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Magnetic field enhancement in superconducting tubes
iv
ABSTRACTS OF PAPERS TO APPEAR IN J. PHYS. CHEM. SOLIDS
The exact diamagnetic susceptibility is calculated as a function of the magnetic field for a magnetic breakdown model which has been previously presented. The susceptibilityis obtained by numerically evaluating the appropriate derivative of the Helmholtz free energy using the exact eigenvalues of the model Hamiltonian. The susceptibilitycalculated by this method includes the contributions from both the zero-field diamagnetism and the de Haas-van Alphen effect. The periodicities in the susceptibility are r e l a ted to the semiclassical electron orbits c o r r e s ponding to this model: for low magnetic fields the periods a r e d e t e r m i n e d by two closed orbits, one within the other; for high fields a single period is observed c o r r e s p o n d i n g to the broken down case of two identical i n t e r s e c t i n g elliptical orbits. The behavior in the transition region is compatible with the expression for the breakdown probability derived by s e v e r a l authors. An approximate calculation of the o s c i l l a t o r y part of the diamagnetism is also c a r r i e d out using the s e m i c l a s s i c a l method of Falicov and Stachowiak. When the influence of the energy gap on the orbit g e o m e t r y is taken into account, their method yields r e s u l t s which a r e in good a g r e e m e n t with the exact susceptibility. Evaluation of the steady diamagnetism for the model using the e x p r e s s i o n for the susceptibility derived by Wannier and Upadhyaya yields r e s u l t s which a r e in a g r e e m e n t with the numerical calculations and, in addition, exhibits anomalous features of the z e r o - f i e l d diamagnetism in the neighborhood of c r i t i c a l points of the F e r m i surface.
(Received 20 May 1968)
14.
P R O C E S S U S D E T R A N S F E R T D'ACTIVITE" D U Fe(m) D A N S LE T R I O X A L A T O FERRATE DE POTASSIUM A. Ru~i, (Institutde physique atomique, Bucarest, Roumanie)
Le p r o c e s s u s de t r a n s f e r t d'activit~ du Fe(III) de Fe(OH)3 & Ks [Fe(C204)~ ~3H20 et & Ks [Fe(C~O,)~ ~ a lieu selon une cin~tique off chaque i s o t h e r m e c o r r e s p o n d & un palter c a r a c t~rtstique, d'une facon analogue au recuit du p r o duit irradi~. La pr~sance de l'eau de c r i s t a l l i s a t i o n a la m~me influence sur le p r o c e s s u s de t r a n s f e r t que clans le cas des cristaux irradi~ par neutrons. Les petites valeures des ~nergies d'activation calcul~es pour le processus de transfert montrent que celui-ci peut intervenir pr~feren-
Vol. 6, No. 8
tiellement dans le processus de recuit. Les spectres des ~ner~es d'activation en presence de l'eau de cristallisation indiquent un seul groupe de pics clans le cas de la substance dop~e tandis que dans le cas de la substance [rradi~e on observe netement deux groupes de pics.
En conformit@ avec ces observations on peut consid@rer que dans le p r o c e s s u s de recuit th~rmique du fer de recul, la derni~r ~tape c ' e s t & dire le passage du Fe(III) de la f o r m e simple clans la f o r m e complexe, peut ~tre repr~sent~e par un p r o c e s s u s de t r a n s f e r t . The process of transference of activity of Fe(III) from Fe(OH)a to Ks [Fe(CeO~)3_'3H20 and Ks ~Fe(C~O~)3 ~ takes place in accordance with a kinetic reaction in which each isotherm corresponds to a characteristic stage in a manner analogous to an annealing of the irradiated product. The presence of water of crystallization has the same effect on the transfer process as tn the case of crystals irradiated by neutrons. The low values of the activating energy calculated for the transfer process show that the latter can intervene preferentially in the annealing process. The spectra of the activating energy in the presence of water of crystallizationindicate a single peak group in the case of the dipped substance, while in the case of the irradiated substance we distinctly observe two peak groups. In line with these observations we may consider that in the thermic annealing of iron the last stage -- i . e . , the passing of Fe(rIl) from the simple to the complex form, may be represented by a process of transfer.
(Received 26 F e b r u a r y 1968) (Revised 10 May 1968)
15.
MAGNETIC FIELD ENHANCEMENT IN SUPERCONDUCTING TUBES E . F . Young and R. L Gayley (State University of New York at Buffalo, Buffalo, New York)
The magnetic behavior of tubes of superconducting material cooled in an axial magnetic field has been studied in an attempt to understand
Vol. 6, No. 8
ABSTRACTS
OF PAPERS
TO APPEAR
the i n c r e a s e in f i e l d s t r e n g t h that o c c u r s in the h o l e s of t h e s e tubes. It was found that the m a g n i tude of this effect is d e t e r m i n e d 'largely by the shape and s i z e of the tube and that it is q u a l i t a t i v e l y the s a m e for a v a r i e t y of m a t e r i a l s . The r e s u l t s show that what is c h a r a c t e r i s t i c of a given tube is the amount of flux that w i l l move into the hole r a t h e r than the field i n c r e a s e that will occur.
IN J. PHYS.
CHEM.
SOLIDS
v
d i f f e r e n t heavy ligands in t e t r a h e d r a l s y m m e t r y differ s u b s t a n t i a l l y f r o m the f r e e - e l e c t r o n value, e x p e c t e d for such s y s t e m s . The g - s h i f t s a r e s a t i s f a c t o r i l y explained by i m p o r t a n t c o n t r i b u t i o n s of ligand s p i n - o r b i t coupling in the p r e s e n c e of a l a r g e d e g r e e of covalency. ( R e c e i v e d 3 May 1968)
( R e c e i v e d 14 M a r c h 1968) ( R e v i s e d 27 May 1968) 18. 16.
THE MOBILITIES OF HOLES AND ELECTRONS IN IODINE SINGLE CRYSTALS B. F i t t o n ( D e p a r t m e n t of N a t u r a l P h i l o sophy, Glasgow U n i v e r s i t y , Glasgow, Scotland)
The m o b i l i t i e s w e r e m e a s u r e d by the obs e r v a t i o n of the t r a n s i t t i m e s of o p t i c a l l y g e n e r a t e d c u r r e n t p u l s e s moving a c r o s s the c r y s t a l under s p a c e - c h a r g e l i m i t e d conditions. The m a j o r i t y c a r r i e r s w e r e holes at r o o m t e m p e r a t u r e . T h e s e had a m o b i l i t y , m e a s u r e d in the b - d i r e c t i o n , which v a r i e d as exp - ( A E / k T ) with ~E = 0.08 eV over the t e m p e r a t u r e r a n g e 190 to 280°K. The m o b i l i t y was 0.66 c m 2 / V s e c at 293°K. The t r a n s i t of e l e c t r o n s was a l s o obs e r v e d in the t e m p e r a t u r e r a n g e 140 to 260CK. The e l e c t r o n m o b i l i t y v a r i e d as T -°'~ o v e r this r a n g e , with u.. = 0.6 cm e / V s e c at 250 ~K. The h o l e s c r e a t e d by light a b s o r p t i o n in e i t h e r of the two m a i n iodine a b s o r p t i o n bands have e s s e n t i a l l y the s a m e m o b i l i t y , i n d i c a t i n g hole t r a n s p o r t in a c o m m o n v a l e n c e band. ( R e c e i v e d 6 May 1968) 17.
GYROMAGNETIC FACTORS AND COVALENCY IN TETRAHEDRAL d s COMPLEXES L . D . Kandel, M. C . G . P a s s e g g i and T. Buch ( D e p a r t m e n t o de Q u i m i c a , F a c u l t a d de C i e n c i a s , U n i v e r s i d a d de Chile) g - F a c t o r s of Fe(III) c o m p l e x e s with
PHOTOCONDUCTIVITY IN CADMIUM IODIDE R . M . Yu (H. W. W i l l s P h y s i c s L a b o r a t o r y , U n i v e r s i t y of B r i s t o l , England)
E x p e r i m e n t a l m e a s u r e m e n t s of the s p e c t r a l d i s t r i b u t i o n of photoconductivity in single c r y s t a l s of c a d m i u m iodide have been c o m p a r e d with the d i s t r i b u t i o n c a l c u l a t e d f r o m De V o r e ' s t h e o r y to e s t i m a t e the p h e n o m e n o l o g i c a l p a r a m e t e r s g o v e r n i n g the p h o t o - s e n s i t i v i t y of this m a t e r i a l . F o r solution grown c a d m i u m iodide c r y s t a l s s u b j e c t e d to an e x c i t a t i o n r a t e of 5 x 101-~ photons s e c - ~ m -2 the l i f e t i m e of p h o t o - e l e c t r o n s is of the o r d e r of 1.5 nsec and the s u f r a c e r e c o m b i n a t i o n v e l o c i t y is e s t i m a t e d to be of the o r d e r of 400 km s e c - 1 . The photon e n e r g y c o r r e s p o n d i n g to p e a k photoconductivity is 3.2 eV at 290 K. It d e c r e a s e s h n e a r l y with t e m p e r a t u r e at the r a t e of - l . 5 x 10 -5 eV °K- 1 , which is s i m i l a r to the t e m p e r a t u r e shift of the o p t i c a l a b s o r p t i o n edge. At peak p h o t o s e n s i t i v i t y , the p h o t o c u r r e n t is p r o p o r t i o n a l to the 0.7th power of the light i n t e n s i t y o v e r two o r d e r s of m a g n i tude of i l l u m i n a t i o n i n t e n s i t y . The p h o t o c u r r e n t light i n t e n s i t y v a r i a t i o n a l s o depends on the photon e n e r g y . F o r the s a m e value of p h o t o c u r r e n t the r i s e and d e c a y t i m e s a r e s h o r t e r f o r photoc u r r e n t s e x c i t e d by photons of h i g h e r energy. O
.
.
( R e c e i v e d 2 May 1968)
ABSTRACTS OF PAPERS TO APPEAR IN J. PHYS. CHEM. SOLIDS
The exact diamagnetic susceptibility is calculated as a function of the magnetic field for a magnetic breakdown model which has been previously presented. The susceptibilityis obtained by numerically evaluating the appropriate derivative of the Helmholtz free energy using the exact eigenvalues of the model Hamiltonian. The susceptibilitycalculated by this method includes the contributions from both the zero-field diamagnetism and the de Haas-van Alphen effect. The periodicities in the susceptibility are r e l a ted to the semiclassical electron orbits c o r r e s ponding to this model: for low magnetic fields the periods a r e d e t e r m i n e d by two closed orbits, one within the other; for high fields a single period is observed c o r r e s p o n d i n g to the broken down case of two identical i n t e r s e c t i n g elliptical orbits. The behavior in the transition region is compatible with the expression for the breakdown probability derived by s e v e r a l authors. An approximate calculation of the o s c i l l a t o r y part of the diamagnetism is also c a r r i e d out using the s e m i c l a s s i c a l method of Falicov and Stachowiak. When the influence of the energy gap on the orbit g e o m e t r y is taken into account, their method yields r e s u l t s which a r e in good a g r e e m e n t with the exact susceptibility. Evaluation of the steady diamagnetism for the model using the e x p r e s s i o n for the susceptibility derived by Wannier and Upadhyaya yields r e s u l t s which a r e in a g r e e m e n t with the numerical calculations and, in addition, exhibits anomalous features of the z e r o - f i e l d diamagnetism in the neighborhood of c r i t i c a l points of the F e r m i surface.
(Received 20 May 1968)
14.
P R O C E S S U S D E T R A N S F E R T D'ACTIVITE" D U Fe(m) D A N S LE T R I O X A L A T O FERRATE DE POTASSIUM A. Ru~i, (Institutde physique atomique, Bucarest, Roumanie)
Le p r o c e s s u s de t r a n s f e r t d'activit~ du Fe(III) de Fe(OH)3 & Ks [Fe(C204)~ ~3H20 et & Ks [Fe(C~O,)~ ~ a lieu selon une cin~tique off chaque i s o t h e r m e c o r r e s p o n d & un palter c a r a c t~rtstique, d'une facon analogue au recuit du p r o duit irradi~. La pr~sance de l'eau de c r i s t a l l i s a t i o n a la m~me influence sur le p r o c e s s u s de t r a n s f e r t que clans le cas des cristaux irradi~ par neutrons. Les petites valeures des ~nergies d'activation calcul~es pour le processus de transfert montrent que celui-ci peut intervenir pr~feren-
Vol. 6, No. 8
tiellement dans le processus de recuit. Les spectres des ~ner~es d'activation en presence de l'eau de cristallisation indiquent un seul groupe de pics clans le cas de la substance dop~e tandis que dans le cas de la substance [rradi~e on observe netement deux groupes de pics.
En conformit@ avec ces observations on peut consid@rer que dans le p r o c e s s u s de recuit th~rmique du fer de recul, la derni~r ~tape c ' e s t & dire le passage du Fe(III) de la f o r m e simple clans la f o r m e complexe, peut ~tre repr~sent~e par un p r o c e s s u s de t r a n s f e r t . The process of transference of activity of Fe(III) from Fe(OH)a to Ks [Fe(CeO~)3_'3H20 and Ks ~Fe(C~O~)3 ~ takes place in accordance with a kinetic reaction in which each isotherm corresponds to a characteristic stage in a manner analogous to an annealing of the irradiated product. The presence of water of crystallization has the same effect on the transfer process as tn the case of crystals irradiated by neutrons. The low values of the activating energy calculated for the transfer process show that the latter can intervene preferentially in the annealing process. The spectra of the activating energy in the presence of water of crystallizationindicate a single peak group in the case of the dipped substance, while in the case of the irradiated substance we distinctly observe two peak groups. In line with these observations we may consider that in the thermic annealing of iron the last stage -- i . e . , the passing of Fe(rIl) from the simple to the complex form, may be represented by a process of transfer.
(Received 26 F e b r u a r y 1968) (Revised 10 May 1968)
15.
MAGNETIC FIELD ENHANCEMENT IN SUPERCONDUCTING TUBES E . F . Young and R. L Gayley (State University of New York at Buffalo, Buffalo, New York)
The magnetic behavior of tubes of superconducting material cooled in an axial magnetic field has been studied in an attempt to understand
Vol. 6, No. 8
ABSTRACTS
OF PAPERS
TO APPEAR
the i n c r e a s e in f i e l d s t r e n g t h that o c c u r s in the h o l e s of t h e s e tubes. It was found that the m a g n i tude of this effect is d e t e r m i n e d 'largely by the shape and s i z e of the tube and that it is q u a l i t a t i v e l y the s a m e for a v a r i e t y of m a t e r i a l s . The r e s u l t s show that what is c h a r a c t e r i s t i c of a given tube is the amount of flux that w i l l move into the hole r a t h e r than the field i n c r e a s e that will occur.
IN J. PHYS.
CHEM.
SOLIDS
v
d i f f e r e n t heavy ligands in t e t r a h e d r a l s y m m e t r y differ s u b s t a n t i a l l y f r o m the f r e e - e l e c t r o n value, e x p e c t e d for such s y s t e m s . The g - s h i f t s a r e s a t i s f a c t o r i l y explained by i m p o r t a n t c o n t r i b u t i o n s of ligand s p i n - o r b i t coupling in the p r e s e n c e of a l a r g e d e g r e e of covalency. ( R e c e i v e d 3 May 1968)
( R e c e i v e d 14 M a r c h 1968) ( R e v i s e d 27 May 1968) 18. 16.
THE MOBILITIES OF HOLES AND ELECTRONS IN IODINE SINGLE CRYSTALS B. F i t t o n ( D e p a r t m e n t of N a t u r a l P h i l o sophy, Glasgow U n i v e r s i t y , Glasgow, Scotland)
The m o b i l i t i e s w e r e m e a s u r e d by the obs e r v a t i o n of the t r a n s i t t i m e s of o p t i c a l l y g e n e r a t e d c u r r e n t p u l s e s moving a c r o s s the c r y s t a l under s p a c e - c h a r g e l i m i t e d conditions. The m a j o r i t y c a r r i e r s w e r e holes at r o o m t e m p e r a t u r e . T h e s e had a m o b i l i t y , m e a s u r e d in the b - d i r e c t i o n , which v a r i e d as exp - ( A E / k T ) with ~E = 0.08 eV over the t e m p e r a t u r e r a n g e 190 to 280°K. The m o b i l i t y was 0.66 c m 2 / V s e c at 293°K. The t r a n s i t of e l e c t r o n s was a l s o obs e r v e d in the t e m p e r a t u r e r a n g e 140 to 260CK. The e l e c t r o n m o b i l i t y v a r i e d as T -°'~ o v e r this r a n g e , with u.. = 0.6 cm e / V s e c at 250 ~K. The h o l e s c r e a t e d by light a b s o r p t i o n in e i t h e r of the two m a i n iodine a b s o r p t i o n bands have e s s e n t i a l l y the s a m e m o b i l i t y , i n d i c a t i n g hole t r a n s p o r t in a c o m m o n v a l e n c e band. ( R e c e i v e d 6 May 1968) 17.
GYROMAGNETIC FACTORS AND COVALENCY IN TETRAHEDRAL d s COMPLEXES L . D . Kandel, M. C . G . P a s s e g g i and T. Buch ( D e p a r t m e n t o de Q u i m i c a , F a c u l t a d de C i e n c i a s , U n i v e r s i d a d de Chile) g - F a c t o r s of Fe(III) c o m p l e x e s with
PHOTOCONDUCTIVITY IN CADMIUM IODIDE R . M . Yu (H. W. W i l l s P h y s i c s L a b o r a t o r y , U n i v e r s i t y of B r i s t o l , England)
E x p e r i m e n t a l m e a s u r e m e n t s of the s p e c t r a l d i s t r i b u t i o n of photoconductivity in single c r y s t a l s of c a d m i u m iodide have been c o m p a r e d with the d i s t r i b u t i o n c a l c u l a t e d f r o m De V o r e ' s t h e o r y to e s t i m a t e the p h e n o m e n o l o g i c a l p a r a m e t e r s g o v e r n i n g the p h o t o - s e n s i t i v i t y of this m a t e r i a l . F o r solution grown c a d m i u m iodide c r y s t a l s s u b j e c t e d to an e x c i t a t i o n r a t e of 5 x 101-~ photons s e c - ~ m -2 the l i f e t i m e of p h o t o - e l e c t r o n s is of the o r d e r of 1.5 nsec and the s u f r a c e r e c o m b i n a t i o n v e l o c i t y is e s t i m a t e d to be of the o r d e r of 400 km s e c - 1 . The photon e n e r g y c o r r e s p o n d i n g to p e a k photoconductivity is 3.2 eV at 290 K. It d e c r e a s e s h n e a r l y with t e m p e r a t u r e at the r a t e of - l . 5 x 10 -5 eV °K- 1 , which is s i m i l a r to the t e m p e r a t u r e shift of the o p t i c a l a b s o r p t i o n edge. At peak p h o t o s e n s i t i v i t y , the p h o t o c u r r e n t is p r o p o r t i o n a l to the 0.7th power of the light i n t e n s i t y o v e r two o r d e r s of m a g n i tude of i l l u m i n a t i o n i n t e n s i t y . The p h o t o c u r r e n t light i n t e n s i t y v a r i a t i o n a l s o depends on the photon e n e r g y . F o r the s a m e value of p h o t o c u r r e n t the r i s e and d e c a y t i m e s a r e s h o r t e r f o r photoc u r r e n t s e x c i t e d by photons of h i g h e r energy. O
.
.
( R e c e i v e d 2 May 1968)