Magnetic and caloric effects in a hard superconductor

Goedemoed,

Physica

S. H.

Van Kolmeschate, De Klerk, Gorter,

30

1225-1228

C.

D.

C. J.

1964

LETTER

Magnetic § 1. After properties

and caloric effects in a hard superconductor

the publication

of our foregoing

of superconducting

The apparatus

TO THE EDITOR

was similar

niobium,

note in Physics

we investigated

to the foregoing

r) on the magnetic

one, but since the investigations

carried out between

the poles of an electromagnet

of two sets, parallel

to the field, one of them containing

were wound in such a way that the influence

Letters

a new sample in higher fields.

the mutual induction the niobium

were

coils consisted

sample. The coils

of the pole tips of the magnet

on them was

negligible. The sample glued together A carbon suspended ature).

of 100 parallel a constantan

thermometer

wires of 0.1 mm diameter on the surface gas atmosphere

each experiment in the sample.

to the temperature

of the bundle. (about

The sample

was

3 mm at room temper-

the sample was heated up in zero field, by means of the

wire, to a temperature

flux

and 33 mm length,

wire.

was painted

Before

returned

around

in a glass tube in a helium

constantan residual

consisted

After

well above

T,;

the heating

of the liquid

so we were sure that there was no

current

helium

was switched

bath within

off the sample

a fraction

of a second.

k2

-I -4nM I ’ -!O

0

-5

Fig.

1. Hysteresis

n

’

18

1

-tL5

loops for impure

-

kOe

10

niobium.

0 4.2”K, v 3.31”K, q 2.11”K, A 1.03”K The curves are interrupted in the regions where flux jumps have been observed.

5 2. Magnetization

curves

and hysteresis

loops were

measured

atures. Some of them are shown in fig. 1. From the much flatter

at several

maxima

temper-

of the curves

and from the negative slope of the magnetization in decreasing fields it follows that this sample was much “harder” than the one of our foregoing paper. This follows also

-

1225 -

1226 S.H. GOEDEMOED, C. VAN KOLMESCHATE, D. DE KLERK AND C. J. GORTER from the residual resistance:

RIO/R 300 = 0.199;

for the foregoing

sample we had

R~CJ/R~OCJ = 0.127.

Smooth curves were found at the higher temperatures. Below 3°K regions were found where the magnetization curve showed a dip. Here the scattering of the experimental points was much larger. These are the regions where “flux jumps” occur. They will be discussed separately. From the linear parts of the magnetization curves at the higher fields, we could extrapolate values for the upper critical field H,,. The H,, versus T diagram derived from them shows a straight line for T > 3”K, leading to T, = 8.9”K. At temperatures below 3°K the curve is rounded off, extrapolating to 9400 Oe at absolute zero. The diagram is somewhat better in agreement with the Ginzburg-Abrikosov theoretical curve 2) than with the one of Gorkov 3). If we suppose that the thermodynamic critical field H, at absolute zero is 1944 Oe4) 5) and if we assume that the transition curve is a parabola with T, = 8.9”K, we find that the parameter H,,/H, is equal to 4.2 at the boiling point of liquid helium and 4.8 at absolute zero. Recently DeSor bo investigated a number of niobium samples contaminated with various amounts of oxygen and nitrogen 6). They all had different values of T, and of H, and H,, at 4.2”K. Smooth curves are obtained if his values of T, and H, are plotted against the corresponding H,, data. We don’t know what the impurity in our sample is, but it appears that our T,-values fits very nicely to his curve. The corresponding H, at 4.2’K, read from his curve, is 1410 Oe, and this leads to HcJHc = 4.5 at 4.2”K. § 3. It was possible to observe the temperature of the sample during the variation of the magnetic field. This was done by measuring the voltage over the carbon thermometer with the help of an oscilloscope. It took about 15 s to increase the field from zero to 10 kOe. Plots of H, M and T as functions of time at 4.2”K are given in fig. 2. Here the four quadrants of the hysteresis loop are plotted separately. The T- and H-curves represent the direct measurements; the M-curves were constructed with the help of fig. 1. The experiments at lower temperatures showed that the flux jumps, mentioned above, are accompanied by pronounced temperature jumps, up to several tenths of a

k

/ \ -t2

Fig. 2. Variation

4

6

8 s -_~2

4

6

8 I _Lz

4

6

0s-_t2

4

6

0s

of field, magnetization and temperature with time for the four quadrants of the hysteresis loop at 4.2”K.

MAGNETIC

AND

CALORIC

EFFECTS

IN A HARD

SUPERCONDUCTOR

1227

degree. (one occasional jump occurs at the end of the third quadrant of fig. 2). They have always the same character. The rise is very steep and they go down exponentially with a l/e-time of about 0.1 s. The steep rise indicates a very good thermal conductivity of the sample (we estimate an upper limit for the equilibrium time of 0.02 s). The decrease after the maximum shows that the heat is carried off by the helium gas surrounding the sample in a fraction of a second. These facts were checked by discharging a condenser through the constantan wire. This caused a very similar rise and fall of the carbon thermometer. (it should be realized that the constantan heater is at the centre of the sample, and that the thermometer is on the outer surface). The fact that the heat is carried off in a time long as compared to the thermal equilibrium time of the sample, and short as compared to the time needed to increase the field to the maximum value, indicates that the temperature curves of fig. 2 may be considered as equilibrium curves. By applying a constant current through the constantan wire, we could interconnect the temperature rise and the heat development per unit time dQ/dt. So it was possible, at least in the temperature region where no flux jumps occur, to integrate the total amount of heat, generated during the magnetization process. At the boiling point of liquid helium, it turned out that the total amount of heat, developed in the second and third quadrants of the hysteresis loop is equal to the sum of - / MdH in these quadrants within the limits of experimental precision. For the first quadrant of the loop we have, according to the first law of thermodynamics : -/MdH=TAS-AQ+AF where all the quantities are taken per unit volume. The first term on the right hand side of the equation represents the reversible heat, required in the magnetization process (the magnetocaloric effect). If the electronic specific heats of the two phases are supposed to be proportional to T and Ts we have TAS=4AF--

tz 1-

tz

with t = T/Te. The term AF is the difference in thermal free energy between the normal and the superconducting states: AF = H,~/&c. At the boiling point of liquid helium we derive from our experimental data:

leading to :

- /M

dH = 3.57 x 105 erg/cm3

-

AQ = 2.07 x 10s erg/cm3 AF = 0.70 x 105 erg/cm3 TAS = 0.80 x 10s erg/cm3 H, = 1325 Oe.

Our value for H, is 12 per cent lower than that of pure niobium at 4.2’K, which is equal to 1510 Oe. It is 6 per cent lower than the value derived from DeSorbo’s curve (see above) which leads to Ho = 1410 Oe. An explanation for this discrepancy may be that the magnetic moment and the heat development data of fig. 2 are based on different experiments. The magnetic moments were determined with a ballistic galvanometer, some ten seconds after a certain field value had been adjusted (see our foregoing note l)). The magnetization in case of a continuously varying field, however, may show retardation effects. An indication for the occurrence of such effects may be that, in the second and fourth quadrants of fig. 2, heat development is still observed a second after the field has

1228 become -

JM

MAGNETIC

AND

CALORIC

zero. If our dQ-value dH

= 4.02

EFFECTS

is assumed

x lOserg/cms,

IN A HARD

to be correct

whereas

SUPERCONDUCTOR

a H, of 1510 Oe would

H, = 1410 gives

- JM

dH = 3.77

lead to x

105

erg/cm3. The authors

wish to express

their thanks

to Mr. J. W. Met selaar

during

the experiments

and calculations,

during

the experiments

and the construction

for carrying

out the glass blowing

Gerritse Received

to Mr. T. Nie boer

for his assistance

for technical

of the apparatus,

assistance

and to Mr. A. R. B.

work. S. H. GOEDEMOED

21-4--64

C.VANKOLMESCHATE D.DE

KLERK

C. J.GORTER Kamerlingh Onnes Laboratorium,Leiden,Nederland

REFERENCES 1) Goedemoed,

S. H., Van

der

Giessen,

A., De Klerk,

D. and Gorter,

C. J., Physics

Letters

3 (1963) 250. 2) Gin z b ur g, V. L., Zh. eksp. i tear. Fiz. 30 (1956) J.E.T.P. 3 (1956) 621. 3)

Gorkov,

593;

L. P., Zh. exp. i tear. Fiz. 37 (1959) 853; English

English

translation:

translation:

Soviet

10 (1960) 593. 4) Chou,

C., White,

5) Stromberg, 6)

DeSorbo,

D. and Johnston,

T. F. and Swenson, W., Phys.

H. L., Phys. Rev. 109 (1958) 788. C. A., Phys. Rev. Letters 9 (1962) 370.

Rev. 132 (1963)

107.

Soviet

Phys.

Phys. - J.E.T.P.

-