The enthalpy of impure niobium in the mixed superconductive state

Goedemoed,

Physica

S. H.

Van

Kolmeschate,

Kes,

P. H.

De Klerk,

32

1183-1188

C.

D.

1966

THE

ENTHALPY

OF IMPURE

NIOBIUM

SUPERCONDUCTIVE by S. H. GOEDEMOED, Ckmunur~ication

No. 348~ from

IN THE

STATE

C. VAN KOLMESCHATE, D. DE KLERK the Kamerlingh

MIXED

P. H. KES

Onnes Laboratoriurn,

Leiden,

and

Nederland

Synopsis From

the simultaneous

ment during calculate

the

Gorter’s

criterion

holds

measurements

the magnetization

process

of the magnetization

enthalpy 1). This is done for an impure for flux jumping2)

in the first quadrant

and the heat develop-

of a second type superconductor can be checked.

of the hysteresis

niobium It appears

it is possible

sample. that

to

As a result this criterion

loop.

1. Introduction. When a superconductor of the second type is placed in an external magnetic field H, which is cycled up from zero (the superconductor being in the pure superconducting state: B = 0) to He, (the field at which the bulk superconductivity disappears: B = Ha) it is seen that at a certain field HC, the flux is beginning to penetrate the superconductor. During the variation of H, - between H C, and Hc, - there are two mechanisms of heat development: a) IYi,, caused by normal electron currents generated by the motion of f hlx 3) 4) ; b) JYR?” (ma g ne t o - ca 1oric effect) due to the decoupling of the superconducting electron pairs. When the magnetic moment M of the superconductor and the heat during the development W = Wiry + W rev are measured simultaneously magnetization process it is possible to calculate the variation in the enthalpy E(H,)(= U - MH,): dE(H,)

= E(Ha) -

E(0) =i[W/I& 0

-

M) dH,.

(1)

E(0) is the enthalpy in the pure superconducting state (H, = 0; B = 0); W is negative when heat is removed from the sample and positive in the opposite case. From the dE(H,) values Gorter’s criterion for flux jumpings) may be checked. This criterion is: If dE(H,) > dE,(= dE(H,J) a sudden transi-

1183 -

1184

S.

H. GOEDEMOED,

c.

VAX

KOLMESCHATE,

tion may occur, which is seen as a flux jump

1’. I-I. lilis

AND

(a discontinuous

1). DE

IiLEItli

variation

of

~$1and a peak in W 6)). 2. Experimmt. The experimental setup has bccii clcscril~cd l)rc\iouslj,5) ‘;). The sample consists of a hundred Nb wires ($ := 0.01 cm; I =:: 3.3 cm), has bran painted glued around a constantan tvire; a carbon thermometer on the surface of this bundle. The whole sample has been mounted in a glass tube, heat contact with the surrounding bath being accomplished by inserting a small amount of He gas into the tube (3 mm Hg at room temperature). The carbon thermometer on the sample is OIIC’ of thr) I~~nchr~ of a Wheatstone bridge, which is balanced in zero field at the temperature of the experiment. The unbalance voltage V of the bridge causal 1)~ the heating of the sample on variation of the field is fed to one 1)air of thtl vertical deflectors of a dual beam oscilloscope. So the deflection of this hcam depcntls on the temperature difference between the sample at (H:,, Jlia) and at during the flux pene(H, = 0, ff, = 0), h ence on the heat development tration. The correspondence between I/ and 11’ is found 1)y means of an electric current I through the constantan wire. Then V = a(T) 12

(2)

where ~(7‘) depends on among other things the geometry of the sample and the tube and on the thermal conductivity A”e of the helium gas (the thermal conductivity in the sample As being much larger than lL~~Is). With the calibration (2) it is now possible to compute from CVthe heat development per unit volume :

in which u is the volume of the supcxrconductor; f\’ is tht> rvsistancc of that part of the constantan wire that contributes to the locating of the sample. It is assumed that V corresponds to T/t-for each value of Hz,. The correctness of this assumption was demonstrated earlier 5). In eq. (2a) R is unknown; it may be determined from the results of the second and third quadrants of the hysteresis loop. When H, is cycled down from + Hc, to -Hr, it follows from ccl. (1) and E(+H,J = E(-Hc2) = II,, that -m/I,., II?.,

The magnetization curves are derived in the following way: two identical coils connected in series and wound in opposite directions have been mounted

THE ENTHALPY

OF IMPURE

NIOBIUM

around the glass tube in the homogeneous

IN THE MIXED

1185

ST.4TE

part of H, - one of them surround-

ing the sample. The net flux enclosed by the two coils is proportional to the magnetization of the sample. The e.m.f. of induction caused by the variation of M is fed into an integrating circuit, the output of which is connected to the second pair of vertical deflection plates of the oscilloscope. The horizontal deflection of the beams of the scope has been made proportional to H, by means of another coil in the homogeneous part of the field. The integrated e.m.f. of induction in this coil is fed to the horizontal deflection plates. By photographing the two traces on the scope during the magnetization process M and W are measured simultaneously. 3. Results. The curves for AE(H,), --M and -W/fi& la...h) for temperatures between 3°K and 7°K.

are shown in fig.

k erg ml3 150

150

100

100

G

50

0

200

150

100

50

0

0 5

H Fig. 1. The velopment

cnthalpy W/f?,

5

&

/1E(heavy

line),

(thin lint) as functions bctwecn

H

magnetization

5

111 (dotted

5

H

line)

kOe

and heat

de-

of the applied field H, at several temperatures 3 and 7°K.

The experiments above 4.2”K (fig. la) b) c)) have:been carried out by heating the sample by means of a suitable electric current through the constantan wire. In these cases the temperature at:Hcz is found to be somewhat lower than in zero field. This may be ascribed to the change in thermal conductivity of the sample at the transition from the superconducting to the normal state. This implies that the thermal conductivity is smaller in the normal state than in the superconducting state the leak along the

1186

S.

H. GOEDEMOED,

C. VAN

KOLMESCHATE,

P. II. KES AND

D. DE KLEKK

constantan wire becoming larger. Since the heat flow in the sample is perpendicular to the applied field Ha, this change becomes effective only when the fluxoids begin to overlap, that is near Hc,. Indeed, if the zero level of W/ri-, - there is a small magnetoresistance of the carbon thermometer ~ is taken equal to the one derived from the experiments at and below 4.2”K,

a good correspondence

(on the base of theoretical

expectation)

to those low temperature results is found (see below). The broken lines at the end of the W/Ha curves have been drawn according to those considerations. At the temperatures 3.O”K and 3.5”K (fig. 1g)Iz)) flux jumps are seen in the regions which are indicated by hatching (for the actual curves of n/rand W see ref. 6). Since in a flux jump the amount of heat involved is no longer proportional to the oscilloscope deflection6) the only reliable way to check Gorter’s criterion is to ignore all the flux jumps (both in M and W/Ei,) and to interpolate the curves smoothly.

600

400

200

0

Fig.

This is more difficult the lower the temperature (especially for the W/ri,curves) because the flux jump region broadens with falling temperature. By adapting the shapes of the curves at the lower temperatures to the character of the experimental data at the higher temperatures it is possible

THE ENTHALPY

to get fairly temperatures

OF INPURE

NIOBIUM

IN THE

MIXED

reliable interpolations at 3.5”K and 3.O”K, present insurmountable difficulties.

1187

STATE

but

still

lower

The curves of fig. 1 show the growth of a hump in dE(H,) at the lower temperatures. Below about 4°K this hump becomes a maximum and, indeed, the flux jumps at 3.5”K and 3.O”K take place in the region where dE(H,) > > LIE,. The absence of flux jumps at 4.O”K and 3.7”K, where also in small regions dE(H,) > AEn, might be attributed to the accuracy of the experiments. The same may be said for the fact that the maximum in the dE(H,)-curve at 3.5”K is somewhat less pronounced than the one at 3.7”K. In order to get an estimate of the experimental accuracy the values of -J

Hc, M dH,

and

He, - J W/Qa dH, 0

0

are plotted against temperature (fig. 2) ; the difference of these curves should be equal to LIE,. By taking the temperature dependence of the bulk critical field H,(T) (as calculated from the specific heat measurements of Ferreira e.a. 7) carried out on a similar Nb sample) a dE,-curve could be constructed (A&

= H”,/8n -

T ;

(H;,8z))

which gives the best fit to the experimental LIE, = 1845 Oe. Indeed the deviations of the experimental values the curve are such that a correction toward the dE(H,) curves of fig. 1 more consistent with each

values if H,(T

= 0) =

of fp2 W/E;T,dH, from curve would make the other.

4. Discu&on. The results of our experiments in the first quarter of the hysteresis loop are in remarkably good agreement with Gort er’s criterion. The flux jumps at 3.5”K and 3.O”K occur in theregionswheredE(H,) > AE,. The fact that no flux jumps are found at 3.7”K and 4.O”K, where also a region occurs where dE(H,) > LIE, may be ascribed to the lack of accuracy of our experimental data (see above); or it may prove that the criterion of flux jumping does not entail the necessity of flux jumping: it may very well be that something like a “minimum instability” is required. For instance at 3.O”K the flux jumping begins at a somewhat larger field than the crossover of the dE(H,) curve. It should be realized that the flux jumping process in our sample is a rather complicated phenomenon. The jumps are so big that a rather large number of wires must be involved, but not all of them (see also ref. 6). Go r t er’s argument implies that no decrease of temperature occurs during the jump and that one wire - or a number of wires - completely passes into the normal state before it passes again into a more or less strain free mixed state. Extra complications will occur if the individual wires of the sample

1188

THE

ENTHALPY

OF IMPURE

NIOBIUM

IN THE

MIXED

STATE

have somewhat different properties, which should of course be expecteds). It may also be a small increase of the temperature that plays an essential role; or maybe the enthalpy of the currents in the normal state cannot be neglected, and this may lead to a decreased probability of flux jumping. We also made some calculations on the second and third quadrants of the hysteresis loop *). It was found that Gort er’s criterion does not apply there, the flux jumps occur exactly where oE(H,) < AE, and no flux jumping is observed where AE(H,) > AE,. This indicates that the mechanism of the flux jumps observed here is not identical with the one encountered in the first quadrant. As a matter of fact the breaking out of flux occurring at low fields in the second quadrant does not require that the whole of the almost fluxless region near the surface of the wire passes into the normal state at the jump. In the third quadrant the situation is complicated by the flux annihilation processa) 10) 11) which may lead to a rather different type of flux jump. Rccrivrd

23-12-65

REFERENCES

1) 2)

Wasim,

S. M., Grenier,

C. G. and Zebouni,

Garter,

C. J., Commun.

Kamerlingh

3)

407. Kim,

Y. B., Hempstead,

C. F. and Strand,

A. R., Phys.

4)

Kim,

Y. U., Hempstead,

C. F. and Strnad,

A. Ii., Phys.

5)

Goedemoed,

S. H., Van

N. H., Phys. Letters 19 (1965)

Onnrs

Kolmeschate,

Lab.,

Leiden,

Suppl.

C., De Klerk,

165.

No. 123~; Physica

31 (1965)

Rev. 129 (1963) 528. Rev. 131 (1963) 2486. D. and Garter,

C. J., Physica

30

( 1964)

6)

1225. Goedemoed, Leiden

S. H., Van

No. 3425;

7)

Ferreira

8)

Kremlev,

9)

Heasley,

Kolmeschate,

Physica

da Silva,

J., to be published

M. G., Samoilov, M. R., Fietz,

D., Commun.

in Physica.

W. A., Rollins,

J. and Rollins,

R. W., Silcox,

Clevelend,

R. W., Rev. mod.

J. E., Campbell,

*) An experimental

W. J. and De Klerk,

B. N. and Skulatchenko,

Phys. of type II superconductivity, 10) Silcox, 11) Evetts,

C., Mctselaar,

31 (1965) 573.

Ohio, U.S.A.

IV-106

8 (1956)

73.

W. W., Conf. on the

(August

28 and 29, 1964).

Phys. 3(i (1964) 52.

A. M. and Dew-Hughes,

difficulty

S. S., Cryogenics J. and Webb,

D., Phil. Mag. IO (1964) 339.

was that near zero field the ai. of our electromagnet

becomes

very

small so that the value of rV/tii, becomes uncertain. Recent experiments in a superconducting solenoid, which is operated at constant l?, showed that, indeed, the values of W/as in the second quadrant near Ha = 0 are larger than we had anticipated. But this does not influence about

G or tcr’s

criterion.

our quantitative

results appreciably

and certainly

not our conclusions