SIZE DISTRIBUTION AND ESR OF UNIFORM MICROCRYSTALS OF PLATINUM

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SIZE DISTRIBUTION AND ESR OF UNIFORM

MICROCRYSTALS OF PLATINUM

D. Gordon, R. Marzke, W. Glaunsinger

To cite this version:

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JOURNAL DE PHYSIQUE Colloque Cl, supplément au ri> 7, Tome 38, Juillet 1977, page C2-87

SIZE DISTRIBUTION AND ESR

OF UNIFORM MICROCRYSTALS OF PLATINUM

D. A. GORDON, R. F . MARZKE

Department of Physics, Arizona State University Tempe, Arizona 85281, U.S.A.

and

W. S. GLAUNSINGER

Department of Chemistry, Arizona State University Tempe, Arizona 85281, U.S.A.

Résumé. — Nous avons étudié la distribution de tailles et la résonance électronique (RPE) de microcristaux __ de platine. Leur diamètre moyen est typiquement de 20 A avec un écart type inférieur à 4 À. Les tailles suivent une distribution normale logarithmique avec <r= 1,2 ±0,02.

Une résonance a été observée entre 17 et 291 K et elle est attribuée aux microcristaux de platine. Le facteur g est 2,001 9 ± 0,000 2 et la largeur de raie est environ 20 G. La dépendance de la susceptibilité RPE envers la température est en bon accord avec une loi Curie. La taille, le facteur g et la largeur de la raie ne dépendent pas de la température, de la fréquence et de la puissance micro-onde, et le signal RPE sature lorsque la puissance augmente. Ce comportement s'interprète par une raie de largeur inhomogène composée de paquets de spins très étroits, et la largeur inhomogène peut être due à l'interaction hyperfine.

Abstract. — The size distribution and ESR of uniform platinum microcrystals have been investigated. The mean size is typically about 20 A, with a standard deviation of less than 4 A. The sizes follow a log-normal distribution, with a =1.2 ±0.02. An ESR signal has been observed in the range 17-291 K and is attributed to the platinum microcrystals. The g-factor is 2.0019 + 0.0002, and the width is about 20 G. The temperature dependence of the ESR susceptibility is in good agreement with a Curie law. The lineshape, g-factor, and linewidth are independent of temperature and microwave power and frequency, and the ESR signal saturates with increasing power. This behaviour is interpreted in terms of an inhomogeneously broadened line having a negligible spin-packet width where the overall linewidth may result from hyperfine broadening.

1. Introduction. — Among the most intriguing properties of small metal particles having dimen-sions < 100 A is their magnetic and ESR behaviour, which can be entirely different from that of bulk metals due to the importance of quantization of electronic energy levels. In a collection of small metal particles containing metal atoms having an odd number of valence electrons per orbital, it is expected that half the particles will contain an even number of electrons per band (even particles), whereas the other half will contain an odd number

(odd particles). Assuming equal spacing of

electro-nic energy levels, theoretical calculations [1] pre-dict that the magnetic susceptibility follows the

Curie-law for the odd particles when kB T/8 < 1,

where 8 is the mean level spacing, while in the even particles the susceptibility is exponentially attenuated. Similar low-temperature magnetic behaviour is predicted for other level-distribution ensembles. It is also possible to observe ESR in small particles of heavy metals due to the strong

inhibition of the electron-phonon interaction, which results in relaxation times orders of magnitude longer than those in bulk metals [2], Hence, ESR should be easier to detect in small metal particles than in bulk metals, an expectation supported by reports of ESR in small gold [3] and silver [4] particles.

Recently, we obtained the first evidence of quantum-size effects in platinum by measuring the magnetic susceptibility of very uniform platinum m i c r o c r y s t a l s h a v i n g a m e a n d i a m e t e r of 22.4 ± 3 . 2 A [5]. We found that the susceptibility becomes temperature dependent near 85 K and obeys the Curie-law below about 20 K. The observ-ed low-temperature behaviour corresponds to about one unpaired electron per particle having spin-only paramagnetism, and the magnetic data are in agreement with the theory of Denton et al. [1]. In view of the success of our susceptibility study, we have extended our research on small platinum particles to include a careful determination of their

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C2-88 D. A. GORDON, R. F. MARZKE AND W. S. GLAUNSINGER particle size distribution and an investigation of

their ESR behaviour, and below we summarize the main results of this research.

2. Experimental.

-

The preparation of platinum hydrosols for electron microscopy and platinum microcrystals embedded in a gelatin matrix for the ESR work has been described elsewhere [5]. Compositions, determined by gravimetric analysis, varied from 15-30 wt. % Pt for different preparations.

Sample purity was examined by emission and absorption spectroscopy, and it was found that common transitional impurities were present in concentrations below 20 ppm.

The particle size distribution was measured using a JEM-100B high resolution electron microscope.

ESR spectra were recorded using a reflection X-band (10 GHz) spectrometer employing 100 kHz field modulation. The temperature was varied in the range 17-298 K using an Air Products LTD-3-110 liquid-helium flow system. The temperature was measured to +- 3 K with a chrome1 vs. gold - 0.07 at

% iron thermocouple. An adjustable single- crystal ruby standard, positioned near the sample in the microwave cavity, was used for relative intensity measurements [6], while absolute intensities and gfactors were measured using calibrated samples of Varian strong pitch and phosphorous-doped silicon. Ambient-temperature ESR spectra were also recorded at K-band (24 GHz) using a superhe- terodyne spectrometer employing 400 Hz field modulation.

3. Results and discussion. - 3 - 1 PARTICLE SIZE DISTRIBUTION.

-

A typical particle size distribution is shown in figure 1. The particles are nearly spherical, and their mean diameter is 20.9

A,

with a standard deviation of only 3.9

A.

Also shown for c o m p a r i s o n a r e G a u s s i a n a n d log-normal distributions [7] having the same mean and standard deviation as the experimental distribution. The differences between the two model distributions are not very pronounced for such a small standard

PCRTlCLE SIZE DSSlRlWTlM

1

FIG. 1.

-

Typical particle size distribution (-) of platinum microcrystals showing the number of particles vs. particle diameter. The particle-diameter interval was 0.8 A, and a total of 630 particles were counted. Gaussian (..-) and log-normal (- - -)

distributions having the same mean and standard deviation are also shown.

deviation, but it appears that the log-normal distribution better reproduces the slight asymmetry of the experimental distribution. When the distributions are compared in cumulative form P I , as shown in figure 2, it is obvious that the straight line characteristic of the log-normal distribution provi- des the better fit to the experimental distribution. It is not surprising that the log-normal distribution is appropriate, since the platinum particles were formed in the hydrosol state. The parameter a in the log-normal distribution, which was found in a previous study to lie in the range 1.4 to 1.6 [7], has for our platinum sample the low value of 1.2 & 0.02. Other platinum preparations have displayed compa- rable uniformity.

Percentoge with diameter c x

FIG. 2. - Log-probability plot for the particle size distributions of figure 1 . u = 1.2 +- 0.02. 0 Experimental ;

-

- - Gaussian ;

log-normal.

3.2 ESR.

-

ESR signals have been observed in all platinum preparations, and typical X-band spectra at 291 and 17 K are shown in figure 3. Also shown for comparison are Lorentzian and Gaussian functions, and it is clear that the experimental lineshape lies between these two functions. Weak structure in the wings, which is more apparent at higher modulation amplitudes, has been observed in several samples. No ESR signal could be detected in the gelatin matrix, in the chloroplatinic acid used to prepare the microcrystals, or in a gold- microcrystal preparation conducted in the same manner as the platinum-microcrystd preparation except that chloroauric acid was substituted for

FIG. 3. - Unsaturated first-derivative ESR spectra of platinum microcrystals at 291 and 17 K. Also shown with the 291 K spectrum are Lorentzian (L) and Gaussian (G) lineshapes having the same peak-to-peak amplitude and width as the experimental

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SIZE DISTRIBUTION AND ESR OF UNIFORM MICROCRYSTALS OF PLATINUM C2-89 chloroplatinic acid. The g-value, determined from

the zero-crossing point, is 2.001 9 +- 0.000 2. The unsaturated linewidth for all samples was in the range 12-20 G, and the sample chosen for careful study had a linewidth of 20 C 1 G. The lineshape and g-value are independent of temperature and microwave power and frequency. The linewidth is also independent of temperature and frequency and increases only slightly with increasing power at high powers (= 20% increase at 20 mW).

The amplitude of the ESR line exhibits a

temperature-dependent decrease with increasing power above about 50 dB. This saturation behavior is illustrated in figure 4. The saturation curves were determined by comparing the sample signal to that of the ruby standard at various power levels and normalizing to unity at the low-power value. It is clear that relatively low powers must be used to avoid saturation.

I

I I I I I I I

70 60 5 0 40 30 20 10 Microwave Power Attenuation (dB)

integrated intensity by a factor of five. Annealing for an additional 4 hours at 200 OC in air produced no further reduction in integrated intensity. Howe- ver, annealing in vacuum at 110 OC for 30 hours reduced the integrated intensity by factor of eight. In all cases the linewidth was unchanged. The annealed platinum samples were resuspended by heating in a dilute aqueous HC1 solution to 100 OC and examined in the electron microscope. There was some evidence of crystallite growth ; however, many of the particles remained isolated.

Since the ESR signal was observed only in

platinum microcrystal samples and not in gold samples or pure gelatin, it is probably due to one of three sources : conduction electrons in the platinum microcrystals ; paramagnetic centers in the gelatin matrix whose formation or manifestation requires the presence of the platinum ; or local- moment-forming impurities in the platinum microcrystals. The first possibility is the most interesting, and we consider next whether it is consistent with the experimental results.

There are several difficulties with ascribing the resonance to conduction electrons in the platinum particles. First, assuming half the particles have an unpaired electron, only about one tenth of these odd particles would be contributing to the signal. Second, the Curie law temperature dependence of the integrated ESR intensity is not in agreement with

the previously reported results of Faraday measurements [5], which indicated a transition to a

temperature-independent susceptibility above about 100 K. Third, the observed g-shift is very small

despite the large spin-orbit coupling for platinum. Regarding the first two objections it may be

FIG. 4. - Saturation behaviour of the ESR line at several _{argued that only the smallest particles in the size} temperatures. Zero dB corresponds to approximately 650 mW of _distribution_{of figure 1}

_-

_{the five}_percent_having microwave power incident on the sample, or H I = 2 G. The

dashed line shows the 1/H, limiting slope at high powers diameters less than about

A-

are contributing to expected for inhomogeneously broadened ESR lines having a the resonance ; for these particles we can expect a negligible spin-packet width [ I I ] (circles,291 K ; squares, 1 9 0 K ; _{mean level separation}₆₂₃₀₀_{K even though for}

triangles, 138 K).

the complete size distribution 6

-

100 K. This The temperature dependence of the magnetic

susceptibility was determined by comparing the unsaturated integrated ESR intensity to that of the

ruby standard. The relative susceptibility approxi- mates a Curie law down to 17 K.

The number of spins contributing to the ESR

signal was estimated by comparing the unsaturated integrated ZSR intensity at 13 K to that of calibrated samples of Varian strong pitch and phosphorous- doped silicon. The results for both intensity stan- dards agreed to within a factor of two, giving a mean value of 0.04 unpaired electrons per particle, or 1018 spins per gram of sample.

Finally, the platinum samples were annealed at 110 and 200 "C for various time intervals and the resulting unsaturated ESR signal monitored.

Annealing at 200 OC in air for 30 min. reduced the

would account for the fact that the integrated ESR

intensity displays Curie behaviour up to room temperature. Curie-like behaviour has previously been reported for ESR in very small particles of

silver 181 and lithium [9].

It should be pointed out that a small gshift and fraction of particles contributing to the resonance has also been observed for small silver particles [4]. However, for small silver particles the linewidth varies linearly with frequency, as predicted by Kawabata [10]. The',frequency-independent linewidth in the platinum microcrystals is not in accord with Kawabata's theory, so that another explana- tion of the platinum ESR must be sought. Below we

suggest a model which can account for the experimental linewidth and saturation behavior of the platinum ESR signal.

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C2-90 D. A. GORDON, R. F. MARZKE AND W. S. GLAUNSINGER

ESR liqe is exhibited in the saturation behaviour. At high microwave power the relative ESR ampli- tdde shown in figure 3 behaves as 1/H1, as required for an inhomogeneously broadened line having a npgligible spin-packet width [ I l l . The observed independence of the lineshape and linewidth on temperature, power (I) and frequency also supports

inhomogeneous broadening [ l 1

,

121. A well-known

example of such broadening occurs for EPR from F-centers in alkali halide crystals, where the linewidth 1123 and saturation behavior [ l l j can be accounted for by hyperfine interactions between the F-center electron and the nuclear moments of the surrounding ions. For the platinum microcrystals we visualize the unpaired electron observed in our ESR experiments as being delocalized with equal probability over all the platinum atoms in a particle. Isotropic hyperfine broadening would then lead to a peak-to-peak linewidth given by [12]

where HBe'"' is the effective hyperfine field at the unpaired electron, I is the nuclear spin,

N

is the number of nuclei over which the unpaired electron is distributed, and NI is the number of those nuclei having magnetic moments. Taking for Hv'"' the value 770 G, which was found for the d-electron corepolarization hyperfine field for a platinum atom in bulk platinum [13], and taking I = 1/2, N = 50

(appropriate to a particle of diameter 10

A),

and

NI = 17, we find AHp-, .= 60 G. The agreement is

considered to be reasonable in view of the uncer- tainties in HWhl, N and NI for the platinum micro-

crystals. Although a Gaussian lineshape is expected in the above analysis, the observed lineshape could arise from a distribution of particle sizes among those microcrystals contributing to the ESR, since the hyperfine width AH,-, is proportional to d-3/2,

where d is the particle diameter. A mechanism of inhomogeneous broadening involving a distribution of g-factors would seem to be ruled out by the observed frequency independence of the linewidth. Although the experimental results are generally consistent with the possibility that the ESR signal is due to conduction electrons in the platinum microcrystals, other possibilities will now be considered. The signal may be due to paramagnetic centers in the gelatin matrix which are absent in the gelatin starting material but are introduced with the preparation of the platinum particles ; alternatively, they may be present initially in the gelatin but may remain unobservable unless, for example, they are (I) Here we neglect the small increase in linewidth with increasing power at high powers. Such an increase could result from a distribution of particle sizes where the linewidth depends upon particle size. Then saturation of the narrower signals at high powers would result in the observation of the broader signals, which would result in an apparent broadening of the ESR line.

relaxed through an interaction with the platinum. In either case they could be of interest because of their proximity to an interaction with the microcrystals. Another interesting possibility is that the source of the resonance may be local moments within the microcrystals themselves.

Efforts to eliminate from consideration any of these mechanisms have not yet been successful. Spectrographic analysis indicates that of the transition ' metals, iron, silver and possibly copper

are present in the platinum samples in high enough concentrations to account for the observed intensity of the ESR signal. The iron and copper impurities are present in similar amounts in the gelatin starting material and in the gold microcrystal samples, where the resonance has not been observed. In view of the small g-shift and the lack of observable g-shift- distribution broadening it appears that of the transition impurities the S-state ion Fe3+ is the most likely candidate as the source of the ESR signal. In addition to transition impurities, dangling bonds and trapped electron centers are also possibilities.

For paramagnetic centers in the matrix, the linewidth of the ESR line would presumably be

determined by dipolar hyperfine interactions with protons in the gelatin. Proton magnetic resonance signals from gelatin have been found to have a linewidth of about 15 gauss, indicating that the proton hyperfine interaction would lead to broadening of the correct magnitude. In an attempt to determine whether the ESR line broadening was due to protons or to platinum nuclei, ENDOR measurements were carried out under various experimental conditions, but no ENDOR signal was observed.

An additional piece of information which may shed light on the question of whether the ESR signal we have seen comes from platinum conduction electrons or paramagnetic centers in the temperature dependence of the relaxation time product TI T,,

obtainable from the saturation data.

We have found that the expressions of Portis [ I 11

for inhomogeneous broadening when om TI

>

1 and w, TI < 1 both fit the data within experimental error over the entire power range. Here w m is the modulation frequency. For the case om TI> 1 we

have obtained the product T I T2 from the saturation

parameter, s = 1/4 y2 HT T I T2, by determining the

value of H I for which the relative ESR amplitude has decreased to 0.5, in which case s = 3. The

product TI T2 equals 2.7 x 10-12, 2.4

x

lo-" and 8 x 10 " s'. at 291, 190 and 138 K , respectively. We consider two possibilities. If, as for F-centers [ l l ] ,

T, is independent of temperature, we can conclude

from our saturation data at 138, 190 and 291 K that

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SIZE DISTRIBUTION AND ESR OF UNIFORM MICROCRYSTALS OF PLATINUM C2-91 appropriate. We are currently collecting saturation M. L. Parsons for sample analyses and Mr. data at other temperatures in order to better define J- Wheatley for electron microscopy. This work the temperature dependence of the relaxation times. was supported in part by a Faculty Grant-in-Aid

Acknowledgments.

-

We wish to thank Dr. from Arizona 'State University.

References

[I] DENTON, R., M~JHLSCHLEGEL, B. and SCALAPINO, D. J.,

Phys. Rev. B 7 (1973) 3589.

[2] HOLLAND, B. W., in Colloque Ampere XIV. (Norfh- Holland, Amsterdam) (1967) 468.

[3] MONOT, R., CHATELAIN, A. and BOREL, J.-P., Phys. Lett. 34A (1971) 57.

[4] MONOT, R., NARBEL, C. and BOREL, J.-P., NUOVO Cimento

19B (1974) 253.

[5] MARZKE, R. F., GLAUNSINGER, W. S., and BAYARD, M.,

Solid State Commun. 18 (1976) 1025.

[6] GLAUNSINGER, W. S. and SIENKO, M. J., J. Chem. Phys. 62 (1975) 1883.

[7] GRANQVIST, C. G. and BUHRMAN, R. A., Solid State

Commun. 18 (1976) 123.

[8] MONOT, R. and MILLET, J.-L., J. Physique Lett. 37 (1976) L-45.

191 TAUPIN, C., Ph. D., University of Paris (1%8). [lo] KAWABATA, A., J. Phys. Soc. Japan 29 (1970) 902.

[ l l ] PORTIS, A. M., Phys. Rev. 91 (1953) 1071.

[12] JSW, A. F., KITTEL, C., LEVY, R. A. and PORTIS, A. M.,

Phys. Rev. 91 (1953) 1066.

[I31 CLOGSTON, A. M., JACCARINO, V. and YAFET, Y., Phys.