sp cimen an

to me s re the voltage-temp rature c rve Chan es in c r ent direction by p riodic

c r ent reversals or p riodic c r ent on an of c cles are u ed to cor ect f or off set

voltages in order that the me s rements can b made d rin one c cle of c an in the

sp cimen temp rature The ef fect of thermo lectric voltage s ould also b c ec ed

d) Other simpl fied method with p riodic c ec s

Simpl fied method without temp rature me s rement mig t also b ac e ted, if an

o erator with s f ficient exp rien e p rorms the me s rement u in a given a p ratu

an if the f ol owin con ition is satisfied If a simpl fied la oratory practice can b s own,

throu h p riodic c ec s, to ac ieve the same res lt as the method in this p rt of

IEC 617 8, within its stated u certainty, then the simpl f ied practice may b u ed in place

of this referen e method These p riodic c ec s could b ac ompl s ed by doin one of

the fol owin :

1) an interla oratory comp rison where one la oratory u es the ref eren e method an

another la oratory u es their simpl f ied method;

2) a sin le la oratory comp rison where one la oratory "c ec s" their simpl f ied method

3) p riodic me s rement of a smal set of ref eren e samples with wel -k own RRR values

u in the simpl fied method;

4) reg lar/f req ent me s rements with multiple sp cimen , one of whic is a referen e

sample that would not b mou ted/dismou ted an would b me s red every time as

a cal brator

A 4 Bending strain de endency of RRR f or Nb-Ti composite superconductor

In general, the resistivity (ρ) of a pure metal s c as co p r at a very-low temp rature

in re ses as its a pl ed strain in re ses In general, a lower ρ wire has a larger p rcentage

c an e in ρ than a hig er ρ wire There is almost no eff ect of strain on the ro m temp rature

resistivity of a metal This me n that the c an e in r

when the sp cimen is mou ted on the me s rement man rel Sin e the b n in strain is

in ersely pro ortional to a radiu of b nt c rvature, the smaler the diameter of the

me s rement man rel the larger is the b n in strain b in a pl ed to the sp cimen

The in re se in resistivity, ∆ρ, at 4 K as a fu ction of cold workin ratio, r

CW[%] for pure

co p r is s own in Cha ter 8 of referen e [2] Sin e the value of r

CW

is a proximately eq al

to the value of ten i e strain, ε, when ε is smal , the res lt is expres ed as in Formula (9) The

de en en y of the co p r resistivity in re se on b n in strain can b o tained by re lacin

the b n in strain by an eq ivalent ten i e strain

Fig re A.2 s ows the relation hip b twe n r

RR

an b n in strain for Nb-Ti comp site

s p rcon u tors with pure Cu matrix, o tained f rom the me s red values of the

intercomp rison test p r ormed in 19 3 an 19 4 The l nes in the fig re are the relation hips

calc lated ac ordin to Formula (9) for e c sp cimen The me s red values b sical y agre

with the calc lated values, an hig r

RR

materials are sen itive to b n in strain Usin

Formula (9), Fig re A.3 s ows the de en en y of rou d Cu wires where r

decre ses by a out 10 % for a b n ing strain of 2 %, with resp ct

to the zero strain value

_ _ _ _ _ _

1

Numb rs ins u re bra k ts ref er to th Biblo ra h

Figure A.2 – Be ding strain depe de c of RRR v lu for

pure Cu matrix of Nb-Ti composite s perconductors

(comparison betwe n me s re v lue a d c lc late v lue )

Figure A.3 – Be din strain depe de c of RRR v lue for rou d Cu wire

Figure A.4 – Be ding strain depe de c of normal ze RRR v lue f or rou d Cu wire

Figure A.5 – Be ding strain depe de c of RRR v lue for re ta g lar Cu wire

Figure A.6 – Be ding strain depe de c of normal ze RRR v lu f or

re ta gular Cu wire

To evaluate a hig -r

RR

material, it is therefore desira le to u e a straig t b se plate or a

man rel with a large coi diameter so that the evaluation can b p rf ormed with the le st

p s ible b n in strain b in a pl ed In ad ition to this, sp cial care s ould b taken with

the sp cimen so that there is no sig ificant strain a pl ed to it d rin han l n

The minimum diameters, d

min, of the me s rement man rel for rou d an rectan ular wires

are l sted in Ta le A.1 an Ta le A.2, resp ctively

Table A.1 – Minimum diameter of the me s reme t ma drel f or round wire

Minimum diameter d

in[mm]

A 5 Procedure of cor e tion of be ding strain ef f ect

Clau e A.5 des rib s the proced re of cor ection of b n in strain eff ect on the resistan e at

low temp rature given in 7.3 For a sp cimen of thic nes 2 mou ted on a man rel of radiu

ε = (1/2)ε (A.6)

for a rectan ular wire an

f or a rou d wire The in re se in the resistivity of pure co p r at 4,2 K is calc lated by

s bstitutin this ε value into F rmula (9) Then, the cor ected resistan e at low temp rature is

calc lated u in Formula (8)

Annex B

(inf or mative)

Uncertainty considerations

B.1 Ov rview

In 19 5, a n mb r of international stan ard organization , in lu in IEC, decided to u ify the

u e of statistical terms in their stan ard It was decided to u e the word “u certainty” f or al

q antitative (as ociated with a n mb r) statistical expres ion an el minate the q antitative

u e of “precision” an “ac urac ” The word “ac urac ” an “precision” could sti b u ed

q al tatively The terminolog an method of u certainty evaluation are stan ardized in

ISO/IEC Guide 9 -3:2 0 [3]

It was left to e c Tec nical Commit e to decide if they were goin to c an e existin an

f uture stan ard to b con istent with the new u if ied a pro c Su h c an e is not e s an

cre tes ad itional confu ion, esp cial y f or those who are not fami ar with statistic and the

term u certainty At the Ju e 2 0 TC 9 me tin in Kyoto, it was decided to implement these

c an es in f uture stan ard

Con ertin “ac urac ” an “precision” n mb rs to the eq ivalent “u certainty” n mb rs

req ires k owled e a out the origin of the n mb rs The coverage f actor of the original

n mb r may have b en 1, 2, 3, or some other n mb r A man facturer’s sp cification that can

sometimes b des rib d by a rectan ular distribution wi le d to a con ersion n mb r of

3

1 The a propriate coverage f actor was u ed when con ertin the original n mb r to the

eq ivalent stan ard u certainty The con ersion proces is not somethin that the u er of the

stan ard ne d to ad res f or compl an e to TC 9 stan ard , it is only explained here to

inf orm the u er a out how the n mb rs were c an ed in this proces The proces of

con ertin to u certainty terminolog do s not alter the u er’s ne d to evaluate their

me s rement u certainty to determine if the criteria of the stan ard are met

The proced res outlned in TC 9 me s rement stan ard were desig ed to lmit the

u certainty of an q antity that could in uen e the me s rement, b sed on TC 9 exp rts’

en ine rin ju gment an pro agation of er or analy is Where p s ible, the stan ard have

simple l mits for the in uen e of some q antities so that the u er is not req ired to evaluate

the u certainty of s c q antities The overal u certainty of a stan ard was then con rmed

by an interla oratory comp rison

B.2 Def initions

Statistical definition can b f ou d in thre sources: ISO/IEC Guide 9 -3:2 0 , ISO/IEC Guide

9 :2 0 [4] an the NIST Guidel nes f or Evaluatin an Expres in the Un ertainty of NIST

Me s rement Res lts (NIST) [5] Not al statistical terms u ed in this p rt of IEC 617 8 are

expl citly defined in ISO/IEC Guide 9 -3:2 0 F r example, the terms “relative stan ard

u certainty” an “relative combined stan ard u certainty” are u ed in ISO/IEC Guide

9 -3:2 0 (5.1.6, An ex J), but they are not f ormal y def i ed in ISO/IEC Guide 9 -3:2 0

(se [5])

B.3 Consideration of the uncertainty conc pt

Statistical evaluation in the p st f eq ently u ed the co f ficient of variation (COV), whic is

the ratio of the stan ard deviation an the me n (N.B the COV is of ten cal ed the relative

stan ard deviation) Su h evaluation have be n u ed to as es the precision of the

me s rements an give the closenes of re e ted tests The stan ard u certainty (SU)

de en s more on the n mb r of re e ted tests an les on the mean than the COV an

theref ore in some cases gives a more re lstic picture of the data s ater an test ju gment

The example in Ta le B.1 s ows a set of electronic drif t an cre p voltage me s rements

f rom two nominal y identical exten ometers u in the same sig al con itioner an data

ac uisition s stem The n = 10 data p irs are taken ran omly f rom the spre d he t of

3 0 0 cel s Here, exten ometer n mb r one (E

1

is at zero of fset p sition whi st

exten ometer n mb r two (E

2) is deflected to 1 mm The output sig als are in volts Ta les

B.2, B.3, B.4 an B.5 are the me n values, exp rimental stan ard deviation , stan ard

u certainties an COV values of two output sig als, resp ctively

Table B.1 – Output sig als from two nominal y ide tic l e te someters

Table B.3 – Experime tal sta dard de iations of two output signals

E perimental stan ard deviatio (σ )

[V]

1n

i

i

nσ

Table B.4 – Sta dard unc rtaintie of two output signals

Stan ard u c rtainty (u)

Xσ

the ad antage of u in the stan ard u certainty, whic is in e en ent of the me n value

B.4 Uncertainty e aluation example f or TC 90 standards

The o served value of a me s rement do s not u ual y coin ide with the true value of the

me s ran The o served value may b con idered as an estimate of the true value The

u certainty is p rt of the "me s rement er or whic is an intrin ic p rt of any me s rement

The mag itu e of the u certainty is b th a me s re of the metrological q al ty of the

me s rements an improves the k owled e a out the me s rement proced re The res lt of

an ph sical me s rement con ists of two p rts: an estimate of the true value of the

me s ran an the u certainty of this “b st estimate ISO/IEC Guide 9 -3:2 0 , within this

context, is a g ide f or a tran p rent, stan ardized doc mentation of the me s rement

proced re One can at empt to me s re the true value by me s rin “ he b st estimate” an

u in u certainty evaluation whic can b con idered as two typ s: Typ A u certainties

(re e ted me s rements in the la oratory in general expres ed in the form of Gau sian

distribution ) an Typ B u certainties (previou exp riments, l terature data, man f acturer’s

information, etc of ten provided in the form of ectan ular distribution )

The calc lation of u certainty u in the ISO/IEC Guide 9 -3:2 0 proced re is i u trated in

the fol owin example:

a) The u er derives in the first ste a mathematical me s rement model in the f orm of

identified me s ran as a fu ction of al input q antities A simple example of s c model

is given f or the u certainty of a f orce, F

W+ d

R+ d

Re,

where F

m, d

W, d

R, an d

Re

re resent the force exp cted d e to an a pl ed stan ard mas ,

the man f acturer’s data, re e ted c ec s of stan ard mas /day an the re rod cibi ty of

c ec s on dif ferent day , resp ctively

Here the input q antities are: the me s red f orce of stan ard mas u in dif ferent

b lan es (Typ A), man f acturer’s data deviation (Typ B), re e ted test res lts u in the

digital electronic s stem (Typ B), and re rod cibi ty of the final values me s red on

diff erent day (Typ B)

b) The u er s ould identify the typ of distribution for e c input q antity (e.g Gau sian

distribution for Typ A me s rements an rectan ular distribution for Typ B

me s rements)

c) Evaluate the stan ard u certainty of the Typ A me s rements:

Au

nσ

is the ran e of rectan ular distributed values

e) Calc late the combined stan ard u certainty for the me s ran by combinin al the

stan ard u certainties u in the expres ion

In this case, it has b en as umed that there is no cor elation b twe n input q antities If

the model eq ation has terms with prod cts or q otients, the combined stan ard

u certainty is evaluated u in p rtial derivatives an the relation hip b comes more

complex d e to the sen itivity co f ficients [6] [7]

f ) Optional − the combined stan ard u certainty of the estimate of the ref er ed me s ran

can b multipl ed by a coverage factor (e.g 1 for 6 % or 2 for 9 % or 3 f or 9 %) to

in re se the pro a i ty that the me s ran can b exp cted to l e within the interval

g) Re ort the res lt as the estimate of the me s ran ± the exp n ed u certainty, together

with the u it of me s rement, an , at a minimum, state the coverage f actor u ed to

compute the exp n ed u certainty an the estimated coverage pro a i ty

To faci tate the computation an stan ardize the proced re, u e of a pro riate certified

commercial software is a straig tforward method that red ces the amou t of routine work [8]

[9]

2

In p rtic lar, the in icated p rtial derivatives can b e si y o tained when s c a

software to l is u ed Further ref eren es f or the g idelnes of me s rement u certainties are

given in [5] [10] an [1 ]

_ _ _ _ _ _

2

Ref ere c s [8] a d[9] giv e ample(s) of s ita le pro u ts a aia le c mmercialy This informatio is giv n f or

th c n e ie c of u ers of this d c me t a d d e n t c n titute a e d rs me t b IEC of th s pro u ts

Un ertainty in the resid al resistan e ratio is comp sed of the stan ard u certainty in the

ro m temp rature resistan e (u

1

an that in the cryogenic resistan e (u

2) In the fol owin

the coverage factor k is as umed to b 1 for simpl city

The resid al resistan e ratio of the s p rcon u tin wire is given by r

= R

1R

2 If the

resid al resistan e ratio, ∆r

, is

22

11

R RR

RR

RR

m

1are the deviation of the voltage, temp rature an a pl ed c r ent,

resp ctively The a proximation in Formula (C.4) is b sed on the fact that the eff ect of

diff eren e of temp rature f om 2 3 K (2 °C) on sen itivity co ff i ients is smal Its ef fect on

the final target u certainty is 0,2 % at most (for me s rement at 2 3 K (0 °C) The

cor esp n in deviation of the ro m temp rature can b divided as

[K]

m2m1

m

TT

∆

(C.5)

where ∆T

m1

is a diff eren e b twe n the me s red ro m temp rature and the sp cimen

m2

is the deviation cau ed by the b lometer Th s, the stan ard

u certainty in the ro m temp rature resistan e is given by

21

2

12

2

1

12

m22

12

m12

11

RTU

R

u

IU

uRu

Iu

1

d e to the diff eren e of the ro m temp rature

f rom the sp cimen temp rature an is f ormal y expres ed as

.9

0 3,0

1m11

RT

uI

In the cryogenic resistan e me s rement, the sp cimen voltage is me s red twice with a

c an e in the c r ent direction It s ould b noted that the voltage at the tran ition is

determined by drawin two straig t l nes an an a precia le u certainty may ap e r in these

analy es This u certainty is denoted by b Then, the stan ard u certainty in the cryogenic

temp rature resistan e is simi arly given by

I2[A] is the typ B

u certainty in the c r ent In the a ove,

an secon terms are doubled b cau e the me s rements are done twice Hen e, when the

sample is me s red in a b n in - re con ition, the relative combined stan ard u certainty is

When the sample c r ent is me s red u in a voltmeter an a stan ard resistor, the

u certainties of the voltage an resistan e af fect the u certainty of me s rement If the value

of the voltage an its stan ard u certainty are U an u

U, an if the value of the resistan e an

its stan ard u certainty are R an u , (U

1I

12

)2

u

I12

in Formula (C.6) an (U

2/I2

)2

When the cryogenic resistan e is me s red in a b nt con ition, the res lt ne d to b

comp n ated f or the strain eff ect u in the given eq ation with the distan e b twe n the two

voltage ta s (L), the diameter (d), co p r ratio (r

Cu) an the radiu of a man rel (R

d) u ed for

the me s rement We as ume that a rou d wire of diameter d is wou d on a me s rement

man rel of radiu R

d With the aid of Formula (8) an (9) the value of the comp n ated

cryogenic resistan e is given by

Formula (9) was neglected The q antity r

Cu

is a ratio that co p r oc upies in a cros

-sectional are of the wire an can b given by r

Cu

＝c/ 1 + c) u in the co p r ratio, c If the

secon term in Formula (C.10) is denoted by δR

2, the contribution to the combined stan ard

2

dd2

CuCu2

ru

du

Lu

Ru

Rr

dL

R

where u

L [m] u [m] u

rCu

d [m] are the typ B stan ard u certainties of distan e

b twe n voltage ta s, diameter, co p r ratio an radiu of man rel, resp ctively L is

req ired to b me s red within the u certainty

= 3 0 Hen e, the relative combined stan ard u certainty of cryogenic

resistan e d e to the b n in strain cor ection is estimated at most to b

*

22

2

0,513 10 R

Table C.1 – Unc rtainty of e c me s reme t

11

<

1 1I

0 5,0

11

<

∆I I

m2T

K1

22

22

CuCu

<

RR

B

0,0

dd

<

C.2 Summary of round robin test of RRR of a Nb-Ti composite superconductor

The rou d ro in test of RRR was car ied out on a Cu/Nb-Ti comp site s p rcon u tor The

sp cification of the test s percon u tor are:

• diameter: 0,8 mm, 0,8 mm in lu in in ulatin layer;

Particip tin in titutes were provided with sp cimen that were ne rly straig t Some

sp cimen were me s red in the as- eceived con ition an some were me s red wou d on a

b b in u der a strained con ition The n mb r of p rticip tin in titutes was 13 f om five

cou tries an the n mb r of determination was 7 R

2was me s red folowin the method

defined in 7.2 an 7.3, an those in A.3 The detai s of the me s rements are des rib d in

referen e [12] The ef fect of the strain was cor ected u in Formula (8) an (9) The

distribution of the me s red r

RR

is s own in Fig re C.1 Almost al of the data, ex e t for

thre , were con entrated fairly s arply The average was 17 ,5, the stan ard deviation was

4,4 an the COV value was 2,4 % If the thre extra rdinary data are omited, the average

was 17 ,2, the stan ard deviation was 3,1 an the COV value was 1,7 %

Hen e, it is re sona le to define the target relative combined stan ard u certainty of this

method not to ex e d 2,5 % b sed on the COV value in the rou d ro in test

Figure C.1 – Distribution of o s rve r

RR

of Cu/Nb-Ti composite s percond ctor

C.3 Reason f or large COV v lue in the intercomparison test on Nb

3

Sn

composite superconductor

The COV value of the intercomp rison test for Nb

3

Sn samples was 6,0 % [13] This value is

mu h larger than that f or Nb-Ti (2,4 %), althou h there is no contribution f om ad itional

u certainty in cor ection of the strain eff ect For clarification of this re son an intercomp rison

test was p rf ormed b twe n two la oratories f or thre Nb

3

Sn samples, two of whic were c t

f om the same b tc of he t tre tment The r

o tained u in the referen e method agre d

within 1 % b twe n the two la oratories f or the thre samples as s own in Ta le C.2, whi e

the r

values were diff erent b twe n the two samples o tained f om the same b tc [14]

This in icates that the large COV value in the former intercomp rison test originated fom

in omogeneity of samples, whi e the test method itself was f airly ac urate This

in omogeneity may b d e to the hig sen itivity to he t tre tment con ition or d e to

defects of the diff usion b r ier Sin e a r

RRvalue is commonly req ired to b gre ter than a

minimum value in order to p s , the existen e of in omogeneities may req ire that several

sp cimen of a given wire b me s red an re orted

Table C.2 – Obtaine value of R

1, R

2(T

c) [Ω]

r

R R

R

1(2 3 K) [Ω] R

2(T

c) [Ω]

o tained in the intercomp rison

test for RRR me s rement in Nb-Ti can also b u ed to estimate the u certainty of r

in

Nb

3

Sn with Formula (C.8) In ad ition, the res lt s own in Ta le C.2 in icates that the main

dif feren e b twe n the me s rements in the two la oratories comes f rom the o served

values of R

1 This is con idered to b cau ed by the u certainty in the ro m temp rature

Bibl ogr aphy

[1] MURASE S SAITOH T MATSUSHITA T an OSAMURA K Stan ardization of the

method f or the determination of the resid al resistan e ratio (RRR) of Cu/Nb-Ti

comp site s p rcon u tors P ro of ICEC16/I CM C, Kitak u h , May 19 6, p.17 5

[2] SIMON N.J DREXLER E.S REED R.P Pro erties of Co p r a d Co p r Al l oys at

Cry g nic Temp ratures NIST Monogra h, 17 (19 2)

[3] ISO/IEC Guide 9 -3:2 0 , Unc rtainty of me sureme t – Part 3: Guid e to the

expres ion of u c rtainty in me sureme t (GU M:19 5)

[4] ISO/IEC Guide 9 :2 0 , Intern t ion l voc b l ary of metrol og – Basic a d g n ral

c n e ts a d as o iated terms (VIM)

[5] TAYLOR, B.N an KUYATT, C.E Guidel nes f or Evaluatin an Expres in the

Un ertainty of NIST Me s rement Res lts NIST Tec nical Note 12 7, 19 4 (Avai a le

at <ht p:/ ph sic nist.gov/Pubs/g idel nes/TN12 7/n12 7s.pdf>)

[6] KRAGTEN, J Calc latin stan ard deviation an confiden e intervals with a

u iversal y a pl ca le spre d he t tec niq e, An l yst, Vol 1 9, 2161 (19 4)

[7] EURACHEM / CITAC Guide CG 4 Secon edition:2 0 , Quantifyin Un ertainty in

Analytical Me s rement

[8] Avai a le at <ht p:/www.metrodata.de/>

[9] Avai a le at <ht p:/www.is max.com/>

[10] CHURCHIL , E HARRY, H.K an COL E ,R Expres ion of the Un ertainties of Final

Me s rement Res lts NBS Sp cial Publcation 6 4 (19 3)

[1 ] JAB NOTE Edition 1:2 0 , Estimation of Me s rement Un ertainty (Electrical Testin /

Hig Power Testin ) (Avai a le at <htp:/www.ja or.jp )

[12] MATSUSHITA T OTABE E.S MURASE S OSAMURA K an HUA CY Adv in

Su erc nd XI Tok o, Sprin er, 15 7 (19 9)

[13] MURASE S SAITOH T MORIAI H MATSUSHITA T an OSAMURA K Ad an es in

Sup rcon u tivity XI Tok o, Sprin er, 151 (19 9)

_ _