Journal of Rescarch of the National Burwau of StandardsVolume 90, Number 2, March-April 1985

Standards for Measurementof the Critical Fields of Superconductors

F. R. FickettNational Bureau of Standards, Boulder, CO 80303

Accepted: November 21, 1984

The origins, definitions, and measurement of the various critical magnetic fields associated with super-conductors are reviewed. The potential need for a consensus standard for the measurement of these fields isevaluated. Measurement techniques as practiced both in industry and in the national laboratories and extrapo-lation techniques commonly used to determine the upper critical fields of the newer materials are presented.Sources of error in the experimental determination of critical fields are assessed for the various commontechniques. A comprehensive bibliography of the modern literature on critical field measurement and inter-pretation is included.

Key words: critical field; critical parameters; magnetic field; standards; superconductors.

1. Introduction

The literature of the field of superconductivity is re-plete with numerous critical magnetic fields. Several(He, Hcl, Hc2) have universal application and acceptance,while many others are defined for subtle and specificpurposes [e.g., Bgn(O)]. Our goal is to evaluate whetherthere is a need for a measurement standard for criticalfield similar to one developed recently for critical cur-rent [1].' We consider only superconductive materialsthat are either commercial items now or those that havethe potential of being so in the foreseeable future. Thiscriterion might seem to allow us to ignore many of themore difficult aspects of the problem, such as the effectof surface superconductivity. Yet, our survey of theliterature indicates that frequently these effects do ap-pear in rather mundane measurements and can alter theresults significantly. Thus, we have included most of theeffects that have been observed to date during attempts

About the Author, Paper: F. R. Fickett is a physicistwith the NBS Electromagnetic Technology Divisionin Boulder, CO. His work was supported by the De-partment of Energy through the Office of FusionEnergy and the Division of High Energy Physics.

to determine the critical fields. However, for practicalpurposes, effects that take place below a critical currentvalue of about 104 A/cm2 are seldom of interest, whichremoves us from the more esoteric regions of the J-Hand T-H curves. There are, of course, exceptions such aspinning studies. Similarly, the more exotic materials,such as the Chevrel-phase conductors, are not of imme-diate practical importance. However, that situationcould easily change. Thus, although our concentrationis on the conductors that are commercially available,these new materials with great potential are also consid-ered.

The terminology used here for the general referencesto the field of superconductivity is that presented in theseveral review documents on terminology prepared byour group [2,33 and in the new ASTM standard forsuperconductor terminology [4]. Definitions of the vari-ous critical fields are given both in the discussion of thetheory and of the extrapolation techniques.

In the recent past, the differentiation of B and H wasa matter left to those who worried about the basic phys-ics of magnetism. Use of the cgs system was entirelyacceptable and magnetism and superconductivity didnot coexist. Under these conditions, the gauss and theoersted were effectively equivalent and, in fact, wereoften used interchangeably. At present, however, SIunits are rapidly gaining acceptance and more is beingwritten regarding the relationships of magnetism and

95

'Numbers in brackets refer to literature references.

superconductivity [5nj Both situacions require that weuse more care in the application of these terms. Thereader interested in the basics of magnetism is referredto our recent publication on magnetic effects at lowtemperatures [61. Table I lists definitions and unit con-

veis-rons for magnetic quantities.The determining equation (in SI) is:

B = 9(H + jW ), {(1)

where B is the magnetic flux density (or magnetic in-

Table 1. Units for magnetic properties.

Gaussian & cgs emu' Conversi,Factor, C'

Dion St & rationalized mks'

Magnetic flux density,magnetic induction B gauss (G) tesla (T), Wb/m

mO xwf 2 .Uzl, G cm veber (Wb'i, volt second (¶/s)

Magnetic field strength,magnetizing force

(Volume) magnetizations

(Volume) magnetization

Magnetic polarization,intensity of magnetization

(Mass) magnetization

H

M

J, I. M

o-, A

oersted (Oe)'

emu/cm"h

G

ernulerml

emufg

10'/4v

10'

4wX/407

417X ¶0"

4sr1 0

ampere per meter (A/mYl

A/m

A/m

T, Wb/m

Am/kgWbnm/kg

(Volume) sascepLtbi.ity X, r dimersion less, cur ,' 47(4n)I X 10

dimeas or.lesshenry per meter (H/m), Wb/(A.m)

(Moss) susceptibility XPs. cmd/g, emu/g 4 wX 10"' mJAg(4r)2X lI0-I Hm3/kg

(Mtolar) susceptibility cm /mol, emu/Mal

Magnetic moment

Magnetic dipole moment

Permeability

Re cal wie pe amtiabilI ly'

(Volume) energy density,energy product

Demagnetization factor

emu, erg/Gm

emu, erg/G

dimensioniess

Am2, joule per tesla (J/T)

4rX 10< °

4wrX 10-7

not deined

H' U

D. A'

erg/cm'

dimensionless 1/4,,r

Wb.nm

H/m

dimensioaless

J/m3

dimensionless

'Gaussian units and cgs eu are tlhe same for uasgnetic propercies. The defining relation ih ?=NY+4wM.bMultiply a number in Gussianb units by C io convert it to SI (e.g., I Gx 0-3Tri -4i ri51 (S terhc in rcntcf 'Ig Vairert h.. been adopted by the National Bureau of Standards. Where two conversion factors arc giveh, the upper one is recogsizetd

under. or consistent with, SI a.l d is based on the defnition B =y,,(H+-f). where lu=4wX 10`H/Hm. The lower one is not recognized under SI and is based onthe defusition B s=ja,+J. where the symbol /.r Mis often used in place of J.

ganuss= 133 gamma (y).Dfinerosionally, oersted=gauss.JA/m was often expressed as "aorpere-lwrn per metetr when used for magnetic field strcngtnhtugne~c nimoment per Iri vcltino.

hthe designartnt. 'emun is aot a ua-t.tRecognized under SI, even thougn based on the difnttion B = uoH +J. See foomnote..F,=lItFs= l-ix, all in SI. !, is equal to Gcatsians p

R. IB. Goldfarb and F. R. Fickel. National Bureau of Standards, Boulder, CO 80303, July 1984

96

Property Symbol

Mwagnetk flux cI

4 wX 10'(4zrX 10-"

m3/molH m3/mol

I

duction) in teslas, H is the magnetic field strength inamperes/meter, M is the (volume) magnetization inamperes/meter, and Mo is the permeability of free space(47rX io-' henrys/meter). The important distinctionhere is that H is an applied field, M is a property of thematerial and, thus, B is a mixed quantity. Because of thisdistinction, we suggest that the proper quantity for thecritical fields discussed here is H; it is the applied fieldvalue at which the transition occurs. This choice leadsto the unfortunate side effect which has plagued us foryears-few researchers have an innate feel for the unitsof amperes/meter. This, in turn, leads to the common fixused by many authors of multiplying the number by Mo

and then using the units of teslas, which are more famil-iar. As an aside: the correct abbreviation for the tesla isT and the correct plural name is teslas (not capitalized)

17].Another subject that sometimes leads to confusion in

the realm of magnetic measurements is the de-magnetization factor, N. In magnetizable bodies, thepoles that appear under the influence of the applied fieldgive a return field through the body that has the effectof lowering the actual value of H within the material.This is a geometric effect and is discussed in detail in ourpublication [6]. It is of concern with superconductorsonly as long as they are in the perfect Meissner statebelow Hc,, a region that is seldom of practical interest.However, in this region the effect is important and mustbe accounted for either in the data processing or bychoice of a sample geometry that minimizes the effect (along ellipsoid with its long axis parallel to the appliedfield).

At first glance, the importance of critical field in prac-tical applications is not obvious. Certainly high valuesare desired for applications in very high field magnets,but only if reasonable critical currents can also beachieved. However, the upper critical field and its be-havior as a function of temperature and critical currentare topics of major importance to the theoretical under-standing of type II superconductivity, which in turn willalmost certainly lead to better materials for the future. Aprime example of this is the effort now afoot to create ahigher critical field in NbTi alloys by third elementadditions [8]. The work is crucially dependent on accu-rate determination of the critical fields. Another exam-ple is the application of critical field values in the treat-ment of scaling of strain effects in high fieldsuperconductors.

In the remainder of this paper we will discuss how thevarious critical fields arise in theory and how they arerelated to other parameters. The techniques used for thedetermination of the fields are reviewed with discussionof the accuracy, precision, and experimental difficultiesinvolved. Since high critical fields are most often deter-

mined by extrapolation rather than direct measurement,some time is spent discussing the various extrapolationschemes and their merits and problems, including con-troversies that have arisen related to the measurementand interpretation of modern data. The final sectionpresents our conclusions and suggestions for how best toapply the concept of standards to this measurementproblem.

2. Theory and DefinitionsThe theoretical background for the various defini-

tions associated with critical magnetic fields is ade-quately covered in many texts on superconductivity.Cody [9] provides a particularly complete listing of theequations. Here we present just enough theory to allowus to define the terms that are essential to understandingthe problems involved with the determination of criticalfields. Where we have an option we will choose thesimplest workable definition and leave the subtle detailsto the theorists. All the terms arise in one way or an-other from the Bardeen-Cooper-Schrieffer (BCS) orGinzburg-Landau-Abrikosov-Gorkov (GLAG) the-ories. Application of these concepts to the theory ofpractical materials, such as the multifilamentary super-conductors; is an active area of research at the presenttime [10-12].

Type I superconductors are included here for com-pleteness, but are nearly totally neglected thereafter,since our concern is with the high-field type II materials.

2.1 Basic Behavior

Here we present the basics of type I and type II super-conductivity. The complications that arise in the variouslimits are discussed in section 2.2. To start, we definefive parameters:

Penetration depth, X. This characteristic length is ameasure of the depth of flux penetration into a super-conductor. The currents which prevent flux penetrationinto the interior of the material flow in a layer of thisthickness. The exact temperature dependence of thisparameter is open to debate, but it decreases mono-tonically with increasing temperature and rapidly dropsto zero near the critical temperature. Typical measuredvalues at 4 K for NbTi and Nb,Sn are hundreds ofnanometers, but with a large spread. For elemental su-perconductors, X is tens of nanometers.

Coherence length, g. This length is a measure of thetypical size of the Cooper pairs. Looked at differently, itcan be taken as the minimum thickness of the interfacebetween superconducting and normal regions. Specificsdepend on the particular theoretical treatment. The

97

GLAG coherence length is temperature dependent, be-ing inversely proportional to the temperature differencefrom the critical value. In impure materials, the coher-ence length value is also influenced by the electronmean free path. Typical values are around 5 nm for typeII superconductors and considerably larger for type I(Al - 1600 nm, Pb -83 nm).

Ginzburg-Landau parameter, K. This is the dimen-sionless ratio of the two parameters above.

K = V/t. (2)

This picture is valid for either type of superconductor atthis point, i.e., below the first critical field value. Thebehavior of various parameters for each of the two typesis shown in figure 2.

Type I superconductors. These materials are puremetals and the critical field transition is first order. Thecoherence length is larger than the penetration depth,and a mixed state (see below) is energetically un-

Type I Type UI

It is roughly temperature independent. K is used as theparameter that distinguishes between type I and type IIsuperconductors; those with a value < 1/V/2 are type I.

Flux quantum, 40. The fundamental unit of mag-netic flux.

*o=h/2e=2.068X 10-'5 Wb. (3)

Normal state resistivity, Pn The classical electrical re-sistivity as measured just above the superconductingtransition unless stated otherwise.

The general behavior of a superconductor in a field isshown in figure 1. The shape is chosen to minimizedemagnetization effects. The conductor is in the Meiss-ner state with B =0 in the bulk of the material. Thesuperconductor distorts the field lines in its vicinity.

Figure 1-Superconductor behavior in the Meissner state showing theeffect of the penetration depth [2].

W

0

I.-LBcowJ

M

(ax-J

0

12

0,

X

d-JILlU.

auJU

-I

TEMPERATURE, T

WU;

I-

0LiA:

co

zUJa

X

IL

2

N

I-

0

C I "C2APPLIED FIELD, H

I

0-Jw

a.C-

TEMPERATURE, T

Figure 2-The parameters most often used in the determination ofcritical field and how they vary with field for both type I and typeII superconductors.

98

MCAPPLIED FIELD, H

"ci "C 2APPLIED FIELD, H

/ MI.d Sit.t

/ I ?11"

favorable. Thus, at H. the superconducting state col-lapses entirely. The critical field is temperature de-pendent, with an approximately parabolic dependenceon TIT,. Below the critical field the flux density is zeroin the bulk and the magnetic susceptibility (G/H) is -I

(SI units), i.e., the material is perfectly diamagnetic. Theresistive transition is sharp for these materials, suf-ficiently so that some are used as temperature standards.

Type Ii superconductors. These are the materials ofprimary commercial interest. All of the high field super-conductors are a subgroup of this type. The materialstend to be alloys and compounds. They also have aregion of perfect diamagnetism that extends only up toa rather small lower critical field, H.,, at which a secondorder transition to the mixed state occurs. The behaviorof the related properties is shown on the right side offigure 2. The fact that the penetration depth is greaterthan the coherence length gives rise to a negative sur-face energy between the superconducting and normalregions and the mixed state becomes energetically fa-vorable at a relatively low field (H,1). The structure ofthis state is as shown in figure 3. It starts when quantizedflux bundles, usually of magnitude 4r,, penetrate the inte-rior of the material. The flux is concentrated in thenormal core which is surrounded by circulating super-currents and, in the limit of zero applied field, it decaysto zero in a distance from the core equal to the pene-tration depth. The density of superconducting electronpairs, which is zero in the core, reaches its equilibriumvalue in a distance approximately equal to the coherence

length. With increasing applied field, the number ofthese flux vortices increases and they form a triangulararray, the flux lattice, with an equilibrium separationthat varies as B -t. At the upper critical field, ,C2, theflux lattice vanishes and bulk superconductivity is de-stroyed. The effect of this scenario on the bulk proper-ties can be seen in figure 2, The resistance (measuredwith sufficiently low current) does not show the trans-formation until H.2 because continuous superconductingpaths still exist through the material up to this point.However, the amount of current that can be carried, thecritical current density, decreases rapidly as the uppercritical field is approached, as shown by the data infigure 4. HJ2 is temperature dependent, and the slope of

II g2

w

ccc-)

-J

C-)

OP

1

0.1

/Nrmnal Core

cScreeningCurrents

- Srpe r C rndd ¶in gMaterial

TDP VIEW

SIDE VIEW

Figure 3-Flux penetration in the mixed state of type II super-conductors &howintg the vortex structure and the flux lattice (131.

0.001 L0.4 0.8 1.2 1.6

CRITICAL FIELD iCoHc2 . T

Figure 4-Variation of the critical current near the upper critical field.Data from [14].

the curve near T. is an important parameter in the de-tailed theory of these materials. For some materials,very high values of H,2 may occur as shown in figure 5;it has been said that critical field values on the order ofa 100 T are not ruled out by existing theory [1I].

There are two classes of superconductors in this cate-gory, intrinsic and impurity dominated. In theory almostany superconductor can be put into the latter categoryby the introduction of impurities or disorder to raise thenormal state resistivity. Huhm and Matthias [12] suggestas an approximate criterion for intrinsic super-conductors that the critical temperature should exceed

99

ooooo00000 U000000000000000

I-0400

C-Jw

-J

ScEI-0ccMa

70

60

50

40

30

20

10

5 10 15 20

TEMPERATURE, K

Figure 5-Behavior of critical field with temperature for several mod-ern superconductors.

8 K. The relationship between the critical field and crit-ical temperature of the two types is quite different. Forthe intrinsic materials

Surface critical field, H, 3. Above H, 2 a material maystill carry a small supercurrent in a surface layer ofthickness approximately equal to the coherence length.This occurs in situations that are usually not encoun-tered in the measurement of practical materials, such aswhen the field is parallel to a free conductor surface. Itis not seen if the field is perpendicular to the sample norif the sample surface is in intimate contact with normalconductor. The surface current persists with increasingfield up to the surface critical field. H.3 is related to H,,by

H. 3 = alc2, (6)

where a is about 1.7. Figures 6 and 7 show the effect onthe magnetization and the field-temperature plots. If therequisite conditions are met, the effect can cause seriouserrors in critical field determinations, especially if themeasurement is made by a resistive technique.

Magnetic, spin, and scattering effects. Many effectswork to alter the simple picture of the origin of theupper critical field presented above. Foremost amongthese is the paramagnetism of the normal state, but con-tributions also arise from the paramagnetism of the su-perconducting state, spin-orbit scattering effects, andelectron-phonon coupling. Because of this, the fullGLAG theory expression for the upper critical field forhigh values of K,

(7)

defines a critical field that is higher than that usually(4) measured. Normal state paramagnetism causes the

where y is the electronic specific heat coefficient (pro-portional to the density of states). The impurity domi-nated materials give

H. 2 - p.y T,. (5)

Thus it is possible (with some assumptions) to separatethe two classes of materials by plotting H12 against yT,.

2.2 Complications

In addition to the rather straightforward consid-erations above, the type II materials have other, morecomplex, aspects to their behavior. The theoretical basisof most of these is presented here, again, in just enoughdetail to describe the effect. The interested readershould consult the pertinent references. Explanation ofthese effects requires the introduction of new criticalfields. These fields are usually not directly measurable.

HC1 HC 2 HC3

APPLIED FIELD, H

Figure 6-Magnetization curve for a type II material showing the ex-tension to H,,.

100

H, 2 x (YT,)2 ,

�La H,*,(0)=3.llXl0'p� yT, (teslas),

X

U-

a

a-a-

TcTEMPERATURE, T

Figure 7-Applied field as a function of temperature for a type IIsuperconductor showing the region of sheath conduction below

If, 3,

actual value to be lower. It is possible to calculate thisparamagnetically limited transition field with the result,

po H,(0) = 1.84 T, (teslas). (8)

ning force (defined as Jc B) on applied field:

F,=JcB=oHc`2(T) f(h), (12)

where h is the ratio of the applied field to the uppercritical field and n is an empirical constant that variesfrom - 1.5 to 2.5. The function f(h) that describes theshape of the pinning curve is most often seen in the formhP(I -h) 9 with the parameters p and q dependent on thespecific materials.

Strain sensitivity. Practical superconducting materi-als, especially the intermetallics, are usually sensitive tostrain. Their critical current and field are degraded byeither compressive or tensile strain. Typical behavior ofthe measured critical field is shown in figure 8. Thehorizontal axis is labeled intrinsic strain, illustrating animportant point from the aspect of measurement; thesuperconducting material in a commercial wire may al-ready be under strain (usually compressive) because offorces exerted by the stabilizer and other components ofthe composite. Thus, measurement of H.2 on these prac-tical materials becomes more of a problem than onemight first imagine and leads to the definition of evenmore terminology. Most of this work comes under theheading of strain scaling studies and several empirical"laws" have emerged [19,20] to describe the behavior.These scaling laws have the exact form of eq (12), butthe temperature dependence of H, 2 is replaced by astrain dependence. Their application requires correctdetermination of the critical field even though, in gen-eral, they do not apply in either the low field (<0.2 H,2)or the high field (>0.9 HC2) regions. Two new defini-

Another symbol for this field that is sometimes used isHpP2 (0). Further modifications to the theory to accountfor paramagnetic effects lead to another critical field,

H ''@)=H .2 (0) (I+ a3)

where a is the Maki parameter given by

a= V2 [H *,(0)/Hp(0)]

1-Jw

(9) L--(

(10) erC.)

which later theoretical development has shown to be

a=2.35 ypn=0.533 [-dMJf, 2 /dT]JT=Tc (11)

Flux pinning. This property determines the criticalcurrent of the high field materials, a high value of Jcrequires that the fluxoid lattice be held in place. Near theupper critical field the value of J, is strongly affected byfield. The formulation originally proposed by Fietz andWebb [16] with further development by Kramer [17] ismost often used to express the dependence of the pin-

1.0

0.9

w

!--J

Ui]

0.8'--0.6% 0 0.6%

INTRINSIC STRAINFigure 8-The effect of strain on the determination of the critical field.

Data from (181.

101

tions appear in these writings: H, 20, which designates the"as received" value of H,2 for a practical material andH,,2 ,,, which gives the maximum value of H, 2 understrain; the peak of the curve in figure 8. This value isassumed to be that of the strain-free state of the super-conductor. Since one is dealing with practical materialshere, it should be pointed out that they do not often havea uniform composition or microstructure and H.2 maywell vary throughout the material. Thus, a sufficientlyhigh measurement current is used so that a "bulk" valuewill be obtained (see the discussion of extrapolationtechniques below) and this fact is often brought to theattention of the reader by use of H,*,(e) as the criticalfield designation (e is the strain parameter).

3. Measurement and DataAnalysis Techniques

Here we are concerned with measurement of the up-per critical field, H,,, although the techniques describedcould be applicable to the determination of other fieldsas well. The correct measurement of critical field, es-pecially in practical superconductors, presents a diffi-cult task both experimentally and in the interpretation ofthe resulting data. Different measurement methods maygive different values for a given sample, and even thesame method may give varying results depending on thechoice of parameters, such as measuring current, used ina resistive determination. The cause of these variations isnot an error in the concept or the measurement, but ismost often due to material effects such as in-homogeneities in the superconductor. Thus, it some-times happens that the measurement result that is mostcorrect physically is not the most meaningful in a prac-tical sense. Critical field determination, unlike the mea-surement of other superconductor parameters, suffersfrom the additional problem that one can seldom actu-

Superconducting

Figure 9-Techniques for deter- Rmiuing critical field values fromresistance and magnetizationdata plots [3]. SA .

ally achieve the fields necessary to see the transitiondirectly and, thus, extrapolation techniques must beused which, themselves, are subjected to interpretation.

The literature on upper critical field measurements ismixed with regard to the care given in presenting thedetails of the experiment and the data analysis methods.Two authors have discussed aspects of the measurementproblem in detail [21,22]. Many of their ideas and obser-vations have been incorporated into the following sec-tions.

3.1 Defining the Transition

Transitions between the superconducting and normalstates are seldom as clean as the curves of figure 2 sug-gest. At best, the transitions have a width to them and atworst they are nearly lost in the noise. The techniquesmost commonly employed involve extrapolations ofparts of curves as shown in figure 9. In practice, a moreelaborate system is used as illustrated in figure 10, inwhich the "center" of the transition is taken as the mid-point between two points that may represent 25 and75%, as in the figure, or some other choice such as10-90%. This approach is helpful because the early partsof the transition may be obscured by noise and becauseof the unsymmetrical nature of the curve, but it is anarbitrary definition. In fact, it has been suggested that,for the resistive determination of critical field in prac-tical materials, this technique is misleading, and theproper value should be taken as that at which the transi-tion first appears with increasing field at a properlychosen current density [21]. This arrangement is used toavoid the problem of H,2 variations throughout the su-perconducting material of the sample as discussed be-low. The author presents data showing that a significantdifference in H.2 value is found by the two techniquesapplied to commercial-type conductors. A similar com-parison using single crystal Cu-Mo-S [23] found differ-

SuperconductingI

M

NormalState

,.

NormalSlate

HOc

H H

102

Extranolated R..nrnni1.00 r ..............

& l'INHOMOGENEOUS

0.75 - ---------------------------------- ''- - SUPERCONDUCTORS

ef Superconducting , Normal

State State Figure 10-Illustration of method of

0.50 ~~~~~~~~~~~~~~~~~~~~~~~~~determining the critical parame-0.50 ------------------------------------ - ter value in the case of a broad

1/ - jMyz transition [13).

0.25 .............-.... . ._ / PURE SUPERCONDUCTORS

T/Tc

ences of up to 20% between measurements using the Ttwo definitions.

A further problem can arise in the situation oftenencountered where one does not want to allow the sam-ple to enter the normal state because of the possibility of 80damage. The approach in this case is to choose an arbi- XX0

trary criterion of detected voltage over a fixed length of 0the wire as defining the critical parameter. This tech- Nb 3 Snnique was chosen for the ASTM standard for critical =current measurement [1]. The reasoning behind the Hchoice and some of the related problems are discussed in 60 _an earlier publication [24]. The effect of the specific ochoice of criterion on the measured critical current isshown in figure 11; clearly a 1 gV criterion results in asignificantly lower critical current value than a 100 IjV 0 -criterion. As discussed in the reference, a low criterion Li 40_is not always desirable in practical application because it Amay not be possible to measure it unambiguously. On <the other hand, a very high one may put one too close to 1 /quenching the sample. 21o 20-

/ ~10 O /1~~10

Figure 11-The effect of choice of criterion on the value reported for 0 100 200the critical current of a practical conductor. Numbers on the curvesgive the actual full-scale voltage in microvolts that corresponds to100% on the vertical axis. CURRENT, A

103

Because of its significance in understanding in-homogeneity effects, the width of the transition is animportant feature of the data. All commercial materialsshow relatively broad transitions as indicated by themeasurements shown in figure 12, especially those forthe Nb3 Sn samples. The interpretation is alwaysstrongly dependent on the measurement technique.

3,2 Measurement Techniques

A wide variety of measurement techniques has beenused for the detection of the upper critical field of super-conductors. The choice among them depends on the

Tc of Nb3 Sn

CommercialWire NBS

ReferenceSample

80

tTC=16.9 K

goal of the measurement and the time (and money)available. As always, the easiest measurements are themost difficult to interpret and the most subject toerror-another manifestation of Murphy's Law. Thetechniques that have been used generally fall into fiveclasses: electrical, magnetic, electromagnetic, thermal,and acoustic. For each of these we will discuss the the-ory behind the measurement, the ease of use, problemswith the technique, and the data interpretation required.The apparatus for each method will be touched onbriefly in the next section. We do not go into great detailhere because a new book on materials properties mea-surement at low temperatures which thoroughly covers

Tc=1 8 .00 K

16.0 17.0 18.0TEMPERATURE, K

8.5 9.0 9.5

TEMPERATURE, K

a,-

140 cU

_

120 n

100 >-Z-

80 <

0X

I-

Figure 12-Comparisons betweencommercial materials and refer-ence samples measured byseveral techniques [25].

104

t)Z.

L..

0

IL

w

C,)

0)

..

each of the techniques, although not always their spe-cific application to superconductors, has recently be-come available [26].

In the discussion that follows, one should keep inmind the fact that practical superconductors are in-homogeneous materials. The critical field of the super-conductor may vary with the relative direction of theapplied field and the conduction path. Isolated regionsof superconducting material may occur, or regions maybe coupled only through a percolation network or bythe proximity effect. Normal conductor, usually copper,is almost always present, with a resistivity that is a factorof 100 or more below its room temperature value. Eachof these factors will affect a given measurement methoddifferently. The ideal measurement method would allowus to determine the microscopic variation of H,2throughout the material, to measure the exact volumefraction of each superconducting species in the com-posite, and to determine the connectivity of the variousregions. Thts would, of course, be accomplished withapparatus of minimum cost and greatest ease of oper-ation. We may have to wait some time for this.

Resistive method. This measurement is by far theeasiest to perform on commercial materials and it is themost commonly used. Care should be taken to have along enough piece of wire that the minimum detectablevoltage represents a reasonably low electric field crite-rion. Current transfer and current sharing effects can beminimized by having the voltage-measuring contacts ona significant length of the sample that is in a region ofuniform field and distant from the current contacts bymany wire diameters. This technique is probably theonly common one that can reasonably be used in pulsed-field systems for the direct measurement of very highcritical fields [27]. The values of Hc measured at lowcurrent levels can be high because the voltage will re-main at zero with only a few strands still super-conducting. In a few unusual situations (field parallel tosurface, no normal metal jacket), it is also possible forsurface superconductivity effects to cause the transitionto be observed at very high field values. Even whensurface effects are not of concern, the choice of mea-suring current is not a trivial problem. Larbalestier [21]presents data showing the value of H1 c2 for cold-workedNbTi to vary from more than 11.6 T to less than 10.9 Tas the measuring current density is raised from 0.005 to10 A/cm 2 , and the curve is not leveling out even then.

MVagnetic methods. A number of techniques use de-tection of the change in magnetization of a sample as ameans of monitoring the critical field transition. Earlymethods are described by Hein and Falge [28] and morerecent ones in the book mentioned above [26]. At Ha

both the magnetization and the susceptibility becomeeffectively zero. Magnetometer techniques measure themagnetization of the sample directly. The sample is in-serted into a pickup coil in the field region. The field isset to a fixed value and the sample is moved either out ofthe coil completely (ballistic method) or caused to oscil-late within the coil (vibrating sample). The voltage in-duced in the coil is integrated to give the magnetization.A variation of this system is found in the swept-fieldtechnique in which the sample remains fixed within thepickup coil and the magnetic field is ramped at a fixedrate. Use of a balanced coil system (see below) allowsextraction of the magnetization signal.

The various inductive techniques all use sus-ceptometers; they measure the incremental sus-ceptibility (AM/AH) by applying a small low-frequencyac field to the sample in the presence of a large back-ground dc field and detecting the induced signal, eitherwith a secondary coil (mutual inductance) or by thechange in inductance of the primary (self inductance).The mutual inductance method is the most commonlyused, and most often the secondary coil system is madeup of two counterwound coils that are connected inseries with the sample contained in one of them. Thisarrangement allows canceling of the primary field signalwith the sample in the normal state prior to a mea-surement. Such systems are said to be balanced.

All of the systems just described require calibration ifthey are to be used for direct measurements rather thanfor tracking the sample through a transition. The easiestmethod uses a properly shaped test specimen of type Isuperconductor, such as lead, and assumes it is perfectlydiamagnetic at 4 K. Room temperature standards ofsusceptibility and magnetic moment are also availablefrom the National Bureau of Standards. Magnetic meth-ods are seldom actually used to determine H,2 of prac-tical materials, but they are used extensively in the deter-mination of ac losses in superconductors. They areuseful for samples of bulk material and for chips orpowders. When used with wires, the samples are eitherbundles of cut wires with their axes parallel to the ap-plied field or noninductively-wound coils in which thewire axis is normal to the field. Again, the in-homogeneous nature of practical superconducting ma-terials can give problems in magnetic measurements.The most common occurs in superconductors where ahigh-.H, phase precipitates at the grain boundaries oflower critical field material. The magnetic techniquessee this layer, and the resulting signal is indistinguishablefrom that which would be seen if the entire grain wereactually in the superconducting state. In the "normal"situation of simply inhomogeneous superconductors,the inductive signal will tend to have a broader spreadthan the resistive one and, in general, will give a lower

105

critical field value for a given material. Also, the mag-netization change, AM; tends to be very small for high-H., materials.

Specific heat. Measurement of the variation of thespecific heat as a function of temperature through thesuperconducting transition is generally considered to bethe best experimental method for characterizing super-conducting materials of all sorts. It is the only one thatcan potentially indicate the amount of superconductingmaterial present and, at least in concept, indicate thepresence of superconductors with different transitiontemperatures or fields. However, it requires a relativelycomplex experimental apparatus for accurate mea-surements. Its use in the measurement of critical fields isfurther complicated by the effect of the field on thethermometry and the lengthy measurement times, but ithas been used successfully for measurements on Nb3 Snin an 18 T field [29]. The temperature variation of thespecific heat for an idealized superconductor is shown infigure 13. An excellent review of the theory and experi-ment with specific applications to superconductors isgiven by Stewart [30] and a general treatment of specificheat at low temperatures by Sparks [26]. Briefly, thediscontinuity at the critical temperature arises from thedifferent contributions to the specific heat made by nor-mal and superconducting electrons. The lattice con-tribution is small at these temperatures; it varies as T'and is unaffected by the transition. The electronic con-tribution, on the other hand, is linear in Tin the normalstate and takes an exponential form in the super-conducting state with the exponent given by -A/kT,where A is the energy gap associated with the super-conducting state. Furthermore, BCS theory gives theresult

Me

e-,LU0-

U,~

060

T/Tc

Figure 13-FBehavior of the specific heat with temperature through asuperconducting-to-normal transition [3].

ae-AATc/yT0 =2.43 (13)

for the ratio of the specific heats of the superconductingand normal states at T0 in zero field. This allows one toestimate the amount of the sample that is super-conducting, although the exact number may not holdtrue for some of the more exotic materials [30]. Further-more, if data can be taken to well below the transitiontemperature, a much more accurate determination of thenormal component of the sample can be made. Becauseof the temperature dependences just described, the onlycomponent of significance well below the transition isthe yT term of the normal material. The ratio of thisterm to the value of yT above the transition is then adirect measure of the fraction of the sample that is notsuperconducting.

Other methods. The three techniques just mentionedare the only ones in common use for critical field deter-mination. However, a few other methods have beenused on occasion. Foner and colleagues [31,32] describean rf (5 to 20 MHz) technique, useful for measuring H,2in powdered or odd-shaped samples, in which losses inan induced rf current are measured with a bridge ar-rangement. The technique is said to effectively monitoronly the superconducting regions of the sample so that,in concept, it would allow determination of multiplecritical field values of materials within a composite. Thefirst of the papers also makes reference to a microwavetechnique.

The use of ultrasonics for critical field determinationis discussed by Neuringer and Shapira [33]. The paperpresents an in-depth analysis of the theory and experi-mental data showing the rapid increase in the attenu-ation of a 10 MHz signal on field-induced transition tothe normal state in a NbZr alloy.

Comparisons. A few experiments have comparedthe critical temperature (not critical field) of a singlesample as determined by several of the methods outlinedabove. They have (wisely) used samples of either puretype I material [34], carefully prepared niobium [25, seefig. 12], or single-phase alloys [33]. In all cases quitegood agreement was obtained between measurementsby all of the techniques, indicating that, in general, lackof agreement among different techniques applied tocomplex materials is due to the inhomogeneous natureof the composite rather than problems with technique.In fact, differences between the inductive and resistivemethods have been used recently to investigate crackformation in the reaction layer of a Nb3Sn multi-filamentary composite [35].

106

3.3 Apparatus

The specific apparatus required for the measurementof critical field by any of the techniques discussed hereare adequately described in the references. General lowtemperature experimental methods are the subject ofnumerous texts (see [26] and references therein). Herewe mention only two apparatus topics that are specificto critical field measurements, sample configuration andhigh-field magnet systems. For ease of discussion weassume that the sample is a wire and we use the resistivetechnique as our model, although the comments shouldusually apply to any other arrangement.

The measurement of critical parameters requires thatthe sample be mounted in such a manner that it will beas strain-free as possible after cooldown, but which as-sures that it will not be able to move under the effect ofthe applied field and current, while still maintaininggood thermal contact with the bath. Figure 14 showsthe most common sample mounting schemes. Each hasits own pros and cons which have been discussed indetail elsewhere [24]. A particularly difficult problemhas to do with the transfer of current in and out of thefilaments in response to proximity to current contactsand to changes in field magnitude or orientation. Caremust be taken that the measurement region is one in

Short Straight

Hairpin

Coil

Long Straight

Figure 14-Commonly used configuration for samples for the mea-surement of critical parameters by the resistive method.

which the current has attained a stable distribution. Ifthe measurement involves sweeping a field, one shouldbe aware that current transfer among filaments will beoccurring during the sweep.

Magnet systems that attain fields much in excess of10 T are not generally available. This makes direct mea-surement of the critical field of the more interestingmaterials at low current densities impossible. Thus, mostlaboratories use approaches that involve the extrapo-lation techniques discussed below. In the larger labora-tories, steady fields of 12 T are available in reasonablevolumes using superconducting magnets and fields to20 T with normal magnets. Hybrid superconducting-normal systems exist that reach fields as high as 30 T.Beyond that is the region attainable only with pulsedmagnet techniques. These magnets allow one to achievefields in the 50 T range for very short periods of time(tens of ms) and the rapid field changes introduce awhole new set of problems into the measurement.

3.4 Sources of Error

It is possible to do a detailed error analysis for each ofthe critical field measurement methods described. How-ever, it will nearly always show that the measurementitself can easily be made with an accuracy near 5% andsomewhat better precision (near 2%) if care is taken inthe determination of the magnetic field and its uni-formity and in the suppression of electronic noise. Thislevel of accuracy is usually quite adequate for most pur-poses outside of the basic research laboratory. The realproblem is the uncertainty in the critical field due tostress and nonuniformity of material in the sample andthe effect of choices of criterion and measuring currentor other experimental parameters on the final result, beit H.2 or the transition width. Reasonable care in thepreparation, characterization, and mounting of the sam-ples is called for here. In pulsed field techniques caremust be taken to prevent inductive heating of the mate-rial. Other rise-time effects appear to be negligible in thepulsed measurements [27]. In the more conventionalmeasurements, slowly sweeping field or temperatureseems to introduce no errors. At least it has been shownthat the value and width of the transition is essentiallythe same whether one holds temperature fixed andsweeps the field or vice versa [36].

3.5 Extrapolation Methods

The value of the critical field for modern super-conducting materials at the temperatures of interest isusually very high and, thus, unattainable in most labora-tories. Several extrapolation methods are commonlyused to allow determination of H,2 at 0 or 4 K from otherdata on the critical parameters. The two common meth-

107

ods are the use of data on the variation of H42 with Tnear the critical temperature. where H, is relativelylow, and extrapolation using pinning theory of the crit-ical current-versus-field behavior. Each of these meth-ods depends critically on the use of theory to guide theextrapolation and each has reasonable success with cer-tain materials and fails rather dramatically with others.For this reason, it is not possible to say that any onetechnique is "correct." It depends on the material towhich it is applied. Also, these problems with cor-rectness of the extrapolation are in addition to the prob-lems already discussed related to the determination ofthe transition value from the experimental data. A smallproblem with terminology arises here also in that theextrapolated upper critical field is nearly universallydesignated H t2, a term already used (see eq (7)) to indi-cate the theoretical critical field in the absence of para-magnetic limiting. In some cases there is no problemwith this dual usage, but in others there definitely is theopportunity for some confusion.

Criticalfield versus temperature. This technique re-lies on the result from GLAG theory:

H*2(0)=a[dHc2dT]Tr.r:Tl, (14)

where a is a constant equal to 0.69 for dirty materials andto 0.72 for clean ones. To use this method, the criticalfield value is measured in the region near T. and theresulting plot is used to get the slope and the criticaltemperature. Typical data from the literature are shownin figure 15. The success of this method depends on howclosely the material obeys the simple GLAG theory.The relationship in eq (14) can also be modified to ac-count for various effects like paramagnetic limiting be-fore the extrapolation is made, but this requires a knowl-edge of the material properties that may not exist. Also,the value of the differential is strongly dependent on themeasuring current, with changes of as much as 30%reported for an order of magnitude change in the cur-rent [22]. As an example, note the widely different val-ues obtained for the critical field of NbSn in the twoplots in figure 15. One cannot really say that currentdensity was the cause of the difference, but it is a strongpossibility. Thus, the chance of agreement of an extrap-olated measurement of this type with the upper criticalfield measured directly depends on the measurementparameters and also on the extent to which the subjectmaterial can be described by the various theoreticaltreatments available. In this latter situation, the commonmaterials are in not too bad shape. Commercial qualityNb3Sn is agreed to be a simple GLAG-theory material,while the NbTi alloys show only a small amount ofparamagnetic limiting of H,,. On the other hand V3 Ga

has a strong paramagnetic limit and the more exoticmaterials, such as Pb-Mo-S, cannot in general be fit tothe theory even with the extensive modifications avail-able for use in the literature.

There is another reason that one desires to have accu-rately measured data on the quantity dHW,/dT near T,: itallows an experimental determination of the electronicspecific heat coefficient, Ay, that figures prominently inmuch of the theory. Comparison of eqs (15) and (5)show that the differential divided by the normal re-sistivity gives the value for gamma, assuming the propertheoretical value has been used for the proportionalitycoefficient. Application of this concept to numerousNbTi alloys is given by Hawksworth and Larbalestier

[8].

Critical current versusfield. Methods of assuring thata sample is at a fixed temperature other than that of aliquid helium bath are not easy to achieve experi-mentally. This fact makes the measurements just de-scribed quite difficult. An alternative technique is to usecritical current data taken as a function of magnetic fieldat relatively modest fields and use pinning theory toextrapolate the data to zero critical current, whichshould occur at H42. The success of this method dependsnot only on the correct measurement of the critical cur-rent, but also on knowledge of the exact behavior of thepinning force with field strength. For NbTi alloys, theexpression,

FJ=c H,`h(l-h), (15)

has proven useful in some instances [39], although thevalue of the exponent is not certain, being in the range2.0 to 2.5 in most cases. Under the proper circumstancesa simple linear extrapolation of J. to zero is acceptable1221. The material most investigated by this technique isprobably Nb3 Sn. The pinning force expression as de-rived by Kramer (see the discussion for eq (12)) for thismaterial is

(16)

where K, is a constant for the conductor. The value of K,and its dependence on H,2, ic and other parameters maychange slightly depending on the particular theoreticalmodification chosen for the scaling [11]. In any event, itis conventional to rewrite eq (16} as

(J, H)' =K,1Hoa512(H( H-H), (17)

so that the equation becomes effectively linear in H. Thequantity on the left hand side of the equation is thenplotted as a function of applied field and a linear extrap-olation made to zero. This method is illustrated by the

108

F,=K, h1(l-h)2,

4 8 12 16 20

TEMPERATURE. K

Figure 15-Typical data showingthe behavior of the slope of H0 2

versus Tnear T, for several com-mon materials. The upper graphis from [37] measured with a cur-rentdensityof I.OA/mm'. Theex-trapolated value of Foll for theNb,Sn sample is 18.45 T. Thelower graph, from [381, showsdata taken at a current density of0.02 A/mm 2 and a fit to thosedata using the simple GLAGtheory expression (eq (14)).

4 8 12 16

TEMPERATURE. K

plot of 4.2 K data shown in figure 16 in which the actualbehavior of the curve is also shown, indicating the de-parture observed at low current values. This conductoris the same one as shown in the lower part cf figure 15.The present extrapolation results in a significantly lowervalue for H, 2. In another instance the same author ob-

served this method to give values for Nb 3Sn that weretoo high compared to those obtained by direct mea-surement [20]. Furthermore, it has been seen that theextrapolation is not useful for highly aspected conduc-tors such as tapes [11]. Application of the method toother high field materials requires a reevaluation of the

109

8

6

I.-

04

2

00

30

I-CujC-

XS01.

20

10

00

20

Figure 16-Determination of theupper critical field of Nb3 Sn bythe Kramer plot extrapolation[38]. The dashed line shows theextrapolation. Measured valuesare also shown in this region.Note that this sample is also theone for which data are shown inthe lower part of figure 15.

24

MAGNETIC FLUX DENSITY, T

constants used in eq (12) and effectively requires a moredetailed analysis than the linear plot [19].

3.6 Reporting of Data

Since part of our goal is to evaluate the structure of astandard for critical field measurement, one consid-eration that is always of importance is the content of anadequate report of measurement. The many problems(or potential problems) outlined above seem to call for avery detailed report if an adequate assessment of theresults is to be made by a reader interested in applyingthem to his own problem or evaluation. We suggest thefollowing listing be used as a guide to the necessarycomponents of a report. Clearly, not all parts will berequired in every case.

How the transition was determined from the rawdata, including voltage or electric field criteria (whereappropriate) and the point on the transition curve cho-Sen for the reported value.

Width of the transition between stated limit points.

Details of sample geometry, internal structure,orientation with respect to the measuring field, mount-ing method considering questions of induced strain andthermal contact (for variable temperature methods).

Variable temperature methods require carefulassessment of the effect of magnetic fields on the ther-mometry. Methods of calibration used to account forthis effect should be described.

Results

The critical field with correct symbol [e.g., ].(T),

Measured directly or extrapolated.

Temperature of stated value (may or may not betemperature of measurement).

Estimated accuracy of the value given.

Experiment

Measurement technique used.

Each measurement method has its own set ofreporting requirements. Most are the typical error andparameter choices related to any measurement withsuch a system. A few are of prime importance for crit-ical field measurement reports.

Resistive transition-the current density, voltageprobe separation, distance of voltage taps from thecurrent contacts.

Magnetic technique-the exact method used, sam-ple mass, magnitude of measurement fields (for in-ductive methods), calibration technique and accu-racy, noise on unprocessed signal.

110

400 ~1

I

-

m

CY-o

3001

200i

100

1 1 1

Nb3 Sn conductor

10,000 filaments0.4 mm diameter

Ba 2

n1 I I "n IU U-%0 12 16

-

Specific heat-thermometer calibration and re-lationship to sample temperature, sample mass, ad-denda loss evaluation, heater power levels.

Modern data collection techniques frequently involveprocessing of the data very early, perhaps even before itis seen by the experimenter. All such processing stepsshould be mentioned.

A point that is often neglected is the accuracy of theapplied magnetic field measurement. Calibration ofmagnets, including evaluation of field inhomogeneityand, in the case of superconducting magnets, the effectof frozen-in flux is a difficult task. It is suggested that acalibration check be made every several months andcertainly when the magnet system is first put into ser-vice.

Extrapolation

Details of an extrapolation technique should begiven including:

The exact method used, including modifications tothe theory employed and the actual equations.

The range of actual data used in the extrapolation.

If at all possible, a graph showing the data and theresult of the extrapolation (see fig. 16).

4. Conclusions

As we mentioned at the beginning, the purpose of thisinvestigation is to evaluate the desirability and feasibilityof creating a standard for measurement of the criticalfield of practical superconducting materials. The type ofstandard under consideration is that typically producedby organizations such as ASTM to assist in commerce.Two standards already exist in the field of super-conductivity, one for general definitions [43 and theother for the measurement of critical currents below600 A 11]. Such standards are created by consensusamong all interested parties and must be able to be usedby industrial laboratories in their day-to-day operation.A further consideration is that there should be a demon-strated need for the standard, at least in the forseeablefuture.

A standard of this type can take several forms. It maybe any of the following: a list of definitions; a manualoutlining accepted measuring and reporting methods; adetailed method of measurement in which apparatus,technique, and report format are specified; or it may bean artifact or standard reference material. Whatever theform, it is essential that the standard be backed up with

adequate research to document the need for each re-quirement of the standard. This is not a trivial problem,and it is often neglected in the rush to create a standardto solve a particular problem. Our feelings regarding theneed for and structure of a standard are given below, Insummary it seems that the time is not yet ripe for afull-fledged standard, but there is some justification forcreating a list of standard definitions and, perhaps, an"operation manual" or similar document. A standardreference material approach might also prove useful, butwould be quite expensive.

4.1 Need for a Standard

Standards of the sort discussed here are usually cre-ated in response to a need expressed by the community.In the case of critical field, there has been a limitedexpression of need. The commercial materials now inuse are, in general, adequately characterized by theircritical current versus field characteristic. Critical fieldinformation is of most use to that group of researcherswho are trying to construct better practical materials forhigh field applications by modification of the crys-tallographic or electronic structure of various existingmaterials, This group should agree among themselveson the requirements for an acceptable measurement ofthe critical field, but that is not adequate reason forcreating a standard. It is entirely conceivable that veryhigh field materials may become feasible in the future,and the need could become great for a critical fieldstandard for commercial versions of those super-conductors. We do feel that a few definitions related tothe critical field measurement should be added to thegeneral definitions standard, mostly the various mod-ifications of H, discussed above. Furthermore, it is pos-sible that certain groups, such as DoE, might want tospecify a critical field measurement method and dataanalysis technique for a particular material. This couldbe done, but it would require that some of the researchmentioned below be performed first if the documentwere to have very wide application.

4.2 Measurement Standards

As should be clear from the analysis above, the cre-ation of a detailed single measurement standard for crit-ical field is probably impossible given the current stateof knowledge regarding the factors that influence H,2and the inhomogeneous nature of the superconductingportion of the practical conductor composite. However,if an attempt were to be made, there are a few items thatshould be considered. The only measurement techniquethat is likely to be widely used in industry is the resistivemethod applied at 4.2 K. A clever application of aninductive technique might also be possible, but none has

111

appeared to date. Similarly, the possibility of routinedirect measurement is remote because of the expense ofhigh field magnets. Thus, extrapolation techniqueswould have to be used and most likely those would becritical current versus field extrapolations with the mea-surements made at 4.2 K. Extensive research on thepinning force phenomenon would be necessary. Signifi-cant advances in understanding the effect of crys-tallographic and metallurgical variations on the criticalfield would be required. All these requirements could bemitigated somewhat by the use of a standard referencematerial as discussed below, but research on the mea-surement methods and their related errors would still beneeded. A standard method should use a relatively highcurrent density, probably in excess of 100 A/mm 2 ,which would avoid some of the problems, but wouldresult in lower critical field values.

4.3 Standard Reference Materials

This approach to the standardization of critical fieldmeasurements is probably the most appealing for thepresent circumstances. Unfortunately, it is also a veryexpensive solution. The idea is to make a series of verywell characterized materials that could then be distrib-uted for the calibration of apparatus. Such materialscould also be used to evaluate the various extrapolationtechniques. The characterization would require verycareful work, expertise in several measurement andanalysis techniques, access to high field magnets, and aconsensus as to the proper choices for the importantparameters. However, considerable progress is now be-ing made in understanding the interactions between themetallurgy and the superconducting properties of thesematerials which may well result in an advanced (prac-tical) superconductor with well-documented homoge-neity and internal structure in the near future. This con-ductor, if it can be made in significant quantities, wouldbe an ideal candidate for a critical field SRM.

It is a pleasure to acknowledge the help of the entireNBS Superconductors and Magnetic Materials group,headed by A. F. Clark, through many conversations andsuggestions. Special thanks are due R. B. Goldfarb forassistance with the subtleties of the field of magneticunits and J. W. Ekin for helping to keep the practicalitiesof the topic in the foreground. Much of the informationon early experimental techniques was obtained from un-published notes carefully prepared by D. T. Read. Mrs.V. Grulke cheerfully prepared the manuscript, withonly occasional comments about amateur word-processor users.

References

Listed here are references from the recent literaturein which the measurement or interpretation of criticalfield data are discussed. Those used as text referencesare numbered and make up the first part of the listing.The others, listed alphabetically following the textreferences, serve to provide background information.Only a few of the many excellent theoretical treatmentsare included.

[I] ASTM Standard for the Measurement of Critical Current(1983).

[2] Powell, R. L., and A. F. Clark, Definitions of terms for practicalsuperconductors, 1. Fundamental states and flux phenom-ena, Crogenics 17, 697-701 (1977).

[3] Powell, R. L., and A. F. Clark, Definitions of terms for practicalsuperconductors, 2. Critical parameters, Cryogenics 18,137-141 (1978).

[4] ASTM Standard for Superconductor Terminology (1983).[5] Matsumoto, H., and H. Unezawa, Interplay between magnetism

and superconductivity, Cryogenics 23, 37-51 (1983).(6] Fickett, F. R., and R. B. Goldfarb, Magnetic properties, Chap-

ter 6 of Materials at Low Temperatures, American Societyfor Metals, Metals Park, Ohio (1983).

[71 Nelson, R. A., SI: The international system of units, publishedby the American Association of Physics Teachers, StonyBrook, NY (1983).

[8] Hawksworth, D. G., and D. C. Larbalestier, Enhanced values ofH,2 in NbTi ternary and quaternary alloys, Adv. Cryo. Eng.26, 479-486 (1980).

[91 Cody, 0. D., Phenomena and theory of superconductivity,Chapter 3 of Superconducting Magnet Systems, H. Brechna,ed., Springer-Verlag, New York, pp. 159-229 (1973).

[10] Beasley, M. R., New perspective on the physics of high-fieldsuperconductors, Adv. Cryo. Eng. 28, 345-359 (1982).

[11] Suenaga, M., and D. 0. Welch, Flux pinning in bronze-processed Nb 3Sn wires, in Filamentary A15 Super-conductors, M. Suenaga and A. F. Clark, eds., Plenum Press,New York, pp. 131-142 (1980).

[12] Hulm, J. K., and B. T. Matthias, Overview of superconductingmaterials development, Chapter I of Superconducting Mate-rials Science, S. Foner and B. B. Schwartz, eds., PlenumPress, New York, pp. 1-61 (1981).

[13] Ekin, J. W., Superconductors, Chapter 13 of Materials at LowTemperatures, American Society for Metals, Metals Park,Ohio (1983).

[14] Huhm, J. K.; J. E. Kunzier and B. T. Matthias, The road tosuperconducting materials, Physics Today, pp. 34-44 (Jan.1981).

[15] Hulm, J. K., and B. T. Matthias, High-field, high-current super-conductors, Science 208, 881-887 (1980).

[16] Fietz, W. A., and W. W. Webb, Hysteresis in superconductingalloys-temperature and field dependence of dislocation pin-ning in niobium alloys, Phys. Rev. 178, 657-667 (1969).

[17] Kramer, E. J., Scaling laws for flux pinning in hard super-conductors, J. Appl. Phys. 44, 1360-1370 (1973).

[18] Ekin, 1. W., Mechanical properties and strain effects in super-conductors, Chapter 3 of Superconductor Materials Science,S. Foner and B. B. Schwartz, eds., Plenum Press, NewYork, 1981, pp. 455-509.

112

[19] Ekin, J. W., Four-dimensional J-B-T-c critical surface for super-conductors, J. Appl. Phys. 54, 303-306 (1983).

[20] Rupp, G., Parameters affecting prestrain and Bc, in multi-filamentary Nb3Sn conductors, Adv. Cryo. Eng. 26,522-529 (1980).

[211 Larbalestier, D. C., Superconducting materials-A review ofrecent advances and current problems in practical materi-als, IEEE Trans. Mag. MAG-17, 1668-1686 (1981).

[22] Evetts. J. E., The characterization of superconductingmaterials-Conflicts and correlations, IEEE Trans. Mag.MAG-19, 1109 (1983).

[23] Lee, Z. H., K. Noto, Y. Watanabe, and Y. Muto, A new aniso-tropy of the upper critical fields Hz in the Cu,8,M6 S, singlecrystal, Physica 107B, 297-298 (1981).

[24] Goodrich, L. F., and F. R. Fickett, Critical current mea-surements: A compendium of experimental results, Cryo-genics 22, 225-241 (1982).

[251 Schooley, J. F., and R. J. Soulen, Definition of the criticaltemperature of practical superconductors, in Developmentof Standards for Superconductors, F. R. Fickett and A. F.Clark, eds., NBSIR 80-1629 (1979) pp. 20-26.

[26] Materials at Low Temperatures, R. P. Reed and A. F. Clark, eds.,American Society for Metals (1983).

[27] Fischer, O.; H. Jones, G. Bongi, M. Sergent, and R. Chevrel,Measurements of critical fields up to 500 kG in the ternarymolybdenum sulphides, J. Phys. C; Solid State Phys. 7,L450-L453 (1974).

[28] Hein, R. A., and R. L. Falge, Differential paramagnetic effect insuperconductors, Phys. Rev. 123, 407-415 (1961).

[29] Stewart, G. R.; B. Cort and G. W. Webb, Specific heat of A15Nb 3Sn in fields to 18 Tesla, Phys. Rev. B 24, 3841 (1981).

[30] Stewart, G. R., Measurement of low-temperature specific heat,Rev. Sci. Instrum. 54, 1 (1983).

[31] Foner, S.; E. J. McNiff, Jr., B. T. Matthias, and E. Corenzwit,Properties of high superconducting transition temperatureNb 3 Ali,-Ge. alloys, Proc. Eleventh International Confer-ence on Low Temperature Physics I1, 1025-11032 (eds. J.F. Allen, D. M. Finlayson, and D. M. McCall) St. Andrews(1968).

[32] Foner, S., High field superconductors, Colloq. Int'l. CNRS 242,423-429 (1975).

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