- Email: [email protected]
Influence of the thermal annealing on the electrical resistivity and thermal diffusivity of Pd:Ag nanocomposites
November 2001
Materials Letters 51 Ž2001. 357–362 www.elsevier.comrlocatermatlet
Influence of the thermal annealing on the electrical resistivity and thermal diffusivity of Pd:Ag nanocomposites C.A.S. Lima a,) , R. Oliva b, G. Cardenas T. b, E.N. Silva c , L.C.M. Miranda c a
b
Laboratorio de Procesamiento Termo-Optico de Materiales, Depto. de Fısica, Facultad de Ciencias Fısicas y Matematicas, ´ ´ ´ UniÕersidad de Concepcion, ´ Casilla 160-C, Concepcion, ´ Chile Departamento de Polımeros, Facultad de Ciencias Quımicas, UniÕersidad de Concepcion, ´ ´ ´ Casilla 160-C, Concepcion, ´ Chile c Depto. de Fısica, UniÕersidade Estadual de Maringa, ´ ´ 87020-900, Maringa, ´ PR, Brazil Received 12 September 2000; received in revised form 21 February 2001; accepted 1 March 2001
Abstract In this paper, we report on the influence of thermal annealing on the electrical and thermal properties of nano-clustered Pd:Ag particles packed into compressed thin wafers. The nano-crystalline Pd:Ag compacts were prepared by solvent evaporation of non-aqueous metal colloids prepared by clustering of metal atoms in organic solvents at low temperature. Samples of Pd:Ag nano-clustered powder so obtained were then compressed into roughly 250 mm thick, 10 mm diameter wafers, and annealed at different temperatures, for about 1 h. The dependence of the electrical resistivity and of the thermal diffusivity of the resulting compacts on their corresponding annealing temperatures were investigated using a LCR impedance meter and a photoacoustic thermal diffusivity measurement apparatus. q 2001 Elsevier Science B.V. All rights reserved. Keywords: Nano-composites; Metal colloids; Thermal annealing; Electrical resistivity; Thermal diffusivity; Porous materials
1. Introduction Although the research into the formation and behavior of metal colloids is one of the classical areas of physical chemistry, the field of metal colloid research is experiencing these days a huge renaissance in interest due to its potential applications in nano-technology. From the point of view of basic research, interest in the so-called nano-particles is particularly important for understanding the transi-
) Corresponding author. Tel.: q56-41-203-085; fax: q56-41224-520. E-mail address: [email protected] ŽC.A.S. Lima..
tion and consequent changes in properties from an atomic or molecular-sized particle to a bulk particle. Furthermore, due to their very high surface areas, small size particles are particularly important in catalysis. Catalytic processes on activated surfaces involving simple molecules continue to be an area of considerable activity both experimental and theoretical w1–9x. The advent of simpler techniques for producing nano-structured metallic and bi-metallic surfaces, with enhanced catalytic activity, gave new breadth to this field w10x. In this paper, we report on the electrical and thermal properties of nano-crystalline Pd:Ag compacts, as obtained from solvent evaporation of nonaqueous metal colloids prepared by the clustering of
00167-577Xr01r$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 5 7 7 X Ž 0 1 . 0 0 3 2 1 - 4
358
C.A.S. Lima et al.r Materials Letters 51 (2001) 357–362
metal atoms in organic solvents at low temperature w10–12x. This method has been proven efficient for producing a new class of stable colloids, from which nano-sized powder is readily obtained. The properties of the resulting colloids and metallic films produced from them are not predictable a priori, and may turn out to be insulating, metallic or semiconducting, allowing therefore important applications to be envisaged. For example, films produced by this method may optically resemble metal films but had been only poor electrical conductors. The understanding of the physical properties of the films and wafers produced from these colloids is our long-term goal in this area. In particular, we have special interest in understanding how the processing conditions affect the physical properties of these systems. This is the point we address ourselves in what follows, by reporting on the influence of thermal annealing of nano-crystalline Pd:Ag compacts on their electrical and thermal properties.
2. Experimental The Pd:Ag nanocompacts were prepared from powders retrieved from Pd:Ag nanocolloidal dispersions in acetone whose preparation followed an adaptation of our previously reported method for clustering metal atoms in organic solvents at low temperatures w10–12x. Fig. 1 shows schematically the specially designed reactor used in our procedures for production of the Pd:Ag nanoparticles. It consists essentially vacuum co-deposition Žcondensation. of evaporated Pd and Ag atoms onto liquid nitrogen frozen acetone. The reactor contains two alumina– tungsten crucibles. In each production run, they were separately charged, with around 100 mg each, with analytical grade Pd ŽAldrich Chemical, USA, 99.99% purity. and Ag ŽAldrich Chemical, 99.99% purity. shots. In a connecting inlet flask, with controllable output, 100 ml of Aldrich Chemical, 99.9% purity, HPLC grade acetone was placed and repeatedly
Fig. 1. Schematic view of the reactor used for producing Pd:Ag nanoparticles.
C.A.S. Lima et al.r Materials Letters 51 (2001) 357–362
freeze-pump-thaw degassed for five cycles. The reactor was pumped to 10y4 Torr, while separate electrodes connected to each crucible allowed them to be heated to red-hot condition, one to the boiling point of Pd and the other to that of Ag Žaround 31408C and 22128C, respectively.. A liquid nitrogen filled dewar was placed around the reactor vessel allowing Pd, Ag and acetone to co-deposit. The full operation for each production run took around 1.5 h. The rate of acetone supply was kept at around 2 mlrmin. At the end of the co-deposition process a blackish matrix was obtained. The liquid nitrogen dewar was then removed allowing the matrix to melt slowly, in approximately 1 h. Upon complete meltdown the black dispersion was allowed another 0.5 h to slowly reach room temperature. Overall, the described procedure allowed us to obtain stabilized colloidal dispersions where the typical Pd–Ag cluster dimensions were found to spread around an average of 46 I, as determined by TEM measurements. The retrieval of the colloidal fine powder was done through vacuum accelerated solvent evaporation. The Pd:Ag nanocompacts samples were produced by compressing Ž700 kgrcm2 . the ultrafine Pd:Ag powder into 10 mm diameter wafers roughly 250 mm thick. The samples were then thermally processed. The selected thermal annealing temperatures were 1508C, 3008C, 5508C, and 9508C. At each selected temperature, the sample was left annealing for 1 h. For comparison, one sample was not annealed, that is, it was left untreated as prepared. The electrical resistivity measurements were carried out on LCR impedance meter ŽPhilips, model PM6304. at 1 kHz. The thermal diffusivity was measured using the typical transmission configuration of the photoacoustic ŽPA. detection. All of our measurements were carried at room temperature Ž258C. on samples that had been previously thermally annealed at the temperatures indicated above. For a survey on the photoacoustic thermal diffusivity measurement we refer to some of the existing review articles w13–15x. Of the existing PA detection schemes, we resorted to the so-called open-photoacoustic cell ŽOPC. configuration w16,17x as illustrated schematically in Fig. 2. It consists of a 250 W halogen–tungsten lamp whose polychromatic beam is mechanically chopped ŽSRS model 540. and focused onto the sample. The sample is mounted di-
359
Fig. 2. Schematic cross-section of the open photoacoustic cell using the front air chamber of a common electret microphone as a transducer medium for the thermal diffusivity measurements.
rectly onto a circular electret microphone. The typical design of an electret microphone consists of a metalized electret diaphragm Ž12 mm thick fluoroethylene propylene with a 50–100 nm thick deposited metal electrode. and a metal backplate separated from the diaphragm by an air gap Ž45 mm wide.. The metal layer and the back plate are connected through a resistor, R. The front sound inlet is a circular hole, 3 mm diameter, and the front air chamber adjacent to the metalized face of the diaphragm is roughly 1 mm deep. As a result of the periodic heating of the sample due to the absorption of modulated Žchopped. light incident upon it, the pressure in the front chamber oscillates at the chopping frequency, causing diaphragm deflections, which generates a voltage, V, across the resistor. This output voltage from the microphone is connected to a lock-in amplifier ŽSRS model 830. in which the signal amplitude and phase are both recorded as a function of the modulation frequency. For relatively thick and optically opaque samples, as in the case of our Pd:Ag compacts, it can be shown w16,17x that the thermal diffusivity, a , can be experimentally determined from the measurements of the PA signal amplitude, S, as a function of the modulation frequency, by fitting the corresponding PA signal data to the expression,
'
S s Ž Arf . exp Ž ya f . .
Ž 1.
Here, A is a constant and a s Žp l 2ra .1r2 with l being the sample thickness. From the fitted value of a, the thermal diffusivity a is readily obtained.
360
C.A.S. Lima et al.r Materials Letters 51 (2001) 357–362
3. Results and discussion In Fig. 3, we show a typical result for the OPC signal amplitude data taken, at room temperature, as a function of the modulation frequency, in this case for a sample annealed at 1508C. The solid line in Fig. 3 corresponds to the data best fitting to the theoretical expression for the OPC signal amplitude given by Eq. Ž1.. The result we got from this data fitting for the value of a was a s Ž0.945 " 0.007. mm2rs. The same procedure was applied to all samples investigated, and the corresponding results for the thermal diffusivity, as a function of the annealing temperature, are summarized in Fig. 4. Also shown in Fig. 4 are the results we got for the electrical resisitivity of our Pg:Ag nanocompacts, as a function of the annealing temperature. The solid curve superimposed onto the electrical resistivity data corresponds to the data best fitting to an exponential decay. As we can see from Fig. 4, the room temperature electrical resistivity decreases very fast in the samples that were subject to thermal treatment, prior to the measurements, at temperatures up to 4008C. From then on, it becomes virtually constant approaching a
final value of about 1 V cm. We can understand this rapid decrease of the electrical resistivity with increasing annealing temperature on the basis that while thermally annealing a sample at a given temperature we are essentially removing the original solvent Žacetone. clogged to the sample nanopores, a process which for acetone should be essentially accomplished at around 4008C. An additional removal at higher annealing temperatures may take place and can be attributed to thermal dissociation of the remaining Žbounded. acetone, or its fragments. This might account for the much smaller decrease observed in the resistivity of the samples annealed between 4008C and 5508C Žhighest dissociation temperature in acetone. when it does level off. It should also be taken into account that this removal facilitates cluster accreation so that grain growth is also expected to occur. In contrast, the thermal diffusivity dependence on the annealing temperature exhibited a more distinct behavior. It initially decreases with increasing annealing temperature, reaches a minimum at around 4008C, and then increases with increasing annealing temperature. To understand this behavior of the thermal diffusivity, we recall that it is defined as a s krr c, where k is the sample
Fig. 3. Open photoacoustic cell ŽOPC. signal amplitude as a function of the square root of the modulation frequency for a Pd:Ag nanocompact annealed at 1508C. The solid line is a least squares fit to the data using Eq. Ž1. of the text.
C.A.S. Lima et al.r Materials Letters 51 (2001) 357–362
361
Fig. 4. Electrical resistivity and thermal diffusivity data for our Pd:Ag nanocompacts, measured at room temperature Ž258C. in samples previously subject to thermal treatment, plotted as a function of the annealing temperature. The fit to the resistivity curve is discussed in the text. The curve through the thermal diffusivity data corresponds to a spline interpolation.
thermal conductivity, r is the sample mass density and c is its specific heat. The initial decrease of a with increasing annealing temperature is, in our view, due to the densification of our sample resulting from the removal of the residual solvent left in the sample. This is consistent with the observed sharp decrease of the electrical resistivity up to 4008C. On the other hand, the expected increase in grain size resulting from the annealing process entails that the sample porosity should also increase as the sample is annealed at higher temperatures. The observed increase of a with increasing annealing temperature above 4008C may be associated with this expected increase in the sample porosity. In fact, for an air-filled porous material, the thermal diffusivity is seen to increase with increasing porosity w18,19x, since the room temperature air thermal diffusivity is relatively high, namely, a air s 21 mm2rs.
In particular, it was shown that the electrical resistivity exhibits a sharp exponential decrease with increasing annealing temperature up to 4008C. Above this temperature, the electrical resistivity remains practically constant. The observed dependence of the thermal diffusivity with increasing annealing temperature was, however, more complex. The thermal diffusivity, whose inverse is essentially a measure of the sample thermalization time, is known to be extremely dependent on the effects of compositional and microstructural variables w19–21x as well as on the sample processing conditions. This can be appreciated from the tabulated values of a w18x for a wide range of materials, such as, metals, minerals, foodstuffs, biological specimens and polymers. The sensitivity of the thermal diffusivity of our Pd:Ag nanocompacts to the effects of the thermal treatment they were subject to, at increasingly higher annealing temperatures, reflects this unique character of this physical parameter.
4. Conclusions In this paper, we have reported on the influence of the thermal annealing of nano-crystalline Pd:Ag compacts on their electrical and thermal properties.
Acknowledgements Author C.A.S. Lima acknowledges support from Proyecto APhotothermal assessment of thermophysi-
C.A.S. Lima et al.r Materials Letters 51 (2001) 357–362
362
cal parameters of strategic new materialsB-Ap. Gestion Fondecyt a98.011.024-1.2, granted to him by the Direccion ´ de Investigacion ´ de la Universidad de Concepcion ´ and author L.C.M. Miranda thanks the Brazilian Agency CNPq for the partial financial support of this work.
References w1x w2x w3x w4x w5x w6x w7x w8x
A.V. Walker, D.A. King, Phys. Rev. Lett. 82 Ž1999. 5156. J.L. Whitten, H. Yang, Surf. Sci. Rep. 24 Ž1996. 55. B. Hammer, J.K. Norslov, Nature 376 Ž1995. 238. F.M. Muller, T.A. Stegink, R.C. Thiel, L.J. de Jongh, G. Schmid, Nature 367 Ž1994. 716. J. Neuegbauer, N. Scheffler, Phys. Rev. Lett. 71 Ž1993. 577. R. Wu, A.J. Freeman, G.B. Olson, Phys. Rev. B47 Ž1993. 6855. P. Krueger, J. Pollmann, Phys. Rev. B47 Ž1993. 1898. C.R. Brundle, J.Q. Broughton, in: D.A. King, D.P. Woodruff ŽEds.., The Chemical Physics of Solid Surfaces and Heterogeneous Catalysis, vol. 3A, Elsevier, Amsterdam, 1990, Chap. 3.
w9x H.P. Bonzel, G. Pirug, J.E. Muller, Phys. Rev. Lett. 58 Ž1987. 2138. w10x K.J. Klabunde, G. Cardenas-Trivino, Metal AtomrVapor Approaches to Active Metal ClustersrParticles. SpringerVerlag VCH Publ., Weinheim, Germany, 1996, p. 237, Chap. 6. w11x G. Cardenas-Trivino, K.J. Klabunde, E.B. Dale, Proc. Opt. Eng. SPIE 821 Ž1987. 206. w12x G. Cardenas-Trivino, V. Vera L., C. Munoz, Mater. Sci. ˜ Bull. 33 Ž1998. 645. w13x A. Rosencwaig, Photoacoustics and Photoacoustic Spectroscopy, Wiley, New York, 1980. w14x C.K.N. Patel, A.C. Tam, Rev. Mod. Phys. 53 Ž1981. 517. w15x H. Vargas, L.C.M. Miranda, Phys. Rep. 161 Ž1988. 43. w16x M.D. Silva, I.N. Bandeira, L.C.M. Miranda, J. Phys. E: Sci. Instrum. 20 Ž1987. 1476. w17x L.F. Perondi, L.C.M. Miranda, J. Appl. Phys. 62 Ž1987. 2955. w18x Y.S. Touloukian, R.W. Powell, C.Y. Ho, M.C. Nicolasu, Thermal Diffusivity, IFIrPlenun, New York, 1973. w19x G. Ziegler, D.P.H. Hasselman, J. Mater. Sci. 16 Ž1981. 495. w20x C.A.S. Lima, M.B.S. Lima, L.C.M. Miranda, J. Baeza, N. Freer, J. Reyes, J. Ruiz, AIP Conf. Proc. 463 Ž1999. 339. w21x C.A.S. Lima, M.B.S. Lima, L.C.M. Miranda, J. Baeza, J. Freer, N. Reyes, J. Ruiz, M.D. Silva, Meas. Sci. Technol. 11 Ž2000. 504.
Materials Letters 51 Ž2001. 357–362 www.elsevier.comrlocatermatlet
Influence of the thermal annealing on the electrical resistivity and thermal diffusivity of Pd:Ag nanocomposites C.A.S. Lima a,) , R. Oliva b, G. Cardenas T. b, E.N. Silva c , L.C.M. Miranda c a
b
Laboratorio de Procesamiento Termo-Optico de Materiales, Depto. de Fısica, Facultad de Ciencias Fısicas y Matematicas, ´ ´ ´ UniÕersidad de Concepcion, ´ Casilla 160-C, Concepcion, ´ Chile Departamento de Polımeros, Facultad de Ciencias Quımicas, UniÕersidad de Concepcion, ´ ´ ´ Casilla 160-C, Concepcion, ´ Chile c Depto. de Fısica, UniÕersidade Estadual de Maringa, ´ ´ 87020-900, Maringa, ´ PR, Brazil Received 12 September 2000; received in revised form 21 February 2001; accepted 1 March 2001
Abstract In this paper, we report on the influence of thermal annealing on the electrical and thermal properties of nano-clustered Pd:Ag particles packed into compressed thin wafers. The nano-crystalline Pd:Ag compacts were prepared by solvent evaporation of non-aqueous metal colloids prepared by clustering of metal atoms in organic solvents at low temperature. Samples of Pd:Ag nano-clustered powder so obtained were then compressed into roughly 250 mm thick, 10 mm diameter wafers, and annealed at different temperatures, for about 1 h. The dependence of the electrical resistivity and of the thermal diffusivity of the resulting compacts on their corresponding annealing temperatures were investigated using a LCR impedance meter and a photoacoustic thermal diffusivity measurement apparatus. q 2001 Elsevier Science B.V. All rights reserved. Keywords: Nano-composites; Metal colloids; Thermal annealing; Electrical resistivity; Thermal diffusivity; Porous materials
1. Introduction Although the research into the formation and behavior of metal colloids is one of the classical areas of physical chemistry, the field of metal colloid research is experiencing these days a huge renaissance in interest due to its potential applications in nano-technology. From the point of view of basic research, interest in the so-called nano-particles is particularly important for understanding the transi-
) Corresponding author. Tel.: q56-41-203-085; fax: q56-41224-520. E-mail address: [email protected] ŽC.A.S. Lima..
tion and consequent changes in properties from an atomic or molecular-sized particle to a bulk particle. Furthermore, due to their very high surface areas, small size particles are particularly important in catalysis. Catalytic processes on activated surfaces involving simple molecules continue to be an area of considerable activity both experimental and theoretical w1–9x. The advent of simpler techniques for producing nano-structured metallic and bi-metallic surfaces, with enhanced catalytic activity, gave new breadth to this field w10x. In this paper, we report on the electrical and thermal properties of nano-crystalline Pd:Ag compacts, as obtained from solvent evaporation of nonaqueous metal colloids prepared by the clustering of
00167-577Xr01r$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 5 7 7 X Ž 0 1 . 0 0 3 2 1 - 4
358
C.A.S. Lima et al.r Materials Letters 51 (2001) 357–362
metal atoms in organic solvents at low temperature w10–12x. This method has been proven efficient for producing a new class of stable colloids, from which nano-sized powder is readily obtained. The properties of the resulting colloids and metallic films produced from them are not predictable a priori, and may turn out to be insulating, metallic or semiconducting, allowing therefore important applications to be envisaged. For example, films produced by this method may optically resemble metal films but had been only poor electrical conductors. The understanding of the physical properties of the films and wafers produced from these colloids is our long-term goal in this area. In particular, we have special interest in understanding how the processing conditions affect the physical properties of these systems. This is the point we address ourselves in what follows, by reporting on the influence of thermal annealing of nano-crystalline Pd:Ag compacts on their electrical and thermal properties.
2. Experimental The Pd:Ag nanocompacts were prepared from powders retrieved from Pd:Ag nanocolloidal dispersions in acetone whose preparation followed an adaptation of our previously reported method for clustering metal atoms in organic solvents at low temperatures w10–12x. Fig. 1 shows schematically the specially designed reactor used in our procedures for production of the Pd:Ag nanoparticles. It consists essentially vacuum co-deposition Žcondensation. of evaporated Pd and Ag atoms onto liquid nitrogen frozen acetone. The reactor contains two alumina– tungsten crucibles. In each production run, they were separately charged, with around 100 mg each, with analytical grade Pd ŽAldrich Chemical, USA, 99.99% purity. and Ag ŽAldrich Chemical, 99.99% purity. shots. In a connecting inlet flask, with controllable output, 100 ml of Aldrich Chemical, 99.9% purity, HPLC grade acetone was placed and repeatedly
Fig. 1. Schematic view of the reactor used for producing Pd:Ag nanoparticles.
C.A.S. Lima et al.r Materials Letters 51 (2001) 357–362
freeze-pump-thaw degassed for five cycles. The reactor was pumped to 10y4 Torr, while separate electrodes connected to each crucible allowed them to be heated to red-hot condition, one to the boiling point of Pd and the other to that of Ag Žaround 31408C and 22128C, respectively.. A liquid nitrogen filled dewar was placed around the reactor vessel allowing Pd, Ag and acetone to co-deposit. The full operation for each production run took around 1.5 h. The rate of acetone supply was kept at around 2 mlrmin. At the end of the co-deposition process a blackish matrix was obtained. The liquid nitrogen dewar was then removed allowing the matrix to melt slowly, in approximately 1 h. Upon complete meltdown the black dispersion was allowed another 0.5 h to slowly reach room temperature. Overall, the described procedure allowed us to obtain stabilized colloidal dispersions where the typical Pd–Ag cluster dimensions were found to spread around an average of 46 I, as determined by TEM measurements. The retrieval of the colloidal fine powder was done through vacuum accelerated solvent evaporation. The Pd:Ag nanocompacts samples were produced by compressing Ž700 kgrcm2 . the ultrafine Pd:Ag powder into 10 mm diameter wafers roughly 250 mm thick. The samples were then thermally processed. The selected thermal annealing temperatures were 1508C, 3008C, 5508C, and 9508C. At each selected temperature, the sample was left annealing for 1 h. For comparison, one sample was not annealed, that is, it was left untreated as prepared. The electrical resistivity measurements were carried out on LCR impedance meter ŽPhilips, model PM6304. at 1 kHz. The thermal diffusivity was measured using the typical transmission configuration of the photoacoustic ŽPA. detection. All of our measurements were carried at room temperature Ž258C. on samples that had been previously thermally annealed at the temperatures indicated above. For a survey on the photoacoustic thermal diffusivity measurement we refer to some of the existing review articles w13–15x. Of the existing PA detection schemes, we resorted to the so-called open-photoacoustic cell ŽOPC. configuration w16,17x as illustrated schematically in Fig. 2. It consists of a 250 W halogen–tungsten lamp whose polychromatic beam is mechanically chopped ŽSRS model 540. and focused onto the sample. The sample is mounted di-
359
Fig. 2. Schematic cross-section of the open photoacoustic cell using the front air chamber of a common electret microphone as a transducer medium for the thermal diffusivity measurements.
rectly onto a circular electret microphone. The typical design of an electret microphone consists of a metalized electret diaphragm Ž12 mm thick fluoroethylene propylene with a 50–100 nm thick deposited metal electrode. and a metal backplate separated from the diaphragm by an air gap Ž45 mm wide.. The metal layer and the back plate are connected through a resistor, R. The front sound inlet is a circular hole, 3 mm diameter, and the front air chamber adjacent to the metalized face of the diaphragm is roughly 1 mm deep. As a result of the periodic heating of the sample due to the absorption of modulated Žchopped. light incident upon it, the pressure in the front chamber oscillates at the chopping frequency, causing diaphragm deflections, which generates a voltage, V, across the resistor. This output voltage from the microphone is connected to a lock-in amplifier ŽSRS model 830. in which the signal amplitude and phase are both recorded as a function of the modulation frequency. For relatively thick and optically opaque samples, as in the case of our Pd:Ag compacts, it can be shown w16,17x that the thermal diffusivity, a , can be experimentally determined from the measurements of the PA signal amplitude, S, as a function of the modulation frequency, by fitting the corresponding PA signal data to the expression,
'
S s Ž Arf . exp Ž ya f . .
Ž 1.
Here, A is a constant and a s Žp l 2ra .1r2 with l being the sample thickness. From the fitted value of a, the thermal diffusivity a is readily obtained.
360
C.A.S. Lima et al.r Materials Letters 51 (2001) 357–362
3. Results and discussion In Fig. 3, we show a typical result for the OPC signal amplitude data taken, at room temperature, as a function of the modulation frequency, in this case for a sample annealed at 1508C. The solid line in Fig. 3 corresponds to the data best fitting to the theoretical expression for the OPC signal amplitude given by Eq. Ž1.. The result we got from this data fitting for the value of a was a s Ž0.945 " 0.007. mm2rs. The same procedure was applied to all samples investigated, and the corresponding results for the thermal diffusivity, as a function of the annealing temperature, are summarized in Fig. 4. Also shown in Fig. 4 are the results we got for the electrical resisitivity of our Pg:Ag nanocompacts, as a function of the annealing temperature. The solid curve superimposed onto the electrical resistivity data corresponds to the data best fitting to an exponential decay. As we can see from Fig. 4, the room temperature electrical resistivity decreases very fast in the samples that were subject to thermal treatment, prior to the measurements, at temperatures up to 4008C. From then on, it becomes virtually constant approaching a
final value of about 1 V cm. We can understand this rapid decrease of the electrical resistivity with increasing annealing temperature on the basis that while thermally annealing a sample at a given temperature we are essentially removing the original solvent Žacetone. clogged to the sample nanopores, a process which for acetone should be essentially accomplished at around 4008C. An additional removal at higher annealing temperatures may take place and can be attributed to thermal dissociation of the remaining Žbounded. acetone, or its fragments. This might account for the much smaller decrease observed in the resistivity of the samples annealed between 4008C and 5508C Žhighest dissociation temperature in acetone. when it does level off. It should also be taken into account that this removal facilitates cluster accreation so that grain growth is also expected to occur. In contrast, the thermal diffusivity dependence on the annealing temperature exhibited a more distinct behavior. It initially decreases with increasing annealing temperature, reaches a minimum at around 4008C, and then increases with increasing annealing temperature. To understand this behavior of the thermal diffusivity, we recall that it is defined as a s krr c, where k is the sample
Fig. 3. Open photoacoustic cell ŽOPC. signal amplitude as a function of the square root of the modulation frequency for a Pd:Ag nanocompact annealed at 1508C. The solid line is a least squares fit to the data using Eq. Ž1. of the text.
C.A.S. Lima et al.r Materials Letters 51 (2001) 357–362
361
Fig. 4. Electrical resistivity and thermal diffusivity data for our Pd:Ag nanocompacts, measured at room temperature Ž258C. in samples previously subject to thermal treatment, plotted as a function of the annealing temperature. The fit to the resistivity curve is discussed in the text. The curve through the thermal diffusivity data corresponds to a spline interpolation.
thermal conductivity, r is the sample mass density and c is its specific heat. The initial decrease of a with increasing annealing temperature is, in our view, due to the densification of our sample resulting from the removal of the residual solvent left in the sample. This is consistent with the observed sharp decrease of the electrical resistivity up to 4008C. On the other hand, the expected increase in grain size resulting from the annealing process entails that the sample porosity should also increase as the sample is annealed at higher temperatures. The observed increase of a with increasing annealing temperature above 4008C may be associated with this expected increase in the sample porosity. In fact, for an air-filled porous material, the thermal diffusivity is seen to increase with increasing porosity w18,19x, since the room temperature air thermal diffusivity is relatively high, namely, a air s 21 mm2rs.
In particular, it was shown that the electrical resistivity exhibits a sharp exponential decrease with increasing annealing temperature up to 4008C. Above this temperature, the electrical resistivity remains practically constant. The observed dependence of the thermal diffusivity with increasing annealing temperature was, however, more complex. The thermal diffusivity, whose inverse is essentially a measure of the sample thermalization time, is known to be extremely dependent on the effects of compositional and microstructural variables w19–21x as well as on the sample processing conditions. This can be appreciated from the tabulated values of a w18x for a wide range of materials, such as, metals, minerals, foodstuffs, biological specimens and polymers. The sensitivity of the thermal diffusivity of our Pd:Ag nanocompacts to the effects of the thermal treatment they were subject to, at increasingly higher annealing temperatures, reflects this unique character of this physical parameter.
4. Conclusions In this paper, we have reported on the influence of the thermal annealing of nano-crystalline Pd:Ag compacts on their electrical and thermal properties.
Acknowledgements Author C.A.S. Lima acknowledges support from Proyecto APhotothermal assessment of thermophysi-
C.A.S. Lima et al.r Materials Letters 51 (2001) 357–362
362
cal parameters of strategic new materialsB-Ap. Gestion Fondecyt a98.011.024-1.2, granted to him by the Direccion ´ de Investigacion ´ de la Universidad de Concepcion ´ and author L.C.M. Miranda thanks the Brazilian Agency CNPq for the partial financial support of this work.
References w1x w2x w3x w4x w5x w6x w7x w8x
A.V. Walker, D.A. King, Phys. Rev. Lett. 82 Ž1999. 5156. J.L. Whitten, H. Yang, Surf. Sci. Rep. 24 Ž1996. 55. B. Hammer, J.K. Norslov, Nature 376 Ž1995. 238. F.M. Muller, T.A. Stegink, R.C. Thiel, L.J. de Jongh, G. Schmid, Nature 367 Ž1994. 716. J. Neuegbauer, N. Scheffler, Phys. Rev. Lett. 71 Ž1993. 577. R. Wu, A.J. Freeman, G.B. Olson, Phys. Rev. B47 Ž1993. 6855. P. Krueger, J. Pollmann, Phys. Rev. B47 Ž1993. 1898. C.R. Brundle, J.Q. Broughton, in: D.A. King, D.P. Woodruff ŽEds.., The Chemical Physics of Solid Surfaces and Heterogeneous Catalysis, vol. 3A, Elsevier, Amsterdam, 1990, Chap. 3.
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