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Upper limit on electron-phonon interaction in vanadium carbide
Volume 33A, number 3
UPPER
PHYSICS LETTERS
LIMIT
ON ELECTRON-PHONON IN VANADIUM CARBIDE
19 October 1970
INTERACTION
D. W, BLOOM and L. FINEGOLD * Department of Physics and Astrophysics, University of Colorado, Boulder, Colorado, 80302, USA R. G. LYE R . I . A . S . , Martin Corporation, 1450 S.Rolling Road, Baltimore, Maryland, 21227, USA and R. RADEBAUGH, J . D . SIEGWARTH Cryogenics Division, NBS-Institute for Basic Standards, Boulder, Colorado, 80302, USA Received 16 September 1970
Single crystals of VCx (x = 0.87, 0.84. 0.81. 0.76) were not superconducting above 30 inK. indicating that the electron-phonon enhancement of the densities of states determined from electronic specific heats is less than 30%.
We have conducted a s e a r c h down to 30 mK for s u p e r c o n d u c t i v i t y in four vanadium c a r b i d e s i n g l e c r y s t a l s a m p l e s having the c o m p o s i t i o n s VC0.87 , VC0.84 , VC0.81 and VC0.76. The c y l i n d r i c a l s a m p l e s (about 10 x 4 m m d i a m e t e r ) w e r e m a c h i n e d f r o m l a r g e r single c r y s t a l s a m p l e s foe which the low t e m p e r a t u r e s p e c i f i c heats had p r e v i o u s l y been m e a s u r e d [1] (except f o r VC0.84 which c a m e f r o m a s i m i l a r l a r g e r s p e c i m e n ) . The s a m p l e s w e r e grown at R. I. A. S. [2] u s i n g a floating zone technique [3]. D e t a i l e d c h e m i c a l a n a l y s e s of r e p r e s e n t a t i v e s a m p l e s indicate they contain a p p r o x i m a t e l y 0.01 wt% each of oxygen and n i t r o g e n and t r a c e s (i. e. < 0.1 wt%) of m e t a l l i c i m p u r i t i e s including c h r o m i u m and iron. (In o th e r e x p e r i m e n t s , the m a g n e t i z a t i o n - field r e l a t i o n was l i n e a r to 8 kOe, indicating negligible f e r r o m a g n e t i c impurity). X - r a y m e a s u r e m e n t s of the l a t t i c e p a r a m e t e r s have shown that the d i f f e r e n c e in c o m p o s i t i o n , 5x, between opposite ends of a given s a m p l e is l e s s than 0.01 f o r all four s a m p l e s [1]. The s a m p l e s w e r e f a s t e n e d [4] with 0.13 m m d i a m e t e r c o p p e r w i r e and v a r n i s h to a p a i r of 0.81 m m d i a m e t e r copper w i r e s w e r e in good t h e r m a l contact with the m i x i n g c h a m b e r of a 3 H e - 4He dilution r e f r i g e r a t o r at the National B u r e a u of Standards. The s a m p l e s w e r e s u r rounded by, but not p h y s i c a l l y touching, a nylon * To whom reprint requests should be sent.
coil form on which were wound a pair of coils. The mutual inductance between the coils was monitored at 17 Hz $. The applied primary field was less than 0 . 3 0 e and the sample chamber was shielded from external magnetic fields by a superconducting lead tube closed at one end.
(The r e l a t i o n [6] Hc(0) = Tc(¥/0.168)1/2 b et w een the c r i t i c a l field at 0 K, the t r a n s i t i o n t e m p e r a t u r e in z e r o field Tc(0) and the e l e c t r o n i c s p e c i f i c heat c o e f f i c i e n t ~, g i v es H c - 4.5 Oe for Tc(0 ) ~ 30 mK.) The t e m p e r a t u r e was m e a s u r e d by c a r b o n r e s i s t a n c e t h e r m o m e t e r s I $ mounted on the s a m p l e holder and on the mixing c h a m b e r , and by a c e r i u m m a g n e s i u m n i t r a t e pill i m m e r s e d in the mixing c h a m b e r . As a check of the a p p a r a t u s an aluminum c y l i n d e r was mounted in one of the s a m p l e s p a c e s : The mutual inductance of the c o i l s changed discontinuously at 1.19 K (c.f. 1.196 K[8]). None of the s a m p l e s b e c a m e s u p e r c o n d u c t i n g above 30 ± 1 inK. Using the equation McMillan [9] has d e r i v e d f o r s t r o n g - c o u p l e d s u p e r c o n d u c t o r s , the t r a n s i t i o n t e m p e r a t u r e Tc = (0D/l.45)exp~[-l.04(l+~)]/[;~- ~* (i+0.62~)]}
(1) A commerciallyavailable mutual inductance bridge was used [5]. $$ The resistors were ground nominal 27 ~ resistors similar to those described by Robichaux and Anderson [7]. 137
V o l u m e 33A, n u m b e r 3
PtIYSICS
w h e r e ~ is the e l e c t r o n phonon i n t e r a c t i o n p a r a m e t e r , ~* is the C o u l o m b p s e u d o p o t e n t i a l r e p u l s i o n p a r a m e t e r of M o r e l and A n d e r s o n [10] and 0 D is the D e b y e c h a r a c t e r i s t i c t e m p e r a t u r e d e t e r m i n e d f r o m s~pecific heat m e a s u r e m e n t s ~. The p a r a m e t e r ~ is u s u a l l y taken to be 0.13 for t r a n s i t i o n m e t a l s [9] a n d t h i s v a l u e w a s a d o p t e d h e r e . A s s u m i n g a m a x i m u m of T c of 30 m K , e q . (1) g i v e s a m a x i m u m v a l u e f o r ;~ of 0.29 for t h e f o u r
s a m p l e s . (An u p p e r l i m i t of /z* ~. 0.19 is g i v e n by an a p p r o x i m a t e c a l c u l a t i o n [12, eqs. (10), (11) and (3)] b a s e d on the T h o m a s - F e r m i m o d e l w h e n c e , f r o m eq. (1) w i t h T c - 30 mK, a ~ 0.35). S i n c e the e l e c t r o n i c d e n s i t y of s t a t e s N 7 ( 0 ) d e t e r m i n e d f r o m s p e c i f i c heat m e a s u r e m e n t s is e n h a n c e d [9] by the factor (1+~) o v e r the b a r e d e n s i t y of s t a t e s N(0), that is N y ( 0 ) = ?,r(0) (1 + ~) , our results show that the specific-heat electronicdensities-of-states reported previously for VC x [I 1 a r e p r o b a b l y e n h a n c e d b y l e s s t h a n 29% o v e r the "bare" band-structure values. The NSF Science Development Program supported the research and abalysis at the University: N A S A R e s e a r c h D i v i s i o n , Code RRM M a t e r i a l s {'l'he 0 D v:liues g i v e n in ref. [11 have b e e n multil)licd 1,y 0 v ~ t / 3 H i l .
138
LETTE
RS
19 O c t o b e r i 9 7 0
Research Branch (Contract NASw- 1290) supported the specimen preparation a t R. I. A. S.; a n d t h e N a t i o n a l B u r e a u of S t a n d a r d s f u n d e d t h e l o w - t e m perature experimental measurements. The initiaI i m p e t u s w a s d u e to D. H. L o w n d e s [13]. T h e m a g netic susceptibility of t h e s e s a m e s a m p l e s w i l l b e reported elsewhere.
]~Qfc)'cncc I II D.H. L o w n d c s . l , . F i n c g o h t nnd I { . G . l , y c . Phil. Mag. 21 (1970) 245. [21 R e s e a r c h I n s t i t u t e ['~r ~M\anced Studies, l ~ a [ t i n ~ ) ~ Md. [3[ W. PrcehL t~l/(t (,~, 1~. tt,dl~,x .t. (;rv~t:d Gr(~x~th :~ (196>) NI N. [ ! I D. W. BhJom. Ph. I). 'i'tm,si.~ ['lliV(~l'SiLy ()[' (~(~h)l';icl(, (1970). I5] W . l , , P i ! l i n g c r . P S.,}:lstr:im : l n d , I . G . [ ) a u n t , ire,,. Sol. I n s t r . 2,9 (195S) 159. (q R. M e s e r v e y and B. I-~,.S c h ~ a r t z in S u p e r c o n d u c t l ~ it3'. E(1.. R. lJ. P n r k s tl)ekker, I n c . . New York. 1969) Vol. 1 p. I(;!;. 71 J. F. Robi(3hat,~x and A. ~?. Antlers(m, [{c~. Sci. Insi r, It) {19(;U) 1512. s I , l . F . C o c h r a n ;rod i). E, Map~H]wr. P h y s . I/ev. 12i i1961) 1(;sx. [~)l W . l ~ . M c M i l h m . P h y s . I{cx. i/;,- il!nlb) 32,1. 11(}] P. Morel :rod P . W . Ande, r s o n . P h y s . Rev. !25 (1:i(~3, 1263. [11 I 1~. Toth, p r i v a t e COlllllltlnic/Iti()ll. It :2} K. A n d r o s . E . B u c h e r , J . P . Mait:l and R . C . S c h e r wood, P h y s . F.ev. 178 (19(;9) 702. t l;~1 D . t t . I ~ o w n d e s , P h . D . T h e s i s , U n i v e r s i t 3 ~,1 C o l o r a d o (19(iS).
UPPER
PHYSICS LETTERS
LIMIT
ON ELECTRON-PHONON IN VANADIUM CARBIDE
19 October 1970
INTERACTION
D. W, BLOOM and L. FINEGOLD * Department of Physics and Astrophysics, University of Colorado, Boulder, Colorado, 80302, USA R. G. LYE R . I . A . S . , Martin Corporation, 1450 S.Rolling Road, Baltimore, Maryland, 21227, USA and R. RADEBAUGH, J . D . SIEGWARTH Cryogenics Division, NBS-Institute for Basic Standards, Boulder, Colorado, 80302, USA Received 16 September 1970
Single crystals of VCx (x = 0.87, 0.84. 0.81. 0.76) were not superconducting above 30 inK. indicating that the electron-phonon enhancement of the densities of states determined from electronic specific heats is less than 30%.
We have conducted a s e a r c h down to 30 mK for s u p e r c o n d u c t i v i t y in four vanadium c a r b i d e s i n g l e c r y s t a l s a m p l e s having the c o m p o s i t i o n s VC0.87 , VC0.84 , VC0.81 and VC0.76. The c y l i n d r i c a l s a m p l e s (about 10 x 4 m m d i a m e t e r ) w e r e m a c h i n e d f r o m l a r g e r single c r y s t a l s a m p l e s foe which the low t e m p e r a t u r e s p e c i f i c heats had p r e v i o u s l y been m e a s u r e d [1] (except f o r VC0.84 which c a m e f r o m a s i m i l a r l a r g e r s p e c i m e n ) . The s a m p l e s w e r e grown at R. I. A. S. [2] u s i n g a floating zone technique [3]. D e t a i l e d c h e m i c a l a n a l y s e s of r e p r e s e n t a t i v e s a m p l e s indicate they contain a p p r o x i m a t e l y 0.01 wt% each of oxygen and n i t r o g e n and t r a c e s (i. e. < 0.1 wt%) of m e t a l l i c i m p u r i t i e s including c h r o m i u m and iron. (In o th e r e x p e r i m e n t s , the m a g n e t i z a t i o n - field r e l a t i o n was l i n e a r to 8 kOe, indicating negligible f e r r o m a g n e t i c impurity). X - r a y m e a s u r e m e n t s of the l a t t i c e p a r a m e t e r s have shown that the d i f f e r e n c e in c o m p o s i t i o n , 5x, between opposite ends of a given s a m p l e is l e s s than 0.01 f o r all four s a m p l e s [1]. The s a m p l e s w e r e f a s t e n e d [4] with 0.13 m m d i a m e t e r c o p p e r w i r e and v a r n i s h to a p a i r of 0.81 m m d i a m e t e r copper w i r e s w e r e in good t h e r m a l contact with the m i x i n g c h a m b e r of a 3 H e - 4He dilution r e f r i g e r a t o r at the National B u r e a u of Standards. The s a m p l e s w e r e s u r rounded by, but not p h y s i c a l l y touching, a nylon * To whom reprint requests should be sent.
coil form on which were wound a pair of coils. The mutual inductance between the coils was monitored at 17 Hz $. The applied primary field was less than 0 . 3 0 e and the sample chamber was shielded from external magnetic fields by a superconducting lead tube closed at one end.
(The r e l a t i o n [6] Hc(0) = Tc(¥/0.168)1/2 b et w een the c r i t i c a l field at 0 K, the t r a n s i t i o n t e m p e r a t u r e in z e r o field Tc(0) and the e l e c t r o n i c s p e c i f i c heat c o e f f i c i e n t ~, g i v es H c - 4.5 Oe for Tc(0 ) ~ 30 mK.) The t e m p e r a t u r e was m e a s u r e d by c a r b o n r e s i s t a n c e t h e r m o m e t e r s I $ mounted on the s a m p l e holder and on the mixing c h a m b e r , and by a c e r i u m m a g n e s i u m n i t r a t e pill i m m e r s e d in the mixing c h a m b e r . As a check of the a p p a r a t u s an aluminum c y l i n d e r was mounted in one of the s a m p l e s p a c e s : The mutual inductance of the c o i l s changed discontinuously at 1.19 K (c.f. 1.196 K[8]). None of the s a m p l e s b e c a m e s u p e r c o n d u c t i n g above 30 ± 1 inK. Using the equation McMillan [9] has d e r i v e d f o r s t r o n g - c o u p l e d s u p e r c o n d u c t o r s , the t r a n s i t i o n t e m p e r a t u r e Tc = (0D/l.45)exp~[-l.04(l+~)]/[;~- ~* (i+0.62~)]}
(1) A commerciallyavailable mutual inductance bridge was used [5]. $$ The resistors were ground nominal 27 ~ resistors similar to those described by Robichaux and Anderson [7]. 137
V o l u m e 33A, n u m b e r 3
PtIYSICS
w h e r e ~ is the e l e c t r o n phonon i n t e r a c t i o n p a r a m e t e r , ~* is the C o u l o m b p s e u d o p o t e n t i a l r e p u l s i o n p a r a m e t e r of M o r e l and A n d e r s o n [10] and 0 D is the D e b y e c h a r a c t e r i s t i c t e m p e r a t u r e d e t e r m i n e d f r o m s~pecific heat m e a s u r e m e n t s ~. The p a r a m e t e r ~ is u s u a l l y taken to be 0.13 for t r a n s i t i o n m e t a l s [9] a n d t h i s v a l u e w a s a d o p t e d h e r e . A s s u m i n g a m a x i m u m of T c of 30 m K , e q . (1) g i v e s a m a x i m u m v a l u e f o r ;~ of 0.29 for t h e f o u r
s a m p l e s . (An u p p e r l i m i t of /z* ~. 0.19 is g i v e n by an a p p r o x i m a t e c a l c u l a t i o n [12, eqs. (10), (11) and (3)] b a s e d on the T h o m a s - F e r m i m o d e l w h e n c e , f r o m eq. (1) w i t h T c - 30 mK, a ~ 0.35). S i n c e the e l e c t r o n i c d e n s i t y of s t a t e s N 7 ( 0 ) d e t e r m i n e d f r o m s p e c i f i c heat m e a s u r e m e n t s is e n h a n c e d [9] by the factor (1+~) o v e r the b a r e d e n s i t y of s t a t e s N(0), that is N y ( 0 ) = ?,r(0) (1 + ~) , our results show that the specific-heat electronicdensities-of-states reported previously for VC x [I 1 a r e p r o b a b l y e n h a n c e d b y l e s s t h a n 29% o v e r the "bare" band-structure values. The NSF Science Development Program supported the research and abalysis at the University: N A S A R e s e a r c h D i v i s i o n , Code RRM M a t e r i a l s {'l'he 0 D v:liues g i v e n in ref. [11 have b e e n multil)licd 1,y 0 v ~ t / 3 H i l .
138
LETTE
RS
19 O c t o b e r i 9 7 0
Research Branch (Contract NASw- 1290) supported the specimen preparation a t R. I. A. S.; a n d t h e N a t i o n a l B u r e a u of S t a n d a r d s f u n d e d t h e l o w - t e m perature experimental measurements. The initiaI i m p e t u s w a s d u e to D. H. L o w n d e s [13]. T h e m a g netic susceptibility of t h e s e s a m e s a m p l e s w i l l b e reported elsewhere.
]~Qfc)'cncc I II D.H. L o w n d c s . l , . F i n c g o h t nnd I { . G . l , y c . Phil. Mag. 21 (1970) 245. [21 R e s e a r c h I n s t i t u t e ['~r ~M\anced Studies, l ~ a [ t i n ~ ) ~ Md. [3[ W. PrcehL t~l/(t (,~, 1~. tt,dl~,x .t. (;rv~t:d Gr(~x~th :~ (196>) NI N. [ ! I D. W. BhJom. Ph. I). 'i'tm,si.~ ['lliV(~l'SiLy ()[' (~(~h)l';icl(, (1970). I5] W . l , , P i ! l i n g c r . P S.,}:lstr:im : l n d , I . G . [ ) a u n t , ire,,. Sol. I n s t r . 2,9 (195S) 159. (q R. M e s e r v e y and B. I-~,.S c h ~ a r t z in S u p e r c o n d u c t l ~ it3'. E(1.. R. lJ. P n r k s tl)ekker, I n c . . New York. 1969) Vol. 1 p. I(;!;. 71 J. F. Robi(3hat,~x and A. ~?. Antlers(m, [{c~. Sci. Insi r, It) {19(;U) 1512. s I , l . F . C o c h r a n ;rod i). E, Map~H]wr. P h y s . I/ev. 12i i1961) 1(;sx. [~)l W . l ~ . M c M i l h m . P h y s . I{cx. i/;,- il!nlb) 32,1. 11(}] P. Morel :rod P . W . Ande, r s o n . P h y s . Rev. !25 (1:i(~3, 1263. [11 I 1~. Toth, p r i v a t e COlllllltlnic/Iti()ll. It :2} K. A n d r o s . E . B u c h e r , J . P . Mait:l and R . C . S c h e r wood, P h y s . F.ev. 178 (19(;9) 702. t l;~1 D . t t . I ~ o w n d e s , P h . D . T h e s i s , U n i v e r s i t 3 ~,1 C o l o r a d o (19(iS).