26 Phase Diagram For Binary Alloys. Contents 2.1. INTRODUCTION SYSTEM, PHASES, STRUCTURAL CONSTITUENTS AND EQUILIBRIUM...

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1 26 Contents 2.1. INTRODUCTION SYSTEM, PHASES, STRUCTURAL CONSTITUENTS AND EQUILIBRIUM PHASE DIARGAM PHASE RULE (GIBBS RULE) TIME-TEMPERATURE COOLING CURVE INTERPRETATION OF PHASE DIAGRAM Volume Fraction Dangers in interpretation of phase diagrams CLASSIFICATION OF PHASE DIAGRAM Soluble component Eutectic reaction Peritectic reaction Eutectoid reaction Peritectoid reaction Monotectic reaction TERNARY DIAGRAM PHASE DIAGRAM AND PROPERTIES OF ALLOYS PHASE DIAGRAM FOR ALLOTROPIC METALS INTERMEDIATE PHASE HUME-ROTHERY S RULES BISMUTH-CADMIUM (Bi-Cd) ALLOY PHASE DIAGRAM LEAD-CADMIUM (Pb-Cd) ALLOY PHASE DIAGRAM LEAD-BISMUTH (Pb-Bi) ALLOY PHASE DIAGRAM REFERENCES... 57

2 2.1. INTRODUCTION 27 The properties of a material depend to a large extent on the type, number, amount, form of the phases present and it can be changed by altering these quantities. It is essential to know the conditions under which these phases exit and the conditions under which a change in phase will occur. A great deal of information concerning the phase changes in many alloy systems have been accumulated and the best method of recording the data is in the form of phase diagrams; also known as equilibrium diagrams or constitutional diagrams. In order to specify completely the state of a system in equilibrium, it is necessary to specify three independent variables. These variables which are controllable are temperature, pressure and composition. 1 A phase diagram, Shows at a glance the phases which exist in equilibrium for any combination of temperature and alloy composition. Shows the relationship between the composition, temperature and structure of an alloy in series. Provide with the knowledge of phase composition and phase stability as a function of temperature, pressure and composition. Permits to study and control processes such as phase separation, solidification of metals and alloys, purification of materials, the growth and doping single crystal, etc. Marks Liquidus (i.e., the line in an equilibrium which indicates the temperature of the beginning of solidification or completion of melting) and solidus (i.e., the lines in an equilibrium diagram which indicate the temperatures of the completion of solidification or the beginning of melting.) Equilibrium diagrams have the following limitations: They do not tell us anything about the size of the micro constituent present. It does not tell us what form is taken by the ferrite or cementite, ejected from the austenite on cooling. Diagrams do not give any information about the physical and mechanical properties of materials.

3 28 Chapter SYSTEM, PHASES, STRUCTURAL CONSTITUENTS AND EQUILIBRIUM A system is a substance so isolated from its surroundings that it is unaffected by these and is subjected to changes in overall composition, temperature, pressure or total volume only to the extent allowed by the investigator. In the other words, a system is that part of the universe which is under consideration. Thus, it may or may not have fixed boundaries depending on the system. If the system cannot exchange mass and energy with its surroundings then it is termed as an isolated system. If the system can exchange energy but not mass with its surroundings, we call it a closed system. If the system can exchange both mass and energy with its surroundings, we call it an open system. A system is classified according to the number of components that constitute the system. A system having one component is called a Unary system and the system having two, three and four components are known as Binary, Ternary and Quaternary systems respectively. A phase is a physically separable part of the system with distinct physical and chemical properties. Phases have the same structure or atomic arrangement, composition and properties throughout. There is a definite interface between the phase and any surrounding or adjoining phases. A single phase system is called homogenous system; systems with two or more phase are called heterogeneous system. When two phases are present in a system, it is not necessary that there will be a difference in both physical and chemical properties; a disparity in one or the other set of properties is sufficient. The phases in alloy are not necessarily uniformly distributed throughout the structure. There are certain ways in which these phases may be associated to form the structure. The association of phases in a recognizably distinct fashion may be referred as a structural constituent of the alloy. It is customary to call those parts of the microstructure that have a clearly identifiable appearance under the microscope, the constituents of the structure. There are three types of equilibria: stable, metastable, and unstable. These three conditions are illustrated in a mechanical sense in Fig.2.1.

4 29 Fig. 2.1: Mechanical equilibria: (a) Stable (b) Metastable (c) Unstable Stable equilibrium exists when the object is in its lowest energy condition. Metastable equilibrium exists when additional energy must be introduced before the object can reach true stability. Unstable equilibrium exists when no additional energy is needed before reaching metastability or stability. Although true stable equilibrium conditions seldom exist, the study of equilibrium system is extremely valuable because it constitutes a limiting condition from which actual conditions can be estimated PHASE DIARGAM A diagram that depicts existence of different phases of a system under equilibrium is termed as phase diagram. It is also known as equilibrium or constitutional diagram. Equilibrium phase diagrams represent the relationships between temperature and the compositions and the quantities of phases at equilibrium. In general practice it is sufficient to consider only solid and liquid phases, thus pressure is assumed to be constant (1 atm.) These diagrams do not indicate the dynamics when one phase transforms into another. However, it depicts information related to microstructure and phase structure of a particular system in a convenient and concise manner. A phase diagram is actually a collection of solubility limit curves. For almost all alloy systems, at a specific temperature, a maximum of solute atoms can dissolve in solvent phase to form a solid solution. The limit is known as solubility limit. In general, solubility limit changes with temperature. If solute available is more than the solubility limit that may lead to formation of different phase, either a solid

5 30 Chapter-2 solution or compound solution. For pure metals, the diagram will be a vertical straight line. The melting temperature, the boiling temperature and allotropic transformation are shown as points on the line. Fig.2.2 shows that the metal melts at temperature a and boils at temperature b. Any allotropic change will take place at temperature in between a and b. Fig. 2.2: Equilibrium diagram for pure metals. Phase diagrams are classified as, Unary (or one component) phase diagram plotted as pressure on the vertical axis and temperature on the horizontal axis variables. It is also called a Pressure- Temperature (or P-T) diagram. Binary (or two-component) is one in which temperature and compositions are variable parameters, and pressure is held constant-normally 1 atm. Ternary (or three-component) phase diagram has three components. The three components are usually compositions of elements, but may include temperature or pressure also. Ideally, the phase diagram will show the phase relationships under equilibrium conditions, that is, under conditions in which there will be no change with time. Equilibrium conditions may be approached by extremely slow heating or cooling, so that if a phase change is to occur, sufficient time is allowed. The data for the construction of equilibrium diagram are determined by the following methods.

6 31 Chapter-2 (1) Thermal Analysis or Plot of cooling curves At constant composition, a cooling curve is plotted between temperature and time. The resulting cooling curve will show a change in slope when a phase change occurs because of the evolution of heat by the phase change. This method is used to determine the initial and final solidification temperature. (2) Metallographic Method Samples of an alloy are heated upto different temperatures and time is given to attain equilibrium. They are then quickly cooled. By this way they retain hightemperature structure. Now these samples are examined microscopically to study the phases present at different temperatures. This method is difficult to apply to metals at high temperatures because the rapidly cooled samples do not always retain their high-temperature structure and considerable skill is then required to interpret the observed microstructure correctly. This method is best suited for verification of a diagram. (3) X-Ray Diffraction Lattice dimensions are measured by this method. This method indicates the appearance of a new phase. The new phase appears due to change in lattice dimensions or due to appearance of new crystal structure PHASE RULE (GIBBS RULE) The number of phases present in any alloys depends upon the number of elements of which the alloy is composed. From thermodynamics considerations of equilibrium, Gibbs derived the following phase rule. P + F = C + N Where, P = Number of phases in the alloys (e.g. solid, liquid etc.) F =Degree of freedom of system (e.g. temperature, pressure, concentration, composition of phases) C = Number of components forming the system (i.e., elements or compounds) N = Number of external factors

7 32 Chapter-2 Generally temperature and pressure are considered as external factors which determine the state of alloy. In metallurgical systems, where pressure is remaining fixed at one atmosphere, the pressure variable is often omitted. The external factor is only temperature which is variable. Thus phase rule can be modified as, P + F = C + 1 or F = C P + 1 Since the degree of freedom F cannot be less than zero, therefore, P C + 1 Hence, the number of phases present will not be more than the number of components TIME-TEMPERATURE COOLING CURVE One of the most widely used methods for the determination of phase boundaries is thermal analysis. The temperature of a sample is monitored while allowed to cool naturally from an elevated temperature (usually in the liquid field). The shape of the resulting curves of temperature versus time is then analyzed for deviations from the smooth curve found for materials undergoing no phase changes (see Fig.2.3). When a pure element is cooled through its freezing temperature, its temperature is maintained near that temperature until freezing is complete (see Fig.2.4). The true freezing/melting temperature, however, is difficult to determine from a cooling curve because of the non-equilibrium conditions inherent in such a dynamic test. This is illustrated in the cooling and heating curves as shown in Fig.2.5, where the effects of both supercooling and superheating can be seen. The dip in the cooling curve often found at the start of freezing is caused by a delay in the start of crystallization. The continual freezing that occurs during cooling through a two-phase liquid-plussolid field results in a reduced slope to the curve between the liquidus and solidus temperatures (see Fig.2.6). By preparing several samples having compositions across the diagram, the shape of the liquidus curves and the eutectic temperature of eutectic system can

8 33 Chapter-2 be determined (see Fig.2.7). Cooling curves can be similarly used to investigate all other types of phase boundaries Fig. 2.3: Ideal cooling curve with no phase change Fig. 2.4: Ideal freezing curve of a pure metal. Fig. 2.5: Natural freezing and melting curves of a pure metal.

9 34 Fig. 2.6: Ideal freezing curve of a solid-solution alloy Fig. 2.7: Ideal freezing curves of (1) a hypoeutectic alloy, (2) a eutectic alloy and (3) a hypereutectic alloy superimposed on a portion of a eutectic phase diagram.

10 2.6. INTERPRETATION OF PHASE DIAGRAM 35 For a binary system of known composition and temperature that is at equilibrium, the following three conclusions are the rules necessary for interpreting phase diagram, The phases that are present The chemical compositions of each phases ( Tie line rule I ) The Lever rule (the percentages or fractions of each phase or Tie line rule II ) (1) Phases present The establishment of what phases are present is relatively simple. One just locates the temperature-composition point on the diagram and notes the phase(s) with which the corresponding phase field is labelled. (2) Chemical composition of phase (Tile line rule I) Let us consider the chemical composition of alloy at temperature t p as shown in the Fig.2.8 (a). Chemical composition of the phases, at any temperature, in two phase region, is determined by rule I, i.e., by drawing a horizontal line OP from temperature t p. The line OP is called tie line. From points O and P draw vertical lines to the base line. The vertical lines cut the base line at points a and b respectively. The amount of solid and liquid present can be read directly. (3) Lever rule (Tie line rule II) This rule helps to calculate the relative proportions of solid and liquid material present in the mixture at any given temperature. The number and composition of phases can be obtained from the phase diagram. If the composition and temperature position is located within a two-phase region, things are more complex. In a two-phase region, one can determine the relative amount of each phase that is present from the phase diagram, using a relationship known as lever rule (or the inverse lever rule), which is applied as follows: Construct the tie line across the two-phase region at the temperature of the alloy. The overall alloy composition is located on the tie line.

11 36 The fraction of one phase is computed by taking the length of the line from the overall alloy composition to the phase boundary for the other phase and dividing the total tie line-length. One can determine the fraction of the other phase in the same manner. In case if phase percentages are desired, each phase fraction is multiplied by 100. When the composition axis is scaled in weight percent; the phase fractions computed using the lever rule are mass fractions-the mass (or weight) of a specific phase divided by the total alloy mass (or weight). The mass of each phase is computed from the product of each phase fraction and the total alloy mass. In order to determine the relative amounts of two phases, erect an ordinate or vertical line at a point on composition scale which gives the total composition of the alloy. The intersection of this ordinate with the given isothermal line denotes the fulcrum of a simple lever system. From Fig. 2.8(a) it is clear that the ordinate KL intersects the temperature line at a point M. However, the relative lengths of lever arm OM and MP (see Fig.2.8 (b)) multiplied by the amount of phases present must balance. From Fig. 2.8(a) it is clear that the length MP represents the amount of liquid and the length OM represents the amount of solid. Therefore, The percentage of solid present = (OM/OP) x 100 = (OP MP)/OP x 100 The percentage of liquid present = (MP/OP) x 100 = [(OP OM)/OP] x 100 From Fig.2.8 OM+MP=OP, which represents the total composition of alloy between liquidus and solidus, say at temperature t p. The OMP (isothermal) can be considered a tie line since this line joins the composition of two phases in equilibrium at a specific temperature t p. We may note that in Fig.2.8 bivariant regions occur above solidus and below liquidus. Obviously, both temperature and composition can thus vary without causing phases appearing or disappearing. The regions between the solidus and liquidus, however, are universal and consist of two phases. This means either temperature or composition can be varied independently without the disappearance of a phase. Lever rules are valid for any two-phase region of the constitutional diagram and have no sense for single phase regions. Using these rules together with the phase rule, one can read any intricate constitutional diagram consisting of many branches and regions. 12

12 37 Fig. 2.8: Lever rule derivation using the phase diagram Volume Fraction In order to relate the weight fraction of a phase present in an alloy specimen as determined from a phase diagram to its two-dimensional appearance as observed in a micrograph, it is necessary to convert between weight-fraction values and areal-fraction values, both in decimal fractions. This conversion can be developed as follows and the weight fraction of the phase is determined from the phase diagram, using the lever rule. Total volume of all phases present = sum of the volume portions of each phase. It has been shown by stereology and quantitative metallography that areal fraction is equal to volume fraction. (Areal fraction of a phase is the sum of areas of the phase intercepted by a microscopic traverse of the observed region of the specimen divided by the total area of the observed region.)

13 Therefore, 38 The phase density value for the preceding equation can be obtained by measurement or calculation. The densities of chemical elements and some line compounds can be found in the literature. Alternatively, the density of a unit cell of a phase comprising one or more elements can be calculated from information about its crystal structure and the atomic weights of the elements comprising it as follows: Dangers in interpretation of phase diagrams An essential point to remember in phase diagrams is that during normal or fast cooling, results may not be as expected in the diagram. Both the theory and the experiments to construct phase diagrams rely on the assumption that the system is in equilibrium, which is rarely the case, as this only occurs properly when the system is cooled very slowly. In order to reach full equilibrium, the solute in the solid phases must stay completely uniform throughout the cooling. However, in most systems, if the system is not cooled quickly, the phase diagram will give fairly accurate results. In addition, near the eutectic, the results become even closer to the phase diagram as the liquid solidifies at nearly the same time. The non equilibrium conditions can sometimes be of benefit, however, as microstructures at higher temperatures in a phase diagrams may sometimes be preserved to lower temperatures by fast cooling, i.e. quenching or unstable microstructures may occur during fast cooling which can be useful when hardening an alloy CLASSIFICATION OF PHASE DIAGRAM An equilibrium diagram has been defined as a plot of the composition of phases as a function of temperature in any alloy system under equilibrium conditions. Equilibrium diagrams may be classified according to the relation of the components in the liquid and solid states as follows:

14 (1) Components completely soluble in the liquid state, 39 and also completely soluble in the solid state. but partly soluble in the solid state (EUTECTIC REACTION). but insoluble in the solid state (EUTECTIC REACTION). The PERITECTIC REACTION. (2) Components partially soluble in the liquid state, but completely soluble in the solid state. and partly soluble in the solid state. (3) Components completely insoluble in the liquid state and completely insoluble in the solid state Soluble component Many systems are comprised of components having the same crystal structure and the components of some of these systems are completely miscible (completely soluble in each other) in the solid form, thus forming a continuous solid solution. When this occurs in a binary system, the phase diagram usually has the general appearance of that shown in Fig.2.9. The diagram consists of two single-phase fields separated by a two-phase field. The boundary between the liquid field and the two-phase field in Fig.2.9 is called the liquidus; that between the two-phase field and the solid field is the solidus. In general, a liquidus is the locus of points in a phase diagram representing the temperatures at which alloys of the various compositing of the system begin to freeze on cooling or finish melting on heating; a solidus is the locus of points representing the temperatures at which the various alloys finish freezing on cooling or begin melting on heating. The phases in equilibrium across the two-phase field (the liquid and solid solutions) are called conjugate phases. If the solidus and liquidus meet tangentially at some point, a maximum or minimum is produced in the two-phase field, splitting it into two portions as shown in Fig.2.10.

15 40 Fig. 2.9: Schematic binary phase diagram showing miscibility in both the liquid and solid states Fig. 2.10: Schematic binary phase diagrams with solid-state miscibility where the liquidus shows (a) a maximum temperature and (b) a minimum temperature.

16 41 Chapter-2 It is possible to have a gap in miscibility in a single-phase field; this is shown in Fig Point TC, above which phases α1 and α2 become indistinguishable, is a critical point. Lines a-tc and b-tc, called solvus lines, indicate the limits of solubility of component B in A and A in B respectively. The configurations of these and all other phase diagrams depend on the thermodynamics of the system. Fig. 2.11: Schematic binary phase diagram with a minimum in the liquidus and a miscibility gap in the solid state The following are the important properties of the solid solution. Thermal and electrical properties are reduced by the formation of solid solutions. Malleability and ductility are generally decreased by the formation of solid solution. All alloying elements increase strength and hardness of materials. Modulus of elasticity or stiffness of the solvent is not too much affected by the increasing amounts of the solute or solvent.

17 42 Properties like density, specific gravity, specific heat, thermal expansion vary directly in proportional to the amount of the solute and the solvent present in the solution Eutectic reaction When two metals are completely soluble in the liquid state but partly or completely insoluble in the solid state, is called as eutectic system. In a eutectic reaction when a liquid solution of fixed composition solidifies at a constant temperature, forms a mixture of two or more solid phases without an intermediate pasty stage. This process is reverse on heating. In eutectic system there is always a specific alloy, known as eutectic composition that freezes at a lower temperature than all other compositions. The freezing point of a pure metal will be lowered by the addition of second metal, if second metal is soluble in the pure metal A when liquid and insoluble are solidified. This is called Raoult s Law. The extent of lowering the freezing point is proportional to the molecular weight of the solute. At the eutectic temperature two solids form simultaneously from a single liquid phase. The eutectic temperature and composition determine a point on the phase diagram called the eutectic point. If a small amount of metal B is added to metal A, the freezing point is lowered. Thus each metal lowers the freezing point of other. By connecting all points where the solidification starts, we get the liquidus line and by connecting all the breaks of the cooling curve we get solidus line. The horizontal line starting from temperature T E is solidus line. The point where the liquids lines intersect (i.e., at E) is called Eutectic point. T E is called eutectic temperature and 70A-30B is called eutectic composition. The alloys to left of the eutectic composition are known as hypoeutectic alloys and right side alloys are called hyper eutectic alloys. Consider the solidification of two metals A and B. Let it eutectic composition is 30A- 70B as shown in Fig Consider the temperature along the eutectic composition as it (30A-70B alloy) cools from temperature T 0, it remains liquid until point E is reached. The straight line (PQ) which contains point E is called eutectic-temperature line. Now liquid starts to solidify at point E and temperature will remain constant T E, until the alloy is completely solid. The liquid will solidify into a mixture of two phases.

18 43 Chapter-2 Let us consider that small amount of pure metal A is solidified. The remaining liquid will be richer in metal B. The liquid composition will slightly shift to right. To maintain the equilibrium value of liquid, the metal B will solidify. If metal B solidifies slightly in excess liquid composition will shift to left. Hence metal A will again solidify to maintain equilibrium. Thus at constant temperature T E, the liquid solidifies alternatively, pure metals A and B. This mixture of metals A and B is known as eutectic mixture, which is extremely fine (visible under microscope only). The eutectic reaction is, Fig. 2.12: Eutectic equilibrium diagram The eutectic mixture consists of two different solid phases; the mixture may be two pure metals, two solid solutions, two intermediate phases or any combination of above. Now, consider composition other than eutectic composition, say, alloy of composition 80A-20B. This alloy remains uniform liquid solution until point L 1 at temperature T 1. At this point the liquid L 1 is saturated in metal A. As the temperature is lowered, the excess of metal A will solidify.

19 44 Chapter-2 Again consider same composition, 80A-20B, at temperature T 2. Applying rule I, at this temperature, we find that composition of solid phase is 100% A and composition of liquid phase is 60A-40B. Similar explanation can be given for the alloy on the right of point E Peritectic reaction The phase diagram for the system having partial solid solubility is called peritectic phase diagram. In this diagram the horizontal line BDF is called peritectic line and point D is termed as peritectic point. Other lines AFG is liquidus line, ABDG is solidus line, BC and DE are solvus lines. (See Fig. 2.13). Fig. 2.13: Peritectic type phase diagram Let us consider the composition along line MM 1. At point r, solidification will start i.e., at temperature T 1 a solid solution α 1 will form having composition s. When the temperature is further lowered, the points will move towards B and point r towards F. At peritectic temperature T 2, the composition of solid solution α is B and composition of liquid is F. At temperature T 2, two phases react with each other and give a new solid. This is called peritectic reaction.

20 Eutectoid reaction Unlike Eutectic or Peritectic transformations which are liquid-solid transformations, Eutectoid involves a solid-solid transformation. Eutectoid reaction is an isothermal reversible reaction in which a solid phase is converted into two or more intimately mixed solids on cooling, the number of solids formed being the same as the number of components in the system. This is called eutectoid reaction Peritectoid reaction The Peritectoid reaction is the transformation of the two solids into a third solid. It is isothermal reversible reaction in which a solid phase reacts with a second solid phase to produce yet a third solid phase on cooling. This is called peritectoid reaction Monotectic reaction In this case the two liquid solutions are not soluble in each other over a certain composition range, i.e., there is a miscibility gap in liquid state between the two metals. In this type one liquid decomposes into another liquid TERNARY DIAGRAM When a third component is added to a binary system, illustrating equilibrium conditions in two dimensions becomes more complicated. One option is to add a third composition dimension to the base, forming a solid diagram having binary diagrams as its vertical sides. This can be represented as a modified isometric projection. Here, boundaries of single-phase fields (liquidus, solidus, and solvus lines in the binary diagrams) become surfaces; single and two-phase areas become volumes; three-phase lines become volumes and

21 46 Chapter-2 four-phase points can exist as an invariant plane. The composition of a binary eutectic liquid, which is a point in a two-component system, becomes a line in a ternary diagram. Although three-dimensional projections can be helpful in understanding the relationship in a diagram, reading values from them is difficult. Therefore, ternary systems are often represented by views of the binary diagrams that comprise the faces and twodimensional projections of the liquidus and solidus surfaces, along with a series of twodimensional horizontal sections (isotherms) and vertical sections (isopleths) through the solid diagram. Vertical sections are often taken through one corner (one component) and a congruently melting binary compound that appears on the opposite face; when such a plot can be read like any other true binary diagram, it is called a quasibinary section. One possibility is illustrated by line 1-2 in the isothermal section shown in Fig A vertical section between a congruently melting binary compound on one face and one on a different face might also form a quasibinary section (see line 2-3). All other vertical sections are not true binary diagrams and the term pseudo binary is applied to them. A common pseudo binary section is one where the percentage of one of the components is held constant (the section is parallel to one of the faces), as shown by line 4-5 in Fig Another is one where the ratio of two constituents is held constant and the amount of the third is varied from 0 to 100% (line 1-5). Isothermal Sections: Composition values in the triangular isothermal sections are read from a triangular grid consisting of three sets of lines parallel to the faces and placed at regular composition intervals (see Fig.2.15). Normally, the point of the triangle is placed at the top of the illustration, component A is placed at the bottom left, B at the bottom right, and C at the top. The amount of component A is normally indicated from point C to point A, the amount of component B from point A to point B, and the amount of component C from point B to point C. This scale arrangement is often modified when only a corner area of the diagram is shown.

22 47 Fig. 2.14: Isothermal section of a ternary diagram with phase boundaries deleted for simplification. Fig. 2.15: Triangular composition grid for isothermal section; x is the composition of each constituent in mole fraction or percent. Projected Views: Liquidus, solidus, and solvus surfaces by their nature are not isothermal. Therefore, equal-temperature (isothermal) contour lines are often added to the

23 48 Chapter-2 projected views of these surfaces to indicate their shape (see Fig ). In addition to (or instead of) contour lines, views often show lines indicating the temperature troughs (also called "valleys" or "grooves") formed at the intersections of two surfaces. Arrowheads are often added to these lines to indicate the direction of decreasing temperature in the trough. Fig. 2.16: Liquidus projection of a ternary phase diagram showing isothermal contour lines PHASE DIAGRAM AND PROPERTIES OF ALLOYS The properties of alloys may vary according to phase diagrams. The alloys containing finer grains are hard and have high yield strength and ultimate strength. Their thermal and electric conductivities are low. An alloy containing coarse grains or large grains has low hardness, yield strength, ultimate strength and high values of thermal and electrical conductivities. In Fig.2.17 (a), the hardness is maximum and conductivity is minimum at eutectic point. This is due to the fact that eutectic is a finely divided mixture of two metals A and B. The size of the crystals which solidify first on right or left side of the point P, is much larger, thus the hardness is lesser and conductivity is more. In Fig.2.17 (b), the properties are on the maximum (hardness) and minimum (conductivity) extremes where the atomic percentage is 50% A and 50% of B. This is due to

24 49 Chapter-2 the fact than maximum strength occurs when the lattice is subjected to maximum strain. The maximum strain occurs where the atomic percentage is 50% of both the metals. The variation of properties is Fig.2.17 (c) and Fig.2.17 (d) is similar to, rather combination of cases Fig.2.17 (a) and Fig.2.17 (b). Fig. 2.17: Phase diagram and properties of alloys PHASE DIAGRAM FOR ALLOTROPIC METALS For all alloy systems involving metals, allotropic transformations of one or both components (metals) results change its structure, properties and shape of equilibrium diagrams. There are many metals which are allotropic in nature. Equilibrium diagram of an alloy system consisting of two allotropic metal A and B is shown in Fig For convenience, consider metal A is fcc at high temperature and bcc at low temperature, where as metal B is fcc at high temperatures and hcp at low temperatures. At very high temperature, the two metals form liquid solution L. There exist only one homogeneous solid solution β below the solidus line XY. The remaining portion of diagram below β is called eutectoid diagram having eutectoids point D. When the alloy of composition D is cooled further below temperature T 1 the single solid phase changes into two new solid phases α and γ. The rate of change (in the reaction) is quite low as compared to eutectic reaction i.e., one liquid changing to two solids upon cooling. The behavior of eutectoid diagram is similar to that of eutectic diagram. The line ADB is called liquidoid while line ACDEB is called solidoid.

25 50 Fig. 2.18: Phase diagram for allotropic metals When temperature is lowered below liquidoid line between C and D, solid solution β decomposes into solid solutions of α and β which are in equilibrium. Their compositions are given by lines AD (β- phase) and AC (α-phase). At temperatures below liquidoid line between D and E, β and γ phases are in equilibrium. Upon cooling, the composition of solid solution β, varies according to line BD and composition of solid solution γ, along line BE INTERMEDIATE PHASE An intermediate phase may occur over a composition range (intermediate solid solution) or at a relatively fixed composition (compound) inside the phase diagram and are separated from other two phases in a binary diagram by two phase regions. Many phase diagrams contain intermediate phases whose occurrence cannot be readily predicted from the nature of the pure components. Intermediate solid solutions often have higher electrical resistivity and harness than either of the two components. Number of phase transformations may takes place for each system. Phase transformations in which there are no compositional alternations are said to be congruent transformations, and during incongruent transformations at least one of the phases will experience a change in composition. Examples for, (i) congruent transformations: allotropic

26 51 Chapter-2 transformations and melting of pure materials (ii) incongruent transformations: all invariant reactions, and also melting of alloy that belongs to an isomorphous system. Intermediate phases are sometimes classified on the basis of whether they melt congruently or incongruently HUME-ROTHERY S RULES While developing an alloy, it is frequently desirable to increase the strength of the alloy by adding a metal that will form a solid solution. Hume-Rothery has framed empirical rules that govern the choice of alloying elements in the formation of substitutional solutions. We may note that if an alloying element is chosen at random, it is likely to form an objectionable intermediate phase instead of a solid solution. Hume-Rothery s Rules are described below. (1) Chemical affinity factor Greater the chemical affinity of two metals the more restricted is their solid solubility. When there chemical affinity is great, two metals tend to form an intermediate phase rather than a solid solution. (2) Relative valency factor If the alloying element has a different valence from that of the base metal, the number of the valence electrons per atom, called the electron ratio, will be changed by alloying. Crystal structures are more sensitive to a decrease in the electron ratio than to an increase. Therefore, a metal of high valence can dissolve only a small amount of lower valence metal while the lower valence metal may have good solubility for a higher valence metal. (3) Relative size factor If the side of two metallic atoms differ by less than 15%, the metals are said to have a favourable size factor for solid solution formation. So far as this factor is concerned, each of the metal will be able to dissolve appreciably in the other metal. If the size factor is greater than 15%, solid solution formation tends to be severely limited and is usually only a fraction of 1%.

27 (4) Lattice-type factor 52 Only metals that have the same type of lattice (e.g., F.C.C) can form a complete solid solubility. The size factor must usually be less than 8%. A qualitative estimate of the solid solubility of one metal in another can be obtained by considering these four factors. It should be noted that an unfavourable relative size factor alone is sufficient to limit solid solubility to a low value. If the relative size factor is favourable then the other three factors should be considered in deciding the probable degree of solid solubility. It must be emphasized that numerous exceptions to these Hume-Rothery rule are known BISMUTH-CADMIUM (Bi-Cd) ALLOY PHASE DIAGRAM The phase diagram of Bi-Cd is shown in the Fig Fig. 2.19: Phase diagram for the Bi-Cd system This phase diagram shows: Minimum melting temperature = 417 K Cadmium vapors are somewhat toxic. 14

28 53 Chapter LEAD-CADMIUM (Pb-Cd) ALLOY PHASE DIAGRAM The phase diagram of Pb-Cd is shown in the Fig Fig. 2.20: Phase diagram for the Pb-Cd system This phase diagram shows: The solubility of Cd in solid Lead is 3.3 wt. % at 248 ºC, 2.5 wt. % at 232 ºC and 0.3 wt. % at room temperature. The eutectic point is at a temperature of 248 C and a Cd content of 17.5%. Discontinuous precipitation is observed in this system

29 54 Chapter LEAD-BISMUTH (Pb-Bi) ALLOY PHASE DIAGRAM One of the most or less complete phase diagrams for the binary Pb-Bi system is shown in the Fig Fig. 2.21: Phase diagram for the Pb-Bi system This diagram shows: An eutectic point at 55.5 wt. % Bi with a melting temperature of 124 C (397 K); A peritectic point at 32.2wt. % Bi with a melting temperature of 184 C (457 K); The solubility limits in solid state: 21.5 wt. % Bi in Pb (α- phase region) and 0.5 wt.% Pb in Bi (γ- phase region); Intermetallic compound phase (β-phase region); b Liquidus and solidus lines; Liquidus and solidus lines. 18 M. Hansen and K. Anderko presented the Pb-Bi phase diagram with some experimental results. 19 Some parameters were changed in comparison with the diagram shown in Fig.2.22 as follows:

30 55 The eutectic point at 56.7 wt.% Bi (56.3 at.% Bi) with a melting temperature of C (398 K); The peritectic point at 36.2 wt.% Bi (36 at.% Bi); The solubility limits in the solid state are reported to be 23.4 wt. % (23.3 at. %) Bi in Pb. In 1973, the Pb-Bi phase diagram with refinements of the boundaries of the ε-phase, given by B. Predel and W. Schwerman, and boundaries of γ (Bi)-phase, given by M.V. Nosek, was published by R. Hultgren. This diagram is reproduced as shown in Fig Fig. 2.22: Phase diagram for the Pb-Bi system This diagram shows: The melting point of Bi at C ( K); The melting point of Pb at C (600.6 K); The solubility limit of Pb in Bi in the solid state- 5 at. %; The solubility limit of Bi in Pb in the solid state- 24 at. %; An eutectoid point at 72.5 at.% Pb and C (227 K); ε-phase region. 20,21

31 56 Chapter-2 In 1992, N. A. Gokcen proposed a few modifications for some characteristic points as shown in Fig Fig. 2.23: Phase diagram for the Pb-Bi system This diagram shows: more precise melting points of elements: T melt Bi = ºC ( K); T melt Pb = ºC ( K); the eutectic point at 45.0 at.% Pb and T melt LBE = ºC ( K); the peritectic point at 71 at.% Pb and 187 ºC ( K); The lower limits of the elements solubility in the solid state at.% Pb in Bi and 22 at.% Bi in Pb

32 2.16. REFERENCES Introduction to Physical Metallurgy by Sidney H Avner, 2 nd ed., Tata McGraw-Hill Edition (1997). 2. Alloy Phase Diagrams and Microstructure, Metals Handbook, Desk Edition, Second Edition, J.R. Davis, Ed., ASM International, p , (1998). 3. H. Baker, Introduction to Alloy Phase Diagrams, Alloy Phase Diagrams, Vol. 3, ASM Handbook, ASM International, p.1-1 to 1-29, (1992). 4. T. B. Massalski, forewords to various monographs of Phase Diagrams of Binary Alloys, ASM International, (1987). 5. H. Okamoto and T. B. Massalski, Impossible and Improbable Forms of Binary Phase Diagrams, Desk Handbook: Phase Diagrams for Binary Alloys, H. Okamoto, Ed., ASM International, p.xxxix-xliii, (2000). 6. F. N. Rhines, Phase Diagrams in Metallurgy: Their Development and Application, McGraw-Hill, (1956). 7. Metallographic and Microstructures, Vol. 9, 9 th ed., ASM Handbook, ASM International, (1985). 8. J. E. Morral, Two-Dimensional Phase Fraction Charts, Scr. Metall., Vol. 18 (No. 4), p , (1984). 9. J. E. Morral and H. Gupta, Phase Boundary, ZPF, and Topological Lines on Phase Diagrams, Scr. Metall., Vol. 25, No. 6, p , (1991). 10. Alloy phase diagram, Vol. 3, ASM Handbook, ASM International, The Materials Information Company, (1992). 11. A. Prince, Alloy Phase Equilibria, Elsevier, (1966). 12. Materials Science by S. L. Kakani, Amit Kakani,New Age International Publisher, New Delhi, (2004). 13. Materials Science & Engineering by I.P. Singh, Subhash Chander, R.K. Prasad, Jain Brothers, (2007). 14. C. Lu and K. T. McDonald, (1998). 15. M. Hansen, Constitution of binary alloys, 2 nd ed., McGraw-Hill, New York, (1958). 16. J. Dutkiewicz, Z. Moser, and W. Zakulski, in Binary Alloy Phase Diagrams, (T. B. Massalski, H. Okamoto, P. R. Subramanian and L. Kacprzak, eds.), ASM International, Metals Park, OH, Vol. 2, p , (1990).

33 58 Chapter E. C. Rollason and V. B. Hysel, Monthly J. Inst. Metals 5: 187 (1938). 18. Smithells, C. J. Metals, Reference Book, 2 nd ed., Vol. I. Interscience Punl. Inc. New York, Butterworths Scientific Publ., London, (1955). 19. Hansen, M., K. Anderko Constitution of Binary Alloys, 2 nd ed., McGraw- Hill Book Co., Inc., New York, USA, (1958). 20. Predel, B., W. Schwerman, Z. Metallk., 58, p.553, (1967). 21. Hultgren, R., et al., Selected Values of the Thermodynamic Properties of Binary Alloys, ASM, Metals Park, Ohio, USA, (1973). 22. Gokcen, N. A., J. Phase Equilibria, 13, p.21, (1992).