Binary Solid Solution

Steven Dutch, Natural and Applied Sciences, University of Wisconsin - Green Bay
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Many materials are similar enough in their crystal lattice structures that they can mingle freely on the atomic scale. Metal alloys are a common example. Such materials are called solid solutions. Common examples in geology include the plagioclase feldspar series, olivine, and many of the carbonates.

Note: just because things form solid solutions doesn't mean they formed from liquids! The carbonates are a good example. Calcite (CaCO3), magnesite (Mg(CO3)2), siderite (FeCO3), rhodocrosite (MnCO3) and smithsonite (ZnCO3) form a fairly complete solid solution series but generally do not form from the liquid state.

solsol00.gif (1848 bytes) Although most texts use the plagioclase series, possibly the best solid solution illustration is the olivine series. Forsterite (Mg2SiO4) forms a  solid solution series with fayalite (Fe2SiO4)

Mg has a smaller ionic radius than Fe, therefore Mg and O are attracted more strongly than Fe and O, so forsterite has a higher melting point than fayalite (shown by the respective open squares).

As liquid olivine cools, it eventually begins to solidify. We could logically expect that to happen somewhere between the melting points of forsterite and fayalite (though not all solid solutions behave this way). The resulting solid would not be pure forsterite, but since forsterite has the higher melting point, we would expect the solid to be richer in forsterite than the melt. The melt and solid compositions when crystallization first begins are shown in red and blue, respectively.

SOLSOL01.GIF (1952 bytes) The removal of forsterite-rich solid will cause the melt to become richer in fayalite, so we expect its composition to shift down (as it cools) and toward fayalite. As the melt becomes richer in fayalite, we expect the resulting solid to become richer in fayalite as well.
SOLSOL02.GIF (2279 bytes) Eventually, the solid becomes rich enough in fayalite that it matches the initial melt composition. When that happens, the system is completely solidified. The last remnant of liquid will be quite a bit richer in fayalite than the initial melt.
solsol03.gif (2445 bytes) It's essential to track three points: the solid composition, the melt composition, and the overall system composition. All three are always on a horizontal ine at any given temperature.

The melt point represents 100% liquid, the solid point represents 100% solid, and the system represents a mix of solid and liquid. Therefore, the relative amounts of solid and liquid can be determined as shown here.

SOLSOL04.GIF (2886 bytes) A complete solid solution diagram looks like this. When the system plots in the purple field it is all liquid, in the yellow field it is a mixture of liquid and solid, and in the blue field it is entirely solid.

The upper bound of the liquid+solid field is called the liquidus, and the lower bound is called the solidus.

In a simple binary eutectic, if you know the melting points of the end members and the position of the eutectic, you can largely predict the system, though the exact curvatures of the liquidus curves have to be determined experimentally. With a solid solution, we can intuitively guess some of the behavior of the system, but there is no way to predict exactly what the composition of the solid phase will be without experimental data.

SOLSOL05.GIF (2216 bytes) As a system of given composition cools, it eventually encounters the liquidus (a). Solid (b) begins to form. As forsterite rich crystals solidify, the melt becomes enriched in fayalite and slides down the liquidus. The solid composition slides down the solidus. Eventually, the solid composition equals that of the initial melt (d). At that point the system has completely solidified. The last remnant of the melt is on the liquidus at c.

The overall system, of course, does not change composition but drops straight down from a to d. Between a and d, the position of the overall system relative to the melt and solid points gives the proportions of melt and solid.

SOLSOL06.GIF (3724 bytes) Sometimes solid solutions can have maxima or minima between the end members. These are no problem: the solid and liquid compositions will still slide down the liquidus and solidus curves. Treat each section as a simple solid solution.

The only complication: what happens if a system exactly matches the maximum or minimum? In that case, it simply crystallizes a solid of that composition.

Tin and lead are an example of a system with a minimum. Solder has a composition at the minimum point. This ensures that the solder has the lowest possible melting point, and that a solid of uniform composition crystallizes.

A Solid Solution Animation

The diagram at left illustrates the Forsterite-Fayalite (Olivine) system. Observe the solid composition, the liquid composition, and the overall system composition as the system evolves.

 


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Created December 1, 1997, Last Update December 1, 1997

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