Chapter 61 Reading Phase Diagrams and Mineral Mixtures

Year 3 · Descriptive Mineralogy · G336-L1

Read phase diagrams, apply a binary lever rule and plot ternary compositions while distinguishing components from phases.

Complementary observations used in systematic mineral identification. Original Geology Hub teaching diagram.

This independent lesson follows the topic framework of the supplied University of Peshawar BS Geology curriculum, session 2004–05 onward. It is newly written study material, not an official university course or qualification.

Learning objectives

Distinguish phase, component and bulk composition.
Read equilibrium fields and phase boundaries.
Apply a lever rule with clearly stated assumptions.

The information contained in a phase diagram

A phase is a physically and chemically distinct part of a system; a component is an independent chemical building block used to describe its composition. Ice and liquid water are two phases of a one-component system. A pressure-temperature diagram locates equilibrium stability fields and boundaries. At a boundary, the neighboring phases can coexist at equilibrium. A rock can preserve a mineral outside its equilibrium field because reaction is slow, so the diagram predicts stable relationships rather than guaranteeing an instantaneous natural response.

For a nonreacting choice of independent components, the general Gibbs phase rule is F = C − P + 2, where F counts independent intensive variables, C components and P phases. Constraints change the count. At fixed pressure, one degree of freedom is removed. Use the rule only after identifying what variables are free and what system is being considered. A phase rule is a consistency tool, not a substitute for knowing the actual positions of phase boundaries.

Composition adds another dimension

A binary diagram commonly plots temperature against composition at fixed pressure. Fields can contain liquid, one solid or a combination of phases. In a two-phase field, a tie line gives the compositions of the coexisting phases. Their amounts follow mass balance. A eutectic describes a particular invariant relation in an appropriate fixed-pressure binary system; it does not mean every mixture has the same melting behavior. Solid solution allows a mineral composition to vary within a structural family.

A ternary composition plot has three end members whose normalized proportions sum to 100 percent. The corners are pure end members, edges are binary mixtures and interior points contain all three. Read proportions along lines parallel to the opposite edges using the diagram convention. Temperature contours or field boundaries may be superimposed on the triangle. Always inspect whether a plotted composition represents an entire rock, an individual mineral or a projected subset of components.

What changes when pressure or composition is fixed

The phase rule counts freedom after the system is defined. For pure water at equilibrium, solid, liquid and vapor meet at a triple point where neither pressure nor temperature can change independently while all three phases coexist. Along a two-phase boundary, changing pressure requires a corresponding temperature change to retain coexistence. Within a single-phase field, pressure and temperature can vary independently over the field. The familiar diagram therefore encodes relations among variables rather than merely naming three states of matter.

In a fixed-pressure binary temperature-composition diagram, the horizontal coordinate is bulk or phase composition depending on what is being plotted. Cooling an all-liquid mixture first crosses the liquidus into a field containing liquid plus crystal. A horizontal tie line at that temperature connects their compositions. The crystal may differ substantially from the bulk composition; the remaining liquid must change to conserve the total amounts of components. Confusing these three compositions is a common source of incorrect cooling paths.

Mass balance in eutectic and solid-solution examples

A simple eutectic model has two solids that crystallize together from the remaining liquid at a particular temperature and liquid composition under fixed conditions. Before that point, one solid can form while the liquid evolves toward the eutectic. In a solid-solution system, a crystal can contain variable proportions of components, so both liquid and solid compositions may move during cooling. These are different diagram topologies and should not be read with an identical shortcut.

For an invented tie line, solid is 10 percent B, liquid is 70 percent B and bulk is 25 percent B. The liquid fraction is (25 − 10)/(70 − 10) = 0.25, leaving 0.75 solid. Check the result: 0.75 × 10 + 0.25 × 70 = 25. If crystals are physically removed, the remaining system no longer retains the original bulk composition. Such fractionation requires a different bookkeeping path from closed-system equilibrium crystallization.

Reading a ternary liquidus projection

In a ternary plot, a point with component masses 10, 15 and 25 grams normalizes to 20, 30 and 50 percent. Temperature can be represented above the composition triangle as a liquidus surface or projected as isotherms. A boundary curve separates primary crystallization fields in an appropriate simplified model. Crossing it may introduce another crystallizing phase, so the liquid path follows different constraints. The Tulane ternary diagram notes illustrate this geometry.

A natural rock contains more components than a simple triangle can display. A projection may exclude or combine constituents to make a useful diagram, but that choice limits what can be inferred. State the components, normalization and fixed variables before interpreting stability. Zoning, incomplete reaction and inherited crystals can preserve a history that differs from the final equilibrium assemblage. A phase diagram is most informative when paired with textures and composition measurements rather than read as a complete history by itself.

Worked activity

At one temperature in an invented binary system, solid has 20 percent B and liquid 80 percent B; bulk composition is 50 percent B. The solid fraction is (80 − 50)/(80 − 20) = 0.5, and the liquid fraction is 0.5. Check by mass balance: 0.5 × 20 + 0.5 × 80 = 50 percent B. For a second bulk composition of 35 percent B, solid fraction is 45/60 = 0.75. These are illustrative phase relations, not a measured mineral system. Plot both bulk points on a sketch and show why tie-line lengths determine the fractions.

Practice and interpretation

Label axes, fixed variables and units before interpreting any diagram. Mark an imagined heating or cooling path and explain which boundary it crosses first. Then distinguish the composition of a surviving crystal from the changing composition of the remaining liquid. For a ternary exercise, normalize 20, 30 and 50 grams of three components; the percentages are already 20, 30 and 50. If the masses total something else, divide each mass by their sum before plotting.

Self-check

Is a component the same as a phase?
What does a tie line give?
Can equilibrium be assumed from a mineral name alone?

Check your answers

No. Components describe composition; phases are distinct physical and chemical portions of the system.
The compositions of coexisting phases at the specified conditions.
No. Reaction kinetics, history and bulk composition must also be considered.

Sources and further study

The explanations and teaching examples are original. Use these institutional resources to check terminology and explore the subject further.

Chapter 61 multiple choice questions

Choose one best answer for each question. Open each answer panel after making your choice.

Ice and liquid water coexist in an equilibrium system containing only H2O. How should the system be described?
1. Two components and one phase
2. Two components and two phases
3. One component and two phases
4. One component and one phase
Answer and explanation
C. One component and two phases The chemical component is H2O, while ice and liquid are distinct phases. Components and phases count different aspects of the system.
Using F = C − P + 2, how many degrees of freedom does a one-component, two-phase system have before another constraint is imposed?
1. Zero
2. Two
3. Three
4. One
Answer and explanation
D. One Substitution gives F = 1 − 2 + 2 = 1. A further constraint, such as fixed pressure, can reduce the independent variables.
At fixed conditions, a binary mixture has bulk composition 35 percent B, solid at 20 percent B and liquid at 80 percent B. What is the solid fraction?
1. 0.75
2. 0.25
3. 0.50
4. 0.35
Answer and explanation
A. 0.75 The lever rule gives (80 − 35)/(80 − 20) = 45/60 = 0.75. The remaining liquid fraction is 0.25.
A ternary mixture contains 20, 30 and 50 grams of its three components. What normalized percentages should be plotted?
1. 10, 15 and 25 percent
2. 20, 30 and 50 percent
3. 20, 30 and 100 percent
4. 40, 30 and 50 percent
Answer and explanation
B. 20, 30 and 50 percent The masses total 100 grams, so their numerical values are already percentages. Ternary proportions must sum to 100 percent.
A mineral persists outside the equilibrium field shown on a diagram. What is a valid geological explanation?
1. Phase diagrams require every natural rock to equilibrate instantly
2. The mineral must have a different chemical name in every field
3. Reaction may have been too slow to reach equilibrium
4. Pressure and temperature can never change after crystallization
Answer and explanation
C. Reaction may have been too slow to reach equilibrium Kinetics and history can preserve minerals outside their equilibrium stability conditions. The diagram describes equilibrium relationships rather than instantaneous natural behavior.

All 84 chapters

Search This Blog

Geology Hub