Alloying Element Partition and Growth Kinetics of Proeutectoid Ferrite in Hot-Deformed Fe-0.1C-3Mn-1.5Si Austenite

Alloying element partition and growth kinetics of proeutectoid ferrite in deformed austenite were studied in an Fe-0.1C-3Mn-1.5Si alloy. Very small ferrite particles, less than several microns in size, were formed within the austenite matrix, presumably at twin boundaries as well as at austenite grain boundaries. Scanning transmission electron microscopy–energy-dispersive X-ray (STEM-EDX) analysis revealed that Mn was depleted and Si was enriched in the particles formed at temperatures higher than 943 K (670 °C). These were compared with the calculation of local equilibrium in quaternary alloys, in which the difference in diffusivity between two substitutional alloying elements was assumed to be small compared to the difference from the carbon diffusivity in austenite. Although the growth kinetics were considerably faster than calculated under volume diffusion control, a fine dispersion of ferrite particles was readily obtained in the partition regime due to sluggish growth engendered by diffusion of Mn and Si.

Appendix

Equation of isoactivity surface of carbon in quaternary austenite

It is demonstrated that Eq. [2] represents the isoactivity surface of carbon that passes through the bulk alloy composition. To begin with, the logarithm of the activity of carbon in austenite is expanded to the first order about the austenite end of the interfacial tie-line (point b in Figure 6) as

$$ \ln a_{1} = \ln a_{1}^{\gamma } + \left. {{\frac{{\partial \ln a_{1} }}{{\partial x_{1} }}}} \right|_{b} \left( {x_{1} - x_{1}^{\gamma } } \right) + \left. {{\frac{{\partial \ln a_{1} }}{{\partial x_{2} }}}} \right|_{b} \left( {x_{2} - x_{2}^{\gamma } } \right) + \left. {{\frac{{\partial \ln a_{1} }}{{\partial x_{3} }}}} \right|_{b} \left( {x_{3} - x_{3}^{\gamma } } \right) $$

(A1)

Since this surface passes through the bulk alloy composition, i.e., a _C(o) = a _C(b), it is expressed by the equation

$$ x_{1}^{0} - x_{1}^{\gamma } = - {\frac{{\partial \ln a_{1} / \partial x_{2} }}{{\partial \ln a_{1} /\partial x_{1} }} }\left({x_{2}^{0} - x_{2}^{\gamma } } \right) - {\frac{{\partial \ln a_{1} /\partial x_{3} }}{{\partial \ln a_{1} /\partial x_{1} }} }\left( {x_{3}^{0} - x_{3}^{\gamma } } \right) $$

(A2)

when points b and o are not far from each other.

On the other hand, substitution of Eqs. [5] through [7] into Eq. [2] yields

$$ x_{1}^{\gamma } - x_{1}^{0} = \left( {x_{2}^{\gamma } - x_{2}^{0} } \right) \cdot {\frac{{D_{12}^{\gamma } }}{{D_{22}^{\gamma } - D_{11}^{\gamma } }}} + \left( {x_{3}^{\gamma } - x_{3}^{0} } \right) \cdot {\frac{{D_{13}^{\gamma } }}{{D_{33}^{\gamma } - D_{11}^{\gamma } }}} $$

(A3)

Since$D_{22}^{\gamma } < < D_{11}^{\gamma }$ and $D_{33}^{\gamma } < < D_{11}^{\gamma }$, Eq. [A3] is reduced to

$$ x_{1}^{\gamma } - x_{1}^{0} = \left( {x_{2}^{\gamma } - x_{2}^{0} } \right) \cdot \left( { - {\frac{{D_{12}^{\gamma } }}{{D_{11}^{\gamma } }}}} \right) + \left( {x_{3}^{\gamma } - x_{3}^{0} } \right) \cdot \left( { - {\frac{{D_{13}^{\gamma } }}{{D_{11}^{\gamma } }}}} \right) $$

(A4)

When solute 1 ( = carbon) is interstitial and solutes 2 ( = Mn) and 3 ( = Si) are substitutional, Brown and Kirkaldy[28] have shown that

$$ {\frac{{D_{12}^{\gamma } }}{{D_{11}^{\gamma } }}} = {\frac{{\partial \ln \mu_{1} /\partial x_{2} }}{{\partial \ln \mu_{1} /\partial x_{1} }}} = {\frac{{\partial \ln a_{1} /\partial x_{2} }}{{\partial \ln a_{1} /\partial x_{1} }}} $$

(A5)

and

$$ {\frac{{D_{13}^{\gamma } }}{{D_{11}^{\gamma } }}} = {\frac{{\partial \ln \mu_{1} /\partial x_{3} }}{{\partial \ln \mu_{1} /\partial x_{1} }}} = {\frac{{\partial \ln a_{1} /\partial x_{3} }}{{\partial \ln a_{1} /\partial x_{1} }}} $$

(A6)

hold. Hence, Eqs. [A2] and [A4] are identical.