The Richard Stockton College of New Jersey
Chemistry Program, School of Natural Sciences and Mathematics
PO Box 195, Pomoma, NJ
CHEM 3410: Physical Chemistry I — Fall 2008
Homework 9— Solutions
1. (a) Point A represents the melting point of pure Ge. Point B is the melting point of pure Si.
(b) At point C you would observe the solid solution (a single-phase mixture of Ge and Si solid).
At Point D you would have two phases: a liquid Ge–Si solutions and a solid Ge–Si solution.
At point E there would be a single liquid solution phase.
(c) Line F is the liquidus curve. Upon cooling it represents the temperature where solid will begin
to form out of the liquid.
(d) The cooling curve for line H is shown below. The first solid b egins to form at point A while
the last liquid solidifies at point B.
(e) Along line I, pure Si liquid is being cooled. For a single component system, there is a unique
melting point where you would observe a thermal arrest. The temperature would not continue
to decrease until all the liquid had solidified. A schematic of this is shown in the figure below.
(f) The free energy curves for the two phases must be drawn in a manner that clearly indicates
which phase(s) is stable.
The solid solution phase is stable for all compositions at 900◦C . The free energy curve for
the solid must be below the liquid for all compositions.
At 1200◦C , there are 3 regions of phase stability: liquid is stable from 0 to 18 wt% Si,
there is a two-phase equilibrium of solid + liquid between 18 wt% and 43 wt% Si, and the
solid solution is the stable phase at compositions above 43 wt% Si. The two phase region is
highlighted with a heavy common tangent line. This line indicates that the chemical potential
of Si in the solid is equal to that of Si in the solid in the two phase region (along the common
tangent). It also means the chemical potential of Ge in the solid equals the chemical potential
of Ge in the liquid in this composition range.
The liquid solution phase is stable for all compositions at 1450◦C . The free energy curve for
the liquid must be below the solid for all compositions.
