Observation of structures in the chromium Kα1 line with spherically bent crystal spectrometer

Volume 33A, n u m b e r 5

PHYSICS

OBSERVATION OF STRUCTURES WITH SPHERICALLY BENT

LETTERS

IN THE CRYSTAL

16 November 1970

CHROMIUM Ka 1 LINE SPECTROMETER

K. D a s G U P T A and P. F. GOTT Department of P h y s i c s , Texas Tech University. Lubbock. Texas, USA

Received 10 October 1970

S t r u c t u r e s in the K~ 1 line of c h r o m i u m have been o b s e r v e d with a high-resolution, h i g h - d i s p e r s i o n s p h e r i c a l l y bent c r y s t a l s p e c t r o m e t e r with high light gathering power.

It i s w e l l - k n o w n f r o m t h e X - r a y s p e c t r o s c o p i c d a t a t a k e n w i t h a two c r y s t a l s p e c t r o m e t e r t h a t t h e s h a p e of Kot l i n e s of t r a n s i t i o n e l e m e n t s d e part significantly from the Lorentzian form. The a s y m m e t r y o r t h e t a i l i n g of Kot l i n e of c h r o m i u m o n t h e l o n g w a v e l e n g t h s i d e , t a k e n w i t h a two q u a r t z c r y s t a l s p e c t r o m e t e r i s s h o w n i n fig. l ( a ) . T h e a s y m m e t r y i n d e x of C r K a 1 m e a s u r e d w i t h o u r two c r y s t a l s p e c t r o m e t e r a g r e e s w e l l w i t h t h e a s y m m e t r y i n d e x f o u n d by P a r r a t t [1]. R e c e n t l y , S h a h a n d D a s G u p t a [2], u s i n g a t h r e e crystal spectrometer, reported the observation o s s t r u c t u r e s i n t h e l o n g w a v e l e n g t h t a i l i n g of C r K a 1 l i n e a s s h o w n in fig. l ( b ) . In t h i s l e t t e r we r e p o r t t h e o p e r a t i o n a n d t h e e s s e n t i a l f e a t u r e s of a n e w l y d e s i g n e d s p h e r i c a l l y bent crystal spectrometer which revealed the s t r u c t u r e s of t h e C r K a 1 l i n e a s s h o w n i n fig. l ( c ) . T h i s i s a l s o a c o n f i r m a t i o n of t h e e a r l i e r f i n d i n g s o s s i m i l a r s t r u c t u r e s o b s e r v e d by S h a h a n d D a s G u p t a [2]. T h e r e s o l u t i o n i n X - r a y s p e c t r o s c o p y i s e s s e n t i a l l y d e t e r m i n e d by t h e ( 1 , - 1 ) r o c k i n g c u r v e w i d t h of t h e a n a l y z e r c r y s t a l . T h e r o c k i n g c u r v e w i d t h i s a f u n c t i o n of t h e m o s a i c i t y , t h e i n t e n s i t y of t h e t h e r m a l d i f f u s e s c a t t e r i n g , i m p e r f e c t i o n s of t h e c r y s t a l . T h e r e s o l u t i o n i n c r e a s e s w i t h t h e i n c r e a s e i n t h e o r d e r of B r a g g reflection. With our spherically bent crystal spectrometer, we have increased the resolution b y i n c r e a s i n g t h e o r d e r of B r a g g r e f l e c t i o n . T h e e s s e n t i a l p a r t of t h e i n s t r u m e n t i s t h e s p h e r i c a l l y b e n t c r y s t a l w h i c h i s a t h i n p i e c e of m i c a (0.14 m m ) p r e s s e d b e t w e e n t w o c u r v e d p i e c e s of g l a s s , of r a d i u s 101 c m . A s l i t of 40 m i c r o n w i d t h a n d 0.3 m m h e i g h t h a s b e e n u s e d a s t h e s e c o n d a r y s o u r c e . T h e r a d i u s of t h e R o w l a n d c i r c l e of t h e s p e c t r o m e t e r i s 50.5 c m , w h i c h i s h a l f t h e r a d i u s of t h e s p h e r i c a l l y b e n t c r y s t a l . F o r s c a n n i n g t h e C r K a 1 a n d Kot 2 l i n e s , t h e c e n t e r of t h e 276

spherically bent crystal is placed from the slit a t a d i s t a n c e e q u a l to t h e c a l c u l a t e d c h o r d l e n g t h c o r r e s p o n d i n g to t h e m e a n w a v e l e n g t h of C r K a 1 a n d K a 2. T h e e f f e c t i v e w i d t h of t h e b e n t c r y s t a l , w h i c h i s e x p o s e d to X - r a y s , i s 2.0 m m . T h e a x i s of t h e c o n e of t h e i n c i d e n t X - r a y b e a m , of t h e B r a g g r e f l e c t e d b e a m , a n d t h e n o r m a l to t h e bent crystal all lie in the same horizontal plane. T h e s l i t , t h e c e n t e r of t h e b e n t c r y s t a l a n d t h e f o c u s e d i m a g e a l l l i e on t h e f o c u s i n g R o w l a n d c i r c l e . S u c h a n a l i g n m e n t of t h e s p e c t r o m e t e r w i t h a m i c a c r y s t a l h a s b e e n t e s t e d f o r t h e 5th a n d 8th o r d e r s of r e f l e c t i o n . T h e c a l c u l a t e d a n g u l a r s e p a r a t i o n b e t w e e n t h e p e a k of C r K a and

5

,,

5

5

/

c)

:/ ¢ irl\

'\,

N~xx

I ev Fig. l(a) CrK0t 1 with two c r y s t a l s l(b) CrKOt 1 with t h r e e c r y s t a l s in (1,1,2) position l(e) T r a c i n g of the strip c h a r t r e c o r d of the CrKOt 1 line with spherically bent mica c r y s t a l in 8th o r d e r of reflection. The energy' separation between s t r u c t u r e s (1) and (2) = 0.2 eV, (1) and (3) = 0.5 eV, (1) and (4) = 0.9 eV and (1) and (5) = 1.4 eV in fig. l(b) and s i m i l a r s e p a r a tions a r e 0.2, 0.6, 0.9 and 1.2 eV in fig. l(e). Struct u r e s do not appear with the two c r y s t a l s p e c t r o m e t e r as shown in fig. l(a).

Volume 33A, number 5

PHYSICS LETTERS

the peak of CrKot 2 is 830 seconds of a r c in the 8th o r d e r of r e f l e c t i o n and the m e a s u r e d value with our i n s t r u m e n t is 826 ± 2 seconds of a r c . In our study of the C r K a 1 line, the c e n t e r of the bent c r y s t a l is set at a distance f r o m the slit equal to the calculated chord length c o r r e s p o n d i n g to the wavelength of the CrKot 1 peak. The c r y s t a l is r o t a t e d with a m o t o r and a s t r i p c h a r t r e c o r d of the s p e c t r u m is taken in the conventional m a n n e r . The h o r i z o n t a l width of the slit is 40 m i c r o n s . T h i s i n t r o d u c e s at any fixed Bragg setting an e r r o r of ~: 4 seconds of a r c due to the a n g u l a r d i v e r g e n c e of 8 seconds at the c r y s t a l caused by the finite width of the slit. This i n t r o d u c e s an e r r o r of 0.1 eV in the m e a s u r e m e n t of the width of C r K a 1 in the 8th o r d e r . This is also a cont r o l l i n g factor of the r e s o l u t i o n of the s p e c t r o m e t e r , and s t r u c t u r e s with a s e p a r a t i o n l e s s than 0.1 eV cannot be o b s e r v e d for C r K a 1 in the 8th o r d e r . It i s , however, p o s s i b l e to u s e a slit

NOTES

ON A B S O R P T I O N

16 November 1970

of width as s m a l l as 10 m i c r o n s which will i n c r e a s e the r e s o l u t i o n but which will significantly r e d u c e the count r a t e . The a s t i g m a t i s m a s s o c i a t ed with the conventional c y l i n d r i c a l l y bent c r y s t a l is r e d u c e d due to the focusing g e o m e t r y of the s p h e r i c a l l y bent c r y s t a l . This l a t t e r p r o p e r t y c o n t r i b u t e s to a higher c o n c e n t r a t i o n of X - r a y s and t h e r e f o r e s p e c t r o s c o p y is p o s s i b l e in higher o r d e r s of r e f l e c t i o n at high r e s o l u t i o n and at high i n t e n s i t y . We b e l i e v e that for high r e s o l u t i o n s p e c t r o s c o p y in the £ n g s t r o m o r d e r wavelength region, the s p h e r i c a l l y bent c r y s t a l at higher o r d e r s of r e f l e c t i o n could profitably r e p l a c e the conventional two c r y s t a l s p e c t r o m e t e r .

References [1] L.G. Psrratt, Phys. Rev. 44 0933) 695. [2] M. Shah and K. Das Gupta, Phys. Letters 24A (1969) 570.

BAND

EDGE

OF SbSI

H. KAMIMURA *, S. M. SHAPIRO and M. BALKANSKI Laboratoire de Physique des Solides, Facult~ des Sciences, Paris, France Equipe de Recherche Associ$e au C.N.R.S.

Received 19 October 1970

Existing absorption edge data of paraelectric SbSI are analyzed and found to follow the Urbach rule. As a result of our analysis the frequency of the phonon which interacts most strongly with the exciton is found to be ~ 220 cm -1.

The object of this b r i e f study lies in c l a r i f y ing the e l e c t r o n i c s t r u c t u r e of SbSI above an4 below the c r i t i c a l t e m p e r a t u r e (T c = 20°C). As a f i r s t step we i n v e s t i g a t e d the a b s o r p t i o n data, c u r r e n t l y available [1, 2]. The a b s o r p t i o n coefficients v e r s u s frequency for E ± c and E / / c were m e a s u r e d at T = 25°C, slightly above the c r i t i c a l t e m p e r a t u r e . The log of the a b s o r p t i o n coefficient is a l i n e a r function of energy in the r e g i o n of the coefficient f r o m 100 cm -1 to 600 c m -1 (fig. 1). This l i n e a r dependence is explained by the Urbach rule [3]: K = K 0 e x p ( a / k B T * ) (E - E o ( T ) )

(1)

* Permanent address: Department of Physics, Faculty

of Sciences, University of Tokyo, Tokyo, Japan.

where K is the a b s o r p t i p n coefficient, T* is the effective t e m p e r a t u r e defined by: T* = ( h w ' / 2 k B) coth(hco'/2kBT)

(2)

where ~ ' is the f r e q u e n c y of the phonon with which the exciton i n t e r a c t s most strongly. The d e p a r t u r e f r o m l i n e a r i t y in the low f r e q u e n c y region may be a t t r i b u t e d to i m p u r i t i e s within the s a m p l e [4]. In our t r e a t m e n t we let cr and w' be a d j u s t a b l e p a r a m e t e r s which a r e d e t e r m i n e d f r o m the data. F r o m the slope of the l i n e a r dependence in fig. 1, we a r e able to d e t e r m i n e the values of ( r / k B T * which a r e a l m o s t i d e n t i c a l for the two p o l a r i z a tions. This value is 30 eV -1. Using this value of a / k B T * , we can g r a p h i c a l l y solve eq. (2) for h ~ ' . We find the solution of hw' for the value of 277