Quite a large number of phase diagrams of metal systems are available, but repeated investigations, with refinements in apparatus and techniques, lead to their frequent revision. No one method is best for all alloy systems, or even to locate all the boundaries in one alloy system.

A diffusion couple is used to get the number and the order of the phases in a system; thermal analysis is able to locate the liquidus lines with precision, and also the univariant equilibriums in a system; x-rays or metallographic methods are used to locate the boundaries between fields involving only solid phases.

No phase diagram is considered fully reliable until similar findings have been observed by at least two independent methods, and that diagram does not violate the phase rule, and other rules of construction based on thermodynamic reasoning.

The followings are some of the methods used in the determination of the phase diagrams:


1. Thermal analysis

2. Dilatometry

3. Microscopic methods

4. X-ray diffraction methods


5. Electrical-resistivity methods

Method # 1. Thermal Analysis:

Thermal analysis is the simplest and the most widely used method for the determi­nation of phase diagrams. Here, when a molten metal, or alloy is cooled very slowly, its tempera­ture is determined with time. A simple experimental set-up is used for this propose as illustra­ted in the Fig. 3.3.


It is possible to control the rate of cooling (or heating, if used) of the metal or alloy. If a body does not undergo any phase change, for example, a non-crystalline solid such as normal window glass (which is called a super cooled liquid) does not undergo freezing, then the temperature-time graph, i.e., the cooling curve is a smooth curve, Fig. 3.40 (a).


A phase change is accompanied by the evolution of heat. For example, when a pure metal solidifies, there takes place evolution of latent heat of freezing, which causes thermal arrest. Fig. 3.40 (b), and thus, the temperature remains constant near its freezing point till freezing are complete, and then the normal cooling takes place.

Experimentally, a liquid pure metal gets undercooled before freezing begins. The latent heat of freezing raises the temperature again almost (but little lower) to the equilibrium freezing temperature. This rise of temperature is called decalescence, Fig. 3.41 (a).


The change from the thermal arrest to further cooling is not always abrupt, instead, a ‘rounding’ (see Fig. 3.41 a) of this part of the curve is common because of the presence of the impurities, or improper experimental set-up. When a pure metal is heated, there takes place overheating before melting proceeds.


The thermal arrest temperature, now, is slightly higher than the equilibrium melting temperature. Fig. 3.41 (a) illustrates a range between the horizontal sections of the heating and cooling curves. This range could be reduced to a fraction of a degree, provided rates of cooling and heating are very slow.

As seen in Fig. 3.4, the bivariant transformations such as the freezing of a solid solution occurs over a range of temperature, i.e., instead of a thermal arrest, there takes place a retardation in the cooling rate. The ideal curve in Fig. 3.4 gets modified to the curve in Fig. 3.41 (b) due to undercooling and coring.

The true liquidus temperature is obtained by extrapolating the curve back to intersect with the initial part of the cooling curve as indicated in Fig. 3.41 (b). This temperature comes out to be closer to the actual liquidus temperature. The estimation of the solidus temperature present at the end of the solidification range, is hardly ever distinct because of the ‘rounding’ of the curve, which owes it to the coring effects.

A more accurate determination of the solidus temperature can be done by finding the break in the heating curve of the previously homogenised alloys. This break is at a higher temperature than that determined by cooling curve, as coring effects have been removed by homogenisation.


The thermal analysis data is supplemented with microscopic examination. In this method, the alloy is heated close to the solidus and quenched to ascertain microscopically the appearance of the first chilled liquid. Using the break points in the heating and the cooling curves of a series of compositions over the entire binary range, the liquidus and solidus boundaries can be determined as illustrated in Fig. 3.5 and 3.6, and has been drawn here in Fig. 3.42 for an isomorphous system.


The curve in Fig. 3.43 (a) is a characteristic cooling curve of a eutectic alloy. Good amount of undercooling as well as decalescence occur. The horizontal part of the curve, thus, lies at a slightly lower than true eutectic temperature, but merges gradually with it. Fig. 3.43 (c) shows cooling curve of a hypereutectic alloy having characteristics of the solid solution as well as of pure eutectic curves.

The horizontal isotherm of peritectic alloy is normally very small, and the ‘rounding’ of the ends of this horizontal occurs to make the estimation difficult. Undercooling is seen to be more prominent in eutectoid reaction than with eutectic, or monotectic, but still more in peritectic alloys. Changes in solid state such as a solvus curve are difficult to be obtained by thermal analysis.


The experimental set-up for thermal analysis could be a bit elaborate, Fig., 3.3, where cooling or- heating rates are controlled, as it helps to estimate the extent of undercooling, or over-heating, and because the cooling curve may be drawn straight with all deviations from the linear path assumed to be due to phase changes.

A differential thermocouple helps to control the rates of heating or cooling. It helps to determine the exact difference in melting points between the two alloys that melt, or transform at nearly the same temperature.

Thermal analysis of low melting alloy can be done even with a thermometer, a watch (with a second hand) and apparatus to melt the alloy. The heat is switched off when the alloy is molten, and the thermometer placed with its bulb in the centre of the sample. The temperature is read at uniform intervals of time, or the time required for a definite fall of temperature (1° or 5°, 10°). Then the cooling curve could be plotted on a graph.

The ‘inverse rate curve’ helps to mark more clearly the breaks (thermal arrests) in the cooling curve. Here, the time needed for one degree, or some fixed number of degrees of drop of temperature is plotted as a function of temperature, as illustrated in Fig. 3.44.


Thermal analysis method needs the following precautions to be carefully observed:

1. The chemical composition of the samples should be accurately determined.

2. The melt should not get contaminated from the atmosphere, the crucible, thermocouple sheath, etc.

3. There should be provision for stirring the molten alloy to obtain uniformity of temperature and to reduce supercooling.

4. As the data relates to the equilibrium conditions, the rate of cooling should be as slow as possible.

5. Temperature fluctuations inside the furnace should be avoided.

The thermal analysis is more commonly used for:

(i) Drawing the liquidus, if under-cooling, or overheating is not large as well as heat of the phase change is not too small, when detection becomes difficult.

(ii) For isothermal reactions.

(iii) It is more frequently used for the preliminary investigations of the alloy systems, i.e., gives rough approximation of the complete liquidus, and can indicate the presence of eutectic, peritectic, or congruently melting intermediate phase. All isothermal reactions occurring in the solid-state are indicated.

Dip Sampling:

This is one of the oldest methods of investigation. Liquidus points are easily detected by this method, particularly where thermal analysis method proves unsatisfactory due to severe undercooling.

Here the alloy is held at a fixed temperature in the two phase field of solid and liquid till equilibrium is attained. The solid crystals (depending on its relative density to liquid) separate by settling (or floating). The liquid can be decanted, and the clear liquid is analysed for the composition.

The procedure is repeated at a series of fixed temperatures to obtain the complete curve. For example, to determine the liquidus of a hyper-eutectic Al-Si alloy, the alloy is held in two-phase field of L + β (silicon-rich) at a fixed temperature. β-phase forms individual idiomorphic particles, which float on the top of the melt, and can be carefully skimmed. This method of dip sampling becomes difficult to be used if the solidifying dendritic-network interferes with separation of solid from liquid.

Method # 2. Dilatometry:

Dilatometry is based on the volume (length) change associated with most phase changes. Fig. 3.45 schematically shows the main features of a dilatometer. The temperature and dilation (change in length) of the sample are simultaneously monitored as a function of time. The simplest dilatomer usually consists of a silica tube with one end closed and provision for the sample to rest firmly upon the closed end inside the tube.


A silica rod rests upon the other end of the sample (Silica is used because of its very low coefficient of thermal expansion). A dial gauge secured to the outer tube and with its lever arm resting upon the protruding end of the silica rod serves to record the length changes.

A furnace may be used to enclose the sample assembly for temperature control. Dial gauges have been replaced by optical lever, or interferometers, etc. Now a day, a differential dilatometer is used wherein the length of the sample is compared with that of a bar of the similar metal of nearly the same expansivity but which does not undergo phase change within the temperature of interest.

With the latest sophisticated equipments, length changes of the order of 10-4 mm can be easily measured. The dilatometric method is always used in conjunction with metallography to cross-check the microstructure after transformation.


Fig. 3.46 illustrates changes in length of low carbon steel due to phase changes during heating and cooling. There is appreciable hysteresis here in temperatures of transformation during heating and cooling. Extremely slow heating and cooling rates minimise the errors due to undercooling and overheating.

Method # 3. Microscopic Methods:

There are various methods using microscopic techniques in determining the phase diagrams. Moreover, microscopic techniques are also used to verify the phase diagrams determined by other methods, where microscopic exa­mination of cast and heat-treated alloys at small composition intervals across the system is done. It is a worth-while but laborious work.


Microscopic method though is suited to general survey work, but more often complete solvus and solidus curves are determined by this method. A number of samples of an alloy, for example of ‘x’ composition of the alloy system as illustrated in Fig. 3.47, are taken and are kept for long periods, each at a different temperature from T1 to T9 so that equilibrium is attained.

The samples are then quenched fast to retain their high temperature microstructures, and then examined metallographically for quality and quantitative studies. Samples held at temperatures, T1, T2, T3 show presence of two phases, α and β; those held at T4, T5 and T6 show presence of single phase, α; while those held at T7, T8 and T9 show evidence of presence of liquid phase.

Thus, it can be concluded that for alloy of composition ‘x’, the solvus lies between temperature T3 and T4, and that the solidus lies between T6 and T7. If now different soaking temperatures in between T6 and T7 range, which are very close to each other, are used, it is possible to arrive at exactly the transformation temperature, i.e., the solidus temperature of alloy ‘x’.

Same procedure helps to obtain the exact solvus temperature. Complete solidus and solvus curves are determined by repeating this process with a series of alloys of progressively changing compositions. It is a good practice to approach the equilibrium point from two directions.

The main advantage of the microscopic method is its directness, i.e., we can observe the change. There is always more confidence in what we see than in what we infer from cooling curves, dilatometric curves, etc.

As high temperature microscopy has limitations, and thus, it is difficult to apply the microscopic method to metals, while at high temperatures. Microscopic examination is done of ‘quenched samples’, which may not always retain their high-temperature microstructures.

Thus, the directness of the method has limitations. Moreover, a considerable skill and mature judgement is needed for inferences to be drawn from microstructures. These two are main disadvantages of this method.

Method # 4. X-Ray Diffraction Methods:

X-rays are used while alloys are in solid-state to:

(i) Identify composition of a phase

(ii) Crystal structure of the phase

(iii) Lattice parameter of the crystal structure.

And, thus, are used to locate the solvus lines in phase diagrams. The method of lattice parameter measurement depends on the fact that crystal dimensions, i.e., lattice parameter increases with the increase of the solute content in the solid solutions, till it gets saturated.

Fig. 3.48 (b) shows that lattice parameter increases progressively in a-phase field, but remains constant in α + β field, because it is the lattice parameter of saturated α – phase at that temperature. This inflection point, thus, refers to the point on the solvus curve at that temperature.


A number of small samples of alloys of different compositions are prepared and homogenised completely. These are then annealed at a temperature, say T1 for a long period (a few days) to attain equilibrium.

These samples are quenched rapidly to retain high temperature phases (if high temperature phases are not retained then high temperature x-ray camera may be used). X-ray diffraction studies are then done on these samples at room temperature. As indicated in Fig. 3.48 (b), a composition like ‘x’ (Fig. 3.48 a) may indicate presence of second phase beyond it (no increase of lattice parameter of α beyond composition x occurs).

Practically, if the lattice parameter of the α- phase is first estimated as a function of the composition, then just a single measurement of the lattice parameter of α when the alloy has been annealed and established in the α + β field, indicates the composition of the α-phase on the solvus line at the temperature of annealing, here T1.

By annealing an (α + β) alloy at a series of temperatures (one at a time), and determining the lattice parameter after each annealing treatment, leads to a succession of points on the solvus line. This is a highly precised and simple method.

Method # 5. Electrical Resistivity Method:

The technique of measurement of electrical resistivity is often used to locate the solvus and horizontal isotherms in the solid state of the alloys.

The electrical resistivity of a solid solution changes nonlinearly with the increase in concentration of the solute. But the electrical resistivity of a phase-mixture is not characteristic of any one of the conjugate phases, but changes linearly with the volume fraction of the phases, Fig. 3.49 (b). The sudden change in the slope of the graph indicates the location of the phase boundary (solvus).


A series of alloys of progressively increasing solute content are prepared and homogenised. These alloys are heated to a temperature and kept for a long time to attain equilibrium (a few days). The electrical resistivity is measured either at the temperature of soaking (this practice is more preferred), or after quenching from this temperature (to retain the high temperature phases).

Resistivity is then plotted as a function of composition as indicated in Fig. 3.49 (b). The abrupt change in the slope indicates the solvus point. The procedure can be repeated for different temperatures to obtain different points on solvus line.

If a number of samples of one composition, after preparation and homogenising, are annealed for a long time each at a different temperature to attain equilibrium. Electrical resistivity is measured of each sample (either at that temperature, or after quenching from that temperature), then a graph is plotted between resistivity as a function of temperature, Fig. 3.49 (c).

The inflection in the curve indicates the location of a phase boundary, and the arrest in temperature indicates univariant transformation such as eutectic, Fig. 3.49 (c). Simple electrical resistivity measuring instrument could be used as here electrical resistivity relative to that of other samples is needed. It is a good practice, here too, to take readings approaching to equilibrium from two directions.

Some Other Methods:

A ferromagnetic phase has much higher saturation magnetic intensity as compared to a paramagnetic phase. If one of the phases present is ferromagnetic, then value of magnetic intensity indicates the appearance or disappearance of a phase. This method is used, in conjunction with some other method.

The fracture at liquation method is a simple method to locate solidus points and the eutectic temperature. A sample in the form of a bar is put under light static load. It is heated slowly and the temperature at which fracture occurs is determined. It indicates the solidus temperature for that composition in an alloy system. The result is only accepted if the fracture is clearly intercrystalline.