Elementary Geochemistry

Phase Diagrams

The figure above shows the phases of water at different pressures and temperatures. Clearly shown is that at constant pressure of 1atm, and with increasing pressure, water will melt (solid to liquid) at 0°C and will evaporate at 100°C.

1 atm is then the vapor pressure of water at 100°C, or the pressure that water will evaporate at the given temperature. The curve connecting the triple point and critical point is called the vapor-pressure curve. Liquid water and water vapor may coexist at any point in this curve. This curve also shows that the vapor pressure of water increases as temperature increases.

The triple point is where all three phases (solid, liquid and gas) are exhibited by water. The critical point is the pressure and temperature combination where liquid water and water vapor may not be distinguished as separate phases.

The above illustration is a Phase Diagram of a One-Component System, the sole component being water. In this particular diagram, we are concerned with two variables (two intrinsic properties that affect the phases of the component), pressure and temperature. At different pressure and temperature combinations, water may exhibit any of three phases (homogenous parts of a system).

Gibbs' Phase Rule

Gibbs’ Phase Rule can be summarized in this equation f = c – p +2

Where:

f is the number of degrees of freedom

c is the number of components

p is the number of components

Applying the rule to the water system, since there is only one component, c will be 1, and the equation will be f = 1 – p + 2 or f = 3 – p. This also means that the maximum number phases is 3 because f can not be less than zero.

At any point within the ice, water and vapor regions (light blue, blue and gray), or when there is only one phase (p=1), f = 3 – 1 or f = 2. This means that there are 2 degrees of freedom, or 2 variables may be changed(increase or decrease temperature and pressure) without affecting the number of phases.

Example, given a point at the vapor region (blue), both pressure and temperature (2 variables) may be changed, and the number of phases (one phase – vapor) will not change. We say then that at that point, the system is divariant (having two degrees of freedom).

At any point along the vapor-pressure curve, the number of phases will be 2 (liquid and vapor). The equation will then be f = 3 – 2 or f = 1. This means that only one variable can be changed without affecting the number of phases.

At a point along the vapor-pressure curve, if the temperature is increased, the system will be completely of vapor (liquid phase will be lost). And if the temperature is decreased, the system will completely be of liquid water (gas phase will be lost). If the pressure is increased or decreased, the temperature will compensate to the change in pressure so that no phase will be lost.

This means that at a point in the vapor-pressure curve, only one component (pressure) may be changed without affecting the number of phases. The system, at this point, is said to be univariant (having one degree of freedom).

Two-Component System

Now let’s add salt to water so we have a two-component system. We will now have another variable (intrinsic property), which is the concentration of salt in the solution. We will also have to add another dimension to our diagram, so our phase diagram will be three-dimensional. The vapor-curve will then be a vapor-pressure surface, and the triple point will be extended to a curve.

The equation, given that there are two components will be f = 2 – p + 2 or f = 4 – p. This means that the maximum number of phases is 4 (remember that f can not be less than zero). These phases are vapor, ice, salt, and solution. Note that liquid water is not listed as separate phase from salt ions because phase is defined as a homogenous unit, and a solution of salt and water is considered a single phase.

There are systems where two phases may not coexist at any temperature and pressure combinations. Example would be the CaSO₄-H₂O system. Given that there are two components (CaSO₄ and H₂O), the equation will be f = 2 – p + 2 or f = 4 – p. Again, the maximum number of phases that can exist at any given pressure and temperature for this system is 4 (f can not be less than zero, paulit-ulit?).

However, there are five possible phases in this system: vapor, solution, ice, gypsum (CaSO₄.H₂O) and anhydrite (CaSO₄). Following Gibbs’ phase rule, anhydrite does not coexist with ice because it is not stable at very low temperatures.

In most geological applications, pressure is assumed to be constant, and so the constant in Gibbs’ is reduced by 1 and so the equation reads f = c – p + 1

Eutectics

Magma has about 9 or 10 major components, and to represent that in a phase diagram, we would need a model of 9 or 10 dimensions. Lucky for us, crystallization of magma occurs in a series of steps involving fewer components that we can use binary and ternary diagrams for these steps.

Let us take the crystallization of a mixture of anorthite (CaAl₂Si₂O₈) and diopside (CaMgSi₂O₆) as shown on the diagram below. Note that the y and x axes are temperature and percentages of the components, respectively, because we assume that pressure is constant.

Am still completing this lecture... Sorry guys

Elementary Geochemistry

Exam - Computer Methods

Final Exam

The Phase Rule