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Neutron critical scattering in iron with very high temperature stability
Volume 29A, number 9
PHYSICS
LETTERS
4. G. Busch and S. Yan, Phys. Kondens. Materie 1 (1963) 37. 5. G. Urbain and E. ~2}elacker Adv. Phys. 16 (1967) 429. 6. G. Busch and Y. Ti~che, Phys. Kondens. Materie 1 (1963) 78. 7. J . E . Enderby and L. Walsh, Phil. Mag. 14 (1966) 991.
References 1. A.S. Epstein, H. Fritzsehe and K. Lark-Horovitz, Phys. Rev. 107 (1957) 412. 2. M. Cutler and C. E. Mallon, J. Chem. Phys. 37 (1962) 2 677. 3. J . N . Hodgson, Phil. Mag. 8 (1963) 735.
NEUTRON VERY
28 July 1969
CRITICAL SCATTERING HIGH TEMPERATURE
IN IRON STABILITY
WITH
R. C I S Z E W S K I
Warsaw Technical University, Institute of Physics, Warsaw, Poland and K. B L I N O W S K I
Institute of Nuclear Research, Warsaw, Poland Received 3 0 M a y 1969
Neutron small angle scattering for different temperatures with + O.lOC temperature stability has been determined, using neutrons of 1.14A wavelength. Predicted by J. Kocinski's theory some diffraction maxima were found. A c c o r d i n g to K o c i n s k i ' s t h e o r y [1] f o r c r i t i c a l m a g n e t i c s c a t t e r i n g of n e u t r o n s , c o n t r a r y to van H o v e ' s , d i f f r a c t i o n m i n i m a in the c r o s s - s e c t i o n should appear for angles
o. --.. ~o/R,
(t)
w h e r e n i s an i n t e g e r ; k t h e i n c i d e n t n e u t r o n wavelenght; R the correlation range defined as 1
R : a [ 4 ~ v { ( T o - T ) / T o } 2 ]-3
(2)
T O i s the t e m p e r a t u r e of t h e s a m p l e and T t e m p e r a t u r e of the f l u c t u a t i o n s . In a p r e v i o u s p a p e r [2] t h e f l u c t u a t i o n t e m p e r a t u r e in i r o n w a s found to b e a b o u t T c - 6°C a n d c o n s e q u e n t l y R ~ 30/~; at t h e c r i t i c a l point. F o r X u s e d in t h i s e x p e r i m e n t , i . e . , 1.14/~, t h e f i r s t m i n i m u m s h o u l d a p p e a r at 01 = 2 ° 1 0 ', t h e s e c o n d at 02 = 4o20 '. B e t w e e n t h e s e two minima there should exist the first maximum, i . e . , at 3o15'. T h e s m a l l a n g l e s c a t t e r i n g m e a s u r e m e n t s in iron have been performed using a double crystal n e u t r o n s p e c t r o m e t e r . In f r o n t of t h e n e u t r o n d e t e c t o r a S o l l e r c o l l i m a t o r w i t h 13 m i n of a r c horizontal angular divergency has been used. T h e s a m p l e t e m p e r a t u r e s t a b i l i t y h a s in g e n e r a l been kept with better than ± 0.1°C accuracy.
Fig. L Small-angle critical magnetic scattering of neutrons in iron. Sample temperature stability ~ O.l°C. The c i r c l e s c o v e r the statistical e r r o r of the counts. For sample temperature To = Tc a trace of the 2nd maximum can be observed.
F o l l o w i n g K o c i n s k i ' s c a l c u l a t i o n s one can e s t i m a t e t h e i n t e n s i t y c h a n g e due to the t e m p e r a t u r e d e v i a t i o n . When t h e s a m p l e t e m p e r a t u r e f o r T o = T c d e c r e a s e s a b o u t 0 . 2 5 o c the i n t e n s i t y in t h e p e a k w i l l d e c r e a s e ~ 10%. In o t h e r 8 r e g i o n s w h e r e t h e p e a k d o e s not a p p e a r the i n t e n s i t y i s much less sensitive for the same temperature instability. 513
Volume 29A, number 9
PHYSICS
LETTERS
F o r t h e s e e x p e r i m e n t a l c o n d i t i o n s t h e 1st maximum appeared for a different angle value t h a n t h e one m e n t i o n e d a b o v e ( s e e fig. 1) w h i c h gives a new value for the fluctuation temperature, n a m e l y T = T c - 10oC. T h e f a c t t h a t none of K o c i n s k i ' s m i n i m a h a s b e e n o b s e r v e d can b e e x p l a i n e d by t h e a s s u m p t i o n that the differential cross-section for neutron c r i t i c a l s c a t t e r i n g i s a s u m of two t e r m s , t h e f i r s t one g i v e n by van H o v e and t h e s e c o n d one by K o c i n s k i , i . e . [3]. R Cl ~ 1 +'C2 f s i n ~ r l s i n ~ 2 r l dr. (3) ~ 0
28 July 1969
After performing some theoretical calculations a r e p o r t g i v i n g f u l l i n t e r p r e t a t i o n of t h e s e and other experimental results will be published.
References 1. J.Kocinski, Aeta Phys. Polon. 30 (1966) 591. 2. K. Blinowski and R. Ciszewski, Phys. Letters 28A (1968) 389. 3. J. Kocinski and K. Wentowska, Acta Phys. Poton., to be published.
+~2
* * * * *
BULK ARRAYS
MEAN F I E L D F L U C T U A T I O N S IN R E S I S T A N C E OF OF S U P E R C O N D U C T I N G POINT CONTACTS ABOVE Tc T. D. CLARK*
Philips Research Laboratories, Eindhoven, Netherlands and D. I t T I L L E Y
Physics Department, Unive~'sity of Essex, Colchester, Essex, UK Received 30 May 1969
The resistance of ball a r r a y s increases according to the "bulk n Curie-Weiss law. We attribute the inc r e a s e to fluctuations in the contact regions.
A b o v e T c t h e r e s i s t a n c e of a d i s o r d e r e d superconducting region should satisfy R / ( R N - R ) = A -1 [(T - T c ) / T c ] n with n = 1 f o r a t h i n f i l m , a n d n = ½ f o r a b u l k r e g i o n [1]. We b e l i e v e we h a v e o b s e r v e d t h e b u l k b e h a v i o u r , 1 n = ~, in p o i n t c o n t a c t a r r a y s . Fig. 1 s h o w s t h e top of t h e r e s i s t i v e t r a n s i t i o n of a c y l i n d r i c a l a r r a y of 1 0 0 ~ m tin b a l l s , l e n g t h 5 m m and c r o s s s e c t i o n 4 m m . B e l o w 3.7OK a " p h a s e s l i p " t a i l ~ lOK in width i s s e e n (2) and f o r T << T c a w e l l d e f i n e d s u p e r c u r r e n t d e v e l o p e d . ( 4 7 ~ A at 1.57OK). T h e e x p e r i m e n t a l p o i n t s up to t h e i n f l e x i o n at a b o u t 6 . 5 ° K in fig. 1 fit t h e " b u l k " C u r i e - W e i s s law. F i g . 2 s h o w s ~ / ( R N - R ) ] 2 p l o t t e d v e r s u s T. T h e d a t a a r e p l o t t e d l o g a r i t h m i c a l l y in fig. 3. T h e p o i n t s b e l o w 3 . 8 4 ° K in fig. 3 r i s e a b o v e t h e * Permanent address: Mullard Research Laboratories, Salfords, Redhill, Surrey, UK. 514
950
R~
~45
~O@
OBSBOeI~Oe
lO ~
BeeOg
Q
°e go
935
4:0
~o
e:o
7;0
~.o
9o 3-.K 15o
Fig. I. Resistancefrom Tc to onset of phononlimited
resistance.
PHYSICS
LETTERS
4. G. Busch and S. Yan, Phys. Kondens. Materie 1 (1963) 37. 5. G. Urbain and E. ~2}elacker Adv. Phys. 16 (1967) 429. 6. G. Busch and Y. Ti~che, Phys. Kondens. Materie 1 (1963) 78. 7. J . E . Enderby and L. Walsh, Phil. Mag. 14 (1966) 991.
References 1. A.S. Epstein, H. Fritzsehe and K. Lark-Horovitz, Phys. Rev. 107 (1957) 412. 2. M. Cutler and C. E. Mallon, J. Chem. Phys. 37 (1962) 2 677. 3. J . N . Hodgson, Phil. Mag. 8 (1963) 735.
NEUTRON VERY
28 July 1969
CRITICAL SCATTERING HIGH TEMPERATURE
IN IRON STABILITY
WITH
R. C I S Z E W S K I
Warsaw Technical University, Institute of Physics, Warsaw, Poland and K. B L I N O W S K I
Institute of Nuclear Research, Warsaw, Poland Received 3 0 M a y 1969
Neutron small angle scattering for different temperatures with + O.lOC temperature stability has been determined, using neutrons of 1.14A wavelength. Predicted by J. Kocinski's theory some diffraction maxima were found. A c c o r d i n g to K o c i n s k i ' s t h e o r y [1] f o r c r i t i c a l m a g n e t i c s c a t t e r i n g of n e u t r o n s , c o n t r a r y to van H o v e ' s , d i f f r a c t i o n m i n i m a in the c r o s s - s e c t i o n should appear for angles
o. --.. ~o/R,
(t)
w h e r e n i s an i n t e g e r ; k t h e i n c i d e n t n e u t r o n wavelenght; R the correlation range defined as 1
R : a [ 4 ~ v { ( T o - T ) / T o } 2 ]-3
(2)
T O i s the t e m p e r a t u r e of t h e s a m p l e and T t e m p e r a t u r e of the f l u c t u a t i o n s . In a p r e v i o u s p a p e r [2] t h e f l u c t u a t i o n t e m p e r a t u r e in i r o n w a s found to b e a b o u t T c - 6°C a n d c o n s e q u e n t l y R ~ 30/~; at t h e c r i t i c a l point. F o r X u s e d in t h i s e x p e r i m e n t , i . e . , 1.14/~, t h e f i r s t m i n i m u m s h o u l d a p p e a r at 01 = 2 ° 1 0 ', t h e s e c o n d at 02 = 4o20 '. B e t w e e n t h e s e two minima there should exist the first maximum, i . e . , at 3o15'. T h e s m a l l a n g l e s c a t t e r i n g m e a s u r e m e n t s in iron have been performed using a double crystal n e u t r o n s p e c t r o m e t e r . In f r o n t of t h e n e u t r o n d e t e c t o r a S o l l e r c o l l i m a t o r w i t h 13 m i n of a r c horizontal angular divergency has been used. T h e s a m p l e t e m p e r a t u r e s t a b i l i t y h a s in g e n e r a l been kept with better than ± 0.1°C accuracy.
Fig. L Small-angle critical magnetic scattering of neutrons in iron. Sample temperature stability ~ O.l°C. The c i r c l e s c o v e r the statistical e r r o r of the counts. For sample temperature To = Tc a trace of the 2nd maximum can be observed.
F o l l o w i n g K o c i n s k i ' s c a l c u l a t i o n s one can e s t i m a t e t h e i n t e n s i t y c h a n g e due to the t e m p e r a t u r e d e v i a t i o n . When t h e s a m p l e t e m p e r a t u r e f o r T o = T c d e c r e a s e s a b o u t 0 . 2 5 o c the i n t e n s i t y in t h e p e a k w i l l d e c r e a s e ~ 10%. In o t h e r 8 r e g i o n s w h e r e t h e p e a k d o e s not a p p e a r the i n t e n s i t y i s much less sensitive for the same temperature instability. 513
Volume 29A, number 9
PHYSICS
LETTERS
F o r t h e s e e x p e r i m e n t a l c o n d i t i o n s t h e 1st maximum appeared for a different angle value t h a n t h e one m e n t i o n e d a b o v e ( s e e fig. 1) w h i c h gives a new value for the fluctuation temperature, n a m e l y T = T c - 10oC. T h e f a c t t h a t none of K o c i n s k i ' s m i n i m a h a s b e e n o b s e r v e d can b e e x p l a i n e d by t h e a s s u m p t i o n that the differential cross-section for neutron c r i t i c a l s c a t t e r i n g i s a s u m of two t e r m s , t h e f i r s t one g i v e n by van H o v e and t h e s e c o n d one by K o c i n s k i , i . e . [3]. R Cl ~ 1 +'C2 f s i n ~ r l s i n ~ 2 r l dr. (3) ~ 0
28 July 1969
After performing some theoretical calculations a r e p o r t g i v i n g f u l l i n t e r p r e t a t i o n of t h e s e and other experimental results will be published.
References 1. J.Kocinski, Aeta Phys. Polon. 30 (1966) 591. 2. K. Blinowski and R. Ciszewski, Phys. Letters 28A (1968) 389. 3. J. Kocinski and K. Wentowska, Acta Phys. Poton., to be published.
+~2
* * * * *
BULK ARRAYS
MEAN F I E L D F L U C T U A T I O N S IN R E S I S T A N C E OF OF S U P E R C O N D U C T I N G POINT CONTACTS ABOVE Tc T. D. CLARK*
Philips Research Laboratories, Eindhoven, Netherlands and D. I t T I L L E Y
Physics Department, Unive~'sity of Essex, Colchester, Essex, UK Received 30 May 1969
The resistance of ball a r r a y s increases according to the "bulk n Curie-Weiss law. We attribute the inc r e a s e to fluctuations in the contact regions.
A b o v e T c t h e r e s i s t a n c e of a d i s o r d e r e d superconducting region should satisfy R / ( R N - R ) = A -1 [(T - T c ) / T c ] n with n = 1 f o r a t h i n f i l m , a n d n = ½ f o r a b u l k r e g i o n [1]. We b e l i e v e we h a v e o b s e r v e d t h e b u l k b e h a v i o u r , 1 n = ~, in p o i n t c o n t a c t a r r a y s . Fig. 1 s h o w s t h e top of t h e r e s i s t i v e t r a n s i t i o n of a c y l i n d r i c a l a r r a y of 1 0 0 ~ m tin b a l l s , l e n g t h 5 m m and c r o s s s e c t i o n 4 m m . B e l o w 3.7OK a " p h a s e s l i p " t a i l ~ lOK in width i s s e e n (2) and f o r T << T c a w e l l d e f i n e d s u p e r c u r r e n t d e v e l o p e d . ( 4 7 ~ A at 1.57OK). T h e e x p e r i m e n t a l p o i n t s up to t h e i n f l e x i o n at a b o u t 6 . 5 ° K in fig. 1 fit t h e " b u l k " C u r i e - W e i s s law. F i g . 2 s h o w s ~ / ( R N - R ) ] 2 p l o t t e d v e r s u s T. T h e d a t a a r e p l o t t e d l o g a r i t h m i c a l l y in fig. 3. T h e p o i n t s b e l o w 3 . 8 4 ° K in fig. 3 r i s e a b o v e t h e * Permanent address: Mullard Research Laboratories, Salfords, Redhill, Surrey, UK. 514
950
R~
~45
~O@
OBSBOeI~Oe
lO ~
BeeOg
Q
°e go
935
4:0
~o
e:o
7;0
~.o
9o 3-.K 15o
Fig. I. Resistancefrom Tc to onset of phononlimited
resistance.