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LORENZ NUMBER IN METALLIC GLASSES
T. Mizoguchi, T. Kudo, S. Takayama
To cite this version:
T. Mizoguchi, T. Kudo, S. Takayama. LORENZ NUMBER IN METALLIC GLASSES. Journal de Physique Colloques, 1980, 41 (C8), pp.C8-501-C8-502. �10.1051/jphyscol:19808125�. �jpa-00220222�
JOURNAL DE PHYSIQUE Colloque C 8 , suppZdment au n08, Tome 41, aoCt 1980, page C8-501
LORENZ NUMBER I N M E T A L L I C G L A S S E S
*+ *
T. Mizoguchi , T. Kudo and S. Takayama
* ~ a c u ~ t ~ of Science, Gakushuin University Mejiro, Tokyo 171, Japan
+L.A. M. S. E.S., Universite' Louis Pasteur, 4, r u e BZaise Pascal, 67070 Strasbourg Ce'dex, France Central Research Laboratory, Hitachi Ltd., Kokubunji, Tokyo 185, Japan.
R6sum6.- Les conductivit6s thermique et Qlectrique, K et o , ont 6t6 mesurdes a 273 K pour plu- sieurs verres m6talliques du type mdtal-m6talloide et du type mgtal-mstal. Les nombres deLorenz L = K / ~ T obtenus sont en bon accord avec la valeur thdorique simple, (r2/3)(k /e)2=2.45. I O - ~ W Q / K ~ , que l'on attend d'un modsle de gaz de Fermi. Ceci indique que les Qlectrons ge conduction jouent un r6le dr*mitlant pour la conductivitd thermique dans les verres m6talliques, bien que le libre parcours moyen n'excsde pas les distances interatomiques entre premiers voisins.
Abstract.- The thermal and electrical conductivities, K and o , of several metallic glasses in both metal-metalloid and metalmetal systems were measured at 273 K. The Lorenz numbers L = K/UT are found to be in good agreement with the simple theoretical value, (~~/3)(k~/e)~=2.443.10-~ wQ/K' which is expected from a Fermi gas model. This indicates that conduction electrons play a dominant role for thermal conductivity in the metallic glasses even though the mean free path is as short as the nearestneighbour atomic distances.
Oneof the characteristic features of metallic quid quenching. The electrical conductivity was glasses (amorphous alloys) is the high electrical measured by 4 electrode method. The thermal con- resistivi~y (typically !93 '1. 200 uQ.cm) which is ductivity was measured by a comparative method.
almost temperature independent. This is conside- The instrumental constant was calibrated with a red to be a direct consequence of the irregular standard sample, a piece of pure copper. It is ve- atomic arrangement in amorphous phase, which li- ry important to reduce the radiation loss in order mits the mean free path of the conduction elec- to get reliable data with this method. We investi- trons to being com?arable to the nearest neighbour gated the effect of radiation heat loss for diffe- atomic distances. In crystalline metals conduction rent cross sections and lengths of samples. The electrons have a mean free path of the order of loss was reduced to a level comparable with the
"J 10' d at room temperature and play a dominant errors due to uncertainties in the dimensions of
role in thermal conductivity as well as in elec- the sample.
trical conductivity. It is of interest to examine The experimental results are shown in Table 1 if the Wiedemann-Franz law holds in the metallic and Fig. 1 . There is a clear correlation between glasses where the mean free path of conduction the observed electrical and thermal conductivities electrons is extremely short. at O°C in many metallic glasses. The Lorenz num-
In order to obtain the Lorenz number, bers for these metallic glasses are found to be in L = K/uT, the thermal and electrical conductivi- good agreement with the simple theoretical value ties, K and a, of metallic glasses were measured. (r2/3) (kg/e)2 = 2.45 x lo-' W Q / K ~ ,
The ribbon specimens ("J 50 pm thick and "J 1 mu which is expected from a Fermi gas model. This in- wide) of several compositions of metallic glasses, dicates that conduction electrons play a dominant Pd77. 5Si 16.5Cu63 Fe7311013B1 7, Fe30B233 Zr70C~30, role in the thermal conduction of the metallic Zr 70 Ni 30 and Ti50Be40Zr10 were prepared by li- glasses even though the mean free path is as short
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19808125
C8-502 JOURNAL DE PHYSIQUE
as the nearest neighbour atomic distance. The con- tribution of phonons for thermal conductivity in these metallic glasses seems to be less than 10 Q 20 % of the total thermal conductivity at 273 K.
The Wiedemann-Franzlaw holds only when the re- laxation time of conduction electrons is equal for both electrical and thermal conductSon. This is the case for crystalline metals at a temperature higher than the Debye temperature OD or at very low temperature where the impurity scattering becomes dominant. The situation is quite different
in metallic glasses where the mean free path of conduction electrons is so short due to structural and compositional disorder that the Wiedemann-Franz law should hold in the whole temperature range.
In crystalline metals, the electronic thermal conductivity often shows a maximum at low tempera- tures where the dominant mechanism of electron scattering changes over from impurity scattering to phonon scattering /I/. In metallic glasses, the elastic scattering due to atomic disorder domina- tes the scattering process within the almost en- tire temperature range /2/. Therefore the electri- cal conductivity is almost temperature independent and the thermal conductivity by electrons is pre- dicted to be linear with temperature. The contri- bution of phonons, however, cannot be neglected at low temperature 131. Pleasurement of thermal conductivity of metallic glasses in a wide tempe- rature range would be interesting.
The authors are grateful to Dr Durand, Dr Kawabata and Dr Egami for valuable discussions.
131 Matey, 3.R. and Anderson, A.C., Phys. Rev. B*
(1977) 3406.
Table 1
I
Sample O(IO-~QC~)-~~(~~-8gQlK2~l
Table 1 : The thermal conductivity K, the electri- cal conductivity 0 and the Lorenz number L at 273 K in several metallic glasses.
Fig. I : The thermal conductivity K versus the electrical conductivity d at 273 K for several metallic elasses :
retical relation,- K = (n2/3) (kg/e)Z~~.
References
/I/ Rosenberg, H.?1., Phil. Trans. Roy. Soc.
(London) A 247 -( 1955) 44 1 .
/2/ Cote, J.P. and Heisel, L.V., Dhys. Rev. Lett.
39 (1977) 102.
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