Appl. Phys. A 81, 673–677 (2005)
Applied Physics A
DOI: 10.1007/s00339-005-3254-9
Materials Science & Processing
i. beszeda1,u e.g. gontier-moya2 ´ a.w. imre3
Surface Ostwald-ripening and evaporation of gold beaded films on sapphire 1 Department
of Solid State Physics, University of Debrecen, 4010 Debrecen, Hungary UMR CNRS 6137, Universit´e Paul C´ezanne Aix-Marseille III, Marseille, France 3 Institut für Materialphysik, Westfälische Wilhelms-Universität, 48149 Münster, Germany 2 L2MP,
Received: 3 November 2004/Accepted: 2 March 2005 Published online: 10 May 2005 • © Springer-Verlag 2005
The kinetics of morphological evolutions of gold nanoparticles on alumina, resulting from evaporation and surface Ostwald-ripening coarsening, have been investigated by means of Auger electron spectroscopy. When the fraction of the covered area is small, the kinetics of evaporation can be related to the desorption of adatoms. In the temperature range 943–1043 K we obtained the evaporation flux J(m−2 s−1 ) = 4.8 × 1027 exp[−196 ± 9 (kJ/mol)/RT ]. The experimental activation energy of evaporation of gold from a sapphire surface, Q evap = 196 ± 9 kJ/mol, is lower than the tabulated value of enthalpy of sublimation of gold, ∆Hsubl = 368 kJ/mol. At lower temperatures, in the range 623–778 K, Ostwald-ripening experiments, carried out on nanosized clusters, yield the mass transfer surface diffusion coefficients of gold on alumina, Ds (m2 /s) = 2.6 × 10−14 exp[−58 ± 9 (kJ/mol)/RT ]. These results, providing information on the evolution of granular gold films such as those used in catalysts or sensors, are compared to previous data on similar systems. ABSTRACT
PACS 68.47.Jn;
1
68.43.Jk; 68.55.-a
Introduction
Oxide supported metal nanoparticles are used to promote or to select the activity of catalysts and sensors. Recent reviews [1–3] describe different aspects of these systems. The nucleation and growth of metal particles on an oxide surface by vacuum deposition can be related to a combination of two processes: adsorption and migration of metal atoms on the oxide surfaces [1, 4, 5]. Thus, the behavior of such films depends on the physical quantities which characterize these processes. From a practical point of view, it is of great interest to know the mass transport parameters, in order to predict the effective morphological evolutions. Related to desorption, the model proposed by Kaganovskii and Beke [6, 7] describes the evaporation of beaded films considered as sources of adatoms. Alternatively, in conditions of mass conservation, the Ostwald-ripening model, extended to the case of particles u Fax: +36-52-316-073, E-mail:
[email protected]
deposited on a substrate [8–10], is related to the migration of adatoms. Auger electron spectroscopy (AES) can be used to follow the variation of the ratio of covered/uncovered substrate areas, which is proportional to the square of the average particle radius. By appropriate choices of the annealing temperatures and the islands morphology, the evaporation and Ostwald-ripening processes can be investigated separately in reasonable times. We present here the experimental measurements carried out on a model sytem: gold on sapphire. 2
Theoretical
2.1
Evaporation of a beaded film
Morphological changes of beaded films on substrates, in consequence of evaporation, can be treated by the model of Kaganovskii and Beke [6, 7], illustrated in Fig. 1. Such beaded films are described by their effective thickness, h eff = 2πϕ(Θ)Ns R3 /3, where Θ and Ns are the contact angle and density of beads, ϕ(Θ) is a geometrical parameter (ϕ(Θ) = 1 − 3/2 cos θ + 1/2 cos3 θ ) and R3 is the average cubic radius. The surface is considered as a two-dimensional layer of width δ = ν ω, where ν is the surface density of sites, and ω the atomic volume. The motion of adatoms is characterized by the intrinsic surface diffusion coefficient, Dsi , and by the surface diffusion length, λs = (Dsi τ)1/2 , where τ is the mean residence time of adatoms on the surface. When the following three conditions fulfill [6, 7]: (i) the surface diffusion fields of islands are overlapping (i.e., the average distance between the beads, , is less than 2λs ), (ii) the evaporation of adatoms is responsible for the diminution of the effective thickness (i.e., the area covered by beads is small compared to the total area), (iii) the surface diffusion process is slower than the detachment rate of atoms from the periphery of beads (surface diffusion control (SDC) regime), then the effective thickness decreases with time, from its initial value h(0), as [6, 7]: h eff (t) = h(0) −
δcs δDs t = h(0) − J ω t = h(0) − 2 t . τ λs
(1)
In these relations, cs is the fraction of adatoms in equilibrium with a plane film, J is the evaporation flux given by J = νcs /τ , Ds is the mass transfer surface diffusion coefficient given by
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Applied Physics A – Materials Science & Processing
and hence, from (3) and (4) we obtain the relation between the gold and oxygen signals: IAu (t) IOx ( f) − IOx (t) = . IAu (0) IOx ( f) − IOx (0) FIGURE 1
Consequently, the normalized effective thickness can be described by:
Model of the beaded film [1]
Ds = Dsi cs . Using AES, the normalized effective thickness, h eff (t)/h(0) can be expressed as a function of the Auger signal of the metal deposit, IM [7]: δcs IM (t) 3/2 = 1− t IM (0) h(0)τ δDs Jω t = 1− t. = 1− h(0) h(0)λ2s
h eff (t) = h(0)
(5)
IAu (t) 3/2 IOx ( f) − IOx (t) 3/2 = IAu (0) IOx ( f) − IOx (0) δcs Jω δDs = 1− t = 1− t = 1− t. h(0)τ h(0) h(0)λ2s
h eff (t) = h(0)
(2)
Consequently, the time dependence of the Auger signal of the deposit yields δcs /τ , or J ω, or δDs /λ2s . The last expression is preferred when it is possible to measure λs and Ds independently, such as in the method, developed by Beke and Kaganovskii, where the shift of a boundary between a coated and a free surface is followed as a function of time [7, 11]. In the present work, gold beaded films were deposited on sapphire substrate. The gold and aluminium Auger peaks are quite close to each other (69 and 51 eV, respectively) and the resolution of our Auger spectroscope was not sufficient to separate them clearly. Therefore we measured the oxygen signal, coming from the substrate, and a simple calculation was made in order to relate it to that of gold necessary in (2). The gold signal is proportional to the surface fraction covered by beads, i.e., depends on the number of particles, n , and on their average area, S: IAu (0) = k1 nS(0) and IAu (t) = k1 nS(t) ,
2.2
(6)
Ostwald-ripening of a beaded film
In case of mass conservation, a decrease of the total coverage may be observed as a result of the surface Ostwaldripening process. Using the same symbols as in the previous section, the average radius of particles, R, can be expressed as [8–10] R(t) 4 8Ds γω2 ν = 1+ (7) t 4 R(0) 45R (0) ln(L)ϕ(Θ)kT where γ is the surface energy of the metal, k the Boltzman constant, T the temperature and L is a constant with a value close to 2.5 [8]. Using the AES technique, the gold Auger intensities are proportional to the area covered by particles: IAu (0) = k1 Ns (0)R2 (0) and IAu (t) = k1 Ns (t)R2 (t) ,
so the normalized Au intensity is IAu (t) Ns (t)R2 (t) = . IAu (0) Ns (0)R2 (0)
(8)
where k1 is a proportionality constant. The normalized gold Auger intensity can be written in the form
The mass conservation implies an additional relation [12]:
S(t) IAu (t) = . IAu (0) S(0)
Ns (t) R3 (0) = 3 . Ns (0) R (t)
(3)
(9)
Similarly, the oxygen Auger intensities can be described as
From (8) and (9) the normalized Au intensity becomes:
IOx (0) = k2 [Stotal − nS(0)], IOx (t) = k2 [Stotal − nS(t)] and IOx ( f) = k2 Stotal ,
IAu (t) R(0) = . IAu (0) R(t)
where k2 is a new proportionality constant for oxygen detection, Stotal is the area of the exposed surface under the electron beam and IOx ( f) is the final oxygen signal obtained after complete evaporation of the deposit. Calculating the differences
Inserting (10) into (7) one gets the time dependence of the normalized Auger intensity of the deposit:
IOx ( f) − IOx (t) = k2 nS(t) and IOx ( f) − IOx (0) = k2 nS(0)
IAu (0) IAu (t)
4 = 1+
8Ds γω2 ν t 45R4 (0) ln(L)ϕ(Θ)kT
(11)
or, using (5), the time dependence of the normalized oxygen intensity:
we get: IOx ( f) − IOx (t) S(t) = IOx ( f) − IOx (0) S(0)
(10)
(4)
IOx ( f) − IOx (0) IOx ( f) − IOx (t)
4 = 1+
8Ds γω2 ν 4 45R (0) ln(L)ϕ(Θ)kT
t.
(12)
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Surface Ostwald-ripening and evaporation of gold beaded films on sapphire
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Experimental
Small plates of α-alumina single crystals, with a polished 101¯ 2¯ surface, were used as substrates. After they had been ultrasonically rinced in alcohol and in distilled water, they were covered with a thin film of gold. The effective thickness of the deposit was 8 nm for evaporation experiments, but only 0.5 nm for Ostwald-ripening experiments. The deposition was carried out from a Knudsen cell directly in the vacuum chamber of Auger device. A quartz balance was used for the calibration of the vapor flux. The sample was fixed to a heating element made of a tantalum wire and a thermocouple pressed on the surface of the sample to determine the actual temperature. The oxygen peak intensity at 503 eV was recorded at regular intervals. During annealings the residual pressure was between 3 – 6 × 10−9 mbar. Several deposition–annealing– evaporation cycles were performed on the same sample. For this reason, each cycle was completed with a heat treatment at elevated temperature (1173 K), to obtain a clean substrate surface where also the signal IOx ( f) was each time measured. 4
Results and discussion
4.1
Evaporation of gold beaded films
The kinetics of evaporation was measured at different temperatures, in the range 943– 1043 K. Figure 2 illustrates a typical IOx (t) curve. The data points marked with open squares, measured at room temperature, have a constant intensity. The increasing part of the curve (filled squares) corresponds to the evaporation at 943 K, and the intensity becomes constant again in the final part obtained at elevated temperature. Figure 3 presents the ( IAu (t)/IAu (0))3/2 vs. time curves, calculated from the oxygen signals, at measured temperatures. For clarity, only the fitted lines are presented. The slopes of these plots can be determined according to (6) as −δcs /h(0)τ = −Jωh(0) = −δDs /h(0)λ2s . Their values are listed in Table 1. The corresponding evaporation fluxes, J, are calculated, using h(0) = 8 nm and ω = 1.69 × 10−29 m3 , and
Oxygen Auger intensity vs. time. The initial part ( symbols) corresponds to low temperature, the increasing part ( symbols) to the evaporation at 943 K, while at long times the intensity reaches a plateau (at elevated temperature, + symbols)
[IAu (t)/IAu (0)]3/2 vs. time curves, calculated from the oxygen
signals
also reported in Table 1. Plotting the logarithm of these values vs. the reciprocal temperature, a linear function could be obtained, which is presented in Fig. 4a. The evaporation flux is given by: J (943– 1043 K) = 4.8 × 1027 −(196 ± 9)kJ/mol × exp m−2 s−1 RT
(13) In Fig. 4b, we compare the evaporation fluxes, J, of gold to those of palladium [13]. We can see that the evaporation of gold adatoms is faster than that of palladium. For example, an evaporation rate of 1017 m−2 s−1 requires about T ≈ 973 K for gold and T ≈ 1073 K for palladium adatoms. In the same figure we have plotted also the maximum evaporation fluxes from bulk metals (sublimation), calculated from the classical relation J = p/(2πmkT)1/2, where p is the equilibrium vapour pressure of the metal at the temperature T, obtained from the tabulated values of the enthalpy and entropies of vaporisation of metals [14] , and m is the atomic mass. We observe that the evaporation of gold and palladium adatoms from alumina surfaces is considerably faster than the sublimation of bulk metals. The question arises whether this difference is caused by the small particle size. Estimating the term 2γω/RkT for the different temperatures and particle sizes used in our experiments, we can conclude that the small radii would not explain the high evaporation rate of Au. The practical importance of these results, particularly when evaporation is to be avoided, is worth to being noted. T (K)
slope = −δDs /h 0 λ2s
J (m−2 s−1 )
943 973 1003 1023 1033 1043
0.00012057 0.00031202 0.00065676 0.00102588 0.00107005 0.00140612
5.7 × 1016 1.5 × 1017 3.1 × 1017 4.8 × 1017 5.1 × 1017 6.6 × 1017
FIGURE 2
FIGURE 3
Slopes of (IAu (t)/IAu (0))3/2 vs. time curves and the corresponding evaporation fluxes at different temperatures TABLE 1
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Applied Physics A – Materials Science & Processing Ds (m2 /s)
T (K)
3.1 × 10−19 6.8 × 10−19 6.5 × 10−19 4.7 × 10−19 5.5 × 10−19 1.1 × 10−18 2.0 × 10−18 1.4 × 10−18 1.7 × 10−18 2.0 × 10−18 2.2 × 10−18 2.1 × 10−18 7.2 × 10−18 2.1 × 10−18
623 623 648 673 673 683 698 713 723 723 743 748 773 778
TABLE 2 Mass transfer surface diffusion coefficients of gold on alumina, obtained at different temperatures
FIGURE 4 (a) Temperature dependence of the evaporation fluxes, extracted form (6). (b) Evaporation fluxes of gold and palladium. × and symbols present the experimental data on Au and Pd. Dashed and solid lines correspond to maximum evaporation fluxes from the bulk Au and Pd metals (sublimation), calculated from the relation J = p/(2πmkT)1/2 [14]
the Arrhenius lines show some interesting facts: 1) at low temperatures (around 573 K–673 K), as compared to palladium, copper, nickel, and even silver, the gold atoms are the most mobile on alumina surfaces (if we assume that the extrapolation of the Arrhenius lines to lower temperatures is correct). 2) The very low activation energy for gold, compared to other metals ( Q s (Au) = 58 kJ/mol, Q s (Pd) = 203 kJ/mol [12], Q s (Ag) = 200 kJ/mol [17], Q s (Cu) = 380 kJ/mol [20], Q s (Ni) = 604 kJ/mol [19]), results only in a moderate effect of temperature on the surface transport of gold atoms.
4.2
Surface Ostwald-ripening of gold particles
Ostwald-ripening was investigated at different temperatures in the range 623 – 778 K. As an example, the IOx (t) curve obtained at 623 K is plotted in Fig. 5. The 4
( f)−IOx (0) is shown in Fig. 6. corresponding quantity IIOx Ox ( f)−IOx (t) From the slope of the straight line, using the following values, h = 0.5 nm, R(0) = 3.5 nm [15], θ = 135◦ [15], γ = 1.5 J/m2 [16], ω = 1.69 × 10−29 m3 , L = 2.5 [8] and ν = ω−2/3 , reported in (12), the mass transfer surface diffusion coefficient was determined. The values obtained at different tempertures are listed in Table 2. Figure 7a shows Ds for gold surface diffusion on alumina vs.the reciprocal temperature and the Arrhenius relation is determined as:
4.3
Surface diffusion length
An expression of λs can be obtained by a combination of the expressions of the evaporation flux J = νcs /τ and the surface mass transfer diffusion Ds = cs Dsi : λs = (Ds ν/J)1/2 .
(15)
The temperature dependence of this parameter can be related to an ‘activation energy’, Q λs , such as: Q λs = (Q s − Q evap )/2
(16)
Ds (623 − 778K) = 2.6 × 10−14 −(58 ± 9)kJ/mol × exp m2 s−1 . (14) RT
Surface diffusion of metals on oxides may be responsible for the coarsening of deposited particles, and for a loss of activity in the case of catalysts and sensors. This remark emphasizes the interest of such surface diffusion data obtained on a model system (clean and well defined surface). We have compared these results with other published data (Pd [12], Ag [17], Ni [18, 19] and Cu [18, 20] on alumina surfaces) in Fig. 7b. The relative positions of
FIGURE 5 The oxygen Auger-intensity vs. time during surface Ostwaldripening at 623 K. The intensity practically reaches a plateau, according to (7). The increasing intensity in the long time-part corresponds to an elevated temperature (to obtain a clean surface)
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Surface Ostwald-ripening and evaporation of gold beaded films on sapphire
677
For these noble metals on sapphire systems it can be concluded that diffusion processes play an important role at low temperatures, due to an increase of the surface diffusion lengths. Comparison with copper and nickel on sapphire shows a significant difference. In these ‘reactive’ systems Q λs is positive [18–20], and so λs increases when the temperature increases. This can be explained by a surface reaction (for example metal–oxygen bonding) which controls the desorption of adatoms. 5
The normalized oxygen intensity, [(IOx ( f) − IOx (0))/(IOx ( f) − IOx (t))]4 = [IAu (0))/(IAu (t)]4 vs. time, corresponding to (12), at 623 K
FIGURE 6
Conclusions
Evaporation and Ostwald-ripening of gold particles deposited on sapphire have been followed by AES, and the evolution kinetics have been interpreted by models involving mass transport of adatoms. The evaporation fluxes measured in the temperature range 943 – 1043 K yield an activation energy of 196 kJ/mol. From the mass transfer surface diffusion coefficients of gold on alumina, determined in the temperature range 623– 778 K, an activation energy of 58 kJ/mol was obtained. The surface diffusion length, deduced from a combination of the two types of experiments, is found to increase when the temperature decreases, with an activation energy of about −70 kJ/mol. In addition to their interest for technological applications, these results illustrate the difference in kinetics of noble metals, compared to reactive metals, deposited on alumina surfaces. ACKNOWLEDGEMENTS This work has been supported by the Hungarian Grant FKFP 0188/2001 and a post doctoral grant of the French Ministery of Research.
REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 FIGURE 7 (a) The temperature dependence of the gold mass transfer surface diffusion coefficients. (b) Comparison of surface diffusion data of Au with those of Ni [18, 19], Cu [18, 20], Pd [12] and Ag [17]
15 16
In the case of gold, from (14) and (13) it comes: Q λs = (58 − 196)/2 ≈ −70 kJ/mol .
14
17
(17)
From the negative Q λs in (17) one can conclude that λs increases with decreasing temperature. A similar result was obtained for palladium on sapphire ( Q λs = −87 kJ/mol) [12].
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