Presence of golden ratio relationships in Fe-Fe3C, Cu-Zn and Cu-Sn alloy systems

Iron-carbon, copper-zinc and copper-tin are the three most significant alloy systems. Iron-carbon system is commonly known for steels, copper-zinc for brasses and copper-tin for bronzes. This paper shows how eutectoid, peritectic, eutectic, cementite-intermetallic, maximum solubility of carbon in ferrite, maximum solubility of carbon in austenite points in Fe-Fe3C phase diagram are linked to one another through golden ratio relationships. This paper also shows the ratios between proportions of Cu and Zn at maximum solubility of Zn in Cu at 456 and 0°C and the ratio of proportions of Cu-Sn at ε-Cu3Sn (IMC) in Cu-Zn and Cu-Sn phase diagrams, respectively, are related to golden ratio. It is predicted that the occurrence of these relationships at vital points in mentioned systems is in accordance with Constructal law of design in nature and golden ratio is the reason for uniqueness and usefulness of these points. © 2015 WIT Press.