Title: More on the Lever Rule

Example Lever Rule Walkthrough

https://www.youtube.com/watch?v=XZEQ0eSFRqg

Walkthrough of the Iron-Carbon Practice Problem - Question 1

What is the weight% of carbon in the austenite phase of an iron-carbon alloy at 1300C and 2.5 global weight% of carbon?

First lets place the specific composition and temperature point on the phase diagram.

This puts us in the two phase region where both austenite and liquid exist.  The composition of the austenite will be determined by the solidus line (or line between austenite and the two phase region).  For 1300 C, the composition value is 1.25 weight % carbon.  This is the precentage of carbon present in the austenite phase that exits in equilibrium with the liquid.  Globally there is more carbon than in the solid phase because the liquid has more carbon dissolved in it.

Walkthrough of the Iron-Carbon Practice Problem - Question 2

What is the weight% of carbon in the liquid phase of an iron-carbon alloy at 1300C and 2.5 global weight% of carbon?

So the weight% of carbon in the liquid will be determined by the liquidus or the line between the two-phase region and the pure liquid region.  At 1300 C this is about 3 weight% carbon which is more than the global total as the liquid is more carbon rich than the solid phase.

Walkthrough of the Iron-Carbon Practice Problem - Question 3

If instead I was at 500C with the same composition (2.5 gloabl weight % of carbon), what percentage of the material is ferrite (alpha phase)? (hint: we are not asking for the composition of carbon but the fraction of the solid and you can round to the nearest whole percentage)

Lets redraw our location on the phase diagram.

Here we are now in the two-phase region with both ferrite and cementite.  To determine what percentage of the solid is made up of the ferrite phase we use the lever rule.

1) draw a line at the temperature through the two phase region

2) identify the compositions at which it intersects with the boundaries of the two phase region
composition_ferrite = 0 weight% C, composition_cementite = 6.69 weight% C

3) apply the lever rule formula: The fraction phase_A present = (composition_B - composition_global)/(composition_B - composition_A)

For this problem that means fraction of ferrite is (6.69 - 2.5)/(6.69-0) or ~63%