Lecture :3
Chapter 9
Phase diagrams
Phase Equilibria:
Equilibrium: The state of a system where the phase characteristics remain constant
over indefinite time periods. At equilibrium the free energy is a minimum.
Free energy : a thermodynamic quantity that is a function of both the internal energy
and entropy (or randomness) of a system. At equilibrium, the free energy is a
minimum.
 A system is at equilibrium if its free energy is at a minimum under some specified
combination of temperature, pressure, and composition. What this mean?
 A change in temperature, pressure, and or composition for a system at equilibrium
will result in an increase in the free energy and in a possible spontaneous change
to another state whereby the free energy is lowered.
Phase Equilibrium: it is refers to equilibrium as it applies to systems in which more
than one phase may exist.
 Phase equilibrium is reflected by a constancy with time in the phase characteristics
of a system.
 Ex: sugar- water syrup is contained in a closed vessel and the solution is in contact
with solid sugar at 20C.(returned to previous fig.)
 If the system is at equilibrium, the composition of the syrup is 65 wt%
C12H22O11 – 35 wt% H2O. What this mean?
 If the temp. of the system is suddenly raised to 100C the equilibrium is
temporarily upset in that the solubility limit has been increased to 80 wt%
C12H22O11.
 Thus some of the solid sugar will go into solution in the syrup this will continue
until the new equilibrium syrup concentration is established at the higher
temp.
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Note: this sugar syrup is a simple example of phase equilibrium using a liquid-solid
system. In many materials systems of interest, phase equilibrium involves solid
phases only .
Summary
Microstructure
phases present
The relative phase amounts
their composition
their spatial arrangement or distribution
 From all that : the free energy consideration and phase diagrams provide
information about equilibrium of the system but they do not indicate the time
period of new equilibrium state.
 For solid systems the state of equilibrium is never achieved completely because the
rate of approach to equilibrium is extremely slow, so the system is said to be in a
nonequilibrium or metastable state .
 Metastable: nonequilibrium state that may persist for avery long time.
 H.w: What
is the difference between the states of phase equilibrium and
metastability?
Phase equilibrium diagrams:
Phase diagrams: a graphical representation of the relationships between
environmental constraints (e.g. temperature and sometimes pressure), composition,
and regions of phase stability, ordinarily under condition of equilibrium.
 The phase diagram can be classified into :
1) One-component (or unary) phase diagrams.
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2) Binary phase diagrams.
3) Triple phase diagrams.
 The phase diagrams depended on temperature, pressure , and composition -and
phase diagrams are constructed when various combinations of these parameters
are plotted against one another.
1) One-component (or unary) phase diagrams
 This is the simplest phase diagram which used one component system.
{composition is constant (i.e. the phase diagram is for a pure substance) and
pressure and temperature are variables.}
 Unary phase diagrams sometimes called a pressure –temperature (or P-T) diagram .
Ex:
The phase diagram of "H2O" as shown below:
From this fig.
 There are three region of different
phases-solid , liquid, and vapor .
 Each of the phases will exist under
equilibrium
conditions
temp.-pressure
ranges
over
the
of
its
corresponding area.
 Any phase can be transform to another
phase if temp. and /or pressure are
altered.
 For ex. At one atmosphere pressure, during heating the solid phase transform to the
liquid phase, i.e. melting occurs.
 If we plot a horizontal line from one atm. We found that line intersection the solidliquid boundary at 0 °C, and intersection the liquid - vapor at 100 °C.
Note:
Upon heating
solid transform
liquid transform
Vapor phase(or
vaporizer)
Upon cooling (condensation)
vapor
liquid
solid .
 All three phases are intersect at common point this point called triple point or
(invariant point) .
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 This means that at this point all phases are simultaneously in equilibrium with one
another.
 Why water has a triple point ?
 Ex.
Assume P=constant, cut the above diagram by horizontal line and draw a curve
represented the change in phases.
Ex 1:
If the pressure is increased, does the melting point of the material of the diagram
increase? -------------, decrease ------------ or stay constant -----------------.
Ex 2:
Draw a curve represented the change in phases of water at constant pressure and
altered temperature a function of time.
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