Temperature and phase dependence of positron lifetimes in CH3OH and CD3OD

PHYSICS

Volume 33A, number l

w h e r e A i s t h e s p i n - o r b i t s p l i t t i n g (0.04 eV f o r silicon) and A is the conventional band parameter [1], t h e e f f e c t i v e m a s s v a l u e c a l c u l a t e d f r o m w h i c h l i e s b e t w e e n 0.23 a n d 0 . 2 5 m o [ 1 - 3 ] . T h e o b s e r v e d i s o t r o p y of t h e e f f e c t i v e m a s s f o r t h e c e n t r a l peak c e r t a i n l y is c o n s i s t e n t with the f o r m of eq. (1), but t h e o b s e r v e d m a s s v a l u e i s s o m e w h a t l a r g e r t h a n t h a t c a l c u l a t e d f r o m eq. (1). U s e of t h e m o n o c h r o m a t i c l a s e r b e a m a n d a s t r o n g microwave power makes the carrier temperature considerably higher than the lattice temperature. In t h a t c a s e , t h e e f f e c t i v e m a s s s h i f t i s l i k e l y to o c c u r [3]. In f a c t , t h e e f f e c t i v e m a s s e s of t h e J = } s e t a l s o g e t c l o s e t o t h o s e of u n s t r e s s e d light and heavy holes. U n d e r the white light il-

TEMPERATURE

AND LIFETIMES

PHASE IN S. Y. CHUANG

21 September 1970

L ET T E RS

l u m i n a t i o n , M j :: ± ~ ( J = ~ ) a n d M j = ± ~ ( j : ½ ) signals disappear. T h e r e l a t i v e i n t e n s i t i e s of t h e t h r e e r e s o nances are evidently non-Boltzmann. Detailed s t u d y of d y n a m i c a l b e h a v i o r s of t h e J :: ~ b a n d h o l e s i s n o w in p r e p a r a t i o n .

S @ ~'~n CUS

[l t G. Dresse[haus. A.F. Kip ~md C. Kittel, Phys. Ill,',. 98 (1955) 368. [21 B. Lax, tt.0. Zeiger and R. N, Dexter, Phys. Rev. 104 (1956) 637. [3] J . C , Hensel and G. Feher, Phys. Rex'. 129 (1~63i 1041.

DEPENDENCE CH3OH AND

OF

POSITRON

CD3OD

and S. J. TAO

The New England Institute. Ridgcfi¢ld,

Connecticut,

USA

I{ceeived 3 August 197()

It has been found that the lifetime 72 and the relative intensity 12 of o - P s show a marked discontinuity at the solid-solid phase transition as well as at the solid-liquid phase transition in both CH3OH and CD3OD.

T h e e f f e c t of p h a s e t r a n s i t i o n on the l i f e t i m e of P s a s w e l l a s on t h e P s f o r m a t i o n in m a n y s u b s t a n c e s h a s b e e n r e p o r t e d and p a r t of the r e s u l t s have been summarized in a recent review [1]. The water-ice system in particular has been investigated intensively both by lifetime measurements and by angular correlation experiments. The most interesting and still unexplained fact in the waterZice system is that the lifetime of o-Ps increases while the formation of Ps decreases upon melting. This effect is even stronger in D20 [2]. Since simple theories such as the "free volume model" [3] and the "Ore model" can not explain this effect, it indicates that molecular reorientations and intermolecular interactions must play an+important role in the slowing down process of e as well as Ps at phase transitions. In order to clarify this point, we have carefully measured positron lifetimes in both CH3OH and CD3OD as function of temperature. The reason to choose these samples is that they are all small molecules with OH or OD in their structure

56

w h i c h i s s i m i l a r to w a t e r m o l e c u l e s . In a d d i t i o n to t h i s , m e t h a n o l u n d e r g o e s a s o l i d - s o l i d p h a s e t r a n s i t i o n . T h e low t e m p e r a t u r e s o l i d p h a s e i s a n i s o t r o p i c with a low s y m m e t r i c c r y s t a l s t r u c t u r e w h i l e t h e high t e m p e r a t u r e s o l i d p h a s e h a s an o r t h o r h o m b i c c r y s t a l s t r u c t u r e [4]. T h e i s o t r o p i c s o l i d p h a s e , of s o - c a l l e d r o t a t i o n p h a s e , i s a t t r i b u t e d to the r o t a t i o n of the OH o r OD g r o u p in s o l i d l a t t i c e s . It i s w e l l knox~m t h a t c o m p a r i s o n between isotopic molecules can give information a b o u t the r o t a t i o n b a r r i e r s [5]. H e n c e c o m p a r i s o n of the r e s u l t s of l i f e t i m e m e a s u r e m e n t s of p o s i t r o n s in m e t h a n o l and i t s i s o t o p i c m o l e c u l e s can g i v e i n f o r m a t i o n c o n c e r n i n g t h e e f f e c t of m o l e c u l a r r o t a t i o n of t h e f a t e of P s . The lifetime-measurement apparatus has been describedpreviously[6]. It has a resolution of a fwhm of 400 psec of "60 Co" prompt curve at 22Na setting and has a linear range of 25 nsec. The samples under investigation were carefully degassed. The temperature-control system was s i m i l a r to the one r e p o r t e d p r e v i o u s l y !17] T h e

PHYSICS LETTERS

Volume 33A, number 1

50

TH t

17(~1:,

TD 4" 1

MDMH I' I

CH3OH

-=--o-

i

=

solid- solid p h ase t r a n s i t i o n (X point), - 117°C f o r CH3OH and - l l 0 ° C f o r CD3OD , and a l s o show a sh ar p discontinuity at the m e l t i n g point, - 9 8 ° C f o r CH3OH a n d - 1 0 1 o c f o r CD3OD. 2. F o r both s a m p l e s , I 2 s t a r t s to i n c r e a s e at a t e m p e r a t u r e about ten d e g r e e s below the X point and r e a c h e s a m a x i m u m at the ~ point. T h i s can he ex p l ai n ed by the fact that the r e o r i e n t a t i o n of the OH o r OD group s t a r t s at a t e m p e r a t u r e l o w e r than the X point. ~'1 shows a m i n i m u m at the X point which can be u n d e r s t o o d as due to the sudden i n c r e a s i n g of P s f o r m a t i o n at X point. 3. F o r both s a m p l e s , ~-2 i n c r e a s e s while I 2 d e c r e a s e s upon m e l t i n g which is s i m i l a r to the r e s u l t s of H 2 0 and D 2 0 [2]. 4. When c o m p a r i n g T2 and I 2 for CH3OH and CD3OD , t h e r e is no si g n i f i can t d i f f e r e n c e f o r the two s u b s t a n c e s in the low t e m p e r a t u r e solid phase. But in the i s o t r o p i c solid phase, w h er e m o l e c u l a r r o t a t i o n b e c o m e s significant, both T2 and I 2 of CH3OH a r e l a r g e r than that of CD3OD. F r o m the above r e s u l t s , it is c l e a r that the m o l e c u l a r r o t a t i o n and i n t e r m o l e c u l a r i n t e r a c t i o n s a l t e r the f o r m a t i o n and annihilation of P s in CH3OH and CD3OD.

40 I

%'

,

30

20 i

i

i

d

i

i

"/'2(nsec) 2.70 2.30

1 I

1.90

I

I 1.50 ,

/ ~:, Inse¢ ) 0.38 r , I

0.30

I,

. l L

,

-150

i

-130

, i

~ - ~ = ~ ~ -

tit'

i,t1=

-llO

- I,

,

-90

TEMP.(°C)

21 September 1970

,

-70

Fig. 1. The lifetimes T1, "r2 and the relative intensity 12 as a function of temperature for CH3OH and CD3OD. TH and TD are transition points of CH3OH and CD3OD respectively; and MH and MD are melting points of CH3OH and CD3OD respectively. stability of t e m p e r a t u r e was within 0.5°C f o r each m e a s u r e m e n t . The l i f e t i m e s p e c t r a under i n v e s t i gation can be d e c o m p o s e d into two l i f e t i m e c o m ponents. The s h o r t l i f e t i m e component 71 i s due to the annihilation of f r e e p o s i t r o n s and p - P s . The long l i f e t i m e component ~2' with a r e l a t i v e i n t e n s i t y / 2 , i s due to the p i c k - o f f annihilation of o - P s . The r e s u l t s a r e shown in fig. 1. Some i m p o r t a n t p h e n o m e n a a r e s u m m a r i z e d as follows: 1. Both r 2 and 12 show a sudden change at the

F u r t h e r i n v e s t i g a t i o n along this line is c u r r e n t ly being u n d e r t a k e n in our l a b o r a t o r y . T h i s work was p a r t i a l l y su p p o r t ed by AEC C o n t r a c t (30-1) 3661.

Refe~'el,t.ces [1] V. I. Goldanskii, At. Energy Rev. 6 (1968) 3. [2] K. Petersen, M. Eldrup and G. Trumpy, Phys. Letters 31A (1970) 109. [3] W. Brandt, S. Berko and W. W. Walker, Phys. Rev. 120 (1960) 1289. [4] K. J. Tauer and W. N. Lipscomb, Aeta. Cryst. 5 (1952) 606. [5] A. R. Ubbelohde, J. Phys. Chem. Solids 18 (1961) 90. [6] S. Y. Chuang and S. J. Tao, J. Chem. Phys. 52 (1970) 749. [7] S. Y. Chuang, W.H. Holt and B. G. Hogg, Can. J. Phys. 46 (1968) 2309.

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