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P + F = C+1 Pressure is fixed Max. 3 phases in a binary system Max. 2 phases in a one-component system
Equilibrium – lowest free energy
Fig. 6.2 Schematic diagram showing stable, unstable and metastable conditions
Fig. 6.1 Binary join CaO-SiO2 in the ternary system Ca-Si-O
MgO is an one-component system
’FeO’ is a two-component system Fe-O ’FeO’ is Fe1-xO + Fe
The condensed phase rule:
The distinction between different crystalline crystalline phases is usually clear e.g. CaCO3 and SiO2 MgSiO3 and Mg2SiO4 are also different phases What about solid solutions? Al2O3 + Cr2O3 One phase The liquid state: Lower number of homogeneous phases Gasses: 1 phase only same crystal structure mix from 0 to 100% Cr2O3
P+F=C+2=3
Fig.6.3 Schematic pressure versus temperature phase diagram of a one-component system.
Fig. 6.4 The system H2O
The SiO2 system
α-quartz
573 ◦C
It is the minimum number of constituents needed in order to describe completely compositions of the phases present
CaO-SiO2 is a two component system
Binary join in the ternary system Ca-Si-O
β-quartz
870 ◦C
β -tridymite
1470 ◦C
β -cristobalite
1710 ◦C
liquid
Polymorphs at ambient pressure
Fig. 6.5 The system SiO2
Diamond anvil cell
3500 kbar = 350 GPa pressure at the centre of the earth
The monotectic reaction
l2
l1
l 1 ⇔ l2 + B
also an invariant reaction
Fig. 6.21 Phase diagram MgO-SiO2
Technologically important phase diagrams
Fig. 6.22 The Fe-C diagram
The system Li2O-SiO2: metastable phase separation and synthetic opals
Spinodal decomposition Two liquids with a very fine texture
Fig. 6.26 Phase diagram Li2SiO3-SiO2. Metastable immiscibility dome
Fig. 6.27 Purification of Si by zone refining: impurities contrate in melt
Yttria-stabilized zirconia, a solid electrolyte
Fig. 6.28 Phase diagram ZrO2-Y2O3 Zr1-2xY2xO2-x oxygen vacancies
Two-component condensed systems
P + F = C +1 = 3
Fig. 6.6 Simple eutectic binary system
Mechanical mixtures
Lever rule
m1*(dist xy) = m2*(dist yz)
Fig. 6.7 Principle of moments
Glass production
Na2O-SiO2 glasses are water soluble!
CaO, MgO, Al2O3 and B2O3 solves this problem
SiO2 glass is also used e.g. in the laboratory
Fig. 6.25 Phase diagram Na2O-SiO2
Syntectic reaction: V ⇔ L1 + L2
Eutectoid reaction:
α ⇔ β + γ
Peritectoid reaction: α ⇔ β + γ
Ca3SiO5 has a lower limit of stability Eutectoid reaction Fast cooling so Ca3SiO5 does not decompose
Ca3SiO5 is the key ingredient in rapid-hardening Portland cement
Number of components?
The number of components of a system is the number of constituents that can undergo independent variation in different phases Alternatively
Coring
Concentration gradients in grains
Fig. 6.11 The plagioclase feldspar system, anorthite-albite
indifferent points
Fig. 6.12 Binary colid solution systems with (a) thermal minima and (b) thermal maxima in liquidus and solidus curves
Fig. 6.16 Binary system with incongruently melting compound and partial solid solution formation
Polymorphs αA αA βB βB
Fig. 6.17 Simple eutectic system with solid-solid phase transitions
Fig. 6.23 Partial diagram for the lime-rich composition in the system CaO-SiO2
Na-S battery
Fig. 6.24 Na-S phase diagram and open circuit cell voltage as a function of degree of discharge/cathode composition for the Na/S cell
AB melts congruently (solid and melt have the same chemical composition)
AB melts incongruently (solid and melt have different chemical compositions) The peritectic reaction also an invariant reaction
Chapter 6 Interpretation of Phase Diagrams
Gibb’s phase rule:
P + F = C+2
What do we mean by phase? A phase is homogeneous The number of phases in a sample is number of physically distinct and mechanically separable (in principle) portions
Fig. 6.18 Binary solid solutions systems with polymorphic phase transitions
Fig. 6.19 Binary eutectic system with polymorphic transitions and partial solid solution formation
Fig. 6.13 Simple eutectic system showing partial solid solubility of the end members
Fig. 6.14 The system Mg2SiO4 – Zn2SiO4
Fig. 6.15 Binary system with partial solid solution formation
Example 1
Example 2