Liquid Titanium Solute Diffusion Measured by Pulsed Ion-Beam Melting

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Introduction
Ti alloys are important commercial materials in the aerospace industry because of their high strength to weight ratio. The manufacture of Ti components often involves melting to obtain the desired alloy composition and casting. In understanding the process of alloy solidification and solute partitioning, the liquid diffusivity is a critical parameter. In addition to the absence of experimental measurements of Ti solute liquid diffusivities in the literature 1,2 , there is also a general deficit in knowledge of the thermophysical properties of the liquid phase, including latent heat, specific heat, and thermal conductivity. This paper reports on direct experimental determination of liquid diffusivities of some common alloying elements in Ti.
Liquid diffusivity is a particularly challenging property to measure accurately. Two potentially serious problems associated with liquid diffusivity measurements are convective contamination and container wall interactions 1 . The elevated melting point (T m ) and high reactivity of Ti exacerbate both of Liquid Ti Solute Diffusion Measured by pulsed Ion-Beam Melting 1 October, 1999 page 2 these problems. Convective contamination generally occurs when temperature gradients in the liquid create instabilities leading to the formation of convective cells. High temperatures and extended times increase the likelihood of cell formation. Although it is exceedingly difficult to completely eliminate convective contamination in terrestrial diffusion measurements, these effects can be minimized by using fine capillaries that limit the formation of convection cells. Although container wall interactions have been ruled out in some diffusion experiments with low T m materials 3 , there is a general concern that fine capillaries introduce additional problems due to wall interactions-a particularly troublesome concern when working with reactive materials at high temperatures. Although microgravity diffusion measurements can effectively eliminate buoyancy convective currents, surface tension-driven flows (Marangoni) may remain.
Liquid diffusivity measurements following pulsed melting can minimize many of these difficulties. The thin film geometry and short melt duration permit the avoidance of convection currents.
The planar geometry permits accurate measurement of the sub-micron diffusion distances resulting from the short melt duration using techniques such as Rutherford backscattering spectrometry (RBS) or secondary ion mass spectrometry. While molten, the liquid is surrounded by a solid of the same composition, so container wall interactions are minimized. The primary difficulties inherent in this method are the accurate measurement of the melt duration, the temporal melt-depth profile, and the liquid temperature. These parameters are generally deduced from time-resolved reflectivity measurements (TRR) and heat-flow simulations. ranging from 100 to 230 keV with common alloying elements in Ti including the alpha stabilizer Sn, the beta stabilizer Mo, and two elements, Zr and Hf, in the same family as Ti (Table I) TEM images were obtained on a Hitachi 8100 microscope operating at 200 keV.

Data Analysis
The ion beam current signal collected by the Faraday cup was split into its three constituent parts as shown in Fig. 2. The relative fractions of the ion species were determined by time-of-flight extraction from the ion current 4 . For these simulations, the depth and time dependent energy deposition of each ion species was handled independently. Silicon heat-flow simulations 4 were performed to determine the total ion beam energy by scaling the ion beam current to match the Si melt duration determined by reflectivity ( Fig. 3 and Table II). Because the thermophysical properties of Si are well known, the accuracy of this part of the analysis is good. The ion beam current profile and calculated fluence were then used as input for Ti heat flow simulations 4 to determine the Ti melt profile ( Fig. 4 and Table II). Uncertainties in this calculation are larger, since the thermophysical properties of Ti (Table III) are not as well known, especially for the liquid and phase transitions. The heat-flow simulation program did not attempt to model any solid state phase transitions. To account for the heat of transformation without modeling directly the solid state transition, the solid specific heat between the transition temperature and T m was increased to recover the correct solid enthalpy at T m . The Ti melt duration was typically less than half that of Si, primarily because of Ti's higher melting point and solid heat capacity.
Initial impurity profiles following ion implantation were extracted from RBS data. Simulations using the Edgeworth function 11 for the implanted concentration profile and the detector resolution were fit to the data. The Edgeworth fitting parameters were then used to model the implanted solute profile (Fig. 5), effectively deconvoluting the RBS instrument function from the raw RBS solute profiles.
The Ti melt profile and initial solute concentration profile were then used as inputs to a onedimensional diffusion equation 12 to obtain the final solute concentration profile (Fig. 5). RBS profiles, calculated from the diffusion simulation results, were compared to the experimental RBS profile from the melted specimen ( Fig. 6). Diffusivities from 3 to 11 x 10 -5 cm 2 /s were input into the diffusion simulation and chi-squared minimization (weighted by counting statistics) was used to identify the best-fit diffusivity.

Results
The results of the liquid Ti solute diffusion calculations are shown in Table II. The maximum solute penetration depth was only one quarter of the maximum melt depth in the Ti (Fig. 4), indicating that convective mixing was not a large factor. The good agreement between the best-fit diffusivities for each solute is demonstrated by the low standard errors 13 (Table IV). Both the Mo and Hf data sets seem to have one outlier when compared with the tightness of the Sn and Zr data sets, but application of Chauvenet's  13 indicates that these data points cannot be excluded. The total error 13 (Table IV) was calculated by including an additional 5% systematic uncertainty from determination of the melt duration, the ion-beam energy, and the simulated melt profile.

Discussion
Upon slow heating, Ti undergoes a solid-state phase transformation from alpha to beta at 1155 K.
All simulations reported in this work assumed melting and solidification of the high temperature beta phase. Very rapid melting and solidification could preclude the formation of the high-temperature beta phase, in which case the alpha would melt and solidify at its metastable melting point 14 (Fig. 7). The simulated melt depth for this sample is 1300 nm, which is in good agreement with the measured value. If the low-temperature alpha phase had instead melted and solidified at the metastable transformation temperature, the simulated melt depth would be 1500 nm. Unfortunately, the uncertainty in the experimental depth measurement is larger than the difference between the two simulations due to the surface roughness ( Figs. 7 and 8).
The surface roughness in Fig. 8 (Table III)  The low solute solubility of Mo in α−Ti (Table I) (Table I), well below the melting point of 1941 K where liquid diffusion ceases. No Mo precipitates were observed in cross-sectional TEM (Fig. 7).
A correlation has been observed between diffusivity and the standard free energy of solution. 1 These observations indicate that the more exothermic the mixing reaction the smaller the liquid diffusivity.
The heats of reaction calculated by Miedema 17 are more exothermic for Sn-Ti (-62 kJ/mol) and Mo-Ti (-6 kJ/mol) than those for Zr-Ti and Hf-Ti (both 0 J/mol). Thus, at the outset of the experiment, it was expected that the Zr and Hf would have higher diffusivities due to their chemical similarity and presumed limited interaction with Ti. However, the observed diffusivities of Sn and Mo were higher than Zr and Hf.
Other thermodynamic parameters can also be used to assess the solution behavior. Strong solute/solvent interactions may lead to the formation of solvent clusters around solute atoms and reduced diffusion rates 18 . Clustering is generally indicated by negative solute partial molar volumes. Turnbull 19 Liquid Ti Solute Diffusion Measured by pulsed Ion-Beam Melting 1 October, 1999 page 7 tabulated the molar volumes of different solutes in Al, but volumetric data were not available for liquid Ti alloys. Observation of the initial liquidus slope in the binary phase diagram can give an independent indication of the exothermicity of the solute/solvent interaction. Generally speaking, for regular solution phase diagrams, the more negative the initial liquidus slope (minus the slope of a straight line connecting the melting points of the pure elements), the more attractive the interaction between the solute and solvent in the liquid. Considering the phase diagrams of Ti-Mo, Ti-Zr, and Ti-Hf, the liquidus slope is significantly more negative for Ti-Zr and Ti-Hf than for Ti-Mo. This trend is consistent with the observed diffusivities (Table IV). The complexity of the Ti-Sn phase diagram lead to its exclusion from the above comparison.
One important parameter in reporting the diffusivity is the temperature. Heat-flow simulations were done to determine the average liquid surface temperature during the course of the experiment (Table   II). It is important to point out that the temperature determination is the least accurate parameter obtained from the heat flow simulations. Calculations indicate that the average surface temperature ranges from T m + 300 K to T m + 550 K. The temperature dependence of the liquid diffusivity can be described as weakly activated or even linear 1 , leading to the general conclusion that the measured diffusivity corresponds to the average melt temperature. For the measurements in Table II,  There is some synergy between buoyancy-and Marangoni-driven convection, because both tend to create convective currents with the same orientation. However, due to the small contributions from these processes, the overall effect of convection on the measurements is negligible. Note that in Fig. 4, the maximum solute depth before and after melting is compared with the total melt depth. If convection were present, one would observe solute within the deepest regions of the melt 22 , but none was detected. This supports the claim that convective contamination is not a significant issue in this type of experiment.

Summary
The Ti liquid solute diffusivity was determined by pulsed ion-beam melting of Ti ion implanted with Sn, Mo, Zr, and Hf. One-dimensional diffusion simulations were utilized to match the final experimental concentration profile given the initial concentration profile and the Ti melt profile. Ti liquid solute diffusivities in cm 2 /s over the temperature range of 2200 to 2500 K are as follows: D Sn = 9.1 ± 0.5, D Mo = 7.7 ± 0.6, D Zr = 5.2 ± 0.3, D Hf = 6.2 ± 0.6. The solidification of the Ti was slow enough to allow the formation of the high temperature beta phase, which later transformed to the low temperature alpha phase.
Calculations of buoyancy and Marangoni convection currents indicate that convective contamination was unlikely.