Multicomponent phase diagrams

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Two-component, liquid/liquid phase diagrams

Since plagioclase is one of the most common minerals in the earth's crust, we will discuss the phase diagram for the plagioclase system. The phase relations in the plagioclase system are shown in Figure 3 at constant pressure equal to that of the atmosphere (atmospheric pressure is 1 bar). In Figure 3 the upper curve is called the liquidus and the lower curve is called the solidus. At temperatures above the liquidus everything is liquid, below the solidus everything is solid (crystals of plagioclase solid solution). At temperatures between the solidus and liquidus crystals of plagioclase solid solution coexist in equilibrium with liquid.
Partial miscibility in binary systems at a pressure of 1 bar. The horizontal lines are the Tie lines. (a) water/phenol. Data by Hill and Malisoff; (b) n-hexane/aniline. Data by Keynes and Hildbrand; Koningsveld, Fig. 38, p. 47.
Keynes and Hildbrand; Koningsveld, Fig. 38, p. 47.

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Two-component, liquid/solid phase diagrams
Figure 1 shows the simplest of two component phase diagrams. The components are A and B, and the possible phases are pure crystals of A, pure crystals of B, and liquid with compositions ranging between pure A and pure B. Compositions are plotted across the bottom of the diagram. Note that composition can be expressed as either a percentage of A or a percentage of B, since the total percentage must add up to 100. (Compositions might also be expressed as mole fraction of A or B, in which case the total must add up to 1). Temperature or pressure is plotted on the vertical axis. For the case shown, we consider pressure to be constant, and therefore have plotted temperature on the vertical axis.

The curves separating the fields of A + Liquid from Liquid and B + Liquid from Liquid are termed liquidus curves. The horizontal line separating the fields of A + Liquid and B + Liquid from A + B all solid, is termed the solidus. The point, E, where the liquidus curves and solidus intersect, is termed the eutectic point. At the eutectic point in this two component system, all three phases, that is Liquid, crystals of A and crystals of B, all exist in equilibrium. Note that the eutectic is the only point on the diagram where this is true.

How to Read a Phase Diagram: This two-phase diagram features two types of curves. Lines separating partially liquid phases from fully liquid phases are known as liquidis lines while the line separating partially melted phases from solids are known as solidus. The point where all three lines meet (point E in this diagram) is known as the eutectic point. Near the eutectic point, a samples behavior is very dependent on its composition. For example, wetting behavior may differ dramatically between the situation of solid a wetting with liquid b vs solid b wetting with liquid a.

The horizontal axis shows the relative composition between the two phases while the vertical axis indicates the temperature of the system. Melting far from the eutectic point may occur over a range of temperatures between solidus and liquidus where both phases are fully melted.

If one has a mixture of composition X at temperature <math>T_2</math>, the percent of A in solid form would be given as the following: % solid A = b/(a+b)*100. The remaining portion of A in the mixture is melted.

Peritectic Point: This is similar to the eutectic point but opposite. At this point three-phase reaction occurs in which, upon cooling, a liquid and a solid phase transform to give one different solid phase. L+<math>alpha</math>-><math>beta</math>


Peritectic means to "grow around" and refers to the fact that upon cooling, the low temperature product of the peritectic reaction (sanidine) will tend to grow around the higher temperature reactant crystals (leucite).

Lever Rule: To determine compositions of phases and the relative proportions of phases to each other in binary phase diagrams the LEVER RULE is used.

To determine the composition of "I" you must complete the following steps:

  1. Draw a line through "I" perpendicular to the base of the diagram. This line represents a line of constant composition and is referred to as an isopleth.
  2. The liquid at "I" consists of a mixture of A and B, the proportions of which can be determined simply by measuring the length of three lines, AI', BI' and AB and then ratio these lengths.
     %A = I'B/AB *100
     %B = I'A/AB *100

This gives us the bulk composition of the liquid at this point. If the composition point for the moves then we get a new bulk composition for that point represented by the new liquid.

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Three-component phase diagrams

Micibility gap in the system water/phenol/aniline at 1 bar. Critical line: C12C1C2C3C13; ridge of bimodal surface: C13ThC12. Redrawn from Schreinemakers. Koningsveld, Fig. 86, p. 83.
Koningsveld, Fig. 86, p. 83.
Calculated ternary isotherms for two binary eutectic temperatures. Koningsveld, Fig. 100, p. 95.
Koningsveld, Fig. 100, p. 95.

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