Bulk and surface properties of liquid Ag–X (X = Ti, Hf) compound forming alloys
Introduction
The development of new materials requires sometimes the knowledge of thermodynamic and thermophysical data which due to the experimental difficulties have not been measured. For this purpose different estimation methods are available [1], [2], [3], [4], [5], [6]. An example are silver based alloys containing the additions of the IV group transition metals, Ti, Zr, and Hf. Ti-based alloys are principally used in aircraft, spacecraft, naval ships and medicine [7], [8]. Hf and its alloys are constituent or subsystems of complex metallic glasses [9], [10], [11], superconducting alloys [12] or are used for nuclear propulsion [13]. For many years the traditional silver solders have been used for joining ceramics and glasses with metallic materials [14]. Recently, the Ag–Ti, Ag–Zr and Ag–Hf alloys have been studied as active brazers with ceramic substrates in composite materials suitable for application where aggressive thermal and mechanical conditions are predominant [15], [16], [17], [18].
The thermodynamic and thermophysical properties of Ag–Ti [19], [20], [21], [22], [23], [24] and the Ag–Hf [21], [22], [23], [24], [25], [26], [27] systems have been studied by few authors. Although the Ag–Ti phase diagram [19], [20] is still incomplete, it is similar to that of the Ag–Zr system [28], exhibiting the presence of two intermetallic phases, AgTi and AgTi2. In the case of the Ag–Hf system, the existence of AgHf and AgHf2 intermetallic compounds has been recognised [21], [22] and its unknown phase diagram [26] should be similar to those of the Ag–Ti and Ag–Zr systems. The Hume-Rothery empirical factors, such as size ratio (VTi/VAg ≈ 0.945 and VHf/VAg ≈ 1.1427) [1], valency difference (=2;3 and =3) and electronegativity difference (≈0.4 and ≈0.6) [29] together with an experimental evidence on the presence of the AgTi, AgTi2, AgHf and AgHf2 intermetallic compounds [21] in the solid state clearly indicate a compound forming tendency and suggest short range ordering in the liquid phases [30].
The high melting points of the IV group metals Ti, Zr and Hf and their strong chemical affinity for oxygen, in pure state or alloyed, make high temperature experimental measurements difficult. The existing thermodynamic data on all three systems, Ag–Ti, Ag–Zr and Ag–Hf are scarce, incomplete and show a considerable scatter. The present paper deals with modelling of thermodynamic and thermophysical properties of Ag–Ti and Ag–Hf liquid alloys. Results on Ag–Zr liquid alloys [31] will also be reported in order to understand better the mixing behaviour, the energetics and structure of these alloy systems.
The excess entropy and the excess Gibbs free energy of Ag–Hf and Ag–Ti liquid alloys have been calculated using the model based on the free volume theory [3] and, as input data, their enthalpy of mixing [22] combined with the physical properties of alloy constituents [1]. The concentration and temperature dependence of the surface and transport properties have been theoretically investigated using a quasi-chemical solution model [32], in the case of both systems at T = 1473 K, while in the case of the Ag–Ti system at T = 1773 K, the compound formation model (CFM) was applied [33], [34]. The nature of mixing and the degree of order in their melts are expressed in terms of the microscopic functions: the concentration–concentration fluctuations in the long wavelength limit, Scc(0) [35], and the Waren–Cowley short-range order parameter, α1 [36], [37], in the frame of a statistical mechanical theory. All calculated values are compared with the corresponding results obtained for Ag–Zr molten alloys [31].
Section snippets
The CFM and the QCA for regular solution: thermodynamic and surface properties
The existing experimental data of the three compound forming systems Ag–Ti, Ag–Zr and Ag–Hf indicate a similar behaviour on mixing [22]. The CFM formalism related to a weak interaction approximation [34], [30] has been successfully applied to Ag–Zr liquid alloys to describe the asymmetric behaviour of their mixing properties with respect to the AB2-stoichiometry [31]. Due to the close similarity between the Ag–Zr and Ag–Ti systems, the last one has been analysed in the framework of the same
Results and discussion
Although scarce the thermodynamic data on Ag–Ti and Ag–Hf liquid alloys indicate negative deviation of their thermodynamic properties from the Raoult’s law, and thus the related thermophysical properties deviate positively from the corresponding ideal values as was previously observed for the Ag–Zr system [31]. Based on the Mendeleev’s rule, the enthalpy and entropy of a certain system may be estimated by comparison with similar systems according to the position of their constituents in the
Conclusions
The QCA and the CFM have been used to study some thermodynamic and thermophysical properties of Ag–Ti and Ag–Hf molten alloys, namely surface tension, diffusivity and viscosity. Due to the lack of experimental data, some thermodynamic properties of both alloy systems have been derived using the free volume theory. The mixing behaviour of Ag–Ti and Ag–Hf molten alloys has been analysed with special emphasis on their bulk and surface properties. Surface properties of Ag–Ti and Ag–Hf liquid alloys
Acknowledgements
The authors would like to thank Prof. F. Sommer, Max-Planck-Institute for Metals Research, Stuttgart and Prof. K. Fitzner, Laboratory of Physical Chemistry and Thermochemistry, Faculty of Non-Ferrous Metals, Krakow, for helpful discussions on this subject. Dr R. Novakovic is grateful to the JSPS (The Japan Society for the Promotion of Science) for financial support.
References (57)
Thermochim. Acta
(1998)- et al.
J. Alloys Compd.
(2000) - et al.
J. Alloys Compd.
(2001) - et al.
Mater. Sci. Eng. A
(2000) - et al.
Acta Mater.
(2001) - et al.
J. Non-Cryst. Solids
(2003) J. Nucl. Mater.
(1981)- et al.
Diam. Relat. Mater.
(1997) - et al.
J. Europ. Ceram. Soc.
(2003) - et al.
Scripta Mater.
(2003)