• Aucun résultat trouvé

DEBYE BEHAVIOR OF THE THERMAL CONDUCTIVITY OF bcc 3He AT VERY LOW TEMPERATURES

N/A
N/A
Protected

Academic year: 2021

Partager "DEBYE BEHAVIOR OF THE THERMAL CONDUCTIVITY OF bcc 3He AT VERY LOW TEMPERATURES"

Copied!
4
0
0

Texte intégral

(1)

HAL Id: jpa-00218105

https://hal.archives-ouvertes.fr/jpa-00218105

Submitted on 1 Jan 1978

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.

DEBYE BEHAVIOR OF THE THERMAL CONDUCTIVITY OF bcc 3He AT VERY LOW

TEMPERATURES

G. Armstrong, A. Greenberg

To cite this version:

G. Armstrong, A. Greenberg. DEBYE BEHAVIOR OF THE THERMAL CONDUCTIVITY OF bcc

3He AT VERY LOW TEMPERATURES. Journal de Physique Colloques, 1978, 39 (C6), pp.C6-135-

C6-139. �10.1051/jphyscol:1978661�. �jpa-00218105�

(2)

JOURNAL DE PHYSIQUE Colloque C6, supplPment au no 8, Tome 39, aotit 1978, page C6-135

DEBYE B E H A V I O R OF THE THERMAL C O N D U C T I V I T Y OF bcc 3 ~ e A T VERY LOW TEMPERATURES

G. Armstrong and A.S. Greenberg

D e p t . of Physics, Colorado S t a t e Univ., F t . Collins, CO 80523

Rdsum6.- Nous pr6sentons des mesures de conductivit6 thermique de bcc 3 ~ e pour les templratures de 0,03 K P 0,4 K. Nous trouvons que la conductivit6 thermique varie c o m e T~ pour les templratures au-dessous du maximum de conductivitl. Nos r6sultats diffsrent des mesures prlcldentes pour les templratures au-dessous de 100 mK. Pour les temperatures au-dessous de 100 mK, aucune mesure n'a 6t6 publi6e jusqu'ici et nous trouvons que nos rdsultats peuvent Ctre bien dlcrits par le modSle de Debye, quoiqu'il soit hien connu que 3 ~ e solide est loin d'gtre un solide dielectrique harmonique simple.

Abstract.- We report thermal conductivity measurements of bcc 3 ~ e for temperatures between 0.03 K and 0.4 K. We find the thermal conductivity varies as T~ for temperatures below the conductivity ma- ximum. Our results differ from previous such measurements above 100 mK. For temperatures below IOOrnK where no other measurements have been reported, we find our results can adequately be described by the Debye model although it is well known that solid 3 ~ e is very much more complex than a harmonic dielectric solid.

In the limit of very low temperatures the principal relaxation process for thermal phonons in a pure Debye dielectric solid is scattering from crystal boundaries or sample chamber walls. If the dominant thermal transport is assumed to be the flow of a phonon gas with a specific heat CV, then the kinetic theory expression for the thermal con'ducti- vity is

k = - C 1 v X ,

3

v

(1)

where v is usually taken as the first sound velocity and A is the effective mean free path of the phonons.

In the boundary scattering limit for thermal conduc- tion by phonons, v and A are generally assumed to be independent of temperature, and thus the thermal conductivity has the same temperature dependence as the lattice specific heat. For a Debye solid there- fore : k a CV cc T3. However, at very low .temperatu- res there may be a lower than cubic temperature de- pendence of k if the effective mean free path is in- creased as the reflection of the longer wavelength phonons from the sample chamber walls becomes more specular.

In the experiment reported here, the thermal conductivity of bcc 3 ~ e has been measured in a cy- lindrical sample chamber, 2.3 cm in diameter, cast from stycast 1266 /I / with three 400 R Speer resis- tors (grade 1002, .5W) spaced 2.8 cm apart and im- bedded off axis in the epoxy cast. A 3.1 mm diameter bore along the axis of the epoxy cylinder nicked the Speer resistors and formed the sample space for the solid helium. A sintered copper heat exchanger was

joined to the top of the chamber using additional Stycast 1266, and in a similar manner manganin hea- ters and a pressure strain gauge were joined to the bottom of the chamber. The Speer resistors were ca- librated using a melting curve sample of 3 ~ e and the pressure-temperature scale of Trickey, Kirk and Adams /2/.

Figure 1 shows the results of measurements of the thermal conductivity for a solid close to melting pressures which was grown using the bloked capillary technique. The closed (open) circles were taken during cooling (warming). For temperatures below the conductivity peak we find k a T3. In the

inset at the bottom 05 the graph we have plotted the effective mean free path, A = 3.9 x I O - ~ V 2 1 3

m 0 'k/~~(mm), where the Debye temperature, OD = 19 K

D

for v = 24.4 cc/mole, was taken from the data of m

Greywall 131. The resulting mean free path is 1.5 mm

+ .

1 nun independent of temperature, as ex- pected, in the boundary scattering region and is comparable in magnitude to the radius of sample chamber. We see no indication of a shift from di- ffusive to spectacular reflection.

We explored some effects of sample growthand heat treatment procedures figure 2. Four different solids were formed at the molar volume of 23.7 cc/

mole. -For clarity the results from only two samples are displayed. The upper curve is the thermal con- ductivity of a sample slowly cooled along the mel- ting curve

(2

3 hr) and then annealed close to mel- ting

(2

2 hr). The lower curve is a sample that was quenched; that is, rapidly cooled

(2 '*

hr) alont the melting curve.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1978661

(3)

The conductivity of the annealed sample is a factor of 2 higher than the quenched sample. This difference is attributed to a difference in crystal quality which manifests itself in equation ( I ) as a change in A ; A is 2.6 mm and 1.5 mm for the upper and lower curves respectively. The other samples grown at 2 3 . 7 cclmole have conductivities intermediate between the samples shown in figure 2 .

For the sample at 24.4 cclmole and in each of the samples at 2 3 . 7 cclmole, irrespective of the histories of these latter samples, we find the thermal conductivity decreased from the maximum value as k a T3. There are several important obser- vations associated with this result. First, we observe that the rather elementary Debye theory for a dielectric solid in which the crystal is conside- red to be perfectly harmonic, adequately describes our data for temperatures below the thermal conduc- tivity peak. This result emphasizes the long stan- ding dilemma that though 3 ~ e cannot justifiably be treated even approximately as a harmonic solid, nevertheless, the Debye model seems to work.

Secondly, we observe no Poiseuille flow of phonons ; i.e., k a T6. Briefly, the conditions for Poiseuille flow are that the crystal is af high quality and isotopically pure and that normal relaxation processes take place much faster than

TEMPERATURE ( mK)

umklapp processes ; i.e., A << r, where r is the N

sample chamber radius or crystal dimension, and A A >>r2. These conditions are similar to those for

N U

the observation of second sound. For our maximum conductivities, we estimate that A % AN r, thus

U

it is understandable that we do not observe k a T6.

Thomlinson 141, in reporting measurements of the thermal conductivity of bcc 3 ~ e above 100 mK, obser- ved an "enhanced flow" in which the conductivity varied as Tn, 3.4 < n < 3.7, close to the low tempe- rature side of the peak. Our samples are comparable to those of Thomlinson's : we have approximately 50 % larger magnitudes of thermal conductivity

(AN1s same order), similar levels of isotopic impu- rities ( < I 0 ppm) and our sample chamber has a factor of 2 larger radius, but we have not observed a con- ductivity in which the temperature dependence had a power greater than 3 near the peak.

The enhanced phonon flow hat Thomlinson obser- ved near the conductivity peak was probably due to being close to the edge of the window conditions for Poiseuille flow. Apparently, our sample confi~uration is sufficientily different to put us outside the window

In conclusion, we have measured the thermal conductivity of several crystal samples of bcc 3 ~ e containing less than 10 ppm '~e, and we find that on the low temperature side of the thermal conduc-

(4)

tivity maximum we can adequatly describe our re- sults using the harmonic dielectric theory of Debye.

We would like to acknowledge much helpful-ad- vice from Jim Sites of our laboratory and from Doug Osheroff of Bell Labs, as well as translation assistance from Susan Tavener and financial support from the National Science Foundation under grant DMR 76-21341.

References

/I/ Emerson and Cuming, Canton, Mass. 02021. We have reported the very low temperature thermal conductivity of Stycast 1266 to the Review of Scientific Instruments (in press). The solid

' ~ e data has been corrected for the conductivi- ty of the Stycast. In that article we also make relevant comments concerning the melting curve thermometry.

/ 2 / Trikey, S.B., Kirk, W.P. and Adams, E.D. ; Rev.

of Mod. Phys.

9

(1972) 668.

131 Greywall, D.S. Phys. Rev. Lett.

2

(1976) 105.

141 Thomlinson, W.C., Phys. Rev. Lett.

2

(1969)

1330.

Références

Documents relatifs

These may be understood by assuming that at any arbitrary field two bands of phonons will be removed, due to transitions between the doublet levels themselves, and

Abstract.- Mean free path of phonons &amp;p have been estimated from the measurements of the thermal conductivity of pure Pb crystals at temperatures 7.5 -f 0.6 K.. In the

Abstract.- Measurements of the specific heat C of bulk a-As down to 0.3 K are consistent with the absence of a linear term, whilst the thermal conductivity K varies as T 3 between

Neumaier [2,3,4] have shown the usefulness of thermal conductivity measurements in the detection and characterization of clusters embedded in dielectric single crystals, with

impossible to build a shielded room low pass filters to earth should be placed in the electrical leads near the resistance thermometer itself.. In the

530 MHz longitudinal acoustic waves propagating in an amorphous epoxy resin as a function of the temperature. The solid line is calculated taking into account the

The behaviour usually seen in amorphous insulators was observed : in particular the T3 variation of the attenuation at the lowest temperatures, logarithmic increase of

with measurements of the thermostatic and transport properties below the Ntel temperature. The Pomeran- chuk effect has been demonstrated to be a powerful experimental