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Submitted on 1 Jan 1977

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THE PHONON SOFTENING IN METALLIC FINE

PARTICLES

K. Ohshima, T. Fujita, T. Kuroishi

To cite this version:

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JOURNAL DE PHYSIQUE Colloque C2, supplkment au no 7 , Tome 38, Juillet 1977, bage C2-163

THE PHONON SOFTENING IN METALLIC FINE PARTICLES

K. OHSHIMA

Matsumoto Dental College, Shiojiri, Japan T. FUJITA (*) and T. KUROISHI (*) (**)

RhumB. - La resistance electrique des films des petites particules Ag et A1 a Ct6 mesuree entre 1,s et 300 K . L'augmentation de la temperature de transition de supraconduction et la reduction de la temphrature de Debye ont kt6 obtenues et on suggbre l'existence d'un phonon mou venant de la surface dans tout le domaine de tempCrature.

Abstract.

-

The d.c. electrical resistance of films of Ag and A1 fine particles was measured between 1.5 and 300 K . The enhancement of the superconducting transition temperature and the reduction of the Debye temperature were obtained and they suggest the existence of the phonon softening due to the surface in the whole temperature region.

1. Introduction.

-

It has been expected that the important properties of the metallic fine particles are based not only on the effect of finite level spacing of electrons but also on the softening effect due to a free surface. Particularly, the softening effect is thought to be observed in the whole temperature region.

We measured the d.c. electrical resistance of films of Ag and A1 fine particles in temperature range between 1.5 and 300 K. In the superconducting state of the films of fine particles, the transition temperature

T ,

was enhanced in comparison with that of the bulk metal and in the normal state at higher temperatures, the Debye temperature 0, for fine particles was reduced from the bulk value.

Both the enhancement of T , and the reduction of 0, depend on the averaged particle size in the film, of fine particles. We explain these effects by supposing the phonon softening due to the surface of the fine particle.

2. Experimental procedures and results.

-

Metal- lic fine particles were deposited on a glass plate with a pair of electrodes by evaporating A1 or Ag metal in He or Ar gas of pressure 0.1

-

6 torr [I]. The areal density of the deposited layer was about

40

-

200 pg/cm2.

The size distribution of particles in a deposited layer of a film was determined from electron micrographs.

The electron and X-ray diffraction patterns showed the Debye-rings of the f.c.c. structure. It (*) Department of Physics, Nagoya University, Nagoya, Japan.

(**) Present adress : Aichi Cancer Center Research Institute, Nagoya, Japan.

was recognized from the line broadening of the diffraction patterns that the crystal strains in the particles were of the same degree for all specimens independently of the particle size.

We measured the d.c. electrical resistance of the films by a conventional four-probe method over the temperature region from 1.5 to 300 K.

The superconducting transition temperature T , was determined from the inflection point of the resistance-temperature curve for A1 samples and was independent of the thickness of the deposited layer [2]. Observed values of T , with various average particle diameter are shown in figure 1, where the peak and the half width of size distribution are shown by a circle and line segment, respectively. The T, was decreased by increasing the particle size for the A1 samples of 50

-

150

A

and the reduction of the resistance was not observed at above 1.5 K for those larger than

1.50

A.

The resistance observed in normal state was independent of temperature for A1 of 100

A

or less in average diameter, while it was almost constant in low temperature range and increased in high temperatures for A1 of 150

-

250

A

and Ag of

100

-

300

A.

The temperature dependent resistance may be devided into two parts, a residual resistance part Ro and a variable part R ( T ) [I]. The behaviour of R ( T ) is shown in figures 2 and 3 for Ag and Al. The curves calculated by Griineisen's relation for bulk metals are shown for comparison. The slopes observed for fine particles are less steeper than that of the bulk metal.

3 . Discussion.

-

Electron-phonon interaction in a sample composed of many fine particles is charac-

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C2-164 K. OHSHIMA, T. FUJITA AND T. KUROISHI

50 100 150

Particle

Diameter ( A )

FIG. 1. - Superconducting transition temperature vs particle size : a) T, of spherical particle in the surface softening ; b) T, of spherical particle in the fully softened state ; T , of bulk A1 is

regarded as 1.18 K in this calculation.

FIG. 2. - Log R ( T ) VS. reciprocal temperature for silver films. Ordinate is in arbitrary unit.

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THE PHONON SOFTENING IN METALLIC FINE PARTICLES C2-165 terized mainly by the phonon state, because each

fine particle has metallic contact with the neighbours. It is convenient to evaluate the change of the values of Tc and 8, by the deviation of phonon spectrum from bulk one. Then, in the superconducting temperature region, we adopted estimation of the phonon spectrum of fine particles by numerical method of Dickey-Paskin [3] and calculation of T , by the formulation of Garland et al. [4]. The expression for Tc are shown as

where ( m 2 ) is an average squared phonon fre- quency, ( 0 2, ) is ( w ) for bulk material and mob is the highest frequency of the phonon spectrum for bulk material. p* is the Coulomb pseudopotential.

A is a dimensionless electron-phonon coupling constant and A is a constant of the order of unity, both of the constants depend on ( w 2 ). The phonon spectrum of the fine particles is modified from that of the bulk metal by the surface effect. Since the effective potential for an atom decreases near the surface in proportion to the square root of the number of neighbours, the frequency of phonon decreases there according to the Einstein model proposed by Dickey and Paskin 131. Values of averaged frequency of the phonon spectrum are calculated for spherical particles as a function of the diameter. Then, Tc of an aluminium spherical particle with f.c.c. lattice is determined for the various diameters. The calculated Tc is shown as the curve ( a ) in the figure 1. The values of Tc estimated by assuming all of the atoms in a particle to be in the softened or amorphous state are also given for comparison as the curve (b) in the figure 1. These fine particles had grown into more than 50

A

diameters in inert gas at room tempera- ture and showed less crystal strain than bulk by the X-ray diffraction. Then, fluctuation effects upon ultrathin films [4] and effects of dielectric barrier or adsorptive solid upon usual granular or amorphous films deposited at low temperature [5-71 cannot appear so much in the present samples which have smaller surface to volume ratio of the particles than that of the above films. Crystal strains in the present fine particles are of the same degree for all

the specimens independently of their size. Moreo- ver the observed value of Tc are much closer to the curve

(a)

than (b) in the figure 1 and show the size dependence. So, the enhancement of Tc is explain- ed fairly well by assuming the phonon softening due to the surface. We consider that some difference between the observed Tc and the curve (a) is due to the crystal strains [8].

At higher temperatures, as is known from the slope of R ( T ) versus temperature curve in the figures 2 and 3, the temperature dependence of the scattering probability of conduction electrons in the fine particles is smaller than that in the bulk metal. We showed that the scattering of conduction electrons at the grain boundary had no temperature dependence in smaller particles [I]. In larger particles, we consider that this scattering mechanism also has no temperature dependence. The temperature dependent scattering of conduction electrons is caused by the phonon and becomes effective with increasing the particle size. The mean value of the energy of these phonons may be lowe ed as the slope of R ( T ) is less steeper. Then the dodifications of the phonon spectrum in the fine partidles from that in the bulk are not the low frequency cutoff due to the restriction of the particle size but the phonon softening due to the surface. The former gives an increase of the mean value of the energy but the latter gives a decrease. Thus the effective Debye temperature 8, for fine particles is lower than that for the bulk metal 6,. The electrical resistance R ( T ) may be evaluated by Griineisen's relation using 8, instead of 8,

6, is determined by fitting the slope of R ( T ) with that measured. Calculated R ( T ) is indicated as the solid lines in the figures 2 and 3. From the good agreement between the calculated R ( T ) and measured one, the temperature dependent part of the scattering of conduction electrons in fine particles can be explained by the phonon softening or lowering of the 0, due to the surface effect.

Thus, in both low and high temperatures, we have recognized the effect of the phonon softening in fine particles.

References

FUJITA, T., OHSHIMA, K. and KUROISHI, T., J. Phys. Soc. [5] STRONGIN, M. and KAMMERER, 0 . F., J. A p p l . P h y s 39

Japan 40 (1976) 90. (1968) 2509.

OHSHIMA, K., FUJITA, T., WADA, N., YOSHIOKA, H. and [6] HAUSER, J. J . , Phys. Rev. B 3 (1971) 1611.

UYEDA, R., J. Phys. Soc. Japan 26 (1969) 862. [7] DEUTSCHER, G. and PASTERNAK, M., Phys. Rev. B 10 (1974) [3] DICKEY, 3. M. and PASKIN, A., Phys. Rev. B 1 (1970) 851. 4042.

[4] GARLAND, J. W., BENNEMANN, K. H. and MUELLER, F. M., [8] OHSHIMA, K., KUROISHI, T. and FUJITA, T., to be published

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