Bulk and surface properties of liquid Ag–X (X = Ti, Hf) compound forming alloys

Abstract

The thermodynamic data of the Ag–Ti and Ag–Hf systems as well as their phase diagrams are still incomplete. Moreover, up to now the phase diagram of the Ag–Hf system is not yet assessed. As concerns their thermophysical properties, a complete lack of experimental data is evident. Such a state of the art results from the experimental difficulties involved in high temperature measurements on highly reactive systems. Based on the experimental data on the existence of the AgTi, AgTi₂, AgHf and AgHf₂ intermetallic compounds in the Ag–Ti and Ag–Hf systems, respectively and our recently reported theoretical results on the Ag–Zr compound forming system, it is reasonable to expect similar mixing behaviour in these three alloy systems. The mixing behaviour of Ag–Ti and Ag–Hf has been analysed through the study of surface properties (surface tension and surface composition), transport properties (chemical diffusion and viscosity) and microscopic functions (concentration fluctuations in the long-wavelength limit and chemical short-range order parameter) in the frame of Quasi Lattice Theory (QLT) combined with a statistical mechanical theory.

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 (V_Ti/V_Ag ≈ 0.945 and V_Hf/V_Ag ≈ 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, S_cc(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].