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In this article we will discuss about:- 1. Introduction to Pearlite 2. Morphology of Pearlite 3. Hull-Mehl Model 4. Experimental Characteristics 5. Diffusion of Carbon during Pearlitic Growth 6. Interlamellar Spacing, S_{0} 7. Crystallography 8. Effects of Pearlite on Properties of Steels.

**Contents: **

- Introduction to Pearlite
- Morphology of Pearlite
- Hull-Mehl Model
- Nature of Nucleus in Pearlite
- Experimental Characteristics of Transformation
- Rate of Pearlitic Growth
- Diffusion of Carbon during Pearlitic Growth
- Interlamellar Spacing, S
_{0 } - Crystallography of Pearlite
- Kinetics of Pearilte Formation
- Effects of Pearlite on the Properties of Steel

1. Introduction to Pearlite:

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Pearlite is, probably, the most familiar micro-structural feature. When austenite in iron-carbon alloys is transformed isothermally below the eutectoid temperature at small undercooling, it undergoes eutectoid transformation to produce a unique micro- structure termed “pearlite”, which was discovered by Sorby in 1864. Pearlite is a common constituent of a large variety of steels, where it substantially increases the strength.

This constituent-pearlite-consists of alternate plates of cementite and ferrite, with ferrite the continuous phase as illustrated in Fig. 3.19 (a microstructure of furnace cooled eutectoid steel). Pearlite is not a phase, but a mixture of two phases, viz., cementite and ferrite. It is however a constituent because it has a definite appearance under the microscope, and can be clearly identified in a structure consisting of several constituents.

The origin of the name “pearlite” is related to the fact that a polished and etched pearlitic structure has the colourfulness of mother-of-pearl. The colour results from the fact that in the lamellar structure, etching attacks the ferrite phase more severely than cementite, and the raised and the regularly spaced cementite lamellae of the colonies then act as diffraction gratings (Fig. 3.20).

A pearl-like lustre is produced by the diffraction of light of various wave lengths from the different colonies. Colonies of lamellae of various orientations and spacing’s characterize the microstructure. The pearlitic reaction in the steels has been of such predominant importance to metallurgists that at times, pearlite is used as a generic term, and any eutectoid transformation is called pearlitic transformation.

**The amount of cementite and ferrite in pearlite obtained in Fe-0.77% C alloy at 727°C (or slightly below it) can be determined by calculations based on ‘Lever Rule’ as: **

The densities of ferrite and cementite are 7.87 and 7.70 g/m^{3} respectively, i.e., are so close that the volume percentages of ferrite and cementite in pearlite are essentially the same as the weight percentages. The amounts of these phases visible in micrographs are related to area percentages (or even proportional width of them), which in turn are directly related to their volume percentages, i.e., the widths of ferrite and cementite are, in general, in the ratio of around 8:1.

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**The spacing variations of the cementite lamellae in the different regions (or colonies) as seen in Fig. 3.19 may be different due to two reasons: **

(i) The differences in the angles that the lamellae of different colonies make with the plane of polish of the sample as illustrated in Fig. 3.20. The colonies with lamellae perpendicular to the plane of polish show the true spacing, or the closest spacing, others show different spacings.

(ii) The pearlite may have formed over a range of temperatures during continuous cooling of the steel. The interlamellar spacing decreases as the temperature of austenite transformation to pearlite decreases (the ratio of width of ferrite to cementite still remains as 8:1).

In eutectoid steel, no proeutectoid ferrite or cementite forms and the steel begins to transform into lamellar pearlite below the temperature, Ae_{1}. If a steel of composition x x (Fig. 3.21) is allowed to cool slowly, only proeutectoid ferrite will be nucleated between the temperature of A_{3} and temperature T_{x}, as above this temperature range, the steel remains in the metastable y-region of the extended γ/γ + Fe_{3} C phase boundary (Fig. 3.21). Pearlite can be nucleated by what is known as ‘cooperative nucleation’ of cementite and ferrite, once the temperature is lowered below T_{x}.

If the cooling rate is increased (as in normalising compared to annealing) so as to run through the temperature interval of A_{3} and T_{x}, no free ferrite would be able to nucleate, and the structure will be wholly pearlite although the steel is hypoeutectoid in composition. Similar is the case if hypereutectoid steel is cooled faster to produce wholly pearlite in structure. Pearlite composition is a function of the relative width of the ferrite and cementite plates.

Pearlite can lower its carbon content to below eutectoid (0.77% C) levels through increased ferrite width, and also can increase its carbon level through reduced ferrite width. The standard ratio of 8:1 as the relative widths of ferrite to cementite therefore corresponds to eutectoid alloys under slow cooling conditions.

** 2. Morphology of Pearlite****: **

The transformation of austenite to pearlite occurs by nucleation and growth. Nucleation mostly occurs heterogeneously. If the austenite is homogeneous, then the nucleation of pearlite occurs almost exclusively at the grain boundaries of austenite.

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It the austenite is not homogeneous, and contains undissolved carbide particles, or areas having higher concentration (> 0.77% C) of carbon, then the nucleation can occur at the grain boundaries as well as in the centres of austenite grains, where carbide particle is present, or even in areas of higher carbon concentrations, or on the inclusions, if present.

The nucleated pearlitic structure then, grows into the austenite as roughly spherically shaped grains called nodules as seen in a microstructure obtained by split transformation a schematic picture is illustrated in Fig. 3.22 (a). Each of these nodules consists of a number of structural units, in each one of which, the lamellae are largely parallel.

These structural units are generally called pearlite colonies. It is often observed that pearlite nodule grows into only one of the adjoining grains. As seen in Fig. 3.22 (a), grain boundaries are saturated with nuclei, the rest transformation occurs by growth of this grain boundary nucleated colonies into austenite. The early Hull-Mehl model explains it.

** **

** 3. Hull-Mehl Model****: **

In this model, the initial nucleus is a widmanstatten platelet of cementite, and forms at the grain boundary of austenite grains and grows into one of the austenite grains as illustrated in Fig. 3.23. (a). As this thin and small plate grows, it thickens as well as grows in length.

This process is accompanied with removal of carbon atoms from the austenite on both sides of it till, the carbon content in the adjacent austenite, in contact with it, reaches some more, or less fixed low value at which ferrite nucleates and grows along the surface of the cementite plate as illustrated in Fig. 3.24 (a) and (b).

As ferrite plates contain almost zero percent carbon, their growth leads to buildup of carbon at the ferrite-austenite interface (Fig. 3.24 b). This buildup of carbon continues until there is enough carbon to nucleate fresh plates of cementite.

Then, these fresh plates of cementite grow to cause the formation of new plates of ferrite. This process of formation of alternate plates of ferrite and cementite forms a colony. A new cementite nucleus of different orientation may form at the surface of a colony (Fig. 3.23 d), which leads to the formation of another colony. As the second colony grows, the edge wise growth of the first colony continues. In a given colony of pearlite, all the cementite plates have a common orientation in space.

It is also true of all the ferrite plates in a colony. If austenite transforms to pearlite at a constant temperature, then the interlamellar spacing, i.e., the spacings between adjacent lamellae of cementite is the same in all the colonies of pearlite. It has also been experimentally shown that interface between pearlite and austenite is an incoherent high energy interface, which grows into that austenite grain with which the pearlitic ferrite and cementite have no orientation relationship.

Presence of this incoherent interface is essential for the high mobility of the interface to form pearlite. Hillert showed that the morphology of pearlite can be explained by a branching mechanism. He demonstrated by a successive etching, technique that the carbide lamellae of a colony were completely interconnected.

**4. Nature of Nucleus in Pearlite**:

Pearlite is a two-phase structure, consisting of alternate plates of ferrite and cementite. The active nucleus is defined as the first one of ferrite, or cementite, to form with a lattice orientation with austenite, which will later be found in the transformed products. Hillert has described a series of experiments that determined relative crystallographic orientations, and the results indicate that pearlite in steel may be nucleated by either ferrite, or cementite.

In hypereutectoid steels, the proeutectoid cementite nucleates pearlite, and in hypo eutectoid steels, the proeutectoid ferrite nucleates the pearlite. In eutectoid steels, the active nuclei could be either ferrite, or cementite, but may appear to be cemenlite. The actual mechanism of the nucleation is fairly complex.

Hillert’s study indicates that in atleast some cases, there is an initial competition between the two phases with the first phase forming a film and then, the other nucleating on adjoining film, until eventually crystallographic and compositional conditions are evolved that produce an alternating structure of ferrite and cementite. As this structure then grows, the ferrite-cementite spacing adjusts itself by a branching process, until the steady-state spacing characteristic of the transformation temperature is attained.

One may visualise that a pearlite colony grows by two modes of growth. Edge-wise growth would be accomplished by simple diffusion process of carbon, because of concentration gradient ahead of interface, and where each plate simply extends at its thin edge. Sidewise growth however would require, in addition to diffusion, alternate nucleation of ferrite and cementite plates. Pearlite nodules nucleate at grain boundaries and grow into austenite grains radially.

At small undercooling, the number of pearlite nuclei nucleated is small, and nodules can grow edgewise, without the side wise growth (along a given grain boundary) and interfering with one another. At relatively higher undercooling, the nucleation rate is also greater and the grain boundaries become covered with pearlite before a significant amount of transformation can occur.

**5. Experimental Characteristics of Transformation****: **

TTT diagram of a steel illustrates the transformation of austenite to pearlite, etc. The nose of the curve coincides with the temperature of the maximum rate of this transformation. The time interval at the nose of the curve increases, with the increasing austenite grain size (and also in the presence of usual elements such as Cr, Mo, Ni, Mn), i.e. the TTT curve of a steel with coarser grains is on the right to the same steel but having finer grains.

As the nucleation of pearlite occurs predominantly at the austenite grain boundaries, a steel having finer austenite grains has more grain boundary area per unit volume, i.e., has more number of potential nucleation sites for pearlite, and thus, results in higher transformation rate, i.e., lower time at the nose of the curve. The time dependence of the nucleation rate in the early stages has been seen to increase as the square of time.

Fig. 3.26 illustrates the effect of time on the rate of nucleation, where this rate is taken as Fig. 3.26. Time dependence of rate of nucleation number of nuclei formed per unit volume (usually cubic at a temperature (eutectoid steel at 680°C). millimeter) per second. It is not constant even at a temperature.

Fig. 3.27 illustrates that the rate of nucleation increases with decreasing temperature of transformation to become almost maximum at around 550°C. Actually, the rate of nucleation is extremely structure-sensitive, as it is heterogeneous in nature. The rate of nucleation, closely below A_{1}, is very small, and the grain boundary nucleation can then be approximated to be random, since the site saturation may not occur. The growth rate then, has a finite value (10^{-3} to 10^{-4} mm/sec).

Thus, only a few pearlite nuclei form, but due to high growth rate, grow into large pearlite nodules. The nodules grow to sizes larger than the original austenite grains, i.e., the nodule growth takes place across austenite grain boundaries

The overall transformation rate is more sensitive to the early nucleation than to later, since the first formed nodules have greater time to grow. Both, the nucleation rate and the growth rate are strongly temperature dependent as illustrated in Fig. 3.27, but the morphology of the pearlite obtained strongly depends on their ratio.

When N/G ratio is high, the nodules grow, but only a little distance as impingement occurs soon from the neighbouring growing nodules. Although, both N and G increase as the temperature falls, N increases at much faster rate than does G, such that there may be a number of pearlite nodules growing into a single austenite grain. As pearlite colonies have almost equal rates of growth in directions parallel and perpendicular to the lamellae, a pearlite nodule is usually spherical in shape, which under microscope has a circular shape.

The growth rate of a pearlite colony, or nodule (before impingement occurs), is independent of time at a constant temperature. Fig. 3.28 illustrates the effect of time at a constant temperature of transformation of 680°C on the radius of pearlite nodule in an eutectoid steel.

The slope of this straight line is G. It has been found that the growth rate is structure-insensitive, i.e. structural changes such as grain size, presence, or absence of carbide particles have little effect- However, G is markedly dependent on temperature, specifically, the degree of cooling ΔT, below eutectoid temperature.

Fig. 3.27 illustrates that growth rate increases as the temperature falls below eutectoid temperature to reach a maximum at the nose of the TTT curve, and then, decreases with further fall of the temperature, but more or less, the growth rate remains in the range of 10^{-4} to 10^{-2} mm/sec. G is also strongly decreased by the substitutional type of alloying elements. The presence of 0.5% molybdenum in steel decreases the growth rate by about two orders of magnitude.

Interlamellar spacing, S_{0}, in pearlite, is defined as the distance from the centre of ferrite (or cementite) plate to that of the next ferrite (or cementite) plate of a colony, when the plates are perpendicular to the plane of polish of the sample. Interlamellar spacing is constant in pearlite obtained from austenite at a fixed temperature, i.e., it is characteristic of the temperature of formation of pearlite. Interlamellar spacing of pearlite is not structure sensitive, i.e., is independent of austenite grain size, or heterogeneity of austenite. However, it decreases with decreasing temperature of transformation as illustrated in Fig. 3.29.

**Interlamellar spacing of pearlite is.an important parameter in the decomposition of austenite:**

(i) Fundamentally, on account of its importance in analysing the factors affecting the rate of growth, and

(ii) Technologically, because it exercises significant influence on the mechanical properties of unhardened steels.

For example, austenite transformed isothermally to pearlite at 700°C results in the interlamellar spacing of about 10^{-3} mm to yield a micro-structure of hardness about 15 HRC, whereas when transformed at 600°C, yields interlamellar spacing of 10^{-4} mm to have a hardness of 40 HRC. Interlamellar spacing is increased by alloying elements like Ni, Mn, Mo, etc. and is decreased by cobalt.

**6. Rate of Pearlitic Growth: **

The following theory is based on the diffusion of carbon in austenite, which is due to concentration gradient produced parallel to the interface [x y in Fig. 3.30 (b)]. Just on the austenite side of austenite-ferrite interface, iron atoms cross the interface to form ferrite lattice, leaving behind carbon atoms in austenite, which increases the carbon concentration in austenite adjoining the ferrite.

Whereas, the austenite adjoining the cementite lamellae is depleted of carbon as a large numbers of carbon atoms are used-up in making cementite. This results in a falling concentration gradient between a point opposite the centre of ferrite lamella to a point opposite the centre of the neighbouring cementite lamella. These two concentrations at a particular transformation temperature, are obtained by extrapolation of the corresponding phase boundaries into the metastable region of the Fe-Fe_{3}C diagram as illustrated in Fig. 3.21, and is called Hultgren’s extrapolation.

At a transformation temperature, T_{x}, C_{a} represents the composition of austenite in equilibrium with ferrite, and C_{b} represents the composition of austenite in equilibrium with cementite. As C_{a} > C_{h}, so a concentration gradient exists in austenite for the carbon to diffuse from regions which would transform to ferrite to regions that would form cementite.

**According to Fick’s first law of diffusion: **

where, J is the amount of matter (here flux of carbon atoms) crossing an area A per second under a concentration gradient, dn/dx, and D^{γ}_{c}. is the diffusion coefficient of carbon is austenite.

Fig. 3.30 illustrates the growing pearlite colony. It can be safely assumed that during the growth of pearlite, all the carbon atoms inside the austenite volume between the planes OPQR and O’ P’ Q’ R’ diffuse at a steady rate to help in the growth of cementite lamella (which meets the plane OPP’O’ of austenite). The growth rate of cementite lamella can be taken to be growth rate of pearlite.

As cementite has a fixed carbon content of 6.67%, its growth rate is directly proportional to the number of carbon atoms per second leaving the austenite and joining a cementite lamella, as well as inversely proportional to the cross-sectional area of the cementite lamella, that is,

where, G is the growth rate (mm/sec), J is the flux of carbon atoms (amount of matter) into the cementite lamella, and A is the cross-sectional area of cementite lamella.

The growth rate of pearlite can also be taken to be proportional to the flux of carbon atoms per unit area shown by curved surface OPP’O’. Thus, with this surface as the area,

Now, using the concentration gradient to be proportional to (C_{a} – C_{b}) and inversely as half of the interlamellar spacing, so, we get-

where, k is a constant independent of time and temperature. Zener, likewise, derived an expression for growth rate as,

where, C_{p} and C_{y} are the number of solute atoms per unit volume in the two phases. If the extrapolated phase boundaries in Fig. 3.21 are taken to be the straight lines, then,

where, ΔT is the degree of super-cooling below the eutectoid temperature, and as |Δ g| ∝ Δ T, then

where, k’ is a constant independent of time and temperature, and Δ g is the change in free energy. The equation concludes that the growth rate is constant at a constant temperature as is found experimentally in pearlite as illustrated in Fig. 3.28. As the interlamellar spacing, S_{0} is seen to decrease linearly with the temperature, i.e.,

It proves that growth rate is zero at T = Te. As the temperature drops below eutectoid temperature, it increases approximately as (ΔT)^{2}. After reaching a maximum, the growth rate decreases again because the exponential term then dominates, i.e. this term becomes very small at lower temperatures resulting in decrease in growth rate again.

**7. Diffusion of Carbon during Pearlitic Growth****:**

A number of theories have been put forwarded to explain the growth of pearlite. Most of them have taken into account the factors involved in the edge wise growth of pearlite colonies, i.e., growth taking place at the ends of the lamellae. As pearlite grows, the interface x y (Fig. 3.30 b) moves into austenite of constant composition (≈ 0.77% C) with a constant velocity, and leaves behind it parallel plates of ferrite and cementite of constant width, and thus, the growth is primarily a steady state phenomenon.

However, looking at this figure, the carbon concentration is constant (0.77%C) at a relatively small distance into austenite, but on crossing the interface, whole of the carbon segregates to a high value of 6.67% in cementite lamellae and almost nil in ferrite. This necessitates a large amount of diffusion of carbon in a very small volume near the interface to form cementite plates. This massive diffusion of carbon can occur, either in austenite, through ferrite, or possibly along the austenite-pearlite interface.

By virtue of greater solubility of carbon in austenite, larger concentration gradients are possible in austenite than in ferrite. But at the temperature of interest in pearlite transformation, D^{α}_{c}, the diffusion coefficient of carbon in ferrite is larger than D^{γ}_{c} in austenite to make diffusion rates in ferrite around 100 times faster than in austenite. And the diffusion coefficient, D^{b}_{c} for diffusion along austenite-ferrite interface will be the largest, but the cross- sectional area for the diffusion flux is very small here, and a ratio of D^{b}_{c}/D^{L}_{c} (where, L stands for lattice diffusion) greater than 10^{3} is needed to make boundary diffusion dominant, but such a large ratio is not normally expected.

In carbon steels, the diffusion of carbon is responsible for the changes in composition necessary for the transformation, and is thus, the rate controlling. The alloying elements in steels are slow diffusing substitutional elements as compared to interstitial diffusion of carbon. If the alloying element partitions itself between ferrite and cementite, then its diffusion becomes the rate controlling, otherwise diffusion of carbon remains the rate controlling even in alloy steels.

** 8. Interlamellar Spacing, S**_{0}**:**

The dependence of S0 on temperature is very important, not only because it measures an important characteristic of the pearlitic transformation, but also helps to determine its growth rate. The diffusion of carbon in austenite can be rate controlling. The diffusion distance is half the interlamellar spacing, S_{0}. As the spacing increases, the diffusion distance increases, and thus, the concentration gradient decreases, which results in a decrease in growth rate.

If the spacing is small, the growth rate is not always large, because with a decrease in spacing, the area of the ferrite-cementite interface per unit volume of pearlite increases and more energy is used to create the interfaces. Thus, the net driving force for the transformation decreases.

Zener calculated the constant interlamellar spacing in terms of interfacial energy. Here, two extreme cases may arise. In one case, when the spacing is very small, most of the driving force is used up in providing energy required to create large area of interfaces, and the effective driving force, and eventually the growth rate gets reduced.

In the second ease, when the spacing is large, the diffusion distance for carbon to diffuse becomes too large, which again results in reduced growth rate. Then, Zener postulated that optimal spacing is one which corresponds to a maximum rate of growth.

If a unit cube of pearlite is considered as in Fig. 3.30, then in a direction perpendicular to the ferrite- cementite interfaces, for every length S_{0}, there are two ferrite-Fe_{3}C interfaces of unit area each. Thus,

If Δ g_{0} is ideally the free energy change of this transformation without these interfaces, then the net free energy change after taking into account the energy used up in creating ferrite-Fe_{3}C interfaces is,

Thus, the interlamellar spacing corresponding to the maximum growth rate is twice the minimum interlamellar spacing (corresponding to the net driving force being zero). Putting the value of S_{m} from equation (3.16),

where, T_{m} is the transformation temperature, Δ H is the enthalpy of transformation, Δ T is the amount of super-cooling. Putting the value of Δ g_{0} in equation (3.22),

This equation illustrates that interlamellar spacing, S_{0} varies inversely with the degree of undercooling. Fig. 3.29 illustrates experimental values of interlamellar spacing, S_{0} as a function of Δ T. The slope is seen to be – 1, indicating an inverse linear relationship between S_{0} and Δ T. This graph also helps to evaluate the value of ferrite-cementite interfacial energy and has been found to be about 3 J/m^{2}. This estimate is about an order of magnitude more than that expected for a semi-coherent interface.

Fig. 3.32 illustrates growth velocity for a number of steels. To a first approximation, the free energy of austenite to pearlite transformation, Δ g_{0} is proportional to Δ T (equation 3.23), and thus, growth rate, G ∝ (Δ T)^{2}

Thus, growth rate at small undercooling is proportional to (Δ T)^{2} with the diffusion coefficient remaining reasonably constant. At larger undercooling, the growth rate decreases because of significant lowering of diffusivity (at lower temperatures).

The substitutional alloying elements in steels (except cobalt) reduce the growth rate strongly, which is of commercial importance as it increases hardenability. Elements like Cr and Mo which raise A_{1} temperature decrease growth rate more drastically than Mn and Ni which lower A_{1}. This is because Cr and Mo partition between ferrite and cementite, whereas, Ni and Mn remain unchanged in ferrite, cementite and austenite phases.

Thus, the greater impact by Cr and Mo is due to that such elements control the reaction, whereas in non-partitioning elements, it is the carbon which controls the reaction. Mn and Ni still reduce the growth rate as these elements reduce the carbon super saturation at a given growth temperature as well as some interaction effect of these solutes with carbon retards the diffusion rates of carbon in iron. Generally, when alloying elements start partitioning, then diffusion through austenite-pearlite interface plays a dominant role.

** 9. Crystallography of Pearlite****: **

Smith has proposed that the moving pearlite interface in contact with austenite is an incoherent high energy interface, growing into a austenite grain (γ_{1} Fig. 3.25) with which the pearlitic ferrite and cementite has no orientation relationship, which has been confirmed by electron microscopy.

In fact, ferrite and cementite are two inter- penetrating single crystals, neither of which has orientation relationship with the austenite grain in which these are growing, but cementite and ferrite lamellae within a pearlite nodule have between them a well-defined crystallographic orientation relationship.

However, there is an orientation relationship between the adjacent austenite grain in which pearlite has (γ_{2 }in Fig. 3.25) not grown with pearlitic ferrite and cementite, or the proeutectoid phase, depending whether it is eutectoid steel, or hypo as well as hyper eutectoid steel respectively.

**Two important relationships are: **

**For hyper eutectoid steels as well as hypoeutectoid steels: **

**Bagaryatski Relationship: **

In hyper eutectoid steels, pearlitic cementite is related with austenite but not the pearlitic ferrite.

**For Eutectoid Steels: **

Pitsch/Petch relationship (when pearlite nucleates on clean austenite boundary)

** 10. Kinetics of Pearlite Formation****: **

Austenite to pearlite transformation is a heterogeneous nucleation and growth type process, which is dependent on both time and temperature. Johnson and Mehl have shown that the fraction of the austenite transformed to pearlite, can be given as a function of the time by the following equation-

where, f(t) is the fraction of austenite transformed to pearlite,

N is the rate of nucleation,

G is the rate of growth, and

t is the time.

**This equation has been developed based on the following assumptions: **

(i) Rate of nucleation, N (the average nucleation rate) is constant with time,

(ii) Nucleation was taken as a random process,

(iii) Rate of growth, G was assumed to be constant with time,

(iv) Nodules maintain a spherical shape as they grow (until they impinge on each other).

When f(t) is plotted against time for chosen values of N and G, then a sigmoidal curve is obtained as illustrated in Fig. 3.33 (a). If fit) is plotted against ^{4}√NG^{3} t, then loo a sigmoidal curve results. This curve as illustrated in Fig. 3.33 (b) illustrates the basic kinetic behaviour of a nucleation and growth process.

**Practically, Johnson-Mehl treatment has following limitations: **

(i) Nuclei are not randomly present.

(ii) The nodules are not truly spherical,

(iii) N is not constant with time at a temperature,

(iv) G can change from one nodule to other and with time.

Thus, Cahn and Hagel pointed out that not all grain boundary nucleation sites were equivalent. They said that grain corners would be more effective than edges, which themselves shall he more effective than grain surfaces. As the high rate of nucleation occurs at these preferred sites, the site-saturation takes place soon. The new equation based on site saturation of grain corner sites is,

where, η is the number of grain corners per unit volume. But, before one fifth of transformation, the site saturation occurs. The equation (3.27) does not contain N as the rate of nucleation is then not important Under these saturation conditions, the transformation will be complete as soon as pearlite nodules migrate half way across the grains.

**Thus, let cl be the average grain diameter, and G, the average growth rate, then the time for complete volume transformation, t _{f} can be simply given by: **

As d/G is the time taken for one nodule to consume one austenite grain, there should be several nodules per grain to satisfy the above equation. This relationship points that two important parameters controlling the volume rate of pearlite formation are growth rate and grain size.

11. Effects of Pearlite on the Properties of Steel:

The hardness of pearlite increases as the interlamellar spacing decreases. So must be true of strength. Also, it is true that interlamellar spacing is inversely proportional to the degree of undercooling. Thus, yield strength (as well as ultimate tensile strength) is linearly related to the reciprocal of the square root of the interlamellar spacing, or of the degree of undercooling below eutectoid temperature as illustrated in Fig. 3.34.

This is true for steels having carbon down to 0.3% as pearlite occupies very small volume of microstructure in steels up to 0.3% carbon, and yield strength is not greatly influenced. As pearlite work-hardens much more rapidly than ferrite, the flow stress increases as the pearlite content increases even when carbon is low.

As the pearlite content increases in carbon steels, impact transition temperature is substantially increased, i.e. decreases ductility and toughness of the steels as illustrated in Fig. 3.35. The ferrite-cementite interfaces provide sites for easy nucleation of cracks, but crack can propagate in ferrite only for a short distance as it meets cementite. The propagation of crack consumes energy. In such cases, it gives wide transition range.