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Phase Diagrams

Uphill Diffusion of Carbon in Fe-Si-C and Fe-Si-Mn-C Alloys

Fick's laws implicitly assume that the concentration gradient is the driving force for diffusion. If the activity gradient is of opposite sign, however, then it is possible for diffusion to take place against, or up, the concentration gradient.

One of the best-known examples of uphill diffusion was given by L. S. Darken (Trans. AIME, Vol. 180 (1949), pp. 430-438), in which two pieces of carbon steel (see Figure 1) were welded together (Weld Number 2; see Table 2, p. 431). One bar contained 3.80 wt. % Si and 0.49 wt. % C, whereas the other bar contained 0.05 wt. % Si and 0.45 wt. % C.

The carbon in the high-silicon bar was at a much greater "potential" than it would appear to be in concentration terms. After carbon was allowed to diffuse for 13 days at the temperature of 1050 °C (1323 Kelvin), most of the carbon diffused to the low-silicon iron bar. Darken selected the temperature of 1050 °C to ensure that the original ferrite transforms into austenite in the diffusion zone.

Uphill Diffusion of Carbon in Fe-Si-C Alloy

Figure 1. Uphill diffusion of carbon in the Fe-Si-C system, calculated with DICTRA, coupled with SSOL2 and MOB2 databases. Note that carbon diffuses from an austenite of carbon content of about 0.33 wt. % to an austenite of carbon content of about 0.59 wt. %. Darken concluded that the difference in silicon content (3.80 wt. % and 0.05 wt. %, respectively) was clearly responsible for the observed phenomenon of uphill diffusion.


Another well-known example of uphill diffusion given by L. S. Darken in the same paper (Trans. AIME, Vol. 180 (1949), pp. 430-438) involves a pieces of carbon steel that contained 3.80 wt. % Si (see Figure 2) and was welded together to a piece of carbon steel that contained 6.45 wt. % Mn (Weld Number 3; see Table 2, p. 431). The silicon-containing bar had 0.49 wt. % C, whereas the manganese-containing bar had 0.58 wt. % C. The carbon was allowed to diffuse for 10 days at the temperature of 1050 °C.

Uphill Diffusion of Carbon in Fe-Si-Mn-C Alloy

Figure 2. Uphill diffusion of carbon in the Fe-Si-Mn-C system, calculated with DICTRA, coupled with SSOL2 and MOB2 databases. The carbon diffuses from an austenite of carbon content of about 0.32 wt. % to an austenite of carbon content of about 0.72 wt. %. In this example, uphill diffusion is even more pronounced, due to the high silicon content of one side (3.80 wt. %) and the high manganese content (6.45 wt. %) of the other. Silicon increases and manganese decreases the activity of carbon.

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L. S. Darken, Diffusion of Carbon in Austenite with a Discontinuity in Composition, Trans. AIME, Vol. 180 (1949), pp. 430-438

Uphill Diffusion of Carbon in Fe-Si-C Alloy

Uphill Diffusion of Carbon in Fe-Si-Mn-C Alloy

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