Evaluation of evaporation losses during electron-beam melting of Ti-Al-V alloys

Abstract

Electron-beam cold-hearth melting (EBCHM) is finding increasing application for the production of titanium alloys due to its ability to dissolve or eliminate inclusions with high melting temperatures. However, the melting of titanium alloys under vacuum results in the marked vaporization of volatile alloying elements, such as aluminum, having vapor pressures exceeding that of titanium. In this article, the evaporation rates of Al, Ti, and V from Ti-rich Ti-Al-V melts, in particular, Ti-6Al-4V, are evaluated on the basis of the thermodynamics of liquid solutions of the melt components. First, the ideal evaporation rate is estimated based on Langmuir's equation and thermodynamic calculations of the activity of the alloying elements. Second, the rate-limiting influence of diffusion of aluminum to the surface of the melt on the evaporation kinetics is considered.The rate of ideal evaporation of component i into vacuum (W i ) varies with temperature according to Langmuir's equation:[1] [2] in which X i , ␥ i , and M i are the molar fraction, activity coefficient, and molar mass of the evaporating species, respectively; P i is the partial pressure of vapor of component i over the multicomponent melt; R is the gas constant; T is the absolute temperature; and is the vapor pressure above the melt of pure element i. The vapor pressures of pure Al, Ti, and V can be estimated using the Clausius-Clapeyron equation:The constants A, B, and C in Eq.[3] are listed in Table I for Al, Ti, and V.The activity coefficients of the components, ␥ i , may be expressed through the partial excess Gibbs energy ; i.e.,In turn, the values of ⌬G -i ex are related to the integral thermodynamic functions ⌬G ex , which are as follows for a ternary system (with components 1, 2, and 3):If the Redlich-Kister equation is used to express the excess Gibbs energy of the Al-Ti, Al-V, and Ti-V binary systems, ⌬G ex of the Al-Ti-V ternary solution can be expressed for the general case as [6] in which X Al , X V , and X Ti denote the mole fractions of components in the melt; ␣ 1 , ␣ 2 , and ␣ 3 are interaction parameters for the ternary solution; and the terms for binary A-B systems are temperature-dependent model parameters; viz.[7]In practice, the maximum number n in the series expansions for ⌬G rarely exceeds 3, and the number of terms in Eq. [7] is taken less than that indicated. The thermodynamic properties of the Ti-Al, Al-V, and Ti-V binary liquid solutions are known and presented in Reference 2. The corresponding model parameters for Ti-Al, Al-V, and Ti-V systems are given in Table II.In view of the typical absence of experimental information on the thermodynamic properties of ternary solutions, the corresponding interaction parameters are usually put to zero, and the extra terms are omitted in Eq. [6]. Such thermodynamic evaluations were performed in Reference 2 for the Al-Nb-Ti, Al-Ta-Ti, and Al-Ti-W ternary systems. In the case of the Al-Ti-V ternary system, the same approximation was used in the present work, taking into account the fact that the...

The role of modeling in the development of advanced processes for metallic aerospace alloys

“…Agreement between measured and predicted evaporation rates was achieved by using the activity coefficient of aluminum (γΑl) in the Ti-6Al-4V melt as essentially a fitting parameter. The possible drawback of this approach was noted by Ivanchenko et al [14], whose thermodynamic calculations suggested that γ Αl was approximately five times higher than the value esti mated by Powell et al…”

“…Based on the solution of the one-dimensional diffusion equation, several very recent investigations have provided an alternate method to describe the competition between diffu sion of solutes to the melt surface and subsequent evapora tion [14,17]. For example, Semiatin et al [17] used a solution from Carslaw and Jaeger [18] to estimate the total solute loss from a melt pool of depth d, surface area A, and initial solute composition Co (in kg/m 3 ), i.e., Total Flux = AdCo×…”

“…2 for predicting aluminum losses in titanium alloys are values of the activity coefficient γAl and diffusivity DAl. In Reference [17], activity coefficients estimated from a ther modynamic database [14] were used. The diffusivity of alu- 3.…”

Diffusion models for evaporation losses during electron-beam melting of alpha/beta-titanium alloys

“…As in previous investigations, [4][5][6][7] this flux was assumed to be given by the Langmuir equation: [5] [3]…”

“…For example, Akhonin et al [6] developed an approach to treat both the evaporation kinetics, including "boundary-layer" diffusion, and the pertinent mass balance in a model that could be applied to industrial melting operations. Ivanchenko et al [7] conducted careful work to establish the activity coefficients that should be used in the Langmuir equation and presented some initial semi-infinite diffusion-model results for the evaporation kinetics during EBM of Ti-64.…”