A phase diagram is essential to a metallurgist's "toolkit'. They tell us in what state and where we will find each element within a material when in "equilibrium" (i.e. it's lowest energy and most stable state) for a given composition, temperature (and pressure). This can be reached by heating at a given temperature or by cooling very slowly.
A phase is defined as a portion of a system with the same structure, properties and composition, and that is different to the rest of a system.
Why are they relevant to a jeweler? A phase diagram is important because it helps to tells us:
Will the alloy be single phase or two phase?
Can the alloy be age hardened?
At what temperature should we anneal our metal to restore ductility?
Will adding more alloying additions introduce a deleterious phase?
Explaining Phase Diagrams
Single Phase Solid Solution: Gold–Silver Phase Diagram
For some compositions, the phase diagram is quite simple – the two elements form a complete single phase solid solution across all possible compositions. Gold & Silver form such a solid solution, where the silver sits as a substitutional soluite on the gold lattice or vice versa.
The lines on the diagram illustrate the boundary between two regions, and the regions between the lines are for a particular stable phase or combination of phases:
Liquidus – The temperature at which the liquid begins to solidify on cooling or when the material is entirely liquid on heating.
Solidus – The temperature at which the solid begins to melt on heating or when the material is entirely solid on heating.
The region between the solidus and liquids is a two-phase region where the liquid and solid co-exist. This is the melting range. Normally, a narrow melting range is desirable.
We can determine the proportion and composition of solid and liquid at a particular temperature using the phase diagram. It is not necessary to know, but you can read more here.
Two-phase solid solution: Gold–Copper Phase Diagram
Gold and copper form a series of "ordered" intermetallic phases, and the liquids and solidus have a complicated shape (a pronounced dip in the middle). Compared to Gold-Silver, the melting range is narrow.
On cooling, gold and copper initially form a single-phase alloy at all compositions. But at lower temperatures, around 400˚C, ordered intermetallic phases are formed. These low-temperature phases are stronger, harder, and less ductile. They are relevant to why we quench after annealing.
A binary eutectic system: Ag-Cu phase diagram
Compared to gold and silver, silver and copper have limited solubility. As we've seen elsewhere, silver atoms are very different in size from copper atoms.
In the central region of composition "space," there is a two-phase microstructure. A silver-rich phase and a copper-rich phase will form, and the proportion of them depends on the overall composition. Both phases contain both copper and silver. These two-phase microstructures are often stronger and more difficult to work with.
The key feature of the silver-copper system is that it contains a eutectic point. At this point, the solidus and liquidus meet. Two solid phases form from a single liquid at a single temperature. Normally, only pure metals melt at a single temperature; melting generally occurs over a range in alloys,
Eutectic compositions are typically used as solders because these alloys have a far lower melting point than the two or more pure metals from which they are made.
Three-element alloys – A ternary phase diagram
When there are three elements, we must plot a ternary diagram. In this case, the phase diagram forms a 3D graph. The triangular cross-section of the prism gives us the composition at a particular temperature. These isothermal triangular sections can be plotted at every temperature and vertically stacked to form a 3D graph in the shape of a prism.
We can use Gold-Copper-Silver as an example. This alloy system forms the basis for most karat gold alloys. The ternary diagram shows the stable phases at all compositions for a particular temperature (an isothermal section).
We can re-cut the prism horizontally to find the possible microstructures at a particular temperature for all compositions, or we can cut vertically to find the possible microstructures at a particular range of compositions for all temperatures.
Horizontal sections show that depending on composition, 18, 14, 10, and 9K gold-silver-copper alloys can be either single-phase or two-phase.
Three possible sections would be for 10K (37.5 wt.% Au), 14K (58.5 wt.% Au), and 18K (75 wt.% Au). Again, we can see the significant region of two-phase structures at these three karats.
Summary
Phase diagrams plot the expected phases at a given temperature and composition in the "equilibrium" case.
Phase diagrams can be used to help design alloy compositions and processing treatments to optimize the properties of jewelry alloys.