Specific heat and the lattice transformation in Nb3Sn

Solid State Communications,

Vol.7, pp.37—39,

1969.

Pergainon Press.

Printed in Great Britain

SPECIFIC HEAT AND THE LATTICE TRANSFORMATION IN Nb 3Sn L.J. Vieland and A.W. Wicklund RCA Laboratories, Princeton, New Jersey, U.S.A. (Received 22 July 1968)

The specific heat anomaly associated with the tetragonal—cubic lattice transformation in Nb3 Sn has been measured. Specific heat X-ray, and velocity of sound measurements on single crystal Nb3Sn cannot be reconciled within the framework of current theories of the transformation.

Nb3Sn has been found to undergo a lattice transformation from a low temperature tetragonal phase to the a-tungsten (cubic) structure at Tm = 43°K.’ The lattice instability of the cubic 2 as state is observed in ultrasonic measurements an anomalous decrease in certain elastic constants with decreasing temperature. In particular, the restoring force for the shear mode corresponding to the tetragonal distortion [(C 11 —C12 )/2] is found to approach zero near Tm. Current theories of the transformation3’4 predict a first order phase change near the temperature T’ at which C 11 = C 12, while X-ray evidence’ suggests that the transformation is second order, there being no observable thermal hysteresis.

design. Temperature was measured with a Pt resistance thermometer obtained from Rosemount Engineering Company, and calibrated by the manufacturer. The specific of total the calibrated addendum amounted to 1/_3/ heat of the specific heat for various samples. Near the peak the data were obtained using temperature increments of about 0.2°K. The results are shown in Fig. 1. The closed circles (sample I) are for a 2.6 g 5 polycrystalline vapor grown material, with a relativelyboule broadofsuperconducting transition extending from 17.75K to 18.00K, while the crosses represent data on a sample of sintered Nb3Sn (PS-i) exhibiting a sharp transition at 18.1K. Below 43K and above 58K, the results for the two specimens were indistinguishable. While the absence of a specific heat peak for PS-i suggests that this sample does not undergo a transformation in the temperature range of the measurement, it has been reported that X-ray diffraction patterns for sintered Nb3 Sn exhibit 6 line broadening lowbehavior temperatures (T I 35°K). The inset showsatthe of sample over the entire range, together with data for a 0.8 g annealed single crystal (sample II) on which elastic constant measurements have recently been made.7 The small size of this sample precludes a precise study of the specific heat peak, but its position is consistent with X-ray data taken on material from the same crystal,5 which gave Tm = (43 ±1)K. Assuming the anomalous

We have measured the specific heat of Nb3 Sn over the temperature range 25°Kto 80°K. We find a peak in the specific heat of two high purity vaporongrown samples or at 51K, depending sample, which at we44K attribute to the lattice transformation, and no evidence of a latent heat. We are able to show that the specific heat, elastic constant, and X-ray data cannot be reconciled with the framework of the current theories of the transformation. The measurements were made by the heat pulse technique in a calorimeter of conventional 37

38

SPECIFIC HEAT AND THE LATTICE TRANSFORMATION IN Nb

3Sn

I

I

I

I

I

I

I

I

I

•SAMPLEI xPS-I

I

I

Vol.7, No.1

I~

X• XX

9. •

.

• . ..x x •.

•

X

•

x

S

. .

X

x

S

•.

X S

:

8

••‘

x

14

~

~ 20 30 40

I

I

I

I

I

I

I

I

50 60 70 80 T(°K) I

I

I

I

43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 T (°K) FIG. 1. Specific heat of three samples of Nb3 Sn: I, high purity vapor grown crystal; PS-i, sintered material; II, vapor grown single crystal showing a lattice transformation by X-rays at Tm = 43°K. electronic contribution to the elastic constants to be the same for.samples I and II, the difference in Tm follows in quantitatively from the~ apparent difference Debye temperatures. According to the theories of Labbé and 3 and Cohen etal.,4 the transformation Friedel, is of the Jahn—Teller type, in which the threefold degeneracy of the orthogonal d sub-bands, arising from interaction along the transition metal chains in the ~-W structure, is removed by the strain accompanying the cubic to tetragonal transition. The fundamental postulate of’ the theory is that the free energy difference 3F between the tetragonal and cubic states is uniquely determined

by the strain = (2/3)(c/a — 1). Near Tm, i.e., for small strains, ~F can be expanded 4 + ...in a. power The series in ; 6F = ~4 2 + B ~ + Ce leading term in the expansion is simply related to the first order elastic constant by A = ~ (C ~, —C in internal energy, obtained12). fromThe thedifference Gibbs—Helmoltz equation AU = AF — T (~(AF)/~ T)~, is AU( T) ~ —T 2(T)

+

T

+

dT

e4

~+

...)

,

(1)

dT

where (T) is the equilibrium value of which minimizes the free energy, and we have dropped the term AF, which is of order (AT/T)(Ta(AF)/aT) Dropping higher order derivatives, B we have

Vol.7, No.1

SPECIFIC HEAT AND THE LATTICE TRANSFORMATION IN Nb3 Sn

T

2 CT)

c

of themaximum specific latent heat peak a 0.3K (The heatover which could interval. have escaped detection is of the order of 0.05 J/g-atom). Equation (2) is therefore clearly violated, and it appears that the free energy expansion is not satisfactory.

(2)

AU = ACdT Tc \.dT,JT The area under the specific heat peak (including any latent heat) can, therefore, be related through the general expansion of the free energy in powers of to the experimentally determined strain and temperature dependence of the soft shear mode near Tm -‘-~

39

—

From the model of Reference 4 the peak in specific heat near Tm (exclusive of the latent heat) is found to be 0.8 J/g-atom-K,9 in agreement with the data of Fig. 1. The absence of an observable latent heat is not attributable, therefore, to a smearing of the transition due to domain formation. Within the context of the independent

Acoustic measurements on sample II~show the soft shear mode vanishing linearly with ternperature with a slope dA/dT of 1.1 x 1010 dyn/cm2-K. The slope is constant over a range of 25K, the lowest measured value of C 11 —C12 being about 0.7 per cent of the room temperature value. Taking the strain measured ‘within a fraction of a degree’ of Tm to be 2 X gives for the right hand side of (2) a difference in internal energy of 2J/g-atom, or about ten times larger than obtained directly by integration

sub-band model, the lattice transformation is of second order. Acknowledgements We are greatly indebted to Drs. R.W. Cohen and G.D. Cody for their helpful criticisms of the manuscript, and to Dr. J.J. Hanak for supplying the crystals. —

REFERENCES

J.J.,

1.

MAILFERT R, BATTERMAN B.W. and HANAK

2.

KELLER K.R. and HANAK

3. 4.

LABIlE J. and FRIEDELJ., J. Phys. Radium, Paris 27, 153 (1966). COHEN,R.W., CODY G.D. and HALLORAN J.J., Phys. Rev. Leti. 19, 840 (1967).

5.

HANAK J.J. and BERMAN H.S., Crystal Growth p. 249. (Supplement to Phys. Chem. Solids) Pergamon Press, N.Y. (1967). Samples I and II are specimens 6 and 5 respectively of this reference, after annealing. Data taken on sample II prior to annealing is reported in references 2 and 4, and subsequent to annealing in references 1, 7 and the present work.

6.

BATTERMAN B.W. and BARRETT C.S., Phys. Rev. Lett. 13, 390 (1964).

7.

REHWALD W., to be published. V is found to be 49.7K, with some difficulty reported in interpreting the data below about 60K. The relative contributions of these terms are model dependent. Using the band structure of Cohen et al, we find the error introduced into equation (2) to be about 10 per cent. COHEN R.W. and VIELAND L.J., to be published. The data of reference 7 gives slightly different results than those of reference 4 for the parameters of the theory obtained from the elastic constants above Tm the only important difference beingthe change in T from 32K to 49.7K.

8. 9.

Phys. Leti. 24A, 315 (1967).

J.J., Phys. Rev. 154, 628 (1967).

,

Die Anomalie der spezifischen Wärme von einkristallinem Nb3 Sn, die bei der Transformation vom tetragonalen zum kubischen Gitter auftritt, wurde gemessen. Diese Messungen zusammen mit Messungen der Gitterkonstanten und der Schallgeschwindigkeit können nicht im Rahmen der bestehenden Theorien fur die Transformation erklãrt werden.