Binary Phase Diagrams

Relevant terms

-- component is a pure element (e.g. Fe, Si, or B) or stoichiometric compound (e.g. NaCl, Al2O3, or Si3N4), i.e. a component is a chemically distinct substance.

-- system is the volume occupied by a substance or series of alloys (e.g. Fe-C, Al2O3-Cr2O3, or ice-water).

-- phase is a chemically and structurally homogeneous region of a material.

-- homogeneous region is a region (or volume) in which the properties of a system are uniform.

-- phase diagram is a map of the regions in which the different phases exist when the system is in equilibrium.

-- solid solution describes the substitution of solute in solvent without a phase change.

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Examples

-- pure fcc-Cu is a single component (Cu), single phase (fcc) system.

-- a mixture of ice and water is a single component (H2O) system composed of two phases.

-- a mixture of bcc-Fe (ferrite) and fcc-Fe (austenite) is a single component system composed of two phases.

-- solid solution of Cu-Ni (or NiO-MgO) is a two-component, single- phase system.

One-component system

Simplified case, where phase relationships may be represented on a pressure-temperature diagram.

Phase equilibria can be described by the Gibbs phase ruleF = C P + 2

which relates number of degrees of freedom, F, at equilibrium to number of components, C, in the system, number of phases in equilibrium, P, and the two state variables temperature and pressure.

Fig. 25 - The equilibrium temperature-pressure diagramfor iron.Fig. 26 Pressure-temperature phase diagram for SiO2.

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In a one-component system, such as Fe or SiO2

-- if 3 phases are in equilibrium, then F = 1 3 + 2 = 0. This means that there is no freedom in specifying variables, so that the 3 phases can exist only at a point - triple point.

-- if 2 phases are in equilibrium, then F = 1 2 + 2 = 1. This means that if one variable is changed (T) then the other is automatically fixed (P), so that the 2 phases can exist along a line - phase boundary line.

Two-component system

Most practical materials are composed of two components, and, since pressure is usually fixed at 1 atmosphere, the important variables are temperature and composition. In such cases, the appropriate expression for the phase rule is

F = C P + 1

When pressure is eliminated as a variable, a two-dimensional phase diagram can be constructed, showing the regions of composition and temperature where the different phases are in equilibrium.

Specifying composition

In many practical situations, compositions are specified as weight percentages (wt.%) or weight fractions of components. Alternatively, compositions may be specified in terms of atomic percentages (at.%) or atomic fractions. The relationships are as follows:

Example

Calculate the atomic percentage of C in Fe for a two-component alloy containing 0.8 wt.% C.

= 3.63 at.% C In ceramic systems, compositions are usually expressed as mole fractions. If mole fraction of component A is NA, then

where nA and nB are the numbers of moles of components A and B, respectively.

Isomorphous system

This is the simplest two-component phase diagram.

-- displays complete solubility in both liquid and solid states over the entire composition range.-- for any mixture of the two components, solidification occurs over a temperature range, rather than at a specific temperature, as is the case for a pure component.-- liquidus curve separates single-phase liquid region from two-phase (solid + liquid) region.-- solidus curve separates two-phase (solid + liquid) region from single-phase solid region.Fig. 27 - An idealized binary(A-B) phase diagram with associated definitions.

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Hume-Rothery rules

In order to form a substitutional solid solution over a wide range of compositions, the following conditions must be met:

-- crystal structures of the two components (A and B) must be the same

-- size difference between components must not differ by more than ~15%.

-- valences of the two components must be similar

-- electronegativities of the two components must be comparableThese conditions are satisfied for many metallic and ceramic systems, e.g. Cu-Ni, Ag-Au, NiO-MgO, Al2O3-Cr2O3.

Fig. 28 Binary isomorphoussystems Cu-Ni and NiO-MgO

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Lever rule

The relative amounts of two phases in the semi-solid (solid + liquid) region can be determined by the lever rule.Amount of liquid of comp. Amount of solid of comp.

where Co is the composition of the mixture. A CL C0 CS B wt.% B T

Administrator (A)

Cooling curves

Experimentally, liquidus and solidus curves can be determined by taking cooling curves at different compositions.

-- for pure components, there is a sharp break in the cooling curve (thermal arrest) due to heat of transformation (crystallization).

-- for two-component mixtures, heat is released over a range of temperatures T = (TL TS), so that there is a change in slope of the cooling curve.Fig. 29 (a) A binary isomorphous phase diagram showing cooling curves for (b) pure component A, and (c) alloy 1.

Solidification and microstructure

Under equilibrium conditions, all compositions in an isomorphous system solidify in a similar manner.

Figure 30 Equilibrium solidification of alloy 1 (composition 0.6 B); (a) the cooling path and sketches showing the development of the microstructure, and (b) an expanded section of part (a) showing the compositions of the liquidus and solidus boundaries in the range of 1010C to 1060C.

-- at T1 the alloy begins to solidify, and the first solid crystallites to form have a composition given by the intersection of the horizontal T1 isotherm (tie line) with the solidus curve (xB = 0.70).

-- when the temperature is reduced to T2, the compositions of both liquid and solid phases are given by the intersection of the tie line with the liquidus and solidus curves (xS = 0.68; xL = 0.57).

-- similarly for T3, T4, and T5, until at T5 solidification is complete.

-- final result of solidification is a polycrystalline (many-grained) material.

-- at all temperatures, the amounts of liquid and solid phases are given by the Lever rule.

Example

What are the mass fractions of solid and liquid phases in equilibrium at T2?

Deviations from ideal behavior

The shape of the isomorphous diagram, Figure 27, reflects ideal mixing of the components A and B in both liquid and solid states. This means that the bond energies for A-B pairs must be equivalent to the average of the bond energies for A-A and B-B pairs, i.e. EAB = (EAA + EBB)/2.

-- when EAB < (EAA+ EBB)/2, then the A component prefers B nearest neighbors and vice versa; thus, the favored arrangement is an ordered solution in which the number of A-B bonds is maximized.

-- when EAB > (EAA+ EBB)/2, then the A component prefers As as nearest neighbors and the B component prefers Bs; thus, the favored arrangement is a clustered solution in which the number of A-B bonds is minimized.

If the clustering tendency in the solid phase increases, relative to that of the liquid, a melting point minimum occurs, resulting in the formation of an eutectic phase diagram.

Eutectic systemFigure 31 A binary eutectic phase diagram and the associated terms used to describe regions of a eutectic system.

As in the isomorphous system, the boundaries separating the liquid and solid phase fields and the two-phase fields are called liquidus and solidus boundaries, respectively.-- the two liquidus curves converge at an eutectic point, E, which is the lowest melting point in the system

-- at the eutectic point, the temperature and compositions of the two solid phases ( and ) are fixed. The invariant reaction may be represented as

L +

where and are the terminal solid solutions of B in A (x1) and A in B (x2) at the eutectic temperature.

Not present in an isomorphous system, solvus boundaries appear at both ends of the eutectic phase diagram, representing the temperature dependence of the solid solubility of each component.

Solidification and microstructure

1. Eutectic compositionFig. 32Schematic of the equilibrium microstructures for a Pb-Sn alloy of eutectic composition C3 above and below the eutectic temperature.

Fig. 33 - Photomicrograph showing the microstructure of a Pb-Sn alloy of eutectic composition. 375 x. Fig. 34 - Schematic representation of the formation of the eutectic microstructure in the Pb-Sn system.

Eutectic microstructure consists of alternating layers (lamellae) of (dark) and (light) phases, where and are solid solutions of Sn in Pb and Pb in Sn, respectively

-- microstructure is formed by counter-diffusion of Sn and Pb atoms just ahead of the advancing solid-liquid interface during solidification.

-- scale of the eutectic microstructure decreases with increasing cooling rate from the liquid state.

The weight fractions of and phases at the eutectic point are given by the Lever rule.

2. Off-eutectic compositionFig. 35 Schematic representations of the equilibrium microstructures for a Pb-Sn alloy of composition C4 as it is cooled from the liquid-phase region.

Fig. 36 Photomicrograph showing the microstructure of a Pb-Sn alloy of composition 50 wt.% Sn-50 wt.% Pb. This microstructure is composed of a primary Pb-rich phase (large dark regions) within a lamellar eutectic structure consisting of a Sn-rich phase (light layers) and a Pb-rich phase (dark layers). 400x.Off-eutectic microstructure (composition C4) consists of primary phase (formed during cooling through the semi-solid region) plus ( + ) eutectic (formed at the eutectic temperature, TE).

-- just above TE, the weight fraction of primary phase is

-- just below TE, the total weight fraction of phase (primary + eutectic ) is

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Cooling curves

Cooling curves can be used to determine the locations of eutectic point, liquidus curve, and solidus curve

Fig.37 The use of cooling curves to establish the liquidus and solidus in a binary eutectic alloy under equilibrium conditions.

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Alloy 3 (eutectic composition) experiences a sharp break in the cooling curve, due to isothermal transformation of the liquid phase into two solid phases (+).

Alloys 2 and 4 experience heat release over a range of temperatures T = (TL - TS), prior to isothermal solidification at the eutectic temperature, TE.

Alloys 1 and 5 behave like regular solid solution alloys, in that there is a change in slope of the cooling curve at TL and TS.

Complex systems

Most practical phase diagrams are more complex than the relatively simple isomorphous and eutectic systems considered so far. Figure 38 shows a binary phase diagram that comprises:

-- two eutectic reactions (L + ; L + ), a peritectic reaction (L + ), and an intermediate phase reaction (L ).

-- phase melts congruently, i.e. the compositions of liquid and solid phases are the same.

-- phase melts incongruently, i.e. it decomposes into two phases (L + ), such that composition of the liquid phase is different from that of the solid phase.

Fig. 38 (a) Complex phase diagram containing a peritectic and two eutectic reactions, and (b) invariant reactions in (a) emphasized along with their symbolic representations.

Eutectoid system

An eutectoid reaction is a solid-state reaction, involving the decomposition of a single solid phase () into two solid phases ( + ) having different compositions.

-- decomposition occurs by solute redistribution in the phase just in front of the two phase ( + ) region.

-- solid-state reaction is slower than liquid-state reaction, due to much slower diffusion rate in the solid state.

-- most important commercial system that exhibits an eutectoid reaction is the Fe-Fe3C system

Fe-Fe3C system

Upon heating, pure Fe experiences two solid state reactions:

912C 1394C-ferrite -austenite -ferrite (bcc) (fcc) (bcc)

Fig. 39 The Fe-C phase diagramWith the addition of C, these polymorphic transformations are drastically modified

-- the solubility of C in -austenite is large; maximum of 2.14 wt.% at 1147C.

-- the solubility of C in -ferrite is small; maximum of 0.022 wt.% at 727C.

-- when the solubility of C in and phases is exceeded, an intermediate phase Fe3C, known as cementite, makes its appearance.

Upon cooling from the fully austenitic state, an alloy of composition 0.76 wt.%C, the following eutectoid reaction occurs:

+ Fe3C(austenite) (ferrite) (cementite) pearlite Pearlite is the product of -austenite decomposition, and consists of alternating layers (lamellae) of -ferrite and Fe3C-cementite. -- pearlite is nucleated at the prior austenite grain boundaries, and propagates by a diffusion controlled mechanism -- C atoms diffuse away from the -ferrite regions into the adjacent Fe3C cementite regions.

Fig. 40 Schematics of microstructures for an Fe-C alloy of eutectoid composition (0.76 wt.% C) above and below the eutectoid temperature. Fig. 41 Photomicrograph of an eutectoid steel showing the pearlite microstructure, which consists of alternating layers of -ferrite (light phase) and Fe3C-cementite (dark phase). 500x

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Fig. 42 Schematic representation of the formation of pearlite from austenite; direction of carbon diffusion indicated by arrows.The wt. fractions of the constituent and Fe3C phases in pearlite can be determined using the Lever rule.

wt. fraction Fe3C = 0.11

Off-eutectoid composition

Alloy compositions to the left and right of the eutectoid (0.76 wt.% C) are termed hypoeutectoid and hypereutectoid, respectively.

-- cooling a hypoeutectoid alloy from the fully austenitic region gives rise first to pro-eutectoid -ferrite (along the prior austenite grain boundaries) and then pearlite.

-- similarly for hypereutectoid alloys, except that the pro-eutectoid phase is cementite.

-- the weight fractions of pro-eutectoid ferrite and total ferrite (pro- eutectoid + eutectoid ferrite) can be determined using the Lever rule.

Hypoeutectoid alloys comprise most of the commercially important steels, since they combine high strength (due to pearlite) and good fracture toughness (due to pro-eutectoid ferrite).

Fig. 43 Schematic of the microstructures for an Fe-C alloy of hypoeutectoid composition C0 (< 0.76 wt.% C), as it is cooled from within the austenite phase region to below the eutectoid temperature. Fig. 44 - Photomicrograph of a 0.38 wt.% C steel having a microstructure consisting of pearlite and pro-eutectoid ferrite. 635x.

Effect of cooling rate

Slow cooling from the fully austenitic region gives pearlite (diffusion-controlled transformation). (fcc) (bcc) + Fe3C (orthorhombic)

(austenite) (ferrite) (cementite) -- composed of alternating layers of ferrite () and cementite (Fe3C), Fig. 41.

-- formed by redistribution of C in the phase just ahead of the advancing two-phase ( + Fe3C) interface, Fig. 42.

-- pearlite is strong and tough.

Fast cooling from the fully austenitic region gives martensite (diffusion-less transformation). (fcc) (bct) (austenite) (martensite)

-- martensite has a needle-like morphology and is hard and brittle.pearlite

When heated, Fe3C begins to form as fine precipitates within the martensite needles.

-- this has the effect of reducing hardness and increasing toughness, called tempering.

When heated just below the eutectoid temperature for a long time (~10 hours), a relatively uniform distribution of coarse Fe3C particles is formed in an -ferrite matrix.

-- such a microstructure, called spheroidite, possesses moderate strength and good ductility.Fig. 45 Progress of athermal martensitic transformation in an Fe-1.8 wt.% C alloy after cooling to (a) 24C, (b) -60C, and (c) -100C.

Fig. 46 Microstructure of a tempered martensite (spheroidite) in a steel with 0.7 wt.% C.Isothermal transformation diagram

The pearlite transformation is both temperature and time dependent, whereas the martensite transformation depends solely on temperature, not time. This difference in behavior can be represented conveniently on an isothermal transformation (IT) diagram.

Fig. 47 Schematic of an isothermal transformation (IT) diagram for a eutectoid steel.Indicates microstructural consequences of changing cooling rate from the fully austenitic region

-- slow cooling forms pearlite

-- fast cooling forms martensite

Incubation period is characteristic of pearlitic transformation, since it occurs via a diffusion-controlled mechanism

-- nucleation and growth initiated at prior austenite grain boundaries

Martempering

This is a commercially important quench-and-temper process:

-- quench to a temperature just above Ms and hold to minimize thermal gradients that can lead to surface cracking

-- quench again to ambient temperature to form 100% martensite

-- reheat to tempering temperature to develop fine-scale Fe3C particles

-- resulting tempered martensite has high strength and moderate ductilityFig. 48 Schematic showing the cooling curve superimposed on IT diagram for martempering, or indirect quench process (with a temper step).

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