An Improved Theoretical Model for A-TIG Welding Based on Surface Phase Transition and Reversed Marangoni Flow

Abstract

It is experimentally shown that a thin layer of silica flux leads to an increased depth of weld penetration during activated TIG (=A-TIG) welding of Armco iron. The oxygen-content is found higher in the solidified weld metal and it is linked to the increased depth of penetration through the reversed Marangoni convection. It is theoretically shown for the first time that the basic reason of the reversed Marangoni convection is the phenomenon called “surface phase transition” (SPT), leading to the formation of a nano-thin FeO layer on the surface of liquid iron. It is shown that the ratio of dissolved oxygen in liquid iron to the O-content of the silica flux is determined by the wettability of silica particles by liquid iron. It is theoretically shown that when the silica flux surface density is higher than 15 µg/mm², reversed Marangoni flow will take place along more than 50 pct of the melted surface. Comparing the SPT line with the dissociation curves of a number of oxides, they can be positioned in the following order of their ability to serve as a flux for A-TIG welding of steel: anatase-TiO₂ (best)-rutile-TiO₂ (very good)-silica-SiO₂ (good)-alumina-Al₂O₃ (does not work). Anatase (and partly rutile) are self-regulating fluxes, as they provide at any temperature just as much dissolved oxygen as needed for the reversed Marangoni convection, and not more. On the other hand, oxygen can be over-dosed if silica, and other, less stable oxides (such as iron oxides) are used.

Appendices

Appendix A: The Thermodynamic Limit of the Dissolved Oxygen Content in Liquid Iron from Silica Dissociation

Let us consider the dissociation of silica in liquid iron according to the following exchange reaction:

$$ {\text{SiO}}_{2} ({\text{s}}) + 2 \cdot {\text{Fe}}({\text{l}}) = \left[ {\text{Si}} \right] + 2 \cdot [{\text{FeO}}] $$

(A1)

where [i] means that component i is dissolved in liquid iron. We consider the equilibrium of almost pure liquid Fe (of unit activity) and pure solid silica (of unit activity) with the liquid iron consisting of the approximately stoichiometric amounts of dissolved Si and FeO. Thus, the stoichiometry of reaction [A1] dictates the following relationship: $x_{\text{Si}} \cong x_{\text{FeO}} /2$. Then, the equilibrium constant of Reaction [A1] is written as:

$$ K \cong 0.5 \cdot x_{\text{FeO}}^{ 3} \cdot \gamma_{\text{FeO}}^{2} \cdot \gamma_{\text{Si}} $$

(A2)

with x _i and γ _i being the mole fraction and activity coefficient of component i. From standard thermodynamic data the equilibrium constant of Reaction [A1] follows from[69]:

$$ \ln K \cong 10.411 - \frac{51513}{T} $$

(A3)

The activity coefficient of Si in infinitely diluted solution of liquid Fe is known from assessed thermodynamic data of[70–72] and is written in the form[73]:

$$ \ln \gamma_{\text{Si}}^{\infty } \cong \frac{ - 31775}{T} \cdot \exp \left( { - \frac{T}{1735}} \right) $$

(A4)

The performance of equation type Eq. [A4] has been proven on different high temperature systems.[74–77] This equation is preferred to other equations at high temperatures as it obeys the 4th law of thermodynamics.[78]

Using data on phase diagram and solubility of the Fe-O system,[70,79] the following approximated equation is obtained in the same formalism as Eq. [A4]:

$$ \ln \gamma_{\text{FeO}}^{\infty } \cong \frac{16917}{T} \cdot \exp \left( { - \frac{T}{2991}} \right) $$

(A5)

Substituting Eqs. [A3–A5] into Eq. [A2], the equilibrium solubility of oxygen C _O (mass ppm) as a function of temperature is obtained as:

$$ \ln C_{\text{O}} ({\text{ppm}}) = \,16.27 - \frac{17171}{T} - \frac{11278}{T} \cdot \exp \left( { - \frac{T}{2991}} \right) + \frac{10592}{T} \cdot \exp \left( { - \frac{T}{1735}} \right) $$

(A6)

When Eq. [A6] was written, the relationship $C_{\text{O}} = 2.87 \cdot 10^{5} \cdot x_{\text{FeO}}$ was also taken into account, being valid in diluted solutions of O in almost pure liquid Fe. At the average temperature of the liquid iron of 2260 K (1987 °C) Eq. [A6] provides the value of C_O = 2000 ppm, being higher by one order of magnitude compared to our measured values (see Table II: 153 … 203 ppm). Thus, thermodynamic properties of silica do not limit the dissolution of oxygen in liquid iron under the conditions of our experiments at $\xi > 0.2$.

Appendix B: The Algorithm to Calculate the SPT Line and Surface Tension of the Liquid Fe-FeO Alloy

Let us consider a binary liquid alloy Fe-FeO alloy at a given temperature (T) and at a given bulk mole fraction of the component FeO (x _FeO). According to Butler,[60] the surface of this liquid solution will be in equilibrium with its bulk, if the partial surface tension values of the two components equal:

$$ \sigma_{\text{Fe}} = \sigma_{\text{FeO}} $$

(B1)

The partial surface tension value of component i (i = Fe and/or FeO) has been expressed as[60–64]:

$$ \sigma_{i} = \sigma_{i}^{\rm o} + \frac{R \cdot T}{{\omega_{i} }} \cdot \ln \frac{{x_{i}^{*} }}{{x_{i} }} + \frac{{\beta \cdot \Updelta G_{i}^{\text{E}} (x_{i}^{*} ) - \Updelta G_{i}^{\text{E}} (x_{i} )}}{{\omega_{i} }} $$

(B2)

where $\sigma_{i}^{\text{o}}$ is the surface tension of pure component i (J/m²) being only the function of temperature, R is the universal gas constant (8.3145 J/mol K), β is the ratio of surface to bulk coordination numbers of the atoms, ω_i is the molar surface area of component i (m²/mol):

$$ \omega_{i} = f \cdot V_{i}^{2/3} \cdot N_{\text{Av}}^{1/3} $$

(B3)

where f is a dimensionless geometrical constant, V _i is the molar volume of component i (m³/mol), N _Av is the Avogadro number, x _i and $x_{i}^{*}$ are the mole fractions of component i in the bulk and in the surface, respectively. The partial excess Gibbs energy of component i ($\Updelta G_{i}^{\text{E}}$) is described by the simplest regular solution model:

$$ \Updelta G_{i}^{\text{E}} = \Upomega \cdot (1 - x_{i} )^{2} $$

(B4)

where Ω is the interaction energy (J/mol), described using Eq. [A5] and the relationship: $\Upomega = R \cdot T \cdot \ln \gamma_{\text{FeO}}^{\infty }$:

$$ \Upomega \cong 140,656 \cdot \exp \left( { - \frac{T}{2991}} \right) $$

(B5)

Physical properties of pure liquid Fe and FeO phases needed for calculations are given in Table B1.[80,81] Other model parameters are selected as: β = 9/11, f = 1.00.[82]

Table B1 Physical Properties of Pure Fe and FeO Liquids[80,81]

In the course of model calculations, first the SPT line for the Fe-FeO system is calculated taking into account the material balance equations in both bulk and surface ($x_{\text{Fe}} + x_{\text{FeO}} = 1$ and $x_{\text{Fe}}^{*} + x_{\text{FeO}}^{*} = 1$). At each temperature the bulk x _FeO value is searched for, at which the Butler Eq. [B1] has 3 solutions at 3 different FeO surface concentrations, and two of them (at the lowest and highest FeO surface concentrations) provide the same values for surface tension, being somewhat lower compared to the 3rd mathematical solution (for more details see[63,64]). Then, both surface tension and its T-coefficient are calculated as a function of composition and temperature. All calculations are performed numerically, by a home-made software. The calculated surface tension values are in good agreement with the known experimental[83–87] and previously calculated[88,89] values.

Appendix C: Solubility of Oxygen in Liquid Iron Due to the Dissociation of Al₂O₃

The reaction of dissociation:

$$ {\text{Al}}_{ 2} {\text{O}}_{ 3} ( {\text{s,l)}} + 3{\text{Fe(l)}} = 2 \cdot \left[ {\text{Al}} \right] + 3 \cdot \left[ {\text{FeO}} \right] $$

(C1)

The equilibrium constant equals[69]:

$$ \ln K = 17.963 - \frac{106966}{T} $$

(C2)

The activity coefficient of Al in liquid Fe equals[73,90]:

$$ \ln \gamma_{\text{Al}}^{\infty } \cong \frac{ - 7200}{T} \cdot \exp \left( { - \frac{T}{4700}} \right) $$

(C3)

The equilibrium constant, supposing both Al and O are dissolved via reaction [C1]:

$$ K = \frac{4}{9} \cdot x_{\text{FeO}}^{5} \cdot \gamma_{\text{Al}}^{2} \cdot \gamma_{\text{FeO}}^{3} $$

(C4)

Substituting Eqs. [A5, C2, C3] into Eq. [C4], the equilibrium mole fraction of FeO in liquid iron can be expressed. Using the relationship $C_{\text{O}} = 2.87 \cdot 10^{5} \cdot x_{\text{FeO}}$, the following final equation is obtained:

$$ \ln C_{\text{O}} ({\text{ppm}}) = \,16.32 - \frac{21393}{T} + \frac{2880}{T} \cdot \exp \left( { - \frac{T}{4700}} \right) - \frac{10150}{T} \cdot \exp \left( { - \frac{T}{2991}} \right) $$

(C5)

Appendix D: Solubility of O in Liquid Iron Due to the Dissociation of TiO₂

The reaction of dissociation:

$$ {\text{TiO}}_{2} ({\text{s,l}}) + 2 \cdot {\text{Fe(l)}} = \left[ {\text{Ti}} \right] + 2 \cdot \left[ {\text{FeO}} \right] $$

(D1)

The equilibrium constant for rutile equals[69]:

$$ \ln K = 6.8064 - \frac{48640}{T} $$

(D2)

The activity coefficient of Ti in liquid Fe equals[73,90]:

$$ \ln \gamma_{\text{Ti}}^{\infty } \cong \frac{ - 8700}{T} \cdot \exp \left( { - \frac{T}{8000}} \right) $$

(D3)

The equilibrium constant, supposing both Ti and O are dissolved via reaction [D1]:

$$ K = \frac{1}{2} \cdot x_{\text{FeO}}^{3} \cdot \gamma_{\text{Ti}} \cdot \gamma_{\text{FeO}}^{2} $$

(D4)

Substituting Eqs. [A5, D2, D3] into Eq. [D4], the equilibrium mole fraction of FeO in liquid iron can be expressed. Using the relationship $C_{\rm O} = 2.87 \cdot 10^{5} \cdot x_{\text{FeO}}$, the following final equation is obtained for rutile:

$$ \ln C_{\text{O}} ({\text{ppm}}) = 14.43 - \frac{16213}{T} + \frac{2900}{T} \cdot \exp \left( { - \frac{T}{8000}} \right) - \frac{11278}{T} \cdot \exp \left( { - \frac{T}{2991}} \right) $$

(D5)

For another form of TiO₂ (anatase) the equilibrium constant equals[69]:

$$ \ln K = 8,975 - \frac{51979}{T} $$

(D6)

Substituting Eqs. [A5, D6, D3] and $C_{\rm O} = 2.87 \cdot 10^{5} \cdot x_{\text{FeO}}$ into Eq. [D4], the following final equation is obtained for anatase:

$$ \ln C_{\text{O}} ({\text{ppm}}) =\, 15.15 - \frac{17326}{T} + \frac{2900}{T} \cdot \exp \left( { - \frac{T}{8000}} \right) - \frac{11278}{T} \cdot \exp \left( { - \frac{T}{2991}} \right) $$

(D7)

Appendix E: Solubility of Oxygen in Liquid Iron Due to Dissociation of Fe₂O₃

The reaction of dissociation:

$$ {\text{Fe}}_{ 2} {\text{O}}_{ 3} ( {\text{s,l)}} + 3{\text{Fe(l)}} = 3 \cdot \left[ {\text{FeO}} \right] $$

(E1)

The equilibrium constant equals[69]:

$$ \ln K = 7.976 - \frac{1110}{T} $$

(E2)

The equilibrium constant of reaction [E1]:

$$ K = x_{\text{FeO}}^{3} \cdot \gamma_{\text{FeO}}^{3} $$

(E3)

Substituting Eqs. [A5, E2] into Eq. [E3], the equilibrium mole fraction of FeO in liquid iron can be expressed. Using the relationship $C_{\text{O}} = 2.87 \cdot 10^{5} \cdot x_{\text{FeO}}$, the following final equation is obtained:

$$ \ln C_{\text{O}} ({\text{ppm}}) = 15.226 - \frac{370}{T} - \frac{16917}{T} \cdot \exp \left( { - \frac{T}{2991}} \right) $$

(E4)