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Dissolution Behavior of TiC Heterogeneous Nucleation Site Particles in Ti–6Al–4V in Electrostatic Levitation Method

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Clarifying the dissolution behavior of titanium carbide (TiC) during heating is crucial for establishing suitable heating conditions for prior-β grain refinement of Ti–6Al–4V induced by TiC particles. This study aims to reveal the effects of heating in the electrostatic levitation (ESL) experiments on the dissolution of TiC by establishing the dissolution kinetics of TiC in liquid Ti–6Al–4V. The sintered mixture of Ti–6Al–4V powder and TiC particles was melted and solidified in ESL. The integral value of heating, I (T, t), with the temperature and heating time serves as a valuable index of the amount of heating. The amount of residual TiC, MR, decreases exponentially with the increase of I (T, t), indicating the symmetry of the Johnson–Mehl–Avrami–Kolmogorov equation. A phase field simulation of TiC dissolution revealed that the dissolution time increases in proportion to the 1.8th power of the initial particle diameter. Additionally, the value of MR calculated using the dissolution equation based on the diffusion theory was consistent with the results of the ESL experiments at a diffusion coefficient, D, of about 1 – 3 × 10−11 m2 s−1, which is an intermediate value of D in multiple diffusion forms. The dissolution model also estimates the number of TiC particles which work as the nucleation sites (Active-TiC).

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A TiC :

Area ratio of residual TiC (area pct)

A Ti-rich :

Area ratio of Ti-rich TiC (area pct)

a SL :

Anisotropy of the solid–liquid interface (m2)

B 1 :

Fitting parameter in Eq. [2] (s m−n)

B 2 :

Fitting parameter in Eq. [8] (mass pct)

B 3 :

Fitting parameter in Eq. [8] (K−2s1)

b :

Coefficient in the first term in Eq. [A1] (m−1)

C :

Concentration of carbon (mol pct)

C L :

Concentration of carbon in a liquid phase (mol pct)

C S :

Concentration of carbon in a solid phase (mol pct)

C I :

Concentration of carbon in a solid–liquid interface (mol pct)

\(D\) :

Diffusion coefficient (m2 s1)

D GB :

Diffusion coefficient at a grain boundary (m2 s1)

D L :

Diffusion coefficient in a liquid phase (m2 s1)

D S :

Diffusion coefficient in a solid phase (m2 s1)

d :

Diameter of carbon (m)

d 0 :

Initial diameter of carbon (m)

k :

Coefficient of concentration (−)

M R :

Amount of residual TiC (mass pct)

m C1 :

Mass of carbon in TiC (kg)

m C2 :

Mass of carbon in Ti-rich TiC (kg)

N a rea :

Number of grains per area (mm−2)

N act :

Number of Active-TiC

N R :

Number of residual TiC

N line :

Number of grains per length (mm−1)

N 2D :

Number of prior-β grains in a cross section of a sample

N 3D :

Number of prior-β grains in a sample

n :

Fitting parameter in Eq. [2] (−)

r :

Radius of TiC (m)

r 0 :

Initial radius of TiC (m)

R 2 :

Coefficients of determination (−)

R act :

Nucleation rate (pct)

T :

Temperature of a sample (K)

T M :

Liquidus temperature (K)

T β :

β-transus temperature (K)

t :

Heating time of TiC particles in liquid titanium or Ti–6Al–4V (s)

t C :

Converted a heating time from the value of TM and I (T, t) (s)

t d :

Dissolution time (s)

t M :

Measurement time of a sample temperature by pyrometer (s)

I (T, t):

Integral value of heating (K2 s)

V A :

Volume ratio of added TiC (vol pct)

V R :

Volume ratio of residual TiC (vol pct)

v smp :

Volume of a sample (m3)

W C :

Atomic weight of carbon (g mol1)

W Ti :

Atomic weight of titanium (g mol1)

x :

Distance from a solid phase to a liquid phase (m)

x C :

Distance from the center of carbon (m)

ΔG :

Volumetric driving force (J m3)

ΔT :

Degree of undercooling (K)

η :

Thickness of a solid–liquid interface (m)


Phase field function (−)

μ SL :

Interface mobility between the solid phase of carbon and liquid phase of titanium (m4 J1 s1)

ρ TiC :

Density of TiC (kg m3)

ρ Ti64 :

Density of Ti–6Al–4V (kg m3)

ρ Ti-rich :

Density of Ti-rich TiC (Ti0.67C0.33) (kg m3)

σ SL :

Anisotropic interfacial energy of the solid–liquid interface (J m2)


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This study was performed under the preliminary experiments of Hetero-3D mission, using Japanese Experiment Module, “Kibo,” on the ISS. This work consisted the result of using research equipment (G1001, G1011, G1012, G1017, G1020, G1054, and G1055) with the help of the Joint Research Center for Environmentally Conscious Technologies in Materials Science, Kagami Memorial Research Institute for Materials Science and Technology, Waseda University (JPMXP0723833151). The work done at Nagoya Institute of Technology (NITech) was supported by Adaptable and Seamless Technology Transfer Program through Target-driven R&D (A-STEP) from Japan Science and Technology Agency (JST) Grant Number JPMJTR23R3. Furthermore, we would like to thank Kimura Foundry Co., Ltd. for the financial support.

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Correspondence to Yuji Mabuchi.

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The interfacial movement of solid carbon in liquid titanium was calculated using a phase field software MICRESS® (Version 7.01, Access e.V.) to simulate the dissolution behavior of TiC (Section II–D). In the phase field simulation, the interface movement can be analyzed continuously by using the phase field function, \(\varphi \). In this study, \(\varphi \) was defined as the solid phase fraction, with \(\varphi \) = 1 indicating 100 pct solid phase and \(\varphi \) = 0 indicating 100 pct liquid phase of carbon. The phase field equation implemented in MICRESS software reads as follows[49]:

$$\frac{\partial \varphi }{\partial t}=\sum {\mu }_{{\text{SL}}}\left\{b\Delta G-{a}_{{\text{SL}}}{\sigma }_{{\text{SL}}}\right\} .$$

An interface mobility between the solid phase of carbon and the liquid phase of titanium, \({\mu }_{{\text{SL}}}\), is related to the kinetic coefficient. As shown in Eq. [A1], the distribution of \(\varphi \) was calculated so that the volumetric driving force, \(\Delta G\), decreased to a minimum value and stabilized at the earliest possible time. Generally, the solid phase changes to the liquid phase above TM because the liquid phase is stable whose \(\Delta {G}_{{\text{SL}}}\) is lower than that of the solid phase. The coefficient in the first term in Eq. [A1], \(b\), is defined as follows[49]:

$$b=\frac{\pi }{\eta }\sqrt{\varphi (1-\varphi )},$$

where \(\eta \) represents the thickness of the interface. In the second term of Eq. [A1], \({\sigma }_{{\text{SL}}}\) and \({a}_{{\text{SL}}}\) represent the anisotropic interfacial energy and anisotropy of the solid–liquid interface, respectively.

The value of \(\varphi \) in this study was calculated by coupling the differential equation of Eq. [A1] with the diffusion equation by using MICRESS®. Some parameters such as \(\Delta G\) were referred to a thermodynamic database acquired using Thermo-Calc® from the CALPHAD database. The temperature was maintained above TM of titanium. Therefore, carbon was found to be more stable in the liquid phase, leading to dissolution as shown in Section III–C.

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Mabuchi, Y., Hanada, C., Aoki, H. et al. Dissolution Behavior of TiC Heterogeneous Nucleation Site Particles in Ti–6Al–4V in Electrostatic Levitation Method. Metall Mater Trans B 55, 2467–2484 (2024).

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