- Email: [email protected]
X-ray diffraction study of fine gold particles prepared by gas evaporation technique
SurfaceScience 106(1981)51-57 North-Holland Publishing Company
X-RAY DIFFRACTlON STUDY OF FINE GOLD PARTICLES PFtEPARED BY GAS EVAPORATION TECHNIQUJI
Jimpei HARADA and Ken-ichi OI-ISHRvI.4 Lkparmient of Applied Physics, Nagoya Wnkwsity, Nagoya 464, Japan
Received 8 September 1980
From the analysis of the X-ray Debye-Scherrer lines of the fine gold particles of which sizes are in a range from 60 to 230A, it was found that the thermal expansion coefficient as well as the lattice parameter are not different from those of the bulk crystal, while the characteristic temperature decreases monotonously with the decrease of the particle size. The particle size dependence of the characteristic temperature can be explained by introducing two characteristic temperatures Bcornand &h& on the assumption that the particles are composed of the core and the she& c!?- and &tt were found in good agreement with the characteristic temperature for the bulk crystal and that for the surface obtained by LEED experiment, respectively.
1. Introduction It is known that large mean square displacements of atoms, (u’}, in metal fine particles are observed from X-ray diffraction experiments [l-3] as well as the measurement of electric conductivity [4]. This fact tends to be considered as a result of the softening of the lattice vibrations arising from the large proportion of surface atoms in fine particles. As reported previously [2, 31 however, the following case is often observed; in addition to the contribution of thermal vibrations, some static Iattice distortions are involved in the observed mean square dispIacement of atoms. This depends on the specimen preparation condition. Furthermore, it was found that the particles coalesce each other at low temperature, when the specimen is heated up. Therefore, it is necessary to justify the mean square displacement of atoms obtained by a simple analysis of X-ray data by checking its temperature dependence in a range well below the temperature at which the coalescence of the tine particle occurs. Previously, it was shown that the characteristic temperature of fine gold particles can be determined from an analysis of the temperature dependence data of the mean square displacement of atoms. The reduction of the characteristic temperature was only 15% for the fine gold particles with the mean size of 100 A [3]. In order to understand more precisely the feature of the thermal vibration of fine gold partides the present authors extended the experiment by observing the particle size dependence of the characteristic temperature. 003~2~/81/000~000/$02.50
@ North-Holland Publishing Company
J. Han&a, K. Ohshima I X-ray diffractionstudy of fine gold pariicles
52
Table 1 Gas evaporation Specimen
conditions
Particle size
Gas
(‘Q I II III IV
@x10) 115(30) 150(40) 230@0)
Ar He Ar Ar
Gas pressure
Evaporation
frorr)
(“C)
15 30 20 30
1400 1600 1400 1600
temperature
2. Experimental Fine gold particles with several mean sizes above 60 A were prepared on a glass plate by gas evaporation technique [S]. The preparation condition and mean particle sizes for the specimens are tabulated in table 1. In order to protect from oxidation the specimens were shielded into a vacuum capsule with a Be window. It was mounted on a specimen holder in the vacuum chamber of an X-ray cryostat. The X-ray diffraction measurements were carried out by using a CuKj3 radiation, monochromated by a flat pyrolytic graphite crystal. The mean particle sizes were determined from the width of the Debye-Sherrer lines using Hall’s relation and the lattice parameters were estimated from their peak positions. The effective temperature parameter B which is proportional to the mean square atomic displacements (u*), B = 8.rr2(u2),was determined from plots of the logarithms of the ratio of the observed and calculated intensities as a function of (sin 8/h)2. As found in previous studies [2, 3] anomalies in the line width, peak shift and systematic intensity deviation from the calculation were also noticed. These are the characte~stics of the Debye-Sherrer pattern obtained from fine gold particles prepared by gas evaporation method. Due to these anomalies the accuracies of the mean particle size, lattice parameter and temperature parameter determined by the present study are within 20%, 0.05% and 6%, respectively. The details of this experimental procedure and the data analysis are the same as those of the previous studies [2, 31. The correction of the thermal diffuse scattering under the Debye-Scherrer lines have not been made because the behaviour of long wavelength phonons has not been understood yet in such fine particles. 3. Results
The results were summarized in table 2, where the thermal expansion coefficients UT were determined by the temperature dependence of the lattice parameter in a range from room temperature up to 80°C. As seen from table 2, obvious differences were not noticed in both the lattice parameter and the thermal expansion coefficient between the fine gold particles and the bulk crystal at room temperature.
J. Harada,K. Ohshima / X-ray difiaction study of fine gold partikks
53
3.2. Characteristic temperature Since the temperature parameter B is given by sum of the contribution from static lattice distortion B, and that from true thermal vibration BT, the characteristic temperature 0n was determined by analysing the temperature dependence of parameter B on the basis of the Einstein approximation B=B,fBT,
(1)
with 6h2 BT = mkn&
1 1 exp(Bn/T) - 1 + Z> ’
where m, T, h and kn are of the usual meaning. The measurements of parameter B were taken at eight different temperatures in a range from 108 up to 298 K. The results obtained for three specimens with different particle sizes are shown in fig. 1, where the solid curves are the best fitting results to the observed points by using the least squares method on the
a:
specimen
o; specimen
111(8i=144f3K) IV
(8~~161
TEMPERATURE
f4K)
(K
)
Fig. 1. Plots of the parameters B against temperature T for the three specimens, I, III and IV. The curved lines were determined by using eq. (1). The dashed curve is estimated by the value of the Debye temperature for the bulk crystal (0~ = 168 K).
J. Harada, K. Ohshima
54
I X-ray diffractionstudy of fine gold partkles
Table 2 The lattice parameter at room temperature, the thermal expansion coefficient or, the characteristic temperature & and the static component of parameter B Specimen
Particle size (A)
Lattice parameter
Thermal expansion coefficient or (10-s K-‘)
0~. (K)
Bs (A’)
4077(R) 3.079(2) 4.079(2)
1.7(3) 1B(3)
134(5) 14.5(4) 144(3) 161(4)
- O.Ol(5) 0.01(3) 0.07(2) 0.02(2)
4.079
1.4
168
(A)
I II III IV
60(10) 115(30) 150(40) 235(50) Large (bulk crystal)
-
basis of eq. (1). The dashed curve in the figure shows the calculation for the bulk crystal, where 13~= 168 K was used for the Debye temperature. The parameters & and B, refined in this way were summarized also in table 2. It should be noticed that the parameters B include scarcely the static components B, in the specimens used.
4. Conclusion and discussion It was found that the lattice parameter and thermal expansion coefficient of fine gold particles are not very much different from those of the bulk crystal, while the characteristic temperature r9n decreases monotonously when the size of particles decreases. It is suggested that the crystalline state of fine gold particles is not greatly different from the bulk crystal as a whole. We, then, assume that the fine gold particle is composed of two parts; the core and the shell as illustrated in fig. 2. According to this model, the temperature parameter Br is also given by the sum of two parts,
ar; shell / core
3ar
r
p=T_
0 Fig. 2. The schematic particle composed of two parts; the core and the shell. r, Ar and p are the radius of the particle, its shell and the ratio of the shell volume to the whole volume.
J. Han&,
K. Ohshima / X-ray diffraction study of fine gold panicles
55
where p means the proportion of the number of atoms in the shell to that of the whole volume and is given by p = 3 Al/Y .
(3)
r and Ar represent the mean radius of the fine particle and the thickness of the shell, respectively. Since we have a relation B - Te-2
(4)
at the high temperature limit of the harmonic approximation, eq. (2) can be rewritten in terms of the characteristic temperature 6,
This relation indicates that l/02 should be proportional to the inverse of the particle size l/r. Such plots are shown in fig. 3. We see that the observed points are fairly well on the straight line which was determined by the least squares fitting method. It is possible to determine the characteristic temperature &,,, from the value of I/@ at a limit of l/r = 0 and the @,,r, from the slope of the straight line in fig. 3, if a suitable
5
10 I/R(X
15
20
10-3&-')
Fig. 3. Plots of the inverse square of the characteristic temperature ll& against the inverse of the particle size l/R. The solid curve is estimated by using a least squares fitting method.
56
J. Ha&a,
K. Ohshima I X-ray diffractionstudy of fine gold particles
thickness of the shell Ar is given. In table 3, ecoreand &shell estimated for the several atomic layers assumed for the thickness, are shown where the Debye temperature for the bulk crystal and that for the clean surface determined by the LEED experiment are also given [6,7]. We see that &,,,, = 165(3)K is in good agreement with the Debye temperature for the bulk crystal 0~ = 168 K and 8shell= 97(6) K with the surface Debye temperature 0Surf,= 83(10) K only if the thickness of the shell is assumed as one atomic layer. The agreement of &hellwith 19~~~. is rather surprisingly good if we consider that the surface of the present fine particle is not so clean comparing the clean gold surface by which the LEED experiment has been made. The present result, therefore, should be understood as representing the thermal vibration of the fine particles of which surfaces are covered by some Ar or He inert gas atoms and not the thermal vibration of fine particles themselves. Previously, Kashiwase et al. [l] deduced in their X-ray study of fine silver particles that surface effect on the lattice vibration should be remarkable in the fine particles because the effect is considered to penetrate deeply into the interior of the particles and causes more softening of the lattice vibration. This effect is conceivable since the interatomic forces are known to be of the long range, particularly, in the case of metal. If this effect is really included, experimental points showed deviate upward from the straight line. As seen in fig. 3, no such tendency is observed at least for gold particles with the sizes above 60 A. This tendency is qualitatively in agreement with Buffat and Borel’s observation of the particle size dependence of the melting temperature for fine gold particles [8]. According to their result the decrease of the melting point is not so great when the size of particles is above 50 A. It is concluded from the present X-ray study that the softening of the lattice vibration in fine gold particles is arised from the increase of the proportion of surface atoms to the whole number of atoms but the effect of softening is not so great, as deduced previously [2,3]. It is supposed that the surface of the fine particles is covered by some inert gas atoms and the thermal vibration is clamped. Accordingly, the further study should be made by using more clean surface of fine metal particles. This is left to the future.
Table 3 The four characteristic
temperatures &hell
One atom layer Two atom layers Three atom layers
(K) b-i 09
97(6) 118(6) 129(6)
83(10)
&oreW
&I (K)
165(3)
168
tishell: characteristic temperature for the shell as shown in fig. 2. Bru,+: surface Debye temperature for the bulk crystal. f&E: characteristic temperature for the core as shown in fig. 2. lIM: Debye temperature for the bulk crystal.
J. Harada, K. Ohshima / X-ray difiaction studyof jine goMparricks
References [l] [Z] [3] [4] [5] [6] [7] [8]
Y. Kashiwase, I. Nishida, Y. Kainuma and K. Kimoto, .I. Physique 38 (1977) C2-157. J. Harada, S. Yao and A. Ichimiya, J. Phys. Sot. Japan 48 (1980) 1625. K. Ohshima, A. Hayashi and J. Harada, J. Phys. Sot. Japan 48 (1980) 1631. T. Fujita, K. Ohshima and T. Kuroishi, J. Phys. Sot. Japan 40 (1976) 90. S. Yatsuya, S. Kasukabe and R. Uyeda, Japan. J. Appl. Phys. 12 (1973) 1675. N. Singh and P.K. Sharma, Phys. Rev. B3 (1971) 1141. M. Kostelitz and J.L. Domange, Solid State Commun. 13 (1973) 241. Ph. Buffat and J.-P. Borel, Phys. Rev. Al3 (1977) 72.
57
X-RAY DIFFRACTlON STUDY OF FINE GOLD PARTICLES PFtEPARED BY GAS EVAPORATION TECHNIQUJI
Jimpei HARADA and Ken-ichi OI-ISHRvI.4 Lkparmient of Applied Physics, Nagoya Wnkwsity, Nagoya 464, Japan
Received 8 September 1980
From the analysis of the X-ray Debye-Scherrer lines of the fine gold particles of which sizes are in a range from 60 to 230A, it was found that the thermal expansion coefficient as well as the lattice parameter are not different from those of the bulk crystal, while the characteristic temperature decreases monotonously with the decrease of the particle size. The particle size dependence of the characteristic temperature can be explained by introducing two characteristic temperatures Bcornand &h& on the assumption that the particles are composed of the core and the she& c!?- and &tt were found in good agreement with the characteristic temperature for the bulk crystal and that for the surface obtained by LEED experiment, respectively.
1. Introduction It is known that large mean square displacements of atoms, (u’}, in metal fine particles are observed from X-ray diffraction experiments [l-3] as well as the measurement of electric conductivity [4]. This fact tends to be considered as a result of the softening of the lattice vibrations arising from the large proportion of surface atoms in fine particles. As reported previously [2, 31 however, the following case is often observed; in addition to the contribution of thermal vibrations, some static Iattice distortions are involved in the observed mean square dispIacement of atoms. This depends on the specimen preparation condition. Furthermore, it was found that the particles coalesce each other at low temperature, when the specimen is heated up. Therefore, it is necessary to justify the mean square displacement of atoms obtained by a simple analysis of X-ray data by checking its temperature dependence in a range well below the temperature at which the coalescence of the tine particle occurs. Previously, it was shown that the characteristic temperature of fine gold particles can be determined from an analysis of the temperature dependence data of the mean square displacement of atoms. The reduction of the characteristic temperature was only 15% for the fine gold particles with the mean size of 100 A [3]. In order to understand more precisely the feature of the thermal vibration of fine gold partides the present authors extended the experiment by observing the particle size dependence of the characteristic temperature. 003~2~/81/000~000/$02.50
@ North-Holland Publishing Company
J. Han&a, K. Ohshima I X-ray diffractionstudy of fine gold pariicles
52
Table 1 Gas evaporation Specimen
conditions
Particle size
Gas
(‘Q I II III IV
@x10) 115(30) 150(40) 230@0)
Ar He Ar Ar
Gas pressure
Evaporation
frorr)
(“C)
15 30 20 30
1400 1600 1400 1600
temperature
2. Experimental Fine gold particles with several mean sizes above 60 A were prepared on a glass plate by gas evaporation technique [S]. The preparation condition and mean particle sizes for the specimens are tabulated in table 1. In order to protect from oxidation the specimens were shielded into a vacuum capsule with a Be window. It was mounted on a specimen holder in the vacuum chamber of an X-ray cryostat. The X-ray diffraction measurements were carried out by using a CuKj3 radiation, monochromated by a flat pyrolytic graphite crystal. The mean particle sizes were determined from the width of the Debye-Sherrer lines using Hall’s relation and the lattice parameters were estimated from their peak positions. The effective temperature parameter B which is proportional to the mean square atomic displacements (u*), B = 8.rr2(u2),was determined from plots of the logarithms of the ratio of the observed and calculated intensities as a function of (sin 8/h)2. As found in previous studies [2, 3] anomalies in the line width, peak shift and systematic intensity deviation from the calculation were also noticed. These are the characte~stics of the Debye-Sherrer pattern obtained from fine gold particles prepared by gas evaporation method. Due to these anomalies the accuracies of the mean particle size, lattice parameter and temperature parameter determined by the present study are within 20%, 0.05% and 6%, respectively. The details of this experimental procedure and the data analysis are the same as those of the previous studies [2, 31. The correction of the thermal diffuse scattering under the Debye-Scherrer lines have not been made because the behaviour of long wavelength phonons has not been understood yet in such fine particles. 3. Results
The results were summarized in table 2, where the thermal expansion coefficients UT were determined by the temperature dependence of the lattice parameter in a range from room temperature up to 80°C. As seen from table 2, obvious differences were not noticed in both the lattice parameter and the thermal expansion coefficient between the fine gold particles and the bulk crystal at room temperature.
J. Harada,K. Ohshima / X-ray difiaction study of fine gold partikks
53
3.2. Characteristic temperature Since the temperature parameter B is given by sum of the contribution from static lattice distortion B, and that from true thermal vibration BT, the characteristic temperature 0n was determined by analysing the temperature dependence of parameter B on the basis of the Einstein approximation B=B,fBT,
(1)
with 6h2 BT = mkn&
1 1 exp(Bn/T) - 1 + Z> ’
where m, T, h and kn are of the usual meaning. The measurements of parameter B were taken at eight different temperatures in a range from 108 up to 298 K. The results obtained for three specimens with different particle sizes are shown in fig. 1, where the solid curves are the best fitting results to the observed points by using the least squares method on the
a:
specimen
o; specimen
111(8i=144f3K) IV
(8~~161
TEMPERATURE
f4K)
(K
)
Fig. 1. Plots of the parameters B against temperature T for the three specimens, I, III and IV. The curved lines were determined by using eq. (1). The dashed curve is estimated by the value of the Debye temperature for the bulk crystal (0~ = 168 K).
J. Harada, K. Ohshima
54
I X-ray diffractionstudy of fine gold partkles
Table 2 The lattice parameter at room temperature, the thermal expansion coefficient or, the characteristic temperature & and the static component of parameter B Specimen
Particle size (A)
Lattice parameter
Thermal expansion coefficient or (10-s K-‘)
0~. (K)
Bs (A’)
4077(R) 3.079(2) 4.079(2)
1.7(3) 1B(3)
134(5) 14.5(4) 144(3) 161(4)
- O.Ol(5) 0.01(3) 0.07(2) 0.02(2)
4.079
1.4
168
(A)
I II III IV
60(10) 115(30) 150(40) 235(50) Large (bulk crystal)
-
basis of eq. (1). The dashed curve in the figure shows the calculation for the bulk crystal, where 13~= 168 K was used for the Debye temperature. The parameters & and B, refined in this way were summarized also in table 2. It should be noticed that the parameters B include scarcely the static components B, in the specimens used.
4. Conclusion and discussion It was found that the lattice parameter and thermal expansion coefficient of fine gold particles are not very much different from those of the bulk crystal, while the characteristic temperature r9n decreases monotonously when the size of particles decreases. It is suggested that the crystalline state of fine gold particles is not greatly different from the bulk crystal as a whole. We, then, assume that the fine gold particle is composed of two parts; the core and the shell as illustrated in fig. 2. According to this model, the temperature parameter Br is also given by the sum of two parts,
ar; shell / core
3ar
r
p=T_
0 Fig. 2. The schematic particle composed of two parts; the core and the shell. r, Ar and p are the radius of the particle, its shell and the ratio of the shell volume to the whole volume.
J. Han&,
K. Ohshima / X-ray diffraction study of fine gold panicles
55
where p means the proportion of the number of atoms in the shell to that of the whole volume and is given by p = 3 Al/Y .
(3)
r and Ar represent the mean radius of the fine particle and the thickness of the shell, respectively. Since we have a relation B - Te-2
(4)
at the high temperature limit of the harmonic approximation, eq. (2) can be rewritten in terms of the characteristic temperature 6,
This relation indicates that l/02 should be proportional to the inverse of the particle size l/r. Such plots are shown in fig. 3. We see that the observed points are fairly well on the straight line which was determined by the least squares fitting method. It is possible to determine the characteristic temperature &,,, from the value of I/@ at a limit of l/r = 0 and the @,,r, from the slope of the straight line in fig. 3, if a suitable
5
10 I/R(X
15
20
10-3&-')
Fig. 3. Plots of the inverse square of the characteristic temperature ll& against the inverse of the particle size l/R. The solid curve is estimated by using a least squares fitting method.
56
J. Ha&a,
K. Ohshima I X-ray diffractionstudy of fine gold particles
thickness of the shell Ar is given. In table 3, ecoreand &shell estimated for the several atomic layers assumed for the thickness, are shown where the Debye temperature for the bulk crystal and that for the clean surface determined by the LEED experiment are also given [6,7]. We see that &,,,, = 165(3)K is in good agreement with the Debye temperature for the bulk crystal 0~ = 168 K and 8shell= 97(6) K with the surface Debye temperature 0Surf,= 83(10) K only if the thickness of the shell is assumed as one atomic layer. The agreement of &hellwith 19~~~. is rather surprisingly good if we consider that the surface of the present fine particle is not so clean comparing the clean gold surface by which the LEED experiment has been made. The present result, therefore, should be understood as representing the thermal vibration of the fine particles of which surfaces are covered by some Ar or He inert gas atoms and not the thermal vibration of fine particles themselves. Previously, Kashiwase et al. [l] deduced in their X-ray study of fine silver particles that surface effect on the lattice vibration should be remarkable in the fine particles because the effect is considered to penetrate deeply into the interior of the particles and causes more softening of the lattice vibration. This effect is conceivable since the interatomic forces are known to be of the long range, particularly, in the case of metal. If this effect is really included, experimental points showed deviate upward from the straight line. As seen in fig. 3, no such tendency is observed at least for gold particles with the sizes above 60 A. This tendency is qualitatively in agreement with Buffat and Borel’s observation of the particle size dependence of the melting temperature for fine gold particles [8]. According to their result the decrease of the melting point is not so great when the size of particles is above 50 A. It is concluded from the present X-ray study that the softening of the lattice vibration in fine gold particles is arised from the increase of the proportion of surface atoms to the whole number of atoms but the effect of softening is not so great, as deduced previously [2,3]. It is supposed that the surface of the fine particles is covered by some inert gas atoms and the thermal vibration is clamped. Accordingly, the further study should be made by using more clean surface of fine metal particles. This is left to the future.
Table 3 The four characteristic
temperatures &hell
One atom layer Two atom layers Three atom layers
(K) b-i 09
97(6) 118(6) 129(6)
83(10)
&oreW
&I (K)
165(3)
168
tishell: characteristic temperature for the shell as shown in fig. 2. Bru,+: surface Debye temperature for the bulk crystal. f&E: characteristic temperature for the core as shown in fig. 2. lIM: Debye temperature for the bulk crystal.
J. Harada, K. Ohshima / X-ray difiaction studyof jine goMparricks
References [l] [Z] [3] [4] [5] [6] [7] [8]
Y. Kashiwase, I. Nishida, Y. Kainuma and K. Kimoto, .I. Physique 38 (1977) C2-157. J. Harada, S. Yao and A. Ichimiya, J. Phys. Sot. Japan 48 (1980) 1625. K. Ohshima, A. Hayashi and J. Harada, J. Phys. Sot. Japan 48 (1980) 1631. T. Fujita, K. Ohshima and T. Kuroishi, J. Phys. Sot. Japan 40 (1976) 90. S. Yatsuya, S. Kasukabe and R. Uyeda, Japan. J. Appl. Phys. 12 (1973) 1675. N. Singh and P.K. Sharma, Phys. Rev. B3 (1971) 1141. M. Kostelitz and J.L. Domange, Solid State Commun. 13 (1973) 241. Ph. Buffat and J.-P. Borel, Phys. Rev. Al3 (1977) 72.
57