**1. Introduction**

Titanium is a common microalloy addition to steels. It can be used to inhibit grain growth, reduce the incidence of transverse cracking in niobium-containing steels production, stabilize the alloy against sensitization to intergranular corrosion, and improve the service performance [1–4]. However, a low titanium content is demanded for special kinds of steel production, such as in high-strength tire cord steel, to enhance drawing and twisting performances.

As a product with superior quality to wire rods, tire cord steel is mainly used in radial ply tires. Before it is made, the steel wire is drawn from 5.5 mm to 0.15 mm in diameter and subjected to cyclic stress in the drawing and twisting process. Therefore, breakage of steel wire during fabrication is a crucial issue. This filament break is especially sensitive with the existence of angular and non-deformable Ti inclusions, such as titanium nitride (TiN) or titanium carbonitride (Ti(CN)) [5–9]. This causes a decrease in fatigue performance and can seriously affect traffic safety.

Therefore, the issue of the control of titanium content has received considerable critical attention. To control the titanium content during steel production, it is essential to study the titanium distribution ratio between steel and slag. To date, there has been limited theoretical and experimental studies implemented on the titanium distribution behavior in slags; acquiring relevant parameters at elevated temperatures between steel and slag is arduous and costly. It is quite essential to establish

a thermodynamic model for calculating the titanium distribution ratio between steel and slag. The ion–molecule coexistence theory (IMCT) has been efficaciously applied to describe phosphate capacity, manganese distribution, sulfide capacity, and so on, as shown in Table 1 [10–23]. In the IMCT, the defined mass action–concentration (MAC) is consistent with the classical concept of activity in the slag.

**Table 1.** Applications of the ion–molecule coexistence theory (IMCT) model during ironmaking and steelmaking processes.


To improve the application domain of IMCT, in this paper, a titanium distribution ratio model of CaO–SiO2–Al2O3–MgO–FeO–MnO–TiO2 slags was built based on the IMCT, combined with industrial measurements. From the results, the titanium distribution behavior during ladle furnace (LF) refining in high-strength tire cord steel production is further revealed.
