HAL Id: jpa-00221329
https://hal.archives-ouvertes.fr/jpa-00221329
Submitted on 1 Jan 1981
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of
sci-entific research documents, whether they are
pub-lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
FILM THICKNESS DEPENDENCE OF HEAT
TRANSMISSION INTO HELIUM
P. Taborek, M. Sinvani, M. Weimer, D. Goodstein
To cite this version:
JOURNAL DE PHYSIQUE
CoZZoque C6, suppZe'ment a u n o 12, Tome 42, &cembre 1981 page C6-825
*
FILM THICKNESS DEPENDENCE OF HEAT TRANSMISSION INTO HELIUK
P. Taborek, M. Sinvani, M. Weimer and D. Goodstein
C a Z i f o r n i a I n s t i t u t e o f TechnoZogy, Pasadena, CA 91125, U. S.A
.
Abstract.- A heater i s pulsed a t t h e i n t e r f a c e between a sapphire c r y s t a l and an adsorbed 'He f i l m . For s h o r t pulses, t h e amount o f heat absorbed by t h e f i l m s a t u r a t e s when t h e f i l m thickness reaches a few l a y e r s , j u s t as observed i n phonon r e f l e c t i o n experiments. For longer pulses, however, t h e r e i s l i t t l e d i f f e r e n c e between t h i n f i l m and vacuum r e s u l t s , w h i l e s u b s t a n t i a l heat i s t r a n s f e r r e d t o t h e b u l k 1 iq u i d .
A f t e r a decade o f f a s t heat p u l s e phonon r e f l e c t i o n experiments i n many l a b - o r a t o r i e s , one o f t h e most s t r i k i n g and p e r s i s t e n t r e s u l t s i s what might be c a l l e d t h e t h r e e l a y e r e f f e c t . Narrow heat pulses (50
-
100 nsec) t r a v e r s e a c r y s t a l b a l l i s t i c a l l y , a r e r e f l e c t e d from a surface, and r e t u r n t o be detected by a bolo- meter. The maximum bolometer s i g n a l i s seen when t h e s u r f a c e i s i n vacuum. Ift h e s u r f a c e i s coated w i t h a t h i n f i l m o f helium, t h e s i g n a l diminishes, i n d i c a t i n g t h a t some o f the heat i n c i d e n t upon the surface has been t r a n s m i t t e d i n t o t h e helium. This change i n t h e s i g n a l s a t u r a t e s a t about t h r e e atomic l a y e r s o f adsorbed helium. No f u r t h e r change i s seen as t h e f i l m thickness increases t o i n f i n i t y ( b u l k l i q u i d ) .
We have performed a s e r i e s o f experiments which throw new l i g h t on t h i s t h r e e l a y e r e f f e c t . I n these experiments, an ohmic heater i s evaporated d i r e c t l y o n t o a c r y s t a l s u r f a c e upon which t h e He f i l m thickness may be manipulated. On t h e f a r s u r f a c e o f t h e c r y s t a l , a superconducting t r a n s i t i o n bolometer i n a constant tem- p e r a t u r e s u p e r f l u i d bath detects t h a t p o r t i o n o f t h e heat which e n t e r s t h e c r y s t a l r a t h e r than b e i n g c a r r i e d away by t h e helium. The c r y s t a l i s a sapphire c y l i n d e r ,
57 mm i n diameter and 9.5 mm t h i c k , o r i e n t e d w i t h t h e heater and bolometer along t h e c r y s t a l l o g r a p h i c y - a x i s . Since t h e Dower d i s s i p a t e d i n t h e heater i s shared between t h e c r y s t a l and t h e helium, we c a l l t h i s the "power s h a r i n g " geometry. (1 )
(See F i g . 1 i n s e t ) .
The r e s u l t s o f these experiments may be summarized b r i e f l y as f o l l o w s : when narrow heat pulses (150 nsec) a r e used, t h e bolometer s i g n a l i s much l i k e t h a t i n r e f l e c t i o n experiments, most o f the change being due t o the f i r s t t h r e e l a y e r s (see F i g . 1 ) . On t h e o t h e r hand, when wide heat pulses (- 10 psec) a t t h e same power d e n s i t y are used, t h e bolometer s i g n a l f o r a t h r e e l a y e r f i l m b a r e l y d i f f e r s from t h e vacuum r e s u l t , w h i l e s u b s t a n t i a l transmission i s observed i n t o b u l k
*
Supported i n p a r t by ONR Contract#
N00014-80-C-0447.C6-826 JOURNAL DE PHYSIQUE
I
NARROW PULSEI
-
vacwm---
3 layers -.---
7 l a p s---
10 layers. . .
. . .
.
bulk BOLOMETERFia.
1
:
Phonon signal in
-
power sharing geometry for
various He film thicknesses
on heater. Heater pulse
width 150 nsec, heater power
density 0.2 watts/mm (typical
power density in ref
1
ection
experiments: .02 W/mm2).
TIME Irsec)
liquid (see Fig. 2).
These observations imply that the three layer effect is a consequence of the
kinetics of film desorption. A detailed calculation indicating that this is indeed
the case will be discussed briefly below, and presented in full in a subsequent
publication.
Previous investigators have attributed the three layer effect to other causes
Guo and ~aris") reported a correlation between heat transmission and film thick-
ness. That observation implies that the coupling of heat across the crystal-helium
interface (i.e., the anomalous Kapitza effect) comes into play in the first three
layers or
10
A
of film. Dietsche and ~inder'~)
argue instead that the transmission
of heat is determined by the pressure in the helium gas, which governs the effec-
tive interfacial resistance between the helium film and the gas. The latter hypo-
thesis alone does not explain our long heat pulse power sharing results, since the
pressure in the gas is not affected by our heat pulses.
To account for these and other experiments, we have formulated a model of the
kinetics of thermal behavior in the film-gas system, when heat is injected into the
film. Equations are written for the conservation of energy and mass in the film,
the dynamical variables being the film thickness and temperature. Energy flows
across the film-solid interface mediated by the Kaoitza resistance, which is
assumed to be independent of the film thickness. The equations can be linearized
and solved analytically for reflection experiments. In the power sharing experi-
ments, where the power densities may be much higher, they are solved numerically.
The central result of the calculation is that when heat is injected into the
film, it evolves toward steady state behavior with a characteristic time, r0, which
-
V a c m---
3 layers 7 layen . . .lo
layers bulk Fig. 2 : Phonon s i g n a l i n power s h a r i n g geom- e t r y . Conditions iden- t i c a l t o those i n F i g . 1 except heater p u l s e 12 usec. 0 10 20 TIME (crsec)t h e l a t e n t heat and heat c a p a c i t y o f t h e f i l m . A t l o n g e r times, much l e s s energy i s t r a n s m i t t e d o u t o f t h e s o l i d s i n c e t h e o n l y remaining mechanism t o c a r r y i t away i s t h e excess k i n e t i c energy o f desorbed atoms over adsorbed atoms i n t h e steady s t a t e . I n t h i s way, t h e model accounts f o r the r e s u l t s i n Figs. 1 and 2 o f t h i s paper. I t a l s o p r e d i c t s t h e t h r e e l a y e r e f f e c t i n narrow heat p u l s e r e f l e c t i o n experiments. I n p a r t i c u l a r , i t i s i n q u a n t i t a t i v e agreement b o t h w i t h the r e s u l t s o f Guo and ~ a r i s ( ~ ) , and w i t h those o f Dietsche and Kinder. ( 3 )
I n conclusion, then, we b e l i e v e t h e t h r e e l a y e r e f f e c t i s n o t a consequence o f t h e e v o l u t i o n o f t h e Kapitza e f f e c t . I t
i s
due i n s t e a d t o t h e k i n e t i c s o f t h e d e s o r p t i o n process. No new i n f o r m a t i o n i s revealed about t h e mysterious Kapitza r e s i s t a n c e , b u t we see t h a t h e a t p u l s e techniques u s i n g f a s t heaters and bolometers c o n s t i t u t e an e x c e l l e n t way o f s t u d y i n g t h e important problem o f d e s o r p t i o nk i n e t i c s .
References: 1. T. I s h i g u r o and T. A . F j e l d l y , Physics L e t t e r s
