上海交通大学：《材料与文明》课程教学资源_参考资料_Understanding Mater_Chapter 5 - Alloys and Compounds

5 Alloys and Compounds Pure materials have a number of inherent mechanical properties, as discussed in Chapter 3.These features,such as strength or duc- tility,can be altered only to a limited degree,for example,by work hardening.In contrast to this,the properties of materials can be varied significantly if one combines several elements,that is,by alloying.In this chapter,we shall unfold the multiplicity of the mechanical properties of alloys and compounds with particular emphasis on the mechanisms which are involved.Specifically,we shall discuss a number of techniques which increase the strength of materials.Among them are solid solution strengthening,pre- cipitation hardening (age hardening),dispersion strengthening, and grain size strengthening.In order to understand these mech- anisms,we need to study the fundamentals of phase diagrams. 5.1.Solid Solution Strengthening When certain second constituents such as tin or nickel are added to copper,the resulting alloy has a noticeably larger yield strength than pure copper,as depicted in Figure 5.1.The added atoms (called solute atoms)may substitute up to a certain limit regular lattice atoms (called solvent or matrix).The resulting mixture is then said to be a substitutional solid solution.In many cases,the size of the solvent atoms is different from the size of the solute atoms.As a consequence,the lattice around the added atoms is distorted,as shown in Figure 5.2.The movement of dislocations upon application of a shear stress is then eventually obstructed and the alloy becomes stronger but less ductile.(Only in cop- per-zinc alloys do both strength and ductility increase simulta- neously.)This mechanism is called solid solution strengthening. Solid solution strengthening is greater (up to a certain limit)the more solute atoms are added (see Figure 5.1).Specifically,the yield strength of an alloy increases parabolically with the solute

5 Pure materials have a number of inherent mechanical properties, as discussed in Chapter 3. These features, such as strength or duc￾tility, can be altered only to a limited degree, for example, by work hardening. In contrast to this, the properties of materials can be varied significantly if one combines several elements, that is, by alloying. In this chapter, we shall unfold the multiplicity of the mechanical properties of alloys and compounds with particular emphasis on the mechanisms which are involved. Specifically, we shall discuss a number of techniques which increase the strength of materials. Among them are solid solution strengthening, pre￾cipitation hardening (age hardening), dispersion strengthening, and grain size strengthening. In order to understand these mech￾anisms, we need to study the fundamentals of phase diagrams. When certain second constituents such as tin or nickel are added to copper, the resulting alloy has a noticeably larger yield strength than pure copper, as depicted in Figure 5.1. The added atoms (called solute atoms) may substitute up to a certain limit regular lattice atoms (called solvent or matrix). The resulting mixture is then said to be a substitutional solid solution. In many cases, the size of the solvent atoms is different from the size of the solute atoms. As a consequence, the lattice around the added atoms is distorted, as shown in Figure 5.2. The movement of dislocations upon application of a shear stress is then eventually obstructed and the alloy becomes stronger but less ductile. (Only in cop￾per–zinc alloys do both strength and ductility increase simulta￾neously.) This mechanism is called solid solution strengthening. Solid solution strengthening is greater (up to a certain limit) the more solute atoms are added (see Figure 5.1). Specifically, the yield strength of an alloy increases parabolically with the solute Alloys and Compounds 5.1 • Solid Solution Strengthening

5.2·Phase Diagrams 75 300 Be (%) 200 Sn FIGURE 5.1.Change in yield strength due to 100 Ni adding various ele- ments to copper.The Zn yield strength,o,in- creases parabolically Cu 10 20 with the solute concen- Concentration,c,of solute (mass%) tration. concentration,c,that is,as c12.Further,solid solution strength- ening is larger the greater the size difference between the solute and solvent atoms.Finally,the ability to lose strength at high temperatures by creep (Chapter 6)is less of a problem in solid solution strengthened alloys compared to their constituents. Many alloys,such as bronze or brass,receive their added strength through this mechanism. 5.2。Phase Diagrams At this point,we need to digress somewhat from our main theme (namely,the description of strengthening mechanisms through alloying).In order to better understand the mechanical (and other)properties of alloys or compounds,materials scientists fre- quently make use of diagrams in which the proportions of the involved constituents are plotted versus the temperature.The use- fulness of these phase diagrams for the understanding of strengthening mechanisms will become evident during our dis- cussions.(A phase is defined to be a substance for which the structure,composition,and properties are uniform.) FIGURE 5.2.Distortion of a lattice by inserting (a)a larger (such as Sn) and (b)a smaller (such as Be)sub- stitutional atom into a Cu matrix. (a) (b) The distortions are exaggerated

concentration, c, that is, as c1/2. Further, solid solution strength￾ening is larger the greater the size difference between the solute and solvent atoms. Finally, the ability to lose strength at high temperatures by creep (Chapter 6) is less of a problem in solid solution strengthened alloys compared to their constituents. Many alloys, such as bronze or brass, receive their added strength through this mechanism. At this point, we need to digress somewhat from our main theme (namely, the description of strengthening mechanisms through alloying). In order to better understand the mechanical (and other) properties of alloys or compounds, materials scientists fre￾quently make use of diagrams in which the proportions of the involved constituents are plotted versus the temperature. The use￾fulness of these phase diagrams for the understanding of strengthening mechanisms will become evident during our dis￾cussions. (A phase is defined to be a substance for which the structure, composition, and properties are uniform.) 5.2 • Phase Diagrams 75 Cu 10 20 100 200 300 Concentration, c, of solute (mass%) Zn Ni Sn Be  y (%) FIGURE 5.1. Change in yield strength due to adding various ele￾ments to copper. The yield strength, y, in￾creases parabolically with the solute concen￾tration. (a) (b) FIGURE 5.2. Distortion of a lattice by inserting (a) a larger (such as Sn) and (b) a smaller (such as Be) sub￾stitutional atom into a Cu matrix. The distortions are exaggerated. 5.2 • Phase Diagrams

76 5.Alloys and Compounds 5.2.1 A particular phase diagram in which only two elements (such as Isomorphous copper and tin)or two compounds(such as Mgo and NiO)are in- volved is called a binary phase diagram.If complete solute solubil- Phase ity between the constituents of a compound or an alloy is encoun- Diagram tered,the term isomorphous binary phase diagram is utilized.Figure 5.3 depicts the Cu-Ni isomorphous binary phase diagram as an ex- ample.Referring to Figure 5.3,we note that at temperatures above 1455C (i.e.,the melting point of nickel),any proportion of a Cu-Ni mixture is liquid.On the other hand,at temperatures below 1085C (the melting point of copper),alloys of all concentrations should be solid.This solid solution of nickel in copper is designated as a-phase. In the cigar-shaped region between the liquid and the a-solid-so- lution areas,both liquid and solid copper-nickel coexist(like cof- fee and solid sugar may coexist in a cup).This area is appropriately termed a two-phase region.The upper boundary of the two-phase region is called the liquidus line,whereas the lower boundary is re- ferred to as the solidus line.Within the two-phase region,the free- dom to change the involved parameters is quite limited.The degree of freedom,F,can be calculated from the Gibbs phase rule: F=C-P+1, (5.1) where C is the number of components and P is the number of phases.!In the present case,there are two components(Cu and Ni)and two phases (a and liquid),which leaves only one degree T [c] Liquid 1455 1210 c+L 1085 FIGURE 5.3.Copper-nickel isomorphous bi- nary phase diagram.The composition Solid here is given in mass percent(formerly Q called weight percent)in contrast to atomic percent.This section uses exclu- sively mass percent.For simplicity,the Cu 23 34 Ni latter is generally designated as % Mass Ni In(5.1)the pressure is assumed to be constant as it is considered in virtually all of the cases in this chapter.If the pressure is an additional variable,then the Gibbs phase rule has to be modified to read F=C-P+2. (5.1a)

A particular phase diagram in which only two elements (such as copper and tin) or two compounds (such as MgO and NiO) are in￾volved is called a binary phase diagram. If complete solute solubil￾ity between the constituents of a compound or an alloy is encoun￾tered, the term isomorphous binary phase diagram is utilized. Figure 5.3 depicts the Cu–Ni isomorphous binary phase diagram as an ex￾ample. Referring to Figure 5.3, we note that at temperatures above 1455°C (i.e., the melting point of nickel), any proportion of a Cu–Ni mixture is liquid. On the other hand, at temperatures below 1085°C (the melting point of copper), alloys of all concentrations should be solid. This solid solution of nickel in copper is designated as -phase. In the cigar-shaped region between the liquid and the -solid-so￾lution areas, both liquid and solid copper–nickel coexist (like cof￾fee and solid sugar may coexist in a cup). This area is appropriately termed a two-phase region. The upper boundary of the two-phase region is called the liquidus line, whereas the lower boundary is re￾ferred to as the solidus line. Within the two-phase region, the free￾dom to change the involved parameters is quite limited. The degree of freedom, F, can be calculated from the Gibbs phase rule: F
C  P 1, (5.1) where C is the number of components and P is the number of phases.1 In the present case, there are two components (Cu and Ni) and two phases ( and liquid), which leaves only one degree 5.2.1 Isomorphous Phase Diagram 76 5 • Alloys and Compounds Mass % Ni T [C]  + L Cu 23 34 Ni 1085 1210 1455 Liquid Solid  FIGURE 5.3. Copper–nickel isomorphous bi￾nary phase diagram. The composition here is given in mass percent (formerly called weight percent) in contrast to atomic percent. This section uses exclu￾sively mass percent. For simplicity, the latter is generally designated as %. 1In (5.1) the pressure is assumed to be constant as it is considered in virtually all of the cases in this chapter. If the pressure is an additional variable, then the Gibbs phase rule has to be modified to read F
C  P 2. (5.1a)

5.2·Phase Diagrams 77 of freedom for varying any parameter.In other words,if we choose the temperature,then the composition of the a and the liquid phases is determined.As an example,if we specify the tem- perature to be 1210C,then the composition of the liquid is about Cu-23%Ni (or more precisely,23 mass percent)and the com- position of the a-solid-solution is about Cu-34%Ni,as can be inferred from Figure 5.3.The horizontal line in the two-phase re- gion which connects the just-mentioned compositions at a given temperature is called the tie line (see also Figure 5.4). The question then arises,how much of each phase is present in the case at hand?For this we make use of the lever rule.Let us assume a starting composition of 31%Ni and again a tem- perature of 1210C,as shown in Figure 5.4.A fulcrum (A)is thought to be positioned at the intersection between the tie line (considered here to represent the lever)and the chosen compo- sition (31%Ni).Similarly as for a mechanical lever,the amount of a given phase is proportional to the length of the lever at the opposite side of the fulcrum.Accordingly,by inspecting Figure 5.4 we conclude that 3/11 or 27%of this alloy at 1210C is lig- uid(34-31)/(34-23)and8/11or73%is solid(31-23)/(34-23). The composition of a solid (and the corresponding liquid) changes continuously upon cooling,as demonstrated in Figure 5.5. At the start of the solidification process of,say,a 28%Ni alloy,the solid (as little as there may be)contains about 40%Ni.At this in- stance,the alloy is still almost entirely in the liquid state (see Tie Line Number 1 in Figure 5.5).As the temperature is lowered (by cooling the alloy,for example,in a mold),the nickel concentration of the a-solid-solution decreases steadily and the amount of solid increases;see Tie Line 2 as an example.Eventually,upon further cooling,the entire alloy is in the solid state and the a-solid-solu- tion now has the intended composition of 28%Ni (Tie Line 3). T c] L Liquidus x+L 1210 C he line or"lever" Fulcrum FiGURE 5.4.Part of the Cu-Ni phase dia- gram to demonstrate the lever rule.The Solidus section of the lever between the fulcrum and the solidus line represents the 23 31 34 amount of liquid.(The analogue is true Mass%Ni→ for the other part of the lever.)

of freedom for varying any parameter. In other words, if we choose the temperature, then the composition of the  and the liquid phases is determined. As an example, if we specify the tem￾perature to be 1210°C, then the composition of the liquid is about Cu–23% Ni (or more precisely, 23 mass percent) and the com￾position of the -solid-solution is about Cu–34% Ni, as can be inferred from Figure 5.3. The horizontal line in the two-phase re￾gion which connects the just-mentioned compositions at a given temperature is called the tie line (see also Figure 5.4). The question then arises, how much of each phase is present in the case at hand? For this we make use of the lever rule. Let us assume a starting composition of 31% Ni and again a tem￾perature of 1210°C, as shown in Figure 5.4. A fulcrum () is thought to be positioned at the intersection between the tie line (considered here to represent the lever) and the chosen compo￾sition (31% Ni). Similarly as for a mechanical lever, the amount of a given phase is proportional to the length of the lever at the opposite side of the fulcrum. Accordingly, by inspecting Figure 5.4 we conclude that 3/11 or 27% of this alloy at 1210°C is liq￾uid ((34–31)/(34–23)) and 8/11 or 73% is solid ((31–23)/(34–23)). The composition of a solid (and the corresponding liquid) changes continuously upon cooling, as demonstrated in Figure 5.5. At the start of the solidification process of, say, a 28% Ni alloy, the solid (as little as there may be) contains about 40% Ni. At this in￾stance, the alloy is still almost entirely in the liquid state (see Tie Line Number 1 in Figure 5.5). As the temperature is lowered (by cooling the alloy, for example, in a mold), the nickel concentration of the -solid-solution decreases steadily and the amount of solid increases; see Tie Line 2 as an example. Eventually, upon further cooling, the entire alloy is in the solid state and the -solid-solu￾tion now has the intended composition of 28% Ni (Tie Line 3). 5.2 • Phase Diagrams 77 23 31 34 1210 Mass % Ni T [C] L Liquidus Tie line or “lever” Solidus Fulcrum  + L  FIGURE 5.4. Part of the Cu–Ni phase dia￾gram to demonstrate the lever rule. The section of the lever between the fulcrum and the solidus line represents the amount of liquid. (The analogue is true for the other part of the lever.)

78 5.Alloys and Compounds T Q+L [C] nonequilibrium solidus line FIGURE 5.5.Equilibrium (solid lines) and nonequilibrium (dashed line) solidus curve in a part of the Cu-Ni 2023 28 34 40 binary phase diagram. Mass Ni The just-described mechanism tacitly implies that the compo- sition of the solid changes instantly upon cooling,as depicted in Figure 5.5.This occurs,however,only when the Cu and Ni atoms are capable of freely exchanging their lattice positions until even- tually the respective equilibrium state has been reached.The mechanism by which atoms change their position is called dif fusion.Diffusion occurs preferentially once the temperature is high and when the difference in concentration between two parts of an alloy is large.(We shall deal with diffusion in more detail in Chapter 6.)The equilibrium concentration of the alloy,as de- picted in Figure 5.5,is only achieved upon extremely slow cool- ing.In most practical cases,however,the composition of an al- loy during cooling is governed by a nonequilibrium solidus line, an example of which is depicted in Figure 5.5 by a dashed curve. Actually,this nonequilibrium solidus line is different for each cooling rate.Specifically,a faster cooling rate causes an increased deviation between equilibrium and nonequilibrium solidus lines. There are practical consequences to the nonequilibrium cooling process just described.Referring back to Figure 5.5,it is evident that a Cu-28%Ni alloy,upon conventional cooling in a mold,has a composition of 40%Ni wherever the solidification has started. Next to this region,one observes layers having successively lower Ni concentrations which solidified during later cooling (compara- ble to the skins of an onion).This mechanism is referred to as seg- regation or coring.In specific cases,solidification and segregation occur in the form of tree-shaped microstructures,as depicted in Figure 5.6.This process may commence on the walls of a mold or on crystallization nuclei such as on small particles.Because of its characteristic appearance,the microstructure is referred to as den- dritic and the respective mechanisms are called dendritic growth

The just-described mechanism tacitly implies that the compo￾sition of the solid changes instantly upon cooling, as depicted in Figure 5.5. This occurs, however, only when the Cu and Ni atoms are capable of freely exchanging their lattice positions until even￾tually the respective equilibrium state has been reached. The mechanism by which atoms change their position is called dif￾fusion. Diffusion occurs preferentially once the temperature is high and when the difference in concentration between two parts of an alloy is large. (We shall deal with diffusion in more detail in Chapter 6.) The equilibrium concentration of the alloy, as de￾picted in Figure 5.5, is only achieved upon extremely slow cool￾ing. In most practical cases, however, the composition of an al￾loy during cooling is governed by a nonequilibrium solidus line, an example of which is depicted in Figure 5.5 by a dashed curve. Actually, this nonequilibrium solidus line is different for each cooling rate. Specifically, a faster cooling rate causes an increased deviation between equilibrium and nonequilibrium solidus lines. There are practical consequences to the nonequilibrium cooling process just described. Referring back to Figure 5.5, it is evident that a Cu–28% Ni alloy, upon conventional cooling in a mold, has a composition of 40% Ni wherever the solidification has started. Next to this region, one observes layers having successively lower Ni concentrations which solidified during later cooling (compara￾ble to the skins of an onion). This mechanism is referred to as seg￾regation or coring. In specific cases, solidification and segregation occur in the form of tree-shaped microstructures, as depicted in Figure 5.6. This process may commence on the walls of a mold or on crystallization nuclei such as on small particles. Because of its characteristic appearance, the microstructure is referred to as den￾dritic and the respective mechanisms are called dendritic growth 78 5 • Alloys and Compounds L  + L  1 2 3 4 20 23 28 34 40 Mass % Ni nonequilibrium solidus line T [C] FIGURE 5.5. Equilibrium (solid lines) and nonequilibrium (dashed line) solidus curve in a part of the Cu–Ni binary phase diagram

5.2·Phase Diagrams 79 and interdendritic segregation.In general terms,the center of the dendrites is rich in that element which melts at high temperatures (in the present case,Ni),whereas the regions between the dendrites contain less of this element.The resulting mechanical properties have been found to be inferior to those of a homogeneous alloy. Further,the nonequilibrium alloy may have a lower melting point than that in the equilibrium state,as demonstrated by Tie Line 4 in Figure 5.5.This phenomenon is called hot shortness and may cause partial melting (between the dendrites)when heating the al- loy slightly below the equilibrium solidus line. It is possible to eliminate the inhomogeneities in solid solu- tions.One method is to heat the alloy for many hours below the solidus line.This process is called homogenization heat treat- ment.Other procedures involve rolling the segregated solid at Liquid Solid Secondary dendrites (a) (b) FIGURE 5.6.Microstructure of an alloy revealing dendrites:(a) schematic,(b)photomicrograph of a nickel-based superalloy

and interdendritic segregation. In general terms, the center of the dendrites is rich in that element which melts at high temperatures (in the present case, Ni), whereas the regions between the dendrites contain less of this element. The resulting mechanical properties have been found to be inferior to those of a homogeneous alloy. Further, the nonequilibrium alloy may have a lower melting point than that in the equilibrium state, as demonstrated by Tie Line 4 in Figure 5.5. This phenomenon is called hot shortness and may cause partial melting (between the dendrites) when heating the al￾loy slightly below the equilibrium solidus line. It is possible to eliminate the inhomogeneities in solid solu￾tions. One method is to heat the alloy for many hours below the solidus line. This process is called homogenization heat treat￾ment. Other procedures involve rolling the segregated solid at 5.2 • Phase Diagrams 79 (a) Solid Secondary dendrites Liquid FIGURE 5.6. Microstructure of an alloy revealing dendrites: (a) schematic, (b) photomicrograph of a nickel-based superalloy. (b)

80 5.Alloys and Compounds high temperatures (called hot working)or alternately rapid so- lidification,which entails a quick quench of the liquid alloy to temperatures below the solidus line. Only very few binary phase diagrams are isomorphous as just described.Indeed,unlimited solid solubility is,according to Hume-Rothery,only possible if the atomic radii of the con- stituents do not vary more than 15%,if the components have the same crystal structure and the same valence,and if the atoms have about the same electronegativity.Other restrictions may ap- ply as well.Actually,most phase diagrams instead consist of one or more of the following six basic types known as eutectic,eu- tectoid,peritectic,peritectoid,monotectic,and monotectoid.They are distinguished by involving reactions between three individ- ual phases.This will be explained on the following pages. Complete solute solubility as discussed in this section is not restricted to selected metals only.Indeed,isomorphous phase di- agrams also can be found for a few ceramic compounds,such as for NiO-MgO,or for FeO-MgO,as well as for the orthosilicates Mg2SiO4-Fe2SiO4,in which the Mg2+and the Fe2+ions replace one another completely in the silicate structure. 5.2.2 Eutectic Some elements dissolve only to a small extent in another element. Phase In other words,a solubility limit may be reached at a certain solute concentration.This can be compared to a mixture of sugar and cof- Diagram fee:One spoonful of sugar may be dissolved readily in coffee whereas,by adding more,some of the sugar eventually remains undissolved at the bottom of the cup.Moreover,hot coffee dissolves more sugar than cold coffee;that is,the solubility limit (called solvus line in a phase diagram)is often temperature-dependent. Let us inspect,for example,the copper-silver phase diagram which is depicted in Figure 5.7.When adding small amounts of copper to silver,a solid solution,called a-phase,is encountered as described before.However,the solubility of copper into silver is restricted.The highest amount of Cu that can be dissolved in Ag is only 8.8%.This occurs at 780C.At any other temperature, the solubility of Cu in Ag is less.For example,the solubility of Cu in Ag at400°℃is only1.2%. A similar behavior is observed when adding silver to copper. The solubility limit at 780C is reached,in this case,for 8%Ag in Cu.Moreover,the solubility at 200C and lower temperatures is essentially nil.This second substitutional solid solution is ar- bitrarily called the B-phase. In the region between the two solvus lines,a mixture of two solid phases exists.This two-phase area is called the a+B region. To restate the facts for clarity:The a-phase is a substitutional solid solution of Cu in Ag comparable to a complete solution of

high temperatures (called hot working) or alternately rapid so￾lidification, which entails a quick quench of the liquid alloy to temperatures below the solidus line. Only very few binary phase diagrams are isomorphous as just described. Indeed, unlimited solid solubility is, according to Hume–Rothery, only possible if the atomic radii of the con￾stituents do not vary more than 15%, if the components have the same crystal structure and the same valence, and if the atoms have about the same electronegativity. Other restrictions may ap￾ply as well. Actually, most phase diagrams instead consist of one or more of the following six basic types known as eutectic, eu￾tectoid, peritectic, peritectoid, monotectic, and monotectoid. They are distinguished by involving reactions between three individ￾ual phases. This will be explained on the following pages. Complete solute solubility as discussed in this section is not restricted to selected metals only. Indeed, isomorphous phase di￾agrams also can be found for a few ceramic compounds, such as for NiO–MgO, or for FeO–MgO, as well as for the orthosilicates Mg2SiO4–Fe2SiO4, in which the Mg2 and the Fe2 ions replace one another completely in the silicate structure. Some elements dissolve only to a small extent in another element. In other words, a solubility limit may be reached at a certain solute concentration. This can be compared to a mixture of sugar and cof￾fee: One spoonful of sugar may be dissolved readily in coffee whereas, by adding more, some of the sugar eventually remains undissolved at the bottom of the cup. Moreover, hot coffee dissolves more sugar than cold coffee; that is, the solubility limit (called solvus line in a phase diagram) is often temperature-dependent. Let us inspect, for example, the copper–silver phase diagram which is depicted in Figure 5.7. When adding small amounts of copper to silver, a solid solution, called -phase, is encountered as described before. However, the solubility of copper into silver is restricted. The highest amount of Cu that can be dissolved in Ag is only 8.8%. This occurs at 780°C. At any other temperature, the solubility of Cu in Ag is less. For example, the solubility of Cu in Ag at 400°C is only 1.2%. A similar behavior is observed when adding silver to copper. The solubility limit at 780°C is reached, in this case, for 8% Ag in Cu. Moreover, the solubility at 200°C and lower temperatures is essentially nil. This second substitutional solid solution is ar￾bitrarily called the -phase. In the region between the two solvus lines, a mixture of two solid phases exists. This two-phase area is called the   region. To restate the facts for clarity: The -phase is a substitutional solid solution of Cu in Ag comparable to a complete solution of 5.2.2 Eutectic Phase Diagram 80 5 • Alloys and Compounds

5.2·Phase Diagrams 81 T rc] 1085 L 1000 962 x+L 28.1% L+B 800 B 8.8% 780C 92% 600 snAlOS a+β 400 200 FIGURE 5.7.Binary copper-silver phase Ag 20 40 60 80 Cu diagram containing a eutectic transfor- Mass Cu mation. sugar in coffee.Consequently,only one phase (sweet coffee)is present.(The analogue is true for the B-phase.)In the a +B re- gion,two phases are present,comparable to a mixture of blue and red marbles.The implications of this mixture of two phases to the strength of materials will be discussed later. We consider now a silver alloy containing 28.1%copper called the eutectic composition (from Greek eutektos,"easy melting"). We notice that this alloy solidifies at a lower temperature(called the eutectic temperature)than either of its constituents.(This phe- nomenon is exploited for many technical applications,such as for solder made of lead and tin or for glass-making.)Upon slow cooling from above to below the eutectic temperature,two solid phases (the a-and the B-phases)form simultaneously from the liquid phase according to the three-phase reaction equation: L28.1%Cua8.8%Cu+B92%Cu. (5.2) This implies that,for this specific condition,three phases (one liq- uid and two solid)are in equilibrium.The phase rule,F=C-P+ 1 [Eq.(5.1)]teaches us that,for the present case,no degree of free- dom is left.In other words,the composition as well as the temper- ature of the transformation are fixed as specified above.The eutec- tic point is said to be an invariant point.The alloy therefore remains at the eutectic temperature for some time until the energy differ- ence between solid and liquid (called the latent heat of fusion, AHf)has escaped to the environment.This results in a cooling curve which displays a thermal arrest (or plateau)quite similar to that of pure metals where,likewise,no degree of freedom remains dur- ing the coexistence of solid and liquid.A schematic cooling curve for a eutectic alloy is depicted in Figure 5.8

sugar in coffee. Consequently, only one phase (sweet coffee) is present. (The analogue is true for the -phase.) In the   re￾gion, two phases are present, comparable to a mixture of blue and red marbles. The implications of this mixture of two phases to the strength of materials will be discussed later. We consider now a silver alloy containing 28.1% copper called the eutectic composition (from Greek eutektos, “easy melting”). We notice that this alloy solidifies at a lower temperature (called the eutectic temperature) than either of its constituents. (This phe￾nomenon is exploited for many technical applications, such as for solder made of lead and tin or for glass-making.) Upon slow cooling from above to below the eutectic temperature, two solid phases (the - and the -phases) form simultaneously from the liquid phase according to the three-phase reaction equation: L28.1% Cu
8.8% Cu 92% Cu. (5.2) This implies that, for this specific condition, three phases (one liq￾uid and two solid) are in equilibrium. The phase rule, F
C  P 1 [Eq. (5.1)] teaches us that, for the present case, no degree of free￾dom is left. In other words, the composition as well as the temper￾ature of the transformation are fixed as specified above. The eutec￾tic point is said to be an invariant point. The alloy therefore remains at the eutectic temperature for some time until the energy differ￾ence between solid and liquid (called the latent heat of fusion, Hf) has escaped to the environment. This results in a cooling curve which displays a thermal arrest (or plateau) quite similar to that of pure metals where, likewise, no degree of freedom remains dur￾ing the coexistence of solid and liquid. A schematic cooling curve for a eutectic alloy is depicted in Figure 5.8. 5.2 • Phase Diagrams 81 1000 800 600 400 200 Ag 20 40 60 80 Cu Mass % Cu T [C] 962 L 28.1 % 8.8 % 780C 92 %  +   Solvus L +   1085  + L FIGURE 5.7. Binary copper–silver phase diagram containing a eutectic transfor￾mation

82 5.Alloys and Compounds FIGURE 5.8.Schematic representa- tion of a cooling curve for a eu- tectic alloy (or for a pure metal). The curve is experimentally ob- amiejadwL tained by inserting a thermome- ter (or a thermocouple)into the liquid alloy and reading the tem- perature in periodic time inter- vals as the alloy cools. Time The microstructure,observed by inspecting a eutectic alloy in an optical microscope,reveals a characteristic platelike or lamel- lar appearance;see Figure 5.9.Thin a and B layers (several mi- crometers in thickness)alternate.They are called the eutectic mi- croconstituent.(A microconstituent is a phase or a mixture of phases having characteristic features under the microscope.)This configuration allows easy interdiffusion of the silver and the cop- per atoms during solidification or during further cooling. Alloys which contain less solute than the eutectic composition are called hypoeutectic (from Greek,"below").Let us assume a Ag-20%Cu alloy which is slowly cooled from the liquid state.Upon crossing the liquidus line,initially two phases(a and liquid)are pre- sent,similar as in an isomorphous alloy.Thus,the same consider- ations apply,such as a successive change in composition during B B (a) (b) FiGURE 5.9.(a)Schematic representation of a lamellar or platelike mi- crostructure as typically observed in eutectic alloys.(b)Photomicro- graph of a eutectic alloy,180x(CuAl2-Al).Reprinted with permission from Metals Handbook,8th Edition,Vol.8(1973),ASM International, Materials Park,OH,Figure 3104,p.156

FIGURE 5.9. (a) Schematic representation of a lamellar or platelike mi￾crostructure as typically observed in eutectic alloys. (b) Photomicro￾graph of a eutectic alloy, 180 (CuAl2–Al). Reprinted with permission from Metals Handbook, 8th Edition, Vol. 8 (1973), ASM International, Materials Park, OH, Figure 3104, p. 156. The microstructure, observed by inspecting a eutectic alloy in an optical microscope, reveals a characteristic platelike or lamel￾lar appearance; see Figure 5.9. Thin  and  layers (several mi￾crometers in thickness) alternate. They are called the eutectic mi￾croconstituent. (A microconstituent is a phase or a mixture of phases having characteristic features under the microscope.) This configuration allows easy interdiffusion of the silver and the cop￾per atoms during solidification or during further cooling. Alloys which contain less solute than the eutectic composition are called hypoeutectic (from Greek, “below”). Let us assume a Ag–20% Cu alloy which is slowly cooled from the liquid state. Upon crossing the liquidus line, initially two phases ( and liquid) are pre￾sent, similar as in an isomorphous alloy. Thus, the same consider￾ations apply, such as a successive change in composition during 82 5 • Alloys and Compounds Temperature Time FIGURE 5.8. Schematic representa￾tion of a cooling curve for a eu￾tectic alloy (or for a pure metal). The curve is experimentally ob￾tained by inserting a thermome￾ter (or a thermocouple) into the liquid alloy and reading the tem￾perature in periodic time inter￾vals as the alloy cools.       (a) (b)

5.2·Phase Diagrams 83 (a) (b) FiGURE 5.10.(a)Schematic representation of a microstructure of a hy- poeutectic alloy revealing primary a particles in a lamellar mixture of a and B microconstituents.(b)Microstructure of 50/50 Pb-Sn as slowly so- lidified.Dark dendritic grains of lead-rich solid solution in a matrix of lamellar eutectic consisting of tin-rich solid solution (white)and lead- rich solid solution (dark)400X,etched in 1 part acetic acid,1 part HNO3,and 8 parts glycerol.Reprinted with permission from Metals Handbook,8th Ed.Vol 7,page 302,Figure 2508,ASM International, Materials Park,OH(1972). cooling,dendritic growth,and the lever rule.When the eutectic tem- perature(780C)has been reached,the remaining liquid transforms eutectically into a-and B-phases.Thus,the microstructure,as ob- served in an optical microscope,should reveal the initially formed a-solid-solution (called primary a,or proeutectic constituent)inter- spersed with lamellar eutectic.Indeed,the micrographs depicted in Figure 5.10 contain gray,oval-shaped a areas as well as alternating black (@)and white(B)plates in between.A schematic cooling curve for a Ag-20%Cu alloy which reflects all of the features just dis- cussed is shown in Figure 5.11(a).For comparison,the cooling curve for an isomorphous alloy is depicted in Figure 5.11(b). Silver alloys containing less than 8.8%Cu solidify similar to an isomorphous solid solution.In other words,they do not con- tain any eutectic lamellas.However,when cooled below the solvus line,the B-phase precipitates and a mixture of a-and B- phases is formed,as described previously in Section 5.2.1. Hypereutectic alloys(from Greek,"above")containing,in the present example,between 28.1 and 92%Cu in silver,behave quite analogous to the hypoeutectic alloys involving a mixture of pri- mary B-phase (appearing dark in a photomicrograph),plus plate- shaped eutectic microconstituents

cooling, dendritic growth, and the lever rule. When the eutectic tem￾perature (780°C) has been reached, the remaining liquid transforms eutectically into - and -phases. Thus, the microstructure, as ob￾served in an optical microscope, should reveal the initially formed -solid-solution (called primary , or proeutectic constituent) inter￾spersed with lamellar eutectic. Indeed, the micrographs depicted in Figure 5.10 contain gray, oval-shaped  areas as well as alternating black () and white () plates in between. A schematic cooling curve for a Ag–20% Cu alloy which reflects all of the features just dis￾cussed is shown in Figure 5.11(a). For comparison, the cooling curve for an isomorphous alloy is depicted in Figure 5.11(b). Silver alloys containing less than 8.8% Cu solidify similar to an isomorphous solid solution. In other words, they do not con￾tain any eutectic lamellas. However, when cooled below the solvus line, the -phase precipitates and a mixture of - and - phases is formed, as described previously in Section 5.2.1. Hypereutectic alloys (from Greek, “above”) containing, in the present example, between 28.1 and 92% Cu in silver, behave quite analogous to the hypoeutectic alloys involving a mixture of pri￾mary -phase (appearing dark in a photomicrograph), plus plate￾shaped eutectic microconstituents. 5.2 • Phase Diagrams 83      FIGURE 5.10. (a) Schematic representation of a microstructure of a hy￾poeutectic alloy revealing primary  particles in a lamellar mixture of  and  microconstituents. (b) Microstructure of 50/50 Pb-Sn as slowly so￾lidified. Dark dendritic grains of lead-rich solid solution in a matrix of lamellar eutectic consisting of tin-rich solid solution (white) and lead￾rich solid solution (dark) 400 , etched in 1 part acetic acid, 1 part HNO3, and 8 parts glycerol. Reprinted with permission from Metals Handbook, 8th Ed. Vol 7, page 302, Figure 2508, ASM International, Materials Park, OH (1972). (a) (b)