One method of examining the phase relationships within a ternary system is by the construction of isothermal sections through the diagram, parallel to the base.

An isothermal section is a representation of the stable phases for different compostions which have been quenched to the same temperature.

The isothermal sections to be examined are derived from the liquidus diagram, where we are looking at the phases present between the liquidus and the solidus.

The best way to view Isothermal Sections is by examining a simple ternary system.

1. Simple Ternary System
   A simple ternary system with a single eutectic. The individual isotherms (in blue) are labelled T5 through T1, such that T5 > T4 > T3 > T2 > T1. The cotectic curves (in magenta) separate the three primary phase fields A + L, B + L and C + L from each other.

2. Isothermal Section at T > temperature of melting of Pure B (TB)
   In this section, made at a temperature above the highest temperature on the diagram, so we are above the liquidus, there exists a single "one-phase field" consisting entirely of melts throughout the system, regardless of the compostion. Another way of looking at this is that no matter what the composition of the system, it will be 100% melt.

3. T5 Isotherm
   For this section, which is at a temperature that intersects the liquidus but not a cotectic curve, the one-phase melt field has become smaller and we have the addition of two "two-phase fields": B + Liq and C + Liq. The boundaries of the melt field are the appropriate contour line representing the isotherm for this section. In each of the two-phase fields, radiating tie lines (in red) are shown connecting coexisting melt and crystal compositions. These tie lines link solid crystals, of fixed composition, (the point from which the tie lines radiate) with liquid of a variety of compositions, represented along the liquidus.

4. T4 Isotherm
   The one-phase melt field has decreased in size, as the temperature of the iosthermal section is lowered. At the same time the two-phase fields of B + Liq and C + Liq have increased and been joined by the two-phase field A + Liq.

5. T3 Isotherm
   The one-phase field continues to shrink while the three two-phase fields increse in size.

6. T2 Isotherm
   In this isothermal section the isotherm has intersected the cotectic curves (in magenta) as well as the liquidus surface. In addition to the one-phase melt field, which continues to decrease in size, and the three two-phase fields, three three-phase fields are present. In each three-phase field a melt of fixed composition (on the cotectic) and crystals of two solids coexist, e.g. A + B + Liq, A + C + Liq and C + B + Liq. Note that only one melt composition can exist in a three-phase field, whereas any number of melts (on the contour line along the boundary of teh melt field) can exist in a two-phase field.

7. T1 Isotherm
   The one-phase melt field has decreased, the two-phase fields have gotten smaller and the three-phase fields have increased.

8. Isothermal section at T < temperature of the eutectic (TE)
   For this isothermal section, which is at a temperature below the temperature of the eutectic, i.e. below the solidus, then the entire diagram is a three-phase field, A + B + C, with no melt remaining and the system at every compostion will consist entirely of some combination of A, B and C.