Engineering Materials – NOTES – Chapter 9 – Phase Diagrams


What is a phase diagram?

A phase diagram shows us the microstructure within a material as a function of the material composition (% alloying elements) and material temperature.


Why are phase diagrams important?

·        They can help us understand the thermal history of a material and the effect of that history on material properties.

·        They are needed to help us understand how we develop and preserve nonequilibrium microstructures.

·        The different microstructures represented on a phase diagram produce different material properties when that microstructure is preserved in the material.



Some basic terms and concepts:

·        Component:  The compounds (metals) of which an alloy is composed.  Includes the solvent (primary material whose crystal structure is maintained) and the solvent (the material introduced into the solid solution)

·        Solubility Limit:  The maximum concentration of solute atoms that may be dissolved in the solvent.  (For example:  How much sugar can you add to water and have it dissolve?  Can you change the limit of how much sugar you can add?  How? Fig. 9.1)

·        Phase:  A chemically and structurally homogeneous portion of a system.  (for example, in Fig. 9.1, we see two phases: liquid solution (syrup) and solid sugar.  Note that both phases may exist together in the same region of the diagram.  The diagram borders exist where one or more phases cease to exist or where a change in phase occurs)

·        Microstructure:  The structure and arrangement of crystals at the microscopic level.

·        Phase Equilibrium:  The phase characteristics of a system do not change with time (all other conditions being the same).  (We typically deal with metastable systems which are not quite at equilibrium, but change very little with time).



We have already defined phase diagrams (above).  Let’s take a look at one and see if we can understand it.  Example Fig. 9.2 (sketch on board also)







Some basic terms for phase diagram interpretation:

·        We will be looking only at binary phase diagrams (two elements).  The display of anything more than two elements gets complicated!

·        For metal alloys, solid solutions are indicated by lowercase Greek letters (a, b, g, etc.)

·        Phase boundaries separate the different phases.  The liquidus line defines the boundary where only the liquid  (L) phase is present.  The solidus line defines the boundary where only the solid phase is present. (Note in Fig. 9.2 the phases come together at the melting point for Copper (1085C) and at the melting point for Ni (1453C).


Interpretation of Phase Diagrams

The information that we can find from a phase diagram includes:

1.      The phases present

2.      The composition of the phases

3.      The percentages or fractions of the phases


Phases Present

Locate the temperature-composition point on the graph to see which phases are present. (Point B in Fig. 9.2 shows a and L (Liquid) phases present)


Determination of Phase Compositions

What is the concentration of each component?

·        Single phase present:  The composition of the phase is simply the overall composition of the alloy (composition of point A in Fig. 9.2 is 60%Ni, 40% Cu at 1100C).

·        Two phase regions:  Procedure:

o       Draw a horizontal “tie line” to intersect the liquidus and solidus lines at the given temperature.

o       The composition of the liquid portion of the two phase region is determined by the composition at the point where the tie line intersects the liquidus line (CL in Fig. 9.2)

o       The composition of the solid portion of the two phase region is determined by the composition at the point where the tie line intersects the solidus line (Ca in Fig. 9.2)


Determination of Phase Amounts

How much of each phase is present in a two phase region?  Use the tie line and lever rule

·        The percentage of each phase is computed as the ratio of the length of the tie line from the overall composition to the opposite phase (not the phase of interest) boundary, divided by the overall length of the tie line. 

The lever rule give a mass fraction of each phase (if the composition scale is wt%).  Sometimes it is useful to express phase amounts as volume fractions (to compare with visual microstructure examinations).  The conversions between mass and volume fractions are given in Equations 9.6 and 9.7 on pp 256-57 of the text!

Example:  9.5(e):







Development of Microstructure in Isomorphous Alloys

(Isomorphous – system with complete liquid and solid solubility 0-100%!)

Equilibrium Cooling – As an isomorphous alloy is cooled very, very slowly, it undergoes a phase change from liquid to solid form.  Note that the composition of each form in the two phase region changes as the temperature drops.  Fig. 9.3  SLOW cooling allows for the material to stabilize in its composition as the temperature cools.


But what if we cool the material faster?


Nonequilibrium Cooling – If the liquid cools too fast for it to stabilize as it cools, we develop a cored structure.  The structure does not have uniform composition.  Consider Fig. 9.4.  At point b’, the solid for a 35%Ni-65%Cu mixture forms with 46% Ni.  With rapid cooling, this solid remains with this composition while successive solids with gradually reduced amounts of Ni form around this center core.  This produces a shift in the solidus line (the liquid has a higher percentage of Cu) and results in less than optimal properties.  This can be a problem in castings.  The coring can be resolved by heat-treating at a temperature just below the solidus line (point d’ in Fig. 9.4) to produce atomic diffusion leading to a more homogeneous composition.


Mechanical Properties – An isomorphous solid will have show solid-solution strengthening.  Each component is initially strengthened by the creation of a solid solution up to some maximum strength that is higher than the individual strength of either component (Fig. 9.5).  The tradeoff is a loss of ductility.


Binary Eutectic Systems – Fig. 9.6 – A binary eutectic system consists of two materials with 3 single phase regions and an invariant point (E in Fig. 9.6) at which an eutectic reaction occurs.  Some important characteristics include:

·        Limited solubility of the components in one another.  In Fig. 9.6, the a phase is Ag dissolved in Cu.  The b phase is Cu dissolved in Ag.  Note that the maximum solubility for each of these phases is less than 10%.

·        The solid two-phase region a + b, is NOT a solution!  This is more like a composite where grains of a (mostly Cu with some small amount of Ag) are mixed in with grains of b (mostly Ag with some small amount of Cu).

·        The boundary line at 779C in Fig. 9.6 separates several regions.  Between 8 and 71.9% Ag, the b phase melts at this temperature while a stays solid.  Between 71.9 and 91.2%, the opposite happens.  At 71.9%, everything melts in a eutectic reaction!

·        Tie lines and lever rules can be used to calculate percent compositions, etc. similar to isomorphous material phase diagrams.  (see example 9.2 and 9.3).


Development of Microstructure in Eutectic Alloys

What happens when you cool a eutectic alloy?

Several possibilities:

·        Cooling a composition that is below the maximum solubility limit (Fig. 9.9).  If we cool through the a region, the b phase never appears because the second component (Sn in Fig. 9.9) is completely soluble in the first component.

·        Cooling a composition above the room temperature solubility limit but below max solubility.  (Fig. 9.10)  a phase solidifies, followed by the precipitating out of b phase within the a crystals as the temperature drops below the solvus line. 

·        Cooling through the invariant point (eutectic composition).  Both a and b phases precipitate together forming alternating layers of these phases (Fig. 9.11 and 9.12)

·        Cooling through a point between the invariant point and max solubility limit (Fig. 9.14 and 9.15).  One phase solidifies in solid “blobs”.  Crossing the eutectic line solidifies the remainder of the material in a eutectic structure around the blobs. (blobs are primary a, eutectic structure is called eutectic a.)

This whole thing can start to really complicated with the introduction of intermediate phases or compounds (Fig. 9.17)


The Iron-Carbon System

This is what we have been waiting for!


BE aware that the primary structural materials in all technologically advanced cultures are iron and steel!


Regions of the iron-carbon phase diagram (Fig. 9.21)

a – ferrite:  The room temperature state of iron with no carbon.  BCC crystal structure

g – austinite – FCC structure for iron between 912 and 1394C.

d – ferrite – iron converts back to a BCC structure at 1394C to its melting point at 1538C.  Of no technological importance so we will ignore this phase!

Fe3C – iron carbide or “cementite”.


We will look at the iron-carbon phase diagram only up to 6.7% carbon.  All steels have carbon contents lower than this.  Above this, we get pure cementite.  In some terms, we can consider Fig. 9.21 to go from 0 to 100% cementite on the x-axis.


Note the ability of carbon to dissolve in iron is better for the FCC structure (g, austenite up to 2.14 wt%) than for the BCC structures (a ferrite up to 0.022wt %).


Note that austenite is NOT magnetic, while ferrite is!


Cementite is very hard and brittle and it adds these characteristics to steel.


Ferrous alloys:  3 classifications:

Commercially pure iron: less than 0.008 wt% C.

Steels: carbon content between 0.008 and 2.14 wt% (rarely exceeds 1%)

Cast irons: carbon content between 2.14 and 6.7 wt%.  Typically less than 4.5 wt% C.


Development of Microstructure in Iron-Carbon Alloys

Eutectoid Composition:  The cooling of steel is similar to the eutectoid materials we studied earlier.  Consider Fig. 9.23.  A steel with 0.76 wt% carbon will cool through the invariant point (eutectic composition).  The austenite (g) changes to alternating layers of ferrite (a, with 0.022 wt% C) and cementite (Fe3C, with 6.7 wt%C).  These alternating light and dark layers are called pearlite because it looks like mother of pearl (Fig. 9.24).  The dark layers are the hard cementite and the light layers are the soft and ductile ferrite.


Hypoeutectoid Alloys:  These are alloys with a composition between 0.022 and 0.76 wt%C (to the left of the eutectoid).  These cool from the single phase austenite region, through a two phase ferrite + austenite region into the ferrite + cementite region (Fig. 9.26).  As the material cools through the 2 phase region (a + g) the a (ferrite) grains grow in size.  Upon crossing the eutectoid line, the remaining austenite converts to pearlite.  The result is a microstructure with grains of ferrite (proeutectoid ferrite) mixed with grains of pearlite (cementite plus eutectoid ferrite). (Fig. 9.27 – Note that all the dark regions are pearlite.  The alternating layers do not show up as well in some of the regions due to the closeness of the layer spacing) (The lever rule can be used to determine the ratio of these two.  The lower the carbon content, the more ferrite and less pearlite due to the fact that the 2 phase region will contain more a and less g (austenite).


Hypereutectoid Alloys:  Alloys with carbon content between 0.76 and 2.14 wt% (to the right of the eutectoid).  ).  These cool from the single phase austenite region, through a two phase cementite + austenite region into the ferrite + cementite region (Fig. 9.29).  As the material cools through the 2 phase region (Fe3C + g) the Fe3C (cementite) grains grow in size.  Upon crossing the eutectoid line, the remaining austenite converts to pearlite.  The result is a microstructure with grains of cementite (proeutectoid cementite) mixed with grains of pearlite (containing eutectoid cementite). (Fig. 9.30 – Note that all the dark regions are pearlite.  The cementite regions are the light regions.  It is hard to distinguish hypo and hyper eutectoid alloys from one another by simply examining their microstructure)


Nonequilibrium Cooling:  Can you predict what will happen if we cool the steel more rapidly?  (more in Chapter 10!)


The Influence of Other Alloying Elements

Alloys do many things for steels (including increasing their cost!).  Relative to this chapter, alloys change the eutectoid temperature (Fig. 9.31).  Most alloys raise it, a few (Mn and Ni) lower it.  Alloys also change the eutectoid composition (Fig. 9.32), with all common alloys lowering the C wt% of the eutectoid composition.


Homework Problems:  9.1, 9.5(c), 9.10, 9.16, 9.21, 9.48, 9.49, 9.51, 9.67