Diffusion of carbon in austenite

Abstract

The concentration dependence of the diffusivity D of carbon in austenite causes complications in the kinetic analysis of various diffusion-controlled reactions that arise in steels (see, for example, Ref. 1). The existence of substantial carbon concentration gradients at the transformation interfaces involved in such reactions makes it imperative to account for the variation of D with x (where x is the mole fraction of carbon), and it has been demonstrated that, for most purposes, a weighted average diffusivity <mml:math><mml:mrow><mml:mover><mml:mi>D</mml:mi><mml:mi>¯</mml:mi></mml:mover></mml:mrow></mml:math> can adequately represent the effective diffusivity of carbon that is needed for the application of the theory of diffusion-controlled growth. Trivedi and Pound first considered this problem in detail, and obtained <disp-formula id="e1"> <label>(1)</label> <mml:math> <mml:mrow> <mml:mover> <mml:mi>D</mml:mi> <mml:mi>¯</mml:mi> </mml:mover> <mml:mo>=</mml:mo> <mml:munderover> <mml:mi>∫</mml:mi> <mml:mrow> <mml:msubsup> <mml:mi>x</mml:mi> <mml:mi>γ</mml:mi> <mml:mi>γα</mml:mi> </mml:msubsup> </mml:mrow> <mml:mrow> <mml:mover> <mml:mi>x</mml:mi> <mml:mi>¯</mml:mi> </mml:mover> </mml:mrow> </mml:munderover> <mml:mi>D</mml:mi> <mml:mtext> d</mml:mtext> <mml:mi>x</mml:mi> <mml:mo>/</mml:mo> <mml:mo>(</mml:mo> <mml:mover> <mml:mi>x</mml:mi> <mml:mi>¯</mml:mi> </mml:mover> <mml:mo>−</mml:mo> <mml:msubsup> <mml:mi>x</mml:mi> <mml:mi>γ</mml:mi> <mml:mi>γα</mml:mi> </mml:msubsup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> </disp-formula> where <mml:math><mml:mrow><mml:mover><mml:mi>x</mml:mi><mml:mi>¯</mml:mi></mml:mover></mml:mrow></mml:math> is the average carbon content of the alloy and <mml:math><mml:mrow><mml:msubsup><mml:mi>x</mml:mi><mml:mi>γ</mml:mi><mml:mi>γα</mml:mi></mml:msubsup></mml:mrow></mml:math> is the maximum permissible carbon content in the austenite at the transformation interface.