Chapter 6Chapter 6Interpretation of Phase Diagrams

Phase diagrams summarize in graphical form the ranges of temperature (or pressure) and composition over which phases or mixtures of phases are stable under conditions of thermodynamic equilibrium.

Phase diagram contains information of compound’s composition, solid solution, phase transition and melting temperature.

Phase rule:Phase rule: P + F = C + 2P + F = C + 2P: number of phases C: number of components F: degree of freedom

Total number of degree of freedom: (C-1)P + 2

Number of relations: C(P-1)

Net degree of freedom: F = (C-1)P + 2 – C(P-1) = C – P + 2

P-1 relations: 1 = 2 = 3 = 4 = 5 = …….= P i: free energy

PV = nRT3 variables, 1 equation

C1 + C2 + …..+ Cc = 100%

One needs P-1 equations to describe the equilibrium between phases

P: number of phasesP: number of phasesHow to distinguish phases?   crystalline phases: MgSiO3, Mg2SiO4

   polymorphism - - -   solid solution ( one phase )   defects ordered defects: distinguished phases disordered defects: one phase (considered as solid solution) WO3-x (WnO3n-1: W20O59, W19O56)   liquid (miscibility or immiscibility)   gas: one phase  

C: number of componentsC: number of components

a) CaO-SiO2 : two componentsb) MgO (heating below mp): one componentc) “FeO” appears to be one component, but

two components

∵ 3Fe2+ 2Fe3+ + Feo

∴ FeO is in fact Fe1-xO (wüstite) + x Fe

Phase diagram of CaO-SiOPhase diagram of CaO-SiO22

F: degree of freedomF: degree of freedomIndependent variable to describe a system

For example: boiling water

P = 2, C = 1F = C – P + 2 = 1 - 2 + 2 = 1

So only temperature or pressure is enough to describe the system, that is, T and P are dependent variables.

Thermodynamically stable Thermodynamically stable or kinetically stableor kinetically stable

metastable

unstable

stable(kinetically stable)

How do you know a compound is How do you know a compound is thermodynamically stable or kinetically stable?thermodynamically stable or kinetically stable?

eg. 1. Ca3SiO5 is prepared above 1300oC. At 1100oC, Ca3SiO5 CaO + Ca2SiO4

Ca3SiO5 is thermodynamically stable above 1300o

C but is kinetically stable at 1100oC.

eg. 2. At ambient temperature and pressure, graphite is thermodynamically stable and diamond is kinetically stable.

Usually metastable products can be obtained by quenching the reaction before it reaches equilibrium.

One component systemOne component system

F = C –P +2 = 3 – POne phase, P = 1, F = 2 It takes two independent variables to describe th

e system. Ex. Ideal gas law: PV = nRT

Two phases, F = 1, e.g. Boiling water. Need to know P or T.

Three phases: no variables.

One component systemOne component system BE: gives the change of transition temperature with pressure. (F = 1)

FC: change of melting point of polymorph Y with pressure. (F = 1)

AB, BC: sublimation curves for X and Y. (F = 1)

CD: vapour pressure curve for the liquid. (F = 1)Points B, C are triple points. (F = 0)In area X, Y etc, F = 2

Phase diagram of waterPhase diagram of water

Phase diagram of SiOPhase diagram of SiO22

-quartz -quartz -tridymite -cristobalite liquid SiO2573oC 870oC 1470oC 1710oC

At 500 bar

-quartz -quartz liquid SiO2

∵ -tridymite and -cristobalite have lower density than quartz

At 1600 bar

However, many metastable phases can be obtained by quenching.

Condensed SystemCondensed System For most systems and applications of interest i

n solid state chemistry, the condensed phase rule is applicable, pressure is not a variable and the vapour phase is not important.

Condensed Phase Rule: P + F = C + 1

e.g. SiO2 (Fig 6.5) 1 + F = 1 + 1 => F = 1

So that temperature is the only factor for the change of polymorphs

Eutectic Binary SystemEutectic Binary System

y: invariant pointxyz: liquidus curvecyd: solidus curve

In order to determine the relative amounts of two phases in a mixture, the level rule is used

What happens if the system is heated from pointse and f ?

eutectic point

Level RuleLevel Rule

(amount of liquid) x (distance of hf) = (amount of B) x (distance of Bf)

liquid B

hf

B

(amount of B) = hf/Bh

(amount of liquid) = Bf/Bh

(amount of B) = hf/Bh (amount of liquid) = Bf/BhComposition of liquid = h

BLiquid

Amount of liquid in varies T

• T1: 0.43 (43% liq.)• T2: liq in f = Bf/Bj = 0.53• T3: 0.71• T4: melt complete

Eutectic ReactionReactions at f point:• T > T1 : 57% B (43% liq.)• T < T1 : 70% B (30% A)mixture of A & B crystalliz

ed• The reaction described a

bove are those that should occur under equilibrium conditions.

A method to lower melting pointA method to lower melting point

From the eutectic binary system, it can be considered that B is added to lower the melting point of A.

For example, NaCl is added to lower the melting point of ice (to –21 o

C)

Binary systems with the formation of Binary systems with the formation of compoundscompounds

Point x: peritectic point.Compound AB melts congruently or incongruently.

Describe what happens when system is cooled at composition n ?

Non-equilibrium productsNon-equilibrium products Describe what happens when system is

cooled at composition n ?

When the system is cooled at composition n, one should getAB + B (equilibrium product)But if A + L AB + L is very slow, one will getA + AB + B ( non-equilibrium products)

Phase diagram of CaO-SiOPhase diagram of CaO-SiO22 system system

Immiscible LiquidsImmiscible Liquids

Formation of metastable 2-liquid systemFormation of metastable 2-liquid system

It happens when “2-liquid B + liquid” is very slow upon cooling

Binary system with complete range of Binary system with complete range of solid solutionsolid solution

CoredCored (phenomenon of non-equilibrium)(phenomenon of non-equilibrium)

When the system is cooled at composition b, the central part that forms first may have composition a and on moving out radially from the centre the crystal becomes increasingly rich in B.

Still forms a single crystal (the same structure type of A and B) but with concentration gradient.

What forms solid solution?What forms solid solution?

A and B have the same structure type and ions in them have similar size.

e. g. CaAl2Si2O8 and NaAlSi3O8 in plagioclase feldspar system

The plagioclase feldspar systemThe plagioclase feldspar system

Glass formationGlass formation Recently, there has been much scientific and

technological interest in glassy semiconductors and metals, materials with unusual electrical and mechanical properties.

If the liquid is cool rapidly (quenched) to room temperature, there may not be time for any crystallization to occur and a glass forms.

Partial Solid SolutionPartial Solid Solution

If ions are quite different in size complete solid solution may not be possible.e.g. forsterite (Mg2SiO4) vs willemite (Zn2SiO4)

Partial Solid SolutionPartial Solid Solution

A slightly complicated partial A slightly complicated partial solid solutionsolid solution

A complicated Partial Solid SolutionA complicated Partial Solid Solution

Binary system with polymorph transitionsBinary system with polymorph transitions

exampleexample

Another exampleAnother example

The Fe-C diagramThe Fe-C diagram