The increasing interest in the last years in nanotechnologies, related to produce, investigate and find functionality for various types of nanomaterials, enriched the data basis concerning their properties at nano-, meso- and macroscale. New properties that can be obtained controlling both, size and arrangement of particles are one of the current scientific and technological issues. Along with this trend, an urgent need for phase diagrams of nanosized alloy systems is evident. Thermodynamic databases have been mainly used for phase diagram optimisation, but they can be also applied for the calculations of thermophysical properties, such as surface tension and viscosity. The CALPHAD (Calculation of Phase Diagrams) approach has been widely recognized in different fields of materials science and engineering [1, 2]. The existing databases have to be extended in view of new requirements to be useful for all classes of nanomaterials. The thermodynamics of solid-liquid phase equilibria in a small particle systems has been initially studied analysing the melting phenomena of pure metals and alloys [3, 4]. It has been established that the melting points of some pure metals decrease with decreasing the size of their metallic particles [5]. The large surface / volume ratio in nano-sized particle systems has significant effects on their thermodynamic properties and phase relations [6]. As a starting point, the phase diagrams of some simple nano-sized metallic systems have been evaluated qualitatively from the macroscopic thermodynamic point of view [5, 7]. The phase diagrams of segregating binary nano-sized alloy systems, such as Cu-Pb [5], Au-Si [7], Ag-Cu [8] have been calculated as a function of temperature (T), composition (c), size (d) and taking into account that the phase relations are dependent upon the size of particle and its surface property. Surface tension of small particles may change due to the curvature, which may decrease with decreasing size, yielding the liquidus temperature drop. For example, in the case of pure gold, this effect would occur for particles less than 10 nm [9]. Accordingly, the assessment of phase diagram of nano-sized particles less than 10 nm should consider the surface tension drop. The next step should include thermodynamic description of nano-sized compound forming alloy systems, followed by advanced ceramics and composite materials and their phase diagram calculations. As in the case of other materials, it is highly necessary to understand the macroscopic properties in correlation with their particular microstructure. The granular and nanoscale materials are studied to discover how their properties differ from their macroscopic counterparts. In various solids as metal and alloys, ceramics for microelectronics, etc. it was found that the thermodynamic, mechanical, dielectric, magnetic, optical and transport properties strongly dependent on their dimension (i.e. thickness in case of thin film structures, particle size in powders, grain size in case of bulk materials), particularly when reducing their geometric dimensions in the range of nanoscale [10-13]. The finite size effects are particularly important for systems with long-range interactions. For example, in case of the ferroelectrics, a reducing of the dipolar interaction and consequently of the Curie transition temperature (Figs.1 a-b) with reduction of the grain size [12] or film thickness was reported [14] as a general behaviour. This size dependance of the Curie temperature and other size-dependent properties in ferroelectrics can be explained by the thermodynamic approach (Landau-Ginzburg-Devonshire) by considering size-dependent Landau coefficients, boundary conditions or surface effects [15]. In the case of metallic alloy systems, by employing the standard thermodynamics for calculating the macroscopic characteristics in nanosystems, some anomalies were found, particularly because the physical characteristics do not scale linearly with respect to the system size [7-9]. Various generalised entropy functions and a better definition of the temperature have been proposed in order to generalise the formalism of the statistics of discrete systems [16-17]. Therefore, they were not applied for solving specific problems of the solid state nanosystems. Another possible approach is the Nanotermodynamics, originally proposed 40 years ago by Hill [6], which considers the entropy a not extensive function and thus the chemical potential is dependent on the number of constituents. It is expected that such new models, applied for specific solid state nanomaterials to provide better instruments and a more accurate description of the overall macroscopic properties related to their discrete nanostructure. [1] N. Saunders, A.P. Miodownik, CALPHAD Calculation of Phase Diagrams, A comprehensive Guide, Pergamon Materials Series, Elsevier Sci., Oxford OX5 1GB, 1998. [2] T. Tanaka, K. Hack, S. Hara, MRS BULLETIN, April 1999. [3] P.R. Couchman, W.A. Jesser, Nature, 269 (1977) 481. [4] J.G. Lee, H. Mori, H.Yasuda, Phys. Rev. B, 66 (2002) 012105-1. [5] T. Tanaka, S. Hara, Z. Metallkd. 92(5) (2001) 467. [6] T. L. Hill, Thermodynamics of Small Systems, Dover, New York (1994) [7] T. Tanaka, S. Hara, Z. Metallkd. 92(11) (2001) 1236. [8] J.P. Hajra, S. Acharya, J. of Nanoscience and Nanotechnology, 4 (7) (2004) 899. [9] J. Lee, M. Nakamoto, T. Tanaka, J. Mater. Sci. 40 (2005) 2167. [10]. J. Schmelzer jr, S. A. Brown et al., Finite-Size Effects in the Conductivity of Cluster Assembled Nanostructures, Phys. Rev. Lett. 88 (2002) 226802. [11] A.E. Berkowitz, R.H. Kodama et al., Anomalous properties of magnetic nanoparticles, J. Magn. Magn. Mater. 591 (1999) 196-197. [12] Z. Zhao, V. Buscaglia et al., Size effect on ferroelectric behavior of dense nanocrystalline BaTiO3 ceramics, Phys. Rev. B 70 (2004) 024107. [13] D. Wolpert et al., Finite Size Effects In Ferroelectric Nanosystems: Absence of mode softening, Tech. Proc. Nanotech. Conf. and Trade Show 2003, Vol. 2, 76 (2003). [14] D.D. Fong, G.B. Stephenson et al., Ferroelectricity in ultrathin perovskite films, Science 304 (2004) 1650. [15] D. Ricinschi et al., Landau theory-based analysis of grain-size dependence of ferro-para phase transition and its thermal hysteresis in BaTiO3 ceramics, J. Phys.: Condens. Matter 11 (1999) 1601. [16] A Coniglio, A Fierro, M Nicodemi, M Pica Ciamarra and M Tarzia, Statistical mechanics of dense granular media, J. Phys.: Condens. Matter 17 (2005) S2557. [17] V. Colizza, A. Barrat and V. Loreto, Definition of temperature in dense granular media, Phys. Rev. E 65 (2002) 050301.
Nanothermodynamics-a possible approach for describing the properties of nanosystems
Novakovic R
2005
Abstract
The increasing interest in the last years in nanotechnologies, related to produce, investigate and find functionality for various types of nanomaterials, enriched the data basis concerning their properties at nano-, meso- and macroscale. New properties that can be obtained controlling both, size and arrangement of particles are one of the current scientific and technological issues. Along with this trend, an urgent need for phase diagrams of nanosized alloy systems is evident. Thermodynamic databases have been mainly used for phase diagram optimisation, but they can be also applied for the calculations of thermophysical properties, such as surface tension and viscosity. The CALPHAD (Calculation of Phase Diagrams) approach has been widely recognized in different fields of materials science and engineering [1, 2]. The existing databases have to be extended in view of new requirements to be useful for all classes of nanomaterials. The thermodynamics of solid-liquid phase equilibria in a small particle systems has been initially studied analysing the melting phenomena of pure metals and alloys [3, 4]. It has been established that the melting points of some pure metals decrease with decreasing the size of their metallic particles [5]. The large surface / volume ratio in nano-sized particle systems has significant effects on their thermodynamic properties and phase relations [6]. As a starting point, the phase diagrams of some simple nano-sized metallic systems have been evaluated qualitatively from the macroscopic thermodynamic point of view [5, 7]. The phase diagrams of segregating binary nano-sized alloy systems, such as Cu-Pb [5], Au-Si [7], Ag-Cu [8] have been calculated as a function of temperature (T), composition (c), size (d) and taking into account that the phase relations are dependent upon the size of particle and its surface property. Surface tension of small particles may change due to the curvature, which may decrease with decreasing size, yielding the liquidus temperature drop. For example, in the case of pure gold, this effect would occur for particles less than 10 nm [9]. Accordingly, the assessment of phase diagram of nano-sized particles less than 10 nm should consider the surface tension drop. The next step should include thermodynamic description of nano-sized compound forming alloy systems, followed by advanced ceramics and composite materials and their phase diagram calculations. As in the case of other materials, it is highly necessary to understand the macroscopic properties in correlation with their particular microstructure. The granular and nanoscale materials are studied to discover how their properties differ from their macroscopic counterparts. In various solids as metal and alloys, ceramics for microelectronics, etc. it was found that the thermodynamic, mechanical, dielectric, magnetic, optical and transport properties strongly dependent on their dimension (i.e. thickness in case of thin film structures, particle size in powders, grain size in case of bulk materials), particularly when reducing their geometric dimensions in the range of nanoscale [10-13]. The finite size effects are particularly important for systems with long-range interactions. For example, in case of the ferroelectrics, a reducing of the dipolar interaction and consequently of the Curie transition temperature (Figs.1 a-b) with reduction of the grain size [12] or film thickness was reported [14] as a general behaviour. This size dependance of the Curie temperature and other size-dependent properties in ferroelectrics can be explained by the thermodynamic approach (Landau-Ginzburg-Devonshire) by considering size-dependent Landau coefficients, boundary conditions or surface effects [15]. In the case of metallic alloy systems, by employing the standard thermodynamics for calculating the macroscopic characteristics in nanosystems, some anomalies were found, particularly because the physical characteristics do not scale linearly with respect to the system size [7-9]. Various generalised entropy functions and a better definition of the temperature have been proposed in order to generalise the formalism of the statistics of discrete systems [16-17]. Therefore, they were not applied for solving specific problems of the solid state nanosystems. Another possible approach is the Nanotermodynamics, originally proposed 40 years ago by Hill [6], which considers the entropy a not extensive function and thus the chemical potential is dependent on the number of constituents. It is expected that such new models, applied for specific solid state nanomaterials to provide better instruments and a more accurate description of the overall macroscopic properties related to their discrete nanostructure. [1] N. Saunders, A.P. Miodownik, CALPHAD Calculation of Phase Diagrams, A comprehensive Guide, Pergamon Materials Series, Elsevier Sci., Oxford OX5 1GB, 1998. [2] T. Tanaka, K. Hack, S. Hara, MRS BULLETIN, April 1999. [3] P.R. Couchman, W.A. Jesser, Nature, 269 (1977) 481. [4] J.G. Lee, H. Mori, H.Yasuda, Phys. Rev. B, 66 (2002) 012105-1. [5] T. Tanaka, S. Hara, Z. Metallkd. 92(5) (2001) 467. [6] T. L. Hill, Thermodynamics of Small Systems, Dover, New York (1994) [7] T. Tanaka, S. Hara, Z. Metallkd. 92(11) (2001) 1236. [8] J.P. Hajra, S. Acharya, J. of Nanoscience and Nanotechnology, 4 (7) (2004) 899. [9] J. Lee, M. Nakamoto, T. Tanaka, J. Mater. Sci. 40 (2005) 2167. [10]. J. Schmelzer jr, S. A. Brown et al., Finite-Size Effects in the Conductivity of Cluster Assembled Nanostructures, Phys. Rev. Lett. 88 (2002) 226802. [11] A.E. Berkowitz, R.H. Kodama et al., Anomalous properties of magnetic nanoparticles, J. Magn. Magn. Mater. 591 (1999) 196-197. [12] Z. Zhao, V. Buscaglia et al., Size effect on ferroelectric behavior of dense nanocrystalline BaTiO3 ceramics, Phys. Rev. B 70 (2004) 024107. [13] D. Wolpert et al., Finite Size Effects In Ferroelectric Nanosystems: Absence of mode softening, Tech. Proc. Nanotech. Conf. and Trade Show 2003, Vol. 2, 76 (2003). [14] D.D. Fong, G.B. Stephenson et al., Ferroelectricity in ultrathin perovskite films, Science 304 (2004) 1650. [15] D. Ricinschi et al., Landau theory-based analysis of grain-size dependence of ferro-para phase transition and its thermal hysteresis in BaTiO3 ceramics, J. Phys.: Condens. Matter 11 (1999) 1601. [16] A Coniglio, A Fierro, M Nicodemi, M Pica Ciamarra and M Tarzia, Statistical mechanics of dense granular media, J. Phys.: Condens. Matter 17 (2005) S2557. [17] V. Colizza, A. Barrat and V. Loreto, Definition of temperature in dense granular media, Phys. Rev. E 65 (2002) 050301.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
