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 ofhigh 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