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Submitted on 1 Jan 1978
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PRESSURE DEPENDENCE OF PHONON
LINESHAPES OF SOLlD DEUTERIUM IN THE
ORDERED STATE
R. Jochemsen, V. Goldman, Isaac Silvera
To cite this version:
JOURNAL DE PHYSIQUE
Collogue C6, suppl6ment au no 8, Tome 39, aozit 1978, page
C6-97
PRESSURE DEPENDENCE OF PHONON LINESHAPES OF S O L I D DEUTERIUM I N THE ORDERED STATE R. Jochemsen, V.V. Goldman and I s a a c F. S i l v e r a
flatumkundig Laboratoriwn, U n i v e r s i t e i t van Amsterdam, VaZckenierstraat
65, 1018 EAmsterdam
Pays Bas
R6slrmb.- On p r e s e n t e d e s r C s u l t a t s expbrimentaux e t t h b o r i q u e s s u r l e s s p e c t r e s d ' a b s o r p t i o n de l ' i n f r a - r o u g e l o i n t a i n du D (J = 1) s o l i d e , dans l ' b t a t d ' o r i e n t a t i o n ordonnbe en f o n c t i o n d e l a d e n s i t b . 2
A b s t r a c t . - R e s u l t s of experimental and t h e o r e t i c a l s t u d i e s of t h e p r e s s u r e dependence of t h e f a r i n f r a r e d a b s o r p t i o n spectrum of s o l i d ( J = 1) deuterium i n t h e o r i e n t a t i o n a l l y ordered s t a t e a r e p r e s e n t e d .
1 . INTRODUCTION.- The ground s t a t e of pure J = 1 deuterium
i s
t h e w e l l known Pa3 s t r u c t u r e , i n which t h e molecules a r e o r i e n t a t i o n a l l y ordered on f o u r s u b l a t t i c e s . T h i s space group should have two d i s - t i n c t i n f r a r e d (IR) a c t i v e phonons. The p r i n c i p a l mechanism f o r IR a b s o r p t i o n i s one i n which t h ee l e c t r i c quadrupole (EQ) f i e l d of a J = I molecule induces a d i p o l e moment on neighbouring molecules. However, t h e a b s o r p t i o n spectrum of ordered J = 1 D 2 a t z e r o p r e s s u r e d i s p l a y s t h r e e peaks superim- posed on a broad monotonically i n c r e a s i n g background
/
1,2/. The main p a r t of t h i s background a b s o r p t i o n does n o t a r i s e from t h e EQ induced mechanism. T h i s was shown by comparing t h e measured spectrum of pure s o l i d J = 0 D p , which does n o t have an EQ moment, w i t h t h e J = 1 D spectrum. S u b s t r a c t i o n of2
t h i s background y i e l d s t h e a b s o r p t i o n spectrum due t o t h e EQ induced mechanism i n t h e J = 1 s o l i d , which h a s been i n t e r p r e t e d i n t h e f o l l o w i n g way /2/ : 1)- The two lower f r e q u e n c y p e a k s r e p r e s e n t
t
t h e two IR allowed t r a n s v e r s e T and l o n g i t u d i n a l t
T' phonon t r a n s i t i o n s . The TU mode i s s h a r p l y peaked, u
whereas t h e h i g h e r frequency T' mode u i s s e v e r e l y broadened by a n h a n n o n i c i t i e s . 2)- The t h i r d peak a r i s e s from a libron-phonon combination barid.
3)- The remaining i n t e g r a t e d i n t e n s i t y i s due t o two and o t h e r multi-phonon p r o c e s s e s .
A s r e a s o n a b l e agreement between experiment and t h e o r y was o b t a i n e d b o t h i n t h e i n t e g r a t e d i n - t e n s i t y and i n t h e l i n e s h a p e s , which were c a l c u l a t e d i n t h e s e l f c o n s i s t e n t phonon approximation w i t h anharmonic c o r r e c t i o n s / 3 , 2 / . We have now extended our measurements t o p r e s s u r e s up t o 5.5 kbar and we p r e s e n t t h e r e s u l t s i n t h i s n o t e .
2. EXPERIMENT.- To p r e s s u r i z e D2 samples a c y l i n - d r i c a l BeCu c e l l was b u i l t w i t h two s a p p h i r e windows. The IR r a d i a t i o n p a s s e s through t h e h i g h p r e s s u r e c e l l and i s d e t e c t e d by a 3 ~ e - c o o l e d bolometer. The s o l i d samples a r e compressed by l i q u i d helium. A t e v e r y p r e s s u r e t h e s o l i d i f i c a t i o n temperature of D
2
i s much h i g h e r than t h a t of He, so d i f f u s i o n of He i n t o D2 i s n o t expected. The m e l t i n g l i n e of M i l l s and G r i l l y / 4 / and t h e i s o c h o r e s of Sapin and Segal
/5/ f o r He were used t o determine t h e p r e s s u r e .
3. RESULTS.- Our r e s u l t s i n d i c a t e t h a t t h e h i g h p r e s s u r e a b s o r p t i o n h a s t h e same o v e r a l l f e a t u r e s a s t h e z e r o p r e s s u r e spectrum, t h a t is, i t shows t h r e e peaks and a background which i n c r e a s e s with frequency. T y p i c a l a b s o r p t i o n s p e c t r a i n J = 1 D
2 a t two e l e v a t e d d e n s i t i e s a r e shown i n f i g u r e 1 . Our measurements l e a d t o t h e f o l l o w i n g c o n c l u s i o n s :
1 . The low frequency T~ mode remains r e l a t i v e l y U
s h a r p , i n d i c a t i n g t h a t no decay mechanism i s present f o r t h i s phonon. I t a l s o i n d i c a t e s t h a t our way of p r e s s u r i z i n g t h e D samples does n o t g i v e r i s e t o
2
l a r g e inhomogeneous s t r a i n s i n t h e c r y s t a l s . The phonon frequency a s a f u n c t i o n of molar volume y i e l d s a l i n e a r f i t on a log-log p l o t w i t h a -2 I n v GrGneisen c o n s t a n t y =
---
a
= 1.87. I n v 2. The l a r g e background c a n a g a i n b e s u b t r a c t e d by u s i n g t h e a b s o r p t i o n i n J =0
D c r y s t a l s of equal 2t h i c k n e s s . This background a b s o r p t i o n which was found t o be d e n s i t y independent, i s shown schemati- c a l l y by t h e dashed l i n e i n f i g u r e 1 .
t
T h i s work was p a r t i a l l y supported by t h e Founda- t i o n f o r Fundamental Research and Matter of t h e Netherlands (FOM).FREQUENCY (cm-'1
Fig. 1 : Absorption in solid Dp for two densities. We plot ad = -In T, where a is the absorption coef- ficient, d is the sample thickness and T is the power transmission. Solid lines : (J = 1)
D2.
Dashed lines : (J = 0) D2
3. The relative multi-phonon contribution to the total absorption seems to decrease, pointing to a decrease of the zero-point motion 121.
4. The frequency splitting between the
:
T
phonon peak and the highest frequency peak increases con- sistently with the one-libron energy, which is pro- portional to (p)5/3 due to the R - ~ EQ interaction.We have also calculated the one-phonon absorption lineshapes as a function of density using a selfconsistent phonon basis with an approximation for the phonon self-energy which includes three phonon processes as a leading term 131, and an iso- tropic potential which was recently proposed 161 for solid molecular H2. The EQQ interaction itself affects the modes in question by a fraction of one percent and was therefore neglected. The results are shown in figure 2.
t
The calculations show the T phonons to be u
perfectly sharp in spite of cubic anaharmonicity. On the other hand the longitudinal phonons are re- latively broad and change character withincreasing density. Although it is difficult to tell at this stage how specific these lineshapes are to the ac- tual approximation for the self-energy, it is clear that the phonon width remains broad even at 10 cc/mole where one expects anharmonic effects to wane.
I
V.10 cclmole ZE
Z-
V.16 cclmole V.17 cclmole 50 100 150 200 250 300 FREQUENCY (cm-I)Fig.
2
: Calculated phonon absorption lineshapes in solid ordered D.
The:
T
phonons have been broadened for cf arity.Comparing these calculations with the expe- t
riment, the positions of the TU phonons are 7 % below the measurements of the whole density range. A comparison of the T' lineshapes will have to await a more complete analysis of the libron-phonon intensities as well as multiphonon processes. Cal- culations of these quantities are now in progress.
ACKNOWLEDGEMENTS.- Special thanks are due to the Computer Center of the University of Groningen where most of the numerical work was performed.
References
/I/ Hardy, W.N., Silvera, I.F., Klump, K.N. and Schnepp, O., Phys. Rev. Lett.
2
(1968) 291 /2/ Jochemsen,R.,
Berlinsky, A.J., Goldman,V.V.
and Silvera, I.F., Commun Phys.
2
(1977) 181 / 3 / Goldman,V.V.,
Horton, G.K. and Klein,M.L.,
Phys. Rev. Lett.
26
(1970) 1424/4/ Mill, R.L. and Grilly E.R., Phys. Rev.
