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Grain-growth kinetics of nanostructured gold
Thin Solid Films 515 (2006) 353 – 356 www.elsevier.com/locate/tsf
Grain-growth kinetics of nanostructured gold O. Yevtushenko, H. Natter, R. Hempelmann * Physical Chemistry, Saarland University Saarbruecken, 66123, Germany Available online 18 January 2006
Abstract Nanocrystalline gold is electrodeposited from non-cyanide non-sulfite bath by pulse techniques. The thermal stability of nanocrystalline gold is investigated in situ by high-temperature X-ray diffraction. The experimental growth kinetics of gold crystallites can be described in terms of a growth model with size-dependent impediment. D 2005 Elsevier B.V. All rights reserved. Keywords: Electrodeposition; Thermal stability; Crystallite growth kinetics
1. Introduction
2. Experimental details
Nanocrystalline materials differ in some physical and chemical properties from polycrystalline materials of the same chemical composition. The reason of this phenomenon is the large volume fraction of interfaces resulting from small crystallite sizes or quantum size effect [1,2]. Undoubtedly it opens the fascinating possibility to change and control material properties simply by adjusting the grain-size appropriately during the production process [3]. As examples, the hardness of nano-Au increases [4] and corrosion resistance in nano-Ni enhances [5] with decreasing crystallite size. An increase of the temperature causes crystal growth and therefore the physical and chemical properties to change [6,7]. For this reason the thermal stability of nanocrystalline materials is one of the most important properties which are of interest for basic research as well as for industrial applications at elevated temperatures. The kinetics of grain growth can be studied by means of in situ high-temperature Xray diffraction [6 –9]. The X-ray diffraction lines contain information about the crystallite size, the structure, packing order of the atoms in the lattice, microstrain etc. The advantage of an in situ experiment is the analysis of the same part of the sample and the observation of changes in X-ray line shapes due to only the increase of the temperature.
Nanocrystalline gold with different crystallite sizes has been prepared from a non-cyanide non-sulfite electrolyte using pulsed electrodeposition technique [10]. We have prepared the electrolyte in the following way: H[AuCl4] reacts with ammonium hydroxide to gold (III) hydroxide, which can be reduced by 3-mercapto-1-propanesulfonic acid (MPS) in a time of approximately 3 h to gold (I). The resulting solution is colorless and exhibits long time stability. The electrolyte consists of 5 g * L 1 HAuCl4 (Au-50%), 10.5 g * L 1 MPS (90%), 160 mL (50%) NH4OH and has a strongly basic pH. We used stainless steel anodes and copper cathodes (99.9% purity). All pulse electrodeposition (PED) experiments are performed at a temperature of 348 K with the following pulse parameters: t on—pulse duration time 1 ms, t off—time between two pulses 20 ms and average current density 50 mA * cm 2. For the characterization of the deposited samples, we used high-temperature X-ray diffraction (Siemens D-5000 diffractometer). In order to achieve high time resolution a position sensitive detector (Braun Inc., Germany) was used. The isothermal measurements were recorded every 60 s. The annealing time expended in heating the sample to the fixed temperature is calculated to be 21 s. This is a very short time in comparison with the time of the whole measurement and therefore no corrections to the time of isotherms data are applied. TEM (Jeol, JEM-2010) pictures of deposited samples are made to obtain the information about the morphology of gold.
* Corresponding author. Tel.: +49 681 302 4750; fax: +49 681 302 4759. E-mail address: [email protected] (R. Hempelmann). 0040-6090/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2005.12.098
354
O. Yevtushenko et al. / Thin Solid Films 515 (2006) 353 – 356
The microstrain is determined by the model described by Cheary and Coelho [11]. For the evaluation of crystallite size we use a modified Warren Averbach analysis [12,13].
fraction decreases the impurities in the grain boundaries are more enriched:
3. Kinetics of grain growth
With the same initial conditions as above, the solution of this differential equation is sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a3 a3 Dðt Þ ¼ þ D20 ð7Þ expð 2b3 t Þ b3 b3 pffiffiffiffiffiffiffiffiffiffiffiffi Using DV ¼ a3 =b3 this can be expressed as ffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Dðt Þ ¼ D2V D2V D20 expð k3 t Þ ð8Þ
At high temperatures the crystallites grow during a relatively short period of time and then the crystallite size does not change essentially any more with time. The theoretical basis for understanding of isothermal grain growth was proposed by Burke and Turnbull [14]. They deduced the grain growth from the movement of grain boundaries and assumed atom transport across the boundaries under a pressure due to surface curvature. A brief discussion of the models can be found in [15]. In our work we compare three theoretical models of grain growth kinetics. 1. The generalized parabolic grain-growth model proposed by Burke and Turnbull [14]. They assumed that in an ideal system after an annealing time t the crystallite size increases with a temperature dependent constant k 1 = na 1 and the crystallite growth can be described by the differential equation: dDðt Þ a1 ¼ dt D ðt Þ
ð1Þ
where D is the average grain diameter; with D(t) = D 0 for t = 0, the solution of the differential equation is Dðt Þn Dn0 ¼ k1 t:
ð2Þ
The empirical grain-growth exponent, n, varies between values of 2 and 4. 2. The grain-growth model with impediment. Grey and Higgins [16] took into account the experimental observation of a limiting grain size. In this model, as a result of crystallite growth, the driving pressure vanishes at a certain stage and Eq. (1) should be supplemented by a growthretarding term b 2 : dDðt Þ a2 ¼ b2 dt D ðt Þ
ð3Þ
With the initial grain size D 0, the solution of Eq. (3) is D0 Dðt Þ a2 a2 b2 D0 þ 2 ln ¼t ð4Þ b2 a2 b2 Dðt Þ b2 At t Y V the grains do not grow anymore, i.e., dD(t) / dt = 0; hence D V = a 2 / b 2 and Eq. (4) can be expressed as D0 Dðt Þ DV D0 k2 t ¼ þ ln ð5Þ DV DV Dðt Þ with k 2 = b 22 / a 2 = a 2 / D V2. 3. Michels at al. [17] suggested that the retarding constant should be a function of the grain size in grain-growth processes of nanocrystalline metals. They assumed that in the process of grain growth when the grain-boundary volume
dDðt Þ a3 ¼ b3 Dðt Þ dt Dðt Þ
ð6Þ
with the rate constant k 3 = 2b 3 = 2a 3 / D V2. This equation is the grain-growth model with size-dependent impediment. The time depending constant k 3 contains the information about the retarding constant. The temperature dependent rate constants k 1, k 2, k 3 contain the information about the grain boundary mobility M, which is described through the self-diffusion coefficient D s M¼
Ds kb T
ð9Þ
The diffusivity follows the Arrhenius law with the activation energy Q, but according to Eq. (9) the mobility and kinetic rate constants k 1, k 2, k 3 exhibit an additional T 1 dependence such as: Q T kD2V ”exp ð10Þ RT Hence, the activation energies of the grain boundary selfdiffusion processes can be obtained from the slope of a plot ln(TkD V2) versus T 1 [15]. 4. Results and discussion For preparation of gold nanostructured samples we use the pulse electrodeposition technique (PED) in galvanostatic mode. According to the Kelvin equation [18] by applying a high current density we get a high overvoltage which is responsible for a high nuclei formation rate. The high deposition rate can be achieved only for a short period of time (t on-time), in our experiments t on = 1 ms, because the metal ion concentration in the vicinity of the cathode decreases and therefore the process would become diffusion-controlled. For this reason, we switched the current pulse off for 20 ms (t off-time). During the t off-time the metal ions diffuse from the bulk electrolyte to the cathode and compensate the metal ion depletion. In this break we observe a second effect: due to the exchange currents Ostwald ripening sets in and causes the crystallite growth. The smallest crystallite size was observed for a current density of 50 mA cm 2 and a temperature of 348 K (Table 1). We assume that a higher desorption rate of gold adatoms and a higher adsorption rate of inhibitor in form of sulfur –gold complexes cause the smaller crystallite sizes. This behavior is also
O. Yevtushenko et al. / Thin Solid Films 515 (2006) 353 – 356 Table 1 Dependence of the gold crystallite size on the temperature of the electrolyte and current density d (nm)
T (K)
J (mA cm 2)
30 23 22 21 21 26 24 23 19 19 23 21 16 16 16
298
5 10 25 50 100 5 10 20 50 100 5 10 25 50 100
323
348
shows a thermal stability up to 523 K. At this temperature, an increase in crystallite size to 47 nm can be observed. To investigate the growth mechanism we measured a series of isotherms. The X-ray patterns were recorded in situ in reflection (h –2h) mode, at the following temperatures: 553, 573, 623, 673 and 723 K. The volume-weighted diameters of the gold crystallites resulting from the Warren Averbach analysis are displayed in Fig. 2; they show a fast increase in the grain size value at short times, which exhibits a pronounced temperature dependence. At lower temperatures, only a moderate and comparatively smooth grain growth behavior can be observed, which stops after a short period of time. To observe the growth kinetics of gold nanocrystallites, fits to the experimental data are performed. Fig. 2 shows the comparison between measured data and the theoretically calculated ones based on the kinetic models offered by Burke and Turnbull [14], Grey and Higgins [16] and Michels et al. [17]. The dashed lines represent the fits with the generalized parabolic grain-growth model (Eq. (2)), the dotted lines are the results of the fits with the growth model with impediment (Eq. (5)) and the solid lines shows the fit results using the grain growth model with size-dependent impediment (Eq. (8)). As follows from Fig. 2, not all applied models achieve a good agreement with the experimental data. Especially the generalized parabolic growth model and the growth model with impediment cannot be brought into agreement with the experimental data and yield unrealistic and unphysical parameters. In contrast to nanocrystalline iron which had been prepared without any grain refiners [15] the gold samples have impurities such as sulfur and arsenic and therefore only the model which takes into account the impurities in the grain boundaries can describe the experimental data. However, the growth model with size dependent impediment describes the experimental data very well. From the evaluation of the temperature dependence of the rate constants obtained for the last mentioned theoretical model it
crystallite size / nm
reported by Lin and Weil [19]. The sulfur atoms act as grain refiner, they cover gold nuclei and prevent further crystallite growth by interaction of their free electron pairs with the metal surface. A decrease of the crystallite size down to 10 nm is obtained by adding NaAsO2 (c = 0.25 g * L 1) to the bath. This is a very strong crystallite size decreasing additive, effective already at very low concentration. It was also shown by Dinan and Cheh [20] that during gold electrodeposition from phosphate bath arsenic containing additives decrease the crystallite size. In our study we investigated the crystallite growth of the electrodeposited gold at high temperatures. The gold sample with initial size of 16 nm deposited from the bath with NaAsO2 (c = 0.25 g * L 1) as additive was heated from room temperature up to 873 K with a rate of 2 K/min. Initially gold has a microstrain 0.35%, after heating nano-gold up to 873 K this parameter decreases to 0.01%. The TEM picture of above mentioned gold is shown on Fig. 1. The nanocrystalline gold
355
573 K 623 K 673 K 723 K 553 K 0
20
40
60
80
100
120
time / min
Fig. 1. TEM picture of a gold sample deposited from the bath with NaAsO2 (c = 0.25 g * L 1) as additive before heating.
Fig. 2. Temperature and time evolution of the volume-weighted average crystallite diameters of gold. The lines represent fits with different kinetic graingrowth models; the dashed lines represent fits with the generalized parabolic grain-growth model, the dotted lines are the results of fits with the growth model with impediment and the solid lines show the fit results using the grain growth model with size-dependent impediment.
356
O. Yevtushenko et al. / Thin Solid Films 515 (2006) 353 – 356
experiment
ln(Tk3D¥2)
linear fit
with size dependent impediment and the activation energy of nanocrystallite gold growth can be determined. Temperature stability of gold is of large importance for industrial applications. Therefore further investigations in this field are in progress now. Acknowledgments
1000/T [K-1] Fig. 3. Temperature dependence of the rate constants in extended Arrhenius representations for nano-gold sample.
is possible to determine the activation energy of the grain growth of nano-gold. We have made extended Arrhenius evaluations using the model with the retarding term proportional to the size. According to the Eq. (10) the experimental value of activation energy of 29.5 kJ * mol 1 for nano-gold crystallite growth can be calculated from the Arrhenius plot (Fig. 3). The linear correlation coefficient of the experimental data is 0.991. The grain boundary selfdiffusion coefficient of poly-crystalline gold in the temperature range of 640 – 717 K obeys the Arrhenius low with an activation energy of 84.9 kJ * mol 1 [21], that is more than two times higher than the experimentally received value of activation energy of nano-gold grain growth. The disagreement between the experimental results and the literature ones can be related to the difference in the grain boundary structure between nanostructured and coarse grained materials and therefore to the difference in the grain boundary self-diffusion.
The present work is initiated and performed at the Universita¨t des Saarlandes (Germany) in the framework of the Sonderforschungsbereich 277 (Grenzfla¨chenbestimmte Materialien) and we thank Deutsche Forschungsgemeinschaft for financial support. For experimental assistance we thank S. Kuhn. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]
5. Conclusion [18]
Nanocrystalline gold can be prepared by pulse electrodeposition. It is shown that the crystallite size depends on physical and chemical process parameters, such as temperature and current density. XRD turns out to be a very advantageous method to observe crystallite growth phenomena. The kinetics of gold grain growth is described in terms of the growth model
[19] [20] [21]
R. Birringer, Mater. Sci. Eng. A117 (1989) 33. H. Gleiter, Prog. Mater. Sci. 33 (1989) 223. C. Suryanarayana, F.H. Froes, Metall. Trans. A23 (1992) 1071. S. Okuda, F. Tang, Nanostruct. Mater. 10 (1998) 169. R. Rofagha, R. Langer, A.M. El-Sherik, U. Erb, G. Palumbo, K.T. Aust, Scr. Metall. Mater. 25 (1991) 2867. H. Natter, R. Hempelmann, Electrochim. Acta 49 (2003) 51. H. Natter, M. Schmelzer, R. Hempelmann, J. Mater. Res. 13 (1998) 1186. S. Morup, J.Z. Jiang, F. Bodker, A. Horsewell, Europhys. Lett. 56 (3) (2001) 441. J.M. Hanchar, K.L. Nagy, P. Fenter, R.J. Finch, D.J. Beno, N.C. Sturchio, Am. Mineral. 85 (2000) 1217. M. Paunovic, M. Schlesinger, Fundamentals of Electrochemical Deposition, John Wiley and Sons, Inc., Pennington, 1998, p. 197. R.W. Cheary, A.A. Coelho, J. Appl. Crystallogr. 25 (1992) 109. B.E. Warren, L.E. Averbach, J. Appl. Phys. 21 (1950) 536. H. Natter, R. Hempelmann, J. Phys. Chem. 100 (1996) 19525. J.E. Burke, D. Turnbull, Prog. Met. Phys. 3 (1952) 220. H. Natter, M. Schmelzer, M.-S. Lo¨ffler, C.E. Krill, A. Fitch, R. Hempelmann, J. Phys. Chem. 104 (2000) 2467. E.A. Grey, G.T. Higgins, Acta Metall. 21 (1973) 309. A. Michels, C.E. Krill, H. Ehrhardt, R. Birringer, D.T. Wu, Acta Mater. 47 (1999) 2143. E. Budevski, G. Staikov, W.J. Lorenz, Electrochemical Phase Transformation and Growth, VCH, Weinheim, 1996. K. Lin, R. Weil, J. Electrochem. Soc. 133 (1986) 4. T.E. Dinan, H.Y. Cheh, J. Electrochem. Soc. 139 (1992) 2. Landolt-Boernstein, Numerical data and functional relationships in science and technology, Diffusion in solid metals and alloys, vol. 26, Springer-Verlag, Berlin, 1990, p. 640.
Grain-growth kinetics of nanostructured gold O. Yevtushenko, H. Natter, R. Hempelmann * Physical Chemistry, Saarland University Saarbruecken, 66123, Germany Available online 18 January 2006
Abstract Nanocrystalline gold is electrodeposited from non-cyanide non-sulfite bath by pulse techniques. The thermal stability of nanocrystalline gold is investigated in situ by high-temperature X-ray diffraction. The experimental growth kinetics of gold crystallites can be described in terms of a growth model with size-dependent impediment. D 2005 Elsevier B.V. All rights reserved. Keywords: Electrodeposition; Thermal stability; Crystallite growth kinetics
1. Introduction
2. Experimental details
Nanocrystalline materials differ in some physical and chemical properties from polycrystalline materials of the same chemical composition. The reason of this phenomenon is the large volume fraction of interfaces resulting from small crystallite sizes or quantum size effect [1,2]. Undoubtedly it opens the fascinating possibility to change and control material properties simply by adjusting the grain-size appropriately during the production process [3]. As examples, the hardness of nano-Au increases [4] and corrosion resistance in nano-Ni enhances [5] with decreasing crystallite size. An increase of the temperature causes crystal growth and therefore the physical and chemical properties to change [6,7]. For this reason the thermal stability of nanocrystalline materials is one of the most important properties which are of interest for basic research as well as for industrial applications at elevated temperatures. The kinetics of grain growth can be studied by means of in situ high-temperature Xray diffraction [6 –9]. The X-ray diffraction lines contain information about the crystallite size, the structure, packing order of the atoms in the lattice, microstrain etc. The advantage of an in situ experiment is the analysis of the same part of the sample and the observation of changes in X-ray line shapes due to only the increase of the temperature.
Nanocrystalline gold with different crystallite sizes has been prepared from a non-cyanide non-sulfite electrolyte using pulsed electrodeposition technique [10]. We have prepared the electrolyte in the following way: H[AuCl4] reacts with ammonium hydroxide to gold (III) hydroxide, which can be reduced by 3-mercapto-1-propanesulfonic acid (MPS) in a time of approximately 3 h to gold (I). The resulting solution is colorless and exhibits long time stability. The electrolyte consists of 5 g * L 1 HAuCl4 (Au-50%), 10.5 g * L 1 MPS (90%), 160 mL (50%) NH4OH and has a strongly basic pH. We used stainless steel anodes and copper cathodes (99.9% purity). All pulse electrodeposition (PED) experiments are performed at a temperature of 348 K with the following pulse parameters: t on—pulse duration time 1 ms, t off—time between two pulses 20 ms and average current density 50 mA * cm 2. For the characterization of the deposited samples, we used high-temperature X-ray diffraction (Siemens D-5000 diffractometer). In order to achieve high time resolution a position sensitive detector (Braun Inc., Germany) was used. The isothermal measurements were recorded every 60 s. The annealing time expended in heating the sample to the fixed temperature is calculated to be 21 s. This is a very short time in comparison with the time of the whole measurement and therefore no corrections to the time of isotherms data are applied. TEM (Jeol, JEM-2010) pictures of deposited samples are made to obtain the information about the morphology of gold.
* Corresponding author. Tel.: +49 681 302 4750; fax: +49 681 302 4759. E-mail address: [email protected] (R. Hempelmann). 0040-6090/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2005.12.098
354
O. Yevtushenko et al. / Thin Solid Films 515 (2006) 353 – 356
The microstrain is determined by the model described by Cheary and Coelho [11]. For the evaluation of crystallite size we use a modified Warren Averbach analysis [12,13].
fraction decreases the impurities in the grain boundaries are more enriched:
3. Kinetics of grain growth
With the same initial conditions as above, the solution of this differential equation is sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a3 a3 Dðt Þ ¼ þ D20 ð7Þ expð 2b3 t Þ b3 b3 pffiffiffiffiffiffiffiffiffiffiffiffi Using DV ¼ a3 =b3 this can be expressed as ffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Dðt Þ ¼ D2V D2V D20 expð k3 t Þ ð8Þ
At high temperatures the crystallites grow during a relatively short period of time and then the crystallite size does not change essentially any more with time. The theoretical basis for understanding of isothermal grain growth was proposed by Burke and Turnbull [14]. They deduced the grain growth from the movement of grain boundaries and assumed atom transport across the boundaries under a pressure due to surface curvature. A brief discussion of the models can be found in [15]. In our work we compare three theoretical models of grain growth kinetics. 1. The generalized parabolic grain-growth model proposed by Burke and Turnbull [14]. They assumed that in an ideal system after an annealing time t the crystallite size increases with a temperature dependent constant k 1 = na 1 and the crystallite growth can be described by the differential equation: dDðt Þ a1 ¼ dt D ðt Þ
ð1Þ
where D is the average grain diameter; with D(t) = D 0 for t = 0, the solution of the differential equation is Dðt Þn Dn0 ¼ k1 t:
ð2Þ
The empirical grain-growth exponent, n, varies between values of 2 and 4. 2. The grain-growth model with impediment. Grey and Higgins [16] took into account the experimental observation of a limiting grain size. In this model, as a result of crystallite growth, the driving pressure vanishes at a certain stage and Eq. (1) should be supplemented by a growthretarding term b 2 : dDðt Þ a2 ¼ b2 dt D ðt Þ
ð3Þ
With the initial grain size D 0, the solution of Eq. (3) is D0 Dðt Þ a2 a2 b2 D0 þ 2 ln ¼t ð4Þ b2 a2 b2 Dðt Þ b2 At t Y V the grains do not grow anymore, i.e., dD(t) / dt = 0; hence D V = a 2 / b 2 and Eq. (4) can be expressed as D0 Dðt Þ DV D0 k2 t ¼ þ ln ð5Þ DV DV Dðt Þ with k 2 = b 22 / a 2 = a 2 / D V2. 3. Michels at al. [17] suggested that the retarding constant should be a function of the grain size in grain-growth processes of nanocrystalline metals. They assumed that in the process of grain growth when the grain-boundary volume
dDðt Þ a3 ¼ b3 Dðt Þ dt Dðt Þ
ð6Þ
with the rate constant k 3 = 2b 3 = 2a 3 / D V2. This equation is the grain-growth model with size-dependent impediment. The time depending constant k 3 contains the information about the retarding constant. The temperature dependent rate constants k 1, k 2, k 3 contain the information about the grain boundary mobility M, which is described through the self-diffusion coefficient D s M¼
Ds kb T
ð9Þ
The diffusivity follows the Arrhenius law with the activation energy Q, but according to Eq. (9) the mobility and kinetic rate constants k 1, k 2, k 3 exhibit an additional T 1 dependence such as: Q T kD2V ”exp ð10Þ RT Hence, the activation energies of the grain boundary selfdiffusion processes can be obtained from the slope of a plot ln(TkD V2) versus T 1 [15]. 4. Results and discussion For preparation of gold nanostructured samples we use the pulse electrodeposition technique (PED) in galvanostatic mode. According to the Kelvin equation [18] by applying a high current density we get a high overvoltage which is responsible for a high nuclei formation rate. The high deposition rate can be achieved only for a short period of time (t on-time), in our experiments t on = 1 ms, because the metal ion concentration in the vicinity of the cathode decreases and therefore the process would become diffusion-controlled. For this reason, we switched the current pulse off for 20 ms (t off-time). During the t off-time the metal ions diffuse from the bulk electrolyte to the cathode and compensate the metal ion depletion. In this break we observe a second effect: due to the exchange currents Ostwald ripening sets in and causes the crystallite growth. The smallest crystallite size was observed for a current density of 50 mA cm 2 and a temperature of 348 K (Table 1). We assume that a higher desorption rate of gold adatoms and a higher adsorption rate of inhibitor in form of sulfur –gold complexes cause the smaller crystallite sizes. This behavior is also
O. Yevtushenko et al. / Thin Solid Films 515 (2006) 353 – 356 Table 1 Dependence of the gold crystallite size on the temperature of the electrolyte and current density d (nm)
T (K)
J (mA cm 2)
30 23 22 21 21 26 24 23 19 19 23 21 16 16 16
298
5 10 25 50 100 5 10 20 50 100 5 10 25 50 100
323
348
shows a thermal stability up to 523 K. At this temperature, an increase in crystallite size to 47 nm can be observed. To investigate the growth mechanism we measured a series of isotherms. The X-ray patterns were recorded in situ in reflection (h –2h) mode, at the following temperatures: 553, 573, 623, 673 and 723 K. The volume-weighted diameters of the gold crystallites resulting from the Warren Averbach analysis are displayed in Fig. 2; they show a fast increase in the grain size value at short times, which exhibits a pronounced temperature dependence. At lower temperatures, only a moderate and comparatively smooth grain growth behavior can be observed, which stops after a short period of time. To observe the growth kinetics of gold nanocrystallites, fits to the experimental data are performed. Fig. 2 shows the comparison between measured data and the theoretically calculated ones based on the kinetic models offered by Burke and Turnbull [14], Grey and Higgins [16] and Michels et al. [17]. The dashed lines represent the fits with the generalized parabolic grain-growth model (Eq. (2)), the dotted lines are the results of the fits with the growth model with impediment (Eq. (5)) and the solid lines shows the fit results using the grain growth model with size-dependent impediment (Eq. (8)). As follows from Fig. 2, not all applied models achieve a good agreement with the experimental data. Especially the generalized parabolic growth model and the growth model with impediment cannot be brought into agreement with the experimental data and yield unrealistic and unphysical parameters. In contrast to nanocrystalline iron which had been prepared without any grain refiners [15] the gold samples have impurities such as sulfur and arsenic and therefore only the model which takes into account the impurities in the grain boundaries can describe the experimental data. However, the growth model with size dependent impediment describes the experimental data very well. From the evaluation of the temperature dependence of the rate constants obtained for the last mentioned theoretical model it
crystallite size / nm
reported by Lin and Weil [19]. The sulfur atoms act as grain refiner, they cover gold nuclei and prevent further crystallite growth by interaction of their free electron pairs with the metal surface. A decrease of the crystallite size down to 10 nm is obtained by adding NaAsO2 (c = 0.25 g * L 1) to the bath. This is a very strong crystallite size decreasing additive, effective already at very low concentration. It was also shown by Dinan and Cheh [20] that during gold electrodeposition from phosphate bath arsenic containing additives decrease the crystallite size. In our study we investigated the crystallite growth of the electrodeposited gold at high temperatures. The gold sample with initial size of 16 nm deposited from the bath with NaAsO2 (c = 0.25 g * L 1) as additive was heated from room temperature up to 873 K with a rate of 2 K/min. Initially gold has a microstrain 0.35%, after heating nano-gold up to 873 K this parameter decreases to 0.01%. The TEM picture of above mentioned gold is shown on Fig. 1. The nanocrystalline gold
355
573 K 623 K 673 K 723 K 553 K 0
20
40
60
80
100
120
time / min
Fig. 1. TEM picture of a gold sample deposited from the bath with NaAsO2 (c = 0.25 g * L 1) as additive before heating.
Fig. 2. Temperature and time evolution of the volume-weighted average crystallite diameters of gold. The lines represent fits with different kinetic graingrowth models; the dashed lines represent fits with the generalized parabolic grain-growth model, the dotted lines are the results of fits with the growth model with impediment and the solid lines show the fit results using the grain growth model with size-dependent impediment.
356
O. Yevtushenko et al. / Thin Solid Films 515 (2006) 353 – 356
experiment
ln(Tk3D¥2)
linear fit
with size dependent impediment and the activation energy of nanocrystallite gold growth can be determined. Temperature stability of gold is of large importance for industrial applications. Therefore further investigations in this field are in progress now. Acknowledgments
1000/T [K-1] Fig. 3. Temperature dependence of the rate constants in extended Arrhenius representations for nano-gold sample.
is possible to determine the activation energy of the grain growth of nano-gold. We have made extended Arrhenius evaluations using the model with the retarding term proportional to the size. According to the Eq. (10) the experimental value of activation energy of 29.5 kJ * mol 1 for nano-gold crystallite growth can be calculated from the Arrhenius plot (Fig. 3). The linear correlation coefficient of the experimental data is 0.991. The grain boundary selfdiffusion coefficient of poly-crystalline gold in the temperature range of 640 – 717 K obeys the Arrhenius low with an activation energy of 84.9 kJ * mol 1 [21], that is more than two times higher than the experimentally received value of activation energy of nano-gold grain growth. The disagreement between the experimental results and the literature ones can be related to the difference in the grain boundary structure between nanostructured and coarse grained materials and therefore to the difference in the grain boundary self-diffusion.
The present work is initiated and performed at the Universita¨t des Saarlandes (Germany) in the framework of the Sonderforschungsbereich 277 (Grenzfla¨chenbestimmte Materialien) and we thank Deutsche Forschungsgemeinschaft for financial support. For experimental assistance we thank S. Kuhn. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]
5. Conclusion [18]
Nanocrystalline gold can be prepared by pulse electrodeposition. It is shown that the crystallite size depends on physical and chemical process parameters, such as temperature and current density. XRD turns out to be a very advantageous method to observe crystallite growth phenomena. The kinetics of gold grain growth is described in terms of the growth model
[19] [20] [21]
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