#invariant points

[materialsscienceandengineering]

The Silver-Calcium Binary System

Phase Poll #7 concluded last week - apologies for being a little late with this post! You guys were almost equally split this time between silver (at 51% of the votes) and calcium (at 49%), which puts us squarely in the middle of the phase diagram, pretty near to the equiatomic intermetallic AgCa.

Unfortunately, when it comes to the Ag-Ca system, there’s not much to say. Not to worry though, I wanted to use this opportunity to talk a little more about the components of phase diagrams! Invariant points have already been covered by this blog, but I’m going to touch on them again to give the definition as points on phase diagrams with no degrees of freedom - they only occur at specific compositions, temperatures, and pressures, etc. In the above diagram, there are several eutectic points, and a couple peritectic points.

Congruent melting, meanwhile, is a phase transition wherein the composition of the liquid is the same as the composition of the solid. In incongruent melting, contrarily, a phase melts to a composition of liquid different than that of the solid. The former case is common in binary systems, with intermediary phases and two-phase regions wherein solids precipitate from the liquid before full melting occurs.

Returning to the silver-calcium system specifically, there aren’t many applications that make use of binary mixtures of the two elements. Silver-calcium batteries, despite the name, are still primarily lead-acid batteries with small amounts of calcium and silver added (as in, even less than 1%). Historically, silver-calcium alloys have been prepared as an intermediary step in the creation of silver catalysts. Another interesting feature of note in this phase diagram is the high temperature calcium phase. While calcium is fcc at room temperature, it has a phase transition above 450°C.

Sources/Further reading: ( 1 ) ( 2 ) ( 3 ) ( 4 ) ( congruent melting ) ( understanding phase diagrams ) ( phase diagram definitions )

More phase diagrams: ( image 1 ) ( mole fraction and mass fraction )

[materialsscienceandengineering]

What is eutectoid

A eutectoid is a phase transition that involves the transformation of one solid phase into two distinct solid phases. I’ve posted briefly about it before here, but you can also check out this link for more information and another example.

[materialsscienceandengineering]

A metatectic point on a phase diagram, also known as a catatectic point, is an invariant point wherein a single solid phase transitions into a liquid phase as well as a second solid phase (or vice versa). It is similar to a peritectic point, however the single solid phase exists at a higher temperature than the mixture of solid and liquid phases, which is the opposite or a peritectic. 

Examples of this behavior (a solid becoming partially liquid) does not typically occur in metallic systems, however it can occur in other instances, such as the phase diagrams of fatty acids.

Image source.

[materialsscienceandengineering]

A peritectoid point on a phase diagram is an invariant point where two separate solid solutions transition into a single, different, solid phase, or vice versa. It is an important reaction in the decomposition of quasicrystalline phases for certain alloys. 

Image source.

[materialsscienceandengineering]

A eutectoid point ( 2 ) on a phase diagram is an invariant point wherein a single solid solution transforms into two distinct solid solutions, or vice versa. Unlike a eutectic point, none of the phases involved are liquids.

Image source.

[materialsscienceandengineering]

A eutectic point ( 2 ) on a phase diagram is an invariant point wherein a pure liquid transitions into a mixture of two solid solutions and vice versa. It is the lowest melting point of any ratio of the components on a phase diagram.

Image source.

[materialsscienceandengineering]

Invariant points on phase diagrams are points with no degrees of freedom, with a unique temperature, pressure, and composition. In other words, they are points on phase diagrams that can only occur at a particular set of conditions that cannot be varied. 

Common invariant points are shown in the images above and include: eutectic and eutectoid points, peritectic and peritectoid points, monotectic and monotectoid points, syntectic points, and catatectic/metatectic points. [Note: if the name of the invariant point ends in -tectic, the phase change involves both liquids and solids, if the name ends in -tectoid, the phase change only involves solids.]

Image sources: ( 1 ) ( 2 )

[materialsscienceandengineering]

A monotectic point ( 2 ) ( 3 ) on a phase diagram is an invariant point where a single liquid phase transitions into a different liquid phase and a solid phase, or vice versa. The two liquids involved are immiscible, like oil and water, so monotectic points also involve miscibility gaps. 

Image source.