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ELECTRON-ELECTRON SCATTERING IN TUNGSTEN
B. Nilaratna, A. Myers
To cite this version:
B. Nilaratna, A. Myers. ELECTRON-ELECTRON SCATTERING IN TUNGSTEN. Journal de
Physique Colloques, 1978, 39 (C6), pp.C6-1064-C6-1065. �10.1051/jphyscol:19786471�. �jpa-00217952�
JOURNAL D E PHYSIQUE
Colloque
C6,supplPment au no 8, Tome 39, aolit 1978, page
C6-1064ELECTRON-ELECTRON SCATTERING I N TUNGSTEN
B.P. N i l a r a t n a and A.Myers
Department of Physics, University of Leeds, Leeds LS2 952: U.K.
Rgsum6.- On a f a i t l e s mesures du temps moyen d e d i f f u s i o n d e s g l e c t r o n s s u r l e s o r b i t e s dans l a r g g i o n du t r o u o c t a s d r i q u e d e l a s u r f a c e d e Fermi du tungstPne, e t on en a d s d u i t l a v a r i a t i o n du temps ( T ) d e l a d i f f u s i o n l o c a l e . Une a n i s o t r o p i e c o n s i d g r a b l e du temps de l a d i f f u s i o n e s t o b s e r v s e avec une dgpendance e n T2 i n d i q u a n t une c o n t r i b u t i o n dominante du p r o c e s s u s d e d i f f u s i o n g l e c t r o n - E l e c t r o n .
A b s t r a c t . - Measurements of t h e e l e c t r o n s c a t t e r i n g time averaged over o r b i t s on t h e h o l e octahedron p a r t of t h e Fermi s u r f a c e of t u n g s t e n have been made and t h e v a r i a t i o n of t h e l o c a l s c a t t e r i n g time ( r ) deduced. Considerable a n i s o t r o p y i n t h e s c a t t e r i n g time i s obser- ved t o g e t h e r w i t h a T2 dependence which..-is taken t o b e i n d i c a t i v e of a dominant e l e c t r o n - e l e c t r o n s c a t t e r i n g p r o c e s s .
Measurements of t h e o r b i t a l l y averaged s c a t t e r i n g r a t e
-
1 > were f i r s t r e p o r t e d i n tungs- t e n some y e a r s ago / l / when a T2 temperature depen- dence was observed. The t e c h n i q u e used i n t h a t and t h e p r e s e n t work employed t h e p a r a l l e l f i e l d r a t i o frequency s i z e e f f e c t ( r f s e ) which has been des- c r i b e d p r e v i o u s l y121.
I n t h e p r e s e n t work t h e e a r l i e r measurements have been extended t o cover t h e temperature r a n g e 1-14 K on a number of o r b i t s over t h e h o l e octahedron p a r t of t h e Fermi s u r f a c e i n t h e (110) p l a n e . A t y p i c a l p l o t of <-
1 > a g a i n s tT
temperature (T) i s s e e n i n f i g u r e 1 i n which a T2 dependence i s observed up t o s 8 K w i t h a h i g h e r t e m p e r a t u r e dependence observed a t h i g h e r tempera- t u r e s . T h i s behaviour h a s been p r e v i o u s l y observed i n t u n g s t e n / 3 / and i s b e l i e v e d t o r e s u l t from a dominant e l e c t r o n - e l e c t r o n c o n t r i b u t i o n (crT2) a t low t,emperatures which i s modified a t h i g h e r tempe- r a t u r e s by an electron-phonon c o n t r i b u t i o n ( a ~ ~ )
.
A f u r t h e r complication w i t h t h i s s u r f a c e i s t h a t t h e temperature v a r i a t i o n of t h e amplitude of t h e r f s e s i g n a l showed anomalous behaviour a s r e p o r t e d p r e v i o u s l y
/
l / . The e x i s t e n c e of t h i s anomalous behaviour implied an obviously erroneous d e c r e a s i n g s c a t t e r i n g time w i t h d e c r e a s i n g temperature a n d , i n t h e absence o f any e x p l a n a t i o n f o r t h e anomaly, no meaningful examination of t h e d a t a could b e made.An e x p l a n a t i o n h a s been g i v e n r e c e n t l y /4/ i n terms of o v e r l a p between t h e r f s e s i g n a l s o r i g i n a - t i n g from t h e c e n t r a l - e x t r e m a l o r b i t s on t h e Fermi s u r f a c e and from non-central o r b i t s . This work also p r o v i d e s a means of o b t a i n i n g t h e temperature de- pendence of c > d e s p i t e t h e anomalous behaviour.
These v a l u e s of <
F
1 > have been i n v e r t e d t o g i v e t h e l o c a l v a l u e s of t h e s c a t t e r i n g r a t e (7
1 ) . The i n v e r s i o n h a s been made u s i n g t h e r e l a t i o nwhere t h e i n t e g r a t i o n i s t a k e n around t h e o r b i t i n k-space and v 1 i s t h e component of t h e e l e c t r o n
-
v e l o c i t y i n t h e p l a n e of t h e o r b i t . The f i t t o t h e 1
50 measured v a l u e s of <
-
> was made by e x p r e s s i n gT i n t h e form
-
1 E C C K (B,$)T i , k i R i ~ ( 2 )
where iKk(8,$) d e n o t e s t h e c u b i c harmonic of 2 t h o r d e r having i i r r e d u c i b l e r e p r e s e n t a t i o n s . The a d d i t i o n a l terms appearing i n (1) a r e t h e e f f e c -
T21Kzl
t i v e c y c l o t r o n mass m: and t h e v e l o c i t y component F i g u r e 1 . : P l o t of t h e e l e c t r o n s c a t t e r i n g r a t e v 1
.
Values of m+ on t h e h o l e octahedron p a r t of< > with temperature
C
l''lin
the 1°' t h e Fermi s u r f a c z have been taken from /5/. Valuesp i L e .
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786471
of t h e e l e c t r o n v e l o c i t y on t h i s s u r f a c e were a l s o g i v e n i n t h a t work b u t t h e component v was not c a l c u l a t e d . I n t h e p r e s e n t work t h e v a l u e s of v
l
have been o b t a i n e d a f t e r modifying t h e scheme f o l -
l
lowed i n 151. The "best" f i t t o t h e v a l u e s of < - > 1 was o b t a i n e d u s i n g a f i v e term c u b i c harmonic f i t . C a l c u l a t i o n s u s i n g more terms f i t t h e s c a t t e r i n t h e experimental d a t a w h i l e c a l c u l a t i o n s w i t h l e s s t h a n f o u r terms lead t o a poor f i t t o t h e o v e r a l l t r e n d i n t h e d a t a . The f i v e term c u b i c harmonic f i t l e a d s t o a v a r i a t i o n of
-
1 a s shown i n f i g u r e 2. It can be seen t h a t t h e r e i s v e r y c o n s i d e r a b l e a n i s o t r o p y i n t h e l o c a l s c a t t e r i n g r a t e .F i g . 2 : P l o t of t h e l o c a l s c a t t e r i n g r a t e
-
1 a t 4 K over the { 110) p l a n e , l a n g l e s being measuredTfromc0a. The u n i t s of - a r e 1 0 ~ s - 1 .
There a r e , however, s e v e r a l d i f f i c u l t i e s i n t h e d e t e r m i n a t i o n of
-
1 which a r e p r e s e n t on t h i s s u r - f a c e and which a r e n o t encountered i n simple m e t a l s e . g . copper. These d i f f i c u l t i e s a r e probably inhe- r e n t and a r e a s f o l l o w s :( i ) t h e complex, m u l t i s h e e t Fermi s u r f a c e l e a d s t o s i g n a l o v e r l a p p r e v e n t i n g h i g h p r e c i s i o n measure- ments of m+ of t h e kind which can be made i n many o t h e r m e t a l s ;
( i i ) t h e r e a r e f a i r l y wide v a r i a t i o n s i n t h e e l e c - t r o n v e l o c i t y over t h e h o l e octahedron ( a s shown i n /5/ and t h e weighting from r e g i o n s of h i g h v e l o c i t y i s , of c o u r s e , low;
( i i i ) t h e r e i s anomalous behaviour i n t h e r f s e si- g n a l amplitude on t h i s s u r f a c e and t h i s l i m i t s t h e accuracy of t h e measurement of c - 1 > f o r some o r b i t s .
~ h u s some c a u t i o n should b e e x e r c i s e d i n
v a r i a t i o n of t h e s c a t t e r i n g r a t e i s b e l i e v e d t o be given i n f i g u r e 2.
There have been no published t h e o r e t i c a l c a l c u l a t i o n s of t h e e l e c t r o n - e l e c t r o n s c a t t e r i n g r a t e over t h i s o r any o t h e r s u r f a c e and s o no comparison with t h e o r y i s p o s s i b l e . I t i s hoped, however, t h a t such c a l c u l a t i o n s w i l l be attempted now t h a t t h e s c a t t e r i n g r a t e a n i s o t r o p y has been o b t a i n e d . This might con£ i r m t h e view t h a t t h e T*
c o n t r i b u t i o n a r i s e s from an e l e c t r o n - e l e c t r o n s c a t t e r i n g c o n t r i b u t i o n and not from o t h e r e f f e c t s a s has been suggested / 6 / .
References
/ l / Thompson, R.S. and Myers, A.,J.Phys. F
3
(1973)L64.
/2/ Myers, A . , P o r t e r , S.G. and Thompson, R.S., 3 . Phys. F
2
(1972) 24./3/ Boiko, V . V . , Gantmakher, V.F. and Gasparov, V.A., JETP - 38 (1974) 604.
141 Beacock, P.E. and Myers, A., J.Phys. F
L
(1977) 2135./5/ Feenan, P . J . , Myers, A. and Sang, D.,Solid S t a t e Comun.
2
(1975) 35.161 Wagner, D.K., Phys. Rev.
B 5
( 1972) 336.c o n s i d e r i n g t h e curve p a r t i c u l a r l y i n t h e r e g i o n about
