One-Component Phase Diagrams

Introduction

A one-component pressure–temperature phase diagram maps which phase of a pure substance is stable under equilibrium conditions. Solid, liquid and vapour occupy regions separated by coexistence curves. The curves meet at a triple point, while the liquid–vapour line ends at a critical point. Reading the diagram requires attention to both axes and to whether a path crosses a phase boundary; simply heating a substance does not always make it pass through every familiar phase.

Core explanation

Within a single-phase region, one phase has the lowest chemical potential at the chosen temperature and pressure. Along a boundary between phases α and β, their chemical potentials are equal and both can coexist. Crossing a boundary changes the stable phase. For a typical substance, the solid–vapour sublimation line, solid–liquid fusion line and liquid–vapour vaporisation line meet at the triple point. The Clapeyron equation gives each line's local slope from its enthalpy and volume change.

The triple point is a particular pressure and temperature where solid, liquid and vapour have equal chemical potential. For a pure, nonreacting substance, it is invariant: at equilibrium one cannot vary temperature or pressure independently while keeping all three phases present. Add heat at that fixed pressure and temperature and phase amounts can change, but the coexistence coordinates stay fixed until one phase disappears. This is different from a two-phase boundary, where moving along the curve changes P and T together.

The liquid–vapour coexistence line terminates at a critical point. Approaching it, liquid and vapour properties become increasingly similar and the distinction between them disappears at the endpoint. Above the critical temperature, compressing the fluid cannot produce a separate liquid–vapour phase boundary in the ordinary sense. A fluid in the supercritical region can change continuously from more gas-like to more liquid-like properties without crossing a first-order liquid–vapour line. The word supercritical describes a thermodynamic region, not a new third phase with a separate coexistence boundary.

The solid–vapour and solid–liquid lines do not normally terminate at the same kind of liquid–vapour critical point in an ordinary simple diagram. Some substances have multiple solid polymorphs, adding more solid regions and triple points. A textbook three-phase sketch is therefore a useful basic topology, not a complete chart of all possible material phases. One should identify the specific substance and pressure range before interpreting an unfamiliar diagram.

A path at fixed pressure is a horizontal line on a graph with pressure on the vertical axis and temperature on the horizontal axis. If that pressure lies below the triple-point pressure, heating a stable solid can cross the sublimation boundary directly into vapour without a stable liquid region. At a pressure above the triple point, a fixed-pressure heating path may cross the fusion line and then the vaporisation line, giving solid → liquid → vapour. The exact path depends on the location and shape of boundaries.

A path at fixed temperature is vertical on the same axis choice. Increasing pressure generally favours a lower-volume phase, though the actual sequence depends on the substance and region. The solid–liquid slope can be negative, as for ordinary ice melting, or positive for many other substances. A diagram must be read from its curves rather than from a universal slogan that pressure always causes one named phase.

Metastable states can exist temporarily beyond an equilibrium boundary, such as supercooled liquid, because nucleation requires overcoming a kinetic barrier. An equilibrium phase diagram marks the lowest-chemical-potential state, not the timescale on which a sample must transform. A measured sample may therefore lag behind the boundary without changing the equilibrium topology.

Step-by-step reasoning

Check which axis is P and which is T. Locate the three main regions, the triple-point junction and the critical endpoint. For a specified heating or compression path, draw a line at constant pressure or temperature and mark only the boundaries it actually crosses. Distinguish equilibrium stable phase from possible metastable persistence.

Visual explanation

Draw P vertically and T horizontally. From one triple point, sketch a sublimation curve toward lower P and T, a fusion line toward higher P, and a vaporisation curve toward higher T ending in a filled critical-point dot. Shade solid, liquid and vapour regions. Draw one horizontal path below the triple pressure showing sublimation and another above it showing melting followed by boiling.

Real-world analogy

A map has regions separated by roads, a three-road junction and one road ending at a landmark. A phase diagram likewise has stable regions, coexistence lines, a triple junction and a critical endpoint. The analogy helps navigation but not the chemical-potential equality that defines each boundary.

Real-world example

Freeze-drying operates by lowering pressure so ice can sublime without a stable bulk liquid step under the chosen conditions. Its operation is guided by the water phase diagram, although heat and mass-transfer rates still govern the practical drying time. The phase diagram tells what equilibrium transition is possible, not how fast it proceeds.

Why?

Why does the liquid–vapour boundary end? At the critical point, liquid and vapour cease to be distinguishable thermodynamic phases. Beyond that endpoint, properties can change smoothly with pressure and temperature, so there is no equality of two separate liquid and vapour chemical potentials defining a coexistence line.

Common misconception

Every heating path does not pass through liquid. Below the triple-point pressure, sublimation can intervene. The critical point is not the same as the triple point: one ends liquid–vapour coexistence, while the other is where three distinct phases coexist. Metastability also does not mean the equilibrium diagram is wrong.

Worked example

Imagine a pure substance with triple-point pressure 0.20 bar. At fixed 0.10 bar, start with stable solid and raise temperature. Because this path lies below the triple point, the stable equilibrium route can cross the solid–vapour line into vapour; it cannot pass through the liquid stability region of the simple diagram. At fixed 1.0 bar, a different horizontal path may cross solid–liquid and then liquid–vapour boundaries. No numerical transition temperatures can be inferred without the actual diagram.

Quick check

1. Can three equilibrium phases of a pure substance coexist at a range of arbitrary pressures, and what happens to the liquid–vapour boundary at the critical point? Answer: No. In the simple one-component diagram, triple coexistence fixes a particular pressure and temperature. The liquid–vapour boundary ends at the critical point because the distinction between liquid and vapour disappears there.

Exam focus

State axis orientation before drawing a path. Label boundary types, triple point and critical point, and use Clapeyron sign for slope questions. Avoid predicting kinetic transformation times from an equilibrium diagram.

Advanced insight

The Gibbs phase rule for a nonreacting one-component system gives F=3−P: two independent intensive variables in a single-phase region, one along a two-phase boundary and none at triple coexistence. This counting explains the diagram topology and will be derived later, while critical behaviour requires care because the phase distinction itself vanishes.

Summary

One-component P–T diagrams show stable phase regions separated by coexistence curves. Three curves meet at an invariant triple point, while the liquid–vapour curve ends at a critical point. Heating or compression paths depend on the coordinates and may bypass liquid below the triple pressure. The diagram describes equilibrium, not transformation speed.

Practice questions

1. Why can heating a solid below its triple-point pressure produce vapour without stable liquid? Answer: The fixed-pressure path crosses the sublimation line while the liquid region exists only at higher pressures in the simple phase diagram. 2. Does a supercritical fluid have a separate liquid–vapour coexistence boundary above the critical point? Answer: No. Liquid-like and gas-like properties can vary continuously there because the two phases are no longer distinct. 3. A sample remains liquid briefly below its equilibrium freezing line. Does this contradict the phase diagram? Answer: No. It can be metastably supercooled because nucleation is kinetically delayed; the diagram identifies the stable equilibrium phase.