Part IV – April 1969 - Papers - Thermal Diffusion above the Eutectoid Temperature in Titanium-Hydrogen Type Systems

A simple model has been developed which describes the steady-state solute distribution in Ti-H type systems above the eutectoid temperature in the presence of a temperature gradient. The solute distribution is dependent on the shape of the phase boundaries. An interesting result, and one that is not observed at steady state in thermal diffusion below the eutectoid temperature, is the existence of a two-phase region. The heat of transport for hydrogen in a titanium, Q*a, over the temperature range 275" to 650.C is determined to be 4500 * 230 cal per mole. The heat of transport for hydrogen in B titanium, QB* over the temperature range 320" to 590.C is found to be 630 ± 200 cal per mole. It is also shown that thermal diffusion provides a method by which phase bounduries above the eutectoid may be determined in Ti-H type systems. IN modern technology materials are being used at constantly increasing temperatures under greater temperature gradients. Thus atomic migration in metal alloys due to a temperature gradient (thermal diffusion) may in some cases occur to an observable extent. The thermal diffusion of hydrogen in zirconium has in recent years received considerable attention1-' because of the use of zirconium alloys in nuclear power reactors. The thermal diffusion kinetics below the eutectoid (547°C) are fairly well understood. At steady state the solid solution, a, and hydride, 6, phases are completely separated with the hydride precipitating at the lower temperatures. No experimental work has been carried out in the a + B region although Droege4 suggested that a complete separation of the two phases, as observed at temperatures below the eutectoid, might not always occur. In the present investigation a simple model has been used to determine the steady-state solute distribution under a temperature gradient in Zr-H type systems heated above the eutectoid temperature. The solute distribution is shown to be dependent on the shape of the phase boundaries in the constitutional diagrams and several typical cases are discussed. The model has been applied to Ti-H. This system was chosen in preference to Zr-H because of its much lower eutectoid temperature (-300°C as compared with 547.C), thereby reducing experimental errors due to oxidation and hydriding. The heats of transport for hydrogen in the a and B phases of titanium also have been determined since they were required to compare the proposed thermal diffusion model with experiment. THEORY In the presence of a temperature gradient the atomic flux in a single-phase region of a two-com-ponent system of which the atoms of only one component are diffusing is given by:' J = - U\dx + RT3 dx) which can be written as: j-D(dn/dt +Q*n/RT2)dt/dx [11 J - -D\dT + RT2)dx [1] where D = diffusion coefficient, n = solute concentration, T = absolute temperature, R = gas constant, dT/dx = temperature gradient, and Q* = heat of transport. At steady state (J = 0) Eq. [I] leads to the solute distribution: n = noexp Q*/RT where no = a constant depending on total solute content. The heat of transport Q* can be experimentally determined from the steady-state distribution. In the present paper we shall determine the solute distribution in systems having the constitutional diagram exemplified by Ti-H shown in Fig. l.' As shown, N,(T) and NB(T) are the equilibrium solute concentrations in the a and 0 phases at temperature T. Lines AA' and CC' define the region of interest to us. The following assumptions are made: 1) Steady-state conditions prevail. 2) In a single-phase region all points on an isotherm have the same thermodynamic potential so that the composition over an isotherm is uniform. If a two-phase region exists, thermodynamic equilibrium is found only at phase interfaces. However, we assume the component of the concentration gradient along an isotherm to be small so that the composition in each phase is approximately the same as at the interface and is given by the constitutional diagram, Fig. 1. 3) There is appreciable diffusion of only one component. 4) We shall consider only the case where Qa*, QB*, and Qg*, the heats of transport for solute diffusion in the a, B, and 6 phases, respectively, are positive. This has been observed for the thermal diffusion of hydrogen in zirconium3 and titanium.10 We will show that the steady-state solute distribution above the eutectoid is primarily determined by the heats of transport and the temperature dependence of Na(T) and Np(T). It may be quite different from the steady-state distribution below the eutectoid. For example, we will see that, under certain conditions,