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Submitted on 1 Jan 1978
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APPRAISAL OF THE CMN/HELIUM KAPITZA
RESISTANCE
J. Harrison
To cite this version:
JOURNAL DE PHYSIQUE Colloque C6, supplement au n" 8, Tome 39, aout 1978, page C6-275
APPRAISAL OF THE CMN/HELIUM KAPITZA RESISTANCE*
J.P. Harrison
Physios Department, Queen's University, Kingston, Ontario, Canada
Résumé.- On souligne que la résistance thermique entre le CMN et l'He3 pur, l'He contenant des impuretés d'He"* ou l'He3 dilué dans l'He1*, peut-être comprise en terme d'une résistance
spin-ré-seau du type "goulot" de phonon (phonon bottleneck) à l'intérieur du CMN et d'une résistivité de contact thermique dépendant d'un effet de taille. Le résultat qui en découle est que le goulot de phonon à l'intérieur du CMN dépend fortement du fait que le CMN est en contact soit avec des atomes d'He3 soit avec des atomes d'He1* à l'interface.
Abstract.- It is argued that the thermal resistance between cerium magnesium nitrate (CMN) and pure He3,He3 containing He1* impurity or dilute He3 in He"* can be understood in terms of the phonon bottle-necked spin-lattice resistance within the CMN and a size dependent thermal boundary resistivity. The fact that emerges is that the phonon bottleneck within the CMN is strongly dependent upon whether the CMN is in contact with He or He"1 atoms at the interface.
INTRODUCTION.- The thermal resistance between CMN and liquid helium has been of great interest for the following reasons :
(i) CMN was used as a refrigerant of liquid He3 and dilute mixtures of He3 in He1* in the early
experiments on those liquids /l/.
(ii) CMN has been the primary thermometer in most of those experiments.
(iii) The resistance was shown by Abel et al to be anomalously small when the CMN was powdered and the helium was pure He3 12/.
(iv) A model introduced by Peshkov /3/ and Wheatley /A/ to explain the anomalously small re-sistance, namely magnetic coupling between cerium spins and He3 quasiparticles, has had considerable influence on subsequent thinking about low tempe-rature Kapitza resistance in other systems.
It is the purpose of this paper to reappraise the experimental results obtained to date on the CMN/helium sustem.
DISCUSSION OF RESULTS - PURE He3.- Figure -1 illus-trates the results obtained by Abel et al /2/ for a cell containing powdered CMN (< 400 pm) and He . Their relaxation time data have been reduced to a thermal resistance by means of the equation T = RC„C„/(C„ + C„) where C„ and C„ are the heat
capa-b H capa-b il capa-b tl .
cities of CMN and helium. For Cg the average of the
several sets of heat capacity measurements collec-ted together by Folinsbee et al 15/ has been used.
Fig. 1 : Thermal resistance between < 400ym CMN and He3, (a) and (b) pure He3 ; (c) He3 + 300 ppm
He1* (1/2 monolayer) ; (d) He3 + 500 ppm He1* (1
mono-layer) ; (e) He" + 5% He3 : (f) He* + 1.3% H e3. Left scale for He results and theory (dashed lines) ; right scale for dilute He3 results and theory.
The dashed lines are the expected resistances that should add in series for heat transfer from He3
quasiparticles to cerium spins /6/. They are He3
quasiparticle/He3 phonon resistance (labelled He3)
the thermal boundary resistance and the CMN spin-lattice resistance. This last resistance results from the well known phonon bottleneck in CMN /7/ ; in turn the bottleneck is governed by temperature independent scattering at the crystallite bounda-ries at low temperatures and by temperature depen-dent scattering by praseodynium impurities at hi-gher temperatures. The anomalously low measured This work has been supported by the National
Research Council of Canada
resistance below 10 mK and its linear temperature dependence led to the acceptance of magnetic cou- pling as an alternate heat transfer path from qua- siparticles to cerium spins. Black et a1
181
repea- ted the relaxation time measurements with the same cell with pure He3 and with ~e~ containing suffi- cient ~e' to cause 1/2and 1 monolayer coverage of He4 on the CMN powder (curves (b), (c) and (d)). They confirmed the low temperature anomaly with pure He3 and discovered the now familiar monolayer effect (see figure I). However no explanation has been offered until now for the anomalouslyhigh
resistance in these experiments for T > 5 mK. Since this work there have been several measurements of the resistance between CMN and pure He3. The agree- ment between the measurements and the expected CMN spin-lattice resistance has been good in magnitude and temperature dependence. However for powdered
CMN the thermal boundary resistance was missing ; this has been explained as a size effect /g/. No evidence for the linear dependence of R on T was observed in the subsequent experiments.
DILUTE He3 IN He"
.-
When during the 1960's expe- rimental interest shifted from pure He3 to dilute He3 in ~e' it was found that the relaxation time between dilute He3 in He4 and CMN was very long. Figure 1 shows some representative results obtained by Wheatley /10/ for the thermal resistance between powdered CMN (< 400 um) and dilute ~ e Again the ~ . dashed lines are the theoritically predicted resis- tances that should combine in series 161. They are the He3 quasiparticle/~e" phonon (labelled dilute He3), thermal boundary and CMN spin lattice resis- tance~. The measured resistance is much larger than expected ; the same conclusion applies to Weatley's results for 1 m CMN and < 37 pm CMN and Chapel- lierts recent work with < 100 pm CMN.IMPLICATION OF THE EXPERIMENTS.- Only one sample cell has produced a measured resistance proportio- nal to temperature. That could have been an artifice resulting from a range of powder diameters in the cell. Generally pure He3/cMN results have shown good agreement with the CM{ spin-lattice resistance expected for a boundary limited phonon bottleneck at low temperatures. The anomaly seems to be the
caseofthe bottlenecked phonons relaxing after 10 traverses ofthe smallcrystallites at low temperatures or by the usual scattering by praseodynium impurities at higher temperatures. It is amazing that with that one assumption the results for all three sizes measured by Weatley and that size used by Chape-
llier are described in temperature dependence and magnitude (within factor 2 for Chapellier's result). The conclusion is that for the CMNIhelium thermal resistance there is a dependence upon which isotope of helium forms the surface layer on the CMN but that this is not a case of coupling energy across the surface but rather of coupling spins and pho- nons within the CMN. This result seems to be an analogue of the results described by Kelly and Richardson 1121 and by Cowan and Monod 1131 for the spin lattice relaxation in liquid He3 confined in small pores.
References
/l/ Abel, W.R., Anderson, A.C., Black, W.C. and Wheatley, J.C. Physics
1
(1965) 331. /2/ Abel, W.R., Anderson, A.C., Black,WC. andWheatley, J.C., Phys. Rev. Lett.
5
(1966) 273./ 3 / Peshkov, V.P., Zh.Ehsp. Theor. Fiz.
66
(1964) 1510 (Sov. Phys. JETP2,
(1964) 1023.) /4/ Wheatley, J.C., Phys. Rev.165
(1968) 304. 151 Folinsbee, J.T., Harrison, J.P. and McColl, D.B., J. Low Temp. Phys.
2,
(1977) 25. 161 Harrison, J.P. (to be published)./ 7 / Miedema, A.R. and Mess, J.W., Physica
30
(1964) 1849 ; Anderson, A.C. and Robichaux, J.E., Phys Rev. B3,
(1971) 1410.181
Black, W.C., Mota, A.C., Wheatley, J.C., Bishop J.H. and Brewster, P.M., J. Low Temp. Phys. 4 (1971) 391.-
/g/ Harrison, J.P. and McColl, D.B., J. Phys. (1977) L297.
/10/ Wheatley, J.C., Proc. of the 1966 Calorimetry Conference (ed. Lounasmaa, O.J.) Ann Acad. Sci. Fenn., Series A.6.210, (1966) 15. /11/ Chapellier, M. (to be published).
1121 Kelly, F.J. and Richardson, R.C., Proc. of LT-13 (ed. by Timerhaus, K.D., O'Sullivan, W.J. and Hammel, E.F., Plenum Press, N.Y.) Vol.
I, (1974) p. 167. -
1131 Monod, P. and Cowen, J.A. (Unpublished report, 1967).
