Phase Diagrams

Phase Diagrams

A phase in a material is a region which differ in its microstructure and or composition from another region. It is homogeneous in crystal structure and atomic arrangement and has same chemical and physical properties throughout. It has a definite interface and able to be mechanically separated from its surroundings. A component is a chemically recognizable species such as iron (Fe) and carbon (C) in carbon steel, water (H2O) and salt (NaCl) in salt solution in water.

An alloy is a combination, either in solution or compound, of two or more components (elements), at least one of which is a metal. An alloy with two components is called a binary alloy. An alloy with three is a ternary alloy and an alloy with four components is a quaternary alloy. The alloy is a material with properties different from those of its components.

A phase is a portion of a system which has uniform physical and chemical characteristics. It is defined as a homogeneous and physically distinct part of a system bounded by a surface and is mechanically separable from other parts of the system. A phase can be gaseous, liquid, or solid. It is perfectly homogeneous and distinct from every other phase which is present in the system. There is a definite boundary between any two phases. This boundary is known as the interface. When two phases are present in a system, it is not necessary that there be a difference in both physical and chemical properties, a disparity in one or the other set of properties is sufficient.

Boundaries in a system are (i) solid-liquid (fusion), (ii) liquid-gas (vapourization), and (iii) solid- gas (sublimation), (iv) solid-solid, and (v) liquid-liquid. Important points are (i) critical point, beyond this a gas cannot be liquefied, (ii) boiling point, at this point, vapour pressure of the gas is atmospheric pressure, (iii) melting point, at this point solid and liquid phase coexist (equilibrium), and (iv) triple point, at this point solid, liquid and gas phase coexist.

Two distinct phases in a system have distinct physical and / or chemical characteristics (e.g., water and ice, water and oil) and are separated from each other by definite phase boundaries. A phase can contain one or more components. A system consisting of only one phase is said to be homogeneous. A system consisting of more than one phase is said to be heterogeneous. Two or more phases are in equilibrium with one another are mixtures or heterogeneous systems. In a heterogeneous system, there can be no transfer of energy or mass from one phase to another. This means that at equilibrium, the different phases have the same temperature and pressure and their respective compositions remain constant all along.

Several systems show intermediate phases, compounds which form between components. Example is iron carbide (Fe3C). If the components are both metallic, they are called inter-metallic compounds. Thermodynamically, compounds form since the particular combination of components is able to form as a single phase with specific lattice having lower free energy than, say, a mixture of two phases. Because of a single phase of fixed composition, intermediate phases have unique melting points (like pure components). The higher degree of thermodynamic stability means that compounds frequently have higher melting points. The atomic percent of components in a compound is called its stoichiometry.

Compounds are written in the form AxBy where x and y are integers. The atomic percent of the components in an intermediate compound can easily be stated by inspection, x/(x + y) and y/(x + y), e.g. Fe3C contains 25 atomic percent C. In general, the integer values x and y are small, since the number of atoms which define the repeating unit of the crystal lattice is small.

A liquid solution occurs when a substance (solute) dissolves in a liquid, such as salt into water. A solid solution is similar, such as when salt dissolves in ice. The substance which dissolves into solution (salt in salt solutions, carbon in steel) loses its identity and is hidden from view as its atoms become incorporated into the solution. Solutions have the same molecular structure or atomic structure from point to point within themselves. Each solution is called a phase.

A solution (liquid or solid) is phase with more than one component. A mixture is a material with more than one phase. Solute (minor component of two in a solution) does not change the structural pattern of the solvent, and the composition of any solution can be varied. In mixtures, there are different phases, each with its own atomic arrangement. It is possible to have a mixture of two different solutions.

Solvent is the host or major component in solution, while the solute is the minor component. Solubility limit of a component in a phase is the maximum quantity of the component which can be dissolved in it (e.g., alcohol has unlimited solubility in water, sugar has a limited solubility, oil is insoluble). The same concepts apply to solid phases: Copper and nickel are mutually soluble in any quantity (unlimited solid solubility), while the carbon has a limited solubility in iron. Fig 1a shows the solubility curve for sugar in water.

Fig 1 Solubility curve of sugar in water and phase diagram of water

A phase diagram is a diagram which depicts existence of different phases of a system under equilibrium. It is actually a collection of solubility limit curves. It is also known as equilibrium or constitutional diagram. It represents the relationships between temperature, compositions, and the quantities of phases at equilibrium. It does not indicate the dynamics when one phase transforms into another. The equilibrium constitution is the state of lowest Gibbs free energy G, for a given composition, temperature and pressure. An alloy in this state shows no tendency to change, it is thermodynamically stable.

The terminology used in phase diagrams include liquidus, solidus, solvus, terminal solid solution, invariant point (reaction), intermediate solid solution, and inter-metallic compound, etc. Phase diagrams are classified according to the number of component present in a particular system.

A liquidus line (or lines) is defined as the line on a phase diagram which defines the liquid region of a material or substance. Above the liquidus line, the substance is considered to be completely liquid. The solidus line is the line (or lines) on a phase diagram below which only solid is present. Technically, it is the locus of temperatures below which only solid is stable. A solvus line is a line on a phase diagram which separates a homogeneous solid solution from a field of several phases which can form by exsolution or incongruent melting.

invariant points represent invariant reactions. An invariant reaction for a binary alloy is one occurring when three phases are in equilibrium. Application of the Gibbs phase rule to this system under constant pressure conditions indicates that it has no degrees of freedom and, hence, the composition of the phases and the temperature of the reaction are all fixed. Hence, invariant reactions occur only at particular conditions of concentration, temperature, and pressure etc. In binary systems, there are several invariant reactions. Eutectic, peritectic, monotectic, peritectoid and eutectoid reactions are all invariant reactions which take place at an invariant temperature for the system.

Invariant reactions result in different product phases such as terminal phases and intermediate phases. Intermediate phases are either of varying composition (intermediate solid solution) or fixed composition (inter-metallic compound). Occurrence of intermediate phases cannot be readily predicted from the nature of the pure components. Inter-metallic compounds differ from other chemical compounds in that the bonding is primarily metallic rather than ionic or covalent, e.g., Fe3C is metallic, whereas MgO is covalent. When using the lever rules, inter-metallic compounds are treated like any other phase.

Intermediate solid solution is a solid solution or phase having a composition range which does not extend to either of the pure components of the system. A terminal solid solution is a solid solution which exists over a composition range extending to either composition extremity of a binary phase diagram. Inter-metallic compounds are defined as solid phases involving two or more metallic or semi-metallic elements with an ordered structure and frequently a well-defined and fixed stoichiometry.

A monotectic point on a phase diagram is an invariant point where a single liquid phase transitions into a different liquid phase and a solid phase, or vice versa. The two liquids involved are immiscible, like oil and water, so monotectic points also involve miscibility gaps.

The eutectic point is the lowest temperature at which the liquid phase is stable at a given pressure. A eutectic system is a homogenous, solid mixture of two or more substances that form a super-lattice which melts or solidifies at a temperature lower than any of the individual ingredients’ melting point. In the iron-carbon phase diagram, this point is indicated by a temperature of 1,148 deg C and a carbon content of 4.26 %.

The lower limit of a single-phase solid field formed by two falling phase boundaries intersecting in a ‘V’ is called a eutectoid point. It is the location on a phase diagram indicating the eutectoid composition and eutectoid temperature of an alloy. The eutectoid point also indicates the location at which three solid phases co-exist. In the iron-carbon phase diagram, this point indicates a temperature of 727 deg C and a carbon content of 0.76 %.

Peritectic point is the point on a phase diagram where a reaction takes place between a previously precipitated phase and the liquid to produce a new solid phase. When this point is reached, the temperature remains constant until the reaction has run to completion. A peritectic point is also an invariant point. A peritectoid point is similar in appearance to a peritectic, being an inverted ‘V’ corresponding to an upper limit of formation of a single solid phase. But the difference is that the two-phase field above is formed of two solid phases (whereas in a peritectic, one is liquid).

For remembering which is which, one is to note that (i) ‘eutec–‘ means a normal ‘V’ meeting a horizontal line, while ‘peritec–‘ means an inverted ‘V’ meeting a horizontal line, (ii) ‘–tic’ means a liquid phase is involved, while ‘–toid’ means all phases are solid. Compared to eutectics and eutectoids, peritectics and peritectoids are of much less engineering significance.

Solid solution alloy is a phase, where two or more elements are completely soluble in each other. This phase depends on the ratio of the solvent (matrix) metal atom size and solute element atom size, e.g., gold- silver alloy, cupper- nickel alloy. Two types of solid solutions can be formed, substitution or interstitial.

Substitution solid solutions – If the atoms of the solvent metal and solute element are of similar sizes (not more, than 15 % difference), they form substitution solid solution, where part of the solvent atoms are substituted by atoms of the alloying element, e.g., copper and nickel. Some substitution solid solutions can form ordered phase where ratio between concentration of matrix atoms and concentration of alloying atoms is close to simple numbers like AuCu3 and AuCu (Au – gold, Cu – copper)

Interstitial solid solution – In interstitial solid solution, the atoms of the added element enter the interstices of the parent lattice. In other words, they fit into the spaces between the atoms of the parent metal. This is less common occurrence and is only possible if the atoms of the added element are small compare with those of the parent metal. Good example is that of carbon in iron to form that various step solid solutions. If the atoms of the alloying elements are considerably smaller than the atoms of the matrix metal, then interstitial solid solution forms, where the matrix solute atoms are located in the spaces between large solvent atoms.

In certain alloys containing three metals not as ternary alloy, both types of solid solution can exit. For example, in austenitic manganese steel there is a substitution solid solution of manganese in iron and also an interstitial solid solution of carbon in iron. Solid solution formation normally causes increase of electrical resistance and mechanical strength and decrease of plasticity of the alloy.

Phase diagram is one of the most powerful tools for studying the development of microstructure. It is also called equilibrium phase diagram or constitutional diagram. A phase diagram embodies information derived from the thermodynamic principles, specialized for a particular range of compositions and presented in a form which makes the data readily accessible. The diagram shows the phases present in equilibrium, as well as the composition of the phases over a range of temperatures and pressures.

Phase diagrams is a type of graph which shows the equilibrium conditions between the thermodynamically-distinct phases. It shows which phases are present in the material system at different temperature, pressure, and compositions. It also shows which phases are present and where the process boundaries are within the composition space. Equilibrium phase diagrams represents relations between temperature, pressure, compositions, and quantities of phases at equilibrium. These diagrams allow to predict phase transformations which occur during temperature change (e.g., upon cooling).

In the phase diagram graph, the coordinates of temperature are on the vertical axis while the coordinates of composition or concentration are on the horizontal axis. The phase diagram graph identifies those temperature-composition coordinates where a certain phase exists. A phase diagram graph also gives out temperature-composition coordinates where only phase mixtures can exist.

Phase diagrams are very important tools in the study of alloys for solutions of several practical problems in metallurgy. These diagrams define the regions of the stability of a phase which can exist in an alloy system under the condition of constant atmospheric pressure. For a binary system, the coordinates of these diagrams are temperature and composition. The inter-relationships between the phases, the temperature, and the composition in an alloy system are normally presented by phase diagram only under equilibrium conditions. Such conditions occur during slow heating and cooling rates of the alloys, when the kinetics of transformations do not play an important role.

Phase diagrams provide Important information which is useful in materials development and selection. It shows phases present at different compositions and temperatures under slow cooling (equilibrium) conditions. It indicates equilibrium solid solubility of one element / compound in another. It suggests temperature at which an alloy starts to solidify and the range of solidification. It signals the temperature at which different phases start to melt. With a phase diagram, quantity of each phase in a two-phase mixture can be obtained.

When the temperature varies in a process, the equilibrium condition of the material keeps changing, e.g., as boundaries on the phase diagram are crossed, hence, phase transformations take place. These transformations determine which phases are present after processing, and how they are distributed amongst one another, i.e., the final microstructure. This in turn controls the material properties. So, for a complete understanding of properties and processing, one needs to know more about the microstructure which is given by a phase diagram. Control of properties relies on managing not just which phases are present, but also their morphology. For example, in a two-phase solid, the shape of the phases and their dispersion within one another frequently has a strong influence on the properties. Phase diagrams give important information needed to predict the phase transformations and final microstructure which result from a given thermal history. The real microstructure is normally not at equilibrium, but phase diagrams give a starting point from which other (non-equilibrium) microstructures can frequently be inferred.

The key concepts in phase transformations are (i) phase transformations are driven by the resulting change in free energy also known as the driving force, (ii) at the phase boundaries, the free energies of the states on either side of the boundary are equal, i.e., the driving force is zero, (iii) phase changes almost always involve diffusion as the kinetic mechanism by which atomic rearrangement occurs, (iv) phase transformations occur through a two-stage process of nucleation and growth, in which nucleation can be spontaneous (homogeneous), or take place on some kind of interface (heterogeneous), (v) TTT (time-temperature-transformation) diagrams capture the extent of an isothermal transformation as a function of the held temperature and time, giving characteristic C-curves for diffusion-controlled phase transformations, and (vi) in continuous cooling, there is a critical cooling rate which just avoids the onset of the diffusional transformations. To relate these concepts to phase diagrams and cooling in real industrial processes, one is to begin with examples of slow cooling, in which the material state can track equilibrium.

Degree of freedom is defined as the minimum number of independent variable factors such as temperature, pressure, and concentration of the phases, which is required to be fixed in order to define the condition of a system completely. A system having 1,2,3 or 0 degrees of freedom is called univariant, bivariant, trivariant, and nonvariant respectively.

Gibbs’ phase rule which is derived from thermodynamic principles, describes the possible number of degrees of freedom (F) in a closed system at equilibrium, in terms of the number of separate phases (P) and the number of chemical components (C) in the system. It is represented by F + P = C + 2, F is number of degrees of freedom or variance, P is number of phases, and C is number of components.

Hume-Rothery rules, named after William Hume-Rothery, are a set of basic rules which describe the conditions under which an element can dissolve in a metal, forming a solid solution. There are two sets of rules, one refers to substitutional solid solutions, and the other refers to interstitial solid solutions.

For substitutional solid solutions, the Hume-Rothery rules are (i) the atomic radius of the solute and solvent atoms differ by no more than 15 %, (ii) the % difference=(solute−solventsolvent)×100%≤15%.crystal structures of solute and solvent are to  be similar, (iii) the complete solubility occurs when the solvent and solute have the same valency (a metal is more likely to dissolve a metal of higher valency, than vice versa), and (iv) the solute and solvent need to have similar electro-negativity. If the electro-negativity difference is too large, the metals tend to form intermetallic compounds instead of solid solutions.

For interstitial solid solutions, the Hume-Rothery rules are (i) solute atoms need to have a smaller radius than 59 % of the radius of solvent atoms, (ii) the solute and solvent need to have similar electro-negativity, and (iii) two elements need to have the same valence. The larger is the difference in valence between solute and solvent atoms, the lower is the solubility.

Fundamentally, the Hume-Rothery rules are restricted to binary systems which form either substitutional or interstitial solid solutions. However, this approach limits assessing advanced alloys which are normally multi-component systems. Free energy diagrams (or phase diagrams) offer in-depth knowledge of equilibrium restraints in complex systems. In essence the Hume-Rothery rules are based on geometrical restraints.

An isomorphous system is one in which two elements are completely soluble in each other in solid and liquid state. In this system substitutional solid state solution can be formed and single type of crystal structure exist. The solid has the same structure for all compositions. The phase diagram for copper-nickel is an isomorphous alloy system. Isomorphous systems are not common, although there are number of isomorphous systems used. The copper-nickel system is an example.

The simplest and easiest type of phase diagram to understand is that for a one-component system, in which composition is held constant (i.e., the phase diagram is for a pure substance). This means that pressure and temperature are the variables. This one component phase diagram is known as unary phase diagram. It is also sometimes called a pressure–temperature (P-T) diagram. It is represented as a two-dimensional plot of pressure (ordinate, or vertical axis) versus temperature (abscissa, or horizontal axis). Very frequently, the pressure axis is scaled logarithmically.

A simple and clear example on one component phase diagram is pressure–temperature phase diagram for water which is shown in Fig 1b. Here it can be noted that regions for three different phases, solid, liquid, and vapour, are defined on the plot. Each of the phases exist under equilibrium conditions over curves shown on the plot (as labelled AT, BT, and CT) which are phase boundaries. At any point on one of these curves, the two phases on either side of the curve are in equilibrium or coexist) with one another. That is, equilibrium between solid and vapour phases is along curve AT, equilibrium between the solid and liquid phases is along curve BT, and the equilibrium between the liquid and vapour phases is along the curve CT. Also, upon crossing a boundary (as temperature and / or pressure is changed), one phase transforms to another.

A binary phase diagram contains only two components. These diagrams can have phases with complete solubility (isomorphous), eutectic with intermediate phases or compounds or phases involving eutectoid and peritectic reactions.

Two components (binary) phase diagrams are those diagrams when the composition of materials contain two or more than two components, binary diagrams is constructed at which the temperature and the composition are variables and the pressure is constant (0.1 MPa). Binary phase diagrams are the graphs which represent the relationships between temperature and the compositions and quantities of phases at equilibrium, which influence the microstructure of an alloy.

Binary isomorphous phase diagram is used when the composition contains two components, found in a number of metallic and ceramic systems. In the isomorphous systems, which include the copper-nickel system (Fig 2) and NiO-MgO (nickel oxide- magnesium oxide) system, only one solid phase forms, and the two components in the system display complete solid solubility.

Fig 2 Copper nickel phase diagram

Tie line is an isotherm in the two-phase region. Intersects of this line with phase boundary lines (e.g., liquidus and solidus) give the compositions of the corresponding phases (e.g., liquid and solid solutions. The tie line in the two-phase region is analogous to a lever balanced on a fulcrum.

Lever rule says that 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. In an alloy or a mixture with two phases, liquid and solid, which themselves contain two elements, A and B, the lever rule states that the mass fraction of the solid phase is given by equation phase percent = (opposite arm of the lever / total length of tie-line) x 100.

The lever rule is a rule used to determine the mole fraction or the mass fraction of each phase of a binary equilibrium phase diagram. It can be used to determine the fraction of liquid and solid phases for a given binary composition and temperature which is between the liquidus and solidus line. The lever rule is a mechanical analogy to the mass balance calculation.

At a point in a phase diagram, phases present and their composition (tie-line method) along with relative fraction of phases (lever rule) can be computed. Procedure to find equilibrium concentrations of phases is shown in Fig 3 and include first a tie-line or isotherm (UV) is drawn across two-phase region to intersect the boundaries of the region. Then perpendiculars are dropped from these intersections to the composition axis, represented by U1 and V1, from which each of each phase is read. U1 represents composition of liquid phase and V1 represents composition of solid phase at intersection U meets liquidus line and V meets solidus line.

Fig 3 Isomorphous binary system showing tie-line

Procedure to find equilibrium relative quantities of phases as per lever rule include (i) a tie-line is constructed across the two-phase region at the temperature of the alloy to intersect the region boundaries, and (ii) the relative quantity of a phase is computed by taking the length of the tie line from overall composition to the phase boundary for the other phase, and dividing by the total tie-line length.

The difference between eutectic and isomorphous is that eutectic contains three phases, but isomorphous contains only two phases. Fig 4 shows a simple example of eutectic system (lead- tin system).

Fig 4 Eutectic phase diagram of lead-tin alloy

Alloys containing between 2 % tin and 19 % tin also solidify to produce a single solid solution ‘alpha’, however, as the alloy continues to cool, a solid-state reaction occurs, permitting a second solid phase ‘beta’ to precipitate from the original ‘alpha’ phase on this phase diagram, the ‘alpha’ is a solid solution of tin in lead, however, the solubility of tin in the ‘alpha’ solid solution is limited. At 0 deg C, only 2 % tin can dissolve in ‘alpha’. As the temperature increases, more tin dissolves into the lead until, at 183 deg C, the solubility of tin in lead has increased to 19 % tin. This is the maximum solubility of tin in lead. The solubility of tin in solid lead at any temperature is given by the solvus curve. Any alloy containing between 2 % tin and 19 % tin cools past the solvus, the solubility limit is exceeded, and a small quantity of ‘beta’ forms.

Ternary phase diagram – A ternary phase diagram shows possible phases and their equilibrium according to the composition of a mixture of three components at constant temperature and pressure. It is a phase diagram for systems consisting of three components. It represents as a pseudo-binary diagram. In a pseudo-binary diagram, equilibria are represented between three or more components using two compounds. Ternary phase diagrams are frequently encountered in ceramic and metallic systems. Fig 5 shows the ternary Al2O3-SiO2-MgO phase diagram at 0.1MPa pressure. The system includes two eutectics, two thermal divides, and incongruent melting of several phases.

Fig 5 Ternary Al2O3-SiO2- MgO phase diagram

Time-temperature-transformation (TTT) diagram also known as isothermal transformation diagram, sigmoidal diagram, C-curve, or S-curve are plots of temperature versus time (normally on a logarithmic scale). They are generated from percentage transformation versus time measurements, and are useful for understanding the transformations of an alloy steel at higher temperatures.

A TTT diagram is only valid for one specific composition of material, and only if the temperature is held constant during the transformation, and strictly with rapid cooling to that temperature. Though normally used to represent transformation kinetics for steels, they also can be used to describe the kinetics of crystallization in ceramic or other materials. Time-temperature-precipitation diagrams and time-temperature-embrittlement diagrams are also being used to represent kinetic changes in steels.

TTT diagram is associated with mechanical properties, micro-constituents / microstructures, and heat treatments in carbon steels. Diffusional transformations like austenite transforming to a cementite and ferrite mixture can be explained using the TTT diagram.

Phase transformations are of two kinds namely, congruent and incongruent. Congruent transformation involves no compositional changes. It normally occurs at a temperature, e.g., allotropic transformations, melting of pure a substance. In case of incongruent transformations, at least one phase undergoes compositional change, e.g., all invariant reactions, and melting of isomorphous alloy. Intermediate phases are sometimes classified on the basis of whether they melt congruently or incongruently, e.g., MgNi2 melts congruently whereas Mg2Ni melts incongruently since it undergoes peritectic decomposition.

Precipitation strengthening reactions by which a material can be strengthened by obstructing movement of dislocations. In these reactions, second phase particles are effective. Second phase particles are introduced mainly by two means, direct mixing and consolidation, or by precipitation. Most important pre-requisite for precipitation strengthening is that there is required a terminal solid solution which has a decreasing solid solubility as the temperature decreases.

Three basic steps in precipitation strengthening are solutionizing, quenching, and aging. Solutionizing is the solution heat treatment, where the alloy is heated to a temperature between solvus and solidus temperatures and kept there till a uniform solid-solution structure is produced. Quenching is the process, where the sample is rapidly cooled to a lower temperature (room temperature). Resultant product is the super-saturated solid solution. Aging is the last but critical step. During this heat treatment step finely dispersed precipitate particles form. Aging the alloy at room temperature is called natural aging, whereas at higher temperatures is called artificial aging. Most alloys need artificial aging, and aging temperature is normally between 15 % to 25 % of temperature difference between room temperature and solution heat treatment temperature.

In case of nucleation and growth, the structural changes / phase transformations take place by nucleation followed by growth. Temperature changes are important among variables (like pressure, composition) causing phase transformations as diffusion plays an important role. Two other factors which affect transformation rate along with temperature are (i) diffusion-controlled rearrangement of atoms because of compositional and / or crystal structural differences, and (ii) difficulty encountered in nucleating small particles through change in surface energy associated with the interface. Just nucleated particle has to overcome the positive energy associated with new interface formed to survive and grow further. It does by reaching a critical size.

Homogeneous nucleation occurs within parent phase. All sites are of equal probability for nucleation. It requires considerable under-cooling (cooling a material below the equilibrium temperature for a given transformation without the transformation occurring). In heterogeneous nucleation, the probability of nucleation occurring at certain preferred sites is much higher than that at other sites, e.g., during solidification, inclusions of foreign particles (inoculants), walls of container holding the liquid. In solid-solid transformation, foreign inclusions, grain boundaries, interfaces, stacking faults and dislocations are the preferred site. When product particle makes only a point contact with the foreign surface, the foreign particle does not play any role in the nucleation process. If the product particle completely wets the foreign surface, there is no barrier for heterogeneous nucleation, in intermediate conditions such as where the product particle attains hemispherical shape.

After formation of stable nuclei, growth of it occurs until equilibrium phase is being formed. Growth occurs by two methods, thermal activated diffusion controlled individual atom movement, or a thermal collective movement of atoms. First one is more common than the other. Nucleation rate is temperature dependent. Transformation rate is a function of both nucleation rate and growth rate. Time needed for a transformation to completion has a reciprocal relationship to the overall transformation rate.

In time-temperature-transformation (TTT diagram), transformation data are plotted as characteristic S-curve. At small degrees of super-cooling, where slow nucleation and rapid growth prevail, relatively coarse particles appear. At larger degrees of super-cooling, relatively fine particles result.

Martensitic growth kinetics consist of diffusion-less, athermal collective movement of atoms. It can also result in growth. Martensitic transformation takes place at a rate approaching the speed of sound. It involves congruent transformation, e.g., FCC (face centred cubic) structured cobalt transforms into HCP (hexagonal close packing) structured cobalt or FCC structured austenite into BCT (body centred tetragonal) structured martensite. Because of its crystallographic nature, a martensitic transformation only occurs in the solid state. Consequently, Ms and Mf are presented as horizontal lines on a TTT diagram. Ms is temperature where transformation starts, and Mf is temperature where transformation completes. Martensitic transformations in iron-carbon alloys and titanium are of great technological importance.

Iron-carbon phase diagram

The iron-carbon (Fe-C) phase diagram is important in engineering as it provides the basis for understanding all cast irons and carbon steels and their heat treatment. In case of pure iron, the low temperature form of iron is called ferrite (or alpha-iron), with a BCC (body-centred cubic) structure. On heating pure iron changes to austenite (or gamma-iron) at 910 deg C, and switches to FCC structure. Pure austenite is stable up to 1,394 deg C, when it changes back to BCC structure delta-iron, before melting at 1,538 deg C. A key characteristic of the iron-carbon system is the extent to which iron dissolves carbon in interstitial solid solution, forming single phases. This is where the changes between BCC and FCC are significant. The interstitial holes are larger in FCC than in BCC. This leads to low solubility of carbon in BCC ferrite and delta-iron, and much higher solubility in FCC austenite.

The iron–carbon phase diagram s shown in Fig 6. The diagram shows on the right side actually shows two diagrams namely (i) the stable iron-graphite diagram (red lines), (ii) and the metastable Fe-Fe3C (iron- cementite) diagram. Cementite is metastable, and the true equilibrium is to be between iron and graphite (C). Although graphite occurs extensively in cast irons, it is normally difficult to get this equilibrium phase in steels. The stable condition normally takes a very long time to develop specially in the low temperature and low carbon range. Hence, the normal equilibrium diagram which is normally used is the metastable Fe-Fe3C diagram since it is relevant to the behaviour of the majority of steels in practice.

Fig 6 Iron-carbon phase diagram

The details of the stable and metastable phase diagrams of the iron-carbon system, especially on the iron-rich side, are known much better than any other binary systems with similar complexity. However, there are still substantial areas where the phase diagram has not been well established such as in the temperature, composition, and pressure ranges not related directly to ironmaking and steelmaking.

There are some important metallurgical phases and micro-constituents in the iron-carbon system. In the Fe–Fe3C system, carbon is an interstitial impurity in iron. It forms a solid solution with alpha (alpha ferrite), gamma (austenite), and delta (delta ferrite) phases of iron.  These are important phases in Fe – Fe3C phase diagram. Between the single-phase fields, there are found regions with mixtures of two phases, such as ferrite and cementite, austenite and cementite, and ferrite and austenite. At the highest temperatures, the liquid phase field can be found and below this are the two-phase fields of liquid and austenite, liquid and cementite, and liquid and ferrite. In heat treatment of steels, the liquid phase is always avoided. At the eutectic point (4.26 % carbon), liquid alloy on cooling gets directly converted into austenite and cementite without any two-phase field. Similarly, at the eutectoid point (0.76 % carbon), austenite phase on cooling gets directly converted into ferrite and cementite without any two-phase field.  Some important boundaries at single-phase fields have been given special names which facilitate the understanding of the diagram. Main phases of iron and steels in equilibrium are the following phases.

Ferrite or alpha-iron phase – It is a stable form of iron at room temperature. It is relatively soft low temperature phase and is a stable equilibrium phase. It transforms to FCC austenite (gamma phase) at 910 deg C. Ferrite is a common constituent in steels and has a BCC structure, which is less densely packed than the FCC structure. It is soft, and fairly ductile.  It is magnetic below 768 deg C. It has low strength and good toughness.

Austenite or gamma iron phase – Austenite is a high temperature phase. It is a solid solution of carbon in the FCC iron. Hence, it has FCC structure, which is a close packed structure. It is a non-magnetic and ductile phase. It transforms to BCC delta ferrite at 1,394 deg C. It is not stable below the eutectoid temperature (727 deg C) unless cooled rapidly. Austenite has good strength and toughness.

Delta ferrite phase – It is solid solution of carbon in BCC iron. It is stable only at temperature higher than 1,394 deg C. It melts at 1,538 deg C. It has paramagnetic properties.

Cementite – It is Fe3C or iron carbide. It is an inter-metallic compound of iron and carbon. It has a complex ortho-rhombic structure and is a meta-stable phase. It is a hard, brittle phase. It has low tensile strength, good compression strength and low toughness. It decomposes (very slowly, within several years) into alpha ferrite and C (graphite) at the temperature range of 650 deg C to 700 deg C.

On comparing austenite with ferrite, the solubility of carbon is more in austenite with a maximum value of 2.14 % at 1,148 deg C. This high solubility of carbon in austenite is extremely important in heat treatment. When solution treatment in the austenite followed by rapid quenching to room temperature allows formation of a super-saturated solid solution of carbon in iron. The ferrite phase is restricted with a maximum carbon solubility of 0.025 % at 727 deg C. Since the carbon range available in common steels is from 0.05 % to 1.5 %, ferrite is normally associated with cementite in one or other form. Similarly, the delta-phase is very restricted and is in the temperature range between 1,394 deg C and 1,538 deg C. It disappears completely when the carbon content reaches 0.5 %.

Alloy of eutectoid composition (0.76 % C) when cooled slowly, forms pearlite, which is a layered structure of two phases namely alpha‐ferrite and cementite. Pearlite is the ferrite-cementite phase mixture. It has a characteristic appearance and can be treated as a micro-structural entity or micro-constituent. It is an aggregate of alternating ferrite and cementite lamellae which degenerates (spheroidizes or coarsens) into cementite particles dispersed with a ferrite matrix after extended holding below 727 deg C. It is a eutectoid and has a BCC structure. It is a partially soluble solution of iron and carbon. Mechanically, the pearlite has properties intermediate to soft, ductile ferrite and hard, brittle cementite. It has high strength and low toughness.

Hypo-eutectoid alloys contain pro-eutectoid ferrite (formed above the eutectoid temperature) along with the eutectoid pearlite which contain eutectoid ferrite and cementite. Hyper-eutectoid alloys contain pro-eutectoid cementite (formed above the eutectoid temperature along with pearlite which contain eutectoid ferrite and cementite.

In case of non-equilibrium solidification of iron-carbon system some additional type of micro-structures can also be formed.  Some of these microstructures are given below.

Bainite – It is a phase between pearlite and martensite. It is a hard meta-stable micro-constituent and consists of non-lamellar mixture of ferrite and cementite on an extremely fine scale. Upper bainite is formed at higher temperatures and has a feathery appearance. Lower bainite is formed at lower temperatures and has an acicular appearance. The hardness of bainite increases with decreasing temperature of its formation. It has good strength and toughness.

Martensite – It is a very hard form of steel crystalline structure. It is named after the German metallurgist Adolf Martens. It is formed by rapid cooling and is hard and brittle. It is a body-centered tetragonal (BCT) form of iron in which some carbon is dissolved. It is formed during quenching, when the face centered cubic lattice of austenite is distorted into the body centered tetragonal structure without the loss of its contained carbon atoms into cementite and ferrite. It is super saturated solution of carbon atoms in ferrite. It is a hard metastable phase. It has lath morphology when carbon is less than 0.6 %, plate morphology when carbon is more than 1 %, and mixture of those in between. It is having high strength and hardness and low toughness.

Sorbite / troostite – Structures of the lower pearlite stage with very fine flakes are referred to as sorbite and troostite. These are the transformation structures of the pearlite stage which correspond to the increasing cooling rates. However, it changes the structure ratio and the formation of pearlite with regard to flake distance. The structure cannot be seen under an optical microscope.

Widmanstatten ferrite – It is obtained when hypo-eutectoid plain carbon steel is cooled down rapidly form a temperature above the A3 temperature. Because of the fast cooling, there is little time available for the ferrite crystals to nucleate not only on the grain boundary but also within the large austenite grains. The crystals quickly grow into some preferred crystal direction inside the grain and hence become longish. The structure is either in the form of needles (laths) or plates which tend to align along the same direction within one grain.

There are several temperatures and critical points in the Iron-carbon diagram which are important both from the basic and the practical point of view. These are the temperatures when during cooling, or heating, the transformations of phase as well magnetic transformation take place in them. The temperatures at which the transformations occur in the solid state are called critical temperatures, or critical points. Major temperatures and critical points are given below.

A0 temperature – It is the Curie temperature when the magnetic to non-magnetic change of cementite occurs on heating. The structure can develop defects such as dislocations, faults, and vacancies. Cementite is metallic and ferromagnetic with a Curie temperature of around 210 deg C. When alloyed, metallic solutes substitute on to the iron sites, smaller atoms such as boron replace carbon at interstitial sites.

A1 temperature – It is the temperature (727 deg C) when the eutectoid transformation takes place. At this temperature pearlite changes to austenite on heating and vice versa.

A2 temperature – It is called the Curie temperature of ferrite (768 deg C). At this temperature, ferromagnetic ferrite on heating changes to paramagnetic. At this temperature, no change in microstructure is involved.

A3 temperature – It is the temperature at which ferrite just starts forming from austenite, on cooling hypo-eutectoid steel or last traces of free ferrite changes to austenite, on heating. Hence, it is the temperature corresponding to gamma + alpha / gamma phase boundary for hypo-eutectoid steel and is a function of carbon content of the steel, as it decreases from 910 deg C at 0 % carbon to 727 deg C at 0.76 % carbon. It is also called the upper critical temperature of hypo-eutectoid steels. The temperature interval between A1 and A3 temperatures is called the critical range in which the austenite exists in equilibrium with ferrite.

Acm temperature – It is the temperature, in a hypereutectoid steel, at which pro-eutectoid cementite just starts to form (on cooling) from austenite. It represents the temperature of gamma / gamma + Fe3C phase boundary and, is a function of carbon. Acm line shows that solid solubility of carbon in austenite decreases very rapidly from a maximum of 2.14 % at 1,148 deg C to a maximum of 0.76 % at 727 deg C, because of the higher stability of cementite at lower temperatures. The extra carbon precipitates from austenite as pro-eutectoid cementite in hyper eutectoid steels (also called secondary cementite in cast irons). Separation of cementite from austenite (on cooling) is also accompanied with the evolution of heat.

A4 temperature – It is the temperature at which austenite transforms to delta iron. The lowest value for this temperature is 1,394 deg C which is in case of pure iron. This temperature increases as the carbon percent is increased.

Ms temperature – It is the temperature at which transformation of austenite to martensite starts during cooling.

Mf temperature – It is the temperature at which martensite formation finishes during cooling. All of the changes, except the formation of martensite, occur at lower temperatures during cooling than during heating and depend on the rate of change of temperature.

Austenite- ferrite transformation – Under equilibrium conditions, pro-eutectoid ferrite is formed in iron-carbon alloys containing up to 0.76 % of carbon. The reaction occurs at 910 deg C in pure iron, but takes place between 910 deg C and 727 deg C in iron-carbon alloys. However, by quenching from the austenitic state to temperatures below the eutectoid temperature, ferrite can be formed down to temperatures as low as 600 deg C. There are pronounced morphological changes as the transformation temperature is lowered, which normally apply in general to hypo-eutectoid and hyper-eutectoid phases, although in each case there are variations because of the precise crystallography of the phases involved. For example, the same principles apply to the formation of cementite from austenite, but it is not difficult to distinguish ferrite from cementite morphologically.

Austenite-cementite transformation – There are different morphologies of cementite which are formed at progressively lower transformation temperatures. The initial development of grain boundary allotriomorphs is very similar to that of ferrite and the growth of side plates or Widmanstatten cementite follows the same pattern. The allotriomorph has a shape which does not reflect its internal crystalline symmetry. This is because, it tends to nucleate at the austenite grain surfaces, hence forming layers which follow the grain boundary contours. The cementite plates are more rigorously crystallographic in form, despite the fact that the orientation relationship with austenite is a more complex one. As in the case of ferrite, most of the side plates originate from grain boundary allotriomorphs, but in the cementite reaction more side plates nucleate at twin boundaries in austenite.

Austenite-pearlite reaction – Pearlite is the most familiar microstructure in the iron carbon phase diagram. It was discovered by Sorby, who correctly assumed it to be a lamellar mixture of iron and iron carbide. It is a very common constituent of a wide variety of steels, where it provides a substantial contribution to strength. Lamellar eutectoid structures of this type are widespread in the metallurgy of steels. These structures have much in common with the cellular precipitation reactions. Both types of reaction occur by nucleation and growth, and are, hence, diffusion controlled. Pearlite nuclei occur on austenite grain boundaries, but it is clear that they can also be associated with both pro-eutectoid ferrite and cementite. In commercial steels, pearlite nodules can nucleate on inclusions.

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