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Low temperature specific heat measurements of ZrV2 and HfV2
Volume 36A, number 5
Low
PHYSICS LETTERS
TEMPERATURE
SPECIFIC
OF
HEAT
27 September 1971
MEASUREMENTS
ZrV 2 AND HfV 2
b. RAPP Department of Physics, Royal Institute of Technology, Stockholm 10044, Sweden
and L . J . VIELAND RCA Zaboratories, Princeton N.J. 08540, USA Received 3 August 1971
The C15 compounds ZrV2 and HfV2 show bulk superconductivity at 7.3 and 8.4°K respectively, indicating a strong dependence of Tc on the electron per atom number for C15 compounds. High electronic contributions to the specific heat are observed.
Superconducting t r a n s i t i o n t e m p e r a t u r e s (Tc:s) a r o u n d 9°K have been o b s e r v e d [1,2] for the cubic Laves p h a s e (C15) compounds Z r V 2 and HfV 2. T h e s e compounds, however, a r e difficult to p r e p a r e in single phase f o r m . F u r t h e r m o r e , for Z r V 2, p o l y m o r p h i s m has been r e p o r t e d [3]. It is p o s s i b l e that the p r e s e n c e of a second p h a s e may influence T c in alloys as m e a s u r e d r e s i s t i v e l y [4, 5] or m a g n e t i c a l l y [1,2, 6]. Such an influence has been o b s e r v e d [7] in the r e l a t e d C15 compounds ZrMo 2 and ZrW 2 w h e r e a r c quenched s a m p l e s w e r e m a g n e t i c a l l y s u p e r c o n d u c t i n g in the 4He r a n g e , due to the p r e s e n c e of a m i n o r i t y b.c.c, phase, although the bulk of the s a m p l e s c o n s i s t e d of C15 m a t e r i a l , n o r m a l at these t e m p e r a t u r e s . The aim of the p r e s e n t i n v e s t i g a t i o n was t h e r e f o r e to e s t a b lish whether s u p e r c o n d u c t i v i t y in ZrV 2 and HfV 2 is a bulk p r o p e r t y of the C15 compounds. Specific heat m e a s u r e m e n t s at low t e m p e r a t u r e s was chosen a s a s u i t a b l e e x p e r i m e n t a l technique for this p u r p o s e . The s t a r t i n g m a t e r i a l s w e r e supplied by M a t e r i a l s R e s e a r c h Ltd. in the form of l u m p s of Hf containing 1 wt% Z r and 2000 pprn of other i m p u r i t i e s and V l u m p s and Z r rod of 99.9% n o m i n a l p u r i t y each. Samples of about 5g were p r e p a r e d by r e p e a t e d m e l t i n g in an a r c f u r n a c e . Weight l o s s e s w e r e negligible. The s a m p l e s w e r e s u b s e q u e n t l y a n n e a l e d in a vacuum below 3 x 10 -6 m m Hg for 12 h o u r s at 1200oc for Z r V 2 and for 10 h o u r s at 1360°C for HfV 2. An X - r a y i n v e s t i g a t i o n of c r u s h e d powder of these
s a m p l e s c o n f i r m e d that the C15 p h a s e s were d o m i n a n t in both alloys. A few (4-6) e x t r a l i n e s , all very weak, showed that a second phase was p r e s e n t in both alloys. F o r Z r V 2 p a r t i a l a g r e e m e n t with d - v a l u e s o b s e r v e d for a hexagonal second phase of the compound [8] was noted. A l though fewer e x t r a l i n e s w e r e o b s e r v e d in HfV 2 the X - r a y p a t t e r n indicated that the s t r u c t u r e of the second phase might also be hexagonal. In c o n t r a s t no additional p h a s e s w e r e o b s e r v e d [9] in HfV 2 when a n n e a l e d below 1200oc. The l a t tice p a r a m e t e r s for C14 phases o b s e r v e d in ZrV2 and suggested for HfV2 [3] did not fit the present data. Specific heat results obtainedby heat pulse calorimetry are shown in fig. 1. The data are normalized to a gram-atomic basis assuming the presence of only material of stoichiometric composition. The normal state specific heat (Cn) is assumed to be of the form Cn = ?,T + b T 3, the coefficients s a t i s f y i n g the r e q u i r e m e n t that the e n tropy above Tcl be independent of the s u p e r conducting phase t r a n s i t i o n . F o r HfV 2 the e n tropy b a l a n c e r e q u i r e d extrapolation of the s u p e r c o n d u c t i n g state data below 5OK. This was done by n o r m a l i z i n g to the specific heat of Nb [10], which shows a c o m p a r a b l e specific heat jump at Tc, m a k i n g use of the law of c o r r e sponding s t a t e s , i.e., C s / C n = f ( T / T c ) . The Tc a r r o w s in fig. 1 m a r k the onset of the two d i s tinct t r a n s i t i o n s s e e n inductively on both s a m pies. The upper t r a n s i t i o n s (Tcl) of 9.4°K and 369
Volume 36A, n u m b e r 5
PHYSICS
LETTERS
27 September 1971
Table 1 Results for C15 HfV 2 and ZrV 2. . . . . . . . . . . . . . . . . . . .
Lattice parameter (,~)
Tc (OK)
. .2 . . . . . . . 66.6 . . . . . . HFV
7~387-i 0.602
8.4
ZrV 2
7.448
7.3
Compound
composition (at% V) 66.6
~ 0.003
8.5OK r e s p e c t i v e l y c o r r e s p o n d to t h o s e p r e v i o u s l y r e p o r t e d f o r t h e C15 c o m p o u n d s [ 1 , 2 , 5]. H e r e t h e y a r e s e e n to b e a t t r i b u t a b l e to t h e m i nor phase. S i n c e t h e s p e c i f i c h e a t c o n t r i b u t i o n of t h e m i n o r p h a s e i s s m a l l , l i t t l e e r r o r i s l i k e l y to r e s u l t f r o m a s s u m i n g , in d e r i v i n g t h e b u l k p r o p e r t i e s of t h e C15 p h a s e , t h a t t h e d e n s i t i e s of states, Debye temperatures, and molar specific h e a t s C(T/Tc) a r e t h e s a m e f o r two p h a s e s . T h e n f r o m t h e r a t i o of t h e i d e a l i z e d s p e c i f i c h e a t a n o m a l i e s a t T c l a n d Tc2, t h e v o l u m e f r a c t i o n of m i n o r p h a s e f o r Z r V 2 i s a b o u t 7~c. T h i s I
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70
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T2[oK z) Fig. 1. Specific heat of HfV 2 (right scale) and ZrV 2 (left scale). CircLes r e p r e s e n t m e a s u r e m e n t s in zero field and c r o s s e s in 105 kG. The a r r o w s denote the onset of inductively observed t r a n s i t i o n s . 370
i9:0 :k 2.0
190 * 10
1.9
16.5 ~ 1.0
219
1.7
÷ 5
is the magnitude expected from the X-ray observations and agrees with a quantitative analys i s of t h e s e c o n d p h a s e in s i m i l a r l y a n n e a l e d Z r V 2 [8]. In c o n t r a s t , a b o u t 60% of t h e i n d u c t a n c e c h a n g e o b s e r v e d in t h e T c m e a s u r e m e n t i s associated with the higher transition. T h e d a t a f o r t h e C15 p h a s e s a r e s u m m a r i z e d in t a b l e 1. T h e e n t r i e s a r e b a s e d on i d e a l i z e d , sharp transitions constructed by linear extrapol a t i o n of Cs/T v e r s u s T c u r v e s , u s i n g e n t r o p y c o n s e r v a t i o n to d e t e r m i n e t h e m e a n Tc. L o w v a l u e s of 0 D a n d u n u s u a l l y h i g h 7 v a l u e s a r e n o t e d . T h e 7 v a l u e f o r HfV 2 i s in a g r e e m e n t w i t h t h a t g i v e n in a r e c e n t l e t t e r [5] (2.1 × 104 e r g / c m 3 - O K 2) b u t n o f u r t h e r d e t a i l s of t h e specific heat measurement were reported. T h e T c v a l u e s in t a b l e 1 a r e a t l e a s t a f a c t o r 20 l a r g e r t h a n t h o s e in a p r e v i o u s i n v e s t i g a t i o n of f o u r C15 c o m p o u n d s [7]. T h e c o r r e s p o n d i n g e l e c t r o n / a t o m n u m b e r s of 4.7 f o r Z r V 2 a n d HfV 2 a n d 5.3 in [7] i n d i c a t e t h a t M a t t h i a s ' r u l e [11] i s o p e r a t i v e in C15 c o m p o u n d s in c o n t r a s t to e a r l i e r o b s e r v a t i o n s [12]. T h e h e l p b y D r . T. C l a e s o n w i t h i n d u c t a n c e measurements, and by A.Wicklund with the specific heat measurements, is gratefully acknowledged. P a r t of t h i s w o r k h a s b e e n f i n a n c e d b y S t a t e n s • o Naturvetenskapliga Forsknmgsrad.
IO
F I
"
A C / T TO (normalized specific heat jump)
f . _~x~ °" "
20 ~ ~ ~ .~, ~xx x
°i
(mJ/g. at. OK2)
0D (OK)
References ~
~o o:]-
,),
04o
[1] B. T. Matthias, V. B. Compton and E. Corenzwit, J. Phys. Chem. Solids 19 (1961) 130. [2] V. Sadogapan, E. Pollard and H C. Gatos, Solid State Comm. 3 (1965) 97. [3] W. M. Rumbai1, J. L e s s - C o m m o n Metals 20 (1970) 191. [4] K. Yasohama and N. Usui, Japan, J. Appl. Phys. 7 (1968) 1128. [5] K. Inoue and K. Taehikawa, Low temperature physics conference, LT12 Kyoto (1970), to be published; Appl. Phys. L e t t e r s 18 (1971) 235. [6] J. T. A. Pollock, R. Shull and H. C. Gatos, Phys. Stat. Sol. (a) 2 (1970) 251. [7] 0. Rapp, J. L e s s - C o m m o n Metals 21 (1970) 27. [8] A. P e b l e r and E. A. G u l b r a n s e n , T r a n s . AIME 239 (1967) 1593•
Volume 36A, number 5
P HY SI CS L E T T E R S
[9] E. Rudy and St. Windisch, J. L e s s - C o m m o n Metals 15 (1968) 13. [10] A. T. Hirschfeld, H. A. Leupold and H. A. B o o r s e , Phys. Rev. 127 (1962) 1501.
27 September 1971
[11] B. T. Matthias, P r o g r e s s in low t e m p e r a t u r e physics Vol. 2, ed. J. C. Gorter (North-Holland, A m s t e r d a m , 1957) pp. 138-150. [12] B. W. R o b e r t s , Intermetallic compounds, ed. J. H. Westbrook (John Wiley, New York, 1967) p. 599. * * * * *
371
Low
PHYSICS LETTERS
TEMPERATURE
SPECIFIC
OF
HEAT
27 September 1971
MEASUREMENTS
ZrV 2 AND HfV 2
b. RAPP Department of Physics, Royal Institute of Technology, Stockholm 10044, Sweden
and L . J . VIELAND RCA Zaboratories, Princeton N.J. 08540, USA Received 3 August 1971
The C15 compounds ZrV2 and HfV2 show bulk superconductivity at 7.3 and 8.4°K respectively, indicating a strong dependence of Tc on the electron per atom number for C15 compounds. High electronic contributions to the specific heat are observed.
Superconducting t r a n s i t i o n t e m p e r a t u r e s (Tc:s) a r o u n d 9°K have been o b s e r v e d [1,2] for the cubic Laves p h a s e (C15) compounds Z r V 2 and HfV 2. T h e s e compounds, however, a r e difficult to p r e p a r e in single phase f o r m . F u r t h e r m o r e , for Z r V 2, p o l y m o r p h i s m has been r e p o r t e d [3]. It is p o s s i b l e that the p r e s e n c e of a second p h a s e may influence T c in alloys as m e a s u r e d r e s i s t i v e l y [4, 5] or m a g n e t i c a l l y [1,2, 6]. Such an influence has been o b s e r v e d [7] in the r e l a t e d C15 compounds ZrMo 2 and ZrW 2 w h e r e a r c quenched s a m p l e s w e r e m a g n e t i c a l l y s u p e r c o n d u c t i n g in the 4He r a n g e , due to the p r e s e n c e of a m i n o r i t y b.c.c, phase, although the bulk of the s a m p l e s c o n s i s t e d of C15 m a t e r i a l , n o r m a l at these t e m p e r a t u r e s . The aim of the p r e s e n t i n v e s t i g a t i o n was t h e r e f o r e to e s t a b lish whether s u p e r c o n d u c t i v i t y in ZrV 2 and HfV 2 is a bulk p r o p e r t y of the C15 compounds. Specific heat m e a s u r e m e n t s at low t e m p e r a t u r e s was chosen a s a s u i t a b l e e x p e r i m e n t a l technique for this p u r p o s e . The s t a r t i n g m a t e r i a l s w e r e supplied by M a t e r i a l s R e s e a r c h Ltd. in the form of l u m p s of Hf containing 1 wt% Z r and 2000 pprn of other i m p u r i t i e s and V l u m p s and Z r rod of 99.9% n o m i n a l p u r i t y each. Samples of about 5g were p r e p a r e d by r e p e a t e d m e l t i n g in an a r c f u r n a c e . Weight l o s s e s w e r e negligible. The s a m p l e s w e r e s u b s e q u e n t l y a n n e a l e d in a vacuum below 3 x 10 -6 m m Hg for 12 h o u r s at 1200oc for Z r V 2 and for 10 h o u r s at 1360°C for HfV 2. An X - r a y i n v e s t i g a t i o n of c r u s h e d powder of these
s a m p l e s c o n f i r m e d that the C15 p h a s e s were d o m i n a n t in both alloys. A few (4-6) e x t r a l i n e s , all very weak, showed that a second phase was p r e s e n t in both alloys. F o r Z r V 2 p a r t i a l a g r e e m e n t with d - v a l u e s o b s e r v e d for a hexagonal second phase of the compound [8] was noted. A l though fewer e x t r a l i n e s w e r e o b s e r v e d in HfV 2 the X - r a y p a t t e r n indicated that the s t r u c t u r e of the second phase might also be hexagonal. In c o n t r a s t no additional p h a s e s w e r e o b s e r v e d [9] in HfV 2 when a n n e a l e d below 1200oc. The l a t tice p a r a m e t e r s for C14 phases o b s e r v e d in ZrV2 and suggested for HfV2 [3] did not fit the present data. Specific heat results obtainedby heat pulse calorimetry are shown in fig. 1. The data are normalized to a gram-atomic basis assuming the presence of only material of stoichiometric composition. The normal state specific heat (Cn) is assumed to be of the form Cn = ?,T + b T 3, the coefficients s a t i s f y i n g the r e q u i r e m e n t that the e n tropy above Tcl be independent of the s u p e r conducting phase t r a n s i t i o n . F o r HfV 2 the e n tropy b a l a n c e r e q u i r e d extrapolation of the s u p e r c o n d u c t i n g state data below 5OK. This was done by n o r m a l i z i n g to the specific heat of Nb [10], which shows a c o m p a r a b l e specific heat jump at Tc, m a k i n g use of the law of c o r r e sponding s t a t e s , i.e., C s / C n = f ( T / T c ) . The Tc a r r o w s in fig. 1 m a r k the onset of the two d i s tinct t r a n s i t i o n s s e e n inductively on both s a m pies. The upper t r a n s i t i o n s (Tcl) of 9.4°K and 369
Volume 36A, n u m b e r 5
PHYSICS
LETTERS
27 September 1971
Table 1 Results for C15 HfV 2 and ZrV 2. . . . . . . . . . . . . . . . . . . .
Lattice parameter (,~)
Tc (OK)
. .2 . . . . . . . 66.6 . . . . . . HFV
7~387-i 0.602
8.4
ZrV 2
7.448
7.3
Compound
composition (at% V) 66.6
~ 0.003
8.5OK r e s p e c t i v e l y c o r r e s p o n d to t h o s e p r e v i o u s l y r e p o r t e d f o r t h e C15 c o m p o u n d s [ 1 , 2 , 5]. H e r e t h e y a r e s e e n to b e a t t r i b u t a b l e to t h e m i nor phase. S i n c e t h e s p e c i f i c h e a t c o n t r i b u t i o n of t h e m i n o r p h a s e i s s m a l l , l i t t l e e r r o r i s l i k e l y to r e s u l t f r o m a s s u m i n g , in d e r i v i n g t h e b u l k p r o p e r t i e s of t h e C15 p h a s e , t h a t t h e d e n s i t i e s of states, Debye temperatures, and molar specific h e a t s C(T/Tc) a r e t h e s a m e f o r two p h a s e s . T h e n f r o m t h e r a t i o of t h e i d e a l i z e d s p e c i f i c h e a t a n o m a l i e s a t T c l a n d Tc2, t h e v o l u m e f r a c t i o n of m i n o r p h a s e f o r Z r V 2 i s a b o u t 7~c. T h i s I
I
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°
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--]
70
60
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~-
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T2[oK z) Fig. 1. Specific heat of HfV 2 (right scale) and ZrV 2 (left scale). CircLes r e p r e s e n t m e a s u r e m e n t s in zero field and c r o s s e s in 105 kG. The a r r o w s denote the onset of inductively observed t r a n s i t i o n s . 370
i9:0 :k 2.0
190 * 10
1.9
16.5 ~ 1.0
219
1.7
÷ 5
is the magnitude expected from the X-ray observations and agrees with a quantitative analys i s of t h e s e c o n d p h a s e in s i m i l a r l y a n n e a l e d Z r V 2 [8]. In c o n t r a s t , a b o u t 60% of t h e i n d u c t a n c e c h a n g e o b s e r v e d in t h e T c m e a s u r e m e n t i s associated with the higher transition. T h e d a t a f o r t h e C15 p h a s e s a r e s u m m a r i z e d in t a b l e 1. T h e e n t r i e s a r e b a s e d on i d e a l i z e d , sharp transitions constructed by linear extrapol a t i o n of Cs/T v e r s u s T c u r v e s , u s i n g e n t r o p y c o n s e r v a t i o n to d e t e r m i n e t h e m e a n Tc. L o w v a l u e s of 0 D a n d u n u s u a l l y h i g h 7 v a l u e s a r e n o t e d . T h e 7 v a l u e f o r HfV 2 i s in a g r e e m e n t w i t h t h a t g i v e n in a r e c e n t l e t t e r [5] (2.1 × 104 e r g / c m 3 - O K 2) b u t n o f u r t h e r d e t a i l s of t h e specific heat measurement were reported. T h e T c v a l u e s in t a b l e 1 a r e a t l e a s t a f a c t o r 20 l a r g e r t h a n t h o s e in a p r e v i o u s i n v e s t i g a t i o n of f o u r C15 c o m p o u n d s [7]. T h e c o r r e s p o n d i n g e l e c t r o n / a t o m n u m b e r s of 4.7 f o r Z r V 2 a n d HfV 2 a n d 5.3 in [7] i n d i c a t e t h a t M a t t h i a s ' r u l e [11] i s o p e r a t i v e in C15 c o m p o u n d s in c o n t r a s t to e a r l i e r o b s e r v a t i o n s [12]. T h e h e l p b y D r . T. C l a e s o n w i t h i n d u c t a n c e measurements, and by A.Wicklund with the specific heat measurements, is gratefully acknowledged. P a r t of t h i s w o r k h a s b e e n f i n a n c e d b y S t a t e n s • o Naturvetenskapliga Forsknmgsrad.
IO
F I
"
A C / T TO (normalized specific heat jump)
f . _~x~ °" "
20 ~ ~ ~ .~, ~xx x
°i
(mJ/g. at. OK2)
0D (OK)
References ~
~o o:]-
,),
04o
[1] B. T. Matthias, V. B. Compton and E. Corenzwit, J. Phys. Chem. Solids 19 (1961) 130. [2] V. Sadogapan, E. Pollard and H C. Gatos, Solid State Comm. 3 (1965) 97. [3] W. M. Rumbai1, J. L e s s - C o m m o n Metals 20 (1970) 191. [4] K. Yasohama and N. Usui, Japan, J. Appl. Phys. 7 (1968) 1128. [5] K. Inoue and K. Taehikawa, Low temperature physics conference, LT12 Kyoto (1970), to be published; Appl. Phys. L e t t e r s 18 (1971) 235. [6] J. T. A. Pollock, R. Shull and H. C. Gatos, Phys. Stat. Sol. (a) 2 (1970) 251. [7] 0. Rapp, J. L e s s - C o m m o n Metals 21 (1970) 27. [8] A. P e b l e r and E. A. G u l b r a n s e n , T r a n s . AIME 239 (1967) 1593•
Volume 36A, number 5
P HY SI CS L E T T E R S
[9] E. Rudy and St. Windisch, J. L e s s - C o m m o n Metals 15 (1968) 13. [10] A. T. Hirschfeld, H. A. Leupold and H. A. B o o r s e , Phys. Rev. 127 (1962) 1501.
27 September 1971
[11] B. T. Matthias, P r o g r e s s in low t e m p e r a t u r e physics Vol. 2, ed. J. C. Gorter (North-Holland, A m s t e r d a m , 1957) pp. 138-150. [12] B. W. R o b e r t s , Intermetallic compounds, ed. J. H. Westbrook (John Wiley, New York, 1967) p. 599. * * * * *
371