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Submitted on 1 Jan 1978
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LAYERING AND THERMAL CONDUCTIVITY OF
4He FILMS ON UNIFORM GRAPHITE
S. Polanco, J. Quateman, M. Bretz
To cite this version:
JOURNAL DE PHYSIQUE Colloque C6, suppldment au no 8, Tome 39, aolit 1978, page C6-344
LAYERING AND THERMAL C O N D U C T I V I T Y O F 4 ~ e F I L M S ON UNIFORM GRAPHITE'
S.E. Polanco, J.H. Quateman and M. Bretz
Randall Zaboratory of Physics, the University of Michigan Ann Arbo~, Michigan 48109, USA
Rdsum6.- Nous avons mesurd P la fois la chaleur spdcifique, la pression gazeuse et la rdsistivitd thermique afin de prQciser la formation des couches et le ddbut de la superfluiditd sur un substrat de graphite UCAR-ZYX d'une trSs grande uniformitd. Nous avons observd des maxima trSs marquds de chaleur spdcifique dus 1 la ddsorption d'une couche lors d'une augmentation de tempdrature. Ces ma-
xima permettent de determiner le remplissage de chaque couche ainsi qu'une ddtermination prdcise du nombre de couches pour nos mesures de rLsistivitd thermique. Lorsque le nombre de couches absorbdes ddpasse cinq, on peut observer des amorces de superfluiditd et des flaques tridimensionelles qui sont compatibles avec les modSles de "percolation".
Abstract.- We have combined heat capacity, vapor pressure and thermal resistance measurements to cha- racterize layering and onsets of superfluidity on a highly uniform graphite substrate, UCAR-ZYX. Strong desorption heat capacity peaks correspond to individual atomic layers "stripping off" the substrate as T is raised. These are used to find layer capacities, which in turn allow a precise la- yer determination for our thermal resistance data. Precursors to superfluidity and evidence for 3D liquid puddling are compatible with percolation models of superfluid onset for helium films thicker than about 5 atomic layers.
Recently it was demonstrated that the orde- pressure was monitored through the 0.028"ID fill ring transition of helium monolayer films
111
shar- line and found to increase dramatically with T. phens dramatically when Grafoil is replaced by abetter graphite substrate, UCAR-ZYX 121. Although the specific surface area for adsorption of this exfoliated single pyrolytic crystal is only about 118th that of Grafoil, the microcrystallites are an order of magnitude larger resulting in the shar- pened 2.9 K specific heat peak. Previous multila- yer studies on Grafoil showed a truncated X peak 131 and mass flow onsets /4/ displaced from the universal curve measured for '~e films on other
substrates. In these studies the layer thickness was approximated by a Frenkel-Halsey-Hill pressure
isotherm fit /5/ which assumes liquid-like film Fin. 1 : Heat capacity of 27.47 STPcc He film-va- behaviour. We have extended the multilayer work to po; in a ZYX calbrimeier (dotted line is to guide
the eye). Solid line is desorption heat capacity ZYX and find several well defined layers. These after corrections for 3D vapor and expected film
presumably result from the excellent mosaic align- contributions. Lower curve gives (dNv/dT) obtained from vapor pressure and dead volume of calorimeter. ment and reduced cavity heterogeneity of ZYX 161.
Desorption heat capacity signals are combined with pressure measurements to accurately determine the temperature dependent layer capacity. The film thermal resistance is plotted vs these layer num- bers for comparison with theory.
Figure 1 shows the total heat capacity of our calorimeter when charged with 27.47 STPcc, or about 7 layers. During data acquisition the vapor
'
Research is supported by NSF contract # DMR 76-20369 and Rackham predoctoral grant. We thank D.N. Bittner for project assistance.
The large volume/area ratio (x 28 that for Grafoil) causes subsequent layers to "strip off" the surfa- ce as temperature is raised 171. Corrections from the empty calorimeter CE, 3D vapor C and assumed
v'
multilayer heat capacity Cf(from reference 131) are subtracted from the data to give the corrected heat capacity curve of figure 1. This, combined with (dNv/dT),q, the slope of the coverage vs temperatu- re (obtained from the equilibrium vapor pressure) are used to determine the isosteric heat of adsorp-
tion q from the relation/8/ fluid film onset. One of us (Polanco) has construc- St
C = C
+
Cf + CE + (qst-kT) (dNv/dT) ted a thin walled stainless cell containing a sin-eq v eq
Since C is many times larger than Cf and the gle ZYX wafer. Standard conductivity procedures /9/ eq
film thins so readily, any truncated specific heat yield a family of lines in temperature difference
anomaly will be lost in the background. AT vs input power Q as coverage is varied at cons- Figure 2 reflects distinct layering in the tant T. The slopes of these lines at small Q com- resultant isosteric heat q of the helium film. prise the data of figure 3.
st
26 24 22 20 18 16 14 25 COVERAGE (STPCC)
Fig. 2 : Isosteric heat of adsorption, qst/k plot- Fig. 3 : The thermal resistance ~ / 6 of the ZYX ted vs film thickness as determined from vapor pres- cell is given vs layer thickness for films at selec- sure of system. Arrows denote film coverages of ted temperatures from 1.19 to 1.81 K. Asterisks for heat capacity peaks in figure I. Double headed ar- each curve indicate first appearance of thermal rows are normalization points between the qst curve precursor effects to full superfluidity where ther- and a 2 K isotherm of chem. pot. taken on the ther- mal resistance disappears.
ma1 conduction ZYX cell.
It is apparent that q provides a significantly
St
better determination of layer capacity than does the 2 K isotherm which is also included in the fi- gure. There are
7
distinct layers present in this particular film with layer completion at the verti- cal arrows. These arrows also denote the coverages for the several heat capacity peaks of figure I. Layer capacities are not quite those expected from the Grafoil multilayer films work /3/. Fillings are 6.9, 5.5, 3.35, 3.25, 2.8 and 2.8 STPcc for layers 1-6 respectively. This reduction in layer capacity with film thickness is consistent with the falling qst. We note, however, that qst rises appreciably during 7th layer formation finally approaching 5 K at the highest coverage. (An exponential fit to the low T heat capacity data of figure 1 independently gives q = 5 K ) . It appears then, that the filmSt
would rather be 7 layers thick than 5 layers ! We suggest that 3D liquid puddles are forming in the film at this thickness and beyond. The suggestion
is substantiated by observation of a greatly en- hanced 1.4 K heat capacity peak (and no further lower T peaks) for another film which we investi-
gated at 36 STPcc.
Precise film thermal resistance measurements are underway which probe the character of the super-
At the lowest coverages thermal resistance is high and the lines extropolate from larger
0
to the origin. But as the film thickens these lines abrup- tly extrapolate to finite4
at zero AT. We denote these places by the asterisks of figure 3 and in- terpret them as precursors to the full superflui- dity where thermal resistance disappears. The pre- cursor region is extensive, being 1/2 layer at1.6 K and more at higher T.
References
/ I / Bretz,M., Dash,J.G., Hickernell,D.C., McLean,E.O. and Vilches,O.E., Phys. Rev.
A8
(1973) 1589/ 2 / Bretz,M., Phys. Rev. Lett.
38
(1977)501/ 3 / Bretz,M., Phys. Rev. Lett.
21
(1973) 1447 / 4 / Herb,J.A. and Dash,J.G., Phys. Rev. Lett.2 9 (1972) 8 4 6
-
/ 5 / See Halsey,G.D., Jr., J. Chem. Phys.
1 6 (1948) 931
-
/ 6 / Nielsen,M. and Dowell,M.W., private communications
/ 7 / Wennerstrom,P. Torne,A. and Lindqvist,T.
(to be published) saw similar behaviour when 4 distinct layers of 3 ~ e desorbed from a neon coated copper surface
/ 8 / Dash,J.G., Films on Solid Surfaces (1975) Academic Press
/ 9 / Cappelletti,R.L. and Ishikawa,M., Rev. Sci. Inst.
4 4 (1973) 301
