# Materials Science Homework 1.

a) the first liquid phase forms at about 183 Celsius degree

b) this liquid phase contains alpha+liquid

c) the complete melting occurs at about 275 Celsius degrees.

d) the composition of the last solid prior to melting is alpha

2.

a) 18.3 percent Sn ….. 100% alpha

97.8% percent Pb…..100% beta

at 25% percent Sn one has (100/(97.8-18.3))*(97.8-25) = 100/1.09 =91.5 % alpha and

100-91.5 =8.5 % beta

b) 18.3% percent Sn ….100% primary alpha

61.9% percent Sn…..100% eutectic

at 25% percent Sn one has (100/(61.9-18.3))*(61.9-25) = 100/1.18 =84 % primary alpha and

100-84 =16% eutectic

c) at 61.9% Sn …. 100% eutectic

at 25% Sn ……..x% eutectic

x% = 25*100/61.9 = 40.38 wt% eutectic

3.

a) The proeutectoid phase is the phase formed before eutectoid transformation

b) 0.02%C ……. 100% ferrite

6.7%C……….100% cementite

at 0.25%C one has (100/(6.7-0.02))*(6.7-0.25) =100/1.03 =96.5% ferrite

and 100-96.5 =3.5% cementite

Hence in 8.3 kg austenite one has 8.3*0.965 =8.0095 kg ferrite and

8.3-8.0095 =0.29 kg cementite

c) at 0.76% C…..100% eutectoid

0.02% C……100% ferrite

at 0.25%C one has (100/(0.76-0.02))*(0.76-0.25) =100/1.45 = 68.9% pearlite and

100-68.9 =31.08% proeutectoid

d) see attached figure