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CHEM 21112
Phase Equilibria (5L)
CHEM 21112 Basic Physical Chemistry II
Course content:
Quantum mechanics (9 h)
Surface and colloid chemistry (6 h)
Atomic and molecular spectroscopy (9h)
Phase equilibria (6 h):
Thermodynamical description of mixtures, partial molar quantities; partial molar volume and
Gibbs free energy. Phases, components and degree of freedom, the phase rule, phase
diagrams; interpretation, lever rule. Liquid-liquid phase diagrams; phase separation, critical
solution temperatures. Temperature-composition diagrams; distillation of mixtures, zeotropes
and azeotropes. Liquid solid phase diagrams; eutectics and three component systems.
Textbooks
"Physical Chemistry"
P.W. Atkins
Oxford University Press
"Elements of Physical Chemistry"
P.W. Atkins
Oxford University Press
Equilibrium
two opposing
processes occurring
at the same rate
a system at
equilibrium is in
balance
H2O(l)
H2O(g)
Equilibrium is a state in which there are no observable
changes as time goes by.
Chemical equilibrium is achieved when:
• the rates of the forward and reverse reactions are equal and
they are not zero.
• the concentrations of the reactants and products remain constant
Chemical equilibrium
N2O4 (g)
2NO2 (g)
Physical equilibrium
the changes that occur are physical processes
H2O(l)
H2O(g)
Chemical equilibrium
chemical equilibrium involves different substances
as reactants and products
N2O4 (g)
2NO2 (g)
Phase
Specific state of matter that is uniform
through out in composition and physical state
Phase
State of matter
A homogenous portion of a system
that has uniform physical and
chemical characteristics
1) The mixture of ice and water
two phases, solid and liquid
2) The mixture of oxygen gas and nitrogen gas
(the system is Homogeneous)
3) CaCO3(s)
CaO(s) + CO2(g)
one phase, gas phase
= 3 phases (2 solid,1 gas)
Phase Changes
•
•
•
•
•
Sublimation: solid → gas.
Vaporization: liquid → gas.
Melting or fusion: solid → liquid.
Condensation: gas → liquid.
Freezing: liquid → solid.
Phase Changes
Energy Changes Accompanying Phase Changes
Enthalpy
Enthalpy (H) ~ heat content (q) @ constant pressure
∆H = thermal (heat) energy change = q
Physical process
H2O (l) + energy  H2O (g)
∆Hvap = 44 kJ/mole
heat of vaporization
What does the sign of the enthalpy tell you?
Endothermic process or reaction
∆H > 0 or positive
Exothermic process or reaction
∆H < 0 or negative
Gas-Liquid Equilibration
Heating Curves
• Plot of temperature change versus heat added is a
heating curve.
• During a phase change, adding heat causes no
temperature change.
– These points are used to calculate ∆Hfus and ∆Hvap.
Heating Curves
Vapor Pressure
Explaining Vapor Pressure on the Molecular
Level
• Some of the molecules on the surface of a liquid have
enough energy to escape the attraction of the bulk
liquid.
• These molecules move into the gas phase.
• As the number of molecules in the gas phase
increases, some of the gas phase molecules strike the
surface and return to the liquid.
• After some time the pressure of the gas will be
constant at the vapor pressure.
Volatile liquid is a liquid that can easily
evaporate at one atmospheric pressure and
room temperature
Molecules of volatile liq escape the liquid
phase into gaseous phase.
A volatile liquid has a strong tendency to
vapourize or evaporate into vapour, creating
high vapour pressure.
On contrary a less volatile liquid has low
vapour pressure because of lower tendency
to vapourize
Vapour pressure
increases with
increasing temperature
due to its KE
When a liquid evaporates in a
closed vessel, its gaseous
molecules formed above the
liquid have high KE and exert a
vapour pressure.
sublimation
Microscopic equilibrium between gas and
liquid. Note that the rate of evaporation of the
liquid is equal to the rate of condensation of
the gas.
Microscopic equilibrium between gas and solid.
Note that the rate of evaporation of the solid is
equal to the rate of condensation of the gas.
Types of Molecules: the types of molecules
that make up a solid or liquid determine its
vapor pressure. If the intermolecular forces
between molecules are:
1
ethyl ether (C4H10O)
Pvapor (25oC) = 520 torr
ethyl alcohol (C2H6O)
Pvapor (25oC) = 75 torr
•relatively strong, the vapor pressure will
be relatively low.
•relatively weak, the vapor pressure will be
relatively high.
Temperature:
at
a
higher
temperature, more molecules have
enough energy to escape from the
liquid or solid. At a lower temperature,
fewer molecules have sufficient
energy to escape from the liquid or
solid.
Low
Temperature
2
High
Temperature
Vapor Pressure and Boiling Point
• Liquids boil when the external pressure equals the
vapor pressure.
• Temperature of boiling point increases as pressure
increases.
• Two ways to get a liquid to boil: increase temperature
or decrease pressure.
– Pressure cookers operate at high pressure. At high pressure
the boiling point of water is higher than at 1 atm.
Therefore, there is a higher temperature at which the food is
cooked, reducing the cooking time required.
• Normal boiling point is the boiling point at 760 mmHg
(1 atm).
Phase Diagrams
• Phase diagram: plot of pressure vs. Temperature
summarizing all equilibria between phases.
• Given a temperature and pressure, phase diagrams
tell us which phase will exist.
Features of a phase diagram:
– Triple point: temperature and pressure at which all
three phases are in equilibrium.
– Vapor-pressure curve: generally as pressure
increases, temperature increases.
– Critical point: critical temperature and pressure
for the gas.
H2O
Standard phase diagram for one component system
B
CO2
Critical
point ???
O
A
?????
Phase Diagrams
Gibbs Free Energy ?
2nd Law of Thermodynamics
A reaction is spontaneous if ∆S for the
universe is positive.
∆Suniverse = ∆Ssystem + ∆Ssurroundings
∆Suniverse > 0 for spontaneous
process
First calc. entropy created by matter
dispersal (∆Ssystem)
Next, calc. entropy created by energy
dispersal (∆Ssurround)
29
Entropy, S
One property common to
spontaneous processes is
that the final state is more
DISORDERED or RANDOM
than the original.
Spontaneity is related to an
increase in randomness.
The thermodynamic property
related to randomness is
ENTROPY, S.
Reaction of K
with water
30
31
The entropy of
liquid water is
greater than
the entropy of
solid water
(ice) at 0˚ C.
32
Entropy, S
So (J/K•mol)
H2O(liq)
69.95
H2O(gas) 188.8
S (gases) > S (liquids) > S (solids)
Second law states:
• Entropy of the Universe must increase in
a spontaneous process
∆Suniv 〉 0
spontaneous
∆Suniv = 0
equilibrium
∆Suniv = ∆Ssys + ∆Ssurr
Do we have to keep calculating ∆Suniv ?
Not necessarily!
A convenient way of using second law……
From last lecture……..
Phase
Specific state of matter that is uniform
through out in composition and physical state
Phase Diagrams
•
•
Phase diagram: plot of pressure vs. Temperature summarizing all equilibria
between phases.
Given a temperature and pressure, phase diagrams tell us which phase will
exist.
Gibbs Free Energy
- New state function
Gibbs Free Energy
The Gibbs Free Energy is a new
state function, defined as:
G = H − TS
At constant temperature and pressure,
∆G is
∆G = ∆H − T∆S
We only have to think about the
system, NOT the Universe……
Josiah Willard Gibbs
(1839-1903)
Gibbs Free Energy
‘G’ is extremely useful for chemistry and
biochemistry, since so much takes place at
constant temperature and pressure.
The condition of constant T and P is very important
when using G. Otherwise, the entropy change of the
surroundings might be different leading to a different
result.
At constant T and P, consideration of ∆G will answer the question
“Will a given reaction be spontaneous?”
∆G < 0
∆G > 0
∆G = 0
process is spontaneous
reverse process is spontaneous
Equilibrium
The Gibbs Free Energy is a direct measure of spontaneity
Phase Equilibria
X(phase 1)
X(phase 2)
At equilibrium, ∆G = 0
H20 (g)
So,
µ(phase 1) = µ(phase 2)
H20 (l)
Chemical Potential (µ)
Chemical potential of component A, µA, is defined as the
partial molar Gibbs free energy:
 ∂G 

µ A = 
 ∂n A  T ,P ,n j ≠ n A
This is the change in G with respect to a infinitesimal
change in the amount of component A with all other
parameters held constant.
It is essentially the free energy increase (or decrease)
associated with adding a little of A to the system.
α
β
µ i( α )
dni
dG = µ i( α ) dn i( α ) + µ i(β ) dn i(β )
dn
(α)
i
= −dn i
dn
(β )
i
= + dn i
dG = −µ dn i + µ dn i
(α)
i
(β)
i
dG
(β)
(α)
= µi − µi
dn i
if µ i( α ) > µ i( β )
, µ i(β )
dG
=0
dn i
µ
(α)
i
=µ
(β )
i
Phase Equilibria
X(phase 1)
X(phase 2)
At equilibrium, ∆G = 0
H20 (g)
So,
µ(phase 1) = µ(phase 2)
H20 (l)
Equation of a phase boundary
G
Master Equation
(α)
m
=G
(β )
m
dG = Vdp − SdT
((αα))
m
m
dG
dG
V dp
dp −−SS dT
dT
== V
((αα))
m
m
((αα))
m
m
and
dG
(β )
m
= V dp − S dT
(β )
m
(β )
m
dG
(α)
m
= dG
(β)
m
V dp − S dT = V dp − S dT
(α)
m
(α)
m
(α)
m
dp(V
(β)
m
(β )
m
− V ) = dT (S
(β )
m
(α)
m
(α)
m
dp S
=
dT V
(α)
m
−S )
(β )
m
(β )
m
(β )
m
−S
−V
dp ∆Sm
=
dT ∆Vm
Clapeyron equation
What Clapeyron equation says….?
dp ∆Sm
=
dT ∆Vm
The Phase Diagrams of H2O and CO2
When water freezes,
it expands.
The density of solid
water is less than the
density of liquid
water.
Ice floats
Why?
Density = 0.92 g/mL
Density = 1.00 g/mL
Fig. 3-UN4
Ice: stable hydro- Liquid water:
transient hydrogen
gen bonds
bonds
Phase
From last few lectures……..
Specific state of matter that is uniform
through out in composition and physical state
Phase Diagrams
•
•
Phase diagram: plot of pressure vs. Temperature summarizing all equilibria
between phases.
Given a temperature and pressure, phase diagrams tell us which phase will exist.
Gibbs Free Energy
- New state function
Chemical Potential (µ)
At equilibrium, ∆G = 0
µ(phase 1) = µ(phase 2)
What Clapeyron equation says….?
dp ∆Sm
=
dT ∆Vm
Standard phase diagram for water (H2O)
Special case
!!!!!
TA curve = known as melting point or
freezing point
Represent the equilibrium between ice
and liquid
Has a negative slope
Water as the liquid is denser than the solid
(ice floats on water).
That means that an increase of pressure
favors the formation of liquid and that the
melting point of water falls with increasing
pressure.
This unique properties of water is due to
the network of hydrogen bonding in ice is
more extensive than in liquid
H2O
Standard phase diagram for one component system
B
O
A
CO2
H2O
CO2
dp ∆Sm
=
dT ∆Vm
dp ∆Sm
=
dT ∆Vm
ΔSpc
qrev, pc
q rev ,pc
∆Spc =
Tpc
∆H pc
=
Tpc
dp ∆H m
=
dT T∆Vm
Clausius-Clapeyron Equation
Rudolf Clausius
1822 – 1888
Emile Clapeyron
1799 - 1864
German Mathematical
Physicist
French Engineer
Clausius-Clapeyron equation
− ∆H m 1
ln p =
+ const.
R T
p2 − ∆H m
ln
=
p1
R
1 1
 − 
 T2 T1 
P1 and P2 are the vapor pressures at T1 and T2 respectively
Common Applications
• Calculate the vapor pressure of a liquid at
any temperature (with known vapor
pressure at a given temperature and known
heat of vaporization)
• Calculate the boiling point of a liquid at a
nonstandard pressure
p2 − ∆H m
ln
=
p1
R
1 1
 − 
 T2 T1 
∆H can be determined from measurements of vapor
pressure at multiple temperatures.
ln P(atm)
From Clausius-Clapeyron equation we see that –∆Hm/R is the slope
lnP vs 1/T.
− ∆H m 1
ln p =
+ const.
R T
liquid
water
solid
ice
∆Hvap
∆Hsub
water
vapor
1/T
Phase Diagrams
Normal: Occurs at 1 atm.
Critical Point: A combination of temperature and pressure
beyond which a gas cannot be liquefied.
•
Critical Temperature: The temperature beyond which a
•
Critical Pressure: The pressure beyond which a liquid
gas cannot be liquefied regardless of the pressure.
cannot be vaporized regardless of the temperature.
Supercritical Fluid: A state of matter beyond the critical
point that is neither liquid nor gas.
Triple Point: A point at which three phases coexist in equilibrium.
www.abertay.ac.uk/careers
Critical Temperature and Pressure
• Gases liquefied by increasing pressure at some
temperature.
• Critical temperature: the minimum temperature
for liquefaction of a gas using pressure.
• Critical pressure: pressure required for
liquefaction.
Critical Temperature, Tc
Transition to Supercritical CO2
Supercritical CO2 Used to Decaffeinate
Coffee
EXAMPLES OF
GREEN CHEMISTRY
• Safer dry cleaning
– Initially gasoline and kerosene were used
– Chlorinated solvents are now used, such
as perchloroethylene
– Supercritical/liquid carbon dioxide (CO2)
The Phase Diagrams of H2O and CO2
• Water:
– The melting point curve slopes to the left because ice is less
dense than water.
– Triple point occurs at 0.0098°C and 4.58 mmHg.
– Normal melting (freezing) point is 0°C.
– Normal boiling point is 100°C.
– Critical point is 374°C and 218 atm.
• Carbon Dioxide:
– Triple point occurs at -56.4°C and 5.11 atm.
– Normal sublimation point is -78.5°C. (At 1 atm CO2
sublimes it does not melt.)
– Critical point occurs at 31°C and 73 atm.
The Phase Diagrams of H2O and CO2
Phase
From last few lectures……..
Specific state of matter that is uniform
through out in composition and physical state
Phase Diagrams
•
•
Phase diagram: plot of pressure vs. Temperature summarizing all equilibria
between phases.
Given a temperature and pressure, phase diagrams tell us which phase will
exist.
Gibbs Free Energy
- New state function
Chemical Potential (µ)
At equilibrium, ∆G = 0
µ(phase 1) = µ(phase 2)
What Clapeyron equation says….?
dp ∆Sm
=
dT ∆Vm
p2 − ∆H m
ln
=
p1
R
1 1
 − 
 T2 T1 
Phase Rule
Four phases of a single substance
cannot coexist in mutual equilibrium.
F=C–P+2
INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE
F = C – P +2
Degree of
freedom or the
number of
independent
variables
The number
of phase
Number of
component
2 variables
(temperature
and pressure)
F=C–P+2
F = # degrees of freedom
The number of intensive parameters that must be
specified in order to completely determine the system
P = # of phases
Phases are mechanically separable constituents
C = minimum # of components
Chemical constituents that must be specified in order to
define all phases
2 = 2 intensive parameters
Usually temperature and pressure
OR
The number of chemical
species that can explained
the composition of all phase
in a system
The least number of
different substances
required to describe the
composition of all phases in
the system
1) water, CO2 = one
component
2) Aqueous solution of
potassium nitrate = 2 system
component because have
potassium nitrate salt and
water.
COMPONENT
DEGREE OF FREEDOM (F)
The number of variables that may
be changed independently without
causing the appearance of a new
phase or disappearance of an
existing phase
UNIVARIANT
TYPES
BIVARIANT
EXAMPLES
CaCO3(s)
CaO(s)
F = C – P +2
=2–3+2
= 1 (univariant)
+ CO2(g)
Calculate the degree of freedom (F)
Means: only one
variable, either
temperature or pressure
can be changed
independently
The number of components is not
always easy to determine at first
glance, and it may require careful
examination of the pyhsical
conditions of the system at
equilibrium
Standard phase diagram for water (H2O)
ONE COMPONENT
SYSTEM
Standard phase diagram for carbon dioxide
(CO2)
Example 1 – Liquid region
In a single phase region (two degrees of freedom), both temperature and pressure
can be varied independently within the limits of the phase boundaries without
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changing
the phase
F=C–P+2
Example 2 – Freezing line
When two phases are in equilibrium (one degree of freedom), either temperature
or pressure can vary independently, but not both
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F=C–P+2
Example 3 – Triple point
At the triple point (three phase equilibrium) there are no degrees of freedom.
Therefore, in this situation, neither temperature or pressure may be varied without
altering
one or
two
of the
phases
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POLICY
RESEARCH
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Phase diagrams of mixtures
Two component systems are better described by binary
phase diagrams
In these equilibrium diagrams we have a composition
variable in addition to the usual temperature and pressure
variables.
We therefore need a three dimensional diagram to plot all
three variables.
To simplify
binary phase diagrams are usually drawn at
atmospheric pressure, showing variations of
temperature and composition only.
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Raoult’s law – in
explaining the effect
of non-volatile solute
on vapour pressure of
solvent and its melting
and boiling point
Two completely
miscible liquid – ideal,
non-ideal, positive
and negative
deviation
TWO COMPONENT
SYSTEM
Composition diagram
vs boiling point
composition for ideal,
non-ideal, negative n
positive deviation
Eutectic system and
cooling curves
Fractional distillation
and azeotropic
system
Single component systems
Ex. H2O, CO2
Two component systems
Liquid – liquid phase diagrams
F=C–P+2
F=4–P
F' = 3 – P
Ideal solutions [obeys Raoult's law ]
F=C–P+2
F=4–P
F' = 3 – P
3 types :
1. Complete Miscible liquid
2. Half miscible liquid
3. Immiscible liquid
Methanol and ethanol
Liquid in
liquid
ether and
water
Oil and
water
Ideal solution- mostly involve the
substance that have similar
physicochemical properties. Ex:
MeOH/EtOH, benzene/toluene
Complete Miscible liquid
 2 types of completely miscible liquids which are ideal and non-ideal solutions
 An ideal solution is a solution that obeys Raoult’s law and non-ideal solution disobey.
 A solution is a ideal solution when:
A
A
=
A
B
 The intermolecular attractions between the mixture of same molecules are
equal with the mixture of different molecules.
 The volume of the mixture is the total volume of both liquids.
 No heat changes (no endo-exothermic process)
 Obeys Raoult’s law
Liquid – liquid phase diagrams
• Consider a solution of two liquids, say
benzene and toluene held at a constant
temperature.
• Benzene and toluene form very nearly ideal
solutions
Ideal solution obeys Raoult's law
where pi is the partial pressure of component i above
the liquid mixture (or the vapor pressure of i in the
mixture),
Xi is the mole fraction of component i in the liquid, and
pi* is the vapor pressure of pure component i.
IDEAL SOLUTIONS
(obeys Raoult’s law)
VAPOUR PRESSURE/
COMPOSITION
DIAGRAM
BOILING POINT/
COMPOSITION
DIAGRAM
Vapor Pressure Diagram
Temperature versus composition
We call this line a “tie line”
It intersects the upper curve at the composition of the vapor
in equilibrium with the liquid at the same temperature
Mixtures of volatile liquids
The Liquid–Vapor Temperature– Composition Phase Diagram
of Benzene and Toluene at 1.00 atm.
EXAMPLE !!!!!
Which vapour
sample rich at
this point?
composition
Fractional distillation
Boiling diagrams provide an explanation for fractional distillation.
“Theoretical plates”
Distillation – Fractional
Vapor
line
Temperature °C
110
Liquid
line
100
90
80
Mole % Toluene 0
Mole % Benzene 100
20
80
40
60
60
40
80
20
100
0
Composition (mole%)
As the hot vapors leave the distilling flask,
they condense on the first cold surface, completing
one vaporization-condensation cycle.
Vapors from the
Distilling flask
Suppose we distill the same 80:20 mixture of toluene
to benzene we did in the simple distillation example
Distillation – Fractional
Vapor
line
Temperature °C
110
Liquid
line
100
90
80
Mole % Toluene 0
Mole % Benzene 100
20
80
40
60
60
40
80
20
100
0
Composition (mole%)
This surface begins to heat from the condensed vapors
which are now 55:45 toluene-benzene
Vapors from the
Distilling flask
This benzene enriched liquid now has a boiling point of ~94
°C (lower than the incoming vapors) and it begins to boil off
this higher surface
Distillation – Fractional
Vapor
line
Temperature °C
110
Liquid
line
100
90
80
Mole % Toluene 0
Mole % Benzene 100
20
80
40
60
60
40
80
20
100
0
Composition (mole%)
These vapors are even further enriched in benzene (now
30:70, toluene:benzene) and condense on the next cold
surface
Vapors from the
Distilling flask
Distillation – Fractional
Vapor
line
Temperature °C
110
Liquid
line
100
90
80
Mole % Toluene 0
Mole % Benzene 100
20
80
40
60
60
40
80
20
100
0
Composition (mole%)
This condensed liquid has an even lower boiling point (86
°C) and as this surface heats it begins to boil off this next
higher surface
Vapors from the
Distilling flask
Distillation – Fractional
Vapor
line
Temperature °C
110
Liquid
line
100
90
80
Mole % Toluene 0
Mole % Benzene 100
20
80
40
60
60
40
80
20
100
0
Composition (mole%)
This vapor now condenses on the next cold surface (now
20:80, toluene:benzene) and the cycle continues
Vapors from the
Distilling flask
Distillation – Fractional
1:99 toluene:benzene
Vapor
line
Temperature °C
110
Liquid
line
100
90
80
Mole % Toluene 0
Mole % Benzene 100
20
80
40
60
60
40
80
20
100
0
Composition (mole%)
This cycle will continue until the top of the column is reached
The liquid collected after seven cycles is now 99% benzene!
Vapors from the
Distilling flask
80:20 toluene-benzene
Distillation – Fractional
1:99 toluene:benzene
Vapor
line
Temperature °C
110
Liquid
line
100
90
80
Mole % Toluene 0
Mole % Benzene 100
20
80
40
60
60
40
80
20
100
0
Composition (mole%)
Each vapor-condensation (or mini-distillation) cycle is
known as one theoretical plate
Vapors from the
Distilling flask
80:20 toluene-benzene
The length of distillation column required to provide one
theoretical plate of separation is known as the height
equivalent theoretical plate (HETP)
Single component systems
Ex. H2O, CO2
Two component systems
Liquid – liquid phase diagrams
F=C–P+2
F=4–P
F' = 3 – P
Ideal solutions [obeys Raoult's law ]
Non Ideal solutions [Azeotrope mixture]
negative/positive deviation
NON-IDEAL SOLUTIONS
• Negative deviation
• Positive deviation
 Intermolecular forces between molecules in the solution are stronger than
those in pure liquid
 Therefore, vapour pressure of the solution is lower than vapour pressure of its
components or pure liquid.
Example :
A
A
=
B
B
WEAKER THAN
A
B
the molecules in the solution have lower tendency to escape into vapour phase.
Therefore the process is EXOTHERMIC
Boiling diagrams for non-ideal solutions
Azeotrope
mixture
Ex:
Formed when the intermolecular forces between molecules in the mixture are
weaker than those in pure liquids.
A
A
=
B
B
STRONGER THAN
A
Vapour pressure of the solution is higher
than expected
B
The solution has a greater
tendency to evaporate or
escape into vapour
The process is endothermic
"low boiling azeotrope."
AZEOTROPE
It is known as a constant boiling
mixture or an azeotropic mixture or
an azeotrope.
An azeotrope is a mixture of two (or more)
miscible liquids that when boiled produce the
same composition in the vapor phase as that
is present in the original mixture.
Single component systems
Ex. H2O, CO2
Two component systems
Liquid – liquid phase diagrams
F=C–P+2
F=4–P
F' = 3 – P
Ideal solutions [obeys Raoult's law ]
Non Ideal solutions [Azeotrope mixture]
negative/positive deviation
Liquid – Solid phase diagrams
Eutectic systems
Liquid –solid phase diagrams
The knowledge of temperature-composition
diagrams for solid mixtures guides the design
of important industrial processes, such as the
manufacture of liquid crystal displays and
semiconductors.
Liquid –solid phase diagrams
Eutactic composition: the mixture with lowest melting point.
A solid with a eutactic composition melts, without changing
the composition, at the lowest temperature of any mixture.