Kinetics of Evaporation of Alloying Elements under Vacuum: Application to Ti alloys in Electron Beam Melting

Introduction

The demand of Ti alloys experiences a rapid growth easily explained by the extremely interesting properties of this metallic material for aerospace, automotive, energy and biomedical engineering. High corrosion resistance associated to a high strength to density ratio makes titanium an excellent candidate for high performance applications, so that many research centers are still developing new grade of Ti alloys to actually broaden the field of potential applications. The success of the titanium industry leads to an enthusiastic development of new melting technologies and large-scale plants [1]. Hence, new melting/remelting processes such as Electron Beam Melting (EBM), Plasma Melting (PM) and Cold Crucible Induction Melting (CCIM) have emerged as either an alternative or a complement to traditional Vacuum Arc Remelting (VAR).Two of them operate in high vacuum (VAR at 10⁻³ mbar –0.1 Pa – and EBM at 10⁻⁴ mbar –0.01 Pa) enabling a complete degassing and impurities removal such as Cl, H or N. This is especially true for EBM since the combination of high vacuum and superheating at the electron beam impingement on the liquid surface makes the melting and casting process particularly conducive to volatilization [2]. Therefore, one of the main drawbacks of these vacuum processes remains the control of the composition of the cast ingots or slabs. It concerns the alloying elements which show a high vapor pressure with respect to titanium matrix, such as Al (one of the basic component in Ti alloys). The initial load composition must then be adjusted to account for such melt losses and to produce the desired ingot composition.

Based on the kinetic theory of gases, the volatilization flux density of a solute element i is expressed by the Langmuir law [3]:

where Pieq is the vapor pressure of i in equilibrium with the liquid phase, T_s is the temperature of the liquid surface, M_i the molecular weight of i. The equilibrium vapor pressure can be expressed from the saturated vapor pressure Pi∘ (this thermodynamic property strongly depends on the temperature) using γi activity coefficient:

with x_i,s being the molar content of i at the liquid surface. If the surface content differs from the bulk composition, a transfer resistance in liquid phase must be taken into account as an additional resistance to the overall kinetics of evaporation.

The net evaporation rate can be calculated by applying the Langmuir–Knudsen law, which considers the difference between the Langmuir evaporation flux and the recondensation flux due to collisions with non-condensable molecules and with those of the metal vapor itself. A recondensation coefficient b_i is introduced to represent the fraction of evaporated atoms which recondense, leading to:

If b_i=1, the net evaporation flux falls to zero, and a thermodynamic equilibrium is established between the liquid and its vapor. This situation corresponds, for instance, to volatilization under atmospheric pressure of argon, where the main resistances to volatilization occur in the liquid or/and gas boundary layers. Conversely, if the recondensation coefficient b_i is zero, the net flux is equal to the Langmuir flux, corresponding to free transport of the vapor atoms. A former experimental and numerical study [4] has proved that a furnace pressure lower than 1 Pa guaranties a recondensation coefficient much lower than 1 and accordingly we will consider the Langmuir’s law as the volatilization law in the vacuum melting processes.

Few studies have investigated the evaporation rate of Al in Ti64 alloy during EBM process. Takagi [5] made the calculation of the Al activity coefficient from the depletion of Al content in a very small liquid bath (100 g) heated by EB and obtained values in the range between 0.0495 and 0.0543 at 1,970 °C, revealing a strong negative deviation from Raoult law. The authors demonstrated that the evaporation takes place from a well-mixed pool of uniform composition (negligible mass transfer resistance within the liquid pool). Powell et al. [6] used a 310 kW EB pilot furnace to estimate activity coefficient and found a value equal to 0.063 at bath temperature between 1,670 and 2,150 °C. Semiatin et al. [7] discussed the assumption of interface-reaction-controlled kinetics making the Langmuir evaporation the only driving force. In contradiction with the authors mentioned above, their work aims to make clear that the diffusion resistance in a liquid bath heated by EB can play a dominant role on the overall evaporation rate. Other literature, such as in Isawa et al. [8] studying Al evaporation behavior in an electron beam cold hearth remelting have taken the activity coefficient to be γ_Al=0.028 to reasonably predict aluminum behavior. In addition to experimental-based studies, the literature shows some attempts to calculate the activity coefficient of Al in Ti64 in liquid phase at high temperature from thermodynamic databases. Hence, using Kohler’s ternary solution model and Miedema’s model, formula for calculating the activity coefficient of elements in ternary alloys has been introduced by Yan et al. [9]. The calculated activity coefficient in Ti64 alloy was found equal to 0.1179 at 1,800 °C. Ivanchenko et al. [10] have also determined the activity coefficient of Al by theoretical calculation using the COST database and give the value as 0.30 at 1,800 °C.

Since certain doubts remain about the driving mechanisms of evaporation and since most of the activity coefficients values for alloying elements in Ti alloys are unknown, an accurate experimental procedure using a laboratory EBM furnace has been conducted with the objective to carefully measure the volatilization losses and to deduce the activity coefficients in liquid phase at a high temperature (1,860 °C), corresponding to the temperature range encountered in most of the vacuum melting processes. The first application has been performed to aluminum element in Ti64 and the obtained value is then compared to the literature data available.

Experimental procedure

Set of experiments was conducted in a 100 kW laboratory Electron Beam Melting furnace (ALD – Lab100) shown in Figure 1. The 100 kW EB gun was used at powers between 4 kW and 16 kW with constant beam voltage of 40 kV. The beam path was controlled by the Escosys pilot program, which allows automatic control of beam displacement, as well as a choice of beam pattern shape, path, size, resolution of pattern, and frequency. FLIR X6540SC infrared camera with a wavelength of 2–5 μm was positioned at the top side of the furnace to ensure that a homogeneous temperature was achieved across the surface of the liquid bath over time. The thermal camera temperature was calibrated with the temperature findings of a two wavelengths pyrometer and the appropriate emissivity of 0.23 was used at the wavelength of 5 μm. This value matches well with the emissivity measured by Rai et al. [11].

Figure 1:

The 100 kW electron beam melting furnace.

A roughly 1 kg of Ti64 was put in a semi-hemispherical water cooled copper crucible (diameter: 12.7 cm, depth: 4 cm) as shown in Figure 2. With the aim of applying a heat power distribution as homogenous as possible on a disk surface, beam condition was set as follow: 80 Hz of frequency with a 512 individual spots per scan pattern.

Figure 2:

Schematic of the water cooled crucible.

An original device to collect and condensate the metallic vapor was set up and is shown in Figure 3. Its design allows simultaneous collection of the evaporating elements at three different angles and two different distances from center of the liquid pool surface. After testing different materials, Si wafer was chosen for gathering the evaporated elements. There are two different positions of the device as close and open positions. Before exposure time, it was in the close position to avoid any deposition of evaporated elements on the substrate. The device was on the open position during exposure time (60 s) to collect the evaporating elements on the Si wafers.

Figure 3:

Device for collecting the metallic vapor. (a) Schematic the device for deposition in open position. (b) Location of the 6 Si wafers. r_sphere=20 or 30 cm θ=70° (H); 50° (M); 30° (L).

Each experiment is composed of three steps, reported in Figure 4. The button-shaped specimen was first heated at 0.07~0.09 A of beam current until the pressure in the furnace reached 5.10⁻⁵ mbar (0.005 Pa) (Step 1-Heating) leaving the sample surface free of any pollution and a cleaner residual atmosphere (degassing). Then the button was melted at 0.2 A of beam current (Step 2-Melting). Melting time was 4 min for every experiment. Finally beam current was increased to 0.4 A (P_EB=16 kW) and the melt was kept for 4 min (Step 3–Evaporation) to reach a thermal steady state, according to the constant outlet-inlet temperature difference of the cooling water as shown in Figure 4. Then surface temperature measurements by both pyrometer and infrared camera were carried out within 20 s. After temperature recording, the exposure experiment was conducted for 60 s (Step 3-Evaporation). Beam was switched off after exposure. After cooling down for 2 h, vacuum was broken and bottom and deposit substrates were removed.

Figure 4:

Three steps of the experimental procedure, beam current and difference of outlet-inlet temperature of the cooling water with time.

Experimental results

Three experiments have been successfully performed for the Ti64 alloy, where measurements of the bath temperature, weight and composition of the deposition layers, and variation of the liquid composition have been achieved.

Temperature and liquid pool shape measurements

Since the electron beam technology ensures reproducible heating conditions, the surface temperature of the pool remains the same for any trials. Measured temperature profile is plotted In Figure 5, it shows that the temperature can be considered as uniform up to 4.0 cm from center of the button (mean temperature is 1,860 °C), then it falls down due to the cooling at the edge. After cooling the button was cut in half and polished revealing the solidification front (shown in red in Figure 5). With the aim of reconstructing the 3D shape of the liquid pool, a bottom was sliced into 6 sections and polished. The solidification lines were merged thanks to SolidWorks software and the volume of the liquid pool was estimated to be equal to 100 cm³.

Figure 5:

Liquid pool profile (red line) in a center plane of the button (left) and temperature profile measured with the thermocamera (right).

Deposit layer on the Si wafer

The composition and the weight of the deposit layer are in need for the calculation of the mass flux density of condensation. An essential prerequisite is a well adhesion of the metallic evaporating atoms on the substrate. Among all the experiment performed, we concluded that the wafer positioned at 20 cm from the liquid bath cannot be selected because of an irregular and bumpy as well as brittle layer. On the contrary, most of the Si wafers at 30 cm from the pool surface shown perfectly flat mirror-like layer (see Figure 6). Depending on the θ angle, the thickness of the deposition layer range between 1 and 2 μm. An example of SEM image of the cross section of the layer is given in Figure 6.

Figure 6:

Top view of a Si wafer after deposition (left) and SEM image of the cross section of the deposition layer at 30L location (right).

The weight of deposition layers mdep was determined using two different methods. First, mass evolution of Si wafer before and after exposure experiment was measured with a high accuracy weight balance. Second, the deposition layer was dissolved into an (HCl, HNO₃) acid solution, the metallic elements were analyzed by ICP and the weight and the chemical composition of deposition layer were then deduced. ICP analysis confirms that the layer is composed of Ti and Al without any traceable amount of V. Although the measured (weight balance) and calculated (ICP) weights match well, the ICP analysis turned out to be the most suitable choice for accurate and reliable assessment of the weight change, because absorption of humidity can introduce errors in mass balance measurement.

The mass flux density of Al condensation φAl, dep on the Si wafer is then calculated by:

(4)φAl, dep(θ,rsphere)=mdepωAl, depSwafertdep

with tdep=60s, m_dep and ω_Al,dep the weight and the Al content of the deposit, and S_wafer the surface of the silicon wafer.

Table 1 sums up the analysis results of the three performed experiments.

Table 1:

Composition/weight of the deposition layers and deposition rate of Al.

Experiment no.	Location	Analysis method			φAl, dep(θ) (kg/m2/s)
		ICP
		Ti (mg)	Al (mg)	Total (Ti+Al)
Ti64-17	30L	1.480	1.344	2.824	4.42×10−5
	30M	3.392	2.744	6.136	9.03×10−5
	30H	5.282	3.892	9.174	1.28×10−4
Ti64-19	30L	1.381	1.257	2.638	4.14×10−5
	30M	3.154	2.315	5.469	7.62×10−5
Ti64-20	30L	1.652	1.393	3.045	4.58×10−5
	30M	3.733	2.875	6.608	9.46×10−5

Variation of the composition of the liquid bath

Liquid bath composition has been analyzed in several locations before (for two experiments in which the EB was switched off before evaporation collection (step 3)) and after vapor exposition step by Glow Discharge Optical Emission Spectrometry, GDOES accurately calibrated to Ti64 alloy. An example of chemical analysis within the bath is presented in Figure 7, which emphasizes the excellent homogeneity of Al content after solidification.

Figure 7:

GDOES analysis at 6 locations within the Ti64-20 bath.

The mean value of Al content within the liquid pool has been calculated for each experiment and the results are reported in Table 2.

Table 2:

Mean Al content of the liquid bath.

	# Experiment	Mean Al wt%	Averaged Al wt%
Before exposure	Ti64-8	3.77	3.80
	Ti64-10	3.84
After exposure	Ti64-17	3.52	3.36
	Ti64-19	3.27
	Ti64-20	3.29

The averaged values were used as a target for numerical simulation, they are 3.80 wt% (x_Al=0.0657, molar content) and 3.36 wt% (x_Al=0.0582) before and after evaporation step respectively.

Discussion

In order to estimate the Al activity coefficient two different approaches have been followed. The first method is based on the deposition rate of Al on the wafers according to three different angles whereas the second approach relies on the depletion of aluminum in the liquid pool.

Deposition rate on Si wafers

Several authors have studied the angular distribution of atomic flux emitted by a point source of metallic vapor [12, 13]. More recently, Chaleix [14] achieved accurate measurements of copper, titanium and aluminum evaporated by EB and drew the normalized distribution of deposition rate according to the law:

(5)φAl, dep(θ)=φAl, dep°cosn(π2−θ)

with n an exponent to be adjusted, and φAl, dep∘ the flux density above the liquid bath (θ=90°), usually not measured because of the EB path. The value n=2 gives the best fit of the experimental distribution as it is shown in Figure 8 in polar coordinates.

Figure 8:

Experimental distribution of the Al deposition rate in polar coordinates and its fit with n=2.

The total mass flux of evaporation ϕAl is easily calculated by integration of the flux density onto the evaporation surface (half sphere) at r_sphere:

(6)ϕAl=∫∫∑φAl, depdS=∫0π/22πrsphere2φAl, dep(θ).sinθdθ

After integration, we obtain:

(7)ϕAl=2πrsphere2n+1φAl, dep∘(kgAl/s)

Moreover the flux of evaporation is emitted by the bath surface according to the Langmuir law (1):

(8)ϕAl=γAlxAl, sPAl∘MAl2πRTsπrbath2

Equations (7) and (8) lead to an expression of the activity coefficient:

(9)γAl=2n+1rsphererbath2φAl, dep∘2πRTsxAl, sPAl∘MAl

with φAl, dep∘=φAl, dep(θ)cosnπ2−θ and n =2

In eq. (9), the saturated vapor pressure of Al has been calculated according to the law given in Reference Book [15] and used in particular by Powell [6]:

log10PAl∘=−16450T−1.023log10T+14.48T in\ Kelvin\ and\ P∘in\ Pa

Experimental measurements of φAl, dep(θ) lead to the assessment of the activity coefficient of Al in liquid Ti64 (Table 3), with a mean value γAl‾=0.044 and a standard deviation equal to 0.008.

Table 3:

Calculation of γAl in Ti64 according eq. 9.

Experiment no.	Location	φAl, dep(θ) (kg/m2/s)	γAl
Ti64-17	30L	4.42×10−5	0.046
	30M	9.03×10−5	0.048
	30H	1.28×10−4	0.061
Ti64-19	30L	4.14×10−5	0.036
	30M	7.62×10−5	0.034
Ti64-20	30L	4.58×10−5	0.042
	30M	9.46×10−5	0.046

Depletion of Al in the liquid pool

This approach requires to simulate the hydrodynamic-thermal and solute behavior of the button during melting and evaporation, and to estimate the activity coefficient leading to the best fit between the calculated and the measured depletion of Al in the bath.

To simulate the evaporation of the alloying elements in electron beam furnace, the numerical model has to address the following phenomena:

1. Momentum and heat transfer inside the Ti bottom

2. Marangoni effect due to high thermal gradient on the liquid pool surface

3. Electron beam energy deposition at the top surface of the bottom

4. Solidification of the alloy

5. Turbulence development in the liquid pool

6. Heat loss through the radiation and cooling circuit of the crucible

7. Mass transfer in the liquid pool

8. vaporation of matrix and alloying elements from the top surface of the liquid pool according to the Langmuir law

All these phenomena have been modeled and solved using a Finite-Volume method implemented within OpenFOAM® open-source framework. Phase change of the material is described using variable porosity and a drag term is introduced in the momentum equation using Darcy law. Permeability of the matter is estimated with Kozeny–Carman equation. To describe turbulence, the standard k-epsilon model was modified to include damping terms, appearing after averaging of Darcy term in the momentum equation. Radiative heat loss is estimated using grey-body model with a constant emissivity. Cooling of the crucible is modeled using simple 1D model with a constant heat transfer coefficient and assumption of reducing contact quality toward the bottom. Electron beam energy is uniformly distributed over beam patterns according to the experimental conditions. The mass transfer inside the liquid pool is described using standard convection-diffusion equation. Diffusivity of aluminum within titanium is calculated using Stokes–Einstein–Sutherland equation. Eddy diffusivity is determined from turbulent viscosity and turbulent Schmidt number, which is set equal to 1. The simulations were performed in a transient 2D formulation since all the operating conditions and geometry are axisymmetric. Further details of the model and validation are presented in Ref. [16].

Figure 9 presents the main features of the hydrodynamics and thermal behavior of the button when the steady state is reached i. e. after 4 min of melting (step 3). It clearly shows a well-mixed liquid pool with maximum fluid flow limited to the surface layer where temperature gradients promote Marangoni stresses. The calculated volume of the liquid pool which is equal to 96 cm³ and its shape agree well with the experimental measurements (see Figure 5, experimental pool volume was estimated to 100 cm³). The temperature profile matches satisfactorily with the one measured by thermocamera having uniform temperature in the central region of the button surface up to 4.5 cm and then a sharp drop in temperature. However discrepancies can be observed at the edge with a relatively weak assessment of the shape of the pool and accurate location of the temperature drop. It can be partly explained by the deformation of the free surface driven by capillary forces and experimentally observed in this region, which is not modeled so far.

Figure 9:

Velocity and streamlines distribution in the liquid pool (left) and calculated surface temperature profile.

After matching the experimental value of the mean Al contents in the pool after 60 s of evaporation with calculated (from x°_Al=0.0657 to xAl60=0.0582) an activity coefficient γAl=0.0495 has been obtained. The simulation of Al transport highlights a good mixing in the bulk of the liquid pool, but a more detailed analysis reveals weak solute gradients near the liquid surface at mid-radius. In this area the relatively weak fluid flow do not fully allow the transport of the Al flux evaporated on the liquid surface. The additional resistance in the liquid phase can be easily estimated from the simulation of evaporation over a perfectly stirred bath, and a relative value equal to 3 % of the interface reaction resistance was found. The rate-controlling influence of solute transport in the melt to the liquid surface can be considered as weak in the electron beam button melting.

Figure 10 (left) draws the relative aluminum depletion after 60 s of exposure time along vertical z lines at regular r positions inside the button. Location of the line corresponds to location inside the button, while shift in x-direction corresponds to percentage of Al losses (1−xAl60/xAl0). The Al content into the bulk of the pool appears effectively uniform, and weak Al gradient in the vicinity of the liquid surface at mid-radius can be noticed.

Figure 10:

Aluminum depletion after 60 s of exposure time along vertical lines at regular r positions (left) and mean molar content of Al versus time (right).

On the right-hand side of Figure 10 the two experimental values of Al content before and after exposition time have been reported with red circle markers. The calculated evolution of the mean Al content in the pool shows a roughly linear variation in this small range of variation (10 %) and confirms that the activity coefficient (γAl=0.0495) allows us to simulate the measured Al depletion.

Conclusion

The kinetics of volatilization of titanium alloys under vacuum has been studied with a first application to Ti64, one of the most common grades. The study focusses on the evaporation of aluminum and the assessment of its activity coefficient at high temperature in liquid phase. Experiments were performed in a laboratory electron beam furnace where the metallic liquid surface remains free of pollution thanks to a vacuum residual pressure lower than 10⁻² Pa.

Two different approaches for the estimation of activity coefficient have been pursued. The first innovative method is based on the deposition rate of Al on Si wafers located at different angles. We found that a deposition according to a cos2π/2−θ law describes well the experimental distribution of the weight of the deposition layer. The second approach relies on the depletion of aluminum in the liquid pool at two separate times of the volatilization process. This method requires an excellent reproducibility of the experiments, and in the future, deep sampling in the liquid pool has been planned to be performed so as to measure the depletion for the same experimental trial.

Both approaches provide values of the Al activity coefficient at T=1,860 °C in a fairly narrow range [0.044–0.0495], in good agreement with the range reported in the literature [0.028–0.065]. Furthermore numerical simulation of the Al behavior in the liquid pool reveals (in the specific case of electron beam button melting) a weak transport resistance in the surface boundary layer.

The two methods will be applied to other grades of Ti alloys where the kinetics of evaporation has not been addressed so far and where the activity coefficients are unknown. A study of the influence of the temperature of the bath surface could be also investigated.