# Unary Phase Diagram

Phase diagrams are important and essential tools to understand compositional concentrations of two or more elements.

• These are influenced by temperature and pressure.
• Melting point of tungsten is 3400°C and that of aluminum 657°C, hence the two elements cannot blend together as their solid-liquid or intermediate phases restrict them to do so.
• However melting point of copper (1083°C) and nickel (1453°C); lead (327°C) and tin (232°C) in their equilibrium phase diagrams indicate the possibility of mixing.

# Phase Diagrams

Definition: Plots showing relations between phases in equilibrium versus composition, pressure and temperature are called phase diagrams. These are also known as equilibrium diagrams.

Temperature is plotted on ordinate (y-axis) and composition (in binary phase diagrams) or pressure (in unary phase diagram) on abscissa (x-axis) in a phase diagram. The composition is expressed in percent weight.

We can see from these diagrams the change in phases with respect to the changes in temperature or composition. Phase diagrams are always drawn at equilibrium state because a system always tries to be stable. The alloy systems involve a number of components. Based on these, the phase diagrams are classified as under:

1. Unary phase diagram (single component system)
2. Binary phase diagram (two components system)
3. Ternary phase diagram (three components system),
4. Quaternary phase diagram (four components system), and so-on.

Now we shall discuss them one by one.

# Unary Phase Diagram

Such phase diagrams are drawn for a single component system. Question of composition and compositional variable does not arise in it. Hence the phase map indicates temperature Ton y-axis and pressure p on x-axis.

Unary Phase Diagram of Iron: Consider the case of iron (Fe) whose phase diagram is shown in Figure 1. The diagram indicates different phases as a function of temperature and pressure. The gases, liquids, and solid forms of iron are single phases.

The boundaries AB, CDE, FDE, GHJ and GHK are phase boundaries for two phase equilibrium. Here D = 1 which implies that either temperature or pressure may be varied. If we want to maintain two phase equilibrium on these boundaries, then pressure and temperature both are required to be changed accordingly.

Triple point and constraint system: Three phase boundaries meet at points D and H. These points are known as triple points. Here, D = 0 and three phase equilibrium exists. As the degree of freedom is zero i.e. system is constraint, neither pressure nor temperature can be varied.

Crystal forms of iron such as BCC (α), FCC (y) and BCC (δ) are obtained at increasing temperatures. BCC (α) form converts to HCP (e) form near a pressure of about 15 GPa.

Unary Phase Diagram of Carbon: The carbon possesses different phases as shown in Figure 2. These are:

(i) Graphite          (iii) Metallic carbon

(ii) Diamond        (iv) Liquid

The graphite is stable solid phase at normal pressures, while the diamond is stable solid phase at high pressures, whereas the metallic carbon exists only at very high pressures. Thus the production of synthetic diamond requires very high pressure.

## Binary Phase Diagram

Such diagrams are a result of two components systems. In addition to pressure and temperature, a third variable `composition’ is also involved now. It, therefore, necessitates a three dimensional diagram to depict phases.

However for simplicity of plotting phase diagrams on paper; the temperature is taken on ordinate and composition on abscissa for a specified pressure. The specified pressure is generally atmospheric. As pressure variable is avoided arbitrarily, Gibb’s Phase Rule equation may be written as

D = C – P + 1 ………..(Equation 2)

Two component systems obeying Hume-Rothery’s conditions, and exhibiting complete solid solubility as well as liquid solubility result into binary phase diagrams. The two involved components dissolve in all proportions into each other in solid and liquid states.

A schematic binary phase diagram is shown in Figure 3. The two components are A and B. Percentage weight composition of A varies between 0 to 100 from left to right while that of B varies between 0 to 100 from right to left on horizontal axis named as composition or c-axis. Temperature is plotted on ordinate.

Solidus and Liquidus: There are two single phase regions, viz. the solid and the liquid. Solid phase region lies below TsMNTL, boundary. The liquid phase region lies above TsQTL, boundary. There is also present a two-phase region marked L + S. It lies between the above two boundaries. Solid and liquid phases co-exist in this region.

The boundary TSMNTL between solid phase and (L + S) phase, is called solidus while TSQTL between liquid phase and (L + S) phase, is known as liquidus. Ts is the temperature below which the system is in solid phase, and TL is the temperature above which the liquid phase exists.

Tie line: The horizontal line QN at temperature T1 is called the tie-line. Another horizontal line RS is tie-line at T2 temperature. If our interest is to obtain mix composition of components A and B at T1 temperature, we consider tie-line QN.

The intersection of this tie-line with liquidus at Q gives liquid composition Cl, and intersection with solidus at N gives solid composition Cs. From Equation 2, the degrees of freedom are

D = 2 – 1 + 1 = 2 for single phases, and D = 2 – 2 + 1 = 1 for two phase region.

Variables for two-phase region: As D = 1 for two-phase region, only one out of three variables named below may be varied. These are

1. Temperature
2. Liquid composition Cl, and
3. Solid composition Cs.

We are not free to choose any percent combination of two components at any arbitrary temperature. Either temperature is to be pre-fixed or composition of one phase is to be specified initially.

## Binary Isomorphous Phase Diagram

By isomorphous system we mean a system in which there is complete solid and liquid solubility of two components. Copper-nickel system is one such example. It is shown in Figure 4.

Liquidus, solidus, and different phases are shown in it as a function of temperature and composition. The melting point of Cu is 1085°C and that of Ni is 1453°C. All other details are similar to as explained in earlier paragraphs, and hence are self-explanatory.

## Types of Binary Phase Diagrams

Depending on small or large, complete or incomplete, and limited or unlimited solid solubility of elements and compounds; and also the melting points of the two components; the binary phase diagrams may be further classified as follows.

1. Eutectic phase diagram
2. Eutectoid phase diagram
3. Peritectic phase diagram
4. Peritectoid phase diagram

Eutectic, eutectoid, peritectic and peritectoid terms are related to phase transformations, and are discussed in following sections with their respective phase diagrams.

## Eutectic Phase Diagram

An eutectic phase diagram is obtained when the melting points of the two components of phase diagram are neither very close nor much different. Only liquid solubility exists in such cases.

The solid solubility may be negligible or partial. Solid solubility is never zero even in an unfavorable condition. Thus, there are two cases of eutectic phase diagrams viz.

• Complete liquid solubility with negligible solid solubility. Cadmium-bismuth system is the example, and
• Complete liquid solubility with partial solid solubility. Lead-tin system is the example of this case.

Phase Diagram of Lead-Tin System: The phase diagram of lead-tin alloy system is shown in Figure 5. Melting points of lead (Pb) and tin (Sn) are 327°C and 232°C respectively. In the solid α phase, a very small amount of tin is dissolved in lead.

The other solid phase is β in which very small quantity of lead is dissolved in tin. Both the components dissolve in each other sufficiently in (α + β) phase.

Two-phase regions (α + β) and (α + L), (α + β) and L; (α + β) and (β + L) are separated by a horizontal line BDE. This line corresponds to a temperature Te known as eutectic temperature.

Composition at point D is called eutectic composition Ce. At this point, the liquid phase L transforms to (α + β) phase during cooling and vice-versa during heating. It can be expressed by an eutectic reaction as given below:

Invariant point: Composition of Sn and Pb at points B, D and E are shown at eutectic temperature. These cannot be varied because degree of freedom for three phases in equilibrium is zero. It can be verified by equation 2 which yields

D = 2 – 3 + 1 = 0

The eutectic temperature and eutectic reaction are called invariant temperature and invariant reaction respectively to indicate D = 0.

Phase boundaries and solvus: In Figure 5, different phases are separated by various phase boundaries, whose details are given below.

• Boundary CD between L and α + L phases is liquidus I.
• Boundary DF between L and β + L phases is liquidus II.
• Boundary BC between α and α + L phases is Solidus I.
• Boundary EF between β and β + L phases is Solidus II.
• Boundary AB between α and α + β phases is Solvus I.
• Boundary EG between β and α + β phases is Solvus II.

Compositions of alloys left to the point D are called hypoeutectic alloys, and those to the right are known as hypereutectic alloys.

## Eutectoid Phase Diagram

The transformation of liquid phase into solid phase on cooling and vice versa has been described in the previous section. In eutectoid system, a solid phase replaces the liquid phase of eutectic system. The eutectoid reaction involves transformation of a solid phase into two other solid phases on cooling and vice versa, and is expressed as

Hypo-eutectoid and hyper-eutectoid: Recall equation 3 whose phase L has been replaced here by y phase. If this replacement is done in Figure 5, it will constitute α + L phase as α + y, and β + L phase as β + y phase respectively.

Te will now be known as eutectoid temperature, and the composition at point D will be called eutectoid composition. The alloy compositions left to point D is known as hypo-eutectoid, and towards right of D is called hyper-eutectoid.

Illustration: An eutectoid reaction takes place at 723°C in iron-carbon system where eutectoid composition contains 0.83% carbon. Here, the austenite, a solid solution of carbon in y-iron decomposes into two solid phases named ferrite (alpha-iron) and the cementite (Fe3C). These are shown later in Figure 7. Eutectoid reaction occurs in other systems also such as Cu-Be, Al-Mn, Cu-Sn, Cu-Al etc.

## Peritectic Phase Diagram

Such a phase diagram is obtained when the melting points of two components differ too much from each other.

The gold-lead system is an example. Here the melting points of gold and lead are 1063°C and 327°C respectively. Thus a vast difference of 736°C exists.

Another example is that of silver (Ag) and platinum (Pt) system whose phase diagram is shown in Figure 6. The difference in melting point of platinum (1769°C) and silver (961°C) is more than 800°C. Various solid phases, two phase regions and liquid phase are shown.

Horizontal tie-line ABC denotes peritectic temperature Tp which is 1185oC. The composition Cp at point B is called peritectic composition. At this point, the solid liquid phase β + L transforms to a single solid phase α on cooling, and vice-versa. The degree of freedom is zero here. So the peritectic reaction is an invariant reaction, as follows:

Different phase boundaries are names in a similar manner as described for eatectic phase diagram.

## Peritectoid Phase Diagram

Such phase diagrams involve transformation of two solid phases into a different solid phase on cooling, and vice-versa. Contrary to peritectic reaction where solid-liquid phase β + L changes to another solid phase α; here solid-solid phase changes to another solid phase. It is given by

## Interpretation of Phase Diagrams

From a binary system of known composition and temperature at equilibrium, the following three kinds of information are available, viz.

• the phases that are present,
• the compositions of these phases, and
• the percentages or fractions of the phases.

The procedures for making these determinations are given below.

Determination of the phases present: To determine what phases are present, we should locate the temperature-composition point on the diagram and note the phase(s) with which the corresponding phase field is labeled.

For example, an alloy of composition 60 wt% Ni + 40 wt% Cu at 1100°C would be located at point A in Figure 4. Since this is within the A region, only the single a-phase will be present.

On the other hand, a 35 wt% Ni + 65 wt% Cu alloy at 1250°C (point B) will consist of both a and liquid phases at equilibrium.

Determination of Phase Composition

First of all, we should locate the temperate-composition point on the phase diagram. Different methods are used for single and two-phase regions. If only one phase is present, the composition of this phase is simply the same as the overall composition of the alloy.

For example, 60 wt% Ni + 40 wt% Cu alloy at 1100°C (point A, Figure 4), only a-phase is present, having a composition of 60 wt% Ni + 40 wt% Cu.

Isotherm: For an alloy having composition and temperature located in a two-phase region, one has to draw a series of horizontal lines, one at every temperature. Each of these is known as a tie line or isotherm.

These tie lines extend across the two-phase region and terminate at the phase boundary line on either side. To compute the equilibrium concentrations of the two phases, the following procedure is adopted.

1. A tie line is constructed across the two phase region at the temperature of the alloy.
2. The intersections of the tie line and the phase boundaries on either side are noted.
3. Perpendiculars are dropped from these intersections to the horizontal composition axis, from which the composition of each of the respective phases is read.

Illustration: For example, we consider 35 wt% Ni-65 wt% Cu alloy at 1250°C, located at point B in Figure 4, and lying within the α + L region. The tie line has been constructed across the α + L phase region.

The perpendicular from the intersection of tie line with liquidus boundary meets the composition axis at 31.5 wt% Ni-68.5 wt% Cu, which is the composition of the liquid phase CL. Likewise for the solidus-tie line intersection, we can find a composition for the α solid-solution phase Cα, of 42.5 wt% Ni-57.5 wt% Cu.

Determination of Phase Amount

We see from the previous example for the 60 wt% Ni-40 wt% Cu alloy at 1100°C (point A in Figure 4) that only α-phase is present; hence the alloy is completely (or 100%) α.

For a two-phase region, the tie line must be utilized in conjunction with a procedure that is called lever rule which is applied as follows.

• The tie line is constructed across the two-phase region at the temperature of the alloy.
• The overall alloy composition is located on the tie line.
• The fraction of one phase is computed by taking the length of tie line from the overall alloy composition to the phase boundary for the other phase, and dividing by the total tie line length.
• The fraction of the other phase is determined in the same manner.

If phase percentages are desired, each phase fraction is multiplied by 100. For more details, see article on lever rule.

Illustration: Let us examine an alloy of composition C2 as it is cooled along the vertical line xx’ in Figure given below. Down to the intersection of xx’ and the solvus line, changes that occur are similar to the previous case, as we pass through the corresponding phase regions (as demonstrated by the insets at point d, e and f).

## Iron-Carbon Phase Diagram

The iron-carbon system, being the most important and common in engineering applications, will be described in detail.

It has already been discussed that carbon has different forms. Iron (Fe) with carbon (C) in graphite form is more stable than iron with iron carbide (Fe3C) component in Fe-Fe3C phase diagram. Fe3C is contained by steels having widely varying carbon content, hence we shall study the metastable phase diagram of Fe-Fe3C.

Weight percent of carbon is plotted on x-axis against the temperature on y-axis as shown in Figure 7. Various solid phases are marked by α and y symbols. Single liquid phase L, solid-liquid phases y+ L etc. and the solid-solid phases α + Fe3C and y+ Fe3C etc. are shown in it.

Eutectoid Point: In Figure 7, point A is eutectoid point. The eutectoid temperature is 723°C and eutectoid composition is 0.83% carbon. Eutectoid reaction is expressed by

Eutectic Point: The eutectoidal mixture of ferrite and cementite is called pearlite. This is a microconstituent. Fraction of ferrite in eutectoid steel is 88%.

Point B is eutectic point whose coordinates are Ce = 4.3% carbon and Te = 1175°C. The eutectic reaction is expressed as

Peritectic reaction occurs at point C where peritectic composition is 0.18% carbon and peritectic temperature is 1495°C. Here, the invariant reaction is

Effect of Percentage of Carbon on Melting Point: Melting point of iron in its purest form is 1539°C. It lowers down with an increase in the percentage of carbon and is lowest (about 1175°C) at 4.3% carbon.

The α-phase is called ferrite, Fe3C is cementite and y-phase is known as austenite. Iron and steel are also termed as ferritic steel in α – region, austcnitic steel in y – region and cast iron when carbon percentage exceeds 2%.

## Applications of Phase Diagrams

Phase diagrams are of great utility in various applications. Some of their important uses are given below.

Alloy Making : Correct compositions of alloying elements at specified temperatures are obtained with the help of phase diagrams.

Zone Refining : Purification of materials is done by the principle of phase separation. Concentration of impurity in semiconductors is controlled by zone refining.

3. Softening of Refractories : Presence of impurities lower down the melting points of high temperature resisting ceramics known as refractory. For example Mg0 as an impurity lowers the melting point of alumina Al203. Phase diagram helps in sorting-out this problem so that the presence of impurities may be avoided.

4. Tempil Sticks : Phase diagrams help to know the eutectic temperature and eutectic composition which is utilized to make eutectic alloys. As these alloy melt at constant temperature, hence they are suitable for temperature measurement. Commercially they are known as tempil sticks.

5. Solder Wire: The eutectic alloy of Pb-Sn (38% – 62%) is used as soldering material to join two metals.

6. Safety Devices: Safety against fire is of utmost importance in petroleum industry, gas filling plants and other hazardous industries. Low melting eutectic alloys are useful in such cases. The phase diagram helps in making proper composition of such alloys of Bi, Cd, Pb and Sn etc.

7. Semiconductor Devices: Eutectic alloys of Au-Si, Ga-Al-As etc. are used in the manufacturing of transistors, thermistors, junction rectifiers and the solar batteries etc.