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Submitted on 1 Jan 1978
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FREQUENCY OF PHONONS EMITTED INTO
LIQUID He BY A SOLID
A. Wyatt, G. Crisp
To cite this version:
JOURNAL DE PHYSIQUE Colloque C6, supplement au n° 8, Tome 39, aout 1978, page C6-244
FREQUENCY OF PHONONS EMITTED INTO LIQUID He BY A SOLID
A.F.G. Wyatt* and G.N. Crisp+§
Department of Physios, University of Exeter, Exeter, Devon, England.
+
Department of Physios, University of Nottingham, Nottingham, England.
Résumé.- Nous avons mesuré la distribution angulaire des phonons émis par NaF avec un bolomètre qui détecte toutes les fréquences et une jonction tunnel supraconductrice qui est sensible aux phonons de Ho> > 2A. Les deux distributions sont très différentes et nous concluons que les fréquences des phonons dans le canal de fond continu sont plus faibles que dans le pic.
Abstract.- We have measured the angular distribution of phonons emitted from NaF with a bolometer which detects all frequencies and a superconducting tunnel junction which is only sensitive to pho-nons with fto) > 2A. The two distributions are substantially different and we conclude that the phonon frequencies in the background channel are lower than those in the peak.
INTRODUCTION.- It is now established that there are two channels for the transmission of phonons from a solid into liquid He /l/. In the classical channel the parallel component of the wave vector (qj]) is conserved and it should be safe to assume that pho-non frequency (oo) is also conserved. However the se-cond channel does not conserve q.. and phonons are radiated into all angles in the liquid He. Although q is not conserved in this background channel it does not necessarily follow that oo is not conserved.lt
is certainly possible to think of processes in which there are interface states that can absorb momentum but nevertheless scatter phonons elastically. As higher frequency phonons have a higher transmission coefficient for this channel we would expect in this case that the spectrum of phonon frequencies in the background would be at least as high as in the peak. On the other hand there could be inelastic scatte-ring from interface states or a non linear interac-tion at the interface which results in multiphonon production. In both cases the background spectrum would be significantly lower than the peak one. These possibilities are shown in figure I.
A measurement of the relative spectra in the peak and background would therefore help elucidate the microscopic processes which give rise to the background channel. Further most experiments on pu-lsed phonons in liquid He rely on injecting phonons in the background channel so it is of paramount im-portance in interpreting these experiments to know the frequency of the phonons being used.
Conside-rable problems of interpretation arise if it is as-sumed that the injected phonons have the same tem-perature as those in the solid which emitted them /2,3,4/.
(a)
(b)
(c)
Fig. I : Possible processes for the transmission of a phonon from a solid into the background distribu-tion in the liquid He. a) inelastic scattering w > u) ; dotted lines indicate delayed emission into the solid or liquid He.b) elastic scattering w = u_ but
a, = q„; c) non linear interaction a).=0)2+w, and q..
- q12 + V
EXPERIMENTAL METHOD.- In order to investigate this matter we have measured the angular distribution of phonons emitted from a NaF crystalwith:bothbolometer and tunnel junction detectors. The graphite bolome-ter is sensitive to all phonon frequencies whereas the superconducting Al tunnel junction only detects phonons with Kw > 2A where A is the superconduc-ting energy gap /5/. The single crystal of NaF had a thin film Au heater on its back face and could ro-tate about a vertical axis. The bolometer and tunnel junction detectors were 8 mm away. The arrangement is shown schematically in figure 2. The crystal had an emitting area of ^ 2 mm2 which is considerably
larger than that used in the earlier angular butions measurements /l/ and so the measured distri-butions are broader. The measurements were taken
§ Present Address: Institute of Oceonagraphic Sciences, Taunton, England.
w i t h t h e He a t a p r e s s u r e of 20 b a r s o t h a t t h e r e was no s c a t t e r i n g i n t h e He. A s t h e superconducting tun- n e l j u n c t i o n i s s e n s i t i v e t o magnetic f i e l d , t h e o r i g i n a l magnetic r o t a t o r was u n s u i t a b l e and t h e c r y s t a l had t o be r o t a t e d w i t h a superconducting s t e p p i n g motor. This meant t h a t a continuous angu- l a r s c a n could n o t be made and i n s t e a d a t each an- g l e t h e c r y s t a l was s t a t i o n a r y and t h e r e c e i v e d s i - g n a l a s a f u n c t i o n of time was taken. The i n i t i a l s l o p e of t h i s s i g n a l was taken t o b e p r o p o r t i o n a l t o t h e phonon f l u x . I I l
I
I I l I -40 -30 -20 -10 0 10 20 30 40 Angle l degree F i g .2
: The angular d i s t r i b u t i o n e m i t t e d by a s i n - g l e c r y s t a l of NaF measured w i t h a bolometer and superconducting A t u n n e l j u n c t i o n . I n s e t is a sche- m a t i c of t h e experimental arrangement.RESULTS.- The r e s u l t s a r e shown i n f i g u r e
2,
where we have normalised t h e curves a t normal i n c i d e n c e . The c u r v e d e t e c t e d by t h e bolometer i s very s i m i l a r t o those r e p o r t e d e a r l i e r/l/
e x c e p t f o r t h e i n c r e a - s e i n width of t h e peak. The new r e s u l t found w i t h t h e t u n n e l j u n c t i o n shows t h a t t h e background i smuch s m a l l e r w i t h t h i s d e t e c t o r than w i t h t h e gra- p h i t e bolometer, from which we conclude t h a t t h e r e a r e r e l a t i v e l y l e s s phonons w i t h
U w
> 2AA1 (=4.2
IQi n t h e background t h a n i n t h e peak.
DISCUSSION.- This conclusion e x p l a i n s a number of r e s u l t s found u s i n g t h i n f i l m Au h e a t e r s . Whereas t h e NaF s i n g l e c r y s t a l s e p a r a t e s i n t h e space t h e peak and background phonons, t h e p o l y c r y s t a l l i n e Au f i l m w i l l r a d i a t e peak and background phonons i n t o a l l a n g l e s . As most of t h e energy i s t r a n s m i t t e d i n
t h e background channel then a t any a n g l e both peak and background phonons w i l l be p r e s e n t b u t t h e back- ground ones w i l l b e dominant. The phonons t h e n from such a h e a t e r w i l l have a lower c h a r a c t e r i s t i c tem- p e r a t u r e than t h e Au f i l m . This was f i r s t c l e a r l y seen i n t h e d i s p e r s i o n of phonon p u l s e s
131.
I t a l s o accounts f o r t h e small s i g n a l d e t e c t e d by t u n n e l j u n c t i o n s which was found by comparing measured and c a l c u l a t e d responses121.
Furthermore t h e tempera- t u r e of t h e phonons found u s i n g t h e h i g h p a s s L i l t e - r i n g e f f e c t of t h e He was a l s o lower than t h e c a l - c u l a t e d h e a t e r temperature121.
F i n a l l y t h e low back- ground v a l u e s found i n t h e t r a n s m i s s i o n from He i n t o a s o l i d/4/
can be understood i f t h e phonon frequen- c i e s a r e low.The problem remains t o d e c i d e between i n e l a s t i c s c a t t e r i n g from s u r f a c e s t a t e s and non l i n e a r proces- s e s a t t h e i n t e r f a c e . The frequency down-conversion and time d e l a y s s e e n i n r e f l e c t i o n experiments
/6,7/
would seem t o favour s u r f a c e s t a t e s . However non l i n e a r p r o c e s s e s a r e c o n s i s t e n t w i t h good t r a n s l a - t i o n a l symmetry which g i v e s r i s e t o t h e w e l l d e f i n e d c r i t i c a l cone.
ACKNOWLEDGMENTS.- These experiments were c a r r i e d o u t a t t h e Department of P h y s i c s , U n i v e r s i t y of Nottin- gham. We a r e g r a t e f u l f o r s u p p o r t from t h e Science Research Council under g r a n t
B/RG/4231.
References
/l/
Sherlock, R?A., M i l l s , N.G. and Wyatt, A.F,G. J. Phys. C8
(1975)
300,/2/
Wyatt, A.F.G. Lockerbie, N.A. and Sherlock, R.A. Phys. Rev. L e t t .2
(1974) 1425.
/3/
Sherlock, R.A., Wyatt, A.F.G. and Lockerbie, N.A. J. Phys. C.10
(1977) 2567.
/ 4 / Wyatt, A.F.G. Page, G . I . and Sherlock, R.A., Phys
Rev. L e t t .
