Direct observation of interacting dislocation loops from different sources in Bi2Te3

Volume 23, number 7

PHYSICS

at 200 m y a r e r e p o r t e d in fig. 2 and show a l i n e a r b e h a v i o u r up to f i e l d s of 22 k V r m s / C m f o l l o w e d by a q u a d r a t i c b e h a v i o u r . T h e s i g n a l b e g i n s to s a t u r a t e at h i g h e r f i e l d s . T o e x p l a i n the p r e s e n t e x p e r i m e n t one m u s t t a k e into a c c o u n t two e f f e c t s . T h e f i r s t i s an e f f e c t of the F r a n z - K e l d y s h type, due to the k d e p e n d e n c e of the e x c i t o n w a v e f u n c t i o n s . Such an e f f e c t h a s b e e n s t u d i e d by Duke [3] f o r s e m i c o n d u c t o r s and l e a d s to a shift of the e x c i t o n p e a k to l o w e r e n e r g i e s and to a w i d e n i n g of the e x c i t o n band s u c h a s o b s e r v e d by G r o s s [4] in C u 2 0 and V r e h e n [5] in Ge. A s e c o n d e f f e c t i s due to the i o n i c n a t u r e of the c r y s t a l and i s the d i s p l a c e m e n t of the p o s i t i v e and n e g a t i v e i o n s i n d u c e d by the e l e c t r i c f i e l d . In ferroelectric materials, where such displacem e n t s a r e v e r y l a r g e , they a r e known to be r e s p o n s i b l e f o r the shift of the f u n d a m e n t a l a b s o r p -

DIRECT

LETTERS

14 November 1966

tion due to the a p p l i e d f i e l d [6]. A m o r e d e t a i l e d p a p e r w i l l be p u b l i s h e d in "I1 Nuovo C i m e n t o " . T h e a u t h o r s a r e i n d e b t e d to P r o f f . E . B a s s a n i and G. C h i a r o t t i f o r h a v i n g s u g g e s t e d t h i s i n v e s t i gation and f o r helpful d i s c u s s i o n s and c o m m e n t s .

References 1. W . F r a n z , Z.Naturforsch. 13a (1958) 484; L.W.Keldysh, Soviet Phys. J E T P 7 (1958) 788; T . S . M o s s , J. Appl. Phys. 32 (1961) 2136. 2. G.Chiarotti et al., Nuovo Cimento 26 (1962) 403. 3. G.B.Duke and M.E.Alferieff, Phys. Rev. 145 (1966) 583. 4. E . F . G r o s s , Suppl. Nuovo Cimento X {1956) 672. 5. Q . H . F . V r e h e n , Phys. Rev. 145 (1966) 675. 6. A . F r o v a and P.J.Boddy, Phys. Rev. Letters 16 (1966)688; C.G~ihwiller, private communication.

OBSERVATION OF INTERACTING DIFFERENT SOURCES

DISLOCATION IN Bi2Te 3

LOOPS

FROM

A. SAGAR and J . W . F A U S T J R . Westinghouse Research Laboratories, Pittsburgh, Pennsylvania 15235, USA Received 17 October 1966

Dislocation loops and multi-turn spirals have been observed on the basal plane in Bi2Te 3 by etching technique. Interaction between the expanding loops and obstacles and between loops from different sources has also been observed.

T h e c o n c e n t r i c d i s l o c a t i o n l o o p s and the m u l t i t u r n d i s l o c a t i o n s p i r a l s p r o d u c e d by F r a n k - R e a d s o u r c e s [1] w e r e f i r s t o b s e r v e d by D a s h [2] in s i l i c o n s a m p l e s p l a s t i c a l l y d e f o r m e d at 1000°C, using infrared transmission microscopy; this obs e r v a t i o n h a s s i n c e b e e n c o n f i r m e d by X - r a y t o p o g r a p h i c t e c h n i q u e s [3]. D i s l o c a t i o n m u l t i p l i c a t i o n by o t h e r m e c h a n i s m s [4] (which a r e s o m e what a n a l o g o u s to the F r a n k - R e a d m e c h a n i s m ) h a s a l s o b e e n r e p o r t e d in s o m e a l l o y s u s i n g t r a n s m i s s i o n e l e c t r o n m i c r o s c o p y [5]. T h i s c o m m u n i c a t i o n r e p o r t s the o b s e r v a t i o n of c o n c e n t r i c d i s l o c a t i o n l o o p s and s p i r a l s u s i n g e t c h i n g t e c h n i q u e , on the b a s a l p l a n e in h e a t t r e a t e d and q u e n c h e d B i 2 T e 3 c r y s t a l s . The c r y s t a l s u s e d w e r e g r o w n by h o r i z o n t a l z o n e - l e v e l i n g f r o m a n o n - s t o i c h i o m e t r i c t e l l u r i u m - r i c h m e l t . The 406

s a m p l e s w e r e h e a t e d a t 500°C for a f e w h o u r s to a few d a y s in v a c u u m (better than 10-5 T o r r ) in a s e a l e d q u a r t z tube, and q u e n c h e d by c o o l i n g t h e m to r o o m t e m p e r a t u r e in a few m i n u t e s . The samples were then carefully cleaved. The conc e n t r i c l o o p s and s p i r a l d i s l o c a t i o n s w e r e r e v e a l e d on the c l e a v e d s u r f a c e s of t h e s e q u e n c h e d s a m p l e s by e t c h i n g in the b r o m i n e e t c h [6]. The s p i r a l s and c o n c e n t r i c l o o p s w e r e o b s e r v e d only in the h e a t t r e a t e d and q u e n c h e d s a m p l e s ; s a m p l e s w h i c h w e r e not s u b j e c t e d to this h e a t t r e a t m e n t did not r e v e a l any l o o p s o r s p i r a l s *, a l t h o u g h s e t s of curved dislocation lines presumably originating f r o m s o m e u n i d e n t i f i e d s o u r c e s (which could * This does not exclude the possibility of small p r i s m a tic loops, which would go undetected due to the l i m i ted resolution inherent in this -technique.

Volume 23, number 7

PHYSICS LETTERS

14 November 1966

Fig. 1. (a) (850 ×) Expanding loops from a source surmounting an obstacle by bulging around it. (b) (1000 x) An example of a dislocation spiral. (c) (1000 x) Exapanding loops from a source surmounting an obstacle by leaving closed loops around it. (d) (500 x) Interacting loops from two sources in near-lying parallel slip planes. (e) (1000 x) Interacting loops from two sources in near-lying parellel slip planes. have been a c t i v a t e d by d e f o r m a t i o n during s a m p l e handling) w e r e often o b s e r v e d in a l m o s t all s a m ple s. The p r e c i s e m e c h a n i s m [1,4] r e s p o n s i b l e for these d i s l o cat i o n loops has not yet been e s t a blished; h o w e v e r , heat t r e a t m e n t and quenching s e e m to be an e s s e n t i a l i n g r e d i e n t f o r pr~oducing t he se loops in our s a m p l e s . Some of the typical p h o t o m i c r o g r a p h s obtained a r e shown in f i g . l ( a - e ) . Fig. l(a) shows the case w h er e the expanding loops f r o m a s o u r c e a r e t r y i n g to s u r m o u n t an o b s t a c l e by c u r v i n g around it [7]. Fig. I(c) shows a c a s e w h e r e the e x panding loops have s u c c e e d e d in s u r m o u n t in g an

o b s t a c l e l e a v i n g c l o s e d loops around it. The i n dividual loops around the o b s t a c l e could not be r e s o l v e d in this p h o t o m i c r o g r a p h . F i g s . 1 (d) and (e) show two e x a m p l e s of i n t e r a c t i o n between d i s l o c a tion loops f r o m two d i f f e r e n t s o u r c e s . In both e x a m p l e s , one set of loops a r e m a r k e d by b r o a d e r g r o o v e s than the other, indicating that the two s e t s of d i s l o c a t i o n loops w e r e in d i f f er en t p a r a l l el planes. The d i sl o cat i o n e n c i r c l i n g the loops f r o m the two s o u r c e s in fig. 1 (d) s e e m s to have been f o r m e d when the expanding o u t e r m o s t loops f r o m the two s o u r c e s c o m e v e r y cl o se and i n t e r a c t with each other; the n e a r - l y i n g p o r t i o n s of the 407

Volume 23, number 7

PHYSICS

LET T ERS

two l o o p s a n n i h i l a t e e a c h o t h e r , w h i c h r e s u l t s in the f o r m a t i o n of a s i n g l e loop. F i g . l ( e ) s h o w s a m o r e c o m p l e x e a s e of i n t e r a c t i n g l o o p s f r o m two s o u r c e s . No s u c h a n n i h i l a t i o n t a k e s p l a c e in t h i s c a s e . F i g . l ( b ) s h o w s a n e x a m p l e of t h e d i s l o c a t i o n m u l t i p l i c a t i o n by s p i r a l m e c h a n i s m . T h e o b s e r v a t i o n of d i s l o c a t i o n s p i r a l s w a s v e r y r a r e , although concentric loops were quite frequently observed. 1. F . C . F r a n k a n d W . T . R e a d

SOFT

X-RAY

J r . P h y s . Rev. 79 (1950) 722.

14 November 1966

2. W . C . D a s h , J. Appl. Phys. 27 (1956) 1193. 3. A . A u t h i e r and A . R , L a n g , J. Appl. Phys. 35 (1964)1956 4. J. Bardeen and C. Herring, Imperfections in Nearly Perfect C r y s t a l s , ed. W.ShocMey (John Wiley and Sons, Inc., New York, 1952)p. 261; S.Amelinelcx, W. Bontinck, W. Dekeyeser and F. Seitz, Phil. Mag. 2 (1957) 355. 5. K.H.Westmacott, R.S. B a r n e s and R. E. Smallman, Phil. Mag. 7 (1962) 1585. 6. A . S a g a r and J. W. Faust J r . , J. Appl. Phys. (to be published). 7. E.Orowan, Discussion, Symposium on Internal S t r e s s e s (Inst. Metals: London, 1947) p.451,

EMISSION AND MOMEN~fUM ME~[ALLIC LITHIUM

EIGENFUNCTION

OF

M. J. S ~ O T T a n d N. H. M A R C H

Department of Physics, The University, Sheffield 10 Received

21 October

1966

The form of the momentum eigenfunction in metallic Li is discussed and shown to lead, quite naturally, to the observed and supposedly anomalous, shape of the soft X - r a y e m i s s i o n spectrum, without appeal to the effect of the hole in the K shell. We work with the conduction band momentum e i g e n f u n c t i o n v(k +Kn) =- v(p), d e f i n e d v i a B l o c h waves ~k(r) through:

v(R+K n) exp(i{k+Kn}'r). (1) Kn H e r e the Kn's d e n o t e the r e c i p r o c a l l a t t i c e v e c ~Pk(r) = E

tors. The intensity for a spherical Fermi surface may then be written:

I(E) o: N(E) ('~ ~ q b l s ( k + K n ) d P l s ( k + K m ) (k+Kn) . K n Km (k+Krn) v

(k+Kn) v (k+Km)>av

(2)

~ ~ ( b l s (p) i s t h e m o m e n t u m e i g e n f u n c t i o n f o r the ~ o r e s t a t e w a v e f u n c t i o n , N(E) i s t h e d e n s i t y of o c c u p i e d s t a t e s a n d t h e a v e r a g e i s o v e r the s u r f a c e of c o n s t a n t e n e r g y E(k). T h e d i s p e r s i o n r e l a t i o n i s a l s o o b t a i n e d f r o m v(p) only, by u s i n g the g r o u p v e l o c i t y f o r m u l a * "

VkE : k+ E Kn Mk+ K,~)12

(a)

T h o u g h v(p) h a s c u b i c , r a t h e r t h a n s p h e r i c a l symmetry, existing data [1,2]** have been plot* Implicit in this formula is the assumption of a local periodic potential from which ~k(r) d e r i v e s . ** D r . R . E . Borland has kindly supplied us with m o r e accurate numerical r e s u l t s than those given in ref, 1. He has obtained these by intergrating through the c o r r e c t Wigner-Seitz polyhedron, r a t h e r than the equal volume sphere. 408

t e d a s a f u n c t i o n of IPt in t h e f i g u r e . It i s c e r t a i n f r o m t h e s e r e s u l t s t h a t v(p) i s p r a c t i c a l l y c o n stant over a large region inside the Fermi surf a c e a n d m u s t p a s s t h r o u g h a n o d e a n d be p o s i t i v e at a l l n o n - z e r o r e c i p r o c a l l a t t i c e v e c t o r s . The former result is simply a manifestation of f r e e e l e c t r o n - l i k e b e h a v i o u r , w h i l e t h e l a t t e r i s a c o n s e q u e n c e of the f a c t t h a t t h e h i g h m o m e n t u m c o m p o n e n t s a r e d o m i n a t e d by t h e a t o m i c l i k e n a t u r e of t h e w a v e f u n c t i o n s n e a r to t h e n u clei. B u t v(p) m u s t be c o n t i n u o u s , a n d h e n c e i t i s clear that its general form mu~t be as sketched in t h e c u r v e s h o w n in fig. 1. E x i s t i n g c a l c u l a t i o n s do not t e l l u s t h e p o s i t i o n a n d h e i g h t of t h e p e a k in

v(p) C,2 "

K,

0.2

04

-02

0'6

08

10

1.2

1"4

.-2.

t ,

20

--

P ~ au

-04

-0tl -FO[

~J

Fig. I. Momentum eigenfunction of conduction band in Li. The crosses denote the values calculated from

band theory [1,2].

215