Question

1. Chapter 9: Questions and Problem 9.7 (20 points, 10 points each) (a) Given here are the solidus and liquidus temperatures for the germanium-silicon system. Construct the phase diagram for this system and label each region. (b) Based on the phase diagram you constructed from above data, determine in (i) wt% and in (ii) weight fraction of Liquid phase and Solid phase at Si composition of 20 wt% at 1100C. (40 points) Composition (wt% Si) Solidus Temperature (°C) Liquidus Temperature (°C) 938 938 1005 1147 1065 1226 1123 1278 1178 1315 1232 1346 1282 1367 1326 1385 1359 1397 1390 1408 100 1414 1414 Solution:

Answer 1

i) Phase diagram of GeSi alloy.

- 1400 Liquidus - - - - - - - - Solidus Temperature (°C) Liquidus + Solidus Liquidus Temperature (°C) 7.5 % 20% Solidus 1100 26% 1000 4-Solidus temperature (°C) H -Liquidus temperature (°C) elci 900 900 80 100 20 40 60 Composition (wt% of Si)

ii) Firstly we need to draw a line, 20 wt % of si composition at a temperature of 1100 C.

and, then a red line (known as Tie line) is drawn where it intresects both the liquidus state and solidus state and the wt% where labelled (in the above figure)

so, the weight% of liquidus state is 7.5% and solidus state is at 26 %.

for finding the weight fraction of the alloy, lever rule is followed,

Lever states that,

"It can be used to determine the fraction of liquid and solid phases for a given binary composition and temperature that is between the liquidus and solidus line".

Ws=Wo-W1/W's-W1

where,

Ws is the Wt% of solid = 26%

Wo is the Wt% of silicon at 1100 C = 20%

Wl is the Wt% of liquid = 7.5%

so, a tie line is drawn parallel to the x axis where it intersects both the states

for finding the weight fraction of liquidus phase above equation is followed by modifing according to the liquid region

W=Wo-Ws/WS-W1

Wl = (26-20)/(26-7.5) *100  = 32.5 %

same as follows for Solid region,

Ws = (20-7.5)/(26-7.5) *100  = 67.5 %

the total wt fraction should be equal to 100

So, Ws+Wl =100

67.5 % +32.5 % =100 %

Hence Proved.

Thank you