Isomorphous Alloy Systems

Isomorphous Alloy Systems

Phase diagrams demonstrate the processes in the substance at different compositions, temperatures and pressures. Phase diagrams are recognizable as equilibrious conditions for an alloy, indicating that very slow heating and refrigeration speeds are used to generate data for its building. Due to the almost never-becoming complexity of industrial activities, step diagrams should be used with some caution. These are, however, very useful in predicting transitions in phases and the subsequent microstructures. And, because in many applications the stresses are constant, phase diagrams are typically built at a constant pressure of one atmosphere. External pressure often influences the phase structure.

Binary isomorphic systems are included in this section. The term isomorph means that in both liquid and solid conditions both metals are completely miscible in each other. The methods of calculation that allow the prediction of the current phases, the chemical compositions of the present phases, and the present phase quantities are shown.

4.1 Binary Systems

Phase diagrams and the systems they describe are often classified and named for the number (in Latin) of components in the system (Table 4.1). When a system consists of two components, then a three-dimensional diagram is needed to determine how they vary with temperature and pressure. The P-T-X (pressure, temperature, composition) diagram for two metals that dissolve in each other is shown in Fig. 4.1.  A feature of this diagram is that two-phase and three-phase equilibria extend over a region rather than being limited to a line or point, as in a one-component diagram. This behavior is shown in the P-T section at constant composition (Fig.

4.1b). It is often useful to have a section at constant temperature through the P-T-X diagram. A P-X section of this kind is shown in Fig. 4.1(c) for a temperature below the triple points of both metals. By far the most useful section through the P-T-X diagram is the one at constant pressure, at atmospheric pressure in particular. Figure 4.1(d) shows the diagram obtained in this instance. Therefore, the most commonly encountered phase diagram in metallurgy is a T-X diagram constructed at a pressure of one atmosphere. The Gibbs phase rule applies to all states of matter (solid, liquid, and gaseous), but when the effect of pressure is constant, the rule reduces to:
                                                          F = C – P + 1

Table 4.2 sums up the stable equilibrium of binary systems.
Thermodynamical principles and thermodynamic property of all the phases that make up the system shall regulate the areas (fields) of a phase diagram and the location and shape of the points, lines, surfaces, and intersections in it. The rule of the phase field states that the number of phases in adjacent fields in a multi-component diagram must differ at constant temperature and pressure by one.

4.1.1 Binary Isomorphous Systems

Some systems consist of components with the même crystal structure, and the components of some of these systems are completely miscible in solid form (comprehensively soluble in each other). If this happens in a binary system, the phase diagram usually appears in Figure. 5.3. The diagram consists of two fields with single phases divided by a field of two phases. The boundary of the fluid field and the field with two phases in Fig. 4.2 is known as the liquid; that is the medium between the two-phase field and the solid field. A liquid is generalized to represent the locus of points in the phase diagram at which the alloys of different structures of the system start to freeze at cooling or finish the melting of the system on heating, where the various alloys freeze or start melting when they are cooled. The balancing steps throughout the two-phase sector in Fig. 4.2 Conjugate liquids are referred to as liquid and solid solutions.

Consider briefly how these diagrams are constructed. A pure metal will solidify at a constant temperature, while an alloy will solidify over a temperature range that depends on the alloy composition. Consider the series of cooling curves for the copper-nickel system (Fig. 4.3). For increasing amounts of nickel in the alloy, freezing begins at increasing temperatures A, A1, A2, A3, up to pure nickel at A4, and finishes at increasing temperatures B, B1, B2, B3, up to pure nickel at B4. If the points A, A1, A2, A3, and A4 are joined, the result is the liquidus line, which indicates the temperature at which any given alloy will begin to solidify. Likewise, by joining the points B, B1, B2, B3, and B4, the solidus line, the temperature at which any given alloy will become completely solid, is obtained. In other words, at all temperatures above the liquidus, the alloy will be a liquid, and at all temperatures below the solidus, the alloy will be a solid. At temperatures between the liquidus and the solidus, sometimes referred to as the “mushy zone,” both liquid and solid coexist in equilibrium. 

Very simple phase diagrams of this type can be constructed by using the appropriate points obtained from time-temperature cooling curves, which indicate where freezing began and where it was complete. However, if the alloy system is one in which further structural changes occur after the alloy has solidified, then the metallurgist must resort to other methods of investigation to determine the phase-boundary lines. These techniques are described in Chapter 12, “Phase Diagram Determination,” in this book. 

The components of some systems are fully soluble, or miscible, in a liquid and solid manner in each other forming a set of solid solutions. A few systems consist of the components having the same crystalline structure. When this occurs in a binary system, the phase diagram usually appears in the coppernickel system in the image. Four. 4.4. On the ordinate axis is shown the temperature and on the abscissa axis the alloy composition is shown. The composition is0 wt.% Ni (100 wt.% Cu) on the far left side, 100 wt.% Ni (0 wt.% Cu) in the far right part.

The diagram contains three different phase areas (or fields): a fluid (L) field, a two-phase solid plus fluid field (α+L), and an alpha (α) solid-solution field where α is a strong solution containing copper and nickel. Each field is defined by the phases or phases which are bounded by the phase-boundary lines across the temperature and composition spectrum. The liquid region, L, is a stable liquid solution consisting of both copper and nickel at high temperatures. A solid solution, α, is a substitute solid solution composed of both copper and nickel atoms with a crystalline face-centric cubic structure (fcc).

When an alloy of any given composition freezes, copper and nickel are mutually soluble in each other and therefore display complete solid solubility. Solid solutions are commonly designated by lowercase Greek letters. The boundaries between the regions are identified as the liquidus and solidus. The upper curve separating the liquid, L, and the two-phase, L + α, field is termed the liquidus line. The liquidus is the lowest temperature at which any given composition can be found in an entirely molten state. The lower curve separating the solid solution, α, field and the two-phase, L + α, field is known as the solidus line. The solidus is the highest temperature when all atoms of a given composition can be found in an entirely solid state. A solidus is the locus of points representing the temperatures at which the various alloys finish freezing on cooling or begin melting on heating.

Complete solid solubility is actually the exception rather than the rule. To obtain complete solubility, the system must adhere to the Hume-Rothery rules for solid solutions (see Chapter 2, “Solid Solutions and Phase Transformation,” in this book). In this case, both copper and nickel have the fcc crystal structure, have nearly identical atomic radii and electronegativities, and have similar valences. The term isomorphous implies complete solubility in both the liquid and solid states. Most alloys do not have such simple phase systems. Typically, alloying elements have significant differences in their atomic size and crystalline structure, and the mismatch forces the formation of a new crystal phase that can more easily accommodate alloying elements in the solid state.

The liquidus and solidus lines intersect at the two composition extremities; that is, at the temperatures corresponding to the melting points of pure copper (1085 °C, or 1981 °F) and pure nickel (1455 °C, or 2644 °F). Because pure metals melt at a constant temperature, pure copper remains a solid until its melting point of 1085 °C (1981 °F) is reached on heating. The solid-to-liquid transformation then occurs and no further heating is possible until the transformation is complete. However, for any composition other than the pure components, melting will occur over a range of temperatures between the solidus and liquidus lines. For example, on heating a composition of 50wt%Cu-50wt%Ni, melting begins at approximately 1250 °C (2280 °F) and the amount of liquid increases until approximately 1315 °C (2400° F) is reached, at which point the alloy is completely liquid. A binary phase diagram can be used to determine three important types of information: (1) the phases that are present, (2) the composition of the phases, and (3) the percentages or fractions of the phases.

Prediction of Phases. The phases that are present can be determined by locating the temperature-composition point on the diagram and noting the phase(s) present in the corresponding phase field. For example, an alloy of composition 30wt%Ni-70wt%Cu at 1315 °C (2400 °F) would be located at point a in Fig. 4.4. Because this point lies totally within the liquid field, the alloy would be a liquid. The same alloy at 1095 °C (2000 °F), designated point c, is within the solid solution, α, field, only the single α phase would be present. On the other hand, a 30wt%Ni-70wt%Cu alloy at 1190 °C (2170 °F) (point b) would consist of a two-phase mixture of solid solution, α, and liquid, L.

Prediction of Chemical Compositions of Phases. To determine the composition of the phases present, locate the point on the phase diagram. If only one phase is present, the composition of the phase is the overall composition of the alloy. For example, for an alloy of 30wt%Ni-70wt%Cu at 1095 °C (2000 °F) (point c in Fig. 4.4), only the α phase is present, and the composition is 30wt%Ni-70wt%Cu. For an alloy with composition and temperature coordinates located in a two-phase region, the compositions of the phases can be determined by drawing a horizontal line, referred to as a tie line, between the two phase boundaries at the temperature of interest. Then, drop perpendicular lines from the intersections of each boundary down to the composition axis and read the compositions. For example, again considering the 30wt%Ni-70wt%Cu alloy at 1190 °C (2170 °F) located at point b in Fig. 4.4 and lying with the two-phase, α + L, field. The perpendicular line from the liquidus boundary to the composition axis is 20wt%Ni-80wt%Cu, which is the composition, CL, of the liquid phase. In a similar manner, the composition of the solid-solution phase, Cα, is read from the perpendicular line from the solidus line down to the composition axis, in this case 35wt%Ni-65wt%Cu.

Prediction of Amounts of Phases. The percentages or fractions of the phases present at equilibrium can also be determined with phase diagrams. In a single-phase region, because only one phase is present, the alloy is comprised entirely of that phase; that is, the phase fraction is 1.0 and the percentage is 100%. From the previous example for the 30wt%Ni70wt%Cu alloy at 1095 °C (2000 °F) (point c in Fig. 4.4), only the α phase is present and the alloy is 100% α. If the composition and temperature position is located within a twophase field, a horizontal tie line must be used in conjunction with the lever rule. The lever rule is a mathematical expression based on the principle of conservation of matter. First, a tie line is drawn across the two-phase region at the composition and temperature of the alloy. The fraction of one phase is determined by taking the length of the tie line from the overall alloy composition to the phase boundary for the other phase and dividing by the total tie line length. The fraction of the other phase is then determined in the same manner. 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.

Again, consider the 30wt%Ni-70wt%Cu alloy at 1190 °C (2170 °F) located at point b in Fig. 4.4 containing both the solid, α, and the liquid, L, phases. The same tie line that was used for determination of the phase compositions can again be used for the lever rule calculation. The overall alloy composition located along the tie line is Cα – CL or 35 – 20 wt%. The weight percentage of liquid present is then:

Likewise, the amount of solid present is:
Since these calculations are performed using graphical methods, the results are approximate instead of accurate. The heel rule can be visualized in the scale as shown in the figure, or the reverse heel rule more accurately. 4.5. 4.5. For the scale of balances, α, which has a higher weight percentage and thus a shorter 5 unit lever arm, has to have the longer lever arm in this example 10 units compared to the solid stage.

It is important to emphasize that equilibrium phase diagrams identify phase changes under conditions of very slow changes in temperature. In practical situations, where heating and cooling occur more rapidly, the atoms do not have enough time to get into their equilibrium positions, and the transformations may start or end at temperatures different from those shown on the equilibrium phase diagrams. In these practical circumstances, the actual temperature at which the phase transformation occurs will depend on both the rate and direction of temperature change. Nevertheless, phase diagrams provide valuable information in virtually all metal processing operations that involve heating the metal, such as casting, hot working, and all heat treatments.

The copper-nickel system is an example of solid-solution hardening or strengthening. Most of the property changes in a solid-solution system are caused by distortion of the crystalline lattice of the base or solvent metal by additions of the solute metal. The distortion increases with the amount of the solute metal added, and the maximum effect occurs near the center of the diagram, because either metal can be considered as the solvent. As shown in Fig. 4.6, the strength curve passes through a maximum, while the ductility curve, as measured by percent elongation, passes through a minimum. Properties that are almost unaffected by atom interactions vary more linearly with composition. Examples include the lattice constant, thermal expansion, specific heat, and specific volume.

Copper-nickel alloys have a good combination of properties and corrosion resistance. One of the most notable uses is for clad coinage. A Cu-25% Ni alloy is used for the clad coinage of the U.S. dime, quarter, and halfdollar. The coins contain a copper core that is clad on the surfaces with the copper-nickel alloy (Fig. 4.7). The same alloy is used for the U.S. nickel.

If the solidus and liquids meet tangentially at some point, a maximum or minimum is produced in the two-phase field, splitting it into two portions (Fig. 4.8). It also is possible to have a gap in miscibility in a single-phase field (Fig. 4.9). 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.

4.2 Nonequilibrium Cooling 

As previously mentioned, equilibrium phase diagrams are constructed to reflect extremely slow cooling rates that approach equilibrium conditions. This type of cooling is seldom encountered in industrial practice where faster cooling rates can produce segregation in the solidification products. As an example of a type of segregation called coring, produced by nonequilibrium freezing, consider the 70% Ni-30% Cu alloy in Fig. 4.10 that is rapidly cooled from a temperature, T0. The first solid forms at temperature T1 with a composition of α1. On further rapid cooling to T2, additional layers of composition, α2, form. The overall composition at T2 lies somewhere between α1 and α2 and is designated as α¢ 2. Because the tie line at α¢ 2 L2 is longer than α2 L2, there will be more liquid and less solid in the rapidly cooled alloy than if it had been slowly cooled under equilibrium conditions. As rapid cooling continues through T3 and T4, the same processes occur, and the average composition follows the nonequilibrium solidus determined by points α1, α¢ 2, α¢ 3, º. At T7, freezing is complete and the average composition of the alloy is 30% Cu. The microstructure consists of regions varying from α1 to α¢ 7, producing a cored microstructure. 


4.1 H. Baker, Introduction to Alloy Phase Diagrams, Phase Diagrams, Vol 3, ASM Handbook, ASM International, 1992, reprinted in Desk Handbook: Phase Diagrams for Binary Alloys, 2nd ed., H. Okamoto, Ed., ASM International, 2010

4.2 A.G. Guy, Elements of Physical Metallurgy, 2nd ed., Addison-Wesley Publishing Company, 1959

4.3 F.C. Campbell, Elements of Metallurgy and Engineering Alloys, ASM International, 2008

4.4 Microstructure of Copper and Copper Alloys, Atlas of Microstructures of Industrial Alloys, Vol 7, Metals Handbook, 8th ed., American Society for Metals, 1972

4.5 V. Singh, Physical Metallurgy, Standard Publishers Distributors, 1999

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