The following points highlight the four main types of binary diagrams. The types are: 1. Solid Solution Systems 2. Insoluble in the Solid State 3. Soluble in the Solid State 4. Peritectic Reaction.
Binary phase diagrams are based on two component systems. Here, the two components may be mixed in an infinite number of different proportions, that is, composition also becomes a variable, apart from pressure and temperature. Binary diagrams are usually drawn at one atmospheric pressure, i.e., pressure is made constant, because the variation in pressure results in insignificant effect on the equilibrium. Moreover, it helps to obtain the binary diagram as a convenient two- dimensional figure.
When the pressure variable and the vapour phase are ignored, then the phase rule for the condensed phases (solid and liquid phases only) is modified to the following form, which is more commonly used for metallic systems as alloys are normally made under normal atmospheric condition, i.e., at constant one atmosphere:
F = C – P + 1 …(3.2)
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In binary diagrams, temperature is plotted as the ordinate and the composition as the abscissa. Thus, the phase diagram is a map which shows at a glance the phases which exist in equilibrium for any combination of temperature and alloy composition.
When three phases are in equilibrium in a binary system, (P = 3, C = 2), F = 0, the degree of freedom is zero. In other words, three phase equilibrium is characterised by a fixed composition and temperature, and it is invariant. Two phase equilibrium means (P = 2, C = 2), F = 1, that is, when the temperature is fixed, the compositions of the phases are also fixed, however, the temperature can be varied within certain limits.
When only one phase is present, (P = 1, C = 2), F = 2, i.e., the composition and the temperature can be varied independently without disturbing the number of phases. In the phase diagram, one phase equilibrium is shown as an area (one phase field).
Depending on the nature of the two elements involved (i.e., the crystal structure, the size of atoms, valency) several types of binary equilibria can occur. Moreover, in a single binary-diagram, several kinds of solidification behaviour and solid-state reactions may occur.
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Iron-cementite diagram is one important example having such complex reactions. Fortunately, every separate region of a complex diagram showing one type of alloy behaviour can be treated individually and independently to interpret the complicated diagrams completely.
Some simple type of alloy behaviour can be classified as:
Type I. And are completely soluble in the solid state (Isomorphous system)
Type II. And are completely insoluble in the solid state (Eutectic system)
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Type III. And are partially soluble in the solid state (Eutectic System)
Type IV. And illustrate peritectic reaction.
Type # 1. Solid Solution Systems:
This is the case when two metals (in metallic systems) are completely soluble in each other in all proportions, both in the liquid and the solid states, This is also called isomorphous, because only a single type of crystal structure is obtained for all ratios of the components, that is, they form substitutional solid solutions in all proportions.
Since the copper-nickel alloys are of commercial interest, this system is used here as an example, because it has been found experimentally that all the alloys of these two metals form solid solutions when cooled from liquid state.
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When pure copper in molten state is slowly cooled under equilibrium conditions, the solidification takes place at the freezing point (1083°C) in the manner illustrated schematically in Fig. 3.2. The equilibrium solidification of an alloy, for example 50% (by weight) copper and 50% nickel is slightly different than the freezing of a pure metal.
Here, complete solidification does not occur at a single temperature, but progressively over a small temperature range as illustrated in Fig. 3.4. There takes place accompanying continuous variation of the chemical compositions of the liquid and of the solid alloy. When the liquid alloy on cooling reaches around 1315°C, solidification begins with the formation of nuclei of the solid phase having around 67% nickel and 33% copper.
As the temperature drops, solidification continues with the growth of the solid phase, normally in the form of dendrites. When the solidification is about half completed, the composition of the solid phase is around 60% nickel, 40% copper, and the liquid has changed its composition from 50% nickel and 50% copper to 43% nickel, 57% copper.
When the solidification has completed, the liquid disappears, and the composition of the solid phase becomes the composition of the original liquid phase, 50% nickel, 50% copper, i.e. of the alloy.
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The continuous change of composition of the solid and liquid phases, during the course of equilibrium solidification is made possible because diffusion occurs relatively rapidly at high temperatures. Experimental set up (Fig. 3.3) is used to obtain cooling curves.
If a number of copper-nickel alloys of different fixed compositions (80 Cu 20Ni, 60Cu 40Ni, 40 Cu 60 Ni, 20 Cu 80 Ni) are made, then it is found that they all solidify over different temperature ranges, and by plotting the cooling curves (Fig. 3.5), the temperatures at which the freezing begins and ends for each alloy can be determined as done in Fig. 3.4. It is assumed that each alloy is cooled slowly enough to attain equilibrium at each stage of cooling process.
It is now possible to draw the actual equilibrium diagram by plotting temperature versus composition. The appropriate points (temperatures at which freezing begins and ends) are taken from the series of cooling curves and plotted on the new diagram. For example, in Fig. 3.6, since the left axis represents the pure copper, 1083°C temperature (where freezing begins and ends too) is plotted along this vertical line.
Similarly, 1454°C is plotted for pure nickel. For the alloy, 80 Cu 20 Ni, a vertical line for this composition is drawn (Fig. 3.6). Temperatures 1190° (freezing begins) and 1135° (freezing ends) are plotted along this line (Fig. 3.6). The same procedure is adopted for other three alloys to obtain set of points (Fig. 3.6).
Now, upper line is drawn by connecting the points at which freezing begins, and is called liquidus. The lower line is drawn by connecting the points at which freezing ends, and is called the solidus line. The area above the liquidus line is a single- phase region, and any alloy in that region will consist of a homogeneous liquid solution.
Also, the area below the solidus line is a single phase region, and any alloy in this region will consist of a homogeneous solid solution. Between the liquidus and solidus lines, there exists a two-phase region. Any alloy in this region will consist of a mixture of a liquid solution and a solid solution.
Any point in the phase diagram has a set of coordinates, a temperature and a composition. For example, point X (Fig. 3.6) signifies an alloy of 80% Ni and 20% Cu at a temperature of 1100°C. The composition is indicated by dropping a vertical line from point X until it touches the x-axis, while the temperature is indicated by drawing a horizontal line through point X to meet the y-axis.
The microstructure of any solid solution alloy (say 80 Ni, 20 Cu), cooled under equilibrium conditions, consists of solid-solution crystals, and each crystal will have the same homogeneous composition (80 Ni, 20% Cu) as of the alloy. Under the microscope, such a microstructure is identical to a pure metal (compare schematic Fig. 3.2 (a) and 3.4 (a).
However, a solid solution alloy shall have different properties than pure metal. It should be stronger, harder, have higher electrical resistivity and normally, have different colour of the surface (lustre) than pure metal. Examples of alloy systems with this type of diagram are Ag-Au, Ag-Pt, Cu-Ni, Au-Cu, Au-Ni.
In all binary diagrams, a two-phase region separates two single-phase regions as given by the ‘1-2-1’ rule. As we move from a single-phase region, we cross into a two-phase region, and then again into a single-phase region. This is true unless the phase boundary is a horizontal line, or at singular points.
Phase rule can be applied to this solid solution diagram, by using the modified form as given in equation 3.2. At the freezing point of pure copper (or nickel), C = 1, P = 2, and thus,
F = 1 – 2 + 1
For the single phase regions, any point above the liquidus (P = 1, liquid), or below the solidus (P = 1, solid solution),
F = 2 – 1 + 1
Thus, both temperature and the composition of the phase can be independently varied (within the limits of two phase boundaries). In the two-phase region (between liquidus and solidus), any point has,
F = 2 – 2 + 1
Here, there are three possible variables: temperature, composition of the liquid phase, and the composition of the solid phase. As, F = 1, that means, only one of these three is independent, and other two are dependent.
For example, if temperature is arbitrarily chosen in this region, say by a point Y (Fig. 3.6), the compositions of two phases are automatically fixed (and are given by the ends of the tie-line drawn at that temperature as given by points 1 and 2). If, for example, the composition of one of the ‘phases’ is specified arbitrarily, the temperature and the composition of the other phase are automatically fixed.
Type # 2. Insoluble in Solid State:
Two Components are Completely Soluble in Liquid State, and are Completely Insoluble in Each Other in Solid State:
Many pairs of elements (or even compounds) are unlikely to satisfy one, or more Hume Rothery rules, the conditions for complete substitutional solid solubility. The solid solubility is therefore limited in a number of binary systems, Fig. 3.14(d). However unfavourable are the conditions for solid solubility, total insolubility (i.e., zero) in the solid state is extremely rare and probably non-existent, particularly when these two metals are initially completely soluble in each other in liquid state.
However, in some cases, the solid solubility is so small that for all practical purposes they may be considered insoluble, and only the pure metal may be shown on the phase diagram (as it is difficult to show the small solubility in the diagram).
Bismuth-cadmium system is one such example, showing complete solid insolubility. Bismuth, one of the ‘less-metallic metals’, has complex type of crystal structure, basically rhombic, having some covalent bonding, and van der Waals forces exist between the layers formed. Thus, bismuth is extremely brittle and is reluctant to form mixed crystals with cadmium, which has HCP structure.
Bismuth-cadmium diagram is a typical example of commonly called a eutectiferous series. The term eutectic is derived from the Greek, ‘eutektos’, or ‘capable of being melted easily’, a reference to the fact that an alloy of precisely eutectic composition (60% Bi, 40% Cd) has the lowest melting temperature.
Bismuth-cadmium diagram can be drawn from a number of cooling curves, analogous to drawing of solid solution diagram. Fig. 3.16 (i) illustrates five cooling curves (Pure Bi; 80% Bi 20% Cd; 60% Bi 40% Cd; 25% Bi 75% Cd; Pure Cd). The cooling curve for pure Bi shows one horizontal (constant temperature of 271°C) line, where solidification starts and completes.
Pure Cd shows similar nature with constant temperature of 321°C, where freezing starts and ends. The alloy (80% Bi, 20% Cd) starts freezing with pure Bi crystals, at temperature T1, and more solid Bi forms as the temperature drops, but in the end a certain amount of solidification occurs at a fixed temperature of 144°C.
The alloy (60% Bi, 40% Cd) called eutectic alloy shows that solidification starts and is completed at a single temperature of 144°C, the eutectic temperature. It is the same temperature where end of solidification occurred in 80% Bi 20% Cd alloy at constant temperature. The cooling curve of eutectic alloy resembles that of a pure metal but the product solid consists of two solid-phases.
The alloy (25% Bi, 75% Cd) shows similar solidification behaviour as alloy (80Bi20Cd), but the temperature of the beginning of solidification is different (T3). Here also, end of solidification of a certain amount of liquid occurs at the same constant temperature of 144°C.
All the alloys are left with varying amount of liquids which solidify in the end at a constant temperature (eutectic temperature) except eutectic alloy which begins to solidify and the solidification is completed at this constant eutectic temperature.
The data like arrest temperatures (271°C, T1, T2 (144), T3, 321°C) for each composition from Fig. 3.16 (i) is transferred to Fig. 3.16 (ii), which is a graph between temperature and composition. The melting points, 271°C and 321°C for pure metals Bi and Cd, are marked on vertical lines representing them respectively.
A vertical line for composition 80% Bi, 20% Cd is drawn and the temperatures, T1 and 144°C are marked. Same method is used for other alloys. The line joining the start of freezing temperatures of these alloys, OPQ is called liquidus.
The point at which liquidus lines (OP and QP) intersect, the minimum point P, is called the eutectic point as it indicates the eutectic temperature T2 (144°C here) and the composition of eutectic alloy (60% Bi, 40% Cd). Here, line OSPRQ is the solidus.
It is clear from the phase diagram that the freezing points of both the pure metals are lowered by the addition of the second metal. This is true as per Raoult’s law, provided both the metals are completely soluble in the liquid state, and are insoluble in the solid state. The depression in the freezing points is proportional to the molecular weight of the solute metal.
The phases present in various areas can be marked easily. Above the liquidus, the area has single-phase homogeneous liquid solution. Let us mark the phases present in area OSP. In all binary diagrams, two-phase region separates single-phase regions as given by the “1-2-1” rule.
As we move horizontally from left to right in area OSP, the vertical line OS represents single solid phase of pure metal Bi, and area beyond OP represents single phase liquid solution. Thus, the two phases present in area, OSP are Bi and liquid.
In the same way, as the extreme vertical lines ST and RV represent pure Bi and pure Cd respectively, the area between them, STVR has mixture of two pure phases (Bi and Cd). Thus, mark the single phase area first and follow the ‘1-2-1’ rule to fill the two phase regions.
The alloys to the left of the eutectic composition are called hypoeutectic alloys and to the right are called hypereutectic alloys. Let us now consider first the cooling of the eutectic alloy (60% Bi and 40% Cd) from completely liquid solution state (above eutectic temperature, 144°C) (Fig. 3.16 ii).
No change occurs in the liquid solution till eutectic temperature, (here 144°C) is reached. As it is an intersection point of liquidus and the solidus, the liquid should begin to freeze, and complete the solidification at this constant temperature (as shall be seen that, it is an invariant point). Its cooling curve as shown in Fig. 3.16 (i c) confirms it. The liquid solidifies into a mixture of two solid phases.
These two solid phases are the ones that are observed at the two ends of the horizontal eutectic-temperature line. From the figure, the two solids are indicated by the points S and R, which represent pure metal Bi and pure metal Cd respectively. Suppose the temperature is slightly below the eutectic temperature, and a small amount of pure metal Bi solidifies, then the remaining liquid becomes richer in Cd, i.e., the composition appears to shift slightly to the right.
Now, pure metal Cd solidifies to restore the liquid composition to the equilibrium value. If slightly more amount of Cd is precipitated, then the composition again shifts to the left. Alternate precipitation of solid Bi and solid Cd, thus continues until the last of the liquid has solidified.
During this time, the temperature essentially remains constant at, or just below eutectic temperature (144°C) by the release of latent heat of fusion of the metals. This extremely fine alternate mixture of two solids, visible only under the microscope, is called eutectic mixture (Fig. 3.16 iii d). The change of a liquid solution of eutectic composition (given by point P) on cooling into two different solids at a constant temperature, the eutectic temperature, is called the eutectic reaction.
In Bi-Cd system, the eutectic reaction is given as:
As the eutectic mixture contains pure metals here, the amount of pure Bi and pure Cd in it, shall be equal to the weight per cent of these metals in the eutectic liquid, i.e., weight percent of Bi and of Cd in the mixture shall be 60% and 40% respectively.
However, the eutectic reaction, in general, is written as:
The product mixture of solids could be two pure metals, two solid solutions, two intermediate phases, or any combination of them.
Let us now see the changes occurring in a hypereutectic alloy, for example, 25% Bi 75% Cd alloy, when cooled under equilibrium conditions from liquid solution state at temperature T. Thus, a vertical line at this composition is drawn, Fig. 3.17 (a). This alloy is completely liquid solution up to temperature T3.
At this temperature, nuclei of the solid in equilibrium with the liquid (25Bi/75Cd) are of pure cadmium, since the horizontal line at this point meets the solidus at point ‘u’, which represents 100% cadmium. Hence the dendrites of pure cadmium begin to form. See Fig. 3.16 (ii d).
As the dendrites of pure cadmium form, the remaining liquid become correspondingly richer in bismuth, so that the composition of the liquid moves towards left along liquidus QP. More solidification occurs as the temperature falls to T4, Fig. 3.17 (a), when more pure cadmium solidifies.
Lever rule can be used to calculate the amount of these phases under equilibrium at temperature T4:
This process of solidification of cadmium continues with simultaneous change of composition of liquid along ‘VP’ with the drop of temperature, until the temperature has just fallen to 144°C (the eutectic temperature).
The liquid now has the composition given by point P, i.e. 60% Bi 40% Cd, the eutectic point composition. A schematic microstructure at this stage is illustrated in Fig. 3.16 (ii e). Lever rule is used to calculate the amount of phases now- (At a fraction of a degree above 144°C)
This weight of solid pure cadmium, which solidified before the eutectic reaction takes place is called primary cadmium, or proeutectic cadmium. The alloy is now at point ‘H’, i.e., has just attained the eutectic temperature (144°C).
The remaining liquid in the alloy has eutectic alloy composition (60% Bi, 40% Cd) and is at eutectic temperature (144°C), and thus, the eutectic reaction occurs by which the liquid solidifies as a fine intimate mixture of Bi and Cd.
The microstructure is shown schematically in Fig. 3.16 (ii, f), i.e., has 58.33% weight of primary cadmium and 41.67% of eutectic mixture of Bi and Cd. Every alloy to the right of point P, i.e., hypereutectic alloy shall have dendrites of pure Cd and eutectic mixture.
If the alloy composition is close to eutectic composition, more eutectic mixture is present in the solidified alloy. See Fig. 3.16 (iii e and f.) No change in the microstructure occurs as the alloy cools, after the eutectic reaction has occurred, to room temperature.
A hypoeutectic alloy, for example having 80% Bi and 20% Cd, remains as unchanged liquid solution as temperature falls from T to T1. At T1 nuclei of pure Bi start to freeze. Bismuth being less-metallic metal does not form dendrites but geometrical-shaped crystals, more often roughly cubic in shape (Fig. 3.16 ii b).
As bismuth has been rejected from liquid solution, the latter becomes correspondingly richer in cadmium, that the composition of liquid moves towards the right along the liquidus O → Z → P. At temperature of 200°C pure bismuth is in equilibrium with liquid of composition Z, (75% Bi, 25% Cd).
Lever rule gives their amount:
As the solidification continues with the fall of temperature, the liquid attains a composition of eutectic alloy, given by point P (60 Bi 40 Cd) at 144°C (the eutectic temperature). At this eutectic temperature, liquid of eutectic composition (50% by weight) solidifies by eutectic reaction as eutectic mixture (whose amount shall be equal to the amount of liquid, that is 50% by weight), whose composition will always be of fixed value, namely 60% Bi/40% Cd in this system.
After solidification, the alloy consists of 50% by weight of primary bismuth, or proeutectic bismuth and 50% of eutectic mixture of Bi and Cd (ratio of weights of Bi and Cd in the eutectic mixture is 60 Bi/40 Cd). Fig. 3.16 ii c illustrates it.
There is no change in microstructure of the alloy as it cools to the room temperature. Every alloy to the left of the eutectic point P i.e., the hypoeutectic alloys, after solidification contain cubes of proeutectic, or primary bismuth and eutectic mixture. The only difference will be in the relative amounts of these.
The closer the alloy composition is to the eutectic composition, more is the eutectic mixture in the alloy. Fig. 3.17 (b) illustrates linear relationship between composition of the alloy and the eutectic mixture. Fig. 3.16 (iii b, c and d) illustrate this fact.
It must be emphasised here that any alloy in liquid solution state on either side of the eutectic point, will first deposit which ever metal is in excess of the eutectic composition in the form of primary (proeutectic) crystals until the remaining liquid attains the eutectic composition at the eutectic temperature (144°C). And then, the eutectic reaction occurs, i.e., regardless of alloy composition, the same eutectic reaction occurs whenever eutectic temperature line is reached by the alloy.
Phase rule can be applied to this diagram. At the eutectic point, three phases, liquid, solid bismuth and solid cadmium, can exist in equilibrium. This, for this two component (bismuth and cadmium) system.
F = C – P + 1
= 2-3+1
= 0
Thus, the degree of freedom is zero, i.e., it is an invariant point. Now using phase rule in two phase field of solid cadmium and solid bismuth, (below 144°C),
F = C – P + 1
= 1-2+1
= 1
Thus, if the only possible degree of freedom is arbitrarily chosen, the condition of the alloy must be uniquely established. As pure bismuth and pure cadmium coexist as solid phases between room temperature and 144°C, it would be possible to specify one independent variable, say, the concentration of one component in either of the two phases, the other two variables should be uniquely defined, i.e., fixed.
But here, one variable, the temperature of the system may have any value between room temperature and 144°C. This means, temperature is also another independent variable, i.e., another degree of freedom. But, phase rule indicates only one degree of freedom for the two-solid phase region.
This would be direct violation of phase rule. Whenever, two phases coexist at equilibrium in a binary alloy, the composition of each phase must change in a predictable manner, if the temperature of the alloy is changed. But, the composition of the pure metal cannot change.
The only possible conclusion is that two phases present can never be pure. These must actually be the solid solutions, and the extent of solubility of each component in the other must change continuously as the temperature changes, as illustrated by dotted lines in Fig. 3.17 (a).
Non-equilibrium Cooling in Eutectic Systems: iq
This causes two main effects:
1. Coring:
Commercial castings are much more rapidly cooled, and there is no time for diffusion to occur in the growing crystals of primary solid solution in the systems. This leads to coring as the phase diagrams contain a solidus and a liquidus.
Even the Al-4% Cu alloy rapidly cooled castings show coring of dendrites to have a composition of AI-0.5% Cu in the core (solidified at ≃ 650°C). Whereas the surface has a copper content of 5.5% (solidified at eutectic temperature).
2. Formation of Eutectic as a Result of Coring:
Normally, as an example, the alloy (Al-4.0% Cu) on solidification under equilibrium conditions contains grains of single phase α. But rapid cooling of such an alloy can cause the eutectic to appear in the alloy. Actually, in industrial Al-Cu alloys, marked coring of the dendrites is a rule.
The dashed line in Fig. 3.27 is the depressed solidus due to fast cooling of AI-4% Cu alloy. The eutectic horizontal line is extended to the left to meet it, as it is the left end of the ‘tie line’ for the cored AI-4% Cu alloy. This alloy does not get completely solidified when cooled fast even on reaching the eutectic temperature.
Normally, 5 to 10% of the liquid still remains, which at the eutectic temperature solidifies as a eutectic mixture of α + θ. Due to divorcement of eutectic (divorcement is the process of one of the phases of the eutectic to leave the other phase alone and gels itself deposited on already existing primary phase of itself), θ is left behind as inter-dendritic layers. Phase θ is CuAl2, which is hard and extremely brittle. Its continuous presence at grain boundaries makes the alloy brittle.
θ also increases corrosion of the alloy. For mechanical and economic reasons, slow cooling is not feasible in foundries. Homogenising annealing (for long times) below the eutectic temperature at 540°C is done to remove coring.
Type # 3. Soluble in Solid State:
Two Components are Completely Soluble in Liquid State and are Partially Soluble in Solid State:
Since most metals show limited solid solubility in each other, and if their melting points are not vastly different, a eutectic phase diagram showing partial solid solubility results. These types of diagrams are most common and important phase diagrams for example, Pb-Sn, Cu-Ag, Pb-Sb, Cd-Zn, Sn-Bi, etc.
As an example, Pb-Sn phase diagram is shown in Fig. 3.21. Such a phase diagram can be drawn from a series of cooling curves of alloys of different compositions in a manner analogous to that used for the eutectic, or solid solution diagram.
The melting points of pure lead and pure tin are indicated at points, 327°C, and 232°C respectively. The line ABC is liquidus, and the line CDBEA is solidus. Single phase areas should be labeled first. Above the liquidus, there exists only single-phase liquid solution because these metals have complete liquid solubility.
As these metals are partially soluble in each other in the solid state, solid solutions are formed, and alloys in this system never solidify as crystals of pure lead, or pure tin, but always a solid solution, or mixture of solid solutions.
The solid phase at the left-end of phase-diagram is the lead-rich α, which is the solid solution of tin in lead. Alpha dissolves only a limited amount of tin. In the same way, solid phase at the right-end is the tin-rich β, which is the solid solution of Pb in Sn.
Beta too dissolves very limited amount of lead. As these solid solutions exist next to the axes, these are called terminal solid solutions, or primary solid solutions. Now, using the “1- 2-1” rule, the two-phase regions are labeled.
The region ABE consists of L + α; region CBD consists of L + β and below the eutectic temperature, the region has α + β. Phase alpha can dissolve a maximum of 19% Sn in Pb at the eutectic temperature indicated by point, E, whereas, β can dissolve a maximum of 2.5% Pb in Sn at the eutectic temperature, indicated by point D.
With the decrease in temperature, the maximum amount of solute metal that can be dissolved in the base or primary metal decreases, as indicated by lines EF and DG. These two lines are called solvus lines and indicate the maximum solubility (saturated solid solution) of Sn in Pb (α), or Pb in Sn (β) as a function of temperature.
The liquidus lines, AB and CD intersect at a minimum point, B, which is called the eutectic point. A temperature horizontal through this point B, which also separates the three two-phase regions, corresponding to the temperature, Te (183°C here) is called the eutectic temperature.
At the eutectic temperature, the following eutectic reaction occurs:
The eutectic horizontal is used as a tie line, the ends of which give the compositions of α and β phases present at this temperature (183°C); along with a liquid of 61.9% Sn and 38.1% Pb.
Here, the solid product is an intimate mixture of two solid solutions, α and β. Lever rule can be used to calculate the relative amounts of these two phases just after the eutectic reaction. Eutectic temperature can be used as a ‘tie line’.
This intimate and fine mixture of α and β (Fig. 3.22) is called eutectic mixture or eutectic microconstituent. If a eutectic mixture of pure metals is compared to this, then it is not possible to tell, when viewed under microscope, whether the eutectic mixture is made up of two pure metals, or two solid solutions.
If the eutectic alloy is cooled under equilibrium conditions from below the eutectic temperature to room temperature, then because of the changes in solid solubility with the fall in temperature as indicated by the both solvus lines, some excess α as well as β get precipitated from the two solid solutions in the mixture. At room temperature, under truly equilibrium conditions, the mixture should consist of pure Sn and pure Pb, and their amounts are 61.9% Sn and 38.1% Pb.
Let us discuss cooling of a hypoeutectic alloy (i.e., Sn less than 61.9%) which does not undergo eutectic reaction, like a Pb-10% Sn alloy. Fig. 3.23 (a) illustrates its cooling curve and (b) illustrates some schematic microstructures of the alloy at various temperatures.
The alloy is liquid solution above temperature T1. At T1, nuclei of α (rich in Pb) begin to freeze. As the temperature drops, more α freezes as dendrites. Diffusion is supposed to take place under equilibrium conditions of freezing.
At temperature T2, Lever rule can be used to calculate the amounts of two phases present with their compositions as (microstructure is shown):
As the temperature decreases, more α with increasing amounts of tin in it, solidifies, till at temperature T3, the alloy has 100% solid alpha (10% Sn 90% Pb). This microstructure (at a lower temperature) has been shown. At temperature, T4, alpha is saturated with tin. As the temperature decreases further, solid solubility of tin in lead decreases, and thus, α rejects tin as solid solution β.
Thus, more and more β precipitates from α with the drop of temperature. The phase β precipitates mainly at the high energy areas of grain boundaries, though some of it, may as well precipitate inside the grains of α at inclusions, or defects. The schematic picture is illustrated in Fig. 3.23 (b).
The cooling of an alloy (40% Sn) is shown in Fig. 3.24, where (a) illustrates its cooling curve, and (b) schematic microstructures of the alloy at different temperatures. This alloy remains liquid till the liquidus line is reached at temperature T.
The liquid begins to freeze nuclei of primary, or proeutectic α (rich in Pb). As the temperature decreases, more of α (richer in Pb) solidifies as dendrites.
Lever rule can be used to calculate the amount of phases at temperature, [microstructure shown in Fig. 3.24 (b)]:
As the temperature drops further, more of α solidifies, and the composition of the liquid becomes richer and richer in Sn to follow the liquidus line, until when the temperature of alloy just reaches the eutectic temperature (183°C), the composition of the liquid becomes that of point P, i.e., the eutectic point (61.9% Sn).
Just a fraction of degree above the eutectic temperature, lever rule could be used to calculate the amount of phases, using a part of eutectic horizontal as the ‘tie-line’ (microstructure is illustrated of this stage):
At the eutectic temperature just reached, 48.96 weight % as liquid (of the alloy) has a composition 61.9% Sn, the eutectic composition, and eutectic reaction occurs, i.e., the liquid solidifies to give fine and intimate mixture of α and β. The amount of eutectic mixture formed is 48.96%. After the solidification, the schematic microstructure is illustrated in Fig. 3.24 (b).
The total amount of α (pro-eutectic + eutectic) can be directly calculated (just after the eutectic reaction) by applying Lever rule at just below 183°C, and thus, eutectic temperature line as ‘tie line’ with fulcrum at 40% Sn (alloy composition):
As the alloy cools to room temperature, the changes in solid solubilities of both α and β takes place as indicated by the two solvus lines EF and DG. Excess amount of β from α, and α from β are precipitated (β present in eutectic mixture).
The cooling of a hypereutectic Pb-Sn alloy (80% Sn) is shown in Fig. 3.25. Solidification starts when the liquidus line is reached at T6. Here, first nuclei are of β, (richer in Sn) a solid solution of Pb in Sn.
As the temperature drops further, more dendrites of primary, or proeutectic β (rich in Sn) solidify, the remaining liquid becomes richer and richer in Pb, gradually moving down and to the right [point H to B in Fig. 3.25 (b)] along the liquidus line until it reaches point, B, the eutectic point.
Lever rule can be used to calculate the amount of phases present and their chemical composition just a fraction of degree above the eutectic temperature, Te (183°C). Using BD as the tie-line with fulcrum at alloy composition. The schematic microstructure is also illustrated in Fig. 3.25 (b).
As the remaining liquid (49.16%) is at point B, the right temperature and the composition to undergo eutectic reaction, i.e., to solidify as the fine and intimate mixture of α (19% Sn) and β (97.5% Sn), of the composition appearing at the two ends of the eutectic temperature horizontal line [point E (19% Sn) and point D (97.5% Sn)].
Eutectic reaction occurs at the constant temperature until the solidification is complete. The schematic microstructure at this stage is shown in Fig. 3.25 (b). The amount of microconstituents are: the amount of eutectic mixture = amount of liquid which underwent eutectic reaction = 49.16%; amount of proeutectic β = 50.84%.
The total amount of β (proeutectic + eutectic) = 50.84 + 49.16 x (54.65/100)
= 77.71%
As the alloy cools to room temperature, solid solubilities of Pb in β and Sn in α decrease as indicated by two solvus lines. Some excess β from α, and α from β precipitate out. The amounts of these may be small enough in some cases to be ignored.
Type # 4. Peritectic Reaction:
When two metals are completely soluble in liquid state, show partial solubility in the solid state, and it their melting points are vastly different from each other, then, a peritectic phase diagram may result. The term ‘peritectic’ is from Greek ‘peri’ which means ‘around’ (the surrounding envelope of the new phase).
Although peritectic reaction occurs in commercially important phase diagrams like iron-carbon, copper-zinc, we shall consider Pt-Ag system, which is one of the few systems, based almost solely on a peritectic reaction.
In the peritectic reaction, a liquid and a solid react isothermally to form a new solid on cooling:
The new solid is usually an intermediate phase, but in some cases may be terminal solid solution as in Pt-Ag system, Fig. 3.28. Peritectic reaction looks to be reverse of eutectic reaction, as here two phases disappear to result in third phase, but their behaviours have little in common.
In Pt-Ag system, ADE is liquidus and ABCE is solidus. As there are single and two-phase regions, ‘1-2-1’ rule can be applied to fill in the regions of the diagram. The peritectic horizontal (BCD), i.e. the peritectic temperatures is 1185°C and the peritectic alloy has 46% Ag and 54% Pt.
The solidification of this alloy is illustrated in Fig. 3.28 with some schematic microstructurcs at different temperatures, where (m) illustrates alloy in liquid solution state. As the temperature drops, freezing of nuclei of α begins when alloy reaches the liquidus point F.
Further drop of temperature causes the formation of dendrites of α (richer in Pt), and thus liquid becomes richer in Ag to follow the liquidus line along FD, to attain the composition given by point D (69% Ag) as the temperature becomes the peritectic temperature (1185°C). Under equilibrium conditions, α also attains the composition given by point B (12% Ag) at this temperature.
Lever rule can be used to calculate the amount of these phases at a fraction of degree higher than the peritectic temperature:
The schematic microstructure at this stage is illustrated in 3.28 (n). As this alloy having L + α in these amounts reaches the peritectic temperature, 1185°C, the following peritectic reaction occurs:
The chemical composition of the liquid and a phases are given by the end points (D and B respectively) of the peritectic-reaction horizontal, and the β solid solution has the peritectic composition (46% Ag) (Fig. 3.28 p). This reaction also occurs at a constant temperature under ideal equilibrium conditions.
The physical pictures of this reaction are illustrated in Fig. 3.29. The liquid and α phase react here to produce β phase, Fig. 3.29 (b). Beta phase forms at the surface of dendrites of α, and very soon α phase gets enveloped by covering of β phase (Fig. 3.29 b). Further growth of β-phase is possible as a result of diffusion (through the existing β covering) of platinum atoms from α-phase (from inside to outside) and of silver atoms from liquid to inside (Fig. 3.29 e).
Thus, this change to get homogeneous β phase takes long time. Under the equilibrium conditions, as sufficient time is given, the formation of homogeneous β grains takes place. For complete peritectic reaction to occur, i.e., to get 100% product β-phase in the solid alloy by peritectic reaction, the ratio of liquid (69% Ag) and α (12% Ag) at peritectic temperature should be 59.65/40.35.
If an alloy has more liquid (in hyper-peritectic alloys), or more a (in hypoperitectic alloys), the extra phase remains unreacted along with the product P phase after the peritectic reaction. For a peritectic reaction to occur, thus, it is not necessary that an alloy should have exact peritectic composition (46% Ag), but that its composition should be such that it passes through the peritectic horizontal (that is, between, points B and D in Fig. 3.28).
The cooling of a hypereutectic alloy (60% Ag 40% Pt) is also described in Fig. 3.28. This alloy has more liquid than can react peritectedly. The freezing begins when the alloy is cooled to its liquidus, i.e., point H. More dendrites of α form as the temperature drops further, Fig. 3.28 (d).
As the alloy cools further, more α solidifies till it just approaches the peritectic temperature (1185°C). The amount of phases present at a fraction of degree more than peritectic temperature can be calculated by using Lever rule. Use peritectic temperature horizontal as ‘tie line’ with fulcrum at alloy composition (60% Ag).
The end points of the ‘tie line’, i.e., B and D indicate the phases present (α and liquid respectively) with their chemical compositions, α (12% Ag) and liquid (69% Ag):
The schematic microstructure is illustrated in Fig. 3.28 (e). As the alloy cools further, more solidification occurs of β (of decreasing Pt%), till the alloy reaches the solidus temperature, where the process is completed and the alloy has 100% single phase β (60% Ag). The grains of β are illustrated in Fig. 3.28 (j)
Another important aspect of peritectic reaction, taking example of Pt-Ag phase diagram is that liquid (having less than 69% Ag) solidifies to give α solid, if temperature of solidification is higher than peritectic temperature, but if below this temperature, liquid (Ag > 69%) solidifies to give directly β phase.
A peritectic reaction often results in the formation of an intermetallic compound of fixed composition (incongruent-melting intermediate compound). Here, by the peritectic reaction, resultant solid is this compound. Fig. 3.30 shows part of Au-Pb phase diagram, in which an alloy having composition 65.6% Au and 34.4% Pb starts freezing when its liquidus point A is reached. Further drop of temperature results in solidification of dendrites of pure Au.
Lever rule can be used to calculate the amount of solid pure gold dendrites and the liquid (45% Pb) just above the peritectic temperature, 418°C:
Now, at the peritectic temperature (418°C), 23.56 wt.% of Au reacts with 76.44% of liquid (45% Pb) by peritectic reaction to result in 100% of Au2 Pb solid, the intermetallic compound:
Non-Equilibrium Cooling in Peritectic Systems:
Industrial castings of alloys which undergo peritectic reaction almost always have non-equilibrium structures. For example Fig. 3.29 (c) is redrawn below in Fig. 3.31 (a). The reason of persistence of dendrites of primary alpha phase is due to very nature of the peritectic reaction.
As β phase forms from α-phase and liquid, it envelopes the α-phase dendrites. This encasement by β-phase shields the α-phase from further reaction with the liquid. Diffusion of Pt atoms to come out of α-phase and of Ag atoms to diffuse in from outside liquid is usually insufficient in solid phases, and specially under fast cooling practice of castings in industry. Equilibrium conditions are almost impossible to be attained.
It is a common practice that such solidified alloys are first cold-worked (to reduce the diffusion distance by reducing the inter-dendritic spacing) and then given long homogenising annealing treatment (or, hot-worked if permissible). The diffusion is quicker and equilibrium structures can be obtained.
Alloy Systems Containing One or More Intermediate Phases:
Intermediate phases are the rule than the exception in equilibrium diagrams. It is because of the presence of intermediate phases, that most equilibrium-diagrams show a combination of various invariant reactions.
Intermediate phases normally form because the two metals (components) have chemical affinity for each other. The chemical compositions of these phases are intermediate between the two pure metals, but crystal structures are different from the pure metals, which distinguishes them from primary solid solutions.
When an intermediate phase has a fixed composition, such as Au2Pb (in Au-Pb system), which has a fixed simple ratio of the two kinds of atoms (2 Au for one Pb atom), it is more precise to call it intermetallic compound. But, if an intermediate phase has a range of compositions, it is called intermediate or secondary solid solution, as β phase in brasses.
Based on the melting behaviour on heating, intermediate phases are classified in two types:
(i) Incongruently Melting Intermediate Phase:
Such a phase, on heating, changes into two different phases, normally one solid and another liquid. Phase Au2Pb (Fig. 3.30) on heating results in reverse of peritectic reaction.
(ii) Congruently Melting Intermediate Phase:
Such a phase, on heating melts just like a pure metal (at a constant temperature to produce liquid solution). Such a compound divides a phase-diagram into essentially independent sections, which can be studied easily separately. Fig. 3.32 illustrates Al—Ca phase diagram.
The congruently melting intermediate compound Al2Ca can be visualised to divide the phase diagram into two separate diagrams: one between Al—Al2Ca, and other between Al2Ca—Ca. The Al—Al2Ca diagram also shows the presence of incongruently melting phase (Al3Ca) produced by the peritectic reaction between solid Al2Ca and liquid (14% Ca) at 699°C. Al2 Ca—Ca diagram is a simple eutectic diagram without partial solid solubility.
In Ag-Mg phase diagram, the intermediate phase, MgAg (having equal number of magnesium and silver atoms) is a solid solution as β’ (it is designated as prime as it is an ordered structure stable up to melting point) extends its field from 26 atomic percent to 42 atomic percent Mg. In this diagram, the incongruently melting ɛ intermediate phase, though is produced by peritectic reaction, but is a solid solution having its field from 75 at % to 79 at % Mg.
