Question

9.34 Consider the hypothetical eutectic phase dia- gram for metals A and B, which is similar to that for the lead-tin system, Figure 9.8. As- sume that (1) a and ß phases exist at the A and B extremities of the phase diagram, re- spectively; (2) the eutectic composition is 47 wt% B-53 wt% A; and (3) the composition of the B phase at the eutectic temperature is 92.6 wt% B-7.4 wt% A. Determine the com- position of an alloy that will yield primary a and total a mass fractions of 0.356 and 0.693. respectively.

Answer 1

We have , a phase diagram similar to that of Pb-sn phare diagram In this rypothetic eutectic phase diagram eutectic composition - 47 #8 ,63%, wt%A op Geufcetic 47 wt%B Also, we have Pouimary & Inked 0.356 how fraction and Total &. mars fraction ka = we need to determine allo composition 0.693 at there conditions Centatic --- A a to (UT). 8) (12.6% 8) Let the required composition be co wt. e by lever rule, Wx= cp-co & 0.693 = 226 - C-4 0 926 - 4 and WK - Centertie - Co & 0.356 - 47-co 47-04 Centeke - Ca

calculations - from eph 0 0.693 -- 92.6 -CO 926 -ca 0.693 x 926 - 0.693 x 6 = 926 - Co 0.693 x 92.6 - 92 6 + cos 0.693x C2 $ 9.172 - 12 6 + C = 0, 643 x 4 - 28.428 + Co 0.693 - Ca Now , using this value of Ca in eq o, we get 47-Co 0,367 (47) - 0.356 x (x = 47-6 0.356 47-a 0,356x47 - 0,356 » (Co - 28.428) 0.693 47 - Co 2 16.732 - 0.514 * (con 28.428) = 47-co- 16.732 16.732 - 0.514 Co + 0.514 X 28.428 - 0.519 + 14.612 47-6 47-6 31.344 - 0.514 6 47-co 7 co - 0.514 to 47 - 31.344 [by taking to on Lns] 0.486 Co 15.656 Co 15.656 32.2 % wt. 0.486 Required Allby composition is 32.2 wt%B, 67. 8 wt%A

I have explained the concept by drawing the probable phase diagram.

Here, Lever Rule is used in the calculations.

Final answer for alloy composition is 32.2wt%B, 67.8 wt%A