Phase Diagrams in Materials Science: A Primer, Study notes of Science education

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Primer Materials For Science Teaching

Spring 2018

Phase diagrams 0.44 wt% of carbon in Fe microstructure of a lead–tin alloy of eutectic composition

A phase may be defined as a homogeneous portion of a system that has uniform physical and chemical characteristics What is a phase?

The Gibbs Phase Rule This rule represents a criterion for the number of phases that will coexist within a system at equilibrium. C – # of components (material that is single phase; has specific stoichiometry; and has a defined melting/evaporation point) N – # of variable thermodynamic parameter (Temp, Pressure, Electric & Magnetic Field) P max

• maximum # of phase(s)

P

max

= N + C

Gibbs Phase Rule – example Phase Diagram of Water C = 1 N = 1 (fixed pressure or fixed temperature) P = 2 1 atm. boiling sublimation melting fixed pressure ( 1 atm) solid liquid vapor 0 0 C 100 0 C fixed pressure (0.0060373atm=611.73 Pa) Ice Ih vapor 0.01 0 C fixed temperature (0.01 oC) vapor liquid solid 611.73 Pa 10 (^9) Pa

Binary phase diagram

Full solubility (Cigar shape diagram) Partially solubility (eutectic diagram)

Full Solubility (Cigar shaped diagram)

In Cigar shape diagram there are three different regions:

1. Liquid (single phase)

2. Liquid + solid (double phase)

3. Solid solution (single phase)

• Liquidus - the boundary line between the liquid region and the double phase region.
• Solidus - the boundary line between the solid solution region and the double phase

region.

Example - Equilibrium Cooling

A copper–nickel alloy of composition 35 wt% Ni – 65 wt% Cu is slowly cooled from 1300 oC (a)At what temperature does the first solid phase form?

• Around 1250 oC (b) What is the composition of this solid phase?
• 46 wt% Ni (c) At what temperature does complete solidification of the alloy occur?
• Around 1210 oC (d) What is the composition of the last liquid remaining prior to complete solidification?
• 24 wt% Ni (e) What is the amount of the solid phase at point c

You start to heat solution of 60 wt% of Cr 2 O 3 from room temperature up to 2200 oC a)What is the melting Temp of pure? Al 2 O 3 and of pure Cr 2 O 3?

• 2045 oC for Al 2 O 3 and 2275 for Cr 2 O 3 b)At which Temp the first liquid appears?
• Around 2110 oC- 2120 oC c)What is the weight percentage of Cr 2 O 3 in the first liquid phase formed
• Around 35 % d)At which Temp all of the solution transformed to liquid
• Around 2190 oC e)What is the composition of the last solid just before melting
• Around 85 % Cr 2 O 3 f)What is the amount of liquid and solid phases at the point A (around 2150 o C)

A

W   100  44  56 %

Partially solubility (eutectic diagram) Single phase Double phase Three phases

In Eutectic shape diagram there are features that are not exist in Cigar shape

diagram :

• Solvus - the boundary line between the solid solution region and the double phase

region solid region. This line together with the solidus line indicate the solubility

limit of the solid solution (max component b in α / max component a in b) in each

temperature.

• Eutectic Line- line where three phases co-exist (α, β, L); below this line

(temperature) there is a complete solidification.

• Eutectic Point- a point (composition) on the eutectic where the melting and

solidification are like in a single component diagram; The melting temperature is the

lowest for the Eutectic composition.

• Max Solubility Limit- is the max amount of component b in α / max amount of

component a in b. The max solubility limit is always at the eutectic temperature.

Microstructure obtained with different compositions

lamellae

Primary α eutectic α

You start with 10 kg solution of 10 wt% Sn - 90 wt% Pb at 200 oC a)How many phases do you have?

• 1 , α phase b)You continue to heat. At which temp will the first liquid appear? What is the wt% of Pb in this first liquid?
• Around 280 oC. 78 wt% Pb c)You start to cool your solution. At which temp the first β phase appears? What is the wt% of Pb in this first β phase?
• Around 150 oC. Around 3 wt% Pb d)At 100 o C what is the amount in kg of the α phase? What is the amount of the β phase?
• Using the lever rule to find the amount of b: = 0.5 kg e) What is the wt% Pb of the α and β phase at 100 oC
• 95 % and 2 % respectively %( ) 5 % 98 5 10 5    wt b 

Complex Diagrams